Consider the function f(x) = (x - 3)².
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.

Answer:

C) E = 118°; T = 118°

-----------------------------------

The given figure is a kite since it has two pairs of congruent sides as marked.

Its one pair of opposite angles are congruent. That is:

Sum of all interior angles of a quadrilateral is 360°:

Both the missing angles are 118°.

The minimum number of hours life guarding that Daniel must work to meet his requirements = 12 hours

To the nearest whole number approximately:

If the digit following the decimal is less than 5, only the number preceding the decimal should remain unchanged.

Add one to the number before the decimal and eliminate the decimal part if the digit following the decimal is five or greater.

Given the information,

Babysitting pays Daniel $8 per hour, and life guarding pays him $15 per hour.

Daniel can only work a total of 18 hours per week and must make at least $200.

Daniel has been babysitting for three hours.

Daniel thus makes 3 x 8 = 24 dollars.

He has earned $200 - 24 = 176 dollars from the original $200.

Let's say Daniel was a lifeguard for m hours.

He therefore made m x 15 = 176.

15 × m = 176

m = 11.73

m ≈ 12 hours

So, the minimum number of whole hours = 12

This means, Daniel must work 12 hours lifeguarding to meet his requirements.

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An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. The restocking fee for an item priced at $180 is $10.

To solve this problem, we need to use a proportion to relate the item price to the restocking fee. The problem provides two pairs of corresponding item prices and restocking fees: $200 and $12, and $150 and $9. We can set up a proportion using these pairs:

$200/$12 = $150/$9

We can simplify this proportion by dividing both sides by 3:

$200/$4 = $150/$3

Now we can use the simplified proportion to find the restocking fee for an item priced at $180. We'll use cross-multiplication:

$200 x $3 = $150 x $4

$600 = $600

This tells us that the ratios are equivalent, and the restocking fee for an item priced at $180 is $10.

In other words, the restocking fee is proportional to the item price, and we can use the given pairs of prices and fees to find the fee for any given price using a proportion.

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The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11

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

The graphs

The lines are absolute function graphs, and they can be represented as

y = a|x - h| + k

Where

Vertex = (h, k)

For the blue line, we have

(h, k) = (2, -5) and (x, y) = (0, -4)

So, we have

-4 = a|0 - 2| - 5

2a = 1

a = 1/2

So, the equation is y = 1/2|x - 2| + 5

For the red line, we have

(h, k) = (-2, 3) and (x, y) = (0, -11)

So, we have

-11 = a|0 + 2| + 3

2a = -14

a = -7

So, the equation is y = -7|x + 2| - 11

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A triangular fence having dimensions 2x + 3, y − 6, and 4x − 3, has a perimeter of Option D: 6x + y - 6 feet.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangular fence has measurements -

a = (2x + 3) feet

b = (y - 6) feet

c = (4x - 3) feet

The formula for perimeter of a triangle is -

Perimeter = sum of all three sides

So the equation will be -

Perimeter = a + b + c

Substitute the values in the equation -

Perimeter = (2x + 3) + (y - 6) + (4x - 3)

Perimeter = 2x + 3 + y - 6 + 4x - 3

Perimeter = 6x + y - 6

Therefore, the value for perimeter is 6x + y - 6 feet.

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The formula to calculate the new value after an increase is to multiply the original value by the percentage of the increase.

The formula to calculate the new value after an increase is to multiply the original value by the percent of the increase. For example, if the original value is $100 and the increase is 10%, the new value would be $100 x 1.10 = $110. This formula can be applied to any original value and any percentage increase. It is useful for calculating the new value after applying a percentage increase, such as when calculating a pay raise or the cost of goods after a price increase. The formula can also be applied to calculate the new value after a percentage decrease, by multiplying the original value by 1 minus the percentage of the decrease.

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The complete question is

the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase  by multiplying the original value by the percent for a new value?

Answer:

The graph of the function will shift vertically up by $5.

Step-by-step explanation:

The original function is m(x) = 2x + 15, where x is the number of people in the car. If the per car charge is changed to $20 per car, the new function becomes m(x) = 2x + 20, because the charge per car has increased by $5.

This means that the y-intercept of the new function is 20 instead of 15, which represents the minimum cost for a car, regardless of the number of people inside. So the graph of the new function will be shifted vertically up by $5 from the graph of the original function.

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(a) The probability that all the student pilots successfully land the plane using the simulator is 43%

(b) The probability that none of the student pilots successfully lands the plane using the simulator is 0.0026%

(c) The probability that exactly eight of the student pilots successfully land the plane using the simulator is 30.1%

Probability is a measure of the likelihood of an event occurring.

(a) What is the probability that all the student pilots successfully land the plane using the simulator?

Probability of all pilots successfully landing

=> 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = 0.43 or 43%

So, the probability that all the student pilots successfully land the plane using the simulator is 0.43 or 43%.

(b) What is the probability that none of the student pilots successfully land the plane using the simulator?

The probability of each pilot failing to land the plane is 0.20. We can use the multiplication rule again to calculate the probability of none of the pilots successfully landing the plane.

