Given:
A plane can fly 1200 miles in the same time as it takes a car to go 320 miles. The car travels 110 mph slower than the plane.
We need to determine the speed of the plane.
Speed of the plane:
Let the speed of the plane be x.
Equating the time taken by the plane and the time taken by the car using the formula,
[tex]Time=\frac{Distance}{Speed}[/tex]
Thus, we have;
[tex]\frac{1200}{x}=\frac{320}{x-110}[/tex]
Cross multiplying, we get;
[tex]1200(x-110)=320x[/tex]
Simplifying, we get;
[tex]1200x-132000=320x[/tex]
[tex]880x=132000[/tex]
[tex]x=150[/tex]
Thus, the value of the speed of the plane is 150 mph
Final answer:
The speed of the plane is found by setting up an equation based on the relationship between distance, speed, and time for both the plane and the car. After setting up the equations and equating the times, we find that the plane's speed is 150 mph.
Explanation:
To find the speed of the plane, we can set up an equation based on the relationship between distance, speed, and time. Let's denote the plane's speed as x mph. Then the car's speed would be x - 110 mph. Since they travel for the same amount of time, we can write two equations:
Time for plane = 1200 miles / x mph
Time for car = 320 miles / (x - 110) mph
These two times are equal, so we set the equations equal to each other:
1200 / x = 320 / (x - 110)
To solve for x, cross-multiply and solve the resulting quadratic equation:
1200(x - 110) = 320x
1200x - 132,000 = 320x
1200x - 320x = 132,000
880x = 132,000
x = 132,000 / 880
x = 150 mph
Therefore, the speed of the plane is 150 mph.
This net can be folded to form a cube with a side length of 20 units
IM
What is the surface area of the cube in square units?
Answer:
The net, when folded into a cube, has a total surface area of 2,400 sq.units
Step-by-step explanation:
The length of all sides of a cube are the same.
Now, the surface area of a cube is the sum of the area of all of its faces.
Since the length of all sides are the same and we are told that the length of a side is 20 units, thus, the area of one face is;
A = 20 x 20 = 400 sq.units
So, one the area of a face is 400 sq.units.
Now, since all the faces are the same measurement, thus each face will have an area of 400 sq.units. Cubes have 6 faces, thus the total surface Area is;
Total = 400 x 6 = 2400 sq.units
The net, when folded into a cube, has a total surface area of 2,400 sq.units
Sadie’s family orders a medium pizza with one topping, a large pizza with three toppings, two salads, and an order of breadsticks. What is the cost of the bill before tax or tip?
A. $40.25
B. $43.00
C. $44.00
D. $39.25
Answer:the answers is B
Step-by-step explanation:
please help im clueless
To create a scale drawing of an Olympic standard swimming pool with a scale of 1 inch to 10 meters, the scaled dimensions would be approximately 2.5 inches for the width and 5 inches for the length.
To create a scale drawing of an Olympic standard swimming pool using a scale of 1 inch to 10 meters, we need to find the scaled dimensions. The actual dimensions of the pool are given as 50 meters in length and 25 meters in width.
Width:
Actual width: 25 meters
Scale factor: 10 meters per 1 inch
Scaled width = Actual width / Scale factor
Scaled width = 25 meters / 10 meters per 1 inch
Scaled width = 2.5 inches
Length:
Actual length: 50 meters
Scale factor: 10 meters per 1 inch
Scaled length = Actual length / Scale factor
Scaled length = 50 meters / 10 meters per 1 inch
Scaled length = 5 inches
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HELP ME WITH CALCULUS 1! I am stuck
answer
graph a
speeds up from (0,1) U (2,3) and slows down from (1,2)
if it marks (2,3) incorrectly, it may be from (2,∞) instead
graph b
speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)
if it marks (3,4) incorrectly, it may be from (3,∞) instead
step-by-step explanation
looking at the velocity graphs, when the absolute value of velocity is increasing (moving away from the x axis), the particle must be speeding up. we say absolute value because while velocity has direction, speed only has magnitude, so we need to take the absolute value of velocity to get speed.
for graph a, we can see the velocity moving away from the x axis during the interval (0,1), moving towards the x axis during the interval (1,2) and then moving away again during the interval (2,3)
so it speeds up from (0,1) U (2,3) and slows down from (1,2)
if it marks (2,3) incorrectly, it may be from (2,∞) instead since this is at an endpoint
repeat for graph b where it moves toward the x axis from (0,1), moves away from (1,2), moves towards from (2,3), and moves away again from (3,4)
so it speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)
if it marks (3,4) incorrectly, it may be from (2,∞) instead since this is at an endpoint
A train leaves Little Rock, Arkansas, and travels north at 60 kilometers per hour. Another train leaves at the same time & travels south at 65 kilometers per hour. How long will it take before they are 500 kilometers apart?
Answer:
3.704 Hours
Step-by-step explanation:
This problem can be solved by using concept of relative speed. relative speed is speed of one body in comparison of other.
If two bodies are moving in same direction their relative speed is calculated by taking difference of each other speed.
If two bodies are moving in opposite direction their relative speed is calculated by taking sum of each other speed.
In the problem stated two bodies are moving in north and south direction, hence they are moving in opposite direction, thus their speed can be taken sum of individual speed.
which is
(60+65) Km/Hr = 135 km/hour
Now given in question distance between two bodies is 500 KM
and relative speed = 135 km/hour
using formula of speed distance and time
Time = distance / speed = 500/135 = 3.704 Hours
Therefore it will take 3.704 Hours for both of the trains to be 500 km apart.
The limit of a rational function at 5 equals the value of the rational function at 5 true or false
What is the measure of SRT? 69 79 99 or 101 degrees
Answer:
it would have to be a 99
The solution is, the measure of angle A is 79°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
we know that
the law of cosines establish
c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]
in this problem
a=11 units
b=11 units
c=14 units
C=angle A
so, we get,
cos C=[11²+11²-14²]/[2*11*11]
-----> cos C=0.19008
C=arc cos (0.19008)
------> C=79.04°
the answer is
the measure of angle A is 79°.
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A manager is deciding whether or not to build a small facility. Demand is uncertain and can be either at a high or low level. If the manager chooses a small facility and demand is low, the payoff is $300. If the manager chooses a small facility and demand is high, the payoff is $100. On the other hand, if the manager chooses a large facility and demand is low, the payoff is -$200, but if demand is high, the payoff is $800.
(a) What would be the best decision based on the maximax criterion?
(b) What would be the best decision based on the maximin criterion?
(c) What would be the best decision based on the minimax regret?
Answer:
Check the explanation
Step-by-step explanation:
(a) Best decision based on maximax criterion= large facility
maximum in the two facilities is $300 and $800 of which $800 is the maximum, So larger facility satisfies maximax.
(b) Best decision based on maximin criterion= small facility
minimum in the two facilities is $100 and -$200 of which $100 is the maximum, So smaller facility satisfies maximin.
(c) Best decision based on minimax regret= large facility
maximum in the two facilities is $300 and $800 of which $300 is the minimum, So larger facility satisfies minimax regret.
Final answer:
Explanation of maximax, maximin, and minimax regret criteria for decision-making in uncertain scenarios.
Explanation:
Maximax criterion: This criterion involves selecting the decision with the maximum possible payoff under each possible outcome. In this case, the manager would choose the large facility due to the potential high payoff of $800 in case of high demand.
Maximin criterion: This criterion involves selecting the decision with the maximum possible payoff under the worst-case scenario. Here, the manager would choose the small facility to minimize the loss to -$200 in case of low demand.
Minimax regret: This criterion involves minimizing the maximum regret that could be incurred based on the wrong decision. The manager would need to calculate regrets for each decision and choose the one with the least possible regret
Two circles lie in space. Which of the following can not occur if they were to intersect?
A. Three points
B. Two points
C. One point
D. Infinitely many points
E. None of the above
Answer:
A. Three points
Step-by-step explanation:
Tangent circles will intersect at the one point of tangency.
Circles that cross each other will intersect in two points.
Circles that are coincident will intersect in infinitely many points.
It is not possible for two circles to intersect in exactly 3 points.
From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be conducted. In the new poll, if the proportion favoring the incumbent has not changed, what is the mean and standard deviation of the number preferring the incumbent?(a)mean = 330, standard deviation = 10.59(b)mean = 0.66, standard deviation = 10.59(c)mean = 330, standard deviation = 18.17
Answer:
The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.
Step-by-step explanation:
We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.
A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.
Let p = probability of voters preferring the incumbent = 66%
n = number of voters polled = 500
So, the mean of the number preferring the incumbent is given by;
Mean = [tex]n \times p[/tex] = [tex]500 \times 0.66[/tex]
= 330 voters
And, standard deviation of the number preferring the incumbent is given by;
Variance = [tex]n \times p\times (1-p)[/tex]
= [tex]500 \times 0.66 \times (1-0.66)[/tex]
= 112.2
So, Standard deviation = [tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{112.2}[/tex] = 10.59
Based on the binomial distribution and the probability of 66%, the mean number of likely voters favoring the incumbent is 330, and the standard deviation is approximately 18.17.
Explanation:In this scenario, we are working with a binomial distribution where we have a fixed number of trials, each trial has two possible outcomes (in this case, favoring the incumbent or not), the probability of success is constant, and the trials are independent. Here, a success is a likely voter favoring the incumbent.
To find the mean of the number preferring the incumbent, we use the formula μ = np, where n is the number of trials (or voters), and p is the probability of a success. Thus, the mean is 500 voters times 66%, which gives us:
μ = 500 * 0.66 = 330.
The formula for the standard deviation (σ) of a binomial distribution is σ = √npq, where q is the probability of failure (1 - p). Therefore, standard deviation is:
σ = √(500 * 0.66 * (1 - 0.66)) = 18.17.
The correct answer is: mean = 330, standard deviation = 18.17
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pLLLLSSSS HELPP IM MARKING BRAINLIEST
The water usage at a car wash is modeled by the equation W(x) = 3x3 + 4x2 − 18x + 4, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day.
C(x) = 2x3 + 2x2 − 18x − 11
C(x) = 3x3 + 2x2 − 18x + 11
C(x) = 3x3 + 2x2 − 18x − 11
C(x) = 2x3 + 2x2 − 18x + 11
Answer:
A C(x) =2x³+2x²-18x-11
Step-by-step explanation:
C(x) = W(x) - D(x)
plug W(x) and D(x) into equation
C(x) = 3x³+4x²-18x+4 - (x³+2x²+15)
add like terms now
C(x) =2x³+2x²-18x-11
examine the system of equations 4.2x + 8y=41.8 -4.2 + y= 19.4
use the linear combination method to solve the system of equations what is the value of x
Answer:
-3
Step-by-step explanation:
i know because i took the test
Answer:
-3 a)
Step-by-step explanation:
bc
The poll found that 38% of a random sample of 1012 American adults said they believe in ghosts. What is the lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts?
Answer:
The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549
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].
For this problem, we have that:
[tex]n = 1012, \pi = 0.38[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 - 1.645\sqrt{\frac{0.38*0.62}{1012}} = 0.3549[/tex]
The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549
Bob flips a fair coin. If Bob’s outcome is heads, Chuck draws a card randomly from a Poker deck where the four kings have been removed beforehand; If Bob’s outcome is tails, Chuck draws a card randomly from another Poker deck where the four aces have been removed beforehand. (There are 52 cards in a standard deck, among which there are 4 kings and 4 aces). Finally, if Chuck gets a king David raises a red flag; otherwise David raises a green flag. What is the probability that David raises a green flag?
Answer:
The probability is 0.9583
Step-by-step explanation:
First, we have 2 possibilities, Bob's outcome is heads or Bob's outcome is tails.
If Bob's outcome is heads, the probability that Chuck doesn't get a king is equal 1, because there aren't kings in the poker deck. it means that if Bob's outcome is heads, the probability that David raises a green flag is 1.
On the other hand, if Bob's outcome is tails, the probability that Chuck doesn't get a king is equal to:
[tex]\frac{44}{48}=0.9166[/tex]
Because there are 48 cards in the poker deck (without the 4 aces) and 44 of them aren't kings. So, if Bob's outcome is Tails, the probability that David raises a green flag is 0.9166.
Now, the probability that David raises a green flag is calculated as:
[tex]P=0.5(1)+0.5(0.9166)=0.9583[/tex]
Because there is a probability of 0.5 that Bob's outcome is heads and there is a probability of 0.5 that Bob's outcome is Tails.
Are the ratios 14:18 and 1:3 equivalent?
Answer:
PLEASE MARK AS BRAINLIEST PLZ
NOPE
Step-by-step explanation:
14:18 if you want to find the divisible number it is 2 now divide them both by 2it will be 7:9 and that's the most simple way
Answer:
No
Step-by-step explanation:
A way you can do it is to simplify the ratio, to make it smaller, but still equal to 14:18.
14:18 can be divided by 2, and turn to 7:9
This cannot be simplified so it is not equivalent.
Final answer
No
A large company that must hire a new president prepares a final list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery. a. What is the probability one of the minority candidates is hired
Final answer:
The probability of one of the minority candidates being hired is 40%.
Explanation:
To find the probability that one of the minority candidates is hired, we need to determine the number of favorable outcomes (one of the minority candidates being selected) and divide it by the total number of possible outcomes (selecting any candidate from the final list of five).
Since there are two minority candidates and five candidates total, the probability of selecting one of the minority candidates is
P(one of the minority candidates being hired) = 2/5 = 0.4 = 40%
What do the solutions of a quadratic equation represent graphically? What is the maximum number of solution(s) given by solving a quadratic?
Answer:
The solutions of a quadratic equation on a graph is the point where the graph cuts across the x and y axes. The maximum number of solutions given by solving a quadratic equation is 2 solutions because the maximum power in a quadratic equation is power 2
The solutions of a quadratic equation represent the points where the graph, or parabola, crosses the x-axis. Those points are known as the roots of the equation. A quadratic equation can have up to two solutions.
Explanation:In mathematics, the solutions of a quadratic equation graphically represent the points where the parabola (graph of the equation) crosses the x-axis. These points are commonly known as the roots or zeros of the quadratic equation. The maximum number of solutions a quadratic equation can have is two. This is due to the highest power in a quadratic equation (ax² + bx + c = 0) being '2'. However, it's also possible for it to have one or no solutions, depending on the values of a, b, and c, specifically their discriminant value (b² - 4ac).
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Mike heats some soup to 216 F. In order to eat the soup, he decides to let the soup cook in his kitchen. The following function represents the temperature of the soup, located in the kitchen with the air temperature of 73 F, after x minutes, where k is the constant rate at which the soup is cooking. T(x)= 73 +143 *e^(kx) If the temperature of the soup is 180 F after 8 minutes, then what is the approximate constant rate of cooling?
Answer:
-0.04
Step-by-step explanation:
The initial temperature of the soup is 216° F. After 8 minutes, the temperature of the soup is 180° F.
Set T(x) equal to 180, and set x equal to 8. Then, solve for r.
Therefore, the approximate constant rate of cooling is -0.04.
Answer:
Mark me brainliest please
Step-by-step explanation:
if you have 1,000,000,000 dollars and you want to split between 10 friends how much will they get each
Answer:
Each friend would get 100000000
Step-by-step explanation:
1000000000 ÷ 10 = 100000000
Answer:
$100,000,000
Step-by-step explanation:
divide 1,000,000,000 by 10, be sure to count your zeros.
97% of £698.04 rounded to 2 decimal places
Rewrite the percent as a decimal by moving the decimal point 2 places to the left:
97% = 0.97
Now multiply:
698.04 x 0.97 = 677.0988
Round to 2 decimal places= 677.10
To find 97% of £698.04, you simply multiply £698.04 by 0.97. This gives you an answer of £677.30, rounded to 2 decimal places.
Explanation:The question is asking for 97% of £698.04. To find this, you would need to multiply £698.04 by 0.97 (which is the decimal equivalent of 97%). Let's do this calculation:
£698.04 * 0.97 = £677.30
Here, the result (rounded to 2 decimal places) is £677.30. So, 97% of £698.04 is £677.30.
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Solve the equation.
3* = 27
x=L(Simplify your answer.)
Answer:
3³ = 27
This is because:
3x3x3 = 27
What is 0.1 repeating. Convert to a FRACTION
Answer:
0.1111... = 0.1 = 1/9
Step-by-step explanation:
0.1111.. Is a repeating decimal which can be written as 0.1 and 1/9
It is important to know that the decimals which have only 1 digit repeating all come from the fractions which are ninths.
The fraction form of a number 0.11... is,
⇒ 1/9
We have to given that,
A number 0.1 repeating.
Now, We can find the fraction of number 0.111.. as,
Let us take,
x = 0.1111..... .. (i)
Multiply by 10,
10x = 1.1111.... .. (ii)
Subtract (ii) from (i);
10x - x = 1.111.. - 0.1111....
9x = 1
x = 1/9
Hence, The fraction form of a number 0.11... is,
⇒ 1/9
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2•2•2•n•n what is the product using exponents
Answer:
2³n²
Step-by-step explanation:
An exponent signifies the number of times the base is a factor in the product. Here, 2 is a factor 3 times; n is a factor 2 times. Their exponents will be 3 and 2, respectively:
2•2•2•n•n = 2³n²
A rectangular tank with a square base, an open top, and a volume of 5324 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
Answer:
Step-by-step explanation:
I can't unless you give me the length and width or its impossible
A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?
Answer:
(a) The variance decreases.
(b) The variance increases.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample mean is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample mean is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The standard deviation of sample mean is inversely proportional to the sample size, n.
So, if n increases then the standard deviation will decrease and vice-versa.
(a)
The sample size is increased from 64 to 196.
As mentioned above, if the sample size is increased then the standard deviation will decrease.
So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.
The standard deviation of the sample mean for n = 64 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7[/tex]
The standard deviation of the sample mean for n = 196 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4[/tex]
The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.
Hence, the variance also decreases.
(b)
If the sample size is decreased then the standard deviation will increase.
So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.
The standard deviation of the sample mean for n = 784 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2[/tex]
The standard deviation of the sample mean for n = 49 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8[/tex]
The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.
Hence, the variance also increases.
Variance has decreased in first case and Variance has increased in second case.
Variation based problem:What information do we have?
Mean tensile stength = 78.3 kilograms
Standard variance = 5.6 kilogram
Variance = sigma² / n
A.
Variance of sample mean with sample size 64 = 5.6² / 64
Variance of sample mean with sample size 64 = 0.49
Variance of sample mean with sample size 196 = 5.6² / 196
Variance of sample mean with sample size 196 = 0.16
Variance has decreased.
B.
Variance of sample mean with sample size 784 = 5.6² / 784
Variance of sample mean with sample size 784 = 0.04
Variance of sample mean with sample size 49 = 5.6² / 49
Variance of sample mean with sample size 49 = 0.64
Variance has increased.
