Answer:800 miles
Step-by-step explanation:
Given
Round trip for Penthaven to Jackson takes 6 hr and 24 minutes in absence of wind
[tex]t_1=6+\frac{24}{60}=6.4\ hr[/tex]
When Wind blows from Penthaven to Jackson it takes 6 hr and 40 min i.e.
[tex]t_2=6+\frac{40}{60}=\frac{20}{3}\ hr[/tex]
Speed of wind [tex]v=50\ mph[/tex]
Suppose x be the distance between Penthaven and Jackson and u be the speed of plane
So initially
[tex]6.4=\frac{x}{u}+\frac{x}{u}[/tex]
[tex]6.4=\frac{2x}{u}[/tex]
[tex]x=3.2u \quad \ldots(i)[/tex]
When wind is blowing then,
[tex]\Rightarrow \frac{20}{3}=\frac{x}{u+v}+\frac{x}{u-v}[/tex]
[tex]\Rightarrow \frac{20}{3}=x[\frac{1}{u+50}+\frac{1}{u-50}][/tex]
[tex]\Rightarrow \frac{20}{3}=x[\frac{2u}{u^2-50^2}]\quad \ldots(ii)[/tex]
Substitute the value of x in [tex](ii)[/tex]
[tex]\Rightarrow \frac{20}{3}=\frac{2u[3.2u]}{u^2-50^2}[/tex]
[tex]\Rightarrow 10[u^2-50^2]=9.6u^2[/tex]
[tex]\Rightarrow 0.4u^2=50^2\times 10[/tex]
[tex]\Rightarrow u^2=\frac{50^2\times 10^2}{4}[/tex]
[tex]\Rightarrow u=250\ mph[/tex]
Thus [tex]x=3.2\times 250=800\ miles[/tex]
The minute hand on a clock is 9 centimeterslong and travels through an arc of 252° every 42 minutes. To the nearest tenth of a centimeter, how far does the minute handtravel during a 42-minute period?
Answer: the minute hand travel 39.6 cm
Step-by-step explanation:
Length of minute hand of a clock = 9 cm
Central angle made by the minute hand = 252°
To find: how far the minute hand travel
Therefore
Length of minute hand is equal to the radius of circle
As we know the circumference of a circle is given by
[tex]C= 2\pi r \dfrac{\theta}{360^\circ}[/tex] where C is circumference , r is radius and ∅ is the central angle
So we have
[tex]C= 2 \times \dfrac{22}{7} \times 9 \times \dfrac{252^\circ}{360^\circ} \\\\\Rightarrow C= 2 \times \dfrac{22}{7} \times \dfrac{252^\circ}{40^\circ} \\\\\Rightarrow C= \dfrac{11}{7} \times \dfrac{252^\circ}{10^\circ} = 39.6[/tex]
Hence, the minute hand travel 39.6 cm in 42 minute period
Final answer:
The minute hand of the clock, which measures 9 centimeters in radius, travels approximately 39.3 centimeters along the arc when it moves through a 252-degree central angle in a 42-minute period.
Explanation:
To determine how far the minute hand of a clock travels in a 42-minute period, we need to calculate the arc length, which is a portion of the circumference of the circle traced by the minute hand's tip. We are given that the minute hand is 9 centimeters long, meaning it is the radius of the circle, and it travels through an arc of 252° during a period of 42 minutes.
The formula to calculate the arc length is:
ℓ = θ/360 × 2πr
Where:
ℓ is the arc length
θ is the central angle in degrees
r is the radius of the circle
In this case:
θ = 252°
r = 9 cm
Now, let's substitute these values into the formula:
ℓ = 252/360 × 2 × π × 9
ℓ ≈ 0.7 × 2 × 3.14159 × 9
ℓ ≈ 39.27 cm
So, to the nearest tenth of a centimeter, the minute hand travels approximately 39.3 cm during a 42-minute period.
Mrs. Braddock has a bag containing 6 lipsticks, 4 eye shadows, 6 eye liners, and 5 mascaras. She will randomly choose one item from the bag.What is the probability that she will pull NOT lipstick? p(NOT lipstick). Round percents to nearest whole number
Answer:
The probability that she will not pull lipstick is 71%.
