x = 2y - 3 & 3x - 7y = -14

The range of the test scores in Mr. Miller's math class is 42.

Mathematically, the range refers to the difference between the highest value and the lowest value in a data set.

The range is computed by subtraction of the lowest value from the highest value.

Mr. Miller can use the range to measure the spread or dispersion of the test scores.

Test Scores:

52, 61, 69, 76, 82, 84, 85, 90, 94

Highest score = 94

Lowest score = 52

Range = 42 (94 - 52)

Thus, we can conclude that for the math students in Mr. Miller's class, the range of their test scores is 42.

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Answer:

4

Step-by-step explanation:

We are asked to find a slope whilst given a graph.

To solve for slope, we must pick two coordinate points that are not decimals and following the formula of rise over run, which in basic terms y over x.

So based on what I see, I can see (1, 1) and (2, 5).

The rise over run is as followed :

\(\frac{y2 - y1}{x2 - x1}\)

2 and 1 meaning the first and second number within the coordinate, so substitute :

\(\frac{5 - 1}{2 - 1}\)

\(\frac{4}{1}\)

Divide :

\(4\)

4 is our slope.

Mistake:

2nd Line of Student Work.

Opening Brackets:

4*1 = 4 Correct

Problem is here: 4*5n = 20n, not 5n, Wrong

Octavia should buy 36 small milkshakes to serve her friends but stay in budget.

To determine the number of small milkshakes Octavia should buy to stay within her budget, we need to consider the cost of each type of milkshake and the total amount she can spend.

Let's assume Octavia buys x small milkshakes. Since each small milkshake costs $2.50, the total cost of x small milkshakes would be 2.50x dollars.

Now, let's set up the inequality based on the given information: 2.50x ≤ 90. This inequality represents that Octavia cannot spend more than $90.

To find the maximum number of small milkshakes Octavia can buy, we solve the inequality:

2.50x ≤ 90

Divide both sides of the inequality by 2.50:

x ≤ 36

Therefore, Octavia can buy a maximum of 36 small milkshakes to stay within her budget.

In this case, the number of small milkshakes she should buy to serve her friends while staying in budget would be 36.

Octavia should buy 36 small milkshakes to serve her friends but stay in budget.

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Answer:

An object's initial position

The initial velocity of an object

The time an object was in motion

The acceleration of an object

Step-by-step explanation:

That equation is used to solve for an object's final position.

Answer:

$93 per hour ?

125-405 = 280

280÷3= 93 per hour

Answer: 25%

Step-by-step explanation: do 250/1,000

you get .25. Then convert that into percentage, which is 25%.

a. The unemployment rate is 20%.

b. The labor-force participation rate is 60%.

According to the question,

Working age population- 100,000

Labour force - 60,000

Unemployed - 12000 instructions

a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:

Unemployment Rate = \(\frac{Number of unemployed People}{Labor force}\) × 100

When an unemployed population is 12,000 and the labor force is 60,000,

the unemployment rate is  = \(\frac{12000}{60000}\) × 100 = 20%

b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:

Labor Force Participation Rate = \(\frac{Labor force}{working age population}\) × 100

When the labor force is 60,000 and the working-age population is 100,000

Labor Force Participation Rate = \(\frac{60000}{100000}\) × 100 = 60%

So, a. The unemployment rate is 20%.

b. The labor-force participation rate is 60 %.

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the regression equation y = 5x + 23 is true.

The number 23 represents the fixed or baseline number of people attending the picnic, regardless of the number of flyers used to advertise it (x).

what is regression?

Regression in mathematics refers to a statistical analysis method used to model the relationship between variables. It aims to find the best-fitting mathematical function that describes the relationship between a dependent variable (also known as the response variable) and one or more independent variables (also known as predictor variables or features).

The purpose of regression analysis is to estimate the parameters of the mathematical function that minimize the difference between the predicted values and the actual observed values of the dependent variable. This allows us to make predictions or draw inferences about the relationship between variables based on the available data.

There are different types of regression analysis, including linear regression, polynomial regression, multiple regression, logistic regression, and more. Each type is suited for different types of relationships between variables and has its own assumptions and techniques for parameter estimation.

Regression analysis is widely used in various fields, such as economics, finance, social sciences, engineering, and machine learning, to analyze and understand the relationship between variables, make predictions, and inform decision-making processes.

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Fg(x) = g(x-1)*1 + g(x-2)*4 + g(x-3)*6 + g(x-4)*8 + g(x-5)*7 + g(x-6)*5 + g(x-7)*3, where g(x) is defined as follows: g(x) = 1 - |x|^2 - 2|x|³    + 10|x|²   - 16|x| + 80 if |x| ≤ 1

The given function g(x) is defined piecewise based on the absolute value of x. For |x| ≤ 1, g(x) is equal to 1 - |x|^2 - 2|x|³ + 10|x|²   - 16|x| + 80.

For 1 < |x| ≤ 2, g(x) is defined differently, and for |x| > 2, g(x) has another definition.

The function Fg(x) is defined as the sum of g(x-i) multiplied by the corresponding values in the list f=[1, 4, 6, 8, 7, 5, 3], where i ranges from 1 to 7.

This means that for each point i, the function g(x-i) is evaluated and multiplied by the corresponding value in f, and the results are summed together.

In essence, Fg(x) combines the contributions of g(x) at different shifted positions (x-i) using the values in f.

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Answer:

scale factor = \(\frac{5}{3}\)

Step-by-step explanation:

The scale factor is the ratio of corresponding sides , B  to A

scale factor = \(\frac{50}{30}\) = \(\frac{5}{3}\)

Then

\(\frac{x}{15}\) = \(\frac{5}{3}\) ( cross- multiply )

3x = 75 ( divide both sides by 3 )

x = 25

and

\(\frac{18}{y}\) = \(\frac{5}{3}\) ( cross- multiply )

5y = 54 ( divide both sides by 5 )

y = 10.8

If there is at-least one-song liked by those two girls but disliked by the third, then the "different-ways" this is possible is 132 ways.

There are ⁴C₃ ways to choose the "3-songs" which are liked by "3-pairs" of girls.

There are 3! ways to find the three songs are liked by which pair of girls.

In total, there are ⁴C₃×3! possibilities for the first "3-songs".

There are "3-cases" for fourth song, let that song be "D".

Case 1: Song "D" is disliked by all three girls means there is only one possibility.

Case 2: Song "D" is liked by exactly one girl means there are three possibility.

Case 3: Song "D" is liked by exactly two girls means there are three pairs of girls to choose from.

However, there is an overlap when "other-song" is liked by "same-pair" of girl is counted as "fourth-song" at some point, in which "case-D" will be counted as one of first "three-songs" liked by same girls.

Counting the overlaps, there are "three-ways" to choose pair with overlaps and 4×3=12 ways to choose what the other "two-pairs" like independently.

In total, there are 3×12=36 over-lapped possibilities,

Therefore, there are ⁴C₃ × 3! ×(3+1+3)-36 = 132 ways for the songs to be likely by the girls.

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Answer:

12 dozen

Step-by-step explanation:

create a proportion of: dozen cookies / cups of pecan

let 'd' = dozen cookies

(3/1 ÷ 5/4) = (d ÷ 5)

simplify 3/1 ÷ 5/4 to be:  3/1 x 4/5, which equals 12/5

12/5 = d/5

cross-multiply to get:

5d = 60

d = 12

Detailed solution is attached!!~

To calculate the total charge within the cylinder with dimensions r=1.5 and h=3, we use the potential function V = 5r + 4 cos Ø in cylindrical coordinates.

The total charge can be obtained by integrating the charge density over the volume of the cylinder.

The potential V within the cylinder is given by V = 5r + 4 cos Ø, where r represents the radial distance from the axis of the cylinder and Ø represents the angle in the cylindrical coordinate system. To calculate the total charge within the cylinder, we need to integrate the charge density over its volume.

The charge density ρ can be related to the potential by ρ = -∇²V, where ∇² is the Laplacian operator. In cylindrical coordinates, the Laplacian operator takes the form:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز + ∂²/∂z²

Since the potential function V does not depend on the z coordinate, the Laplacian reduces to:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز

Applying this operator to the potential function V, we find:

∇²V = (1/r) ∂/∂r (r ∂V/∂r) + (1/r²) ∂²V/∂ز

To find the charge density, we substitute this expression into ρ = -∇²V:

ρ = -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز

To calculate the total charge, we integrate the charge density ρ over the volume of the cylinder:

Q = ∫∫∫ ρ dV = ∫∫∫ -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز dV

The integration is performed over the cylindrical coordinates r, Ø, and z, with appropriate limits. Evaluating this integral will give us the total charge within the cylinder.

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Solving for q will give us the optimal quantity that maximizes the profit,  a function that gives the total profit earned can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

Assuming that the revenue and cost are functions of the quantity sold (q), the total profit can be calculated as follows:

Profit(q) = Revenue(q) - Cost(q)

To find the quantity which maximizes the profit, we can take the derivative of the profit function with respect to q and set it equal to zero, and then solve for q:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the quantity that maximizes the profit. However, without knowing the specific forms of the revenue and cost functions, we cannot write a specific profit function or find the quantity that maximizes the profit.

In general, the profit function can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

where the revenue per item and cost per item are functions of q. To find the quantity that maximizes the profit, we need to differentiate the profit function with respect to q and set it equal to zero:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the optimal quantity that maximizes the profit.

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Lane needs to eat 2/10 of the brownie to eat the same amount as Alex.

Alex cut his brownie into tenths and ate 2/10 of it.

Lane cut his brownie into fifths.

What fraction of the brownie does Lane need to eat to eat the same amount as Alex.:

In this problem, we can compare the fraction of brownie that Alex ate with the fraction of brownie that Lane needs to eat to eat the same amount as Alex.

Let’s first simplify the fraction of brownie that Alex ate.2/10 can be simplified by dividing both the numerator and the denominator by the greatest common factor, which is 2.2/10 = 1/5

Now, we need to find the fraction of brownie that Lane needs to eat to eat the same amount as Alex.

To do this, we need to find a common denominator.

The least common multiple of 5 and 10 is 10.

This means we can convert 1/5 into a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2.1/5 = 2/10.

Now, we can see that to eat the same amount as Alex, Lane needs to eat 2/10 of the brownie.

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Answer:

look down

Step-by-step explanation:

let length be" x"

accroding to question

breadth= 2x/3

we know,

Area of rectangle= l × b

384=x × 2x/3

calculate

Answer:

3x - 10 = 13 would be the verbal expression where x = a number

Hope this helps!

Answer:

4.75 kg

Step-by-step explanation:

Bottles of jam given by Sakshi to her friends =7

Bottles of jam prepare by sakshi for herself =12

Total bottles of jam made =7+12=19

Weight of jam in 1 bottles =250 gm

Total weight of jam made by sakshi

=250×19

=4,750 gm

Total weight of jam =4.75 kg.

The expansion of (a + b)8 = a⁸ + 8a⁷b + 28a⁶b² + 56a⁵b³ + 70a⁴b⁴ + 56a³b⁵ + 28a²b⁶ + 8ab⁷ + b⁸.

Recall the binomial theorem for expansion of powers of (a + b) as follows:

(a + b)⁰ = 1, (a + b)¹ = a + b, (a + b)² = a² + 2ab + b²,

and in general,

(a + b)n = nC₀an + nC₁an-1b + nC₂an-2b² + ... + nCn-1abn-1 + nCnbn,

where nCk = n!/[k!(n - k)!], k = 0, 1, ..., n.

The expansion of (a + b)8 is:

(a + b)⁸ = 8C₀a⁸ + 8C₁a⁷b + 8C₂a⁶b² + 8C₃a⁵b³ + 8C₄a⁴b⁴ + 8C₅a³b⁵ + 8C₆a²b⁶ + 8C₇ab⁷ + 8C₈b⁸.

to find the precise coefficients of (a + b)8, apply the formula given above.

n = 8, and so calculate

nC₀, nC₁, ..., nC₈nC₀ = 8C₀ = 1nC₁ = 8C₁ = 8nC₂ = 8C₂ = 28nC₃ = 8C₃ = 56nC₄ = 8C₄ = 70nC₅ = 8C₅ = 56nC₆ = 8C₆ = 28nC₇ = 8C₇ = 8nC₈ = 8C₈ = 1

Therefore, substitute these values to obtain the precise coefficients of (a + b)8.

(a + b)8 = a⁸ + 8a⁷b + 28a⁶b² + 56a⁵b³ + 70a⁴b⁴ + 56a³b⁵ + 28a²b⁶ + 8ab⁷ + b⁸.

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Answer:

x = 3

Step-by-step explanation:

6x - 2 = x + 13

6x - x = 13 + 2

5x = 15

x = 3

The volume of the cone is 1960.64 cubic yards.

We have,

The formula for the volume of a cone is:

V = (1/3)πr²h

where π is approximately 3.14, r is the radius, and h is the height.

Substituting the given values, we get:

V = (1/3) x 3.14 x 12² x 13

V = (1/3) x 3.14 x 144 x 13

V = 1/3 x 3.14 x 1872

V = 1960.64

Rounding to the nearest hundredth, we get:

V = 1960.64

Therefore,

The volume of the cone is 1960.64 cubic yards.

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Answer:

$20.01

Step-by-step explanation:

Simply subtract $29.99 from $50.00 so, your problem should be set up like this:

You substitute the numbers with 10s, but there cannot be more than one.

Answer:

$20.01

Step-by-step explanation:

You should subtract 50.00 and 29.99, and since there are three zeros, you have to borrow from the five, making it a four. Then, you make the first zero into a 10, then borrow from that one, making it a nine, same with the second zero. Then, for the third zero, you only borrow one from the second zero, turning the second one into a nine and the third on into a 10. You then start the subtracting process. This is the first part to the problem:

50.00 - 29.99 = ?

Then, this is what you should have after:

49.91(0) - 29.99 = ?

This is what you get after:

20.01

Then, add the dollar sign. You will get:

$20.01

Hope it helped!

Answer:

(3, -2)

Explanation:

Solving for x in the second equation gives

Putting this into the first equation gives

Expanding the left-hand side gives

With the value of y in hand, we put it in x + 2y = -1 to get

adding 4 to both sides gives

Hence, the solution to the system is (3, -2) and it can be verified by plotting the graph.

Answer:

7

Step-by-step explanation:

4(x + 1)+3x + 7

Distribute

4x+4 +3x+7

Combine like terms

4x+3x   +4+11

7x+15

The coefficient is the term in front of the x

7

Answer: -1/4

Step-by-step explanation:

(-7+3)/(7+9)

-4/16

-1/4

The value of Emma's deposit after 3 years, including simple interest, is $90 + $10.80 = $100.80.

Simple Interest = Principal x Rate x Time

In this case, the Principal is $90 (the initial deposit), the Rate is 4% (0.04 as a decimal), and the Time is 3 years.

Step 1: Calculate the simple interest.
Simple Interest = $90 x 0.04 x 3
Simple Interest = $10.80

Step 2: Add the simple interest to the initial deposit.
Total Value = Principal + Simple Interest
Total Value = $90 + $10.80
Total Value = $100.80

So, the value of Emma's deposit after 3 years is $100.80.

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3a - 2a x 4a + 6a

Using the order operations : Brackets, Exponents, Multiplication/Division, Addition/Subtraction.

=> We do the multiplication first : 2a x 4a = 8a^2.

-> = 3a - 8a^2 + 6a.

Now, we reposition the terms :

3a - 8a^2 + 6a = (3a + 6a) - 8a^2 = 9a - 8a^2.

Therefore, the answer is C.