What is the range of this function?

Answer:

Likely

Step-by-step explanation:

in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.

Let's start by setting up an equation based on the given information.

Let Leah's current age be represented by "x". Then, we know that:

x = 3(x-4)

Expanding the right side of the equation:

x = 3x - 12

Bringing the "x" term to the left side and simplifying:

2x = 12

x = 6

So Leah is currently 6 years old. Now we want to find out how many years it will take for her to be exactly twice as old as she was four years ago. Let's represent this number of years as "y". Then we can set up another equation:

6 + y = 2(6 - 4 + y)

Simplifying:

6 + y = 2(2 + y)

6 + y = 4 + 2y

2 = y

So in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.

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The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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Consequently, 1 pound weighs more than 19 ounces.

What additional weight units are there?

The weight can also be expressed in terms of grams, kilograms, pounds, and tons.

Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.

The weight unit known as an ounce is 1/16th of a pound.

A ton weighs 2000 pounds.

16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.

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Answer:

To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.

First, we will take the derivative of both sides of the equation with respect to x:

d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]

Next, we will differentiate each term on the left side of the equation:

cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx

We can simplify this equation by moving all the terms involving dy/dx to the left side:

cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]

Now we can solve for dy/dx by isolating it on one side of the equation:

dy/dx [2 - sin(y)] = cos(x) - 2xy^2

dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]

Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:

dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]

The area of the remaining portion of the sheet is -4x² + 12x + 6.

Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.

Therefore, the area of the remaining portion can be found as follows:

area of the rectangle = 3(4x + 2)

area of the rectangle = 12x + 6

Therefore,

area of each square cut out = x²

area of the 4 square cut out = 4x²

Therefore,

area of the remaining portion = 12x + 6 - 4x²

area of the remaining portion = -4x² + 12x + 6

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The no of paintings does Mark have left after four days of selling his paintings is 6.

What about selling?

Selling is the process of exchanging goods or services for money or other valuable considerations. It involves persuading a customer to buy a product or service by demonstrating its value and benefits. Selling can occur through various channels such as face-to-face interactions, online transactions, or through advertising and marketing efforts.

The process of selling typically involves several steps, including identifying potential customers, understanding their needs and preferences, presenting the product or service, addressing any objections or concerns, and closing the sale. Effective selling requires strong communication and interpersonal skills, as well as a deep understanding of the product or service being sold and the market in which it is being sold.

According to the given information:

Let: Initial Number of Mark's Paintings = x

The first day he sells 1/4th of them

Let: Initial Number of Mark's Paintings = x

The first day he sells 1/4 th of them

Number of Paintings Left

= (1 - 1/4) * x = 3/4 * x

The second day he sells one-half of the paintings he started the day with Number of Paintings Left = (1 - 1/2) * 3/4 * x = 3/8 * x

The third day he sells one-half of the paintings he started the day with

Number of Paintings Left = (1 - 1/2) * 3/8 * x = 3/16 * x

The fourth day he sells one-half of the paintings he started the day with Number of Paintings Left = (1 - 1/2) * 3/16 * x = 3/32 * x

Number of Paintings Left = x 64

Number of Paintings Left = 3 x 2

Number of Paintings Left = 6

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Mark has 6 paintings left after four days of selling his paintings.

A quantity decreasing over time at a rate proportionate to its present value is referred to as exponential decay in mathematics. In other words, the amount diminishes in each unit of time by a fixed percentage or share of its value.

On the first day, Mark sells 1/4th of his paintings, which is 1/4 * 64 = 16 paintings.

After the first day, he has 64 - 16 = 48 paintings left.

On the second day, Mark sells 1/2 of the paintings he started with, which is 1/2 * 48 = 24 paintings.

After the second day, he has 48 - 24 = 24 paintings left.

On the third day, Mark again sells 1/2 of the paintings he started with, which is 1/2 * 24 = 12 paintings.

After the third day, he has 24 - 12 = 12 paintings left.

On the fourth day, Mark sells 1/2 of the paintings he started with, which is 1/2 * 12 = 6 paintings.

After the fourth day, he has 12 - 6 = 6 paintings left.

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Answer: B

Step-by-step explanation:

Answer:

To solve this problem, we can use the equations of motion for a particle moving in the vertical direction with constant acceleration g. The equation for the height (h) of the particle as a function of time (t) is:

h = ut - 1/2 gt^2

The particle will reach its maximum height when it has zero velocity, which occurs at the peak of its trajectory. The time taken to reach the peak can be found by setting the velocity equal to zero:

0 = u - gt

t = u/g

Substituting this value of t into the equation for h, we get:

h = u(u/g) - 1/2 g(u/g)^2

h = u^2/2g - u^2/2g

h = 0

This tells us that the particle reaches a height of zero at the end of its trajectory, which is not the maximum height. To find the maximum height, we need to consider the distance s between the point of projection and the wall.

Let t1 be the time taken by the particle to reach the wall, and t2 be the time taken to return to the ground. These times can be found by solving the quadratic equation:

s = ut1 + 1/2 gt1^2

0 = ut2 - 1/2 gt2^2

Using the quadratic formula, we get:

t1 = (u + sqrt(u^2 + 2gs))/g

t2 = (u - sqrt(u^2 + 2gs))/g

The maximum height is reached halfway between t1 and t2, which occurs at:

t = (t1 + t2)/2

t = (u/g)

Substituting this value of t into the equation for h, we get:

h = u(u/g) - 1/2 g(u/g)^2 - s

h = u^2/2g - gs/2

Therefore, the greatest height that a particle with initial velocity u can reach on a vertical wall at a distance s from the point of projection is u²/2g - gs²/2u².

The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.

The total number of ways to develop the complex would be 665, 280 ways.

To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.

Using combinations, we have:

Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)

Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)

Now, we find the probability:

Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members

Probability = (C(28, 6) x C(12, 4)) / C(40, 10)

Probability = 0.3633

To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:

The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:

P(11, 5) = 11! / (11 - 5)!

Total ways to develop the complex = 12 x P(11, 5)

= 12 x 55440 = 665,280 ways

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Answer:

Step-by-step explanation:

This is a quadratic and needs to be factored as such. When we factor, we get

cosx = 1/2 and cosx = -1. Refer to the unit circle to find all the angles that have a cosine of 1/2. Those would be in Q1 and Q4; namely, pi/3 and 5pi/3. The angle where the cosine is -1 is at pi.

[tex]x=\pi ,\frac{\pi }{3},\frac{5\pi }{3}[/tex]

Answer:

Step-by-step explanation:

From the data in the table, we can conclude that when x = 4, then the residual will equal -1.

To determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.

So, Residual = Gven value - Predicted value.

When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.

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Answer:

The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.

Step-by-step explanation:

In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.

If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.

Answer:

164 Cakes

Step-by-step explanation:

382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.

.............................

If Mr. Wang and Mrs. Wang have 3 sons and every son has 1 wife, 1 son, and 1 sister, the total number of people in the family, based on mathematical operations, is 14.

The total number of people in the family can be determined using the mathematical operations of multiplication and addition.

Multiplication and addition are two of the four basic mathematical operations.

Multiplication involves the multiplicand, the multiplier, and the product, while addition involves two or more addends added to get the sum.

The number of parents = 2

The number of sons = 3

The number of additional family members for each son = 3

The total number of additional family members = 9 (3 x 3)

The total number of persons in the family = 14 (9 + 3 + 2)

Thus, there are 14 people in the family of Mr. Wang and Mrs. Wang.

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So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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Answer: To determine the unit price, we divide the price by the number of ounces.

For the 1.5-ounce bag:

Unit price = $0.65 / 1.5 ounces = $0.433 per ounce

For the 5.75-ounce bag:

Unit price = $1.30 / 5.75 ounces = $0.226 per ounce

For the 2-pack of 5.75-ounce bags:

Total ounces = 2 x 5.75 = 11.5 ounces

Total price = $2.45

Unit price = $2.45 / 11.5 ounces = $0.213 per ounce

Therefore, the 2-pack of 5.75-ounce bags has the lowest unit price and is the best buy based on price alone.

Step-by-step explanation:

The histogram that displays the data in the table correctly is C. Histogram C.

Look at the data in the table and look for the number of photocopies that are located between 800 and 899. There are 3 of these.

The number located between 900 and 999 are 5 in number including 915, 919, 923, 950, and 989. The number located between 1,000 and 1, 099 is 8 photocopies.

The histogram that shows this is Histogram C.

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With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.

What is Compound interest?

Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.

Now,

Using the given formula:

N = (-log(1 - i * A / P)) / (log(1 + i))

where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250

N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))

N = (-log(1 - 175)) / (log(1.0025))

N = (-log(0.9883)) / (0.0025)

N = 376.48

Rounding up to the nearest whole number, it will take 377 months to pay off the loan.

Therefore, it will take approximately 31 years and 5 months to pay off the loan.

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The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

In the given question,

There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH)

We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:

P(HHT) = (1/2) * (1/2) * (1/2) = 1/8

P(HTH) = (1/2) * (1/2) * (1/2) = 1/8

P(THH) = (1/2) * (1/2) * (1/2) = 1/8

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8

Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

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Answer:

The answer is the Blue car

Step-by-step explanation:

let Red car be x

let blue car be y

x=120km---->1hr

y=130km----->1hr

Average speed =distance(km)/time(hr)=km/hr

let A be average speed

A(x)=120/1=120km/hr

A(y)=130/1=130km/hr

therefore,

the blue car has the greatest average speed

Answer:

=10 m

Step-by-step explanation:

PYTHAGOREAN THEOREM

8^2+6^2=64+36=100

=√100m

=10 m

Answer:

interquartile range = 6

Step-by-step explanation:

the interquartile range is the difference between the upper quartile Q₃ and the lower quartile Q₁

Q₃ is the value at the right side of the box, that is 86

Q₁ is the value at the left side of the box, that is 80

interquartile range = Q₃ - Q₁ = 86 - 80 = 6

The percentage of adults who preferred soccer or basketball is 25%.

The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.

From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.

Thus,

11% + 14% = 25%

Hence, the percentage of adults who preferred soccer or basketball is 25%.

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Answer:

explanation:A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

Answer: To solve the problem, we can use the formula for exponential decay:

N(t) = N0 * (1/2)^(t/T)

where:

N(t) is the amount of the radioactive element at time t

N0 is the initial amount of the radioactive element

t is the time that has elapsed

T is the half-life of the radioactive element

Let's assume that the initial amount of carbon-14 in the bones was N0. After the bones were discovered, they had lost 60.1% of their carbon-14, which means that only 39.9% of the original carbon-14 remained. Therefore, we can write:

N(t) = 0.399 * N0

We want to find the time t that has elapsed since the mastodon died. We can rearrange the formula for exponential decay to solve for t:

t = T * log( N(t) / N0 ) / log(1/2)

Substituting the given values, we get:

t = 5750 * log( 0.399 ) / log(1/2)

Using a calculator, we find that t is approximately 16060 years. Therefore, the bones were approximately 16060 years old at the time they were discovered.

Step-by-step explanation:

Answer:

8√2 cm

Step-by-step explanation:

Answer: n=41

Step-by-step explanation:

If 41 racing cars are randomly selected, what is the probability that the sample mean would be greater than 88.1 gallons? Round your answer to four decimal