Answer:
c =3
Step-by-step explanation:
4c = 12
Divide each side by 4
4c/4 =12/4
c = 3
Hi to whoever is reading this. I really need help on breaking down the expression. I am doing this without a calculator and I don’t Know what steps to take to get the answer.
Answer:
A
Step-by-step explanation:
[tex]81[/tex] is [tex]9^2[/tex] which happens to be [tex](3^2)^2[/tex] or [tex]3^4[/tex].
So [tex]\sqrt[4]{81} =3[/tex]
this eliminates options C and D
It can't be option B as both b and c aren't 4th rooted.
A recipe requires 3/4 cups of sugar for every 14 cookies how many cups of sugar will be needed to bake 168 cookies
Answer:
9 cups
Step-by-step explanation:
3/4 cups of sugar for 14 cookies
There are 168÷14 = 12 set of 14 cookies in 168
So we need 12 times 3/4 sugar
12 × 3/4 = 9 cups of sugar needed
Find the sum of place value and face value of 7 in 1879523
Answer:
Ok. so the Place value is 70000 and the face value is 7. Face value of a digit in a number is the digit itself.
More clearly, face value of a digit always remains same irrespective of the position where it is located
Place value of a digit in a number is the digit multiplied by thousand or hundred or whatever place it is situated.
Hope this helped.
Step-by-step explanation:
A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.262, .622). Identify the point estimate for estimating the true proportion of college students who prefer that drink.
Final answer:
The point estimate for the proportion of college students who prefer drink A is found by averaging the lower and upper bounds of the 95% confidence interval, which yields an estimate of 0.442 or 44.2%.
Explanation:
The point estimate for the true proportion of college students who prefer drink A is the midpoint of the 95% confidence interval. To find the point estimate, you sum the lower and upper bounds of the interval and divide by 2. In this case, the confidence interval is (.262, .622). The calculation for the point estimate is (0.262 + 0.622) / 2, which equals 0.442. Therefore, the point estimate is 0.442, which means that approximately 44.2% of college students prefer drink A.
Claim: Students should be required to take at least one online class.
Counterclaim: Some students can focus better when they are in a traditional classroom setting.
Which statement is the best rebuttal to the counterclaim given?
(A). When working on an online class, students have more freedom to choose an environment that is best for them.
(B). A traditional classroom is the best environment for learning, but an online class can be good for students too.
(C). Students should only be taught in a traditional classroom environment, because it works best for everyone.
Answer:
A. when working on an online class students have more freedom to choose an environment in which they are most comfortable
Step-by-step explanation:
some students do better at home some do better in a traditional setting but being online lets you change your setting to anywhere with online access
Thomas purchased a used vehicle that depreciates under a straight-line
method. The initial value of the car is $7000, and the salvage value is $500. If
the car is expected to have a useful life of another 5 years, how much will it
depreciate each year?
O
A. $1300
O B. $1000
O c. $7000
O D. $5000
Answer: A. $1300
Step-by-step explanation:
The initial value is $7000
The Salvage value is $500
The car will depreciate under a straight-line method, meaning it will lose $6500 value in 5 years.
6500 / 5 = 1300
Tiffany sells cars. She gets an 18% commission. How much will she make on a $ 28,000.00 car?
Answer:
5040$
Step-by-step explanation:
28000 x .18 = 5040
We are given that if Tiffany closes any car on a car she gets 18% as commission. For a car that cost $28,000 her commission will be $5,040
Given data
Commission = 18%
Cost of car = $ 28,000.00
Let us find 18% of $28,000.00
Commission = 18/100* 28,000.00
Commission = 0.18* 28,000.00
Commission = $5,040
Hence her commission will be: $5,040
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what is true about a number with base A and exponent B?
Answer:
A^B = A*A*A*... (B number of times)
49w = −8
what is the value of w
Answer:
w= -0.163265306122449
Step-by-step explanation:
49w = -8
divide both sides by 49
w= -8/49 = -0.163265306122449
check answer by multiplying -0.163265306122449 by 49
49 * -0.163265306122449 = -8
Answer:
w = -8/49
Step-by-step explanation:
49w = −8
Divide each side by 49
49w/49 = -8/49
w = -8/49
Using the common denominator what is the equivalent fraction of 1/8
Answer:
2/16
Step-by-step explanation:
1/8 x 2 = 2/16
Both 2 and 16 divide by 8, so one can know this is correct.
Also, both 8 and 16 are divisible by 8, so one can see this is the common denominator.
A worker has asked her supervisor for a letter of recommendation for a new job. She estimates that there is an 80 percent chance that she will get the job if she receives a strong recommendation, a 40 percent chance if she receives a moderately good recommendation, and a 10 percent chance if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate, and weak are 0.7, 0.2, and 0.1, respectively.
a. How certain is she that she will receive the new job offer?
b. Given that she does receive the offer, how likely should she feel that she received a strong recommendation?
i. a moderate recommendation?
ii. a weak recommendation?
c. Given that she does not receive the job offer, how likely should she feel that she received a strong recommendation?
i. a moderate recommendation?
ii. a weak recommendation?
Answer:
a) P(Job offer) = 0.65
b) P(S|J) = 0.862
P(M|J) = 0.143
P(W|J) = 0.0179
c) P(S|J') = 0.400
P(M|J') = 0.343
P(W|J') = 0.257
Step-by-step explanation:
- Let the event that she gets a job be J
- Let the event that she does not get the job be J'
- Let the event that she receives a strong recommendation be S
- Let the event that she receives a moderate recommendation be M
- Let the event that she receives a weak recommendation be W.
Given in the question,
P(J|S) = 80% = 0.8
P(J|M) = 40% = 0.4
P(J|W) = 10% = 0.1
P(S) = 0.70
P(M) = 0.20
P(W) = 0.10
a) How certain is she that she will receive the new job offer?
P(J) = P(J n S) + P(J n M) + P(J n W) (since S, M and W are all of the possible outcomes that lead to a job)
But note that the conditional probability, P(A|B) is given mathematically as,
P(A|B) = P(A n B) ÷ P(B)
P(A n B) is then given as
P(A n B) = P(A|B) × P(B)
So,
P(J n S) = P(J|S) × P(S) = 0.80 × 0.70 = 0.56
P(J n M) = P(J|M) × P(M) = 0.40 × 0.20 = 0.08
P(J n W) = P(J|W) × P(W) = 0.10 × 0.10 = 0.01
P(J) = P(J n S) + P(J n M) + P(J n W)
P(J) = 0.56 + 0.08 + 0.01 = 0.65
b) Given that she does receive the offer, how likely should she feel that she received a strong recommendation?
This probability = P(S|J)
P(S|J) = P(J n S) ÷ P(J) = 0.56 ÷ 0.65 = 0.862
i. a moderate recommendation?
P(M|J) = P(J n M) ÷ P(J) = 0.08 ÷ 0.65 = 0.143
ii. a weak recommendation?
P(W|J) = P(J n W) ÷ P(J) = 0.01 ÷ 0.65 = 0.0179
c) Probability that she doesn't get job offer, given she got a strong recommendation = P(J'|S)
P(J'|S) = 1 - P(J|S) = 1 - 0.80 = 0.20
Probability that she doesn't get job offer, given she got a moderate recommendation = P(J'|M)
P(J'|M) = 1 - P(J|M) = 1 - 0.40 = 0.60
Probability that she doesn't get job offer, given she got a weak recommendation = P(J'|S)
P(J'|W) = 1 - P(J|W) = 1 - 0.10 = 0.90
Total probability that she doesn't get job offer
P(J') = P(J' n S) + P(J' n M) + P(J' n W)
P(J' n S) = P(J'|S) × P(S) = 0.20 × 0.70 = 0.14
P(J' n M) = P(J'|M) × P(M) = 0.60 × 0.20 = 0.12
P(J' n W) = P(J'|W) × P(W) = 0.90 × 0.10 = 0.09
Total probability that she doesn't get job offer
P(J') = P(J' n S) + P(J' n M) + P(J' n W)
= 0.14 + 0.12 + 0.09 = 0.35
Given that she does not receive the job offer, how likely should she feel that she received a strong recommendation?
This probability = P(S|J')
P(S|J') = P(J' n S) ÷ P(J') = 0.14 ÷ 0.35 = 0.400
i. a moderate recommendation?
P(M|J') = P(J' n M) ÷ P(J') = 0.12 ÷ 0.35 = 0.343
ii. a weak recommendation?
