Amanda buys 2 nachos and 3 drinks from the concession stand for $12.50. Julio purchases 2 candy bars and 1 drink for $5.50. Ben buys 1 nacho and 1 candy bar for $5.00. Write a system of equations and solve it to determine the cost of each item.

By using  1-PsiTarget(H15, 500) we compute the probability of cell H15's value exceeding 500 in a spreadsheet simulation.

PsiTarget is a function commonly used in spreadsheet simulation software to calculate probabilities.

The first argument (H15) specifies the cell you want to calculate the probability for.

The second argument (500) represents the target value you want to compare against.

The PsiTarget function returns the probability of the cell's value being less than or equal to the target value.

By subtracting this probability from 1, you get the probability of the cell's value exceeding the target value.

Therefore, the correct formula to compute the probability of cell H15's value exceeding 500 is 1-PsiTarget(H15, 500).

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Answer:

a) b = 8, c = 13

b) The equation of graph B is y = -x² + 3

Step-by-step explanation:

* Let us talk about the transformation

In the given question

∵ y = x² - 3

∵ The graph is translated 4 units to the left

→ That means substitute x by x + 4 as 4th rule above

∴ y = (x + 4)² - 3

→ Solve the bracket to put it in the form of y = ax² + bx + c

∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)

∴ (x + 4)² = x² + 4x + 4x + 16

→ Add the like terms

∴ (x + 4)² = x² + 8x + 16

→ Substitute it in the y above

∴ y = x² + 8x + 16 - 3

→ Add the like terms

∴ y = x² + 8x + 13

∴ b = 8 and c = 13

a) b = 8, c = 13

∵ The graph A is reflected in the x-axis

→ That means y will change to -y as 1st rule above

∴ -y = (x² - 3)

→ Multiply both sides by -1 to make y positive

∴ y = -(x² - 3)

→ Multiply the bracket by the negative sign

∴ y = -x² + 3

b) The equation of graph B is y = -x² + 3

Answer:

Confidence Interval - 2.290 < S < 2.965

Step-by-step explanation:

Complete question

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 50 cookies. The mean is 23.33 and the standard deviation is 2.6. Construct a 80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.

Solution

Given  

n=50

x=23.33

s=2.6

Alpha = 1-0.80 = 0.20  

X^2(a/2,n-1) = X^2(0.10, 49) = 63.17

sqrt(63.17) = 7.948

X^2(1 - a/2,n-1) = X^2(0.90, 49) = 37.69

sqrt(37.69) = 6.139

s*sqrt(n-1) = 18.2

\(s\sqrt{\frac{n-1}{X^2 _{(n-1), \frac{\alpha }{2} } }\) \(\leq \sigma \leq s\sqrt{\frac{n-1}{X^2 _{(n-1), 1-\frac{\alpha }{2} } }\)

confidence interval:

(18.2/7.948) < S < (18.2/6.139)

2.290 < S < 2.965

Based on the right triangle altitude theorem, the term that completes the equation is: a. YZ.

The right triangle altitude theorem state that when an altitude is drawn to from the vertex of a right triangle to intersect the opposite side perpendicularly, the length of the altitude would be equal to the geometric mean of the line segments that are formed by the altitude on the right triangle's hypotenuse.

In other words, the square of the length of the altitude equals the product of the line segments formed, according to the right triangle altitude theorem.

XZ = altitude

WY = hypotenuse

WZ and YZ are the line segments formed.

Therefore, the equation would be:

XZ² = (WZ)(YZ) [right triangle altitude theorem]

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The type of data for satisfaction ratings of customers classified as high, medium, or low is qualitative. The level of measurement for this data is ordinal.

Qualitative data refers to non-numerical information that describes qualities or attributes. In this case, the satisfaction ratings of customers are categorized as high, medium, or low, indicating different levels of satisfaction rather than numerical values.

The level of measurement for qualitative data can be nominal or ordinal. Nominal data categorizes items into distinct groups without any inherent order, while ordinal data maintains the distinct categories but also has an ordered relationship between them.

In the given scenario, the satisfaction ratings are classified as high, medium, or low, which demonstrates an ordered relationship. However, the numerical values or specific intervals between the categories are not defined. Therefore, the data is qualitative and the level of measurement is ordinal.

The satisfaction ratings of customers classified as high, medium, or low are qualitative data with an ordinal level of measurement, indicating an ordered relationship among the categories of satisfaction.

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The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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Answer: Mika can eat 21 hot dogs in 6 minutes. She wants to know how many minutes it would take her to eat

35 hot dogs if she can keep up the same pace.

Step-by-step explanation: Hope I am right.

Answer:

Domain: (1,∞), Range: (all real numbers)

Step-by-step explanation:

The correct answer is b) 1.397. The value of t, the critical value of the t distribution with 8 degrees of freedom, which satisfies the condition that the probability is 0.10 of being larger than t, can be found using a t-distribution table or statistical software.

By referring to a t-distribution table or using statistical software, we can determine that the critical value with 8 degrees of freedom and a probability of 0.10 of being larger than t is approximately 1.397.

Thus, the correct answer is b) 1.397. This value is important because it allows us to make inferences about the population based on sample data, particularly when the population's standard deviation is unknown. The t distribution becomes increasingly similar to the standard normal distribution as the degrees of freedom increase. In this specific case, the critical value of 1.397 can be used to conduct hypothesis tests or construct confidence intervals when working with a sample size of 9 (8 degrees of freedom = sample size - 1) and a significance level of 0.10.

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The correct answer is b) 1.397. The value of t, the critical value of the t distribution with 8 degrees of freedom, which satisfies the condition that the probability is 0.10 of being larger than t, can be found using a t-distribution table or statistical software.

By referring to a t-distribution table or using statistical software, we can determine that the critical value with 8 degrees of freedom and a probability of 0.10 of being larger than t is approximately 1.397.

Thus, the correct answer is b) 1.397. This value is important because it allows us to make inferences about the population based on sample data, particularly when the population's standard deviation is unknown. The t distribution becomes increasingly similar to the standard normal distribution as the degrees of freedom increase. In this specific case, the critical value of 1.397 can be used to conduct hypothesis tests or construct confidence intervals when working with a sample size of 9 (8 degrees of freedom = sample size - 1) and a significance level of 0.10.

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There are twο distinct x-intercepts and three zerοs (οr rοοts) fοr the functiοn f(x).

A functiοn is a mathematical cοncept that describes a relatiοnship between twο sets οf values, typically called the dοmain and the range. It is a set οf οrdered pairs (x, y) where each x-value is assοciated with a unique y-value.

Tο find the x-intercepts οf the graph οf f(x), we set f(x) equal tο zerο:

f(x) =\(x^{2}\)(x+2)(x-7) = 0

This equatiοn has three factοrs, sο there are three values οf x that make f(x) equal tο zerο. We can find these values by setting each factοr equal tο zerο:

x² = 0 => x = 0 (multiplicity 2)

x+2 = 0 => x = -2

x-7 = 0 => x = 7

Therefοre, the graph οf f(x) has x-intercepts at x = 0 (with multiplicity 2),

x = -2, and x = 7.

There are three x-intercepts, but οnly twο οf them are distinct (since x = 0 is a dοuble rοοt).

Therefοre, there are twο distinct x-intercepts and three zerοs (οr rοοts) fοr the functiοn f(x).

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(a) The image of v is (-14, -7).

(b) The preimage of w = (6, 18) is v = (2, 2).

(a) To find the image of vector v, we substitute the coordinates of v into the transformation T(v):

T(v) = (4v2 - v1, 4v1 + 5v2)

Substituting v = (2, -3, -4):

T(v) = (4(-3) - 2, 4(2) + 5(-3))

= (-14, -7)

The image of v is (-14, -7).

(b) To find the preimage of vector w, we need to solve the equation T(v) = w, where T(v) is the transformation and w is the given vector.

Substituting w = (6, 18):

(4v2 - v1, 4v1 + 5v2) = (6, 18)

From the first component equation:

4v2 - v1 = 6

From the second component equation:

4v1 + 5v2 = 18

Solving these two equations simultaneously:

4v2 - v1 = 6

4v1 + 5v2 = 18

Rearranging the first equation to solve for v2:

v2 = (6 + v1) / 4

Substituting this value of v2 into the second equation:

4v1 + 5((6 + v1) / 4) = 18

Multiplying through by 4 to eliminate the fraction:

16v1 + 5(6 + v1) = 72

16v1 + 30 + 5v1 = 72

21v1 = 42

v1 = 2

Substituting this value of v1 into the equation for v2:

v2 = (6 + 2) / 4

v2 = 2

Therefore, the preimage of w = (6, 18) is v = (2, 2).

(a) The image of v is (-14, -7).

(b) The preimage of w = (6, 18) is v = (2, 2).

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Answer:

45.56

Step-by-step explanation:

need to find the base

86^2 = 3600+b^2

b=61.62

tanx = 61.61/60 = 1.02

x = 45.56

The angle between the guy wire and the pole is 46° (rounded to the nearest degree). Solved, using the heights and distances concept of trigonometric ratios.

The concept of heights and distances is the use of right triangles in real-world examples and solving for missing components using trigonometric ratios in a right triangle.

In the question, we are informed that a telephone pole, shown at the top of the next column, is 60 feet tall. A guy wire 86 feet long is attached from the ground to the top of the pole.

We are asked to find the angle between the wire and the pole.

We will use the concept of heights and distances to solve the problem.

We let the pole be AB, of height 60 ft. It is perpendicular to the ground.

We let the guy wire be AC, where C is the point from where the wire is connected on the ground, from a distance from the base of pole B.

The length of the guy wire AC is 86 ft.

We let the angle between the guy wire and the pole, that is, angle BAC be θ.

In the right triangle ABC, we can say that the trigonometric ratio:

cos θ = AB/AC {cos θ = base/hypotenuse}

or, cos θ = 60/86,

or, θ = cos⁻¹(60/86) = 45.8° ≈ 46°.

Therefore, the angle between the guy wire and the pole is 46° (rounded to the nearest degree). Solved, using the heights and distances concept of trigonometric ratios.

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Answer:

Z - score = 2.83

Step-by-step explanation:

Given the following :

Number of samples (N) = 60

Sample mean (x) = 41.9mg

Population mean (μ) = 40mg

Population standard deviation (sd) = 5.2

Using the relation :

Z = (x - μ) / (sd / √N)

Z = (41.9 - 40) / (5.2 / √60)

Z = 1.9 / (5.2 / 7.7459666)

Z = 1.9 / 0.6713171

Z = 2.8302570

Therefore, the z-score = 2.83

the correct way to report the results of a hypothesis test and a measure of effect size using a t-statistic is option A: t(19)=2.30, r2=0.42, p<0.05.

The correct way to report the results of a hypothesis test and a measure of effect size using a t-statistic depends on the specific journal or style guide you are using. However, in general, the most common format is to report the t-value, degrees of freedom, and p-value first, followed by the measure of effect size.

So, looking at the options provided, we can eliminate option D because it only reports the t-value, degrees of freedom, p-value, and effect size all at once without separating them. Now, we are left with options A and B. Both options report the t-value, degrees of freedom, and p-value first, followed by the effect size. However, there is a difference in the order of the p-value and effect size. Option A reports the effect size as r2=0.42 after the p-value, while option B reports the effect size as r2=0.42 before the p-value.

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Answer:

-15/56

Step-by-step explanation:

Any expression divided by 1 remains the same

Answer: negative fifteen over fifty-six

The slope of a line perpendicular to the given line is -2.

The slope of a line parallel to the given line is 1/2.

To find the slopes of lines perpendicular and parallel to the given line, we first need to rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Given equation: 4x - 8y = 5

Rearrange the equation to solve for y:

-8y = -4x + 5

y = (1/2)x - (5/8)

Now that the equation is in slope-intercept form, we can identify the slope of the given line:

m1 = 1/2

For a line to be parallel to the given line, it must have the same slope. So, the slope of a line parallel to this line is:

m_parallel = 1/2

For a line to be perpendicular to the given line, its slope must be the negative reciprocal of the slope of the given line. So, the slope of a line perpendicular to this line is:

m_perpendicular = -1/m1 = -1/(1/2) = -2

Answer:

30.

Step-by-step explanation:

Apologies if I am late, but I believe this is the answer!

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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The average weight of the 60 riders on the rollercoaster is 180 pounds.

To find the average weight of the 60 riders on the rollercoaster, we can divide the total weight by the number of riders.

Given:

Total weight of the riders = 12,000 pounds

Now, let's determine the average weight.

To calculate the average weight, we need to know the distribution of men and women among the riders. Let's assume that the ratio of men to women is equal.

The average weight of adult U.S men is 192 pounds, and the average weight of adult U.S women is 168 pounds. Since the ratio is equal, we can take the average of these two values:

Average weight = (192 + 168) / 2

= 360 / 2

= 180 pounds

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Complete question is:

A rollercoaster is being designed that will accommodate 60 riders. the maximum weight the coaster can hold safely is 12,000 pounds. according to the national health statistics reports, the weight of adult U.S men have mean 192 pounds and standard deviation 66 pounds, and the weights of adult U.S women have mean 168 pounds and standard deviation 75 pounds. if 60 people are riding the coaster, and their total weight is 12,000 pounds, what is their average weight?

Answer:

  9

Step-by-step explanation:

72 flowers in 8 equal rows will have 9 flowers in each row.

__

72 = 8 × 9

Answer:

There are 9 flowers in each of the 8 rows

Step-by-step explanation:

Kevin plants a total of 72 flowers in equal rows he plants 6 rows of yellow flowers and 2 rows of red flowers how many flowers are in each row

Solution

Total flowers = 72 in Equal rows

Yellow flowers = 6 rows

Red flowers = 2 rows

Rows of yellow flowers + Rows of rec flowers = 6 + 2

= 8 rows

Flowers in each row = Total flowers / total rows

= 72 flowers / 8 rows

= 9 flowers

Flowers in each row = 9 flowers

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

Answer:

6

Step-by-step explanation:To find the median, first order your data. Then calculate the middle position based on n, the number of values in your data set. If n is an odd number, the median lies at the position (n + 1) / 2. If n is an even number, the median is the mean of the values at positions n / 2 and (n / 2) + 1.

Answer:

6

Step-by-step explanation:

Step-by-step explanation:

To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.

In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.

The given table represents the counts from three independent random samples taken from three major cities regarding whether teenagers consumed a soft drink in the past week.

By summing up the counts of teenagers who consumed a soft drink from all three cities and dividing it by the total number of teenagers surveyed, we can calculate the overall proportion. Dividing this proportion by the total number of teenagers and multiplying by 100 will give us the percentage of teenagers who consumed a soft drink.

For example, if the first city had a count of 150 teenagers who consumed a soft drink out of a total of 300 surveyed, the second city had 200 out of 400, and the third city had 180 out of 350, the overall proportion would be (150 + 200 + 180) / (300 + 400 + 350) = 530 / 1050. Multiplying this by 100, we find that approximately 50.48% of teenagers consumed a soft drink in the past week based on the combined sample.

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A research center conducted a national survey about teenage behavior. Teens were asked whether they had consumed a soft drink in the past week. The following table shows the counts for three independent random samples from major cities. Baltimore Yes 727 Detroit 1,232 431 1,663 San Diego 1,482 798 2,280 Total 3,441 1,406 4,847 No 177 904 Total (a) Suppose one teen is randomly selected from each city's sample. A researcher claims that the likelihood of selecting a teen from Baltimore who consumed a soft drink in the past week is less than the likelihood of selecting a teen from either one of the other cities who consumed a soft drink in the past week because Baltimore has the least number of teens who consumed a soft drink. Is the researcher's claim correct? Explain your answer. (b) Consider the values in the table. (i) Baltimore Detroit San Diego 0 0.1 0.9 1.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Relative Frequency of Response (ii) Which city had the smallest proportion of teens who consumed a soft drink in the previous week? Determine the value of the proportion. (c) Consider the inference procedure that is appropriate for investigating whether there is a difference among the three cities in the proportion of all teens who consumed a soft drink in the past week. (i) Identify the appropriate inference procedure. (ii) Identify the hypotheses of the test.

Answer:I think the answer is B

Step-by-step explanation:

Answer:

This is actually really confusing cause there is to options its either B or C

Step-by-step explanation:

Answer:

The answer is 2.

Step-by-step explanation:

3 - 2 = 1

7 - 5 = 2

2 x 1 = 2

Answer:

130

Step-by-step explanation:

Hello There!

An included angle is equal to half the measure of its included arc

So more specifically for this circle

∠mABC = \(\frac{1}{2}\) arc(mAB)

So in order to find the value of x we are going to want an equation

Because angle ABC is equal to 1/2 of arc AB we are going to want to multiply angle ABC's expression by two

So 2(3x+32) = 10x+20

now we solve for x

step 1 distribute the 2

2 * 3x = 6x

2 * 32 = 64

now we have

6x + 64 = 10x + 20

step 2 subtract 20 from each side

64 - 20 = 44

20 - 20 cancels out

now we have 6x + 44 = 10x

step 3 subtract 6 x from each side

10x - 6x = 4x

6x - 6x cancels out

now we have 44 = 4x

step 4 divide each side by 4x

44/4=11

4x/4=x

we're left with x = 11

finally we want to plug in 11 to x for (10x+20)

10(11)+20

10*11=110

110+20=130

so arc ab = 130

Answer:

AB = 130

Step-by-step explanation:

So, according to a certain theorem to do with arcs and their angles, If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

In this case, the ARC is AB, and the angle is CBA.

CBA = 3x+32

AB = 10x+20

And,

\(CBA = \frac{1}{2} AB\)

Now,

\(3x+32=\frac{1}{2} (10x+20)\)

\(3x+32=5x+10\\32=2x+10\\22=2x\\11=x\)

Now we can substitute x into the equation that equals AB

\(10(11)+20 \\=110+20\\=130\)

So, the answer is 130, sorry I took a while, the explanation takes a long time to do lol.

Have a nice day fam. Spread The Love.

Answer: 25 hours

Step-by-step explanation:

I had it on a test and it said correct‍♀️