FITNESS Alejandro is a personal trainer. For his clients to gain the maximum benefit from their exercise, Alejandro calculates their maximum target heart rate using the function f(x) = 0.85(220 – x), where x represents the age of the client. Find the inverse of this function and interpret its meaning in the context of the situation.

Answers

Answer 1

Answer:

1). [tex]f^{-1}(x)[/tex] = (200 - [tex]\frac{x}{0.85}[/tex])

2). Inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.

Step-by-step explanation:

Function representing the maximum heart rate is,

f(x) = 0.85(220 - x)

Here x = age of the client

Equation form of the function will be,

y = 0.85(220 - x)

To get the inverse of the given function, replace 'x' by 'y' and 'y' by 'x' and solve for y.

x = 0.85(220 - y)

220 - y = [tex]\frac{x}{0.85}[/tex]

y = 220 - [tex]\frac{x}{0.85}[/tex]

Now convert this equation into a function.

[tex]f^{-1}(x)[/tex] = (200 - [tex]\frac{x}{0.85}[/tex])

Here inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.


Related Questions

Michael was asked to give examples of the identity property of addition and the identity property of multiplication. Below are his answers.

Identity property of addition: 8 + 1 = 8

Identity property of multiplication: 8(0) = 0

What was Michael’s mistake?

He should have added 0 to 8 and multiplied 1 by 8.
He should have 8 + 1 = 9.
He should have 8(0) = 8.
He should have distributed the 8.

Answers

Answer:

He should have added 0 to 8 and multiplied 1 by 8

Step-by-step explanation:

Michael should have added 0 to 8 and multiplied 1 by 8.

What is multiplication?

Multiplication is the process of adding a number up to a given number.

The identity property of addition is 0 and the identity property of multiplication is 1.

Therefore, Michael should have added 0 to 8 and multiplied 1 by 8.

To learn more about multiplication, click here:

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The area of a rectangle is given by A(x) = x2 + 5x with x being the height and x + 5 being the base. If the area is 14, what is the only viable solution for the height? Why are there not two solutions?​

Answers

Answer:

See below.

Step-by-step explanation:

A(x) = x^2 + 5x

A(x) = x^2 + 5x = 14

x^2 + 5x - 14 = 0

(x + 7)(x - 2) = 0

x + 7 = 0  or  x - 2 = 7

x = -7 or x = 2

x is the height of a rectangle.

The only viable solution is x = 2 because the height of a rectangle cannot be a negative number such as -7.

The only viable solution for the height is x= 2, because height cannot be a negative value.

What  is Rectangle?

A rectangle is a quadrilateral with four right angles.

What is Area?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

What is Quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2} +bx+c=0[/tex]

Given,

Area of the rectangle = [tex]x^{2} +5x[/tex] = 14

Then,

[tex]x^{2} +5x-14=0\\(x+7)(x-2)=0[/tex]

Therefore x = -7 and 2

But the Height cannot be negative therefore x = 2

Hence, only viable solution for the height is x= 2, because height cannot be a negative value.

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pls help it will mean alot!!
due rn!!

Answers

Answer:

f(x) = 4^x

f(4) = 4^4 = 256

Hope this helps!

:)

the answer is 256 but i am not sure

hope this helps and be safe :)

A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot.
4.1 feet
17.0 feet
20.6 feet
21.4 feet

Answers

Answer:20.6

Step-by-step explanation:

20.6

Answer:

C) 20.6

Step-by-step explanation:

just took the test

5. Jack and Jill use rain gauges that are the same size and shape to measure rain on top of a hill. Jack
uses a rain gauge marked in fourths of an inch. Jill's gauge measures rain in eighths of an inch. On
Thursday, Jack's gauge measured inches of rain. Jill and Jack both had the same amount of water,
so what was the reading on Jill's gauge on Thursday? Draw a number line and write a sentence to
explain your thinking.

Answers

Answer:

List the multiples

1/4,2/4,3/4,4/4

1/8,2/8,3/8,4/8,5/8,6/8,7/8,8/8

1/4=2/8

2/4=4/8

4/4=8/8

Those numbers are the common fractions so they would be the only fractions that both Jack and Jill could get.

Step-by-step explanation:

Select The decimal that is equivalent to 7/8

Answers

Answer:

0.875

Step-by-step explanation:

look at the fraction as a division problem

8÷7

Mr. Anderson has 4 recipes for granola. Which recipe has the greatest ratio of honey to oats?

Answers

Answer:

Recipe 3 has the greatest honey to oats ratio amongst the 4 recipes.

Step-by-step explanation:

Complete Question

Mr. Anderson has 4 recipes for granola. Recipe 1

A 2-column table with 3 rows is titled Recipe 1. Column 1 is labeled Honey (tablespoons) with entries 5, 10, 15. Column 2 is labeled Oats (cups) with entries 2, 4, 6.

Recipe 2

A 2-column table with 3 rows is titled Recipe 2. Column 1 is labeled Honey (tablespoons) with entries 6, 10, 14. Column 2 is labeled Oats (cups) with entries 3, 5, 7.

Recipe 3

A 2-column table with 3 rows is titled Recipe 3. Column 1 is labeled Honey (tablespoons) with entries 3, 6, 9. Column 2 is labeled Oats (cups) with entries 1, 2, 3.

Recipe 4

A 2-column table with 3 rows is titled Recipe 1. Column 1 is labeled Honey (tablespoons) with entries 8, 10, 12. Column 2 is labeled Oats (cups) with entries 4, 5, 6.

Which recipe has the greatest ratio of honey to oats?

Solution

Computing the ratio of honey to oats for each of recipes

Recipe 1

Honey | 5 | 10 | 15

Oats | 2 | 4 | 6

Honey to Oats ratio = (5/2) = (10/4) = (15/6) = 2.5 to 1.

Recipe 2

Honey | 6 | 10 | 14

Oats | 3 | 5 | 7

Honey to Oats ratio = (6/3) = (10/5) = (14/7) = 2 to 1.

Recipe 3

Honey | 3 | 6 | 9

Oats | 1 | 2 | 3

Honey to Oats ratio = (3/1) = (6/2) = (9/3) = 3 to 1.

Recipe 4

Honey | 8 | 10 | 12

Oats | 4 | 5 | 6

Honey to Oats ratio = (8/4) = (10/5) = (12/6) = 2 to 1.

Recipe 3 evidently has the greatest honey to oats ratio amongst the 4 recipes.

Hope this Helps!!!

Answer: Recipe 3

Step-by-step explanation:

36 + 1.80 + 2.16 I'm stuck ​

Answers

Answer:

39.96 should be the right answer

Answer: 39.96

Step-by-step explanation:

36+1.80=37.80

Then you add 2.16

37.80+2.16=39.96

Please can people help??!!
Photo below

Answers

i think this is the method for solving it

The temperature during a winter day was less than 8 degrees Fahrenheit. Digby wants to write an any quality for the temperature during the winter day. What constant should Digby use in the inequality?

Answers

Answer:

8

Step-by-step explanation:

y < mx+c

here  y will be the temperature on any particular winter day, x will be the variable on whixh temperature is dependent  and m will be the gradient.

The temperature must always be less than 8 so c will be 8.

y < 8

8 should be the maximum value of the inequaltiy

Answer:

your anwser is 8

Step-by-step explanation:

Solve for 2.
Write the smaller solution first, and the larger solution second.
(3x – 6)(-x + 3) = 0
smaller x =
larger x =

Answers

Answer:

(3x – 6)(-x + 3) = 0

=> 3x - 6 = 0 => x = 6/3 = 2

and

=> -x + 3 = 0 => x = 3

Hope this helps!

:)

Exponential Growth and Decay The expressions below represent either exponential growth or exponential decay. Check all the expressions that represent exponential decay. 5x 3(0.75)2t 35(2.4)x 5000(1.04)3t 0.05x 500(0.005)t

Answers

Answer:

First one: 5x3(0.75)2t

and fourth one: 0.05x500(0.005)t

Step-by-step explanation:

In order to have an exponencial decay, the rate of the exponencial function needs to be lesser than 1.

The rate is the value between parenthesis, so in the first equation, the rate is 0.75, so this is an exponencial decay.

The second equation has rate = 2.4, so this is not an exponencial decay.

The third equation has rate = 1.04, so this is not an exponencial decay.

The fourth equation has rate = 0.005, so this is an exponencial decay.

Answer:

It's A,C,F

Step-by-step explanation:

I answered it :) and got it right.

it was found that out of 45 girls,10 joined singing but not dancing and 24 joined dancing . how many joined but not singing ? how many joined both

Answers

11 are in both singing and dancing.
45-10 singing= 35 not singing
45-24 dancing = 21 not dancing
24+10= 34 in singing OR dancing,
Subtract the 34 from 45
which leaves 11 in both singing AND dancing.

21  girls joined but not singing and 14 girls joined both singing and dancing.

What are Arithmetic operations?

Arithmetic operations can also be specified by the, subtract, divide, and  multiply built-in functions.

Total no. of girls = 45

No. of girls are dancing = 24

No. of girls are singing but not dancing = 10

No. of girl are both singing and dancing = 24-10 = 14

No. of girls are dancing but not singing = 45-24=21

Hence, 21  girls joined but not singing and 14 girls joined both singing and dancing.

Learn more about Arithmetic operations

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The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: \[P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square).\]What is the maximum value of $P$? What is the minimum value of $P$?

Answers

Hint

If we define x to be the value of one of the factors, since 1 + 2 + 3 + 4 + 5 ... + 10 = 11(5) = 55, the value of the other factor has to be 55-x.

To maximize P, you'd like to make x as close as possible to the vertex you found. What if you want to minimize P? Remember x must be an integer.

I hope this helps :)

PLEASE HELP!
Evaluate the expression 5(7 − 4)2 ÷ 3 + 11.

Answers

Answer:

26

Step-by-step explanation:

5(7 − 4)^2 ÷ 3 + 11.

PEMDAS says parentheses first

5(3)^2 ÷ 3 + 11.

Then exponents

5 (9)÷ 3 + 11.

Multiply and divide from left to right

45 ÷ 3 + 11

15 +11

26

35-20x2divide3+11
15x2
30divide3=10
10+11=21

Which of the following is true of the values of x and y in the diagram below? A unit circle is shown. A radius with length 1 forms angle theta = StartFraction pi Over 4 EndFraction. The radius intersects point (x, y) on the unit circle. y < x y > x y + x = 1 StartFraction y Over x EndFraction = 1

Answers

Answer:

y/x = 1 got it right on edg

Step-by-step explanation:

Answer:

y/x = 1  on E2020

Step-by-step explanation:

Have a Great Day :)

Is the percent increase for 50 to 70 = to the percent decrease from 70 to 50

Answers

Answer:

no it is not equal.

Step-by-step explanation:

when you calculate the percentages, you will find  that the increase has 40% while the decrease has about 28.6%

Answer:

No. The amounts of change are the same, but the original amounts are different. The ratio for the percent increase from 50 to 70 is 20/50, or 40%. The ratio for the percent decrease from 70 to 50 is 20/70, or about 29%.

Step-by-step explanation:

SAMPLE RESOND

how to make a dot plot

Answers

Answer:

draw a a big L and put your numbers

Draw a line horizontally and make values and put dots

Can someone please help me with this?

Answers

Answer:

Step-by-step explanation:

find the proportion and solve for the volume.

Chantel is running for a rally race she ran 2,000 feet every day for six days how many yards did Chanel run

Answers

Answer:

4,000 yards

Step-by-step explanation:

2,000 ft * 6 days = 12,000 feet ran in total

Conversion: 3 feet = 1 yard

12,000 ft = 4000 yards

A necklace found at a pawn shop is 192 grams and has a volume of 19.5 cubic centimetres. What metal is the necklace made of?

Answers

Answer:

Bronze

Step-by-step explanation:

To know the metal used to produce necklace, we must calculate the density of the necklace. This is illustrated below below:

Mass of necklace = 192g

Volume = 19.5cm^3

Density =...?

Density of a substance is simply defined as the mass of the substance per unit volume.

Density = Mass /volume

Density = 192g / 19.5cm^3

Density = 9.85g/cm^3

Now comparing the density of the necklace with the density of various metals in the table, we can see that the density of the necklace matches that of bronze.

Therefore, the necklace is made of bronze.

This net will be folded to form a prism. A net of a rectangular prism. From top to bottom, the rectangles are labeled B, D, E, F. The left side is labeled A and the right side is labeled C. Which pairs of faces will be opposite one another when the prism is created? Check all that apply. D and F A and C A and B B and F B and E B and C E and F A and F

Answers

Answer:

D and F

A and C

B and E

Step-by-step explanation:

due to the fact that it is a rectangle prism, and the A is on the left  and  C is on the right, the other alphabet  B,D,E F is straight down, you have to fold the d and f first, then A and C and lastly B and E to form the prism

Answer:

a,b,e

Step-by-step explanation:

Tamika’s math test scores (out of 30) are 25, 28, 26, 25, 8, 29, 28, 24, 23.


a)What is the outlier in this set?

b) Why might Tamika’s teacher decide to remove this outlier when calculating the average for her report card?

c) Which average is affected more by the removal of the outlier, the mean or median? Justify your answer.

I WILL GIVE BRAINLIEST IF YOU ANSWER ALL THE 3 QUESTIONS GOOD.

Answers

Answers:

A.) 8 is the outlier in the set. It is the only number that doesn't match with the others. It is the furthest from the median of the numbers.

B.) The outlier could represent false information. It could greatly drop the number of the mean, or the average, range of the scores.

C.) The mean is affected more. The mean of a set of numbers is the average of the set. The median just locates the middle-most number. The median would not always give an accurate representation of the average of the set like the mean would.

Help me please help me thank you

Answers

Answer: 110, 35, 70, G, J, F, E, B, A, H, C, D, I

Step-by-step explanation:

8. For number 8, you will be using the exterior angle theorem. The exterior angle theorem states that the exterior angle equals the two angles inside the given triangle. Since we have 50 and 60, you will add 50 + 60 to get 110.

9. In this problem, you shall use the vertical angle theorem. The vertical angle theorem is simply that any angles vertical from one another are congruent. So a will be also 35 degrees.

10. This is an image depicting two lines cut by a transversal, creating multiple congruent angles. With this, you will be using the alternate interior angle theorem. Alternate interior angles are angles on different sides of the transversal but inside both of the lines that were cut into, as shown above. So,  b will also equal 70 degrees.

Part B:

1. G

2. J

3. F

4. E

5. B

6. A

7. H

8. C

9. D

10. I

Dghgfty is my morning time for

In the right triangle shown, DF=EF=3DF=EF=3D, F, equals, E, F, equals, 3.

How long is DEDED, E?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
3\sqrt{2}3
2

3, square root of, 2, end square root

(Choice B)
B
3\sqrt 33
3

3, square root of, 3, end square root

(Choice C)
C
666

(Choice D)
D
6\sqrt 26
2

6, square root of, 2, end square root

(Choice E)
E
999
Report a problem
Do 5 problems



Answers

Answer: A or 3 sqrt 2

Step-by-step explanation:

Answer:

3 sqrt 2

Step-by-step explanation:

HELP!!! Cumulative Exam!! Which is the simplified form of m Superscript negative 8 p Superscript 0? StartFraction 1 Over m Superscript 8 Baseline p EndFraction StartFraction 1 Over m Superscript 8 EndFraction StartFraction p over m Superscript 8 EndFraction m Superscript 8

Answers

Answer:

(B)[tex]\dfrac{1}{m^8}[/tex]

StartFraction 1 Over m Superscript 8 EndFraction

Step-by-step explanation:

We want to find the simplified form of: [tex]m^{-8}p^0[/tex]

[tex]m^{-8}p^0=m^{-8}$ X p^0\\p^0=1\\m^{-8}=\frac{1}{m^8} \\$Therefore:\\m^{-8}$ X p^0=\dfrac{1}{m^8} X 1\\=\dfrac{1}{m^8}[/tex]

The correct option is B.

Answer:

I am 80% sure its 1 if not then its 1/p

Step-by-step explanation:

The area of a swimming pool is 120 sq meters. The width of the pool is 8 meters. what is the length of the pool in centimeters ?

Answers

120/8 = 15m
15m = 150cm
Answer 150cm

If (A:20:4:16) is a proportion the find out the value of A fastly​

Answers

Answer: A = 5

Step-by-step explanation:

I'll rewrite this as fractions.

[tex]\frac{A}{20}=\frac{4}{16}[/tex]

Solve for A,

[tex]A=\frac{20*4}{16}\\ A=\frac{80}{16}[/tex]

[tex]A=5[/tex]

Formula for a area of a circle

Answers

Answer:

A=(pie) r^2

Step-by-step explanation:

A = Area

(pie) = 3.14

r^2 = (r is the radius)

Answer:

pi r^2

Step-by-step explanation:

That is your answer

Find the volume of this figure.
12 m
6 m
6m​

Answers

Answer:

432

Step-by-step explanation:

To get volume you need to multiply all of the numbers together (Length, height, and width). You need to multiply 6 and 6 (You get 36) and multply the answer by 12 to get 432.

Hope this helps!

(Also can I get Brainliest? Please?)

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