A line passes through the point (2, -8) and has a slope of -5.
Write an equation in slope-intercept form for this line.

The Mean Value Theorem states that there exists a point c in the interval of the given function such that the derivative of the function at this point is equal to the average rate of change of the function on the interval. In this case, c = 7/2 satisfies the theorem for f(x) = 3x^2 - 5x + 1 on the interval [2, 5].

Using the Mean Value Theorem, we can find c by solving the equation 3c^2 - 5c + 1 = (3(5)^2 - 5(5) + 1 - (3(2)^2 - 5(2) + 1)) / (5 - 2). Simplifying, we get c = 7/2.

The Mean Value Theorem states that there exists a point c in the interval of the given function such that the derivative of the function at this point is equal to the average rate of change of the function on the interval. To find this point c, we must solve the equation

3c^2 - 5c + 1 = (3(5)^2 - 5(5) + 1 - (3(2)^2 - 5(2) + 1)) / (5 - 2).

This simplifies to c = 7/2, which means that this value of c satisfies the conclusion of the Mean Value Theorem for

f(x) = 3x^2 - 5x + 1

on the interval [2, 5]. This means that for any value of x within the interval, the rate of change of the function is always equal to 7/2.

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Answer: 5

Step-by-step explanation:

The area of the square with side length [tex]5x[/tex] is [tex]25x^2[/tex].

The area of the square with side length [tex]2x[/tex] is [tex]4x^2[/tex].

The area of the triangle is [tex]\frac{1}{2}(2x)(5x)=5x^2[/tex].

It follows that [tex]25x^2 +4x^2 +5x^2=850 \implies x=5[/tex]. Note that we reject [tex]x=-5[/tex] since the length cannot be negative.

Answer:

8÷10^3 (8×10^-3)

Step-by-step explanation:

8÷1000 can be considered final answer

And can be written 8÷10^3 or 8×10^-3

[tex]80÷10^4

\\ =80÷10000

\\ = \frac{80}{1000} (multiply \: and \: divide \: left \: and \: right) \\ = \frac{8}{1000} = \frac{1}{125} (cancel \: common \: factor \: 8)

[/tex]

The translated function g(x) can be written as:

g(x) = (x + 2)^2

First, remember that an horizontal shift of N units applied to a function f(x) is:

g(x) = f(x + N)

if N > 0, the shift is to the right.

if N < 0, the shift is to the left.

Here we want a shift of 2 units to the left is:

g(x) = f(x + 2)

Where f(x) = x^3

Then the formula for the function g(x) is:

g(x) = (x + 2)^2

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The value of a and b is -5/4. The value describes the value of each digit in relation to its position in the number.

(a) Mean Value  = [tex]\frac{1}{3-1} \int_1^3 f(x)=\frac{1}{2}-\frac{5}{2}=\frac{5}{4}[/tex]

b) [tex]} \int_3^5 f(x) d x=\int_1^5 f(x) d x-\int_1^3 f(x) d x=10-\frac{5}{2}=\frac{15}{2} \\[/tex]

[tex]& \left.\int_3^5(2 f(x)+6) d x=2 \int_3^5 f(x) d x+6 \int_3^5 d x=2\left(\frac{15}{2}\right)+6 x\right]_3^5=15+6(2)=27 \\[/tex]

c) [tex]} f(x)=a x+b \\[/tex]

[tex]& \left.\int_1^3(a x+b) d x=\frac{a x^2}{2}+b x\right]_{x=1}^3=\frac{9}{2} a+3 b-\frac{a}{2}-b=4 a+2 b=\frac{5}{2} \\[/tex]

Simplifying,

[tex]\left.\int_1^5(a x+b) d x \cdot \frac{a x^2}{2}+b x\right]_{x=1}^5=\frac{25 a}{2}+5 b-\frac{a}{2}-b=12 a+4 b=10 \\[/tex]

[tex]4 a+2 b=5 / 2 \stackrel{n-3}{\rightarrow}-12 a-6 b=-15 / 2[/tex]

Then we get,

[tex]12 a+4 b=10[/tex]

[tex]$ \frac{12 a+4 b=20/2}{ -2 b=5 / 2} b=\frac{-5}{4}[/tex]

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Answer:

Shape A: 647 (area) and 120 (perimeter)

Shape B: 192 (area) and 70 (perimeter)

Step-by-step explanation:

For shape A, we can find the area by:

- splitting the rectangle into 2 (horizontally), one that will have 16 and 12 as the sides, and another with 35 and 13 as the sides. Then, we can multiply the two rectangles and add them to find the area: (16*12) + (35*13) = 647

We can find the perimeter by:

- adding all the numbers: 25+16+12+19+13+35 = 120

For shape B, we can apply the same method as shape A:

- Area: (12*8) + (8*12) = 192

- Perimeter: 12+8+8+7+7+8+8+12 = 70

Answer:

Shape a) Area: (25*16)+(19*13)=400+247=647

 Perimeter: 16+12+19+13+35+25=120

Shape b)Area: (12*8)+(12*8)=96+96=192

              Perimeter: 12+8+7+8+12+8+7+8 = 70

To find volume: calculate volume of each rectangle, then add them.

[tex]V=Length*width[/tex]

I've highlighted which rectangle to calculate.

To find perimeter: add up all sides.

A function is invertible if and only if for every y in the range of the function, there is one and only one x in the domain such that f(x) = y. The inverse of a function is a new function that "swaps" the x and y values of the original function.

So, the inverse of a function represented by the table you provided would be a new function where the x values are -4.4, -0.6, 0.8, 1.2, 2.6 and 6.4 and the y values are -3, -2, -1, 1, 2 and 3 respectively.

The graph of the inverse function would be a reflection of the original function over the line y=x, meaning that it would be the same shape but flipped across the line y = x.

If you measure a flower stem, its termination will be on the eleventh line from the 5 inch mark. The length of the blossom stem is 5 and 11/16 inches.

What is Measurement?

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences. Measurement, then, is the process of establishing how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind.

We have to measure 5 inches on scale we have to follow these steps:

Step 1: Get a ruler for inches. There will be 12 lines on the ruler that represent inches, indicating that it is an inch ruler. A foot is equivalent to 12 inches (0.305 m). Inches are divided into each foot. On the ruler, each inch is divided into 15 smaller marks for a total of 16 marks per inch.

Step 2: Find out what an inch is. 12 inch markings make up a ruler. The longest lines on the ruler serve to identify them, which are usually the numbered marks. Put one end of the nail, for instance, directly on the left side of the ruler when you need to measure it. The nail is 5 inches long if it terminates just over the long line next to the big number 5.

Step 3: Discover the 1/2 inch markings. The 1/2 inch marks, which are half as long as the inch marks, will be the second-longest lines on the ruler. Due to the fact that it is just half an inch, each 1/2 inch mark will be placed halfway between each inch number. This indicates that the 1/2 inch lines are located immediately between the 0 and 1 inch, 1 and 2 inch, 2 and 3 inch, and so on across the ruler. On a 12 inch ruler, there are a total of 24 of these marks.

Step 4 : Recognize the 1/4-inch markers. There will be a smaller line that represents a 1/4 of an inch halfway between each 1/2 inch line. These markers will indicate 1/4, 1/2, 3/4, and 1 inch inside the first inch. Despite having separate lines, the 1/2 inch and 1 inch markers are still included in the 1/4 inch measures since 2/4 of an inch equals half an inch and 4/4 of an inch equals one inch. On a 12 inch ruler, there are a total of 48 of these marks.

Step 5: Recognize the 1/8-inch scale. The tiny marks on the ruler that are situated between the 1/4-inch markers are the 1/8-inch marks. There are markers that stand for 1/8, 1/4, 3/8, 1/2, 5/8, 6/8, 3/4, 7/8, and 1 (or 8/8) of an inch between 0 and 1 inch. On a 12 inch ruler, there are 96 of these marks in total.

Step 6 : Recognize the 1/16-inch scale. The little lines at the midpoint of each 1/8 inch represent the 1/16 inch. These are the ruler's tiniest lines as well. The 1/16-inch mark is located on the very first line on the ruler's left side. There are symbols that stand for 1/16, 2/16, 1/8, 3/16, 4/16, 5/16, 6/16, 3/8, 1/2, 9/16, 10/16, 5/8, 11/16, 12/16, 3/4, 13/16, 14/16, 7/8, 15/16, and 16/16 of an inch, respectively, between 0 and 1 inch. There are 192 of these lines on the ruler in total.

