Use only the commutative property of addition to complete the statement.
2x + 21=

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

[tex]\rm A = P \left ( 1 + \dfrac{r}{n} \right ) ^{nt}[/tex]

Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.

For interest compounded monthly, the value of n is 12.

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be

[tex]\rm A = 500 \left ( 1 + \dfrac{0.09}{12} \right ) ^{12 \times 4}[/tex]

Simplify the equation, then we have

A = 500 (1.0075)⁴⁸

A = 500 x 1.4314

A = $715.70

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.

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Answer:

5/8 of pizza left

Step-by-step explanation:

Answer:

x = -36

Step-by-step explanation:

Subtract 9 from 3.2(x−6)=14⋅−6

Multiply 14 by −6.2(x−6)=−84

Divide each term

Simplify the left side.

Move all terms not containing x to the right side of the equation.

x = -42 + 6

Add -42 & 6

x = -36

Based on the packaging of the cookies, the number of ways you can buy 36 cookies is 12 ways.

The ways you can buy the cookies include:

In conclusion, there are 12 ways to buy the cookies.

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The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is 45 minutes and 3.33 minutes respectively.

x ≥ 0

y ≥ 0

x + y ≤ 80

0.09x + 0.006y ≤ 2.16

From (1)

x ≤ 80 - y

0.09x + 0.006y ≤ 2.16

0.09(80 - y) + 0.006y ≤ 2.16

7.2 - 0.09y + 0.006y ≤ 2.16

7.2 - 0.084y ≤ 2.16

-0.084y ≤ 2.16 - 7.2

-0.084y ≤ -5.04

y ≤ -5.04 / -0.084

y ≤ 60

x + y ≤ 80

x + 60 ≤ 80

x ≤ 80 - 60

x ≤ 20

The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is

Television = $900 / 20

= 45 minutes

Radio = $200/60

= 3.33 minutes

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Answer: 105 degrees

Step-by-step explanation:

two sides of a trapezoid add up to 180 degrees

180 - 75 = 105

After calculating the volume of these two rectangular prisms , we have come to conclude that the total volume of two rectangular prisms is 372 in³.

A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles (top, bottom, and lateral faces) and all pairs of opposite faces are congruent.

A rectangular prism, like all three-dimensional shapes, has volume and surface area. A cuboid is simply another name for a rectangular prism.

A rectangular prism is basically a rectangle,

so the volume = l × b × h

Volume of 1st rectangular prisms = 9 × 6 × 3  

                                                       = 162 in³

Volume of 2nd rectangular prisms = 10 × 7 × 3  

                                                          = 210 in³

Total volume = 162 + 210

                      = 372 in³

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Answer:

x = 0

Step-by-step explanation:

Let's solve the problem,

→ (x/9) + 8 = 8

→ x/9 = 8 - 8

→ x = 0 × 9

→ [ x = 0 ]

Thus, the value of x is 0.

[tex]y = x {}^{2} - 8x + 12 \\ y = x {}^{2} - 8x + 12 + 4 - 4 \\ y = (x {}^{2} - 8x + 16) - 4 \\ y = ( x - 4)^{2} - 4[/tex]

The dimensions of the rectangle are; length 63 inches and width is 20 inches.

Let 'L' be the length of the rectangle.

Let 'W' be the breadth of the rectangle.

As, the length of a rectangle is three more than triple the width.

Thus,

L = 3 + 3W

The formula for the perimeter is;

Perimeter = 2 (L+W)  

The value of perimeter is 166 inches.

Thus,

166 = 2(3 + 3W +W)

166 = 2(3 + 4W)

166 = 6 + 8W

166 - 6 = 8W

W = 20

W = width = 20 inches

L = 3 + 3W

L = 3 + 3(20)

L = 3 + 60

L = 63 inches.

Thus, the dimensions of the rectangle are; length 63 inches and width is 20 inches.

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1. 1/2

2. 3/10

3. 2 and 3/5

4. 1 and 7/12

5. 1 and 1/3

Answer:

Wish i could help

Step-by-step explanation:

According to the solving the amount should be invested in each account should be :$500.

A borrower as well as deposit-taking financial organization paying interest to a lender or depositor on an amount in excess of the original payment at a specified rate. It is not the same as a fee paid by the borrower to the lender or a third party.

Debit your Interest Expense account and credit our Accrued Interest Payable account to record the accrued interest for an accounting period. This increases the value of your expenditure as well as payable accounts.

Let the amount invested at 5 be x.

Let the amount invested at 6% be 2000 - x.

Interest on 5% will be 0.05

Interest on 6% will be 6%(2000 - x) = 120 - 0.06x

This will be:

0.05x + 120 - 0.06x = 105

- 0.01x = -15

x = 1500

The amount invested at 6% will be:

= 2000 - 1500

= 500

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The value of y' according to the given equation in the task content is; 1.

According to the task content, it follows that the equation given is; 2x³y - 3x² = 4y'.

On this note, the value of y' can be determined by substituting the given values of x and y as follows;

2(2)³×1 - 3(2)² = 4y'

16 - 12 = 4y'

y' = 4/4

y' = 1.

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The equations which have no solution are choices A, B, C and D.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.

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The amount of bacteria after 12 hours would be 8 grams

Rate can be defined as  the ratio between two quantities that are related in size but may be in different units.

It is also known as the ratio of comparison between quantities of different units.

From the information given, we have that;

To determine the amount of bacteria after 12 hours, we have;

= 12 × 15/ 100

multiply and find quotient

= 1. 8

In 12 hours, the amount of bacteria is ;

= 6 + 1. 8

= 7. 8 grams

= 8 grams

Thus, the amount of bacteria after 12 hours would be 8 grams

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Step-by-step explanation:

no calculator at hand ?

f(-3.5) means that we have to replace every x in the function expression by -3.5 and then calculate.

f(-3.5) = (-3.5)² - 5(-3.5) + 6 = 12.25 + 17.5 + 6 = 35.75

Answer:

Step-by-step explanation:

-6+2y=10

2y=10+6

2y=16

2y/2=16/2

y=8

so the final answer of first question is y=8

The next one is

6x-2y=-10

as we got from the first question y=8 so

6x-2(8)=-10

6x-16=-10

6x=-10+16

6x/6=6/6

so the final answer is 1

Answer:

[tex]7x + 5y \leqslant 30[/tex]

The value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

Equations are mathematical expressions that are represented by the equal to or equality sign i.e =

Examples of equations are:

a + b = c

y = mx + c

Ax + By = C

y = ax^2 + bx + c

y =  x

The equation is given as

x = [a^2 + a^2]/[ab + 1]

To start with, we evaluate the like terms i.e. we add a^2 and a^2

This is represented as

a^2 + a^2 = 2a^2

Substitute 2a^2 for a^2 + a^2 in the given equation

So, we have

x = [2a^2]/[ab + 1]

The above equation cannot be further simplified

Hence, the value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

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Answer:

3 heartbeats per sec.

Step-by-step explanation:

Number of heartbeats / Total time will give the rate or number of heartbeats per sec.

The condition that will create a biased estimator of a population parameter is D. The expected value of the estimator is not equal to the population parameter.

It should be noted that a parameter is a descriptive measure applied to a whole population. There are numerous population parameters exist. For instance, the population size (N) is one parameter.

For T(x) to be an unbiased estimator of population parameter, it is necessary that the expected value of the estimator is equal to population parameter.

Therefore, the condition that will create a biased estimator of a population parameter is that the expected value of the estimator is not equal to the population parameter.

