Find the volume to each equation
(Directions listed above questions)

Answer:

$20,907

Step-by-step explanation:

To calculate the amount that needs to be placed in an account now to have $22,500 in 3 years, you can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount

P = principal (the initial amount placed in the account)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = number of years

In this case, r = 0.048, n = 52 (since the interest is compounded weekly), and t = 3.

So, we have:

A = 22,500

P = ?

r = 0.048

n = 52

t = 3

Plugging these values into the formula:

22,500 = P * (1 + 0.048/52)^(52 * 3)

Solving for P, we get:

P = 22,500 / (1 + 0.048/52)^(52 * 3)

P = 22,500 / (1 + 0.048/52)^(156)

Rounding to the nearest dollar, we get:

P = $20,907

So, a person should place $20,907 in the account now, if the account pays 4.8% annual interest rate, compounded weekly, to have $22,500 in 3 years.

The volume of the rectangular prism based on the assumed values will be 640 inches³.

It should be noted that to find the volume of a rectangular prism, we have to multiply the length of the prism by the width of the prism by the height of the prism.

Let's assume that the base length of a rectangular prism is 8 inches, the base width is 5 inches and the height of the prism is 16 inches, as we want to find the volume of the rectangular prism.

The volume of the rectangular prism formula, the volume of rectangular prism = length × width × height of the prism

= 8 × 5 × 16

= 640 cubic inches.

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If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted

Let A, B and C be events relative to the sample space S.

The sample space is the set of all possible outcomes of the experiment.

The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.

Here we have to plot the each representing events using the Venn diagram representation

Part a

The event is (A ∩ B)'

Plot the Venn diagram

Part b

The event is (A ∪ B)'

Plot Venn diagram

Part c

The event is (A ∩ C) ∪ B

Plot the Venn diagram

Therefore, the Venn diagram of the each event has been plotted

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Answer:

Step-by-step explanation:13x6

Answer:

20√5x7

Step-by-step explanation:

The Possible effects of incentives for political leaders includes options 1, 2, 3, and 4. These options elaborate the incentives of political leaders.

Favor programs with immediate benefits: Political leaders may be incentivized to prioritize policies or programs that provide immediate benefits to their constituents in order to increase their popularity and chances of reelection.

Implement policies that favor a small, powerful group: Incentives for political leaders may also lead them to implement policies or regulations that favor a small, powerful group, such as major donors or influential interest groups, at the expense of the general public.

Provide policies whose costs outweigh the benefits: Political leaders may be incentivized to implement policies that provide short-term benefits but have long-term costs or consequences, such as a large budget deficit or environmental degradation.

Favor programs with immediate costs: Alternatively, incentives may lead political leaders to prioritize programs or policies with immediate costs, such as increased taxes or reduced spending, to address pressing issues and avoid long-term consequences.

Therefore, options 1, 2, 3, and 4 describe possible effects of incentives for political leaders.

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____The given question is incomplete, the complete question is given below:

Select all the items that describe possible effects of incentives for political leaders. 1.favor programs with immediate benefits 2.implement policies that favor a small, powerful group 3.provide policies whose costs outweigh the benefits 4.favor programs with immediate costs

Answer: A. Parallelogram

Step-by-step explanation:  A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length.

Answer:

see explanation

Step-by-step explanation:

(a)

there is a common difference between consecutive terms, that is

10 - 12 = 8 - 10 = 6 - 8 = 4 - 6 = - 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 12 and d = - 2 , then

[tex]a_{n}[/tex] = 12 - 2(n - 1) = 12 - 2n + 2 = 14 - 2n

(b)

similarly this is an arithmetic sequence

with a₁ = 25 and d = 20 - 25 = 15 - 20 = 10 - 15 = 5 - 10 = - 5

[tex]a_{n}[/tex] = 25 - 5(n - 1) = 25 - 5n + 5 = 30 - 5n

Answer:

Step-by-step explanation:

A because the gcf of 20 is 4 and the gcf of 4 is 4

Answer:

b

..,..............................................is my answer

Answer:

0.606 < p < 0.674

Step-by-step explanation:

[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.64\pm1.645\sqrt{\frac{0.64(1-0.64)}{540}}\\\\CI_{90\%}\approx0.64\pm0.034\\\\CI_{90\%}=\{0.606,0.674\}[/tex]

Thus, we are 90% confident that the true population proportion is between 0.606 and 0.674

A = {f, k, m, y}

B' = {k, x, y}

[tex]A \cup B' = \{f, ~k, ~m, ~y, ~x\}[/tex]

(every element from A and any other element that B' has that A didn't)

A' = {q, x}

B' = {k, x, y}

[tex]A \cap B' = \{x\}[/tex]

(x is the only element that both sets have)

Two pairs of separate sides are parallel in a quadrilateral with a single arrow once per pair of opposite sides.

A quadrilateral has four straight sides and is a two-dimensional form. Parallelograms, isosceles triangles, rectangles, kites, rectangles, and rhombuses are a few examples of quadrilaterals.

Option (c) illustrates a trapezoid in which one set of opposing sides has arrows indicating how they are parallel to one another. Alternative (d) has both couples of opposing sides indicated with arrows, indicating that all side are parallel, while options (a) and (b) don't even have any linear opposite sides.

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Answer:(A=πr2).

Step-by-step explanation:The cubic feet, or volume, of a cylindrical log is given by the volume of a cylinder V=πhr2. A log with radius of 2 feet and height of 10 feet would have a volume of about 125.66 cubic feet (or ft3). The volume can also be thought of as the area of the base times height with the base area being the area of a circle (A=πr2).

The number of ways for the child to select 3 treats is given as follows:

455 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The order in which the treats are chosen is not relevant, hence the combination formula is used to solve this question.

Three treats are chosen from a set of 15, hence the number of ways is given as follows:

C(15,3) = 15!/(3! x 12!) = 455 ways.

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It's important to work through the problems yourself to improve your understanding and problem-solving skills.

For the unit 3 homework on parallel and perpendicular lines, you should have learned about the slope of lines, how to find the slope of a line given two points, and the relationship between parallel and perpendicular lines.

To find the slope of a line given two points, you can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

To determine if two lines are parallel, you can compare their slopes. Parallel lines have the same slope.

To determine if two lines are perpendicular, you can use the fact that the product of their slopes is -1. That is, if m1 and m2 are the slopes of two lines, and m1 * m2 = -1, then the lines are perpendicular.

It's important to practice working through problems using these concepts and formulas to develop your skills and understanding. Additionally, you can seek assistance from your teacher or tutor if you have specific questions or concerns.

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The common difference of the given arithmetic sequence is 8.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given arithmetic sequence is -1, 7, 15,....

Common difference = Second term - First term

= 7-(-1)

= 7+1=8

Common difference = Third term - Second term

= 15-7

= 8

Therefore, the common difference is 8.

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The solution is, the common differences are -3, -20, -10, -2, 5.

In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.

here, we have,

So we just need to take different pairs of consecutive terms and see if their difference is always the same:

1) The differences are:

32 - 35 = -3

29 - 32 = -3

26 - 29 = -3

So yes, this is an arithmetic sequence and the common difference is -3

2) The differences are:

-23 - (-3) = -20

-43 - (-23) = -20

-63 - (-43) = -20

This is an arithmetic sequence, and the common difference is -20

3) The differences are:

-64 -(-34) = -30

-94 -(-64) = -30

-124 -(-94) = -30

This is an arithmetic sequence and the common difference is -30

4) The differences are:

-40 -(-30) = -10

-50 - (-40) = -10

-60 - (-50) = -10

This is an arithmetic sequence and the common difference is -10

5) The differences are:

-9 - (-7) = -2

-11 - (-9) = -2

-13 - (-11) = -2

This is an arithmetic sequence, and the common difference is -2

6) The differences are:

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

This is an arithmetic sequence, and the common difference is 5.

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Answer:

Step-by-step explanation:

The two numbers are 42 and 49.

Let us suppose the numbers are x and y.

From the above question,

=> x + y = 91 ------(1)

Also,

=> x:y = 6:7

If we express y in terms of x,

Then, x/y = 6/7

It can also be written as,

=> y = 7x/6 ------(2)

On substitution of value from (2) into (1),

We get,

=> x + 7x/6 = 91

=> 13x/6 = 91

=> x = 6*7

=> x = 42

Now, Substituting the value of x in (1),

We get,

=> 42 + y = 91

=> y = 91 - 42

=> y = 49

Therefore, The values of the two numbers are 42 and 49.

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Answer:

Step-by-step explanation:

To find the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop, we need to find the lower and upper bounds of the interval that contains the middle 94% of the data. This can be done using the standard normal distribution and the z-score.

First, we'll find the z-score that corresponds to the lower bound. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the lower bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 3%:

z = (x - 6.48) / 0.06

z = -2.33

Next, we'll use the z-score to find the value of x (the lower bound). We'll use the standard normal distribution table to look up the value of -2.33 and find that it corresponds to a cumulative probability of 0.01. So, the lower bound is such that 1% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + (-2.33) * 0.06

x = 6.32

So, the lower bound of the interval that contains the middle 94% of the data is 6.32 millimeters. This is the diameter that separates the bottom 3% of the bolts from the rest.

Next, we'll find the upper bound in a similar way. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the upper bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 97%:

z = (x - 6.48) / 0.06

z = 2.33

Using the standard normal distribution table, we find that the value of 2.33 corresponds to a cumulative probability of 0.99. So, the upper bound is such that 99% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + 2.33 * 0.06

x = 6.64

So, the upper bound of the interval that contains the middle 94% of the data is 6.64 millimeters. This is the diameter that separates the top 3% of the bolts from the rest.

Therefore, the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop are 6.32 millimeters and 6.64 millimeters, rounded to the nearest hundredth.

7.21 × 10⁻⁷

Step-by-step explanation:

(6.94 × 10⁻⁷) + (2.7 × 10⁻⁸) = 7.21 × 10⁻⁷

56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

What is Total price?

In order to calculate the total price of something is by using this formula. Purchase Price = Cost Price + Margin.

To find out how much gas will be needed to make 27 brackets, we need to multiply the amount of gas required for making one bracket by the number of brackets to be made.

So, the total amount of gas needed to make 27 brackets would be:

2.1 cu ft * 27 = 56.7 cu ft

Therefore, 56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

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Answer:

both sides are equal to: [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Trigonometric functions are defined as the ratios between sides based on some angle. There's three main trig functions you want to remember which are defined as:

[tex]sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\\\\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex]

and then there are three other trig functions, which are simply the reciprocals:

[tex]csc(\theta)= \frac{\text{hypotenuse}}{\text{opposite}}=\frac{1}{sin(\theta)}\\\\sec(\theta) = \frac{\text{hypotenuse}}{\text{adjacent}}=\frac{1}{cos(\theta)}\\\\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}=\frac{1}{tan(\theta)}[/tex]

Now in our case we have the angle of 45 degrees and we have the hypotenuse with length 16, and we want to either solve for the opposite (x) or adjacent side (y)

Let's solve for the adjacent side, in which case we want a trig function defined using the hypotenuse and adjacent side, which is our cosine function.

[tex]cos(45)=\frac{y}{16}\implies cos(45)*16=y[/tex] and from here we can use a calculator or the unit circle which gives us an exact value. Using the unit circle, we can determine that: [tex]cos(45)=\frac{\sqrt{2}}{2}[/tex] and plugging that into our equation we get: [tex]y=\frac{\sqrt{2}}{2}*16=8\sqrt{2}[/tex] and we can use a calculator to approximate this: 11.313

Now we can also use the trig functions to find "x", which is the opposite side. In this case we want to use a trig function which is defined using the opposite and hypotenuse side, which is our sine function: [tex]sin(45)=\frac{x}{16}\implies sin(45)*16=x[/tex] and the cool thing about this, is that sin(45) and cos(45) are actually equal, so our "x" and "y' side are exactly equal: [tex]x=8\sqrt{2}[/tex]

We can verify this using the Pythagorean Theorem: [tex](8\sqrt{2})^2+(8\sqrt{2})^2=16^2\\\\(8^2*\sqrt{2}^2)+(8^2+\sqrt{2}^2)=256\\\\(64*2)+(64*2)=256\\\\128+128=256\\\\256=256[/tex]

The angle of the base and the ladder is 69. 34 degrees

Note that the six trigonometric identities are;

From the information given, we have that;

Hypotenuse = 17 meters

Adjacent = 6 meters

The identity to use is the cosine

cos θ = adjacent/hypotenuse

Substitute the  values

cos θ = 6/17

cos θ =,0. 3529

Take inverse of cos

θ = 69. 34 degrees

Hence, the value is 69. 34 degrees

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Answer:

Step-by-step explanation:

we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base  (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.

6 * 8 + 4 * 5 =                     remember PEMDAS

48 + 20 =

68 m²

Based on the information, we can infer that the graph would be a curve like the one shown in the attached image.

First of all, to graph the information about the body temperature of children, we must consult on the internet or other sources what is the body temperature of children. Below is the information:

According to the above, the graph should present a higher frequency at a temperature of 98.6, so the highest point on the graph would be at that temperature. On the other hand, the other temperatures would decrease because they are less frequent among children.

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The set of ordered pairs of option A does not represent a function. The solution has been obtained using the properties of function.

What is a function?

A relationship between a number of inputs and one output per input is referred to as a function. Typically, a function is denoted by the notation f(x), where x is the input. Typically, a function is represented as y = f(x).

We know that for one input, a function can have only one output.

But, in option A, for the same input value 2, there are two output values 2 and 7. Whereas in other options, each input has only one output.

Hence, the set of ordered pairs of option A does not represent a function.

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Answer:

s = 13.6

m∠T = 35.7°

m∠U = 61.3°

Step-by-step explanation:

• Solving for side s:

To find the length of side s, we have to use the cosine rule:

[tex]\boxed{a^2 = b^2 + c^2 - 2bc \ cosA}[/tex],

where:

In this case, the unknown side is s, and the sides adjacent to it have lengths of 8 and 2. The angle opposite to s is ∠S = 83°. Therefore,

[tex]s^2 = 8^2 + 12^2 -2(8)(12) \cdot cos(83^{\circ})[/tex]

⇒ [tex]s = \sqrt{8^2 + 12^2 -2(8)(12)\cdot cos(83^{\circ})}[/tex]

⇒ [tex]s = \bf 13.6[/tex]

• Solving for m∠T:

In order to find m∠T, we can use the sine rule:

[tex]\boxed{\frac{sinA}{a}= \frac{sinB}{b} =\frac{sinC}{c}}[/tex],

which means that the ratios of the sines of angles and their opposite sides are equal for a triangle.

The side opposite to ∠T is US = 8. Therefore:

[tex]{\frac{sinT}{8} = \frac{sin(83^{\circ})}{13.6}}[/tex]

⇒ [tex]sinT= \frac{sin(83^{\circ})}{13.6} \times 8[/tex]

⇒ [tex]T = sin^{-1}( \frac{sin(83^{\circ})}{13.6} \times 8)[/tex]

⇒ [tex]T = \bf 35.7^{\circ}[/tex]

• Solving for m∠U:

Now that we know the values of two angles of the triangle, we can calculate the third angle using the fact that the angles in a triangle add up to 180°:

∠U + ∠S ∠T = 180°

⇒ ∠U + 83° + 35.7° = 180°

⇒ ∠U = 180° - 83° - 35.7°

⇒ ∠U = 61.3°

7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given inequality is:

x + 8 > 15

Subtracting 8 on both sides of the equation:

x + 8 - 8 > 15 - 8

x > 7

Here, 7 is not included and hence it is depicted using an open dot.

Hence, option B is the correct answer.

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Answer:

No

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

x + 32 + 4x + 20 + 4x + 20 = 180

9x + 72 = 180  ( subtract 72 from both sides )

9x = 108 ( divide both sides by 9 )

x = 12

then the 3 angles are

x + 32 = 12 + 32 = 44°

4x + 20 = 4(12) + 20 = 48 + 20 = 68°

4x + 20 = 68°

an obtuse angle is greater than 90°

none of the 3 angles in the triangle are obtuse

Answer:

No

Step-by-step explanation:

All angles of a triangle add up to 180°.

4x + 20 + 4x + 20 + x + 32 = 180

1. Simplify

9x + 72 = 180

2. Subtract 72 from both sides.

9x = 108

3. Divide both sides by 9.

x = 12

Replace x by 12 in each angle.

-  12 + 32 = 44°

-  4(12) + 20 = 68°

-  4(12) + 20 = 68°

All of the angles are less than 90°, so they aren't obtuse.