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3 years ago

10

Simplify each expression using the order of operations. Then, match the expression (term) on the left with its solution (definit

ion) on the right.
Match Term Definition

42 + 3 − 2(3) A) 18

22 ⋅ 8 ÷ 2 + 2 B) 44

(42 + 16) + 12 C) 75

8 ⋅ 32 + 3 D) 13

1 answer:

makvit [3.9K]3 years ago

4 0

The second one is true

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How many liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16%

Naily [24]

1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.

For given question,

Let x be the quantity ( in liters ) of glycerin added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin,

Thus,

Quantity of glycerin in 12 liters + Quantity of glycerin in x

= Quantity of glycerin in resultant mixture.

⇒ 8% of 12 + 100% of x = 16% of (12 + x )

⇒ 0.08 × 12 + x = 0.16 × ( 12 + x )

⇒ 0.96 + x = 0.16 × 12 + 0.16x

⇒ 0.96 + x = 1.92 + 0.16x

⇒ x - 0.16x = 1.92 - 0.96

⇒ 0.84x = 0.96

⇒ x = 1.143 liters

Therefore, 1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.

Learn more about the resulting solution here:

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2 years ago

V-39=-16 what is the answer

kotykmax [81]

V-39=-16
V-39+39=-16+39
V=23

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3 years ago

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Yasmine has a dinner party for her grandparents’ 50th anniversary. The total bill comes to $389.45. If she tips the waiter 18%,

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$459.551

Step-by-step explanation:

18% of 389.45 is 70.101 (the tip)

389.45+70.101=459.551 (the total)

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3 years ago

Ryan, Michelle, and Erwin spent $13.50, $16.50, and $14, respectively, at an amusement park. Ryan bought three tickets for the F

Alex

The matrix equation that represents this situation is

$\left[\begin{array}{ccc}3&2&0\\1&0&4\\3&1&1\end{array}\right]*\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}13.50\\16.50\\14.00\end{array}\right]$

Use technology to find the inverse of matrix A:

$A^{-1}= \left[\begin{array}{ccc}-\frac{2}{5}&-\frac{1}{5}&\frac{4}{5}\\
\frac{11}{10}&\frac{3}{10}&-\frac{6}{5}\\\frac{1}{10}&\frac{3}{10}&-\frac{1}{5}\end{array}\right]$

Multiplying A inverse by B, we get the solution matrix
[tex]\left[\begin{array}{ccc}2.50\\3\\3.50\end{array}\right][\tex]

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A hemispherical tank is filled with water and has a diameter of 6 feet. If water weighs 62.4 pounds per cubic foot, what is the

masha68 [24]

Answer:

The total weight of the water in a full tank, to the nearest pound is 3527 pounds per cubic foot

Step-by-step explanation:

Given:

Diameter of the hemispherical tank = 6 feet

Weight of water per cubic foot = 62. 4 pounds

To Find:

The total weight of the water in a full tank, to the nearest pound?

Solution:

We know that the volume of a sphere is:

$V =\frac{4}{3}\pi r^3$

where

r = is the radius

In the question we are given with diameter,

So

$radius = \frac{diameter}{2}$

radius = $\frac{6}{2}$

Radius = 3

We need the volume of the hemisphere

So the volume of the hemisphere will be half of the volume of teh sphere

$\frac{V}{2} = \frac{2}{3}\pi r^3$

Thus the volume of the hemisphere is

$V =\frac{2}{3} \pi r^3$

Now substituting the values

$V = \frac{2}{3} \pi(3)^3$

$V = \frac{2}{3}\pi(27)$

$V = \frac{54 \pi}{3}$

$V = \frac{169.56}{2}$

V= 56.52 cubic foot

Now, the total weight of water of:

W = 56.52 x 62.4

W= 3526.848 pounds per cubic foot

To the nearest pounds

W= 3527 pounds per cubic foot

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3 years ago