Use the graphs of f and g to find (fg)(−1).

Using arithmetic operations it is obtained that after the increase, the pay will be $13.50 per hour.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To calculate the increase in pay, start by multiplying the current hourly rate of $12.50 by the percentage increase of 8% -

Increase in pay = $12.50 x 8/100

Increase in pay = $12.50 x 0.08

Increase in pay = $1.00

So, the increase in pay is $1.00 per hour.

To find the new hourly rate after the increase, add the increase in pay to the current hourly rate -

New hourly rate = $12.50 + $1.00 = $13.50

Therefore, the increased, pay will be $13.50/hr.

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The derivative of composite functions are listed below:

Case A

Subcase i: y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii: y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i: y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii: y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

Chain rule is powerful resource to find the derivative of a composite function, that is, a function of the form:

f ° u (x) = f[u(x)]

And chain rule is now defined:

df[u(x)] / dx = (df / du) · (du / dx)

There are three cases requiring chain rule, now we proceed to determine the derivative for each expression:

Case A

Subcase i

y = (x³ + 8 · x² - x + 3)⁴

y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii

y = (x² + 4 · x - 2) · (2 · x - 7)³

y' = (2 · x + 4) · (2 · x - 7)³ + 6 · (x² + 4 · x - 2) · (2 · x - 7)²

y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i

y = 5 · x · (2 · x - 1 / x²)²

y' = 5 · [(2 · x - 1 / x²)² + 2 · x · (2 · x - 1 / x²) · (2 - 2 / x³)]

y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii

y = (2 - x) / (x² + 3 · x - 1)

y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

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Answer:

New value =

56 - Percentage decrease =

56 - (14% × 56) =

56 - 14% × 56 =

(1 - 14%) × 56 =

(100% - 14%) × 56 =

86% × 56 =

86 ÷ 100 × 56 =

86 × 56 ÷ 100 =

4,816 ÷ 100 =

48.16

56 decreased by 14% = 48.16

Absolute change (actual difference):

48.16 - 56 = - 7.84

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Answer:

the efficiency of the generator is 81.82%.

Step-by-step explanation:

The efficiency of a generator is defined as the ratio of the electrical power output to the mechanical power input. In this problem, the electrical power output is given as 90 hp, and the mechanical power input is the power supplied by the engine, which is 110 hp. Therefore, the efficiency of the generator can be calculated as follows:

Efficiency = Electrical power output / Mechanical power input

Efficiency = 90 hp / 110 hp

Simplifying the fraction, we get:

Efficiency = 0.8182

To convert this decimal to a percentage, we multiply by 100:

Efficiency = 0.8182 * 100

Rounding to two decimal places, we get:

Efficiency = 81.82%

Therefore, the efficiency of the generator is 81.82%.

Answer:

B 3

notice that beside the 30 degree there is also 90 degree. please see the attachment.

Answer: The correct answer is 4988.

Step-by-step explanation: 4007+981 = 4988 Add the one to the eight then add the 8 to the tens place and add the 9 to the hundreds place.

THIS IS THE CORRECT ANSWER.

If a nurse can visit 5 patients each hour. If he has 37 patients to visit in a day.  the nurse can visit all of his patients if he works for at least 8 hours in a day.

Let's start by figuring out how many hours the nurse would need to visit all 37 patients, assuming he could work for a continuous period of time without taking a break:

37 patients ÷ 5 patients/hour = 7.4 hours

However, since the nurse cannot work a fraction of an hour, we need to round up to the nearest hour. Therefore, the nurse would need to work for 8 hours in order to visit all 37 patients.

So, the nurse can visit all of his patients if he works for at least 8 hours in a day.

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Answer:

14

Step-by-step explanation:

To find the value of (f-g)(2), we first need to compute the function (f-g), which is defined as the difference between f(x) and g(x), and then evaluate it at x=2.

So, (f-g)(x) = f(x) - g(x)

Substituting the given functions, we get:

(f-g)(x) = (3x^2 + 1) - (1-x)

(f-g)(x) = 3x^2 + x

Now, to find (f-g)(2), we substitute x=2 into the expression we just obtained:

(f-g)(2) = 3(2)^2 + 2

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

(f-g)(2) = 12 + 2

(f-g)(2) = 14

Therefore, the value of (f-g)(2) is [14.]

Answer: 2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

[tex]\frac{1}{2} *\frac{10}{1} = \frac{10}{2} = 5[/tex]

Answer:

(a) Pour trouver le nombre d'étudiants qui suivent les trois matières, on peut utiliser la formule suivante:

Therefore , the solution of the given problem of ordered pair comes out to be system of equations is the ordered pair (-4, 1).

Two independent variables that are grouped in a fashion that suggests a particular order are known as "ordered pairs." The 1 and 2 parts each indicate one of an order pair's y-coordinates. The ordered pair is shown in close parenthesis in the example that follows.

Here,

We can solve this system of equations by substitution or elimination.

Here's how to do it using the substitution method:

From the first equation, we know that y = x + 5. We can substitute this expression for y in the second equation to get:

$x - 5y = -9

$x - 5(x + 5) = -9

$x - 5x - 25 = -9

Simplifying the equation, we get:

$-4x = 16$

$x = -4$

Now that we know the value of x, we can substitute it back into the first equation to find y:

y = x + 5 = -4 + 5 = 1$

Therefore, the solution to the system of equations is the ordered pair (-4, 1).

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15 < 4 + x

15 - 4 < x

11 < x

Therefore, the solution to the inequality is x > 11.

The statement 3/4> 13/16 is false and the statement 6/7> 5/8is true.

Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Using the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.

The first statement is:

3/4 > 13/16

Take the LCM:

12/16 > 13> 16

Comparing the numerator we see that, 12 > 13 is false. Hence, the statement is false.

The second statement is:

6/7 > 5/8

Take the LCM:

48/56 > 35/56

Comparing the numerator we see that, 48 > 35 is True.

Hence, the statement is True.

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The congruent angles in the similar figures are as follows:

∠M ≅ ∠R

∠N ≅ ∠S

∠P ≅ ∠T

∠Q ≅ ∠U

Two figures are said to be similar if they are the same shape.  Similar figures have the corresponding sides in proportion to each other.

Similar figures also have the corresponding angles equal to each other.

Therefore, the figures are similar by MNPQ ~ RSTU

Hence,

∠M ≅ ∠R

∠N ≅ ∠S

∠P ≅ ∠T

∠Q ≅ ∠U

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what is combination ?
In mathematics, a combination is a way of selecting items from a collection, such that the order of selection does not matter. The combination formula gives the total number of ways to choose k items from a set of n distinct items without regard to the order in which they are chosen.

The combination formula is given by:

n choose k = n! / (k! * (n-k)!)

Explanation:
If we have 10 color-coded wires, we can choose 2 wires out of them in (10 choose 2) ways.

(10 choose 2) is a combination formula given by:

(10 choose 2) = 10! / (2! * (10-2)!)

= (10 * 9) / 2

= 45

This means that we need to perform 45 tests to cover all possible pairings of 2 wires from 10 color-coded wires.

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The answer is option B, 1(1/2) yards.

How to determine the total amount?

We apply the following total sales calculation to get the total sales amount.

Total sales = original price + original price * sales tax rate

To find out how many yards of cloth remain, we need to subtract the amount used for making curtains from the total amount provided:

Total amount of cloth provided = 5(3/4) yards

Amount of cloth used for curtains = 4(1/4) yards

Remaining amount of cloth = Total amount of cloth provided - Amount of cloth used for curtains

= 5(3/4) - 4(1/4) yards

= 5 yards + 0.75 yards - 4 yards - 0.25 yards

= 1(1/2) yards

Therefore, the answer is option B, 1(1/2) yards.

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Maura will have 5, 206 points at either hotel by booking 301 nights.

