Question 3 (2 points)
Lauren deposited $300 to start her savings account. After one year, she had $312 in
her account. If she did not deposit or withdraw any money that year, how much
interest did she earn?
A

Answer: Let x be the number of points scored by each girl and y be the number of points scored by each boy.

We know that:

3x + 2y = 27 (the total number of points scored by the 3 girls and 2 boys)

3x - 2y = 15 (the difference between the number of points scored by the girls and the number of points scored by the boys)

We can use the second equation to find the value of one of the variables and substitute it into the first equation.

3x - 2y = 15

3x = 15 + 2y

Substitute this into the first equation:

(15 + 2y) + 2y = 27

2y = 12

y = 6

Now that we know that each boy scored 6 points, we can substitute that back into the second equation to find the number of points each girl scored:

3x - 2y = 15

3x - 2(6) = 15

3x = 27

x = 9

So each girl scored 9 points and each boy scored 6 points.

Step-by-step explanation:

On a team have 3 girls and 2 boys

Let say  each girl points scored=x

Let say  each boy points scored=y

Total scored by 3 girls and 2 boys =27

                                              3x +2y=27----------1

The difference between points of  3 girls and 2 boys =15

                                               3x-2y=15---------2

Solve equation 1 and 2

From 2nd equation

we can rewrite as :

                          3x=15+2y---------3

Submit 3rd equation in 1st equation.

             15+2y+2y=27

                          4y=27-15

                          4y=12

                            y=3

Therfore, each boy points scored=3

For find each girl scored points

Submit y=3 in 1st equation.

                     3x+2(3)=27

                              3x=27-6

                              3x=21

                                x=7

Therfore, each girl points scored=7

Therfore,number of points each boy scored by =3points

Therfore,number of points each girl scored by =7points

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Answer: c=√202

Step-by-step explanation:

c = √(9² + 11²)

which also simplifies to 23.769729

I hope this helps!

Answer:

Step-by-step explanation:

The solution of the inequality is x < 60 and graph is shown in the image attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Let x represent the number of days.

Since 25 tables is being shipped daily and we want to find how many days will there be fewer than 1500 tables, we can write:

25x < 1500

x < 1500/25

x < 60

Note: fewer than means less than i.e. <

The graph is shown in the image attached

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The volume of empty space in the box will be 220cm³

The diameter of the candle is equal to the width of the box (the length of the side of the square base of the box), and the height of the box is equal to the height of the candle, assuming that the candle fits tightly inside the box without wasting any room.

You may compute the prism's volume by multiplying it by the square base's area (height).

The area of the circular base can be used to compute the volume of the candle's cylinder (height).

The square box base's side measures 8 cm long, hence its area is equal to that measurement= 8cm²=64cm²

The candle's diameter is two times its radius, hence the radius is 8cm/2=4cm

area of the circular base thus Equals (A = π r²).

=πx4²

=16π²

Since the height of the candle and of the box is 16cm, the difference in volume is 1024-256π

=220cm³

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If the post office is 13 blocks away from the library and each block is 275 meters, approximately, the distance from the post office to the library, in miles, is 2.2 miles.

To determine the distance or the number of miles from the post office to the library, we use unit conversions and mathematical operations (multiplication and division).

Using multiplication, the number of blocks is converted to meters.

The distance is converted from meters to miles by division.

The distance of a block in the city = 275 meters

The number of blocks from the library to the post office = 13 blocks

The distance from the post office to the library = 3,575 meters (13 x 275)

1,609.34 Meters = 1 Miles

The distance in miles from the post office to the library = 2.2 miles (3,575/1,609.34)

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The probability that the first item is not the first to be delivered is 0.6667

Represent the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.

So, the probability that one of the other two items arrives first is

1/3 + 1/3 = 2/3.

