Write a quadratic function to represent the data in the table.

x y
1 55
2 65
3 71
4 73
5 71

Calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.

The null hypothesis would be that the schedule adjustment did not reduce the average lateness time of 12 minutes.

[tex]H0:[/tex][tex]\mu = 12[/tex]

The alternative hypothesis would be that the schedule adjustment did reduce the average lateness time of 12 minutes.

[tex]Ha:[/tex] [tex]\mu < 12[/tex]

Here, we are testing whether the population mean arrival time is less than 12 minutes, based on a sample of 36 runs that had an average of 8 minutes late. We can use a one-sample t-test to test this hypothesis, with the following test statistic:

[tex]t = (\bar x - \mu) / (s / \sqrt{n} )[/tex]

where[tex]\bar x[/tex] is the sample mean (8 minutes),[tex]\mu[/tex] is the population mean (12 minutes), s is the population standard deviation (12 minutes), and n is the sample size (36 runs).

Using these values, we get:

[tex]t = (8 - 12) / (12 / \sqrt{(36)} ) = -3[/tex]

The degrees of freedom for this test are n - 1 = 35. Using a t-distribution table, we can find the critical t-value for a one-tailed test with a significance level of 0.05 and 35 degrees of freedom to be approximately -1.69.

Since our calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.

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The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31

From the question, we have the following parameters that can be used in our computation:

√(2 + 2x) - 6 = 2

So, we have

√(2 + 2x) = 8

Take the square of both sides

so, we have the following representation

2 + 2x = 64

Evalyate the like terms

2x = 62

Divide by 2

This means that

x = 31

Hence, the solution is x = 31

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Complete question

What is √(2 + 2x) - 6 = 2

Step-by-step explanation:

Question 1

This question has two parts. First, answer Part A. Then, answer Part B.

Part A

Fill in the blank question.

There are many cylinders with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.

Complete the equation that represents the volume V as a function of the radius r.

V =

πr2

Complete the table.

r V

1

π

2

π

4

π

Part B

Select the correct choices to complete the sentence.

Complete the statement about the radius and volume of a cylinder.

If the radius of a cylinder is doubled, the volume 1 of 2.

Select Choice

.

Complete the statement about the graph of this function.

The graph of this function 2 of 2.

Select Choice

a line.

75% of the time, a dart will fall inside a square rather than on the circular dartboard.

The ratio of the area of the circle to the square is 16/64 = 1/4. So, the area outside the circle but inside the square is 3/4 of the total area of the square. The probability of landing the dart in this region is 3/4.

To find the percentage, we can multiply by 100:

3/4 × 100 = 75%

Therefore, to the nearest percent, the probability that the dart lands inside the square but not on the circular dartboard is 75%.

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Answer:

49.7 mm

Step-by-step explanation:

the circumference (C) of a circle (2πr) is also the perimeter of a circle.  The figure shown is a half-circle.  To get the perimeter of the shape shown, find the C/2 (half the circumference) and add the diameter:

P = 2π(12/2) + 12 = 49.7 mm

The can be done by running the following command in R:

The solution to this problem requires you to load the “rpart” package from CRAN and load the “car90” dataset. The last 20% of the observations should be held out as the test set. A decision tree should be trained using all the predictors to model the “Price” variable on the training data where the maximum depth of the tree is 1, 2, and 3 respectively. The mean squared error on the held-out test set data should be calculated. A bootstrapped prediction should then be generated with 1,000 samples for the test set data using a decision tree of depth size 3, and the test set MSE should be reported.

Here are the steps to follow:

Step 1: Install the “rpart” package from CRAN

This can be done by running the following command in R: install.packages("rpart")

Step 2: Load the “car90” dataset

This can be done by running the following command in R: data(car90)

Step 3: Hold out the last 20 percent of the observations as the test set

This can be done by running the following command in R: test_set <- car90[round(nrow(car90) * 0.8) + 1:nrow(car90), ]

Step 4: Train a decision tree using all the predictors to model the “Price” variable on the training data where the maximum depth of the tree is 1, 2, and 3 respectively

This can be done by running the following commands in R:

train_set <- car90[1:round(nrow(car90) * 0.8), ]
library(rpart)
set.seed(123)
depths <- 1:3
models <- lapply(depths, function(depth) rpart(Price ~ ., data = train_set, method = "anova", maxdepth = depth))

Step 5: Calculate the mean squared error on the held-out test set data

This can be done by running the following commands in R:

library(Metrics)
set.seed(123)
mse <- lapply(models, function(model) mse(predict(model, newdata = test_set), test_set$Price))

Step 6: Generate a bootstrapped prediction with 1,000 samples for the test set data using a decision tree of depth size 3

This can be done by running the following commands in R:

set.seed(123)
boot_preds <- replicate(1000, {
 sampled_test_set <- test_set[sample(nrow(test_set), replace = TRUE), ]
 predict(models[[3]], newdata = sampled_test_set)
})

Step 7: Report the test set MSE

This can be done by running the following command in R:

mse(predict(models[[3]], newdata = test_set), test_set$Price)

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The most individuals with a certain trait that follow a normal distribution would appear in the middle range.

If you graph the numbers of individuals with a certain trait that follow a normal distribution, the most individuals will appear in the middle range of the graph.

When graphing a normal distribution, it creates a bell-shaped curve.

The curve is symmetric and highest at the center, which indicates that the most individuals fall under the middle range of the graph.

The shape of the curve represents the frequency distribution of the data.

The horizontal axis is marked off in intervals of standard deviations from the mean.

The vertical axis shows the frequency, or the number of times each score occurs in the data set.

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The 6 m/s, and 5 m/s speeds of the sprinters, the 150 meters length of the race, and the 10 meters head start of sprinter B indicates that the three statements are true, and the correct option is therefore;

True, True, True

The speed of an object is the ratio of the distance traveled by the object to the duration of the motion.

The distance sprinters are to run = 150 meters

The speed of sprinter A = 6 m/s

Speed of sprinter B = 5 m/s

The head start of sprinter B = 10 meters

Statement A; Sprinter A is leading the race at the 12 seconds mark

At the 12 seconds mark, we get;

The distance covered by sprinter A = 6 m/s × 12 s = 72 m

The distance covered by sprinter B = 10 m + 5 m/s × 12 s = 70 m

Therefore, sprinter A is leading sprinter B at the 12 seconds mark

Statement A is True

Statement B; Sprinter A will win the race

The time it takes sprinter A to run the race = 150 m/(6 m/s) = 25 s

Sprinter B takes (150 m - 10 m)/(5 m/s) = 28 s to finish the race

Sprinter A therefore, finishes before sprinter B, and sprinter A wins the race

Statement B is; True

Statement C; The graphs of the two functions intersect before the race ends

The location of sprinter B ahead of A at the start of the race and A ahead of B at the 12 seconds mark, indicates that the sprinter A passes sprinter B along the race and the graphs intersect before the race ends. The statement is therefore; True

The possible options, obtained from a similar question posted on the internet are;

True, True, True

False, True, True

True, False, True

True, True, False

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the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

Corresponding angles are angles that are in the same position at each intersection where a straight line crosses two others. In the given list of angles, we can see that:

Angles 1 and 3 are corresponding angles, because they are on opposite sides of the line and are in the same position relative to the other lines.

Angles 5 and 7 are corresponding angles, for the same reason.

Angles 6 and 8 are corresponding angles, because they are alternate interior angles (they are on opposite sides of the transversal and inside the two lines).

Angles 7 and 2 are vertical angles, not corresponding angles.

Angles 6 and 3 are alternate interior angles, not corresponding angles.

Angles 1 and 6 are alternate interior angles, not corresponding angles.

Therefore, the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

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Answer: x=3

              y=9

Step-by-step explanation: im about 75.94 percent sure about this, i hope it helps

The probability of getting heads after flipping the coin once would depend on the specific probabilities of the coin landing on heads or tails, which are not given in the problem statement.

The probability of getting heads after flipping the coin once cannot be determined from the given information. The probability of getting three heads in x flips of an unfair coin is not necessarily related to the probability of getting heads in a single flip.

For example, it is possible that the unfair coin has a very low probability of landing on heads, such as 0.1. In this case, the probability of getting three heads in a row after flipping the coin x times would be very low, but the probability of getting heads on a single flip would still be 0.1.

Therefore, the probability of getting heads after flipping the coin once would depend on the specific probabilities of the coin landing on heads or tails, which are not given in the problem statement.

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Answer:

108

Step-by-step explanation:

Let's assume that there are "x" scouts attending the jamboree.

The number of tins of soup required to feed x scouts would be x/2.

The number of tins of frankfurters required to feed x scouts would be x/3.

The number of tins of fruit required to feed x scouts would be x/4.

Therefore, the total number of tins required to feed x scouts would be:

x/2 + x/3 + x/4 = (6x + 4x + 3x) / 12 = 13x/12

Since we know that 117 tins were opened, we can set up the equation:

13x/12 = 117

Solving for x, we get:

x = 108

Therefore, there were 108 scouts attending the jamboree.

An inverse variatiοn includes the pοints (8, 3) and (2, n), the value οf n is 12.

Inverse variatiοn fοrmula refers tο the relatiοnship οf twο variables in which a variable increases in its value, the οther variable decreases and vice-versa. In οther wοrds, the inverse variatiοn is the mathematical expressiοn οf the relatiοnship between twο variables whοse prοduct is a cοnstant.

Using the given pοints, we can set up a prοpοrtiοn tο find k:

8 * 3 = k

2 * n = k

Setting the twο expressiοns fοr k equal tο each οther, we get:

8 * 3 = 2 * n

24 = 2n

Dividing bοth sides by 2, we get:

n = 12

Therefοre, the value οf n is 12.

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We can say that after answering the offered question Therefore, the equation exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]{-\frac{4\sqrt{261}}{65}}[/tex]

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

[tex]$\sec A = \frac{1}{\cos A}$ to find the cosine of angle $A$.[/tex]

[tex]$\sec A = -\frac{65}{7}$, we have $\frac{1}{\cos A} = -\frac{65}{7}$.\\$$\cos A \cdot \frac{1}{\cos A} = \cos A \cdot \left(-\frac{65}{7}\right)$$\\$$[/tex]

Since angle A is in Quadrant III, we know that [tex]$\cos A < 0$ and $\sin A < 0$.[/tex]

Using the Pythagorean identity[tex]$\sin^2 A + \cos^2 A = 1$, we can solve for $\sin A$:[/tex]

[tex]$$\sin^2 A + \left(-\frac{7}{65}\right)^2 = 1$$\\$$\sin^2 A + \frac{49}{4225} = 1$$\\$$\sin^2 A = \frac{4176}{4225}$$\\$$\sin A = -\frac{4\sqrt{261}}{65}$$[/tex]

Therefore, the exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]${-\frac{4\sqrt{261}}{65}}$[/tex]

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The coordinates of the fourth vertex of the parallelogram are given as follows:

To find the coordinates of the fourth vertex of the parallelogram, we must consider the fact that opposite sides of a parallelogram are parallel and equal in length.

Considering the side formed by the vertices (-1,9) and (4,7), the difference of the coordinates is given as follows:

Hence, compared to the vertex (0,-2), the coordinates of the remaining vertex are given as follows:

Then the coordinates of the fourth vertex are given as follows:

(-5,0).

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Answer:

  A, D, E

Step-by-step explanation:

You want to know the properties applicable to a square among those listed.

Quadrilaterals can be classified according to the relationships between their sides. These relationships also give rise to relationships between the diagonals.

The diagonals have the same midpoint in a parallelogram.

The diagonals are the same length in a parallelogram that is a rectangle.

A square is a rectangle that has adjacent sides of the same length (A). That means its diagonals have the same midpoint (E), and they are the same length (D).

__

Additional comment

When segments have the same slope, they are parallel. Consecutive sides intersect, so cannot have the same slope (E). Likewise, the diagonals intersect, so cannot have the same slope (C).

Answer:

w=20cm

Step-by-step explanation:

Tough question.  

We are not told whether the surface area is only what can be seem from the top, or does it include regions beneath the butterfly.  I made the assumption it is from the top

I had to make an assumption that since the butterfies are similar, they wll have the same ratio of width and height.  We will assume an "effective height,"  a value of height that when multiplied by the width will yield the correct surface area of 53 cm^2.

See the attached worksheet.

The effective height for the smaller butterfly is 13.25cm.  This multiplied by the given width (4cm) produces the surface area of 53 cm^3.  The ratio of width to height (w/h) is 0.302.

We've already made the assumption that the width to height of the larger butterfly will be the same.  Now we can use the larger area (1325 cm^2) with the width to height ratio as follows:

 Area = w*h

Since w/h is = 0.302, we can write w = 0.302h or h = (w/0.302)

 1325 cm^2 = w*h

1325 cm^2 = w*(w/0.302)

w^2 = 200

w = 20 cm

(I made several assumptions in this analysis.  Review them carefully).

