Write a rational expression to determine how many cubbies high the book shelf will be.

Since it is conical, we need to find the surface area of the top of the conical shape.

If we unfold the top part of the cone, we will have a section of a circle:

The circunference of this section is the same as the total circunference of the base of the cone, which we can get from its radius (half its diamtere):

If we visualize the cone by the side, we see that it forms a isosceles triangle which the same height and the base euqal to the diameter:

So, we can calculate "R", the radius of the unfolded cone, using the Pythagora's Theorem:

The circunference of a section of a circle is the circunferece of the total circle times the fraction of the section represents of the total circle. Let's call ths fraction "f", this means that:

The area will follow the same, the area of the section is the fraction "f" times the total area of the circle, so:

So, the surface area of the top of the cone is 204.1 ft². Since each skin covers 15 ft², we can calculate how many skins we need by dividing the total by the area of each skin:

This means that we need 13.60666... skins, that is, 13 is not enough, we need one more, so we need a total of 14 skins.

Answer

8

Step-by-step explanation

we know that the term quotient means that we divided so we think backward if 24 is being divided by 3 what times 3 equals 24 the answer would be 8 because 3x8=24.

The diameter = 2 times the radius

radius = diameter / 2

radius = 25.3/2

radius = 12.65 cm

Result radius = 12.65 cm

Taking a look at the graph, we can notice that point (7000,2875.99) is highlighted.

Using this point, we can conclude that the cost of talking 7000 minutes is $2875.99

Given:-

Now to find the value of,

So by simplyfying according to the given elementary row operation,

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

hand-engraved watch bands:

total watch bands = 20

total profit = $105.00

Step 02:

ratio:

total profit (50 watch bands):

The answer is:

$ 262.50

Answer

Explanation

The variable given is x

Five times the variable is 5x

When 4 is added, the expression becomes 5x + 4, which gives the Left Hand Side of the equation.

For the Right Hand Side, four times the number is 4x

7 more than 4x is 4x + 7

Since the result on the Left Hand Side = Right Hand Side, then the required equation is

Now, to find the number x, we shall solve the above equation as follows

Since we would need to multiply each coordinate by 1/2 to perform the transformation, then the scale factor would be 1/2. The answer is the first option.

Answer:

A. f(-2) = 13

B. f(0) = 1

C. f(7) = -41

Step-by-step explanation:

f(x) = 1 - 6x

A.

f(-2) = 1 - 6(-2)

f(-2) = 1 + 12

f(-2) = 13

B.

f(0) = 1 - 6(0)

f(0) = 1

C.

f(7) = 1 - 6(7)

f(7) = 1 - 6(7

f(7) = -41

I hope this helps!

Let each person get portion "x".

So, 3 person would get "3x" and that would be equal to "1" sandwich.

Thus, we can write the equation:

Let's solve for "x",

Each person will get one-third of a sandwich.

Answer:

a. If the selection is made with replacement, they are NOT independent because they affect each other.

b. The probability of selecting TWO accurate orders is .7157 and the events ARE independent.

Step-by-step explanation:

Add the accurate orders:

315+273+248+125=961

Add the inaccurate orders:

38+56+37+17=148

148/961=0.1540 probability of getting ONE inaccurate order

1.0-0.1540=0.846 probability of selecting ONE accurate order

0.846 * 0.846 = 0.7157 the probability of selecting TWO accurate orders

Therefore, the probability is .7157 and the events ARE independent.

Answer

2.8 - 4.4n - 2n + 7 = 9.8 - 6.4n

Explanation

To answer this, we just bring the terms with n together and the terms without together too.

2.8 - 4.4n - 2n + 7

= 2.8 + 7 - 4.4n - 2n

= 9.8 - 6.4n

Hope this Helps!!!

ANSWER

EXPLANATION

Given;

Rewrite as;

Simplify by moving 1/3 inside the logarithm;

Answer:

2,152

Step-by-step explanation:

So to find this all you have to do is subract 7,419 and 5,267 to get the answer of 2,152

Hope This Helps <3 <3

The amount of flour needed for 72 cookies is 4.5 cups.

46 / 69 and 48/84 are not proportional because the fractions in their simplest forms are 3/4 and 4/7.

The value of x in  2/3 = 1.2 / x is 1.8.

The value of x in 8 / 15 = 24 / x is 45.

7 / 5 ≠ 15 / 10.

6 / 8 = 15/20

In order to determine how many cups of flour is needed for 72  cookies, determine how many cups is needed for one cookies.

Amount of flour needed for one cookie = 3/48

Now, multiply this fraction by 72: 3/48 x 72 = 4.5 cups

If two fractions are proportional, when they are expressed in their simplest form, both fractions would have equal values.

46 / 69 = 2 / 3

48 / 84 = 4/7

Given this equation : 2/3 = 1.2 / x

In order to determine the value of x, cross multiply:

2x = 3 x 1.2

2x = 3.6

x = 3.6 / 2

x = 1.8

Given this equation : 8 / 15 = 24 / x

In order to determine the value of x, cross multiply:

8x = 24 x 15

8x = 360

x = 360 / 8

x = 45

7/5 and 15 / 10

7/5 =  15 /10

The cross product:

(7 x 10) = (5 x 15)

70 ≠ 75

6 / 8 = 15/20

The cross product : (6 x 20) = (8 x 15)

120 = 120

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The total commission earned by Paun is $14,000.

For the given question.

The total sales done by Paun is $50,000.

There is commission of 25% on first $2000.

There is commission of 30% on remaining that is 48,000.

The total commission will be 25% of $2,000 and 30% of 48,000.

