Using the z-distribution, it is found that the data provides convincing evidence that the proportion has increased.
What are the hypotheses tested?At the null hypotheses, it is tested if the proportion has not increased, that is, the difference of the 2017 proportion and the 2014 proportions is not positive, hence:
[tex]H_0: p_2 - p_1 \leq 0[/tex]
At the alternative hypothesis, it is tested if the proportion has increased, hence:
[tex]H_1: p_2 - p_1 > 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given by:
[tex]p_1 = 0.197, s_1 = \sqrt{\frac{0.197(0.803)}{61}} = 0.0509[/tex]
[tex]p_2 = 0.383, s_2 = \sqrt{\frac{0.385(0.615)}{52}} = 0.0675[/tex]
Hence, for the distribution of differences, they are given by:
[tex]\overline{p} = p_2 - p_1 = 0.383 - 0.197 = 0.186[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0509^2 + 0.0675^2} = 0.0845[/tex]
What is the test statistic?It is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which p = 0 is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{0.186 - 0}{0.0845}[/tex]
z = 2.2
What is the decision?Considering a right-tailed test, as we are testing if the proportion is higher than a value, the critical value at the 0.05 significance level is [tex]z^{\ast} = 1.645[/tex].
Since the test statistic is greater than the critical value for the left tailed test, the data provides convincing evidence that the proportion has increased.
More can be learned about the z-distribution at https://brainly.com/question/26454209
Which graph shows the solution to 8y < 4x + 16? A. B. C. D.
Answer:
The answer is D.
Step-by-step explanation:
Find the boundary line, and then just shade the area.
y < 1/2x + 2
Answer:
d
Step-by-step explanation:
2023
Solve the following: A)4x-1/2=x+7
B)3x+2=2x+13/3
(Please help)
Answer:
A) x = 2.5
B) x = 7/3
Step-by-step explanation:
A) 4x - 1/2 = x + 7
4x - x = 7 + 1/2
3x = 7.5
x = 7.5/3
x = 2.5
B) 3x + 2 = 2x + 13/3
x +2 = 13/3
x = 13/3 - 6/3
x = 7/3
I hope this helps!
pls solve the following math from trigonometry
Step-by-step explanation:
[tex] \tan(2x) = 1.5[/tex]
Take the arc tangent,
[tex] \tan {}^{ - 1} ( \tan(2x) ) = \tan {}^{ - 1} (1.5) [/tex]
[tex]2x = 56.3[/tex]
[tex]x = 28.15[/tex]
b.
[tex](3 \cos(x) + 1)(2 \cos(x) + 3) = - 2[/tex]
[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 3 = - 2[/tex]
[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 5 = 0[/tex]
[tex]6 \cos {}^{2} (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0[/tex]
[tex]6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0[/tex]
[tex](6 \cos(x) + 5)( \cos(x) + 1) = 0[/tex]
Set each factor equal to zero.
[tex]6 \cos(x) + 5 = 0[/tex]
[tex]6 \cos(x) = - 5[/tex]
[tex] \cos(x) = - \frac{5}{6} [/tex]
[tex]x = \cos {}^{ - 1} ( \frac{5}{6} ) [/tex]
[tex]x = 146.4[/tex]
For the second factor,
[tex] \cos(x) + 1 = 0[/tex]
[tex] \cos(x) = - 1[/tex]
[tex]x = 180[/tex]
So the answer for the second one is
146.4 and 180.
7. Instructions: Find the missing side of the triangle.
Answer:
50²-30²=x²
2500-900=1600
√1600= 40
x=40
Find the volume of the triangular prism.
4 ft
8 ft
37 ht
Answer:
4 ft
Step-by-step explanation:
So to calculate the volume of a triangular prism, the formula is 4ft
Step-by-step explanation:
volume of prism = area of triangle * length
= 1/2*4*8*37
= 592ft^3
i need help im stuck lol
Answer: Angle A = 120 degrees.
Step-by-step explanation:
Answer:
50 degrees sorry if wrong
Step-by-step explanation:
PLS HELP Solve for x
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
If two secants are drawn from a point outside a circle, then product of one secant segment and its external part equal the product of the other secant segment and its external part.
(Secant-Secant Power Theorem)
(JG)(JH) = (JM)(JK)
(16) X (7) = (8+X)(8)
112=64+8X
8X=48
X=6
What is the value of
-8(17-12)
—————
-2(8-(-2)
-4
-2
2
4
Answer:
4
Step-by-step explanation:
smart
Please help me solve this question
Shannon mistakenly mixed up angles A and B. Notice the side 9 is opposite angle B and not angle A.
She should replace every copy of uppercase A with uppercase B. Also, she should replace lowercase 'a' with lowercase b
This is what her steps should look like
[tex]\frac{\sin B}{b} = \frac{\sin C}{c}\\\\\frac{\sin B}{9} = \frac{\sin 125^{\circ}}{12}\\\\B= \sin^{-1}\left(\frac{9*\sin 125^{\circ}}{12}\right) \approx 37.9^{\circ}\\\\[/tex]
Then we can find angle A like this
[tex]A+B+C = 180\\\\A = 180 - B - C\\\\A \approx 180 - 37.9 - 125\\\\A \approx 17.1^{\circ}\\\\[/tex]
Angle A is approximately 17.1 degrees.
i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help
Answer: 176 cubic cm
Step-by-step explanation:
Formula for finding volume is l x w x h
The first rectangle on the bottom:
2 x 2 x 8 = 32
The second rectangle next to it:
3 x 6 x 8 = 144
Now add the two values to get the volume of the figure
144 + 32= 176
Help me please I do not understand this assignment
Answer:
Step-by-step explanation:
Equation: y = 20x
y = # of gallons
x = minutes
6.
So, you substitute (0, 1, 2, 3 and 4 minutes) for x, to find the number of gallons:
x = 0 mins:
y = 20x
y = 20(0)
y = 0 gallons
(0, 0)
x = 1 min.
y = 20x
y = 20(1)
y = 20 gallons
(1, 20)
x = 2 mins.
y = 20x
y = 20(2)
y = 40 gallons
(2, 40)
x = 3 mins.
y = 20x
y = 20(3)
y = 60 gallons
(3, 60)
x = 4 mins.
y = 20x
y = 20(4)
y = 80 gallons
(4, 80)
7. View the attached graph
8. Predict the amount of water in the tank after 6 mins.
We use the same equation, y = 20x for this question
y = 20x
y = 20(6)
y = 120 gallons
(6, 120)
8. Linear ==> straight line
Non-linear ==> anything other than a straight line (curved line)
As you can see from my attached graph, the relationship between x and y and linear, because the graph has a straight line.
Hope this helps!
What is the first step when rewriting y = –4x2 + 2x – 7 in the form y = a(x – h)2 + k?
2 must be factored from 2x – 7
–4 must be factored from –4x2 + 2x
x must be factored from –4x2 + 2x
–4 must be factored from –4x2 – 7
Answer:
–4 must be factored from –4x2 + 2x
An airplane flies with a constant speed
of 820 miles per hour. How far can it
travel in 1 hour?
820 miles
to find:how far the airplane can travel in an hour.
solution:x= v × t
x= 820 × 1
x= 820 miles
so, the airplane can travel 820 miles per hour.
How many lines of symmetry does the following figure have?
1
3
4
5
Answer:
1
Step-by-step explanation:
It has 1 lines of symmetry
Hopes this helps
#ViolentJax
Hi Please help!
Identify the RATE OF CHANGE and INITIAL VALUE from ONE of the equations listed.
A. y = 3x + 6
B. y = -7x + 5
C. y = 9x + 4
Answer:
C
Step-by-step explanation:
pls tell me if im right or wrong
Hello Brainilest Brains, I was wondering what 87x72 is. Please say the answer in the answer section below. Thanks for the help!
Answer:
6,264
Step-by-step explanation:
Answer:
6264
Step-by-step explanation:
72 x 8 = 576
576 x 10 = 5760
72 x 7 = 504
5760 + 504
6264
i do not know this answer
We know that 2+2 is 4.
34 - 4 is 30.
Therefore, the legnth, a, is half of thirty.
30/2 = 15
a = 15
[tex]\bf a= 15\;\; millimetetrs[/tex]
Step-by-step explanation:
perimeter: 34 millimetetrs
perimeter= [tex]\tt a+2+a+2=34[/tex]
[tex]\tt 2a+4=34[/tex]
[tex]\tt 2a+4-4=34-4[/tex] (Subtract 4 from both sides)
[tex]\tt 2a=30[/tex] (Simplify)
[tex]\tt \cfrac{2a}{2}=\cfrac{30}{2}[/tex] (Divide both sides by 2)
[tex]\tt a=15[/tex]
Therefore, a= 15 millimetetrs.
~
i need help with this question!!
Jason customizes and sells water bottles. He must sell each water bottle for less than $15, otherwise then nobody may buy them. Which number line represents all the possible prices for which Jason could sell a water bottle and make a profit?
Answer:
i cant really tell because there is no real explannation
Step-by-step explanation:
At a football game, 92% of people attending were supporting the home team, while 8% were supporting the visiting team. If 1564 people attending the game supported the home team, what was the total number of people attending the game?
The total number of people attending the game is 1700.
What is Percentage?Percentage in simple terms can be defined as a part per 100.
Percentage is a ratio or number which has to be defined as a fraction of 100.It is denoted by %.
If we are asked to calculate the percent of a number simply divide it by the whole part or number and then multiply with 100.
Percent of people supporting the home team = 92%
Number of people supporting the home team = 1564
Let x be the total number of people attending the game.
⇒ [tex]\frac{1564}{x}[/tex] × 100 = 92
⇒ [tex]\frac{1564}{x}[/tex] = 0.92
⇒ x = [tex]\frac{1564}{0.92}[/tex]
⇒ x = 1700
Hence, the total number of people attending the game will be 1700.
To learn more on Percentage, click:
https://brainly.com/question/28998211
#SPJ2
A new truck can travel 350 miles on 25 gallons of gas.
a
How far can it travel on 60 gallons of gas?
b.
What is the cars gas mileage (miles per gallon)?
Answer:
A. 840 miles
B. 14 miles per gallon
Step-by-step explanation:
A. 14 mi. per gal. x 60 = 840 miles
B. 350 mi./25 gal. = 14 miles per gallon
hope this helps :)
1. The truck can travel 840 miles on 60 gallons of gas.
2. The truck's gas mileage is 14 miles per gallon.
What is Proportion?Proportion refers to the relationship or comparison between two quantities or parts of a whole. It is often expressed as a ratio or a fraction. In mathematics, a proportion states that two ratios or fractions are equal.
a) We have, 25 gallons of gas corresponds to 350 miles.
Let's set up the proportion:
25/350 = 60/x
25x = 350 (60)
25x = 21,000
x = 21,000 / 25
x = 840
Therefore, the truck can travel 840 miles on 60 gallons of gas.
b) The truck can travel 350 miles on 25 gallons of gas.
Gas mileage = Distance / Gas consumed
Gas mileage = 350 miles / 25 gallons
Gas mileage = 14 miles per gallon
Therefore, the truck's gas mileage is 14 miles per gallon.
Learn more about Proportion here:
https://brainly.com/question/26974513
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Pierre has more money than alex.
if Pierre gave Alex £20 they would have the same amount.
if Alex gave Pierre £22, the Pierre would have twice as much as Alex.
How much does each one actually have?
Answer:
p = 2a-22
a= p-20
these will help you find the actual value
Step-by-step explanation:
this is not for the actual value
pierre = p
alex = a
p = a+20
p-20 = a
p+22 = 2a
p = 2a-22
A bakery had 14 bran muffins, 19 banana muffins, and 23 pumpkin muffins left at the end
of the day. The leftover muffins were placed into boxes of assorted muffins. There were
8 muffins in each box. How many boxes of assorted muffins were there?
Determine if these statements are correct. Select True or False.
. To solve, add first, and then divide.
O True O False
To solve, divide first, and then add.
O True O False
There were 7 boxes of assorted muffins.
O True O False
There were 8 boxes of assorted muffins.
O True O False
This is a one-step division problem.
O True O False
Answer:
(I put the answers in bold)
To solve, add first, and then divide.
O True O False
To solve, divide first, and then add.
O True O False
There were 7 boxes of assorted muffins.
O True O False
There were 8 boxes of assorted muffins.
O True O False
This is a one-step division problem.
O True O False
Step-by-step explanation:
To get the answer I added all the numbers to get fifty-six and divided it by eight to get seven.
solve for X: x = −b ± √b²-4ac/2a
two correct answers :
x = -2c
or
x = -2b - 2c
Find the area of the figure.
12 mm
6 mm
5 mm
CAN SOMEONE PLS HELPP
What is the greatest common factor of 6x^2+18x-36
Answer:
6
Step-by-step explanation:
if the mean of 4 6 9 11 10 and k is 8 what is its median
4.289 rounded to the nearest tenth
dd2+2
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Answer: umm what did you say?
Step-by-step explanation:
A
group of friends were working on a student film that had a budget of $1300.
They spent all their budget on equipment and props. They used 55% of their
budget on props. How much money did they spend on equipment?