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Answer:

Step-by-step explanation:

21 divided by 7 is 3 so 3 minus 10 is negative 7

The solution is : 7 when subtract the quotient of 21 and 7 from 10.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

the quotient of 21 and 7

i.e. we have to divide 21 by 7

i.e. 21/7 = 3

so, we get,

the quotient of 21 and 7 is 3

now, we have to Subtract 3 from 10

i.e. 10 - 3

= 7

so, we get,

21 divided by 7 is 3 so 10 minus 3 is  7.

Hence, The solution is : 7 when subtract the quotient of 21 and 7 from 10.

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The co-ordinates of the y-intercept is (0,-9) .

Y-intercept is the point on the graph where the graph passes over the y-axis.

To calculate the y-intercept we have to graphically represent the curve and pick out the points where the graph crosses over the x-axis.

For a graph with an equation in the form y = f(x) , y intercept can be calculated by substituting the value of x as 0 in the equation.

In the graphical representation we can see that the graph passes through  (- 8, 3) and (- 3, - 4.5).

Therefore the slope of the line passing through these points is given by:

[tex]m=\frac{-4.5-3}{-3-(-8)} \\\\m=\frac{-7.5}{5} \\\\m=-\frac{3}{2}[/tex]

Now the equation of the line is given by :

[tex]y-3 =- \frac{3}{2} (x-(-8))[/tex]

[tex]y-3 =- \frac{3}{2} x - 12[/tex]

[tex]y=- \frac{3}{2} x - 9[/tex]

Therefore at x = 0 , the value of y is -9.

So the y-intercept is given by the point (0,-9) .

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The coordinates of the y-intercept are ( 0 , 9 / 5 ) .

Finding equation of line :

( y - 3 ) / ( x + 8 ) = ( 3 + 4.5 ) / ( - 8 + 3 )

( y - 3 ) / ( x + 8 ) = ( 7.5 ) / ( - 5 )

- 5 y + 15 = 7.5 x + 6

- 5 y - 7.5 x + 9 = 0

Equation of line : 5 y + 7.5 x - 9 = 0

Writing equation in Slope - Intercept form

y = m x + c

y = [ ( - 7.5 x ) / ( 5 ) ] + [ 9 / 5 ]

Hence , y - intercept = 9 / 5 .

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The value of integral ₀∫¹ ( eˣ - 2 )² dx is 8 + ( e² - 1) / 2 - 4e.

When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.

Consider the integral expression,

₀∫¹ ( eˣ - 2 )² dx

Using ( a + b )² = a² + b² + 2ab

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int_0^{1}(e^{2x}+4-2e^{x})dx[/tex]

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int^0_{1}e^{2x} dx +\int_0^{1}4 dx - \int_0^{1}4e^{x} dx[/tex]

Now, integration of eˣ is eˣ + c where c is constant.

Therefore,

[tex]\int_{0}^{1} ( e^{x} - 2 )^{2} dx = [ \frac{e^{2x}}{2} ]_0^{1} + [ 4x ]_0^{1} - [ 4e^{x}]_0^{1}[/tex]

₀∫¹ ( eˣ - 2 )² dx = ( e² / 2 - e⁰/2 ) + ( 4 - 0 ) - ( 4e¹ - 4e⁰ )

₀∫¹ ( eˣ - 2 )² dx =  e² / 2 - 1/2 + 4 - 4e + 4

₀∫¹ ( eˣ - 2 )² dx = e² / 2 - 4e + 8 - 1/2

₀∫¹ ( eˣ - 2 )² dx =  = 8 + ( e² - 1) / 2 - 4e

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the slope is represented by m

the x coordinate of the ordered pair is x1

the y coordinate of the preferred pair is y1

y-y1=m(x-x1)

The distance between the school and the hospital on the map  is 8 cm

Here, we want to find the distance between the school and the hospital on the map

The scale is that 4cm to 5km

So ;

if 4 cm = 5km

Then x cm = 10km

x * 5 = 4 * 10

5x = 40

x = 40/5

x = 8 cm

Therefore the distance between the school and the hospital on the map  is 8 cm

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