The remainder spent on phone cards is $187.2
How much money did he spend on phone cards?From the question, we have the following parameters that can be used in our computation:
Amount = $360
He spends ½ on lunch, and a %4 on transportation
The remainder spent on phone cards is calculated as
Phone cards = (1 - 1/2 - 4%) * 360
Evaluate the product
Phone cards = 187.2
Hence, the amount is $187.2
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Find the global maxima and global minima of the function
f(x, y) =x^2 − 2xy + 2y on the rectangle D = {(x, y) ∶ 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}
The required global maximum value is 4 and the global minimum value is 3.
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.
Here,
The critical points can be found by finding the partial derivatives of the function with respect to x and y and setting them equal to zero.
df/dx = 2x - 2y = 0
df/dy = -2x + 4y = 0
Solving the system of equations, we find that the critical points are (1, 2) and (2, 1).
Since (1, 2) is within the bounds of the rectangle D, we need to check the value of f(1, 2) to see if it is a local minimum or local maximum.
f(1, 2) = 1 - 2 + 4 = 3
(2, 1) is also within the bounds of the rectangle D, we need to check the value of f(2, 1) to see if it is a local minimum or local maximum.
f(2, 1) = 4 - 2 + 2 = 4
Since f(1, 2) < f(2, 1), the global maximum is at point (2, 1) and the global minimum is at point (1, 2).
The global maximum value is 4 and the global minimum value is 3.
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Which division problem can be described using this model? Responses 3÷4 , 3 divided by 4, 3÷1/4 3 divided by 1 fourth 1÷1/12 , 1 divided by fraction 1 over 12, 3÷1/12
The model represent here gives the division problem is 3÷1/4.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
We have three section 1+ 1 + 1= 3.
and, Each section have the fraction
= 4/12
= 1/3
so, the model represent here gives the division problem
3÷1/4.
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The water rate for a city in North Carolina is $1.39 per 755 gallons of water used. a) What is the water bill if a resident of that city uses 30,000 gallons? b) How many gallons of water can a customer use if the water bill is not to exceed $150?
The gallons of water a customer can use if the water bill is not to exceed $150 is 81474.82 gallons
What is the water bill if a resident of that city uses 30,000 gallons?
In order to determine the water bill, we need to calculate the price of one gallon of water (rate) using the given information.
Since $1.39 per 755 gallons
rate = 1.39/ 755
The water bill if a resident of that city uses 30,000 gallons will be:
1.39/ 755 * 30000 = $55.23
The gallons of water a customer can use if the water bill is not to exceed $150 will be:
Let x be gallons of water
(1.39/ 755)x ≤ 150
x ≤ 150/(1.39/ 755)
x ≤ 81474.82 gallons
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Patsy Bonner buys 200 shares of Target at $ 56.30 and 100 shares of Pepsico at $68.73. Find the total cost ignoring commissions.
Answer:
[tex]\$25,006[/tex]
Step-by-step explanation:
The total cost of Target shares is [tex](200)(\$56.30)=\$11,260[/tex].
The total cost of Pepsico shares is [tex](200)(\$68.73)=\$13,746[/tex].
Adding these costs together yields [tex]\$11,260+\$13,746=\$25,006[/tex].
You might have noticed that the numbers, or frequencies, on an old radio dial are not evenly spaced. There is, however, some pattern to the placement of these frequencies. You will analyze this data and answer the following questions.
frequency reading on the radio dial (kilohertz)
distance from the left end of the radio dial (centimeters)
53
1.54
60
2.17
70
2.95
80
3.62
100
4.75
120
5.67
140
6.45
170
7.43
1. a. What is the independent variable and what are its units?
b. What is the dependent variable and what are its units?
2. Make a scatter plot of the data. Describe the data set based on the scatter plot.
b. What do you expect to happen to the distance from the left end of the radio as the frequency gets higher?
c. What do you expect to happen to the distance from the left end of the radio as the frequency gets smaller?
Answer:
j3jejej
jwjitygueiejjejrjejejrjrjtjjturuejdvr7uejfnfnnrkrjdvev4j
find the absolute value!! Need asap!!
Answer:
|-1/7| = 1/7 or approx .14
I keep messing up somebody please help me
Answer:
23 and 16
Step-by-step explanation:
The pattern is to subtract 7 each time.
