Answer:
(a) Explained below.
(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).
Step-by-step explanation:
The information provided is:
n (Men who finished the marathon) = 25,221
n (Women who finished the marathon) = 12,883
Compute the proportion of men and women who finished the marathon as follows:
[tex]\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988[/tex]
The combined proportion is:
[tex]\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989[/tex]
(a)
The hypothesis is:
H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.
Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.
Compute the test statistic as follows:
[tex]Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78[/tex]
Compute the p-value as follows:
[tex]p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075[/tex]
The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.
Thus, concluding that the rate of those who finish is the same for men and women.
(b)
Compute the 99% confidence interval for the difference between proportions as follows:
The critical value of z for 99% confidence level is 2.58.
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
[tex]=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\[/tex]
Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).
true or false:
Question attached:
Answer:
true
Step-by-step explanation:
If log25 ~ 2.3219,
evaluate log280.
Answer:
You need to write log_2 80 in terms of log_2 5 , such that:
log_2 80 = log_2 (8*10)
Using the properties of logarithms, you need to convert the logarithm of product in summation of logarithms, such that:
log_2 (8*10)= log_2 8 + log_2 10
Since log_2 10 = log_2 (2*5) , yields:
log_2 (8*10)= log_2 8 + log_2 (2*5)
log_2 (8*10)= log_2 8 + log_2 2 + log_2 5
You need to write 8 as power of 2, such that:
log_2 (8*10) = log_2 (2^3) + log_2 2 + log_2 5
Using the power property of logarithms, log_a b^c = c*log_a b yields:
log_2 (8*10) = 3log_2 2 + log_2 2 + log_2 5
Since log_2 2 = 1 yields:
log_2 (8*10) = 3 + 1 + 2.3219
log_2 (8*10) = 4 + 2.3219 => log_2 (8*10) = 6.3219
Hence, evaluating the given logarithm , using the indicated properties of logarithms, yields log_2 (8*10) = 6.3219 .
Step-by-step explanation:
The value of [tex]log_2{80}[/tex] if [tex]log_25 = 2.3219[/tex] is 6.3219.
What is a logarithm?The logarithm is exponentiation's opposite function in mathematics.
This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.
Given, [tex]log_25 = 2.3219[/tex].
Now, To obtain the value of [tex]log_2{80}[/tex] we'll break it into suitable smaller parts.
Therefore,
[tex]log_2{80} = log_2({8\times10})[/tex].
[tex]log_2{80} = log_28 + log_210[/tex]
[tex]log_2{80} = log_28 + log_2({2\times5})[/tex].
[tex]log_2{80} = log_28 + log_22 + log_25[/tex].
[tex]log_2{80} = 3 + 1 + 2.3219[/tex].
[tex]log_2{80} = 6.3219[/tex].
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Write the slope-intercept form of the equation of each line.
x + 5y - 10
Answer:
y = -1/5x + 2
Step-by-step explanation:
I will assume the "-" is an equal sign. Solve for y.
x + 5y = 10
~Subtract x to both sides
5y = 10 - x
~Divide 5 to everything
y = 2 - 1/5x
~Reorder
y = -1/5x + 2
Best of Luck!
In Riverview Middle School, 20% of the students participate in after-school clubs. For every 100 students, how many are in an after-school club?
2
5
20
80
Answer:
20
Step-by-step explanation:
I hope this helps :))))
A turtle walks of a mile in 40 minutes. What is the unit rate when the turtles speed is expressed in miles per hour (60 minutes)? (needs to be a denominator)
Answer:
1.5 miles per hour.
Step-by-step explanation: Because is a turtle walks a mile in 40 minutes then half of that is 20 or half a mile which that 40 minutes plus 20 minutes is 60 minutes.
Hi there! Someone please help me with this question correctly :)
I’ll mark brainliest and give out points
Answer:
y=x+4
Step-by-step explanation:
So uh, i dont know how to explain, but fairly sure its y=x+4
what is the domain of the function f(x)=|x|
Answer:
All Real
Step-by-step explanation:
WILL GIVE BRAINLIEST
Quadrilaterals PQRS and TUVW are similar
What is the value of b in yards?
O 0.5 yd
0 3.2 yd
O 12.5 yd
0 28.8 yd
Answer:
3.2
Step-by-step explanation:
depending on what W-T looks like it seems the best answer
♡ The Question ♡
Quadrilaterals PQRS and TUVW are similar.
What is the value of b in yards?
* ୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
3.2 yd!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
No Explanation/Step-By-Step provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-No tips provided!
Find the x and y intercept of the line below
3x + 4y = 12
Answer: x intercept (4,0) y intercept (0,3)
Step-by-step explanation:
why are the properties of equality important in solving equations?
Step-by-step explanation:
As equations get more complex it is important to use properties of equality to isolate the variable and solve the equation. Here are the properties of equality you need to isolate terms and solve equations. The Subtraction Property of Equality is used when you have an equation with addition in it
please help!
Find the slope of a line that passes through the
following ordered pairs. Reduce to lowest
terms.
(7, 1) (0, -3)
Question 1 (5 points)
(02.01 LC)
Line segment AB has a length of 5 units. It is translated 3 units to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime? (5 points)
a. 2 units
b. 3 units
c. 4 units
d. 5 units
Answer:
The answer to this question is b. 3 units
Answer:
D. 5 Units
Step-by-step explanation:
A translation is a different way of saying that the shape was moved. So since this is a movement nothing changed about the length of the line segment, meaning the line segment stayed 5 units.
