a right circular cylinder, a, has radius r and height h. another right circular cylinder, b, has radius 3r and height 2h. what is the ratio of the volume of a to the volume of b ?

The price the machinery have initially cost rounded to the nearest dollar is $244,693

The formula for calculating depreciation is expressed according to the formula:

P(t) = P0e^-rt

Given the following parameters

P(t) = $100,000

rate = 12% = 0.12

time =7 years

Substitute

100,000 = P0e^-(0.12)(7)

100000 = P0e^0.84
P0 = 100000/e^0.84
P0 = $244,693

Hence the price the machinery have initially cost rounded to the nearest dollar is $244,693

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A major disadvantage of correlations is that they cannot make a cause-and-effect statement.

Correlations are statistical measures that describe the size and direction of a relationship between variables.

Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.

The disadvantages of correlations include:

Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.

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Answer:

21(10)

Step-by-step explanation:

youll have to do 21 times 10

Answer:

[tex]\frac{210.00}{10}[/tex] = x

Step-by-step explanation:

[tex]\frac{210.00}{10}[/tex] = x

Let x is the number that each person needs to pay.

Answer:

8 1/4 or 33/4

Step-by-step explanation:

How to muliply fractions: just multiply all the denominators together and the numerators together

However, if your mulitplying whole numbers, you have to change those into improper fractions using the formula: Whole number x denomiator + numerator

**Make sure to put the same numerator as you had before when you change to an improper fraction!!!

-4 1/2 = -9/2

-2 1/5 = -11/5

5      -9    -11        5 x -9 x -11        -45 x -11 (use a calculator)       495

--   x  -- x  ---   =   ---------------  =   -------------                              =  ------------

6       2     5         6 x 2 x 5           12 x 5                                         60

                      1         33

=  8.25 or  8  ---- =  --------

                       4         4

Answer:

(10 + 3x) (10 - 3x)

Hope this helps!

Answer:

25% is the correct answer

Answer:

2/15

Step-by-step explanation:

Slope: m=(y2-y1)/(x2-x1)

m = (3 - 7)/(-14 - 16) = (-4)/(-30) = 4/30 = 2/15

The rate of change from 1 hour to 2 hours will be 125 miles per hour. Option C is correct.

What is linear equation?

A relationship between two or more parameters that, shown on a graph, produces a linear model. The degree of the variable will be one.

Given that;

Two points on the graph are (1, 125) and (2, 250).

Now, The slope of the line is calculated as;

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Hence, Slope of the line passes through the points (1, 125) and (2, 250).

m = (250 - 125) / (2 - 1)

m = 125

So, The rate of change from 1 hour to 2 hours will be 125 miles per hour.

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Answer:

0.24 ounces for 3 teabags.

Step-by-step explanation:

Since this is a 1 digit number, we should find out how much each teabag weighs. We can do this by dividing 8 by 100, which gives us 0.08.

Now we can multiply that by 3, which gives us 0.24, so 3 teabags are 0.24 ounces.

Answer:

∠ABC = 40

∠CBC = 50

Step-by-step explanation:

∠ABC + ∠CBD = 90

2x + (3x - 10) = 90

2x + 3x - 10 = 90

5x = 100

x = 20

∠ABC = 2x = 2(20) = 40

∠CBC = 3x - 10 = 3(20) - 10 = 50

The simplified result is :

[tex]4x/x^{2}[/tex] - 1

= 4/x -1

4-x / x.

Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.

An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.

In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression often means applying them.

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The Janitor used 8/15 of the bottle

How to calculate the amount of the solution of the bottle used ?

The Janitor has 3/5 of a spray bottle solution

He uses 1/9 of the solution in a day

The amount of solution used can be calculated as follows

3/5 × 1/9

= 3/45

= 1/15

The initial amount  in the bottle is

3/5 - 1/15

= 8/15

Hence the amount of solution he has used is 8/15

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Answer:    Find the square roots and the multiply that by 4

Step-by-step explanation:

hope this helped

Answer:

Let Pip get = x

Fiona gets = x + 35

Ratio = 6:1

x+35/x = 6

x + 35 = 6x

5x = 35

x = 7

Total money = x + x + 35 = 14+ 35 = £49

Answer:

£49

Step-by-step explanation:

Fiona gets 35 more than Pip so 6-1 =5 and 5 portions = 35

so 1 portion = 7

7x6 = 42

7x1 =7

7+42 = 49

so they got £49

hope this works :)

During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

Given the expression, a³ - b³ / 5, where:

a = 2

b = -3

Substitute the values into the expression

Step 1: (2)³ - (-3)³ / 5

Evaluate

Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)

Step 3: 8 + 27/5

Step 4: 35/5 [addition]

Simplify

Step 5: 35/5 = 5 [division]

Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

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Answer:

5 x + 4 y = 4 b

Step-by-step explanation:

You haven't specified what form you need. Here is the Standard form, but you can also calculate the Slope intercept form points and the Point-Slope form.

Find the equation of the line in standard form with the properties:

slope: m = -5/4

At least two parameters must be provided to determine a line equation:

Since the line is incompletely determined, compute the equation assuming an arbitrary y-intercept b

Substitute the slope m = -5/4 into the slope-intercept equation y = m x + b:

y = -(5 x)/4 + b

Add (5 x)/4 to both sides:

(5 x)/4 + y = b

Multiply both sides by 4:

4 ((5 x)/4 + y) = 4 b

Distribute: 4 ((5 x)/4 + y) = 5 x + 4 y:

Answer: 5 x + 4 y = 4 b

9 pounds of hamburger meat will be needed by Brian.

We are given value for one unit. The calculation is required for more than one units, hence, multiplication will be performed.

As per the given information, amount of hamburger meat required for one person is = 3/4 pound

Amount of hamburger meat required for 12 people = (3/4) × 12

Performing division to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 3 × 3

Performing multiplication to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 9 pounds

Therefore, Brain needs to buy 9 pounds of hamburger meat.

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the linear function that represents the given line is:

y = f(x) = (-2/3)*x - 11

Here we have a line given by a point-slope equation:

y + 7 = (-2/3)*(x + 6)

And we would want to get a function of the form y = f(x). So the first thing we need to do is isolate y in one side of the above equation. If we subtract 7 in both sides we will get:

y = (-2/3)*(x + 6) - 7

Expanding that:

y = (-2/3)*x + (-2/3)*6 - 7

y = -(2/3)*x - 4 - 7

y = (-2/3)*x - 11

Then the linear function that represents the given line is:

y = f(x) = (-2/3)*x - 11

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If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.

An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of function f over the interval [-3, 0]:

a = -3; f(a) = -4.5

b = 0; f(b) = 0

Substituting the given parameters into the formula, we have;

Average rate of change = (0 - (-4.5))/(0 - (-3))

Average rate of change = 4.5/3

Average rate of change = 1.5.

Also, we would determine the average rate of change of function g over the interval [-3, 0]:

a = -3; f(a) = 5

b = 0; f(b) = 14

Substituting the given parameters into the formula, we have;

Average rate of change = (14 - 5)/(0 - (-3))

Average rate of change = 9/3

Average rate of change = 3.

In conclusion, the average rate of change of function f is less than the average rate of change of function g.

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Answer:

The average rate of change of f is less than the average rate of change of g.

Step-by-step explanation:

Plato/Edmentum

Answer:

Question:

A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?

A.) (-1,3),(2,-1),(-1,-1)

B.) (6,0),(6,7)(0,7)

C.) (-1,-1),(-6,-13),(-9,-9)

D.) (-3,-4),(3,-4),(3,4)

Triangle and Coordinate Geometry

As the name suggests 'tri-angle' means it has three angles that are formed only when three sides are joined together.

So the triangle is a planner geometry that has three sides and three interior angles. In a triangle, the sum of all three interior angles is always

180

∘

.

If a triangle

A

B

C

has the sides

a

,

b

,

and

c

, then

The perimeter of the triangle:

P

=

a

+

b

+

c

In coordinate geometry, the distance between two points:

D

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

Answer and Explanation:

Given:

The perimeter of the triangle is

24

units.

There are four options with different-different vertices and one of them is correct, so we choose one option randomly and check it for the given perimeter.

Firstly we chose the option

D

:

The vertices of the triangle are:

P

(

−

3

,

−

4

)

,

Q

(

3

,

−

4

)

,

and

R

(

3

,

4

)

Using the distance formula:

D

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

So

P

Q

=

√

(

3

+

3

)

2

+

(

−

4

+

4

)

2

=

√

6

2

+

0

=

6

u

n

i

t

And

Q

R

=

√

(

3

−

3

)

2

+

(

4

+

4

)

2

=

√

0

+

8

2

=

8

u

n

i

t

And

P

R

=

√

(

3

+

3

)

2

+

(

4

+

4

)

2

=

√

6

2

+

8

2

=

√

36

+

64

=

√

100

=

10

u

n

i

t

So

The perimeter of the triangle

P

Q

R

is:

Perimeter

=

P

Q

+

Q

R

+

P

R

=

6

+

8

+

10

=

24

u

n

i

t

s

Step-by-step explanation:

Answer:

10 days

Step-by-step explanation:

60/50×12 give u the number of days it will last them

Answer:

d)2

Step-by-step explanation:

you would group-like terms and so

4q+q=11-1

5q=10(you would let q stand on it own)

so you divide through by 5

5q/5=10/5

q=2

the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.

We are given that:

The first integer is represented by the variable x.

We need to find the next four consecutive odd integers.

We know that the difference between the two consecutive odd integers will always be 2.

So, this means, we can always get the next odd integers by adding 2 to the previous one.

So, we get that:

x + 2

x + 2 + 2 = x + 4

x + 4 + 2 = x + 6

x + 6 + 2 = x + 8

Therefore, we get that, the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.

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Number of servings of Gerber mixed cereal for baby = 1

Number of servings of Gerber mango tropical fruit dessert for baby = 3

Given information about Gerber products are,

Gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.

Gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.

We have to find the number of servings of each to provide exactly 300 calories and 74 grams of Carbohydrates. So we need to find the appropriate combination of numbers 60 and 80 to make 300 and combinations of 11 and 21 to get 74.

Since 1 x 60 + 3 x 80 = 60 +240 = 300

and 1 x 11 + 3 x 21 = 11 + 63 = 74 ,

we can conclude that 1 serving of Gerber mixed cereal and 3 servings of Gerber mango tropical fruit dessert  will do.

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The values of the variables are:

a = -3

b = 2

c = -4

d = 6

e = -7

Given, the expressions are:

4a + 2 = -10

4a = -10-2

4a = -12

a = -3

substitute a value in the next expression.

a(2+b) = -12

-3(2+b) = -12

-6-3b = -12

-3b = -12+6

-3b = -6

b=6/3

b = 2

now substitute b value in the next expression.

-5c+b= 22

-5c+2 = 22

-5c = 22-2

-5c = 20

c = -20/5

c = -4

substitute c value in the next expression.

7(c+d) = 14

7(-4+d) = 14

-28+7d = 14

7d = 14+28

7d = 42

d=42/7

d=6

In the last expression substitute c and d values to find e.

d-c-e= 17

6-(-4)-e = 17

6+4-e = 17

10-e = 17

-e = 17-10

-e = 7

e = -7

hence we get the values of all the variables.

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Answer:

-15

Step-by-step explanation:

set it up

f(40)=-2x+10

40=-2x+10

subtract ten

30=-2x

divide by -2 to isolate the x

-15=x

Answer:

f(x) = -2x + 10

If f(x)= 40

By using equation,

or, 40=-2x+10

or, 40-10=-2x

or, 30=-2x

or, 30/-2=x

Therefore x=-15

The statement that the ratio 2/5 to 1/3 has a unit rate of 2/15 is; True

A unit rate is defined as a rate for one of something. This can be written as a ratio with a denominator of one.

For example, if you ran 50 meters in 10 seconds, you ran an average 5 meters in 1 second. Both of the ratios, 50 meters in 10 seconds and 5 meters in 1 second, are rates, but the 5 meters in 1 second is a unit rate.

We are given the ratio 2/5 to 1/3. Now, this can be expressed as;

(2/5)/(1/3) = 2/5 * 1/3 = 2/15

Thus, this corresponds with the given unit rate of 2/15.

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