Use the distributive property to evaluate each expression (5-7)(-30

Answer:

6π or 18.84956 (rounded to 18.85)

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

In this question we are trying to calculate the cost of exact amount of fabric used given the cost per area of the fabric.

To answer this question mathematically, we need to know the area of the bulletin board. To do this , we employ a mathematical approach. We know that the bulletin board is circular in shape from the question and thus we calculate the area of this shape.

Mathematically, the area of the circular bulletin board is pi * r^2 where r refers to the radius. From the question, we can identify that this radius is 2.5 feet. let’s insert this into the equation we have.

mathematically A = 2.5^2 * pi = 19.63 sq. feet

The cost of the fabric per square feet is 1.48.

now the cost for this area that we have will be 1.48 * 19.63 = 29.0524

This is nearest to 29

the cow will walk 2 miles

Step-by-step explanation:

half a mile - 0.5 miles

1/4 of an hour = 0.5 miles

2/4 of an hour = 1 Miles

3/4 of an hour = 1.5 miles

4/4 of an hour (one hour) = 2 miles

0.5 × 4 = 2

The first thing to do is identify the unnecessary information (that they met 2 years ago).  

From there, let's go back three years ago.  We'll call Daniel's age x, and Ben's age will be 3x.  Ben's age is also equal to x + 20.

3x = x+ 20

2x = 20

x = 10

Daniel was 10 three years ago, and Ben was 30.  Now, Ben is 33.

Answer: PEMDAS

Step-by-step explanation:

Answer:

10000 cows.

Step-by-step explanation:

Remainder before the 10% loss: (7650/9) x 10 = 8500

Total before any losses : (8500/85) x 100 = 10000

Answer:

5/11

Step-by-step explanation:

The simplified fraction that represents 0.45 with a bar over the 45 is 45/99 => 5/11.

correct option: 5 Over 11

Here, we have,

we have to break down the decimal 0.45.

The digit 4 is in the tenths place, and the digit 5 is in the hundredths place.

To convert this decimal into a fraction, we can write it as:

0.45 = 4/10 + 5/100

Simplifying the fractions:

0.45 = 2/5 + 1/20

Now, to find the fraction equivalent of the repeating decimal 0.45, we need to express it as an infinite geometric series:

0.45 = (2/5) * (1 + 1/5 + 1/25 + ...)

The sum of an infinite geometric series can be calculated using the formula:

Sum = a / (1 - r)

where a is the first term and r is the common ratio.

In this case, a = 1/5 and r = 1/5.

Sum = (1/5) / (1 - 1/5)

Sum = (1/5) / (4/5)

Sum = (1/5) * (5/4)

Sum = 1/4

Therefore, the fraction equivalent of the repeating decimal 0.45 is 1/4.

However, among the given options, the fraction 45/99 is the closest approximation to 1/4.

This is because 45/99 can be simplified to 5/11, which is the closest fraction to 1/4.

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Answer:

9 9/10

Step-by-step explanation:

amount of them

= 3 1/2 + 6 2/5

= 7/2 + 32/5

= 35/10 + 64/10

= 99/10

= 9 9/10

Final answer:

The total amount of paper boxes recycled by Tiffany's class over two months is 9 9/10 boxes, after adding 3 1/2 boxes and 6 2/5 boxes using common denominators.

Explanation:

The student's question involves adding together two fractions to find the total amount of recycled paper boxes. Tiffany's class recycled 3 1/2 boxes one month and an additional 6 2/5 boxes the following month. To find the total, we need to add these two fractions.

First, let's convert these mixed numbers into improper fractions:
3 1/2 = 7/2 (since 3  imes 2 + 1 = 7)
6 2/5 = 32/5 (because 6  imes 5 + 2 = 32)

Next, we find a common denominator (which is 10 here) and add the two fractions:
7/2 = 35/10
32/5 = 64/10
Now, we add 35/10 + 64/10 = 99/10.

Finally, we convert the improper fraction back to a mixed number: 99/10 equals 9 whole boxes and 9/10 of a box.

So, Tiffany's class recycled a total of 9 9/10 boxes over the two months.