51 - 7 = 44
44 - 7 = 37
37 - 7 = 30
30 - 7 = 23
23 - 7 = 16
a hot air balloon decends 305 feet per minute for 4minutes then ascends at a rate of 215 per minute for another 2 minutes. find the total feet in altitude
The total feet in altitude is given by the equation A = -790 feet
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total feet in altitude be represented as A
Now , the equation will be
The hot air balloon descends 305 feet per minute for 4 minutes
So , the total descending will be a negative value , where
The feet in altitude descended = -305 x 4 = -1220 feet
Now , hot air balloon ascends 215 feet per minute for 2 minutes
So , the total ascending will be a positive value , where
The feet in altitude ascended = 215 x 2 = 430 feet
And , the total feet in altitude A = feet in altitude descended + feet in altitude ascended
Substituting the values in the equation , we get
The total feet in altitude A = -1220 + 430
On simplifying the equation , we get
The total feet in altitude A = -790 feet
Hence , the equation is A = -790 feet
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Let X be a continuous random variable taking values between 0 and 2 with probability density function p(x) = 0.5. Find E(X) and Var(X). Plot its Cumulative Distribution Function.
E(X) = 2 and Var(X) = 4/3.
And then, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
Continuous Random Variable ExpectationsThe expected value (mean) of a continuous random variable X with probability density function p(x) is given by:E(X) = ∫x*p(x)dx, where the integral is taken over the range of X.
In this case, since p(x) = 0.5 for all x in [0,2], we have:E(X) = ∫x*0.5dx = 0.5∫xdx = 0.5(x²/2)|0 to 2 = (2²/2 - 0²/2)*0.5 = 2.
The variance of X is given by:Var(X) = E((X - E(X))²) = E(X²) - (E(X))².
We have to calculate E(X²), which can be found as:E(X²) = ∫x²*p(x)dx = 0.5∫x²dx = 0.5(x²/3)|0 to 2 = (2²/3 - 0³/3)*0.5 = 8/3.
So, Var(X) = E(X²) - (E(X))² = 8/3 - (2)² = 8/3 - 4 = 4/3.
The cumulative distribution function (CDF) of a continuous random variable X is given by:F(x) = P(X <= x) = ∫p(t)dt for all t <= x.
In this case, since p(x) = 0.5 for all x in [0,2], we have:F(x) = 0.5x for x in [0,2].
The CDF of X is a monotonically increasing function, and it tells us the probability that X takes a value less than or equal to x.
Now, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
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The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 390 minutes, the monthly cost will be $178. If the customer uses 940 minutes, the monthly cost will be $398.
A) Find an equation in the form y=mx+b where x is the number of monthly minutes used and y is the total monthly of the Splint plan.
B) Use your equation to find the total monthly cost if 866 minutes are used.
Answer: If 866 minutes are used, the total cost will be ------ dollars
The equation can be given as y = 0.4x +22 and the monthly cost is $368.4
What is a linear equation?
A linear equation is an expression whose degree is one. The most general linear equation is y = mx + c. Where m is the slope and c is the y-intercept.
A) To find the equation in the form y = mx + b.
We are given two points (390, 178) and (940, 398).
Now we substitute these points into the standard equation y = mx + c
We get
y = mx + b
178 = m * 390 + b
398 = m * 940 + b
We subtract the two equation we get,
550m = 220
m =0.4
Now we substitute these values in the equation 1 we get
178 = 0.4 * 390 + b
178 = 156 + b
b = 22
So the equation is:
y = 0.4x + 22
B) We are asked to find the cost for 866 minutes we substitute x = 866 in the equation
y = 0.4x + 22
y = 0.4 * 866 + 22
y = 346.4 + 22
y = 368.4
So if 866 minutes are used, the total monthly cost will be $368.4.
The equation can be given as y = 0.4x +22 and the monthly cost is $368.4
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16. The elevation of City of Santa Clara is approximately 75 ft. What is the elevation in centimeters? (1ft = 12in; 1in = 2.54cm)
Answer:To convert the elevation of the City of Santa Clara from feet to centimeters, you can use the conversion factors:
1 ft = 12 in
1 in = 2.54 cm
First, convert feet to inches:
75 ft * 12 in/ft = 900 in
Then, convert inches to centimeters:
900 in * 2.54 cm/in = 2286 cm
So, the elevation of the City of Santa Clara is approximately 2286 cm.
Step-by-step explanation:
Mei is thinking of a 2-digit multiple of 2. Ben is thinking of a 2-digit multiple of 3. Xander is thinking of a 2-digit multiple of 4. Dom is thinking of a 2-digit multiple of 6. Alice is thinking of a 2-digit multiple of 8. They are all thinking of the same number.
The only 2-digit multiple of 2, 3, 4, 6, and 8 is the number 24.
What is multiple ?Multiple is a term that refers to an amount that is greater than one or a collection of two or more items. It is often used to describe a quantity of objects, people, or events that are distinct from each other. For example, a multiple of five would be five, ten, fifteen, twenty, etc. Similarly, a multiple of three would be three, six, nine, twelve, etc.
Therefore, all five people are thinking of the same number: 24.
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The height of a rectangular box is 4 times its length, and its width is 7 in more than its length. The volume of the box is 102 in^3. Use the ALEKS graphing calculator to find the length of the box. Round your answer to two decimal places.
Answer: Let's call the length of the box "x". Then, the height of the box is 4x and the width is x + 7. The volume of the box is given by the equation:
x * 4x * (x + 7) = 102
Expanding and simplifying the equation, we get:
4x^3 + 28x^2 - 102 = 0
To find the length of the box, we need to solve for x in this equation. One way to do this is to use the cubic formula. However, this formula can be quite complex, so a simpler method would be to use numerical methods such as the bisection method or Newton's method.
Step-by-step explanation:
1×0.1+6×0.01+8×0.001 in standard form
Answer:
the answer is 0.168
Step-by-step explanation:
have a good day!
The students in Class 6 vote to pick a class captain. The choice is Anton, Eva, Kofi or Petra. Anton gets 0.2 of the votes. Eva gets 10% of the votes. Petra gets of the votes. Kofi gets 9 votes. How many students are in class 6?
Answer:
There are 15 students in class 6
Step-by-step explanation:
Let's call the number of students in class 6 "n".
We know that:
Anton gets 0.2 * n votes
Eva gets 0.1 * n votes
Petra gets (1 - 0.2 - 0.1) * n votes
Kofi gets 9 votes
The total number of votes is n, so we can write:
n = 0.2 * n + 0.1 * n + (1 - 0.2 - 0.1) * n + 9
Simplifying this equation:
0.6 * n = 9
So:
n = 9 / 0.6
n = 15
Solve the triangle:
Answer:
Step-by-step explanation:
we will find the first angle in the larger triangle;
180⁰-60⁰= 120⁰
120⁰
the second angle will be;
120⁰+30⁰=150⁰
180⁰-150⁰=30⁰
30⁰ this means that the second triangle is isosceles triangle, when we find the hypotenuse of the smaller triangle it will be equal to x since the sides are equal
88/sin60⁰=x/sin90⁰
88sin 90⁰=xsin60⁰
88/0.8660=0.8660x/0.8660
x=101.62
What is the answer to 19-6(-k-2)?
Answer: 6k + 31
Step-by-step explanation:
19 - (-6k - 2(6))
19 - (-6k - 12)
19 + 6k + 12
6k + 31
Answer: 6k + 31
Step-by-step explanation:
= 19-6(-k-2)
= 19+6k +12
= 6k + 31
(2) Melissa and Ron entered a competition as a team Ron's score was 4/9 of Melissa's score. Melissa scored 50 more points than Ron. How many points did Melissa score?
The number of points that Melissa scored would be = 89 points.
How to calculate the number of point scores by Melissa?The competition was carried out by these two individuals that had different scores such as follows:
The total number of scores for Melissa = 50 point + Ron's score. That is , y = 50+X. ---> eq 1
The total number of Ron's score X = 4/9 × y --> 2
substitute y into equation 2.
X = 4/9× (50+X)
X= 22 + 0.44x
0.56x= 22
X= 22/0.56
X= 39.
substitute X into equation 1;
y= 50+39
y = 89
Therefore, the total number of points for Melissa = 89 point.
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Anita attends a private school where she must wear a uniform. This year, the price of the uniform is $86.80, which is 9.6% more than it cost last year. How much were uniforms last year?
Help please
Answer:
The price of the uniforms last year was about $79.20.
Step-by-step explanation:
In order to calculate the price of the uniforms last year, it is important to understand two important thing that can be inferred by what is told in the problem. This year's uniforms are 9.6% more than last year's. The easiest way to understand this line of information is that if we view the prices of the uniform from the perspective of last year's price, we can set the price of last year's uniform as 100% of the original price, and this year's uniform as 109.6% of the original price. Essentially, this year's uniform price is 109.6% of what it would cost you to buy a uniform last year.
Since you are given the information that this year, the uniforms cost $86.80, you know that $86.80 is 109.6% of last year's uniform cost. Now you can write an equation to solve for last year's price.
Set last year's uniform price to be represented by the variable [tex]x[/tex], and you will have the function of [tex]109.6[/tex]% · [tex]x = 86.8[/tex]. In order to solve for [tex]x[/tex], you simply divide both sides of the equation by 109.6%, which you will then get [tex]x = 86.8[/tex] ÷ 109.6%, which can be rewritten as [tex]x=86.8[/tex] ÷ [tex]\frac{109.6}{100}[/tex] or [tex]x=86.8[/tex] · [tex]\frac{100}{109.6}[/tex] ≈ $79.20. Hence, last year's uniforms costed $79.20.
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can someone help me pls
a. The two pentagons are congruent as the transformations they underwent were only translation and rotation, which are rigid motions.
b. The side lengths of ABCDE are given as follows:
CD = 3.2.DE = 4.1.EA = 2.8.AB = 2.2.BC = 1.4.The angle measures of FGHIJ are given as follows:
<F = 59º.<J = 162º.<I = 108º.< H = 117º.<G = 94º.What are the effects of each transformation?Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.Congruence is only changed with a dilation, as the side lengths are changed.
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Helpppopoooooopppppppp
A. The solution set of the system is {7, 3}
About elimination methodThe elimination method is a method used to solve or find a set of solutions to a system of linear equations of two variables by eliminating one of the variables. If the variables are x and y, to determine the x variable we must first eliminate the y variable, or vice versa, if we want to find the y variable, we must first eliminate the x variable.
To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them. Then only can determine other variables that will be determined. So in the elimination method you need to eliminate the variable twice.
To eliminate y in order to find the value of x.
9x-y=60 (i) 9x-y=60
x+y=10 (ii) | times (-1)| -x-y= -10
___________ __________ _
10x=70
x=7
Substitute the value x=7 into equation (ii)
x+y=10
7+y=10
y=3
So the solution set is {7, 3}
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seven times the quotient of 2 and 3
Answer:
4.666667, or you can round it to 4.67, depends on what it's asking!
Step-by-step explanation:
The quotient means to divide, so 2/3 = 0.666667
0.666667 * 7 = 4.666667
Hope that helps.
Select the correct answer. Which expression is equivalent to this polynomial? x2 + 8
A. ( x + 2 2 ) ( x − 2 2 )
B. ( x + 4 i ) ( x − 4 i )
C. ( x + 2 2 ) 2 D.
Answer: C.
Step-by-step explanation:
I need help………………………
Step-by-step explanation:
could you answer to my question
I'll need more than I need help in a picture to answer your question
please answer to this with what you need help with I am only seeing a question which I do not know and what I need to focus
thank you for cooperating - yuri
Consider the following three random experiments: Experiment 1: Toss a coin. Experiment 2: Toss a die. Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9. (a) Specify the sample space of each experiment. (b) Find the relative frequency of each outcome in each of the above experiments in a large number of repetitions of the experiment. Explain your answer.
To fully get the answer on the sample space and relative frequency, let's go directly to the analysis of the experiments as given.
The random experiments and their outcome(a) Sample space:
Experiment 1: Toss a coin: The sample space of this experiment is {heads, tails}.Experiment 2: Toss a die: The sample space of this experiment is {1, 2, 3, 4, 5, 6}.Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9: The sample space of this experiment is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.(b) Relative frequency of each outcome:
Relative frequency of an outcome is the number of times the outcome appears divided by the total number of trials. In a large number of repetitions of an experiment, the relative frequency of each outcome approaches the theoretical probability of that outcome.
Experiment 1: Toss a coin: Since each outcome (heads or tails) is equally likely, the theoretical probability of each outcome is 0.5. In a large number of repetitions of the experiment, the relative frequency of heads and tails would approach 0.5.Experiment 2: Toss a die: Since each outcome (1 to 6) is equally likely, the theoretical probability of each outcome is 1/6. In a large number of repetitions of the experiment, the relative frequency of each outcome (1 to 6) would approach 1/6.Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9: Since each outcome (0 to 9) is equally likely, the theoretical probability of each outcome is 1/10. In a large number of repetitions of the experiment, the relative frequency of each outcome (0 to 9) would approach 1Learn more on relative frequency here https://brainly.com/question/3857836
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is the data below at represented by a comparative bar chart, the bar representing which of these will be the tallest
If the data below are represented by a comparative bar chart, the bar representing the following will be the tallest:
Cat Failed
Which bar will be the tallest?The tallest bar of all of these will be the cat failed bar. A comparative bar chart is often designed to compare a set of observations.
From what we can see in the passage, it is clear that the bar chart representing the cat failed group contains the highest number and will likely have the tallest chart of all the others listed. So, the point is to look out for the observation with the highest number and the cat failed group meets the requirement.
Complete Question:
If the data below are represented by a comparative bar chart, the bar representing which of these will be the tallest?
Passed Failed
Cat. 24. 30
Dog 26. 28
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I NEED HELP ASAP PLEASE!!! Determine which integer will make the inequality x − 3 > 15 true.
S:{15}
S:{17}
S:{18}
S:{30}
Answer:
c) S : {30}
So, it is correct answer.
Step-by-step explanation:
mental math be like :-)
20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 2020 customers, 44 have enough cash to pay for their meal, 1616 have a credit card, and 33 have enough cash and a credit card. Using this information, answer each of the following questions.
Let AA be the event that a randomly selected customer has enough cash and BB be the event that a randomly selected customer has a credit card.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that a customer has enough cash?
the value of P(A∪B) is 17/20.
What is probability?Probability is a number expressing the likelihood or chance that a specific event will occur. Proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, A neighborhood restaurant is serving dinner to 20 patrons.
Both cash and credit are accepted as modes of payment at the restaurant. Of the 20 customers, 3 have enough cash and a credit card to pay for their dinner, 16 have a credit card, and 4 have enough cash to cover the cost of their meal.
From the general formula of probability:
Probability = (desired outcomes)/(Total outcomes)
Let "A" represent the situation in which a randomly chosen consumer has enough cash,
"B" represents the situation in which a randomly chosen customer has a credit card.
thus,
P(A) = 4/20
P(A) = 1/5
P(B) = 16/20
Also given,
P(A∩B) = 3/20
Since,
P(A∪B) = P(A) + P(B) -P(A∩B)
P(A∪B) = 4/20 + 16/20 - 3/20
P(A∪B) = 17/20
therefore, the value of P(A∪B) is 17/20.
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Let f(w) x 10x . We want to estimatef(1.07) using linear approximations. That is, using an appropriate tangent line_ First, we will build the tangent line at (€, y_ Enter as an ordered pair (a,6) The slope of the tangent line comes from f For this problem, f' (c) = And mtan The equation of the tangent line, in slope intercept form, is y = T(c) = Now, f(1.07) ~ T(1.07) Compare to actual value f(1.07)
The linear approximation of f(1.07) using the tangent line is T(1.07) is 10.77, which is slightly lower than the actual value f(1.07) = 11.77.
First, we need to find the derivative of the function f(x) = x + 10x.
The derivative is given by:
f'(x) = 1 + 10
Next, we need to find the tangent line at the point (a, 6), which means we need to find the value of "a" that makes the tangent line pass through (a, 6). To do this, we use the equation of the tangent line:
y - 6 = (1 + 10)(x - a)
y = (1 + 10)(x - a) + 6
Now we need to use the value of "a" to find the value of f(a) and then use this to find the value of the linear approximation of f(1.07).
Let's assume that the value of "a" is 1.
So, f(a) = f(1) = 1 + 10(1) = 11
And the equation of the tangent line is:
y = (1 + 10)(x - 1) + 6 = 11x - 4
Now, to find the value of the linear approximation of f(1.07), we use the equation of the tangent line:
T(1.07) = 11 * 1.07 - 4 = 10.77
Finally, we compare this value with the actual value of f(1.07), which is:
f(1.07) = 1.07 + 10 * 1.07 = 11.77
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The Bitcoin economy had reported year-on-year growth from 2017 to 2019 at a yearly rate of 7%. In 2020 it went into a downward trend. That year the growth turned negative at -5%. If the negative growth doubled the next year, what was the approximate percentage increase or decrease of the bitcoin economy in that year, compared to 2018?
SELECT ONLY ONE
Approximately 9% decrease
Approximately 13% decrease
Approximately 3% increase
Approximately 5% increase
If the Bitcoin economy had a yearly growth rate of 7% from 2017 to 2019, then the value in 2019 would be $1.07^3 = $1.225. If the economy had a negative growth rate of 5% in 2020, then the value in 2020 would be $1.225 x 0.95 = $1.1638. If the negative growth rate doubled in the next year, then the value in the next year would be $1.1638 x 0.9 = $1.04742.
To calculate the percentage change from 2018 to the next year, we can compare the values of the Bitcoin economy in those two years. The value in 2018 would be $1.07^2 = $1.1449. The percentage change would be ((value in next year - value in 2018) / value in 2018) x 100%. Substituting the values, we get ((1.04742 - 1.1449) / 1.1449) x 100% = -8.5%.
Therefore, the approximate percentage decrease of the Bitcoin economy in the next year, compared to 2018, is approximately 9%. The closest option is "Approximately 9% decrease".