Between 11pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
URGENT
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a. In this exercise, we are given that Mystery Pizza has an average οf 4.2 teIephοne orders per hour between 11 P.M. and midnight on Thursday night. Nοw using these given vaIues, we wiII caIcuIate the probabiIity that at Ieast 30 minutes wiII eIapse before having the next teIephone οrder.
Hοw can we calculate the probability of the expected time for an event to occur?Accοrding to probabiIity theory and statistics, the exponentiaI distributiοn is the probabiIity distribution of time between occurrences in the Poissοn distribution. It is a distribution of probabiIities that frequentIy correIates to the amount of time before a specific event takes pIace. It is a prοcess in which events take pIace continuousIy, independentIy, and at an average pace that remains constant throughout the process.
In caIcuIating the area under the curve of its graph (CDF), we wiII have to use the fοIIowing formuIa for the mean and the standard deviation,
Mean and Standard Deviatiοn:
[tex]$\begin{array}{r}{\mu={\frac{1}{\lambda}};}\\ {\sigma={\frac{1}{\lambda}}\,.}\end{array}$[/tex]
where,
x is the randοm variabIeλ is the rate parameter, aIsοthe mean time between the eventFirst, let us calculate the mean and standard deviation using the given Pοisson mean [tex]$\lambda=4.2.$[/tex] Using the fοrmula, we have,
[tex]$\begin{aligned}\rm{\mu=\sigma={\frac{1}{\lambda}}}\\ {={\frac{1}{4.2}\\{=0.2381}\end{aligned}$[/tex]
Sο we have the mean and the standard deviation of 0.2381 hours.
Nοw, we wiII caIcuIate the probabiIity that at Ieast 30 minutes or 0.50 hοurs wiII eIapse before the next teIephone order. Keep in mind that we are caIcuIating the probabiIity for "more than" the x so we wiII use the right-taiIed formuIa for this which is given by,
Right-tailed area(Mοre than x) :
[tex]$P(X\gt x)=e^{-\lambda x};$[/tex]
where,
x is the randοm variableλ is the rate parameter, alsο the mean time between the eventsUsing the fοrmula, we have:
[tex]$\begin{array}{r l}{P(X\gt 0.50)=e^{-\lambda x}}\\ {=e^{-42(0.50)}}\\ {=0.1225\,.}\end{array}$[/tex]
Therefοre, we can concIude that there is a 12.25% chance that at Ieast 30 minutes or 0.5 hours wiII eIapse before another teIephone order.
b. Next, we wiII caIcuIate the probabiIity that Iess than 15 minutes wiII eIapse befοre the next teIephone order. Remember that we are caIcuIating the probabiIity of Iess than x. This means that we wiII be using the fοrmuIa for the Ieft-taiIed area which is given by,
Left-tailed area(Less than οr equal to x):
[tex]$P(X\leq x)=1-e^{-\lambda x}$[/tex]
where,
x is the randοm variableλ is the rate parameter, alsο the mean time between the eveUsing the fοrmula, we have:
[tex]$\begin{array}{r l}{P(X\leq0.25)=1-e^{-\lambda x}}\\ {=1-e^{-42(0.25)}}\\ {=1-0.3499}\\ {=0.6501\,.}\end{array}$[/tex]
Therefοre, there is a 65.01% that Iess than 15 minutes wiII eIapse before the next teIephοne caII.
c. In this part, we wiII caIcuIate the probabiity that between 15− 30 minutes wiII eIapse befοre the next teIephone order. MathematicaIIy, we have,
[tex]$P(0.25\lt X\lt 0.5)=P(X\lt 0.50)-P(X\lt 0.25)$[/tex]
Frοm part a, we have the value for P(X>0.50) which is 0.1225. Now using the cοmplement rule, we can get P(X<50}
[tex]$\begin{array}{c}{{P(X\lt 50)=1-P(X\gt 50)}}\\ {{=1-0.1225=0.8775\,.}}\end{array}$[/tex]
We have nοw the value of P(X<0.50) which is 0.8775.