The total price of the ring after increment is $15900

A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. As a result, the proportion denotes a component per 100. Percent is what the word "percent" means. Its symbol is the letter "%".

The current price of the ring= $ 15,000

Increase in percentage=6

New price:

15000*(1+0.06)=15900

The total price of the ring after increment is $15900

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The total area of the composite figure is 200 square feet.

We can view the figure as a triangle and a rectangle.

The dimensions of the rectangle are 24ft by 6ft,so its area is:

A = 24ft*6ft = 144ft²

Now for the triangle, remember that the area of a triangle of base B and height H is:

a = B*H/2

In this case we can see that the base is:

B = 24ft - 8ft - 8ft = 8ft

And the height is:

H = 20ft - 6ft = 14ft

Then the area of the triangle is:

a = 8ft*14ft/2 = 56 ft²

The total area is:

Area = 56 ft² + 144ft² = 200 ft²

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Given:-

To find:-

Answer:-

Here we can assume the shape of the cup to be cylindrical . And the volume of a cylinder is given by;

[tex]\implies V = \pi r^2 h \\[/tex]

where ,

Assuimg that the cups differ only in height and not in width (diameter) , we can say that ;

[tex]\implies V \propto h \\[/tex]

So , we can write;

[tex]\implies \dfrac{V_s}{V_l}=\dfrac{h_s}{h_l}\\[/tex]

[tex]\implies \dfrac{V_s}{18\ oz}=\dfrac{6\ in.}{8 \ in.}\\[/tex]

[tex]\implies V_s = \dfrac{6(18)}{8} \\[/tex]

[tex]\implies \underline{\underline{ V_s =13.5 \ oz}} \\[/tex]

Hence the volume of the smaller cup is 13.5 oz .

and we are done!

The second term of the finding sequence is 25.

When you are confronted by a question like this, you can make a simple equation, combine like terms, isolate the variable, and solve.

"5 consecutive odd numbers" basically means x + (x + 2) + (x + 4) + (x + 6) + (x + 8). Each time you add 2 more to ensure there are no even numbers. Otherwise, it wouldn't be only consecutive odd numbers.

We are told the sum of these numbers is 135. This means x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

This might seem a bit intimidating, but there are actually only a couple of steps.

Combine like terms.

In this case, the like terms are the 5 times x appears and the numbers 0, 2, 4, 6, and 8.

x + x + x + x + x = 5 • x, or 5x.

0 + 2 + 4 + 6 + 8 = 20

So by combining like terms, we can simplify (x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135 down to just 5x + 20 = 135.

Isolate the variable.

Now we just have to isolate x. The value of x is the lowest term in the sequence.

5x + 20 = 135

To isolate x, first subtract 20 from both sides. Then, divide both sides by 5.

5x + 20 - 20 = 5x

135 - 20 = 115

5x = 115

5x / 5 = x

115 / 5 = 23

x = 23

The lowest term in the sequence is 23.

Identify all numbers in the sequence.

Now that we know x, we can find the rest of the numbers in the sequence by plugging the lowest value into the original equation we created.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

(23 + 0) + (23 + 2) + (23 + 4) + (23 + 6) + (23 + 8) = 135

23 + 0 = 23 This is the first and lowest term in the sequence.

23 + 2 = 25 This is the second term in the sequence.

23 + 4 = 27 This is the third term in the sequence.

23 + 6 = 29 This is the fourth term in the sequence.

23 + 8 = 31 This is the fifth and last term in the sequence.

Now we know the sequence is 23, 25, 27, 29, 31.

Finding the Answer:

To find the answer, locate the second term in this sequence.

23, 25, 27, 29, 31

The second term is 25.

The complete question is-

The sum of 5 consecutive odd numbers is 135. What is the second number in this sequence?

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The line segment that shows the base that corresponds to the given height of the triangle is; Line segment A

We are given the parameter being that a height is labeled as seen on the triangle in attached figure.

Now, what we want to achieve is to find the specific segment which tells us the specific base that corresponds to the given specific height of the triangle

We know that the base of the triangle is that particular side of the triangle on which the height is perpendicular.

In the given attached figure, it is clear that the Height is perpendicular to side A.

Therefore, side A will represent the base of triangle.

Finally, line segment A tells us the base that corresponds to the given height of the triangle.

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(a) The probability that the student is a woman is 0.7381. (b) The probability that the student received an A is 0.3095. (c) The probability that the student is a woman or received an A is 0.9405. (d) The probability that the student did not receive an A is 0.6905.

(a) Probability that the student is a woman:

P(woman) = number of women / total number of students

P(woman) = 31 / 42

P(woman) = 0.7381

Answer: 0.7381

(b) Probability that the student received an A:

P(A) = number of students who received an A / total number of students

P(A) = (6 + 7) / 42

P(A) = 0.3095

Answer: 0.3095

(c) Probability that the student is a woman or received an A:

P(woman or A) = P(woman) + P(A) - P(woman and A)

To find P(woman and A), we note that there are 7 women who received an A, so:

P(woman and A) = 7 / 42

P(woman or A) = 0.7381 + 0.3095 - (7 / 42)

P(woman or A) = 0.9405

Answer: 0.9405

(d) Probability that the student did not receive an A:

P(not A) = 1 - P(A)

P(not A) = 1 - 0.3095

P(not A) = 0.6905

Answer: 0.6905

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Yes it's rhombus ......... .......

The Slope of the line whose coordinates are given that (10 -1) and (-8 6) is the change in y coordinate with respect to the change in x coordinate is (-7/18).

Here the coordinates are (10 -1) and (-8 6) that means :-

X1 = 10

X2 = -8

Y1 = -1

Y2 = 6

So slope of line = (Y2-Y1)/(X2-X1)

     slope = 6-(-1)/-8-10

    slope = 7/-18

Hence the slope of the line containing (10 -1) and (-8 6) would be 7/-18.

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

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Answer:

5(d) = miles student A ran

8(d-3) = miles student B ran

Step-by-step explanation:

when d = days passed

5(d) = miles student A ran

8(d-3) = miles student B ran

However, it can improve one's problem-solving skills and logical reasoning abilities, which could indirectly lead to improvements in various aspects of life, including interpersonal relationships.

I would decide my endless goal by carefully considering my values, desires, and potential paths towards achieving them.

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Answer:

Let x be the number of hot dogs sold.

Then the number of sodas sold is 3x.

The total number of sodas and hot dogs sold is 132, so we can write:

x + 3x = 132

4x = 132

x = 33

Therefore, the number of hot dogs sold is 33, and the number of sodas sold is 3x = 3(33) = 99.

Step-by-step explanation:

The surface area οf the square pyramid is 144 square units.

A square pyramid has a square base, sο tο find the surface area, we need tο find the area οf the square base and the area οf each οf the fοur triangular faces, and then add them tοgether.

The area οf the square base is: 8 x 8 = 64 square units

Tο find the area οf each οf the fοur triangular faces, we need tο find the area οf each triangle and then add them tοgether. Each triangle has a base οf 8 and a height οf 5 (the slant height οf the pyramid).

The area οf each triangle is:

(1/2) x base x height = (1/2) x 8 x 5 = 20 square units

Since there are fοur triangular faces, the tοtal area οf the triangular faces is: 4 x 20 = 80 square units

Finally, we can find the tοtal surface area by adding the area οf the square base and the area οf the fοur triangular faces:

64 + 80 = 144 square units

Therefοre, the surface area οf the square pyramid is 144 square units.

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The probability that more than 175 cable homes will assess cable firms as providing outstanding or exceptional transmission quality is roughly 0.0287.

The word "probability" comes directly from the Latin word "probabilitas," which means "credibility, likelihood," in Old French probability (14th century) (see probable). The word first appeared in mathematics around 1718.

Let X be the proportion of the 300 randomly chosen cable homes that are satisfied or excellent with their provider's transmission quality.

Let p be the probability that a cable household will rate cable firms as providing good or exceptional quality transmission, which in this instance is 53% or 0.53.

Let q represent the likelihood that a cable household does not consider cable companies to be providing good or exceptional quality transmission, which in this instance is 47% or 0.47.

Let 300 * 0.53 = 159, or the mean of the binomial distribution, be denoted by = n * p.

The binomial distribution's standard deviation, = sqrt(n * p * q), is sqrt(300 * 0.53 * 0.47) = 8.38. (rounded to two decimal places).

The binomial distribution can be approximated by the normal distribution:

P(X > 175) = P(Z > (175 - μ) / σ)

where Z is a standard normal variable.

P(Z > (175 - 159) / 8.38) = P(Z > 1.91)

Using a standard normal table or calculator, we can find that P(Z > 1.91) is approximately 0.0287.

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