Im need help on this question

Im Need Help On This Question

Answers

Answer 1
You were right, its the second choice CA=CB+BA

Related Questions

Share £45 in the ratio of 2:3.

Answers

Answer:

18:27

Step-by-step explanation:

2:3= 2 parts to 3 parts

Total is 5 parts

45/5 parts- each part is 9

2(9)=18

3(9)=27

Answer:

[tex]\£ 18: \£27[/tex]

Step-by-step explanation:

[tex]\frac{45}{2+3}[/tex]

[tex]\frac{45}{5}=9[/tex]

[tex]2:3[/tex]

[tex]2 \times 9 : 3 \times 9[/tex]

[tex]18:27[/tex]

Square 100 * square 25 simplified

Answers

Answer:

50

Step-by-step explanation:

Both √100 and √25 are perfect squares:

√100 = 10

√25 = 5

10(5) = 50

6 people will attend a lunch 2 cans of juice should be provided per person determine the total number of cans of juice required

Answers

Answer:

12

Step-by-step explanation:

it's 6 people and 2 cans of juice goes to each person so you can multiply 6× 2 and you get 12 . 12 cans of juice would be required to provide 6 people with 2 cans each .

What was the sampling method that was used in the scenario? A study was done to determine the age, the number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed.

Answers

Answer:

The sampling method that was used in the scenario is systematic sampling.

Step-by-step explanation:

Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and following a static, periodic interval.  

For instance, consider a study where the researcher first selects a name randomly from the alphabetized order and then follow a fixed pattern of selecting every 10th person from the population.

In this case, a study was done to determine the age, the number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas.

The first house was randomly selected from the neighborhood around the park.

Then, the resident of every 8th house in the neighborhood around the park was interviewed.

So, the researcher selects a random house and then keep on selecting the houses in an interval of 8. This way the next house selected with be the 8th, the next the 16th, and so on.

Thus, the sampling method that was used in the scenario is systematic sampling.

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,100 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,100 and $14,700. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)

Answers

Answer:

[tex] P(X<12000)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]

Then we can conclude that the probability that your bid will be accepted would be 0.41

Step-by-step explanation:

Let X the random variable of interest "the bid offered" and we know that the distribution for this random variable is given by:

[tex] X \sim Unif( a= 10100, b =14700)[/tex]

If your offer is accepted is because your bid is higher than the others. And we want to find the following probability:

[tex] P(X<12000)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]

Then we can conclude that the probability that your bid will be accepted would be 0.41

5+10/x=x+8 Solve the equation with steps

Answers

Answer:

2 and -5

Step-by-step explanation:

[tex]5+\dfrac{10}{x}=x+8 \\\\\\-3+\dfrac{10}{x}=x \\\\\\-3x+10=x^2 \\\\\\x^2+3x-10=0 \\\\\\(x+5)(x-2)=0 \\\\\\x=2,-5[/tex]

Hope this helps!

Find the vertex of the graphed function.
f(x) = |x-4| +3
AY
00
6
4
2
Y
4
The vertex is at

Answers

Answer:

The x-coordinate is the solution to x - 4 = 0, which is x = 4 and the y-coordinate is 3 so the answer is (4, 3).

How many arrangements of the letters in the word olive can you make if each arrangement must use three letters

Answers

Answer:

60

Step-by-step explanation:

There are 5 letters that can be first.

There are 4 letters that can be second.

There are 3 letters that can be third.

The number of permutations is 5×4×3 = 60.

4. (07.04 MC)

An observer (0) spots a plane (P) taking off from a local airport and flying at a 23° angle horizontal to her line of sight and located directly above a tower (T). The observer also notices a bird (B)

circling directly above her. If the distance from the plane (P) to the tower (T) is 5,000 ft., how far is the bird (B) from the plane (P)? Round to the nearest whole number.

Answers

Answer:

11779 ft

Step-by-step explanation:

We are given that

[tex]\theta=23^{\circ}[/tex]

Distance between tower and plane,d=5000 ft

We have to find the distance between the plane and bird.

Let x  be the distance between bird and plane

We know that

[tex]tan\theta=\frac{perpendicular\;side}{Base}[/tex]

Using the formula

[tex]tan23=\frac{5000}{x}[/tex]

[tex]x=\frac{5000}{tan23}=11779.3 \approx 11779ft[/tex]

Hence, the distance between the plane and bird=11779 ft

Answer:

11779 ft

Step-by-step explanation:

We are given that

Distance between tower and plane,d=5000 ft

We have to find the distance between the plane and bird.

