The volume of a cube is 3,375 cubic inches. What is the measure of each side of the cube?

Answers

Answer 1

Answer:

The measure of each side of the cube will be 15 inches.

What is volume?

The Volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. Volume is defined as the space occupied by an object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the cube or Cuboid

The cube has all the sides equal means that the length, width, and height of the cube will be the same. Let's suppose the length, width, and height of the cube is a.

The volume of a cube will be given by the formula:-

Volume = side³ = a³

a³ = 3375

a = ∛3375

a = ∛( 15 x 15 x 15 )

a = 15 cubic inches.

Therefore, the measure of each side of the cube will be 15 inches.

To know more about volume follow

brainly.com/question/35100

#SPJ5

Answer 2

Answer:

Answer:

l=w=h=15

Step-by-step explanation:

Volume of a cube= l*w*h

where l=w=h

$l = {}^(3) √( v) \: \: \: l = {}^(3) √(3375) = 15$

15*15*15=3375

Hope this helps ;) ❤❤❤

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What value of n makes the equation 0.3(12 n-16)=0.4(12-3n) true

Answers

I believe that n= 2. please correct me if I am wrong.

Answer:

n=2

Step-by-step explanation:

Find the value of the expression: 70–a^2 for a=–25; 1; 10

Answers

Answer:

a = -25: -555
a = 1: 69
a = 10: -30

Step-by-step explanation:

Put the value where "a" is in the expression and do the arithmetic.

For a = -25: 70 - (-25)² = 70 - 625 = -555
For a = 1: 70 - (1)² = 70 - 1 = 69
For a = 10: 70 - (10)² = 70 - 100 = -30

_____

If you're unsure of your own arithmetic skills, you can always use a calculator.

Jared ate 1/4 of a loaf bread. He cut the rest of loaf into slices. How many slices of bread did he cut?

Answers

Answer: He cut 6 slices of bread.

Step-by-step explanation:

Given : Jared ate $(1)/(4)$ of a loaf of bread.

Then , the reaming portion of the bread will be $1-(1)/(4)=(4-1)/(3)=(3)/(4)$ .

The size of each slice = $(1)/(8)$ of a bread.

N ow , the number of slices he cut the remaining portion = $(3)/(4)/(1)/(8)$

$=(3)/(4)*8=6$

Hence, the number of slices of bread he cut = 6.

3 slices because he ate 1 slice ( 1/4) (2/4) (3/4) (4/4) so 3 slices

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answer in terms of V.)

Answers

Answer:

The dimensions of the aquarium that minimize the cost of the materials:

$x=y=\sqrt[3]{(2V)/(5)}\nz=\sqrt[3]{(25V)/(4)}$

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V= $Length * Breadth * Height=xyz$ ----A

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=5xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

$\nabla C =\lambda \nabla V$

$((\partial C)/(\partial x),(\partial C)/(\partial y),(\partial C)/(\partial z))= \lambda ((\partial V)/(\partial x),(\partial V)/(\partial y),(\partial V)/(\partial z))$

$(5y+2z,5x+2z,2y+2x)=\lambda(yz,xz,xy)$

So,

$5y+2z=\lambda yz$ ----1

$5x+2z=\lambda xz$ -----2

$2y+2x=\lambda xy$ ----3

Multiply 1 ,2 and 3 by x,y and z respectively.

$5xy+2xz=\lambda xyz$ ----4

$5xy+2yz=\lambda xyz$ -----5

$2yz+2xz=\lambda xyz$ ----6

Now equate 4 and 5

5xy+2xz=5xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

$5x(x)+2(x)z=2(x)z+2xz\n5x^2=2xz\n5x=2z\n(5)/(2)x=z$

Substitute the values in A

$V = xyz = x * x * (5)/(2)xV=(5)/(2)x^3\n\sqrt[3]{(2)/(5)V}=x\nx=y=\sqrt[3]{(2)/(5)V}\nz=(5)/(2)x=(5)/(2)(\sqrt[3]{(2)/(5)})=\sqrt[3]{(25V)/(4)}$

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

$x=y=\sqrt[3]{(2V)/(5)}\nz=\sqrt[3]{(25V)/(4)}$

Solve this system of linear equations. Separatthe x- and y-values with a comma.
9x - 10y = -34
3x - 4y = -16

Answers

Answer:

$9x - 10y = - 34 - - - (a) \n 3x - 4y = - 16 - - - (b) \n (a) - 3 * (b) : \n 0x + 2y = 14 \n y = 7 \n 3x - (4 * 7) = - 16 \n 3x = 12 \n x = 4$

answer:( 4, 7 )

Hi there!

»»————-　★　————-««

I believe your answer is:

(4,7)

»»————-　★　————-««

Here’s why:

I have graphed the system on a program.
The two lines intercept at the point (4,7). This means that it is the solution to the system.
See the graph attached.

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

The daily high temperature in Chicago for the month of August is approximately normal with mean 78 degrees F, and standard deviation 9 degrees F. a. What is the probability that a randomly selected day in August will have a high temperature greater than the mean daily high temperature of 78 degrees F?
b. What is the percentile for a day in August with a high temperature of 75 degrees F?
c. What is the 75th percentile for the daily high temperature for the month of August?
d. What is the interquartile range for the daily high temperature for the month of August?

Answers

Answer:

a) $P(X>78) = P(Z> (78-78)/(9)) = P(Z>0)= 0.5$

b) $P(X<75)= P(Z< (75-78)/(9)) = P(Z<-0.333) = 0.370$

So then 75 F correspond to approximately the 37 percentile

c) $z=0.674<(a-78)/(9)$

And if we solve for a we got

$a=78 +0.674*9=84.07$

So the value of height that separates the bottom 75% of data from the top 25% is 84.07 F.

d) $IQR = 84.07-71.93= 12.14$

See explanation below.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the daily high temperature in Chicago for the month of August of a population, and for this case we know the distribution for X is given by:

$X \sim N(78,9)$

Where $\mu=78$ and $\sigma=9$

We are interested on this probability

$P(X>78)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=(x-\mu)/(\sigma)$

Using the z score we got:

$P(X>78) = P(Z> (78-78)/(9)) = P(Z>0)= 0.5$

Part b

For this case we can find the percentile with the following probability:

$P(X<75)$

If we use the z score formula we got:

$P(X<75)= P(Z< (75-78)/(9)) = P(Z<-0.333) = 0.370$

So then 75 F correspond to approximately the 37 percentile

Part c

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X<a)=0.75$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X<a)=P((X-\mu)/(\sigma)<(a-\mu)/(\sigma))=0.75$

$P(z<(a-\mu)/(\sigma))=0.75$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674<(a-78)/(9)$

And if we solve for a we got

$a=78 +0.674*9=84.07$

So the value of height that separates the bottom 75% of data from the top 25% is 84.07 F.

Part d

For this case we know that $IQR = Q_3 - Q_1 = P_(75)-P_(25)$

So then we just need to find the percentile 25.

$P(X>a)=0.25$ (a)

$P(X<a)=0.75$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

$P(X<a)=P((X-\mu)/(\sigma)<(a-\mu)/(\sigma))=0.25$