Part 1
Use the Pythagorean theorem to find the unknown side of the right triangle.

Answer:

Step-by-step explanation:

1) -2

2) 0

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The calculated value of the derivative f'(x) at x = -2/3 if f(x) = 5x√(x + 1) is f'(-2/3) = 0

Given the function

f(x) = 5x√(x + 1)

Factor out 5

So, we have

f(x) = 5[x√(x + 1)]

The derivative is then calculated using the following chain rule

f'(x) = 5[du/dx * dy/du]

When differentiated, we have

f'(x) = 5[√(x + 1) + x/2[√(x + 1)]]

This gives

f'(x) = 5[3x + 2/2[√(x + 1)]]

So, we have

f'(x) = [15x + 10]/[2√(x + 1)]

Substitute -2/3 for x

f'(-2/3) = [15(-2/3) + 10]/[2√((-2/3) + 1)]

Evaluate

f'(-2/3) = [0]/[2√1/3]

Evaluate the quotient

f'(-2/3) = 0

Hence, the value of the derivative is 0

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Answer: r=89.1

Step-by-step explanation: It has been given that,

PQ=PR

So, it is an isosceles triangle, hence ∠Q=∠R. let it be x

Now, we know that the sum of the angles of a triangle = is 180

∘

.

So,

∠P+∠Q+∠R=180

38.2+52.7+x=180

90.9+x=180

taking 90.9 in RHS it becomes -, so

x=180-90.9

x=89.1

Answer:

Step-by-step explanation:

Let's call the weight of Karen's package "w" in pounds.

For the first courier, the cost is given by:

Cost = 20 + 2w

For the second courier, the cost is given by:

Cost = 12 + 3w

We know that these costs are equivalent, so we can set them equal to each other:

20 + 2w = 12 + 3w

Simplifying this equation, we get:

8 = w

So the weight of Karen's package is 8 pounds.

To find the cost, we can plug this weight into either of the equations above:

For the first courier:

Cost = 20 + 2(8) = 36

For the second courier:

Cost = 12 + 3(8) = 36

So it will cost Karen $36 to deliver her package, and the weight of the package is 8 pounds.

The equation that can be solved to predict the number of times Harris will spin a sum less than 10 is B) 12/500 = x/15

Harris should expect to spin a sum of 10 or greater 240 times.

It should be noted that to predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of experiments (500).

The possible sums that can be obtained are: 5, 6, 7, 8, 9, 10, 11, and 12. The probability of getting a sum less than 10 is the sum of the probabilities of getting each of these outcomes, which is:

P(sum less than 10) = P(1 and 4, 1 and 5, 2 and 4, 2 and 5, 3 and 4, 3 and 5)

= 6/15 * 2/5

= 4/25

Multiplying this probability by the total number of experiments (500), we get:

Number of times Harris will spin a sum less than 10 = (4/25) * 500 = 80

Therefore, the correct equation to predict the number of times Harris will spin a sum less than 10 is: 12/500 = x/15

Part B: Based on the information, the possible outcomes that give a sum of 10 or greater are: 10, 11, and 12. The probability of getting a sum of 10 or greater is the sum of the probabilities of getting each of these outcomes, which is:

P(sum of 10 or greater) = P(1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, 6 and 4, 7 and 3, 8 and 2, 9 and 1, 8 and 3, 7 and 4, 6 and 5)

= 12/15 * 3/5

= 36/75

= 12/25

Multiplying this probability by the total number of experiments (500), we get:

Number of times Harris should expect to spin a sum of 10 or greater = (12/25) * 500 = 240

Therefore, Harris should expect to spin a sum of 10 or greater 240 times.

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Answer:

B

Step-by-step explanation:

[tex]x^{2} +7x+49[/tex] is a prime equation.

1. Data is approx bell-shaped and symmetric

2. Median is between 150 to 175

A histogram is a graphical representation of a frequency distribution of a set of continuous data. It is used to display the shape of the data and to show how frequently certain values occur within a given range or interval.

In a histogram, the x-axis represents the range or interval of the data, and the y-axis represents the frequency of occurrence of values within each interval.

The data is divided into a set of bins or intervals, and the height of each bar on the histogram represents the number of data points that fall within that particular bin. The bars of the histogram are typically drawn adjacent to each other, with no gaps between them, to emphasize the continuity of the data.

Therefore, from the histogram used to represent the given data, it can be seen that the data is symmetric and also the median has the values between 150 to 175

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The coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.

A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.

When a point is reflected over the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.

Therefore, to find the coordinates of point B' after reflecting point B over the x-axis, we simply need to change the sign of the y-coordinate of point B.

Starting with point B at (8, -3), reflecting over the x-axis changes the sign of the y-coordinate, so the new point B' is at:

B' = (8, 3)

Therefore, the coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.

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In light of this, the cylinder's total surface area falls between approximately 1017.9 cm²and 1357.2 cm².

A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h." The entire surface area of the cylinder is calculated as follows:

Total Surface Area of Cylinder = 2r (h + r) square units.

The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. It is seen as a prism since its base is a circular. It is frequently used as a container and can either be solid or hollow 13.

The following formula can be used to get a cylinder's total surface area:

A = 2πr² + 2πrh

where r is the cylinder's base's radius, h is the cylinder's height, and is a mathematical constant roughly equal to 3.14159.

Yet, we can locate a variety of potential surface areas using the provided information. With the assumption that the radius is equal to the feedback's half (9 cm), we can

after which, we can determine the surface area as follows:

A = 2π(9)² + 2π(9)(18) (18)

A=  2π(81) + 2π(2916)

A ≈ 1017.9 cm²

The surface area can be calculated as follows if we assume that the radius is equal to two-thirds of the feedback (i.e., r = 12 cm):

A = 2π(12)² + 2π(12)(18) (18)

A ≈ 1357.2 cm²

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The ball will reach its maximum height after 3.5 seconds.

What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and then moves along a curved path under the influence of gravity.

In projectile motion, the object follows a parabolic trajectory, which is a curve described by a quadratic function. The path of the object depends on the initial velocity, angle of projection, and acceleration due to gravity.

The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately.

The height function of the ball thrown The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately. is given by h(t) = 112t - 16t^2, where t is the time in seconds and h(t) is the height of the ball at time t.

To find the maximum height, we need to find the vertex of the parabolic function h(t). The vertex of a parabola given by the equation y = ax^2 + bx + c is located at x = -b/2a.

In the case of our height function h(t) = -16t^2 + 112t, the coefficient of the squared term is -16, and the coefficient of the linear term is 112. Therefore, the time at which the ball reaches its maximum height is given by:

t = -b/2a = -112/(2*(-16)) = 3.5

So, the ball will reach its maximum height after 3.5 seconds.

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Answer:

Step-by-step explanation:

To make x the subject of y = ax^2 + b, we can use the following steps:

1.Subtract b from both sides to isolate the term with x^2:

y - b = ax^2

2.Divide both sides by a to isolate x^2:

(y - b) / a = x^2

3.Take the square root of both sides to solve for x:

x = ± sqrt((y - b) / a))

Therefore, the expression for x as a subject of y = ax^2 + b is:

x = ± sqrt((y - b) / a))

After answering the provided question, we can conclude that As a result, function option A) 5/6 is the correct answer.

A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.

Both Glass A and Glass B initially hold the same amount of liquid. Assume that the total amount of liquid that each glass can hold is equal to 6 units.

As a result, Glass A is initially filled with 3 units of liquid (1/2 of 6 units) and Glass B is initially filled with 2 units of liquid (1/3 of 6 units).

When the liquid from Glass B is poured into Glass A, the total amount of liquid in Glass A increases to 5 units (3 units + 2 units), and the glass is now completely filled.

So, after pouring the liquid from Glass B into it, the fraction of Glass A that is filled is 5/6.

As a result, option A) 5/6 is the correct answer.

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After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.

CB = 8 cm * tan(25°)

≈ 3.45 cm

To find the segment CB, we need to use the tangent of the angle α (25°). We also need to know the length of the segment AB, which is 8 cm. To solve for CB, we use the equation CB = 8 cm * tan(25°). After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.

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Answer:

1) 2160000000

2) 3.24 * 10^14

Step-by-step explanation:

30*8000(5-)1800

240000 * 5 * 1800

1200000 * 1800

2160000000

1500(800-)15000*18000

1200000 * 15000 * 18000

18000000000 * 18000

3.24 * 10^14

Answer:

Here are the angles in each quadrant with a common reference angle of 165°:

First quadrant: angle is 15° (subtract 165° from 180°)

Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)

Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)

Fourth quadrant: angle is 195° (subtract 165° from 360°)

Answer:

Slope = 0.5

Step-by-step explanation:

Slope of a Line passing through two points [tex](x_1 , y_1)[/tex] and [tex](x_2 ,y_2)[/tex] equal [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Since our Line passes through the two points ( -3 , 5 ) and ( 5 , 9 )

Then the Slope = [tex]\frac{9-5}{5-(-3)}=\frac{4}{8} =0.5[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{Slope\ formula\ is :\mathtt{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}\rightarrow \dfrac{rise}{run} = slope}[/tex]

[tex]\textsf{Your labels :}\\\\\mathtt{y_2 \rightarrow 9}\\\mathtt{y_1 \rightarrow 5}\\\\\mathtt{x_2\rightarrow 5}\\\mathtt{x_1\rightarrow-3}[/tex]

[tex]\textsf{Your equation should look like : }\mathtt{slope = \dfrac{9 - 5}{5 - (-3)}}[/tex]

[tex]\textsf{Solving for your answer should be :}[/tex]
[tex]\mathtt{slope = \dfrac{9 - 5}{5 - (-3)}}[/tex]

[tex]\mathtt{slope = \dfrac{9 - 5}{5 + 3}}\\\textsf{(We got a positive (+) symbol because double negatives }(-)\textsf{ make a positive!})[/tex]

[tex]\mathtt{slope = \dfrac{4}{8}}}[/tex]

[tex]\mathtt{slope = \dfrac{4\div2}{8\div2}}[/tex]

[tex]\mathtt{slope = \dfrac{2}{4}}[/tex]

[tex]\mathtt{slope = \dfrac{2\div2}{4\div2}}[/tex]

[tex]\mathtt{slope = \dfrac{1}{2}}[/tex]

[tex]\large\textsf{Thus your \boxed{\textsf{answer}} should most likely be :}\\\\\\\large\boxed{\mathtt{slope = \dfrac{1}{2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: Slope-intercept form : y-y₁=m(x-x₁)

Passes through (-12, 7)

Slope = -5/3

m = slope

Simply plug everything in :)

y - y₁ = m(x - x₁)

y - 7 = -5/3(x + 12)

Simplify.

y - 7 = -5/3x - 20

Add 7 to both sides.

y = -5/3x = -13

~Hope I helped~

Step-by-step explanation:

Answer: h = 7

Step-by-step explanation:

63 = 1/2 * 18 * h

63 = 9 * h

63 = 9h

*Divide 9 on both sides.

7 = h

Answer:

So the composite function that gives the area of a circle in terms of time is:

A(r(t)) = π(0.25+2t+4t²)

The revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016. 2. The revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.

A factor is a number that represents how two quantities are related to one another. It is frequently used to indicate how much one amount exceeds or falls short of another. For instance, if a business's revenue. On the other hand, a percentage is a technique to represent a portion or ratio of something as a fraction of 100. For instance, if a company made money.

The given revenue for the two years is $138200 and $164900.

The factor of the two revenue is:

factor = 164900 / 138200 = 1.193

Hence, the revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016.

percentage = (164900 / 138200) * 100% = 119.3%

Therefore, the revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.

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the measurement of the fourth angle of the quadrilateral is 95 degrees.

To find the measurement of the fourth angle of a quadrilateral when the measures of three angles are given, we can use the fact that the sum of the measures of the angles in a quadrilateral is 360 degrees.

Let's denote the measure of the fourth angle as x. Then we can write an equation:

80 + 120 + 65 + x = 360

Simplifying this equation, we get:

x = 360 - 80 - 120 - 65 = 95

Therefore, the measurement of the fourth angle of the quadrilateral is 95 degrees.

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The amount of money in the account after 17 years is approximately $49,222.26.

Investment is the act of allocating resources, such as money or time, with the expectation of generating a return or profit in the future. Investment can take many forms, such as investing in stocks, bonds, real estate, or businesses.

Investment is an important tool for individuals and businesses to build wealth and achieve financial goals. By investing in assets that appreciate in value or generate income, investors can increase their net worth and achieve long-term financial stability.

When making investment decisions, investors typically consider factors such as risk, return, liquidity, and diversification. Risk refers to the possibility of losing money, while return refers to the potential profit or income generated by the investment. Liquidity refers to how easily an investment can be converted into cash, while diversification refers to spreading investment across multiple assets to reduce risk.

Using the formula [tex]V= Pe^{rt}[/tex], where P = $34300, r = 0.02, and t = 17, we can find the value of the account after 17 years:

V = 34300 * [tex]e^{0.02*177[/tex]

V ≈ $49,222.26

Therefore, the amount of money in the account after 17 years is approximately $49,222.26.

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Hence, they are different because they drawn from the different scales values.

Data in math is a collection of facts and figures that can be in any form—numerical or non-numerical.

Numerical data is the one you can calculate, and it is always collected in number form, such as scores of students in class, wages of workers in an organization or height of players on a football team, etc.

As per the given graphs they are different because they drawn with the help of different scales.

Hence, they are different because they drawn from the different scales values.

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Answer:

Step-by-step explanation:

The perimeter is the distance around the edge of the shape.

    [tex]P=2+4+2+1+4+5=18cm[/tex]

About the equation [tex]7 * 3 = 21[/tex], the generalization we can make is that dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction.

We use generalizations to describe the pattern they see in the relationship of a specific group of numbers. It's a pattern that holds true every time.

In mathematics, generalization can be defined as a statement that is true for an entire class of objects, the process by which we obtain a general statement, or the method by which knowledge is transferred from one setting to another.

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The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week". This is because according to the table, the percentage of people who spent less than 1 hour watching TV is 50%, which means that half of the people surveyed watched less than 1 hour of TV each week.

Therefore, The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".

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Answer:

150.00

Step-by-step explanation:

a = 1/2bh

a = 1/2(2)(10)

a = 10 [tex]m^{2}[/tex]

10x15 = 150

Helping in the name of Jesus.

The expressions whose solutions are represented by the graph are:

A. 5 - X > 4

D. 6x - 7 > 5

The mathematical expressions, whose solutions are represented by the graph are those that fall within the shaded region of the graph. For instance, in the mathematical expression, 5 - x > 4, the shaded region points to 4 and values greater than it.

So, this expression satisfies the condition and can be described as a solution represented by the graph.

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Answer:

-349

Step-by-step explanation:

1)[-6-22]+[-321]

2)(-28)-321

3)-349

If x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.  the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.

To find the inverse function of f(x) = 5x - 3, we need to follow these steps:

Step 1: Replace f(x) with y:

y = 5x - 3

Step 2: Solve for x in terms of y:

y = 5x - 3

y + 3 = 5x

x = (y + 3)/5

Step 3: Replace x with f^(-1)(x) and y with x:

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

Step 4: Check if the inverse function is valid by verifying if f(f^(-1)(x)) = x and f^(-1)(f(x)) = x:

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

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

Since f(f^(-1)(x)) = x + 2 and f^(-1)(f(x)) = x/5, the inverse function is valid.

Therefore, the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.

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The complete question is:

if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.

What are the step to find the inverse to this function?