PLEASE HELP
Parts a, b, c, d, and e

Answers

Answer 1

The values of the composite functions are f(g(2)) = 5.5, h(f⁻¹(5)) = 1, x = 5 for f(h(x)) = 7, R(4) = 4 and k(x) = 2

Evaluating the composite functions

From the question, we have the following parameters that can be used in our computation:

The functions f(x), g(x) and h(x)

Solving the composite functions, we have

f(g(2)) = f(3) i.e. g(2) = 3

This gives

f(g(2)) = 5.5

Next, we have

h(f⁻¹(5))

Here, we have

f⁻¹(5) = 4

So, we have

h(f⁻¹(5)) = h(4)

Evaluate

h(f⁻¹(5)) = 1

Next, we have

f(h(x)) = 7

From the graph, we have

f(0) = 7

This means that

h(x) = 0

From the table, we have

h(5) = 0

This means that

x = 5 for f(h(x)) = 7

Evaluating R(x) at x = 4. we have

R(x) = 2f(x) - 3g(x) + h(x)

This means that

R(4) = 2f(4) - 3g(4) + h(4)

So, we have

R(4) = 2 * 9 - 3 * 5 + 1

R(4) = 4

Evaluating k(x) at x = 5. we have

k(x) = h⁻¹(g(f⁻¹(x)))

This means that

k(x) = h⁻¹(g(f⁻¹(5)))

From the graph, f⁻¹(5) = 4

So, we have

k(x) = h⁻¹(g(4))

Next, we have

g(4) = 5

So, we have

k(x) = h⁻¹(5)

From the table, we have

h⁻¹(5) = 2

This means that

k(x) = 2

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Related Questions

una carga de 10 toneladas se distribuyo en partes iguales entre 6 camiones cuantas lleva cada camion

Answers

If a load of 10 tons was distributed equally among 6 trucks, each truck would carry 1.6667 tons.

What is the unit rate?

In Mathematics, the unit rate is sometimes referred to as unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.

How to determine the unit rate?

In order to determine the unit rate, we would use the following mathematical equation (formula);

Unit rate = Number of ounces/Number of trucks

Unit rate = 10/6

Unit rate = 1.6667 tons.

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Complete Question:

A load of 10 tons was distributed equally among 6 trucks, how many does each truck carry?

Determine the Y intercept:

Answers

The y-intercept of the line is 2.

In the equation y = 9x + 2, x and y are variables that represent the coordinates of any point on the line.

To find the Y-intercept, we need to find the value of y when x equals 0.

When x equals 0, the equation becomes:

y = 9(0) + 2

Any number multiplied by 0 is 0, so the first term drops out and we are left with:

y = 0 + 2

Which simplifies to:

y = 2

Therefore, when x equals 0, y equals 2. This means that the point (0, 2) is on the line. In other words, the line intersects the y-axis at y = 2, which is the Y-intercept of the line.

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Jared's class took a survey to see how many students owned a trampoline. Of the 24 students in the class, 14 students said they owned a trampoline. If you chose a student at random from Jared's class, what is the probability that the student does not own a trampoline?

Answers

The probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.

The probability that the student does not own a trampoline is equal to the number of students who do not own a trampoline divided by the total number of students in the class.

The number of students who do not own a trampoline is equal to the total number of students in the class minus the number of students who own a trampoline:

24 - 14 = 10

Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is:

P(not owning a trampoline) = 10/24

Simplifying the fraction,

P(not owning a trampoline) = 5/12

Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.

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Edgar has several different types of songs in a playlist. Suppose he plays a song at random from the playlist. How much greater is the probability that he plays a rock song than a hip hop song

Answers

The probability that he plays a rock song than a hip hop song is greater than 0.1. The Option B is correct.

How much greater is the probability?

Probability helps to find out the likelihood of the occurrence of an event by measuring the chance of an event happening and is equal to the number of favorable events divided by the total number of events.

Given that:

Total of songs = 40

Prob (playing rock) = 15/40

Prob (playing hip-pop) = 11/40

How much greater probability he plays a rock song than a hip hop song will be:

= 15 / 40 - 11/40

= 15 - 11 / 40

= 4/40

= 1/10

= 0.1

Answers

The equations are classified as follows

System A

consistent and independent this means that the system as a unique solution at (3, 3)

How to classify system B and C

System B

inconsistent this means that the system as a no solution

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

System C

consistent and dependent this means that the system as infinitely many solution

A consistent system is dependent if there are an infinitely many solutions. The two equations represent the same line when you graph them.

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I just need d and e answers for this question.

Answers

The probability that (all 23 are not smokers is 0.0429

P(all 23 are not smokers 0.0429

P(exactly 6 smokers) ≈ 0.1671

How to calculate the probability

a) If 16% of the population are smokers, then the probability that an individual is not a smoker is 1-0.16=0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429

b) The probability that any one individual smokes is 0.16, and the probability that any one individual does not smoke is 0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429 (rounded to four decimal places).

c) Similarly, we can use the binomial distribution to find the probability of exactly 6 smokers in a sample of 23:

P(exactly 6 smokers) = (23 choose 6) * 0.16⁶ * 0.84^17 ≈ 0.1671

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PLS HELP THIS IS DUE TODAY what is 736 x 21

Answers

Answer:

15456

Step-by-step explanation:

My work is attached to this answer

5. Select all expressions that are equivalent to 3^8.
A. 3^2x3^4
B. 3²x3^6
C. 3^16/3^2
D. 3^12/3^4
E. (3^4)²
F. (3¹)^7

Answers

The expressions that are equivalent to 3^8 are:

B 3²x3^6D. 3^12/3^4E. (3^4)²

How to solve the expressions

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B 3²x3^6

= 9 x 729

= 6561

C. 3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E. (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

B 3²x3^6D. 3^12/3^4E. (3^4)²

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Layla works at a trampoline park. Last month, she earned $1,568 in gross income. Her net income was $1,338.79.

Answers

The amount of tax and deductions from the income is $229.21

Calculating the amount of tax and deductions

From the question, we have the following parameters that can be used in our computation:

Gross income = $1,568

Net income = 1,338.79

Using the above as a guide, we have the following:

Deductions = Gross income - net income

Substitute the known values in the above equation, so, we have the following representation

Deductions = $1,568 - 1,338.79

Evaluate the expression

So, we have

Deductions = $229.21

Hence, the amount of tax and deductions from the income is $229.21

Answers

0.00205 can be written in scientific notation as 2.05 x 10^-3.

Answer:

The answer is 2.05×10‐³

Step-by-step explanation:

0.00205 to scientifi notation or standard form

=2.05×10‐³

L Pretest: Unit 2
Question 16 of 45
A relation is called a function when each element in the domain is paired with
just one element from which of the following?
OA. Range
OB. Solution variables
OC. Independent variables
OD. Inputs
SUBMIT

Answers

A relation is called a function when each element in the domain is paired with just one element from the A. Range

Completing the statement

From the question, we have the following parameters that can be used in our computation:

The incomplete definition of relation

A relation takes the form

Domain : x

Range : y

The values from the domain are then paired with the range

If these values are paired just once, then it is a function

Answers

Answer:

James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the Aestheticism movement.

Applying the Right Triangle Altitude Theorem. Which similarity statement is true?

Answers

The true similarity statement are using Right Triangle Altitude Theorem :

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

By the Right Triangle Altitude Theorem,

If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.

Using this,

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.

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The complete question is given below.

Freemont run club surveyed a random sample of 30 of their members about their running habits

Answers

The reasonable estimate would be 25

How to solve for the estimate

We have to solve this using the rule of 3

9 out of 30 members said that they run more than 5 days a week.

We will form the equations

when 9 ran = 30 menbers

when n ran = 84 members

we will then cross multiply

84 x 9 = 30 x n

n = 25.2

When we round this, the reasonable estimate would be 25

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Complete question

Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.

There are 84 Freemont Run Club members.

Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?

may i have the different proofs for this thank you

Answers

The proof for AB ≅ CD is:

Step Statement Reason

1 ∠B ≅ ∠D, BC || AD Given

2 ∠BCA ≅ ∠CAD Alternate Interior angles

3 AC ≅ AC common side

4 ΔABC ≅ ΔADC Angle-Angle-Side rule of congruency

5 AB ≅ CD Corresponding sides of congruent triangle

Consider triangle ABC and triangle ADC.

Here, side BC is parallel to side AD.

From the attached figure we can observe that AC is a transversal.

so, ∠BCA and ∠CAD would be alternate angles formed by two parallel lines and transversal.

By property of Alternate Interior angles,

∠BCA ≅ ∠CAD

Also, we can observe that side AC is common side to ΔABC and ΔADC.

We rewrite this proof as,

Step Statement Reason

1 ∠B ≅ ∠D, BC || AD Given

2 ∠BCA ≅ ∠CAD Alternate Interior angles

3 AC ≅ AC common side

4 ΔABC ≅ ΔADC Angle-Angle-Side rule of congruency

5 AB ≅ CD Corresponding sides of congruent triangle

This is the required proof.

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Help

Applying the Solution to a 3X3 System

At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?

Show up all steps please

Answers

Solving the system of equations, the number of children, parents, and Grandparents who were in attendance are 190, 140 and 70 respectively.

Let C, P and G denotes the number of children, parents and the grandparents in the function.

We get the system of equations,

C + P + G = 400 [equation 1]

P = 2G ⇒ G = P/2 [equation 2]

C = P + 50 [equation 3]

Substituting 2 and 3 in 1,

(P + 50) + P + (P/2) = 400

2P + P/2 = 350

5/2 P = 350

P = 140

C = P + 50 = 140 + 50 = 190

G = P/2 = 140/2 = 70

Hence the number of parents = 140, grandparents = 70 and children = 190.

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PLEASE HURRY

Let v = 5i - 2j Find ||4v||

Answers

The magnitude of the vector 4v is 4 times the magnitude of v, which is equal to 4 √29.

Given the vector v = 5i - 2j, we can find the magnitude or norm of the vector ||v|| using the formula:

||v|| = √(v · v)

where · denotes the dot product of the vector with itself.

Substituting the values of the vector v, we have:

||v|| = √((5i - 2j) · (5i - 2j))

Expanding the dot product using the distributive law, we get:

||v|| = √(25i² - 20ij + 4j²)

Since i² = j² = 1 and ij = ji = 0, we can simplify this expression to:

||v|| = √(25 + 4) = √29

Thus, the magnitude of the vector v is √29.

Now, we need to find the magnitude of the vector 4v. Using the property that ||kv|| = |k| ||v|| for any scalar k and vector v, we have:

||4v|| = |4| ||v|| = 4 √29

In summary, the magnitude of the vector v is √29, and the magnitude of the vector 4v is 4 √29.

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solve the following inequality PKEASE HELP SOLVE!!

Answers

The solution to the given inequality expression is: x ≤ -2

How to solve the Inequality?

The inequality expression is given as:

5(0.5)ˣ + 1 ≤ 21

Subtract 1 from both sides to get;

5(0.5)ˣ ≤ 20

Divide both sides by 5 to get:

(0.5)ˣ ≤ 4

Using logarithm we have:

x In 0.5 ≤ In 4

x ≤ In 4/In 0.5

x ≤ -2

Thus, that is the solution of the inequality expression

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If there were 20 dogs and 60 cats at a pet daycare, how many cats would there be if there were 40 dogs and the ratio stayed the same?

Answers

The quantity of cats that will be in the pet daycare when there are 40 dogs would be = 120 cats.

How to calculate the ratio of cats to dogs in the pet daycare?

Ratio can be defined as the comparison of two values that shows the amount of one value that can be found in the other value.

The initial amount of dogs = 20

The initial amount of cats = 60

The final amount of dog = 40

The final amount of cats = ?

That is;

20 dogs = 60 cats

40 dogs = X cats

make X the subject of formula;

X = 40×60/20

= 2400/20

= 120 cats

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The cost of a first-class postage in 1970 was $0.06 and in year 2013 was $0.46. Determine the average annual rate of increase in the price of postage stamps during the
years 1970 to 2013.
A. 18.47%
B. 4.851%
C. 6.63%
D. 4.84%

Answers

From 1970 to 2013, the price of postal stamps increased at an average yearly rate of 4.851%.

The formula for compound interest is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A represents the total sum, P represents the beginning sum, r represents the yearly interest rate, n is the number of times the interest is compounded annually, and t represents the number of years.

In this instance, we may consider the initial cost of postal stamps in 1970 as the principal and the rise in price as the interest. The yearly rate of rise, r, may be calculated using the formula.

Let P represent the price in 1970 ($0.06) and A represent the price in 2013 ($0.46). Let t be the duration, or 43 years, from 1970 to 2013.

Then, we can write:

[tex]A = P(1 + r)^t[/tex]

Substituting the values, we get:

[tex]0.46 = 0.06(1 + r)^{43[/tex]

Dividing both sides by 0.06, we get:

[tex]7.67 = (1 + r)^{43[/tex]

Taking the 43rd root of both sides, we get:

[tex](1 + r) = 7.67^{1/43}\\(1 + r) = 1.04851[/tex]

Subtracting 1 from both sides, we get:

r = 0.04851 = 4.851%

Therefore, the average annual rate of increase in the price of postage stamps from 1970 to 2013 is 4.851%.

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A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0.4. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot.

Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?

A. Yes, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
B. Yes, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
D. No, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

Answers

Answer: Choice C

C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

====================================================

Explanation:

If the new additive was more effective than the old one, then the difference in proportions (new - old) should be fairly large.

Count the dots over the x axis labels of "0.4" through "0.6"

5 dots over "0.4"1 dot over "0.5"1 dot over "0.6"

That makes 5+1+1 = 7 dots total.

There are 7 instances where the difference of proportions is 0.4 or larger.

This is out of 200 observations, so 7/200 = 0.035 = 3.5% of the differences have 0.4 or larger.

This is not very significant. The general rule of thumb is to use 5% as the threshold. Some stats textbooks will use 10%. Other times your teacher will specify the significance level. The Greek letter alpha is often used.

Because 3.5% < 5%, we consider the new additive to not be that effective compared to the original additive.

I’m confused. Can somebody help me?

Answers

Answer:

The Correct answer is D and F

20 Per Question, Algebra 2, Thanks :)

Answers

The answer to the expression is (x+3)/(x-1)

What is a quadratic expression?

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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Given a trapezoid with a height of 4.3 m and bases of 9.2 m and 3.2 m, what is the area of the trapezoid? Do not include units in your answer. Round your answer to the nearest tenth.

Answers

Answer:

26.5

Step-by-step explanation:

The formula for the area of a trapezoid is:

A = (1/2)h(b₁ + b₂)

where h is the height, b₁ and b₂ are the lengths of the parallel bases.

Substituting the given values:

A = (1/2)(4.3 m)(9.2 m + 3.2 m)

A = (1/2)(4.3 m)(12.4 m)

A = 26.52 m²

Rounding to the nearest tenth:

A ≈ 26.5

Therefore, the area of the trapezoid is approximately 26.5 square meters.

Find P U (Q n R).........................

Answers

P U (Q n R):
Q n R = {5, 11} (common numbers)
P U (Q n R) = {5, 7, 10, 11, 13, 14} (Q n R common numbers + all the numbers from P)

what is the inverse of y=4x+5?

Answers

Y=(x-5)/4

Inverses are just replacing x and y and solving for y ->

X=4y+5
X-5=4y
(X-5)/4=y

Given:

[tex]\sf y = 4x + 5[/tex]

Switch x and y.

[tex]\sf x = 4y + 5[/tex]

Solve for y.

[tex]\sf 4y = x - 5[/tex]

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

[tex]\Rightarrow\boxed{\sf y = \dfrac{1}{4} \ x-\dfrac{5}{4}}[/tex]

Trapezoid ABCD is transformed according to the rule . What is the x-coordinate of A”? -3 -2 2 3

Answers

The x-coordinate of A” is 2

Here, we want to know;

the x-coordinate of the rotation about the origin of a point 90 degrees clockwise.

A rotation of 90 degrees clockwise about the origin will turn the coordinates (x, y) to (-y, x)

Here, The coordinates of A is (3,-2)

So, upon the assigned rotation, it becomes;

A'' = (2,-3)

So, the x-coordinate of A” is 2

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A human heart pumps about 7 × 10-2 liter of blood pe-
heartbeat. The average human heart beats about 72 times per minute.
How many liters of blood does a heart pump in 1 year? 70 years?

Answers

The heart will pumps 31,536 litres in 1 year and pumps 2,207,520 liters in 70 years.

Simple solution to how blood is pumped

There are 72 heartbeats in a minute.

If heart pumps 7 × 10⁻² litre per heartbeat,

then in 1 min,

7 × 10⁻² x 72 = 5.04 litres/minute

In one year (365 days), the heart pumps:

5.04 x 60 x 24 x 365 = 31,536 litres/year

Hence in 1 year, heart pumps 31,536 litres

In 70 years, the heart would pump:

31,536 x 70 years = 2,207,520 litres

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Select the correct answer.
A number is selected at random from the set (2, 3, 4,... 10). Which event, by definition, covers the entire sample space of this experiment?
O A.
O B.
O C.
OD.
The number is even or less than 12.
The number is not divisible by 5.
The number is neither prime nor composite.
The number is greater than 2.
Reset
Next

Answers

The sample space for this experiment is the set {2, 3, 4, 5, 6, 7, 8, 9, 10}.

The event that covers the entire sample space is option D, "The number is greater than 2." This is because every number in the sample space is greater than 2.

Option A, "The number is even or less than 12," does not cover the entire sample space because 9 and 10 are not even and 10 is greater than 12.

Option B, "The number is not divisible by 5," does not cover the entire sample space because 5 and 10 are both divisible by 5.

Option C, "The number is neither prime nor composite," does not cover the entire sample space because 2 and 3 are prime numbers.

Therefore, the correct answer is D.

carly and ramil want to draw a line on the coordinate plane that is parallel to line a. carly uses the rule multiply by 1 add 2 to generate her y coordinates. ramil uses the rule multiply by 2 and add 1 to generate his y-coordinates. which students line will be parallel to line d? without graphing the lines explain how you know

Answers

The students' line that will be parallel to line d is the line with the same slope as d

Which students line will be parallel to line d?

The rules are given as

Carly uses the rule multiply by 1 add 2 to generate her y coordinates. Ramil uses the rule multiply by 2 and add 1 to generate his y-coordinates

This means that the equations of the function are

Carly: y = x + 2

Ramil: y = 2x + 1

If the slope of line d is 1, Carly's line will be parallel to line d and if the slope of line d is 2, Ramil's line will be parallel to line d

This is because parallell lines have equal slopes

PLEASE HELP Parts a, b, c, d, and e

Answers

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PLEASE HELP
Parts a, b, c, d, and e