Which values are within the range of the piecewise-defined function?
f(x) = StartLayout enlarged left-brace 1st Row 1st column 2 x + 2, 2nd column x less-than negative 3 2nd row 1st column x, 2nd column x greater-than negative 3 3rd Row 1st column negative x minus 2, 2nd column x greater-than negative 3 EndLayout

The number of cars adam have by the given data is 63 model cars.

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.

We are given that;

Models of cars= 7/8

Number of cars= 54 more than planes

Now, Let's start by using algebra to represent the problem:

Let x be the number of planes Adam has.

Then, the number of cars he has is 54 more than x, or x + 54.

We know that 7/8 of the models he collects are cars. This means that the remaining 1/8 are planes. Therefore, we can set up the equation:

x + 54 = 7/8 (x + 54 + x)

Simplifying and solving for x, we get:

8x + 432 = 14x + 378

6x = 54

x = 9

This means that Adam has 9 planes.

To find the number of cars, we can substitute x = 9 into the expression we found earlier for the number of cars:

x + 54 = 9 + 54 = 63

Therefore, by solving the equations the answers will be 63 model cars.

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Answer:

Let x be the length of each side of the square base, and let h be the height of the aquarium. Then the volume of the aquarium is:

V = x^2 * h

We are given that V = 20, so we can solve for x:

x^2 * h = 20

x^2 = 20/h

x = sqrt(20/h)

The area of each of the four walls of the aquarium is x*h, and there are four walls, so the total area of glass needed is:

A_glass = 4xh = 4sqrt(20h)

The cost of the glass is 7 dollars/m², so the cost of the glass is:

C_glass = 7A_glass = 74sqrt(20h) = 28sqrt(20h)

The perimeter of the square base is 4x, so the length of the metal frame needed is:

L_frame = 4x + 4h

Substituting x = sqrt(20/h), we get:

L_frame = 4sqrt(20/h) + 4h

The cost of the frame is 10 dollars/m, so the cost of the frame is:

C_frame = 10*L_frame = 10(4sqrt(20/h) + 4h)

The total cost is the sum of the cost of the glass and the cost of the frame:

C = C_glass + C_frame = 28sqrt(20h) + 10(4sqrt(20/h) + 4h)

Simplifying, we get:

C = 28sqrt(5h) + 40sqrt(5h) + 40h

C = 68sqrt(5h) + 40h

Therefore, the total cost C is a function of the height h and can be expressed as C = 68sqrt(5h) + 40h in dollars.

Step-by-step explanation:

Answer:

6.97

Step-by-step explanation:

Answer: $42

Step-by-step explanation:

91/2 metres of fabric would cost $42, because 24 divided by 6 is 4. So, if 4 multiplied by 91/2 is 42.

the expected number of tardies is 1.66, rounded to two decimal places.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, In a certain school, the probabilities of the number of students who are reported tardy are shown

Number tardy: 0           1                2             3               4

Probability:     0.19     0.22          0.37         0.18        0.04

The expected number of tardies can be calculated by multiplying each possible number of tardies by its probability and then summing up the results. That is:

Expected number of tardies = (0 × 0.19) + (1 × 0.22) + (2 × 0.37) + (3 × 0.18) + (4 × 0.04)

Simplifying the expression, we get:

Expected number of tardies = 0 + 0.22 + 0.74 + 0.54 + 0.16

Expected number of tardies = 1.66

Therefore, the expected number of tardies is 1.66, rounded to two decimal places.

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The probability of forming a new word beginning with R and ending with T from the word TOGHETHER is:

1/336

Probability is a measure of the likelihood or chance that an event will occur. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find the probability of forming a new word beginning with R and ending with T from the word TOGHETHER, we need to count the number of ways to choose the first and last letters that satisfy these conditions, and then divide by the total number of possible choices.

First, we need to find the total number of possible three-letter combinations that can be formed from the word TOGHETHER. There are eight letters in the word, so there are 8 choices for the first letter, 7 choices for the second letter (since we've already used one letter), and 6 choices for the third letter (since we've used two letters). Therefore, there are 8 x 7 x 6 = 336 possible three-letter combinations.

Next, we need to count the number of three-letter combinations that begin with R and end with T. There is only one R in the word, so there is only 1 choice for the first letter. Similarly, there is only one T in the word, so there is only 1 choice for the third letter. Therefore, there is only 1 x 1 = 1 possible choice for the first and last letters that satisfy the conditions.

Therefore, the probability of forming a new word beginning with R and ending with T from the word TOGHETHER is:

1/336

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Answer:

a) 1/1

b) 3/2

c) 2/1

d) 17/13

Step-by-step explanation:

a) 1 sun for every 1 moon

b) 12 circles for 8 triangles = 12/8 = 3/2 (divide 12 and 8 by the highest number possible for both at the same time, which is 4 in this case)

c) 8/4 = 2/1

d) 17/13

code: 7591-5917-1759-9175

The latest time you can catch the bus from Rudder Inn to arrive at West Jetty by 14:30 is given as follows:

13:54.

The latest time you can catch the bus from Rudder Inn to arrive at West Jetty by 14:30 is obtained from the table in this problem.

The train arrival times at Rudder Inn are given as follows:

25 minutes and 54 minutes past the hour.

The duration of the ride is given as follows:

9 + 13 = 22 minutes.

Meaning that the 14:25 train will not arrive at West Jetty before 14:30, hence you must take the 13:54 train.

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The complete proof of theorem AB and CB with points of tangency at A and C. AD and DC are radii is mentioned below.

A triangle is a closed geometric figure consisting of three straight line segments that are connected to form three vertices and three angles. Triangles are two-dimensional shapes that can be classified based on their angles and sides.

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Therefore, Janet spent approximately $259.68 on fuel during her vacation in Chile.

Average The arithmetic mean is calculated by adding a group of numbers, dividing the result by their count, and then adding the result. For instance, 2, 3, 4, 5, 7, and 10 have an average value of 5, which is the result of 30 divided by 6.

To estimate how much Janet spent on fuel, we can use the formula:

Fuel cost = Number of gallons used x Cost per gallon

First, we need to calculate the number of miles per gallon (mpg) that the car achieved:

mpg = Number of miles driven / Number of gallons used

mpg = 1075 miles / 43 gallons

mpg ≈ 25

Now we can estimate the fuel cost:

Fuel cost = 43 gallons x $6.039 per gallon

Fuel cost ≈ $259.677

Therefore, Janet spent approximately $259.68 on fuel during her vacation in Chile.

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The percent error rounded to the nearest tenth of a percent is approximately 9.4%.

If the measurement of the object are measured to be M, and the percentage error in the measurement is estimated to be E%, and O is the original measurement of the object to be measured than:

[tex]\rm M \in O \pm E\% \: \rm of \: \rm O[/tex]

where O = original measurement of the object being measured.

This will give the range of values in which the original measurement can fall in. that is

[tex]\rm [ O - \text{E\% of O}, \: \: O + \text{E\% of O}][/tex]

We are given that;

Length of caterpillar=7cm

Now

The percent error is a measure of how inaccurate an estimate is, given by the formula:

percent error = (|estimated value - actual value| / actual value) x 100%

In this case, the estimated value is 7 cm and the actual value is 6.4 cm, so we can substitute these values into the formula:

percent error = (|7 - 6.4| / 6.4) x 100%

Simplifying the expression inside the parentheses, we get:

percent error = (0.6 / 6.4) x 100%

Dividing 0.6 by 6.4 and multiplying by 100%, we get:

percent error = 9.375%

Therefore, by the percent error the answer will be approximately 9.4%

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Step-by-step explanation:

let's just look at the first (outmost left) point.

from f(x) to g(x) it moved 4 units down and 3 units left.

so, this should be the 3rd answer option in your list.

The correct statement which best describes the transformation from f(x) to g(x) is,

⇒ The graph of f(x) was translated left 3 units and down 4 units to obtain g(x).

Given that;

The graph of f (x) and g (x) is shown in figure.

Now, By graph we get;

The transformation from f(x) to g(x) it moved 4 units down and 3 units left.

Hence, The correct statement which best describes the transformation from f(x) to g(x) is,

⇒ The graph of f(x) was translated left 3 units and down 4 units to obtain g(x).

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His potential scores are higher than 78 because he cannot achieve a number high enough to average over 85. (to 100)

The study of possibility is a math discipline that focuses on calculating the possibility or chance that an event will occur. It is a means to put a number on the uncertainty that is always present. A number among 0 and 1, where 0 denotes the event's impossibility and 1 denotes its certainty, is used to describe the likelihood of it happening. For instance, if you flip a coin, the likelihood of getting heads is 0.5, which means that you have a 50% probability of obtaining heads and a 50% probability of obtaining tails. Numerous disciplines use probability, such as statistics, finance, engineering, physics, and computer programming. It is an effective instrument for predicting outcomes, evaluating risks, and making choices based on speculative data.

given

462 grades are needed to achieve 77. (6 x 77).

510 points are needed to achieve 85. (6 x 85).

462<79 + 85 + 75 + 66 + 79 + x < =510

462 < 384 + x < = 510 Completely subtract 384 from the total.

78 < x <=126

His potential scores are higher than 78 because he cannot achieve a number high enough to average over 85. (to 100)

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If a certain blood test is 99.5% effective at detecting Foreign Bloodborne Pathogens:

a. The probability that both tests correctly detect a Foreign Bloodborne Pathogen is approximately 0.990.

b. The probability that all ten tests correctly detect a Foreign Bloodborne Pathogen is approximately 0.951.

c.  The probability that at least one test fails to detect a Foreign Bloodborne Pathogen is 0.993.

The probability that the blood test correctly detects a Foreign Bloodborne Pathogen is 0.995, and the probability that it fails to detect a Foreign Bloodborne Pathogen is 0.005.

1. Probability that both tests correctly detect a Foreign Bloodborne Pathogen:

The probability of both tests correctly detecting the pathogen is the product of the probability of the first test correctly detecting the pathogen and the probability of the second test correctly detecting the pathogen. Since the two tests are independent, we can multiply the probabilities. Therefore, the probability of both tests correctly detecting the pathogen is:

0.995 x 0.995 = 0.990025

So, the probability that both tests correctly detect a Foreign Bloodborne Pathogen is approximately 0.990.

2 Probability that all ten tests correctly detect a Foreign Bloodborne Pathogen:

The probability that all ten tests correctly detect a Foreign Bloodborne Pathogen is the product of the probabilities of each individual test correctly detecting the pathogen, since each test is independent. Therefore, the probability of all ten tests correctly detecting the pathogen is:

0.995^10 ≈ 0.951

So, the probability that all ten tests correctly detect a Foreign Bloodborne Pathogen is approximately 0.951.

3. Probability that at least one test fails to detect a Foreign Bloodborne Pathogen:

The probability that at least one test fails to detect a Foreign Bloodborne Pathogen is the complement of the probability that all 1,000 tests correctly detect the pathogen. Therefore, the probability that at least one test fails to detect a Foreign Bloodborne Pathogen is:

1 - 0.995^1000 ≈ 0.993

So, the probability that at least one test fails to detect a Foreign Bloodborne Pathogen is approximately 0.993.

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Answer: The small box can hold 1 blue book and 1 green book.

The large box can hold 2 blue books and 1 green book.

Step-by-step explanation:

For the small box it states that it can hold 4-6 pounds.

So, to find this I added the weight of 1 blue book (3.1) to the weight of 1 green book (2.4) which gets you the answer 5.5. This is well within the weight limit.

For the large box it states it can hold 8-9 pounds.

So, to find this I added the weight of 2 blue books (3.1 + 3.1 = 6.2) to the weight of 1 green book (2.4) which gets you the answer 8.6. This is well within the weight limit.

I believe this is right, but it could be wrong... check and let me know!!

To find the perimeter, we need to find the sum of the lengths of all sides of the figure defined by the three functions.

Since we do not have any information about the shape of the figure, we cannot determine the perimeter directly. However, we can make some assumptions about the shape of the figure and proceed with the calculation.

Assuming that the figure is a triangle, we can find the lengths of the sides using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the lengths of the sides of the triangle defined by the three functions.

The vertices of the triangle are the points where the three functions intersect. To find these points, we need to solve the system of equations:

f(x) = g(x)

f(x) = h(x)

g(x) = h(x)

Solving these equations, we get:

x = -1, 2/3

Substituting these values of x into the functions, we get the corresponding y-values:

f(-1) = 4, g(-1) = 1, h(-1) = 3

f(2/3) = 23/3, g(2/3) = 16/3, h(2/3) = 47/3

Now, we can use the distance formula to find the lengths of the sides of the triangle:

AB = sqrt((2/3 - (-1))^2 + (23/3 - 4)^2) = sqrt(161/3)

AC = sqrt((2/3 - (-1))^2 + (47/3 - 4)^2) = sqrt(458/3)

BC = sqrt((23/3 - 16/3)^2 + (47/3 - 1)^2) = sqrt(738/3)

The perimeter of the triangle is the sum of the lengths of the sides:

P = AB + AC + BC = sqrt(161/3) + sqrt(458/3) + sqrt(738/3)

So, the perimeter of the triangle defined by the three functions is approximately equal to 19.47 units.

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According to the above, Mary would pay R510 if she pays for the 3m of irrigation tube in cash.

To identify how much Mary would pay for the irrigation tube, we must carry out the following mathematical procedure:

We must find the cost of the 3 meters that Mary wants to buy.

Now we must calculate how much the discount on the value of the tubes is equivalent to:

So the discount equals R90. Therefore, we must subtract this value from the total value that the tubes would be worth.

So the total value would be 510

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1. The amount of money that Danny will have in the account in 1 year is $12,163.42

2. The annual percentage yield (APY) for the savings account will be 4.99%.

To calculate how much money Danny will have in the account in one year, we need to use the formula for compound interest: A = P * (1 + r/n)^(n*t).

In this case, P = $11,500, r = 0.048 (since the annual interest rate is 4.8%), n = 12 (since interest is compounded monthly), and t = 1. Plugging these values into the formula, we get:

= $11,500 * (1 + 0.048/12)^(12*1)

= $11,500 * (1.004)^12

= $12,163.42

The annual percentage yield (APY) is the effective annual rate of return taking into account the effect of compounding. It is calculated as: APY = (1 + r/n)^n - 1

APY = (1 + 0.048/12)^12 - 1

APY = 0.0499

APY = 4.99%

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The volume of the solid obtained by rotating the region bounded by the given curves y = lnx and y = 4, and x = 0 about the specified line is -13.41π.

The volume of the solid obtained by rotating the region bounded by the given curves y = lnx and y = 4, and x = 0 about the specified line is given by:

V = π ∫04 [lnx]2 dx

V = π ∫04 (xlnx-x) dx

V = [π (xln2x-2xlnx+2x-2x2)]04

V = [π (ln24-2.4ln4+8-16)]

V = [π (2.38-9.6+8-16)]

V = -π (4.22)

V = -13.41π

Therefore, the volume of the solid obtained by rotating the region bounded by the given curves y = lnx and y = 4,

and x = 0 about the specified line is -13.41π.

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Answer:

number is 0

Step-by-step explanation:

number = 0

Add = 0+12 = 12.

Subtract = 12-10=02

opposite = 20

Add = 20+12

Answer = 32

That was easy.

Answer:

-2/3

Step-by-step explanation:

1/3 + 2/4 - 3/2

= 4/12 + 6/12 - 18/12

= 10/12 - 18/12

= -8/12

= -2/3

The probability of success trial nearest to four decimal places will be 0.1867.

Let 'p' be the probability of favorable events, 'x' be the number of times getting success, and 'n' be the total number of trials. Then the probability is given as,

[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]

The probability of success is 0.30 and the total number of trials is 17. Then the probability is given as,

P(x = 4) = ¹⁷C₄ x (0.30)⁴ x (1 - 0.30)¹⁷⁻⁴

P(x = 4) = ¹⁷C₄ x (0.30)⁴ x (0.70)¹³

P(x = 4) = 2380 x 0.0081 x 0.00968

P(x = 4) = 0.1867

The probability is 0.1867.

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Answer:

Step-by-step explanation:

32 IS  TRUE

The value of x is given as follows:

x = 22.

Similar polygons are polygons that share these two features presented as follows:

The two triangles in this problem are similar, hence the proportional relationship for the side lengths is given as follows:

x/18 = 11/9

9x = 11 x 18

x = 11 x 2

x = 22.

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Answer:

y = 2.5x

Step-by-step explanation:

I don't know what your choices are, but the equation is

y = [tex]\frac{5}{2}[/tex] x

or y = 2 [tex]\frac{1}{2}[/tex]

or y = 2.5x  They all mean the same thing.

This means that in 1 minute you can package 5/2 or 2.5 calculators.

You find the rate by the change in y over the change in x.

You have two points given (10,25) and (30,75)

[tex]\frac{25}{10}[/tex] = 2.5 or [tex]\frac{5}{2}[/tex]

[tex]\frac{75}{30}[/tex] = 2.5 or  [tex]\frac{5}{2}[/tex]

Helping in the name of Jesus.

The graph of the system of inequalities is the last graph.

Here we have the system of inequalities:

y ≤ -3x+1

y < -x+3      (you wrote an "s" here, i assume it means smaller)

And we want to identify the graph of this system.

In both cases, y is smaller than the linear equation, so in both cases the region shaded will be below the lines.

The only option that shows that is the last option, so we conclude that the correct option is the last one.

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Answer: True

This is because of the commutative property in addition and multiplication. It means that no matter what order factors/addends are in, the product/sum will be the same. This can be seen in problems such as:

5+7 = 12

7+5 = 12

or

9x6=54

6x9=54

The commutative property is not found in subtraction or division, as can be seen in these problems:

10-6=4

6-10=(-4)

or

2÷1=2

1÷2=0.5

Answer: The answers could be 162 mm^2, 189 mm^2, or 84 mm^2

Step-by-step explanation:

(Since the base and height aren't listed, the answers might be wrong.)

A (of a triangle) = 1/2 * b * h

If b = 27 and h = 12, we first divide 12 by 2. 27 * 6 = 162 mm^2

If b = 27 and h = 14, we first divide 14 by 2. 27 * 7 = 189 mm^2

If b = 12 and h = 14, we first divide 14 by 2. 12 * 7 = 84 mm^2

Answer:

Step-by-step explanation:

To find the quadratic function that models the population, we can use quadratic regression. We can assign the variable x as the number of years after 1970, and y as the labor pool in millions of people. We can then input the data into a calculator or a spreadsheet software and use regression analysis to find the quadratic equation that best fits the data.

Using a spreadsheet software, we can input the data and use the trendline feature to find the quadratic function. The resulting equation is:

y = -32.917x^2 + 338.958x + 63.396

Therefore, the quadratic function that best models this population as a function of the number of years after 1970 is:

y = -32.917x^2 + 338.958x + 63.396

where x is the number of years after 1970 and y is the number of millions of people in this labor pool.

b. According to the model, what is the projected size of the labor pool in 2025?

To find the projected size of the labor pool in 2025, we need to plug in x = 55 (since 2025 is 55 years after 1970) into the quadratic function we found in part (a):

y = -32.917x^2 + 338.958x + 63.396

y = -32.917(55)^2 + 338.958(55) + 63.396

y = -32.917(3025) + 18642.19 + 63.396

y = -99588.508 + 18642.19 + 63.396

y = -80982.922

Rounding to the nearest million, we get a projected size of the labor pool in 2025 of 83 million. Therefore, according to the model, the projected size of the labor pool in 2025 is 83 million.

The probability of selecting a hybrid car at random is 3/14 expressed as a fraction.

A fraction is a mathematical expression that represents a part or a quotient of two quantities. Fractions are written in the form of a numerator and a denominator, separated by a horizontal or slanted line. The numerator represents the part of the whole or the quantity being considered, while the denominator represents the total number of equal parts in the whole.

The total ratio of cars in the parking lot is 3 + 11 = 14. This means that 3/14 of the cars in the lot are hybrids.

If there are 280 cars in the lot, then the number of hybrid cars is:

3/14 x 280 = 60

So there are 60 hybrid cars in the lot. The probability of selecting a hybrid car at random is:

P(hybrid) = number of hybrid cars / total number of cars

P(hybrid) = 60 / 280

Simplifying:

P(hybrid) = 3 / 14

Therefore, the probability of selecting a hybrid car at random is 3/14 expressed as a fraction.

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