A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants of a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use (pie=3.14).

Answer:

bsqaure +csqaure =bsqaure

Step-by-step explanation:

A - the sum of the numbers is 5

[tex]A=\{(1,4),(4,1),(2,3),(3,2)\}\\|A|=4\Rightarrow \text{C}[/tex]

Answer:

There are no solutions to the system because the equations represent parallel lines

Step-by-step explanation:

If you get a solution 0 =12

This is never true, so that means there are no solutions.

The lines are parallel.

If you get 2=2, you will have infinite solutions because they are the same line

Answer:

im going to say c is the answer to this question

Answer: C

Step-by-step explanation:

Answer:

The answer is A.) u < 200

next one is B.) u > 200

The alternative hypothesis in your testing would be: u < 20; u > 200.

An alternative hypothesis can be defined as a statement in statistical inference which is used in contradictory form against what is stated in the null hypothesis.

Alternative hypothesis is the alternative t a null hypothesis in hypothesis testing.

Therefore, the alternative hypothesis in your testing would be: u < 20; u > 200.

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If x varies directly with y, then :

●  Increase in x results in increase of y

●  Decrease in x results in decrease of y

●  It is represented by : x ∝ y

[tex]\mathsf{\bigstar\;\;If\;x\;varies\;directly\;with\;y\;then : \large\boxed{\mathsf{\dfrac{x_1}{x_2} = \dfrac{y_1}{y_2}}}}[/tex]

Here : x₁ = 6 and y₁ = 15 and x₂ = x₂ and y₂ = 20

Substituting the values we get :

[tex]\mathsf{\implies \dfrac{6}{x_2} = \dfrac{15}{20}}[/tex]

[tex]\mathsf{\implies x_2 = \dfrac{20 \times 6}{15}}[/tex]

[tex]\mathsf{\implies x_2 = 8}[/tex]

Answer : x = 8 when y = 20

Answer:

x = 8

Step-by-step explanation:

Given that x varies directly as y then the equation relating them is

x = ky ← k is the constant of variation

To find k use the condition x = 6 when y = 15

k = [tex]\frac{x}{y}[/tex] = [tex]\frac{6}{15}[/tex] = 0.4

x = 0.4y ← equation of variation

When y = 20, then

x = 0.4 × 20 = 8

[tex]A=\{1,3,5,\ldots,99\}\\B=\{50,55,\ldots,150\}\\\\A\cap B=\{55,65,75,85,95\}[/tex]

Answer:

[tex]A\bigcap B=\left \{ 55,65,75,85,95 \right \}[/tex]

Step-by-step explanation:

Set A contains odd numbers between 0 and 100.

So, the elements in set A are as, Set A[tex]=\left \{ 1,3,5,7,9,11,13,15,...99 \right \}[/tex]

Set B contains the numbers between 50 and 150, that are evenly divisible by 5.

So, the elements in set B are are as, Set B

[tex]=\left \{ 55,60,65,70,75,80,85,90,... 145\right \}[/tex]

Now, we need to find [tex]A\bigcap B[/tex]

To find  [tex]A\bigcap B[/tex] , we need to find the common elements in Set A and Set B.

The common elements in Set A and Set B is [tex]\left \{  55,65,75,85,95 \right \}[/tex]

So, [tex]A\bigcap B=\left \{ 55,65,75,85,95 \right \}[/tex]

Answer:

The surface area is [tex]SA=384\ mm^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the cube is equal to

[tex]SA=6s^{2}[/tex]

we have

[tex]s=8\ mm[/tex]

substitute

[tex]SA=6(8)^{2}[/tex]

[tex]SA=384\ mm^{2}[/tex]

Answer:

Is the graph shown the initial triangle, or the translated one?

Step-by-step explanation:

ANSWER

461.7 yd²

EXPLANATION

The shaded region represents a sector.

The area of the sector is a fraction of the area of the whole circle.

Area of sector

[tex] = \frac{angle \: \: of \:sector }{360 \degree} \times \pi {r}^{2} [/tex]

We substitute the angle of the sector and the radius of the circle to obtain:

[tex] = \frac{167 \degree}{360 \degree} \times \pi \times {17.8}^{2} [/tex]

[tex] = 461.7 {yd}^{2} [/tex]

Therefore the area of the shaded region to the nearest tenth is 461.7 square yards.

