A sphere has a diameter of 14 units. What is the volume of the sphere in cubic units? If a cylinder has the same radius as the sphere and a height
of 14 units, what is the volume of the cylinder? Use 3.14 for pie

A). The volume of the sphere is about 1,077.02 cubic units, and the volume of the cylinder is about 718.01 cubic units.

B). The volume of the sphere is about 1,436.03 cubic units, and the volume of the cylinder is about 2.154.04 cubic units.

C). The volume of the sphere is about 1,436.03 cubic units, and the volume of the cylinder is about 957.35 cubic units.

D). The volume of the sphere is about 1,077.02 cubic units, and the volume of the cylinder is about 1,615.53 cubic units.

Answer:

-27 and -18

Step-by-step explanation:

Solve algebraically. Use a variable and an expression to represent the numbers.

let the smaller number be "x"

The bigger number is x + 9.

The two numbers are "x" and "x + 9".

The sum of two numbers means when you add them together. If their number is −45, then:

x + x + 9 = −45

Simplify and isolate "x" to solve in the equation.

x + x + 9 = −45        Collect like terms (numbers that have "x") to simplify

2x + 9 = −45        Isolate "x"

2x + 9 - 9 = −45 - 9        Subtract 9 from both sides

2x = −54

2x/2 = −54/2        Divide both sides by 2

x = -27       Value of smaller number

The bigger number is x + 9. Substitute "x" for -27 and solve.

x + 9

= -27 + 9        Add together

= -18        Value of bigger number

Therefore the two numbers are -27 and -18.

Answer:

if -45 + -9 = -54 that means - 54 + 9 = -45

Step-by-step explanation:

Answer:

20 per min

Step-by-step explanation:

Answer: 1200 boxes per 1 hour

Step-by-step explanation: 15 divided by 3 is 5. 300 divided by 100. 100 boxes in 5 minutes. 5 times x is 60. 60 is a hour. 60 divided by 5 is 12. 100 times 12 is 1200. 1200 boxes per 1 hour.

Answer:

x = 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex], then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x × [tex]\sqrt{2}[/tex] = 10 ( divide both sides by [tex]\sqrt{2}[/tex] )

x = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]

  = [tex]\frac{10\sqrt{2} }{2}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

19

Step-by-step explanation:

We have that out of 100 products , 93 are ready for purchase by customers.

The probability of the product being purchased is 93% or 0.93.

The expectation is given by;

E(x)=n*p(x)

If the 20 products are selected, then we have n=20

The expectation is

[tex] \bar x = 0.93 \times 20[/tex]

[tex] \bar x = 18.6[/tex]

Thus approximately 19 customers will be ready to purchase

Final answer:

The expected mean number of products ready for purchase out of 20 selected is 18.6, calculated by multiplying the probability of one product being ready (0.93) by the total number of products (20).

Explanation:

To determine the expected mean number of products ready to purchase out of a selection of 20 products, given that out of each 100, 93 are ready, we use the concept of probability and expected value. The probability that any one product is ready to purchase can be represented as 93/100 or 0.93.

For the expected mean number of products ready to purchase out of 20, we multiply the probability that one product is ready (0.93) by the total number of products chosen (20):

Expected mean number = 0.93 * 20 = 18.6

Therefore, we would expect that, on average, 18.6 out of 20 products selected would be ready to purchase.

Answer:

  5.  C.  {(22, 10), (23, 10), (24, 7), (25, 5)}

  6.  C.  x = -2

Step-by-step explanation:

A relation is not a function if a vertical line intersects a graph of it in more than one place.

__

5. A set of ordered pairs is not a function if any of the first-values is repeated.

In set A, (22, ) is repeated.

In set B, (23, ) is repeated.

In set D, (24, ) is repeated.

In set C, no first-value is repeated, so the relation is a function.

__

6. The line x=-2 is a vertical line, so a vertical line intersect it in an infinite number of places. It is NOT a function.

step-by-step explanation:

1.

8m +4n +7m-2n

=8m+7m+4n-2n

=15m+2n

2.

12(5y+4)

=60y+48   [ Using distributive law]

Therefore it is binomial of one variable.

3.

[tex]-2(\frac{1}{3}x -\frac{1}{5} )[/tex]

[tex]=-\frac{2}{3} x +\frac{2}{5}[/tex]

4.

4d+12

=4(d+3)

5.

-4.5n+3

= -4(5n+3)

Final answer:

The weight gain in days per pound for Lin's puppy is 8 days per pound.

Explanation:

The weight gain in days per pound can be calculated by taking the reciprocal of the rate of weight gain. In this case, Lin's puppy is gaining weight at a rate of 0.125 pounds per day. To find the weight gain in days per pound, we can take the reciprocal of 0.125, which is 1/0.125 = 8 days per pound.

Answer:

[tex]x=5,y=10[/tex]

Step-by-step explanation:

Given:

                      [tex]4x - 2y = 0[/tex]        equation:1

                 [tex]-x - 2y = -25[/tex]        equation:2

Terminating the equations by subtracting equation:2 from equation:1

                     [tex]4x - 2y -(-x - 2y)= 0-( -25)\\\\ 4x-2y+x+2y=25\\\\5x=25\\\\x=5[/tex]

Putting 'x' in equation :1

                                [tex]4(5) - 2y = 0\\\\20-2y=0\\\\2y=20\\\\y=10[/tex]

[tex]x=5,y=10[/tex]

(x²-3²)(x+5) is the binomial that is a factor of the polynomial P(x) = x³ + 5x² − 9x − 45

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is P(x) = x³ + 5x² − 9x − 45.

Factor out the greatest common factor from each group.

x³ + 5x² − 9x − 45.

x cube plus five times of x square minus nine times of x minus forty five.

x² (x+5)-9(x+5)

(x²-9)(x+5)

We can write 9 as a square of three

(x²-3²)(x+5)

A mathematical expression consisting of two terms connected by a plus sign or minus sign

Hence, (x²-3²)(x+5) is the binomial that is a factor of the polynomial P(x) = x³ + 5x² − 9x − 45

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Answer:

375 meters

Step-by-step explanation:

We use the tangent ratio to determine the height of the height of the cliff.

We have that, the boat is 600 meters from the base of a cliff.

We also know that, the angle of elevation to the top of the cliff is 32°

Using the tangent ratio, we have:

[tex] \tan(32) = \frac{h}{600} [/tex]

We solve for h to obtain:

[tex]600\tan(32) = h[/tex]

[tex]h = 374.92[/tex]

Therefore the height of the cliff is approximately 375 meters

The angle of elevation is an angle that is formed between the horizontal line and the line of sight, hence the Height of the cliff is

374.4 meters

Given Data

Opposite/Height of cliff = ??

Adjacent/Distance of boat from base = 600 meters

Angle of elevation ∅  = 32°

By applying SOH CAT TOA

Tan  ∅ = Opp/Adj

Substituting our given Data we have

Tan 32 = Opp/600

0.624 = Opp/600

Cross multiply we have

Opp = 0.624*600

Opp = 374.4 meters

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The y-values of equivalent ratios increase at the same rate as their x-values. The vertical distance between points is constant, and the horizontal distance between points is constant. This forms a straight line.

Explanation:

Equivalent proportions (which are, as a result, equal parts) are two proportions that express a similar connection between numbers. We can make comparable proportions by duplicating or separating both the numerator and denominator of a given proportion by a similar number.

Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions.

Answer:

The y-values of equivalent ratios increase at the same rate as their x-values. The vertical distance between points is constant, and the horizontal distance between points is constant. This forms a straight line.

Step-by-step explanation:

Copy and paste this answer and you will get it correct!!!!! I promise!

