Question 3
5 1
Divide 6 • 12

According to the question we have ,The area covered by the spotlight is 153.86 square feet. The correct option is c.

The diameter of a circle cuts through center whereas the radius extends from the center to the edges of the circle. A circle's diameter effectively splits the shape in half. The radius of a circle is the distance from the middle to any point on the edge. The diameter the radius are inversely proportional, or 2r=d2 r=d. A line connecting two points on either a circle is referred to as a chord.

We have the formula of Area of a circle: A = π\(r^2.\)

According to the question we have ,there is a spotlight above the center of the ground that surrounds a 7-foot-radius lit area.

A = π\(r^2\). = π * \(7^2\)

= 3.14 * 49 = 153.86 square feet.

So, the area covered by the spotlight is 153.86 square feet.

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Answer:

Throughout the clarification segment elsewhere here, the definition of it's concern is mentioned.

Step-by-step explanation:

Central theorem:

Statement:

If x would be any distribution of random sample 30 more wide with either a mean = \(\mu\)

standard deviation = \(\sigma\)

After which \(\bar{x}}\) would have had a roughly normal distribution which

mean = \(\mu\) and

default variance = \(\frac{\sigma}{\sqrt{n}}\)

The amount after 5 years on $100 using the compound interest is $122.

According to the question,

We have the following information:

Principal = $100

Interest Rate = 4%

Time= 5 years

We know that the following formula is used to find the total amount if there is compound interest:

Compound amount = \(P(1+\frac{r}{100})^{t}\) where P is the principal, r is interest rate and t is the time in years

(Note that there are different formulas for compound interest depending on how it is calculated.)

A = \(100(1+\frac{4}{100})^{5}\)

A = \(100(\frac{104}{100})^{5}\\100(1.04})^{5}\)

A = 100*1.22

A = $122

Hence, the amount after 5 years on $100 using the compound interest is $122.

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

XD is an emoticon commonly used to symbolize dying from laughter. It represents 2 closed eyes with the X and mouth with the D.

The solution of the equations is (-2, -1)

2x - 3y = -1

11x  - 9y = -13

Using elimination method let multiply the first equation by -3.

Therefore,

-6x + 9y = 3

11x - 9y = -13

5x = -10

x = -10 / 5

x = -2

let's find y as follows;

2(-2) - 3y = -1

-4 - 3y = -1

-3y = -1 + 4

-3y = 3

y = 3 / -3

y = -1

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Answer:

C = 70000 + 5000x + 900y

Step-by-step explanation:

You are paying

- $70,000 to keep the place running,

- $5000 to cabaret artist per performance, since x represents the number of performances by the cabaret artist per month, it is 5000x in a month

- $900 to jazz ensemble per hour, since y represents the number of hours of jazz per month, it is 900y in a month.

If you sum all the costs and set it to the C, you will get:

C = 70000 + 5000x + 900y

After evaluating the given expression, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d = -4

An Algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.t may contain one or more variables, which are symbols that represent unknown quantities or values that can vary.

Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships. For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".

The given expression is d3a2−(c+b), where a = -2, b = 3, c = -12, and d = -4. Substituting these values, we get:

d3a2−(c+b) = (-4)3(-2)² - (-12 + 3) = -434 - (-9) = -48 + 9 = -39

Therefore, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d=-4.

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Answer:

whats the problem

Step-by-step explanation:

Answer:

yup

Step-by-step explanation:

\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

1) Evaluating that expression

x – 9 = 2(x – 3) + 12​ Distributing

x-9=2x-6+12 Adding 9 and Subtracting 2x from both sides

x-2x=9-6+12 Combining like terms

-x=3+12

-x=15

x=-15

S={-15}

Answer:

Area = 50.24 feet^2

Step-by-step explanation:

radius = 4 feet

Area =?

\(Area =\pi r^2\\\\\)

Substitute values into the given equation

\(Area =3.14\times 4^2\\\\Area =3.14\times 16\\\\Area =50.24\:ft^2\)

Answer:

1/6

Step-by-step explanation:

i used a calculator

Answer:

  $4918

Step-by-step explanation:

You want the tax owed on $90,000 using the given tax rate table.

The tax is the sum of the amounts of tax due in each income range.

  tax = 0.0575(90,000 -17,000) +0.05(17,000 -5000) +0.03(5000 -3000) +0.02(3000)

  = 0.0575(90,000) -(17000(.0575 -.05) +5000(.05 -.03) +3000(.03 -.02))

  = 0.0575(90,000) -(127.50 +100 +30)

  = 5175 -257.50 = 4917.50

Rounded to the nearest dollar, the tax due is $4,918.

__

Additional comment

The tax will be the maximum of ...

You can compute them all and find the maximum, or you can choose the function applicable to the income amount. The result is the same.

<95141404393>

(a) Initial population of deer is 11

(b) Number of deer will became 600 in 24.5 years

(c) The maximum number of possible deer in park is 1001

      based on exponential function.

e^-x is known as an exponential function, it is a decreasing function because, as x increases e^-x decreases

given,   Population of deer after t years is

            P(t) =1001/(1+ 90e^-0.2t)

(a) For initial population we have to put t=0 years

         P(0)= 1001/(1+90 e^0)

                =  1001/(1+90)

                =   1001/91

                ≈    11

(b) Here given, number of deer is 600 we have to calculate t in years

          600 = 1001/(1+90e^-0.2t)

         1+90e^-0.2t = 1001/600

          90e^-0.2t =(1001/600) - 1

          90e^-0.2t =401/600 =0.668

           e^-0.2t = 0.668/90 = 0.0074

       taking ln(log with base e) both side we get

           ln(e^-0.2t)=ln(0.0074)

            -0.2t = -4.90

              t= -4.90/-0.2

              t= 24.53 years

(c)   We have to calculate number of possible deer in the park

              for the population to me maximum (1+90e^-0.2t) should be minimum, and the minimum value of (e^-0.2t),an will be 0(zer0),so    minimum value of (1+90e^-0.2t) will be 1

  Hence, The maximum possible value of deer in the park will be

             1001/1 = 1001

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Answer:

$42

Step-by-step explanation:

7/14=1/2 so he saved 1/2 of 84

The value of sin (α + β) is,

⇒ sin (α + β) = - 135/377

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Angle α in quadrant 3:

y = opposite = 21 and x = adjacent = 20

Then, hypotenuse = √( 21² + 20²)

                            = √ ( 441 + 400)

                            = sqrt( 881)

So, sin α = 21/√881

              = 21 × sqrt(881)/881

And, cos α = 20/sqrt(881) = 20sqrt(881) / 881

Since, Angle β in Quadrant 2:

Hence,  adjacent = -5 and hypotenuse = 13

Then, by Pythagorean,

y = opposite = 12

So, sin β = 12/13, cos β = -5/13

as given,

And, tan β = -13/12

Since, We know that;

sin (α + β) = sin α cos β + cos α sin β

               = 21/√881 × - 5/13 + 20/√881 × 12/13

               = 1/√881 (- 105/13 + 240/13)

               = - 1/√881 (135/13)

              = - 135/377

Hence, The value of sin (α + β) is,

sin (α + β) = - 135/377

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Answer:

y = -3x + 1

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be -3.

Plug in the slope and given point into y = mx + b

y = mx + b

-5 = -3(2) + b

-5 = -6 + b

1 = b

Then, plug in the slope and y intercept into y = mx + b again:

y = -3x + 1 will be the equation of the line

Answer:

Yes.

Step-by-step explanation:

As long as the individual's that have been selected as part of the study were actually selected randomly then yes. If there was no bias or other external factors affecting the probability of getting chosen then these individual's would clearly represent the entire population of Best Buy customers. Therefore, if the data gathered from these individuals results in being 68% of that population that does not buy anything then this would result in a valid claim by Best Buy.

Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

The mean number of scores per game is 8

Step-by-step explanation:

Since we know we can find the mean by adding all the numbers and dividing them by many numbers there were. Once you add 8, 14, 4, 7, 6, 4, and 7, you will get 64. Since there were 8 numbers, you divide 64 by 8 to get 8.

Answer:

I would need to see the models to answer this question.

Answer:

?

Step-by-step explanation:

The solution for \((x^{\frac{4}{3} } x^{\frac{2}{3} } } )^{\frac{1}{3} }\) is \(x^{\frac{2}{9} }\)

Given,

\((x^{\frac{4}{3} } x^{\frac{2}{3} } } )^{\frac{1}{3} }\)

We have to solve this using laws of indices;

Laws of indices;

1. Multiplication;

The indices of two terms that are to be multiplied together and have the same base (in this case, x) are added.

xᵃ xᵇ = x ᵃ ⁺ ᵇ

2. Division;

The indices of two terms that are to be divided and have the same base (in this case, x), are subtracted.

xᵃ / xᵇ = x ᵃ ⁻ ᵇ

3.  Brackets;

The powers are multiplied together if a term with a power is raised to a power by itself.

(xᵃ)ᵇ = x ᵃᵇ

Here,

We can use the first law and third law.

So,

\((x^{\frac{4}{3} } x^{\frac{2}{3} } } )^{\frac{1}{3} }\)

= \((x^{\frac{4}{3}^{-} \frac{2}{3} } )^{\frac{1}{3} }\)

= \((x^{\frac{2}{3} } )^{\frac{1}{3} }\)

= \(x^{\frac{2}{3}.\frac{1}{3} }\)

= \(x^{\frac{2}{9} }\)

That is,

The solution for \((x^{\frac{4}{3} } x^{\frac{2}{3} } } )^{\frac{1}{3} }\) is \(x^{\frac{2}{9} }\)

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9514 1404 393

Answer:

  a) -13

  b) -22

Step-by-step explanation:

It can be convenient to compute the function values first:

  f(1) = 1² -14·1 = -13

  g(1) = 1 +8 = 9

Then the compositions are ...

(a) (f+g)(1) = f(1) +g(1) = -13 +9 = -4

(b) (f-g)(1) = f(1) -g(1) = -13 -9 = -22

Answer: C.

Step-by-step explanation:

Total number of plants in Robert's garden = 8 + 4 + 16 + 22

= 50

Number of tomato plants in Robert's garden = 8

Ratio of total number of plants to the number of tomato plants = 50 : 8

Simplify

50 : 8 = 25:4

Answer:

4, 9, and -1

Step-by-step explanation:

Please give me brainliest

Answer:

4x+9-y

The 4 is your coefficient. X and Y are your variables and 9 is your constant.