Theresa uses a unique box in the shape of a trapezoidal prism for her specialty candles. The area of the base of the box for the smaller candle is 125 cm2 and the box is 12 cm tall. The box used for the larger candle has a base whose area is 160% that of the smaller box, and it is 6 centimeters taller. What percent of the volume of the smaller box is the volume of the larger box?

AM = MB

CM = common side

∠3 = ∠4

△AMC ≅ △BMC

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

CM ⊥ AB

∠3 = ∠4

We have to prove △AMC ≅ △BMC.

Now,

If CM ⊥ AB

AM = MB

Now,

AM = MB

CM = common side

∠3 = ∠4

△AMC ≅ △BMC

Thus,

AM = MB

CM = common side

∠3 = ∠4

△AMC ≅ △BMC

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Answer:

rounded answer (+) 171036

rounded answer (-) 169692

Step-by-step explanation:

Answer: Austin college, 5, Barton college, 3.

Step-by-step explanation:

In the stem 7 there is no 70, but higher, so we just count the leaves on the stem 6; Austin's college contains 5 numbers, and Barton's contains 3.

Answer:

Percent Change

[tex]\sf percent\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]

[tex]\sf \implies \textsf{percent change from 1845-1846}=\dfrac{148-118}{118} \times 100=25.4 \%[/tex]

[tex]\sf \implies \textsf{percent change from 1846-1847}=\dfrac{139-148}{148} \times 100=-6.1 \%[/tex]

[tex]\sf \implies \textsf{percent change from 1847-1848}=\dfrac{151-139}{139} \times 100=8.6 \%[/tex]

(all solutions are given to the nearest tenth)

Answer:

11 soccer balls (rounded estimate; should be close to 11)

Step-by-step explanation:

Because you need to match the limit, you first have to convert in. to ft. That will get you at 2.3 (it is an non-stopping number, so I rounded to the tenths). 11 x 2.3 is  25.3. You can’t go lower, so you have to have that extra soccer ball. Hope this helps.

Answer:

Step-by-step explanation:

Formula for finding slope

Substituting the given points

Answer:

Step-by-step explanation: The probability of rolling an even number is three out of six, or three-sixths. This fraction can be simplified as the numerator and denominator are both divisible by three.

Answer:

420

Step-by-step explanation:

Base is the bottom across

Height is in the middle so multiply them and you get 420 inches

Answer:

4311/9900 = 0.4354

530/900 = 0.58

674/990 = 0.689

4936/990 - 4.985

8099/ 990 = 8.180

Step-by-step explanation:

Just divide and it should give you the decmile version

Answer:

y=-|x+1|+1

Step-by-step explanation:

im not too sure though

Answer:

Step-by-step explanation:

So first you need to find to Constant of Proportionality and to do that you need to divide either 96 by 3 or 160 by 5. The answer you get is the first blank, then to find the second blank you take 14 and multiply it by the first answer.

Answer:

50% or 1/2

Step-by-step explanation:

P(adult)=0.5

P(children)=0.5

0.5*40=20

20/40=2/4=1/2=0.5

0.5*100=50%

Answer:

[tex]5\sqrt{15}[/tex]

Step-by-step explanation:

[tex](\sqrt{3}+\sqrt{48})(\sqrt{20}-\sqrt{5})[/tex]

[tex]\textsf{Use} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]

[tex]\implies (\sqrt{3}+\sqrt{16 \cdot 3})(\sqrt{4 \cdot 5}-\sqrt{5})[/tex]

[tex]\implies (\sqrt{3}+\sqrt{16}\sqrt{3})(\sqrt{4}\sqrt{5}-\sqrt{5})[/tex]

[tex]\implies (\sqrt{3}+4\sqrt{3})(2\sqrt{5}-\sqrt{5})[/tex]

[tex]\implies (5\sqrt{3})(\sqrt{5})[/tex]

[tex]\implies 5\sqrt{3}\sqrt{5}[/tex]

[tex]\implies 5\sqrt{3 \cdot 5}[/tex]

[tex]\implies 5\sqrt{15}[/tex]

Answer:

5√15

Step-by-step explanation:

(√3 + √48)(√20 - √5)

step 1 simplify √48

(√3 + 4√3)(√20 - √5)

step 2 add √3 and 4√3

(5√3)(√20 - √5)

step 3 simplify √20

(5√3)(2√5 - √5)

step 4 subtract √5 from 2√5

(5√3)(√5)

step 5 multiply 5√3 and √5

= 5√15

explanation of each step

step 1 and 3

To simplify radicals you list the factors of the number under the sqaure root

For 48 we have 2 × 2 × 2 × 2 × 3

We then pair the factors off as powers of 2 if possible

We get 2² × 2² × 3 which can further be simplified as 4² × 3

We then list the number with the power on the outside of the radical and leave the numbers with no power on the inside to get 4√3.

This process is used to simplify √20 as well.

step 2 and 4

For these two steps we are adding and subtracting radicals  with the same radicand ( number inside of the square root. ) This is very simply as we keep the radicand the same and just perform the operation to the coeffecients ( number on the outside of the square root )

Eg. a√b + c√b = (a+c)√b or a√b - c√b = (a-c)√b

Hence, 4√3 + √3 = (4+1)√3 = 5√3

Step 5.

Finally we multiply the two radicals. This is very simply as we can use the rule to do so.

a√b × c√d = (a×c)√b×d

Hence, 5√3 × √5 = (5×1)√(3×5) = 5√15

Answer:

Good seats sold=80

Poor seats sold=130

Step-by-step explanation:

g + p = 210 seats.  Then p = 210 - g.

($5)g + ($2)p = $660.  Substite 210 - g for p,

($5)g + ($2)(210 - g) = $660

Simplify, 5g + 420 - 2g = 660 => 3g = 240  =>  g = 80

80 and 130

Answer:

the mean is the closest of 2 or 3

Answer:

The answer is 3.5

The area decreases by 1155.52 square meters

What we must do is calculate the area before and after making the diameter cut.

The area of a circle is equal to:

a = pi * r ^ 2

now the diameter is equal to:

d = 2 * r

therefore r,

r = d / 2

before the cut would be

r = 96/2

r = 48

replacing in the area formula

a1 = 3.14 * 48 ^ 2

a1 = 7234.56 square meters.

after cutting the diameter decreases by 8, that is, 96 - 8 = 88, calculating the radius would be:

r = 88/2

r = 44

now calculating the new area would be:

a2 = 3.14 * 44 ^ 2

a2 = 6079.04 square meters.

now we calculate the difference

a1 - a2 = 7234.56 - 6079.04

= 1155.52 square meters

means that the area decreases by 1155.52 square meters

Answer:

A and E

Step-by-step explanation:

they are both of them correct

Answer:

Group 1: 2x, -4x, 25x

Group 2: -3y, y

Group 3: 10, -6, 100

Group 4: -6x^2, 5x^2

Step-by-step explanation:

In eac group they are the ones that can be combined together, you cannot combine numbers from diffrent groups because they are not like terms.

Answer:

C

Step-by-step explanation:

Mean is all the numbers in the list added / the number of numbers

(Ex: 14, 13, 15, 17

Mean = (13 + 14 + 15 + 17) / (number of numbers in the list)

Mean = 59 / 4

Mean = 14.75)

Range = (The largest number - the smallest number)

Mode is the number that appears the most

The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number

________________________________________________________

Mean of Ernie = 19

Mean of Lori = 17.6

A is False

Range of Ernie = 7

Range of Lori = 8

B is false

Median of Ernie = 18

Median of Lori = 18

C is true

Mode of Ernie = 17

Mode of Lori = 18

D is false

Answer:

Jay has the fastest time because the he gained more meters per second.

Step-by-step explanation:

hope this helps if do mark brainllest pls!

Answer:

A) Jay is faster because he is running 5 m/s