A circle with a radius of 10 inches is placed inside a square with a side length of 20 inches. Find the area of the circle.

a. 143
b. 400
c. 413
d. 314

[tex] \frac{m}{n} . \frac{n}{p} \div \frac{p}{q} \\ = \frac{m}{p} \div \frac{p}{q} \\ = \frac{m}{p} . \frac{q}{p} \\ = \frac{mq}{ {p}^{2} } [/tex]

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

The correct answer is first option

mq/p²

Step-by-step explanation:

It is given that, (m/n) * (n/p) ÷ (p/q)

To find the simplified form of given expression

Let  (m/n) * (n/p) ÷ (p/q) can be written as,

(m/n) * (n/p) ÷ (p/q) =  (m/n) * (n/p) * (q/p)

 = (m * n * q)/(n * p * q)

 = (m * q)/(p * p)

 = mq/p²

Therefore the correct answer is mq/p²

To work out the central angle, you just re-arrange the equation for the length of an arc:

Equation for length of an arc:

[tex]\frac{angle}{360}[/tex] × [tex]diameter[/tex] × π = [tex]length of arc[/tex]

We can arrange this to work out the central angle, q.  But first, lets substitute in all of the values that we know:

angle = q

diameter = 5 x 2 = 10 ft

length of arc = 7

[Substitute in]

[tex]\frac{q}{360}[/tex] × [tex]10[/tex]π = [tex]7[/tex]       (Now just rearrange for q)

[tex]\frac{q}{360}[/tex] = [tex]\frac{7}{10\pi }[/tex]     (multiply both sides by 360 to get q)

[tex]q[/tex] = [tex]\frac{7}{10\pi }[/tex] × [tex]360[/tex]  (now just simplify)

[tex]q[/tex] = [tex]\frac{252}{\pi }[/tex]

   = [tex]80.214[/tex]   (rounded to 3 decimal places)

______________________________

Therefore:

The equation that gives you ange q is:

[tex]q[/tex] = [tex]\frac{length.of.arc}{diamater.times.\pi }[/tex] × [tex]360[/tex]

and q = 80.214  when all of the values are substituted in.

Answer:

B q=7/5

Step-by-step explanation:

Well Q=s/r and they said a Radius of 5 Which puts 5 at the bottom.

Then an arc length of 7 Which =S. so q=7/5

to get the equation of a straight line, all we need is two points, hmmm say this line runs over (0 , -2) and (3 , 0), so let's use those.

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-0}{0-3}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{2}{3}(x-3)\implies y=\cfrac{2}{3}x-2[/tex]

Answer:

See explanation

Step-by-step explanation:

The distance formula is given by:

[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

We want to find the distance between (a,b) and (x,y).

The center of the habitat is missing in the question.

Assuming the center is (a,b) where a and b are real numbers, then we can use the distance formula to obtain:

[tex] d = \sqrt{(x - a)^{2} + {(y - b)}^{2} } [/tex]

For instance if the center of your habitat us (2,-1), then

[tex]d = \sqrt{(x - 2)^{2} + {(y + 1)}^{2} } [/tex]

Answer:

42.5 %

Step-by-step explanation:

You would multiply the probability of the couple having a girl and the test predicting it’s a girl.

0.85 x 0.5= 0.425 = 42.5%

Answer:C

Step-by-step explanation:4x _2y =64 because 8×8= 64

For this case we must find an equation equivalent to:

[tex]\frac {1} {4} x- \frac {1} {2} y = 8[/tex]

We add [tex]\frac {1} {2}[/tex] and on both sides of the equation:

[tex]\frac {1} {4} x = 8 + \frac {1} {2}y[/tex]

We multiply by 4 on both sides of the equation:

[tex]x = 32 + \frac {4} {2}y\\x = 32 + 2y[/tex]

Multiplying by 2 on both sides of the equation:

[tex]2x = 64 + 4y\\2x-4y = 64[/tex]

Answer:

Option B

TW x WU = CW x VW

Fill in the known values:

WU = TU - TW = 21.2 - 14.6 = 6.6

14.6 x 6.6 = 6 x VW

Simplify:

96.36 = 6VW

Divide both sides by 6:

VW = 96.36 / 6

VW = 16.06

Round to one decimal place:

VW = 16.1

The answer is D>

Answer:

D.) 16.1

Step-by-step explanation:

I got it correct on founders edtell

Answer:

its 2 4/9

Step-by-step explanation:

because i did trial and error, i converted all the fractions into decimals until one of the conversions was equal to 2.444444444444...infinite

[tex]2 \frac{4}{9}[/tex] would be the correct answer.

