"mailing labels are sold in packages of 16 envelopes are sold in packages of 20 what is the least number of labels and envelopes you can buy so that there is one label on each envelope with none left over?"

The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)

An expression in maths, a statement involving at least two different numbers (known or unknown) and at least one operation.

Given an expression, -3x²-24x-36;

Factorizing, we get,

-3x²-24x-36 = -3(x²+8x+12)

= -3(x²+6x+2x+12)

= -3[x(x+6)+2(x+6)]

= -3(x+6)(x+2)

Hence, The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)

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Answer:

The answer is Ahope this helps

The equivalent expression to 45÷(2-x) is 45/(2-x).

According to the question,

We have the following expression:

45÷(2-x)

Or in other words, it can be said that 45 is divided by (2-x).

Now, when we are finding the equivalent expression of any expression for that matter then the final expression after solving any expression should be equal to the original one.

For example, the equivalent expression for 3/5 is 6/10 because when we divide the second fraction by we will get 3/5.

Now, in this case, the equivalent expression will be:

45/(2-x)

Because the fraction also means division.

Hence, the correct option is A.

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The average ticket cost for each concert is given as follows:

The ticket costs are obtained by a system of equations, for which the variables are given as follows:

It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:

6a + 6b = 1707

a + b = 284.5.

Three tickets for concert B cost a total of $687, hence the cost for concert B is of:

3b = 687

b = 287/3

b = $95.67.

Replacing into the first equation, the cost for concert A is given as follows;

a = 284.5 - 95.67

a = $188.83.

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Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Given statement solution is :-  Box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

To construct a box-and-whisker plot using the given data, you first need to find the minimum, maximum, median, and quartiles. Here are the steps to create the box-and-whisker plot for the given data set:

Sort the data in ascending order:

12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 18, 20

Find the median (middle value) of the data set. Since the data set has an odd number of values, the median will be the middle value:

Median = 15

Find the lower quartile (Q1), which is the median of the lower half of the data set.

Counting from the start, the lower half of the data set is:

12, 12, 13, 14, 14

Q1 = 13

Find the upper quartile (Q3), which is the median of the upper half of the data set.

Counting from the end, the upper half of the data set is:

17, 18, 20

Q3 = 18

Find the minimum and maximum values in the data set:

Minimum = 12

Maximum = 20

Now that we have the necessary values, we can construct the box-and-whisker plot:

lua

Copy code

       |                 |

 12  |      -------------|    

 13  |                 |

 14  |              ----  

 15  |           -------

 16  |      -------------|    

 17  |                 |

 18  |              ----  

 20  |                 |

       |_________________|

In this box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

8x+25=5x+35 (x=10/3)

Step-by-step explanation:

The equation for Store A would be: y(cost) = 8x(days) + 25

The equation for Store B would be: y = 5x + 35

So, since he wants the cost to be the same, 8x+25=5x+35

1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.

2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Question 1.

In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;

Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6

Mean number of text for Jada = 30/6

Mean number of text for Jada = 5.

Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6

Mean number of text for Diego = 36/6

Mean number of text for Diego = 6.

Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6

Mean number of text for Lin = 24/6

Mean number of text for Lin = 4.

Question 2.

In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;

Standard deviation = √(1/n × ∑(xi - u₁)²)

Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]

Standard deviation for Jada = √(6/6) = 1

Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]

Standard deviation for Diego = √(14/6) = 1.53

Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]

Standard deviation for Lin = √(76/6) = 3.6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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The number of sections of board that he can construct will be equal to 7.

We are given that:

A carpenter has 6 boards.

Length of each board = 7 / 8 yard long

Now, we will use multiplication.

Total length of cardboards available = 7 / 8 × 6 yards

Total length = 42 / 8 yards

Total length = 21 / 4 yards.

Now, 3/4 yard sections of board that he can construct will be:

Number of sections of board = 21 / 4 ÷ 3 / 4

Number of sections of board = 21 / 3

Number of sections of board = 7

Therefore, the number of sections of board that he can construct will be equal to 7.

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Answer:

C) 1/2

Step-by-step explanation:

3/16 + 5/8 is equal to 13/16. Or in decimal form: 0.8125. If you multiply 13/16 by 1/2, you'll get 13/32 (decimal form: 0.40625).

0.40625 rounded to the nearest tenth is 0.5 or 1/2.

Answer:

B. 4.00$

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

john is 20 years old

Step-by-step explanation:

we can take the ages as

john= x

jean= x+12

according to question

x+(x+12)= 52

2x+12= 52

transpose

2x= 52-12

2x= 40

x= 40/2

x= 20

john= 20

jean= 20+12= 32

therefore john is 20 years old and jean is 32 years old

Answer:

the square root of 23 is 4.8 or if you need the longer one it's 4.79583152331

Answer:

z=529

Step-by-step explanation:

Let's solve your equation step-by-step.

√z=23

Solve Square Root.

√z=23

z=232(Square both sides)

z=529

Check answers. (Plug them in to make sure they work.)

z=529(Works in original equation)

Answer:

The solution set is {-3, -6}.

Step-by-step explanation:

x^2 + 18 = -9x

x^2 + 9x + 18 = 0

(x + 3)(x + 6) = 0

x = -3, -6.

Given that we have 47 kids and each kid needs 10 marbles, find out how many bags of 24 marbles will we need.

First, we will multiply 47 by 10 to get the amount of marbles needed.

47 x 10 = 470

So, that means we need 470 marbles in total.

Then, we divide 470 by 24 to see how many bags of 24 marbles 470 marbles is.

470 / 24 = 19.5833

Since, we can't have 19.5833 bags, we have to check what it would be if we only used 19.

19 x 24 = 456

470 - 456 = 14

Since, 18 is the closest number of bags but it has less than 470 it would not be correct.

Therefore, the best answer would be B. 25 since it is better to have extra marbles but not a very wide margin.

Answer:

84

Step-by-step explanation:

TPS + SPR = RPT and TPS = RPT - SPR

The measure of RPT and SPR are given so we just need to place them and do the calculation

TPS = 137 - 53

TPS = 84

Answer: A

Step-by-step explanation: The line is linear as it changes at a constant rate which means it’s also proportional as proportional means as x changed so does y.

An inequality for x considering the figure is written as

the value of x is 82.5

x cannot be right angle because it will be against the rule of angle in a point is 360 degrees

The inequality that represents the figure in terms of x is written using the knowledge that angles in a point is 360 degrees

x + 2x + x + 30 < 360

adding like terms

4x + 30 < 360

solving for x

4x < 360 - 30

4x < 330

x < 82.5

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Answer:

= X + 8.2

Step-by-step explanation:

Answer:

A, B, C,

Step-by-step explanation:

Just use a calculator...?

a)

\(2^-^2*2^8=\frac{1}{2^2}*2^8=\frac{2^8}{2^2}=2^8^-^6=2^6=64\\\)

b)

\(3^-^5*3^1=\frac{1}{3^5}*3=\frac{3}{243}=\frac{1}{81}\)

c)

\(4^4*4^-^3=\frac{4^4}{4^3}=4^1=4\)

d)

\(5^3*5^-^1=\frac{5^3}{5^1}=5^2=25\)

e)

\(6^-^8*6^-^6=\frac{6^6}{6^8}=6^-^2=\frac{1}{6^2}=\frac{1}{36}\)

f)

\(8^2*8^-^4=\frac{8^2}{8^4}=8^-^2=\frac{1}{8^2}=\frac{1}{64}\)

Let's assume the number of cookies Lily bought is represented by "C," and the number of brownies is represented by "B."

According to the problem, the cost of one cookie is $2, and the cost of one brownie is $3. Lily spent a total of $144.

We can set up two equations based on the given information:

C + B = 60 (equation 1, representing the total number of sweets)

2C + 3B = 144 (equation 2, representing the total cost in dollars)

To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.

From equation 1, we can rewrite it as C = 60 - B.

Now substitute this value of C in equation 2:

2(60 - B) + 3B = 144

Simplify the equation:

120 - 2B + 3B = 144

Combine like terms:

120 + B = 144

Subtract 120 from both sides:

B = 144 - 120

B = 24

Now substitute the value of B back into equation 1 to find C:

C + 24 = 60

C = 60 - 24

C = 36

Therefore, Lily bought 36 cookies and 24 brownies.

Answer:

17

Step-by-step explanation:

You have to multiply 2 and 9 first, so the product is 18. Now you have to subtract that from 1 itself and therefore, the final answer is 17.

Hope this helps you!?!

Answer: 25%

Step-by-step explanation:

Divide 17/68 = .25

Move decimal 2 places over = 25%

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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The missing angles on the figure are as follows

The  missing angles ae solved as follows

v = y vertical angles theorem

Examining the figure shows that

v + 90 = 180 angle on a straight line

hence v = 180 - 90 = 90

so we can say that v = y = 90

Also, y + 38 + z = 180 angles in a triangle

90 + 38 + z = 180

z = 180 - 90 - 38

z = 52 degrees

furthermore, w = x base angle of isosceles triangle

w + x + v = 180

w + x + 90 = 180

w + x = 90

hence w = x = 45 degrees

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1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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