If you were given the area of a figure and told that all the dimensions of the figure would be cut in half, how could you find the area of the new similar figure?

Multiply the area of the original figure by 4.
Divide the area of the original figure by 1/2 .
Multiply the area of the original figure by 1/2 .
Divide the area of the original figure by 4.

Answer:

44,886 gallons

Step-by-step explanation:

We need to find the volume

V = l*w*h

V = 30ft*25ft*8ft

V =6000 ft^3

We know that 1 ft^3 = 7.481 gallons

6000 ft^3 * 7.481 gallons/1 ft^3 = 44886 gallons

Answer:

44,883 gallons

Step-by-step explanation:

The amount of water the pool can hold can be found by calculating the volume of the pool.

We know that the pool is rectangular, and it is a three dimensional shape (3 dimensions: length, width and depth). Therefore, we can use the formula for finding the volume of a rectangular prism:

V=l*w*h

We know the length is 30 feet and the width is 25 feet. The height is also the depth, so the height is 8 feet.

l= 30 feet

w=25 feet

h= 8 feet

Substitute these values into the formula.

V= 30 feet * 25 feet * 8 feet

Multiply the numbers together.

V= (30 feet * 25 feet) * 8 feet

V= 750 feet^2 * 8 feet

V=6000 feet^3

Now, let's find how many gallons the pool can hold.

1 ft^3 is equal to 7.4805 gallons. Therefore, we can multiply 6000 ft^3 and 7.4805

6000 ft^3 * 7.4805 gallons/1 ft^3

6000* 7.4805 gallons

44,883 gallons

The pool can hold 44,883 gallons of water.

Answer:

[tex] \boxed{[3 \: \: \: - 12 \: \: \: \: \: \: 15 \: \: \: - 21] } [/tex]

Step-by-step explanation:

[tex]3 \times 1 = 3 \\ \\ 3 \times ( - 4) = - 12 \\ \\ 3 \times 5 = 15 \\ \\ 3 \times ( - 7) = - 21 \\ \\ \\ = > 3.[1 \: \: \: - 4 \: \: \: \: \: \: 5 \: \: \: - 7] =[3 \: \: \: - 12 \: \: \: \: \: \: 15 \: \: \: - 21] [/tex]

Answer:

During the last 5 basketball games, Javier scored 13 , 20, 13, 15, and 24 points

Step-by-step explanation:

Answer:

11 points

Step-by-step explanation:

Range = Highest value - lowest value

Highest value = 24

Lowest value = 13

Range = 24 - 13

Range = 11

Answer:

3x + 9

Step-by-step explanation:

For value of (f+g)(x) add two functions up

x + 3 + 2x + 6 = 3x + 9

Answer:

B

Step-by-step explanation:

1 and 2 thirds gallons per minute

Answer:

5

Step-by-step explanation:

Let the number of the kitchen clock sold =a

Let the number of the cuckoo clock sold =b

Let the number of the two-foot high grandfather clocks sold =c

The new saleswoman sold at least two of each of the three models.

Therefore:

[tex]a\geq 2\\b \geq 2\\c \geq 2[/tex]

In all, she collected $300 from selling these models alone

17a+31b+61c=300

17(2)+31(2)+61(2)=218

300-218=82

Next, we try to express the remainder (82) in terms of 17, 31 and 61

82=17(3)+31

Therefore, she sold:

She sold 5 $17 clocks.

CHECK:

17(5)+31(3)+2(61)=$300

Answer:

6.6 ounces left

Step-by-step explanation:

Take the amount she had and subtract the amount she used

8.3-1.7 =6.6

Answer:

She has 6.6 ounces left.

Answer:

w=6, x=7, t=7, n=90, w=15/2

Step-by-step explanation:

a) 5w = 30

30/5 = 6

w=6

b) 3x-5=16

Add 5 to each side.

3x+5=16+5

3x=21

21/3=7

x=7

c) 10-t=17

10-t=17

17-10-7

-t=-7

Negative and a negative is a positive.

t=7

d) n/5 = 18

n=18 * 5

n=90

e.) 4w-12=2w+3

4w=2w+3+12

4w=2w+15

4w−2w=15

2w=15

w= 15/2

Answer:

6

Step-by-step explanation:

In a right triangle the legs are base and height

area = (1/2) base × height = (1/2) 3 (4) = 6

Answer: 6  square units

Answer:

His percentage profit is 12%

Step-by-step explanation:

Here, we want to calculate the percentage profit made by the business man.

Per kg of what he is selling, he has 3 parts high quality sugar and 5 parts low quality sugar.

Now let’s see how much these costs

For the high quality sugar, it’s total kg mixed per kg will be 3/(3+5) = 3/8

Since high quality sugar costs 10 shillings per kg, 3/8 of a kg will cost 3/8 * 10 = 30/8 = 3.75 shillings

For the low quality, its part will be 5/(3 + 5) = 5/8

since low quality costs 8 shillings per kg, 5/8 of a kg will cost 5/8 * 8 = 5 shillings

Total cost price = 3.75 + 5 = 8.75 shillings

% profit = (selling price - cost price)/cost price * 100%

selling price here is 9.8 shillings per kg

while cost price is 8.75 shillings per kg

% profit = (9.8-8.75)/8.75 * 100%

= 1.05/8.75 * 100% = 0.12 * 100% = 12%

Answer:

C, 1/10 c^3d^4

Remove the cubic root operation by raising all the terms by 1/3

1/100^1/3 c^9^1/3 a^12^1/3

Simplify:

1/10c^3a^4

Answer:

32 servings

Step-by-step explanation:

Take the amount of honey and divide by the size of a serving

8 ÷ (1/4)

Copy dot flip

8 * 4/1

32

There are 32 servings

Answer:

32 servings

Step-by-step explanation:

Answer:

1. 47 2. 49

Step-by-step explanation:

1st is complementary and second is supplementary

Answer:

Step-by-step explanation:

b+43˚=90˚

subtract 43˚ from both sides of the equation

b=47˚

3x+33˚=180˚ (because it's a straight angle)

subtract 33˚ from both sides

3x=147˚

divide both sides by 3

x= 49˚

Answer:

$1,592.74

Martha will need to pay $1,592.74 more

Step-by-step explanation:

Using the compound interest/inflation formula;

A = P(1+r)^(t)

Where;

A = final value

P = initial value = $10,000

r = inflation rate = 3% = 0.03

t = time = 5 years

Substituting the values;

A = $10,000(1+0.03)^(5)

A = $11592.740743

A = $11,592.74

How much more will Martha need to save;

C = final value - initial value = A - P

C = $11,592.74 - $10,000

C = $1,592.74

Martha will need to pay $1,592.74 more

Answer:

1,590.00

Step-by-step explanation: I took the test

Answer:

the answer is 10

Step-by-step explanation:

the other shape is half of all the degreed of the first one

Answer: 10

Step-by-step explanation:

AB:  3.0/2 = 1.5 = EF

BC:  5.0/2 = 2.5 = FG

CD:  4.0/2 = 2.0 = GH

DA:  8.0/2 = 4.0 = EH

1.5+2.5+2.0+4.0 = 10

Step-by-step explanation:

Ok, so the surface area is found by adding up all the areas of each individual shape of the entire solid.

I attached a picture of some of the missing values. That should help a little with visualizing.

Since the three rectangles are all the same values, you can substitute adding them by just multiplying lw (their individual areas) by 3.

The three triangles at the top are all the same as well, so you can multiply their areas ([tex]\frac{1}{2} bh[/tex] ) by 3, too.

Then there's the triangle at the bottom that is by itself, that will just have a 1 in front of it.

Now you can make your surface area equation:

[tex]SA=3lw+3(\frac{1}{2} b_1h_1)+\frac{1}{2} b_2h_2[/tex]

The b1h1 are the three triangles at the top and the b2h2 is the triangle at the bottom.

[tex]SA=3(10)(16)+3(\frac{1}{2})( 10)(6)+\frac{1}{2} (10)(8.7)\\SA=480+90+43.5\\SA=613.5[/tex]

If there's anything you need me to explain further, feel free to comment :)

Answer:

[tex]SA=613.5m^2[/tex]

Answer:

[tex]\Huge \boxed{\mathrm{613.5 \ m^2 }}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

We can find the total surface area by adding the surface area of the triangular prism with the surface area of the triangular pyramid at the top.

Surface area of the triangular prism:

10 × 8.7 × 1/2 + 16 × 10 × 3

⇒ 523.5

Surface area of the triangular pyramid:

6 × 10 × 1/2 × 3

⇒ 90

Adding the surface areas:

523.5 + 90

⇒ 613.5

[tex]\rule[225]{225}{2}[/tex]

Answer:

They would fall in the same year every 10 years

Step-by-step explanation:

Here in this question, we are interrelated in calculating the number of years it will take the alumni reunion and the alumni soccer game to fall in the same year.

Now looking at the number of years, we can see we have every 2 and every 10 years

To get the year in which they happen at the same time, we can simply find the lowest common multiple of 2 and 10 and that would be 10

This can be visualized in a way that;

The reunion has happened now, and will happen in the next 10 years.

Now since the soccer game has happened now, in the next 10 years, we shall be having 5 episodes. This means that it will take up to the 10th year before we have the soccer game and the alumni reunion occurring at the same time and the mathematical reason for this is that , 10 is the lowest common multiple of 10 and 2

Answer:

1 times

Step-by-step explanation:

Hello,

The alumni have reunions every 10 years

But also have football games every 2 years

We have to find how often do the football and reunion fall the same year.

Working with a space of 10 years

In 10 years, reunions happen only once

In 10 years, soccer games happen five times

Assuming we're in the year 2020,

The next reunion would likely occur in year 2030.

But soccer games will happen in year 2022, 2024, 2026, 2028 and finally 2030.

Checking both soccer and reunion coincidence, we can only find one which is in year 2030.

So, soccer games and reunions happen once in 10 years

Answer:

3/4

Step-by-step explanation:

There is 2 Os and 8 in total.

So the probability of selecting O is 1/4

As the question asks everything but O, you subtract that answer from 1. 1-1/4=3/4

Answer: 2,695

Step-by-step explanation:

5-6+8*674/2

Multiply 8 and 674

5-6+5,392/2

Divide 5,392 by 2

5-6 + 2,696

Subtract 6 from 5

-1 + 2,696

Add

2,695

Step-by-step explanation:

5 - 6 = -1

-1 + 8 = 7

7 x 674 = 4,718

4,718 / 2 = 2,359

Answer:

Step-by-step explanation:

2^(3-5)

=2^-2

Answer:

[tex] \frac{ {2}^{4 + 3} }{2^{5 + 4} } [/tex]

[tex] \frac{ {2}^{7} }{2^{9} } [/tex]

= 2^7-9

= 2^-2

Answer:

Center = (7, - 5)

Radius = 3

Step-by-step explanation:

[tex] {x}^{2} + {y}^{2} + 14x - 10y + 65 = 0 \\ {x}^{2} + 14x + {y}^{2} - 10 + 65 = 0 \\ ( {x}^{2} + 14x + {7}^{2}) - {7}^{2} + ({y}^{2} - 10y + {5}^{2}) \\- {5}^{2} + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 - 25 + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 + 40= 0 \\ (x + 7)^{2} + (y - 5)^{2} - 9= 0 \\ (x + 7)^{2} + (y - 5)^{2} = 9 \\ (x + 7)^{2} + (y - 5)^{2} = {3}^{2} \\ equating \: it \: with \: \\ (x - h)^{2} + (y - k)^{2} = {r}^{2} \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3[/tex]

Answer:

C(n)=1.25n

Where n= number of cans

Step-by-step explanation:

C=cost

n=number of cans

Quantity Total cost

1 $1.25

2 $2.50

3 $3.75

4 $5.00

Total cost, c(n) =1.25n

Check

Total cost when n=4

Total cost c(4)=1.25×4

Total cost c(4)=5.00

Answer:

D

Step-by-step explanation:

The total number of students is 15+12= 27

The ratio of girls to total students is 12/27 = 4/9

Answer:

1 1/5 [tex]\geq[/tex] x  OR one and on fifth is greater than or equal to x.

Step-by-step explanation:

2/5 [tex]\geq[/tex] x - 4/5

To isolate x, we need to add 4/5 to each side:

6/5 [tex]\geq[/tex] x is what we get

We can simplify it to:

1 1/5 [tex]\geq[/tex] x

Add 4/5 to both sides

X <= 6/5

X <= 1 1/5

Answer:  

1

Step-by-step explanation:

8-1,2,4.....

25-1,5...

Answer:

To find the average rate of change, we divide the change in the output value by the change in the input value. The Greek letter Δ (delta) signifies the change in a quantity; we read the ratio as “delta-y over delta-x” or “the change in y divided by the change in x”.

Answer:

Find the average rate of change of the function

A General Note: Rate of Change

The units on a rate of change are “output units per input units.” The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

Step-by-step explanation:

b can be used to check her score

Answer:

the answer is show me your kitty cat

Step-by-step explanation: