A machine shop has a fixed set-up cost of $2000 to produce new bolts. The cost of materials and labor to produce each individual bolt is $8.50. Which of the following functions models the average cost per bolt for the company to produce x bolts, where x> 1? C(x) = 2000 + 8.50xC(x) = (2000 + 8.50)xC(x) = 2000 + 8.50/xC(x) = 2000 + 8.50x/x

The work required to pump the water out of the spout is 12,249.7 pi J.

Let's assume that the radius of the tank is 6 ft, the radius of the spout is 12 ft, and the height of the water in the tank is 16 ft.

To calculate the work required to pump the water out of the spout, we'll need to use the equation: W = (4/3)πr2(h+R-r) ρg where W is the work required, π is pi (3.1415), r is the radius of the tank, R is the radius of the spout, h is the height of the water in the tank, and ρg is the density of water (62.5 lb/ft3).

Plugging in our values, we get:

W = (4/3)π(6 ft)2(16 ft + 12 ft - 6 ft) (62.5 lb/ft3)

W = (4/3)π(36 ft2) (34 ft) (62.5 lb/ft3)

W = (4/3)π(2268 ft3) (62.5 lb/ft3)

W = 12,249.7 pi J

Therefore, the work required to pump the water out of the spout is 12,249.7 pi J.

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The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.

There would be two walls with 10 x 16 dimensions so the area is :

= 2 x 10 x 16

= 320 square feet

Two walls with 20 x 10 dimensions :

= 2 x 20 x 10

= 400 square feet

The total area is :

= 400 + 320

= 720 square feet

One gallon of paint can cover 400 square feet so the number of gallons needed is:

= 720 / 400

= 1. 8 gallons

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Full question is:

One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.

Answer:

14.45kg

Step-by-step explanation:

450g=0.45kg

14kg+0.45=14.45kg<20kg

if we  that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:

100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.

If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.

So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:

On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.

However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.

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Step-by-step explanation:

square root of 196 is 14

square root of 169 13

square root of 121 is 11

square root of 225 is 15

square root of 144 is 12

square root of 100 is 10

Answer: D) 4/5

Hope this helps :)

Answer:

Sara

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 21 because 12+2+3+4=21 so i state my answer is 21

Answer:

There are 3 different rectangles (in feet): 2 by 6; 3 by 4; 1 by 12

Step-by-step explanation:

The answer is that there is an infinite number of rectangles with area 12 sq in.

If the length and width must be whole numbers, then you need to find all different pairs of numbers whose product is 12.

2 × 6 = 12

3 × 4 = 12

The two pairs of numbers Vanessa thinks are correct, but there is one more.

12 × 1 = 12

Answer: There are 3 different rectangles: 2 by 6; 3 by 4; 1 by 12

Answer:

yes i can but will have to get back to you in about half a hour just doing maths atm with the teacher

Step-by-step explanation:

Answer:

\( \sec( \frac{x}{3} ) + 4 > 2 - \sec( \frac{x}{3} ) \\ 2 \sec( \frac{x}{3} ) > - 2 \\ \sec( \frac{x}{3} ) > - 1 \\ \boxed{y = \sec( \frac{x}{3} )} \\ \boxed{y = - 1}\)

B) is the right answer.

Answer:

B

Step-by-step explanation:

We want to solve the inequality:

\(\displaystyle \sec\Big(\frac{x}{3}\Big)+4>2-\sec\Big(\frac{x}{3}\Big )\)

First, we can add sec(x/3) to both sides:

\(\displaystyle2 \sec\Big(\frac{x}{3}\Big)+4>2\)

Subtracting 4 from both sides yields:

\(\displaystyle 2\sec\Big(\frac{x}{3}\Big)>-2\)

And dividing both sides by 2 yields:

\(\displaystyle \sec\Big(\frac{x}{3}\Big)>-1\)

Therefore, we can graph the following two functions:

\(\displaystyle y=\sec\Big(\frac{x}{3}\Big)\text{ and } y=-1\)

Where our solutions will be all the intervals where y = sec(x/3) is above the line y = -1.

Answer:

$720 divided by 2 = $360

$360-106=$254

$360+106=$466

$254+$466=$720

Person 1 has $254

Person 2 has $466

To find the limit of a convergent sequence, we can simply take the limit as n approaches infinity. Let's calculate the limits for each of the given sequences:

A. \(\sf\:\lim_{n \to \infty} \frac{5n}{n+7} \\\)

To find the limit, we divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{5n/n}{(n+7)/n} = \frac{5}{1} = 5 \\\)

Therefore, the limit of the sequence A is 5.

B. \(\sf\:\lim_{n \to \infty} \frac{4-7n}{8+n} \\\)

Again, divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{4/n - 7}{8/n + 1} = \frac{0 - 7}{0 + 1} = -7 \\\)

So, the limit of sequence B is -7.

C. \(\sf:\lim_{n \to \infty} \frac{8n - 500\sqrt{n}}{2n + 800\sqrt{n}} \\\)

Divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500\sqrt{n}/n}{2 + 800\sqrt{n}/n} \\\)

As n approaches infinity, the terms involving \(\sf\:\sqrt{n}/n \\\) tend to 0:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500(0)}{2 + 800(0)} = \frac{8}{2} = 4 \\\)

Therefore, the limit of sequence C is 4.

To summarize:

A. The limit of sequence A is 5.

B. The limit of sequence B is -7.

C. The limit of sequence C is 4.

Hi there!

Begin by differentiating f(x) using the power rule:

dy/dx = nxⁿ⁻¹

Therefore:

f(x) = 3x² - 5x + 10

f'(x) = 6x - 5

Set this equation equal to 0 to find the x-intercept:

0 = 6x - 5

5 = 6x

x = 5/6, which is where the graph goes from NEGATIVE to POSITIVE, so there is a MINIMUM at this value.

there seems to be missing text

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

Bryan had 400$ in his bank account before he withdraw

Step-by-step explanation:

60$ ---- 15%(set what you have)

x$ ------100%(set what you need)

(x$ x 15%) 15x =(60$ x 100%)6000( cris cross the sides)(the signs dont matter )

x=400

Answer: Hi!

The equation for inverse proportion is x y = k or x = k/ y.

When finding the value of the constant k, you can use the known values and then use this formula to calculate all of the unknown values.

Hope this helps!

Answer:

I duno

Step-by-step explanation:

I smart

The base length of the parallelogram found using the area formula is 4 units.

What is a parallelogram?

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees. 360 degrees is the sum of all interior angles.

A parallelogram's area is the area that it takes up in a two-dimensional plane. The parallelogram's area is calculated by multiplying the base length by the height.

Each shape's perimeter can be defined as either the entire length or total distance encircling the object. The entire distance between a parallelogram's boundaries is also known as the parallelogram's perimeter.

Given,

The area of the parallelogram A =36 sq. units

The height of the parallelogram  h = 9 units

We are asked to find the base length b.

Now the formula for the area of the parallelogram is:

A = b * h

36 = b * 9

b = 36/9 = 4 units.

Therefore the base length of the parallelogram, found using the area formula is 4 units.

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Answer:

c.    x = -2  or x = -3

Step-by-step explanation:

The vertical asymptotes occur where the denominator = 0.  That happens when the f(x) is undefined.  So,

x^2 + 5x + 6 = 0

(x + 2)(x + 3) = 0

x = -2  or x = -3

If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.

To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:

Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.

Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.

Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.

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Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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The distance between the points B and C is 12m

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

for the coordinates B (-14,-5) and C(-14, 7), then x1 = -14 ,x-2= -14 , y1= -5 and y2= 7

therefore d =√((x2 – x1)² + (y2 – y1)²) = √((-14– -14)² + (-5 – 7)²)

d=√((0)² + 12²)

d=√144

d= 12m

therefore the distance between the points B and C is 12m.

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You have the following function f(x):

f(x) = 4.93/x - 3.35

To calculate f(2.9) you replace x bu 2.9 in the previous function, and proceed with the calculations:

f(2.9) = 4.93/2.29 - 3.35

f(2.9) = 2.15 - 3.35 = -1.2

Then, the answer is f(2.9) = -1.2

Step-by-step explanation:

I hope this answer is helpful ):

None of the chosen pairs will be dependent as nothing is specified.

Independent events are those events whose occurrence does not have any effect on the events that may occur or occurred.

Dependent events are those vents whose occurrence either depends on some other event or has an effect on occurring or occurred vents.

Given, The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.

As not mentioned that what kind of book he chooses first or types of book.

Also which shelf he chooses first choosing the first book is independent

and choosing the second book is also independent so none of the chosen pair will be dependent.

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