What is the square root of 98 rounded to the nearest thousandth

To calculate Frederick's approximate savings if he paid off the loan early, subtract the total amount he would pay if the loan continued for the full term from the original loan amount. The monthly payment amount can be calculated using the compound interest formula. By multiplying the monthly payment by the number of payments, you can find the total amount paid over 20 years. Subtracting this from the original loan amount gives you the approximate savings.

To calculate the approximate amount Frederick would save if he paid off the loan early, we need to find the total amount he would pay if he continued making monthly payments for the full 20 years and subtract the total amount he would pay if he paid off the loan early.

1. First, find the monthly interest rate by dividing the annual interest rate by 12:

i = 0.022 / 12 = 0.00183

2. Next, calculate the monthly payment using the compound interest formula:

P = (r * PV) / (1 - (1 + r)^(-n))

Where P is the monthly payment, r is the monthly interest rate, PV is the loan amount, and n is the number of monthly payments.

3. Substitute the values into the formula:

P = (0.00183 * $70,000) / (1 - (1 + 0.00183)^(-240))

4. Solve for P to find the monthly payment amount:

P ~ $520.63

5. To find the total amount paid over 20 years, multiply the monthly payment by the number of payments:

Total amount paid = $520.63 * 240 = $124,950.98

6. To find the approximate amount saved if the loan is paid off early, subtract the total amount paid from the original loan amount:

Approximate savings = $70,000 - $124,950.98 = -$54,950.98

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Final answer:

Frederick would save approximately $34,692.80 if he paid off the loan early.

Explanation:

To calculate the amount Frederick would save if he paid off the loan early, we need to determine the total cost of the loan and compare it to the amount he would pay if he paid it off in a shorter time period.

First, we need to calculate the monthly payment using the formula:

Monthly Payment = Loan Amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments)))

Substituting the values, we have:

Loan Amount = $70,000

Monthly Interest Rate = 2.2% / 12 = 0.1833%

Total Number of Payments = 20 * 12 = 240

Plugging the values into the formula, we get:

Monthly Payment = $70,000 * (0.1833% / (1 - (1 + 0.1833%)^(-240)))

Calculating this equation gives us a monthly payment of approximately $436.22.

Next, we calculate the total cost of the loan by multiplying the monthly payment by the total number of payments:

Total Cost = Monthly Payment * Total Number of Payments

Plugging in the values, we get:

Total Cost = $436.22 * 240

Calculating this equation gives us a total cost of approximately $104,692.80.

If Frederick paid off the loan early, he would save the difference between the total cost and the original loan amount, which is $104,692.80 - $70,000 = $34,692.80.

Given expression is:

By substituting the value of "g" in the given expression, we get

→ [tex]4g-12[/tex]

→ [tex]4(5) -12[/tex]

→ [tex]20-12[/tex]

→ [tex]8[/tex]

Thus the above answer is correct.

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Answer:

50

Step-by-step explanation:

IN order to find a number that is "x" times greater than another you have to multiply the number by the times greater, for example if you are trying to find a number that is 2 times greater than 8, you multiply 8 by 2=16 so 16 is 2 times greater than 8.

To find the number that is 10 times greater than 5 you just have to multiply 5*10, as the result will be 50, so that would be the answer.

4 x 6 = 24 square feet

24/12 = 2

 so 1 person for every 2 square feet

1 mile - 5280 feet

4 x 5280 = 21120

21120 x 15 = 316800 square feet

316800/2 = 158,400 people

Brad Hamilton's weekly salary as an accounting clerk is $625.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Brad Hamilton's annual salary as an accounting clerk is $32,500

So number of weeks in an year = 52

So, Brad Hamilton's weekly salary as an accounting clerk

                                  = Brad Hamilton's annual salary / number of weeks

⇒ Brad Hamilton's weekly salary = $32,500/52

⇒ Brad Hamilton's weekly salary = $625

Thus, Brad Hamilton's weekly salary as an accounting clerk is $625.

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Answer:

associative property

Step-by-step explanation:

The inverse of y = 5 x² + 10 is , y = √ ( ( x / 5 ) - 2 )

What is an Inverse Function?

An inverse function is a function that undoes the action of the another function. To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

                                                   f⁻¹ ( x ) = y

Given data ,

y = 5 x² + 10

Now interchange the variable x and y , we get

x = 5 y² + 10

Subtract 10 from both sides , we get

x - 10 = 5 y²

Divide by 5 on both sides ,

( x / 5 ) - 2 = y²

Therefore , y = √ ( ( x / 5 ) - 2 )

Hence , the inverse f⁻¹ ( x ) = y = √ ( ( x / 5 ) - 2 )

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Final answer:

Yes, if four points are collinear, they are also coplanar, as they lie on the same straight line and therefore exist in the same plane.

Explanation:

If four points are collinear, this implies that they lie on the same straight line. By definition, a straight line is a one-dimensional figure and hence exists within any given plane. Therefore, four collinear points must also be coplanar, existing on the same plane. In three-dimensional geometry, the concept of coplanarity can be evaluated using a determinant. If this determinant equals zero, it indicates that the four points lie within the same plane.

Moreover, lines and planes in three-dimensional space can be represented by equations, and by combining these into a system of equations, one can ascertain the geometric relationships between the points in question.

The expression 2^4 \u00b7 2^{-7} simplifies to 2^{-3}, which is the same as 1/2^3 or 1/8.

The expression 2^4 \u00b7 2^{-7} can be simplified using the properties of exponents, specifically the law that states when multiplying expressions with the same base, you add the exponents. Here, we are multiplying 2 raised to the power of 4 with 2 raised to the power of -7. Therefore, we add the exponents 4 and -7 together to get 2^{4-7} = 2^{-3}.

To simplify further, remember that a negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Hence, 2^{-3} = 1/2^3 = 1/8. Therefore, 2^4 \u00b7 2^{-7} simplifies to 1/8.

The three significant figure decimal is 4.38.

A group of numbers between integers on a number line are known as decimals. They are merely an additional mathematical representation of fractions.  Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are represented to the right of the decimal point.

Given:

4/3/8 as a decimal

Now, divide 3/8 we get

3/8 = 0.375

      = 0.38

So, the three significant figure decimal is 4.38.

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Answer:

[tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex]

Step-by-step explanation:

We have been given that Vanessa uses the expressions [tex]3x^2+5x+10[/tex] and [tex]x^2-3x-1[/tex] to represent the length and width of her patio.

To find the expression that represents the area of Vanessa's patio we will multiply the length of patio by width of patio as:

[tex](3x^2+5x+10)*(x^2-3x-1)[/tex]

Upon using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex](3x^2*x^2)+(3x^2*-3x)+(3x^2*-1)+(5x*x^2)+(5x*-3x)+(5x*-1)+(10x^2)+(10*-3x)+(10*-1)[/tex]

Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,

[tex](3x^{2+2})+(-9x^{2+1})+(-3x^2)+(5x^{1+2})+(-15x^{1+1})+(-5x)+(10x^2)+(-30x)+(-10)[/tex]

[tex](3x^{4})+(-9x^{3})+(-3x^2)+(5x^{3})+(-15x^{2})+(-5x)+(10x^2)+(-30x)+(-10)[/tex]

[tex]3x^{4}-9x^{3}-3x^2+5x^{3}-15x^{2}-5x+10x^2-30x-10[/tex]

Now let us combine like terms.

[tex]3x^{4}-9x^{3}+5x^{3}-3x^2-15x^{2}+10x^2-5x-30x-10[/tex]

[tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex]    

Therefore, the expression [tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex] represents the area of Vanessa's patio.

The recursive formula is an = a_(n-1) +4.

The correct option is (D).

A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:

The recursive formula to find the nth term of an arithmetic sequence is:

an = an-1 + d for n ≥ 2

where

an is the nth term of a A.P.

d is the common difference.

Given:

14, 18, 22, 26, 30, …

a1=14

and, d= 18-14

d=4

a2= a1 + 4

a2 = 14+4= 18

Similarly, going this way

an = a_(n-1) +4

Hence, the recursive formula is an = a_(n-1) +4

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Answer:

The bar diagram is shown below. Number of peoples who are 18 or older is 163,776.

Step-by-step explanation:

Given information:

Total number of peoples in the city = 332,054

Number of peoples who are under 18 = 168,278

Number of peoples who are 18 or older is

[tex]332,054-168,278=163,776[/tex]

We need to draw a bar diagram.

In the bar diagram x axis represents the age and y-axis represents the number of peoples.

First bar represents the number of peoples who are under 18 i.e., 168,278.

Second bar represents the number of peoples who are 18 or older i.e., 163,776.

We are given a total size of 24 2/3 feet of wrapping paper. Convert this into fraction of denominator 6:

total paper = 24 2/3 = 74/3 = 148/6 feet

Subtract 5/6 foot:

remaining paper = 148/6 – 5/6 = 143/6 feet

Divide by 11:

each piece = (143/6) ft / 11 = 143/66  ft = 2.17 ft

Given

John had a roll containing of wrapping paper  

[tex]=24\tfrac{2}{3}[/tex]

First, he must cut off 5/6 foot because it was torn.

He wants to divide it into 11 pieces.

To proof

As given in question

John had a roll containing of wrapping paper

[tex]=24\tfrac{2}{3}[/tex]

[tex]=\frac{74}{3}[/tex]    ( solving the mixed fraction form)

 First, though, he must cut off 5/6 foot

than we get

[tex]= \frac{74}{3} - \frac{5}{6}[/tex]

Taking the L.C.M of 3 and 6 is 6

[tex]=\frac{148-5}{6}[/tex]

[tex]=\frac{143}{6}[/tex]

=23.83 feet (approx)

He wants to divide it into 11 piece

length of the each piece

[tex]=\frac{23.83}{11}[/tex]

length of the each pieces be 2.16 feet ( approx)

Hence proved