Answer:

Area of shaded sector = 461.5 yd²

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

To find the area of given circle

Here r = 17.8 yd

Area = πr²

 = 3.14 * 17.8²

 = 3.14 * 316.84

 = 994.8776 yd²

To find the area of shaded region

Central angle of sector = 167°

Area of sector = (167/360) * area of circle

 =  (167/360) *994.8776

 = 461.52 ≈ 461.5 yd²

Answer:

mirena started at sea level, dove down 15 feet then rose up 6 feet

Step-by-step explanation:

she starts at zero the goes up -15 feef and then up 6 feet

Answer:

Morena started at sea level, dove down 15 feet, then rose up 6 feet.

Step-by-step explanation:

The expression is composed by three values. The first value indicates the starting point; which is 0, meaning sea level. The second component is -15, this indicates that Morena dove 15 feet below sea level, so she dove down. The third component is 6, this indicate that she drove up 6 feet, so she rose up. The position of Morena should be at 9 feet below sea level. The equation should be:

X = 0 + (-15) + 6

X = 0 - 15 + 6

X = -15 + 6

X = -9 down sea level

X means the Morena's postion

Answer:

( - [tex]\frac{1}{3}[/tex], [tex]\frac{3}{4}[/tex] )

Step-by-step explanation:

Given the 2 equations

9x + 8y = 3 → (1)

6x - 12y = - 11 → (2)

To eliminate the y- term multiply (1) by 1.5

13.5x + 12y = 4.5 → (3)

Add (2) and (3) term by term

(6x + 13.5x) + (- 12y + 12y) = (- 11 + 4.5)

19.5x = - 6.5 ( divide both sides by 19.5 )

x = [tex]\frac{-6.5}{19.5}[/tex] = - [tex]\frac{1}{3}[/tex]

Substitute this value into either of the 2 equations and solve for y

Using (1), then

- 3 + 8y = 3 ( add 3 to both sides )

8y = 6 ( divide both sides by 8 )

y = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

Solution is (- [tex]\frac{1}{3}[/tex], [tex]\frac{3}{4}[/tex] )

Answer:

  A.  4.20% compounded quarterly

Step-by-step explanation:

The effective annual multiplier on an account with annual interest rate r compounded n times per year is ...

  (1 +r/n)^n

When doing multiple evaluations of the same expression, it is convenient to let a spreadsheet or calculator do them from a list of inputs. In the attached, we round the result to 4 decimal places to make comparison easier.

The highest effective rate is 4.2% compounded 4 times per year.

____

Example calculation

  (1 +0.042/4)^4 = 1.0105^4 = 1.0426661426550625 ≈ 1.0427

Answer:

A) Account 1: Interest is compounded quarterly at an annual rate of 4.20%

Answer:

2x+5=3x-3

Step-by-step explanation:

The larger number is represented by X=5, and that number plus x would be 2x+5. The sum of those is 3 less than 3 times x, which is shown by 3x-3. So, 2x+5=3x-3

Answer:

The numbers are 8 and 13. Hopefully that can help with the equation.

Step-by-step explanation:

Answer: 24%

Step-by-step explanation:

2610+8120 = The undergraduates and graduates combined.

That is 10730. You are figuring out the probability the student is a graduate when those two graduates are combined, because that is all the data given. So you would do 2610/10730 in your calculator, resulting in 24.324324324%. As it says rounded to the nearest percent in parentheses, it has to round to the whole number, 24%, and .3 rounds down.

Answer:

the minimum value is 1/2x^2+4x+15/2 (write down the work below)

Step-by-step explanation:

f(x)=1/2*(x+3)*(x+5)=0

multiply the parenthesis by  1/2

(1/2x+3/2)*(x+5)

multiply the parenthesis

1/2x^2+5/2x+3/2x+15/2

calculate the equation

1/2x^2+4x+15/2 is you're answer  

Answer:

Explanation:

When 4 people are chosen at random, the probability that exactly 3 of them favor the new building project may be thought as four cases:

- the first one is against and the other three are in favor

- the second one is against and the other three are in favor

- the third one is against and the other three are in favor

- the fourth one is against and the other three are in favor.

