Answer:
5.0in/secStep-by-step explanation:
[tex]Circumference = 2\pi r\\\\2 \pi \times 40 ft = 80\pi ft = 253.3274123 ft\\\\= 253.3274123 ft \times 12 \: \frac{inches }{feet} \\\\ = 3015.928947 in\\\\\\10 min = 10 min \times 60 \: sec / min = 600 sec\\\\4 \: revolutions / 10 min = 4 \times 3015.928947\: in / 600 sec \\\\ = 5.0 in/sec[/tex]
The linear velocity of the Ferris wheel is 20.1 inches per secnod.
What is the angular velocity of a rotating body?Suppose the body revolves θ angle in t time then the angular velocity of the body is
ω= θ/t
What is the linear velocity of a rotating body?Suppose the rotating body covers 's' distance in 't' which is actually 'rθ' distance in 't' time because, s=rθ.
Then the linear velocity of the rotating body is
v=s/t=r(θ/t)=r ω
i.e. v=r ω.
How to solve the problem?The speed of the Ferris wheel is given by 4 revs in 10 minutes. That means 4(2π) radians in 10 minutes.
Hence, the angular velocity of the Ferris Wheel is
ω= 8π/(10×60) rad/s= π/(75) rad/s
Hence, the linear velocity of the Ferris Wheel is
v=r ω= 40 Feet ( π/(75) rad/s)
= (12×40π)/(75) inch/s
= 20.1062 inch/s
≈20.1 inch/s (rounded to the nearest tenth)
To learn more about the Angular velocity visit- https://brainly.com/question/13649539?referrer=searchResults
#SPJ2
Your math professor gives you a set of 10 problems and tells you that the final exam will consist of a random selection of 5 of them. If you figured out how to do 7 of the problems, what is the probability that you answer correctly (a) all 5 problems
Answer:
0.083
Step-by-step explanation:
To solve the above question, we use the combination method.
C(n, r) = nCr = n!/r!(n - r)!
Probability of answering (all 5 correctly)
= Probability of answering ( 5 out of 7 correctly)/ Probability of answering (5 out of 10 problems)
Probability of answering ( 5 out of 7 correctly) = 7C5
nCr = n!/r!(n - r)!
= 7!/5! (7 - 5)!
= 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (2 × 1)
= 21 ways
Probability of answering (5 out of 10 problems) = 10C5
nCr = n!/r!(n - r)!
= 10!/5! (10 - 5)!
= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (5 × 4 × 3 × 2 × 1)
= 252 ways
Probability of answering (all 5 correctly)
= 21/252
= 0.0833333333
Approximately = 0.083
If a data set produces SSR = 400 and SSE = 100, then the coefficient of determination is a. .10. b. .80. c. .25. d. .40.
Answer: 0.8
Step-by-step explanation:
Given the following :
Sum of Square Error Error (SSE) = 100 which is the difference between the actual and predicted value.
Sum of Square due to regression (SSR) = 400
The Coefficient of determination (R^2) :
(Sum of Square Regression(SSR)) / Sum of Squared total (SST))
Sum of Squared total (SST) = SSE + SSR
Sum of Squared Total = (100 + 400) = 500
R^2 = 400 / 500
R^2 = 0.8
Write an equation of the line below.
Answer:
y = x - 1
Step-by-step explanation:
If you have 200 cupcakes and you give 90 how many do you have left
Answer:
110 cupcakes are left
Step-by-step explanation:
200-90 is 110
Answer:
110 cupcakes
Step-by-step explanation:
If you have 200 cupcakes and you give away 90, that means you only have [tex]200-90[/tex] cupcakes left.
[tex]200 - 90 = 110[/tex]
So you have 110 cupcakes left.
Hope this helped!
A mountain biker gets halfway up a hill and realizes he forgot his water, so he returns to his starting point.
Answer:
True
Explanation:
1/2 (up the hill) - 1/2 (down the hill) = 0
Find the value of 83 - [59 - (22 - 18)].