Hence, If you measure a flower stem, its termination will be on the eleventh line from the 5 inch mark. The length of the blossom stem is 5 and 11/16 inches.

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Answer:

[tex]\frac{7d}{15}[/tex]

Step-by-step explanation:

Answer:

next person to answer give them the brainly crow

Step-by-step explanation:

The lowest corresponding fraction of the integer is its simplest form. so we get the answer is 0.96.

A method is considered efficient if it can generate an answer quickly and without needing a page of computations. A successful strategy is one that solves every issue of a certain class (i.e., one that is generalizable to many problems using the same operation).

The lowest corresponding fraction of the integer is its simplest form.

Take the denominator's LCM as the first step. Step 2: Multiply the numerator and the denominator by the same number to convert the denominators to the LCM Value. Step 3: Subtract the numerator once the denominator is equal. Step 4: If required, simplify the resultant fraction.

5-3 a simpler problem. Then subtract.7 /10

5 / 3 - 7 / 10 =

50 - 21 / 30 = 29 / 30 = 0.96 .

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Answer:

P/E = 125/9= 13.89:1

Step-by-step explanation:

2mm shares at $ 125/share

18mm earnings so earnings per share EPS = 18/2 =9

The P/E ratio is calculated by dividing the stock's current price by its latest earnings per share.

P/E = 125/9= 13.89:1

Answer:

Step-by-step explanation:

The earnings per share can be calculated as

Earnings per Share =Total EarningsTotal Shares=$18,000,0002,000,000=$9.

Therefore the PE ratio is

PE Ratio =$125$9≈13.89.

The model that would explain the utility is U(q) = - 0.02q^2 - 300 + 10q.

The maximum number of workers is 250 and utility is 950

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

The total income as I(q) = 60q - 0.02q^2.

The total cost as C(q) = 300 + 50q.

The utility model can then be calculated as

U(q) = I(q) - C(q)

So, we have

U(q) = 60q - 0.02q^2 - 300 - 50q.

U(q) = - 0.02q^2 - 300 + 10q.

We have

U(q) = - 0.02q^2 - 300 + 10q.

Differentiate and set to 0

-0.04q + 10 = 0

So, we have

-0.04q = -10

This gives

q = 250 --- max workers

Recall that

U(q) = - 0.02q^2 - 300 + 10q.

So, we have

U(250) = - 0.02* 250^2 - 300 + 10 * 250

U(250) = 950 --- amount of utility

See attachment for the graph of I(q)=60q-0.02q^2

On the graph, we have the interpretation to be a maximum income of $45000 at 1500 workers

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When a test is two-sided and one-sided: We will reject the null hypothesis at the = X 0.01 0.050. 10 significance level if the value of interest falls outside a 95% confidence interval. If the value of interest falls outside a 99% confidence interval, the null hypothesis will be rejected at the = 0.010.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used. The confidence interval is the range of values within which you expect your estimate to fall a certain percentage of the time if you repeat your experiment or re-sample the population in the same manner.

Here,

When a test is two-sided and one-sided: If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the = X 0.01 0.050. 10 significance level. The null hypothesis will be rejected at = 0.010 if the value of interest falls outside a 99% confidence interval.

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Answer:

two sided.

.05

.01

Step-by-step explanation:

The amount of money which Jan's remodel would cost is equal to $624.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

Area of rectangle = 12 × 16

Area of rectangle = 192 square feet.

For the total cost, we have the following;

Total cost = Area of remodel × cost per square foot.

Total cost = 192 × 3.25.

Total cost = $624.

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The account balance after 5 years will be $3935.53.

Compound interest is interest that is paid on both principal and interest at regular intervals. The first year of compound interest is similar to the first year of simple interest, but the difference begins in the second year.

Continuously compounded interest means that an account balance is constantly earning interest and reinvesting that interest so that it, too, earns interest.

Given that Jessica invests $3,065 in a savings account with an annual interest rate of 5% compounded continuously.

The account balance after 5 years will be calculated as:-

[tex]P(t) = P_oe^{rt}\\P(t) = 3065\times e^{0.05\times 5}\\P(t) = \$3935.53[/tex]

Therefore, the balance in the account after 5 years will be $3935.53.

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The cylinder has a volume of 150.796 in³. The cylinder has a surface area of 175.929 in².

The quantity of three-dimensional space that an object or closed surface occupies is referred to as volume in mathematics. The cubic units of volume are m³, cm³, in³, and so on.

The sum of all of an object's faces is its surface area in three dimensions. Wrapping, painting, and finally building things to achieve the best possible design are examples of real-world applications of the concept of surface areas.

Given that a volume of cylinder = h × r² × π

                         h = 12 in

                          r = 2 in

                       volume = ?

Volume of cylinder = h × r² ×π

                                 = =12 × 3.14×(2)²

                                       =37.68 × 4

                                       =150.796 in³

B). Surface area of cylinder= 2πr² + 2πrh

                                         =2× 3.14 × (2)²+2× 3.14× 2×12

                                          =175.929in²

The formula V=r²(h) can be used to determine a cylinder's volume. Simply multiplying the area of the circular base shape by the height is all that is required to determine a cylinder's volume.

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The binomial probability formula calculates the probability of getting exactly "x" successes in "n" independent trials, where each trial has a probability "p" of success.

In this case, the success is a French hen, with probability 0.81, and the number of trials is 3 (the number of hens).

The binomial coefficient "n choose x" represents the number of ways to choose "x" successes from "n" trials. It can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where n! is the factorial of n, which is the product of all positive integers up to n.

Plugging in the values from the problem, we have:

P(X=2) = (3 choose 2) * (0.81)^2 * (0.19)^1

= (3! / (2! * (3-2)!) ) * (0.81)^2 * (0.19)^1

= 3 * 0.81^2 * 0.19

= 0.324

So, the probability of getting exactly 2 French hens out of 3 is approximately 0.324.

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The linear function in the form is y = 4x + 1.5 to the situation.

What is meant by function?

Initial fee: $4

Per mile: $1.50

Set up an equation where  = the taxi charges

Using y = mx + b form:

y = 4x + 1.5

The linear function in the form is

y = 4x + 1.5

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The value of f(x) . g(x) is  3x² + 5x - 2 two linear functions multiplied together to form a quadratic function.

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, Are two function f(x)  3x - 1 and g(x) = x + 2.

Now, f(x) . g(x) is nothing but multiplication of f(x) and g(x).

Therefore,

f(x) . g(x) = (3x - 1)(x + 2).

f(x) . g(x) = 3x² + 6x - x - 2.

f(x) . g(x) = 3x² + 5x - 2.

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The volume of the spherical segment above the plane is[tex](1/3) *\pi * (r^2 - (r-h)^2) * h[/tex] and the volume of the ring resulting from drilling a hole through the center of a sphere is [tex]\pi * (R^2 - r^2) * R.[/tex].

A sphere of radius "r" is cut by a plane "h" units above the equator. To find the volume of the solid (spherical segment) above the plane, we first need to find the height of the segment, which is (r - h). Then, we can use the formula for the volume of a spherical segment: [tex](1/3) * \pi * (r^2 - (r-h)^2) * h.[/tex]

A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. To find the volume of the resulting ring, we can use the formula for the volume of a cylindrical ring: [tex]\pi * (R^2 - r^2) * h[/tex], where h is the height of the ring. Since the hole goes all the way through the sphere, the height of the ring is equal to the radius of the sphere, R. So the volume of the ring is [tex]\pi * (R^2 - r^2) * R[/tex].

In the first problem, the volume of the solid (spherical segment) above the plane is [tex](1/3) * \pi * (r^2 - (r-h)^2) * h[/tex]. In the second problem, the volume of the resulting ring is [tex]\pi * (R^2 - r^2) * R.[/tex]

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Using the equation

Since Pat is the CEO of Pat's Pickle-Packing Plant, but can still pack 18 jars of pickles per hour. Kim, a rising star in the industry, packs 24 jars per hour. Kim arrived at work at 9:00 am one day to find that Pat had been packing pickles since

7:30 am. Later that day, Kim had packed exactly the same number of jars as Pat.To find the time and number of jars picked, we solve an equation.

An equation is a mathematical expression that shows the relationship between two variables.

Let

Since Pat picks at a rate of 18 jars of pickles per hour, the number of jars Pat picks is n = 18t

Also, Kim picks at a rate of 24 jars per hour, 1.5 hours later the number of jars Kim picks is n' = 24(t + 1.5)

Since n = n', we have that

18t = 24(t - 1.5)

18t = 24t - 36

18t - 24t = -36

-6t = -36

t = -36/-6

t = 6 hours

Since Kim's time is t - 1.5 = 6 - 1.5 = 4.5 hours

To find the number of jars each picked, substitute t = 6 into n. so, we have that

n = 18t

= 18(6)

= 108 jars

So,

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The required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

It is given that m ∠ AOB = 42 ∘ and m ∠ EOF = 66 ∘ . By the definition of congruent angles, ∠ EOF ≅ ∠ BOC. Therefore, m ∠ BOC = 66 ∘ . In the addition, m ∠ AOC = 108 ∘ , and by definition of the straight angle, m ∠ AOC + m ∠ COD = 180 ∘ . After application of the subtraction of the angle, m ∠ COD = 72 ∘ .

Thus, the required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

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Answer:

It is given that m∠AOB = 42º and m∠EOF = 66º. By the vertical angles theorem, ∠EOF ≅ ∠BOC. By the angle addition postulate, m∠AOC = 108º, and by the linear pair theorem, m∠AOC + m∠COD = 108º. After the application of the subtraction property of equality, m∠ COD = 72º.

Step - by - step

first box: vertical angles theorem

second box: angle addition postulate

third box:  linear pair theorem

fourth box: subtraction property of equality

It is likely that the result of the Gallup poll generally holds true for Yvonne's school.

Yvonne can calculate the sample proportion of teens who report that they seldom or never argue with their friends by using the formula:

P = (number of teens who report that they seldom or never argue with their friends / sample size)

For Yvonne's survey of 150 students, if 108 of them report that they seldom or never argue with their friends, then the sample proportion is:

P = (108/150) = 0.72

This result is very close to the 72% reported in the Gallup poll. Therefore, it is likely that the result of the Gallup poll generally holds true for Yvonne's school.

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The limit of f(x) as x approaches 0 is 1.

The limit of f of x as x approaches 0 can be calculated using limit theorems. First, we rewrite the function as:

f(x) = (x + 1) / (1 / (x - 1))

Then, we can simplify this by multiplying both the numerator and denominator by (x - 1):

f(x) = (x + 1)(x - 1) / 1

Next, we can apply the limit theorem that states the limit of a product is the product of the limits. Thus, we can calculate the limit as:

lim f(x) = lim (x + 1)(x - 1) / 1

= lim (x + 1) * lim (x - 1) / 1

= 0 + 1 * 0 - 1 / 1

= 1 / 1

= 1

Therefore, the limit of f(x) as x approaches 0 is 1.

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A cube is a three-dimensional shape with all sides of equal length, width, and height. If the length of the packaging box is 4xy, then all the sides of the cube have the same length 4xy.

What is the straightforward meaning of volume?

The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.

To find the volume of a cube, we use the formula: volume = side x side x side = (side)^3

Therefore, the volume of the packaging box in terms of x and y is (4xy)^3 = (4xy)(4xy)(4xy) = (4xy)^3 = (4x)^3 * y^3 = 64x^3 * y^3

So the volume of the packaging box is 64x^3 * y^3 cubic units.

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Fully factor the numerator and denominator of each rational expression. Write as one fraction by multiplying the numerators together and multiplying the denominators together.

Multiplication:

Step 1: Factor both the numerator and the denominator.

Step 2: Write as one fraction.  Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.

Step 3: Simplify the rational expression.

Step 4: Multiply any remaining factors in the numerator and/or denominator.

Multiplying Rational Expressions Involving Quadratics with Leading Coefficients of 1

Step 1: Fully factor the numerator and denominator of each rational expression.

Step 2: Write as one fraction by multiplying the numerators together and multiplying the denominators together.

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