Last week, Harry ran 5 laps around the lake. Sophia ran 1 5/6 times as many laps around the lake as Harry did. How many laps around the lake did Sophia run?

To find the area of the circle:

   ⇒ must know the area's formula ⇒ [tex]\pi r^2[/tex]

Let's consider the information given

         ⇒ the radius' length is half of the diameter

             ⇒ thus the radius' length is 3.5 in

Let's calculate the area:

    [tex]Area=\pi r^2=\pi (3.5^2)=12.25\pi in^2[/tex]

The problem asks us to leave the answer in terms of '[tex]\pi[/tex]' which means that we won't multiply '[tex]\pi[/tex]' to the final answer, but leave it there,

Answer: 12.25[tex]\pi in^2[/tex] or Choice (B)

Hope that helps!

Answer:

120 days

Step-by-step explanation:

Remark

It's an inverse relationship. As the number of men go up, the 80 gets smaller. As the number of men goes down, the number of days will get larger.

Equation

80 = k / 15                Multiply both sides by 15

Solution

80*15 = 15 * k/15

1200 = k

That means that k is number that 80 men will produce. It is the number that relates men and days.

So now you want to put 10 men where 15 were before and see what that does to the number of days.

days = 1200/10

days = 120

Answer

It will now take 120 days.

15 men can do a piece of work in 80 days. How long will it take to complete the work if 5 men are reduced?

In this question we are provided that 15 men can do a work in 80 days and we are asked to calculate the time if 5 men are reduced that means we need to calculate the no. of days 10 men will take to do the same work.

There are two methods to solve this question

[tex] \small \red{ \underline{\bf{ Unitary \: Method }}}[/tex]

15 men can do a piece of work in 80 days

1 men can do a piece of work in 80 × 15 days

10 men can do a piece of work in [tex]\dfrac{80 × 15}{10}[/tex] = 120 days

[tex] \rule{40mm}{5pt}[/tex]

[tex] \small \orange{ \underline{\bf{ Method \: of \: proportion}}}[/tex]

Let us assume that 10 men can do a piece of work in x days.

[tex] \begin{array}{cc} \bf{Number \: of \: men} & \bf {Number \: of \: days} \\ 15&80 \\ 10&x\end{array}[/tex]

[tex] \small\bf{ 15 : 10 :: x : 80}[/tex]

[tex] ➲ \: \small\rm{10 \times x = 80 \times 15} [/tex]

[tex]➲ \: \small\rm {x = \dfrac{80 \times 15}{10} = 120 \: days }[/tex]

x = 120

[tex] \rule{72mm}{6pt} [/tex]

well, Mai is 21 today and when she's 25 is 4 years from now, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000\left(1+\frac{0.10}{1}\right)^{1\cdot 4}\implies A=2000(1.1)^4\implies A=2928.2[/tex]

Answer: 1

Step-by-step explanation:

0.8 is the slope of the line M'N'.

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. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

So, the coordinates of M' are (0.82, 0.84) = (1.6, 3.2), and the coordinates of N' are (0.83, 0.85) = (2.4, 4).

Now, we can find the slope of line M'N' using the slope formula:

slope of M'N' = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (1.6, 3.2) and (x2, y2) = (2.4, 4).

slope of M'N' = (4 - 3.2) / (2.4 - 1.6)

the slope of M'N' = 0.8

Therefore, the slope of line M'N' is 0.8.

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Answer: 3.63248

Step-by-step explanation:

I know the answer thats all

Answer:

3.632

Step-by-step explanation:

since 1.244 has 3 decimal places you can round off the answer to 3 d. p.

If  his current total savings is 300m²+120m+180 dollars. The factorization that represent the months and monthly deposit is: 60(5m²+2m+3)

Given:

Expression=300m²+120m+180

Factorize

Extraction of common factor

60(5m²+2m+3)

Expand

60×5m²+60×2m+60×3

=300m²+120m+180

Therefore the factorization that represent the months and monthly deposit is: 60(5m²+2m+3).

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Answer: D

Step-by-step explanation:

Answer: 95 degrees

Step-by-step explanation:

Answer:

You have to add 1.5 to each input number to find its corresponding output number.

Answer:

Becky is 7 years old.

Step-by-step explanation:

Let b - Becky's age

Equation - 3b = 21

Divide both size by 3 to isolate the variable.

21/3 is 7.

If Johnny is 21 years old he is three times as old as Becky then age of Becky is 7 years.

Two or more expressions with an Equal sign is called as Equation.

Given that Johnny is 21 years old

Johnny is three times as old as Becky.

We have to find the age of Becky.

Let x be the age of Becky.

As Johnny is three times as old as Becky.

We can write the equation as below

21=3x

Divide both sides by 3

7=x

Hence, if Johnny is 21 years old he is three times as old as Becky then age of Becky is 7 years.

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Answer: Darkness

Step-by-step explanation: If there is more darkness you will be able to see less so ya

Hi!

