Solve by using substitution. Express your answer as an ordered pair.
1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,
12,883 women finished and 163 dropped out. We want to use a 0.01 significance level to test
the claim that the rate of those who finish is the same for men and women.
a) Test the claim using a hypothesis test (identify the null hypothesis, alternative hypothesis,
test statistic, critical value (or P-value) and conclusion)
b) Test the claim by constructing an appropriate confidence interval.
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).
A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist's estimate? Round the percent to the nearest hundredth if necessary.
Answer:
6%
Step-by-step explanation:
Estimated distance = 80 miles
Actual distance covered = 75.5 miles
We need to find the percent error of the cyclist's estimate. Its formula is given by :
[tex]\%=\dfrac{|\text{actual value-estimated value}|}{\text{actual value}}\times 100[/tex]
Put all the values,
[tex]\%=\dfrac{80-75.5}{75.5}\times 100\\\\=5.96\%[/tex]
or
= 6%
So, the percentage error is 6%.
Answer:
5.96
Step-by-step explanation:
. Austin wants to buy some pens and pencils. He has $30 in his bag. Each pen costs $5 and each pencil costs $1.50. He needs 5 more pencils than pens.Part A how many pencils can $ustin buy at most" Write your answer and your work or explanation in the space below. Part If Austin had $40 in his bag, how many pens could Austin buy at most" Explain how you found the answer in the space below.
Answer:
3 pens
Step-by-step explanation:
Total expenditure (Price x Quantity) on pens & pencils = $30
Let pen quantity be = x , Let pencil quantity be = y
Given : Pen (x) price = 5 , Pencil (y) price = 1.5 , Pencils (y) = Pen (x) + 5
So, 5x + 1.5y = 30
5x + 1.5 (x + 5) = 30 → 5x + 1.5x + 7.5 = 30 → 6.5x + 7.5 = 30
6.5x = 30 - 7.5 → 6.5x = 22.5
x = 22.5 / 6.5 → x = 3.46 ≈ 3 pens
What is the Surface area for a rectangular prism that has the measurements of 2, 12, and 6?
Answer:
216
Step-by-step explanation:
A=2(wl+hl+hw)=2·(12·2+6·2+6·12)=216
Answer: A=216
Step-by-step explanation:
so very sorry if it is not right but, I looked at it and that's what showed up
The Historic Triangle in Virginia connects Jamestown, Williamsburg, and Yorktown. The interior angle at Williamsburg is 120°. The interior angle at Jamestown is twice the measure of the interior angle at Yorktown. Find the measures of the interior angles at Jamestown and Yorktown.
Answer: Interior angles at Jamestown and Yorktown are 40° and 20°, respectively
Step-by-step explanation: Jamestown, Williamsburg and Yorktown form a triangle. The sum of the interior angles of a triangle is 180°.
Suppose interior angle at Yorktown is x. As Jamestown is twice the measure at Yorktown, it means this interior angle is 2x.
Then, the measures will be:
2x + x + 120 = 180
3x = 60
x = 20
Angle at Yorktown is 20°.
So, angle at Jamestown is
2x = 2.20 = 40°
The measures of the interior angles at Jamestown and Yorktown are 40° and 20°, respectively.
please help me i’ve tried so many of these and i can’t figure out how to do it
Answer:
15.4%
Step-by-step explanation:
Calculate the volume of both containers.
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
[tex]V_{A}[/tex] = π × 10² × 11 = 1100π ft³
[tex]V_{B}[/tex] = π × 7² × 19 = 931π ft³
Subtract volume of B from volume of A to find quantity left in A
quantity left in A = 1100π - 931π = 169π ft³
To calculate the percentage left in A after B has been filled
[tex]\frac{left}{full}[/tex] × 100%
= [tex]\frac{169\pi }{1100\pi }[/tex] × 100%
= [tex]\frac{169}{1100}[/tex] × 100%
= 15.4% ( to the nearest tenth )
y/2 = 9 What is the value of y that satisfies the equation
Answer:
y=18
Step-by-step explanation:
pls give brainliest
Write a conjecture that describes the pattern below.
3, 9, 27, 81...
Answer:
3 times 3 is 9
9 times 3 is 27
27 times 3 is 81
Step-by-step explanation:
What is the general form of the equation of the line shown?
Answer:
the general form of the equation of the line will be:
[tex]y-x=2[/tex]
Step-by-step explanation:
Finding the slope:
Taking two points from the line as shown in figure
(-2, 0)(0, 2)Finding the slope between (-2, 0) and (0, 2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)[/tex]
[tex]m=\frac{2-0}{0-\left(-2\right)}[/tex]
[tex]m=1[/tex]
Finding the y-intercept
We know that the y-intercept can be calculated by setting x=0
From the figure, it is clear that at x=0, y=2
Thus, the y-intercept is (0, 2)
We know that the slope-intercept form of the equation line is:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
As we have already determined the slope = m = 1 and the y-intercept b=2.
Substituting the values in the slope-intercept form of the equation line
[tex]y=mx+b[/tex]
[tex]y=(1)x+2[/tex]
[tex]y=x+2[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
As we already know the equation in slope-intercept form
[tex]y=x+2[/tex]
so just simplify the equation to write in standard form
[tex]y-x=2[/tex]
Thus, the general form of the equation of the line will be:
[tex]y-x=2[/tex]
here is this question below
Answer:
10
Step-by-step explanation:
they are actually mutiplicating by 2
so 5x2=10
Answer:
10
Step-by-step explanation:
its all times 2
3x2=6
6x2=12
7x2=14
8x2=16
5x2=10
what is the slope of 6x + y = 60
Answer:
I believe the slope is -6
Step-by-step explanation:
You rearrange the equation to get y by itself
y = 60-6x
then you put the equation in slope intercept form
y = -6x+60
meaning -6 (m) is the slope
At the bookstore, Tim bought a magazine for $4, and five books that all cost the same amount. He spent a total of $129. Which equation expresses how much each book cost?
Answer:
25(b) + 4 = 129
Step-by-step explanation:
b=5
25(5) + 4=129
What is a good estimate for 1,710 2,740 4.322 5,700 7,810 6,395
Answer: If you want to round is so you have a small amount of decimals, you could round to the nearest tenths which would give you 17,102,740 4.3
Step-by-step explanation:
help plzz Charli pays $18.00 for 5 t-shirts he needs your help to answer the following questions.
Answer:
What do you but in the chart? Also, part 2 is 72
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
If each t-shirt costs 3.6 dollars then you would have to multiply 3.6 by 20 shirts which will equal to 72. So Charlie has to pay 72 dollars for 20 shirts.
A serving of walnuts is 2/3 of a cup. How many servings are there in a 5 1/3-cup bag of walnuts?
Answer:
8 servings.
Step-by-step explanation:
The answer is 8 because 2/3 multiplied by 8 or 8/1 equals 16/3 and 16/3 simplified is 5 1/3
ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!
In how many years will $12,000 yield an interest of $4,800 at 10% simple interest? *
A. 25 years
B. 0.04 year
C. 4 years
D. 0.25 years or 3 months
Answer:
Time= 4 years
Step-by-step explanation:
Giving the following information:
Principal (P)= $12,000
Interest rate (r)= 10% = 0.10
Interest earned (I)= $4,800
To calculate the time required to gain $4,800 interest, we need to use the following formula:
T= I / (P*r)
T= 4,800/(12,000*0.1)
T= 4 years
Select all the true statements.
- 1.9 is to the left of -1.48.
-1.9 is to the right of -1.48.
1.9 is closer to 0.
-1.48 is closer to 0.
-1.48 is less than – 1.9.
-1.48 is greater than -1.9.
Answer:
-1.9 is to the left of -1.48.
-1.48 is closer to 0.
-1.48 is greater than -1.9.
Answer:
statements 1,4,5
Step-by-step explanation:
What is the value for 3-2m<7
Answer:
m>−2
Step-by-step explanation:
3-2m<7
subtract 3 from both sides
-2m<4
divide by 2
m>−2
Find the slope of the line passing through the points (-7, -4) and (8,8).
Answer:
Hope its work for you
Step-by-step explanation:
As we know that,
slope=m=(Y2-Y1)/(X2-X1)As given values
take, (X1,Y1)=(-7,-4)
(X2-Y2)=(8,8)
hence X1=-7 , Y1= -4 , X2=8 , Y2= 8
putt the values in the above equation of slope we get ,
m=(8-(-4))/(8-(-7)
m=12/15 AnsAnswer:
0.8
Step-by-step explanation:
Slope=(y2-y1) (8--4) (12)
(x2-x1)= (8--7)= (15)= 0.8
Solve 6x+8+7x-9=90 this is pretty hard tbh
Answer:
x=7
Step-by-step explanation:
6x+8+7x-9=90
13x+8-9=90
13x-1=90
add 1 to both sides
= 13x=91
divide both sides by 13
= x=7
Penelope earned $50 in May. She earned $60 in June.
What is the percent increase or decrease in Penelope's monthly earnings?
A. 30% decrease
B. 25% increase
C. 20% decrease
D. 20% increase
b)25%
espero ter ajudado
is this proportional relationship? please help!!
Answer:
yes, the slope is the same throughout the table
Step-by-step explanation:
Answer:
Yes, the graph shown is a proportional relationship.
Step-by-step explanation:
If you divide the distance (6) by the time (1) you get the same thing (6). Repeat for all the terms in the graphs. Since 6/1 is 6, 12/2 is 6, 18/3 is 6 and 24/4 is 6, The relationship is proportional.
Which are correct statements regarding proofs? Select three options.
In a paragraph proof, statements and their justifications are written in sentences in a logical order.
A two-column proof consists of a list statements and the reasons the statements are true.
A flowchart proof gives a visual representation of the sequence of steps without justifications.
A flowchart proof is a visual way of describing the statements and reasons for a proof.
A two-column proof lists only the given information and what is to be proven.
Answer:
A. a two-column proof consist of a list of statements and the reasons the statements are true.
B. a flowchart proof gives a visual representation of the sequence of steps without justification.
D. a two-column proof list only the given information and what is to be proven.
Step-by-step explanation: This is the correct answer on Edge 2021, just took the quiz. Hope this helps. ^-^
The correct statements are:
In a paragraph proof, statements and their justifications are written in sentences in a logical order.
A two-column proof consists of a list of statements and the reasons the statements are true.
A flowchart proof is a visual way of describing the statements and reasons for a proof.
What is a flowchart?A flowchart is a graphical representation of a process, algorithm, or system that uses symbols, shapes, and arrows to depict the various steps and their interconnections.
We have,
In a two-column proof, each statement is listed in one column, and the justification for the statement is listed in a separate column.
A flowchart proof also provides a visual representation of the sequence of steps, but it includes justifications for each step.
So,
The following statements are incorrect:
A flowchart proof gives a visual representation of the sequence of steps without justifications.
A two-column proof lists only the given information and what is to be proven.
Thus,
The correct statements are:
In a paragraph proof, statements and their justifications are written in sentences in a logical order.
A two-column proof consists of a list of statements and the reasons the statements are true.
A flowchart proof is a visual way of describing the statements and reasons for a proof.
Learn more about flowcharts here:
https://brainly.com/question/14598590
#SPJ5
These fraction are part of a list of students quiz scores. Choose ALL scores that are equal to 80%
A.) 8/20
B.) 8/10
C.) 24/30
D.) 16/20
E.) 16/30
Answer:
B and D
Step-by-step explanation:
I'm pretty sure but definitely B
The greater of two integers is 10 more than twice the smaller integer. The sum of the two integers is -8. Find the integers.
Answer:
-6, -2
Step-by-step explanation:
» Which pair of numbers has an LCM of 60?
2 and 12
5 and 12
6 and 12
3 and 12
Answer: 5 and 12
Step-by-step explanation:
2 and 12 is not it because 12 can be divided by 2 meaning that the LCM of those two numbers will be 12.
6 and 12 is not it because 12 can also be divided by 6 meaning that the LCM of 6 and 12 is also 12.
3 and 12 is also the same, 12 can be divided by 3 so their LCM will be 12.
With 5 and 12, 12 is not divisible by 5 so you will have to find the multiples of 5 and 12 and it will eventually be 60.
Multiples of 5: 5, 10,15,20,25,30,35,40,45,50,55,60,65
Multiples of 12: 12, 24, 36, 48, 60, 72
As it appears in both multiples, 60 is the least number that appears in both multiples so the LCM of 5 and 12 is 60.
Answer:
It's 5 and 12
Step-by-step explanation:
Antwaun waters his lawn 3 times a week. If he watered his lawn 24 times in all, which equation could be used to find how many weeks he has been watering his lawn?
(It's not 8, I know that) PLEASE HURRY
Answer:
Antwanun waters his lawn 3 times a week, he watered his lawn 24 . So what you will need to do is divide 3 in 24 to find how many weeks he has been watering his lawn, You get 8. Mr. Antwanun has been watering for 8 weeks. Equation- Antuwantun waters his lawn 3 times a week so if he watered his lawn 24 times, 3 times a week he would have been watering his lawn for 8 weeks.
Answer:
3x=24
Step-by-step explanation:
3 times a certain amount equals 24 times in total
given f (x) = 5x + 1, find f (-3)
Answer:
f(- 3) = - 14
Step-by-step explanation:
To evaluate f(- 3), substitute x = - 3 into f(x), that is
f(- 3) = 5(- 3) + 1 = - 15 + 1 = - 14
Identify the equation in slope-intercept form for the line containing the point (2,4) and perpendicular to y=1/2x+1/2.
Answer:
y = − 2 x
Step-by-step Explanation:
Y + 2 = − 2 ⋅ ( − 1 ) Write in y = m x + b form.
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
m in perpendicular = − 1 2
(1,-2),y=(1)/(2)x+4
I hope I helped!
Answer:
y = -2x + 8
Step-by-step explanation:
For this problem we need to consider that the equation of a line perpendicular to another line will have a "negative reciprocal" slope so that when they cross, it forms a 90-degree angle, hence perpendicular. Additionally, we will need to use the point-slope form and re-write it into the slope-intercept form to incorporate (2,4) into our equation. With these things in mind, let's do that.
y = (1/2)x + (1/2)
We want a "negative reciprocal" so:
y = -2x + (1/2)
Since -2 is the "negative reciprocal" of 1/2.
And now we want to use the point-slope form to incorporate (2,4)
y - y0 = -2 ( x - x0 )
Where, y0 = 4 and x0 = 2.
y - y0 = -2 ( x - x0 )
y - 4 = -2 ( x - 2 )
y - 4 = -2x + 4
y = -2x + 8
So, the equation that is perpendicular to y = (1/2)x + (1/2) and includes the point (2,4) is y = -2x + 8.
Cheers.