h(x)= 12/2x+16

find h(-8)​

Answer:

-13

Step-by-step explanation:

f(x)=2x-7

f(-3)=2(-3)-7=-6-7=-13

Answer:

14.5

Step-by-step explanation:

10 + (2 x 3)2 ÷ 4 × (3 x 1/2)

10 + (6)2 / 4 * (1.5)

10 + 12 / 4 * 1.5

10 + 3 * 1.5

10 + 4.5

14.5

Answer:

20.5

Step-by-step explanation:

10 + 12 ÷ 4 x 7/2

10 + 3 x 7/2

10 + 21/2

10 + 10.5

20.5

The two steps for calculating the mean:

Add up all the values in the data set.

Divide this number by the number of values.

The mean of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”

There are two steps for calculating the mean \((\bar{x})\):

(1) Add up all the values in the data set.

Sum of all the observations of given data denoted by \(\sum x\)

(2) Divide this number by the number of values.

The total number of values of given data denoted by 'n'

Sample mean:

\($$\overline{x}= \frac{\sum x}{n} $$\)

Example: Find the mean step by step?

42, 13, 31, 87, 24, 58, 76, 69

Solution:

Step 1: Find the sum of the values by adding them all up.

\(\sum x=\) 42 + 13 + 31 + 87 + 24 + 58 + 76 + 69 = 400

Step 2: Divide the sum by the number of values

In the formula, n is the number of values in your data set. Our data set has 8 values.

\($$\overline{x}= \frac{\sum x}{n} $$\)

\($$\overline{x}=\frac{400}{8}\)

\($$\overline{x}\) = 50

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Answer: okay so you add all of the numbers in the data set and then divide by how many numbers there were in the set.

Step-by-step explanation:

a) Using the Avrami equation with n = 1.2 and 90% completion in 180 seconds, the parameter k is found to be approximately 0.00397. b) The rate of transformation, r, is approximately 0.0367 per second.


a) The Avrami equation is given by the equation t = k * (1 – exp(-r^n)), where t is the transformation time, k is a parameter, r is the rate of transformation, and n is a constant (in this case, n = 1.2). Given t = 180 seconds and the transformation is 90% complete, we can rearrange the equation to solve for k: k = t / (1 – exp(-r^n)). By substituting the values, we find k ≈ 0.00397.
b) To determine the rate of transformation, we can rearrange the Avrami equation and solve for r: r = (-ln(1 – (t / k)))^(1/n). Plugging in the values t = 180 seconds and k ≈ 0.00397, and n = 1.2, we can calculate r ≈ 0.0367 per second. This represents the rate at which the transformation progresses per unit time.

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Answer:

-x² + 13x + 2

Step-by-step explanation:

you are on ambitious level, and you cannot answer that yourself ? that is trivial. truly. no hidden traps, just straight forward adding and simplifying. what is the problem, please ?

-7x² + 6x² = -x²

5x + 8x = 13x

-1 + 3 = 2

Answer:

3rd option

Step-by-step explanation:

Given

(- 7x² + 5x - 1) + (6x² + 8x + 3) ← remove parenthesis

= - 7x² + 5x - 1  + 6x² + 8x + 3 ← collect like terms

= - x² + 13x + 2

Answer:

\(delta = {b}^{2} - 4ac = {p}^{2} - 4 \times 3 \times 3 = {p}^{2} - 36\)

The equation has no real roots if delta <0

that is -6<p<6

The integral ∫ \((4x^6)^3\) dx, evaluated by making the appropriate substitution, is (3/168) × \(4^{(11/6)}\) × \(x^{(7/2)}\) + C.

To evaluate the integral ∫ \((4x^6)^3\) dx, we can make the appropriate substitution u = 4\(x^6\).

First, we need to find the derivative of u with respect to x, du/dx.

Taking the derivative of both sides, we get du/dx = 24\(x^5\).

Next, we rearrange the equation to solve for dx: dx = du / (24\(x^5\)).

Now, we substitute u = 4\(x^6\) and dx = du / (24\(x^5\)) into the integral:

∫ \((4x^6)^3\) dx = ∫ \(u^3\) (du / (24\(x^5\))).

Simplifying the integral, we have (1/24) ∫ (\(u^3\) / (\(x^5\))) du.

Since u = 4\(x^6\), we can rewrite the integral in terms of u only:

(1/24) ∫ (\(u^3\) / (\((u/4)^{(5/6)})\)) du.

Simplifying further, we have

(1/24) ∫ (\(u^3\) / (\(u^{(5/6)}\) × (\(4^{(-5/6)})\))) du

This becomes

(1/24) ∫ (\(u^3\) / ((\(u^{(5/6)}\) × (\(4^{(-5/6)})\))) du = (1/24) ∫ (\(u^3\) / (\(u^{(5/6)}\) × (\(4^{(-5/6)})\))) du

Now, we can integrate with respect to u:

(1/24) × [(\(u^{(4/3 + 1)}\) × \((4^{(-5/6)})\)) / (4/3 + 1)] + C

Simplifying further, we get

(3/168) × \(u^{(7/3)}\) × \((4^{(-5/6)})\) + C

Finally, substituting back u = 4\(x^6\), we have

(3/168) × \((4x^6)^{(7/3)}\) × \((4^{(-5/6)})\) + C.

This simplifies to (3/168) × \(4^{(11/6)}\) × \(x^{(7/2)}\) + C.

Therefore, the integral ∫ \((4x^6)^3\) dx, evaluated by making the appropriate substitution, is  (3/168) × \(4^{(11/6)}\) × \(x^{(7/2)}\) + C.

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a) About 99.7​% of organs will be between 205 grams and 415 grams.

b) The percentage of organs weighing between 240 grams and 380 grams is of 95%.

c) The percentage of organs less than 240 grams or more than 380 grams is of 5%.

d) The percentage between 240 grams and 415 grams is of: 97.35%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

The first three questions are quite straight forward, while for the fourth we consider the symmetry of the normal distribution, as follows:

Hence the total percentage is of:

0.95 x 50 + 0.997 x 50 = 97.35%.

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Answer:

c

Step-by-step explanation:

1 2/3 = 5/3 = 20/12

3 1/4 = 13/4 =39/12

The formula of the average velocity is, Average Velocity = (final displacement - initial displacement) / time

The formula for average velocity is:

Average Velocity = (final displacement - initial displacement) / time

or

Average Velocity = (change in displacement) / time

where "displacement" refers to the change in position of an object, and "time" refers to the time interval over which the displacement occurred.

Mathematically, this can be represented as:

v = (x_f - x_i) / t

or

v = Δx / t

where "v" represents the average velocity, "x_f" represents the final position of the object, "x_i" represents the initial position of the object, and "Δx" represents the change in position (i.e., final position - initial position). Finally, "t" represents the time interval over which the displacement occurred.

Therefore, the average velocity = (final displacement - initial displacement) / time

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Answer: 28. (33.75)

32-33. Well, x is 10 if that helps at all

Step-by-step explanation: sorry I can’t be of more help, I haven’t dealt with volume in approximately a year so I’m kind of rusty

Marine regression refers to the retreat of the sea, leading to a decrease in the extent of marine environments and the exposure of previously submerged areas. This phenomenon can have significant impacts on marine life.

The effects of marine regression on marine life are varied and depend on several factors, such as the speed and magnitude of the regression, the adaptability of the species, and the availability of alternative habitats. Marine organisms that rely on coastal areas for breeding, feeding, or shelter may face significant challenges as their habitats shrink or disappear altogether. Some species may be able to migrate to more suitable areas, while others may experience population declines or local extinctions.

Marine regression can disrupt the delicate balance of ecosystems, leading to changes in species composition and interactions. It can also affect the availability of food sources and alter the physical and chemical properties of the water, impacting the survival and reproductive success of marine organisms.

Furthermore, the loss of coastal habitats due to marine regression can have cascading effects on the wider ecosystem, including the loss of nursery grounds for fish and other marine organisms, decreased biodiversity, and altered nutrient cycles.

In summary, marine regression can have profound consequences for marine life, potentially leading to habitat loss, population declines, changes in species interactions, and ecological disruptions. Understanding and mitigating the impacts of marine regression are crucial for preserving the health and diversity of marine ecosystems.

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Answer:

A. Y-68=-5(x-14)

Step-by-step explanation:

Mary is spending money at the average rate of $5 per day. After 14 days she has $68 left. The amount left depends on the number of days that have passed. write an equation for the situation

We find the equation using the point slope equation of a line. This is given as:

y - y1 = m(x-x1)

The slope intercept form will be

y = -5x + b

since the amount decreases by $5 per day...

Our slope is -5 so m=-5

We have a point (x1,y1) = (14, 68)

Hence, we have:

y-68 = -5(x-14)

Option A is correct

Answer: x=45/3

Step-by-step explanation:

A maping diagram can be made of two columns, one represents the domain of a function (values of x or "inputs") and the other colum represents the range of the function (values of y or "outputs")

It can be used to represent any relationship between any two variables.

For the domain {-1, 0, 2}

And the range {1,4}

There are several possible combinations, for example:

The value of x is less than or equal to 2 and 1 half. The correct option is B.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that inequality is 3¹/₂≥1.4x. The inequality will be solved as below,

3¹/₂ ≥ 1.4x

(14)/(10)x ≤ (5/2)

(5/10)x ≤  5/2

x ≤ (5/10) ÷ ( 5/2 )

x ≤ 2.5

x ≤ 2¹/₂

Therefore, the value of x is less than or equal to 2 and 1 half. The correct option is B.

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Answer: x <= 2 1/2

Step-by-step explanation: Got correct on test

The matching answers and corresponding colors for the holiday lights are: (Slope: 3) Dark Blue, (Slope: -4) Violet, (Slope: 1/4) Red.

To find the slope of a line passing through two points \((x_1, y_1)\ and\ (x_2, y_2)\), we can use the formula:

Slope = \((y_2 - y_1) / (x_2 - x_1)\)

Let's calculate the slopes for each pair of points:

1. (8, 3) and (10, 9):

Slope = (9 - 3) / (10 - 8) = 6 / 2 = 3

2. (2, -3) and (1, 1):

Slope = (1 - (-3)) / (1 - 2) = 4 / (-1) = -4

3. (-4, -8) and (-8, -9):

Slope = (-9 - (-8)) / (-8 - (-4)) = (-9 + 8) / (-8 + 4) = -1 / (-4) = 1/4

Now let's compare the slopes to identify the matching answers:

1. Slope: 3 (Dark Blue)

2. Slope: -4 (Violet)

3. Slope: 1/4 (Red)

Thus, the corresponding colors for the holiday lights would be:

1. Dark Blue

2. Violet

3. Red

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We have shown that there are elements m, n ∈ S with m - n divisible by 16.

Answer:Let's consider the remainders of elements of S when divided by 16. These remainders can only be integers between 0 and 15, so there are only 16 possible remainders. However, we have 17 elements in S, so by the Pigeonhole Principle, at least two of these elements must have the same remainder when divided by 16. Let's call these elements m and n. Since they have the same remainder when divided by 16, their difference must be divisible by 16. In other words, m - n is divisible by 16. Therefore, we have shown that there are elements m, n ∈ S with m - n divisible by 16.

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The alternative that should be selected is alternative A.

To determine which alternative to choose, we need to compare their annual cash flows using an annual cash flow analysis and a 10% interest rate. Let's analyze each alternative:

Alternative A: It has an initial cost of $50,000 and generates an annual cash inflow of $15,000 for 10 years. The annual cash inflow remains constant throughout the life of the project.

Alternative B: It has an initial cost of $80,000 and generates an annual cash inflow of $20,000 for 5 years. At the end of the 5-year period, the unit is replaced with an identical one.

Alternative C: It has an initial cost of $100,000 and generates an annual cash inflow of $30,000 for 4 years. At the end of the 4-year period, the unit is replaced with an identical one.

To determine the present value of each alternative, we need to discount the annual cash flows at a 10% interest rate. By calculating the present value of each alternative, we can compare their net present values (NPVs). The alternative with the highest NPV should be selected.

Performing the calculations, we find that the net present value (NPV) of alternative A is the highest, indicating that it is the most financially favorable option. Therefore, alternative A should be selected.

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All parts of the problem given have been explained and provided below.

Variables in any particular dataset are defined as any characteristics, numbers, or quantity that can be measured or counted to give information about any object, on which the dataset is based.

So, the variables in this given dataset are;

Overall score

Recommended

owner satisfaction

Overall miles per gallon

Acceleration (0-60) sec

Categorical or qualitative variables are those which can't be quantified or measured. Their values are defined by an order relation between the different categories.

the categorical variables in this dataset are,

Recommended

Owner satisfaction

Quantitative variables are those which can be measured in an order to provide information about an object.

the quantitative variables in this dataset are,

Overall score

Overall miles per gallon

Acceleration (0-60) sec

In the given dataset, 7 vehicles are recommended,

So their percentage would be,

7/15 × 100 = 46.67%

The average overall miles per gallon of these 15 vehicles is 25.4.

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The length of each side of the base is 3 inches. Thus, the correct option is D.

In terms of geometry, a pyramid is a polygon that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex. If the base of the pyramid is a rectangle then the pyramid is known as a rectangular pyramid.

The lateral area of a regular pentagonal pyramid is 75 square inches and the slant height is 10 inches.

The length of each side of the base is calculated as,

75 = 5 x 1/2 x a x 10

75 = 25a

a = 3 inches

Thus, the correct option is D.

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True.

If adding two positive integers results in a negative number, it means that an overflow has occurred. The overflow flag is set when the result of an operation is too large to be represented with the given number of bits.
If bx and dx both contain positive integers and adding them produces a negative result, the overflow flag will be set. This is because when two positive integers are added, the result should also be a positive integer. If the result is negative, it means there was an overflow during the addition process, and the overflow flag will be set to indicate this issue.

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Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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The coordinates of point P along the directed line segment AB is (10, 13).

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

The line AB.

P is the point between the line AB.

Now,

A = (4, 10) = (a, b) and B = (14, 15) = (c, d)

m : n = 3 : 2

So,

P = (x, y)

The coordinates is given by:

x = (mc + na) / (m + n)

y = (md + nb) / (m + n)

So,

x = (42 + 8) / 5

x = 10

y = (45 + 20) / 5

y = 13

Now,

P = (10, 13)

Thus,

The coordinates of point P is (10, 13).

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The area bounded by the sin (100x² + 49y²) dA is calculated by using integration is 2π (1 - cos 1).

An area bounded by the curve: When the two curves intersect then they bound the region is known as the area bounded by the curve.

Evaluate the integral by making an appropriate change of variables.

The equation of the ellipse is 100x² + 49y² = 1

Let cos t = 10x and sin t = 7y. Then we have

or x = 1/10 cost , y = 1/7 sint.

Then

=> 100 (1/10cost)^2 + 49 (1/7 sint)^2 = 1

=> cos^2 t + sin^2t = 1 which suggests a change of variable will be:

\(\left \{ {{x(r,t) = r/10cost} \atop {y(r,t)=r/7sint}} \right.\)

where 0≤r≤1 and 0≤t≤2\(\pi\). Then we also have,

100x² + 49y² = r²

So,

=> ∫∫ sin (100x^2 + 49y^2)dA

     R

=> \(\\\)2 ∫2\(\pi\) ∫\(1\)  sinr^2 dr dt

       0     0

=> 4\(\pi\) ∫\(1\)  rsinr^2 dr

          0    

Now r² is replaced by r, then we get

=> 2\(\pi\) ∫\(2\)  sinr^2 d(r^2)

          0

=> - 2\(\pi\) cos r^2 \(\left \{ {{r^2=1} \atop {r^2=0}} \right.\)    

=> -2\(\pi\) (cos1-cos0)

=> -2\(\pi\) (-1 + cos1)

=> 2\(\pi\)(1-cos1)

Evaluating the integral by making an appropriate change of variables 2 sin(100x^2 + 49y^2) dA.

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9514 1404 393

Answer:

Step-by-step explanation:

Let q represent the number of quarters (the higher-value item). Then 145-q is the number of dimes. The total collection is worth ...

  0.25q + 0.10(145 -q) = 24.25

  0.15q = 9.75 . . . . . . . . . . . . . . . . subtract 14.50; collect terms

  q = 65 . . . . . . . . . . . divide by 0.15

  d = 145 -q = 80

Ted has 80 dimes and 65 quarters.

___

Check

  80 dimes: $8.00

  65 quarters: $16.25

Total: $8.00 +16.25 = $24.25.

The area of the trapezoid in this problem is given as follows:

15 square feet.

The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:

A = 0.5 x h x (b1 + b2).

The dimensions for this problem are given as follows:

h = 3 ft, b1 = 4 ft and b2 = 6 ft.

Hence the area is given as follows:

A = 0.5 x 3 x (4 + 6)

A = 1.5 x 10

A = 15 square feet.

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Answer:

11.09 years

Step-by-step explanation:

Given data

Principal P= $10200

Rate= 6.25%

Double the principal A = $20,400

The expression for the time taken is

t= ln(A/P)/r

t= ln(20400/10200)/0.0625

t= ln(2)/0.0625

t= 0.69314/0.0625

t= 11.09024 years

Hence the number of years is 11.09 years

4x+20

OPTION A is the correct answer.