Answer:
The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
An experimenter flips a coin 100 times and gets 59 heads.
This means that [tex]n = 100, \pi = \frac{59}{100} = 0.59[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 - 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.4756[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 + 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.7044[/tex]
The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).
Which of the following is true?
1. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.
2. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.
3. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.
4. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.
Answer:
Option A
Step-by-step explanation:
If the quadrilateral ABCD is dilated by a scale factor 'k' to form quadrilateral A'B'C'D',
Scale factor = [tex]\frac{\text{Length of one side of the Image}}{\text{Length of one side of the original}}[/tex]
k = [tex]\frac{BA'}{BA}[/tex]
Distance between B(2, -5) and A(-1, -1) = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(2+1)^2+(-5+1)^2}[/tex]
= 5 units
Distance between B(2, -5) and A'(-5.5, 5) = [tex]\sqrt{(-5.5-2)^2+(5+5)^2}[/tex]
= [tex]\sqrt{(-7.5)^2+(10)^2}[/tex]
= 12.5 units
Scale factor 'k' = [tex]\frac{12.5}{5}[/tex]
k = [tex]\frac{5}{2}[/tex]
Therefore, ABCD is dilated by a scale factor [tex]\frac{5}{2}[/tex] about point B.
BA and it's image BA' are on the same line and passes through center of dilation B.
Similarly, lines CD and C'D' will be parallel because they do not pass through center of dilation.
Therefore, Option (A) will be the correct option.
Midwest Publishing publishes textbooks. The company uses an 800 number where people can call to ask questions about the textbooks and place orders. Currently, there are 2 representatives handling inquiries. Calls occurring when both lines are in use get a busy signal. Each representative can handle 12 calls per hour. The arrival rate is 20 calls per hour.
Required:
a. How many extension lines should be used if the company wants to handle 90% of the calls immediately?
b. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used?
c. What percentage of calls receive a busy signal for the current telephone system with two extension lines?
Answer:
A. 18 calls
B. 0.9
C. 20
Step-by-step explanation:
Number of representatives=2,
Number of extension lines=2,
Average calls each representative can accommodate per hour = 15 calls,
Arrival rate per hour = 30 calls
(a) 90% of the arrival rate = 0.09 × 20 = 18 calls
To handle 18 calls immediately, 18 extension lines should be used
(b) Probability is given by number of possible outcomes ÷ number of total outcomes
Number of possible outcomes = 18, number of total outcomes = 20
Probability (call will receive busy signal) = 18/20 = 0.9
(c) For one extension line, numbers of calls to receive busy signal = 20 - 10 = 10 calls
Number of calls to receive busy signal for the current telephone system with two extension lines = 2 × 10 = 20 calls
Help me please with this maths question thank you
Answer:
Step-by-step explanation:
A)
The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.
B)
The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.
4x + 1 = 2x + 12 Subtract 1 from both sides.
- 1 -1
4x = 2x + 11 Subtract 2x from both sides
-2x -2x
2x = 11 Divide by 2
x = 11/2
x = 5.5
C)
P = L + L + w + w
P = 4(5.5) + 1 + 2(5.5) + 12 + 5.5 + 5.5
P = 22 + 1 + 11 + 12 + 11
P = 23 + 23 + 11
P = 57
Select the correct answer. Which function is continuous across Its domain
Answer:
D is the answer
Step-by-step explanation:
plug the -2's in line 1 & 2 then 4 in 2 and 3
the 1&2 , and the 2 and 3 numbers have to match
Using the conditions for continuity, we find that the function D.) is continuous.
How to check if a function is continuous?A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied:
f(a) exists (i.e. the value of f(a) is finite)the right-hand limit = left-hand limit, and both are finite.right-hand limit = left-hand limit = f(a)Since for -4 <= x < -2, -2 <= x < 4 and 4 <= x <= 8, the function f(x) is defined by straight lines , the function will be continuous for all x ≠ -2 and 4. Now for x = -2, 4, let us check all the three conditions:
A.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 6 = 4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
B.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 -2 = -4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
C.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 25 - 3*4 = 13
left hand limit = 0.5 * (4)² = 8
right hand limit = 25 - 3*4 = 13
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = 4.
D.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 20 - 3*4 = 8
left hand limit = 0.5 * (4)² = 8
right hand limit = 20 - 3*4 = 8
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = 4.
Thus, the function is continuous.
Learn more about continuity here
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Which pair of functions are inverses of each other?
O A. f(x) = f and g(x) = 8x?
O B. f(x) = 4 + 9 and g(x) = 4x - 9
O C. Ax) = 5x – 9 and g(x) = 149
O D. f(x) = 3 - 7 and g(x) = 247
State sales tax y is directly proportional to retail price x. An item that sells for 156 dollars has a sales tax of 14.42 dollars. Find a mathematical model that gives the amount of sales tax y in terms of the retail price x .
What is the sales tax on a 320 dollars purchase.
Answer:
The sales tax on a 320 dollars purchase is of $29.6.
Step-by-step explanation:
State sales tax y is directly proportional to retail price x.
This means that:
[tex]y = cx[/tex]
In which c is the constant of proportionality.
An item that sells for 156 dollars has a sales tax of 14.42 dollars.
This means that [tex]x = 156, y = 14.42[/tex]. We use this to find c. So
[tex]y = cx[/tex]
[tex]14.42 = 156c[/tex]
[tex]c = \frac{14.42}{156}[/tex]
[tex]c = 0.0924[/tex]
Then
[tex]y = 0.0924x[/tex]
What is the sales tax on a 320 dollars purchase?
y when [tex]x = 320[/tex]. So
[tex]y = 0.0924(320) = 29.6[/tex]
The sales tax on a 320 dollars purchase is of $29.6.
The ratio of the number of cherry tomatoes in a tossed salad to people served is 7:15. If Waldo wants to serve 105 people, how many cherry tomatoes will Waldo use
Simplify your answer
Answer:
= F^2 x^2
Step-by-step explanation:
(F(x))^2
Apply the rule: (a) =a (x) = x
= (Fx)^2
Apply exonent rule: (a . b)^n = a^n b^n (Fx)^2 = F^2 x^2
= F^2 x^2
Ivan is playing a skee-ball game. Different points are awarded depending on which hole the ball goes through. When the ball goes in the smallest hole, it is worth 100 points. When it goes in the bigger hole, it is worth 10 points, and when it does not go in either hole, it is worth 1 point. Ivan earned 352 points in the last game.
Which combination will result in a score greater than his current score?
2 balls in the smallest hole, and 8 balls in the bigger hole
4 balls in the smallest hole, and 6 balls in neither hole
3 balls in the smallest hole, 4 balls in the bigger hole, and 3 balls in neither hole
3 balls in the smallest hole, 3 balls in the bigger hole, and 4 balls in neither hole
Answer:
B.
Step-by-step explanation:
I don't know for a fact but i think its B. Sorry if I got it wrong.
First the store raised the price of a pot by 20%. Then they announced a 20% discount on the pot. Is the customer going to pay more or less for the pot now than before.
Answer:
less
Step-by-step explanation:
An increase of 20% makes the price 120% of the original price.
A discount of 20% makes the discounted price 80% of the previous price.
Original price: x
20% increase in price: 1.2 * x
20% discount over the raised price: 0.8 * 1.2 * x
Now we multiply the numbers in the last expression and compare the result with x.
0.8 * 1.2 * x = 0.96x
0.96 is less than x, so the customer pays less than the original price.
If ABC is reflected across the y-axis, what are the coordinates of C?
A. (-8, -4)
B. (8,-4)
C. (-8,4)
D. (4,-8)
Answer:
c....................
csc(π/2) =__
a.0
b.-1
c.1
d.undefined
Hi there!
[tex]\large\boxed{C. \text{ } 1}[/tex]
csc (π/2)
π/2 is located at (0, 1)
csc is equal to 1/y, or the reciprocal of the y-value
Therefore:
csc(π/2) = 1/1 = 1. C is the correct answer.
Choose the algebraic description that maps the image ABC onto A'B'C'.
Solve the given system by the substitution method
5x + y 19
7x-2y = 13
Answer:
x = 3 , y = 4
Step-by-step explanation:
5x + y = 19 --------- ( 1 )
=> y = 19 - 5x
7x - 2y = 13 ------------ ( 2 )
Substitute y in ( 2 ) :
7x - 2( 19 - 5x ) = 13
7x - 38 + 10x = 13
17x = 13 + 38
17x = 51
x = 3
Substitute x in ( 1 ) :
5x + y = 19
5( 3 ) + y = 19
15 + y = 19
y = 19 - 15
y = 4
A table is on sale for $247, which is 76% of the regular price.
What is the regular price?
Answer:
$325
Step-by-step explanation:
Find the regular price by dividing 247 by 0.76:
247/0.76:
= 325
So, the regular price was $325
The value of y varies with x and z, and y=8, when x=4 and z=10. What is the value of y when x=5 and z=11
The slope of diagonal AB is ___ , and it’s equation is ___.
Answer:
The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].
Step-by-step explanation:
Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.
Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].
A marketing researcher wants to test the hypothesis that, within the population, there are differences in the importance attached to shopping by consumers living in the northern, southern, eastern and western United States. Which statistical test should be used
Answer: Analysis of variance
Step-by-step explanation:
Analysis of variance is the statistical test that's used in analyzing the differences among means. The analysis of variance is used to determine if a statistically significant differences exust between the means of the independent groups.
Based on the question given, the null hypothesis will be that no difference in the importance that's attached to shopping by the consumers living in different regions in the United States.
Find the union {6, 11, 15} U Ø
Explanation:
The Ø means "empty set". It's the set with nothing inside it, not even 0.
We can write Ø as { } which is a pair of curly braces with nothing between them.
The rule is that if we union any set A with Ø, then we'll get set A
A U Ø = A
Ø U A = A
In a sense, it's analogous to adding 0. So it's like saying A+0 = A and 0+A = A.