Step-by-step explanation:
The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable number of outcomes
N = total number of outcomes
The contents in Mrs. Braddock's bag are:
Number of lipsticks = n (L) = 6
Number of eye shadows = n (S) = 4
Number of eye liners = n (E) = 6
Number of mascaras = n (M) = 5
Total number of items in the bag = N = 21
Consider that the probability of an event occurring is P. Then the probability of the given event not taking place is known as the complement of that event.
Complement of the given event is, 1 – P.
Compute the probability of selecting a lipstick as follows:
[tex]P(L)=\frac{n(L)}{N}\\\\=\frac{6}{21}\\\\=\frac{2}{7}[/tex]
Compute the probability of not selecting a lipstick as follows:
[tex]P(L^{c})=1-P(L)[/tex]
[tex]=1-\frac{2}{7}\\\\=\frac{7-2}{7}\\\\=\frac{5}{7}[/tex]
Convert this probability into percentage as follows:
[tex]\frac{5}{7}\times 100 = 71.4286\approx 71\%[/tex]
Thus, the probability that she will not pull lipstick is 71%.
Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 32 % . She obtains a random sample of 72 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? Please give your answers precise to two decimal places.
Answer:
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Step-by-step explanation:
For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The probability that an independent restaurant will fail in the first year is 32%.
This means that [tex]p = 0.32[/tex]
72 independent restaurants
This means that [tex]n = 72[/tex]
Mean:
[tex]E(X) = np = 72*0.32 = 23.04[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{72*0.32*0.68} = 3.96[/tex]
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Final answer:
The mean number of independent restaurants in the sample expected to fail within the first year is 23.04, and the standard deviation is approximately 4.28.
Explanation:
To find the mean and standard deviation of the number of restaurants that failed within a year in Kristen's research, we can use the properties of the binomial distribution. The probability of a single restaurant failing (success in this context) is 0.32 (32%). Given a sample size of 72 restaurants, the mean number of restaurants that fail within a year is the product of the sample size and the probability of failure.
The formula for the mean (μ) of a binomial distribution is μ = n * p, where n is the sample size and p is the probability of success. Therefore, the mean number of failed restaurants is 72 * 0.32 = 23.04.
The formula for the standard deviation (σ) of a binomial distribution is σ = √(n * p * (1 - p)). Thus, the standard deviation of failed restaurants is √(72 * 0.32 * (1 - 0.32)) = √(72 * 0.32 * 0.68) ≈ 4.28.
Therefore, the mean number of restaurants that failed within a year is 23.04, and the standard deviation is approximately 4.28.
A random sample of 400 Michigan State University (MSU) students were surveyed recently to determine an estimate for the proportion of all MSU students who had attended at least three football games. The estimate revealed that between .372 and .458 of all MSU students attended. Given this information, we can determine that the confidence coefficient was approximately: a. .92 b. .95 c. .88 d. .90 e. .99
Answer:
a. .92
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 of the interval is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The lower bound is the point estimate [tex]\pi[/tex] subtracted by the margin of error.
The upper bound is the point estimate [tex]\pi[/tex] added to the margin of error.
Point estimate:
The confidence interval is symmetric, so it is the mean between the two bounds.
In this problem:
[tex]\pi = \frac{0.372 + 0.458}{2} = 0.415[/tex]
Sample of 400, which means that [tex]n = 400[/tex]
Margin of error is the estimate subtracted by the lower bound. So [tex]M = 0.415 - 0.372 = 0.043[/tex]
We have to find z.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.043 = z\sqrt{\frac{0.415*0.585}{400}}[/tex]
[tex]z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}[/tex]
[tex]z = 1.745[/tex]
[tex]z = 1.745[/tex] has a pvalue of 0.96.