Let x  be the distance between bird and plane

We know that

Using the formula

Hence, the distance between the plane and bird=11779 ft

Please show work for number 3 and 4!

Answers

Answer:

Three: x = 400

Four : 9

Step-by-step explanation:

Three

a = 10*√2

2a = √(2x)                    Square both sides.

4a^2 = 2x                     Divide both sides by 2

2a^2 = x                       Put a = 10√2 into a^2

2(10√2)^2 = x               Square a

2(100*2) = x                 Multiply the result by 2.

2(200) = x

x = 400

Four

x^(a^2) / x ^(b^2) = x^36

Substitute a + b = 4 in for b.

x^(a^2) / x^(4 - a)^2 = x^36

Subtract powers

x^(a^2 - (4 - a)^2 = x^36

x^(a^2 - (16 - 8a + a^2) = x^36

Gather like terms

x^(8a - 16) = x^36

The powers are now equal

8a - 16 = 36      

Add 16 to both sides

8a = 36 + 16

8a = 52

Divide by 8

a = 6.5

Solve for b

a + b = 4

6.5 + b = 4

b = 4 - 6.5

b = - 2.5

a - b = 6.5 - (- 2.5) = 9

Keisha, a scheduler at Mangel-Wurzel Transport, gets a call from a regular customer needing to move 70.3 m^3 of rock and soil, which Keisha knows from previous experience has an average density of 880 kg/m^3. Keisha has available a dump truck with a capacity of 9 m^3 and a maximum safe load of 5300. kg. Calculate the number of trips the dump truck will have to make to haul the customer's load away.

Answers

Answer:

Step-by-step explanation:

You take 70.3m^3 multiple with 880kg /m^3 divide with 5300.kg will give you the answer cause I tried it and it worked 100% true.

I hope tis helps .

If sin(18+x)=cos58 find value of x

Answers

Answer:

14

Step-by-step explanation:

Since sine and cosine are cofunctions of each other:

[tex]\sin (\theta)= \cos (90-\theta)[/tex]

and vice versa. Therefore:

[tex]18+x=90-58 \\\\18+x=32 \\\\x=32-18=14[/tex]

Hope this helps!

Pleasssseeee hheeelllppp

Answers

Answer:

No

Step-by-step explanation:

They are not congruent or similar because the figures themselves indicate no similar or congruent parts. Although they may seem congruent or similar, without telling us one thing, we cannot assume that they are similar or congruent.

Arrange the equations in the correct sequence to rewrite the formula for displacement, d = vt-at?, to find a. In the formula, dis
displacement, vis final velocity, a Is acceleration, and t is time.

2(vt -d)=at^2

a=2(d – vt)/12

2(d-vt) = at^2

vt-d=1/2 at^2

d-vt = 1/2at^2

a=2(vt-d)/t^2

Answers

Options

[tex]2(vt -d)=at^2[/tex]

[tex]a=\frac{2(d - vt)}{t^2}[/tex]

[tex]2(d-vt) = at^2[/tex]

[tex]vt-d=\frac{1}{2} at^2[/tex]

[tex]d-vt = -\frac{1}{2}at^2[/tex]

[tex]a=\frac{2(vt-d)}{t^2}[/tex]

Answer:

See Explanation below

Step-by-step explanation:

Given

[tex]d = vt - \frac{1}{2}at^2[/tex]

Required

Steps to find a

To solve for a;

The step 1 is :

[tex]d-vt = -\frac{1}{2}at^2[/tex]

This is achieved by adding vt to both sides

The step 2 is:

[tex]vt-d=\frac{1}{2} at^2[/tex]

This is achieved by multiply both sides by -1

The step 3 is:

[tex]2(vt -d)=at^2[/tex]

This is achieved by multiplying both sides by 2

The step 4 is:

[tex]a=\frac{2(vt-d)}{t^2}[/tex]

This is achieved by dividing both sides by t²

Note that, not all steps in the option are used because they are either incorrect or not necessary

Answer:

for edmentum the answer is

Box 1: d-vt=1/2at^2

Box 2: vt-d=1/2at^2

Box 3: 2(vt-d)/t^2

Step-by-step explanation: Almost certain after scrounging Brainly.

Good luck!

