which expression is equivalent to the given expression 13+6×7 after using the distributive property ​

I'm not an expert at this but the answer should be 13.9 or 14

Final answer:

The length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.

Explanation:

In order to find the length of an arc made by an 80° central angle in a circle with a 10 ft. radius, we need to use the formula for the circumference of a circle. The formula for the circumference is C = 2πr, where C is the circumference and r is the radius. In this case, the angle is 80°, so we need to find the fraction of a full circle that the angle represents. Since a full circle is 360°, the fraction is 80/360 = 2/9. Therefore, the length of the arc is 2/9 times the circumference of the circle with a 10 ft. radius.

To find the circumference of a circle with radius 10 ft., we can use the formula C = 2πr. Plugging in the value of the radius, we get C = 2π(10) = 20π ft. Since the length of the arc is 2/9 times the circumference, the length of the arc is (2/9)(20π) ft. Simplifying, we get (40/9)π ft. This is approximately 13.96 ft. Therefore, the length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.

Answer:

-14 - 30 i

Step-by-step explanation:

We recall that when combining complex numbers, we need to combine the real parts among themselves to get the new real part, and the imaginary parts among themselves to get the imaginary part of the new complex that results from the operation.

In our case the firs complex number is "-8" which consists of strictly real part (with zero imaginary part). The second complex number is (6+30 i) which has real part = 6 and imaginary part = 30 i.

now we operate separately on the real parts and on the imaginary parts performing the requested subtraction:

Real part:  -8 - 6 = -14

Imaginary part: 0 i - 30 i = -30 i

Therefore the final complex number that results from this subtraction is: "-14 - 30 i"

Answer:

The option " The sum has degree of 6 , but the difference has a degree of 7 " is correct.

Step-by-step explanation:

Given that the sum and difference of the polynomials [tex]3x^5y-2x^3y^4-7xy^3[/tex] and [tex]-8x^5y+2x^3y^4+xy^3[/tex]

[tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)[/tex]

[tex]=3x^5y-2x^3y^4-7xy^3-8x^5y+2x^3y^4+xy^3[/tex]

[tex]=-5x^5y+0-6xy^3[/tex]

[tex]=-5x^5y-6xy^3[/tex]

Therefore [tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)=-5x^5y-6xy^3[/tex]

In the simplified sum of the polynomials [tex]-5x^5y-6xy^3[/tex]  we have the degree is 6

[tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)[/tex]

[tex]=3x^5y-2x^3y^4-7xy^3+8x^5y-2x^3y^4-xy^3[/tex]

[tex]=11x^5y-4x^3y^4-8xy^3[/tex]

Therefore [tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)=11x^5y-4x^3y^4-8xy^3[/tex]

In the simplified difference of polynomials [tex]11x^5y-4x^3y^4-8xy^3[/tex] we have the degree is 7

Therefore the option " The sum has degree of 6 , but the difference has a degree of 7 " is correct

Answer:

The sum has a degree of 6, but the difference has a degree of 7.

Step-by-step explanation:

Answer:

120 mg

Step-by-step explanation:

750 ml       300mg

300 ml         x mg

750 / 300 = 300 / x

x = (300 x 300) / 750 = 120 mg

Answer:

The number is 8.

Step-by-step explanation:

Write an equation then solve by isolating the variable.

let x be the number

4x + 15 = 47  Subtract 15 from both sides

4x = 47 - 15

4x = 32     Divide both sides by 4

x = 32/4

x = 8

Therefore the number is 8.

Answer:

8

Step-by-step explanation:

Answer:

10.32

Step-by-step explanation:

10.31988

the 9 makes the 1 to a 2 so...

10.32

Find the ratio of the similar known sides:

1.34/2 = 0.67

The smaller triangle is 0.67 the size of the larger one.

Multiply the similar sides by the ratio:

DE = 4 x 0.67 = 2.68

FE = 3 x 0.67 = 2.01

Answer:

Find the ratio of the similar known sides:

1.34/2 = 0.67

The smaller triangle is 0.67 the size of the larger one.

Multiply the similar sides by the ratio:

DE = 4 x 0.67 = 2.68

FE = 3 x 0.67 = 2.01

Step-by-step explanation:

Answer:

C) 12(8+3)

Step-by-step explanation:

Answer:C) 12(8+3)

Step-by-step explanation: i took the test

Answer:

30,000 cm^2.

Step-by-step explanation:

The area  = 3*1 = 3 square meters.

There are 100^2 = 10,000 cm^2 in a square meter

So the area in square centimeters is 3 * 10,000 = 30,000.

Answer:

-12+18x

Step-by-step explanation:

-3(4-6x)=-12+18x

Answer:

5≤u

Step-by-step explanation:

Put the words and numbers into an equation:

-5u+27≤2

Put all like terms on one side:

27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)

Simplify:

25≤5u

Solve:

5≤u

:)

Answer:

4x-19/3

Step-by-step explanation:

1/2(8x+4)+1/3(9-34)

8/2x+4/2+9/3-34/3

4x+2+3-34/3

4x+5-34/3

4x-19/3

Answer:

3x+5

Step-by-step explanation:

Answer:

The total pieces of cake are 24

Step-by-step explanation:

Linear equations

It's a relation between one or more variables and or numbers, connected with the equal sign. An example is 4x-5=7, or 2(x+y)=7-(x-y)

This problem can be easily solved without the use of equations, but we are required to.

We know Mindy and Troy combined ate 9 pieces of cake, we also know that Mindy ate 3 pieces of cake. It leaves 6 pieces to Troy. Since Troy ate 1/4 of the whole cake, then

[tex]\displaystyle \frac{1}{4}X=6[/tex]

Where X is the number of pieces of cake

Solving for X

[tex]X=(4)(6)=24\ pieces[/tex]

search for the best and accurate answers

The four consecutive even integers are 20, 22, 24, 26

Solution:

Let the four consecutive even integers are a , a + 2, a + 4, a + 6

Let "a" be the smallest integer and "a + 6" be the largest integer

To find: the four consecutive even integers

Given that the greatest of four consecutive even integers is 14 less than twice the smallest integer

largest integer = twice the smallest integer - 14

a + 6 = 2(a) - 14

a + 6 = 2a - 14

a - 2a = -14 - 6

-a = -20

a = 20

Thus the four consecutive even integers are:

a = 20

a + 2 = 20 + 2 = 22

a + 4 = 20 + 4 = 24

a + 6 = 20 + 6 = 26

Thus the four consecutive even integers are 20, 22, 24, 26

Answer:

Step-by-step explanation:

a) The maximum number of houses Sam can build in 24 hours is 8, so the constraint is in construction, not decoration. For each small house Sam constructs, he makes $10/3 = $3.33 per hour of work. For each large house Sam constructs, he makes $15/5 = $3.00 per hour. The most money is to be made by building only small houses.

Sam should make 8 small houses and 0 large houses in 24 hours.

__

b) If Sam works 8-hour days, then he can complete at most 80 small houses. The constraint remains in construction, so the answer is the same: build only small houses.

_____

If Sam works more than 16 2/3 hours per day, he can build 100 large houses or more, so the constraint moves to decoration. The decorator makes more money by decorating large houses, so all the effort should go to construction of large houses.

If Sam works between 10 and 16 2/3 hours per day, the best revenue will come from some mix. The problem statement is unclear as to how many hours Sam works in 30 days.

The garden view hotel is 235 feet tall

Step-by-step explanation:

The given is:

We need to find the height of the garden view hotel

Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet

∵ The height of the garden view hotel = x feet

∵ The height of the plaza hotel = y feet

∵ The height of the garden view hotel is 17 less than twice the

    height of the plaza hotel

- That means x is less than 2 × y by 17, equate x by the difference

   of 2 × y and 17

∴ x = 2y - 17 ⇒ (1)

∵ Their combined height = 361 feet

∴ x + y = 361

- Find y in terms of x by subtraction x from both sides

∴ y = 361 - x ⇒ (2)

Substitute y in equation (1) by equation (2)

∵ x = 2(361 - x) - 17

- Simplify the right hand side

∴ x = 722 - 2x - 17

- Add like terms

∴ x = 705 - 2x

- Add 2x to both sides

∴ 3x = 705

- Divide both sides by 3

∴ x = 235

The garden view hotel is 235 feet tall

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The height of the Gardenview Hotel is 235 feet, which we found by first creating a system of equations using the information given and then solving by substitution.

To find the height of the Gardenview Hotel, let's create a system of equations based on the information given. Let G be the height of the Gardenview Hotel and P be the height of the Plaza Hotel. We are told that the Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel, which we can express as G = 2P - 17. Additionally, we know their combined height is 361 feet, so G + P = 361.

Now we can solve the system of equations step by step:

Substitute the expression for G from the first equation into the second equation: (2P - 17) + P = 361.

Combine like terms: 3P - 17 = 361.

Add 17 to both sides of the equation: 3P = 378.

Divide both sides of the equation by 3 to find the height of the Plaza Hotel: P = 126.

Now use the value of P to solve for G using the first equation: G = 2(126) - 17.

Simplify to find the height of the Gardenview Hotel: G = 252 - 17.

Thus, the height of the Gardenview Hotel is 235 feet.

Answer:

1,500

Step-by-step explanation:

75•20

Answer:1500

Step-by-step explanation: 75 times 20 = 1500

To calculate the change in position after 30 seconds, multiply the rate of change per 10 seconds, which is -1 3/10 feet, by the number of 10-second intervals in 30 seconds, resulting in a total change of -3 9/10 feet or -3.9 feet.

If your team changes its position by -1 3/10 feet every 10 seconds in a tug of war game, we need to find out the change in position after 30 seconds.

Since the change in position is consistent over time, we can calculate the total change by multiplying the rate of change per 10 seconds by the number of 10-second intervals in 30 seconds.

The number of 10-second intervals in 30 seconds is:

30 seconds / 10 seconds per interval = 3 intervals.

The total change in position is then:

-1 3/10 feet/change × 3 changes = (-1 × 3)+(3/10 × 3)

= -3 9/10 feet or -3.9 feet.

Your team's change in position after 30 seconds is -3 9/10 feet or -3.9 feet.

The one side of rectangle is 11 feet and other side is 19 feet.

Step-by-step explanation:

Given,

Area of rectangle = 209 square feet

Let one side of rectangle = w

other side of rectangle = 2w-3

Area of rectangle = One side * other side

[tex]209=w*(2w-3)\\209=2w^2-3w[/tex]

[tex]0=2w^2-3w-209\\2w^2-3w-209=0[/tex]

[tex]2w^2+19w-22w-209=0\\w(2w+19)-11(2w+19)=0\\(2w+19)(w-11)=0[/tex]

Either;

2w+19=0        =>2w=-19

Or,

w-11=0            => w=11

As length cannot be negative, therefore,

One side of rectangle = 11 feet

Other side of rectangle = 2w-3 = 2(11)-3 = 22-3 = 19 feet

The one side of rectangle is 11 feet and other side is 19 feet.

Keywords: rectangle, area

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Answer: the person on the left

Step-by-step explanation:

by taking 20% off of the total cost first they are getting the better deal.

The customer gets a better deal from the cashier on the left. Explanation on determining the better deal between two cashiers based on how they apply discounts.

To determine who is getting the better deal, let's compare the total bill after discounts for both cashiers:

Cashier on the left: 20% off, then subtract $10

Cashier on the right: Subtract $10 first, then 20% off

Example Calculation:

If the total bill is $100:
Left cashier: $100 - 20%($100) = $80, then $80 - $10 = $70
Right cashier: $100 - $10 = $90, then 20%($90) = $18, so $90 - $18 = $72

In this scenario, the customer gets a better deal from the cashier on the left.

Answer:

Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did

Step-by-step explanation:

Let

x ----> number of hours worked by Jolianne

t ----> number of hours worked by Andrew

we know that

The number of hours worked by Jolianne multiplied by $10 per hour plus $27 saved must be equal to the number of hours worked by Andrew multiplied by $8

The linear equation that represent this situation is

[tex]10x+27=8t[/tex] ----> equation A

[tex]x=\frac{t}{2}[/tex] -----> equation B

substitute equation B in equation A

[tex]10(\frac{t}{2})+27=8t[/tex]

so

Andrew's table and equation is correct

Jolianne's table and equation are not correct, because Andrew did not work twice as many hours as she did

Answer:

the answer is B :)

Step-by-step explanation:

Answer:

For question 9: Angle 1= 20, angle 2= 70, angle 3= 70, angle 4= 20, angle 5= 20, angle 6= 70, and angle 7= 70.

Step-by-step explanation:

Answer:

D) 7 divided by 3

Step-by-step explanation:

Answer:

7 divided 3

Step-by-step explanation:i got it correct

You would have to sell approximately 52 bracelets per week in order to pay your fee.

190 ÷ 3.60 = 52.7

This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.

To determine the profit you make from selling glow sticks at the Star Wars convention, you can calculate the profit per unit and the total profit considering the costs and selling price.

Here are the key values:

Cost per glow stick: $2.02

Fixed weekly fee for the booth: $190

Selling price per glow stick: $3.60

Now, let's calculate the profit per unit:

Profit per unit = Selling price per unit - Cost per unit

Profit per unit = $3.60 - $2.02 = $1.58

This means you make a profit of $1.58 for each glow stick you sell.

To find the total profit, you need to consider how many glow sticks you sell. Let's assume you sell 'x' glow sticks. Your total profit can be calculated as:

Total Profit = Profit per unit × Number of Units Sold

Total Profit = $1.58x

Now, you need to take into account the fixed weekly booth fee of $190. So, your total profit after deducting the booth fee will be:

Total Profit - Booth Fee = $1.58x - $190

This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.

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Answer:135,136,137

Step-by-step explanation:

408 divided by 3=136

136-1=135

136+1=137

135,136,137

The largest number of the three consecutive even numbers that sum to 408 is 138.

The problem is a classic arithmetic sequence problem in mathematics, where a common difference exists between each number. For consecutive even numbers, this difference is 2. If the sum of three consecutive even numbers is 408, we can form the equation 3n+6=408 (since the first number is 'n', the next is 'n+2', and the following is 'n+4'). Solving this equation gives us n=134, hence the sequence of numbers is 134, 136 and 138. The largest number in this sequence is 138.

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Step-by-step explanation:

the farmer plants 0.4 of the total field which is 2.3 acres

⇒0.4×2.3= 0.92 acres

now draw a grid of area 2.3 acres and in that area shade 0.92 acres.Use a proper scale to draw the grid. It will a be pictorial representation of the proper and its solution.

Answer:3/4

Step-by-step explanation

Person A: -3 +(-1) + 0

+ =-2

And you divide by 12 and get

9/12=3/4

Answer: 3/4

Step-by-step explanation:

Answer:

The required probability is  given by, 0.9919.

Step-by-step explanation:

Let, X be the random variable denoting the no. of pages among those 4 pages which Julia writes where she makes no spelling mistake.

clearly,

X [tex]\sim[/tex] Binomial (4, 0.7)

So,      P(X = x) = [tex]^4C_{x} \times (0.7)^{x} \times (0.3)^{(4 - x)}[/tex]

                            [when  x = 0, 1, 2, 3, 4]

                         = 0 otherwise

According to the question, we are to find out  P(X ≥ 1) .

Now, P(X ≥ 1)

     = 1 - P(X = 0)

     = [tex] 1 - (^4C_{0} \times (0.7)^{0} \times (0.3)^{4})[/tex]

     = [tex] 1 - 0.0081[/tex]

     = 0.9919

So, the required probability is  given by, 0.9919

The probability that Julia will have no spelling mistakes on at least one of the pages is approximately 99.19%.

To determine the probability that Julia will have no spelling mistakes on at least one of the four pages she writes, we can first find the probability that she will make at least one spelling mistake on all four pages and then subtract this from 1.

The probability that there will be a spelling mistake on a page:

= 1 - 0.7 = 0.3.

Since the probability of a spelling mistake on each page is independent, we can multiply the probabilities for the four pages together.

The probability of at least one mistake on all four pages:

= 0.3 x 0.3 x 0.3 x 0.3 = 0.3⁴= 0.0081.

The probability that there will be no spelling mistakes on at least one page

= 1 - 0.0081 = 0.9919 or about 99.19%.

So, the probability is 99.19%.