Looking for the accumulated value if the money is compounded continuously?

Answer:

The minimum value is 18.55 and the maximum value is 18.64. When rounding to one decimal place, you must look at the number two places after the decimal. If this is bigger than 5 round up and lower than 4 round down.

Step-by-step explanation:

Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.

Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:

Total P+I (A) = $4,200.00

Principal (P) = $2,200.00

Compound (n) = Compounding Continuously

Time (t in years) = 14 years

R = 4.619% per year

The calculation steps are as follows:

Solving for rate r as a decimal

r = ln(A/P) / t

r = ln(4,200.00/2,200.00) / 14

r = 0.0461877

Then convert r to R as a percentage:

R = r * 100

R = 0.0461877 * 100

R = 4.62%/year

Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.

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Answer:

(5,1) (4,2) (1,3)

Step-by-step explanation:

since is going a clockwise rotation the -x(5,4,1) all will become positive

9514 1404 393

Answer:

  $60

Step-by-step explanation:

The total she started with is the sum of the amount she spent and the amount remaining:

  $25.80 +$9.25 +$18.85 +$6.10 = $60.00

Ashley brought $60.00 to the mall.

Answer:

The Total money she bring to mall is $ 60.

Step-by-step explanation:

Given that :-

After a shopping trip to the mall. Ashley saw $6.10 in her purse she spent $ 25.80 on a pair of shoes, 59.25 on a necklace, and $18.85 on a belt.

To find :-

How much money did Ashley bring to the mall ?

Solution :-

Total money she bring to the mall = sum of amount she spend and amount remaining.

Total money = $ 25.80 + $ 59.25 + $ 18.85 + $6.10

Hence, The total money she bring to mall is $ 60.00.

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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Answer:

ok so they test 7 components so the probity of getting a bad one for each is 0.2 so we just multiply this 7 times

0.2*0.2*0.2*0.2*0.2*0.2*0.2=0.0000128

Hope This Helps!!!

The required probability will be 0.0000128 that the first defect is found in the seventh component tested.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

We have been given that a company ships computer components in boxes that contain 50 items.

Assume that the probability of a defective computer component is 0.2.

As per the given condition, the required solution would be as:

They test seven components, and the probability of obtaining a defective one for each is 0.2, so we just multiply this by seven.

⇒ 0.2×0.2×0.2×0.2×0.2×0.2×0.2

⇒ 0.0000128

Thus, the required probability will be 0.0000128 that the first defect is found in the seventh component tested.

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Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Given:

The quadratic equation is

\(y=6x^2-9x+22\)

To find:

The correct application of the quadratic formula.

Solution:

If a quadratic equation is \(ax^2+bx+c=0\), then the quadratic formula is

\(x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\)

We have,

\(y=6x^2-9x+22\)

Putting \(y=0\), we get

\(6x^2-9x+22=0\)

Here, \(a=6,b=-9,c=22\). Using the quadratic formula, we get

\(x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}\)

The correct application of the quadratic formula is \(x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}\).

Note: The options are not in proper format.

We are 95% confident that the true population, mean commute time for the commuter students at KSU is between 15.2 and 31.6 minutes.

We are 95% certain that the true population mean falls within this interval based on the 95% confidence interval. Therefore, if it applies to the student population and not the sample, it is not about the population's distribution. This confidence interval is an inference about the population, not the sample. Therefore, we cannot claim that 95% of the population resides inside those two miles. All that matters is how confident we are that the population parameter falls within that range.

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Let's start by defining some variables:

Let's call Jamal's age "J".

Let's call Alex's age "A".

From the problem statement, we know that:

J = A - 5 (Jamal is 5 years younger than Alex)

J * A = 300 (the product of their ages is 300)

We can use the first equation to substitute J in the second equation:

(A - 5) * A = 300

Expanding the left-hand side:

A^2 - 5A = 300

Moving all terms to the left-hand side:

A^2 - 5A - 300 = 0

We can solve for A using the quadratic formula:

A = (-(-5) ± sqrt((-5)^2 - 41(-300))) / (2*1)

A = (5 ± sqrt(25 + 1200)) / 2

A = (5 ± sqrt(1225)) / 2

Since A is a positive integer, we take the positive solution:

A = (5 + 35) / 2 = 20

Now we can use the first equation to find J:

J = A - 5 = 20 - 5 = 15

Therefore, Jamal is 15 years old.

Answer:

Step-by-step explanation:

a) \(5y+ab\)

b) \(f^{3} -3\\\)

c) \(6kq\)

d) \(\frac{3xy}{2w} \\\\\)

e) \(3x-4\sqrt{z} \\\)

f) \(\frac{2p}{5q} \\\\\)

\(a) 5y+ab5y+ab

b) \begin{gathered}f^{3} -3\\\end{gathered}

f

3

−3

c) 6kq6kq

d) \begin{gathered}\frac{3xy}{2w} \\\\\end{gathered}

2w

3xy

e) \begin{gathered}3x-4\sqrt{z} \\\end{gathered}

3x−4

z

f) \begin{gathered}\frac{2p}{5q} \\\\\end{gathered}

5q

2p

\)

Answer:

4%

Step-by-step explanation:

Using the proportional side rule for similar triangles, all the values of x can be found as below.

Similar triangles are triangles which has the same shape but different size.

The length of sides are proportional in similar triangles.

1) Side lengths of bigger triangle are 32 + x and 24 + 9 = 33.

Corresponding proportional sides of smaller triangles are 32 and 24 respectively.

Using proportion,

\(\frac{32+x}{32}\) = \(\frac{33}{24}\)

Cross multiplying,

(32 + x) 24 = 32 × 33

768 + 24x = 1056

4x = 288

x = 12

2) Side lengths of bigger triangle are 33 + x and 20 + 14= 34.

Corresponding proportional sides of smaller triangles are x and 14 respectively.

\(\frac{33+x}{x}\) = \(\frac{34}{14}\)

462 + 14x = 34x

20x = 462

x = 23.1

3) Side lengths of bigger triangle are 30 + x + 5 = 35 + x and 36.

Corresponding proportional sides of smaller triangle are 30 and 20 respectively.

\(\frac{35+x}{30}\) = \(\frac{36}{20}\)

700 + 20x = 1080

20x = 380

x = 19

4) Side lengths of bigger triangle are x + 8 + 2x - 5 = 3x + 3 and 20 + 22.5 = 42.5.

Corresponding proportional sides of smaller triangles are 2x - 5 and 22.5 respectively.

\(\frac{3x+3}{2x-5}\) = \(\frac{42.5}{22.5}\)

67.5x + 67.5 = 85x - 212.5

17.5x = 280

x = 16

5) Side lengths of bigger triangle are 2x+4 +4 = 2x + 8 and x+7+3 = x + 10.

Corresponding proportional sides of smaller triangles are 2x + 4 and x + 7 respectively.

\(\frac{2x+8}{2x+4}\) = \(\frac{x+10}{x+7}\)

(2x + 8) (x + 7) = (x + 10) (2x + 4)

2x² + 8x + 14x + 56 = 2x² + 20x + 4x + 40

22x + 56 = 24x + 40

2x = 16

x = 8

6) Side lengths of bigger triangle are 2x + 8 + 5x - 4 = 7x + 4 and 82.

Corresponding proportional sides of smaller triangles are 2x + 8 and 28 respectively.

\(\frac{7x+4}{2x+8}\) = \(\frac{82}{28}\)

196x + 112 = 164x + 656

32x = 544

x = 17

Hence the values of x in each of the triangles are found.

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Based on the graph the car requires 2.5 gallons of fuel to travel 100 miles.

Given:

The graph shows a proportional relationship between the distance a car travels and the fuel it consumes.

Distance (miles)                   Fuel(gallons)

0                                              0

40                                            1

80                                            2

120                                           3

160                                           4

200                                          5

240                                          6

280                                          7

From the table:

1 gallon fuel = 40 miles

1 mile = 1/40 gallon fuel

multiply by 100 on both sides

100 miles = 100/40 gallons fuel

100 miles = 5/2 gallons fuel

100 miles = 2.5 gallons fuel.

Therefore the car requires 2.5 gallons of fuel to travel 100 miles.

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y-2= -8(x-5)

Step-by-step explanation:

thats the right answer trust me

The total interest for the loan is $4,550. This means that over the course of 5 years, you will pay back the original loan amount of $13,000 plus $4,550 in interest for a total of $17,550.

To calculate the total interest for this loan, we need to use the simple interest formula:
Monthly EMI formula :
Interest = Principal x Rate x Time

In this case, the principal (amount borrowed) is $13,000, the rate is 7%, and the time is 5 years.

So,

Interest = $13,000 x 0.07 x 5

Interest = $4,550

It's important to keep in mind that this calculation assumes that the interest rate remains constant over the entire 5-year period.

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To calculate the length of cable needed, we first need to determine the length of the zip line itself. We can use the distance between the trees and the change in height of the cable to calculate the horizontal and vertical distances.

Let's say the distance between the trees is 200 feet and the change in height is 80 feet. To ensure a 6 to 8 feet of vertical change for every 100 feet of horizontal change, we need to limit the horizontal distance to between 750 and 1000 feet.

We can use the Pythagorean theorem to calculate the length of the zip line:

horizontal distance = √(100^2 - 80^2) = 60 feet

total length of zip line = √(200^2 + 60^2) = 208.44 feet

To account for the required 5% slack in the line, we need to add 5% to the total length:

total length with slack = 208.44 + (0.05 * 208.44) = 218.86 feet

To wrap around each tree, we need an additional 6 feet at each end, so we need to add 12 feet to the total length:

total length with slack and extra cable = 218.86 + 12 = 230.86 feet

Therefore, we need a total length of 230.86 feet of cable.

Step-by-step explanation:

To determine the length of cable needed for the zip line, we first need to calculate the horizontal distance between the two trees. Let's assume that the distance between the trees is d feet. We also need to calculate the vertical change in height of the cable between the two trees. Let's assume that the height difference is h feet.

Given the slope constraint, we know that for every 6 to 8 feet of vertical change, we need 100 feet of horizontal change. This means that the slope of the zip line should be between 6/100 and 8/100. We can use this information to set up a proportion:

vertical change / horizontal change = slope

h / d = 6/100 or h / d = 8/100

Solving for d in each of these equations, we get:

d = h / (6/100) = 100h / 6 = 50h / 3 (for the minimum slope of 6/100)

d = h / (8/100) = 100h / 8 = 25h / 2 (for the maximum slope of 8/100)

To account for the required 5% slack in the line, we need to increase the length of the cable by 5%. This means that the actual length of cable needed is:

L = 1.05d + 12

where 12 feet represents the 6 extra feet of cable needed at each end to wrap around each tree.

Substituting the expressions for d that we derived earlier, we get:

L = 1.05(50h/3) + 12 = (175h/6) + 12 (for the minimum slope of 6/100)

L = 1.05(25h/2) + 12 = (131h/40) + 12 (for the maximum slope of 8/100)

Therefore, the total length of cable needed for the zip line depends on the height difference between the trees and the desired slope of the line. For example, if the height difference is h = 50 feet and we want to use the minimum slope of 6/100, then the total length of cable needed would be:

L = (175(50)/6) + 12 = 1462.5 feet

If we want to use the maximum slope of 8/100, then the total length of cable needed would be:

L = (131(50)/40) + 12 = 73.2 + 12 = 85.2 feet

Note that these values are approximations and do not take into account factors such as the weight of the rider or the tension of the cable.

Interest, is an additional money paid for borrowing money. it could be simple or compound interest.

simple interest= p×T×R/100

when interest is compounded annually

F= p(1+r)^t

F= future value

p= principal

r= rate

t= time

compound interest is calculated based on the initial and accumulated interest.

F= p(n+r)^n

F= 10000(1+0.02)^1

F= 10000×1.02= $10200

interest= 10200-10000

interest = $200

second year

F = 10200(1+0.02)^1

F=10200×1.02= $10404

Interest= 10404-10200

interest= $204

third year

F= 10404(1+0.02)^1

F= 10404(1.02)

F = $10612.08

interest= 10612.08-10404

interest= $208.08

first year

I=10000×1×0.02/100

interest= $2

second year

I= 10000×2×0.02/100

interest= $4

for the third year

I =10000×3 × 0.02/100

interest= $6

Answer:

True

Explanation:

Bridget Riley was one of the most prominent artists associated with the 1960s 'Op Art' movement, which was an art movement that explored optical illusions and effects to create abstract art that played with the viewer's perception. However, there were many other artists associated with this movement, including Victor Vasarely, Richard Anuszkiewicz, and Yaacov Agam, among others.

Answer:

Step-by-step explanation:

After the first year, the number of rabbits will double from 50 to 100.

After the second year, the number of rabbits will double again from 100 to 200.

This doubling process will continue for a total of 5 years, so after 5 years, the number of rabbits will be:

Number of rabbits after 5 years = 50 x 2^5 = 50 x 32 = 1600

Therefore, there will be 1600 rabbits on Groff Farm after 5 years.

Similarly, after 10 years, the number of rabbits will double 10 times:

Number of rabbits after 10 years = 50 x 2^10 = 50 x 1024 = 51200

Therefore, there will be 51,200 rabbits on Groff Farm after 10 years.

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Answer:

16 divided by 2 equals C which is 8.

Step-by-step explanation:

Answer: 0.0493 Chance of Probability

The function represented by the graph with the given transformations is |–x| + 2.

The function represented by the given transformations is |–x| + 2.

Let's analyze the transformations step by step:

Reflection across the x-axis:

Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.

Translation right 2 units:

Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.

Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.

Thus, the function represented by the graph with the given transformations is |–x| + 2.

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Answer: -lx-2l

Step-by-step explanation:

Answer:

3rd option.

Step-by-step explanation:

figure u dont need one

Answer:

seven hundred ten and two hundred and thirty one 700,000+ 10,000+ 200+30+1

Step-by-step explanation:

Answer:

The horizontal line test may be used to determine whether a function is one-to-one.
The vertical line test may be used to determine whether a relation is a function.

Step-by-step explanation:

In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.

Proportion shows the relative number of objects or people in the whole.

Proportions are ratios equated to each other.

They are expressed as fractional values, in decimals, percentages, and fractions.

The percentage of Boomers who want to shop in-store = 84%

The sample size of the Boomer Generation = 75

The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)

Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.

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