Consider the function f(x) = 3x and the function g, which is shown below. G(x)=F(x)-2=3^x-2 How will the graph of g differ from the graph of f? A. The graph of g is the graph of f shifted 2 units up. B. The graph of g is the graph of f shifted 2 units to the right. C. The graph of g is the graph of f shifted 2 units down. D. The graph of g is the graph of f shifted 2 units to the left. Reset Next


H E L P

Answers

Answer:

  C.  The graph of g is the graph of f shifted 2 units down

Step-by-step explanation:

The transformation ...

  g(x) = f(x -h) +k

represents a translation h units right and k units up.

You have h=0 and k=-2, so the graph is shifted 0 units right and 2 units the opposite of up.

The graph of g is the graph of f shifted 2 units down.

Answer:

C

Step-by-step explanation:

I just took the test on edmentum

justify each step x/3-7=11 x/3=18 x=6

Answers

This is the steps for equation solving for the value of x,

x/3-7 = 11

now 7 goes to the other side of equation by changing the sign from - to +,

x/3 = 11 + 7

x/3 = 18

now when we multiply both sides of equation with 3 or 3 goes to the other side of equation and multiply with 18 leaving x alone here for finding the value of x,

and we get, x = 54

at the end of equation we get x = 54, if the equation was in the form 3x - 7 = 11, then we will get x = 6

if segment ac and segment bc are tangent to circle o find the value of x

Answers

Answer:

x = 150°

Step-by-step explanation:

Start by cutting the shape into two triangles by bisecting the 30°

Now we have two triangles that have two angles 90° and 15°

Subtract 15° from 90°, you'll get 75°

Double 75° because x is split into 2

150° = x

Also, were given 3 angles, this is a quadrilateral.

90° + 90° +  30° = 210°

360° - 210° = 150°

Answer:

150°

Step-by-step explanation:

OA⊥AC and OB⊥BC

∠A+∠B+∠C+∠O=360°

90°×2+30°+x=360°

x=360°-210°=150°

Which are the possible side lengths of a triangle?
O 3 cm, 5 cm, 9 cm
O 4 cm, 8 cm, 10 cm
O 6 cm, 9 cm, 17 cm
O 8 cm, 10 cm, 18 cm

Answers

Answer:

4 cm, 8 cm, 10 cm

Step-by-step explanation:

For a triangle to exist, two sides added up must be greater than the third side. The only quantities that satisfy this relationship is the second option.

Which is the better buy?. Store A $180 at 1/3 off Or Store B $110 at 10% off

Answers

Answer: Store B

Step-by-step explanation:

180 / 3 = 60. 180 - 60= $120. Store A cost is $120.

110 * 0.9 = $99. Store B's cost is $99.

Answer:

Store B

Step-by-step explanation:

Store A the price would be about $120.60

Store B price would be about $99

To find store a price, you first find the discount, so

0.33 x 180 = 59.40

Then subtract this from the original price to know the total after the discount

180-59.40=120.60

Do the same thing with the other Store

110 x 0.10 = 11

110-11=99

A study conducted by Harvard Business School recorded the amount of time CEOs devoted to various activities during the workweek. Meetings were the single largest activity averaging 18 hours per week. Assume that the standard deviation for the time spent in meetings is 5.2 hours. To confirm these results, a random sample of 35 CEOs was selected. This sample averaged 16.8 hours per week in meetings. Which of the following statements is correct?

a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
b. The interval that contains 95% of the sample means is 17.1 and 18.9 hours. Because the sample mean is not between these two values, we do not have support for the results of the CEO study by the Harvard Business School.
c. The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
d. The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we do not have support for the results of the CEO study by the Harvard Business School

Answers

Answer:

a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 18, \sigma = 5.2, n = 35, s = \frac{5.2}{\sqrt{35}} = 0.879[/tex]

95% of the sample means:

From the: 50 - (95/2) = 2.5th percentile.

To the: 50 + (95/2) = 97.5th percentile.

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-1.96 = \frac{X - 18}{0.879}[/tex]

[tex]X - 18 = -1.96*0.879[/tex]

[tex]X = 16.3[/tex]

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]1.96 = \frac{X - 18}{0.879}[/tex]

[tex]X - 18 = 1.96*0.879[/tex]

[tex]X = 19.7[/tex]

95% of the sample means are between 16.3 and 19.7 hours. This interval contains the sample mean of 16.8 hours, which supports the study.

So the correct answer is:

a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.

You might need:

A circle is centered at J(3,3) and has a radius of 12.

Where does the point F(-6, -5) lie?

Choose 1 answer:

Answers

Answer:

Step-by-step explanation:

The equation of this circle is (x - 3)^2 + (y - 3)^2 = 12^2.

Let's substitute the coordinates of the given point and compare the results to the above equation:  do they produce a correct statement?

(-6 - 3)^2 + (-5 - 3)^2 = ?

9^2 + 8^2 = 145

Because r = 12, the above result would need to be 144, not 145, if the given point were actually on the circle.  We must conclude that (-6, -5) lies just outside the circle.

81 + 64 = 144  

PLEASEEEE HELLLPPPP COMPARING EXPONENTIAL FUNCTIONS ...an online retailer developed two exponential functions to model the weekly usage of two coupon codes where x os the number of weeks since the start of the year. ​

Answers

Answer:

  A.  The weekly usage of both coupons is decreasing and approaching a horizontal asymptote as x gets larger.

Step-by-step explanation:

You can see that f(x) is a decreasing exponential function because the base is 0.75, a value less than 1. The horizontal asymptote is 10, the constant added to the exponential term.

Obviously, g(x) is decreasing. If we assume it is an exponential function, we know there is a horizontal asymptote. (Every exponential function has a horizontal asymptote.)

__

If you use your graphing calculator's exponential regression function, you can find a good model for g(x) is ...

  g(x) = 950·0.7^x +12

That is, it is an exponential function that decays faster than f(x), but has a higher horizontal asymptote.

_____

Both functions are decreasing and approaching horizontal asymptotes.

Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function in your final answer include the table of function values f(x)=2^x h(x)=x^3+x+8

Answers

Answer:

When x = 10, or when f(x) = 1024, or any value greater than that.

Step-by-step explanation:

For f(x): 1x = 2, 2x = 4, 3x = 8, 4x = 16, 5x = 32, 6x = 64, 7x = 128, 8x = 256, 9x = 512, 10x = 1024

for g(x) 1x = 10, 2x = 19 3x = 38, 4x = 72, 5x = 128, 6x = 230, 7x = 358, 8x = 528, 9x = 746, 10x = 1018

Answer:

When x = 10, or when f(x) = 1024, or any value greater than that.

Step-by-step explanation:

The image of ABC after a reflection across EG is ABC which statement is true about point F ​

Answers

Answer: First option.

Step-by-step explanation:

As the triangle is reflected over the line EG, this means that the distance between each common point of the triangles and the line must be the same for both triangles.

This means that the distance between B and E, is the same distance as the distance between B' and E.

Now, as you know, the midpoint of a segment is a point such that the distance between that point and each endpoint is the same.

So, in the linea AA', the points A and A' are the endpoints, and because F lies in the line of reflection, the distance between A and F is the same distance than in between A' and F.

So F is the midpoint in  the line AA'

The correct option would be the first one, F is the midpoint of AA' because the line EG bisects AA', and F is colinear to E and G.

A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 1 or less, the lot passes inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection

Answers

Answer:

0.1979 or 19.79%

Step-by-step explanation:

If 20% of all bulbs are defective, there is a 20% chance of each bulb being defective and an 80% chance of each bulb not being defective.

This is a binomial probability model with probability of success (bulb being defective) of p=0.20.

In order for the lot to pass inspection, it must contain either zero or one defective bulb, the probability of one of these scenarios occurring is:

[tex]Pass= P(d=0)+P(d=1)\\Pass= 0.80^{14}+14*0.20*0.80^{13}\\Pass=0.1979[/tex]

The probability that the lot will pass inspection is 0.1979 or 19.79%.

A student said that the y-intercept of the function y = 3 · 4x is 4. What is their mistake? What is the actual y-intercept?

Answers

Answer:

The y intercept is 0

Step-by-step explanation:

the equation of a line is given as

[tex]y= mx+c[/tex]

where

m= is the slope

c= is the y intercept

their mistake is that they did not recall that if the "c" is not shown, it is assumed to be zero (0)

5:36, 2:9, 3:18, 1:3 what is the largest ratio? please help me!

Answers

Answer:

[tex]1:3[/tex]

Step-by-step explanation:

[tex]5:36=5/36[/tex]

[tex]\approx 0.13888888888[/tex]

[tex]2:9=2/9[/tex]

[tex]\approx 0.22222222222[/tex]

[tex]3:18=1/6[/tex]

[tex]\approx 0.16666666666[/tex]

[tex]1:3=1/3[/tex]

[tex]\approx 0.33333333333[/tex]

Answer:

1:3

Step-by-step explanation:

GCF of 36, 9, 18, 3 is 36

        5:36

2:9=  8:36

3:18= 6:36

1:3=  12:36

1:3 is the largest ratio.

Pete is making decorations for a dinner party.The instructions tell him to use 9 flowers for a medium-sized decoration.Complete each statement to adjust the flowers for different-sized decorations based on these instructions.

Answers

Answer:i need points

Step-by-step explanation:bleep bop boop

write an equation for an ellipse centered at the origin, which has foci at (+-3,0) and co vertices at (0+-4)

Answers

Answer:

The equation for an ellipse centered at the origin with foci at (-3, 0) and (+3, 0) and co-vertices at (0, -4) and (0, +4) is:

[tex]\frac{x^{2}}{7} + \frac{y_{2}}{16} = 1[/tex]

Step-by-step explanation:

An ellipse center at origin is modelled after the following expression:

[tex]\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]

Where:

[tex]a[/tex], [tex]b[/tex] - Major and minor semi-axes, dimensionless.

The location of the two co-vertices are (0, - 4) and (0, + 4). The distance of the major semi-axis is found by means of the Pythagorean Theorem:

[tex]2\cdot b = \sqrt{(0-0)^{2}+ [4 - (-4)]^{2}}[/tex]

[tex]2\cdot b = \pm 8[/tex]

[tex]b = \pm 4[/tex]

The length of the major semi-axes can be calculated by knowing the distance between center and any focus (c) and the major semi-axis. First, the distance between center and any focus is determined by means of the Pythagorean Theorem:

[tex]2\cdot c = \sqrt{[3 - (-3)]^{2}+ (0-0)^{2}}[/tex]

[tex]2\cdot c = \pm 6[/tex]

[tex]c = \pm 3[/tex]

Now, the length of the minor semi-axis is given by the following Pythagorean identity:

[tex]a = \sqrt{b^{2}-c^{2}}[/tex]

[tex]a = \sqrt{4^{2}-3^{2}}[/tex]

[tex]a = \pm \sqrt{7}[/tex]

The equation for an ellipse centered at the origin with foci at (-3, 0) and (+3, 0) and co-vertices at (0, -4) and (0, +4) is:

[tex]\frac{x^{2}}{7} + \frac{y_{2}}{16} = 1[/tex]

The demand for the video games provided by Mid-Tech Video Games Inc. has exploded in the last several years. Hence, the owner needs to hire several new technical people to keep up with the demand. Mid-Tech gives each applicant a special test that Dr. McGraw, the designer of the test, believes is closely related to the ability to create video games. For the general population, the mean on this test is 100. Below are the scores on this first test for the applicants. 95 105 120 81 90 115 99 100 130 10 The owner is interested in the overall quality of the job applicants based on this test. Compute the mean and the median scores for the 10 applicants. What would you report to the owner

Answers

Answer:

Mean: 94.5.

Median: 99.5

Standard deviation: 33.1

We can tell the owner that the applicants don't have a score significantly below from 100.

Step-by-step explanation:

First, we analize the sample and calculate the statistics (mean, median and standard deviation).

Mean of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(95+105+120+81+90+115+99+100+130+10)\\\\\\M=\dfrac{945}{10}\\\\\\M=94.5\\\\\\[/tex]

The median, as the sample size is an even number, can be calculated as the average between the fifth and sixth value, sort by value:

[tex]\text{Median}=\dfrac{99+100}{2}=99.5[/tex]

The standard deviation is:

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((95-94.5)^2+(105-94.5)^2+(120-94.5)^2+. . . +(10-94.5)^2)}\\\\\\s=\sqrt{\dfrac{9834.5}{9}}\\\\\\s=\sqrt{1092.7}=33.1\\\\\\[/tex]

To tell if this sample has a value significantly lower than the expected score of 100, we should make a hypothesis test.

The claim is that the mean score is significantly lower than 100.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=94.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.1.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{33.1}{\sqrt{10}}=10.467[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{94.5-100}{10.467}=\dfrac{-5.5}{10.467}=-0.53[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

This test is a left-tailed test, with 9 degrees of freedom and t=-0.53, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-0.53)=0.306[/tex]

As the P-value (0.306) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean score is significantly lower than 100.

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