james and terry open a savings account that has a 2.75% annual interest rate compounded monthly. the initial deposit was $5,000 how much will be in the account after 20 years?

After substituting the given values of x and y in the equation, all that can apply are (0, 2), (3, 0), and (6, -2).

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

here, we have,

As per the given information in the question,

The given equation is,

y=-2x+6

Now, substitute the corresponding points and check,

The points are,

(1 ,4) ⇒ 4= -2*1+6

⇒4=4

This is correct.

(2, 3)  ⇒ 3 = -4+6

This is not correct.

(-1, 8)  ⇒ 8= 2+6

This is correct.

(10, -15) ⇒ -15=-20+6

This is not correct.

(0, 3)  ⇒ 3=6

This not correct.

(3,0)  ⇒ 0 = -6+6

This is correct.

(7, -8)  ⇒ -8= -14+6

This  is correct.

(-6,17)  ⇒ 17 = 12+6

This is not correct.

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[tex]\it P(A)=\dfrac{n^o\ de\ casos\ favorables\ de\ A}{n^o\ total\ de\ casos\ posibles}\\ \\ \\ n^o\ total\ de\ casos\ posibles=100\\ \\ n^o\ de\ casos\ favorables=50+30=80\\ \\ P(A)=\dfrac{\ 80^{(20}}{100}=\dfrac{4}{5}[/tex]

Answer:

D

Step-by-step explanation:

[tex]\frac{7-i}{3+i}[/tex]

rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator

the conjugate of 3 + i is 3 - i

note that i² = - 1

= [tex]\frac{(7-i)(3-i)}{(3+i)(3-i)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{21-7i-3i+i^2}{9-3i+3i-i^2}[/tex]

= [tex]\frac{21-10i-1}{9-i^2}[/tex]

= [tex]\frac{20-10i}{9+1}[/tex]

= [tex]\frac{20-10i}{10}[/tex]

= [tex]\frac{20}{10}[/tex] - [tex]\frac{10i}{10}[/tex]

= 2 - i

Answer: To calculate the number of attendees after 4 years, we can use the formula:

Attendance = 1200 * (1 - 0.5%)^4

Where 0.5% is the decimal equivalent of the percentage decrease.

In this case:

Attendance = 1200 * (1 - 0.005)^4

Attendance = 1200 * 0.995^4

Attendance = 1200 * 0.9450625

Attendance = 1134

So, after 4 years, the attendance will be 1134 people.

Step-by-step explanation:

As a result, it is discovered that the answer to the given function problem is slant sample points of y = x -4.

Mathematical studies cover the areas and prospective applications of geometry as well as numbers and their variants, equations, and related structures. A group of inputs that collectively produce a similar result is referred to as a "function." Each input contributes to a single, distinguishable consequence in an output-input connection known as a function. Each activity has a scope, which is also known as a region or city or municipality. Commonly, functions are denoted by the letter f. (x). The origin is X. Across operations, one-to-one action, many-to-one activity, on activity, and on

Here,

Every one of the three asymptotes can be used to construct a rational function because rational functions can take any form.

This is depicted in both the linked graph and the graph of the function f(x that serves as a representation. The function's asymptotes are as follows.

The asymptotes for the vertical slope are x = -4,

The horizontal asymptotes are Y = 0 and.

Slant has an asymptote of Y = x -4.

An exponential function is used in our example function. That isn't generally perceived of as a polynomial, but it may be expressed as an endless degree polynomial. A rational function is typically described in publications as the percentage of polynomials.

As a consequence, the solution to the given function problem is slant sampling points, which are y.

