Question 1(Multiple Choice Worth 2 points)
(Comparing Data MC)

The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.

Which drive-thru typically has more wait time, and why?

Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean

With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.

With a simple random sample, each participant is selected at random from the population, ensuring that everyone has an equal chance of being selected.

This eliminates any potential bias or manipulation, as no one can control or influence the selection process. Additionally, the sample size can be increased to amplify the accuracy and representativeness of the data collected. Therefore, a simple random sample is a reliable method for gathering unbiased data.

With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.

This means that each individual or element in the population has an equal chance of being chosen, ensuring unbiased and representative sample results.

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With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.

With a simple random sample, each participant is selected at random from the population, ensuring that everyone has an equal chance of being selected.

This eliminates any potential bias or manipulation, as no one can control or influence the selection process. Additionally, the sample size can be increased to amplify the accuracy and representativeness of the data collected. Therefore, a simple random sample is a reliable method for gathering unbiased data.

With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.

This means that each individual or element in the population has an equal chance of being chosen, ensuring unbiased and representative sample results.

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Answer: b

Step-by-step explanation:

I didnt get it  but thats the correct answer when i guessed on it

Answer:

The answer is the skin est one there

Step-by-step explanation:

I got the question wrong so I don't know how but this is the correct one

Answer:

9.3 ft

Step-by-step explanation:

The graph of the exponential function across the interval is attached below

To graph the function y = 3ˣ over the interval 1 ≤ x ≤ 2, you can follow these steps:

Choose a suitable scale for the x-axis and y-axis. Since the function grows rapidly, you may need to use a logarithmic scale on the y-axis to show the entire graph.

Plot some key points of the function. To do this, you can choose some values of x within the given interval and calculate the corresponding values of y. For example:

When x = 1, y = 3^1 = 3

When x = 1.5, y = 3^1.5 = 5.2

When x = 2, y = 3^2 = 9

Connect the plotted points with a smooth curve. Since the function is exponential, the curve will be a smooth upward curve that gets steeper and steeper as x increases.

Label the axes and add any necessary annotations or markings. For example, you may want to label the plotted points with their coordinates or add gridlines to help read off values from the graph.

Kindly find the attached graph below

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The equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞ is y = √(x - 3) - 2.

An equation is a mathematical statement that indicates the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields of mathematics, science, engineering, and economics. They can be written in various forms, such as standard form, slope-intercept form, point-slope form, and more.

Here,

To shift the parent function y = √x to the right by 3 units and down by 2 units, we use the transformation:

y = √(x - 3) - 2

This equation has a domain of 3 ≤ x < ∞, since we subtract 3 from x inside the square root function. The range is -2 ≤ y < ∞, since we subtract 2 from the square root function.

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Answer: Profit = .95 or 95 cents

Step-by-step explanation:

What is the question here?

If it is profit then the answer is 3.79-2.84

The likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4%

To illuminate this issue, we will utilize Bayes' hypothesis. Let's characterize the taking after occasions:

A: the persistent is contaminated with HIV

B: the persistent tests positive for HIV

We need to calculate P(A|B), the likelihood that an understanding is contaminated with HIV given that they tried positive for HIV.

By Bayes' hypothesis:

P(A|B) = P(B|A) * P(A) / P(B)

where

1. P(B|A) is the likelihood of testing positive for HIV given that the persistent is tainted with HIV (97%)

2. P(A) is the predominance of HIV within the clinic (8%)

3. P(B) is the likelihood of testing positive for HIV, which can be calculated utilizing the law of adding up to likelihood:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

where

1. P(B|A') is the likelihood of testing positive for HIV given that the persistent isn't tainted with HIV (4%)

2. P(A') is the complement of A, i.e., the likelihood of a quiet not being tainted with HIV (1 - 8% = 92%)

Substituting the values we have:

P(B) = 0.97 * 0.08 + 0.04 * 0.92 = 0.0736

P(B) =  0.0736

Hence,

P(A|B) = 0.97 * 0.08 / 0.0736 ≈ 0.104

P(A|B) = 0.104

So the likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4% (adjusted to three decimal places). 

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The given system of equations can be represented in matrix form as:

| 10 13 15 | | x | | 4 |

| 12 -2 5 | x | y | = |-8 |

| 2 2 -6 | | z | | 4 |

Therefore, the matrix A is:

| 10 13 15 |

| 12 -2 5 |

| 2 2 -6 |

And the vector ⇾b is:

| 4 |

|-8 |

| 4 |

Answer:

7/4

Step-by-step explanation:

i am sooo sure that  the answer is 1.75

Yes, the sample size of 4,706 is large enough to justify the use of the z formula.

To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.

One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.

In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.

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By calculating the CDF of normal distribution, the percentage of scores that are greater than 90 are 14.6%.

The CDF function of a Normal distribution is calculated by translating the random variable to the Normal Standard, and then looking up a value from the precalculated "Phi" function (Φ), which is the cumulative density function of the normal standard. The Normal Standard, often written Z, is a Normal with mean 0 and variance 1. Thus, Z∼N(μ=0,σ²=1).

Let x1, x2, .... be the scores on the test.

X ~ N (82, 64)

P(90 < X < 100) = Φ(18/8) - Φ(1) = 0.146 (using norm.s.dist function in excel)

Step-by-step explanation:

cores Distribution and Percentile

The scores on a test are normally distributed, with a mean of 82 and a standard deviation of 8. What percent of scores are less than 90? Explain

To find the percentage of scores that are less than 90 in a normally distributed test with a mean of 82 and a standard deviation of 8, we can use the cumulative distribution function (CDF) of the normal distribution.

The CDF of a normal distribution gives the probability that a random variable falls below a particular value. In this case, we want to find the probability that a score is less than 90.

The formula for the CDF of a normal distribution is:

CDF(x) = (1/2) * (1 + erf((x - μ) / (σ * sqrt(2))))

where erf is the error function, μ is the mean, σ is the standard deviation, and x is the value we want to find the cumulative probability for.

Plugging in the given values:

μ = 82

σ = 8

x = 90

We can calculate the cumulative probability using the formula:

CDF(90) = (1/2) * (1 + erf((90 - 82) / (8 * sqrt(2))))

Using a calculator or statistical software that provides the error function, we can find that erf(1.0) is approximately 0.6827.

Plugging this value back into the formula, we get:

CDF(90) = (1/2) * (1 + 0.6827) = 0.8414

So, the cumulative probability that a score is less than 90 is approximately 0.8414, or 84.14%.

Therefore, about 84.14% of the scores are less than 90 in this normally distributed test.

The domain is all real numbers, and the range is all real numbers greater than or equal to -4. So, correct option is A.

The given function f(x) = (x + 2)(x + 6) is a quadratic function, and its graph is a parabola that opens upwards. We are given that the vertex of the parabola is at (-4, -4), and it passes through the points (-6, 0) and (-2, 0).

The domain of a function is the set of all possible input values for which the function is defined. Since this is a polynomial function, it is defined for all real numbers. Therefore, the domain of the function f(x) is all real numbers.

The range of a function is the set of all possible output values that the function can take. Since the parabola opens upwards and its vertex is at (-4, -4), the lowest point on the graph is at (-4, -4), and it extends infinitely upwards. Therefore, the range of the function f(x) is all real numbers greater than or equal to -4.

Hence, the correct option is A).

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Complete question is:

The graph of the function f(x) = (x +2)(x + 6) is shown below.

On a coordinate plane, a parabola opens up. It goes through (- 6, 0), has a vertex at (- 4, - 4), and goes through (- 2, 0).

What is true about the domain and range of the function?

A) The domain is all real numbers, and the range is all real numbers greater than or equal to –4.

B) The domain is all real numbers greater than or equal to

–4, and the range is all real numbers.

C) The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.

D) The domain is all real numbers greater than or equal to

–4, and the range is all real numbers such that –6 ≤ x ≤ –2.

Answer: 13%

Step-by-step explanation:

10/74 = 0.13513513513

The approximate volume of the solid is 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is 8.17 × 10^20 π cubic inches.

We have,

1.

The volume V of a cylinder is given by V = πr²h,

where r is the radius and h is the height.

Substituting r = 2.0 × 10^7 feet and h = 4.0 × 10^5 feet.

V = π (2.0 × 10^7)² (4.0 × 10^5)

Simplifying,

V = 1.6 × 10^23 π cubic feet (using scientific notation and leaving the answer in terms of π)

2.

The volume of a cone is given by V = 1/3πr²h,

where r is the radius, h is the height, and we are given the diameter (d = 2r).

Substituting,

d = 1.0 × 10^7 inches, r = d/2 = 5.0 × 10^6 inches, and

h = 5.0 × 10^5 inches, we get:

V = 1/3 π (5.0 × 10^6)² (5.0 × 10^5)

Simplifying,

V = 2.6 × 10^20 π cubic inches

(using scientific notation and leaving the answer in terms of π)

Rounding to the nearest hundredth,  

V = 8.17 × 10^20 π cubic inches.

Thus,

The approximate volume of the solid is V = 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is V = 8.17 × 10^20 π cubic inches.

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The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

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Based on the information, the y-intercept is (0, 6.5).

The function is increasing.

Based on the information, we can use the variable x. This will be:

0 = 6.5 + 5.25%x

-6.5 = 5.25%x

x = -6.5 / 5.25% ≈ -123.81

There's no x intercept due to the negative value which doesn't make sense in this scenario.

In order to find the y-intercept, we set x = 0 and evaluate b(x):

b(0) = 6.5 + 5.25% × 0 = 6.5

Therefore, the y-intercept is (0, 6.5).

The function b(x) is increasing since the coefficient of x is positive (5.25%). This means that as the number of engines produced (x) increases, the time it takes to manufacture the engines also increases.

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Answer:

The answer for speed is 8 miles/hr

Step-by-step explanation:

speed =distance/time

s=20/2.6

s=8miles/hr

Answer:

4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles

Step-by-step explanation:

Pattern blocks are a set of geometric shapes commonly used in math education. The set typically includes six different shapes: triangle, rhombus, trapezoid, hexagon, square, and equilateral triangle. Each hexagon in a pattern block set is made up of six equilateral triangles.

To make 4 hexagons using pattern blocks, we would need to calculate the total number of equilateral triangles required. Since each hexagon is made up of 6 equilateral triangles, we can multiply the number of hexagons by 6 to get the total number of equilateral triangles needed.

4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles

So, you would need 24 pattern block triangles to make 4 hexagons using pattern blocks.

Answer:

Let's use pattern blocks to visualize the situation and say that a hexagon is 1 whole. Since 3 rhombuses make a hexagon, 1 rhombus represents and 2 rhombuses represent . We can see that 6 pairs of rhombuses make 4 hexagons, so there are 6 groups of in 4.

5/3 is greater than 1 (it's 1.67), and the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.

The area model, linear model, and set model are the three major types of fraction models. Evidence demonstrates that allowing pupils to deal with all three models is critical for establishing a conceptual knowledge of fractions.

The student is utilizing the model to calculate the product of 5/2 and 2/3, or (5/2) x (2/3).

To multiply fractions, simply multiply their numerators and then their denominators. So:

(5/2) x (2/3) = (5 x 2) / (2 x 3) = 10/6 = 5/3

Because 5/3 is greater than 1 (it's 1.67), the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.

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Complete question:

The equation that will be  used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ

What is equation?

An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

The population of Log Village is 1800 in 2010, and the population increases each year by 9%.

Initial population(p)= 1800

rate of increase(r)= 9%

Time(t)= x years.

The formula for the population after n years is p(1+r/100)ⁿ.

To determine the equation for the population after x years we have to put the values in the above expression.

So putting all the values we get,

The population, y, of Log Village x years after 2010 is

          y= 1800( 1+9/100)ˣ

          y= 1800(1.09)ˣ

Hence, The equation that will be  used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ

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Answer:

367.2

Step-by-step explanation:

Basically 270% is 2.7 so if you multiply 2.7 by 136 you will get 367.2

Answer: The amount of planes of symmetry a right pyramid with an isosceles triangle base has four.

Hope this helps!

Eliminate x by adding the two equations, yielding [tex]y = 6[/tex]. Then, substitute y into either equation to solve for x, obtaining [tex]x = -3[/tex]. The solution is [tex](-3,6)[/tex].

An equation is a mathematical statement that uses symbols, numbers, and variables to show that two expressions are equal, typically with an equal sign between them.

A variable is a quantity or symbol that can take on different values in a mathematical expression, equation, or formula, typically represented by a letter.

To eliminate a variable in a system of equations, we want to find a way to add or subtract the two equations so that one of the variables is eliminated.

In this case, we can eliminate the variable x by adding the two equations

[tex]x- 7y = -45[/tex]

[tex](-x +8y = 51)[/tex]

[tex]y = 6[/tex]

Now that we have found the value of y, we can substitute it into either of the original equations to solve for x. Let's use the first equation

[tex]x-7y = -45\\x- 7(6) = -45\\x = -45+42\\x = -3[/tex]

Therefore the solution to the system of equations is [tex]x= -3[/tex] and[tex]y= 6[/tex]

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the solution to the system of equations is (x, y) = (-3, 6).

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

To eliminate the variable x, we can add the two equations together. This will result in the x variable being eliminated, leaving us with an equation in terms of y:

(x - 7y) + (-x + 8y) = -45 + 51

Simplifying and solving for y, we get:

y = 6

Now that we know the value of y, we can substitute it into one of the original equations to solve for x. Using the first equation:

x - 7(6) = -45

Simplifying and solving for x, we get:

x = -3

Therefore, the solution to the system of equations is (x, y) = (-3, 6).

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Answer: Year 6

Step-by-step explanation: The year my money would be at least $1300 is year 6.

In what year would the money be at least $1300?

The formula that can be used to determine the number of years that $100 would have a value of $1300 is:

Number of years =  In(FV / PV) / r

Where:

FV = future value

PV = present value

r = interest rate

In(1300 / 1000) / 0.05

0.2623642645 / 0.05

= 5.2 years

Future value in 5 years = $1000(1.05^5) = $1276.28

Future value in 6 years = $1000(1.05^6) = $1340.10

By division rule of fraction, dividing 44.4 by 100 results to 0.444, that is shifts three decimal places (to right).

We can divide 44.4 by 100 using simple rule of division.

Rewriting 44.4 in fractional form we get,

44.4 = 444/10

Dividing 444/10 by 100 we can write it in fractional form as 444/10*100.

Therefore, 44.4 divided by 100 in fractional form can be written as 444/1000.

Applying division rule of fractions,

Dividend is 444 and divisor is 1000.

Since the denominator of the fraction has three zeros (in divisor 1000) by properties of fraction the decimal place of the numerator shifts three places to its right.

Also something divided by one is the same value as its initial value.

Thus as 444 shifts to three decimal places (on its right) it becomes 0.444 as the denominator is 1*1000.

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Answer:

(3,0)

Step-by-step explanation:

the point (5,-5) a translation of 2 units left would be equivalent to x-2.

(5-2,-5)

5 units up is equivalent to y+5

therefore

(5-2,-5+5)

yields

(3,0)

The total number of cards drawn is 16 and As a result, we have the following:

6 face cards, Aces 1, 9 numbered cards

Because there are 12 face cards, half of them are 6 face cards.

There are 4 aces, so we draw 1.

There are 36 numbered cards in total, therefore one-fourth of them are 9 numbered cards.

We draw a total of 6 + 1 + 9 = 16 cards.

We may use the information provided in the problem to determine how many of each card type we have. We chose:

6 face cards make up half of the deck.

1 ace: 1 ace

9 numbered cards are one-fourth of the numbered cards.

As a result, we have:

6 face cards

Aces: 1

9 numbered cards

We can also ensure that the total number of cards drawn (16) corresponds to the number of cards in a regular deck by subtracting the cards we drew from the total number of cards: a deck of playing cards (52)

There are 52 - 16 = 36 cards left.

This means that there are 36 - 6 - 1 - 9 = 20 undrawn cards in the deck.

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The area of the regular pentagon is  490 square units

The formula used for calculating the area of a regular pentagon is expressed with the equation

A = 1/2 pa

Such that the parameters are;

From the information given, we have that;

Perimeter = 5s

Substitute the values,

Perimeter = 5(14)

multiply the values

Perimeter = 70 units

Now, substitute the value into the formula

Area = 1/2 × 70(14)

Area = 980/2

Divide the values

Area = 490 square units

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Vic would think that the amount of butter in Imani's cookies is appropriate since the ratio of flour to butter used in Imani's recipe is the same as the ratio used in Vic's favorite cookie recipe, which is 250:170 grams of flour to butter.

Specifically, in Vic's recipe, there are approximately 1.47 grams of flour for every gram of butter (250/170), while in Imani's cookies, there are approximately ratio 1.19 grams of flour for every gram of butter (750/630). This means that there is relatively more butter in Imani's cookies compared to Vic's recipe. Based on this difference, Vic might expect Imani's cookies to have a richer, denser texture and a stronger buttery flavor than his favorite recipe.

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Yes, the transformation is a rigid motion because the angle measures and the distances between the vertices of the image are the same as the corresponding angle measures and distances in the preimage.

Since the shape and size are the same in both the preimage and the image, and only the position has changed, this transformation is considered a rigid motion. Rigid motions, such as translations, rotations, and reflections, preserve the shape and size of the original figure.

Assuming the shape has been bent, it means that the angle measures and distances between the vertices have been altered. But this is not the case.

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