25% of $2,000 = 25 × 2000/100

25% of $2,000 = $500

30% of 48,000 = 30 × 48,000/100

30% of 48,000 = $14,400

Total commission = $500 + $14,400 = $14,900.

Thus, the total commission earned by Paun is $14,000.

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Answer:

The greatest common factor (GCF) of the numerator (4) and the denominator (16) is 4

GCF(4,16) = 4

4/16 = 4 ÷ 4/16 ÷ 4

= 1/4

hope it helps you

A function is a relation that gives one input for every one output thus the value of g(10) is -31.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given function,

g(x) = -3x - 1

The value of the function at x = 10

g(10) = -3(10) - 1

g(10) = -30 - 1 = -31

Hence "A function is a relation that gives one input for every one output thus the value of g(10) is -31".

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Solution:

A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.

Hence, the number that can be expressed as a product of an integer by itself is;

Therefore, the perfect square is 81.

OPTION B is correct.

Answer:

y = [tex]\frac{5}{4}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{5}{4}[/tex] , then

y = [tex]\frac{5}{4}[/tex] x + c ← is the partial equation

to find c substitute (- 4, - 6 ) into the partial equation

- 6 = - 5 + c ⇒ c = - 6 + 5 = - 1

y = [tex]\frac{5}{4}[/tex] x - 1 ← equation of line

The given equation is

At first, we have to isolate x on one side and the numerical term on the other side, then

Add 1 to both sides

Subtract x from both sides

The solution of the equation is x = 8

Using the discriminant of a quadratic function, it is found that:

6. The range of values is of c ≤ 1/16.

8. The range of values of k is: -9 < k < -1.

10. The discriminant is never negative, hence the function has real roots for all values of k.

A quadratic function is modeled as follows:

y = ax² + bx + c.

The discriminant of the function is given as follows:

Δ = b² - 4ac

For item 6, the function is given as follows:

y = 2x² - 3x + (2c + 1).

The coefficients are given as follows:

a = 2, b = -3, c = 2c + 1.

The function is positive for all values of x if it has at most one real root, hence:

Δ ≥ 0

(-3)² - 4(2)(2c + 1) ≥ 0

9 - 16c - 8 ≥ 0

1 - 16c ≥ 0

16c ≤ 1

c ≤ 1/16

For item 8, the function is given as follows:

y = kx² - (k - 3)x - 1 = 0.

The coefficients are given as follows:

a = k, b = -k - 3, c = -1.

It has no real roots if:

Δ < 0

b² - 4ac < 0

(-k - 3)² - 4(k)(-1) < 0

k² + 6x + 9 + 4k < 0

k² + 10k + 9 < 0

Hence the range is:

-9 < k < -1.

For item 10, the function is given as follows:

y = kx² + (k - 2)x - 2 = 0.

The coefficients are given as follows:

a = k, b = k - 2, c = -2.

It has no real roots if:

Δ < 0

b² - 4ac < 0

(k - 2)² - 4(k)(-2) < 0

k² - 4k + 4 + 8k < 0

k² + 4k + 4 < 0

(k + 2)² < 0.

(k + 2)² is always positive, hence the function will always have real roots.

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Answer

Discriminant of a quadratic functio

A quadratic function is modeled as follows:

y = ax² + bx + c.

The discriminant of the function is given as follows:

Δ = b² - 4ac

For item 6, the function is given as follows:

y = 2x² - 3x + (2c + 1).

The coefficients are given as follows:

a = 2, b = -3, c = 2c + 1.

The fnction is positive for all values of x if it has at most one real root, hence:Δ ≥ 0

(-3)² - 4(2)(2c + 1) ≥ 0

9 - 16c - 8 ≥ 0

1 - 16c ≥ 0

16c ≤ 1

c ≤ 1/16

For item 8, the function is given as follows:

y = kx² - (k - 3)x - 1 = 0.

The coefficients are given as follows:

a = k, b = -k - 3, c = -1.

It has no real roots if:

Δ < 0

b² - 4ac < 0

(-k - 3)² - 4(k)(-1) < 0

k² + 6x + 9 + 4k < 0

k² + 10k + 9 < 0

Hence the range is:

-9 < k < -1.

For item 10, the function is given as follows:

y = kx² + (k - 2)x - 2 = 0.

The coefficients are given as follows:

a = k, b = k - 2, c = -2.

It has no real roots if:

Δ < 0

b² - 4ac < 0

(k - 2)² - 4(k)(-2) < 0

k² - 4k + 4 + 8k < 0

k² + 4k + 4 < 0

(k + 2)² < 0.

(k + 2)² is always positive, hence the function will always have real roots.

Step-by-step explanation:

Solution:

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Write the given values

STEP 3: Substitute the values and simplify

We solve the bracket first:

We solve the division operator next:

We do the addition and subtraction simultaneously to have:

Hence, the result of the simplification gives 3

Problem

The formula A = P +Prt

Solution

We can take common factor and we got:

A= P(1+rt)

And we can divide both sides by 1+rt and we got:

P = A /(1+rt)

We have the following:

now, we must give values to x, to be able to graph

The grahp is:

Given

Tax rate = 28.5 mills

Smith's house is accessed at $80,000

Jones's house is accessed at $67,000

Property taxes are calculated by multiplying the assessed, taxable property value by the mill rate and then dividing that sum by 1,000.

The formula is given by:

Property tax for the Smith's:

Property tax for the Jones':

The extra amount the Smith's pay is the difference in the tax levied on Smith and Jones:

Hence, the Smith's pay $370.5 more than the Jones'