Answer:

6x+8

Step-by-step explanation:

Answer:

6x + 8 is the answer

Step-by-step explanation:

on Edgenuity 2020

Answer:

rise

Step-by-step explanation:

Answer:

2x-8d

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Globalization represents to the worldwide reconciliation of universal exchange, venture, data innovation and societies. Government strategies intended to open economies locally and universally to support advancement in poorer nations and raise ways of life for their kin are what drive globalization. In any case, these approaches have made a universal free market that has principally profited global enterprises in the Western world to the disadvantage of littler organizations, societies and average folks.

Answer:

I took the test the answer is B.

Step-by-step explanation:

Answer:

Length = 22 inches, Width = 5 inches

Step-by-step explanation:

Let P represent the Perimeter, L , the length and W, the width

Perimeter of a rectangle, P = 2 (L + W) ....eq 1

from the question;

L = 2 + 4W .....eq 2

Slotting in the respective values of P and L in eq 1

54 = 2{(2 + 4W) + W}

Expanding the bracket

54 = 2(2 + 5W)

54 = 4 + 10W

Subtracting 4 from both sides of the equation

54 - 4 = 10 W

50 = 10W

Dividing both sides by the coefficient of W which is 10

5 = W

Therefore, W = 5 inches

Slotting in the value of W in eq 2

L = 2 + 4(5)

L = 2 + 20

L = 22 inches

Now lets check our answers by slotting in the values of P, L and W in eq 1

54 = 2 (22 + 5)

54 = 2 (27)

54 = 54

Since both sides of the equation are equal, the values of L and W are correct

Hence Length = 22 inches, Width = 5 inches

Answer:

You will pay $12.23

Step-by-step explanation:

One method:

$17.99 * (1-15%) = $15.29

$15.29 * (1-20%) = $12.23

Final answer:

It will take Shaun 156 hours to mow 78 lawns based on his current rate of mowing 3 lawns in 6 hours.

Explanation:

To determine how many hours it will take Shaun to mow 78 lawns based on the rate at which he mows 3 lawns in 6 hours, we will use a proportion. First, we find the rate at which Shaun mows lawns per hour, which is 3 lawns / 6 hours = 0.5 lawns per hour. Next, we set up a proportion where the total number of lawns he needs to mow (78 lawns) is set equal to the product of the number of hours it takes (which we are trying to find) and the rate at which he mows lawns (0.5 lawns per hour).

So, the proportion is:
78 lawns = x hours ( 0.5 lawns/hour.)

Dividing both sides of the equation by 0.5 lawns/hour gives us:

x hours = 78 lawns / 0.5 lawns/hour

x hours = 156 hours.

Therefore, it will take Shaun 156 hours to mow 78 lawns at his current rate.

A. If you use only the coupon you will have to pay $137.50.

B. Using the Coupon during the sale, the kit is discounted by $112.50

C. The total percent discount is 45% after both discounts.

Step-by-step explanation:

Step 1; The store has the robotics kit for a sale of 25% off $250. So we need to find how much 25% is in terms of $250. To do that we convert 25% into a fraction by dividing it by 100 and multiplying it with $250.

25% of  $250 = [tex]\frac{25}{100}[/tex] × $250 = 0.25 × $250 = $62.50

So we find the cost of the kit due to the store's discount. To do that we subtract the discounted price from the original price.

Robotics kit price after 25% discount = $250 - $62.50 = $187.50.

Step 2; A coupon you have gives you an additional 20% discount. So the robotics kit can be brought for 25% off due to the sale at the store, due to this coupon you get an additional 20%. So you get a 45% discount off $250.

45% of  $250 = [tex]\frac{45}{100}[/tex] × $250 = 0.45 × $250 = $112.50.

So to find the total discount we subtract this $112.50 from the non-discounted cost of $250.

Total discounted price = $250 - $112.50 = $137.50.

Answer:

[tex]-0.8x + 4.8y + 16[/tex]          

Step-by-step explanation:

We have to simplify the given expression:

[tex]4(0.5x + 2.5y-0.7x-1.3y+4)[/tex]

First we group all the like terms of x.

[tex]4((0.5x-0.7x) + 2.5y-1.3y+4))\\=4(-0.2x+ 2.5y-1.3y+4)[/tex]

Next we group all the like terms of y.

[tex]4(-0.2x+ (2.5y-1.3y)+4)\\=4(-0.2x+1.2y+4)[/tex]

Now, we use distributive property for the multiplication,

[tex]4(-0.2x+1.2y+4)\\=(4\times -0.2x) + (4\times 1.2y) + (4\times 4)\\=-0.8x + 4.8y + 16[/tex]

is the required simplified expression.

Answer:

-0.8x + 4.8y + 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we can convert feet to inches

1 foot=12 inches

7 feet=84 inches

Next, we find out inches per hour

84 inches/27 1/2 hours

----------- --------------

27 1/2 27 1/2

=3.054 inches/hour

Answer:

The answer is option C [tex](x+1)^{2} + ( y-2)^2 =25[/tex]

Step-by-step explanation:

i) The answer is option C [tex](x+1)^{2} + ( y-2)^2 =25[/tex]

Answer:

0.525

Step-by-step explanation:

It's easy

Answer:

0.53

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

We want to find an expression that is equivalent to

[tex] {16}^{ \frac{3}{4}x } [/tex]

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

We apply this property of exponents to rewrite our expression:

We set a=16, n=4 and m=3x

This implies that:

[tex]{16}^{ \frac{3x}{4} } = \sqrt[4]{ {16}^{3x} } = (\sqrt[4]{ {16} })^{3x} [/tex]

The first choice is correct.

Answer:

A

Step-by-step explanation:

edg review 2020

The value of h(t) when [tex]t=\frac{15}{32}[/tex] is 10.02.

Solution:

Given function [tex]h(t)=-16t^2+15t+6.5[/tex]

To find the value of h(t) when [tex]t=\frac{15}{32}[/tex]:

[tex]h(t)=-16t^2+15t+6.5[/tex]

Substitute [tex]t=\frac{15}{32}[/tex] in the given function.

[tex]$h\left(\frac{15}{32} \right)=-16\left(\frac{15}{32} \right)^2+15\left(\frac{15}{32} \right)+6.5[/tex]

            [tex]$=-16\left(\frac{225}{1024} \right)+15\left(\frac{15}{32} \right)+6.5[/tex]

Now multiply the common terms into inside the bracket.

           [tex]$=-\left(\frac{3600}{1024} \right)+\left(\frac{225}{32} \right)+6.5[/tex]

Now, in the first term, the numerator and denominator both have common factor 16. So reduce the first term into the lowest term.

          [tex]$=-\left(\frac{225}{64} \right)+\left(\frac{225}{32} \right)+6.5[/tex]

To make the denominator same, take LCM of the denominators.

LCM of 64 and 32 = 64

        [tex]$=-\left(\frac{225}{64} \right)+\left(\frac{225\times2}{32\times2} \right)+6.5\times\frac{64}{64}[/tex]

        [tex]$=-\frac{225}{64} +\frac{450}{64}+\frac{416}{64}[/tex]

        [tex]$=\frac{-225+450+416}{64}[/tex]

       [tex]$=\frac{641}{64}[/tex]

       = 10.02

[tex]$h\left(\frac{15}{32} \right)=10.02[/tex]

Hence the value of h(t) when [tex]t=\frac{15}{32}[/tex] is 10.02.

Answer:

3/10

Step-by-step explanation:

10/10 - 7/10 = 3/10

Final answer:

The fraction of students in the marching band that are girls is 3/10, calculated by first determining the total number of students and then finding the difference between the total and the number of boys.

Explanation:

To figure out what fraction of the students in the marching band are girls, we need to first determine the total number of students in the band based on the given information that 28 boys represent 7/10 of the band. To find the total, we divide the number of boys by the fraction they represent:

Total students = 28 boys ÷ (7/10) = 40 students

Now, to find the number of girls, we subtract the number of boys from the total number of students:

Girls = Total students - Boys = 40 students - 28 boys = 12 girls

To find the fraction that represents the girls in the band, we put the number of girls over the total number of students:

Fraction of girls = Girls ÷ Total students = 12 ÷ 40 = 3/10

Answer:

The solution is -5 or 11

Step-by-step explanation:

We are given the equation;

[tex]4(3-x)^\frac{4}{3}-5=59[/tex]

We are supposed to solve the equation;

Taking 5 to the other side;

[tex]4(3-x)^\frac{4}{3}=59+5[/tex]

[tex]4(3-x)^\frac{4}{3}=64[/tex]

Dividing both sides by 4

[tex](3-x)^\frac{4}{3}=\frac{64}{4}[/tex]

[tex](3-x)^\frac{4}{3}=16[/tex]

We can cube both sides;

[tex]((3-x)^\frac{4}{3})^3=16^3[/tex]

[tex](3-x)^4=4096[/tex]

Then we can get the fourth root on both sides of the equation;

[tex]\sqrt[4]{ (3-x)^4} =\sqrt[4]{4096}[/tex]

We get;

[tex]3-x=+8 or -8[/tex]

Solving for x

[tex]3-x=8 and 3-x=-8[/tex]

Therefore;

[tex]x=-5 or 11[/tex]

Therefore, the solution is -5 or 11

Answer:

Hamburger = $2.5

Fries = $0.80

Step-by-step explanation:

set up a system of equations

y = total cost

x = number of hamburgers

y = number of fries

[tex]24=8x+5y\\16.60=6x+2y[/tex]

find a LCF and multiply the equations. I'll be using the LCF of 5 & 2, which is 10 for y. so I will mulitilpy the first equation by 2 to get 10y and then the second by NEGATIVE 5 (-5) so when I combine both equations the y will cancle out because I'll get -10. Doing this, you should end up with this:

[tex]48=16x+10y\\-83=-30x-10y[/tex]

when you have this combine the equations to get

[tex]-35=-14x[/tex]

then divide both sides by -14 to get

[tex]2.5=x[/tex] this is the cost of one hamburger

then you plug in x into one of the original equations (I'll use the first equation)

[tex]24=8(2.5)+5y[/tex]

then solve for y to get

[tex]0.80=y[/tex] this is the cost for fry

if you plug in both the value for x and y into the original equations (like so)

[tex]24=8(2.5)+5(0.8)\\16.60=6(2.5)+2(0.8)[/tex]

you'll see that they are true (they equal one another)

this means that the cost of a hamburger is $2.50 and the cost of fries is $0.80

The cost of each hamburger is $2.50, and the cost of each serving of fries is $0.80.

Let's use a system of equations to solve this problem. Let h represent the cost of a hamburger and f represent the cost of a serving of fries.

From the information given, we can create two equations:

8h + 5f = 24

6h + 2f = 16.60

Now, we can solve this system of equations. We can start by solving one of the equations for one of the variables and then substituting it into the other equation. Let's solve equation 1 for h:

8h = 24 - 5f

h = (24 - 5f)/8

Now, substitute this expression for h into equation 2:

6[(24 - 5f)/8] + 2f = 16.60

Now, we can simplify and solve for f:

(3/4)(24 - 5f) + 2f = 16.60

Multiply both sides by 4 to eliminate the fraction:

3(24 - 5f) + 8f = 66.40

Now, distribute the 3 on the left side:

72 - 15f + 8f = 66.40

Combine like terms:

-7f = 66.40 - 72

-7f = -5.60

Now, divide by -7 to solve for f:

f = -5.60 / -7

f = $0.80

Now that we've found the cost of a serving of fries (f), we can use this value to find the cost of a hamburger (h) using equation 1:

8h + 5(0.80) = 24

8h + 4 = 24

8h = 24 - 4

8h = 20

h = 20 / 8

h = $2.50

So, the cost of each hamburger is $2.50, and the cost of each serving of fries is $0.80.

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