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## A random sample of 25 statistics examinations was taken. the average score in the sample was 76 with a standard deviation of 12. assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is:

Since the sample size is less than 30, therefore we use
the t statistic.

Let us define the given variables:

N = sample size = 25

X = average score = 76

s = standard deviation = 12

99% Confidence interval

Degrees of freedom = n – 1 = 24

The formula for confidence interval is given as:

CI = X ± t * s / sqrt N

using the standard distribution table, the t value for DF
= 24 and 99% CI is:

t = 2.492

Therefore calculating the CI using the known values:

CI = 76 ± 2.492 * 12 / sqrt 25

CI = 76 ± 5.98

CI = 70.02, 81.98

Answer: The average score ranges from 70 to 82.

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## What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample mean of \$6.88 per basket. assume that the standard deviation is known to be \$1.92 per basket. find a 90% confidence interval for the population mean price per basket that farmers in this region get for their peach crop

Given:
Sample size, n = 40
Sample mean, xb = \$6.88
Population std. deviation, σ = \$1.92 (known)
Confidence interval = 90%

Assume normal distribution for the population.
The confidence interval is
(xb + 1.645*(σ/√n), xb – 1.645*(σ/√n)
= (6.88 + (1.645*1.92)/√40, 6.88 – (1.645*1.92)/√40)
= (7.38, 6.38)

Answer: The 90% confidence interval is (7.38, 6.38)

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## Consider college officials in admissions registration, counseling, financial aid campus ministry, food services, and so on. How much money do these people make each year? Suppose you read in your local newspaper that 45 officials in student services earn an average of \$50,340 each year. Assume that the standard deviation is \$10,780 for salaries of college officials and student services. Find a 90% confidence interval for the population mean salaries of such personnel. Round your answer to the nearest dollar and don;t forget to use the \$ sign.

Since sample size is > 40, we use the z-score
in calculating for the confidence interval.

The formula is given as:

Confidence Interval = X ± z * σ / sqrt (n)

Where,

X = mean = \$50,340

z = z-score which is taken from standard distribution
tables at 90% confidence interval = 1.645

σ
= standard deviation = \$10,780

n = sample size = 45

Substituting to the equation:

Confidence Interval = 50,340 ± 1.645 * 10,780 / sqrt (45)

Confidence Interval = 50,340 ± 1,607

Confidence Interval = \$48,733 to \$51,947

Therefore the salary range of the personnel is \$48,733 to \$51,947.

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## Sat scores are distributed with a mean of 1,500 and a standard deviation of 300. you are interested in estimating the average sat score of first year students at your college. if you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?

Sat scores are distributed with a mean of 1,500 and a standard deviation of 300. you are interested in estimating the average sat score of first year students at your college. if you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?

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## What type of graph uses the length of bars to show how many data points are in an interval??

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## During which interval was the bicyclist speed the greatest? I am not sure about my answer.

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## A motorist drives along a straight road at a constant speed of 15.0 m/s. Just as she passes a parked motorcycle police offi cer, the offi cer starts to accelerate at 2.00 m/s2 to overtake her. Assuming that the offi cer maintains this acceleration, (a) determine the time interval required for the police offi cer to reach the motorist. Find (b) the speed and (c) the total displacement of the offi cer as he overtakes the motorist.

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## Find all solutions in the interval [0, 2pi): sin5x+sinx=sin3x

Find all solutions in the interval [0, 2pi): sin5x+sinx=sin3x

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## What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample mean of \$6.88 per basket. assume that the standard deviation is known to be \$1.92 per basket. find a 90% confidence interval for the population mean price per basket that farmers in this region get for their peach crop.

C. Yes, because the population values appear to be normally distributed.

Step-by-step explanation:

Given is a graph which shows the distribution of values of a population

The graph has the following characteristics

i) Bell shaped

ii) symmerical about mid vertical line

iii) Unimodal with mode = median =mean

iv) As x deviates more from the mean probability is decreasing and also curve approaches asymptotically the x axis

Hence we find that the curve is a distribution of normal

Option C is right

C. Yes, because the population values appear to be normally distributed.

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## The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples 26 different days and records the number of calls. the sample yields a mean of 258.4 calls with a standard deviation of 32.7 calls per day. the 95% confidence interval for the mean number of calls per day has an upper bound of ________. (round your answer to 1 decimal place.)

First we calculate for the total number of possibilities
(permutation) to select 4 disks from the container:

Total number of possibilities = 10 * 9 * 8 * 7

Total number of possibilities = 5040

Now let us find the 4 disks that will result in a range of 7.

Range = highest number – lowest number

The pair of highest and lowest number that will result in
range of 7 is: (1 & 8), (2 & 9), (3 & 10)

As a basis of calculation, let us use the pair 1 & 8.

There are four possible ways to select 1 and three for 8.

Arrangements of maximum and minimum pair = 4 * 3

Arrangements of maximum and minimum pair=12

Now we need to calculate for the remaining 2 disk. There
are 6 numbers between 1 & 8. The total possibilities for selecting 2 disk
from the remaining 6 is:

Possibilities of selecting 2 disk from remaining 6 = 6 *
5

Possibilities of selecting 2 disk from remaining 6 = 30

Therefore, the total possibility to get a range of 7 from
a pair of 1 & 8 is:

Total possibility for a pair = 12 * 30

Total possibility for a pair = 360

Since there are a total of three pairs (1 & 8), (2
& 9), (3 & 10):

Total possibilities of the 3 pairs = 360 * 3

Total possibilities of the 3 pairs = 1080

Therefore:

Probability = Total possibilities of the 3 pairs / Total
number of possibilities

Probability
= 1080 / 5040 = 3 / 14                      (FINAL

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## PLEASE HELPPP Which graph has a negative rate of change for the interval 0 to 2 on the x-axis?

D is correct. x>2 the growth rate of the exponential function exceed the growth rate of the linear function.

Step-by-step explanation:

We are given a linear function and an exponential function in graph.

We need to find interval when growth rate of the exponential function exceed the growth rate of the linear function.  Option A) When x<1

Growth rate of linear function = 2

Growth rate of Exponential function = 0.75

When x<1 , growth rate of exponential function is less than linear function.

Option B) When 0≤x≤1

Growth rate of linear function = 2

Growth rate of Exponential function = 1

When 0≤x≤1  , growth rate of exponential function is less than linear function.

Option C) When 1≤x≤2

Growth rate of linear function = 2

Growth rate of Exponential function = 2

When 1≤x≤2  , growth rate of exponential function is equal to linear function.

Option D) When x>2

Growth rate of linear function = 2

Growth rate of Exponential function = 4

When x>2  , growth rate of exponential function is exceed the growth rate of  linear function.

Thus, x>2 the growth rate of the exponential function exceed the growth rate of the linear function.

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## An experiment is designed to determine if the amount of sugar in a drink affects the likelihood that bees will be attracted to it. Sample A is 100 mL of pure water. Sample B is 100 mL of water with 1 gram of sugar dissolved in it. Sample C is 100 mL of water with 2 grams of sugar dissolved in it. All samples are placed on a picnic table. One observer is assigned to each drink. The observers count the number of bees that visit the drink during a 15-minute interval.

Answer: c. Count the number of tomatoes that are produced by a tomato plant that is grown in clay soil, and compare it to the number of tomatoes that are produced by a tomato plant that is grown in sandy soil.

Explanation:

Scientific design is like a detail procedure for conducting the research. It includes a typical hypothesis or a scientific inquiry which is required to be proved. It includes a method of survey or data collection, and an experimental procedure.

An independent variable can be changed or manipulated by the experimenter the impact of which can be observed on the dependent variable. The dependent variable is the outcome of the experiment.

According to the given situation, soil type is the independent variable and the the yield of tomatoes should be the dependent variable. As the type of soil chosen will directly influence the yield of tomatoes.

On the basis of the above information, c. Count the number of tomatoes that are produced by a tomato plant that is grown in clay soil, and compare it to the number of tomatoes that are produced by a tomato plant that is grown in sandy soil. is the correct option.

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## Mixed numbers from 3 to 7 with an interval of 1/3

To solve this, you have to find the interval in which d > 0. For starters, solve for the x-intercepts of 0, or when d=0. . You can now plug in d=0. . Now, as |x|=y is the same as x=±y, t=±3 or t=3 and t=-3. Next, we determine if our d is positive or negative in the interval (-∞,∞) with subintervals at our x-intercepts, making our intervals (-∞,-3), (-3,3), and (3,∞). To do this, just take one value from each interval and plug it in for t. For interval (-∞,-3), we can use -4 so , making all ds in this interval negative. For (-3,3), the easiest thing to use is 0 so , making all ds in this interval positive. For interval (3,∞), we can use 4 so , making all ds in this interval negative. As we need d>0, we can conclude that in the interval (-3,3) the car is in the air. Lastly, we must consider that t cannot be less than 0 as there is no such thing as negative time, so with 0 as our domain restriction, we can conclude the interval in which the car is in the air is (0,3), also written as t ∈ (0,3).

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## Is my answer, right? The table of values represents a polynomial function f(x). How much greater is the average rate of change over the interval [7, 9] than the interval [4, 6]? x f(x) 4 105 5 384 6 945 7 1,920 8 3,465 9 5,760 Is the answer 605 or am I way off?? \$.\$

The average rate of change A(x) over interval [a, b] is given by: …..

As per the statement:

The table of values represents a polynomial function f(x).

For interval [7, 9]

f(7) = 1920

f(9) = 5760

then

using equation  we have; Substitute the given values we have; Next:

For interval [4, 6]

f(4) =105

f(6) =945

then

using equation  we have; Substitute the given values we have;   Therefore,1500 greater is the average rate of change over the interval [7, 9] than the interval [4, 6]