Answer:
28
Step-by-step explanation:
83 - [59 - (22-18)]
= 83 - [59 - 4]
= 83 - 55
= 28
Which of the following expressions does not represent "four more than one-third x"?
Options:
1/3x + 4
x/3 + 4
1/4x + 3
Please explain well so I can understand it. Thanks! :)
Answer:
1/4x + 3
Step-by-step explanation:
The question said one-third(1/3) not one-fourth(1/4).
1/3x + 4 can also be written as x/3 + 4.
Answer:
1/4x + 3
Step-by-step explanation:
expressions does not represent "four more than one-third x"
1/3x + 4 --- No.
x/3 + 4 --- No.
1/4x + 3 --- Yes. it does not represent 4 + 1/3x. you can tell it by +3
Kara needs to fence her yard. How many feet of fencing is needed?
A. 370 feet
B. 500 feet
C. 13, 700 feet
D. 15, 000 feet
Answer:
newzz new new me he new new
Answer:
oiuhj90pkomnjhb vcfgtyu789i0op,lmkn bvghyu7890opklmnjbhgvfty67890-p[lkjhngvty67u890-op[l;',
Step-by-step explanation:
Gunnar’s car gets 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. PART B: Gunnar’s car is close to empty and only has 0.98 gallon of gas left. He stops at a gas station that charges $2.05 per gallon of gas. How much does it cost for Gunnar to refill his tank? Round your answer to the nearest penny.
Answer:
399.17 miles
Step-by-step explanation:
Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.
Gunnar's car travels with one gallon of gas = 22.4 miles
He can travel with 17.82 gallon of gas = 17.82 × 22.4
= 399.168 ≈ 399.17 miles
Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.
Write the algebraic expression without parentheses. - (- 7 + 7 y) 7 + 7y 7 - 7y -7 + 7y 49y
the answer is 7-7y i think if not the it should be 7+7y
16. In the adjoining figure, if ll|m, then find the value of angle x
Step-by-step explanation:
Hey, there!!
Let's solve it simply,
angle ONP = 60°+55° { as exterior angle is equal to the sum of opposite interior angle}.
Therefore, angle ONP = 115°.
Now, let's solve for x,
x+ 115°=180° { because the sum of co-interior angle is 180°}.
x= 180°-115°
Therefore, the measure of angle x is 65°.
Hope it helps...
Answer:
[tex]\Huge \boxed{{x=65\° }}[/tex]
Step-by-step explanation:
l and m are parralel lines.
The third angle in the triangle is also x, because of corresponding angles.
Angles in a triangle add up to 180 degrees.
Create an equation and solve for x.
x + 60 + 55 = 180
Add the numbers.
x + 115 = 180
Subtract 115 from both sides.
x = 65
After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The population on the island grows exponentially according to the model n(t)-ne", where n(t)is the number of rats at time t in months. After 15 months there are 280 rats on the island a. Find a function that models the population t months after the arrival of the rats. b. What will the population be 3 years after the shipwreck? Round to a whole number. c. When will the population reach 2000 rats?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]n(t) = 120 e^{(0.056t)}[/tex]
b
[tex]n(36) = 901 \ rats[/tex]
c
[tex]t = 50 \ months[/tex]
Step-by-step explanation:
From the question we are told that
The original number of rats that swim from the wreckage to a deserted island is
The population on the island grows exponentially according to the model
[tex]n(t) = n_o e^{rt}[/tex]
The number of rats after t = 15 months is 280
So
[tex]n(15) = 120 e^{15 * r } = 280[/tex]
=> [tex]120 e^{15 * r } = 280[/tex]
=> [tex]e^{15r} = 2.33[/tex]
=> [tex]15r = 0.8459[/tex]
=> [tex]r = 0.056[/tex]
Therefore the population t months after the arrival of the rats is mathematically represented as
[tex]n(t) = 120 e^{(0.056t)}[/tex]
Here t is in months
Considering question b
For t = 3 years = 12 * 3 = 36 months
Then the number of rats that will be present is mathematically represented as
[tex]n(36) = 120 e^{0.056 * 36 }[/tex]
[tex]n(36) = 901 \ rats[/tex]
Considering question c
Now the number of rats considered is n(t) = 2000
So
[tex]n(t) = 2000 = 120e^{0.056t}[/tex]
=> [tex]2000 = 120e^{0.056t}[/tex]
=> [tex]16.67 = e^{0.056t}[/tex]
Taking natural log of both sides
=> [tex]0.056 t = 2.81[/tex]
=> [tex]t = 50 \ months[/tex]
10. Hank bought a four-family residence for rental property. Hank put 20% down on the $300,000 rental unit. How much will he be able to depreciate
using the class recovery period for residential rental property each year?
A. $9,809.09
O B. $15,609.09
O C. $11,893.09
D. $10,909.09
Mark for review Will be highlighted on the review page)
Answer:
D. $10,909.09
Step-by-step explanation:
The class recovery period for residential rental property each year = 27.5 years
The cost basis for the residential property = $300,000
The amount he will be able to depreciate
= Cost basis/ Number of years
= $300000/ 27.5 years
=$10, 909.090909
Approximately ≈ $10,909.09
The amount he will be able to depreciate using the class recovery period for residential rental property each year is: D. $10,909.09.
Using this formula
Depreciation=Rental unit amount/ MACRS residential rental property recovery period
Where:
Rental unit amount=$300,000
MACRS Residential rental property recovery period=27.5 years
Let plug in the formula
Depreciation=$300,000/27.5
Depreciation=$10,909.09
Inconclusion the amount he will be able to depreciate using the class recovery period for residential rental property each year is: D. $10,909.09.
Learn more about recovery period here:https://brainly.com/question/24953839
Solve the simultaneous equation,
2p - 3q = 4
3p + 2q = 9
Answer:
p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]
Step-by-step explanation:
Given equations:
2p - 3q = 4 -----------(i)
3p + 2q = 9 ------------(ii)
Let's solve this equation simultaneously using the elimination method
(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;
[2p - 3q = 4] x 3
[3p + 2q = 9] x 2
6p - 9q = 12 -------------(iii)
6p + 4q = 18 -------------(iv)
(b) Next, subtract equation (iv) from equation (iii) as follows;
[6p - 9q = 12]
- [6p + 4q = 18]
-13q = -6 -----------------(v)
(c) Next, make q subject of the formula in equation (v)
q = [tex]\frac{6}{13}[/tex]
(d) Now substitute the value of q = [tex]\frac{6}{13}[/tex] into equation (i) as follows;
2p - 3([tex]\frac{6}{13}[/tex]) = 4
(e) Now, solve for p in d above
Multiply through by 13;
26p - 18 = 52
Collect like terms
26p = 52 + 18
26p = 70
Divide both sides by 2
13p = 35
p = [tex]\frac{35}{13}[/tex]
Therefore, p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]
2. Find the slope and y-intercept.
a. y = 3x - 4 b. 4x - 5y = 15
given directed line segment AB find the coordinates of p such that the ratio of ap to pb is 2:1 plot point p
Answer:
[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]
Step-by-step explanation:
The question is incomplete; However
[tex]A = (-2, -4)[/tex]
[tex]B = (6, 1)[/tex]
Required
Determine coordinates of P
When line segment is divided in ratios, the following formula calculates the coordinates;
[tex]P(x,y) = \{\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\}[/tex]
In this case;
[tex]m:n = 2:1[/tex]
[tex](x_1,y_1) = (-2, -4)[/tex]
[tex](x_2,y_2) = (6, 1)[/tex]
So, the coordinates of P is calculated as thus
[tex]P(x,y) = \{\frac{2 * 6 + 1 * (-2)}{2+1}, \frac{2 * 1 + 1 * (-4)}{2+1}\}[/tex]
[tex]P(x,y) = \{\frac{12 -2}{3}, \frac{2 -4}{3}\}[/tex]
[tex]P(x,y) = \{\frac{10}{3}, \frac{-2}{3}\}[/tex]
Hence, the coordinates of P is
[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]
The question is incomplete, the points A and B are:
A = (-2, -4)
B = (6, 1)
We want to find a point P in the segment AB such that the ratio of AP to PB is 2:1
We will find that:
[tex]P = (\frac{2}{3} , \frac{7}{3} )[/tex]
The general formula for two points (x₁, y₁) and (x₂, y₂), the coordinates of a point that separates the segment in a ratio j:k is
[tex]P = (\frac{j*x_1 + k*x_2}{j + k} , \frac{j*y_1 + k*y_2}{j + k})[/tex]
So we only need to use that general formula:
[tex]P = P = (\frac{2*(-2) + 1*6}{3} , \frac{2*(-4) + 1*1}{3})\\\\P = (\frac{2}{3} , \frac{7}{3} )[/tex]
If you want to learn more, you can read:
https://brainly.com/question/17623648
solve for p 7(p-9)=34.3
Answer: p = 13.9
Step-by-step explanation: 7(p-9) = 34.3 multiply 7 into p and -9
7p - 63 = 34.3 add 63 into both sides
7p = 97.3 divide 7 into both sides.
