factor [tex](2x^4+y^3)^2[/tex]

in the alphabetical order A-B SO I THINK IT IS 10

(a) Positive derivative interval: From x = -∞ to x = -4, and from x = 0 to x = 3.

(b) Negative derivative interval: From x = -4 to x = 0, and from x = 3 to x = ∞.

(c) x-value(s) where derivative equals zero: At x = -3 and x = 2.

(d) x-value(s) where derivative does not exist: At x = -4 and x = 3.

To find the intervals where the derivative of the function is positive, negative, or equals zero, we first need to find the critical points by setting the derivative equal to zero and solving for x. We can see from the graph that there is only one critical point at x = -2. We then test each interval between the critical points and endpoints to determine if the derivative is positive or negative.

From x = -infinity to x = -2, the derivative is negative. From x = -2 to x = 3, the derivative is positive. From x = 3 to x = infinity, the derivative is negative. Therefore, the answer is (a) the derivative is positive on (-2, 3); (b) the derivative is negative on (-infinity, -2) and (3, infinity); (c) the derivative equals zero at x = -2; (d) the derivative exists for all x.

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The number of vacation packages offered by Peaceful Travel Agency is 10

To determine the number of different vacation packages offered by Peaceful Travel Agency, we need to use the multiplication principle of combination and counting.

Since the agency has 2 cities, 5 months, and 1 airline to choose from, we can multiply the number of options for each category to get the total number of vacation packages:

So, we have

vacation packages = 2 cities x 5 months x 1 airline

vacation packages = 10

Therefore, Peaceful Travel Agency offers 10 different vacation packages.

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The 99% confidence interval estimate of the population proportion p is (0.5323, 0.7877) to 4 decimal places.

What is confidence interval?

A confidence interval is a range of values calculated from a sample of data that is used to estimate an unknown population parameter with a certain level of confidence.

1.To construct a 99% confidence interval estimate of the population proportion p, we can use the following formula:

CI=[tex]$\hat{p}$[/tex]±[tex]\item $z_{\alpha/2}$[/tex]×[tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]

where:

[tex]$\hat{p}$[/tex] is the sample proportion (x/n)

[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 99% confidence level, which is 2.576

n is the sample size

Substituting the given values, we have:

[tex]$\hat{p}$[/tex] = x/n = 66/100 = 0.66

[tex]\item $z_{\alpha/2}$[/tex] = 2.576 (from the standard normal distribution table or calculator)

n = 100

Plugging these values into the formula, we get:

CI = 0.66 ± 2.576 * [tex]\sqrt{(0.66)\frac{(1-0.66)}{100}}[/tex]

CI = 0.66 ± 0.1277

Therefore, the 99% confidence interval estimate of the population proportion p is (0.5323, 0.7877) to 4 decimal places.

2.To estimate the proportion of all Americans that have cats as pets with 95% confidence, we can use the following formula:

CI=[tex]$\hat{p}$[/tex]±[tex]\item $z_{\alpha/2}$[/tex]×[tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]

where:

[tex]$\hat{p}$[/tex] is the sample proportion (0.372)

[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 95% confidence level, which is 1.96

[tex]\item $n$[/tex] is the sample size (710)

Substituting the given values, we have:

​CI=0.372±1.96×[tex]\sqrt{0.372\frac{(1-0.372)}{710} }[/tex]

CI=0.372±0.0325

Therefore, the 95% confidence interval estimate of the proportion of all Americans that have cats as pets is [tex]$(0.3395, 0.4045)$[/tex] to 4 decimal places.

Expressing this in interval notation, we get [tex](33.95$, $40.45$)$[/tex] to 2 decimal places as a percentage.

Thus, we can say with 95% confidence that the proportion of all Americans that have cats as pets is between 33.95% and 40.45%.

3.To determine the sample size required to estimate the population proportion with a margin of error no larger than 0.04 and a 95% confidence level, we can use the following formula:

[tex]n=(\frac{z_{\alpha/2}}{E} )^2[/tex]×[tex]\hat{p}$(1-$\hat{p}$)[/tex]

where:

[tex]\item $n$[/tex] is the required sample size

[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 95% confidence level

[tex]\item $E$[/tex] is the margin of error

[tex]$\hat{p}$[/tex] is the sample proportion

Substituting the given values, we have:

[tex]n=(\frac{1.96}{0.04} )^2[/tex]×[tex]0.1161[/tex][tex](1-0.1161)[/tex]

Rounding up to the nearest whole number, we get:

n=476

Therefore, the required sample size to estimate the population proportion with a margin of error no larger than 0.04 and a 95% confidence level is 476.

4.To determine the sample size required to estimate the population proportion with a margin of error no larger than 0.05 and a 90% confidence level, we can use the following formula:

[tex]n=(\frac{z_{\alpha/2}}{E} )^2[/tex]×[tex]\hat{p}$(1-$\hat{p}$)[/tex]

where:

[tex]\item $n$[/tex] is the required sample size

[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 90% confidence level, which is 1.645

[tex]\item $E$[/tex] is the margin of error, which is 0.05

[tex]$\hat{p}$[/tex] is the sample proportion, which is 21/126 = 0.1667

Substituting the given values, we have:

[tex]n=(\frac{1.645}{0.05} )^2[/tex]×[tex]0.1167[/tex][tex](1-0.1167)[/tex]

n=145.9198

Rounding up to the nearest whole number, the government official should take a sample size of 146 to achieve his desired margin of error.

Therefore, the required sample size to estimate the population proportion with a margin of error no larger than 0.05 and a 90% confidence level is 146.

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which gives us a rate of "4 airplanes per 5 minutes" or "4/5 airplanes per minute."

To change minutes into hours, you can use simple mathematical operations.

There are 60 minutes in one hour. Therefore, to convert minutes into hours, you can divide the number of minutes by 60.

For example, if you have 120 minutes, you can divide 120 by 60 to get 2 hours (120 ÷ 60 = 2). Similarly, if you have 90 minutes, you can divide 90 by 60 to get 1.5 hours (90 ÷ 60 = 1.5).

Here's the formula you can use:

Hours = Minutes ÷ 60

So, to change any number of minutes into hours, divide that number by 60

by the question.

On a normal day, 12 airplanes arrive at an airport every 15 minutes. Write a rate that represents this situation.

The rate of airplanes arriving at the airport can be expressed as "12 airplanes per 15 minutes" or "12/15 airplanes per minute."

We can simplify this fraction by dividing the numerator and denominator by 3,

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Answer: The number of scores represented in the blue section of the boxplot is 12.

Answer: It is 144 but add pi symbol

Step-by-step explanation:

In conclusion the exact volume of the cone is 144π cubic inches.

How to solve and what does volume mean?

The radius of the circular base is half the diameter, which is 12/2 = 6 inches.

The volume of a cone can be found using the formula V = (1/3)πr²2h, where r is the radius and h is the height.

Substituting the given values, we get:

V = (1/3)π(6²2)(12)

V = (1/3)π(36)(12)

V = (1/3)(432π)

V = 144π

Therefore, the exact volume of the cone is 144π cubic inches.

Volume is a measure of the amount of space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be determined by measuring its dimensions, such as length, width, and height, and applying the appropriate formula for the shape of the object.

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The solution to the expression 7 + (one-fifth x 18 – 3) using the order of operations is 7.6 .

The order of operations is:

Perform any calculations inside parentheses first.

Exponents (ie powers and square roots, etc.)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

To solve the expression 7 + (one-fifth x 18 – 3), we need to apply the order of operations, which is a set of rules that determines the sequence in which we perform mathematical operations.

Using the order of operations simplifies the expression as follows:  

Calculate what's inside the parentheses:

one-fifth x 18 – 3 = (1/5) x 18 – 3

= 3.6 - 3

= 0.6

Add 7 to the result:

7 + 0.6 = 7.6

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Answer:  it's 8.6 or 1.4

Step-by-step explanation:

Turn 10% into a decimal form... .10

.10 x 14 = 1.4

10 - 1.4 = 8.6

The expression for the difference quotient is option C and the simplified form of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.

We are asked to find the expression for the difference quotient of the function f(x) when evaluated at x and x + h. The difference quotient is given by:

[tex]$\frac{f(x+h) - f(x)}{h}$[/tex]

where h is a small nonzero number representing the change in the input.

Substituting f(x) with its expression, we get:

[tex]$\frac{(2(x+h)^2 + 4(x+h) - 3) - (2x^2 + 4x - 3)}{h}$[/tex]

Expanding and simplifying the numerator, we get:

[tex]$\frac{2x^2 + 4xh + 2h^2 + 4x + 4h - 3 - 2x^2 - 4x + 3}{h}$[/tex]

Simplifying further, we get:

[tex]$\frac{2x^2 + 4xh + 2h^2 + 4h}{h}$[/tex]

Canceling the common factors of h, we get:

[tex]$2x + 4 + 2h$[/tex]

Therefore, the expression for the difference quotient of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.

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The true total distance chained if the measured distance on the ground is 6000 m would be 6001.8 m.

The measured distance on the ground is 6000 m. However, due to the increase in temperature during the surveying, the chain would have expanded, leading to an increase in the measured length.

The coefficient of linear expansion of steel is 8 x 10^-6 per oC. Therefore, for a temperature increase of 45 - 20 = 25 oC, the increase in length of the chain can be calculated as follows:

ΔL/L = αΔT

Substituting the given values, we get:

ΔL/30.00 = (8 x 10^-6) x 25

ΔL = 0.006 m

This means that the actual length of the chain during the surveying was 30.006 m.

To find the true total distance chained, we need to correct the measured distance on the ground for the increase in chain length. Let D be the true total distance chained. Then we have:

D/30.006 = 6000/30.00

Solving for D, we get:

D = 6000 x 30.006 / 30.00

D = 6001.8 m

Therefore, the true total distance chained is 6001.8 m.

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The value of x in the series given the first three terms x + 5, x + 1 and x is 1/3

Given that, we have

x + 5, x + 1 and x

Using the common ratio, we have

(x + 5)/(x + 1) = (x + 1)/x

So, we have

x² + 5x = x² + 2x + 1

Evaluating the like terms, we have

3x = 1

Divide by 3

x = 1/3

Hence, the value of x is 1/3

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(a) For every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited. (b) for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.

(a) To calculate the odds that a taxpayer will be audited, we need to divide the probability of being audited by the probability of not being audited. The probability of being audited is given as 1.5 percent or 0.015. The probability of not being audited is the complement of the probability of being audited, which is 1 - 0.015 = 0.985. Therefore, the odds that a taxpayer will be audited are:

0.015/0.985 = 0.0152284264

To convert this to odds notation, we divide the probability of being audited by the probability of not being audited:

0.015/0.985 = 0.0152284264 = 0.0152 (rounded to four decimal places)

This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited.

(b) The odds against a taxpayer being audited is the ratio of the probability of not being audited to the probability of being audited. We have already calculated the probability of not being audited to be 0.985, and the probability of being audited to be 0.015. Therefore, the odds against a taxpayer being audited are:

0.985/0.015 = 65.66666667

To convert this to odds notation, we divide the probability of not being audited by the probability of being audited:

0.985/0.015 = 65.66666667 = 66 (rounded to the nearest whole number)

This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.

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The sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.

Sample space refers to the set of all possible outcomes of a random experiment or a probability event. In the context of your card example, the sample space is the set of all possible cards that could be chosen from the labeled set.

In this case, the sample space would be {E, X, P, R, S, I, O, N}, as these are the possible outcomes when selecting one card from the set.

Therefore the sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.

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Answer:

650

Step-by-step explanation:

It's simple

The mass of substance left after 6 days is 9 g

The mass of substance left, N is given by

N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time

Also, λ = 0.693/t' where t' = half-life of iodine = 8 days

So, λ = 0.693/t'

λ = 0.693/8

λ = 0.086625/day

Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 6 days,

N = N₀exp(-λt)

N = 16 gexp(-0.086625/day × 7 days)

N = 16 gexp(-0.606375)

N = 16 g × 0.5453

N = 8.72 g

N = 8.72 → 9 g

So, the mass of substance left after 7 days is 9 g

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Answer:2.75 gallons of water

Step-by-step explanation:

Answer:

One gallon is equal to 16 cups of water.

To find out how many gallons are in 44 cups of water, we can divide 44 by 16:

44 cups ÷ 16 cups/gallon = 2.75 gallons

Therefore, 44 cups of water is equal to 2 and 3/4 gallons.

Step-by-step explanation:

1. Recall that 1 gallon is equal to 16 cups of water. Therefore, to find how many gallons are in 44 cups of water, we can set up a proportion:

1 gallon / 16 cups = x gallons / 44 cups

2. To solve for x, we can cross-multiply and simplify:

16x = 1 * 44

16x = 44

x = 44 / 16

x = 2.75

3. The result of 2.75 gallons represents the equivalent amount of water in gallons. To express this answer as a whole number or mixed number, we can observe that 2.75 is equal to 2 and 3/4:

2.75 = 2 + 0.75

2.75 = 2 + 3/4

Therefore, 44 cups of water is equal to 2 and 3/4 gallons.

Answer: Bob 3 Hours Jack 2 Hours

Step-by-step explanation:

Step-by-step explanation:

The total amount to be refunded to the five clients is:

5 x R665,00 = R3325,00

To find the balance on the company account after the refunds have been paid, we need to subtract the total amount refunded from the current balance:

R2195,00 - R3325,00 = -R1130,00

Therefore, the balance on the company account will be negative and equal to -R1130,00 after the refunds have been paid.

The values of k that would make the product of ᵏ⁄3 × 12 be greater than 12 is: D. for any value of k greater than 3.

The product of two numbers is the result obtained when one number is multiplied by another.

A. For values of k that are less than 1 but greater than 0, i.e 1.5, we have:

0.5/3 * 12 > 12

2 > 12 [false]

B. For values of k that are less than 3 but greater than 1, i.e 2, we have:

2/3 * 12 > 12

8 > 12 [false]

C. For any value of k that is equal to 3, i.e. 3, we have:

3/3 * 12 > 12

12 > 12 [false]

D. For values of k that are greater than 3, i.e 6, we have:

6/3 * 12 > 12

24 > 12 [true]

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Answer: the total direct cost of one item is $0.47.

Step-by-step explanation:

If the packaging employee makes $14 per hour and can package 200 items in one hour, the direct labor cost per item would be:

Direct labor cost per item = Hourly wage rate / Number of items packaged per hour

Direct labor cost per item = $14 / 200

Direct labor cost per item = $0.07

The direct material cost per item is given as $0.40.

Now we can calculate the total direct cost per item:

Total direct cost per item = Direct labor cost per item + Direct material cost per item

Total direct cost per item = $0.07 + $0.40

Total direct cost per item = $0.47

The answer would probaly be 1

Area of sector is 177.8cm².

In geometry, a sector is a region of a circle that is bounded by two radii and an arc, where the radii intersect at the center of the circle. The area of a sector is the fraction of the circle's total area that is enclosed by the sector.

where A is the area of the sector, θ is the central angle of the sector (measured in degrees), r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.

The formula for the area of a sector is:

A = (θ/360) x πr²

Angle made by sector=360-256=104

Radius of circle=14cm

Area of the sector DFE=∅/360×πr²

=104/360×π×14²

=177.8cm²

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Answer : 0.99

Explanation :  15 * 6.6/100 For The Tax.

Total : 15.99

Answer: Step 1: Pick a pair of corresponding points: one point in the shape before the translation and the same point in the shape after the translation.

Step 2: Determine how many units, a, left or right the shape moved.

Step-by-step explanation:

The equation of the new line which is parallel to the given line of equation y= 4/3x+4 is found to be: y + 7  = 4/3(x - 3).

The amount by which a line is inclined towards the horizontal axis is known as its slope. The slope can also provide a measure of a line's steepness and is helpful in assessing if two lines remain parallel or perpendicular.

Standard equation of line:

y = mx + c

m is the slope and c is the y intercept.

equation of a line: y = 4/3x + 4

On comparing both equation:

m = 4/3 and c is 4

Now, we know that : slopes of parallel lines are equal.

m = 4/3 and passing point is given as:  (3,-7).

Using the point slope form:

y - y1 = m(x - x1)

y - (-7) = 4/3(x - 3)

y + 7  = 4/3(x - 3)

Thus, the equation of the new line which is parallel to the given line of equation  y= 4/3x+4 is found to be: y + 7  = 4/3(x - 3).

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Answer:

si y = a 55 es 5.7

Step-by-step explanation:

la otra es 3.9