You are considering taking out a loan of $8,000.00 that will be paid back over 8 years with quarterly payments of $320.19. If the interest rate is 6.3% compounded quarterly, what would the remaining balance be immediately after the fourteenth payment?

The remaining balance would be $___________. (Round to 2 decimal places.)

Answer:

P(5,6) = 63

Step-by-step explanation:

Test each point to see which ordered pair maximizes the objective function:

(0,0): p = 3(0) + 8(0) = 0

(2,7): p = 3(2) + 8(7) = 6 + 56 = 62

(5,6): p = 3(5) + 8(6) = 15 + 48 = 63

(8,1): p = 3(8) + 8(1) = 24 + 8 = 32

Hence, (5,6) is the ordered pair that maximizes the objective function.

Answer: Number 2

Step-by-step explanation: yes

Answer:

D)

hope it helps..........

Answer:

D is the correct answer

hope it is helpful to you ☺️☺️☺️

Answer:

B

Step-by-step explanation:

given scale is 1 inch represents 7.5 feet

then we require to calculate how many 7.5 feet there are in each dimension.

to obtain this divide each dimension by 7.5, that is

13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )

26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )

then dimensions are approximately 1.73 inches by 3.47 inches

Answer:

A

Step-by-step explanation:

Answer:

option  (a) is correct.

2 + m - 1 + m is an equivalent expression  to the given expression  3m+1-m

Step-by-step explanation:

Given expression  3m+1-m

We have to choose an equivalent expression from given options.

Equivalent expression are those expression that looks different but are same.

Like 4+2 = 6  and 3+ 3 = 6

Both have same value but looks differently.

Like terms are term having same variable with same degree.

Consider the given expression  3m+1-m

Simplify by adding like terms,

3m + 1 - m = (3-1) m + 1

Thus, (3-1) m + 1  = 2m + 1

Also 2m + 1 can be written as m + m + 2 - 1

Thus, option  (a) is correct.

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{4}}}\implies \cfrac{4+2}{-6}\implies \cfrac{6}{-6}\implies -1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{-1}(x-\stackrel{x_1}{4}) \\\\\\ y+2=-x+4\implies y=-x+2\)

Answer:

-1.5f - 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

-2.4f + 0.9f - 11 - 9

Step 2: Simplify

Answer:

C

Step-by-step explanation:

x + y + 10 = 0 ( subtract x + 10 from both sides )

y = - x - 10 → (1)

x² + y - 2 = 0 → (2)

substitute y = - x - 10 into (2)

x² - x - 10 - 2 = 0

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 4 = 0 ⇒ x = 4

Answer:

13.5

Step-by-step explanation:

Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

C: EAF Is the correct answer

The average rate of change of the function over the interval is 4

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

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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The options given are correct formulas and should use the distributive law √5(√7-√2) for simplicity.

(√5+√2)(-√7)

distribution characteristics

Given integers A, B, and C. According to the distributive law,

A(B + C) = AB + AC

From the formula we can see that A is distributed over B and C.

Therefore, the sum of the coefficients and terms must be in the parentheses of the distribution properties. Based on the options given, the correct formulas that should use the distribution characteristics for simplicity are √5(√7-√2) and

(√5+√2)(-√7)

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Step-by-step explanation:

As a ream or

500

sheets of paper weigh

4.818

pounds

One sheet of paper weighs

4.818

500

=

0.009636

pounds.

It is apparent that pound is too big a unit for a sheet of paper.

As each pound has

16

ounces, one can say

one sheet of paper weighs

0.009636

×

16

=

0.154176

ounces.

If ounce is too big, as we have

1

pound equal to

28.34952

grams

one sheet of paper weighs

0.154176

×

28.34952

≈

4.371

grams

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\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

Step-by-step explanation:

f(x)=2x

note: putting anything in the f(x) parentheses replaces x in the function with that value

so,

f(-3) = 2(-3) = -6

f(0) = 2*0 = 0

f(2) = 2(2) = 4

Answer:

Find the perimeter of a park that measures 7 miles by 910 miles. Get the answers you need, now! ... Advertisement tasha005111 is waiting for your help. Add your answer and earn points. kaylapoo34 kaylapoo34 Answer: the answer is 130. Step-by-step explanation: ... 15 Niles and Bob sailed at the same time for the same length of time.

Step-by-step explanation:

Answer:B

Step-by-step explanation:

The 90% confidence interval for the proportion of all faculty members at the community college who know sign language is (0.0420, 0.1348)

We can use the formula for a confidence interval for a proportion to calculate the interval

CI = p ± zsqrt(p(1-p)/n)

where:

p is the sample proportion (13/147 = 0.0884)

z is the z-score for the desired confidence level (90% confidence level corresponds to a z-score of 1.645)

n is the sample size (147)

Substituting the values, we get

CI = 0.0884 ± 1.645sqrt(0.0884(1-0.0884)/147)

Simplifying the expression, we get

CI = 0.0884 ± 0.0464

Therefore, the 90% confidence interval for the proportion of all faculty members at the community college who know sign language is

CI = (0.0420, 0.1348)

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Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Answer:

120 bicycles

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

1.81 inches

Step-by-step explanation:

Given that,

The circumference of the largest orange in a bag is \(9\dfrac{5}{8}\ \text{inches}\) and that of smallest orange is \(7\dfrac{13}{16}\ \text{inches}\).

Difference = largest orange - smallest orange

= \(9\dfrac{5}{8}-7\dfrac{13}{16}\\\\=\dfrac{77}{8}-\dfrac{125}{16}\\\\=\dfrac{29}{16}\\\\=1.81\ \text{inches}\)

So,  difference of the circumferences of the smallest orange and the largest orange is 1.81 inches

instantaneous rate of change of the search length 0.1667 seconds per

We need to take the derivative of the function S(n) with respect to n and evaluate it at n=12 in order to determine the instantaneous rate of change of the search length for a set of 12 articles.

Taking the derivative of S(n) with respect to n using the chain rule, we get:

S'(n) = 1.6 * (1/(0.8n)) * 0.8 = 2/n

Evaluating this expression at n=12, we get:

S'(12) = 2/12 = 0.1667 seconds per article

This indicates that the search time will increase by approximately 0.1667 seconds per article if the set contains 12 articles by one unit. Alternately, the search time per article will decrease by approximately 0.1667 seconds if the set's number of articles decreases by one unit from 12.

Therefore, the units for the instantaneous rate of change are "seconds per article", indicating the change in search time for each additional or fewer article in the set.

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Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees

The diagram is not shown; however, the question can still be answered.

The given angles are:

\(\theta_1 = 74.0^o\)

\(\theta_2 = 66.0^o\)

Represent the third angle as \(\theta_3\)

The helicopter and the 2 VORs form a triangle.

So, we make use of the following theorem to calculate the third angle

\(\theta_1 + \theta_2 + \theta_3= 180^o\) ---- sum of angles in a triangle

Substitute known values

\(74.0^o + 66.0^o + \theta_3= 180^o\)

\(140.0^o + \theta_3= 180^o\)

Collect like terms

\(\theta_3= 180 -140.0^o\)

\(\theta_3= 40^o\)

Hence, the third angle is 40 degrees.

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Answer:

Perimeter of rectangle ABCD = 9.64 units

Step-by-step explanation:

The formula used to calculate perimeter of rectangle is:

\(Perimeter\: of\: rectangle=2(Length+ Width)\)

We know that rectangle has opposite sides same i.e Length (AB and CD) are same and Width( AD and BD) are same

We need to find Length and Width to find the perimeter

So, if we find Length AB and Width AC we can find perimeter

Finding Length AB

The length AB can be found using distance formula: \(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We have A =(-6,-4) and B(-4,-4)

So, x_1=-6, y_1=-4, x_2=-4, y_2=-4

Putting values in formula and finding length

\(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-4-(-6))^2+(-4-(-4))^2}\\Distance=\sqrt{(-4+6)^2+(-4+4)^2}\\Distance=\sqrt{(2)^2+(0)^2}\\Distance=\sqrt{4+0}\\Distance = 2\)

So, Length AB = 2

Now, Finding Width AC

The length AB can be found using distance formula: \(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We have A =(-6,-4) and C(-4,-2)

So, x_1=-6, y_1=-4, x_2=-4, y_2=-2

Putting values in formula and finding length

\(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-6-(-4))^2+(-4-(-2))^2}\\Distance=\sqrt{(-6+4)^2+(-4+2)^2}\\Distance=\sqrt{(-2)^2+(-2)^2}\\Distance=\sqrt{4+4}\\Distance = \sqrt{8}\\Distance=2.82\)

So, Width AD = 2.82

Now, We have Length = 2 and Width = 2.82

Finding perimeter of rectangle

\(Perimeter\: of\: rectangle=2(Length+ Width)\\Perimeter\: of\: rectangle=2(2+ 2.82)\\Perimeter\: of\: rectangle=2(4.82)\\Perimeter\: of\: rectangle=9.64\)

So, Perimeter of rectangle ABCD = 9.64 units

Answer:

thx m8

Step-by-step explanation:

:)

Answer:

No idea but ok