Find the sum of the hundred even numbers from 0 to 398

Given

A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. the graph shows the height above the surface of the ground, y, in feet the hammer is x seconds after being thrown from the roof

Solution

The final answer

Option C

Jonas have to repay $13888 after 4 years.

Given

Principle amount of loan (P) = $12,400

Rate of interest (R) = 3%

Time period (T) = 4 years

Also the interest is not compounded, hence it is simple interest.

The formula for simple interest is (PTR)/100

Where,

P = Principle amount

T = time period

R = rate of interest

By substituting the values in the formula we get,

Simple interest =  (12400 x 4 x 3) / 100

Simple interest = 1488

Hence adding this interest to Principle sum we get

12400 + 1488 = 13888

Jonas has to repay $13888 after 4 years.

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Given

The table,

The sample size is 27.

To find:

The mean weight of these 27 babies.

Explanation:

It is given that,

That implies,

The mean weight of 27 babies is,

Hence, the mean weight of 27 babies is 6.1 pounds.

The equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

Let

Since the rectangular plot of ground is 30 meters longer than it is wide, we have that

L = W + 30

Since the area of the rectangular plot is A = LW where

Since A = 20,000 m², we have that

LW = 20,000

(W + 30)W = 20,000

W² + 30W = 20,000

W² + 30W - 20,000 = 0

Using the quadratic formula, we have that

[tex]W = \frac{-30 +/- \sqrt{30^{2} - 4 X (-20000)} }{2 X 1} \\W = \frac{-30 +/- \sqrt{900 + 80000} }{2} \\W = \frac{-30 +/- \sqrt{80900} }{2} \\W = \frac{-30 +/- 284.43}{2} \\W = \frac{-30 +/- 284.43}{2}\\W = \frac{-30 - 284.43}{2} or \frac{-30 + 284.43}{2}\\W = \frac{-314.43}{2} or \frac{254.43}{2}\\W = -157.22 or 127.23\\[/tex]

Since W cannot be negative, we have W = 127.23

Since L = W + 30

L = 127.23 + 30

L = 157.23

So, the dimensions are

So, the equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

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Explanation

Given the function;

We are asked to find the population of the bacteria after 7 days.

Given that t represents the number of days, we can find the population by substituting 7 into the formula. This can be seen below.

Answer: 4374

Answer: E. 2.24

Step-by-step explanation:

6720 - 6720 x 2/3

6720 - 4480

= 2,240

1 kilo = 1000 meters

2240 ÷ 1000

= 2.24

The length of the scraps of wood when placed side by side is 53 inches.

A line plot is a graph that is made up of a number line and check marks above the numbers on the number line. The check marks above the number line represents the frequency of the data. For example, there are two checkmarks above 7. This means that there are two scraps of woods that measure 7 inches.

In order to determine the approximate length of the scraps of wood if they are placed side by side, add the length of each scrap of wood together.

Addition is a mathematical operation that is used to determine the sum of two or more numbers. The sign that is used to denote addition is +.

[tex]5\frac{1}{2} + 6 + (6\frac{1}{2}. 3) + (7. 2) + 8[/tex] =

[tex]5\frac{1}{2} + 6 + 19\frac{1}{2} + 14 + 8[/tex] = 53 inches

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The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.

Given,

The exponents; 3^6 and 3^5.

We have to simplify this into a single power of 3.

In multiplication;

That is,

aᵇ . aⁿ = a^(b + n)

a^b . c^d = a x c ^ (b + d) = ac^bd

So,

3⁶ . 3⁵ = 3^(6 + 5) = 3¹¹

That is,

The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.

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If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras

The distance traveled by Mr. Giordano = 4.5 miles

The time taken = 5 minutes

Speed = Distance / Time

Substitute the values in the equation

Speed = 4.5/5

= 0.9 miles per minutes

The distance traveled by Mr. Baras = 6.3 miles

The time taken = 8 minutes
Speed = Distance / Time

Substitute the values in the equation

Speed = 6.3/8

= 0.78 miles per minutes

Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras

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Answer:744

Step-by-step explanation:

800-7%=744

Answer:

$56

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the ratios (red to blue), of perimeter and area, given that corresponding sides have the ratio red to blue = 5 to 8.

The ratio of perimeters is the ratio of corresponding side lengths:

  red to blue = 5 / 8

The ratio of areas is the square of the ratio of corresponding side lengths:

  red to blue = (5 to 8)² = 25 / 64

__

Additional comment

Ratios are customarily expressed in any of three equivalent forms:

Answer:

  2.7 - h < 2.3

Step-by-step explanation:

You want an inequality to represent the relationship described by "Stella wants to know the number of hours (h) by which she must reduce her 2.7 hour half-marathon time to run in under 2.3 hours."

If h is the number of hours by which the time is reduced, Stella wants ...

  2.7 -h < 2.3 . . . . . . . . . representative inequality

__

Additional comment

The solution would be h > 0.4. Stella must reduce her time by more than 0.4 hours.

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The expected number of juniors in the committee is 1.3

The question is incomplete, the complete question is given below:

A committee of 3 members is selected from a club made up of 13 juniors members and 17 senior members. What is the expected number of juniors in the​ committee?

The expected number of juniors in the committee is computed here as:

Juniors in the committee=13

Seniors in the committee=17

Total number of members=(13+17)=30

Fraction of juniors in total members=13/30

So expected number of juniors in the committee:

=Fraction of juniors in total members*Total number of members to be selected

=(13/30)*3

=1.3

Therefore 1.30 is the expected number of juniors in the committee

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The area in square inches of the tile is 9 / 4 t .

She makes rectangular kitchen tiles with an area of t square inches.

Therefore,

area of the rectangular kitchen tiles = lw

t = lw

l = t / w

w = t / l

Therefore, the tile is 3 / 4 as long and 3 times wide as her kitchen tiles.

Hence,

area of the tile = 3 / 4 t / w × 3(t / l)

area of the tile = 9 / 4 × t² / lw

where

lw = t

Hence,

area of the tile  = 9 / 4 × t² / t

area of the tile  = 9 / 4 × t

Therefore,

area of the tile  = 9 / 4 t

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Linear equations - The team can bring its 24 players

What do you mean by linear equations with one variable?

A linear equation with one variable is one that can be written as ax+b = 0, where a and b are two integers, and x is a variable. This type of problem only has one solution. For instance, the linear equation 4x+4=8 only has one variable.

We are given that,

the total money raised by the lacrosse team is given to be $2863.50

bus rented at a cost of $1087.50

meal budget per person is calculated to be $74

let us assume the number of players the team can bring to the tournament to be "x".

bus rent + (meal budget * number of players) = total money raised

= 1087.50 + (74*x) = 2863.50

= 1087.50 + 74x = 2863.50

= 74x = 2863.50 - 1087.50

= 74x = 1776

= x = 1776 ÷ 74

= x = 24

Thus the team can bring its 24 players.

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Answer:

In second week there is percentage limit (-ve sign) of 20% in people traveling examine to first week.

In 0.33 week there is proportion increase of 50% in human beings traveling compare to 2nd week.

In fourth week there is share limit of 75% in humans visiting evaluate to 1/3 week.

After four years, the investment is worth £8934.34.

The interest you earn on interest is known as compound interest. For instance, if you start with $100 and it generates 5% interest annually, you will conclude the first year with $105 in your account. You'll have $110.25 after the second year is over.

We employ the formula approach to determine the entire amount,

A = P(1+r)^n

The amount invested, or principal(P), is £8,000.

Interest rate r is 2.8%, or 0.028.

n = 4 years have passed.

Now, immediately enter these values into the formula, A = P(1+r)n.

A = 8000 * (1 + 0.028) ^ 4

= 8000 * 1.028 ^ 4

= 8934.34

Consequently, the investment's value after four years is £8934.34.

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Step-by-step explanation:

[tex]area \: of \: circle = \pi\:r^{2} \\ \pi \times6.5^{2} - \pi \times {2.3}^{2} = 36.96\pi = 116.113... {cm}^{2} [/tex]

Answer:

116.129 cm²

Step-by-step explanation:

       [tex]\boxed{\bf Area \ of \ circle = \pi r^2}[/tex]

Area of outer circle:

    R = 6.5 cm

   Area =3.142 * 6.5 * 6.5

             = 132.75 cm²

Area of inner circle:

 r = 2.3 cm

       Area of inner circle =3.142 * 2.3 *2.3

                                        = 16.621 cm²

Area of shaded area = area of outer circle - area of inner circle

                                    = 132.75 - 16.621

                                    =  116.129 cm²

Answer:16

Step-by-step explanation:

x-[tex]\sqrt{x}[/tex]=12

x=16

Given the formula for the circumference of a circle:

C = 2πr

Let's find the circumference of a circle with a diameter of 4 ft.

