Answer:
The 96% confidence interval for the proportion of people who say they jog regularly is between 0.1222 and 0.1578. This means that we are 96% sure that the true population proportion of people who jog is between 0.1222 and 0.1578.
With a 99% confidence level, the interval would be wider.
The smallest number of people we could contact to still have a margin of error of 3% at a 96% confidence level is 566.
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A polling organization contacts 1600 people and of these 14% say that they jog regularly.
This means that [tex]n = 1600, \pi = 0.14[/tex]
Construct and interpret a 96% confidence interval for the proportion of people who say they jog regularly.
96% confidence level
So [tex]\alpha = 0.04[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.056[/tex].
Margin of error:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 2.056\sqrt{\frac{0.14*0.86}{1600}}[/tex]
[tex]M = 0.0178[/tex]
Lower bound:
Sample proportion subtracted by the margin of error. So
[tex]\pi - M = 0.14 - 0.0178 = 0.1222[/tex]
Upper bound:
Margin of error added to the sample proportion. So
[tex]\pi + M = 0.14 + 0.0178 = 0.1578[/tex]
The 96% confidence interval for the proportion of people who say they jog regularly is between 0.1222 and 0.1578. This means that we are 96% sure that the true population proportion of people who jog is between 0.1222 and 0.1578.
Explain what changes if you instead use a 99% confidence level.
With a 99% confidence level, the value of Z would be higher(2.575), which means that the interval would be wider.
What is the smallest number of people we could contact to still have a margin of error of 3% at a 96% confidence level.
This is n for which [tex]M = 0.03[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 2.056\sqrt{\frac{0.14*0.86}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.056\sqrt{0.14*0.86}[/tex]
[tex]\sqrt{n} = \frac{2.056\sqrt{0.14*0.86}}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.056\sqrt{0.14*0.86}}{0.03})^2[/tex]
[tex]n = 565.5[/tex]
Rounding up:
The smallest number of people we could contact to still have a margin of error of 3% at a 96% confidence level is 566.
PLEASE HELP QUICKLY
If AABC is a right triangle, where AB is 27, BC is 36, and AC is 45, which of the following can
be used to find the measure of ZA? Select all that apply.
Answer:
TanA= [tex]\frac{36}{27}[/tex] and sinA=36/45
Step-by-step explanation:
Tan= opposite/adjacent
since 36 is opposite of A and 27 is adjancent to 36 your will use tanA= 36/27
Sin= opposite/hypotenuse
36 is opposite of A and 45 is the hypotenuse
write the ratio 48:30:42 in its simplest form
Someone please help me answer this!!
Answer:
[tex]b^{4}[/tex]Step-by-step explanation:
b^10 / b^6 = b^10-6 = b^4
Hope that helps!
plz help!!!!!!!!!!!!
Please help solve for x
9514 1404 393
Answer:
x = 22.5
Step-by-step explanation:
The angle bisector divides the triangle sides proportionally.
x/30 = 24/32
x = 30(24/32)
x = 22.5
Pharmex is a chain of drugstores that operate around the country. To see how effective its advertising and other promotional activities are, the company has collected data from 50 randomly selected metropolitan regions. In each region, it has compared its own promotional expenditures and sales to those of the leading competitor in the region over the past year. There are two variables: "Promote" reflects Pharmex’s promotional expenditures as a percentage of those of the leading competitor, and "Sales" reflects Pharmex’s sales as a percentage of those of the leading competitor. A portion of the data appears below. Show all work.
Region Promote Sales Region Promote Sales Region Promot Sales
1 77 85 21 103 112 41 100 94
2 110 103 22 95 96 42 96 81
3 110 102 23 103 93 43 88 92
4 93 109 24 89 97 44 109 108
5 90 85 25 97 92 45 109 103
a. Using Excel, create a scatterplot of the data. What do you observe? What type of relationship, if any, is apparent from the scatterplot?
b. Insert a trendline (click on the scatterplot, then click the Layout tab, and choose Trendline). What type of trendline seems to fit best?
c. Under "More Trendline Options," select "Display Equation on chart" and "Display R-squared value on chart." What do you see? What do these numbers mean?
Answer:
Positive relationship exists
Linear trend line
R² = 0.3522
Step-by-step explanation:
Given the data :
Promote (X) :
77
110
110
93
90
103
95
103
89
97
100
96
88
109
109
Sales (Y) :
85
103
102
109
85
112
96
93
97
92
94
81
92
108
103
A.) From the resulting plot, tbe slope of the graph is positive, hence, we can conclude that there exist a positive relationship between the variables 'promote' and 'sale'.
The linear trend line gives the best fit for the data with a correlation Coefficient, R value of 0.5935
The R² value is 0.3522. R² is the Coefficient of determination which gives the percentage of explained variation. For this data, about 35% of variation in sales is given by the best fit line.
equation of (8,-8) (-5,-8)
Answer:
y = - 8
Step-by-step explanation:
The equation of (8,-8) (-5,-8) is y = - 8
Answer:
0
Step-by-step explanation:
(8,-8) (-5,-8)
(8 x -5) ( 8 x -8) (-8 x -5)(-8 x -8) = ?
-40 - 64 + 40 + 64 = 0
Calculator A What is the measure of angle A? 5 cm 3 cm Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. mZA =D B 4 cm C С. 4 1 2 3 4 O
Answer:
53.13⁰
Step-by-step explanation:
Use sine:
sinθ=opposite/hypotenuse
sin∠A=4/5
∠A=sin⁻¹(0.8)=53.13010235415≈53.13⁰
The measure of angle A is 53.13 degrees in right triangle ABC.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle ABC is a right angled triangle
AB=3cm, BC=4cm and AC is 5cm
We have to find the ∠A
By using sine rule we find this
sin∠A = opposite side/hypotenuse
=4/5
sin∠A =0.8
Take sin⁻¹ on both sides
∠A =sin⁻¹(0.8)
= 53.13 degrees.
Hence, the measure of angle A is 53.13 degrees.
To learn more on trigonometry click:
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Which system models the height of the tennis ball and the height of the dog's mouth over time? h = 4.5t + 18 and h = -16t2 + 1.5t + 21 h = 18t + 4.5 and h =-16t2 + 21t + 1.5 h = -16t2 + 4.5t + 18 and h = -16t2 + 1.5t + 14 h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5
Answer:
the first answer is d and the second one is c
Step-by-step explanation:
edge
The height of the tennis ball and the height of the dog's mouth over time are h = 4.5t + 18 and h = -16t2 + 1.5t + 21 respectively. Therefore, the correct option is option A.
What is height?Height is a measurement of vertical distance, or how high or something someone is (how tall they are). For instance, "The altitude of that structure is 50 m" and "The height of such an aircraft in-flight is roughly 10,000 m". Christopher Columbus, for instance, has a height of 5 feet 2 inches.
Height is more frequently referred to as altitude when describing the vertical position from sea level. Additionally, elevation (height over sea level) is known as altitude if the point is connected to the Earth. The height of the tennis ball and the height of the dog's mouth over time are h = 4.5t + 18 and h = -16t2 + 1.5t + 21 respectively.
Therefore, the correct option is option A.
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Zander read 13 3/4pages in 1/4 of an hour. Sydney read 43 1/3 pages in 2/3 of an hour. At these rates, would Zander or Sydney read more pages in 1 hour?
(HELP FASTTT
I need help with this I don’t understand the answer
Answer:
the answer is 6
Step-by-step explanation:
PLZ HELP
Overnight, the temperature drops at a rate of 2° per hour. How long will it take for the
temperature to drop 12°?
Answer:
6 hours
Step-by-step explanation:
2x6=12
Of the 60 books on a bookshelf,24 are non-fiction.what percent of the books are non fiction.
fiction?
WILL MARK BRAINLIEST
What is the value of j?
