Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

cot x sec4x = cot x + 2 tan x + tan3x

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x

1 + sec2x sin2x = sec2x

sine of x divided by one minus cosine of x + sine of x divided by one minus cosine of x = 2 csc x - tan2x + sec2x = 1

Answer:

C(x) = 5x + 20 (for members)

C(x) = 3.5x (for non-members)

Step-by-step explanation:

Cost of membership = $20

Price of a game per month = $5

So, the linear equation to compute the total cost for a member can be computed by:

C(x) = 5x + 20

where x is the number of games per month

On the other hand, non-members can get one more game per month for $7 which means they get 2 games for $7. The price for a single game is $7/2 = $3.5 a month.

The linear equation to compute the total cost for a non-member is:

C(x) = 3.5x

where x is the number of games per month.

The following system of equations can be used to decide whether to become a member or not, by substituting the number of games in place of x and finding out the total cost.

C(x) = 5x + 20 (for members)

C(x) = 3.5x (for non-members)

Answer:

[tex]m\angle E=58^o[/tex]

Step-by-step explanation:

we know that

In the right triangle DEF

[tex]tan(E)=\frac{DF}{EF}[/tex] ----> by TOA (opposite side divided by adjacent side)

[tex]tan(E)=\frac{8}{5}[/tex]

[tex]m\angle E=tan^{-1}(\frac{8}{5})=58^o[/tex]

Answer:

Step-by-step explanation:

This is classic right triangle trig.  We have the reference angle of 59 degrees, we have the side adjacent to that angle of 4 units, and we are looking for CD which is the hypotenuse of the triangle.  That is the cosine ratio:

[tex]cos\theta=\frac{adj}{hyp}[/tex]

Filling in:

[tex]cos(59)=\frac{4}{hyp}[/tex]

Doing some algebraic acrobats there to solve for the hypotenuse gives you:

[tex]hyp=\frac{4}{cos(59)}[/tex]

Use your calculator to solve this in degree mode:

hyp = 7.8 units

Answer:

a.)   depth of the lake = (volume of the lake) / area of lake

            = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet

b.) 11 inches  = 0.9167 feet

    Water gained in cubic feet gained by the lake

         = 624,305,840,400 [tex]\times[/tex]  0.9167  

         = 572,282,434,719.5 cubic feet

c.) the percentage change in the lake volume over that year

      = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet

      =  0.0033

      = 0.33%

Step-by-step explanation:

i) acres to square feet :    1 acre = 43560 square feet

  therefore 14,332,090 acres  = 624,305,840,400 square feet

ii) 1 mile  = 5280 feet

   1 cubic mile  = 5280 [tex]\times[/tex] 5280 [tex]\times[/tex] 5280 = 147,197,952,000 cubic feet

therefore 1180 cubic miles  = 173,693,585,360,000 cubic feet

a.)   depth of the lake = (volume of the lake) / area of lake

            = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet

b.) 11 inches  = 0.9167 feet

    Water gained in cubic feet gained by the lake

    = 624,305,840,400 [tex]\times[/tex]  0.9167   = 572,282,434,719.5 cubic feet

c.) the percentage change in the lake volume over that year

  = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet

   =  0.0033

  = 0.33%

Answer:

a) -2x^2 + 164x

b) 3362 feet

c) (82 , -328)

d) yes

Step-by-step explanation:

y = -2x^2 + 160x

Slope = 4 feet downward for every 1 horizontal foot.

a) h(x) = -2x^2 + 160x - (-4x)

= -2x^2 + 160x + 4x

= -2x^2 + 164x

b) The highest point occurs at the vertex of the parabolic equation. x is the same as the number of the axis of symmetry.

x = -b/2a

From the equation, a = -2 , b= 164

x = -164/ 2(-2)

x = -164/-4

x = 41

Put x = 41 into the value of h(x)

h(x) = -2x^2 + 164x

= -2(41^2) + 164(41)

= -2(1681) + 6724

= -3362 + 6724

= 3362 feet.

The maximum height occurs at 41 feet out from the top of the sloping ground at a height of 3362ft about the top edge of the cliff.

c) h(x) = -2x^2 + 164x

2x^2 - 164x + h = 0 when 0 ≤ x ≤ 41

Solve the equation using the formula (-b+/-√b^2 - 4ac) / 2a

a = 2, b= -164 , c = h

= [-(-164) +/- √(-164)^2 - 4(2)(h) ] / 2(2)

= (164 +/- √26896 - 8h)/ 4

This gives the value of -328 ≤ h ≤ 3362 is used because the rocket hits the sloping ground of (82 , -328)

d) the function still works when it is going down

We first find the function h=f(x) for the rocket's height above the ground. The maximum height is found using the vertex formula with x=(-b)/(2a). We can also determine the function x=g(h) for when the rocket is going up, but this does not work for when the rocket is going down due to needing negative roots.

(a) Because the ground slopes 4 feet downward for every 1 horizontal foot, the ground line equation is y=-4x. So, to find the height of the rocket 'h' above the ground, we subtract the equation of the rocket's path from this equation for height of the ground, which gives h=f(x)=y-(-4x)=-2x²+160x+4x=-2x²+164x.

(b) To find the maximum height (vertex) of the parabolic path the rocket takes, we use x=(-b)/(2a) from the standard quadratic equation format (ax²+bx+c=0). Here, a=-2 and b=164. So, x=(-164)/(2*-2)=41. Therefore, the maximum height is when x=41, and we substitute x=41 into the equation h=f(x) to find the maximum height.

(c) To obtain x as a function of h, we can rearrange our equation for h=f(x) to make x=g(h). This will be a square root function because of the x² in the equation. However, since we only want the going up part, we just consider the positive root.

(d) This function doesn't work for when the rocket is going down as it would require considering the negative root, which isn't included in our function g(h) as it involves square roots.

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The percentage of male workers who preferred a female boss increased at a rate of 0.1667% per year from 1974 to 1998. Using this information, we can predict that 9% of male workers would prefer a female boss in the year 1998.

This question involves linear relationships and prediction in mathematics. In this case, we're looking at an increase from 5% to 9% in male workers who preferred a female boss--this increase occurred over a period of 24 years (from 1974 to 1998). So, the rate of increase in male workers who preferred a female boss over those years was (9% - 5%) / 24 years = 0.1667% per year. Since the percentage was 5% in the beginning year 1974, we need to find the year when this percentage will become 9%. So, 9% = 5% + 0.1667% * (number of years from 1974). Solving this for the number of years gives approximately 24 years. Therefore, the year when 9% of male workers will prefer a female boss would be 1974+24 = 1998

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Answer:

25% of probabilities

Step-by-step explanation:

A= red eye

a=sepia eye

B=longwing

b=apterous

         AB         aB

Ab     AABb     AaBb

ab      AaBb     aaBb

AABb=25%

AaBb=25%

Ab= 25%

aaBb=25%

aaBb= sepia eye with longwig

Answer:

Exact circumference is [tex]7\frac{49}{150}km[/tex]

Approximate circumference is [tex]7.33 km[/tex]

Step-by-step explanation:

We are given;

We are required to determine the exact and approximate circumference of the circle.

Taking π as 3.14

[tex]Circumference=3.14 (2\frac{1}{3}km)[/tex]

                          [tex]=7\frac{49}{150}km[/tex]

The exact circumference of the circle is [tex]7\frac{49}{150}km[/tex]

[tex]7\frac{49}{150}km=7.327 km\\ = 7.33 km (nearest hundredth)[/tex]

Thus, the approximate circumference of the circle is [tex]7.33 km[/tex]

Answer:

Some details are missing in the question, here are the details ; A proton initially has v = -6.5i + 17j + 13k and then 8.00s later has v = -2.8i + 17j - 9.3k (in meters per seconds).

a) proton's average acceleration in unit vector notation = 0.46i - 2.78k

b) Magnitude = 2.85m/s2

c) angle between and the positive direction of the x axis = 279.39 degree (counter clockwise)

Step-by-step explanation:

The detailed and step by step explanation is as shown in the attachment

Answer:

  3

Step-by-step explanation:

Each term of the sequence has 0.5 added to the one before. The first 10 terms are ...

  -1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0

f(10) = 3.0

_____

If you like, you can use the given information about the first term (-1.5) and the common difference (0.5) to write an explicit formula:

  f(n) = f(1) +d(n -1)

  f(n) = -1.5 +0.5(n -1)

Then the 10th term is ...

  f(10) = -1.5 +0.5(10 -1) = -1.5 +4.5 = 3

Answer:3.46$

Step-by-step explanation:

Probability distribution:

[tex]\to x \ \ \ \ \ \ \ -\$5 \ \ \ \ \ \ \ \$0 \ \ \ \ \ \ \ \$5\\\\\to P(x) \ \ \ \ \ \ \ 0.36 \ \ \ \ \ \ \ 0.48 \ \ \ \ \ \ \ 0.16\\\\[/tex]

[tex]\to \mu_{x}= Mean\ (X)= E(X) \ = - \$ 1\\\\\to \sigma^{2}_{x}= \Sigma_{x} x^2 p(x)- (\mu_{x})^2\\\\[/tex]  

         [tex]=(-5)^2 \times 0.36 + 0+ (5)^2 \times 0.16 - (-1)^2\\\\=25 \times 0.36 + 0+ 25 \times 0.16 - 1\\\\=9 + 0+ 4 - 1\\\\= 13-1\\\\=12\\\\[/tex]

Therefore,  

[tex]\to \sigma_{x}=\sqrt{12}= \$ 3.464[/tex]

Therefore, the final answer is "3.464".

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Step-by-step explanation:

∫₋₂² (f(x) + 6) dx

Split the integral:

∫₋₂² f(x) dx + ∫₋₂² 6 dx

Graphically, if f(-x) = -f(x), then ∫₋₂² f(x) dx = 0.  But we can also show this algebraically.

Split the first integral:

∫₋₂⁰ f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Using substitution, write the first integral in terms of -x.

∫₂⁰ f(-x) d(-x) + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₂⁰ f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Flip the limits and multiply by -1.

∫₀² f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Rewrite f(-x) as -f(x).

∫₀² -f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₀² f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

The integrals cancel out:

∫₋₂² 6 dx

Evaluating:

6x |₋₂²

6 (2 − (-2))

24

Henry will have run a total of 1540 miles on his new running shoes after 5 weeks.

To find the total mileage on Henry's shoes after 5 weeks, we need to calculate the distance he runs each week and add them up.

In week 1, Henry runs 20 miles per day, so the total distance he runs in week 1 is 20 miles * 7 days = 140 miles.

In week 2, he adds 12 miles to his daily routine, so he runs 20 miles + 12 miles = 32 miles per day. The total distance he runs in week 2 is 32 miles * 7 days = 224 miles.

We can continue this pattern for the remaining weeks:

Week 3: 44 miles per day, total distance = 44 miles * 7 days = 308 miles

Week 4: 56 miles per day, total distance = 56 miles * 7 days = 392 miles

Week 5: 68 miles per day, total distance = 68 miles * 7 days = 476 miles

The total mileage on Henry's shoes after 5 weeks is the sum of the total distances in each week: 140 + 224 + 308 + 392 + 476 = 1540 miles.

Answer:

Therefore the value of x is

[tex]x=5[/tex]

Step-by-step explanation:

Given:

Consider the figure such that

PQ || BC

AP = 20 , AB = 36

AQ = 5x , AC = 45

To Find:

x = ?

Solution:

In Δ APQ and Δ ABC

∠APQ ≅ ∠ACB {Corresponding angles are equal since PQ is parallel to BC}

∠A≅ ∠A  ……….....{Reflexive Property}  

Δ APQ~ Δ ABC….{Angle-Angle Similarity test}  

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}=\dfrac{PQ}{BC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}\\\\\dfrac{20}{36} =\dfrac{5x}{45}\\\\x=\dfrac{20\times 45}{36\times 5}=5\\\\x=5[/tex]

Therefore the value of x is

[tex]x=5[/tex]

Answer:

26.67 hours

Step-by-step explanation:

Given:

Number of hours of service projects (N) = 40 hours

Time taken to complete the garden project is two-third of the total time.

Therefore, the time taken to complete the garden project can be obtained by multiplying the part to the total time taken.

So, the hours taken for garden project is given as:

[tex]x=\frac{2}{3}\times N\\\\x=\frac{2}{3}\times 40\\\\x=\frac{80}{3}\\\\x=26.67\ hours[/tex]

Therefore, it took 26.67 hours to complete the garden project.

Answer:

Rocket will land on the ground in 3 seconds.

Step-by-step explanation:

Given:

[tex]A(t) = -16t^2 + 32t + 48[/tex]

where [tex]t[/tex] ⇒ time in seconds since launch.

[tex]A(t)[/tex] ⇒ altitude of the rocket after reaching the ground.

we need to find the time at which rocket will land on the ground.

Solution:

Now we can say that;

altitude of the rocket after reaching the ground will be equal to 0.

So;

[tex]A(t)=0[/tex]

Now Substituting [tex]A(t)=0[/tex] in given expression we get;

[tex]0=-16t^2+32+48[/tex]

Now we take -16 common we get;

[tex]0=-16(t^2-2t-3)[/tex]

Now Dividing both side by -16 we get;

[tex]\frac0{-16}=\frac{-16(t^2-2t-3)}{-16}\\\\0=t^2-2t-3[/tex]

Now factorizing the above equation we get;

[tex]0=t^2-3t+t-3\\\\0=t(t-3)+1(t-3)\\\\0=(t+1)(t-3)[/tex]

Now we will find 2 values of t by substituting each separately.

[tex]t+1=0 \ \ \ Or \ \ \ \ t-3 =0\\\\t =-1 \ \ \ \ \ \ Or \ \ \ \ \ \ t=3[/tex]

Now we get 2 values of t one positive and one negative.

Now we know that time cannot e negative hence we will discard it and consider positive value of t.

Hence Rocket will land on the ground in 3 seconds.

Answer:

697.87

Step-by-step explanation:

You are looking for the monthly payment (PMT) on a loan (borrow = loan).

This is the formula you would use for installment loans (loan payment)

PVA = PMT [(1 - (1+APR/n)^-nY)/APR/n]

NOTE:

PMT = regular payment amount  = ?

PVA = starting loan principal (amount borrowed)  = 29542

APR = annual percentage rate (as a decimal)  = 0.063

n = number of payment periods per year  (they told you that it is monthly, so n =12)

Y = loan term in years (can be a fraction) = 4

NOTE: a helpful tip is so start with the original formula and rearrange it to make what you are looking for the subject of the formula.

We're solving for the monthly payment. So rearrange the formula:

PVA = PMT [(1 - (1+APR/n)^-nY)/APR/n]

PMT = [PVA (APR/n)]/(1 - (1+APR/n)^-nY)

PMT = [29542 (0.063/12)] / (1 - (1+ 0.063/12)^-12x4)

∴ PMT = 697.8653...

Round off the answer to as many decimal places as instructed by your lecturer/teacher.

Here we have rounded off to 2 decimal places:

∴ PMT = 697.87

Based on the information given the monthly payment is $697.87 .

Given:

PMT = ?

PVA =29542

APR = 6.3% or  0.063

n =12×4=48

Hence:

PMT = [29542 (0.063/12)] / (1 - (1+ 0.063/12)^-12x4)

PMT = [29542 (0.063/12)] / (1 - (1+ 0.00525)^-12x4)

PMT = [29542 (0.00525)] / (1 - (1.00525)^-48)

PMT = [29542 (0.00525)] / (1-0.777757)

PMT = 155.0955/0.22224274

PMT = 697.865316

PMT= 697.87 (Approximately)

Inconclusion  the monthly payment is $697.87 .

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Answer:

The first one.

Step-by-step explanation:

We can say lines L and K are parallel, because they have the same slope and different y intercepts.

This would mean they will always be moving in the same direction, hence causing them to never touch.

Mean and Mean Absolute Deviation

Step-by-step explanation:

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Here's how to calculate the mean absolute deviation.

Step 1: Calculate the mean.

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

Step 3: Add those deviations together.

Step 4: Divide the sum by the number of data points.

The probability of having wrinkled green peas is 25% or 0.25

Explanation:

Given:

Pea shape - smooth and wrinkled

Pea color - Yellow and green

Smooth is dominant to wrinkled

Yellow color is dominant to green

So, the genotype of smooth pea is SS or Ss

                                 wrinkled pea is ss

The genotype of yellow pea is YY or Yy

                                 green pea is yy

According to the question,

Ssyy X ssYy

Possible gametes of Ssyy - Sy , Sy, sy, sy

Possible gametes of ssYy - sY, sy, sY, sy

Cross between these gametes are shown in the punnett square drawn in the word file attached.

According to the cross,

The probability of having wrinkled green peas is 25% or 0.25

Answer:

(A)  [tex]C(x)=2.15x+525[/tex]

(B) 188 books

(C) 545 books

Step-by-step explanation:

We have been given that Alfred Juarez's fixed cost to produce a typical poetry volume is $525, and his total cost to produce 1000 copies of the book is $2675.

(A) The cost function will be in form [tex]C(x)=ax+b[/tex], where, a is cost of each copy, x is number of books and b is fixed cost.

Upon substituting our given information, we will get:

[tex]2675=1000a+525[/tex]

Let us solve for a.

[tex]2675-525=1000a[/tex]

[tex]2150=1000a[/tex]

[tex]a=\frac{2150}{1000}=2.15[/tex]

Therefore, the cost function would be [tex]C(x)=2.15x+525[/tex].

(B) Since each book sells for $4.95, so amount earned by selling x books would be [tex]4.95x[/tex]

Revenue function would be [tex]R(x)=4.95x[/tex]

We know that break-even is a point, where cost is equal to revenue or when there is a 0 profit.

[tex]R(x)=C(x)\\\\4.95x=2.15x+525[/tex]

[tex]4.95x-2.15x=525[/tex]

[tex]2.8x=525[/tex]

[tex]x=\frac{525}{2.8}[/tex]

[tex]x=187.5\approx 188[/tex]

Therefore, Alfred must produce 188 poetry books to break even.

(C) We know that profit is equal to difference of revenue and cost.

[tex]\text{Profit}=\text{Revenue}-\text{Cost}[/tex]

[tex]P(x)=4.95x-(2.15x+525)[/tex]

[tex]1000=4.95x-(2.15x+525)[/tex]

[tex]1000=4.95x-2.15x-525[/tex]

[tex]1000=2.8x-525[/tex]

[tex]1000+525=2.8x[/tex]

[tex]1525=2.8x[/tex]

[tex]x=\frac{1525}{2.8}[/tex]

[tex]x=544.642857\approx 545[/tex]

Therefore, Alfred must produce and sell 545 books to make a profit of $1000.

Answer:

n≅376

So sample size is 376.

Step-by-step explanation:

The formula we are going to use is:

[tex]n=pq(\frac{z_{\alpha/2}}{E})^{2}[/tex]

where:

n is the sample size

p is the probability of favor

q is the probability of not in favor

E is the Margin of error

z is the distribution

α=1-0.98=0.02

α/2=0.01

From cumulative standard Normal Distribution

[tex]z_{\alpha/2}=2.326[/tex]

p is taken 0.5 for least biased estimate, q=1-p=0.5

[tex]n=0.5*0.5(\frac{2.326}{0.06})^{2}\\n=375.71[/tex]

n≅376

So sample size is 376

Answer:

Step-by-step explanation:

4π r²=144 π

r²=36

r=6 cm

Answer: he bought 2 adult tickets and 7 children tickets.

Step-by-step explanation:

Let x represent the number of adult tickets that he bought.

Let y represent the number of children tickets that he bought.

He brought some adult tickets and some children tickets for a total of 9 tickets. This means that

x + y = 9

The adult tickets cost $10 per ticket and the children tickets cost $8 per ticket if he spent a total of $76, it means that

10x + 8y = 76 - - - - - - - - - - - -1

Substituting x = 9 - y into equation 1, it becomes

10(9 - y) + 8y = 76

90 - 10y + 8y = 76

- 10y + 8y = 76 - 90

- 2y = - 14

y = - 14/ -2

y = 7

x = 9 - y = 9 - 7

x = 2

Yo sup??

Since the two figures are similar therefore their sides are in proportion.

for the first one

factor=2/8=1/4

for the second

factor=10/4=5/2

Hope this helps.

Answer: 7

Step-by-step explanation:

Answer: Debt- Equity ratio is 0.41

Step-by-step explanation: Debt- Equity ratio is calculated by subtracting one from the equity multiplier.

To solve this problem the du pont analysis is used which is Return on equity = Profit margin * Total Asset turnover * equity multiplier

0.1834 = 0.062 × 2.10 * Equity multiplier (EM)

0.1834 = 0.1302

EM = 1.41

Therefore debt-equity ratio = EM - 1

= 1.41 - 1 = 0.41

Final answer:

The Debt-Equity Ratio of Kindle Fire Prevention Corp. is calculated using the Dupont Identity formula, which links ROE to profit margin, asset turnover, and the equity multiplier. Using the provided financial ratios, the calculated Debt-Equity Ratio is 139.86 after rounding to two decimal places.

Explanation:

The student has asked to calculate the debt–equity ratio for Kindle Fire Prevention Corp. using given financial ratios. To find the debt–equity ratio, we use the Dupont Identity which links the Return on Equity (ROE) to profit margin, asset turnover, and the equity multiplier (which is inversely related to the debt-equity ratio).

First, we express ROE as the product of profit margin, asset turnover, and equity multiplier:

ROE = Profit Margin × Total Asset Turnover × Equity Multiplier

Given: ROE = 18.34%, Profit Margin = 6.2%, Asset Turnover = 2.1

We rearrange the formula to solve for Equity Multiplier:

Equity Multiplier = ROE / (Profit Margin × Total Asset Turnover)

Substitute the given values:

Equity Multiplier = 18.34% / (6.2% × 2.1) = 18.34 / (0.062 × 2.1)

Equity Multiplier = 18.34 / 0.1302 = 140.862

Since Equity Multiplier = 1 + Debt-Equity Ratio, we can find the Debt-Equity Ratio by subtracting 1 from Equity Multiplier:

Debt-Equity Ratio = Equity Multiplier - 1 = 140.862 - 1 = 139.862

Therefore, the Debt-Equity Ratio of Kindle Fire Prevention Corp. is 139.86 (rounded to two decimal places).

Answer: The maximum = 3 tons

Step-by-step explanation:

The cost function C(x) = x + 5x + 7

P(×) = 13x - x^2 - 5x -7

If x <3

P= x^2 +8x -7

Differentiating to get x

dp/dx = -2x + 8

X= 8/2

C=4

Maximum will be 3 tons

When x=3

P= 13x - x^2 -5x +7 -3x + 9

When x>3

dp/dx = x^2+5x +2

X = 5/2 = 2.5

Answer:

7

Step-by-step explanation:

[tex]\sum\limits_{t=1}^{3}(4\cdot(\frac{1}{2})^{t-1})[/tex]

This is the sum of the first three terms of a geometric sequence, where the first term is 4 and the common ratio is ½.

We can use a formula to find the sum, or, since there's only three terms, we can find the value of each term then add up the results.

4 · (½)¹⁻¹ = 4

4 · (½)²⁻¹ = 2

4 · (½)³⁻¹ = 1

4 + 2 + 1 = 7

Answer: she invested $17000 in the account earning 6% annual interest.

she invested $13000 in the account earning 7.5% annual interest.

Step-by-step explanation:

Let x represent the amount that she invested in the account earning 6% annual interest.

Let y represent the amount that she invested in the account earning 7.5% annual interest.

Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. This means that

x + y = 30000

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the account earning 6% annual interest.

P = x

R = 6%

T = 1 year

I = (x × 6 × 1)/100 = 0.06x

Considering the account earning 7.5% annual interest,

P = y

R = 7.5

T = 1

I = (y × 7.5 × 1)/100 = 0.075y

Last year she earned $1995 in interest. This means that

0.06x + 0.075y = 1995 - - - - - - - -

Substituting x = 30000 - y into equation 1, it becomes

0.06(30000 - y) + 0.075y = 1995

1800 - 0.06y + 0.075y = 1995

- 0.06y + 0.075y = 1995 - 1800

0.015y = 195

y = 195/0.015 = 13000

x = 30000 - y = 30000 - 13000

x = 17000

Answer:

Our answer is $2000

Step-by-step explanation:

Short term capital loss = $1000

Long term capital loss = $4000

Taxable Income = $30000

Long term capital loss carryover to 2019 = ($1000 + $4000) - $3000 = $2000