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24
Find the median of the given data.
3 5 78 81 90
Median =
=

Answer:

a. factors of 3x²-7x-6 =(x-3) and (3x+2)

b factors of 4x²-49=(2x-7) and (2x+7)

Answer: The solution to the system of equations by substitution is (x, y) = (-1, 1).

Step-by-step explanation:

The smaller amount of total calories consumed is 359 calories.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.

Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".

Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.

Jane consumes:

Half a blueberry muffin: 0.5 * 270 = 135 calories

Whole fruit platter: 190 calories

A third of a glass of milk: (1/3) * 102 = 34 calories

So her total calorie intake is: 135 + 190 + 34 = 359 calories (rounded to the nearest whole calorie).

Rob consumes:

Hashbrowns and eggs: 2 * 190 = 380 calories

Half a glass of orange juice: 0.5 * 40 = 20 calories

So his total calorie intake is: 380 + 20 = 400 calories.

Therefore, the smaller amount of total calories consumed is 359 calories.

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Answer:

Step-by-step explanation:

just guess if not use the internet

Answer:

Step-by-step explanation:

She chose a line plot because it is an easier way to display the amount of students and how many lines of code they each wrote. That way on a line plot, it displays the number of students, and the frequency amount of times the same number of lines of code were written.

Answer:

a. A linear equation would best represent the total cost a shopper will pay for an order.

b. y = .7x + 5 would model this situation.

A graph of the image of ABC under a dilation whose center is P and scale factor is 2 is shown in the image below.

In Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape.

In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 2 centered at P.

Based on the image (see attachment), we can logically deduce that each vertex is 2 times as far from center P as the original vertex and each segment is 2 times as long as the original:

Side length A'C' = 8.2 × 2 = 16.4

Side length A'B' = 5.0 × 2 = 10.0

Side length B'C' = 5.8 × 2 = 11.6

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Answer:

x = 6;

y = 3√3

Step-by-step explanation:

Use trigonometry:

[tex] \ \cos(60°) = \frac{3}{x} [/tex]

Use the property of proportion to find x:

[tex]x = \frac{3}{ \cos(60°) } = \frac{3}{0.5} = 6[/tex]

Use the Pythagorean theorem to find y:

[tex] {y}^{2} = {x}^{2} - {3}^{2} [/tex]

[tex] {y}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27[/tex]

[tex]y > 0[/tex]

[tex]y = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} [/tex]

The number of bald eagles in the state during the winter of 1999 would be 34.

The machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

The cost of a tangible asset is spread out throughout the course of depreciation. It symbolises the asset's value dropping over time as a result of damage, obsolescence, or other circumstances. Depreciation is crucial because it enables firms to account for an asset's cost over the course of its useful life rather than just in the year it was purchased.

Depreciation can be calculated using a number of different approaches, such as the straight-line method, the decreasing balance method, and the sum-of-years' digits method.

The annual depreciation expense is:

Annual Depreciation Expense = (Cost of Asset - Salvage Value) / Useful Life in Units

Annual Depreciation Expense = ($84,600 - $6,000) / 393,000

Annual Depreciation Expense = $0.20 per unit

For second year we have:

Second-Year Depreciation = Annual Depreciation Expense x Units Produced in Second Year

Second-Year Depreciation = $0.20 x 33,300

Second-Year Depreciation = $6,660

Now, the year-end book value is:

Accumulated Depreciation = Annual Depreciation Expense x Number of Years

Accumulated Depreciation = $0.20 x 2

Accumulated Depreciation = $0.40 per unit

For:

Accumulated Depreciation = $0.40 x 33,300

Accumulated Depreciation = $13,320

Also,

Book Value = Cost of Asset - Accumulated Depreciation - Salvage Value

Book Value = $84,600 - $13,320 - $6,000

Book Value = $65,280

Hence, the machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

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The solution is : (-2,7) is the point of intersection.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

To solve the equations by graphing, use the form y=mx + b to find the slope and y-intercept of each equation. Graph the line and find their intersection point.

y = −2x + 3                                     y = −4x − 1

Slope: -2                                        Slope: -4

Y-int: (0,3)                                      Y-int: (0,-1)

Start at (0,3) and go down            Start at (0,-1) and go down 4 units

2 units and 1 to the right.               and 1 to the right. Connect the points.

Connect the points.

Continue this pattern in either direction for both lines until they intersect each point. The point of intersection (x,y) is the solution to the system of equations.

See attached graph.

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Complete question:

A pair of linear equations is shown below: y = −2x + 3 y = −4x − 1 Which of the following statements best explains the steps to solve the pair of equations graphically?

The coordinates of the matrix A with the given base S are:

<1, 2, 0, 2>

The coordinates will be a vector of the form:

<x, y, z, k>

Such that these four values are each of the coefficients that affect each one of the matrices in the base respectively.

Then we can write a system of equations like:

x + y + z + k = 5

x - y - z  = 3

x + y = 3

x = 1

We can replace the last equation in the third one to get:

1 + y = 3

y = 3 - 1

y = 2

Now we can replace x and y in the second equation:

1 + 2 - z = 3

z = 1 + 2 - 3

z = 0

And the with the first equation:

1 + 2 + 0 + k = 5

3 + k = 5

k = 5 - 3 = 2

Then the coordinates of the matrix A are:

<1, 2, 0, 2>

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Answer:

use what u learn from the teacher

Total earnings < Ticket cost,  this inequality represents this situation.

The inequality, A declaration of relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Equations and questions can both be used to formulate and answer inequality problems.

Write two values   being compared in the problem in step one. Decide the first value is greater or less than the second value in step two.In step third Insert  inequalities symbol between the first and second values if the first value is greater than the second.

We calculate who earned enough money to buy a ticket,than need to calculate the total amount earned by each friend.

For  the total amount earned by each friend by multiplying the number of hours worked by hourly rate,

In Friend 1; 5 hours x $9.10 per hour = $45.50

In  Friend 2; 4 hours x $9.10 per hour = $36.40

In Friend 3; 7 hours x $9.10 per hour = $63.70

In Friend 4; 3 hours x $9.10 per hour = $27.30

In Friend 5; 6 hours x $9.10 per hour = $54.60

If each friend earned enough money to buy a ticket, than need to compare their total earnings to the cost of a ticket =$75.99. That is, Total earnings ≥ Ticket cost

Now ,substitute their total earnings for each friend,

In,Friend 1; $45.50 ≥ $75.99 that is Not enough money

In Friend 2; $36.40 ≥ $75.99 that is Not enough money

In Friend 3; $63.70 ≥ $75.99 that is Not enough money

In Friend 4; $27.30 ≥ $75.99 that is Not enough money

In Friend 5; $54.60 ≥ $75.99 that is Not enough money

Nobody   of  friends earned enough money to buy a ticket,

therefore ,Total earnings < Ticket cost.

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Answer:

=4.44444444×10UP38

Step-by-step explanation:

that is your answer:)

The surface area of the square pyramid is 89.4 ft² as the lateral area is  80.4 ft².

The surface area of a square pyramid is calculated by the formula

SA = B + 4ℓ, where B is the area of the base and ℓ is the lateral area.

In this case, the base area is 9 square feet (3 ft x 3 ft). The lateral area is 4ℓ, which is calculated by multiplying the slant height by the perimeter of the base.

The slant height of a square pyramid is calculated by the formula

s = √(h² + (a/2)²), where h is the height of the pyramid and a is the length of one side of the base.

In this case, the height is 3 ft and the length of one side of the base is 3 ft. Therefore, the slant height is

s = √(3² + (3/2)²)

= √(9 + 2.25)

= √11.25

= 3.35 ft.

The perimeter of the base is 6 ft (3 ft x 2). Therefore, the lateral area is

4ℓ = 4 x 3.35 ft x 6 ft

= 80.4 ft².

The surface area of the square pyramid is then

SA = B + 4ℓ

= 9 ft² + 80.4 ft²

= 89.4 ft².

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Karen and Wayne will need to make monthly payments of $66.39 for 3 years to pay off the loan for their new refrigerator for a given sales tax.

The add-on interest loan formula can be used to determine the monthly payment:

(Loan amount + Interest) / the number of payments equals a payment.

We must first determine the refrigerator's total cost, including sales tax:

Final price is $1,598 plus 5% of $1,598.

$1,677.90 is the total price.

Secondly, we must determine the loan's interest rate:

Interest is calculated as Loan Amount * Addition Rate. Ages in years

Interest equals $702.25 when $1,677.90 multiplied by 0.14 by three.

When interest is included, the total loan amount is:

Loan amount = Purchase price plus interest

Total of the loan: $1,677.90 plus $702.25

Amount borrowed: $2,380.15

In the end, we can figure out the monthly payment:

Payment: ($2,380.15) divided by (3 years * 12 months/year) =

monthly payment of $66.39

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Answer:

I think the answer is B?

Step-by-step explanation:

The graph of the original triangle and the after the dilation are shown below:

Triangle dilation graph 8.

Dilation refers to the process of expanding or stretching an object or a space in one or more directions. In mathematics, dilation is a geometric transformation that changes the size of an object or a figure by either enlarging or reducing its dimensions, while preserving its shape and orientation.

In the context of image processing and computer vision, dilation is an operation that is commonly used to enhance and extract features from images. It involves convolving an image with a small structuring element or kernel, which slides over the image and replaces each pixel with the maximum value within the kernel.

For a dilation with a scale factor of 0.5 and centered at the origin, each coordinate of the triangle will be multiplied by 0.5. Thus:

J(8,0) will become J'(4,0)

L(-2,0) will become L'(-1,0)

K(4,4) will become K'(2,2)

The graph of the original triangle and the image after the dilation are shown below:

Triangle dilation graph 6

For a dilation with a scale factor of 2 and centered at the point (8,3), each coordinate of the triangle will be multiplied by 2 and then translated by the vector (8,3). Thus:

A (9,8) will become A'(26,14)

C (0,2) will become C'(8,7)

G (3,3) will become G'(14,9)

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There is no x-coordinate where the graph of the function [tex]f(x) = e^{-x^{2}}[/tex] has a slope of 0. However, the best answer would be (A) 0.

Answer:

x = [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

8x = [tex]\frac{2}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

24x = 2 ( divide both sides by 24 )

x = [tex]\frac{2}{24}[/tex] = [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

To solve for d in the equation d/11 = 14, we can multiply both sides by 11 to isolate d on one side of the equation.

d/11 = 14 (multiply both sides by 11)

d = 11 x 14

Simplifying, we get:

d = 154

Therefore, the solution for d is 154.

Answer: What do you mean where is the arc?

Step-by-step explanation:

we have shown that [tex]$(a^m)^n = a^{mn}$[/tex] for all [tex]$a \in G$[/tex] and [tex]$m, n \in \mathbb{Z}$[/tex].

To prove that in a group G, [tex]$(a^m)^n = a^{mn}$[/tex] for all [tex]$a \in G$[/tex] and [tex]$m, n \in \mathbb{Z}$[/tex], we need to show that both sides of the equation are equal.

We start by simplifying the left-hand side:

[tex]$(a^m)^n = a^{mn}$[/tex]

This is because raising a to the power of m and then to the power of n is the same as raising a to the power of mn. This property is known as the associative property of exponents.

Next, we need to show that the right-hand side of the equation is also equal to [tex]$a^{mn}$[/tex]:

[tex]$a^{mn} = a^{nm}$[/tex]

This is because multiplication is commutative in [tex]$\mathbb{Z}$[/tex], which means that [tex]$mn = nm$[/tex]

Therefore, we have shown that [tex]$(a^m)^n = a^{mn}$[/tex] for all [tex]$a \in G$[/tex] and [tex]$m, n \in \mathbb{Z}$[/tex].

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Answer:

14 units.

Step-by-step explanation:

2(4y - 3) + 2(3y - 1) = 62  Distribute the 2's.

8y - 6 + 6y -2 = 62  Combine like terms

14y -8 = 62  Add 8 to both sides

14y = 70  Divide both sides by 14

y = 5

Now find side QR:

3y - 1

3(5) - 1

15 - 1

14

Helping in the name of Jesus.

According to the calculations we can conclude that Rosa can play 21 more minutes on Monday.

If 9 minutes represents 30% of the time Rosa can play video games, we can use proportional reasoning to find the total time she can play. Let x be the total time she can play in minutes.

9 / x = 30 / 100

We might cross-multiply and simplify to find x's value:

9 * 100 = 30 * x

900 = 30x

x = 900 / 30

x = 30

So Rosa can play a total of 30 minutes each day.

To find how many more minutes she can play on Monday, we subtract the time she has already played from the total time:

30 - 9 = 21

Therefore, Rosa can play 21 more minutes on Monday.

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The general solution to the differential equation is M = (1/2)n² + Bn, where B is an arbitrary constant.

In calculus, differentiation is a process of finding the rate at which a function changes with respect to its input variable. It is the process of finding the derivative of a function, which represents the slope of the tangent line to the graph of the function at a given point.

The derivative of a function f(x) at a point x=a is denoted as f'(a) and is defined as the limit of the difference quotient as the interval between a and a+h approaches zero, where h is a small nonzero number.

The process of differentiation involves applying differentiation rules or formulas, which are a set of rules that make it easier to find the derivative of various functions. Some of the common rules include the power rule, product rule, quotient rule, and chain rule.

To solve the given differential equation:

[tex]\frac{d^{2}M }{dn^{2} } + 2n\frac{dM}{dn} =n[/tex]

We can assume a solution of the form:

[tex]M= An^{p}[/tex]

where A and p are constants to be determined.

Taking the first derivative of M with respect to n, we get:

[tex]\frac{dM}{dn} = Apn^{p-1}[/tex]

Taking the second derivative of M with respect to n, we get:

[tex]\frac{d^{2}M }{dn^{2} }= A(p)(p-1)n^{p-2}[/tex]

Substituting these expressions into the original differential equation, we get:

[tex]A(p)(p-1)n^{p-2} + 2Apn^{p-1}= n[/tex]

Simplifying, we get:

[tex]A(p)(p-1)n^{p-2} + 2Apn^{p}=n^{p+1}[/tex]

Since this equation must hold for all values of n, we can equate the coefficients of each power of n to get two equations:

A(p)(p-1) = 0

2Ap = 1

From the first equation, we get:

p = 0 or p = 1

If p = 0, then M = A, a constant. Substituting into the differential equation, we get:

0 = n

This is not true for all values of n, so p cannot be 0.

If p = 1, then M = An. Substituting into the differential equation, we get:

2An + 2nA = n

Simplifying, we get:

A = 1/2

Therefore, the solution to the differential equation is:

M = (1/2)n² + Bn

where B is a constant of integration.

Thus, the general solution to the differential equation is:

M = (1/2)n² + Bn

where B is an arbitrary constant.

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The standard deviation of the sampling distribution of all samples is 0.057.

What is the standard deviation?

The standard deviation is a measurement of how much a group of values vary or are dispersed. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Here, we have

Given: In 2019, the average high school GPA for incoming University of Maryland freshmen was 4.32 with a standard deviation of 0.285. Suppose UMD freshmen are randomly assigned into groups of 25.

We have to find the standard deviation of the sampling distribution of all samples.

Let x = High-school GPA scores of students in 2019.

E(x) = 4.32, S.D(x) = 0.285, n = 25

Suppose we consider the sampling distribution of the sample mean of all these samples, then we have

E(x) = 4.32

S.D(x) = 0.285/√25

= 0.057

Hence, the standard deviation of the sampling distribution of all samples is 0.057.

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