Probability of all pilots failing to land = 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 = 0.000026 or 0.0026%

So, the probability that none of the student pilots successfully land the plane using the simulator is 0.0026% or 0.000026.

(c) What is the probability that exactly eight of the student pilots successfully land the plane using the simulator?

where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success in one trial, and nCk is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.

In this case, we have n=9, k=8, p=0.80, and (1-p)=0.20. So, the probability of exactly eight pilots successfully landing the plane is:

P(X=8) = 9C8 * 0.80^8 * 0.20^(9-8) = 0.301 or 30.1%

So, the probability that exactly eight of the student pilots successfully land the plane using the simulator is 0.301 or 30.1%.

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1) The mean of the data is 4.45.

2) The mode of the data is 11.

3) The median of the data is 4.

The mean of the data is the ratio of the sum of the given data and the number of the count of the data.

The mode of the data is the number that is repeated maximum number of times. The median of the data is when the data is arranged in an increasing order then the middle most value will be the median of the data.

Given data is 6 11 5 11 4 0 2 0 1.

The mean of the data is,

Mean =  ( 6 + 11 + 5 + 11 + 4 + 0 + 2 + 0 + 1 ) / 9

Mena = 4.45

Mode = 11

Median:- 0,0,1,2,4,5,6,11,11

Median = 4

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Last month 26 of the 280 students won a free lunch. The experimental probability of winning will be 13/140

Probability is the occurence of the events. Some of the events cannot be predicted with certainty. Probability of any event can be defined as P(A) , and there are many types of probability density functions.

Once a month, the cafeteria has each student pick a card from a standard deck of cards. From the deck of cards, each student has to pick a card for every one month.

Students who pick an ace get a free lunch

Given that,

Last month 26 of the 280 students won a free lunch and the percentage of winning is near to 9.2% approximately and it is very near to the 10%.

The experimental probability of winning is the ratio of number of possible outcomes to the total number of outcomes.

So, the experimental probability of winning is 26/280 = 13/140

Therefore, the  experimental probability of winning is 13/140

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The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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Answer:

50 kg of green tea leaves and 50 kg of assam black tea leaves.

Step-by-step explanation:

Let x kg be the amount of green tea and y kg be the amount of Assam tea.

x+y=100 (1) [mass]

price for 1 kg of assam tea= 7.20/600×1000g

= $12/kg

total cost= 100×10

= $1000

8x+12y= 1000 (2) [cost]

(1)×8: 8x+8y= 800 (3)

(2)-(3): (8x+12y)-(8x+8y)= 1000-800

4y= 200

y= 50 (4)

sub (4) into (1):

x+50= 100

x= 50

10:40 am

63 mile distance and 27 mph. starting from 8 am

63/27 => 2 (2/3) hours. 2/3 of an hour is also, 40 minutes.

so 8 am plus 2 hours and 40 minutes means 10:40 am

The measure of <E= 60, <F= 95 and <G= 25 degree.

In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.

Given:

The two triangles are similar.

In triangle JKL using Angle Sum Property

<J + <K + <L = 180

95 + 60 + <K = 180

155 + <K = 180

<K = 180- 155

<K = 25 degree

Thus, the measure <E= 60

and, the measure <F= 95

and, the measure of <G= 25.

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If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.

In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.

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On solving the provided question we can say that from the graphs,

y = f(x) = |x| and g(x) = |x-h| + k

Mathematicians use diagrams to logically bring facts or values ​​using visual representations or charts. A graph point usually reflects a contact between two or more things. Nodes or vertices and corner form a graph, which is a nonlinear data construction. We often glue knots together called vertices. This graph has vertices V=1, 2, 3, 5 and edges E=1, 2, 1, 3, 2, 4 and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) are graphical representations of expanding growth. Logarithmic graph in the format of a triangle 

from the graphs,

y = f(x) = |x|

y = f(x) + k

y = f(x+h)

g(x) = |x-h| + k

now, it will be

k>0 and h<0

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The account would contain 10,230.00 after 1 year.the amount in the account after 1 year, we can use the formula: [tex]P (1 + r/n)^nt[/tex]

To find the amount in the account after 1 year, we can use the formula:[tex]P (1 + r/n)^nt[/tex]

Where,

P = Principal Amount

r = Rate of Interest

n = Number of times the interest is compounded per year

t = Time in years

For this question,

P = 10,000

r = 2.3%

n = 1

t = 1

Therefore,

[tex]10,000 (1 + 0.023/1)^1*1\\10,000 (1.023)^1[/tex]

10,000 x 1.023

= 10,230.00

The complete question is:

If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account contain after 1 year?

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a) Since Todd and Amani started with the same initial deposit, they will never have the same amount in their accounts if they keep to their weekly savings plans because Todd's weekly savings are two times that of Amani.

b) An equation to represent the total amount in each of their accounts at any given time or weeks is as follows:

An equation is a statement of equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine values, variables, and numbers or constants without the equation symbol (=), which differentiates them from equations.

                                        Todd     Amani

Initial deposit in account  $10       $10

Weekly deposits               $4         $2

Let the number of weeks of deposits = w

Let the total deposit in Todd's account in w weeks = t

t = 10 + 4w

Let the total deposit in Amani's account in w weeks = a

a = 10 + 2w

For Todd's and Amani's account to be equal, 10 + 4w = 10 + 2w

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This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).

A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.

A linear equation is so named because plotting the graph of a given linear model yields a straight line.

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Answer: the initial points is 30.
and per pair of shoes is 15.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation connects m and n.

Suppose n=1,

m=3/1=3.

If n=2,

m=3/2=1.5

If n=3,

m=3/3=1. This shows that as n increases, m decreases.

If m was equal to 1,

1=3/n

Thus n=3.

If m=2,

2=3/n

n=1.5

If m=3,

3=3/n

n=1.

This also shows that as m increases, n decreases.

Hope this helps :)

Answer:

When I increased n, m decreased.

When I increase m, n decreases

Step-by-step explanation:

Let's say that m is one and n is 3

1 = [tex]\frac{3}{3}[/tex]  Us this as our base to compare increasing m and n.

Increase n to 6

[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]

When I increased n, m decreased.

Increase m to 3

3 = [tex]\frac{3}{1}[/tex]

When I increase m, n decreases

the boat will coast for a distance of 400 ln(2) ft, which is approximately 277.3 ft.

To find how far the boat will coast, we need to use the concept of differential equations. The equation that describes the velocity of the boat at any time "t" after its motor quits is given by:

dv/dt = -k*v

where "v" is the velocity of the boat at time "t", "k" is the proportionality constant, and the negative sign indicates that the velocity is decreasing with time.

We can solve this differential equation to obtain the velocity of the boat as a function of time:

v(t) = v(0) * e^(-k*t)

where "v(0)" is the initial velocity of the boat (40 ft/sec).

Using the given information, we can set up two equations:

v(10) = 20 (velocity after 10 sec)

v(0) = 40 (initial velocity)

Plugging these values into the equation, we get:

20 = 40 * e^(-10k)

Solving for "k", we get:

k = ln(2)/10

Now, we can integrate the velocity equation to find the distance the boat travels during the coasting period:

d = [tex]\int\limits^{\infty}_{10} {v(t)} \, dt[/tex]

Plugging in the values, we get:

d = (40/k) * [e^(-k*10) - 0] = 400 ln(2) ft

To explain the solution, we used the concept of differential equations to model the motion of the boat as it coasts after its motor quits. We used the given information to solve for the proportionality constant "k", which allowed us to find the velocity of the boat at any time.

Finally, we integrated the velocity equation to find the distance the boat travels during the coasting period. The key to this problem was using the concept of differential equations to model the motion of the boat and setting up the appropriate equations to solve for the unknowns.

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Complete question is:

Suppose that a motorboat is moving at 40 ft/sec when its motor suddenly quits, and then 10 sec later the boat has slowed to 20 ft/sec. Assume, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?

Answer: -1/3

Step-by-step explanation:

Slope = Rise/Run

Answer:

Let's call the length of side 1 "x". Then, the length of side 2 is 2x, and the length of side 3 is x + 4. So, the expression for the three sides of the triangle can be represented as:

x + 2x + (x + 4) = 3x + 4

This expression represents the sum of the lengths of all three sides of the triangle.

Step-by-step explanation:

Answer: x+2x+(4+x)

Step-by-step explanation:

since side one is unknown, we can substitute it with variable x, and side two is twice as much as side one so we do 2x, and side three is four cm longer than side one so we do 4+x at the end

Gwen has £0.75 money left over, as per linear equation if a litre of cola costs £1.25.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

It is given that Gwen has a £5 note and a £2 coin.

Therefore, she has a total of £(5 + 2) = £7

A liter of cola costs £1.25.

Therefore, (7 ÷ 1.25) = 5.6

Therefore, Gwen can buy a total of 5 liters of cola.

Now, Gwen has left money of £[7 - (5 × 1.25)] = £0.75

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Complete question is:

Gwen has a £5 note and a £2 coin

a litre of cola cost £1.25

gwen buys as many liter bottles of cola as she can

how much money will she have left over

Answer:

(x-1)(x+1)(x+3)

Step-by-step explanation:

[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]

Answer:

In 6 seconds: 180 m

20 m: in 2 seconds

Step-by-step explanation:

y = distance

x = time

y is proportional to x:

y = kx

y is proportional to the square of x:

y = kx²

We are given: (3, 45)

45 = k × 3²

45 = 9k

k = 5

The equation is:

y = 5x²

When x = 6,

y = 5(6²)

y = 180

180 m in 6 seconds

When y = 20,

20 = 5x²

x² = 4

x = 2

2 seconds for 20 m

From the given choices, we get:

No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.

The correct option is D.

A computer experiment in which you can select a random sample from the given probability distributions is called a simulation.

Given:

A student wants to simulate 28 birthdays,

but she does not have a calculator or software program available,

so she makes up 28 numbers between 1 and 365.

By comparing with the definition:

From the given choices, we get,

D. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.

Hence, D is the correct option.

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