Each one of those probabilities are equal to:

          ↑                          ↑

      one against          three in favor

Since, there are four equal results: 4 × 0.09611875 = 0.384475

Rounded to 2 significant digits that is 0.38.

The probability that exactly 3 out of 4 people randomly selected from a poll, where 65% of people are in favor of a certain building project, are also in favor of it is approximately 0.3835 or 38.35%.

This question is about the calculation of probability related to a poll result. To calculate the probability that exactly 3 of 4 randomly chosen people favor the new building project, we should consider this as a binomial probability problem, because each person either supports the project or not, and each person is independent of the others. Accordingly, the probability that exactly 3 out of 4 people are in favor is given by the formula:

P(X=3)=C(4,3)*(0.65)^3*(1-0.65)^(4-3)=4*(0.65)^3*(0.35)=(4*0.2746*0.35)=0.3835

So, the probability that exactly 3 of them favor the new building project is approximately 0.3835 or 38.35%.

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Answer:

  2 raisins

Step-by-step explanation:

The mean is calculated in the usual way: the sum divided by the number of numbers.

  mean = (5 +9 +5 +5 +7 +11)/6 = 7

The deviations are the differences from the mean:

  deviation = {5, 9, 5, 5, 7, 11} -7 = {-2, 2, -2, -2, 0, 4}

and the absolute deviation is the absolute value of these numbers:

  absolute deviation = {2, 2, 2, 2, 0, 4}

The mean absolute deviation (MAD) is the average of these values:

  (2 +2 +2 +2 +0 +4)/6 = 2

The mean absolute deviation is 2.

_____

It is generally convenient to let technology do the computation. A spreadsheet or graphing calculator can do this easily.

Answer:

(-) $29.26 per thousand for a 3-year 3.4% loan

(a) $5,240

(b) $153.32

(c) $279.52

Step-by-step explanation:

• Payment per thousand

The payment amount can be computed from the formula ...

A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount, r is the annual rate, n is the number of payments per year, and t is the number of years.

For a $1000 3-year loan at 3.4%, this evaluates to ...

A = 1000(0.034/12)/(1 -(1 +0.034/12)^(-12·3)) ≈ $29.26

The monthly car payment per $1000 borrowed is $29.26.

__

• Rudy's trade-in allowance and down payment will reduce the amount he finances to ...

$10,240 -3000 -2000 = $5,240

__

• $5,240 = 5.24 × $1000, so Rudy's payment will be ...

5.24 × $29.26 = $153.32

__

• The amount of interest Rudy pays is the difference between the amount paid back and the amount of the loan.

(36 mo)×($153.32/mo) - 5240 = $279.52

Monthly Car Loan Payment Per $1000 Borrowed is $29.26

(a) money he will borrow for loan = $ 5240

(b) monthly auto payment = $ 153.32

(c) the total amount of interest he will pay is $279.52

(d) Total payment for car= $ 10,519.52

Given Information :

We find out the monthly car loan payment for every $1000 borrowed.

Lets use monthly payment formula

[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }[/tex]

Where P is the loan amount.

r is the rate of interest and t is the number of years

n is the period

P=1000

Given that  3-year auto loan at 3.4% APR.

t=3, r= 3.4%= 0.034, n=12

Substitute all the values and calculate the monthly loan

[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }\\A=\frac{1000\cdot \frac{0.034}{12} }{1-(1+\frac{0.034}{12})^{-12\cdot 3} }\\A=\frac{1000\cdot \frac{0.034}{12}}{1-\left(\frac{0.034}{12}+1\right)^{-36}}\\A=\frac{2.83333\dots }{1-1.00283\dots ^{-36}}\\A=29.25782[/tex]

Monthly Car Loan Payment Per $1000 Borrowed is $29.26

The cost of car is  $10,240. Allowance = 3000 and down payment = 2000

(a) Auto loan = cost of car - allowance - down payment

[tex]Auto \; loan = 10240 - 3000 -2000=5240[/tex]

(b) Monthly Car Loan Payment Per $1000 Borrowed is $29.26

Monthly car loan payment for $5240 is

[tex]\frac{5240}{1000} * 29.26=153.32[/tex]

(c) first we find out the total loan amount paid in 3 years (36 months)

[tex]36 \cdot 153.3224=5,519.52[/tex]

To find the amount of interest he pay , we subtract the loan amount

[tex]5,519.52-5240=279.52[/tex]

the total amount of interest he will pay is $279.52

(d) Total payment for car = down payment +total loan amount paid

Total payment for car =[tex]5000+5519.52=10,519.52[/tex]

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Answer:

The formula for circumference: 2rpi

PB = r = 29m

The circumference of circle P is:

2(29)pi

=58pi

Answer:

The circumference of circle  =58π m

Step-by-step explanation:

Points to remember

Circumference of circle = 2πr

Where r is the radius of the circle

From the figure we can see a circle with radius PB = 29 m

To find the circumference of circle

Here r = 29 m

Circumference = 2πr

 = 2 * π * 29

 = 58π m

Therefore the  circumference of circle  =58π m

Answer:

Easy its D

Step-by-step explanation:

remember he does not want to pass 2,000

1,400 - 400 = 1,000

1,000 + 1,200 = 2,200

Answer:

No; 1,200 will cause him to exceed 2,000.

Step-by-step explanation:

Given that Brett wants to stay within his daily calorie limit of 2,000 calories, and he has already consumed 1,400 calories and burned 400 calories at the gym, the maximum additional calories he can consume without exceeding his limit is:

2,000 (daily limit) - 1,400 (already consumed) - 400 (burned at the gym) = 1,000 calories

So, Brett can consume a maximum of 1000 more calories to stay within his daily limit of 2,000 calories. Therefore, 1,200 calories is not a viable solution because it exceeds his limit by 200 calories.

The correct answer is:

No; 1,200 will cause him to exceed 2,000 calories.

Hope this helps :))

Answer:

√129

Step-by-step explanation:

The distance formula between two points is:

d² = (x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²

Plugging in:

d² = (4 − (-4))² + (-1 − 7)² + (-2 − (-3))²

d² = 8² + 8² + 1²

d² = 129

d = √129

Answer:

  Q

Step-by-step explanation:

Each line from a vertex to the midpoint of the opposite side is called a median. The point where the medians intersect, point Q, is the centroid.

The centroid of ΔABC is point Q.

Answer:

Q

Step-by-step explanation:

We are given that L,M and N are midpoints of sides AC,AB and BC of a triangle.

We have to find the centroid of triangle ABC.

Centroid of triangle : It is defined as the intersection point of medians of triangle.

Medians of triangle ABC are BL,CN and  AM.

Medians BL, CN and AM are intersect at point Q.

Therefore, centroid of triangle ABC is Q by definition of centroid of triangle.

Answer:Q

Answer:

  x² +4x +4

Step-by-step explanation:

Matching the expressions, you see you have y=2. Put 2 where y is and simplify.

  (x +2)² = x² +2x(2) +(2)² = x² +4x +4

ANSWER

[tex] {x}^{2} + 4x + 4[/tex]

EXPLANATION

We want to expand:

[tex](x { + 2)}^{2} [/tex]

Using the identity:

[tex] {( x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]

We put y=2 into the identity to obtain;

[tex] {( x + 2)}^{2} = {x}^{2} + 2x(2) + {2}^{2} [/tex]

This simplifies to:

[tex]{( x + 2)}^{2} = {x}^{2} +4x + 4[/tex]

Answer:

  A.  4

Step-by-step explanation:

Pick two terms with consecutive x-values and find their ratio. That is the common ratio.

 for x = 2 and x = 1,

 r = 32/8 = 4

The common ratio is 4.

_____

You can check other pairs of terms if you want to confirm.

  r = 2048/512 = 4 . . . . for x=5 and 4.

Answer:

Hi!

The correct answer is A. 4.

Step-by-step explanation:

To find the common ratio of an geometric sequence of set A = {a₁, a₂, a₃, ..., aₙ} you can use the formula:

[tex]r=\frac{a_{i+1}}{a_i}[/tex]

If you pick x = 4 to find the ratio, you have to replace in the formula:

[tex]r=\frac{a_{4+1}}{a_4} =\frac{a_{5}}{a_4}[/tex] // replace the values

[tex]r= \frac{2048}{512} = 4[/tex]

The common ratio of this geometric sequence is 4.

Answer: The first box is circle and second box is rectangle.

Step-by-step explanation:

If you are asking about the shape of the cross section for a right circular cylinder, that is the case. A parabola or triangle can't be sliced so the cross section is parallel or perpendicular to the base.

If the cross section is parallel to the base, it is a circle.

If the cross section is perpendicular to the base, it is a rectangle.

Answer:

The answer should be. ( 7,2 )

Answer: second option.

Step-by-step explanation:

Given the transformation [tex]T:(x,y)[/tex]→[tex](x+3,y+1)[/tex]

You must substitute the x-coordinate of the point B [tex]x=4[/tex]) and the y-coordinate of the point B [tex]y=1[/tex]) into [tex](x+3,y+1)[/tex] to find the x-coordinate and the y-coordinate of the image of the point B.

Therefore, the image of B(4,1) is the following:

[tex](x+3,y+1)=(4+3,1+1)=(7,2)[/tex]

You can observe that this matches with the second option.

Given that the raffle prize is to be divided equally, the amount of money each person will receive will be equal to the total raffle prize (14x^(2)/15) divided by the number of people (7x). Thus, we get:

(14x^(2)/15) / 7x

= (14x^(2)/15) * (1/7x)

= 14x^(2)/15*7x

= 14x^(2)/105x

= 2x/15 (Divide both the numerator and denominator by 7x)

Therefor, each person would receive 2x/15 dollars.

If you know how to cancel when dealing with fractions, you can get to this step much easier, however this way also works. The idea with cancelling would be that when you had (14x^(2)/15) / 7x, you would recognise that 14x^2 may be divided by 7x straight away to get 2x. Then you would have 2x/15 as your answer.

ANSWER

[tex]y = 3x - 17[/tex]

EXPLANATION

The given line has equation;

[tex]y - 3x = 2[/tex]

We solve for y to get;

[tex]y = 3x + 2[/tex]

The slope of this line is 3.

Since tyheline is parallel to this line, it also has slope 3.

The line passes through (6,1), we can use the slope intercept form,

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the point and the slope to get;

[tex]y - 1 = 3(x - 6)[/tex]

[tex]y = 3x - 18 + 1[/tex]

[tex]y = 3x - 17[/tex]

Answer: First Option

[tex]y = 3x - 17[/tex]

Step-by-step explanation:

For a linear equation of the form

[tex]y = mx + b[/tex] the slope of the line is the constant m.

In this case we have the line

[tex]y-3x=2\\y=3x +2[/tex]

Then the slope is [tex]m=3[/tex]

If the equation of the line sought is parallel to the line [tex]y=3x +2[/tex] then by definition both lines have the same slope m = 3

Therefore the equation of the line sought is:

[tex]y = 3x + b[/tex]

Where b is a constant that represents the intersection of the line with the y axis.

[tex]b = y_0 -3(x_0)[/tex]

Where [tex](x_0, y_0)[/tex] is a point belonging to the line sought.

In this case the point is (6, 1)

So

[tex]b =1 -3(6)[/tex]

[tex]b =-17[/tex]

Finally the equation is:

[tex]y = 3x - 17[/tex]

Answer:

56

Step-by-step explanation:

Assumption: You don't watch the same movie twice

I will explain in 2 ways

METHOD 1: Multiplication Rule

On Saturday, you have 8 choices. On Sunday, you have 7 choices because u have already watched 1 movie on Saturday

8×7 = 56

METHOD 2: Permutation

Since 'order' is important, i.e. watching movie A on Saturday & B on Sunday is different from watching B on Saturday & A on Sunday, so it's

8P2 = 56

Using the permutation formula, it is found that you can choose a movie to see this Saturday and one to see this Sunday in 56 ways.

The order in which the movies are chosen is important, as they are respective to different days, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 2 movies will be chosen from a set of 8, hence:

[tex]P_{(8,2)} = \frac{8!}{6!} = 8 \times 7 = 56[/tex]

Hence, you can choose a movie to see this Saturday and one to see this Sunday in 56 ways.

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