p = 13.9
This question can be solved in two ways
the equation given is 7(p-9)=34.3
The first step to take is to divide both sides of the equation by 7
p - 9 = 34.3 / 7
p - 9 = 4.9
The second step is to combine similar terms
p = 4.9 + 9 = 13.9
A second method
the equation given is 7(p-9)=34.3
1. expand the bracket
7p - 63 = 34.3
2. Combine similar terms
7p = 34.3 + 63
7p = 97.3
3. Divide both sides of the equation by 7
p = 13.9
A similar question was solved here: https://brainly.com/question/20432589?referrer=searchResults
Micah was given $200 for his birthday. Each week he spends $15 on comic books. In how many weeks will his birthday money be gone?
Answer:
13 weeks
Step-by-step explanation:
V = -15 x + 200 x 213.33 weeks 6 = -15x + 200 after 13 weeks.
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
The number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.
Given,
Micah was given $200 for his birthday.
Each week he spends $15 on comic books.
We need to find in how many weeks will his birthday money be gone.
How to compare two units in proportion?We need to make sure we get the required value on the left side.
If 1 week = 7 days
Find how many days in 2 weeks
2 weeks = 2 x 7 days = 14 days
We have 2 weeks on the left side.
If 2 items = $5
5/2 x 2 items = 5/2 x $5
5 items = $25/2 = $12.5
Find the total amount Micah has.
= $200
Find the amount spend each week.
= $15
Find how many weeks she must spend to spend $200.
We have,
$15 = 1 week
Multiply 200/15 on both sides.
200/15 x $15 = 200/15 x 1 week
$200 = 13.33 weeks
This means 13 weeks.
Thus the number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.
Learn more about how to find the number of weeks equal to 56 days here:
https://brainly.com/question/2583713
#SPJ2
Find the least whole number that can replace _
to make the statement true.
_ ÷ 17 > 99
The _ can be replaced with?
Answer:
1684
Step-by-step explanation:
x ÷ 17 > 99
x > 17 * 99
x > 1683
The least whole number that is greater than 1683 is 1684.
Answer: 1684
Answer:
1683
Step-by-step explanation:
To undo the problem you do 99 times 17 which is 1683. Then you know that 1683 divided by 17 is 99.
Solve and graph the following inequality
Answer:
x is greater than 4
Step-by-step explanation:
4x + 5 is greater than 13
you want to find out what x is
4 - 4 x + 5 is greater than 13 - 4 ( whatever you do to one side you have to do to the other)
x + 5 is greater than 9
x + 5 - 5 is greater than 9 - 5
x is greater than 4
Need help!!! A rocket scientist is designing a rocket to visit the planets in the solar system. The velocity that is needed to escape a planet’s gravitational pull is called the escape velocity. The escape velocity depends on the planet’s radius and its mass, according to the equation V escape=square root(2gR where R is the radius and g is the gravitational constant for the particular planet. The rocket’s maximum velocity is exactly double Earth’s escape velocity. The earth’s gravitational pull is 9.8 m/s^2 The earth’s radius is 6.37 x10 ^6 For which planets will the rocket have enough velocity to escape the planet’s gravity?
Answer:
Mercury, Venus, Earth, Mars, and Uranus
Step-by-step explanation:
Calculate the escape velocity for each planet, using the equation v = √(2gR).
[tex]\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right][/tex]
The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s. So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.
i need help with this can someone help me
Answer:
#9 x=21
#10 a. QP b. 8 c. 18
Step-by-step explanation:
#9 use the theorem where the ratio between a midline and the base of the triangle is 1:2
as we know the midline and the base is 1:2
this means
2(4x-65)=2x-4
4x-65=x-2
3x=63
x=21
---------------------------------------------------------------
#10
a. RS|| QP (Remember to write the letters accordingly)
b. 8 (As mentioned before of the ratio 1:2)
c. 18
A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to Two-thirds of its maximum volume? Use π = 3.14 and V = four-thirds pi r cubed.
Answer: A
16 minutes
Step-by-step explanation:
The required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.
The rate of change is defined as the change in value with the rest of the time is called rate of change.
Here,
radius = 55 / 2 = 27.5
Since volume is directly proportional to the cube of the radius,
So,
For maximum volume,
V ∝ R³
and
2/3V = v
2/3R³ = r³
r = 27.5 ∛2/3
r = 24
Now,
the radius increases at a rate of 1.5 feet per minute.
Time to reach a radius of 24 feet,
= 24 / 1.5
= 16 minutes
Thus, the required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.
Learn more about rate of change here: https://brainly.com/question/13103052
#SPJ2
In triangle ABC, which side is the longest if these are the measures of the angles? m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°
Answer:
AC
Step-by-step explanation:
First, let's find m∠B and m∠C by solving for x. Since the sum of interior angles in a triangle is 180°, we know that:
60 + 3x - 2 + 2x + 7 = 180
5x + 65 = 180
5x = 115
x = 23° so m∠B = 3(23) - 2 = 67° and m∠C = 2(23) + 7 = 53°. The longest side of a triangle is always opposite to the largest angle of the triangle, and since m∠B is the largest, we know that the side opposite to ∠B is the longest. That side is AC.
In triangle ABC, the longest side is AC, since it is opposite the biggest angle ∠B.
What is the angle sum property of a triangle?According to the angle sum property of a triangle, the sum of the three interior angles is 180°.
What is the relation between sides' length and the size of the angle of a triangle?In a triangle, the longest side is on the opposite side of the biggest angle, and the shortest side is on the opposite side of the smallest angle.
How do we solve the given question?We are given the angles of the triangle ABC. We are asked to find the longest side in the triangle ABC.
By the angle sum property of a triangle, we know that,
m∠A + m∠B + m∠C = 180°
or, 60° + (3x - 2)° + (2x + 7)° = 180°
or, 5x + 65° = 180°
or, 5x = 180° - 65° = 115°
or, x = 115/5 = 23.
∴ m∠A = 60°.
m∠B = (3x - 2)° = (3(23) - 2)° = (69-2)° = 67°.
m∠C = (2x + 7)° = (2(23) + 7)° = (46 + 7)° = 53°.
∵ m∠B is the largest angle, the side opposite to it, that is, AC is the longest side of the triangle.
Learn more about the properties of a triangle at
https://brainly.com/question/11920446
#SPJ2
The average age of Iowa residents is 37 years. Amy believes that the average age in her hometown in Iowa is not equal to this average and decided to sample 30 citizens in her neighborhood. Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311. What is the p-value of the test statistic? Answer choices are rounded to the hundredths place.
Answer:
0.10
Step-by-step explanation:
Average age of Iowa residents = 37 years
Amy believes that the average age in her hometown in Iowa is not equal to this average
Alternative hypothesis : µ ≠ 37
Sample size = 30
t - test statistic = 1.311
The p-value of the test statistic can be obtained using the online p-value calculator :
The p- value obtained using a t-test statistic value of 1.311 and a degree of freedom (df =N-1; 30 - 1 = 29) at a 0.05 significance level = 0.100072 = 0.10 ( nearest hundredth)
Answer:
0.20
Step-by-step explanation:
In order to find the p-value we first need the degrees of freedom because we are running a t-test. The df = n-1 = 30-1 = 29. If Amy is using the alternative hypothesis, µ ≠ 531, this is a two-tailed test. In order to find the p-value, we simply need to find the probability of being as extreme or more extreme as our current test statistic in one-tail and then multiply it by 2. Another way to describe this is it is the tail probability/area. If we go to the df row of 29 and then scan to the right we see 1.311 is in the 0.10 column. So if we multiply this by 2, we find 0.20 or 20% in both of the tails. So the p-value is 0.20.
How many atoms in human body?
If "a" is a negative number, and "ab" is a positive
answer, then what is the sign of "b”?
Answer:
b would be a negative number
Answer: The sign of b is negative or -
Step-by-step explanation:
If you multiply two negative numbers you will have a positive number. And if you multiply a positive and negative numbers you will have a negative answer.
A company that prints Blue Books for exams makes a profit according to the number of books sold. Suppose that the Profit is
Answer:
The answer is not complete. I will explain the concept of profit to you.
Step-by-step explanation:
We can determine profit deducting direct costs (cost price) of commodities from sales (selling prices) of the commodities.
Profit = Selling Price - Cost Price
Example:
A trader buys some dresses for #2,500 in May and agrees to pay for it in three months’ time. He sells off all the dresses in August for #4,500. The profit for the month is #2,000.
The formula for percentage profit is [tex]\frac{profit * 100}{cost price}[/tex]
The formula for gross profit is Revenue – Cost of Sold Items
Profit Margin = [tex]\frac{Total Income}{Net Sales}[/tex] * 100
While Gross Profit Margin can be calculated as [tex]\frac{Gross Profit}{Net Sales}[/tex] * 100
Any of these formulas can be used to calculate profit-related questions.
How many 5 ounce glasses of soda can you get from 3, 2 liter bottles of soda (6 liters total?
Answer:
21
Step-by-step explanation:
tcctvucycyccyctctctchu ycuvuvuvy t r y y g g t g
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .10 significance level. Let p_M and p_F be the proportion of Men and Women who own cats respectively.
Based on a sample of 80 men, 40% owned cats
Based on a sample of 80 women, 51% owned cats
What is the test statistic and the critical value? Reject or Fail to Reject Null hypothesis?
Answer:
The test statistics is [tex]t = -1.40[/tex]
The critical value is [tex]Z_{\alpha } = 2.33[/tex]
The null hypothesis is rejected
Step-by-step explanation:
From the question we are told that
The sample size for men is [tex]n_1 = 80[/tex]
The sample proportion of men that own a cat is [tex]\r p _M = 0.40[/tex]
The sample size for women is [tex]n_2 = 80[/tex]
The sample proportion of women that own a cat is [tex]\r p_F = 0.51[/tex]
The level of significance is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \r p _M = \ r P_F[/tex]
The alternative hypothesis is [tex]H_a : \r p _M < \r p_F[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{(\r p_M - \r p_F)}{\sqrt{\frac{(p_M*(1-p_M)}{n_1 } } + \frac{p_F*(1-pF)}{n_2 } }[/tex]
=> [tex]t = \frac{(0.40 - 0.51)}{\sqrt{\frac{(0.40 *(1-0.41)}{80} } + \frac{0.51*(1-0.51)}{80 } }[/tex]
=> [tex]t = -1.40[/tex]
The critical value of [tex]\alpha[/tex] from the normal distribution table is
[tex]Z_{\alpha } = 2.33[/tex]
The p-value is obtained from the z-table ,the value is
[tex]p-value = P( Z < -1.40) = 0.080757[/tex]
=> [tex]p-value = 0.080757[/tex]
Given that the [tex]p-value < \alpha[/tex] then we reject the null hypothesis