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The function g(x) = 4∛(x+2) - 5 is a transformation of the cube root parent function f(x) = ∛x. The transformation involves a vertical stretch by a factor of 4, a horizontal shift to the left by 2 units, and a vertical shift downwards by 5 units.

The cube root parent function f(x) = ∛x has a single x-intercept at the origin (0,0) and is symmetric about the origin. It has a gradual increase as x moves from negative to positive values.

In contrast, the function g(x) = 4∛(x+2) - 5 has a vertical stretch by a factor of 4, making the graph steeper than the parent function. The horizontal shift to the left by 2 units moves the x-intercept to (-2,0). The vertical shift downwards by 5 units moves the entire graph downward, so the new y-intercept is at (0,-5).

Overall, the function g(x) has been vertically stretched, horizontally shifted to the left, and vertically shifted downward from the parent function f(x).

The value of the term 14 times 39 can be expressed as the value of 2.7857.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Or, how do you increase something by 14 to get 39? If "x" in the phrase "14 times what = 39?" is "what," then the equation to use to solve the issue is as follows:

14 • x = 39

which is spelled out as:

14x = 39

In order to get the x alone, we must take the 14 from the left side of the equation. We multiply both sides by 14 to achieve that.

14x/14 = 39/14

39/14 is 2.7857 and 14x/14 equals x, thus our equation will be as follows:

x = 2.7857

Therefore, the result of 14 times what is 39 is 2.7857.

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Answer:

here's your answer

Step-by-step explanation:

hope it will help you

A. A one-sample z-test for a population mean

A one-sample z-test is used to compare the sample mean to a known population mean. In this case, the researchers have a known population mean (the mean battery life of the older version of the battery) and they are trying to determine if the mean battery life of the new battery is greater than that. Therefore, a one-sample z-test is the appropriate test.

The researchers selected random samples of 32 of the new batteries, subjected the batteries to continuous use, and determined the mean and standard deviation of the battery lives in the sample. The one-sample z-test is used to compare the sample mean to a known population mean. The researchers can use this test to determine if the mean battery life of the new battery is b significantly greater than the known mean battery life of their older version. The z-test will calculate the probability of the observed results occurring if the mean battery life of the new battery is actually equal to the known mean battery life of their older version. If the probability is low enough, the researchers can reject the null hypothesis (that the mean battery life of the new battery is equal to the known mean battery life of their older version) and conclude that the mean battery life of the new battery is greater than the known mean battery life of their older version.

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Answer: -15

Step-by-step explanation:

2.75 inches is equal to 69.85 millimeter

To convert 2.75 inches to millimeter, we can use the following formula:

1 inch = 25.4 millimeter

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in feet = conversion factor × The length in meter

Substitute the values in the equation

2.75 inches = 25.4 × 2.75

Multiply the numbers

= 69.85 millimeter

Therefore, 2.75 inches is 69.85 millimeter

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The value of the missing angle of the diagram above would be = 78°

The total interior angle of a triangle = 180°

The value of the available angles given = 44° and 34°

The value of the third angle of the triangle = ?

That is ;

180 = 44+34+?

make ? the subject of formula;

? = 180 -78

? = 102°

But angle of a straight line = 180°

Therefore, <1 = 180-102 = 78°

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Answer:

3y + 2

Step-by-step explanation:

10 + 2y - 8 + y = 2y + y + 10 - 8 = 3y + 2

The amount having half life=27 days  left after 54 days will be 122 gm.

What is a substance's half-life?

When we refer about half life, we mean the time it takes for exactly half of the radioactive material in question to decay.

More specifically, the time it takes for the radioactive material to lose exactly half of its mass.

Now,

As half-life=27 days

initial amount=488 gm

after 27 days, amount=488/2=244 gm

and after next 27 days amount=244/2

=122 gm

So, After 27+27=54 days the left substance will be 122gm of total initial amount=488gm.

hence,

           The amount left after 54 days will be 122 gm.

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Answer:

Step-by-step explanation:

true

The additive inverse of the polynomial is:

7y^(2) - x^(2)y + 3xy + 7x^(2)

The additive inverse of a number A is a number B such that:

A + B = 0

B = -A

Similarly for polynomials, to find the additive inverse, you just need to multiply it by -1.

Here the polynomial is:

-7y^(2) + x^(2)y - 3xy - 7x^(2)

Then the additive inverse is:

-1*(-7y^(2) + x^(2)y - 3xy - 7x^(2))

7y^(2) - x^(2)y + 3xy + 7x^(2)

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Answer:

              Teresa has 994 songs on her MP3 player.

Step-by-step explanation:

              We know that Rosanne has 142 songs on her MP3 player, and that Teresa has 7 times more songs than Rosanne does. Therefore, we can conclude that the number of songs that Teresa has 142 × 7 = 994 songs on her MP3 player.

Have a great day! Feel free to let me know if you have any more questions :)

The volume of the figure is 18 cubic units

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

The figure

The figure can be divided into two 3-D figures represented below

Cube: side length = 2

Cuboid: 2 by 5 by 1

The volume of the figure is then calculated as

Volume = Volume of cube + Volume of cuboid

So, we have

Volume = 2 * 2 * 2 + 2 * 5 * 1

Evaluate

Volume = 18

Hence, the volume is 18 cubic units

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Generally, a size 1 diaper will weight around 8-14 lbs may it be for infants or adults.

By absorbing or containing waste materials to prevent soiling of outer clothing or the surrounding environment, diapers are a type of underwear that enable the wearer to urinate or defecate without using a toilet.

Diapers must be changed when they become soiled or wet, usually by a second person like a parent or caregiver. Skin issues around the diapered area can arise from failing to change a diaper as frequently as necessary.

Cloth or synthetic disposable materials are used to create diapers. Infants, toddlers who haven't learned to use the toilet, and kids who have bedwetting issues are the main groups of people who wear diapers. Adults who have incontinence or other conditions that call for their use may also do so.

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Answer:

Step-by-step explanation:

Y=6m/1-m

x=3(m+1)/1-m

The length of each side of the octagon with area of 576 square centimeters and an apothem of 16 centimeters is  9  centimeters .

Compared to lower sided shapes, an octagon's area is a little more complicated. A normal octagon's area is equal to 4 as. Where "s" stands for the octagonal side and "a" for the apothem, which runs straight from the pentagon's center to one of its sides.

The formula for the area of a regular octagon is:

A = 4 × apothem × side

Using this formula and the given values, we can solve for the length of each side of the octagon:

576 = 4 × 16 × side

Dividing both sides by 4 × 16, we get:

side = 576 ÷ (4 × 16)

Simplifying the right-hand side, we get:

side = 576 ÷ 64 = 9 cm.

Therefore, the length of each side of the octagon is  9 cm .

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Answer:

Step-by-step explanation:

In a recent year, Saudi Arabia produced 8.2 million barrels of crude oil per day, compared to 6.4 million barrels per day for the United States. This was 28% more than what the United States produced.

Saudi Arabia now consumes 1.8 million more barrels of crude oil per day than the United States does. Crude Oil from Saudi Arabia: In January 2023, production was reported at 10,319,000 barrels per day, down from 10,475,000 barrels per day in the previous year.

In November 2022, crude oil production in Saudi Arabia was 10,468 thousand barrels per day, down from 10,957 thousand barrels per day the year before.

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Answer:

The difference between -2and-3 and 1 and -3 is 1

The perimeter of the triangle is the sum of the lengths of all three sides. Therefore, the expression for the perimeter is:

(10f + 6) + (2f-4) + (9g + 1)

Simplifying the expression:

= 12f + 9g + 3

Therefore, the expression for the perimeter of the triangle is 12f + 9g + 3 centimeters.

Answer:

5.6

Step-by-step explanation:

Answer:

5.6

Step-by-step explanation:

5.6 to the nearest 10th

Using compound interest formula when the CD matures on Melissa's 14th birthday, there will be $3187.69 available.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Use the formula for compound interest to calculate the amount of money that will be available when the CD matures -

[tex]A = P(1 + r/n)^(nt)[/tex]

Where A is the amount of money available when the CD matures, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, the initial principal is $2000, the interest rate is 6%, and the CD will be held for 8 years (from Melissa's 6th to 14th birthday).

It is not given how many times per year the interest is compounded, so assume it is compounded annually.

Using these values in the formula -

[tex]A = $2000(1 + 0.06/1)^(1*8)A = $2000(1.06)^8A = $3187.69[/tex]

Therefore, the value is obtained as $3187.69.

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You'll need a drill bit with a diameter slightly smaller than 0.249325 inches.

A chart or formula can be used to determine the correct drill bit size for a 1/4-20 tap.

The following formula is a common method:

drill bit size = tap's major diameter - (constant x pitch)

The major diameter of a 1/4-20 tap is 0.250 inches, and the pitch (distance between threads) is 0.050 inches. Using 0.0135 as a constant (a common value for coarse threads), the calculation would be:

0.250 drill bit size (0.0135 x 0.050)

Size of drill bit = 0.250 - 0.000675

0.249325 in drill bit size

As a result, you'll need a drill bit with a diameter slightly smaller than 0.249325 inches. In practice, a drill bit size of 7/32 inch would suffice for the majority of applications.

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The fraction n/8 is between 4/5 and 1. To calculate all the possible values of n, use the following equation:  n = (4/5)*8 = 6.4

Since n is a fraction, the possible values are 6, 6.4, 6.8, 7.2, 7.6, 8, and 8.4.
The possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.

To find the possible values of n, we can cross-multiply and compare the fractions.

1/2 < n/8 < 4/5

Cross-multiplying gives us:

8 < 2n < 32

Dividing by 2 gives us:

4 < n < 16

The possible values of n are the integers between 4 and 16, which are 5, 6, and 7.

Therefore, the possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.

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The probability of at least one of the cars starting on a cold morning is 0.84 or 84%.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is used to quantify the chances or odds of a particular event happening or not happening.

In probability theory, the probability of an event is represented as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. The probability of an event that is neither impossible nor certain is represented by a number between 0 and 1, where a probability of 0.5 indicates that the event is equally likely to happen or not happen.

Probability can be calculated using various methods, including empirical or experimental probability, theoretical probability, and subjective probability. Empirical or experimental probability is based on observations or experiments, while theoretical probability is based on mathematical models or formulas. Subjective probability is based on personal beliefs or opinions.

Probability is used in many areas of study, including statistics, economics, engineering, and physics, among others. It is also used in everyday life, such as when making decisions or predicting outcomes. For example, probability can be used to determine the likelihood of winning a game of chance, the chances of an accident happening, or the probability of a disease occurring.

To find the probability of at least one of the two cars starting on a cold morning, we can use the complement rule, which says that the probability of an event happening is equal to 1 minus the probability of the event not happening.

In this case, the event of interest is at least one car starting on a cold morning. The complement of this event is neither car starting on a cold morning. The probability of neither car starting on a cold morning is:

0.4 * 0.4 = 0.16

Therefore, the probability of at least one car starting on a cold morning is:

1 - 0.16 = 0.84

So the probability of at least one of the cars starting on a cold morning is 0.84 or 84%.

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Three expressions containing exponents so that each expression equals 81 are,

1) 9²

2) 3⁴

3) 8² + 17

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We have to write three expressions containing exponents so that each expression equals 81.

Hence, We get;

Three expressions containing exponents so that each expression equals 81 are,

1) 81 = 9 × 9 = 9²

2) 81 = 3 × 3 × 3 × 3 = 3⁴

3) 81 = 8 × 8 + 17 = 8² + 17

Thus, Three expressions containing exponents so that each expression equals 81 are,

1) 9²

2) 3⁴

3) 8² + 17

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The mass of 1 whole pizza will be 384 g.

What is Proportion ?

A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. It is a formula or claim that shows that two ratios or fractions are equivalent.

He has cut 1st pizza into 24 slices and other pizza into 8 slices.

Let the mass of small slice to be "x" g

So, the mass of large slice will be " 32+x " g

Now, Ben has two identical pizzas, it means the mass of both pizzas will be same.

So, mass of 1st pizza = mass of other pizza

                        24 x   =  8 ( 32+x )

                        24x = 256 + 8x

                        16x = 256

                         x = 16

Hence, the mass of 1 whole pizza = 24 × 16 = 384 g.

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There are 2 tablespoons in an ounce. So for 2 ounces, you will need 4 tablespoons, for 4 ounces 8 tablespoons, and so on.

A tablespoon is a unit of volume measurement in United States, and some other countries. It is equal to approximately 15 milliliters (0.51 fluid ounces). One tablespoon can be further divided into three teaspoons, meaning that one tablespoon is equal to three teaspoons.

In the United States, one tablespoon is equal to 0.5 ounce, which is equal to 14.3 grams. This is slightly different in the UK, where one tablespoon is equal to 0.6 ounces (which is equal to 17.7 grams). To convert tablespoons to ounces, you can use the following formula is 1 tablespoon = 0.5 ounces.

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