So that's why {6, 11, 15} U Ø = {6, 11, 15}
There's nothing to add onto the set {6, 11, 15}, so we just get the same thing back again.
what type of number cannot be written as a fraction p/q, where p and q are intergers and q is not equal to zero
Answer:
irrational numbers
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.
Hi there!
»»————- ★ ————-««
I believe your answer is:
Irrational Number
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The definition that is given in the question was the definition of a irrational number.A number that cannot be written as a fraction with two integers is called a irrational number. Some examples of irrational numbers are non-terminating decimals that do not repeat and non-perfect squares. A number that CAN be written as a fraction with two integers is called a rational number.⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
The sum of the first ten terms of an arithmetic progression consisting of
positive integer terms is equal to the sum of the 20th, 21st and 22nd term.
If the first term is less than 20, find how many terms are required to give
a sum of 960.
Answer: [tex]n=13[/tex]
Step-by-step explanation:
Given
Sum of the first 10 terms is equal to sum of 20, 21, and 22 term
[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]
No of terms to give a sum of 960
[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]
Value of first term is less than 20
[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]
Answer:
15
Step-by-step explanation:
In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))
Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.
When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.
To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.
Then in the expression: (n÷2)×(2a+(n-1)×d)
substitute:
n = 14 (must be an even number for the equation to work)
a = 15
d = 7
This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)
substituting:
n = 15
a = 15
d = 7
This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.
I hope this has helped you.
P.S. Everything in the previous solution was right apart from the start of the last section and the answer
when a number is added to 1/5 of itself, the result is 24. the equation that models this problem is n+1/5n=24. what is the value of n?
Find the simple interest on the following. 1 ) Rs 1,760 for 3 years 6 months at the rate of 12% p.a.
Plss help me
Answer:
739.2
Step-by-step explanation:
Find the area of the irregular figure. Round to the nearest hundredth.
Answer:
[tex]67.5\text{ [square units]}[/tex]
Step-by-step explanation:
The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.
Formulas:
Area of rectangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=bh[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]By definition, the base and height must intersect at a 90 degree angle.
The rectangle has a base of 10 and a height of 5. Therefore, its area is [tex]A=10\cdot 5=50[/tex].
The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 2\cdot 5=5[/tex].
Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 5\cdot 5=12.5[/tex].
Thus, the area of the total irregular figure is:
[tex]50+5+12.5=\boxed{67.5\text{ [square units]}}[/tex]
What are the solutions to the system of equations graphed below
A few people gather together to play a game in which one needs to roll 3 six-sided dice. One person notices that the sum of the number of spots on three dice comes up as 11 (the event E1) more often than it does 12 (the event E2) even though it looks like it should be even. This person argues as follows: E1 occurs in just six ways:
{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}, and E2 occurs also in just six ways: {(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}.
Therefore E1 and E2 have the same probability P(E1) = P(E2). Why isn’t it?
Answer:
Yes, P(E1)=P(E2)
Step-by-step explanation:
We are given that
Number of dice=3
Total outcomes of 1 die=6
Therefore,
Total number of outcomes =[tex]6^3=216[/tex]
E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}
E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}
We have to show that E1 and E2 have the same probability P(E1) = P(E2).
Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]
Using the formula
[tex]P(E_1)=\frac{6}{216}[/tex]
[tex]P(E_1)=0.0278[/tex]
[tex]P(E_2)=\frac{6}{216}[/tex]
[tex]P(E_2)=0.0278[/tex]
Hence, P(E1)=P(E2)
Matthew participates in a study that is looking at how confident students at SUNY Albany are. The mean score on the scale is 50. The distribution has a standard deviation of 10 and is normally distributed. Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
a) 93.32%
b) 6.68%
c) 0.07%
d) 43.32%
Answer:
b) 6.68%
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean score on the scale is 50. The distribution has a standard deviation of 10.
This means that [tex]\mu = 50, \sigma = 10[/tex]
Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
The proportion is 1 subtracted by the p-value of Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 50}{10}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668
0.0668*100% = 6.68%
So the correct answer is given by option b.
Find the interquartile range of the data set represented by this box plot.
25
20
45
35
Answer:
25
Step-by-step explanation:
im pretty sure i think only ok i think no saying bad things in the comment
what is the sum of the complex numbers -9-i, and -5-i?
Answer:
-14-2i
Step-by-step explanation:
-9-i+(-5-i)
collect like terms(real-real, imaginary-imaginary)
=(-9-5)+(-i-i)
=-14-2i
Jason wants to fill a cylindrical water tank to its full capacity. He knows that the volume of the tank is equal to the product of , the square of the radius of the tank, and the height of the tank. Jason measured the height of the tank and found it to be 15 feet. He also measured the radius of the cylindrical tank and found it to be 10 feet. If Vrepresents the volume of the cylindrical tank, then which of the following equations can be used to calculate the volume of the tank?
Answer:
B) [tex]\sqrt{\frac{v}{15\pi } } = 10[/tex]
Step-by-step explanation: