Decreasing the number of years of a loan decreases the amount of interest repaid over the term of the loan. Suppose a dental hygienist has the option of a 30-year loan or a 25-year loan of $345,000 at an annual interest rate of 3.75%.
(a)
a) Calculate the monthly payment (in dollars) for each loan. (Round your answers to the nearest cent.)
30-year loan
25-year loan

b) Calculate the savings in interest (in dollars) by using the 25-year loan. (Round your answer to the nearest cent.)

The total company fund before any bonuses were paid is $995 and there were 20 staffs.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Let y represent the total company fund and x represent the number of staffs.

From the first statement:

y - 50x = -5  (1)

Also:

y - 45x = 95    (2)

From equation 1 and 2:

x = 20, y = 995

The total company fund before any bonuses were paid is $995 and there were 20 staffs.

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Part 1)  [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.

Part 2)  The series converges

======================================================

Work Shown:

[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]

[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]

Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series  

[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]  

either converge together or diverge together due to the Limit Comparison Test.

But the simpler series is known to converge (p-series test).

Therefore, the original series converges as well.

The two series likely don't converge to the same value, but they both converge nonetheless.

Answer is b. ( -1, -5)

Answer is b. (-1, -5)

Step by step

Substitute the x and y values into both equations to find equality

 Answer b. Makes both equations equal

2x + y = -7

2(-1) + (-5) = -7

-2 -5 = -7

-7 = -7
it equals now let’s do the 2nd one

x - y = 4

-1 -(-5) = 4

4 = 4

This one equals too. I did the math on the other three answers and they did not equal. 

Option A is correct. The gross profit that has been calculated for this year is given as 17545

22050 × 97.5%(100-2.5%) = 21498.75

= 21498.75 × 0.975 = 20961.28

= 20961.28 x 0.975 = 20437.24

= 20437.24 x  0.975  = 19926.31

= 19926.31 ×  0.975  = 19428.15

= 19428.15 x  0.975  = 18942.45

= 18942.45 x  0.975  = 18468.80

= 18468.89 ×  0.975  = 18017

= 18007 × 0.975  = $17545

Hence we can see at the end of the solution that the value of the gross profit in 2028 = $17545

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Answer: Option (3)

Step-by-step explanation:

[tex]\frac{1}{6a^2}-\frac{5b}{3a^3}+\frac{b^2}{4a}\\\\=\frac{2a}{12a^3}-\frac{20b}{12a^3}+\frac{3a^2 b^2}{12a^3}\\\\=\frac{3a^2 +b2 +2a-20b}{12a^3}[/tex]

Answer:

c = -75

Step-by-step explanation:

cd + (-6c) = 150

d = 4

c(4) + (-6c) = 150

4c - 6c = 150

-2c = 150

c = -75

The volume of the rectangular box is the product of the base area and the height 3x - 1

The given parameters are:

Length = 3x + 4

Width = 3x

Height = 3x - 1

The base area of the rectangular box is calculated as

Base area = Length * Width

Substitute the known values in the above equation

Base area = 3x(3x + 4)

This means that the volume of the rectangular box is the product of the base area and the height 3x - 1

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Answer:

The third one

Step-by-step explanation:

It cannot be the first 2 as the corners wouldn't line up. It cannot be the last one as B and R are not the same angles

Answer: 5 units

Step-by-step explanation:

x+2+2x-7=13

solve for x

3x=18

x=6

∴SR: 2x-7

=2(6)-7

=12-7

=5

Answer:

SR = 5

Step-by-step explanation:

[tex]TR=x+2+2x-7=3x-5[/tex]

[tex]3x-5=13[/tex]

[tex]3x=13+5[/tex]

[tex]x=18/3=6[/tex]

[tex]SR=2x-7=2(6)-7=12-7=5[/tex]

Hope this helps

Answer:

[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]

Step-by-step explanation:

We are given the trigonometric equation of:

[tex]\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}[/tex]

Let u = 4x then:

[tex]\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}[/tex]

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

[tex]\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]

Convert u-term back to 4x:

[tex]\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]

Divide both sides by 4:

[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]

The regression equation based on the information given about the sugar contents will be 0.18x - 20.84.

It should be noted that from the information, the accompanying data are the caloric contents and the sugar contents of 11 high-fiber breakfast cereals.

The sugar content will be:

a. 160 calories

= 0.18x - 20.84.

= 0.18(160) - 20.84

= 7.96

b. 90 calories

= 0.18x - 20.84.

= 0.18(90) - 20.84

= -4.64

c. 175 calories

= 0.18x - 20.84.

= 0.18(175) - 20.84

= 10.66

d. 208 calories

= 0.18x - 20.84.

= 0.18(208) - 20.84

= 16.6

Therefore, the sugar contents is illustrated above.

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The system of inequalities be

3x+2y ≤ 25, 4x+6y ≤ 37

1) Maximum number of sundaes possible exists 9.

2) Maximum number of milkshakes possible exists 6.

3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.

A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.

Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.

Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.

Let x represent the number of sundaes he creates and y the number of milkshakes he creates.

We represent in tabular form,

                    Sundae(x)      Milkshake(y)     Total

Ice-cream          3                         2             3x+2y

Strawberries      4                        6             4x+6y

System of inequalities:

Sundaes and milkshakes with at most 25 ice-cream scoops exist

33x+2y ≤ 25.

Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.

1) Maximum number of sundaes possible:

Maximum number of sundaes possible when y = 0

From the graph y = 0 at x = 9.25

Therefore, the maximum number of sundaes possible exists at 9.

2) Maximum number of milkshakes possible:

Maximum number of milkshakes possible when x = 0

From the graph x = 0 at y = 6.167

Therefore, the maximum number of milkshakes possible exists at 6.

3) Combination that utilizes the most of both Ice-cream and Strawberries:

A combination of both is possible there exists an intersection of both the equation.

From the graph, the intersection point exists x = 7.6 and y = 1.1.

Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.

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Answer: $51156

Step-by-step explanation:

a = b x p%

how much will the price increase

a = 49,000 x 4.4%

= 49,000 x 0.044

= $2156

price of next model

49,000 + 2156 = $51156

Grandma should be able to make three slices of French toast by slicing one of the original slices into two.

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Answer:

21

Step-by-step explanation:

(-4)(-2)+2(6+5)

(8)+2(11)

10+11

21

Hope this helps! :)

Answer:32

Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32

Answer:

11 and 2/3

Step-by-step explanation:

The given expression be [tex]$(5)^{7/3[/tex] then the value exists ³√5⁷.

The base number exists raised to a power of the exponent numerator and estimated to the root of the exponent denominator.

Given: [tex]$(5)^{7/3[/tex]

The given expression contains an exponent of (7/3)

When we exist transforming from exponential form to radical form you always place the numerator as our constant's exponent in the radical ( [tex]$5^{\frac{7}{3} }$[/tex] exists named the radicand because it exists found in the radical) and the denominator in front of the radical, where it would be named the index.

The formula would be: [tex]$(\sqrt[n]{x})^{q}=x^{\frac{p}{q}}$[/tex]

Therefore, the correct answer is ³√5⁷.

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The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

The given parameters are:

Rate, r = doubles every two days

Initial number of strain, a = 1

This means that the function is an exponential function.

An exponential function is represented as:

A(d) = a * r^d

Since the strain doubles every two days, we have:

A(d) = a * r^(d/2)

Substitute the known values in the above equation

A(d) = 1 * 2^(d/2)

Evaluate the product

A(d) = 2^(d/2)

When there are 256 bacterial cells, the equation becomes

2^(d/2) = 256

Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

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Answer:

f(-6)= -19 and g(-4)= -187

Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.

Length

2.6 x 40 = 260

260 cm = 2.6 m

Width

4.5 x 40 = 180

180 cm= 1.8 m

Area

1.8 x 2.6 = 4.68 m

Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

Step-by-step explanation:

68% of all values are within 1 SD (110 ± 15).

95% of all values are within 2SD (110 ± 2×15 = 30)

99.7% of all values are within 3 SD (110 ± 3×15 = 45)

a)

95 is 110 - 15, so exactly 1 SD apart from the mean value.

68% or 0.68 is the probability of all values between 95 and 125.

so, 34% or 0.34 is the probability of all values between 95 and 110. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 95 is

0.34 + 0.5 = 0.84

b)

125 is 110 + 15, so exactly 1 SD apart from the mean value.

so, as per a) 34% or 0.34 is the probability of all values between 110 and 125. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 125 is

0.5 - 0.34 = 0.16

Answer:

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

Step-by-step explanation:

You have to move the variables (r and t) with u to isolate s.

[tex]rs+t=u[/tex]

   [tex]-t[/tex]       [tex]-t[/tex]

------------------------

[tex]rs=u-t[/tex]

÷ [tex]r[/tex]       ÷ [tex]r[/tex]

------------------------

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

Answer:

a) x + 10 = 45

b) 3 = 6 - x

c) d = s * t

Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.

SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.

This is all we're really doing.

Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.

Just keep doing this with all the equations.

Hope this helped!

Answer:

the slope of the line passing through the points (-4,-4) and (2, 5) m=3/2.

Step-by-step explanation:

Hello!

To find the slope between two points use the formula

The required coordinates of the unit circle for s = -11π/6 is (√3/2, 1/2). Using trigonometric functions, the required answer is calculated.

There are six trigonometric functions.

They are sin θ, cos θ, tan θ, sec θ, cosec θ, and cot θ.

Where θ - 0 to 360° or 0 to 2π

For a unit circle, the coordinates are given in the form of trigonometric functions as below:

x = cos θ and y = sin θ

Here it is given that s = θ = -11π/6

So, on substituting,

x = cos θ = cos (-11π/6)

⇒ x = √3/2

y = sin θ = sin (-11π/6)

⇒ y = 1/2

Thus, the required coordinate pair is (√3/2, 1/2).

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The length of the apothem of the regular pentagon shown is 5.2 meters

Represent the central angle of the regular pentagon using x

The value of the central angle of the regular pentagon is then calculated as:

x = 360/n

Where n represents the number of sides

i.e n = 5

So, we have:

x = 360/5

Evaluate the quotient

x = 72

Represents the apothem with y.

The apothem is then calculated as:

tan(x/2) = (Side length/2)/Apothem

This gives

tan(72/2) = (7.6/2)/y

Evaluate the quotient

tan(36) =3.8/y

Multiply both sides by y

y tan(36) = 3.8

Divide both sides by tan(36)

y = 3.8/tan(36)

Evaluate the quotient

y = 5.2

Hence, the length of the apothem of the regular pentagon shown is 5.2 meters

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Because the parabola intercepts the x-axis only once, we conclude that the discriminant is 0.

For a quadratic equation:

y = a*x^2 + b*x + c

The discriminant is:

D = b^2 - 4ac

In the graph we can see that the parabola intercepts the x-axis in its vertex, then the parabola has only one real zero, then we conclude that the discriminant is equal to zero.

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Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:

a) 900,000.

b) 78,125.

c) 10,000.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:

[tex]n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1[/tex]

Hence the number is:

N = 9 x 10^5 = 900,000.

For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5[/tex]

Hence the number is:

N = 5^7 = 78,125.

For item c, if the first 3 digits are 277, the parameters are:

[tex]n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10[/tex]

Hence the number is:

N = 10^4 = 10,000.

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The probability that they are female and use public transport is [tex]\mathbf{=\dfrac{1}{3}}[/tex]

The probability that they are female and walk/cycle to college is [tex]\mathbf{=\dfrac{1}{9}}[/tex]

Probability is an area of mathematics that deals with numerical representations of how probable an event is too probable to occur or how probable a statement is to be true.

Probability is synonymous with possibility. It is a mathematical field that is concerned with the occurrence of a random event. The value ranges from zero to one. The definition of probability is to predict the degree to which something is likely to occur.   To determine the likelihood of a particular event occurring, we must first determine the total number of possible outcomes.

Mathematically:

[tex]\mathbf{Probability = \dfrac{number \ of \ required \ outcomes}{total \ number \ of \ possible \ outcomes}}[/tex]

From the table in the image attached below.

The probability that they are female and use public transport is:

[tex]\mathbf{=\dfrac{9}{27}}[/tex]

[tex]\mathbf{=\dfrac{1}{3}}[/tex]

Also, the probability that they are female and walk/cycle to college is:

[tex]\mathbf{=\dfrac{3}{27}}[/tex]

[tex]\mathbf{=\dfrac{1}{9}}[/tex]

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The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.

It should be noted that inequalities are simply used to compare two expressions that are unequal.

It can be seen that the solution set that's illustrated is:

x² + y² <= 16

-1/4x² + 2 <= y

Therefore, the inequality system that has the solution set shown will be option C.

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