Where r is the radius.

To find the radius, we have:

The radius of the circle is 2 ft.

Take π = 3.14

Hence, to find the circumference of the circle, C, substitute 2 for r, 3.14 for π, and evaluate.

Thus, we have:

Therefore, the circumference of the circle is 12.56 ft

ANSWER:

C. 12.56 ft

The number of tiny toys that Toby's Tiny Toys need to sell to reach its break-even point is 13,475.

The break-even point is the production and sales units that will ensure that Toby's Tiny Toys does not incur a loss or generate a profit.

At the break-even point, the total revenues are equal to the total costs (fixed and variable).

Selling price per unit = $16.50

Variable expenses per unit = $12.50

Contribution margin per unit = $4 ($16.50 - $12.50)

Fixed expenses = $53,900

Break-even point in units = Fixed costs/Contribution margin per unit

= 13,475 ($53,900/$4)

Thus, we can conclude that Toby’s Tiny Toys needs to sell 13,475 to break even.

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The number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.

The overall revenues and entire costs are equal at the break-even point (fixed and variable).

The production and sales units that will verify that Toby's Tiny Toys does not suffer a loss or make a profit are the break-even point.

$16.50 is the selling price per unit.

Variable costs amount to $12.50 per unit.

The contribution margin = $16.50 - $12.50 = $4 per unit equals

Fixed costs is $53,900.

Break-even point = Fixed costs / Contribution margin

Break-even point = $53,900/$4

Apply division operation to get

Break-even point = 13,475

Thus, the number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.

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Slope of the line graph here is undefined.

When a line is vertical, its slope is ambiguous. A vertical line lacks the horizontal distance required for a positive, negative, or zero slop to exist. Since there is no horizontal change, there is no slope for vertical lines because 0 cannot be divided into any integer.

It is obvious that the x-coordinates are the same if we have a pair of coordinates, (x1, y1) and (x1, y2) through which a line passes. They are the same vertical line's points. As a result, the slope of such a line will be ambiguous.

Examples of undefined slope in real-world situations include elevators that only go up and down, and a mountain cliff that is vertical for a certain amount of height but impossible for climbers to scale.

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Answer: 3 hours

Let john take x hours to finish the work

Let nelly take y hours to finish the work

given, y =x+3

Portion of work done by john alone in one hour = 1/x

Portion of work done by Nelly alone in one hour = 1/y

∴Portion of work done by both john and nelly in one hour = 1/x + 1/y

[tex]= \frac{1}{x} + \frac{1}{x+3}\\=\frac{x+3+x}{x*(x+3)}\\=\frac{2x+3}{x^2+3x}[/tex]

Total time taken by John and nelly to finish the work = 2 hours

[tex]\therefore [2(2x+3)]/[x^2 + 3x] = 1\\= > 4x + 6 = x^2 + 3x\\= > x^2 -x -6 =0\\= > x^2 - 3x + 2x -6 =0\\= > x(x-3) + 2(x-3)=0\\= > (x+2)(x-3)=0[/tex]

Hence either x = -2 or x = 3

Since x is time taken, it cannot be negative, hence x = 3

∴Time taken by john to finish the work = 3 hours

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We have the following:

We must apply the simple interest formula which is the following:

Where, P is the principal 3000

r is the interest rate 0.12

t is time in years

A is the total value

replacing:

The answer is $3360 at the end of the 1 year period

Answer:

first plot the positive 2 on the y axis

plot (0,2)

Then from (0,2) go up 2 and right 2.

Answer in attached image

The width of the house driveway in the scale drawing is 4 inches.

Scale drawing is drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale).

Therefore, he measured a house and its lot and made a scale drawing.

The scale of the drawing was 1 inch : 5 feet.

The houses driveway is 20 feet wide in real life.

Therefore,

5 feet = 1 inch

20 feet = ?

cross multiply

Therefore,

width of the driveway on the scale drawing =  20 × 1 / 5

width of the driveway on the scale drawing =  20 / 5

width of the driveway on the scale drawing =  4 inches.

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Answer:

65

Step-by-step explanation:

2:26

1:x

26/2 = x = 13

The heli uses 13 gallons per hour.

5:y

13x5 = y = 65

Hope that helps