We want to solve for [tex]b[/tex]

Given:

[tex]a=\sqrt{b+6}[/tex]

Square both sides:

[tex]a^2=\sqrt{b+6} ^2[/tex]

Simplify:

[tex]a^2=b+6[/tex]

Subtract [tex]6[/tex] from both sides:

[tex]a^2-6=b+6-6[/tex]

Simplify:

[tex]a^2-6=b[/tex]

Flip:

[tex]b=a^2-6[/tex]

Hence, [tex]b[/tex] is the subject of the formula.

Answer:

Part A: x = -39/4 or -9.75

Part B: y = 1/2 or .5

Step-by-step explanation:

Part C: Multiply the bottom equation by 2, obtaining 4x + 10y = -34. Subtract the top equation (4x + 4y = -37) from this equation, obtaining 6y = 3. Solving this, y = 1/2

(y = .5). Substitute this value of y into the equation 4x + 4y = -37, and then solve for x:

4x + 4(1/2) = -37

4x + 2 = -37

4x = -39, so x = -39/4 or -9.75

Answer:

18.4 kilograms per class.

Step-by-step explanation:

Since each class recycled the same amount, we divide the total (36.8 kilograms) by the number of classes (2). 36.8/2 = 18.4 This means that each class recycled 18.4 kilograms of paper.

Answer:

Putting all the x's to one side.

Step-by-step explanation:

By doing this, you would get:

10 = 2.5x

so,

4 = x

Answer:

We subtract 5x from both sides

Step-by-step explanation:

Step 1:  Subtract 5x from both sides

[tex]5x + 10 = 7.5x[/tex]

[tex]10 + 5x - 5x = 7.5x - 5x[/tex]

[tex]10 = 2.5x[/tex]

Step 2:  Divide both sides by 2.5

[tex]\frac{10}{2.5} = \frac{2.5x}{2.5}[/tex]

[tex]4 = x[/tex]

Answer:  We subtract 5x from both sides

Answer:

D) 18 freshman, 18 sophmores, 30 juniors, 30 seniors

Step-by-step explanation:

ratio given:

320 : 300 : 500 : 510

320 = 300 and 500 = 510

therefore ratio of 300 : 300 : 500 : 500

Ratio of 300 : 500 = 18 : 30

18 : 18 : 30 : 30

Answer:

The last one

Step-by-step explanation:

You just have to find the percentage of each

First find the total

300+320+500+510=1630

1)freshman: (320÷1630)×100

2) sophomore:(300÷1630)×100

3) juniors:(500÷1630)×100

4)seniors:(510÷1630)×100

Answer:

169 cm²

Step-by-step explanation:

Answer:

54 degrees

Step-by-step explanation:

21/36 <- divide 21 by 36 first

=0.58333

Around 54 degrees

Answer:

It’s b

Step-by-step explanation:

Answer:

375 m

Step-by-step explanation:

25 x 15 =

375

Answer:

$57.93

Step-by-step explanation:

14 x 12 = 168

168/2.9

The values of a and b are 33% and 42.7% respectively.

Given:

The number of students that like blue uniform is only as 32,

The number of students that like gold uniform is only as 25,

The number of students that like blue and gold uniforms is 12

The number of students that like neither blue nor gold uniform as 6.

Then, the total number of students interviewed are 75 students.

The relative frequency of the students who like blue is 25, therefore,

25/75= 1/3= 0.33

= 33%

The relative frequency of the students that like blue but not gold is 32, therefore,

32/75= 0.427

=42.7%

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Answer:

y = - 2x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3 ) and (x₂, y₂ ) = (1, 1 )

m = [tex]\frac{1-3}{1-0}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - 2x + 3 ← equation of line

Answer:

B

Step-by-step explanation:

The questions says that the graph is shifted down 7 units, which means it will affect the y-intercept.

Remember: If it's shifted up, it's positive & if it's shifted down, it's negative.

Answer:

B

Step-by-step explanation:

f(x)=9x

g(x)=9^x-7

if shifted down its negative ,if shifted up its positive.

Answer:

75.4

Step-by-step explanation:

S = r^2 * alpha * pi

where alpha is central angle = 135

S = 8^2 * 135/360 * pi = 12 * pi ~ 75.4

Answer:

7 2/5 and/or -37/5

Step-by-step explanation:

It can also be 7.04 also

Answer:

480

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

3+4 as the denoninators are the same

Answer:

[tex]\Longrightarrow: \boxed{\sf{\dfrac{7}{k} }}[/tex]

Step-by-step explanation:

You have to find the numerator number by adding it to the denominator.

[tex]:\Longrightarrow \sf{\dfrac{3}{k}+\dfrac{4}{k}=\dfrac{?}{k} }[/tex]

[tex]\Longrightarrow: \sf{\dfrac{3+4}{k}}[/tex]

First, add the numbers from left to right.

[tex]\sf{\dfrac{3+4}{k}=\boxed{\sf{\dfrac{7}{k}}}[/tex]

I hope this helps, let me know if you have any questions.

Answer:

Step-by-step explanation: