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Answer:

If the amount is P, with the interest rate of 12%, the interest over the year is:

In this case the quarterly interest rate is:

With the same amount and 3% quarterly rate, the yearly interest would be:

The quarterly interest rate in this case is:

If the quarterly interest rate is r, it should be little less than 3% to yield a 12% yearly rate.

So Kraig is wrong.

Answer:

$21,616.26.

Step-by-step explanation:

24000 =P(1 + 0.03/4)^14

P = 24000 / (1 + 0.03/4)^14)

21,616.26.

=

The present value that will grow to ​$24000 if interest is 3​% compounded quarterly for 14 quarters is $21,482.40

To find the present value that will grow to $24,000 at 3% interest compounded quarterly for 14 quarters, we use the formula for compound interest:

[tex]PV = FV / (1 + r/n)^{(n*t)}[/tex]

Where:

PV = Present Value

FV = Future Value ($24,000)

r = Annual interest rate (3% or 0.03 as a decimal)

n = Number of compounding periods per year (quarterly, so n = 4)

t = Number of years (14 quarters = 14/4 = 3.5 years)

Substitute the values into the formula:

PV = [tex]$24,000 / (1 + 0.03/4)^{(4*3.5)}[/tex]

PV = [tex]$24,000 / (1 + 0.0075)^{(14)}[/tex]

PV = [tex]$24,000 / (1.0075)^{14}[/tex]

PV ≈ $21,482.40 (rounded to the nearest cent)

Therefore, the present value required for it to grow to $24,000 in 14 quarters at 3% interest compounded quarterly is approximately $21,482.40.

In this explanation, we used the formula for compound interest to calculate the present value (PV). The formula accounts for the future value (FV), the annual interest rate (r), the number of compounding periods per year (n), and the time in years (t). By plugging in the given values and performing the calculations, we arrived at the present value of approximately $21,482.40.

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Answer:

A, B, B

Step-by-step explanation:

Answer:

x = 12 m = 87

Step-by-step explanation:

x = Dave

(7x + 3) + x = 99

8x + 3 = 99

      -3     -3

8x = 96

----    ----

8       8

  x = 12

7(12) + 3

84 + 3

   87

Dave has 12 dollars, Martha has 87.

Answer:

TRUE If substituting the test point produces a false solution, we shade on the opposite side of the line.

FALSE Elimination will give you an exact answer to a system of equations.

Step-by-step explanation:

Weird, I thought I already answer this xD

Answer:

The answer is 36°.

Hope it helps.

Step-by-step explanation:

• • •

Both? or just the westbound?

Answer:

b is correct answer

Step-by-step explanation:

when we write logarithmic terms we change the result from number which is power of 3

Answer:

220ft tall

Step-by-step explanation:

From the question we are given the following:

Adjacent side of the triangle = 80feet

Angle of elevation = 70°

Required

Height of the building (Opposite)

Using the SOH CAH TOA identity:

tan theta = opp/adj

tan 70 = H/80

H = 80tan70

H = 80(2.7474)

H = 219.79ft

Hence the building is 220ft tall

Answer:

6(4x + 2y)

Step-by-step explanation:

24x = 2 * 2 * 2 * 3 * x

18y = 2 * 3* 3 * y

Common factors = 2 * 3 = 6

24x + 18y = (6*4x) + (6*2y)   {6 is common in both terms}

               = 6*(4x + 2y)

The height of the given triangle is 3.7 yds. Therefore option A is the correct answer.

We need to find the height of the given triangle.

The formula to find the area of the triangle is Area=√s(s-a)(s-b)(s-c).

Where s is the semiperimeter, a,b and c are sides of the triangle.

Now, s=6+10+14/2=15 yds

Area of a triangle=√15(15-6)(15-10)(15-14)=25.9

Area of triangle=1/2×14×h=25.9 square yds

⇒h=3.7 yds

Therefore, the height of the given triangle is 3.7 yds.

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Answer:

SR = 22 cm

Step-by-step explanation:

area = bh/2

(21 cm)(h)/2 = 231 cm^2

21h = 462 cm

h = 22 cm

SR = 22 cm

Answer:

Step-by-step explanation:11/2x(8-4)=22

Answer:

$445.20

Step-by-step explanation:

First, find his pay after the 5% raise:

400(1.05)

= 420

Find his pay after the 6% raise:

420(1.06)

= 445.2

So, his weekly pay is now $445.20

Answer:

2*6*11

Step-by-step explanation:

I am not sure what your question is because I think you are asking the factor of these numbers. so u do 2+16+48 which is 66 and if you prime factorize it then you get 2*6*11. so the answer is 2*6*11.

Answer:

7238.23

Step-by-step explanation:

v=4/3πrcubed

solve it and get the answer

Answer:

1980

Step-by-step explanation:

13 sides

Number of sides n=13

The sum of interior angles of polygon =(2n−4)×90o

=(2×13−4)×90o

=(26−4)×90o

=22×90o

We get,

=1980

The image of this question is missing and so i have attached it.

Answer:

dd/dt = 4.47 ft/s

Step-by-step explanation:

From the image attached, let's denote the following;

d = horizontal distance beneath pulley

h = height of pulley

l = diagonal from the pulley to the head of the person

v = velocity of rope rising

Using pythagoras theorem;

l² = d² + h²

Differentiating with respect to time and considering h = c^(te) gives;

2l(dl/dt) = 2d(dd/dt)

We are given;

d = 20 ft

h = 10 ft

v = 4 ft/s

We know that velocity in this case is change in diagonal distance with time. Thus;

v = dl/dt = 4 ft/s

From earlier, we saw that;

2l(dl/dt) = 2d(dd/dt)

Thus, reducing it gives

(dl/dt)(l/d) = dd/dt

Now, l² = d² + h²

l = √(d² + h²)

Also, v = dl/dt = 4

Thus;

4(√(d² + h²))/d = dd/dt

4(√(20² + 10²))/20 = dd/dt

dd/dt = 4.47 ft/s

Answer:

Height of the cone = 5 cm

Step-by-step explanation:

Volume of the rectangular prism with a cone shaped hole = Volume of the rectangular prism - Volume of the cone

Volume of the rectangular prism = Length × Width × Height

                                                       = 5 × 5 × 7

                                                       = 175 cm³

Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here, r = Radius of the cone

h = Height of the cone

Volume of the cone = [tex]\frac{1}{3}\pi (\frac{3}{2})^{2}(h)[/tex]

                                 = 0.75πh cm³

Volume of the rectangular prism with a hole = 163.22 cm³

175 - 0.75πh = 163.22

0.75πh = 175 - 163.22

0.75πh = 11.78

h = 5 cm

Answer: 25

Step-by-step explanation:

80 - 55 = 25 super bouncy balls given away

So he gave away 25 balls.

Answer:

13

Step-by-step explanation:

Complementary angles add to 90 degrees

A+ B = 90

26+x  + 38+x = 90

Combine like terms

2x+64=90

2x+64-64 = 90-64

2x = 26

Divide by 2

2x/2 = 26/2

x = 13

Answer:

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they order a nonalcoholic beverage, or they order an alcoholic beverage. The probability of a customer ordering a nonalcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

At a Noodle & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.43.

This means that [tex]p = 0.43[/tex]

Find the probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

This is:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{7,0}.(0.43)^{0}.(0.57)^{7} = 0.0195[/tex]

[tex]P(X = 1) = C_{7,1}.(0.43)^{1}.(0.57)^{6} = 0.1032[/tex]

[tex]P(X = 2) = C_{7,2}.(0.43)^{2}.(0.57)^{5} = 0.2336[/tex]

[tex]P(X = 3) = C_{7,3}.(0.43)^{3}.(0.57)^{4} = 0.2937[/tex]

[tex]P(X = 4) = C_{7,4}.(0.43)^{4}.(0.57)^{3} = 0.2216[/tex]

Then

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0195 + 0.1032 + 0.2336 + 0.2937 + 0.2216 = 0.8716[/tex]

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

Answer:

3

Step-by-step explanation:

5×3=15 she would have 4 left but can't make a full star

The distance between Rachel and Amos after one hour is 15 miles.

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

Distance travelled by Rachel after one hour = 9 mph * 1 h = 9 miles

Distance travelled by Amos after one hour = 12 mph * 1 h = 12 miles

Let x represent the distance between Rachel and Amos, hence:

x² = 9² + 12²

x = 15

The distance between Rachel and Amos after one hour is 15 miles.

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Using the Pythagorean Theorem, they will be 15 miles apart after one hour.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this problem, considering their directions, their distance is the hypotenuse of a right triangle of legs 9 miles and 12 miles, hence:

[tex]d^2 = 9^2 + 12^2[/tex]

[tex]d = \sqrt{9^2 + 12^2}[/tex]

d = 15 miles

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Answer:

11 is the median of the entire data set

6 is the median of the lower half and 16 is the median of the upper half data scores...

Subtract 16 from 6 gives 10 so the answer is C) 10

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

Explanation:

The first step is to sort the data from smallest to largest. Luckily, that's already been done for us.

Next, we find the median. This is the middle most number of the set. In this case, the median is 11 since we have 3 values below it (2,6,7) and 3 values above it (15,16,17).

Let

L = {2,6,7}

U = {15,16,17}

where L and U are the lower and upper sets respectively.

In other words, anything in set L is lower than the median while anything in set U is above the median. The median itself (11) is not part of either set.

Notice how 6 is the midpoint of set L, while 16 is the midpoint of set U.

This means Q1 = 6 and Q3 = 16

Therefore,

IQR = Q3 - Q1

IQR = 16 - 6

IQR = 10

which is why choice C is the final answer.

6(x-3)=3x+9

6x-18=3x+9

6x-3x=18+9

3x=27

x=27 ÷3

x=9

Hope this will help you

The solution is x = 9, which is an option (B).

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Let's simplify the equation by distributing 6 on the left-hand side:

6x - 18 = 3x + 9

Now, let's isolate the x terms on one side and the constant terms on the other side:

6x - 3x = 9 + 18

3x = 27

x = 9

Therefore, the solution to the equation 6(x - 3) = 3x + 9 is x = 9, which is option B.

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Answer:

3.5 cm

Step-by-step explanation:

v = πr²h

r = radius

π = 22/7

h = height

192.5 = 22/7 x 5 x r²

divide both sides of the equation by (7/22 x 1/5)

192.5 x 7/22 x 1/5 = r²

r² = 12.25

find the square root of both sides

r = 3.5cm

Answer:

answer is 10 (very easy)

Answer:

380. 1

Step-by-step explanation:

A=π r2=π. 11^2= 380.13271