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Nancy purchased a hot tub at a total price of $6995.

She made a $1200 down

payment and financed the rest at 10. 4% compounded monthly.

Nancy can repay

the loan in 36 months or 48 months.

How much interest will Nancy save is she

repays the loan in 36 months instead of 48 months?

Using linear equation, Isaac saved $33.3 and June ran 20.25 miles in 3 days.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Let Eve saved = $x

then Isaac saved= 5x+x=$6x

where x=$5.55

Hence,

           Isaac saved=$33.3

Let June ran y mile in one day

so, In three days she ran = 3y mile where y=6.75 miles

Hence,

           June ran 20.25 miles in 3 days.

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The names possible to describe the shape Mr Meyer drew are square and rhombus.

A square is a quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles).

A rhombus is a quadrilateral whose four sides are all the same length.

We know a square has 4 sides that are equal and 4 right angles.

And Its properties are acquired by the shape Rhombus with equal sides, and opposite sides that are parallel to each other and angles are of right angle (90 degrees).

And many Quadrilaterals have a right angle but not 4 equal sides.

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Answer:

The volume is 1449 ft^3

Step-by-step explanation:

Split each section, the living room and hallway, into two different rectangular prisms to solve for.

The larger rectangle will have a length of 15ft, a width of 12ft, and a height of 7ft as shown in the diagram. Multiply length, width, and height to find the volume of 1,260ft.

15*12*7=1,260

The smaller rectangle will have a length of 9ft. That's found by subtracting 15 from 24. The width will be 3ft. That's found from subtracting 9 from 12. The height is still 7. Multiple each together to find the second rectangle's volume of 189ft.

24-15=9

12-9=3

9*3*7=189

Add both volumes together and you have the volume of the whole space.

1,260+189=1449ft^3

Answer:

24

Step-by-step explanation:

12*8*5 =480 current surface

double = 960

so make the 12 into 24 height.

done

the customer saved 45% on the price of the radio compared to the original price.

25%

The original price of the radio = 100%

The 20% discount = 100%-20% = 80%

The 25% discount = 80%-25% = 55%

Overall percentage reduction = 100%-55% = 45%.

The original price of the radio was 100%. On the final day, the ale was discounted by 25%, which reduced the price to 80%. This was then further discounted by 20%, bringing the price to 55%. Therefore, the overall percentage reduction on the price of the radio was 45%. This means that the customer saved 45% on the price of the radio compared to the original price.

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He used 1/8 of the paint for the birdhouse. This was calculated by adding the 3/8 of paint used for the bookhelf and 1/4 of paint used for the wagon together and then subtracting this amount from the total amount of paint. The result was 1/8 of the paint that was left for the birdhouse.

1. We know that Mr. Riva used 3/8 of the paint for the bookhelf and 1/4 for the wagon.

3/8 + 1/4 = 5/8

2. Since he had 1/8 of the paint left, we can subtract the amount he used from the total amount of paint:

1 - 5/8 = 1/8

3. Therefore, Mr. Riva used 1/8 of the paint for the birdhouse.

Mr. Riva used 1/8 of the paint for the birdhouse. This was calculated by adding the 3/8 of paint used for the bookhelf and 1/4 of paint used for the wagon together and then subtracting this amount from the total amount of paint. The result was 1/8 of the paint that was left for the birdhouse.

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The "dead spot" is 19.04 thousand miles from the center of the earth

To find the "dead spot" where no net gravitational force acts upon the object, we need to find the value of x that makes F equal to 0.

We know that F = −K x2 + 0.012K (239 − x)2

So, we set F equal to 0 and solve for x:

0 = −K x2 + 0.012K (239 − x)2

0 = −K x2 + 0.012K (239 − x)2

K x2 = 0.012K (239 − x)2

x2 = 0.012 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 x2 - 676.8 x + 568.976

x2 - 2.888 x2 = 676.8 x - 568.976

-1.888 x2 = 676.8 x - 568.976

x2 = 361.6 x - 303.504

x = √(361.6 x - 303.504)

x = √(361.6 x - 303.504)

x = 19.04

So the "dead spot" is 19.04 thousand miles from the center of the earth

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Answer: 25, 25, 50, 50

Step-by-step explanation: Hello! Because it is a parallelogram, there are two pairs of congruent sides.  This means that if one of the sides is twice the size of the other, then the side congruent to the side that is twice the size of the smaller side is also twice the size of the smaller side.  

Let's represent a as the two smaller sides and b as the two larger sides

2a = b, 2a + 2a = b + b, 1/2(b) = a

Since the parallelogram is 150 cm, you know that 100 + 50 = 150.

50 is half the quantity of 100 and both add up to 150.

You now know that a + a = 50 and b + b = 100

a = a and b = b.

Divide 50 and 100 by two to find the length of each side.

50/2 = 25, 100/2 = 50.

The lengths of each side of the parallelogram are: 25, 25, 50, 50.

Answer:

Step-by-step explanation:

23 barrels an 3 budgets

The value of the mathematical statement 159.12 divided by 6.8 is 23.4

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

159.12 divided by 6.8

When represented using numbers and expressions, we have

159.12/6.8

Using a calculator, the value of the quotient is

23.4

Hence, the solution is 23.4

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Variables in mathematics are used to represent values or quantities that can change or vary.

The values are:

a) g(3b) = 9b² - 3b

b) f(2) + 1 = 9

What is a function?

A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as a range). The inputs are usually represented by variables, such as 'x' in the examples you provided.

The given functions are

f(x) = 3x +2 and g(x) = x² - x,

a) g(3b) = (3b)² - (3b) = 9b² - 3b

b) f(2) = 3(2) + 2 = 6 + 2 = 8

so f(2) + 1 = 8 + 1 = 9

Hence, the values are:

a) g(3b) = 9b² - 3b

b) f(2) + 1 = 9

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Answer: The answer is 6.51

Answer:

6.51

Step-by-step explanation:

10.5%  to change to a decimal divide by 100%

.105 x 62 = 6.51

That the nimber value i

Answer:

An exponential decay function has the form y = a*b^(-kt) where a is the initial value, b is the base of the exponential function (in this case, 1 - the decay rate as a decimal), k is the decay rate and t is the time.

Given that the initial value is 980, the decay rate is 1% every 2 days and the time is 5 weeks. The first step is to convert the time to the same unit of time as the decay rate, in this case, days: 5 weeks * 7 days/week = 35 days.

The decay rate per day is 1/100 because 1% as a decimal is 0.01, so the decay rate per day is 0.01/2 = 0.005

Now we can plug in the values in the function:

y = 980 * (1 - 0.005)^(-0.005*35)

y = 980 * 0.995^(-17.5)

y ≈ 574.64

So, the value of the quantity after 5 weeks to the nearest hundredth is 574.64

It's worth noting that in this case, the base (1 - decay rate) is less than 1, which implies that the value of the quantity decreases over time.

Answer:

Step-by-step explanation:

Hello! Here are the steps to solve 4x - 8 = 3x + 13

4x - 8 = 3x + 13
    + 8         + 8
____________

4x       = 3x + 21
-3x        -3x
____________
x = 21

There is one solution because there is only one possibility for x.  Let's check the answer.

4(21) - 8 = 3(21) + 13
84 - 8 = 63 + 13
76 = 76

x = 21, x does equal 21 and the answer that there is only one solution is correct.

No solutions would mean that after you solved the equation, you would get something like 9 = 7, 2 = 5, etc. which is not true.  No solutions would mean that you would receive a false equation.

Infinite solutions would mean that after you solved an equation, such as 2x = 2y, you would get x = y.  There are infinite solutions for this because you can substitute infinite numbers in for x and y.  1 = 1, 2 = 2, 3 = 3, 4 = 4, 5 = 5, etc.

Answer:

X and y are the variables in the expression

Step-by-step explanation:

Variables are letters that represent an unknown value

For example, x + 4 = 7

In this equation, x is the variable because it is letter representing the unknown value

⇒ In 7x+ 4y+1 , x and y are the variables in the expression

The value of x when Sum of LHS = RHS is 4.

The letter "x" may be used in algebra to represent an unknown value. It might be called a "variable" or "unknown." If we make an effort, we can determine the value of x in the equation x + 2 = 7! The letter "x" is not required for a variable; it can also be "y," "w," or any other letter, name, or symbol.

The algebraic statement should typically take one of the following shapes: addition, subtraction, multiplication, and division. To find the value of x, first bring the variable to the left side, then shift every other value to the right side.

x + 5 + x+ 5+ x+ 5 = 27

3x + 15 = 27

3x = 27 - 15

x = 12/3

x = 4

Thus, The value of x when Sum of LHS = RHS is 4.

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Correct question:

Given both sides are equivalent expression and LHS sum = RHS. Find The value of x?

For the sample (a) Mean is 30.8, the median is 31 and the standard deviation is 3.96, (b) the coefficient of skewness using Pearson's method is -0.151, and (c) the coefficient of skewness using the software method is 0.075.

Given values,

36, 26, 33, 28, 31

no. of values, n = 5

(a)

Mean, μ = Σx/n

= (36+26+33+28+31)/5 = 30.8

Now, Median, M = (n+1)/2th value

M = (5+1)/2 th = 3rd value

M = 31

Standard deviation(s) = [tex]\sqrt{ }[/tex]Σ(x-μ)²/n-1

= [tex]\sqrt{ \frac{(36-30.8)^{2}+(26-30.8)^2+(33-30.8)^2+(28-30.8)^2+(31-308)^2 }{4} }[/tex]

s = 3.96

(b) the coefficient of skewness using Pearson’s method

= 3(μ-M)/s = 3(30.8-31)/3.96 = -0.151

(c) the coefficient of skewness using the software method

= 1/s³(n-1)Σ(x-μ)³ = [tex]\frac{(36-30.8)^{3}+(26-30.8)^3+(33-30.8)^3+(28-30.8)^3+(31-30.8)^3 }{4(3.96)^3}[/tex]

= 0.075

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The area of the triangle is 60 in²

An isosceles triangle is a triangle with two equal sides. The area of an isosceles triangle is given by:

A = 1/2[√(a² − b² ⁄4) × b],

Where a is the measure of equal sides and b is the base of triangle

From the given info, a = KL = LM = 13 in and b = KM = 10 in

A = 1/2[√(13² − 10² ⁄4) × 10]

A = 1/2[√(169 − 100 ⁄4) × 10]

A = 1/2[√(169 − 25) × 10]

A = 1/2[√(144) × 10]

A = 1/2[12 × 10]

A =  1/2[120]

A = 60 in²

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As per the given length and width, the perimeter of rectangle is 16x² + 22x + 39

In math the term perimeter of rectangle is defined as the length of the outline of a shape.

In order to find the perimeter of a rectangle or square you have to add the lengths of all the four sides, then the formula is written as,

=> P = 2(l + w)

here l refers length and w refers the width of the rectangle.

Here we have given that the length of the rectangle in terms of x is 8x² +4x +7 and its width is 7x + 8.

Then the perimeter is calculated as,

=> P = 2(8x² +4x + 7 + 7x + 8)

When we simplify the expression, then we get,

=> P = 2(8x² + 11x +15)

When we multiply 2 with the expression, then we get,

=> P = 16x² + 22x + 39

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Answer :

a=93

b=19

Step-by-step explanation:

For (a)

Triangle total angles = 180

So we have

40+57+x = 180

x= 180 - 97

x= 83

Now,

x+ a =180( straight Angel)

83+a = 180

a = 93

Or,

You can use exterior angle theorem:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles

a = 40+57

= 93

For (b)

Using the exterior angle theorem

b+38 =57

b = 57 - 38

= 19

Answer:

The correct answer is a= 97°

b=19°

Answer:

see below

Step-by-step explanation:

total sum of all angles is 360

becuase they are all parallel, so the sum of A & D multiply by 2 = 360

so a+d = 180

5x+18 +3x+10 = 180

8x+28 =180

8x=152

x=19

A = 5*19+18 =113

D=3*19+10 =67

Total VAT imposed on the Hungarian Secret boxes by Hungarian Government during time of purchase is 6480 Hungarian Forint

A consumption tax known as value-added tax (VAT) is imposed on products and services at every step in the supply chain where value is added, from the point of initial production to the point of sale.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

The total cost of the Secret Boxes is 30480.

The VAT is 27 %

So, the price of the Secret Boxes without Taxex is x

Therefore ,

x + 27% of x  = 30480

⇒ x + 27x/100 = 30480

⇒ 127x/100 = 30480

⇒ x = 24000

Total VAT imposed on the boxes = 30480 - 24000 = 6480

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The probability that a randomly selected female senior will have a lower score than a male senior with a score of 1512 is approximately 0.788, or 78.8%.

What is the probability?

Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. An event with a probability of 0 cannot occur, while an event with a probability of 1 is certain to occur.

To find the probability that a randomly selected female senior will have a lower score than a male senior, we need to use the standard normal distribution table, which gives the probability that a randomly selected value from a normal distribution with a mean of 0 and a standard deviation of 1 will be less than a certain value.

We can use the z-score formula to standardize the female senior's SAT score, which is given by:

z = (x - mean) / standard deviation

Where x is the female senior's SAT score, mean is the mean of the distribution of SAT scores for college bound female seniors, and standard deviation is the standard deviation of the distribution of SAT scores for college bound female seniors.

So the z-score for a female senior with a score of 1512 (the same as the mean of the male seniors) is:

z = (1512 - 1486) / 311 = 0.8

Looking at the standard normal distribution table, we can see that the probability that a value from a standard normal distribution is less than 0.8 is approximately 0.788.

Hence, the probability that a randomly selected female senior will have a lower score than a male senior with a score of 1512 is approximately 0.788, or 78.8%

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The standard deviation of the weight of 4 men would be: 5 lbs.

The standard deviation of a sample of size 4 is the square root of the variance divided by the sample size. In this case, the standard deviation of the weight of 4 men would be:

√(100 / 4) = √(25) = 5 lbs

Please note that the standard deviation of a population is denoted by the Greek letter sigma (σ) and the standard deviation of a sample is denoted by the letter s.

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The mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

The mean of a geometric distribution is given by:

Mean = 1/p

Here, p is the probability of success on a single trial.

In this case, p = 0.80

So, the mean of the geometric distribution = 1/0.80 = 1.25

The variance of a geometric distribution is given by:

Variance =[tex](1-p) / p^2[/tex]

By substituting the value of p = 0.80, we get:

Variance = [tex](1-0.80) / 0.80^2 = 0.20 / 0.64 = 0.3125[/tex]

So the variance of the geometric distribution = 0.3125

Therefore, the mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

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The interest will she earn in 1year is $45 if Rachel has $900 in a savings account. The interest rate is 5% per year and is not compounded.

What is Simple Interest ?

Simple Interest can be defined as the ratio of product of principal amount, time, rate and hundred.

Given ,

Rachel has $900 in a savings account. The interest rate is 5% per year and is not compounded.

we have to find interest will she earn in 1year

so we know that,

I  = PTR

I = 900*(0.05)*1

I = $45

So, The interest could be $45.

Therefore, The interest will she earn in 1year is $45 if Rachel has $900 in a savings account. The interest rate is 5% per year and is not compounded.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{h}{2}=\cfrac{8}{h}\implies h^2=16\implies h=\sqrt{16}\implies h=4[/tex]