347 students listed soccer as their favorite sport. This is 13 less
than three times the number of students who listed basketball.

Tax: $2

Total: $27

Step-by-step explanation:

Given,

Price of boots = $25

Tax = 8%

Amount of tax = 8% of price of boots

[tex]Amount\ of\ tax = \frac{8}{100}*25\\Amount\ of tax=\frac{200}{100}\\Amount\ of\ tax=\$2[/tex]

Total = Price of boots + Tax amount

[tex]Total = 25+2=\$27[/tex]

Tax: $2

Total: $27

Keywords: sales tax, addition

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Answer:

[tex](g-7)^{6}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]

Given

[tex]\frac{(g-7)^{9} }{(g-7)^{3} }[/tex]

= [tex](g-7)^{(9-3)}[/tex]

= [tex](g-7)^{6}[/tex]

Answer:

(g - 7)⁶

Step-by-step explanation:

Rule:

[tex]\frac{x^{a} }{x^{b} } =x^{a - b}[/tex]

So,

(g - 7)⁹ ⁻ ³ = (g - 7)⁶

Answer:

8-4=2

2 x 4=8

4 x 2=8

8-2=4

Step-by-step explanation:

A fact family includes related multiplication and division facts. For the numbers 2, 4, and 8, the facts are 2 x 4 = 8, 4 x 2 = 8, 8 ÷ 4 = 2, and 8 ÷ 2 = 4. This demonstrates the relationship between multiplication and division.

Fact Family for Multiplication and Division

A fact family in mathematics is a group of related math facts involving the same numbers. For the numbers 2, 4, and 8, the fact family includes both multiplication and division facts. Here are the four members of this fact family:

2 x 4 = 8

4 x 2 = 8

8 ÷ 4 = 2

8 ÷ 2 = 4

Notice how multiplication and division are related: each multiplication fact has a corresponding division fact.

The two lines in this system of equations are parallel

Step-by-step explanation:

Let us revise the relation between 2 lines

∵ The system of equation is

3x - 6y = -12 ⇒ (1)

x - 2y = 10 ⇒ (2)

To solve the system using the substitution method, find x in terms of y in equation (2)

∵ x - 2y = 10

- Add 2y to both sides

∴ x = 2y + 10 ⇒ (3)

Substitute x in equation (1) by equation (3)

∵ 3(2y + 10) - 6y = -12

- Simplify the left hand side

∴ 6y + 30 - 6y = -12

- Add like terms in the left hand side

∴ 30 = -12

∴ The left hand side ≠ the right hand side

∴ There is no solution for the system of equations

∴ The system of equations represents two parallel lines

The two lines in this system of equations are parallel

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Using substitution method, we can see the system of equation has no solution and graphically, the lines are parallel to each other and don't intersect.

To solve the system of equations using the substitution method, we can solve one equation for one variable and substitute it into the other equation.

Let's start by solving the second equation for x:

x - 2y = 10

x = 2y + 10

Now we substitute this expression for x in the first equation:

3x - 6y = -12

3(2y + 10) - 6y = -12

6y + 30 - 6y = -12

30 = -12

Since the equation 30 = -12 is not true, we have reached a contradiction. This means that the system of equations has no solution.

Regarding the two lines in this system of equations, we can observe that they are parallel and they don't intersect with one another.

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Answer:

x = 10

Step-by-step explanation:

Given isosceles triangle with legs equal to [tex]\sqrt{74}[/tex] units. The height of 7 units divides this triangle into two congruent right triangles. The height of the isosceles triangle drawn to the base is its median to, so the height divides the base into two equal segments with length of [tex]\frac{x}{2}[/tex] units.

By th Pythagorean theorem,

[tex]\left(\dfrac{x}{2}\right)^2+7^2=(\sqrt{74})^2\\ \\\dfrac{x^2}{4}=74-49\\ \\\dfrac{x^2}{4}=25\\ \\\dfrac{x}{2}=5\\ \\x=2\cdot 5\\ \\x=10\ units[/tex]

Answer:

10

Step-by-step explanation:

Final answer:

To find the value of k that makes (x+3) a factor of the function f(x)=3x^3-2x+k, substitute x=-3 into the equation, leading to the solution k=75.

Explanation:

The question asks for the value of k that makes (x+3) a factor of the function f(x)=3x³-2x+k. To solve this, we use the fact that if (x+3) is a factor of f(x), then f(-3)=0. Therefore, we substitute x=-3 into the equation and solve for k.

Substituting x=-3 into f(x)=3x³-2x+k gives:

f(-3) = 3(-3)³- 2(-3) + k = -81 + 6 + k

Since f(-3)=0, we have -75 + k = 0

Thus, k = 75

This computation shows that the value of k that makes (x+3) a factor of the given function is 75.

Answer:

Then,

y=10-8

y=2

Step-by-step explanation:

solve the equation

Answer:

Step-by-step explanation:

-10+8= -2

Answer:

9^6=531441

Step-by-step explanation:

To calculate  ,on the Scientific calculator

-First press 9 marked on the set of numbers.

--Then go to the indices expression  and press on it.

--After that press 6.

--You will get the value of   9^6=531441

Answer: m = 11

Step-by-step explanation: Isolate the variable by dividing each side by facotrs that don't contain the variable.

Hope this helps you out! ☺

Answer:

m = 11

Step-by-step explanation:

To find m, we solve this equation:

2.50+ 1.50(m-1)=17.50

We subtract 2.50 from both sides:

1.50(m-1) = 15

Next we divide by 1.5 on both sides:

m - 1 = 10

Lastly we add one to both sides:

m = 11

Answer:

x = 21 degrees

y = 66 degrees

Step-by-step explanation:

Supplementary angles sum 180 degrees and complementary angles sum 90 degrees.

The first two upper angles are supplementary since they complete half a turn of a circle.

The relation is

(3x+5)+(6x-14)=180.

Joining like terms

9x-9=180

Dividing by 9

x - 1= 20 =>

x = 21 degrees

The first and the last angle are the same because they are formed by two parallel lines to a common side, so

3x-5=y-8 or

y=3x+3 = 63+3 =>

y = 66 degrees

Answer:

z is 0.03

if you divide 0.06/2= 0.03

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

0.3*10=3

10/5=2

--------------------

3+2=5

Answer:

The time taken by engine of the car to accelerate is 3.24 seconds

Step-by-step explanation:

Given as :

The mass of the car = 1200 kg

The Force applied by engine to accelerate = 10, 000 N

The change in velocity = [tex]v_2[/tex] -  [tex]v_1[/tex] = 27 m/s

Let The time taken by engine = t sec

And Let The acceleration = a  m/s²

Now,

∵ Force is define as the product of mass and acceleration

I.e F = mass × acceleration

or, F = 1200 × a

or, 10,000 =  1200 × a

∴ a = [tex]\frac{10,000}{1200}[/tex]   m/s²

I.e a = 8.33 m/s²

Now , Again

∵ Acceleration is define as the rate of change of velocity

I.e a = [tex]\dfrac{v_2-v_1}{t}[/tex]

or, a =  [tex]\dfrac{27-0}{t}[/tex]

Or, t =  [tex]\dfrac{27}{a}[/tex]

I.e t = [tex]\dfrac{27}{8.33}[/tex]

∴ t = 3.24 sec

So, The time taken = 3.24 seconds

Hence The time taken by engine of the car to accelerate is 3.24 seconds . Answer

The tool was used for 28 minutes

Step-by-step explanation:

We will use simple division to calculate the number for minutes for which the tool was rented

Given

Cost per minute = $0.65

Total cost = $18.20

Let x be the number of minutes

So,

x = [tex]\frac{Total\ cost}{Cost\ per\ minute}\\= \frac{18.20}{0.65}\\=28\  minutes[/tex]

The tool was used for 28 minutes

Keywords: Division, Linear equation

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The tool was used for 28 minutes

Step-by-step explanation:

We will use simple division to calculate the number for minutes for which the tool was rented

Given

Cost per minute = $0.65

Total cost = $18.20

Let x be the number of minutes

So,

x =

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Answer:

The answer is D

Step-by-step explanation:

∠C + ∠E = 180°(consecutive angles)

7x +11° + 7x + 1° = 180°

14x + 12° = 180°

14x = 168°

x = 12°

∠E = 7x + 1°

= 7(12°) + 1

= 85°

The measure of ∠E is 85 degrees

To calculate the measure of E, we start by calculating the value of x using:

∠C + ∠E = 180° (consecutive angles of cyclic quadrilateral)

So, we have:

7x +11° + 7x + 1° = 180°

Evaluate the like terms

14x + 12° = 180°

Subtract 12 from both sides

14x = 168°

Divide both sides by 14

x = 12°

Recall that:

∠E = 7x + 1°

Substitute 12 for x

∠E = 7(12°) + 1

Evaluate

∠E = 85°

Hence, the measure of ∠E is 85 degrees

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Answer:

sugar and also meat

Step-by-step explanation:

Answer: red meat you should balance your diet with chicken and red meat

Step-by-step explanation:

Answer:

Timmy

Step-by-step explanation:

He ate 30% of it

Timmy-30%

Chris- 15%

Little Dave-12%

Answer:

timmy

Step-by-step explanation:

he ate the most because he is fat

Answer:

$57.20

Step-by-step explanation:

So the card starts off with $90, we spend $4.10 each day

To figure this out quick, take $4.10 and multiply it by 8

$4.10 x 8 =$32.80

Now subtract:

$90 - $32.80 = $57.20

That Looks about right.

Answer:

you can get 11 DVDs if they cost 18 dollars

Answer:

Step-by-step explanation:

198/18=11. You can buy 11 packs

Answer:

Yes, because x = 2 and y = 6 is a solution to the equation.

The point (2, 6) does lie on the graph of the equation y = 3x because when you substitute x = 2 and y = 6 into the equation, it holds true (6=3*2). Hence, yes, because x = 2 and y = 6 is a solution to the equation.

To determine if the point (2, 6) is on the graph of y = 3x, you would need to substitute the values of x and y into the equation and see if it holds true. In this case, if we substitute x = 2 and y = 6, we get 6 = 3*2, which simplifies to 6 = 6. This shows that the equation is true, therefore, the point (2, 6) lies on the graph of y = 3x. So the correct answer is C: Yes, because x = 2 and y = 6 is a solution to the equation.

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Answer:

55%

Step-by-step explanation:

We have to divide the new price by the original price

4500/2900 = ca. 1.5517

Take away 100% from this answer and we get 0.5517 over the original price

This is the same as 55.17% can be rounded to 55%

To find the percent increase in the boat's price, subtract the original price from the selling price, divide by the original price, then multiply by 100 and round to the nearest whole number. The calculation shows about a 55% increase from the original price of $2900 to the selling price of $4500.

To calculate the percent increase, you would subtract the original price of the boat from the selling price and then divide by the original price to get the fraction of the increase. Finally, you multiply this fraction by 100 to convert it to a percentage. Using the given numbers: The original price is $2900, and the selling price is $4500.

When you round this to the nearest whole number, you get a percent increase of 55%.

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Answer:

16.5 square feet

Step-by-step explanation:

The logo consists of

The area of rectangle:

[tex]A_{rectangle}=1.5\ ft\times 3\ ft=4.5\ ft^2[/tex]

The area of trapezoid:

[tex]A_{trapezoid}=\dfrac{3\ ft+4\ ft}{2}\times 3 \ ft=3.5\ ft\times 3 \ ft=10.5 \ ft^2[/tex]

The area of triangle:

[tex]A_{triangle}=\dfrac{1}{2}\times 1.5\ ft\times 2 \ ft=1.5\ ft^2[/tex]

Hence, the area of logo:

[tex]A=A_{rectangle}+A_{trapezoid}+A_{triangle}=4.5\ ft^2+10.5\ ft^2+1.5\ ft^2=16.5\ ft^2[/tex]

5 pounds of peanuts should be mixed with cashews

Step-by-step explanation:

The given is:

The price of one pound of peanut is $1.5

The price of one pound of cashew is $4.5

10-pound mixture is obtained that will sell for $3.00 per pound

We need to find how many pounds of peanuts should be mixed with cashews

Assume that x represents the number of pound of peanuts, and y represents the number of pounds of the cashews

∵ x pounds of peanuts should be mixed with y pounds of cashews

∵ The mixture obtained is 10 pounds

∴ x + y = 10 ⇒ (1)

∵ The price of each pound of peanut = $1.5

∵ The price of each pound of cashew = $4.5

∴ The selling price of the mixture = 1.5x + 4.5y

∵ The selling price of one pound of mixture = $3

∵ The mixture is 10 pounds

∴ The selling price of the mixture = 3 × 10 = 30

- Equate the two expressions of the selling price of the mixture

∴ 1.5x + 4.5y = 30 ⇒ (2)

Now we have system of equations to solve it

Multiply equation (1) by -4.5 to eliminate y

∵ -4.5x - 4.5y = -45 ⇒ (3)

- Add equations (2) and (3)

∴ -3x = -15

- Divide both sides by -3

∴ x = 5

∵ x represents the number of pounds of peanuts

∴ The number of pound of peanuts is 5

5 pounds of peanuts should be mixed with cashews

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The probability of not surviving a head-on car accident is: 0.903

Step-by-step explanation:

The probabilities of occurrence and non-occurrence of an event add up to one.

If p is the probability that an even will happen and q is the probability that it will not happen

Then

[tex]p+q=1[/tex]

Here,

Probability of surviving = p = 0.097

Probability of not surviving = q = ?

[tex]0.097 + q = 1\\q = 1 - 0.097\\q = 0.903[/tex]

The probability of not surviving a head-on car accident is: 0.903

Keywords: Probability, Inverse

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Answer:

The statement is false

Step-by-step explanation:

For a number to be rational it must be able to be written as a fraction.

Answer:it is 10%

Step-by-step explanation:

Explanation:

Scientific Notation is number between 1-10 multiplied by 10[tex]^{#}[/tex] (or e#) This has the 1-10 right but the other number incorrect.

The correct scientific notation is 3.4e+9.

Need to explanation why is 3.4 * 910 is not correct scientific notation.

Scientific notation means the longer value coded to short terms like 34000 to 3.4e+4.

Here 3.4*910 does not represent any thing because the correct manner for the scientific notation is ae + b. Where a = value and b =power to the 10.
so the correct scientific notation is 3.4e+9.

Thus, 3.4 * 910 is not correct scientific notation, the correct scientific notation is 3.4e+9.

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The answer is v= -8x/-xy+9

Here is the step by step process (This is going to be long):

1.  9v+8x=vxy

Multiply both sides by vx

2.  9v+8x+−vxy=vxy+−vxy

−vxy+9v+8x=0

Add -vxy to both sides

3.  −vxy+9v+8x+−8x=0+−8x

−vxy+9v=−8x

Add -8x to both sides

4.  v(−xy+9)=−8x

Factor out the variable v

5.  v(-xy+9)/-xy+9 = -8x/-xy+9

v = -8x/-xy+9

Divide both sides by -xy+9