We can nοw get the P(0.25<X<0.50) by subtracting P(X<0.50) by P(X<0.25) frοm part b.. So we have,
[tex]$\begin{array}{r}{P(0.25\lt X\lt 0.50)=P(X\lt 0.50)-P(X\lt 0.25)}\\ {=0.8775-0.6501}\\ {=0.2274\,.}\end{array}$[/tex]
Sο we have P(0.25<X<0.50)=0.2274. Therefore, we can concIude that there is a 22.74% chance that between 15 and 30 minutes wiII eIapse before having a teIephone order.
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Related Questions
Can you help me to solve these two questions?
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The equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.
What do a curve's tangent and normal lines represent?A line that meets a curve at a point and has the same slope as the curve there is said to be the tangent line to that curve. A line that is perpendicular to the tangent line at a given position is the normal line to a curve at that location. In other words, the normal line's slope equals the tangent line's slope's negative reciprocal. The normal line is helpful for determining the direction of greatest change of the curve at a place whereas the tangent line gives information about the instantaneous rate of change of the curve at that point.
The given function is f(x) = 1/x.
The slope of the function is the derivative of the function thus,
f(x) = 1/x
f'(x) = -1/x²
f'(7) = -1/49
The equation of the line is given as:
y - y1 = m(x - x1)
where, m is the slope of the equation.
The equation of the tangent line is:
y - f(7) = f'(7)(x - 7)
y - 1/7 = -1/49(x - 7)
y = (-1/49)x + 8/49
b. The equation of the normal line to the graph is given as:
The slope of the normal line is negative and opposite of the tangent line.
That is,
m = 49.
y - f(7) = 49(x - 7)
y - 1/7 = 49(x - 7)
y = 49x - 342
Hence, the equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.
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if cos is the 4 quadrant
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The exact value of sin∅ if cos∅ =3/8 and in the fourth quadrant is 292⁰
What are the angles in the 4th quadrant?We should recall that the the angles of the 4th quadrant range from 270° to 360°. that is to say that in the fourth quadrant, 270≤x≤360
The given angle is cos∅ =3/8
cos∅ = 0.375
Find the angle we take the cos inverse
That ∅ = Cos⁻¹0.375
∅ = 68⁰
In the fourth quadrant, cos is positive that 360-68 = 292⁰
Then the exact value of sin is 292⁰
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Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
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Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
The local zoo buys from a supplier with an invoice amount if 17,200. The term of the sale are 5/22 n/30. What is the net amount on the order of the bill is paid by the 22nd day
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The net amount on the order if the bill is paid by the 22nd day is $16,340.
What is trade credit?The terms of payment that a supplier offers to a buyer are referred to as rade credit terms. These conditions outline the deadline for payment as well as any early payment discounts. For instance, if a supplier offers "2/10 net 30" terms, the customer can choose to pay the whole amount up front or receive a 2% reduction if they pay within 10 days.
The parameters of a trade credit agreement can significantly affect a company's cash flow. If a company can benefit from an early payment discount, they can save expenses and increase cash flow.
The term of sale is given as 5/22 n/30.
Here, the discount is 5%, thus the invoice amount is:
Discount = 0.05 x $17,200 = $860
Now, the net amount is:
Net Amount = Invoice Amount - Discount
Net Amount = $17,200 - $860
Net Amount = $16,340
Hence, the net amount on the order if the bill is paid by the 22nd day is $16,340.
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in a batch of 10,000 clock radios 500 are defective. A sample of 10 clock radios is randomly selected without replacement from the 10,000 and tested. The entire batch will be rejected if at least one of those tested is defective. what is the probability that the entire batch will be rejected?
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Answer:
Step-by-step explanation:
This is an example of a hypergeometric distribution problem, where we have a population of 10,000 clock radios with 500 defective ones, and we want to calculate the probability of getting at least one defective radio in a random sample of 10 without replacement.
The probability of getting no defective radios in the sample is:
(9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
This is because, for the first radio, there are 9500 good radios out of 10,000, and for the second radio, there are 9499 good radios out of 9,999, and so on.
The probability of getting at least one defective radio in the sample is then:
1 - (9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
which is approximately equal to 0.401.
Therefore, the probability that the entire batch will be rejected is 0.401.
Please help me with this question
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The slope-intercept version of the equation for the tangent line to f(x) at the position (-5, -1) is y = (-1/5)x -2. Thus,
m = -1/5
y = (-1/5)x -2
What can you infer from a tangent line?A tangent line is a straight line that οnly has οne cοntact with a functiοn. (See earlier.) The instantaneοus rate οf change οf the functiοn at that exact place is shοwn by the tangent line. At each given pοint οn the functiοn, the slοpe οf the tangent line is equal tο the derivative οf the functiοn at that same lοcatiοn.
We must determine the derivative οf the functiοn and evaluate it at x = -5 in οrder tο determine the slοpe οf f(x) = 5/x at the pοint (-5, -1).
f(x) = 5/x
f'(x) = [-5/x²]
When we enter x = -5, we obtain:
f'(-5) = [-5/(-5)²] = -1/5
As a result, the tangent line to f(x) at the point (-5, -1) has a slope of -1/5.
y - y1 = m(x - x1)
y - (-1) = (-1/5)(x - (-5))
y + 1 = (-1/5)(x + 5)
y = (-1/5)x -10/5
y = (-1/5)x -2
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Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?
92 19 41 24 75 53 70 3 67 64 9
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Step-by-step explanation:
To find the range, we need to subtract the smallest value from the largest value in the dataset:
Range = Largest value - Smallest value
Range = 92 - 3
Range = 89
To find the variance and standard deviation, we need to calculate the mean first:
Mean = (Sum of all values) / (Number of values)
Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11
Mean = 45.09 (rounded to two decimal places)
Next, we need to calculate the variance:
Variance = (Sum of squared differences from the mean) / (Number of values - 1)
Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)
Variance = 1071.45 (rounded to two decimal places)
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = Square root of variance
Standard deviation = Square root of 1071.45
Standard deviation = 32.74 (rounded to two decimal places)
The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.
PLS HELP FAST 50 POINTS + BRAINLIEST
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Answer:
Anna had 23 sweets in her bag at the start of the day.
Step-by-step explanation:
Let's use working backwards to find out how many sweets were in the bag at the start of the day.
At the end of lesson 4, Anna had 1 sweet left in her bag. So, before she gave a sweet to her teacher in lesson 4, she had 2 sweets left in her bag.
In lesson 3, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 3, she had 2 x 2 + 1 = 5 sweets in her bag.
In lesson 2, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 2, she had 5 x 2 + 1 = 11 sweets in her bag.
In lesson 1, she gave out half of the sweets in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 1, she had 11 x 2 + 1 = 23 sweets in her bag.
Therefore, Anna had 23 sweets in her bag at the start of the day.
1+1 = 2 2x2 = 4 = what was left at the start of lesson 4
4 + 1 = 5
5 x 2 = 10 = what was left at the start of lesson 3
10 + 1 = 11
11 x 2 = 22 = what was left at the start of lesson 2
22 + 1 = 23
23 x 2 = 46
So at the start of the day there was 46 sweets
The pens in a box are repackaged equally into 9 packs. Each pack has more than 15 pens.
1. Find an inequality to represent n, the possible number of pens in the box.
2. Explain why you chose this inequality.
Answers
Therefore, the possible number of pens in the box is p, where p is greater than 135.
What is inequality?Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.
Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.
Here are some general steps to solve an inequality:
Simplify both sides of the inequality as much as possible. This may involve combining like terms, distributing terms, or factoring.Get all the variable terms on one side of the inequality symbol and all the constant terms on the other side. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol.Solve for the variable by isolating it on one side of the inequality symbol. If the variable has a coefficient, divide both sides of the inequality by that coefficient.Write down the solution as an inequality. If you have solved for x, the solution will be in the form of x < a or x > b, where a and b are numbers.Check your solution by testing a value in the original inequality that is within the range of the solution. If the inequality holds true for that value, then the solution is correct. If not, then you may need to recheck your work or adjust your solutionby the question.
Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:
p/9 > 15
Multiplying both sides by 9, we get:
p > 135
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Solve for h -110=13+3(4h-6)
Answers
Answer:
H= -35/4
Decimal form: -8.75
Explanation:
Subtract 13 from both sides. { -110 - 13 =3(4h - 6) }Simplify -110 -13 to -123 { -123 = 3 (4h - 6) }Divide both sides by 3 { -123/3 = 4h - 6 }simplify 123/3 to 41 { -41 = 4h - 6 }add 6 to both sides { -41 +6 = 4h }simplify -41 + 6 to -35 { -35 = 4h }divide both sides by 4 { - 35/4 = h }switch sides { h= - 35/4 }The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 385 grams and a standard deviation of 8 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to 2 decimal places
Answers
The weight that corresponds to the highest 5% is also approximately 398.12 grams.
What is Z-Score?
A score's connection to the mean within a group of scores is statistically measured by a Z-Score.
To find the weight that corresponds to each event, we need to use the standard normal distribution and convert each value to a z-score using the formula:
z = (x - μ) / σ
Here are the calculations for each event:
The weight that corresponds to the 25th percentile:
-0.68 = (x - 385) / 8
Solving for x gives:
x = 379.44 grams (rounded to two decimal places)
Therefore, the weight that corresponds to the 25th percentile is approximately 379.44 grams.
The weight that corresponds to the 95th percentile. we find that the z-score is approximately 1.64 (rounded to two decimal places). Then we can use the formula above to solve for x:
1.64 = (x - 385) / 8
x = 398.12 grams (rounded to two decimal places)
Therefore, the weight that corresponds to the 95th percentile is approximately 398.12 grams.
The weight that corresponds to the highest 5%:
1.64 = (x - 385) / 8
x = 398.12 grams (rounded to two decimal places)
Therefore, the weight that corresponds to the highest 5% is also approximately 398.12 grams.
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Sharon used 8 roses and 6 tulips to make a bouquet. The tape diagram below shows the relationship between the number of roses and the number of tulips in the bouquet.
Answers
Answer:
Step-by-step explanation:
its C
HELP Whats the Answer to this Stand Deviation Question?
Answers
Answer: he would be 2 standard deviations above the
Step-by-step explanation:
the annual rainfall in 2017 in opuwo was 420mm.
the annual rainfall in 2018 was 12% more than in 2017.
find the annual rainfall in 2018.
Answers
Thus, Opuwo received 470.4mm of precipitation annually in 2018.
What is the procedure for determining rainfall?Depth x Radius x Radius x 3.14 will give you the typical rainfall amount. The apex of the bucket's region can be located. To calculate the amount of rain, divide the capacity by this region.
To find the annual rainfall in 2018, we can use the fact that it was 12% more than in 2017.
Let R be the annual rainfall in 2017 (which we know to be 420mm). Then, the annual rainfall in 2018 can be expressed as:
R + 0.12R
Simplifying this expression, we get:
1.12R
Therefore, the annual rainfall in 2018 was:
1.12 x 420mm = 470.4mm
So the annual rainfall in 2018 in Opuwo was 470.4mm
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I need help with this
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Answer:
D
Step-by-step explanation:
when an angle is supplementary to another angle, it means that both of the angles added together equal 180 degrees.
120+60=180.
Solve each of the following equations for the indicated variable f = (1+i)"-1 for i
Answers
Answer:
If i = -1 then the answer is f = 0
0 = ( 1 + -1 ).
f equaling 0 makes the statement true 0=0
Step-by-step explanation:
the answer is supposed to be 799 & 7188, but I don't know how to get there
Answers
Doing simple algebra with the two summations we can see that:
[tex]\Sigma x = 799\\\\\Sigma x^2 = 7,188[/tex]
How to find the values of the two summations?First, we know that there are 97 passengers, and we know that the summation:
[tex]\Sigma (x - 5) = 314[/tex]
Where x represents the weights.
Then we can rewrite that sum as:
[tex]\Sigma (x - 5) = \Sigma x - 97*5[/tex]
And replace that in the original equation to get:
[tex]\Sigma x - 97*5 = 314\\\Sigma x = 314 + 5*97 = 799[/tex]
So that is the first summation, now let's get the second one, we can rewrite the summation as:
[tex]\Sigma (x - 5)^2 = \Sigma x^2 - 10x +25 \\\\\Sigma x^2 - \Sigma 10x + \Sigma 25[/tex]
Where remember we have 97 terms, and the summation is equal to 1623, then:
[tex]\Sigma x^2 - \Sigma 10x + 25*97 = 1623[/tex]
Now we can replace the second term by the thing we found earlier:
[tex]\Sigma x^2 - 10\Sigma x + 25*97 = 1623\\\\\Sigma x^2 - 10*799 + 25*97 = 1623\\\\\Sigma x^2 = 1623 + 10*799 - 25*97\\\\\Sigma x^2 = 7,188[/tex]
That is the answer.
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Hi, any one can solve it ?
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For given function f(x)= x³ + 2x , the complete table is mentioned below. f⁻¹(3)= 1, f⁻¹(-12) = -2.
Describe function ?In mathematics, a function is a rule that assigns a unique output value for every input value in a specified set. It is a fundamental concept in algebra, calculus, and other areas of mathematics.
A function is typically denoted by a symbol, such as f(x), where x is the input variable, and f(x) is the output variable. The set of all input values for which the function is defined is called the domain, and the set of all output values is called the range.
To complete the table of values, we simply plug in the given values of x into the expression for f(x) and evaluate:
x f(x)
0 0
1 3
2 14
To find f⁻¹(3), we need to solve for x in the equation f(x) = 3:
x³ + 2x = 3
x³ + 2x - 3 = 0
We can use trial and error to find that x = 1 is a solution to this equation:
1³ + 2(1) - 3 = 0
Therefore, f⁻¹(3) = 1.
To find f⁻¹(-12), we need to solve for x in the equation f(x) = -12:
x³ + 2x = -12
x³ + 2x + 12 = 0
We can use trial and error to find that x = -2 is a solution to this equation:
(-2)³ + 2(-2) + 12 = 0
Therefore, f⁻¹(-12) = -2.
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Evaluate (can't write decimal answer).
[tex]sin(20)sin(70)-sin(14)cos(26)-cos(6)cos(84)[/tex]
Answers
The evaluation of sin(20)sin(70) - sin(14)cos(26) - cos(6)cos(84) is approximately -1.
How to solve trigonometry?Use the trigonometric identities to simplify the expression:
sin(20)sin(70) - sin(14)cos(26) - cos(6)cos(84)
= (sin(20)cos(20)) / 2 - (sin(14)sin(64)) / 2 - (cos(6)cos(6)) / 2
= [(sin(40) - sin(80)) / 2] - [(cos(50) - cos(78)) / 2] - [(1 + cos(12)) / 2]
= (sin(40) - cos(50) + cos(78) - sin(80) - 1 - cos(12)) / 2
Now, use a calculator to evaluate each trigonometric function:
sin(40) = 0.6428, cos(50) = 0.6428, cos(78) = 0.2079, sin(80) = 0.9848, cos(12) = 0.9781
Substituting these values:
= (0.6428 - 0.6428 + 0.2079 - 0.9848 - 1 - 0.9781) / 2
= -2.755 / 2
= -1.3775
Therefore, the value of the given expression is approximately -1.
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The area of shape A is 3cm2 what is the area of shape B?
Answers
28.5cm^2 is the area of shape B.
What is area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition polyhedra of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus.sought a general definition of surface area.
(3×7)+(1.5×5)
21+7.5
28.5cm^2
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Cody has $7 dollars. he wants to buy at least 4 snacks. Hot dogs (x) and $2 each. Peanuts (y) are $1 each. which ordered pair is a solution
Answers
Since we can't find an ordered pair (x, y) that satisfies all the conditions, there is no solution to this problem.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true. Equations can be used to model relationships between variables, solve real-world problems, and make predictions.
Here,
Let's start by defining the variables:
x: number of hot dogs
y: number of peanuts
We need to find an ordered pair (x, y) that satisfies the following conditions:
x and y are both integers
x is greater than or equal to 0
y is greater than or equal to 0
2x + y ≤ 7 (total cost of snacks can't exceed $7)
x ≥ 4 (at least 4 snacks)
We can use trial and error to find a suitable ordered pair. Let's start with x = 4 and see if we can find a corresponding y value that satisfies the conditions:
If x = 4, then the total cost of hot dogs is 4 * $2 = $8.
We need to spend no more than $7, so we have $7 - $8 = -$1 left for peanuts.
Since we can't spend a negative amount of money, there is no solution for x = 4.
Let's try x = 5:
If x = 5, then the total cost of hot dogs is 5 * $2 = $10.
We have $7 - $10 = -$3 left for peanuts, so there is no solution for x = 5 either.
Finally, let's try x = 6:
If x = 6, then the total cost of hot dogs is 6 * $2 = $12.
We have $7 - $12 = -$5 left for peanuts, so there is no solution for x = 6 either.
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Complete question:
Cody has $7 dollars. he wants to buy at least 4 snacks. Hot dogs (x) and $2 each. Peanuts (y) are $1 each. Find the solution for this question of equation?
Consider the function h(x) = a(−2x + 1)^5 − b, where a does not=0 and b does not=0 are constants.
A. Find h′(x) and h"(x).
B. Show that h is monotonic (that is, that either h always increases or remains constant or h always decreases or remains constant).
C. Show that the x-coordinate(s) of the location(s) of the critical points are independent of a and b.
Answers
Answer:
A. To find the derivative of h(x), we can use the chain rule:
h(x) = a(-2x + 1)^5 - b
h'(x) = a * 5(-2x + 1)^4 * (-2) = -10a(-2x + 1)^4
To find the second derivative, we can again use the chain rule:
h''(x) = -10a * 4(-2x + 1)^3 * (-2) = 80a(-2x + 1)^3
B. To show that h is monotonic, we need to show that h'(x) is either always positive or always negative. Since h'(x) is a multiple of (-2x + 1)^4, which is always non-negative, h'(x) is always either positive or negative depending on the sign of a. If a > 0, then h'(x) is always negative, which means that h(x) is decreasing. If a < 0, then h'(x) is always positive, which means that h(x) is increasing.
C. To find the critical points, we need to find where h'(x) = 0:
h'(x) = -10a(-2x + 1)^4 = 0
-2x + 1 = 0
x = 1/2
Thus, the critical point is at x = 1/2. This value is independent of a and b, as neither a nor b appear in the calculation of the critical point.
Annie is concerned over a report that "a woman over age 40 has a better chance of being killed by a terrorist than of getting married." A study found that the likelihood of marriage for a never-previously-wed, 40 -year-old university-educated American woman was 2.5% . To demonstrate that this percentage is too small, Annie uses her resources at the Baltimore Sun to conduct a simple random sample of 546 never-previously-wed, university-educated, American women who were single at the beginning of their 40 s and who are now 45 . Of these women, 20 report now being married. Does this evidence support Annie’s claim, at the 0.01 level of significance, that the chances of getting married for this group is greater than 2.5% ? Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0Ha: p=0.025: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.025
Answers
Due to the directed nature of the alternative hypothesis, a one-tailed test is being used (greater than).
what is null hypothesis ?The null hypothesis, which is an assertion or assumption that there is no significant difference or association between two or more variables or populations, is used in statistical hypothesis testing. It is frequently indicated by the letter H0 and is typically the hypothesis that is tested against a competing hypothesis. The objective of the hypothesis test is to either reject or fail to reject the null hypothesis based on the evidence or data seen. The null hypothesis serves as the default or baseline assumption. If the alternative hypothesis is supported by evidence, the null hypothesis is likely to be rejected.
given
The test's null and alternate hypotheses are as follows:
H0: p 0.025 (The percentage of American women with university educations who had never previously been married at the start of their 40s and are now 45 and married is less than or equal to 2.5%)
Ha: p > 0.025 (More than 2.5% of American women with college degrees who were unmarried at the start of their 40s and are now 45 and married are never before married).
Due to the directed nature of the alternative hypothesis, a one-tailed test is being used (greater than).
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an adjusted r-squared value of 0 represents no ability of the model to explain the dependent variable.
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An adjusted R-squared value of 0 indicates that the model has no ability to explain the variation in the dependent variable using the independent variables included in the model.
In other words, the model does not fit the data well and cannot make accurate predictions. An adjusted R-squared value of 1 represents a perfect fit, where the model explains all of the variation in the dependent variable using the independent variables. However, it is important to consider other factors such as the sample size, the quality of the data, and the appropriateness of the model to make valid conclusions about the model's ability to explain the dependent variable.
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For each of the following propositions, either i. use a case-based proof to demonstrate that the proposition holds true or ii. Use a counterexample to demonstrate the proposition does not hold.
(a) Assume x is an integer that is not divisible by 3, and y is an integer that is not divisible by 3. Then the sum of x and y cannot be divisible by 3.
(b) Assume x is an integer that is not divisible by 3, and y is an integer that is divisible by 3. Then the sum of x and y cannot be divisible by 3.
Answers
In both cases, the sum of x and y is not divisible by 3, we have demonstrated that the proposition is true. and the proposition is false, and we have shown a counterexample where the sum of two integers, one of which is not divisible by 3 and the other is divisible by 3, can be divisible by 3.
(a) To prove that the sum of two integers, x and y, neither of which is divisible by 3, cannot be divisible by 3, we can use a case-based proof.
Case 1: x and y leave a remainder of 1 when divided by 3.
Let x = 3m + 1 and y = 3n + 1, where m and n are integers. Then, the sum of x and y is 3m + 3n + 2, which leaves a remainder of 2 when divided by 3. Therefore, x + y is not divisible by 3.
Case 2: x and y leave a remainder of 2 when divided by 3.
Let x = 3m + 2 and y = 3n + 2, where m and n are integers. Then, the sum of x and y is 3m + 3n + 4, which leaves a remainder of 1 when divided by 3. Therefore, x + y is not divisible by 3.
Since in both cases, the sum of x and y is not divisible by 3, we have demonstrated that the proposition is true.
(b) To prove that the sum of two integers, x and y, where x is not divisible by 3 and y is divisible by 3, cannot be divisible by 3, we can use a counterexample.
Let x = 2 and y = 6. Then, x is not divisible by 3 and y is divisible by 3. However, x + y = 8, which is not divisible by 3.
Therefore, the proposition is false, and we have shown a counterexample where the sum of two integers, one of which is not divisible by 3 and the other is divisible by 3, can be divisible by 3.
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A screen has a zoom of 140%, which means that images on the screen are 140% as long and 140% as wide as when they are printed on a sheet of paper. An image of a house is 17 cm tall when printed on a sheet of paper. How tall would the image of the house be on the screen? Give your answer in centimetres (cm).
Answers
Answer:
23.8 cm
Step-by-step explanation:
17 * 140% = 17 * 1.4 = 23.8 cm
The image of the house would be 23.8 cm tall on the screen.
To calculate the height of the image of the house on the screen, we can use the given zoom factor of 140%.
The zoom factor of 140% means that the images on the screen are 140% as long and 140% as wide compared to when they are printed on a sheet of paper.
To calculate the height of the image on the screen, we need to multiply the printed height by the zoom factor (140% or 1.4).
Height on the screen = Printed height * Zoom factor
Height on the screen = 17 cm * 1.4
Height on the screen = 23.8 cm
Therefore, the image of the house would be 23.8 cm tall on the screen.
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Three dice are rolled. What is the probability of getting the sum as 13?
Answers
When three dices are rolled.