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Teen obesity:
The 2013 National Youth Risk Behavior Survey (YRBS) reported that 13.7% of U.S. students in grades 9 through 12 who attend public and private schools were obese. [Source: Kann, L., Kinchen, S., Shanklin, S.L., Flint, K.H., Hawkins, J., Harris, W.A., et. al.(2013) YRBS 2013]
Suppose that 15% of a random sample of 300 U.S. public high school students were obese. Using the estimate from the 2013 YRBS, we calculate a standard error of 0.020. Since the data allows the use of the normal model, we can determine an approximate 95% confidence interval for the percentage of all U.S. public high school students who are obese.
Which interval is the approximate 95% confidence interval?
A) 0.097 to o.177
B) 0.117 to 0.157
C) 0.110 to 0.190
D) 0.013 to o.170
Answer:
95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].
Step-by-step explanation:
We are given that 15% of a random sample of 300 U.S. public high school students were obese.
Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample % of U.S. public high school students who were obese = 15%
n = sample of U.S. public high school students = 300
p = population percentage of all U.S. public high school students
Here for constructing 95% confidence interval we have used One-sample z proportion statistics.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
95% confidence interval for p = [[tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]0.15-1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] , [tex]0.15+1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] ]
= [0.110 , 0.190]
Therefore, 95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].
The correct answer is option (c). The approximate 95% confidence interval is [tex]\[0.1108 \text{ to } 0.1892\][/tex]
To determine the approximate 95% confidence interval for the percentage of all U.S. public high school students who are obese, we'll use the standard error provided and the normal model.
The formula for the confidence interval is:
[tex]\[\hat{p} \pm Z \cdot \text{SE}\][/tex]
Now, we calculate the margin of error:
[tex]\[\text{Margin of Error} = Z \cdot \text{SE} = 1.96 \cdot 0.020 = 0.0392\][/tex]
Then, we determine the confidence interval by adding and subtracting the margin of error from the sample proportion:
[tex]\[\hat{p} - \text{Margin of Error} = 0.15 - 0.0392 = 0.1108\][/tex]
[tex]\[\hat{p} + \text{Margin of Error} = 0.15 + 0.0392 = 0.1892\][/tex]
Therefore, the approximate 95% confidence interval is:
[tex]\[0.1108 \text{ to } 0.1892\][/tex]
Las tres quintas partes de los animales de un parque natural son mamíferos y, de ellos, cinco sextos son carnívoros ¿Qué fracción del total de animales representan los mamíferos carnívoros? Explicá cómo lo pensaste
The carnivores mammals are (1/2) of the total animals in the natural park.
Step-by-step explanation:
Let the total no. of animals be 'a'
The amount of mammals = (3/5)a
The amount of carnivores= (5/6) (3/5) a
= (1/2) a
So, the carnivores mammals are (1/2) of the total animals in the natural park.
Find the Lowest Common Multiple of 3, 5 and 6.
Answer:
30
Step-by-step explanation:
6*5= 30
3*10= 30
5*6= 30
The Lowest Common Multiple of 3, 5, and 6. is 30
The lowest common multiple of a group of numbers is the smallest number that is a multiple of all the numbers.
Given the integers 3, 5 and 6, to get the Lowest common multiple, we will need to take the product of all the integers as shown:Lowest common multiple = 3 * 5 * 6 = 60But note that 60 is not the lowest value that can go easily in the integers, hence the LCM of the numbers will be 5*6 = 30Learn more here: https://brainly.com/question/4913940
Which letter represents the maximum of the data set on the box plot?
A
B
C
D
E
30
35
40
45
50
How many stripes does each zebra have if there are 6 zebras at the zoo, 162 stripes in all, and all the zebras have the same number of stripes?
Answer:
27 stripes
Step-by-step explanation:
162/6=27
Since each zebra has the sam amount of stripes, you will divide the amount of stripes my the amount of zebras.