This is not 2.4. This is "2.44444..." because of the line over the 4 after the decimal place (this applies for any decimal such as [tex]2.48\overline{47} = 2.484747474747...[/tex]).

In general, the over-lined part can be written as a fraction of 9 (99, 999, 9999, etc. if the over-lined part has more than one digit, in increasing order of digits), which is why [tex]2 \frac{4}{9}[/tex] is the correct answer.

Answer:

[tex]\large\boxed{(2b+3)\times(5b-1)\times(5b+1)}[/tex]

Step-by-step explanation:

The formula of a volume of a rectangular box:

[tex]V=lwh[/tex]

l - lenght

w - width

h - height

[tex]V=50b^3+75b^2-2b-3=25b^2(2b+3)-1(2b+3)\\\\=(2b+3)(25b^2-1)=(2b+3)(5^2b^2-1^2)\\\\=(2b+3)\bigg((5b)^2-1^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2b+3)(5b-1)(5b+1)[/tex]

Therefore the dinemsions of thisp prism are:

[tex](2b+3)\times(5b-1)\times(5b+1)[/tex]

Answer:

the one with ++-

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

Where P = pages and x = minutes, your rule is as follows:

[tex]P=\frac{10}{3} x[/tex]

Simply plug in your last minute value to find your last page value.

[tex]P=\frac{10}{3} (72)\\P=240[/tex]

Answer:

1180 cans

Step-by-step explanation:

Heywards collected = 980 cans

Ballards collected 200 fewer cans than Heywards.

Total cans collected by Ballard = ?

Therefore the sum of Heywards collected cans and Ballards fewer cans will give us the total cans collected by Ballard.

=980+200

=1180

Ballard collected 1180 cans....

Answer:

a. [tex]c(x) = 2x + 105[/tex]

b.  [tex]c(50) =\$205[/tex]

Step-by-step explanation:

The variable cost of $ 2 implies that for each manufactured calculator the total cost increases $ 2.

The fixed cost of $ 105 implies that regardless of the number of manufactured calculators there will always be a cost of $ 105.

If we call x the number of manufactured calculators then the total cost c(x) will be:

[tex]c(x) = 2x + 105[/tex]

Then, the cost of manufactured 50 calculators a day is:

[tex]c(50) = 2(50) + 105[/tex]

[tex]c(50) = 100 + 105[/tex]

[tex]c(50) =\$205[/tex]

Answer:

The length is 16.1 ft and the width is 4.7 ft

Step-by-step explanation:

Let

x -----> the total length of the tables

y -----> the width of the tables

we know that

The area is equal to

[tex]A=xy[/tex]

[tex]A=75\ ft^{2}[/tex]

so

[tex]75=xy[/tex] -----> equation A

[tex]x=3y+2[/tex] -----> equation B

substitute equation B in equation A

[tex]75=(3y+2)y[/tex]

[tex]3y^{2} +2y-75=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]y=4.7\ ft[/tex]

Find the value of x

[tex]x=3(4.7)+2=16.1\ ft[/tex]

therefore

The length is 16.1 ft and the width is 4.7 ft

Answer:

The length and width of the serving table is 16.1 ft and 4.7 ft respectively.

Step-by-step explanation:

Consider the provided information.

Let the width of the table is x and length of the table is y.

The total length of the tables will be two more than three times the width.

This can be written as:

y = 2+3x

The area of the table is 75 ²ft

The area of rectangle is:

length × width = Area

Substitute width = x and length = 2+3x in above formula.

(x)(2+3x) = 75

2x+3x²-75 = 0

3x²+2x-75 = 0

The above equation is in the form of ax²+bx+c=0. Now use the quadratic formula to find the root of the equation.

[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute a=3, b=2 and c=-75 in above formula.

[tex]x_{1,2}=\frac{-2\pm\sqrt{2^2-4(3)(-75)}}{2(3)}[/tex]

[tex]x_{1,2}=\frac{-2\pm\sqrt{904}}{6}[/tex]

[tex]x_{1,2}=\frac{-2\pm30.07}{6}[/tex]

[tex]x_{1}=\frac{-2+30.07}{6}[/tex]

Ignore the negative value of x as width should be a positive number.

[tex]x=4.7\ ft[/tex]

Now substitute the value of x in y = 2+3x.

y = 2+3(4.7)

y = 16.1 ft

Hence, the length and width of the serving table is 16.1 ft and 4.7 ft respectively.

Answer:

6

Step-by-step explanation:

[tex]-\frac{2}{3} x+9=\frac{4}{3} x-3\\\\[/tex]

First, multiply both sides by 3.

[tex]-2x+27=4x-9\\[/tex]

Next, combine like terms.

[tex]-2x+27=4x-9\\-2x+36=4x\\36=6x[/tex]

Solve for x.

[tex]36=6x\\6=x[/tex]

The value of "x" in the equation is 6.

To find the value of "x" in the equation -2/3x + 9 = 4/3x - 3, we need to isolate "x" on one side of the equation. Let's solve step-by-step:

Step 1: Get rid of fractions by multiplying all terms by the least common multiple (LCM) of the denominators, which is 3.

3 * (-2/3x) + 3 * 9 = 3 * (4/3x) - 3 * 3

Simplify:

-2x + 27 = 4x - 9

Step 2: Move "4x" and "27" terms to one side and " -2x" and " -9" terms to the other side.

Add 2x to both sides:

-2x + 2x + 27 = 4x - 9 + 2x

Simplify:

27 = 6x - 9

Step 3: Move the constant term " -9" to the other side of the equation by adding 9 to both sides:

27 + 9 = 6x - 9 + 9

Simplify:

36 = 6x

Step 4: Solve for "x" by dividing both sides by 6:

x = 36 / 6

x = 6

The value of "x" in the equation is 6.

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Answer:

40°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for third angle

third angle = 180° - (90 + 50)° = 180° - 140° = 40°

Answer: B. 40

Step-by-step explanation: A triangle’s angles will always add up to 180 degrees. Add the 2 angles that are given. 90 + 50 = 140. Subtract this number from 180. 180 - 140 = 40. The third angle is 40 degrees.

Answer:

0.7557

Step-by-step explanation:

In this question use the Table of Standard Normal Probabilities for Negative z-scores and the Table of Standard Normal Probabilities for Positive z-scores

Where z=2.27 NORMDIST(2.27)=0.9884 (read from table for positive z-scores)

Where z=-0.73 NORMDIST(-0.73)=0.2327 (read from table for negative z-scores)

You know P(-0.73<z<2.27)= 0.9884-0.2327=0.7557

The probability that P(–0.73 < z < 2.27) is 0.7557.

The z score is used to determine by how many standard deviations, the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation,n= sample\ size\\\\\\[/tex]

From the normal distribution table, P(-0.73 ≤ z ≤ 2.27) = P(z < 2.27) - P(z<-0.73) = 0.9884 - 0.2327 = 0.7557

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Answer:

The factored form of the equation is (x + 4)(x – 6) = 0.

Step-by-step explanation:

(x – 4)(x + 2) = 16

Foil the left side

x^2 +2x-4x-8 =16

Combine like terms

x^2 -2x-8 = 16

Subtract 16 from each side

x^2 -2x-8-16 =16-16

x^2 -2x-24 =0

Factor the left hand side

What two numbers multiply to -24 and add to -2

-6*4 =-24

-6+4 = -2

(x-6) (x+4) =0

Solving using the zero product property

x-6 =0   x+4=0

x=6        x=-4

Answer:

C: on ed

Step-by-step explanation:

Answer:

=20.0

Step-by-step explanation:

We can first find the value of the angle at B using the sine formula.

a/sine A=b/Sin B

9/sin 15=12/sin B

Sin B=(12 sin 15)/9

Sin B=0.345

B=20.18°

Therefore angle C =180-(15+20.18)

=144.82°

a/Sin A=c/Sin C

9/Sin 15=c/Sin 144.82

c=(9 sin 144.82)/sin15

=20.0

Step-by-step explanation:

It is impossible for a triangle to have side lengths of 4, √415, and 16.

The sum of the shortest two sides must be greater than the longest side.  However, 4 + 16 < √415.  

It is impossible to make a triangle with side lengths  4, √415, and 16 because the two side length of the triangle is always greater than the third length of the triangle.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have side lengths of a triangle.

As we know from the definition of the triangle the sum of the two side length of the triangle is always greater than the third length of the triangle.

Also, the sum of the interior angle of a triangle is 180 degrees.

As the three lengths are 4, √415, and 16

AB + BC < AC

Let suppose:

AB = 4 units

BC = 16 units

AC = √415 units

4 + 16 < √415

Thus, it is impossible to make a triangle with side lengths  4, √415, and 16.

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Answer:

9 is (2/9) of the way from A = 5 to B = 23.

Step-by-step explanation:

Note that there are 23-5, or 18, units separating 5 and 23.

2/9 of that distance is (2/9)(18), or 4.

Adding 4 to 5, we get 9.

9 is (2/9) of the way from A = 5 to B = 23.

If this is not clear, I'd suggest you draw this situation and prove to yourself that 9 is (2/9) of the way from A = 5 to B = 23.

Answer:

9

Step-by-step explanation:

The equation is A+K (B-A). So 5+ 2/9 (23-5) = 9

Answer:

26,250

Step-by-step explanation:

25,000 + 5% = 26,250

:) please mark Brainliest

The Smiths' new car purchase price before taxes cannot exceed $23,809.52 considering they have $25,000 and need to pay a 5% sales tax on the purchase.

To calculate the maximum purchase price of the new car before taxes that the Smiths can afford, we need to account for the 5% sales tax they will have to pay on top of the purchase price. Since the Smiths have saved $25,000, this is the total amount they have available to pay for the car including the sales tax.

To find the purchase price before tax, call this price 'P'. The total cost including the sales tax will be P + 0.05P (which is the sales tax). This total cost must not exceed $25,000. Therefore, we can set up the following equation:

1.05P <= $25,000

Divide both sides of the equation by 1.05 to isolate P:

P <= $25,000 / 1.05

P <= $23,809.52

So, the purchase price of the Smiths' new car before taxes cannot exceed $23,809.52.

Answer:

Yes, it is a function.

Step-by-step explanation:

Since each x-value is used only once, the relation is a function.

Yes, The relation represented in table is a function.

A relation between a set of inputs having one output each is called a function.

Given that;

The table is,

x |  5  10  15

y | 3    8    8

Now,

Clearly, Each inputs having one output in the table as;

⇒ f (5) = 3

⇒ f (10) = 8

⇒ f (15) = 8

So, The table represent the function.

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Answer:

the answer is 42.875

Step-by-step explanation:

3.5^3 = 42.875

Answer:

[tex]\large\boxed{V=42\dfrac{7}{8}\ ft^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cube:

[tex]V=a^3[/tex]

a - edge

We have

[tex]a=3\dfrac{1}{2}\ ft[/tex]

Convert to the improper fraction:

[tex]a=\dfrac{3\cdot2+1}{2}=\dfrac{7}{2}\ ft[/tex]

Substitute to the formula of a volume:

[tex]V=\left(\dfrac{7}{2}\right)^3=\dfrac{7^3}{2^3}=\dfrac{343}{8}=42\dfrac{7}{8}\ ft^3[/tex]

Answer:

Part 1) The ordered pair is (0,0)

Part 2) The ordered pair is (-2,-4)

Part 3) The ordered pair is (4,8)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a direct variation

[tex]y=2x[/tex]

Complete the ordered pairs

Part 1) we have (0,?)

For x=0

Substitute in the equation and solve for y

[tex]y=2(0)=0[/tex]

therefore

The ordered pair is (0,0)

Part 2) we have (-2,?)

For x=-2

Substitute in the equation and solve for y

[tex]y=2(-2)=-4[/tex]

therefore

The ordered pair is (-2,-4)

Part 3) we have (4,?)

For x=4

Substitute in the equation and solve for y

[tex]y=2(4)=8[/tex]

therefore

The ordered pair is (4,8)

Answer:

2x^4 - 9x^3 -8x^2 + 15x

Step-by-step explanation:

(x^2-5x)(2x^2+x-3) distribute first

2x^4

x^2 + x = x^3

5 * 2x^2 x= 10x^3

5x^1+1 = 5x^2

5 * 3x = 15x Put them all together

2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x Like terms

2x^4 + x^3 -10x^3 - 3x^2- 5x^2 + 15x Add similar terms

= 2x^4 + x^3 - 10x^3 - 8x^2 + 15x more adding terms

2x^4 - 9x^3 -8x^2 + 15x

Hope my answer has helped you, if not i'm sorry.

For this case we must multiply the following expression:

[tex](x ^ 2-5x) (2x ^ 2 + x-3)[/tex]

We apply distributive property term to term taking into account that:

[tex]+ * - = -\\- * - = +\\x ^ 2 * 2x ^ 2 + x ^ 2 * x-x ^ 2 * 3-5x * 2x ^ 2-5x * x + 5x * 3 =[/tex]

For powers of the same base, we place the same base and add the exponents:

[tex]2x ^ 4 + x ^ 3-3x ^ 2-10x ^ 3-5x ^ 2 + 15x =[/tex]

We add similar terms:

[tex]2x ^ 4-9x ^ 3-8x ^ 2 + 15x[/tex]

Answer:

OPTION D

[tex]2x ^ 4-9x ^ 3-8x ^ 2 + 15x[/tex]

Answer:

1-4x

Step-by-step explanation:

Answer:

Step-by-step explanation:

The product of four and a number x: 4 · x = 4x

One minus the product of four and a number x: 1 - 4x

Answer:

the solution set of n2 - 14n = -45 is {5, 9}

Step-by-step explanation:

We have the following equation: n^2 - 14n = -45

Rearrange:

n^2 - 14n +45 = 0

Factorizing:

(n-9)(n-5) = 0

Therefore, the solution set of n2 - 14n = -45 is {5, 9}

Answer:

Step-by-step explanation:

[tex]S = 1/2, 1, 3/2, 4, 5/2, 3, 7/2...\\a_n = \frac{n}{2}\\a_{15} = \frac{15}{2}[/tex]

Complementary angle add up to 90 degrees.

Angle A = x + 6

Angle B = x

They both add up to 90.

x + 6 + x = 90

2x + 6 = 90

2x = 90 - 6

2x = 84

x = 84/2

x = 42

Angle A = x + 6

Angle A = 42 + 6

Angle A = 48 degrees

Answer:

[tex]4x[/tex]

Step-by-step explanation:

We want to find the simplest rational exponent form of

[tex]\sqrt{x} \cdot 4\sqrt{x}[/tex]

Recall that: [tex]\sqrt{a}=a^{\frac{1}{2} }[/tex]

We rewrite the expression in the exponent form to get:

[tex]x^{\frac{1}{2}}\cdot 4x^{\frac{1}{2}[/tex]

We can regroup the product to get:

[tex]4 x^{\frac{1}{2}\cdot x^{\frac{1}{2}[/tex]

We apply the rule: [tex]a^m\cdot a^n=a6{m+n}[/tex] to get:

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{\frac{1}{2}+\frac{1}{2}}[/tex]

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{1}[/tex]

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4x[/tex]