The data given represents the number of gallons of coffee sold per hour at two different coffee shops.

_________
Perks A Lot
10 3.5 3
5 2.5 7
8 5.5 9.5
6 9 4.5
______________
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
_____________

Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour.

Perks A Lot, with a median value of 5.75 gallons
Wide Awake, with a median value of 4.5 gallons
Perks A Lot, with a mean value of 5.75 gallons
Wide Awake, with a mean value of 4.5 gallons

Answer:

\( Area = 112.1 m^2 \)

Step-by-step Explanation:

Given:

∆WXY

m < X = 130°

WY = x = 31 mm

m < Y = 26°

Required:

Area of ∆WXY

Solution:

Find the length of XY using Law of Sines

\( \frac{w}{sin(W)} = \frac{x}{sin(X)} \)

X = 130°

x = WY = 31 mm

W = 180 - (130 + 26) = 24°

w = XY = ?

\( \frac{w}{sin(24)} = \frac{31}{sin(130)} \)

Multiply both sides by sin(24) to solve for x

\( \frac{w}{sin(24)}*sin(24) = \frac{31}{sin(130)}*sin(24) \)

\( w = \frac{31*sin(24)}{sin(130)} \)

\( w = 16.5 mm \) (approximated)

\( XY = w = 16.5 mm \)

Find the area of ∆WXY

\( area = \frac{1}{2}*w*x*sin(Y) \)

\( = \frac{1}{2}*16.5*31*sin(26) \)

\( = \frac{16.5*31*sin(26)}{2} \)

\( Area = 112.1 m^2 \) (to nearest tenth).

Answer:

6400

Step-by-step explanation:

Substitute the given value into the expression

p²q²

= 10² × 8²

= 100 × 64

= 6400

Step-by-step explanation:

given that p=10

you would times 10 by itself so:

10x10=100

now the same for the q=8

8x8=64

now i think you would have to times 100 with 64 if not than there's your answer

which equals to 6400 (if you times it)

hope that helps

Approximately 57.83% of trees would be below 191 inches in diameter.

Approximately 37.48% of trees would be between 176 and 196 inches in diameter.

A diameter of approximately 194.83 inches represents the top 35% of the trees.

To find the percentage of trees below 191 inches in diameter, we need to calculate the cumulative probability below that value.

Using the mean and standard deviation given:

Mean (μ) = 187 inches

Standard Deviation (σ) = 20.4 inches

We can standardize the value 191 inches using the z-score formula:

z = (x - μ) / σ

z = (191 - 187) / 20.4 ≈ 0.1961

Next, we find the cumulative probability using the z-score:

P(Z < 0.1961)

Using a standard normal distribution table or calculator, we find that P(Z < 0.1961) ≈ 0.5783.

b) To find the percentage of trees between 176 and 196 inches in diameter, we need to find the cumulative probability between these values.

First, we calculate the z-scores for both values:

z1 = (176 - 187) / 20.4 ≈ -0.5392

z2 = (196 - 187) / 20.4 ≈ 0.4412

Next, we find the cumulative probabilities for each z-score:

P(Z < -0.5392) ≈ 0.2946

P(Z < 0.4412) ≈ 0.6694

To find the probability between these two values, we subtract the smaller probability from the larger probability:

P(-0.5392 < Z < 0.4412) = 0.6694 - 0.2946 ≈ 0.3748

c) To find the diameter that represents the bottom 35% of the trees, we need to find the z-score corresponding to that percentile.

Using a standard normal distribution table or calculator, we find the z-score that corresponds to the bottom 35% is approximately -0.3853.

Next, we can solve for the diameter using the z-score formula:

-0.3853 = (x - 187) / 20.4

Solving for x, we get:

x ≈ 179.17 inches

So, a diameter of approximately 179.17 inches represents the bottom 35% of the trees.

d) To find the diameter that represents the top 35% of the trees, we can use the same approach as in part c) but with the z-score corresponding to the top 35% (which is the same as the bottom 65%).

Using a standard normal distribution table or calculator, we find the z-score that corresponds to the top 35% (bottom 65%) is approximately 0.3853.

Using the z-score formula:

0.3853 = (x - 187) / 20.4

Solving for x, we get:

x ≈ 194.83 inches

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Answer:

60 + 2 + 0.6 + 0.08 + 0.006

Step-by-step explanation:

you break it up into columns and whatever is before it becomes a 0 as a place holder.

i hope this helps :))

Answer: 15 with 8 over 100

Step-by-step explanation:  15.08 has 2 digits  after decimal = something over 100  =\(15\frac{8}{100}\)

Following equation represents the parabola in the graph:

x=1/12(y+4)^2-2

From the graph, we see that;

Focus = (-4, -2)

We use the equation x=h−p  to find the directrix.

General form of equation of a parabola is;

(y - k)² = 4p(x - h)

where;

focus is (h + p, k)

directrix is x = h - p

If we are talking about the function y = ax² + bx + c, then since it is a continuous function on the whole real line, it must cross the y–axis at (0 , c).

However x = y² + 1 is a parabola(not a function) that does not cross the y–axis.

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we have f(x) = sin(3x) + x - 1 as the equation that satisfies the given conditions.

To find the equation for f(x) given the information provided, we need to integrate the given derivative f''(x) and use the initial conditions f'(0) and f(0).

Given: f''(x) = -9sin(3x)

Integrating f''(x) with respect to x will give us f'(x):

f'(x) = ∫(-9sin(3x)) dx

To integrate -9sin(3x), we can use the fact that the integral of sin(ax) with respect to x is -1/a * cos(ax). In this case, a = 3.

f'(x) = -9 * (-1/3 * cos(3x)) + C1

      = 3cos(3x) + C1

Using the initial condition f'(0) = 4, we can solve for C1:

4 = 3cos(3 * 0) + C1

4 = 3 * 1 + C1

C1 = 4 - 3

C1 = 1

Therefore, we have f'(x) = 3cos(3x) + 1.

To find f(x), we integrate f'(x) with respect to x:

f(x) = ∫(3cos(3x) + 1) dx

The integral of 3cos(3x) with respect to x is (3/3) * sin(3x) = sin(3x).

The integral of 1 with respect to x is x.

f(x) = sin(3x) + x + C2

Using the initial condition f(0) = -1, we can solve for C2:

-1 = sin(3 * 0) + 0 + C2

-1 = 0 + 0 + C2

C2 = -1

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Answer:

Okay to start with we know this side isn't congruent to our side with 55 degrees looking at this side we can see that x is not 95 degrees because it is an acute angle so A is crossed out. Next this side isn't congruent like I said so B is crossed out. C is possible but the angle wouldn't be as wide as it is if we had 59 degrees so C is incorrect. Leaving us with D 70 degrees hope this helps and sorry if I got it wrong!

Step-by-step explanation:

Simplifying

25x + -15 = 2y

Reorder the terms:

-15 + 25x = 2y

Solving

-15 + 25x = 2y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + 25x = 15 + 2y

Combine like terms: -15 + 15 = 0

0 + 25x = 15 + 2y

25x = 15 + 2y

Divide each side by '25'.

x = 0.6 + 0.08y

Simplifying

x = 0.6 + 0.08y

Answer:

21

Step-by-step explanation:

all the details are in the attached picture.

Answer: Jack travels 5 miles + 3*(janice's miles)  

If Jack travels 30 miles, then

30 = 5 + 3*Janice

subtract 5 from both sides

25=3*Janice

divide both sides by 3

Janice travelled 25/3 miles, or 8.33333 miles

Hope it helps Can you mark me Brainliest pls

Answer:

He traveled 23 miles in all

Answer:

Step-by-step explanation:

nancy: 22

jay: 11 cause nancy has twice as many apples as jay.

ava has 8 apples cause jay has 3 more apples than ava :)

The range of a function can have more numbers, fewer numbers, or the same number of numbers as the domain. Alice is correct.

The domain of a function refers to the set of input values, while the range refers to the set of output values. In general, the range is determined by the behavior of the function and how it maps the inputs to the outputs.

There are cases where the range can have the same number of numbers as the domain. For example, in a function where each input maps to a unique output value, the range will have the same number of elements as the domain.

However, there are also cases where the range can have fewer numbers than the domain. This happens when multiple inputs map to the same output value. In such cases, the range will have fewer elements than the domain.

In other words, Alice's statement is correct. The range of a function can have more numbers, fewer numbers, or the same number of numbers as the domain, depending on the behavior of the function.

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Weight represents the top 10% of the zucchinis is 5.9

The formula for calculating a z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

We're looking for:

Weight is 10% of zucchinis at the top.

Top 10% = 90% of the population

90th percentile Z score is 1.282.

Hence

1.282 = x - 5 / 0.7

1.282 × 0.7 = x - 5

0.8974 = x - 5

x = 5 + 0.8974

x = 5.8974

5.9 ounces, roughly.

The top 10% of the zucchinis have a weight of 5.9 ounces.

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Answer:

X=50

Step-by-step explanation:

If you algebraically plug in 50 you come to an answer of X=50

Answer:

\(\frac{1}{5}\)

Step-by-step explanation:

Slope is defined at the \(\frac{rise}{run}\) of a linear function, or, the change in y, divided by the change in x

In this case the function rises by 1, and runs 5, or the slope is \(\frac{1}{5}\)

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

Answer:

1)=-18x^5+60x^4-50x^3

2)k=3m/2-12

3)6x^2(x+2)(x-2)

Step-by-step explanation:

Hope dis helps :)

could i have brainliest

Answer:

As x approaches 6:

\( \frac{6 - x}{ {x}^{2} - 36 } = - \frac{x - 6}{(x - 6)(x + 6)} = - \frac{1}{x + 6} = - \frac{1}{6 + 6} = - \frac{1}{12} \)

The limit of the given function as x approaches 6 is -1/12. This is achieved by factoring and revising the original function, and then substituting into the revised function.

The student is asking for the limit of the function (6-x) / (x²-36) as x approaches 6. In mathematics, this is a problem of calculus and specifically involves limits. Let's solve this by first factoring the denominator to get (6-x) / ((x-6)(x+6))

By realizing we can revise the numerator as -(x-6), we make it obvious that the limit can be directly computed by substituting x=6 after canceling out the (x-6) terms. The result is -1/12, therefore the limit of the function as x approaches 6 is -1/12.

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Answer:

8/4 or 2/1 simplified

Step-by-step explanation:

The option: (12.038, 12.062)

Hi, I'd be happy to help you calculate the 97% confidence interval for the given data. To find the 97% confidence interval for a sample of 204 soda cans with a mean amount of 12.05 ounces and a standard deviation of 0.08 ounces, follow these steps:

1. Identify the sample size (n), mean (µ), and standard deviation (σ): n = 204, µ = 12.05, σ = 0.08
2. Determine the confidence level, which is 97%. To find the corresponding z-score, you can use a z-table or calculator. The z-score for 97% confidence is approximately 2.17.
3. Calculate the standard error (SE) using the formula: SE = σ / √n. In this case, SE = 0.08 / √204 ≈ 0.0056.
4. Multiply the z-score by the standard error to find the margin of error (ME): ME = 2.17 × 0.0056 ≈ 0.0122.
5. Find the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the mean, respectively: Lower bound = 12.05 - 0.0122 ≈ 12.0378, Upper bound = 12.05 + 0.0122 ≈ 12.0622.

So, the 97% confidence interval for this sample is approximately (12.0378, 12.0622), which is closest to the option (12.038, 12.062).

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Answer:

2x+5 is the expression

Answer:

The expression is 2x + 5

A repeating zero multiplicity factor (x a)k, k > 1, results in x = an of k. The multiplicity of a polynomial is the number of times a certain factor appears in the equation when it has been factored.

A single zero is present where the graph crosses the x-axis and appears practically linear at the intercept. It is a zero with even multiplicity if the graph hits the x-axis and then deflects off of it. It is an odd multiplicity zero if the graph crosses the x-axis at zero. Degree n is equal to the multiplicities added together.

Set your initial factor to zero and solve in step one. Step 2: Keep solving by setting all of your factors in your factored form polynomial equal to zero and repeating this step for each factor. There are no practical solutions for this issue. Step 3: Make a list of your polynomial's zeros.

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Answer:

\(a^{12}\)

Step-by-step explanation:

Identity Used :   \(a^x \times a^y = a^{x+ y}\)

       \(a^5 \times a^7 = a^{5 + 7} = a^{12}\)

The function g(x) is a transformation (flipped upside down and horizontally stretched) of the quadratic parent function, f(x) = x2. g(x) = -0.5x².

Flipping upside down, is found by taking the negative of the original function; that is, the rule for this transformation is −f (x).

Since, g(x) is an upside down function of f(x), g(x) = -f(x).

If we multiply a function by a coefficient, the graph of the function will be stretched.

A function h(x) represents a horizontal compression of f(x) if h(x) = f(cx) and c > 1.

A function h(x) represents a horizontal stretch of f(x) if h(x) = f(cx) and 0 < c < 1.

Since, g(x) is clearly a stretched transformation of f(x), c < 1.

The possible function g(x) = -0.5x².

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Answer:

0.0027 = 0.27% probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

At a large state university, the heights of male students who are interscholastic athletes is approximately Normally distributed with a mean of 74.3 inches and a standard deviation of 3.5 inches. Sample of 10:

This means that \(\mu_I = 74.3, s_I = \frac{3.5}{\sqrt{10}}\)

Those who are "non-interscholastics" have mean of 70.3 inches and a standard deviation of 3.2 inches. Sample of 12.

This means that \(\mu_N = 70.3, s_N = \frac{3.2}{\sqrt{12}}\)

What is the probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes?

This is the probability that:

N - I > 0

Distribution N - I:

\(\mu = \mu_N - \mu_I = 70.3 - 74.3 = -4\)

\(s = \sqrt{s_I^2+s_N^2} = \sqrt{(\frac{3.5}{\sqrt{10}})^2+(\frac{3.2}{\sqrt{12}})^2} = 1.44\)

Probability:

One subtracted by the p-value of Z when X = 0.

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0 - (-4)}{1.44}\)

\(Z = 2.78\)

\(Z = 2.78\) has a p-value of 0.9973

1 - 0.9973 = 0.0027

0.0027 = 0.27% probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes

The probability for the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes in state university is 0.0027.

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

For the above data, the value of mean would be

\(m=70.3-74.3\\m=-4\)

The selected sample size are 10 interscholastic athletes and 12 non-interscholastics. The value of standard deviation is,

\(\sigma=\sqrt{(\dfrac{3.5}{\sqrt{10}})^2+(\dfrac{3.2}{\sqrt{10}})^2}\\\sigma=1.44\)

The Z score can be find out using the following formula.

\(Z=\dfrac{X-\mu}{\sigma}\\Z=\dfrac{0-(-4)}{1.44}\\Z=2.78\)

The z score of 2.78 has the p value equal to 0.9973. For sample mean of non-interscholastics to be greater, the probability,

\(P=1-0.9973\\P=0.0027\)

Thus, the probability for the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes in state university is 0.0027.



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The amount Anne has is $31.

The amount James has is $66.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

James amount = x

Anne amount = y

x + y = 97

x = y/2 - 2

Now,

y/2 - 2 + y = 97

y/2 + y = 97 + 2

y + 2y = 99 x 2

3y = 198

y = 66

Now,

x = y/2 - 2

x = 66/2 - 2

x = 33 - 2

x =31

Thus,

Anne has $31.

James has $66.

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The line which contains the points (4,0) and (0,-2), value of y when x =3 is,  -1/2

The equation of a straight line is a relationship between x and y coordinates, The two point form of a straight line is y-y₁ =  y₂-y₁/x₂-x₁(x-x₁).

Given that,

The points, (4,0) and (0,-2)

Equation of line for given two points,

y-y₁ =  y₂-y₁/x₂-x₁(x-x₁)

y-0 =  -2 - 0/0-4(x-4)

y = 1/2(x - 4)

2y = x - 4

when x = 3,

y =  1/2(3 - 4)

y = - 1/2

Hence, the value of y is -1/2

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