To find the number of points, we shall assume that nights are denoted as n. The number of points for Hotel Elegance will be shown as :

= Signing up points + ( Number of points per night x Number of nights)

= 89 + 17 n

The number of points for Hotel Paradiso is:

= 691 + 15 n

The number of nights that Maura needs to stay for the points to be the same is :
89 + 17 n = 691 + 15 n

17 n - 15 n = 691 - 89

2 n = 602

n = 602 / 2

n = 301 nights

The number of points would be :

= 691 + 15 n

= 691 + 15 x 301

= 5, 206 points

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The solution is,

y = 2(x+1)^2+6

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

y = -(x-1)^2/2 -4

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

here, we have,

y = 2(x+1)^2+6

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

y = -(x-1)^2/2 -4

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

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The event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Option D

To determine which event is most likely to occur, we need to compare the probabilities of each event happening.

Rolling a multiple of 4 on an eight-sided die:

There are 8 possible outcomes when rolling an eight-sided die, and 2 of them are multiples of 4 (4 and 8). So, the probability of rolling a multiple of 4 is 2/8, or 1/4.

Spinning a spinner and landing on pink:

There are 4 possible outcomes when spinning the spinner, and only one of them is pink. So, the probability of landing on pink is 1/4.

Winning a raffle that sold a total of 100 tickets, if you buy 53 tickets:

The total number of possible outcomes is the total number of tickets sold, which is 100. The number of favorable outcomes is the number of tickets the person bought, which is 53. So, the probability of winning the raffle is 53/100.

Reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew:

The total number of possible outcomes is the total number of candies in the bag, which is 50 + 10 = 60.

The number of favorable outcomes is the number of strawberry chews in the bag, which is 50. So, the probability of pulling out a strawberry chew is 50/60, which simplifies to 5/6.

Comparing the probabilities, we can see that the event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Therefore, this event is the most likely to occur.

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Answer:

19

Step-by-step explanation:

111111111

+

1111111111

count how many 1ns are there.

ans is 19

Using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

What is meant by Pythagoras' theorem?

The Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse. In essence, Pythagoras' theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.

The given figure is a right triangle.

The length of road A = 16.01 km

The length of road B = 10 km

a) The length of road C can be found using Pythagoras' theorem.

From figure,

A² = B² + C²

16.01 ² = 10² + C²

C² = 156.32

C = 12.5 km

b) Speed of bike = 19.5 km/h

   Length of road C = 12.5 km

Time = Length/speed = 12.5/19.5 = 0.64 hours

 Length of road B =10 km

Time = Length/speed = 10/19.5 = 0.51 hours

c) Length of road A = 16.01

Time taken = Length/speed = 16.01/19.5 = 0.82 hours.

Therefore using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

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The term B. One Optimal Solution best describes the system of inequalities 2x + y < 15, 3x + y < 12, f(x, y) = 2x + 2y.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two inequalities 2x + y < 15 and 3x + y < 12.

has one optimal solution as if we subtract these two inequalities, 'y' will get canceled and we can have the value of 'x' from that we can determine 'y' also.

Q. Which term best describes the solution of the situation represented by the system of inequalities? 2x + y < 15, 3x + y < 12, f(x,y) = 2x+2y

A. alternate optimal solutions

B. One Optimal Solution

C. Unbounded

D. Infeasible

The sample space lists all possible outcomes of rolling a number cube twice, where W represents a roll with a value of 6 or higher, and L represents a roll with a value of 5 or lower.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The answer to Question 3 is List 2, which gives the sample space for pulling 2 marbles from the bag with replacement.

The answer to Question 4 is two ninths. Since there are three cards with one D each, the probability of selecting a D on the first draw is 1/3. Since the cards are replaced, the probability of selecting a D on the second draw is also 1/3. Therefore, the probability of selecting D and D in that order is (1/3) * (1/3) = 1/9. However, since the order of selection does not matter, we must also consider the probability of selecting D and D in the reverse order, which is also 1/9. Therefore, the total probability is 1/9 + 1/9 = 2/9.

The answer to Question 5 is four thirty sixths or one ninth. The only ways to get a sum of 5 are by rolling a 1 and a 4, a 2 and a 3, or a 3 and a 2. Each of these outcomes has a probability of 1/6 * 1/6 = 1/36, so the total probability is 3 * 1/36 = 1/12 = 4/36.

The answer to Question 6 is Rolling a number cube twice.  For example, WW represents rolling a 6 or higher on both rolls, and LL represents rolling a 5 or lower on both rolls.

Therefore, The sample space lists all possible outcomes of rolling a number cube twice, where W represents a roll with a value of 6 or higher, and L represents a roll with a value of 5 or lower.

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Answer:

Step-by-step explanation:

list 4

Booth's additional funds needed (AFN) for the coming year is $365.

What is additional funds?

Additional Funds Needed (AFN) is a way of calculating how much new funding will be required, so that the firm can realistically look at whether or not they will be able to generate the additional funding and therefore be able to achieve the higher sales level.

Use the following formula to calculate Booth's additional funds needed (AFN) -

AFN = (A*/S)ΔS - (L*/S)ΔS - MS1(RR)

where -

A* = Total assets excluding spontaneous liabilities

S = Sales

ΔS = Increase in sales

L* = Total spontaneous liabilities

MS1 = Net income (1 - RR), where RR is the retention ratio (1 - payout ratio)

Start by calculating A* and L*.

Since we are told that spontaneous liabilities increase at the same rate as sales, we can use the percentages provided to calculate the required increases in each account -

Accounts receivable: ΔAR = 0.5(S1 - S0) = 0.5(2000 - 1000) = 500

Inventories: ΔINV = 0.5(S1 - S0) = 0.5(2000 - 1000) = 500

Accounts payable: ΔAP = 0.5(S1 - S0) = 0.5(1000 - 500) = 250

Accruals: ΔACC = 0.5(S1 - S0) = 0.5(1000 - 500) = 250

A* = Total assets - spontaneous liabilities

= $1000 - ($200 + $50 + $250 + $50 + $250)

= $200

L* = Spontaneous liabilities

= $200 + $50 + $250 + $50

= $550

Next, calculate the increase in fixed assets that would be required if Booth operated at full capacity -

ΔFA = (FCR)(ΔS)

where FCR is the fixed assets capacity ratio, given by -

FCR = Actual sales / Full capacity sales

= $1000 / (2 x $1000)

= 0.5

ΔFA = (0.5)(1000)

= 500

Now calculate AFN using the formula -

AFN = (A*/S)ΔS - (L*/S)ΔS - MS1(RR)

= ($200 / $1000)(1000) - ($550 / $1000)(1000) - ($30)(0.5)

= $365

Therefore, the value is obtained as $365.

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The Booth Company's sales are forecasted to double from $1,000 in 2016 to $2,000 in 2017. Here is the December 31, 2016, balance sheet:

Cash  $  100  Accounts payable  $   50

Accounts receivable  200  Notes payable  150

Inventories  200  Accruals  50

Net fixed assets  500  Long-term debt  400

Common stock  100

Retained earnings  250

Total assets  $1000  Total liabilities and equity  $1000

Booth's fixed assets were used to only 50% of capacity during 2016, but its current assets were at their proper levels in relation to sales. Spontaneous liabilities and all assets except fixed assets must increase at the same rate as sales, and fixed assets would also have to increase at the same rate if the current excess capacity did not exist. Booth's after-tax profit margin is forecasted to be 3% and its payout ratio to be 50%. What is Booth's additional funds needed (AFN) for the coming year? Round your answer to the nearest dollar.

True, false, true, true, false and true are the answers of statements a to f respectively.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

(a) A linear transformation [tex]T:R^n\rightarrow R^m[/tex] is completely determined by the effect on the columns of the n x n identity matrix is true from the fact that the columns of any n x n matrix A completely determine the linear transformation T defined by T(x) = Ax for any vector x in Rⁿ.

(b) False. There exist linear transformations from Rⁿ to Rⁿ that are not matrix transformations.

(c) True. The range of the matrix transformation H Ax is the set of all possible linear combinations of the columns of A.

(d) True. A linear transformation  [tex]T:R^n\rightarrow R^m[/tex]  is one-to-one if and only if T(x) = T(y) implies x = y for any vectors x and y in Rⁿ.

(e) False. The matrix transformation x → Ax is one-to-one if and only if the equation Ax = 0 has only the trivial solution (i.e., x = 0).

(f) True. The matrix transformation x → Ax is one-to-one if and only if the kernel of the linear transformation T(x) = Ax is trivial, which is equivalent to the columns of A being linearly independent.

Hence, true, false, true, true, false and true are the answers of statements a to f respectively.

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Answer:

The correct statement is (B), You can safely carry out the test if your sample size is large and there are no outliers.

Step-by-step explanation:

Step 1: Given Information

A one-sample test about a population mean using a significance level.

Next,  OR Step 2

To identify the correct statement:

(a) False, because if a distribution is moderately skewed, then you can still carry out the test if the sample size is large ( or more).

(b) True, because if the sample size is larger ( or more) and there are no outliers, then you can still safely carry out the test.

(c) False, the sample size should be large ( or more) since the distribution is moderately skewed.

(d) False, the one-sample  test can only be used if the population standard deviation is unknown. You apply the onesample  test if the population standard deviation is known.

(e) False, -procedures are not robust, because they are heavily influenced by outliers.

Thus the answer to your problem is, B.

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Answer:

The geometric mean of 16 and 36 is 24

it would take approximately 11 hours to complete the order if the number of working machines increased by a factor of 2.

An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations, but does not contain an equals sign. Algebraic expressions are used to represent mathematical relationships and are an important tool in algebra and other areas of mathematics.

Algebraic expressions can be simple, such as x + 2, which consists of a variable (x), a constant (2), and an addition operation. More complex algebraic expressions can contain multiple variables, constants, and operations, such as 2x² + 3xy - 4.

Variables in algebraic expressions represent unknown values that can vary or change, while constants are fixed values that do not change. Mathematical operations, such as addition, subtraction, multiplication, and division, are used to combine variables and constants in algebraic expressions.

We can use the following formula to solve the problem:

(number of machines) x (time to complete the order) = constant

Let's call the constant k. If six machines working simultaneously can complete the order in 22 hours, we have:

6 x 22 = k

k = 132

Now, let's double the number of machines to 12 and find the new time it would take to complete the order:

12 x t = 132

where t is the new time it would take to complete the order with 12 machines. Solving for t, we get:

t = 132/12

t ≈ 11

Therefore, it would take approximately 11 hours to complete the order if the number of working machines increased by a factor of 2.

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Final answer is that there are 500 students in Math 6.

what is percentage ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the % symbol. For example, 50% means 50 out of 100, or 0.5 as a decimal.

According to question:
A. Joey's answer of 180 is not correct. If 300 students are currently mastering their math lessons and this represents 60% of the total number of students in Math 6, we can use the following equation to find the total number of students in Math 6:

60% of the total number of students = 300

0.6 × Total number of students = 300

Total number of students = 300 ÷ 0.6

Total number of students = 500

Therefore, there are 500 students in Math 6, not 180.

B. It is possible that Joey used a method called "guess and check" to arrive at his answer of 180. This method involves guessing a number, plugging it into an equation or problem, and checking to see if it is the correct answer. While this method can be useful in some cases, it is not a reliable method for solving this problem since there are an infinite number of numbers to guess from and the probability of guessing the correct answer is low.

C. To solve this problem correctly, we can use a percent equation. We know that 60% of the students in Math 6 are mastering their math lessons, so we can write:

0.60 × Total number of students = 300

To solve for the total number of students, we can divide both sides of the equation by 0.60:

Total number of students = 300 ÷ 0.60

Total number of students = 500

Therefore, the final answer is that there are 500 students in Math 6.

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0.0248 is the probabilty that he or she is allergic to multiple foods .

What is probability and its formula?

The probability serves as a gauge for the possibility that an event will occur. It quantifies the certainty of the event.

                         The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.

P(food allergy and history of severe reaction) = 0.08 x 0.38

= 0.0304

b) P(allergic to multiple foods) = 0.08 x 0.31

= 0.0248

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