Total number of outcomes = = 216
Sum of 13 can be achieved in the following ways:
From the digits 6,4,3
So, there are 3! ways = = 6
From the digits 6,2,5
So, there are 3! ways = = 6
From the digits 5,4,4
So, there are ways = 3
From the digits 6,6,1
So, there are ways = 3
From the digits 3,5,5
So, there are ways = 3
So, total numbers whose sum is 13=
So, Probability = .
Therefore, the probability of getting sum as 21 on rolling three dice = .
The roof on a house requires that every 2 yards gets covered by 3 shingles. You currently have 60 boxes that contain 120 shingles each. The roof of the house is estimated at 4500 yards that must be covered. Which sentence best describes the amount of shingles needed?
Answers
To cover the house roof, as we only need 6,750 shingles and we have 7,200 shingles available.
What are arithmetic operations ?
Arithmetic operations are basic mathematical operations used to perform calculations involving numbers. The four basic arithmetic operations are:
Addition: This operation involves combining two or more numbers to get a total or sum. The symbol used for addition is "+".Subtraction: This operation involves finding the difference between two numbers. The symbol used for subtraction is "-".Multiplication: This operation involves finding the product of two or more numbers. The symbol used for multiplication is "×" or "*".Division: This operation involves dividing a number into equal parts or finding how many times one number fits into another. The symbol used for division is "÷" or "/".According to the question:
To determine the amount of shingles needed to cover the roof of the house, we can use the fact that every 2 yards requires 3 shingles. Therefore, for 4500 yards, we need to divide by 2 and then multiply by 3 to get the total number of shingles needed.
(4500 yards) / (2 yards/2) * (3 shingles/2 yards) = 6,750 shingles
Since we have 60 boxes that contain 120 shingles each, we can calculate the total number of shingles we have:
60 boxes * 120 shingles per box = 7,200 shingles
Therefore, we have more than enough shingles to cover the roof, as we only need 6,750 shingles and we have 7,200 shingles available.
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Assume that a piece of land is currently valued at $50,000. If this piece of land is expected to appreciate at an annual rate of 5% per year for the next 20 years, how much will the land be worth 20 years from now?
Answers
The value of the land 20 years after it appreciates at annual rate at 5% is $132676.47.
What is appreciation of assets?An asset's value increases over time through a process called appreciation. Depreciation, on the other hand, reduces an asset's value throughout its useful life. The rate at which an asset's value increases is known as the appreciation rate. An increase in the value of financial assets, such as stocks, is referred to as capital appreciation. When a currency appreciates, it means that its value increases when compared to other currencies on the foreign exchange markets.
The annual rate is given as 5%.
The new value after 20 years can be calculated using the formula:
[tex]A = P * (1 + r/n)^{(nt)}[/tex]
Substituting the values we have:
[tex]A = $50,000 * (1 + 0.05/1)^{(1*20)}\\A = $50,000 * 1.05^{20}\\A = $132,676.47[/tex]
Hence, the value of the land 20 years after it appreciates at annual rate at 5% is $132676.47.
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I have two fair dice each numbered 1 to 6. I am going to throw the two dice. What is
the probability that the sum of the numbers on the dice will be a square number?
Answers
The probability that the sum of the numbers on the dice will be a square number is 1/6.
What is the mathematical probability?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.
We can first make a list of every conceivable result when rolling two dice in order to determine the likelihood that the sum of the numbers on the two dice will be a square number:
[tex](1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6[/tex])
[tex](2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)[/tex]
[tex](4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)[/tex]
[tex](6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)[/tex]
The sums can then be listed, and the square numbers can be identified:
2, 3, 4, 5, 6, 7
3, 4, 5, 6, 7, 8
4, 5, 6, 7, 8, 9
5, 6, 7, 8, 9, 10
6, 7, 8, 9, 10, 11
7, 8, 9, 10, 11, 12
The likelihood that the sum of the numbers on the dice will be a square number is 6 out of a total of 36 potential outcomes.
P(square sum) = 6/36 = 1/6.
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