The probability that the first item is not the first to be delivered is

1 - 2/3 = 1/3

Evaluate

1 - 2/3 = 0.6667

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Answer: 43

Step-by-step explanation:

Multiply 8.6 and 10 then subtract 7 then you do 4.3 times 10 then you subtract then subtract the values you get

The approximate area (shaded region) of the remaining portion of the circle in square feet is 55.94 ft².

We know that,

the side of square=2*[r*√2/2]=r*√2 that is being taken out.

diameter = 14 ft and radius , r = 7 ft.

the side of square=7*√2=9.89 ft

[area of the remaining portion of the circle]=[ area of a circle]-[area of a square]

[area of a square] = (7√2)²=98 ft²

[ area of a circle] = π*r²= π x 7^2 = 153.94 ft²

therefore,

[area of the remaining portion of the circle]=153.94 - 98=55.94 ft²

the answer is 55.94 ft².

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The option that is a statistical question is how many miles do the students in your class run each week? (option b)

A statistical question is a question that can be answered by collecting data that have varying values.

For example, the number of miles that the students in your class run each week is statistical question because each student would run. This is because data would be collected from more than one student and the students would have varying miles that they run.

The number of pets your grandparents have is not a statistical questions because they can only have a set number of pets.

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Answer:

B. How many miles do the students in your class run each 

Step-by-step explanation:

2 packs include 12 baseball cards, and there are 6 baseball cards per pack.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

given, There are 24 baseball cards In 4 packs complete the table to find the rate that gives the number of cards in 2 packs.

Since

There are baseball cards in 4 packs = 24

Thus,

Baseball cards in 1 pack = 24 / 4

Baseball cards in a pack = 6

Baseball cards in 2 packs = 12

therefore, there are 12 baseball cards in 2 packs also the rate of baseball cards per pack is 6.

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Complete question:

To find the y intercept of a polynomial function solve the function for the input value of zero.

We know that a polynomial function is a function that contains only positive integer exponents of a variable.  

The highest power of a polynomial function is the degree of polynomial function.

A polynomial is generally represented as P(x).

The domain of a polynomial function is entire real numbers (R).

We know that the y-intercept is the value of the function for which the function has an input value of zero.

To find the y intercept of a polynomial function P(x) we substitute x = 0 and solve the polynomial function.

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Answer: 0.2m/h

Step-by-step explanation: We can say when the turtle travels 1/10 of a mile in 1/2 of an hour, he's traveled 0.1 miles in 30 minutes.

If you're looking for the turtle's rate in miles per hour, just double both the time and the distance traveled.

You will end up with 0.2 miles per hour or 2/10 of a mile per hour.

Answer:7 games

2 cases= x games

you give 4 or 2 from each case

divide 10 by 2 and get 5 them add 2 to your answer and get 7 GAMES

BOOM!!

The area of the border is 72 square inches - 80 square inches = -8 square inches.

What is rectangle ?

A rectangle is a four-sided geometric shape with four right angles. The opposite sides of a rectangle are of equal length and parallel to each other, and the opposite angles are equal. The length and width of a rectangle are its two dimensions, with the length being the longer side and the width being the shorter side.

To find the area of the border, subtract the area of the photograph from the total area of the photograph and the frame. The total area of the photograph and the frame is the area of the frame (which is just the border) plus the area of the photograph.

The area of the photograph is 8 inches * 10 inches = 80 square inches

The area of the frame is the perimeter of the photograph (28 + 210) multiplied by the width of the border, which is 2 inches. So the area of the frame is 2*(28 + 210) = 2*36 = 72 square inches.

Therefore, the area of the border is 72 square inches - 80 square inches = -8 square inches.

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Answer: Use cross product property

Step-by-step explanation:

I solved it out for you below! I hope it helps! If you need a better explanation maybe ask your teacher? :)

S + R represents the total trips done by these trucks.

Volume is defined as the amount of space occupied by an object that is bound by a boundary. It must be noted that the volume is a mathematical term that is only applicable to 3D (three-dimensional) objects or spaces. As such, the units commonly used for volume are cubic units, that is, m3, cm3, in3, etc.