P(W|J') = P(J' n W) ÷ P(J') = 0.09 ÷ 0.35 = 0.257
Hope this Helps!!!
She has 62% certainty of getting the job. If she gets it, there are high chances (~90%) that the recommendation was strong. In case of rejection, she's slightly more likely to have received a strong recommendation than a moderate or weak one.
Explanation:The subject of this problem involves the understanding of conditional probabilities and the principle of total probability. Let's denote the events as follows:
A1: the recommendation is strong A2: the recommendation is moderate A3: the recommendation is weak B: she gets the new job offer
a. The total probability that she will receive the job offer is calculated as follows:
P(B)=P(A1)P(B|A1)+P(A2)P(B|A2)+P(A3)P(B|A3) = 0.7*0.8+0.2*0.4+0.1*0.1=0.62, so she is 62% certain that she will receive the job offer.
b. If she does receive the offer, the probabilities that she got a strong, moderate and weak recommendation are calculated using Bayes' Theorem:
P(A1|B)=P(B|A1)P(A1)/P(B)=0.8*0.7/0.62 =~ 0.9 P(A2|B)=P(B|A2)P(A2)/P(B)=0.4*0.2/0.62 =~ 0.13 P(A3|B)=P(B|A3)P(A3)/P(B)=0.1*0.1/0.62 =~ 0.016
c. If she doesn't get the job, the probabilities are calculated similarly:
P(A1|Not B)=P(Not B|A1)P(A1)/P(Not B)=0.2*0.7/0.38 =~ 0.37 P(A2|Not B)=P(Not B|A2)P(A2)/P(Not B)=0.6*0.2/0.38 =~ 0.32 P(A3|Not B)=P(Not B|A3)P(A3)/P(Not B)=0.9*0.1/0.38 =~ 0.24Learn more about Conditional Probability here:
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A deck of cards contains 52 cards.two decks are put together and divided among eight players.how many cards does each person get
Answer:
13 cards
Step-by-step explanation:
One deck has 52 cards.
2 decks have 2 * 52 cards, or 104 cards.
104 cards are divided among 8 players.
104/8 = 13
Answer: 13 cards
Mrs.Mroc has 35 students in her science class.If her class increases to 42 students next
year, what will be the percent of change?
Answer:
20%
Step-by-step explanation:
Find the increase (subtract original number with final):
42-35= 7
Find the percent change (divide the increase by original number, then multiply by 100 to find the percentage):
[tex]\frac{7}{35}[/tex]*100=20
The percent change from 35 students to 42 students is 20%. This is calculated by using the formula for percent change: ((New Amount - Original Amount) / Original Amount) * 100.
Explanation:In this case, we are trying to calculate the percent change in the number of students in Mrs. Mroc's class. The formula for percent change is:
((New Amount - Original Amount) / Original Amount) * 100
The New Amount is 42 (the number of students next year), and the Original Amount is 35 (the current number of students). So the percent change would be (((42-35)/35)*100), which equals 20%.
So, if Mrs. Mroc's class increases from 35 students to 42 students next year, the percent change will be 20%.
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1. Walking to improve health. In a study investigating a link between walking and improved health (Social Science & Medicine, Apr. 2014), researchers reported that adults walked an average of 5.5 days in the past month for the purpose of health or recreation. a) Specify the null and alternative hypotheses for testing whether the true average number of days in the past month that adults walked for the purpose of health or recreation is lower than 5.5 days. b) Is the test one-tailed or two-tailed? c) Using α = .01, specify the critical value (CV), the rejection region, and draw the distribution.