Which expression is the simplest form of
(x4/7)^7
Answer:
7
Step-by-step explanation:
What is the product of 7/10 and 3 2/3?
1 3/5
1 13/15
2 17/30
3 7/15
David roller skates 33 miles in 2
3/4 hours. What is his average speed in
miles per hour?
Answer:
12 miles per hour
Step-by-step explanation:
Two hundred wildebeests and 150 gazelles grazed on the savannah what was the ratio of gazells to wildebeests grazing on the savannah/
Answer:
150:200
Step-by-step explanation:
You can simplify it too. 3:4
Given that 7x−7y=18
Find x when y=−6
Give your answer as an improper fraction in its simplest form.
Answer:
-24/7
Step-by-step explanation:
7x -7(-6) = 18
7x + 42= 18
7x = -24
x= -24/7
Which scatterplot BEST suggests a linear relationship between X and Y? URGENT!!!!!!!!!!!!!!! HELP PLEASE AND FAST!!!!!!
The scatterplot that best represent a linear relationship between the variables, X and Y, is: graph C.
What is a Linear Relationship?On a scatterplot, the trendline that shows a linear relationship between two variables will have a straight line pattern that either slopes up or down.
The scatter plot in graph C shows a trendline that slopes along a straight line. Therefore, the answer is C.
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3. Which polynomial has a leading coefficient of 4 and a degree of 3?
1 . 3x4 - 2x2 + 4x - 7
2. 4x4 - 3x3 + 2x2
3 .4 + x - 4x2 + 5x
4. 2x + x2 + 4x3
Answer:
4
Step-by-step explanation:
write the equation of the line that passes through two points in slope intercept form (-8,1) and (2,-4)
Answer: Answer and explanation in pic
Step-by-step explanation:
(n+8)/5=(n-1)/2 what is n
Answer:
Step-by-step explanation:
n=7
Evaluate start fraction 2 over 3 end fractionx for x = three-fourths
A. one-half
B. eight-ninths
C. The fraction states 9 over 8.
D. 2
Answer:
A
Step-by-step explanation:
Help i will give brainliest to the first one to have a REAL answer
Answer:
y = -32
Step-by-step explanation:
-6 (y+15) = -3y + 6
-6y - 90 = -3y + 6
-3y - 90 = 6 + 90
= -3 = 96
y = -32
Answer:
Y=28
Step-by-step explanation:
Distribute-6(y+15) > -6y-90
-6y-90=-3y+6 add the -3y to the -6y and the -90 to the 6
-3y=-84
Then just divide -84 by -3
May anyone help I’ll give 15 :)
Answer:
B. No. -6.5 is to the left of -6.3 on a number line. He should have switched the last two numbers.
Step-by-step explanation:
When flipping a coin, the probability of getting tails is 50% and heads 50%. What is the probability of getting heads
or tails?
50%
60%
75%
100%
Answer:
50%
Step-by-step explanation:
Most people assume the toss of a coin is always a 50/50 probability, with a 50 percent chance it lands on heads, and a 50 percent chance it lands on tails
Answer:
100%
Step-by-step explanation:
There is a 50% chance of getting heads, and 50% chance of getting tails.
If these two options are added together, you get 100%. There are only two options on a coin flip anyways, so the probability of getting heads or tails would be 100%.
You are selling candy bars for a fundraiser. you want to sell at least $200. If snickers cost $2 per bar and M&M's cost $3 per bag, then write an inequality that represents all the possible combinations you can sell to meet your goal.
Answer:
Step-by-step explanation:
Goal = > $2500
Amount raised = $700
Amount needed to raise = $2500 - 700 = $1800
Number of candy bars needed = x
Price of a candy bar = $1.50
1.5x > 1800
x > 1800 ÷ 1.5
x > 1200
Answer: They need to sell more than 1200 candy bars.
2X+20 and X+60 I have to solve for X
Answer:
x = 40
Step-by-step explanation:
I don't understand, but I think you mean 2x + 20 = x + 60
So that's what I'm going to solve for if that's wrong tell me what you mean.
2x + 20 = x + 60 (subtract 20 on both sides)
2x = x + 40 (subtract x on both sides)
x = 40
HOPE THIS HELPS!
IF YOU HAVE A QUESTION ABOUT THIS COMMENT.
Answer:
x = 26.6
Step-by-step explanation:
1. 2x+20+x+60
2. Combine like factors (x' s, and 20+60)
3. 3x+80
4. divide 80 from 3 (80/3)
5. 26.6
What is the y-intercept of -x + 4 = y? *
Answer:
4
Step-by-step explanation:
Im sure it is as y=mx +c c being the interceot and mx as the gradient
Answer:
(0,4)Step-by-step explanation:
Keesha has 12 glue bottles and 42 craft sticks.
What is the greatest number of supply bags
she can make if she puts an equal amount of
both in each bag?
Answer:
4 i believe
Step-by-step explanation:
The solution of a+b>12 is a>−3. What is the value of b?
Answer:
we conclude that when we substitute b = 15, the solution of the inequality becomes:
[tex]a>-3[/tex]
Therefore, the value of b = 15.
The solution graph is also attached.
Step-by-step explanation:
Given the inequality expression
[tex]a+b>12[/tex]
Putting b = 15 in the inequality expression
[tex]a+b>12[/tex]
[tex]a+15>\:12[/tex]
subtract 15 from both sides
[tex]a+15-15>12-15[/tex]
simplify
[tex]a>-3[/tex]
Thus, we conclude that when we substitute b = 15, the solution of the inequality becomes:
[tex]a>-3[/tex]
Therefore, the value of b = 15.
The solution graph is also attached.