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Answer:

            4  to  1

Step-by-step explanation:

                                                Tablespoon of cocoa   to Tablespoon of sugar

                                                                          8             :                2

                                                                          [tex]\frac{8}{2}[/tex]              :                [tex]\frac{2}{2}[/tex]

                                                                          4             to                1

When recipe is doubled:                             ( 8 x 2)         to        (2 x 2)

                                                                         16             :              4

                                                                         [tex]\frac{16}{4}[/tex]             :               [tex]\frac{4}{4}[/tex]

                                                                          4           to              1

It can be observed that the ratio remains the same

Answer:

7/8

12.5%

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

f(30)=-11

f(30)=-3/5(30)+k

-11=-18+k

+18 +18

7=k

Answer:

Number of republicans = 207 Number of democrats = 245

Step-by-step explanation:

Here you go

(x + 38) + x = 452 x + 38 + x = 452 2x = 452 - 382x = 414x = 414 / 2 x = 207

Answer:

Increases by 71% to the nearest whole number

Step-by-step explanation:

=((12-7) /7 )x100

=57×100

=0.714286×100

=71.4286%change

=71.4286%increase

The PCR in terms of t is 6,912in3t, rounded to the nearest hundredth.

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a) The percentage of shoppers that have computer access at home is given as follows: 44%.

b) The percentage of shoppers that do not have an e-mail account is given as follows: 66%.

A percentage is obtained as a proportion, dividing the number of desired outcomes by the number of total outcomes, and then multiplying this amount by 100%.

Out of 150 shoppers, 48 + 18 = 66 have computer access at home, hence the percentage is given as follows:

66/150 x 100% = 44%.

Out of 150 shoppers, 18 + 81 = 99 do not have an e-mail, hence the percentage is given as follows:

99/150 x 100% = 66%.

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Answer:

2 miles / half-hour

Step-by-step explanation:

You will notice that the y intercepts the x at every half-hour interval

Ex: 2 at 30 min, 4 at one hour, 6 at one hour 30 minutes...

Answer:

D

Step-by-step explanation:

add -2 to the other side of the equation to isolate y

On solving the provided question, we can say that he equation is

[tex]40/2000=32/X = > X=1600\\[/tex]

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation is

[tex]40/2000=32/X \\40X=32*2000\\40X=64000\\X=64000/40\\X=1600\\[/tex]

IS THE PROJECTED INCREASE FROM 1860 TO 1892.

THUS THE TOTAL POPULATION IS EXPECTEDTO BE 22000+1600=23600.

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Answer:

Step-by-step explanation:

8. ( - 3, 6 )

10. ( - 7, 9 )

Expressions that perform similarly but differ in appearance are said to be equivalent expressions.

When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s).

It is comparable to perform 3+2minus, 3, plus, 2, and 2 3 232, minus, 3. Despite being in opposite sequence, the numbers add out to 1 less than 1.

Each of the fractions 1 start fraction, 1 divided by, 2 end fraction, and 5 10 10 5 start fraction, 5 divided by, 10 end fraction, is identical. Despite the difference in the numerals, they both add up to 5.

Algebraic expressions 2 + 2 2x+22, x, plus, 2 and 2(x+1)2, left parenthesis, x, plus, 1 and right parenthesis, are equal. All xx values have the same value according to the expression:

x     2(x + 1 )                  2x + 2

0     2(0 - 1 ) = 2            2(0) + 2 = 2

1      2(1 + 1 ) = 4             2(1) + 2 = 4

2      2(2 + 1 ) = 6           2(2) + 2 = 6

3      2(3 + 1 ) = 8           2(3) + 2 = 8.

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The average rate of change of filling the water heater is solved to be

The results indicate that 1 1/3 is the ratio of the rate of change of water height to time.

The average rate of change for the points t = 3 and t = 6  is solved using the formula

m = (y₀ - y₁) / (x₀ - x₁)

m = (3 - 7) / (3 - 6)

m = (-4) / (-3)

m = 4/3

m = 1 1/3

The values means that the rate of change of of height of water to time it takes is equal to 1 1/3

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Answer:

16052.47m²

Step-by-step explanation:

area of a circle=πr²

π=314

3.14×71.5×71.5=16052.465m²

=16052.47m²

Answer:

16,060.61 m² (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Given:

Substitute the given radius into the area of a circle formula and solve for A:

[tex]\implies A= \pi \cdot 71.5^2[/tex]

[tex]\implies A= 5112.25 \pi[/tex]

[tex]\implies A= 16060.6070...[/tex]

[tex]\implies A= 16060.61\; \sf m^2\;(2 \; d.p.)[/tex]

Therefore, the area of the circle is 16,060.61 m² (2 d.p.).

In 37 years and 6 months, Jacob will be 1.5 years older than his uncle Todd.

In 37 years and 6 months, Jacob will be 1.5 years older than his uncle Todd.

Hello, using the information provided, write an equation to get the answer to this question:

33 years old Todd

12 years old Jacob

So, Jacob's age plus the amount of years asked equals 1.5 Todd's age (1.5 x 33).

(12+x)

12 +x = 1.5 (33) (33)

working out x

12 +x = 49.5

x= 49.5 -12

: x = 37.5 years

Given that 12 months make up a year, 0.5 years is equal to half a year.

12 times 0.5 years equals 6 months.

In 37 years and 6 months, Jacob will be Todd's age by a factor of 1.5.

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Answer:

12j + 6

Step-by-step explanation:

You have to multiplied this polynomial expression in order to expand it:

2(6j + 3)

12j + 6

Answer:

12j + 6

a(b+c) = ab + bc

2(6j+3)

2*6 = 12

12j

2*3 = 6

12j + 6

The specified dimensions of the interior and exterior walls, indicates that the dimensions of the building is 28 feet 10 5/8 inches

The dimensions of a building includes the lengths, height, and width of the building.

The wall measurements for the building are;

The thickness of the interior walls = 2 × 4 (3 1/2'')

The thickness of the sheetrock on both sides of the interior walls = 1/2''

The dimensions of the exterior walls = 2 × 6(5 1/2'')

The thickness of the sheet rock on the interior of the interior walls = 1/2''

The thickness of the sheeting on the exterior of the exterior walls = 7/16''

The thickness of the brick on the exterior of the exterior wall = 3 5/8''

The specified dimension of one of the rooms = 11' 3''

The dimension of the second room = 15'7''

The outside dimension of the house, D, is therefore;

D = The sum of the dimensions of the rooms + The dimension of the inner wall + 2 × The thickness of the outer wall

Therefore;

D = 11'3'' + 15'7'' + 3 1/2'' + 1/2'' + 1/2'' + 2 × (5 1/2'' + 1/2'' + 7/16'' + 3 5/8'')

D = 11'3'' + 15'7'' + 4 1/2'' + 20 1/8'' = 28' 10 5/8''

The dimension of the building, D = 28 feet 10 5/8 inches

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The 10,000 loan has 132.56 in monthly payments, and the loan's total interest is 5363.27.

Until the loan is repaid in full at the conclusion of its term, the principle and interest that make up each level payment are shown on a loan amortisation schedule, which is the whole table of periodic loan payments.

The formula for monthly payments for the loan is,

[tex]$M . P .=\frac{P(r / n)}{1-(1+r / n)^{-n t}}$[/tex]

where, P is the initial amount

r is the rate

n is the period in a year

is the number of years

Now it is given that,

Principle amount borrowed P =  10,000

Rate of interest, r = 7% = 0.07

Monthly Payment, so n = 12

Time, t = 4 years

Thus, Monthly payment of the loan is given as,

[tex]M . P .=\frac{P(r / n)}{1-(1+r / n)-n t}[/tex]

Putting the values we get,

[tex]\text { M.P. }=\frac{10,000(0.07 / 12)}{1-(1+0.07 / 12)-12 * 4}[/tex]

Simplifying we get,

[tex]\text { M.P. }=\frac{(70 / 12)}{1-(12.07 / 12)^{-48}}[/tex]     or,

[tex]\text { M.P. }=\frac{5.833}{1-(1.005)^{-48}}[/tex]

Thus, we get

[tex]\text { M.P. }=\frac{5.833}{1-0.756}[/tex]    or,

[tex]\text { M.P. }=\frac{5.833}{0.244}[/tex]

Solving we get,

[tex]\text { M.P. }=\$ 132.56[/tex]

This is the loan's needed monthly payment.

The difference between the total amount of monthly payments made and the original sum will now be the total amount of interest paid.

Thus,

Total interest of the loan = T.M.P - P

Therefore,

Total Monthly Payments = M.P x t x n

Putting the values we get,

Total Monthly Payments = 132.56 x 4 x 12

⇒ Total Monthly Payments = $6363.27

Therefore,

Total interest of the loan = 6363.27 - 10,000

⇒ Total interest of the loan = $5363.27

As a result, the 10,000 loan's monthly payment is 132.56, and its overall interest cost is 5363.27.

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Answer:

2.88 markup per rose

Step-by-step explanation:

12.24/12 = 1.02 per rose

46.8/12 = 3.9 per rose

3.9 - 1.02 = 2.88 markup per rose

The rate of change of function A is greater than the rate of change of function B. This is the statement which best compares the rate of change of the two functions.

What is rate of change?

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

The formula for rate of change is:

[tex]m=\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]

The points for first function A are

(7,21) and (8,24).

So, the rate of change is:

[tex]m=\frac{24-21}{8-7}[/tex]

m= 3/1 = 3

The points for second function B are

(2,4) and (3,6).

So, the rate of change is:

[tex]m=\frac{6-4}{3-2}[/tex]

m= 2/1 = 2

The rate of change of function A is 3, while the rate of change of function B is 2.

Hence, the rate of change of function A is greater than the rate of change of function B.

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Answer: 6

Step-by-step explanation:

Since M is the midpoint of LN, M divides LN by exactly half.

This means that LM and MN have the same length.

Using this, we can set up the equation:

3x=2x+2

x=2

Since we now know the value of x, let's use it to find LM.

LM = 3x = 6

So the answer is 6.

Two calculations that she can do to find the cost are:

Remember that if we have a value A, and we want to apply a discount X (where X is a percentage) then the value after the discount is:

A' = A*(1 - X%/100%)

Here we know that the initial value of the pants is c dollars, and the discount is of the 15%, then the expression that we need to solve is:

cost = c*(1 - 15%/100%)

Now we can simplify that expression to get:

cost = c*(1 - 0.15)

cost = c*0.85

These the calculations that she needs to do.

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Therefore , the solution of the given problem of range comes out to be option b is y ≤ -5 .

The variable range is calculated by determining its maximum observed value and deducting its minimum observed value (minimum). Possible range or variational bounds: different pricing for steel; different designs; The breadth or scope of a process or action: insight a weapon's projectile's maximum or anticipated range. A list or set's range is the integer between its lowest and maximum. Aligning all the numbers will help you find the region. The lowest number should then be subtracted from the greatest number.

Here,

Given :

=> y = -3x² - 12x -17 or

=> f(x) =  -3x² - 12x -17

To find the range :

=> If a < 0 the range of f(x) ≤ y

=> If a > 0 the range of f(x) ≥ y

As a =-3

So ,  vertex(xv ,yv ) = (-2 , -5)

=> y ≤ -5

Therefore , the solution of the given problem of range comes out to be option b is y ≤ -5 .

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On solving the provided question we cans ay that equation will be => x *(x+1) = 12 => x = 6, -2

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

a pack of pencils, a pack of pens, and a notebook for = $12.

the pack of pens cost = $1 more than the pack of pencils,

let,

x = cost of pen

y = cost of note book

equation will be

x *(x+1) = 12

x^2 + x = 12

(x+2)(x-6) = 0

x = 6, -2

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The length of AB is AB = 8 units.

What is distance between two points?

The length of a straight line in the coordinate plane that connects two points in space is what is referred to as their distance. We use the absolute value to calculate the distance between any two points because it is impossible for this distance to be negative.

Consider, the given points A (-4, -3), B (4, -3), C (4, -7), D (-4, -7).

We have to find the length of AB.

Consider, the distance formula,

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

where,

[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the points.

Here,

[tex](x_1, x_2) = (-4, -3)\\(x_2, y_2) = (4, -3)[/tex]

Plug these values in the above formula,

[tex]d = \sqrt{(4-(-4))^2+(-3-(-3))^2} \\d = \sqrt{8^2 +0^2} \\d = \sqrt{8^2} \\d = 8[/tex]

Hence, the length of AB is AB = 8 units.

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