The scatter plot below shows the relationship between hours spent on video games and hours spent on homework last week for students in Ginny's class.
Which of the following is the best estimate of the average change in homework time that was associated with a 111 hour increase in time spent on video games?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
-4−4minus, 4 hours
(Choice B)
B
-\dfrac{4}{3}−
3
4
minus, start fraction, 4, divided by, 3, end fraction hours
(Choice C)
C
-\dfrac{1}{3}−
3
1
minus, start fraction, 1, divided by, 3, end fraction hours
(Choice D)
D
-\dfrac{1}{6}−
6
1
minus, start fraction, 1, divided by, 6, end fraction hours
Answer:Choice B -4/3
Step-by-step explanation:
I need help I don’t understand
At Sunshine Middle school,60% of 800 students participate in music. How
students participate in music.
Answer:
75%
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRAINESLT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
I'd like help you but I'm not sure about this question. But I have a solution, kinda, You could say. If you go to gg and click the camera icon next to the search bar and take a photo of this problem, they will find immediate answers for you that other people have solved, I hope that helps
Solve the system of equations using the linear combination method.
ſc+d_17
Tc-d-3
Enter your answers in the boxes
C
d
Answer: Please rewrite your question or send a pic. It is not clear what you are asking.
Step-by-step explanation:
At a carnival, it costs $0.30 for each chance to throw a ring over a bottle to win a prize. If Anita and Jerome get an even amount of chance and together they have $3.60, how many throws will they get each?
Answer:
c - amount of chances
Step-by-step explanation:
0.30c + 0.30c = 3.60
0.60c = 3.60
c = 6
They will get 6 throws each.
Given two points (2, 7) and (1, -2) on a line, calculate the slope of the line.
A. slope 7
B. slope 8
C. slope 9
D. slope 10
Answer:
Step-by-step explanation:
Slope of line passing through (2, 7) and (1, -2) = (-2-7)/(1-2) = 9
Principal, $2000; Annual interest rate, 5.3%; time, 5 years
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
yes!!? hiii, what do u need?
2x + 7 ≥ x + x + 1
Please solve this and show all of your work!
Answer:
Step 1 : Equation at the end of step 1 : (2x - 1) • (x + 7) = 0 Step 2 : Theory - Roots of a product : 2.1 A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. We shall now solve each term = 0 separately
Step-by-step explanation:
convert 3245ml to liters
Answer:
3.245L
Step-by-step explanation:
3245÷1000 = 3.245L
8. What does the y-intercept represent?
A. It shows that during the week a movie is released, it is rented about 20 times.
B. It shows that 6 weeks after a movie is released, it is rented about 3 times.
C. It shows that 3 weeks after a movie is released, it is rented about 6 times.
D. It shows that 20 weeks after a movie is released, it is rented 0 times.
Please help me RANDOM ANSWERS WILL BE REPORTED
Answer:
About 51 miles per hour
Step-by-step explanation:
What is the probability of rolling a 4, 5 or 6 on a die?
1/36
2/12
1/2
6/9
Someone please help me
9514 1404 393
Answer:
b, d, c, a, e
Step-by-step explanation:
A formula should always come with a definition of the variables it uses. Here, you're supposed to somehow magically figure out what the variables are.
A = P(1 +r/n)^(nt)
A is the amount of the investment of principal P after t years, compounding annual rate r n times per year.
__
Then your blanks get filled like this:
1. A -- b the value
2. P -- d the principal
3. r -- c the annual interest rate
4. n -- a number of times compounded per year
5. t -- e number of years
In the Special Right Triangle below, solve for the value of y. Y = _____ (keep your answer in simplest radical form)
Options
5
5√2
10
10√2
Answer:
Value of Y = 5√2 units
Step-by-step explanation:
Given:
Perpendicular = X
Base = Y
Hypotenuse = 10
Find:
Value of Y
Computation:
Cos θ = Base / Hypotenuse
Cos 45 = Y / 10
1/√2 = Y / 10
Value of Y = 5√2 units