Answer:

h(-5) = -13

Step-by-step explanation:

h(x) = 3x + 2

Let x = -5

h(-5) = 3(-5) +2

        = -15 +2

        = -13

Answer:

H(-5)= -13

Step-by-step explanation:

1) Plug in -5 for the variable X

2) Then Solve

h(-5)= 3(-5) + 2

h(-5)= -15 + 2

H(-5)= -13

Hope this Help!

Answer:

An "association" exists between two categorical variables if the row (or column) conditional relative frequencies are different for the rows (or columns) of the table. ... If the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.

Step-by-step explanation:

The area of the circle with a radius of 3 is approximately 28.26 square units using the approximation [tex]\( \pi \approx 3.14 \).[/tex]

The area [tex]\(A\)[/tex] of a circle with radius [tex]\(r\)[/tex] is given by the formula:

[tex]\[ A = \pi r^2 \][/tex]

Given that the radius [tex]\(r\)[/tex] is 3, we can substitute this value into the formula:

[tex]\[ A = \pi \times (3)^2 \][/tex]

[tex]\[ A = \pi \times 9 \][/tex]

Using the approximation [tex]\( \pi \approx 3.14 \),[/tex] we can calculate:

[tex]\[ A \approx 3.14 \times 9 \][/tex]

[tex]\[ A \approx 28.26 \][/tex]

Therefore, the area of the circle with a radius of 3 is approximately [tex]\(28.26\).[/tex]

Answer:

6xy - 8x + 5y - 4z

Step-by-step explanation:

6xy - 20y + 7z - 8x + 25y - 11z

Group the ones with the variable first to make an equation:

6xy - 8x - 20y + 25y + 7z - 11z

Solve the equation

6xy - 8x +5y - 4z

Answer:

A function is a relation where there is only one output for every input. In other words, for every value of x, there is only one value for y. Function Rule. A function rule describes how to convert an input value (x) into an output value (y) for a given function. An example of a function rule is f(x) = x^2 + 3.

Step-by-step explanation:

The concept of a function relies on the idea of a functional dependency, where the output is entirely determined by the input.

A rule is considered a function when it satisfies the fundamental condition of assigning a unique output value to each input value. In other words, for every input, there should be exactly one corresponding output.

A key aspect of a function is that it avoids ambiguity and ensures a consistent mapping between inputs and outputs. Each input value must have a specific and unambiguous output value associated with it. This property distinguishes a function from a general relation, where multiple inputs may have the same output.

Additionally, a function must be well-defined, meaning that it produces a predictable and consistent output for any given input within its domain. The rule should be defined for all valid inputs, without any gaps or exceptions.

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Answer:

x =17

Step-by-step explanation:

Given shape is of a irregular hexagon.

Sum of all angles of an irregular hexagon

[tex]=(6 - 2) \times 180 \degree = 4 \times 180 \degree = 720 \degree \\ \\ \therefore \: (6x - 2)\degree + (7x + 19)\degree + 116 \degree \\ \: \: \: + (5x + 36)\degree + (8x - 1)\degree + 110 \degree \\ \: \: \: = 720 \degree \\ \\ \therefore \:(26x + 52)\degree + 226\degree = 720 \degree \\ \\ \therefore \:26x\degree + 278\degree = 720 \degree \\ \\ \therefore \:26x\degree = 720 \degree - 278\degree \\ \\ \therefore \:26x\degree = 442 \degree \\ \\ \therefore \:x = \frac{442\degree}{26\degree} \\ \\ \huge \red{ \boxed{\therefore \:x = 17}}[/tex]

Answer:

Because theres nothing to solve for x is all real numbers

Step-by-step explanation:

There is no way to solve it as theres nothing to solve for. You just plug in the x's with any number you want and it still will be there

Answer:

6 in.

Step-by-step explanation:

Hello there!

Work the triangle formula backward:

15 x 2=30

30/5=6 in

:)

Answer:

d dfghjkl

Step-by-step explanation:

i just knowvghnm,.

Answer: Adult 84

Children 34

Junior 2

Step-by-step explanation:

Adults tickets = $5

Children tickets = $.10

Junior tickets = $2

Total ticket sold = 120 at $119

Total tickets price

= Adults + junior + children

= 5 + 2 + 0.10 = 7.1

No of tickets sold for adults

= 5 / 7.1 × 119

= 84

No of tickets sold for children

= 2/7.1 × 119

= 34

No of tickets sold for junior

= 0.10/7.1 × 119

= 2

Total ticket sold

= 84 + 34 + 2

= 120

Final answer:

During the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.

Explanation:

Let's assume that the number of adult tickets sold is x, the number of junior tickets sold is y, and the number of children's tickets sold is z.

According to the information given, the cost of an adult ticket is $5, the cost of a junior ticket is $2, and the cost of a children's ticket is $0.10 (10 cents).

The total number of tickets sold is 120, so we can write the equation:

x + y + z = 120

Additionally, the total amount collected from the ticket sales is $119, so we can write the equation:

5x + 2y + 0.10z = 119

We now have a system of equations that we can solve to find the values of x, y, and z.

By using substitution or elimination methods, we can find that x = 22, y = 67, and z = 31.

Therefore, during the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.

Answer:

The number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.

Step-by-step explanation:

Given:

A local theater sell all 500 tickets for a total of $8,070.

The price of tickets were $15 for students, $12 for children, and $18 for adults.

The adult tickets sold were three times as many as children’s tickets.

Now, to find the number of student tickets, children tickets and adult tickets  sold.

Let the number of students ticket be [tex]x.[/tex]

Let the number of children ticket be  [tex]y.[/tex]

So, the number of adults ticket be [tex]3y.[/tex]

Now, the total number of tickets sold:

[tex]x+y+3y=500\\\\x+4y=500\\\\x=500-4y\ \ \ ...(1)[/tex]

Now, the total cost of tickets:

[tex]x(15)+y(12)+3y(18)=8070\\\\15x+12y+54y=8070\\\\15x+66y=8070\\\\Substituting\ the\ value\ of\ x\ from\ equation\ (1):\\\\15(500-4y)+66y=8070\\\\7500-60y+66y=8070\\\\7500+6y=8070\\\\Subtracting\ both\ sides\ by\ 7500\ we\ get:\\\\6y=570\\\\Dividing\ both\ sides\ by\ 6\ we\ get:\\\\y=95.[/tex]

Thus, the number of children ticket is 95.

According the adult tickets sold were three times as many as children’s tickets.

Therefore, the number of adult tickets = 95 × 3 = 285.

Now, substituting the value of [tex]x[/tex] in equation (1) to get the number of student tickets:

[tex]x=500-4y\\\\x=500-4(95)\\\\x=500-380\\\\x=120.[/tex]

Hence, the number of student tickets is 120.

Therefore, the number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.

The problem can be solved by creating a system of equations representing each type of ticket sales and their respective prices. Three equations are formed from the information provided and are then solved to find the numbers of each type of ticket sold.

This problem can be solved using a system of equations, representing each type of ticket sales and their prices. Let's define the variables. Let's let x represent the number of student tickets, y represent the number of children's tickets, and z represent the number of adult tickets.

We know that the total number of tickets sold is 500, so we can form the equation:
x + y + z = 500.
Moreover, we know that the total amount of money made from the tickets is $8070, so we can form the equation:
15x + 12y + 18z = 8070.
Lastly, we know that the theater sold three times as many adult tickets as children's tickets, forming the equation:
z = 3y.

Using these three equations, we can substitute and simplify to find the values of x, y, and z, representing the numbers of student, children, and adult tickets sold respectively.

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The ball will come to ground after 6 seconds.

We have a function of time given by -

f(x) = [tex]-16t^{2} +96t[/tex]

that gives the height of the ball in feet at ' t ' second.

We have to find out after how much time the ball will hit the ground.

The type of motion discussed in the above question is a two - dimensional projectile motion.

We have - h(t) = f(x) = [tex]-16t^{2} +96t[/tex]

Now, in order to find out the time at which the ball will hit the ground again, we will equate h(t) = f(x) = 0

[tex]-16t^{2} +96t=0\\-16t(t - 6)=0\\-16t =0\;\;\;\;\;\;t -6 = 0[/tex]

Now, time can never be 0.

Hence -

t - 6 = 0

t = 6 seconds.

Hence, the ball will come to ground after 6 seconds.

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Independent variable is the variable that you change.

Dependent variable is the variable you measure that results from or depends on the independent variable.

Since you want "r" to be the independent variable, you isolate/get the variable "q" by itself in the equation: [this is because "r" would be the variable that changes, and "q" would be the variable you find/measure that depends on "r"]

10q - 5r = 30             Add 5r on both sides

10q = 5r + 20          Divide 10 on both sides to get "q" by itself

[tex]q=\frac{5r+30}{10}[/tex]

[tex]q=\frac{5r}{10} +3[/tex]

[tex]q=\frac{1}{2} r+3[/tex]

The value of r is the independent variable is [tex]\rm \dfrac{10q-30}{5}[/tex].

Given that,

Equation; [tex]\rm 10q-5r = 30[/tex]

We have to determine,

The value of r is the independent variable.

According to the question,

A variable whose values do not change is known as independent changes. They have their own value, which is not changed with the equation.

To determine the value of r is the independent variable following all the steps given below.

Therefore,

The value of r is the independent variable is,

[tex]\rm 10q-5r = 30\\\\10q=30+5r\\\\q = \dfrac{30+5r}{10}\\\\q = \dfrac{5}{5} \times \dfrac{6+r}{2}\\\\ q = \dfrac{1}{2}r + \dfrac{6}{2}\\\\ q = \dfrac{1}{2}r + 3\\\\[/tex]

Hence, The value of r is the independent variable is [tex]\rm \dfrac{1}{2}r + 3[/tex].

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Answer:

The distance the tip of the second hand travels in 10 minutes is 502 cm.

Step-by-step explanation:

Given : The second hand on a clock is 8 cm long.

To find : What is the distance the tip of the second hand travels in 10 minutes?

Solution :

The circumference of clock is [tex]C=2\pi r[/tex]

The radius is r=8 cm

[tex]C=2\times 8\times \pi[/tex]

[tex]C=16\pi[/tex]

i.e. in 1 minute it cover  [tex]16\pi[/tex]

In 10 minutes it cover  [tex]16\pi\times 10[/tex]

In 10 minutes it cover  [tex]160\times 3.14[/tex]

In 10 minutes it cover  [tex]502.4[/tex]

Therefore, the distance the tip of the second hand travels in 10 minutes is 502 cm.

Answer: Tank B can hold 27.4 gallons

Step-by-step explanation:

Volume of a cylinder = πr^2h

Given that Cylindrical tank A has 9/10 of the radius and 9/10 of the height of cylindrical tank B

Let the radius of A = r

Radius of B = R

Height of A = h

Height of B = H

r = 0.9R and h = 0.9H

Volume of A = πr^2h

= π(0.9R)^2(0.9H)

= 2.29R^2H

Given that tank A can hold 20 gallons, approximately

20 = 2.29R^2H

R^2H = 20/2.29 = 8.73 ..... (1)

Volume of B = πR^2H

Substitutes R^2H in equation (1) into Volume of B

Volume of B = 3.143 × 8.73

Volume of B = 27.4 gallons

Answer: Tank B can hold 27.43 gallons

Step-by-step explanation: Please see the attachments below

Answer:

64 inches

Step-by-step explanation:

We know the following:

- A chessboard is made of 64 white and black squares.

- The 64 squares are arranged in 8 rows and 8 columns.

- Each square is 2 inches thick.

From the first point, we see that a chessboard is a square. This means its length and width are equal.

This is also why the number of rows is equal to the number of columns.

It has been established that there are 8 rows (and 8 columns). Each row is made up of 8 squares.

Therefore, the length of 8 squares (a row) is:

L = 8 * 2 = 16 inches.

Hence, each row (and column) is 16 inches long.

Therefore, Perimeter will be:

P = 4L

P = 4 * 16

P = 64 inches

The perimeter of the chessboard is 64 inches.

Final answer:

The student needs to calculate the perimeter of a chessboard. Multiplying the side of one square (2 inches) by the number of squares (8) gives the length of one side (16 inches). The perimeter is then 4 sides multiplied by 16 inches, resulting in 64 inches.

Explanation:

The student is asking about the perimeter of a chessboard. To find the perimeter, we need to calculate the total length of the chessboard's borders. Since the chessboard has 8 squares along each side and each square has a side length of 2 inches, the length of one side of the chessboard is 8 squares × 2 inches/square = 16 inches. The chessboard is a square with four equal sides, so the perimeter (P) is 4 times the length of one side.

P = 4 × 16 inches = 64 inches

Therefore, the perimeter of the chessboard is 64 inches.

Given:

The base of the given triangle has two part:

Left( left side of the hypotenuse) = 25

Right ( right side of the hypotenuse) = x

The altitude (h) = 60

To find the value of x.

Formula:

By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,

[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]

Now,

Putting,

left = 25, altitude = 60 and right = x we get,

[tex]\frac{25}{60} =\frac{60}{x}[/tex]

or, [tex](25)(x )=(60)(60)[/tex] [ by cross multiplication]

or, [tex]x = \frac{3600}{25}[/tex]

or, [tex]x = 144[/tex]

Hence,

The value of x is 144.

Answer:

x = 144

Step-by-step explanation:

Height Theorem

60² = 25·x

3600 = 25x

x = 3600 : 25

x = 144

Answer:

0.043

Step-by-step explanation:

We are given that

Initially when t=0

Then, A=22 million

The population of a country after t years is given by

[tex]A=22e^{kt}[/tex]

When t=8 then A=31 million

Substitute the values

[tex]31=22e^{8k}[/tex]

[tex]\frac{31}{22}=e^{8k}[/tex]

[tex]1.409=e^{8k}[/tex]

[tex]8k=ln(1.409)=0.343[/tex]

[tex]k=\frac{0.343}{8}=0.043[/tex]

Answer:

42,008

Step-by-step explanation:

The ending balance after 2 years will be equal to $42008.

The amount of interest calculated on the principal amount over a whole year of the loan amount is called simple interest.

In finance and economics, interest is the payment of an amount over repayment of the original sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.

Given that the amount is $35600 at 9% interest for 2 years. The total balance after 2 years will be,

SI = ( P x R x T ) /100

SI = ( 35600 x 9 x 2 ) / 100

SI = 6408

Ending amount = 6408 + 35600

Ending amount = $42008

Therefore, the ending balance after 2 years will be equal to $42008.

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The surface area of the cylinder with a height of 5 inches and a radius of 3 inches is calculated using the formula A = 2πrh + 2πr² and comes out to approximately 150.796 in² when rounded to the nearest thousandth.

To calculate the surface area of a cylinder, we use the formula A = 2πrh + 2πr², where 'r' is the radius and 'h' is the height of the cylinder. Given the height 'h' is 5 inches and the radius 'r' is 3 inches, we substitute these values into the formula.

Calculating the lateral surface area (the area of the side):
A_lateral = 2πrh = 2π(3 in)(5 in) = 30π in².

Calculating the area of the two bases:
A_bases = 2πr² = 2π(3 in)² = 18π in².

Now, add the lateral area and the area of the bases to find the total surface area:
A_total = A_lateral + A_bases = 30π in² + 18π in² = 48π in².

Using π ≈ 3.14159, the total surface area is: A_total ≈ 48(3.14159) = 150.796 in². Rounded to the nearest thousandth, the surface area of the cylinder is 150.796 in².

Answer:

350 ft long facing the barn and 175 ft wide

Step-by-step explanation:

Let a and b be the length and width of his rectangular fence. Since he has 700 feet of fencing and one side does not need fencing. We have the following constraint equation:

a + 2b = 700

a = 700 - 2b

We want to maximize the following area formula

A = ab

We can substitute a = 700 - 2b

[tex]A = (700 - 2b)b = 700b - 2b^2[/tex]

To find the maximum value of this, simply take the 1st derivative, and set it to 0

A' = 700 - 4b = 0

b = 700 / 4 = 175 ft

a = 700 - 2b = 700 - 350 = 350 ft