Two dump trucks hauling rock to a construction site is given by the expression. xS + yR

S +R

Truck 1 can haul x cubic yards

Truck 2 can haul y cubic yards.

Truck 1 makes P trips to the construction site, while truck 2 makes R trips.

Hence the trips made by truck 1 and truck 2 should be the addition of the trips made by the trucks individually.

So the total trips is represented by S + R

Therefore, S + R represents the total trips done by these trucks.

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Answer:4√81=±3

Step-by-step explanation:

If (x+5)^4 = 81,

then (x+5)^2 = ± sqrt(81), so

        (x+5)^2 = ±9

Focusing on (x+5)^2 = 9 for the two real roots, we have

 (x+5)^2 = 9

       x+5 = ± sqrt(9)

       x+5 = ± 3

       x+5 = 3 gives you x = -2

       x+5 = -3 gives you x = -8

There are two complex roots too, but I'm not sure if you're studying that too.   If so, then you'd solve (x+5)^2 = -9:

       x+5 = ± sqrt(-9)

       x+5 = ±3i

       x = 5 ± 3i as the two complex roots.

The next time they will flash together will be at 4:00 AM.If they flash together at 1:00 AM.

According to the given information we are trying to find the smallest time interval at which both the lighthouses will flash together.The first lighthouse flashes every 15 minutes, and the second lighthouse flashes every 18 minutes.

To find the LCM of 15 and 18, we can list out the multiples of each number and find the smallest multiple that is common to both.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, ...

As we can see, the smallest multiple that is common to both lists is 90. This means that the two lighthouses will flash together every 90 minutes.Since they both flash at 1:00 AM, we can add 90 minutes to 1:00 AM to find the next time they will flash together:
1:00 AM + 90 minutes = 4:00 AM

So, the next time they will flash together will be at 4:00 AM.

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The solution to the fractions are;

7. 5/6

8. 6/5

A fraction can be described as the part of a whole variable, number or element.

There are several types of fractions, which includes;

From the information given, we have that;

1 1/3 × 5/12

convert to improper fraction

4/3 × 5/12

Multiply the values

5/6

(7/10 + 1/5) ÷ ( 6/4 - 3/4)

find the lowest common denominators

( 7 + 2 /10) ÷ (6 - 3 /4)

subtract or add the numerators

9/10 ÷ 3/4

take inverse of the divisor and multiply

9/10 × 4/3

6/5

Hence, the values are 5/6 and 6/5 respectively.

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Answer:

Step-by-step explanation:

I don't know I'm just asking the question

If the four players choose their numbers independently and uniformly at random from [0,1], then the expected value of the sum of the two middle numbers is 1/2, and the expected value of the sum of the two extreme numbers is 1/2. Therefore, in order to minimize the expected

One of the most straightforward methods for gathering information from the entire population is random sampling. Every member of the subset has an equal chance of being chosen as part of the sampling process when using random sampling. For instance, if an organization employs 300 people overall, a sample group of 30 workers will be chosen to participate in the survey. In this instance, the population is the entire workforce of the organization, and the sample is 30 employees. Since all of the employees who were picked to participate in the survey were chosen at random, every worker has an equal chance of getting chosen.

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The conclusions that can be made from this table include:

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, factory A for those who need repairs is 0.05 in the first year. In this case, among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.

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Answer:

well the best I can say is maybe multiply all of the numbers

[tex]5 \times 7 \times 9 = x \div 3[/tex]

35*9=x÷3

315÷3

just do the 315÷3 and you should get an answer

The distance PR across the river is 177 feet

The complete question is added as an attachment

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

The equivalent ratio represented as

PR : 125 = PR + 170 : 245

Express the ratio as a fraction

So, we have the following representation

PR/125 = (PR + 170)/245

Cross multiply

This gives

245PR = 125PR + 21250

Evaluate the like terms

120PR = 21250

Divide both sides by 120

PR = 177

Hence, the distance is 177 feet

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When a  transformation is applied to a figure to create a new figure then Dilation do not preserve congruence but do preserve orientations.

