given the function h(x)=3x+1 and g(x)= x/3 find

a) h^-1 (x)
b)gh^-1 (7)

Answer:

linear inequation with 1 variable

Answer:

10

Step-by-step explanation:

median is the middle number

these numbers in order are 2, 5, 6, 8, 12, 15, 19, 22 and the middle numbers are 8 and 12

to ind the middle number of those two numbers, you find the mean (averge) of those numbers

mean: 8+12=20/2=10

lmk if its right!

Answer:

Accuracy is how close a measured value is to an accepted value. Precision is how close measurements are to one another. To make measurements, you have to evaluate both the accuracy and the precision to get a correct value.

Expression 5 + (12.8 ÷ 3.2) represents the phrase 5 + the quotient of 12. 8 and 3. 2 and option (a) is the correct answer.

Expressions refer to a phrase with at least two numbers or variables with any mathematical operations such as addition, exponents, etc. x - 6, 9 + 4y, and 6a are all examples of mathematical expressions.

Equations refer to a sentence when two expressions are equated with the help of '='. x - 6 = 6a is an example of an equation.

In phrase 5+ the quotient of 12. 8 and 3. 2

We divide the phrase into different mathematical operations.

The first operation is of addition with 5, we can write the beginning as 5 + ...

The next operation is division in the phrase the quotient of 12. 8 and 3. 2 which is added to the expression and we get 5 + (12.8 ÷ 3.2)

And we get our answer.

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The complete question might be :

Which expression represents the phrase 5+ the quotient of 12. 8 and 3. 2?

a. 5 + (12.8 ÷ 3.2)

b. 5 - (12.8 + 3.2)

c. 5 + (12.8 * 3.2)

d. none of the above

Answer:

Step-by-step explanation:

Answer:

1.92

Step-by-step explanation:

2.40 is more than 1.92

Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.

A fraction is not defined when the denominator is zero.

In this problem, the expression is given by:

cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.

The denominators are zero in two cases:

Hence the equation is not defined for an angle of 90º.

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Answer:

m = \(\frac{16}{3}\) , z = \(\frac{24}{5}\)

Step-by-step explanation:

Δ PQT and Δ PRS are similar ( by AA postulate ), so the ratios of corresponding sides are equal, that is

\(\frac{PQ}{PR}\) = \(\frac{PT}{PS}\) , substitute values

\(\frac{m-2}{m}\) = \(\frac{5}{8}\) ( cross- multiply )

8(m - 2) = 5m ← distribute parenthesis on left side

8m - 16 = 5m ( subtract 5m from both sides )

3m - 16 = 0 ( add 16 to both sides )

3m = 16 ( divide both sides by 3 )

m = \(\frac{16}{3}\)

and

\(\frac{QT}{RS}\) = \(\frac{PT}{PS}\) , substitute values

\(\frac{3}{z}\) = \(\frac{5}{8}\) ( cross- multiply )

5z = 24 ( divide both sides by 5 )

z = \(\frac{24}{5}\)

Answer:

\((x+5)^{3}\)

Step-by-step explanation:

Hope this helps

The expression for the word problem is ( x + 5 )².

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given word problem is the cube of the sum of a number and 5. The expression will be formed as below:-

Let the unknown number be x.

E = ( x + 5 )²

Therefore, the expression for the word problem is ( x + 5 )².

The complete question is given below:-

The cube of the sum of a number and 5. Write the mathematical expression.

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Answer:Exact Form:

23/6

Decimal Form:

3.83

Mixed Number Form:

3 5/6

Expressions are mathematical statements represented with the variables

The value of 12x^-3 y-1 for x=-1 and y=5 is - 12/5

The expression is given as:

\(12x^{-3} y^{-1}\)

When x = -1, the expression becomes

\(12 * -1^{-3} y^{-1}\)

Evaluate the exponent

\(- 12 y^{-1}\)

When y = 5, the expression becomes

\(- 12 * 5^{-1}\)

Evaluate the exponent

- 12/5

Hence, the value of 12x^-3 y-1 for x=-1 and y=5 is - 12/5

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(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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The order in which they performed be

14 + 16 . . . . add 5 + 9  

30 . . . . . . . add 14 + 16

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. There are four possible math operations here: addition, subtraction, multiplication, and division.

Given: 40/8 + 3² + (15 - 7) × 2

The order of operations instructs you to begin by assessing parenthesized expressions. This is done by deducting 7 from 15.

40/8 + 3² + 8 × 2 . . . . (15 - 7) = 8

Then you evaluate exponential terms.

 40/8 + 9 + 8 × 2 . . . . . 3² = 9

Next, multiply and divide from left to right. In this case, division comes before multiplication.

 5 + 9 + 8 × 2 . . . . . divide 40/8 = 5

 5 + 9 +16 . . . . . . multiply 8 × 2 = 16

The order in which they performed be

14 + 16 . . . . add 5 + 9  

30 . . . . . . . add 14 + 16

The complete question is:

Using the order of operations, what are the steps for solving this expression?

40/8+3^2+(15-7)*2

Arrange the steps in the order in which they are performed.​

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Answer:

5

Step-by-step explanation:

2x - 7 + 7 > 3 + 7

2x/2 > 10/2

x > 5

(my device doesn't have the sign for greater than or equal to so imagine i used it)

Answer:

9

Step-by-step explanation:

2^(7–7) =1 1 ≥ 3? No

2^(8–7) =2 2 ≥ 3? No

2^(9–7) =4 4 ≥ 3? Yes

The answer is 1400, good luck

The final image will fit in a similar portfolio with an area of 160 square inches.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

The dimensions for this problem are given as follows:

24 inches, 36 inches.

With the reduction with a scale factor of 1/3, the dimensions are given as follows:

8 inches,  12 inches.

With the enlargement by a factor of 1.25, the dimensions are given as follows:

10 inches and 15 inches.

Hence the area is given as follows:

15 x 10 = 150 square inches.

As the area of 150 square inches is less than 160 square inches, the final image will fit in a similar portfolio with an area of 160 square inches.

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Answer:

x = 25

Step-by-step explanation:

\( \triangle DGH\sim\triangle DEF... (given) \)

\( \frac{DG}{DE} =\frac{GH}{EF} \)

\( \frac{52}{91} =\frac{x+3}{2x-1} \)

\( \frac{4}{7} =\frac{x+3}{2x-1} \)

4(2x - 1) = 7(x + 3)

8x - 4 = 7x + 21

8x - 7x = 21 + 4

x = 25

Answer:

163

Step-by-step explanation:

Given the following :

Number of visitors on Friday = 3,260

Number increased by 15% on Saturday

Projected percentage increase on Saturday = 20%

Actual percentage increase in number of visitors = 15%

Number of visitors on Saturday :

(100 + 15)% × 3260

115% * 3260

(115/100) * 3260

= 3749 visitors

Projected percentage increase = 20%

Projected number:

((100 + 20)% * 3260

120% * 3260

(120/100) * 3260

= 3912

Difference : (3912 - 3749) = 163

Answer:

4800

Step-by-step explanation:

I attached a picture of the work.

We need to made a function that will help us solve this

f(x)=dx; d = $ per hour, x = # of hours

step 1) identify d (in this case, the money made per hour) which = 10

f(x)=10x

step 2) identify x (# of hours total) which = 480

f(x)=10(480)

step 3) solve the equation

f(x)=4800

independent variable:

the number of hours

dependant variable:

the amount of money made after 12 weeks

Answer:

A linear equation in the slope-intercept form is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, we know that the rate of change (the slope) is -5

Then we just replace a by -5

y = -5*x + b

Now we also know that this line passes through a point, and the point is (3, 0)

This means that the point (3, 0) is a solution for the line equation, so when x = 3, we also have y = 0.

Replacing these values in our equation we get:

0 = -5*3 + b

0 = -15 + b

15 = b

Now we know the value of b, so we can replace it in the line equation to get:

y = -5*a + 15

Which is the complete equation of the line.

The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

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Answer:

27mph

Step-by-step explanation:

Let's assume the speed of the first car is x mph. Since the second car is traveling 6 mph slower, its speed would be (x - 6) mph.

To find out how far each car has traveled, we can use the formula: distance = speed × time.

For the first car:

Distance traveled by the first car = speed of the first car × time

d₁ = x mph × (4 hours + 20 minutes)

Since we need to work with a single unit of time, let's convert 20 minutes to hours:

20 minutes = 20/60 = 1/3 hours

Substituting the values:

d₁ = x mph × (4 + 1/3) hours

d₁ = x mph × (13/3) hours

d₁ = (13x/3) miles

For the second car:

Distance traveled by the second car = speed of the second car × time

d₂ = (x - 6) mph × (4 hours + 20 minutes)

d₂ = (x - 6) mph × (13/3) hours

d₂ = (13/3)(x - 6) miles

Since they are traveling in opposite directions, the sum of their distances is equal to the total distance between them:

d₁ + d₂ = 260 miles

Substituting the expressions for d₁ and d₂:

(13x/3) + (13/3)(x - 6) = 260

To simplify the equation, let's multiply both sides by 3 to get rid of the denominators:

13x + 13(x - 6) = 780

13x + 13x - 78 = 780

26x - 78 = 780

26x = 780 + 78

26x = 858

x = 858/26

x ≈ 33

The speed of the first car is approximately 33 mph. Substituting this value back into the equation for the speed of the second car:

Speed of the second car = x - 6 ≈ 33 - 6 ≈ 27 mph

Therefore, the first car is traveling at approximately 33 mph, and the second car is traveling at approximately 27 mph.

Answer:

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Step-by-step explanation:

A. Yes. She solved the problem correctly.

B. No. She multiplied the dividend by the divisor instead of finding the reciprocal.

C. No. She multiplied the denominators instead of finding a common denominator.

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Her workings

7 ÷ 2/ 5

=1/ 7 × 2/ 5

= 2/35

Dividend=7

Divisor=2/5

The correct working

7 ÷ 2/ 5

=7 × 5/2

=35/2

Answer:

D

Step-by-step explanation:

I got an 100% on the quiz I took with this question :)

Hope I could help good luck on passing!!

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \£990\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &4 \end{cases} \\\\\\ A=990[1+(0.02)(4)]\implies A=990(1.02)(4)\implies A=4039.2\)

Answer:

(-21, -59.5)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

2x - 3x = 21

-6x + 2y = 7

Step 2: Solve for x

2x - 3x = 21

Step 3: Solve for y

The TI-84 Plus calculator can be used to find various percentiles and guarantee values for a certain type of automobile tire. The 19th percentile of tire lifetimes is approximately 35.38 thousand miles. The 71st percentile is approximately 42.85 thousand miles. The first quartile, which represents the 25th percentile, is approximately 37.07 thousand miles. To ensure that only 2% of the tires violate the guarantee, the tire company should guarantee a minimum of approximately 31.35 thousand miles.

To find the percentiles and guarantee values using the TI-84 Plus calculator, we can utilize the normal distribution function. Given that the lifetime of the automobile tires is normally distributed with a mean (μ) of 39 thousand miles and a standard deviation (σ) of 6 thousand miles, we can apply these values to the calculator.

(a) To find the 19th percentile, we input the following command: invNorm(0.19, 39, 6). The calculator will provide an output of approximately 35.38 thousand miles.

(b) For the 71st percentile, we use the command: invNorm(0.71, 39, 6). The calculator will yield an approximate value of 42.85 thousand miles.

(c) The first quartile, representing the 25th percentile, can be obtained by entering: invNorm(0.25, 39, 6). The calculator will give an output of approximately 37.07 thousand miles.

(d) To determine the guarantee value for which only 2% of the tires violate the guarantee, we use the command: invNorm(0.02, 39, 6). The calculator will provide an approximate value of 31.35 thousand miles.

These calculations give us the requested percentiles and guarantee value for the tire lifetimes, rounded to at least two decimal places.

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The required distance of the point from the line is given as 2 units.

Given that,

Line ℓ has equation y=7. Find the distance between ℓ and point D(-5,-7).

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
For the line l y = 7, the distance from the point D(-5, -7) is given as,
D =| l |/ |l|
D = y - 7 / √y²
Now put y = -7 in the above equation,
D = |-7 - 7 | / √7²

D = 14 / 7
D = 2

Thus, the required distance of the point from the line is given as 2 units.

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Answer:

14014

Step-by-step explanation:

base of stone pyramid=154

height=91

b×h

154×91=4014

Answer:

1. 24p + 18

Step-by-step explanation:

One of the formulas used to find the perimeter of a rectangle is:

P = 2(l + w)

Where P is the perimeter, l is the length, and w is the width. We can substitute in the given values:

P = 2[(4p + 4) + (8p + 5)]

Now we can combine the like terms:

P = 2[12p + 9]

And simplify:

P = 24p + 18

This is the same as option 1.