It is given that y varies directly as x. If y = 5 when x = 4 determine the constant of variation.

A) -4/5
B) 4
C) 5
D) 5/4

Answer:

$800

Step-by-step explanation:

Kevin earns a base pay = $325 /week

He also make some extra earning in the form of commission. Let this extra earning be “$X”

Thus, Base pay + Extra earning through commission = $1125 -------------Equation (A)

Substituting the values in equation A, we get –  

$325 + $X = $1125

$X = $1125 - $325

= $ 800

The radius of the large storage shed is approximately 2.023 feet to the nearest hundredth of a foot.

To find the radius of the large storage shed, we need to use the formula for the volume of a cone, which is given by: [tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

where V is the volume, r is the radius of the base, h is the height and [tex]\( \pi \)[/tex]is approximately 3.14. We are given that the volume V is 51.4 cubic feet and the height h is 12 feet. We need to solve for r.

First, let's rearrange the formula to solve for r: [tex]\[ r^2 = \frac{3V}{\pi h} \][/tex]

Now, plug in the given values:

[tex]\[ r^2 = \frac{3 \times 51.4}{3.14 \times 12} \][/tex]

[tex]\[ r^2 = \frac{154.2}{37.68} \][/tex]

[tex]\[ r^2 \approx 4.093 \][/tex]

Now, take the square root of both sides to find r:

[tex]\[ r \approx 2.023 \][/tex]

So, the radius of the large storage shed is approximately 2.023 feet to the nearest hundredth of a foot.

Answer:C

$35 + (−$7) + (−$5)

hope this helps :}

Answer:

Number of boxes that will fit =2340

Step-by-step explanation:

The shipping box volume can be calculated by the formula V = Lxwxh ,where L ,w ,h are length ,width  and height of the box.

The length of the shipping box =[tex]3\frac{3}{4} =\frac{15}{4} ft.[/tex]

Width = 3 ft.

Height =[tex]3\frac{1}{4} =\frac{13}{4} ft.[/tex]

Volume of shipping box =[tex]\frac{15}{4} .3 .\frac{13}{4} =\frac{585}{16} = 36.6 ft[/tex].cubic ft.

Volume of shipping box can also be calculated by multiplying base area with the height of box.

Base area of box = [tex]\frac{15}{4} .3=\frac{45}{4} square ft.[/tex]

Volume of box = base area x height =[tex]\frac{45}{4} .\frac{13}{4} = 36.6 cubic ft.[/tex]

Volume of packing cubes =[tex]\frac{1}{4} .\frac{1}{4} .\frac{1}{4} =\frac{1}{64}[/tex] cubic ft.

Number of fish boxes that will fit in the shipping box = volume of shipping box ÷ volume of fish food box = 36.6 ÷ [tex]\frac{1}{64}[/tex] =2340 .

The annual interest rate is 4.5%.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$5000, simple interest=$2250 and time period= 10 years.

Here, 2250= (5000×R×10)/100

225000=50000R

R=225000/50000

R=4.5%

Therefore, the annual interest rate is 4.5%.

To learn more about the simple interest visit:

https://brainly.com/question/25845758.

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The geometric mean of given numbers 9 and 11, using the formula is 9.95.

If a and b are two numbers

Their geometric mean = [tex]\sqrt{a*b}[/tex]

Given numbers are 9 and 11

So, the geometric mean of 9 and 11 will be:

[tex]\sqrt{9*11} \\\\\sqrt{99} \\\\9.95[/tex]

Therefore, the geometric mean of given numbers 9 and 11 is 9.95

To get more about the geometric mean visit to:

https://brainly.com/question/47038

Final answer:

The surface area of a pyramid with a base side of 2.5 inches and a slant height of 3 inches is calculated by finding the area of the base and the four triangular faces separately and then adding them together, resulting in a total surface area of 21.25 square inches.

Explanation:

To find the surface area of a pyramid with a square base of 2.5 inches and a slant height of 3 inches, we need to calculate the area of the base and the area of the four triangular faces.

For the base, which is a square:

Area of base = side × side = 2.5 inches × 2.5 inches = 6.25 square inches

For each triangular face:

Area of one triangle = (base × slant height) / 2 = (2.5 inches × 3 inches) / 2 = 3.75 square inches

Since there are four such triangles, we multiply the area of one triangle by 4:

Total area of four triangles = 3.75 square inches × 4 = 15 square inches

Finally, add the area of the base and the total area of the triangular sides to get the total surface area:

Total surface area = area of base + total area of triangles = 6.25 square inches + 15 square inches = 21.25 square inches

The surface area of the pyramid is therefore 21.25 square inches.

The area of the parallelogram is approximately [tex]\( 1216.35 \)[/tex] square centimeters, with a longer side of 45 cm and height 27.03 cm.

To find the area of the parallelogram given the dimensions and conditions described, we can follow these steps:

1. Identify Key Dimensions:

  - The shorter side [tex]\( a = 29 \)[/tex] cm.

  - The longer side is divided into two segments: 33 cm and 12 cm. Therefore, the longer side [tex]\( b = 33 + 12 = 45 \)[/tex] cm.

2. Determine the Height Corresponding to the Longer Side:

  - We need to find the height [tex]\( h \)[/tex] of the parallelogram with respect to the longer side [tex]\( b = 45 \)[/tex] cm.

3. Utilize the Perpendicular Segment Information:

  - The perpendicular from the point of intersection of the diagonals to the longer side divides it into two segments: 33 cm and 12 cm.

  - This perpendicular segment represents the height [tex]\( h \)[/tex] from the base to the opposite side.

4. Use Geometric Properties of the Parallelogram:

  - In a parallelogram, the point of intersection of the diagonals divides each diagonal into two equal segments.

  - Since the perpendicular divides the longer side into two segments, we can use these to find the height [tex]\( h \)[/tex].

Given that the point of intersection of the diagonals and the perpendicular segment splits the longer side into two segments (33 cm and 12 cm), we note that this splitting essentially occurs at the mid-point of the segments because the diagonals bisect each other.

5. Calculate the Area:

  - The area [tex]\( A \)[/tex] of a parallelogram is given by the formula:

    [tex]\[ A = \text{base} \times \text{height} \][/tex]

  - Here, the base is the longer side [tex]\( b = 45 \)[/tex] cm, and the height [tex]\( h \)[/tex] needs to be calculated using the right triangle formed by the height and the segments.

6. Determine Height Using Right Triangle:

  - We use the properties of the right triangle formed by the height and the segments:

    [tex]\[ h^2 + \left(\frac{33 - 12}{2}\right)^2 = 29^2 \][/tex]

  - This simplifies to:

    [tex]\[ h^2 + 10.5^2 = 29^2 \][/tex]

    [tex]\[ h^2 + 110.25 = 841 \][/tex]

    [tex]\[ h^2 = 841 - 110.25 \][/tex]

    [tex]\[ h^2 = 730.75 \][/tex]

    [tex]\[ h = \sqrt{730.75} \][/tex]

    [tex]\[ h \approx 27.03 \text{ cm} \][/tex]

7. Calculate the Area:

  - Now that we have [tex]\( h \approx 27.03 \)[/tex] cm, the area [tex]\( A \)[/tex] of the parallelogram is:

    [tex]\[ A = b \times h = 45 \times 27.03 \approx 1216.35 \text{ cm}^2 \][/tex]

Therefore, the area of the parallelogram is approximately [tex]\( 1216.35 \text{ cm}^2 \)[/tex].

In order to find how many pieces of 1/3 feet rope you can make out of 7 feet rope, you have to divide 7 feet by 1/3 feet.

7/ (1/3) = 21 pieces

Therefore, you can make 21 1/3 – feet ropes.

Answer: Hello there!

Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.

we know that:

x + y = 92

x*y = 2107

now we have a system of equations that we need to solve:

the first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:

x = 92 - y

now we can replace it in the second equation and find the value of y.

x*y = 2107

y*(92 - y) = 2107

92y - y^2 = 2107

now we need to solve a cuadratic equation!

-y^2 + 92y - 2107 = 0

using the Bhaskara formula, we get:

[tex]y = \frac{-92 +/- \sqrt{92^{2} -4 *(-1)*(-2107) } }{-2} = \frac{-92 +/- \sqrt{36} }{-2} = \frac{-92 +/- 6}{-2}[/tex]

so we have two solutions:

y = (-92 + 6)/(-3) = 43

y = (-92 - 6)/(-2) = 49

because y is the oldest one, we need to take the biggest solution, this is y = 49.

so the oldest parent has 49 years.

if you want to find the age of the other parent, replace this in the first equation:

y + x = 92

49 + x = 92

x = 92 - 49 = 43

Nolan correctly identified the square  numbers before and after 18.

The square roots of them are 4 and 5.

Clearly, square root of 18 should lie between 4 and 5 only.

He, then carefully squared 4.1, 4.2, 4.3 etc. and identified that 4.3 squared is nearer to 18.

Since, Nolan is finding estimated square root, his steps are cool and he didn't make any error.

Answer: C

Step-by-step explanation:

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