Answer:
a) We need to conduct a hypothesis in order to check if the true average number of days in the past month that adults walked for the purpose of health or recreation is lower than 5.5 days (a;ternative hypothesis) , the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 5.5[/tex]
Alternative hypothesis:[tex]\mu < 5.5[/tex]
b) For this case since we want to determine if the true mean is lower than an specified value is a one tailed test
c) For this case the significance level is given [tex]\alpha=0.01[/tex] and we want to find the critical value, so we need to find a critical value on the normal standard distribution who accumulate 0.01 of the area on the right tail and if we use excel or a table we got:
[tex]z_{cric}= -2.326[/tex]
And the rejection zone would be: [tex] (\infty ,-2.326)[/tex]
And the region is on the figure attached
Step-by-step explanation:
Part a: State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true average number of days in the past month that adults walked for the purpose of health or recreation is lower than 5.5 days (a;ternative hypothesis) , the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 5.5[/tex]
Alternative hypothesis:[tex]\mu < 5.5[/tex]
Part b
For this case since we want to determine if the true mean is lower than an specified value is a one tailed test
Part c
For this case the significance level is given [tex]\alpha=0.01[/tex]and we want to find the critical value, so we need to find a critical value on the normal standard distribution who accumulate 0.01 of the area on the right tail and if we use excel or a table we got:
[tex]z_{cric}= -2.326[/tex]
And the rejection zone would be: [tex] (\infty ,-2.326)[/tex]
And the region is on the figure attached
Fine the value of d. 2d-5= 17
Answer:
d = 11
Step-by-step explanation:
Find the area of the shaded sector. Round to the nearest tenth and use 3.142 or the pi button on your calculator for pi.
answers: (all answers are squared)
44.0 in2
66.0 in2
263.9 in2
22.0 in2
Given:
Given that the radius of the circle is 12 inches.
The angle of the shaded sector is 210°
We need to determine the area of the shaded sector.
Area of the shaded sector:
The area of the shaded sector can be determined using the formula,
[tex]Area =(\frac{\theta}{360}) \pi r^2[/tex]
Substituting [tex]\theta=210[/tex] and r = 12, we get;
[tex]Area =(\frac{210}{360}) (3.142)(12)^2[/tex]
Simplifying, we get;
[tex]Area =(\frac{210}{360}) (3.142)(144)[/tex]
[tex]Area =263.9 \ in^2[/tex]
Thus, the area of the shaded sector is 263.9 square inches.
Hence, Option c is the correct answer.
nancy bought 7 1/2 gallons of milk for the school cafeteria.she bought only half-gallon containers. how many half gallon containers did she buy
Below are two parallel lines with a third line intersecting them. What is x
Answer:
136=x
Step-by-step explanation:
When an angle is shown, the one opposite of it is equal to the forst equation. The bottom angles are equal to 360ñ so if you take 46x2=92. Subtract 92 by 360 to get 268. Divide it by 2 to get one of the bigger angles, which is 134 degrees. And as for the top, one angle on the bottom is equal to the same spot on the top. so, 136=x
Answer :
x = 134°
Step by step :
46° + x = 180°
x = 180° - 46°
x = 134°
Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for Inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month? 32 +1.645,8908 32 + 1.9620 0.64 + 1.282,16.620.) © 264 265 CHAT 0.04 + 1.00, layanan
Answer:
0.64 ± 0.1117 or
[tex]0.64\pm 1.645*\sqrt{\frac{0.64*(0.36)}{50}}[/tex]
Step-by-step explanation:
Sample size (n) = 50
Z-score for a 90% confidence interval (z) = 1.645
Proportion of students that read at least one book (p):
[tex]p=\frac{32}{50}=0.64[/tex]
The confidence interval is given by:
[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]
Applying the given data:
[tex]0.64\pm 1.645*\sqrt{\frac{0.64*(1-0.64)}{50}}\\ 0.64\pm 0.1117[/tex]
The confidence interval is 0.64 ± 0.1117
The 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month is [tex]0.64\pm 0.11178[/tex].
Given information:
From a random sample of 50 (n) students, Alma found that 32 students read at least 1 book last month.
Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book.
It is required to find the 90 percentage confidence interval for the proportion of all students in her district who read at least 1 book last month.
Now, from tha table, the z-score of 90 percent confidence level is,
[tex]z=1.645[/tex]
The probability p for the proportion of students who read atleast one book is,
[tex]p=\dfrac{32}{50}\\p=0.64[/tex]
So, the 90 percent confidence interval will be calculated as,
[tex]p\pm z\sqrt{\dfrac{p(1-p)}{n}}=0.64\pm 1.645\times \sqrt{\dfrac{0.64(1-0.64)}{50}}\\=0.64\pm 0.11178[/tex]
Therefore, the 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month is [tex]0.64\pm 0.11178[/tex].
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What are the possible outcomes of flipping a coin once
Answer:
1/2 chances if getting heads 1/2 for getting tails
Answer:
heads or tails
An archer is able to hit the bull's-eye 53% of the time. If she shoots 10 arrows, what is the probability that she gets exactly 4 bull's-eyes?
To find the probability that the archer gets exactly 4 bull's-eyes out of 10 shots, use the binomial probability formula. The probability is approximately 0.221.
Explanation:To find the probability that the archer gets exactly 4 bull's-eyes out of 10 shots, we can use the binomial probability formula. The formula is:
P(x) = nCx * p^x * (1-p)^(n-x)
Where:
P(x) is the probability of getting exactly x successesn is the number of trialsx is the number of successes we want to find the probability forp is the probability of a single successIn this case, n = 10, x = 4, and p = 0.53 (since the archer hits the bull's-eye 53% of the time).
Plugging these values into the formula:
P(4) = 10C4 * (0.53)^4 * (1-0.53)^(10-4)
Calculating this gives us P(4) ≈ 0.221
Final answer:
To find the probability of exactly 4 bull's-eyes out of 10 shots for an archer with a 53% success rate, use the binomial probability formula, resulting in approximately a 20.6% chance.
Explanation:
The probability that an archer who hits the bull's-eye 53% of the time getting exactly 4 bull's-eyes out of 10 shots can be calculated using the binomial probability formula: P(X = k) = nCk × p^k × (1 - p)^(n - k), where:
n is the number of trials (10 arrows)
k is the number of successes (4 bull's-eyes)
p is the probability of success on a single trial (0.53)
nCk is the number of combinations of n things taken k at a time
Applying these values:
Calculate the number of combinations for getting 4 successes out of 10 trials:
10C4 = 210.
Calculate the probability of getting exactly 4 bull's-eyes:
P(X = 4) = 210 × (0.53)^4 × (0.47)^6.
Compute the result:
P(X = 4) ≈ 0.206 (rounded to three decimal places).
The archer has approximately a 20.6% chance of hitting exactly 4 bull's-eyes out of 10 shots.
HELP PLEASEEEE! I kinda need this done asap so can anyone explain it to me? :)
Answer:
The Answer is 25.5 in
Step-by-step explanation:
What you basically do is
17² * 17²= 289
19² * 19²= 361
Then add 289+361=650
Then u have to Divide
Then you should get 25.495
Then Round to the nearest Tenth and you Get (25.5 in)
Hope This was Right
Answer:
25.49
Step-by-step explanation:
To find the hypotenuse for right triangles, we use the Pythagorean Theorem or
[tex]A^{2} +B^{2} = C^{2}[/tex]
Keep in mind we only use this for right triangles
With that in mind, lets solve for side c
[tex]A^{2} + B^{2} = C^{2} \\19^{2} +17^{2} = C^{2} \\(19*19) + (17*17) = C^{2} \\361+ 289 = 650\\C^{2} = 650\\\sqrt{650} = C\\C = 5\sqrt{26} or 25.49[/tex]
Hope This Helps!
A plant grows 12 mm every four months how many centimeters will it grow in one year?
Step-by-step explanation:
One year is 12 months. 12 mm is 1.2 cm.
Write and solve a proportion
1.2 cm / 4 months = x / 12 months
x = 3.6 cm
How do the areas of triangle ABC and DEF compare?
O The area of ABC is 1 square unit less than the area of
ADEF
O The area of AABC is equal to the area of ADEF.
O The area of ABC is 1 square unit greater than the
area of ADEF.
O The area of ABC is 2 square units greater than the
area of ADEF.
Answer:
C: The area of ABC is 1 square unit greater than the
area of ADEF
Step-by-step explanation:
Due to the area of triangle ABC and triangle DEF, the ABC triangle has dimensions that are 1 square unit greater that the area of ADEF. This is because the lines have different lengths. Good Luck on the Rest of Your Questions!!
Answer: C
Step-by-step explanation:
sara pays $4100 tuition and fees for each of the two semesters, plus an additional $41" for textbooks each semester. what is the monthly cost?
Answer:
The monthly cost is $690.17.
Step-by-step explanation:
Each semester costs $4100.
In each semester, there are $41 spent on textbooks.
In a year:
2*4100 + 2*41 = $8282
Monthly cost
A year has 12 months. So
8282/12 = 690.17.
The monthly cost is $690.17.
A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs.
They sold each ticket for $45.
Let y represent the net profit (in dollars) when they have sold 2 tickets.
Which of the following information about the graph of the relationship is given?
Answer: slope and x-intercept
y-intercept and a point that is not an intercept is the information about the graph of the relationship is given. So, the correct answer is E. y-intercept and a point that is not an intercept
Let's analyze the information given in the problem:
1. The charity organization sold 18 tickets to cover necessary production costs.
2. They sold each ticket for $45.
3. They want to determine the net profit when they have sold 2 tickets.
We are given a specific point on the graph: (x = 2, y = net profit when 2 tickets are sold).
Now, let's calculate the net profit when 2 tickets are sold:
Net profit when 2 tickets are sold = Total revenue - Total production costs
Total revenue = 2 tickets * $45 per ticket = $90
Total production costs = $18 (to cover necessary production costs)
Net profit = $90 - $18 = $72
Now, let's look at the options:
A. Slope and x-intercept: We do not have the slope or the x-intercept of the graph.
B. Slope and y-intercept: We do not have the slope or the y-intercept of the graph.
C. Slope and a point that is not an intercept: We have a point on the graph, but we do not have the slope.
D. x-intercept and y-intercept: We do not have the x-intercept or the y-intercept of the graph.
E. y-intercept and a point that is not an intercept: We have the y-intercept (net profit when 0 tickets are sold, which is $18) and a point on the graph (net profit when 2 tickets are sold, which is $72).
F. Two points that are not intercepts: We have one point on the graph (net profit when 2 tickets are sold, which is $72), but we do not have another point.
So, Based on the information given, the correct option is:
E. y-intercept and a point that is not an intercept
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Correct Question is:
A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs.
They sold each ticket for $45.
Let y represent the net profit (in dollars) when they have sold 2 tickets.
Which of the following information about the graph of the relationship is given?
A. Slope and x- intercept
B. Slope and y-intercept
C. Slope and a point that is not an intercept
D. x-intercept and y intercept
E. y-intercept and a point that is not an intercept
F. Two points that are not intercepts
you start at (6, 8). You move down 6 units and left 1 unit. Where do you end?
Find BC
(round to the nearest hundredth)
Given:
In ΔABC, ∠C = 90°, ∠A = 50° and AB = 3 unit.
To find the value of BC.
Formula:
By Trigonometric Ratio we get,
[tex]sin \ \theta=\frac{opposite}{Hypotenuse}[/tex]
Now,
With respect to θ = 50°, AB is the hypotenuse and AB is the opposite side.
So,
[tex]sin \ 50^{\circ}=\frac{BC}{AB}[/tex]
[tex]sin \ 50^{\circ}=\frac{BC}{3}[/tex]
[tex]BC = 3 \times sin 50^{\circ}[/tex]
[tex]BC = 2.298 = 2.3[/tex] (approx)
Hence,
The value of BC is 2.3 units.
The graph of a line passes through the points (0,5) and (-10,0). What is the equation
of the line?
CLEAR
CHECK
y = 2x - 10
y = 5x + 5
y= 1 / 8x 10
y = -2x + 5
Answer:
Y=1/2x +5
Step-by-step explanation:
(0,5) (-10,0)
0-5/-10-0=1/2
(0,5) (x, y)
Y-5/x-10=1/2(crossmultiply)
2y-10=x
2y= x +10(divide all sides by 2)
Y=1/2x+5
State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed limit. They plan to set up a radar trap and check the speeds of 80 cars. Taking a random sample of eighty cars is considered sufficiently large for the distribution of the sample proportion to be normally distributed. Would a random sample of 50 cars have been large enough and why?
Answer:
With n = 50, both conditions(np > 5, n(1-p) > 5) are satisfied, so a random sample of 50 cars would have been large enough.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to the normal distribution if:
np > 5, n(1-p) > 5
70% of the drivers traveling on a major interstate highway exceed the speed limit.
So p = 0.7.
Would a random sample of 50 cars have been large enough and why?
With n = 50
np = 50*0.7 = 35 > 5
n(1-p) = 50*0.3 = 15 > 5
With n = 50, both conditions(np > 5, n(1-p) > 5) are satisfied, so a random sample of 50 cars would have been large enough.