If $5000 is put into a savings account that pays
3.5% interest compounded monthly, how much
money, to the nearest ten cents, would be in that
account after 6 years, assuming no money was
added or withdrawn?

we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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Answer:

it would be 3(16-8x) also know as A

Step-by-step explanation:

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Answer:

This is my answer,

Step-by-step explanation:

The equation is y=2x, and the horizontal line will always be half of the vertical line (1:2). We can prove this by plugging in y or x. For example, if y is 12, 12=2x. X would equal six.

The correct statement that describes the given work shown is;

the work was done correctly.

We know from geometry that the sum of angles on a straight line is 180°. The two angles we are given form a straight line and as such, we have the expression;

(5x + 109) + (14x + 242) = 180

Adding like terms gives us;

19x + 351 = 180

Subtract 351 from both sides to get;

19x = -171

Divide both sides by 19 to get;

x = -9

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Answer:A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

The domain and range of the function  f(x) = 3/x + 2 are  (-∞, 0) ∪ (0, ∞) and  (-∞, 2) ∪ (2, ∞). The vertical and horizontal asymptotes are x = 0 and y = 2 respectively

In mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.

To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.

The function f(x) = 3/x + 2

The domain of the function is (-∞, 0) ∪ (0, ∞)

The range of the function is (-∞, 2) ∪ (2, ∞)

The x - intercept is (-3/2, 0)

The y - intercept does not exist

The vertical asymptotes is x = 0

The horizontal asymptotes is y = 2

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Step-by-step explanation:

1) 6s^2

(s mean the length of each side, s=7)

= 6x7^2

= 294

2) 2(3)(2)+2(1)(2)+2(3)(1)

（l=length, w=wide, h=height)

= 12+4+6

= 22

3) 4(π)12^2

(r=radius)

= 576

The area of the shaded which is obtained using the composite figure formed the shaded region and the area under the curve of the specified function is; (2·π - 3·√3)/2 square units

A composite figure is one that is composed of two or more simpler figures.

The area can be considered of comprising of a composite figure of the area under the curve of the function and the area of the shaded region

The function representing the curve under the shaded region can be presented as follows;

y = 3·cos(x) + 1

The interval specified under the curve can be expressed as follows;

0 ≤ x ≤ π/3

Therefore, the area under the curve can be found as follows;

\(\int\limits^\frac{\pi}{3} _3 {3\cdot cos(x) + 1} \, dx = [3\cdot sin(x) + x]^{\frac{\pi}{3} }_0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3} - 0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3}\)

sin(π/3) = (√3)/2

Therefore; 3·sin(π/3) + π/3 = 3·(√3)/2 + π/3 = (2·π + 9·√3)/6

The area of the rectangle = (4 - 0) × (π/3 - 0) = 4·π/3

The area of the shaded region = Area of the rectangle - Area under the curve of the specified function

Therefore, area of the shaded region = 4·π/3 - (2·π + 9·√3)/6 = (2·π - 3·√3)/2

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Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

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Answer:

Prime Factors of 545 are 5, 109, and usually expressed as 5 x 109. 4.

hope this is right! :) -liaa

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  \(x\leq 2\)

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

Answer:

10.5

Step-by-step explanation:

Answer:

Here is the answer:

Step-by-step explanation:

10.5

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

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

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Answer:

p = 20

Step-by-step explanation:

\(\rm \implies \dfrac{p}{2} - 9 = 1 \\ \\ \rm \implies \dfrac{p}{2} - 9 + 9 = 1 + 9 \\ \\ \rm \implies \dfrac{p}{2 } = 10 \\ \\ \rm \implies \dfrac{p}{ \cancel{2}} \times \cancel{2} = 10 \times 2 \\ \\ \rm \implies p = 20\)

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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Answer:

this question is inappropriate

The height will be 6 feet, so the correct option is C.

Here we know that the diameter of the flagpoler is the linear equation:

D(h) = 12 - 0.5*h

Where the variable h is the number of feet above the base.

If the diameter is 9 inches, then we need to solve

9 = 12 - 0.5*h

For the variable h, so let's do that:

9 = 12 - 0.5*h

9 - 12 = -0.5*h

-3/-0.5 = h

6  =h

The correct option is C, the number of feet above the base is 6 feet.

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if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

1843.2

Step-by-step explanation:

area=width*length

38.4=width

48=length

38.4*48=1843.2

Answer: 29 feet from across the kitchen to one hole to the other.

After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

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Answer:

-5.3

Step-by-step explanation:

Simplify the expression.

f ( x ) = 3x - 1

g ( x ) = 2x - 3

_____________________

g ( x ) = f ( 2 )

2x - 3 = 3(2) - 1

2x - 3 = 6 - 1

2x - 3 = 5

2x - 3 + 3 = 5 + 3

2x = 8

2x ÷ 2 = 8 ÷ 2

x = 4

Answer:

The width is 15 inches long