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2 years ago

MATH: Composition of two functions...help needed with this problem

Mathematics

1 answer:

Evgesh-ka [11]2 years ago

3 0

The equation of Q(n) is $Q(n) = \frac89 * (88n + 23)$

<h3>How to determine the formula of Q(n)?</h3>

The functions are given as:

$R(d) = \frac89 d$

$P(n) = 88n + 23$

From the question, we understand that:

d = P(n)

This means that:

d = 88n + 23

Substitute d = 88n + 23 in R(d)

$R(n) = \frac89 * (88n + 23)$

Also, from the question

Q(n) = R(n)

So, we have:

$Q(n) = \frac89 * (88n + 23)$

Hence, the equation of Q(n) is $Q(n) = \frac89 * (88n + 23)$

Read more about composite functions at:

brainly.com/question/10687170

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Karina wants to fill the base so that it is 85% full. What is the volume of the base that she is filling? (Find 85% of the volum

Mazyrski [523]

Question:

Karina has recently begun kickboxing and purchased training equipment as modeled in the diagram below. The cylindrical base is 15 inches tall with a diameter of 22 inches.

Karina wants to fill the base so that it is 85% full. What is the volume of the base that she is filling? (Find 85% of the volume).

Answer:

$Section = 4847.3205\ in^3$

Step-by-step explanation:

Given

$h = 15in$ -- height

$d = 22in$ -- diameter

Required

85% of the volume

First, calculate the radius

$r = \frac{1}{2} * d$

$r = \frac{1}{2} * 22= 11in$

The volume (V) is then calculated using:

$V = \pi r^2h$

$V = 3.142* 11^2 * 15$

$V = 5702.73\ in^3$

85% of the volume is:

$Section = 85\% * V$

$Section = 85\% * 5702.73\ in^3$

$Section = 4847.3205\ in^3$

3 0

2 years ago

5. A pair of jeans costing

Levart [38]

So $39.50 is the price when you are paying full price, which can be represented by 100%. If you’re paying 25% less, than you are only paying 75% of the original price. Simply multiply $39.50 by 75%(expresses as 0.75) to determine the sale price. 39.50(.75)=29.62 The closest value to that is $29.50, so D is the answer.

6 0

3 years ago

Round to 2 decimal places *

EleoNora [17]

Answer: The circumference of the dome is therefore 149.15 feet or 47.5π feet

Step-by-step explanation:

A scale is basically referred to as the ratio of the dimensions of an object as represented in a draft to the real or true dimensions of the object being drafted.

The figure(s) on the left of the ratio sign represents the size and dimensions of the model with respect to the actual size or dimensions of the object. On the other hand, the figure on the right hand size represents the actual dimensions and size of the real object.

So, if an object is being drawn with the ratio, 1cm : 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always be represented by 1cm in the drawing. If the object is being drawn with a scale of 5cm : 1cm then the actual size of the object will be increased in the drawing. That is, for every 1cm in the actual dimensions of the object, there will be a 5cm representation in the drawing.

Now, the architect draws with a scale of 0.25 inches : 1 foot. If the diameter of the hemispherical dome is 23.75 inches in the scale model, then the actual diameter of the dome is:

0.25 inches ------- 1 foot

23.75 inches ------- ? feet

= 23.75/0.25 × 1

= 95 feet

Therefore, the actual diameter of the dome is 95 feet. We are now required to find the circumference of this dome.

The dome is a hemisphere which literally means half of a sphere. So, if the formula for finding the circumference of a sphere is πd, that of a hemisphere will then be πd/2. Since the diameter is already known to be 95 feet, the circumference of the hemisphere =

(π × 95)/2

=47.5π feet

If π = 3.14, then the circumference = (3.14 × 95)/2 = 149.15 feet

The circumference of the dome is 149.15 feet or 47.5π feet

5 0

3 years ago

Find the x value 4x-28 9x

andriy [413]

Answer: -5.6

Step-by-step explanation:

Simplifying

(4x + -28) = 9x

Reorder the terms:

(-28 + 4x) = 9x

Remove parenthesis around (-28 + 4x)

-28 + 4x = 9x

Solving

-28 + 4x = 9x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9x' to each side of the equation.

-28 + 4x + -9x = 9x + -9x

Combine like terms: 4x + -9x = -5x

-28 + -5x = 9x + -9x

Combine like terms: 9x + -9x = 0

-28 + -5x = 0

Add '28' to each side of the equation.

-28 + 28 + -5x = 0 + 28

Combine like terms: -28 + 28 = 0

0 + -5x = 0 + 28

-5x = 0 + 28

Combine like terms: 0 + 28 = 28

-5x = 28

Divide each side by '-5'.

x = -5.6

Simplifying

x = -5.6

5 0

3 years ago

45% of all 1st graders at Sierra Elementary School are female students. This year there are 54 female 1st graders at Sierra Elem

Anit [1.1K]

Answer:

There are 120 1st graders at Sierra Elementary School this year

Step-by-step explanation:

Let n represent the total number of 1st graders at Sierra Elementary School

Since 45% of all 1st graders at Sierra Elementary School are female students and this year there are 54 female 1st graders, 45% of n is equal to 54

→ n( $\frac{45}{100}$ ) = 54

→ 45n = 5400

→ n = 120

3 0

3 years ago

Read 2 more answers