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Answer:

6 3/4 cm³

Step-by-step explanation:

I'm assuming value means volume, so if I'm wrong, let me know ;).

To find volume, you multiply length x height x width. So you multiply 2 1/4 three times.

Convert 2 1/4 to an improper fraction.

2 1/4 = 9/4

9   x   3        27

--        --     =

4   x    1        4

Now convert 27/4 to a mixed fraction.

27/4 = 6 3/4

So the volume of the cube is 6 3/4 cm³.

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hope it helps

Answer:

Step-by-step explanation:

The formula for this is

[tex]N=N_0(.5)^{\frac{t}{H}[/tex] where

N is the amount of the element left after a certain amount of time (for us it is measured in days),

N₀ is the initial amount of the element in grams,

t is the number of days gone by, and

H is the half life of the element. Filling in:

[tex]N=42(.5)^{\frac{16}{8}[/tex] which simplifies a bit to

[tex]N=42(.5)^2[/tex] and a bit more to

N = 42(.25) which gives us a remaining amount of

N = 10.5

Answer:

B=23.19

Step-by-step explanation:

First, find the last side of the triangle using the Pythagorean theorem.

[tex]a^{2} +b^{2} =c^{2} \\21^{2} +9^{2} =c^{2} \\441+81=c^{2} \\\sqrt[3]{58}=c[/tex]

Then, find the missing angle, lets name it B.

The angle B can be found using the inverse sine function.

B=arcsin(opp/hyp)

[tex]B=arcsin(\frac{9}{\sqrt[3]{58} } )\\B=23.19[/tex]

Answer:

Length = 5 feet

Breadth = (5/3) feet

Height(depth) = 2 feet

Volume of the entire tank = Length x Breadth x Height  

                                         = [tex]5 \times \frac{5}{3} \times2 = \frac{50}{3}[/tex]   ----------(1)

Water is filled upto a height of (1/3) feet

Volume of water in the tank = Length x Breadth x Height  

                                           = [tex]5 \times \frac{5}{3} \times \frac{1}{3} = \frac{25}{9}[/tex]     -------------(2)

Volume of space needed to be filled = (1) - (2)

                                                         = [tex]\frac{50}{3} -\frac{25}{9} = \frac{150-25}{9} = \frac{125}{9} cubic feet[/tex]

                                           OR

Height of tank needed to be filled = 2 - (1/3) = (5/3) feet

Volume of space =  Length x Breadth x Height of empty tank

                           =  [tex]5 \times \frac{5}{3} \times \frac{5}{3} = \frac{125}{9} cubic \ feet[/tex]

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Explanation:

As mentioned earlier (in a previous post) the triangle with sides 2,5,7 is not a right triangle. So we can rule out choice A.

For choice B, we have a = 6, b = 8, c = 10, and that leads to...

a^2+b^2 = c^2

6^2+8^2 = 10^2

36+64 = 100

100 = 100

The true equation at the end means the beginning equation is true as well for those a,b,c values. Therefore, we have a right triangle and the answer is choice B

Choices C and D are similar to choice A. They make a^2+b^2 = c^2 to be false.

Answer:

J

Step-by-step explanation:

[tex]y \alpha x \\ \frac{y}{x} = k \\ \frac{21}{3} = \frac{105}{x} \\ x = 15[/tex]

Answer:

6 pencils in each group

Step-by-step explanation:

Total = 88

Gave away = 46

Balance = 88 - 46 = 42

Divided into 7 groups, means : 42/7 = 6

So each group has 6 pencils

Answer:

There are 35 of each color.

Step-by-step explanation:

If the number of each color is the same  there are 140 / 4 = 35 balloons of each color.

Answer:

Option a.

Step-by-step explanation:

By looking at the options, we can assume that the function y(x) is something like:

[tex]y = \sqrt{4 + a*x^2}[/tex]

[tex]y' = (1/2)*\frac{1}{\sqrt{4 + a*x^2} }*(2*a*x) = \frac{a*x}{\sqrt{4 + a*x^2} }[/tex]

such that, y(0) = √4 = 2, as expected.

Now, we want to have:

[tex]y' = \frac{x*y}{2 + x^2}[/tex]

replacing y' and y we get:

[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]

Now we can try to solve this for "a".

[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]

If we multiply both sides by y(x), we get:

[tex]\frac{a*x}{\sqrt{4 + a*x^2} }*\sqrt{4 + a*x^2} = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}*\sqrt{4 + a*x^2}[/tex]

[tex]a*x = \frac{x*(4 + a*x^2)}{2 + x^2}[/tex]

We can remove the x factor in both numerators if we divide both sides by x, so we get:

[tex]a = \frac{4 + a*x^2}{2 + x^2}[/tex]

Now we just need to isolate "a"

[tex]a*(2 + x^2) = 4 + a*x^2[/tex]

[tex]2*a + a*x^2 = 4 + a*x^2[/tex]

Now we can subtract a*x^2 in both sides to get:

[tex]2*a = 4\\a = 4/2 = 2[/tex]

Then the solution is:

[tex]y = \sqrt{4 + 2*x^2}[/tex]

The correct option is option a.

Answer:

D. 78°

Step-by-step explanation:

50°+28°= 78°

_______

Answer:

The researcher determines relationships among variables.

The individuals are observed the exact way they act in real life.

Step-by-step explanation:

An observational study can be defined as a type of study in which a researcher observes and measures the effect of a diagnostic test, risk factors, or treatments on individuals without intervening, changing or manipulating who are or aren't exposed to it (controlled conditions).

Hence, the statements which best describes a characteristic of an observational study are;

I. The researcher determines relationships among variables.

II. The individuals are observed the exact way they act in real life.

Additionally, an unobtrusive data collection is a data collection technique used mainly in the social sciences to obtain or gather data without the researcher directly interfering or interfacing with the subject being studied. Thus, it doesn't influence the behavior, action or response of the subjects under study.

Answer:

2.15cm^3

Step-by-step explanation:

V = Mass / Density

21.93g / 10.2 g/cm^3

2.15cm^3

Answer:

A, B, D, E, F

Step-by-step explanation:

48/64 can be simplified into all of them except C

Answer:

1 : 6

Step-by-step explanation:

Answer: See the attached image

You have the correct idea for the boxes you've filled out. For the first three boxes in column 1, I would be specific which segments you are dividing. So for instance, in the first box, it would be EG/EB = 55/11 = 5. Then the second box would be EF/EC = 35/7 = 5, and so on. The order of the boxes doesn't matter. The three boxes then combine together to help show that the triangles are similar. Specifically [tex]\triangle EFG \sim \triangle ECB[/tex]. The order of the letters is important to help show how the angles pair up and how the sides pair up. We use the SSS similarity theorem here.

The second problem is the same idea, but we use one pair of congruent angles. So we'll use the SAS similarity theorem this time.

Answer:

A,B,F

Step-by-step explanation:

I did the test and got it right, hope this helps

Answer:

1 11/12

Step-by-step explanation:

convert to common denominators.

1 1/6 = 7/6 = 14/12

3/4 = 9/12

14+9=23

23/12

1 11/12

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hope it helps

Answer:

x-intercept (-3;0) and (1;0)

y-intercept (0;1)

35 is the answer

have a wonderful day

Answer:

4p +2

Step-by-step explanation:

(2p + 1)(2)

Distribute

2p * 2 + 1*2

4p +2

Answer:

4p+2

Step-by-step explanation:

See the steps below:)

Answer:

53

Step-by-step explanation:

848 students/16 buses=53 students per bus

Welcome back....♡

Surface area = 2( 4 × 2 ) + ( 3 × 4 )

+ 2( 4 × 4 ) + 3( 10 × 4 )

+ 3( 4 × 7 )

Surface area = 16 + 12 + 32 + 120 + 84

Surface area = 264 in^2

Answer: hi your question is incomplete below is the complete question

Use the Divergence Theorem to calculate the surface integral S F dS   with F x y z = , , and S is a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral

answer : surface integral = 384/5 π

Step-by-step explanation:

Representing  the vector field as

F ( x, y , z ) = ( a^3 + y^3 ) + ( y^3 + z^3 ) + ( Z^3 + x^3 ) k

assuming the sphere ( s) with radius = 2 be centered at Origin of the vector field.

Hence the divergence will be represented as :

Attached below is the detailed solution