This means that:
[tex]1 - \frac{\alpha}{2} = 0.96[/tex]
[tex]\frac{\alpha}{2} = 1 - 0.96[/tex]
[tex]\frac{\alpha}{2} = 0.04[/tex]
[tex]\alpha = 0.08[/tex]
Confidence level:
[tex]1 - \alpha = 1 - 0.08 = 0.92[/tex]
So the correct answer is:
a. .92
To determine the confidence coefficient for the proportion of MSU students who attended at least three football games, the margin of error is calculated from the given interval range and related to the Z-value of a standard normal distribution. The coefficient that matches the margin of error from the calculation is approximately 0.95, indicating a 95% confidence level.
The confidence interval for the proportion of Michigan State University (MSU) students who attended at least three football games is given as (0.372, 0.458). To determine the confidence coefficient used to calculate this interval, we need to look at the width of the interval and how it relates to the standard error of the proportion.
The width of the confidence interval is 0.458 - 0.372 = 0.086. Since we know that the total width of the interval spans the range of twice the margin of error, one margin of error is then 0.086 / 2 = 0.043.
Using the Z-table for the normal distribution, we can find which confidence coefficient corresponds to a Z-value that gives a margin of error of 0.043, considering that the formula for the margin of error in this case would be: Z * sqrt((p*(1-p))/n). For a sample size of 400, and approximating p by the midpoint of the confidence interval (0.372 + 0.458)/2 = 0.415, the computation would look roughly like this:
Z * sqrt((0.415*(1-0.415))/400) = 0.043
After solving this equation for Z, we can then locate the corresponding confidence level on the standard normal (Z) distribution table. This process would lead to finding that the closest confidence coefficient that would generate the margin of error of 0.043 with the given sample size and point estimate proportion is approximately 0.95, or 95%.
Therefore, the confidence coefficient is 0.95, which corresponds to option b. 0.95.
Write a verbal description for each algebraic expression 100-5n
Step-by-step explanation:
One hundred minus five n
A sociologist develops a test to measure attitudes towards public transportation, and 25 randomly selected subjects are given the test. The sample mean score is 76.2 and the sample standard deviation is 21.4. The population is normally distributed. What is the 95% confidence interval for the mean score of all such subjects? Round to 3 decimal places.
Final answer:
The 95% confidence interval for the true mean score of subjects' attitudes towards public transportation is between 67.361 and 85.039, computed using a t-score for a sample size of 25.
Explanation:
To calculate the 95% confidence interval for the mean score of all subjects regarding their attitudes towards public transportation, we will use the following formula for a confidence interval when the population is normally distributed but the population standard deviation is not known:
CI = ± t*(s/√n), where CI is the confidence interval, ± denotes plus or minus, t is the t-score that corresponds to the desired level of confidence and degrees of freedom (df = n - 1), s is the sample standard deviation, and √n is the square root of the sample size.
For our sample size of n = 25, the degrees of freedom is df = 24. Consulting a t-distribution table or using statistical software to find the t-value for df = 24 at a 95% confidence level, we assume a t-value approximately equal to 2.064 (this may slightly vary depending on the source of the t-distribution table). Plugging in the values:
CI = ± 2.064*(21.4/√25), thus the margin of error is approximately 2.064 * 4.28
The confidence interval is then the sample mean ± the margin of error:
76.2 ± (2.064 * 4.28)
This calculation yields a confidence interval for the population mean score of:
Lower Bound = 76.2 - 8.83872 ≈ 67.361
Upper Bound = 76.2 + 8.83872 ≈ 85.039
Therefore, rounding to three decimal places: 67.361 (Lower Bound) and 85.039 (Upper Bound).
We are 95% confident that the true mean score of all subjects' attitudes towards public transportation lies between 67.361 and 85.039.
Two angles are complementary. Angle 1 measures 33.5 degrees. What is the measure of Angle 2? *
Juan Pablo demora 7 minutos en dar una vuelta a la cancha de fútbol y Pedro demora 2 minutos más corriendo a la misma velocidad que Juan Pablo. ¿Cuánto tiempo demorará Pedro en dar 12 vueltas?
Answer: 108 minutes
Step-by-step explanation:
This translates to:
Juan Pablo takes 7 minutes to do a full lap on a football field, Pedro needs 2 more minutes ruuning at the same speed thanJuan Pablo.
How much time does Pedro need to do 12 laps?
The fact that Pedro runs at the same speed than Juan Pablo, and needs more time, may mean that the radius of the laps of Pedro are a little bit bigger than the ones of Juan Pablo (which means that the total distance that pedro runs is bigger)
If Juan Pablo does a lap in 7 minutes, then Pedro does a lap in 7 minutes + 2 minutes = 9 minutes.
Then to do 12 laps, he needs 12 times that amount of time, this is:
12*9 min = 108 minutes
Awnser this please.
Answer:
1.5 hours
Step-by-step explanation:
make each half hour represent t
Cost C(t) = 24 + 14t
66 = 24 + 14t
42 = 14t
t = 3
3 half hours = 1.5 hours
Answer:
1 and a half hours of work
Step-by-step explanation:
You minus 66 and 24 to get 42. Then you divide 42 and 14
The scores on a test are normally distributed with a mean of 150 and a standard deviation of 30. What is the score that is 1 standard deviation below the mean?
A score of 120 is one standard deviation below the mean of 150 on a test with a standard deviation of 30.
Explanation:The score that is 1 standard deviation below the mean is found by subtracting the standard deviation from the mean. In the context of this normal distribution of test scores, with a mean of 150 and a standard deviation of 30, we calculate the score one standard deviation below the mean as follows:
Score = Mean – Standard Deviation = 150 – 30 = 120
This calculation indicates that a score of 120 is one standard deviation below the mean on this test.
A broken thermometer reads 33° F, but Kira knows that the temperature is at least 33° F, if not even colder. Which of the following inequalities, shows the possible temperatures? t ≤ 33° F t ≥ 33° F t > 33° F t < 33° F
Answer:
t ≤ 33
Step-by-step explanation:
The answer can be 33 or below.
The cost medium pizza with no toppings is $7.50. The cost of each topping is $0.50. a) what is the equation that represents this relation if C represents the cost of pizza and N represents the number of topping?
Answer:$7.50+$0.50xN or C+$0.50xN
Step-by-step explanation:
Because the pizza is 7.50 and the extra toppings are 0.50 cents so the number of toppings is n and the cost for the pizza is c so C+0.50xN.
Good Luck!!
1. Write an expression that represents the area of a rectangle given that the Length = (x+3) and the width = (3x + 4).
2. The area of a rectangle is 28x2 – 13xy – 6y2 square units. If the length of the rectangle is 7x + 2y units, then find the breadth of the rectangle, hence find the perimeter of the rectangle
Answer:
(7x+2y)- length (4x-3y)- width
22x-2y is the perimeter.
Step-by-step explanation:
Which represents a quadratic function?
f(x) = −8x3 − 16x2 − 4x
f (x) = three-quarters x 2 + 2x − 5
f(x) = StartFraction 4 Over x squared EndFraction minus StartFraction 2 Over x EndFraction + 1
f(x) = 0x2 − 9x + 7
Answer:[tex]f(x)=\frac{3}{4}x^2+2x-5[/tex]
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
b
What’s the correct answer for this?
Answer:
A
Step-by-step explanation:
Plate X will result in the lightest place since it's density and thickness both are less.
On Monday, 288 students went on a trip to the zoo. All 7 buses were filled and 8 students had to travel in cars. How many students were in each bus?
Answer:
40 kids
Step-by-step explanation:
288 minus the 8 kids that had to hide in cars= 280. 280 divided by the seven busses is 40
73 POINTS need help
A large mall is built in the shape of a square. At each corner of the mall stands a pillar which is topped by a pyramid-shaped section of red tin roof, as shown in the picture below.
The pyramid is a square pyramid, measuring 21.5 feet on each of its base edges. The height of each of the triangular lateral face is 13.4 feet. Use this information to answer the following questions.
What is the area of the roof? [Type your answer as a number. Do not round.]
blank square yards
Answer:
2304.8 ft^2
Step-by-step explanation:
The lateral area of one of the pyramid is 21.5 * 13.4 * 4/2 = 576.2
There are 4 of them, so we multiply that by 4 : 576.2 * 4 = 2304.8
statistical analyst for the Wall Street Journal randomly selected six companies and recorded both the price per share of stock on January 1, 2009 and on April 30, 2009. The results are presented below. Suppose the analyst wished to see if the average price per share of stock on April 30, 2009 is greater than the average price per share of stock on January 1, 2009 at α=.025. Apr. 30, 2009 33 33 34 30 33 38 Jan. 1, 2009 21 25 30 33 23 27 For the hypothesis stated above, what is the P-value?
Answer:
p value= 2.228
Step-by-step explanation:
since average of two groups is being compared two-sample t-test will be performed.
degrees of freedom= 12-2=10
at α=.025 from t table
p value= 2.228
The speed of pickup of ride sharing services like Uber and Lyft seems to have surpassed that of ambulance services. The mean response time of ambulances across the United States is 15.3 minutes with a standard deviation of 12.8 minutes. For ride sharing services, the mean pick-up time across the United States is 8 minutes with a standard deviation of 5.2 minutes. Based on these estimates, which of the following gives the standard deviation of the sampling distribution of the difference in the sample means for samples of 30 ambulance rides and 40 ride sharing rides (Ambulance – Ride Sharing)?
Answer:
The correct answer is (C).
Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately≈2.912 minutes.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The correct answer is (C).
Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} = \sqrt{\frac{12.8^2}{30}+\frac{5.2^2}{40}} \approx 2.912
n
1
s
1
2
+
n
2
s
2
2
=
30
12.8
2
+
40
5.2
2
≈2.912 minutes.
A brokerage charges ? regardless of whether an investor buys or sells assets, and ? are incurred with every transaction
Answer:
Yes, that's true.
Step-by-step explanation:
A brokerage fee is the commission paid to a salesperson or broker for selling insurance or securities, respectively. The amount of this fee is usually calculated as a percentage of the transaction price, though it may be a flat fee.
brokerage fee compensates a broker for executing a transaction. It is usually, but not always, a percentage of the transaction value. In finance, stockbrokers most often come to mind, but real estate agents and business brokers frequently charge brokerage fees
Answer:
A brokerage charges brokerage account fees regardless of whether an investor buys or sells assets, and trade commissions are incurred with every transaction.
Which of the following is the equation of a direct variation that has a constant of variation equal to -1/2?
A. y= x- 1/2
B. -1/2 y=x
C. y= -2x
D. y= -1/2x
I think it is c. y= -2x hope you have a good day!
observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3
Answer:
We have two relations
2*x*y = 6 (2 times x times y is equal to six)
x - y = 3 ( the difference between x and y is trhe)
Where whe have two variables, x and y.
To solve this system, the first step is isolation one of the variables in one of the equations, let's isolate x in the second equation.
x - y = 3
x = 3 + y
now we can replace this in the other equation and then solve it for y.
2*x*y = 6
2*(3 + y)*y = 6
6y + 2y^2 = 6
now we have the quadratic equation:
2y^2 + 6y - 6 = 0
the solutions are:
[tex]y = \frac{-6 + -\sqrt{6^2 - 4*2*(-6)} }{2*2} = \frac{-6 +- 9.2}{4}[/tex]
the solutions are:
y = (-6 + 9,2)/4 = 0.8
y = (-6 - 9.2)/4 = -3.8
if y = 0.8, then:
x = 3 + y = 3.8
if y = -3.8
x = 3 + y = 3 - 3.8 = -0.8
so we have two possible solutions:
(-0.8, -3.8) and (3.8, 0.8)
What is the lateral surface area of the square pyramid below?
a
48 in²
b
105 in²
c
96 in²
d
57 in²
Answer:
lateral surface area = 48 inches²
Step-by-step explanation:
The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.
area of a triangle = 1/2 × b × h
The slant height of the triangle is gotten using Pythagoras theorem
lateral surface area = 4 × (1/2 × 3 × 8)
lateral surface area = 4 × 24/2
lateral surface area = 4 × 12
lateral surface area = 48 inches²
Answer:
48 in
Step-by-step explanation:
<3 hoped this helped <3
Which of the following has a constant of proportionality of 2?
A) y = 2 x
B) 2 y = x
C) y = x + 2
D) y + 2 = 2 x
Answer:
A) y = 2 x
Step-by-step explanation:
The equation for direct variation is
y = kx where the constant of proportionality is k
y = 2x
Help whats 2+2 please i cant figure it out its baby two right
2 + 2 =4 is four tgvjixyi9
Answer:
It’s 4 or fish
Step-by-step explanation:
Find an equation of the circle that has center(-3,4) and passes through(1,-2)
Answer:
(x +3)^2 +(y -4)^2 = 52
Step-by-step explanation:
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
We are given the value of (h, k), and we can find the value of r^2. Using the values of h and k, our equation is ...
(x +3)^2 +(y -4)^2 = r^2
Since we know this equation is satisfied by the point (1, -2), we can use this point in the equation to find r^2:
(1 +3)^2 +(-2 -4)^2 = r^2
16 +36 = r^2 = 52
The equation of the circle is ...
(x +3)^2 +(y -4)^2 = 52
Area =
22ft for diameter
Here is your answer! uwu
A shipment to a warehouse consists of 500 PS4. The manager chooses a random sample of 50 PS4 and finds that 3 are defective. How many PS4 in the shipment are likely to be defective?
Answer:
30 PS4 in the shipment are likely to be defective
Step-by-step explanation:
We take the estimate from the sample and estimate to all the PS4 in store. This means that we can solve this question using a rule of 3.
From the sample of 50 PS4, 3 are defective. How many are expected to be defective out of 500?
50PS4 - 3 defective
500 PS4 - x defective
[tex]50x = 3*500[/tex]
[tex]x = \frac{1500}{50}[/tex]
[tex]x = 30[/tex]
30 PS4 in the shipment are likely to be defective
Answer:
don't take my word but I think 150
Step-by-step explanation:
Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that less than thirty percent of the teen girls smoke to stay thin? g
Answer:
We conclude that less than thirty percent of the teen girls smoke to stay thin.
Step-by-step explanation:
We are given that the Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old).
After four years the girls were surveyed again. Sixty-three said they smoked to stay thin.
Let p = percentage of the teen girls who smoke to stay thin.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 30% {means that at least thirty percent of the teen girls smoke to stay thin}
Alternate Hypothesis, [tex]H_A[/tex] : p < 30% {means that less than thirty percent of the teen girls smoke to stay thin}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample % of teen girls who smoke to stay thin = [tex]\frac{63}{273}[/tex] = 0.231
n = sample of teen girls = 273
So, test statistics = [tex]\frac{0.231-0.30}{\sqrt{\frac{0.231(1-0.231)}{273} } }[/tex]
= -2.705
The value of z test statistics is -2.705.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical value of -1.645 for left-tailed test.
Since our test statistics is less than the critical value of z as -2.705 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that less than thirty percent of the teen girls smoke to stay thin.
About 23% of the surveyed girls smoked to maintain or lose weight. Social and cultural factors contribute to this behavior, which often leads to health issues. Broader and more comprehensive studies are needed for a conclusive answer.
Explanation:Yes, there's some evidence to suggest fewer than thirty percent of teen girls smoked to stay thin. Only 63 girls out of the 273 surveyed stated they smoked for weight issues, which equates to around 23%. However, this result is not conclusive, as it is based solely on the girls who participated in this particular study. For a more comprehensive conclusion, we would need to evaluate multiple studies with larger participant samples.
In broader context, the challenges teens face with self-image are due in part to sociocultural factors, such as the beauty ideal of thinness often emphasized in media. The image of thin models contributes significantly to body image concerns and associated behaviours like smoking to maintain or lose weight. Such behaviours can lead to health problems including, but not limited to, type 2 diabetes, heart disease, and even cancer.
Also, obesity is a rising epidemic affecting many, with its highest rates found in the United States. Increasing awareness about these issues and promoting healthier methods of maintaining weight can help in addressing these problems.
Learn more about Teen smoking for thinness here:https://brainly.com/question/12743744
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Which is the graph of the linear equation y= -1/3x +5
Answer:
x=-3(y-5)
Step-by-step explanation: