Juanita used the steps shown below to correctly solve an equation. A step is missing.
-3(c-6) + 4c = 5(2c + 9)
?
c+ 18 = 10c +45
c-27 = 10 c
-27= 9c
-3 = c
O-3c-6 + 4c = 10c + 9; associative property of addition
O-3c+ 18+ 4c = 10c + 45; associative property of addition
O-3c-6 + 4c = 10c + 9; distributive property
O-3c + 18+ 4c = 10c +45; distributive property

Answer: Hi this is neither.

The answers to both the subparts using the binomial theorem are shown:

Probability:

(A) Summation notations:

(B) Simplified terms of the expansion:

Therefore, the answers to both the subparts using the binomial theorem are shown:

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For any function f(x), the average rate of change on the interval [x1,x2] is given by [f(x2) - f(x1)]/(x2-x1)

For f(-1) = 2.5 and f(3) = 40, the average rate of change on the interval [-1,3] is given by:

step 1 - (40 - 2.5)/[3-(-1)] = 37.5/4 = 9.375

step 2 - (37.5)/4

step 3 - Solving the fraction we find that the average rate of change is 9.375 (or 75/8)

There are two more quarters than dimes and as many nickels as dimes and quarters together. The total amount of money is 3. 75 dollars, then nickels dimes and quarters are there each, D =7 dimes , Q =  9 quarters, and N  =  16 nickels

tart by defining the variables for this problem :

Q : number of quarters

D : number of dimes

N : number of nickels

There are two more quarters than dimes so the equation :

Q = D+2

And as many nickels, as quarters and dimes together so the equation :

N = Q+ D

The total amount of money is $3.75  so the equation :

0.25Q + 0.10D + 0.05N =3.75

Solve the following system :

Q = D + 2 (I)

N = Q + D (II)

0.25Q + 0.10D + 0.05N =3.75(III)

In the equation (II)  find Q in terms of N and D :

N = Q + D (II)

Q = N - D (IV)

If  use (I) in (IV) :

Q = N - D

D + 2 = N - D

2D = N - 2

N = 2D + 2 (V)

If use (I) and (V) in (III)

0.25Q + 0.10D + 0.05N =3.75

(0.25) . (D + 2) + 0.10D + (0.05) . (2D + 2) = 3.75

0.25D +0.50 + 0.10D + 0.1D + 0.1 = 3.75

0.45D = 3.75

D = 3.75/ 0.45

D = 7

if D = 7 -----------replacing in (I)

Q = D + 2

Q = 7 + 2

Q   = 9

If  replace this values in (II)

N = Q + D

N = 9 + 7

N = 16

there are D =7 dimes,

                 Q =  9 quarters

                  N  =  16 nickels

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The equation of each line is labelled as shown in the image attached below, where:

y = 2x + 7 is line b

x + 5y = 10 is line d.

x + y = -9 is line f.

y = x is line c.

x = -5 is line a.

y = -5 is line e.

The equation of a line can be rewritten as y = mx + b, if the line has a slope of m and a y-intercept of b.

For vertical lines, the equation is written as x = b, where b is where the line cuts across the x-axis.

For horizontal lines, the equation is written as y = b, where b is the point on the y-axis the line intercepts.

The equation y = 2x + 7 is a line that has a slope of 2 and a y-intercept of 7. This line is labelled as line b in the image below.

x + 5y = 10 is rewritten as y = -1/5x + 2. The slope is 1/5 and the y-intercept is 2. This equation is labelled as line d.

x + y = -9 is rewritten as y = -x - 9. The slope is -1 and the y-intercept is -9. It is represented by the line labelled line f.

y = x has a slope of 1 and passes through the origin, (0, 0). It is labelled as line c.

x = -5 is the vertical line that is labelled as line a.

y = -5 is the horizontal line that is labeled as line e.

See image  below.

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Answer:

5001 and 4999

Step-by-step explanation:

25,000,000 is the square of 5,000 and 24,999,999 is one less than it. Notice that the situation resembles the expression [tex]x^2-1[/tex] in which x would be 5,000.

[tex]x^2-1[/tex] can be factored into [tex](x+1)(x-1)[/tex], and substituting x with 5000 yields: [tex](5000+1)(5000-1)[/tex]. This can also be written as [tex](5001)(4999)[/tex]. Therefore, the integers would be 5001 and 4999.

Unit rate for the given expression 625 ft² in 2/3 hours is equal to

975ft² /hour.

As given in the question,

Given expression :

650 ft² in 2/3 hours

Unit rate for the given expression 625 ft² in 2/3 hours is equal to

In 2 /3 hours  = 650 ft²

Simplify the given expression for the unit rate

  1 hour = 650 / 2 / 3 ft² / hour

Multiply 650 to 3 and divide it by 2 we get,

   1 hour = ( 650× 3 ) / 2 ft² / hour

⇒ 1 hour = 1950 / 2 ft² / hour

⇒  1 hour = 975 ft²/hour

Therefore, unit rate for the given expression 625 ft² in 2/3 hours is equal to 975ft² /hour.

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The distance of AX, A(-4, 5), X(1, -2) is 8.6

The distance formula is used to find the distance (shortest path) between two points.

The distance formula is

[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} } \\d = \sqrt{(-4 - 1)^{2} + (5 - (-2))^{2} } \\d = \sqrt{(-5)^{2} + (7)^{2} } \\d = \sqrt{25 + 49}\\ d = \sqrt{74}[/tex]

d = 8.6

Therefore, the distance of AX, A(-4, 5), X(1, -2) is 8.6

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The most appropriate choice for histogram will be given by-

a) Team tigers has taller players than team panthers

Team panthers has shorter players than team tigers.

b) team tigers have height that vary more.

c) So team panthers have more players about the same height.  

What is histogram?

Histogram is a type of bar graph which makes use of the range of classes in the horizontal x axis and the frequency of classes in the vertical y axis.

Here,

a) The bars in the histogram of team tigers are relatively taller than the bars in the histogram of team panthers. So, team tigers has taller players than team panthers.

The bars in the histogram of team panthers are relatively shorter than the bars in the histogram of team tigers. So, team panthers has shorter players than team tigers.

b) For team tigers, there are no players between 66-69 inches height and, two players between 69-72 inches height and five players between 72-75 inches height. So fluctuations between the heights of two consecutive bars for team tigers is more.

For team panthers, it can be seen that the fluctuation between the heights of heights of two consecutive bars is not that much.

So team tigers have height that vary more.

c) In team panthers, there are one player in 63-66 inches and 69-72 inches, three players in 66-69 inches and 75-78 inches and two players between 72-75 inches and 78-81 inches. So team panthers have more players about the same height.  

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Complete Question

The diagram has been attached here

Look at the two histograms below. They give you information about the heights of players on two basketball teams, the Tigers and the Panthers. Use the histograms to answer the following questions.

a)Which team has taller players? Which has shorter players? Explain your thinking.

b)Which team has heights that vary more? Explain your thinking.

c)Which team has more players that are about the same height?

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5 is in hundreds place and its place value is 500, 4 is in tens place and its place value is 40, 8 is in ones place and its place value is 8.

I hope this helps :)

The linear function equation exists the slope-intercept form. A linear equation exists represented as: h(x) = mx + b  then [tex]$\mathbf{h}(\mathrm{x})=-\frac{1}{5} \mathrm{x}+3$\\[/tex].

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let the independent variable be x.

The value of the function at 0 is 3.

If h(0) = 3

When the independent variable decreases by 5, the independent variable increases by 1.

So, the slope (m) exists -1/5.

Where, m = -1/5 the slope

b = 3 - the y-intercept

A linear equation exists represented as: h(x) = mx + b then [tex]$\mathbf{h}(\mathrm{x})=-\frac{1}{5} \mathrm{x}+3$\\[/tex].

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The solutions for the inequalities are:

z < -6 or z > 3 and -9 ≤ x ≤9

We are asked to solve the inequalities given.

For the inequality 4z−5<−29 or 4z+3>15, we have to solve for z. i.e., find the value for z.

4z−5<−29 or 4z+3>15

⇒ 4z < -29 + 5 or 4z > 15 -3

⇒ 4z < -24 or 4z > 12

⇒ z < -24/4 or z > 12/4

⇒ z < -6 or z > 3

The solution for z are the values above 3 and less than -6.

For 8x+8 ≥ −64 and −7−8x ≥ −79, we need to solve for x.

8x+8 ≥ −64 and −7−8x ≥ −79

⇒ 8x ≥ -64 -8 and -8x ≥ -79 + 7

⇒ 8x ≥ -72 and -8x ≥ -72

⇒ x ≥ -72/8 and -x ≥ -72/8

⇒ x ≥ -9 and x ≤ 9

⇒ -9 ≤ x ≤9

The solution for x are between -9 and 9.

The question is not complete. The complete question is given below:

Solve the system of inequalities.

4z−5<−29 or 4z+3>15

8x+8≥−64 and −7−8x≥−79.

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Answer:

Step-by-step explanation:

Brandon takes 1/4 of a 24-hour period to read 1/3 of his book. At this rate, how many hours will it take Brandon to complete the book?

1/4 of 24 hours = 0.25 × 24 = 6 hours

so:

Brandon takes 6 hours to read 1/3 of his book. To read the full book, going at the same reading rate:

6 × 3 = 18

It takes Brandon 18 hours to read the book.

All three fruits are not apples is 0.027

Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection.

P (X) = n/N

Given :

A fruit basket contains 5 apples

oranges=6

peaches=3

To find  :

compute the chance that all 3 fruits are not apples ?

Solution :

P(all 3 are apples) =(5x4x3)/(14x13x12)

⇒ 60/ 2184

⇒ 0.027

the chance that all 3 fruits are not apples is  0.027

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After reflection across the line x = -2, point L(-6,2), M(-6,0), K(-1,3) and J(3,0) becomes L'(1,2), M'(1,0), K'(-3,3) and J'(-1,0)

The line x = -2 will be parallel to y-axis. Let us say that there is a general point A(a,b). If this point is reflected across the line x = -2 then the y coordinates should remain same for the reflected point but x coordinate will change.

The new x coordinate will be parallelly opposite to the initial point and also at the same distance from the line as the initial point

From the Figure, we can see,

The coordinates of,

The point L is (-6,2),            

The point M is (-6,0),

The point K is (-1,3) and,

The point J is (3,0).

After reflection across the line x = -2, the coordinates of,

The point L' is (1,2),      

The point M' is (1,0),

The point K' is (-3,3),    

The point J' is (-1,0)

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The t distribution's degrees of freedom are equal to n - 1 by standard deviation.

What does math standard deviation mean?

The degrees of freedom for the t distribution when creating a confidence interval for the population mean using the sample's standard deviation equals n - 1.

Degrees of freedom = n - 1

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Answer:

Part A: C. 3c - 2 = c + 22

Part B: The cat weighs 12 pounds, and the dog weighs 34 pounds.

Step-by-step explanation:

Create a system of equations:

d = 3c - 2, d = 22 + c

And substitute to get the answer to part A:

22 + c = 3c - 2

If you solve the system, you get d = 34 and c = 12 as the answer to part B.

The cat weighs 12 pounds, and the dog weighs 34 pounds.

Answer: The weight of the dog is 34 pounds and The weight of the cat is 12 pounds The answer should be B I think that's the answer

Step-by-step explanation:

Answer: $63

Step-by-step explanation:

If the electrician gains $18 an hour and works for 3 and a half hours, once you add the money for the total time up you will get $63.

$9 (for the 30 minutes) + $18 x 3 (for the 12-2 full working hours).

Hope this helps^^

[7th Grader]

Answer:

M = 7p - 147

Step-by-step explanation:

Nicole is selling wing plates to fund raise. She's selling the plates for $7 each. She spent $147 on the ingredients and package for the plates. Which equation represents M, her profit of money, after selling p plates of wings?​

profit - sales - cost of goods sold

where p = number of plates sold

M = 7p - 147

It took me 120 minutes to answer 25 questions. How long did each question take?

120/25 = 4.8 minutes per question

Answer:

53.998x

Step-by-step explanation:

9.31x  · 5.8

9.31 · 5.8x

=53.999x

If T = 1, then the number T2580 represents 2580 as the right answer. This is the basic rules of linear equation.

The first order of equations are linear equations. For lines in the coordinate system, linear equations are defined. It is referred to as a linear equation in one variable when the equation contains a homogeneous variable of degree 1 (i.e., only one variable).

There may be multiple variables in a linear equation. Linear equations in two variables, and so forth, are what the equation is known as if it contains two variables. 2x-3=0, 2y=8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are a few examples of linear equations.

The three forms of linear equations are

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r + 6 expression represents the number of marbles that Conrad has.

Algebraic expression

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

For example, 3x² − 2xy + c is an algebraic expression.

Given that Conrad has 6 more marbles than Rory. If r represents the numbers of marbles that Rory has.

Number of marbles Rory has = r

Therefore number of marbles Conrad has = r + 6

r + 6 expression represents the number of marbles that Conrad has.

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Answer:

The value would double

Step-by-step explanation:

4/5 is half of 8/5

Answer:

4/5 is half of 8/5 so it got doubled

Answer: y = x -7

Step-by-step explanation: -x + y = 5

y = x + 5

y = x + a

-5 = 2 + a

a = -7

y = x - 7

The slope-intercept form for this linear function is y = 8x + 47.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

From the linear function, we have:

Points on x-axis = (-3, 2).

Points on y-axis = (23, -17).

Substituting the given points into the formula, we have;

Slope, m = (-17 - 23)/(2 + 3)

Slope, m = -40/5

Slope, m = -8

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + c

Where:

At point (-3, 23), we have:

y = mx + c

23 = 8(-3) + c

23 = -24 + c

c = 23 + 24

c = 47

Therefore, the slope-intercept form is as follows:

y = mx + c

y = 8x + 47

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We are trying to find the Least Common Multiple. This is a number that both 4 and 8 can be multiplied by a whole number to achieve, more specifically, the minimum of that list of numbers. This one is really simple. Since 8 is a multiple of 4 (4 x 2 = 8), the LCM is 8! (8 is also a multiple of 8 because 8 x 1 = 8).

So the answer is 8.

Equivalent or not equivalent result for each pair of given expressions are as follow:

a.5x-7+3x and 3x-7 +5x is equivalent.

b. 4y +9 +3y and 3y + 9 + 4y is equivalent.

c. 6z -2z +4 and 4 +2z-6z is not equivalent.

As given in the question,

Each pair of given expressions are equivalent or not equivalent :

a. 5x-7+3x and 3x-7 +5x

5x-7+3x

=(5x +3x) -7

= 8x -7

3x-7 +5x

= (3x +5x) -7

= 8x -7

This pair is equivalent.

b. 4y +9 +3y and 3y + 9 + 4y

4y +9 +3y

=(4y+3y)+9

= 7y +9

3y + 9 + 4y

=(3y +4y) +9

= 7y +9

This pair is equivalent.

c. 6z -2z +4 and 4 +2z-6z

6z -2z +4

=4z + 4

4 +2z-6z

= 4 -4z

This pair is not equivalent.

Therefore, equivalent or not equivalent result for each pair of given expressions are as follow:

a.5x-7+3x and 3x-7 +5x is equivalent.

b. 4y +9 +3y and 3y + 9 + 4y is equivalent.

c. 6z -2z +4 and 4 +2z-6z is not equivalent.

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