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Ede4ka [16]
3 years ago
8

The density of a certain material is such that it weighs 70 pounds for every 8.5 gallons of volume. Express this density in kilo

grams per liter. Round your answer to the nearest hundredth.
Mathematics
1 answer:
STALIN [3.7K]3 years ago
4 0

The correct answer is 0.99kg/L

Explanation:

To find the density, the first step is to convert the weight (mass) and the volume into the appropriate units.

The volume is 8.5 gallons and this needs to be converted to litters. In this case, multiply the volume in gallons by 3.785 because each gallon contains 3.785 liters.

8.5 x 3.785 = 32.1725 liters

The mass is 70 pounds and this needs to be converted to kilos. In this case, divide the pounds by 2.204 considering each kilo contains 2.204 pounds.

70 ÷ 2.2046 = 31.751 kilos

Now, find the density by dividing the mass into the volume.

Density= 31.751 kg ÷ 32.1725 L

Density = 0.98 kg/L

This means the density is 0.9.868 kg/L and this can be rounded as 0.99 kg/L

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vichka [17]
Hello!

Due to the definition of the Alternate Interior Angles Theorem, (x+23)+(x+54)=180 degrees:

x + 23 + x + 54 = 180
2x + 77 = 180
2x = 103
x = approximately 52 degrees  or exactly 51.5 degrees

I hope this helps :))
4 0
3 years ago
Let N be the universal set and A, B, C, D be its subsets given by A={x:xisaevennaturalnumber},B={x:xNandxisamultipleof3} C={x:x
Svet_ta [14]

Answer:

A^{'} = {1,3,5,7,9,....}

B^{'} = {1,2,4,5,7,8,10,11,13,14......}

C^{'} = {1,2,3,4,5}

D^{'} = {10,11,12,13,14,15,......}

Step-by-step explanation:

Solution:

It is given that, Universal set is the set of all Natural Numbers.

and

Set A, Set B, Set  C, Set D are subsets of Universal set.

A = {x:x is even natural numbers} = {2,4,6,8,10,.....}

B = {x:x ∈ N and x is a multiple of 3} = {3,6,9,12,15,....}

C = {x:x∈ N and x < 5} = {6,7,8,9,10,.....}

D = {x:x ∈ N and x > 10} = {1,2,3,4,5,6,7,8,9}

U = {1,2,3,4,5,6,7,8,9,10,11,........}

Complements:

A^{'} = U-A = {1,2,3,4,5,6,7,8,9,10,11,........} - {2,4,6,8,10,.....}

A^{'} = {1,3,5,7,9,....}

B^{'} = U-B =  {1,2,3,4,5,6,7,8,9,10,11,........} - {3,6,9,12,15,....}

B^{'} = {1,2,4,5,7,8,10,11,13,14......}

C^{'} = U-C = {1,2,3,4,5,6,7,8,9,10,11,........} - {6,7,8,9,10,.....}

C^{'} = {1,2,3,4,5}

D^{'} = {1,2,3,4,5,6,7,8,9,10,11,........} - {1,2,3,4,5,6,7,8,9}

D^{'} = {10,11,12,13,14,15,......}

8 0
2 years ago
The top tree broke and fell over.the remaining tree teunk is 3 feet tall.the tip of the tree rests on the ground 14 feet from th
Bas_tet [7]

Answer:

14.3 feet.

14.3 feet

Step-by-step explanation:

The problem forms a right triangle in which:

The Vertical Leg of the Right Triangle = 3 feet

The Horizontal Leg of the Right Triangle =14 feet

We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,

Using Pythagoras Theorem

Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=14^2+3^2\\Hypotenuse^2=205\\Hypotenuse=\sqrt{205}\\Hypotenuse=14.32\\ \approx 14.3 feet $(to the nearest tenth of a foot).\\Therefore, the lenght of the broken part of the tree to the nearest tenth of a foot is 14.3 feet.

5 0
3 years ago
Solve for x {x+4]= 6
wlad13 [49]

The solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.

<h3>What is a quadratic equation?</h3>

Any equation of the form \rm ax^2+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}

We have an equation:

x(x + 4) = 6

By distributive property:

x² + 4x = 6

x² + 4x - 6 = 0

a = 1, b = 4, c = -6

Plugging all the values in the formula:

\rm x = \dfrac{-4 \pm\sqrt{4^2-4(1)(-6)}}{2(1)}

After calculating:

\rm x = \dfrac{-4 \pm\sqrt{40}}{2}

\rm x=-2+\sqrt{10},\ \ \ or \ \ \ x=-2-\sqrt{10}

Thus, the solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ1

6 0
2 years ago
Read 2 more answers
This jar has 1 red, 74 yellow, and 25 green gumballs. What are the chances of picking a green gumball? the red one? ​
kari74 [83]

Answer: green = 25/100, red = 1/100

Step-by-step explanation: add ALL of the gumballs, there's your denominator, now you have 0/100 (1+74+25), count the amount of marbles you want to get the probability of, lets say green, there's your numerator (25) = 25/100

5 0
3 years ago
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