Marvin used the money he received from high school graduation gifts to start a new savings account with a simple interest rate of 7. 5%. After 12 years, the account had earned $288. If there were no other deposits or withdrawals, what was the original amount placed in the account?

well, let's recall that a year has 12 months, so 9 months is really 9/12 of a year

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1413\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1413)(0.05)(\frac{3}{4}) \implies I = 1413(\frac{3}{80})\implies I\approx 52.99[/tex]

4.5 is the length of each part in feet. This can be solved by using the concept of feet.

foot, plural feet, any of a wide range of ancient, medieval, and modern linear measurements (often 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.

The foot measured [tex]11^{\frac{1}{42}[/tex] inches in antiquity. The typical man's foot measures 12 inches in length nowadays.

Given that:

The length of the wooden board is given as = 108 inches.

As it is cut in 2 equal parts, it becomes: 108/2 = 54 inches in each

We have to calculate the length of each part in feet, so divide 54 by 12.

As we know,

12 inches = 1 feet

Thus, 54 inches = 54/12 feet = 4.5 feet

So, the length of each part is 4.5 feet.

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Answer:

[tex] \sf \: x = 7[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ 2x + 5 = 3x - 2

Then the value of x will be,

→ 2x + 5 = 3x - 2

→ 2x - 3x = -2 - 5

→ -x = -7

→ [ x = 7 ]

Hence, the value of x is 7.

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

Profit and Loss is a financial statement that shows a company's revenue, costs, and expenses over a certain period of time, such as a month or a year. The purpose of a P&L statement is to show the company's financial performance and to determine whether the company is making a profit or incurring a loss.

The proportion that the retailer makes after selling a good at a price greater than its cost is the product's profit margin. P% indicates it.

Profit Percentage P% = {(selling price – cost price) / cost price} x 100.

The selling price of the purse is $35 and the original cost of the purse is $22.50. So the profit is $35 - $22.50 = $12.50

Profit as a percent = (Profit / Original cost) * 100

Profit as a percent = ($12.50 / $22.50) * 100 = 55.6%

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

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The number of hours after which the candle is burned completely is

68 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Candle height = 11(1/3) inches

Each hour the height decreases by 1/6 inch.

Now,

The equation to find the number of hours x after which the candle is burnout is 11(1/3) - (1/6)x = 0

Solve for x.

11(1/3) - (1/6)x = 0

11(1/3) = (1/6)x

34/3 = (1/6)x

x = (34 x 6) / 3

x = 34 x 2

x = 68

Thus,

After 68 hours the candle is completely burnt.

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As per the conditions given by the question, the 95% confidence interval of the true proportion who said that they would take a ride in a self-driving car is (53.3856%, 62.6144%).

Now, According to the question:

What is confidence interval?

A confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

To find the 95% confidence interval of the true proportion, we need to use the following formula:

point estimate +/- (margin of error * z-score)

The point estimate in this case is the sample proportion, which is 58%. The margin of error is 2.4%, and the z-score for a 95% confidence interval is 1.96.

Plugging these values into the formula, we get:

58% +/- (2.4% * 1.96)

This simplifies to:

58% +/- 4.6144%

So the 95% confidence interval is:

(53.3856%, 62.6144%)

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Answer:

$6.51

Step-by-step explanation:

To make a percent a decimal, divide by 100

62% = .62

.62 x 10.50 = 6.51

We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.

The coefficient of the expression X²Y in the product 7x² 5y X² 3y is 35.

7x² 5y X² 3y

= 7x² X² (5y 3y)

= 7x² X² (2y)

= 7x² X² 2y

= 14x² 2y

= 28xy

= 35

The given expression is 7x² 5y X² 3y. This can be rearranged as 7x² X² (5y 3y). This is equal to 7x² X² (2y). This can further be rearranged as 7x² X² 2y. This is equal to 14x² 2y. This can be further rearranged as 28xy. This is equal to 35. Therefore, the coefficient of X²Y in the product 7x² 5y X² 3y is 35.

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Writing the whole number in the numerator and 1 in the denominator. Fraction in simplest form is 8

How to Find the Most Basic Form

Determine the GCF of the fraction’s numerator and denominator.

Divide the created GCF by the numerator and denominator.

Fill in the blanks with the simplified fraction of the supplied fraction.

The most basic form, If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase “lowest terms” when referring to the simplest form.

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No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.

The sum of the angles of a triangle must always add up to 180 degrees. To determine if a set of angles can form a triangle, add the angles together. If the sum is 180, the angles can form a triangle. In this case, 30 + 60 + 90 = 180, which does not equal 180. Therefore, these angles cannot form a triangle.

No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.

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The total cost for your fun day out is $23.82.

In mathematics →

Given is that you decided to go snowboarding for the day and you have to figure out your budget. Tickets are $75.00 per day and there is a 5% convenience charge when you order your ticket. You also have to pay for a bus ticket that is $12 for the day. You mom gives you a 15% off coupon that applies to the lift ticket only.

Assume that the total cost for your fun day out is ${x}. Then, we can write the equation as -

{x} = 15% of (75 + {5% of 75}) + 12

{x} = 15% of (75 + {5/100 x 75}) + 12

{x} = 15% of (75 + {1/20 x 75}) + 12

{x} = (15/100) x (75 + 75/20) + 12

{x} = (3/20 x 78.75) + 12

{x} = 11.82 + 12

{x} = 23.82

Therefore, the total cost for your fun day out is $23.82.

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By using systems of linear equations by elimination, it can be determined that x = 0.5 y +2 and 2.2x-1.8y-1.6=0 are equivalent to x=0.818182 and y+0.727273.

Using elimination, let's fix your system. 0.6 x=1.2+0.3 y, 2.2 x-1.8 y-1.6=0 in the graph, and y=2 x-4, y=1.222222 x-0.88888

Step 1: Divide both sides by 0.6 to find the solution for x = 0.6 x=1.2 + 0.3 y.

[tex]$$\begin{aligned}& \frac{0.6 x}{0.6}=\frac{0.3 y+1.2}{0.6} \\& x=0.5 y+2\end{aligned}$$[/tex]

Let's figure out what x is, 2.2 x-1.8 y-1.6=0.

First, multiply both sides by 1.8 y.

[tex]$$\begin{aligned}& 2.2 x-1.8 y-1.6+1.8 y=0+1.8 y \\& 2.2 x-1.6=1.8 y\end{aligned}$$[/tex]

Add 1.6 to both sides in step two.

[tex]$$\begin{aligned}& 2.2 x-1.6+1.6=1.8 y+1.6 \\& 2.2 x=1.8 y+1.6\end{aligned}$$[/tex]

3. Multiply both sides by 2.2.

[tex]$\frac{2.2 x}{2.2}=\frac{1.8 y+1.6}{2.2}$[/tex]

x=0.818182 y+0.727273

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Answer:

C is a function

Step-by-step explanation:

for a relation to be a function each value of x must map to exactly one unique value of y

A

2 → 5 and 2 → 2 ← not a function

B

- 1 → 6 and - 1 → 7 ← not a function

C

all values of x map to exactly one unique y ← function

D

3 → 1 and 3 → 2 ← not a function

Answer:

40%

Step-by-step explanation:

1 and 3/5 as a fraction is 8/5 which as a percent is 160%.

25% of 16 is 4

160%/4 = 40%

The height of the screen will be;

⇒ h = 28 inches

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches.

Here,

The diagonal of the screen television = 53 inches

And, The width of the screen television = 45 inches

Let the height of the television = h

So, By the Pythagoras theorem, we get;

⇒ AC² = AD² + DC²

Where, AC = Diagonal of television.

AD = Height of the television

DC = Width of the television.

Substitute all the values, we get;

⇒ 53² = h² + 45²

⇒ 2809 = h² + 2025

⇒ 2809 -2025 = h²

⇒ h² = 784

⇒ h = √784

⇒ h = 28 inches

Thus, The height of the screen = 28 inches

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∠EFH and ∠ACD are angles of alternate exterior angles in the figure as  alternate external angles are those that are generated on the outer side of the parallel lines .

When two straight lines connect at a 90° angle or are perpendicular to one another, an angle is formed. The symbol denotes a right angle. In the picture up above, many right angle formations are visible. Shapes include the correct angles. Triangles classified as right triangles have one of their internal angles at a 90 degree right angle. The three interior angles of a triangle add up to 180 degrees, so the three interior angles of a right triangle must always add up to 90 degrees because one of them is always 90 degrees.

given

The pair of angles known as alternate external angles are those that are generated on the outer side of the parallel lines but on the transverse side.

sum up to 180 degrees, you can calculate the size of the inner angle adjacent to it if you know the size of the outer angle (since together they are the angle on a straight line). The internal angles at the other two vertices are added to create the outer angle of a triangle.

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Answer:22 days

Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,

Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)

so, 2000/90 = we will get number of days

therefore 22.22 days

Which emplies 22 days.

The steps for measuring the angle b is shown below, <b= 41.

If a triangle side is created, the outside angle that results is equal to the sum  of the two opposite internal angles.

If an equivalent angle is measured at each triangle vertex, the exterior angles always add up to 360 degrees.

Given:

exterior angle = 113

and, opposite interior angle =72

Using Exterior angle property we have

72 + b = 113

Subtract 72 from both side

72 + b -72 = 113 -72

b = 113- 72

b = 41

Hence, the measure of b is 41 degree.

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The percentages for this problem are calculated as follows:

The percentages in this problem are obtained applying proportions, multiplying the total amount by the decimal equivalent of the percentage.

Hence the amount that represents 100% of 36 seconds is obtained as follows:

1 x 36 = 36 seconds.

(as a percentage of 100% has a decimal equivalent of 1).

The amount that represents 25% of 36 seconds is obtained as follows:

0.25 x 36 = 9 seconds.

(as a percentage of 25% has a decimal equivalent of 1).

The percentage of 125% of 36 students can be obtained combining the two previous expressions as follows:

1.25 x 36 = 1 x 36 + 0.25 x 36 = 36 + 9 = 45 seconds.

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Therefore , the solution of the given problem of scatter plot comes out

to be  2 regions contain 2 x 40 (or 80) students.

Several dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).

Here,

A box plot separates a data set into four areas, each identified by five lines. The lowest line displays the result, while the highest line displays the result. 25% of the data points are distributed across each region, and the median score is indicated by the middle line.

In this box plot, for instance, there are lines at 10, 30, 48, 70, and 100. The fact that no student received a score exactly equal to 30, 48, or 70 allows us to deduce the following:

Because the middle two sections represent the interquartile range (IQR), which comprises the middle 50% of the data, they are frequently "boxed" together.

We are informed that 120 students received test scores below 70. Additionally, since there are three regions with scores below 70 and each region has a 25% weighting, 3 x 25% (or 75% of the students) had scores below 70.

In other words, 75% of 120 students.

If there are 120 students total throughout the three regions, then each

region has 40 pupils, or one-third of the total.

The box plot indicates that there are two areas, and since each region has 40 students, there are 80 students total in the two regions.

As a result, two zones with two sets of 40 students each make up the solution to the scatter plot problem.

Therefore , the solution of the given problem of scatter plot comes out

to be  2 regions contain 2 x 40 (or 80) students.

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A measurement which could be the side lengths of a right triangle include the following: C. √24 in, √6 in, √30 in.

In order to determine which measurements could be the side lengths of a right triangle, we would have to apply Pythagorean's theorem.

Mathematically, Pythagorean's theorem is given by this formula:

x² + y² = z²

From the side lengths of the first triangle, we have the following:

(√6)² + (√30)² = (√33)²

6 + 30 = 33

36 = 33 (False).

From the side lengths of the first triangle, we have the following:

(√27)² + (√18)² = (√48)²

27 + 18 = 48

45 = 48 (False).

From the side lengths of the first triangle, we have the following:

(√6)² + (√24)² = (√30)²

6 + 24 = 30

30 = 30 (True).

From the side lengths of the first triangle, we have the following:

(√18)² + (√21)² = (√48)²

18 + 21 = 48

39 = 48 (False).

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Answer: 8:15pm

Step-by-step explanation:

9+6=15 +105 = 120, 120/60=2 hours (total duration), 6:15 + 1 hour = 7:15 + 1 hour = 8:15pm

Answer:

35 [tex]\frac{0}{1}[/tex]

Step-by-step explanation:

If a value of y relates only to one value of x, then the function does have an inverse function.

A relation between such a collection of inputs and outputs is known as a function.

Thus, if a value of y relates only to one value of x, then the function does have an inverse function.

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Logical partition - A partition within an extended partition

System partition - The partition where you place the boot loader

Primary partition - The section of the hard drive that will become the bootable drive

IBM and Microsoft initially kept internal lists of designated partition types to be used in the MBR partition table. As the market for PC operating systems and disc tools expanded and became more open, other suppliers also needed to give their products specialised partition kinds. Third parties began to merely allocate partition types on their own behalf in a largely uncoordinated trial-and-error fashion because Microsoft neither documented all of the partition types already given by them nor wished to retain foreign assignments. This resulted in several conflicting assignments, which occasionally caused serious compatibility issues between certain products. [1]

In the 1990s, a number of industry professionals including Hale Landis, Ralf D. Brown, Matthias R. Paul, and Andries E. Brouwer began investigating partition kinds.

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Answer:

The diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers

Step-by-step explanation:

To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to know the distance from the Moon to the Sun and the distance from the Moon to Earth.

Since the distance from the Moon to the Sun is much greater than the distance from the Moon to Earth, the angle subtended by the Sun at the Moon will be much smaller than the angle subtended by Earth at the Moon.

Therefore, the size of Earth as seen from the Moon will be much larger than the size of the Sun as seen from the Moon.

To find the ratio of the size of Earth to the size of the Sun as seen from the Moon, we can use the formula:

size ratio = (distance to Earth / distance to Sun) x (Sun's diameter / Earth's diameter)

Substituting in the given values, we get:

size ratio = (384400km / 149600000km) x (1391000km / Earth's diameter)

Simplifying, we get:

size ratio = 0.00257 x (1391000km / Earth's diameter)

To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to solve for Earth's diameter. Dividing both sides of the equation by 0.00257, we get:

Earth's diameter = (1391000km / 0.00257) = 54304839.858km

Therefore, the diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers.

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The length of the line is 5 units.

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

Given that, endpoints are (-1,4) and (2,0) of the line segment.

The length= √(2+1)²+(0-4)²

                 =5units

Hence, The length of the line is 5 units.

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The true statements after a dilation of scale factor 3 are,

∠A corresponds to ∠A' and Triangle ABC is similar to triangle A'B'C'.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, The points of ABC are (negative 3, 3), (- 1, 1), and (- 3, 1).

The points of A'BC' are (- 9, 9), (- 3, 3), and (- 9, 3) after a dilation of 3, (x, y) ⇒ (3x, 3y).

We know dilation maintains the similarity of the dilated figures.

Therefore, The statements that are true,

∠A corresponds to ∠A' as dilation maintains similarity.

Triangle ABC is similar to triangle A'B'C'.

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Answer:

Options A,B,C,E

Step-by-step explanation: