You are given information about the amount of each purchase at a department store. Find the mean, median, mode, range and standard


deviation when each purchase decreases by 15%.



Mean: $51. 72


Median: $37. 25


Mode: $21. 36


Range: $415. 85


Standard Deviation: $11. 91



When each purchase is


decreased by 15%, the mean is ____ the median is ______ the mode is______ the range is______and the standard


deviation is______

(a) The sampling distribution of x is approximately normal with mean 82 and standard deviation 3. (b) P(x > 87.4) = 0.0708. (c) P(x ≤ 75.1) = 0.0990. (d) P(79.3 < x < 84.7) = 0.1675.

(a) The sampling distribution of x is approximately normal due to the central limit theorem, with a mean of μ = 82 and a standard deviation of σ/sqrt(n) = 27/sqrt(81) = 3.
(b) To find P(x > 87.4), we first standardize the value using the formula z = (x - μ) / (σ / sqrt(n)) = (87.4 - 82) / (27 / sqrt(81)) = 1.48. We then find the probability using a standard normal distribution table or calculator, which is approximately 0.0708 or 7.08%.
(c) To find P(x ≤ 75.1), we again standardize the value using the formula z = (x - μ) / (σ / sqrt(n)) = (75.1 - 82) / (27 / sqrt(81)) = -1.29. We then find the probability using a standard normal distribution table or calculator, which is approximately 0.0990 or 9.90%.
(d) To find P(79.3), we first standardize the value using the formula z = (x - μ) / (σ / sqrt(n)) = (79.3 - 82) / (27 / sqrt(81)) = -0.96. We then find the probability using a standard normal distribution table or calculator, which is approximately 0.1675 or 16.75%.

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Answer:

3$

Step-by-step explanation:

Let x be t-shirts and y socks.

4x + 3y= $37

2y + 5x= $41

x= (37 - 3y) ÷ 4

2y + 5((37-3y)÷4)=41

y=3

First, we need to define rational numbers

Rational numbers are numbers that can be express as a quotient or fraction

From the question given, The square root of 16 is 4, this can be express as 4/1

Hence, it is a rational number

Therefore the correct option is A

Increasing government spending (G) will lead to the largest increase in equilibrium GDP in a simple fixed-price Keynesian model with an MPC of 0.8.

In the Keynesian model, an increase in government spending directly stimulates aggregate demand, leading to an increase in GDP. The magnitude of the increase in GDP depends on the marginal propensity to consume (MPC), which represents the fraction of additional income that households spend. In this case, with an MPC of 0.8, 80% of any increase in income will be spent.

When government spending increases, it injects additional income into the economy. Households, with a high MPC, will spend a significant portion of this additional income on consumption goods and services. This increased consumption will, in turn, stimulate further economic activity, leading to a multiplier effect and a larger increase in GDP.

Therefore, increasing government spending would have the greatest impact on increasing equilibrium GDP in this scenario.

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If we allow the number of edges between any two nodes to be more than two, we would need to use the adjacency matrix to accurately store that graph information.

The adjacency matrix is a matrix representation of a graph where the rows and columns represent the vertices and the values in the matrix represent the number of edges between two vertices.

In this case, we could have values greater than 1 in the matrix to represent multiple edges between two vertices.

On the other hand, the adjacency list data structure would not be able to accurately store this information, as it represents each vertex and its adjacent vertices in a linked list format.

It would be difficult to represent multiple edges between two vertices using this data structure.

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Answer:

In this case, the y-intercept is (0, 4)

Step-by-step explanation:

The y-intercept of the line is the point where the line intersects with the y-axis when x = 0. In this case, the y-intercept is (0, 4), which means that if you ordered a bowl of yogurt with no toppings, it would cost $4.00.

The slope of the line represents the rate of change of the cost of the yogurt with respect to the number of toppings. In this case, the slope is 0.25, which means that for each additional topping you add, the cost of the yogurt increases by $0.25.

So, the equation of the line that represents the scenario is y = 0.25x + 4. This means that the cost of the yogurt (y) is equal to 0.25 times the number of toppings (x) plus 4.

The measure of one interior angle of a regular 16-gon is 157.5 degrees. This is obtained by using the formula (n-2) * 180° / n, where "n" represents the number of sides of the polygon. In this case, (16-2) * 180° / 16 = 157.5°..

To find the measure of one interior angle of a regular 16-gon, we can use the formula for the measure of an interior angle of a regular polygon:

Interior Angle = (n-2) * 180° / n

where "n" is the polygon's number of sides.

For a regular 16-gon, substituting the value of "n" into the formula, we get:

Interior Angle = (16 - 2) * 180° / 16

= 14 * 180° / 16

= 2520° / 16

= 157.5°

Therefore, the measure of one interior angle of a regular 16-gon is 157.5 degrees.

To understand the calculation, let's break it down. Equal interior angles and sides define a regular polygon. The sum of the interior angles of any polygon is given by the formula (n-2) * 180°, where "n" is the number of sides. In a regular polygon, all the interior angles are congruent, so to find the measure of one angle, we divide the sum by the number of sides.

In the case of a regular 16-gon, we subtract 2 from 16 to get 14, multiply it by 180°, and then divide by 16 to find that each interior angle measures 157.5°.

Therefore, the measure of one interior angle of a regular 16-gon is 157.5 degrees.

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Answer:

The scale factor of a dilation is 3.

Step-by-step explanation:

Given the length ST of the rectangle RSTU

The length ST of the rectangle = 8 units

It is clear that the corresponding length S'T' = 23 is 3 times the length of the original length ST = 8

i.e.

S'T' = 3(ST)

S'T' = 3(8)      ∵ ST = 8

S'T' = 24

It indicates that the RSTU has been dilated by a scale factor of 3.

As the scale factor 3 > 1, it also indicates that the dilated rectangle R'S'T'U is enlarged.

Therefore, the scale factor of a dilation is 3.

To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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Answer: 11.4 cm

Step-by-step explanation:

190/25 = 7.6

7.6 x 1.5 = 11.4

Answer

the two cities are 11.4 cm apart on the map

Answer:

Length of AB is 4

because

AB = AC - BC

Answer:

388

Step-by-step explanation:

i looked it up

Answer:

45 bottles per minute

Step-by-step explanation:

the number of bottles per minute would equal the rate of change, or 'slope'

the slope formula is 'the difference of the two y-values / difference of the two x-values'

(270-135) / (6-3) = 135/3 or 45 bottles per minute

Answer:

\( \huge \boxed{ \boxed{ - \frac{1}{2} }}\)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question we have

\(m = \frac{6 - 8}{12 - 8} = - \frac{2}{4} = - \frac{1}{2} \\ \)

We have the final answer as

\( - \frac{1}{2} \\ \)

Hope this helps you

Answer:

10/12

Hope it helps.

Answer:

the third one

Step-by-step explanation:

y represents the number plus 5 and the x represents the other number

The numbers 3, 4, and 7 likely refer to specific shapes that are programmed into the toy's code and represented by specific patterns of 1s and 0s.

To understand how codecs work, it is helpful to think of them as translators. When digital information is transmitted, it is often compressed to reduce the amount of data that needs to be transmitted.

In the case of Tracy the turtle's shape toy, the codecs are responsible for encoding the shapes into digital information that can be transmitted to the toy's display. The toy's display then decodes this information to display the shapes. The numbers 3, 4, and 7 likely refer to specific patterns of 1s and 0s that represent the shapes programmed into the toy.

In mathematical terms, codecs use various algorithms to compress and decompress digital information. These algorithms often involve complex mathematical formulas that are used to analyze and reduce the amount of data that needs to be transmitted.

Codecs are an essential component of digital communication and are used in everything from video streaming to text messaging.

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Complete Question:

Does anyone know 3. 4. 7 Kid's Shapes Toy for Tracy the turtle in codecs?

Answer:

x=2

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable x.

The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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If the null hypothesis is true and there is no treatment effect, the expected value on average for the F-ratio would be 1.00. The correct answer is option (b) 1.00

In hypothesis testing using the F-test, the F-ratio is calculated by dividing the variance between groups (treatment effect) by the variance within groups (random variation). When the null hypothesis is true and there is no treatment effect, the numerator (variance between groups) and the denominator (variance within groups) would be similar, resulting in an F-ratio close to 1.

Therefore, the correct answer is b. 1.00, as the expected value for the F-ratio would be around 1 when the null hypothesis is true and there is no treatment effect.

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The forecast for week 6 if Y is forecast for demand of chips sale and X is the week 18. The correct answer is 1) 18 KD.

This forecast assumes a linear relationship between the demand for chips sale and time. To use the equation Y=2X+6 for forecasting the demand of chips sale, we need to plug in the value of X, which is the week for which we want to create the forecast. Here, we want to forecast for week 6, so X=6.

Substituting the value of X=6 in the equation, we get:

Y=2(6)+6

Y=12+6

Y=18

Therefore, the forecast for week 6 using the given equation is 18.

Hence, option 1) 18 KD is the correct answer.

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The number of cups of cat food the feeder can hold is 12 cups.

The total volume of the feeder is calculated as follows;

total volume = volume of cylinder + volume of cone

The volume of the cylindrical part of the feeder is calculated as;

V = πr²h

where;

V = π(2.5 in)²(7.5 in)

V = 147.3 in³

The  volume of the cone part of the feeder is calculated as;

V = ¹/₃ πr²h

V = ¹/₃ π(2.5 in)²( 4 in )

V = 26.2 in³

Total volume =  147.3 in³ + 26.2 in³

Total volume = 173.5 in³

The number of cups of cat food the feeder can hold is calculated as follows;

n =  (173.5 in³) / 14.4 in³

n = 12 cups

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Answer:

35.344

Step-by-step explanation:

Answer:

It takes 1 year.

Step-by-step explanation:

You have to apply simple interest formula, I = (P×R×T)/100 where I represent interest amount, P is principle, R is interest rate and T is number of years :

\(I = \frac{PRT}{100} \)

\(200 = \frac{4000 \times 5 \times T}{100} \)

\(20000 = 20000T\)

\(T = 1\)

We, know that :

\( \underline{\boxed{\sf Interest \: amount = \dfrac{Principal \times Rate \times Time}{100}}}\)

\( \underline{\boxed{\sf I = \dfrac{P \times R \times T}{100}}}\)

By putting values, we have

\( \sf : \implies 200 = \dfrac{4000 \times 5 \times T}{100}\)

\( \sf : \implies 200 \times 100 = 20000 \times T\)

\( \sf : \implies 20000 = 20000 \times T\)

\( \sf : \implies \cancel{\dfrac{20000}{20000}} = T\)

\( \sf : \implies 1 = T\)

\( \underline{\boxed{\sf T = 1 \: year}}\)

It takes 1 year for him to earn $ 200 in simple interest.

(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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Answer:

I believe the answer is function

Step-by-step explanation:

Answer:

C. 84

Step-by-step explanation:

12+15+11+20+5=63

12/63= 0.1904...

.1904 x 441= 83.96

Answer:

$54 × 30/100

=$16.20

$54-$16.20

=$37.80

Answer:

8 times due to 48 divided by 6 is 8

Step-by-step explanation: