A business sets up a sinking fund so they will have a $61,000.00 to pay for a replacement piece of equipment in 9 years when the current equipment will be sold for scrap. If they make deposits at the end of every 2 months for 9 years in the investment that pays 5.9% compounded every 2 months, what size should each payment be?

The every 2 months payments are $
.

Answers

Answer 1

Using compound interest, each payment should be $948.86, rounded to two decimal places.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

[tex]A = P (1 + r/4)^t[/tex]

To determine the size of each payment that needs to be made at the end of every 2 months, we can use the formula for the future value of an annuity:

[tex]FV = Pmt x [(1 + r)^{n - 1}] / r[/tex]

When we enter these values into the formula, we obtain:

In this instance, we know that the sinking fund's future value should be $61,000, the interest rate each 2-month period is 5.9%/6 = 0.983%, and there are a total of 54 periods (9 years x 12 months/year / 2 months/period = 54 periods) in the sinking fund's life.

[tex]$61,000 = Pmt x [(1 + 0.00983)^{54 - 1}] / 0.00983[/tex]

Solving for Pmt, we get:

[tex]Pmt = $61,000 x 0.00983 / [(1 + 0.00983)^{54 - 1}][/tex]

= $61,000 x 0.00983 / 0.6346

= $948.86

Therefore, each payment should be $948.86, rounded to two decimal places.

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Related Questions

Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.

Answers

The answer of the given question based on to determine that the quadrilateral must be a parallelogram the answer is given below.

What is Parallelogram?

A parallelogram is  type of quadrilateral ( polygon with four sides) with two pairs of parallel sides. This means that the opposite sides of parallelogram are parallel and congruent.

Yes, we can determine that the given quadrilateral is a parallelogram based on the information given.

We are told that opposite sides of the quadrilateral are congruent (that is, AB is congruent to CD, and BC is congruent to DA), which is a property of parallelograms. We are also told that opposite angles of the quadrilateral are congruent (that is, angle A is congruent to angle C, and angle B is congruent to angle D), which is another property of parallelograms.

Therefore, based on these two pieces of information, we can conclude that the quadrilateral must be a parallelogram. This is because these properties are unique to parallelograms and do not apply to other types of quadrilaterals, such as rectangles, rhombuses, or trapezoids.

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Lori is 8 years old. In 5 ​years, her cousin Philip will be twice as old as Lori will be. Write the ratio of​ Philip's age now to​ Lori's age now.

Answers

Answer: 13:26

Step-by-step explanation:

8 + 5 = 13. Philip will be twice as old as Lori will be.

13 x 2 = 26

So, the ratio will be 13:26

Hope this helps!


13:26 is the ratio of Phillips age now to Loris age now

The faunal exam scores in a statistics class were normally distributed with a mean of 63 And a standard deviation of 5 . Find the probability that a randomly selected students scored of then 65 on the exam

Answers

Probability that a randomly selected students scored of then 65 on the  faunal exam is 65.54%.

Explain about the normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically towards either the extreme. The distribution's mean is another name for the center of the range.

mean μ = 63

standard deviation  σ = 5

x = 65

Find z-score:

z = (x - μ)/σ

z = (65 - 63)/5

z = 2/5

z = 0.4

Using z score table:

Probability that a randomly selected students scored of then 65 on the  faunal exam is :

P(x = 65) = P(z = 0.4)

P(x = 65) = 0.6554

Thus, Probability that a randomly selected students scored of then 65 on the  faunal exam is 65.54%.

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22. A small coffee company claims to include 11 ounces of coffee in every bag of ground coffee it produces. Out of a random sample of 250 bags, 50 of the bags contain only 10.9 ounces. Which inferences from the results of the random sample are reasonable? Choose all that are correct.

A. It can be inferred that 5% of the bags from a second random sample will contain more than 11 ounces.

B. It is likely that a second random sample of bags will show a much lower percentage of bags with only 10.9 ounces.

C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.

D. It is likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

E. It is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

Answers

From the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

What is meant by percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

Given,

Amount of coffee in A bag of ground coffee = 11 ounces

Number of bags = 250 bags

Number of bags which contain 10.9 ounces of coffee = 50

The percentage of bags which contain 10.9 ounces of coffee

= (50/250) × 100 = 20%

This percentage shows that the company's claim is not true because they claim every bag contains 11 ounces of coffee.

Therefore from the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

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fx=x square -4 find codomain​

Answers

So, the codomain of the function is the set of all real numbers: codomain = R.

What is function?

In mathematics, a function is a rule that maps a set of inputs (domain) to a set of outputs (codomain) in such a way that each input is associated with exactly one output. A function can be represented using various notations, including equations, graphs, and tables. A function can be thought of as a machine that takes an input and produces an output. The input is usually represented by the variable x, and the output is represented by the variable y. The relationship between the input and output is defined by the function rule. Functions are used in many areas of mathematics, science, and engineering to describe various phenomena, such as motion, growth, and decay. They are also used to model and analyze data in statistics and economics, and to design and control systems in engineering and computer science.

Here,

The codomain is the set of all possible output values of a function.

For the given function, f(x) = x² - 4, we can see that the output values are obtained by squaring the input value, subtracting 4, and therefore can be any real number.

To find the codomain of the function f(x) = x² - 4, we need to determine the range of the function, which is the set of all possible output values.

Let y = f(x) = x² - 4.

To find the range, we need to solve for y:

y = x² - 4

y + 4 = x²

Taking the square root of both sides, we get:

x = ±√(y + 4)

Therefore, the range of the function is the set of all real numbers greater than or equal to -4, since y + 4 must be non-negative for real values of y:

range = {y | y + 4 ≥ 0} = {y | y ≥ -4}

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Domain
V
m
d
1 of 5 (1 point) | Question Attempt: 1 of 1
Relation 1
t
Function
O Not a function
O Function
Relation 3
Domain Range
d
pencil
sky
sky
sky
Not function.
b
V
N
Range
Domain
Z
X
y
k
O Function
O Not a function
Relation 2
Relation 4
Domain Range
3
-1
-6
-1
-5
4
7
-9
-1
2
Range help please ASAP

Answers

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Write the equation of the conic section shown below.

Answers

The equation of the conic section shown below is x² + y² + 10x + 2y - 20 = 0

Describe Circle?

A circle is a two-dimensional geometric shape that consists of a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius.

A circle can be defined by its center point and radius or by its circumference, which is the distance around the perimeter of the circle. The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14.

The center of the circle is (-5,-1) and its radius is the distance from the center to any point on the circle. Using the distance formula, we can find the radius:

r = √((0 - (-1))² + (-10 - (-5))²) = √(1 + 25) = √(26)

So, the equation of the circle in standard form is:

(x + 5)² + (y + 1)² = 26

Alternatively, in general form, it can be written as:

x² + y² + 10x + 2y - 20 = 0

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The graph shows the cube root parent function

Answers

The true statement is A, for x < 0 the function is negative.

Which statements describe the graph of the function?

On the image we can see the graph of the parent cube root function.

y = ∛x

And we want to see which statements are true. Remember that the function is negative if the graph is below the x-axis and positive if it is above, using that we can analyze the graph.

First, notice that for x < 0 the graph is below the x-axis, then the first statement is true.

When x < 0, the function is negative.

So the only correct option is A.

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The guitar Francisca wants is on sale at two different stores. The original price of the guitar at both stores is $160. At which store is the guitar less expensive? How much less expensive?​

Answers

Answer:

The guitar Francisca wants is on sale at two different stores. The original price of the guitar at both stores is $160. At which store is the guitar less expensive? How much less expensive?

Suppose that you put 2 dimes, 2 nickels, and 1 penny into a bag. a coin will be drawn from the bag and replaced 175 times. what is a reasonable prediction for the number of times a dime will be drawn?

Answers

A reasonable prediction for the number of times a dime will be drawn is approximately 90.

What is probability?

Probability is the measure of how likely it is that an event will happen. The event is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. Probability is used in many areas, such as mathematics, science, engineering, and finance. For example, in mathematics, probability is used to determine the likelihood of an event occurring or a certain outcome occurring.

When 2 dimes, 2 nickels, and 1 penny are placed into a bag, there are 5 total coins. Therefore, the probability of drawing a dime is 2/5. When a coin is drawn and replaced 175 times, the probability of drawing a dime will remain the same (2/5) and the expected value of drawing a dime is 175*2/5 = 90. Since this is a reasonable prediction, it is a valid solution.

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3. Sergio's savings account statement showed a previous balance of $234.95 and interest of $1.06. The statement also showed deposits of $123.42 and $50.66 and withdrawals of $323.09. What is his new balance?

Answers

Sergio's new balance is $87

How to calculate the new balance?

Sergio's savings showed a previous balance of $234.95 and interest of $1.06

The statement also showed deposits of $123.42 and $50.66 and withdrawals of $323.09

The new balance can be calculated by adding the previous balance, interest, deposits in the statement and then subtract the sum total from the withdrawal amount

234.95 + 1.06 + 123.42 + 50.66 - 323.09

= 410.09 - 323.09

= 87

Hence Sergio's new balance after adding the deposits, previous balance then subtracting from the withdrawal is $87

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Find each length for a 30°−60°−90°
triangle.

Find the shorter leg and the hypotenuse if the longer leg is 9 inches

Shorter leg = ________ √ _________ in.

Hypotenuse = ________√ ________in.

Find the longer leg and the hypotenuse if the shorter leg is 4 cm.

Longer leg = _______√ _________cm.

Hypotenuse = __________cm.

(40 points)

Answers

In accordance with the provided assertion, (A) the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches (B) the longer leg is 4√3 cm and the hypotenuse is 8 cm.

What do maths lengths mean?

The measurement or size of a thing end to end is referred to as its length. To put it another way, it is the bigger of the higher two or three dimensions of a geometric form or object.

For a 30°−60°−90° triangle, the ratios of the side lengths are:

Shorter leg: opposite 30° angle = xLonger leg: opposite 60° angle = x√3Hypotenuse: opposite 90° angle = 2x

Using these ratios, we can solve the problems:

If the longer leg is 9 inches, we have:

Longer leg = x√3 = 9

x = 9/√3 = 3√3

Shorter leg = x = 3√3

Hypotenuse = 2x = 2(3√3) = 6√3

Therefore, the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches.

    2. If the shorter leg is 4 cm, we have:

Shorter leg = x = 4

Longer leg = x√3 = 4√3

Hypotenuse = 2x = 2(4) = 8

Therefore, the longer leg is 4√3 cm and the hypotenuse is 8 cm.

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A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 90 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 20 cm deep?

Answers

The speed at which the water level is rising when the water is 20 cm deep is 0.04285 m/min

How to solve this

Using differentiation:

dV/dt = 0.3

find dh/dt

the width of the water level is dependent on the height

at height 0, width of 20

height 60, width of 80

when height increases by 1, width increases by 1

dh/dt = dw/dt

V = 0.5*(0.2 + (0.2+h))*h*10

V = 5*(0.4 + h)*h

V = 5h^2 + 2h

dV/dt = 5*2h(dh/dt) + 2(dh/dt)

when h = 0.5

0.1 = 5*2*0.5*(dh/dt) + 2(dh/dt)

0.1 = 5(dh/dt) + 2(dh/dt)

7(dh/dt) = 0.3

dh/dt = 0.04285 m/min

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Question 7
Type in the correct coordinates for the image after each reflection. WHEN YOU TYPE IT
IN... USE THE APPROPRIATE FORM. NO SPACES BETWEEN SYMBOLS AND NUMBERS.
USE PARENTHESIS.
Example: (2,-3)
Preimage
(1,5)
(-4,7)
(6,-2)
(-3,-8)
Reflect x-axis
(1,-5)
(4,-7)
(6,2)
(-3,8)
Reflect y-axis
(-1,5)
(4,7)
(-6,-2)
(3,-8)
Reflect yax
(5,1)
(7,-4)
(-2,6)
Iz pis
(-8,-3)

Answers

The coordinates of the image of the points following the reflection transformation can be presented as follows;

Preimage   [tex]{}[/tex] Reflect x-axis    Reflect y-axis    Reflect y = x

(1, 5)  [tex]{}[/tex]           (1, -5)                   (-1, 5)                 (5, 1)

(-4, 7) [tex]{}[/tex]          (-4, -7)                 (4, -7)                  (7, -4)

(6, -2)[tex]{}[/tex]           (6, 2)                   (-6, 2)                 (-2, 6)

(-3, -8) [tex]{}[/tex]         (-3, 8)                  (3, -8)                 (-8, -3)

What is a reflection transformation?

A reflection transformation is a transformation in which a preimage point is flipped across a line of reflection.

The coordinates of the image of the point (x, y), following a reflection across the x-axis is the point (x, -y)

The coordinates of the image of the point (x, y) following a reflection across the y-axis is the point (-x, y)

The coordinates of the image of the point (x, y) following a reflection across the line, y = x is the point (y, x)

The coordinates of the images of the specified points after the specified reflections are therefore;

The values in the table of the coordinates of the Preimages and images can therefore, be obtained as follows;

Preimage point (1, 5);

The image after a reflection across the x-axis is therefore;

(1, 5) [tex]\underrightarrow{R_{x-axis}}[/tex] (1, -5)

The image after a reflection across the y-axis, therefore;

(1, 5) [tex]\underrightarrow{R_{y-axis}}[/tex] (-1, 5)

The image after a reflection across the line y = x is therefore;

(1, 5) [tex]\underrightarrow{R_{y = x}}[/tex] (5, 1)

Preimage point (-4, 7);

The image after a reflection across the x-axis is therefore;

(-4, 7) [tex]\underrightarrow{R_{x-axis}}[/tex] (-4, -7)

The image after a reflection across the y-axis, therefore;

(-4, 7) [tex]\underrightarrow{R_{y-axis}}[/tex] (4, 7)

The image after a reflection across the line y = x is therefore;

(-4, 7) [tex]\underrightarrow{R_{y = x}}[/tex] (7, -4)

Preimage point (6, -2);

The image after a reflection across the x-axis is therefore;

(6, -2 [tex]\underrightarrow{R_{x-axis}}[/tex] (6, 2)

The image after a reflection across the y-axis, therefore;

(6, -2) [tex]\underrightarrow{R_{y-axis}}[/tex] (-6, -2)

The image after a reflection across the line y = x is therefore;

(6, -2) [tex]\underrightarrow{R_{y = x}}[/tex] (-2, 6)

Preimage point (-3, -8);

The image after a reflection across the x-axis is therefore;

(-3, -8) [tex]\underrightarrow{R_{x-axis}}[/tex] (-3, 8)

The image after a reflection across the y-axis, therefore;

(-3, -8) [tex]\underrightarrow{R_{y-axis}}[/tex] (3, -8)

The image after a reflection across the line y = x is therefore;

(-3, -8) [tex]\underrightarrow{R_{y = x}}[/tex] (-8, -3)

Please find above the completed table including the coordinates of the images following the reflection across the x, y-axis and the line y = x

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3.
A bag contains:
• 5 red marbles
.
6 blue marbles
3 green marbles

4 black marbles
2 yellow marbles
A marble will be drawn from the bag and replaced. If the experiment is repeated 100
times, what is a reasonable prediction for the number of times a green or black
marble will be drawn?

Answers

Answer:

300

Step-by-step explanation:

because you do it for 1 hundred years you multiply it by 100 and it would be 3x100=300

30. When the polynomial f(x) = (p-1)x³ + px² + qx +r, where p, q and r are constants, is divided by (x + 2) and (x - 1), the remainders are - 5 and 4 respectively. If (x + 1) is a factor of f(x), find the values of p, q and r. Hence, factorize f(x) completely.​

Answers

Answer:

Step-by-step explanation:

Using the remainder theorem we get:

[tex]f(-2)=-5[/tex],  [tex]f(1)=4[/tex], and [tex]f(-1)=0[/tex]

So we get

[tex]f(-2)=(-8)(p-1)+4p-2q+r=-5[/tex]

                 [tex]-8p+8+4p-2q+r=-5[/tex]

                              [tex]-4p-2q+r=-13[/tex]  [tex](a)[/tex]

[tex]f(1)=(p-1)+p+q+r=4[/tex]

                       [tex]2p+q+r=5[/tex]               [tex](b)[/tex]

[tex]f(-1)=-(p-1)+p-q+r=0[/tex]

                                 [tex]-q+r=-1[/tex]    [tex](c)[/tex]

We need to solve (a), (b) and (c) simultaneously to find p,q, and r.

from [tex](c)[/tex]  [tex]r=q-1[/tex]. Sub this into (a) and (b):

[tex]-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12[/tex]    [tex](d)[/tex]

      [tex]2p+q+(q-1)=5 \rightarrow q=3-p[/tex]              [tex](e)[/tex]

Sub (e) into (d) we get

[tex]-4p-(3-p)=-12 \rightarrow p=3[/tex]

Sub [tex]p=3[/tex] into [tex](e) \rightarrow q=0[/tex]

Sub  [tex]p=3,q=0[/tex] into [tex](c) \rightarrow r=-1[/tex]

SOLUTION: [tex]p=3,q=0,r=-1[/tex]    

So [tex]f(x)=2x^3+3x^2-1[/tex]

by dividing (x+1) into f(x) we get  (I am not showing working for this division)

[tex]f(x)=(x+1)(2x^2+x-1)[/tex]

[tex]\rightarrow f(x)=(x+1)(2x-1)(x+1)[/tex]

In triangle LMN, m = 4.1 inches, I = 3.9 inches and to the nearest 10th of a degree.

Answers

The possible value of angle M is 30.6°.

What is Law of Sines?

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given is a triangle LMN.

Given,  m = 4.1 inches, I = 3.9 inches

∠L = 151°. We have to find ∠M.

Using law of sines,

l / sin L = m / sin M

3.9 / sin (151°) = 4.1 / sin (M)

sin (M) = [4.1 × sin (151°)] / 3.9

           = 0.5097

M = sin⁻¹ (0.5097) = 30.64° ≈ 30.6°

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The question is incomplete. The complete question is,

In triangle LMN, m = 4.1 inches, I = 3.9 inches and ∠L = 151°. Find all possible values of ∠M to the nearest 10th of a degree.

A team with 8 games out of 12 games played. What is the reduced ratio of the following:
__________ 1. Win to games played?
__________ 2. Win to losses?
__________ 3. Loss to games played?

Answers

Therefore , the solution of the given problem of ratio comes out to be 1:3 is the decreased loss-to-games-played ratio.

Explain ratio.

A collection of integers "a" as well as "b" that seem to be equal can be defined using the straightforward fraction calculation "a / b," at which "b" may be larger than zero. A ratio is created by combining two ratios. The ration would be 1:1 if there were just one male and three women. There are 1/4 guys and 3/4 women in the group. Portions can be a divide between different things, a number, or a specific portion of the volume of a component.

Here,

In events played, win:

Out of the 12 games contested, 8 were victories. We can split the numerator and denominator by 4 to decrease the ratio:

=> 8/12 = 2/3

The decreased win-to-games-played ratio is 2:3.

win to loss ratio

If a squad has 8 victories, they have 4 defeats (since they have played 12 games in total). As a result, the winning/losing split is as follows:

8:4, which is further diminished by multiplying the number and denominator by 4:

=> 2:1

The decreased win-to-loss ratio is 2:1.

Played events lost:

If a squad has 4 losses and has played a total of 12 games, the ratio of losses to games played is as follows:

=> 4/12 = 1/3

=> 1:3 is the decreased loss-to-games-played ratio.

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At a restaurant any slice of pizza cost $250 the restaurant is serving pepperoni and sausage pizza which expression represents the cost of x number of pepperoni slices and wine number of sausage slices of pizza

Answers

Assuming that a slice of pizza costs the same regardless of its topping, the expression that represents the cost of x number of pepperoni slices and y number of sausage slices of pizza would be:

$250 * (x + y)

Here, (x + y) represents the total number of slices of pizza ordered, and multiplying by $250 gives the total cost of the order in dollars.

find the value of each variable using sine and cosine.

Answers

Answer:

p ≈ 11.3 , q ≈ 4.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos20° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{p}{12}[/tex] ( multiply both sides by 12 )

12 × cos20° = p , then

p ≈ 11.3 ( to 1 decimal place )

using the sine ratio in the right triangle

sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{12}[/tex] ( multiply both sides by 12 )

12 × sin20° = q , then

q ≈ 4.1 ( to 1 decimal place )

Find the future value (in dollars) of a 2-year investment of $6,525 into a simple interest rate account that has an annual simple interest rate of 3.7%.

Answers

$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

The formula to calculate the future value of an investment with simple interest is:

FV = P(1 + rt)

where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.

P = $6,525

r = 0.037

t = 2 years

Plugging these values into the formula, we get:

FV = $6,525(1 + 0.037×2)

FV = $6,525(1.074)

FV = $7,008.

Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.

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Find the value of x.

Answers

Answer: x = 60 degrees

Step-by-step explanation:

As we see, there is a 90 degree angle formed the top left corner. You divided it by 2 and it is formed by both triangles and u get 45 degrees.

Now, according to angle sum property:

angle A + Angle B + Angle C = 180 degrees

therefore, 75 + 45 + angle c = 180

and by linear equation , angle c = 180 - [75 + 45]

                                                       =  180 -120

                                                       = 60

therefore, x = 60

Answer:

60 degrees

Step-by-step explanation:

A right triangle is 180 degrees. 60+75+a= 180degrees. It shows a right angle, with a line right at the middle. half of 90 is 45, so put that in the equation and you get 60+75+45=180 degrees. to solve for ? you want to take 45 + 75 + ? = 180 degrees 45 plus 74 is 135 so take 180-135 is 60. the ? will be 60 degrees.

I hope this helps : )

Question 3
Joanne's Printing Services charges $49.95 to print 200 business cards. Each additional set of
100 cards costs $14. This is represented in the piecewise function below, where x is 1 set of
100 cards:
r(x) =
5 pts
29.95
when x is an integer and x < 2
29.95 + 14(x - 2) when x is an integer and x > 2
Determine the cost of 6 sets of cards.

Answers

The cost of 6 sets of cards is $105.95

How to get the cost of 6 sets of cards?

Each set has 100 cards, then in 6 sets there are 6*100 = 600 cards.

We know that the first 200 cards costs $49.95, and from then, the cost per set is $14.

So we have a piecewise function which can be written as:

y = $49.95   if x ≤ 200

y = $49.95 + $14*(x - 200) if x > 200.

Then we have 200 cards and 4 sets, then the total cost will be:

$49.95 + 4*$14 = $105.95

That is the cost of the 6 sets.

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bill is in the process of installing an above ground swimming pool in his yard. if the diameter of the pool is 35 feet what is the approximate circumference of the pool\

Answers

The formula to find the circumference of a circle is:

Circumference = 2 x π x radius

where π (pi) is a mathematical constant approximately equal to 3.14, and the radius is half of the diameter.

If the diameter of the pool is 35 feet, then the radius is 35 / 2 = 17.5 feet.

Therefore, the circumference of the pool is:

Circumference = 2 x π x radius
Circumference = 2 x 3.14 x 17.5
Circumference ≈ 109.9 feet

So, the approximate circumference of the pool is 109.9 feet.

PLEASE HELP, WILL GIVE BRAINLIEST!!!!

see image bellow

Answers

Answer:

onomatopoeia

Step-by-step explanation:

onomatopoeia are words that are sounds

Answer:

Onomatopoeia

Step-by-step explanation:

Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds. (For example, they should do their first squat 30 seconds into the drill.) How many times during the 200 second drill should the little monsters do an overhead press and a squat at the same instant?

Answers

The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

What are mathematical operations?

The term "operation" in mathematics refers to the process of computing a value utilising operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds.

The prime factorization of 12 is 2² x 3, and the prime factorization of 30 is 2 x 3 x 5.

To find the smallest common multiple, we need to take the highest power of each prime factor that appears in either factorization. Thus, the smallest common multiple of 12 and 30 are:

2² x 3 x 5 = 60

This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.

To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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ALGEBRA 1 HW!! 35 POINTS!!I WILL GIVE BRAINLYEST FOR ANSWERS​​

Answers

The value of the ratio g(24)/g(21) is 729, and other solutions are shown below

The pattern of the infinite sequence

The domain and the range of h(n)

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

Domain: All set of whole numbersRange: All set of whole numbers

The values of h(5) and h(11)

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

The explicit function of h(n)

In (b), we have

h(n) = n

The values of s(4) and s(7)

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

s(n) = 2n

The table of the infinite sequence

Complete the table for f(5) and f(7)

From the table, we can see that

As n increases, the value of f(n) is divided by 2 to get the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

The domain of f(n)

The possible values of n are real numbers

So, we have

Domain: All set of real numbers

The observation of the function

Above, we have

As n increases, the value of f(n) is divided by 2 to get the next term

This means that

As n gets larger and larger, the value of f(n) get halved

A doubling sequence g(n)

The value of g(4)

From the question, we have

First term, a = 9

Common ratio, r = 2

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

Completing the statements

Based on the function definitions, the statements when completed are

g(n) = g(n - 1) * 2g(n) = g(n - 2) * 4g(n) = g(n - 3) * 8

The value of the ratio

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

Divide the equations

g(24) = 2(9)^23

-------     ----------

g(21) = 2(9)^20

Evaluate

g(24)/g(21) = 729

Hence, the value of the ratio is 729

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6.)Walmart is running a sale on baseball hats. Sergio bought one on sale for 25% off its regular price of $45. If sales tax is 10.25%, what is the total cost of the hat?

Answers

Answer: 37.21 dollars

Step-by-step explanation: 25% of 45 is 11.25 so after the sale it is 33.75 then you multiply by .1025 which gives you 3.46 rounded then add it
33.75+3.46= 37.21

The beach is 141 miles away. Your gas tank hold 18 gallons, and you use 3/8 of a tank to get to the beach.


a) What is your mpg (Miles per gallon)?

b) If gas costs $3.15 per gallon, how much did you spend to get to the beach?


*NEED ANSWERS NOW* FOR 28 POINTS im in 8th grade

Answers

You therefore paid $21.26 to travel to the beach.

How is a mile calculated?

One mile is 5,280 feet long. To determine how many steps this should require walking a mile, simply split 5,280 feet by the length of your typical stride. For instance, if your typical stride is 2 feet, walking a mile will need 2,640 steps.

a) We must divide the total amount of miles travelled by the quantity of gas consumed in order to compute mpg (miles per gallon). If 141 miles are covered by 3/8 of a tank, we may calculate the tank's total capacity as follows:

18 gallons = 8/8 tank (full tank)

So, 3/8 tank = (3/8) x 18 = 6.75 gallons

Therefore, the mpg is:

mpg = distance traveled ÷ gas used

mpg = 141 miles ÷ 6.75 gallons

mpg = 20.89 miles per gallon (rounded to two decimal places)

b) The entire amount of gas consumed must be multiplied by the gallon price in order to get the cost of gas. Gas is expensive at:

Cost of gas = gas used x price per gallon

Cost of gas = 6.75 gallons x $3.15/gallon

Cost of gas = $21.26

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Find the probability that the sum is as stated when a pair of dice is rolled. Odd or doubles

Answers

There is approximately a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 3 odd numbers among the possible outcomes of each die (1, 3, 5), so there are 3 x 3 = 9 ways to obtain an odd sum:

(1,2), (1,4), (1,6), .... (6,1), (6,3), (6,5)

There are 6 possible outcomes for rolling the same number on both dice, so there are 6 ways to obtain doubles:

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

We counted (1,1), (3,3), and (5,5) twice in the above two categories, so we need to subtract 2 from the total count.

Therefore, there are 9 + 6 - 2 = 13 ways to obtain an odd sum or doubles.

Therefore, the probability of rolling an odd sum or doubles is:

P(odd sum or doubles) = 13/36

Thus, there is about a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

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