Rotations, reflections, translations, and dilation are only a few of the many transformations. Dilation do not preserve congruence but do preserve orientations. Rotations, reflections, and translations all preserve congruence and are referred to as isometries.

Maintaining congruence refers to a transformation where the side lengths and angle measurements of the Image and Pre-Image are the same.

An object's orientation refers to how its related parts are ordered. As long as the components of an item remain in the same sequence, rotation and translation retain orientation. Orientation is not maintained by reflection.

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Using arithmetic operations it is found that -

It took Castenea 10 hours and 36 minutes to finish the first book Eragon.

The number of pages in Castenea's second book Eldest is 707.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of pages in Eragon is = 530 pages

The rate for Castanea's reading is = 1 page/72 seconds

The time taken by Castanea to finish the first book is -

Time Taken = Number of Pages × Time taken to read 1 page

Use the arithmetic operation of multiplication.

Substitute the values in the equation -

Time Taken = 530 × 72

Time Taken = 38160 seconds

To convert seconds into minutes use the arithmetic operation of division.

38160 / 60 = 636 minutes

To convert minutes into hour use the arithmetic operation of division.

636 / 60 = 10.6 hour

Therefore, it took Castanea 10 hours 36 minutes to finish the first book.

The time took by Castanea to finish the second book = 14 hours 8 minutes and 24 seconds

To convert hours into minutes use the arithmetic operation of multiplication.

14 × 60 = 840 minutes

To convert minutes into seconds use the arithmetic operation of multiplication.

848 × 60 = 50880 seconds

Use the arithmetic operation of addition to get the total seconds -

50880 + 24 = 50904 seconds

The rate for Castanea's reading is = 1 page/72 seconds

The number of pages in Castanea's second book is -

Number of Pages = Time Taken in total/Time taken to read 1 page

Use the arithmetic operation of division.

Substitute the values in the equation -

Number of Pages = 50904/72

Number of Pages = 707

Therefore, there were seven pages in the second book.

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Since J and M are base angles of trapezoid JKLM, the measure of k is 168°.

The base angles of an isosceles trapezoid are congruent and equal. This ultimately implies that, an isosceles trapezoid has base angles that are always equal in magnitude.

By equating the given base measures of isosceles trapezoid JKLM, we can determine the specific value of x and angle k as follows;

m∠J = m∠M

4x + 1 = 12x - 95

By re-arranging and collecting like terms, we have the following:

12x - 4x = 95 + 1

8x = 96

By dividing both sides of the equation by 8, we have the following:

x = 96/8

x = 12.

Therefore, the measure of k is given by:

m∠k = 180 - 12

m∠k = 168°.

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The perimeter of the entire figure is 40 inches

It is important to note that the formula for area of a figure is expressed as;

A = a²

Where;

A + A = 100

a² = 100

Take the square root of both sides

a = √100

a = 10 inches

The formula for calculating the perimeter of a square is expressed as;

Perimeter = 4a

Substitute the value of a, we have;

Perimeter = 4(10)

expand the bracket

Perimeter = 40 Inches

Hence, the perimeter is 40 Inches

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Knowing that digital camera merchants typically mark up their products by 40%, even when a camera's actual cost is $175.50 The price of one rupee is $438.75.

Your boss has chosen to give old models of digital cameras a discount in order to make place for new ones. She wants to offer them for sale at the store's original price, without a markup, in order to move them quickly. You are requested by her to alter the price tags and create signage indicating the percentage of the reduction. A digital camera costs $175.50 at the manufacturer's suggested retail price, with shops adding 40% to that figure.

cost = ($175.50 / 40 ) × 100 = $438.75

In mathematics, the cost price formula, often known as C.P., is used to determine an object's exact price.The price that a buyer pays for a good, service, or commodity, according to the definition of C. P.In the estimation of profit and loss calculations for a specific purchase, it is frequently utilized.

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