An account paying 4. 6% interest compounded quarterly has a balance of $506,732. 32. Determine the amount that can be withdrawn quarterly from the account for 20 years, assuming ordinary annuity. A. $9,722. 36 b. $6,334. 15 c. $23,965. 92 d. $7,366. 99.

Answer:

900

Step-by-step explanation:

multiply 2x2x3x3x5x5

4x9x25 which is 900

According to given condition, E and F are independent events.

To determine if events E and F are independent, we need to check if the occurrence of one event affects the probability of the other event.

Let's first calculate the probability of event E, which is the probability of getting at least one head and one tail in three coin flips. We can use the complement rule to find the probability of the complement of E, which is the probability of getting all heads or all tails in three coin flips:

P(E) = 1 - P(all heads) - P(all tails)

P(E) = 1 - \((1/2)^{3}\) - \((1/2)^{3}\)

P(E) = 3/4

Now, let's calculate the probability of event F, which is the probability of getting at least two heads in three coin flips. We can use the binomial distribution to find the probability of getting two or three heads:

P(F) = P(2 heads) + P(3 heads)

P(F) = (3 choose 2)\((1/2)^{3}\) + \((1/2)^{3}\)

P(F) = 1/2

To check if E and F are independent, we need to calculate the joint probability of E and F and compare it to the product of the probabilities of E and F:

P(E and F) = P(at least one head and one tail, at least two heads)

P(E and F) = P(2 heads) + P(3 heads)

P(E and F) = (3 choose 2)\((1/2)^{3}\)

P(E and F) = 3/8

P(E)P(F) = (3/4)(1/2)

P(E)P(F) = 3/8

Since the joint probability of E and F is equal to the product of their individual probabilities, we can conclude that E and F are independent events. In other words, the occurrence of one event does not affect the probability of the other event.

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Answer:

no

no

yes

Step-by-step explanation:

A mean is an arithmetic average of a set of observations. The mean number of visits the students made to the library in the last month is 2.32 visits.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

For the given frequency table, the sum of the mean and the total number of values can be written as,

Sum = (0×284) + (1×218) + (2×76) + (3×64) + (4×42) + (5×320) = 2330

Total number of values = 284 + 218 + 76 + 64 + 42 + 320 = 1004

The mean for the table can be written as,

Mean = sum/ Total number of values = 2330/1004 = 2.32

Hence, the mean number of visits the students made to the library in the last month is 2.32 visits.

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Answer:

-8 and 3, or -3 and 8

Step-by-step explanation:

xy = -24

x - y = 11

x = y + 11

y(y + 11) = -24

y^2 + 11x + 24 = 0

(y + 8)(y + 3) = 0

y = -8 or y = -3

x = 3 or x = 8

the numbers are -8 and 3, or -3 and 8

Answer:

R200

Step-by-step explanation:

selling price of each earring

R200

Answer:

4x+2=22

4x+2-2=22-2

4x=20

4x/4=20/4

x=5

Answer:

T=.25k+.97t

This is because you 25 cents of gas is multiplied by k, which leaves the other section of the equation.

Answer:

x = 3

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

Since we know triangles ABC and DEC are similar, we can use the ratio method to find x.

\( \frac{ec}{bc} = \frac{ed}{ba} \\ \frac{25}{5} = \frac{18 - x}{x} \\ \frac{18 - x}{x} = 5 \\ 18 - x = 5x \\ 18 = 5x + x \\ 6x = 18 \\ x = \frac{18}{6} \\ = 3\)

Multiplication is the process of multiplying. Jay lost 30 pounds in a period of 6 months.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

A.) The newly recorded temperature in January will be six times the temperature in February, therefore, we can write,

January = 6 × February = 6×(-3°F) = -18°F

Hence, the newly recorded temperature in January will be equal to -18°F.

B.) Change in water level on each day of the drought was equal to -4 inches, while the drought lasted for 1 week(7days), Thus, the net change in water level can be written as,

net change = 7 × -4 = -28inches

Hence, the net change in the water level during the drought was equal to -28 inches.

C.) Jay went on a diet for six months and lost 5 pounds each month, therefore, the net change in the weight will be equal to,

Net Change = 6 × 5 = 30 pounds

Hence, Jay lost 30 pounds in a period of 6 months.

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Answer:

Length of the longest side: 65 cm

Step-by-step explanation:

First side = x;

"Other side (with respect to first side)" = y;

Third side = z

When the first side is multiplied by 4, it is 10cm longer than 3 times the third side : 4x = 10 + 3z

We receive an equilateral triangle when one side increases by 11, and the other decreases by 11. Therefore when x + 11, and y - 11, x + 11 = z, and y - 11 = z.

x + 11 = z               x - z = 11  

y - 11 = z       →      y - z = 11

4x = 10 + 3z         4x - 3z = 10

Matrix:

\(\begin{bmatrix}1&-1&0&|&-11\\ 0&-1&1&|&11\\ 4&-3&0&|&10\end{bmatrix}\)

If we reduce this matrix, our dimensions are 43, 54, and 65. Therefore the length of the longest side of the original triangle would be 65.

The sides of an equilateral triangle are equal.

The longest side of the original triangle is 65 cm

Let the sides of the original triangle be a, b and c.

From the question, we have:

\(\mathbf{4a = 10 + 3c}\) --- the first side multiplied by 4, is 10 more than the third side multiplied by 3

The equations that relate the increment or decrement of the side lengths are:

\(\mathbf{a + 11 = c}\)

\(\mathbf{b - 11 = c}\)

Make a, the subject in \(\mathbf{a + 11 = c}\)

\(\mathbf{a = c - 11}\)

Substitute \(\mathbf{a = c - 11}\) in \(\mathbf{4a = 10 + 3c}\)

\(\mathbf{4(c - 11) = 10 + 3c}\)

Open brackets

\(\mathbf{4c - 44 = 10 + 3c}\)

Collect like terms

\(\mathbf{4c - 3c = 10 + 44}\)

\(\mathbf{c = 54}\)

Recall that: \(\mathbf{a = c - 11}\)

So, we have:

\(\mathbf{a= 54 - 11}\)

\(\mathbf{a= 43}\)

Also, recall that: \(\mathbf{b - 11 = c}\)

So, we have:

\(\mathbf{b - 11 = 54}\)

\(\mathbf{b = 11 + 54}\)

\(\mathbf{b = 65}\)

So, we have:

\(\mathbf{a= 43}\)

\(\mathbf{b = 65}\)

\(\mathbf{c = 54}\)

By comparing the side lengths, we have:

The longest side of the original triangle is 65 cm

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Answer:

E

Step-by-step explanation:

Because the y-intercept is (0,-20)

The special right triangle is the right triangle that have acute angle values

that simplify the process of finding its dimensions.

The correct values are;

1. The angle the ladder makes with the ground, is approximately 66.93°

2. The length of YZ is approximately 19.18 ft.

3. CB = 7 ft. and AB = 7·√3 ft.

Reasons:

1. The length of the ladder = 15 ft.

Height of the ladder above the ground, h = 13.8 ft.

Required:

The angle the ladder makes with the ground.

Solution:

The angle the ladder makes with the ground is given by the equation;

\(sin(\theta) = \dfrac{Length \ of \ the \ ladder}{Height\ of \ the \ ladder \ above the \ ground} = \dfrac{13.8}{15} = 0.92\)

\(\theta = arcsin\left(0.92 \right) \approx 66.93^{\circ}\)

2. The given parameters are;

XY = 11

∠Z = 35°

YZ = Required

In a right triangle, the side facing the acute angle is a leg of the triangle.

Therefore;

XY is the opposite side to ∠Z

\(sin(\angle Z) = \dfrac{XY}{YZ}\)

Which gives;

\(sin(35^{\circ}) = \dfrac{11}{YZ}\)

\(YZ= \dfrac{11}{sin(35^{\circ}) } \approx 19.18\)

YZ ≈ 19.18 ft.

3. AC = 14 ft.

∠A = 30

Required:

The length of the other two sides

Solution:

Where by AC is the hypotenuse side, we have;

CB = AC × sin(∠A)

Therefore;

CB = 14 × sin(30°) = 7

CB = 7 ft.

AB =  AC × cos(∠A) = 14 × cos(30°) = 7·√3

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1. The angle the ladder makes with the ground, is approximately 66.93°

2. The length of YZ is approximately 19.18 ft.

3. CB = 7 ft. and AB = 7·√3 ft.

If on the following Tuesday, Terry fills out scale again and receives a score of 28 , then Terry's scores on the Self-Monitoring Scale do not appear to be Reliable .

The Terry's scores on the Self-Monitoring Scale do not appear to be reliable, because there is a significant difference between his score on Friday and his score on the following Tuesday.

The Reliability is defined as the consistency of measurement over time or across different conditions.

In this case, if Terry's scores on the Self-Monitoring Scale were reliable, we would expect them to be consistent or stable over time.

However, his score on Tuesday is significantly lower than his score on Friday suggests that there may be some inconsistency in his responses .

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Answer:

I don't think there is a point to math lol

Answer:

it depends on what job you want

I think we should be able to choose what classes we take in high school but then Idek what i want to do sooo that's also a problem

Answer:

17%of 23000

17/100×23000

1 yrs depreciation is 3910

then

after 4 years depreciation is 4×3910

=15640

the worth of after 4 yrs is 23000-15640

=Rs 7360

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

1.)Gcf of 89 and 76

\(gcf(89and76)\)

2)step 2

\( = \frac{89 \times 76}{lcm(89and76)} \)

3.)step 3

\( = \frac{6767}{6767} = 1\)

4.)answer

\(1\)

In the given figure, we can observe that two triangles are formed: ΔASB and ΔTSC.

It is given that:

Length of ST = 54 ft

Length of TB = 25 ft

Length of SC = 18 ft

To find: The length of SA

The length of TA can be found as follows:

Using the Pythagorean theorem,

In ΔTSC,TS² + SC² = TC²

54² + 18² = TC²

2916 + 324 = TC²

3240 = TC²

TC = 60 ft

Now, in ΔTSA,

TS² + SA² = TA²

60² + SA² = TA²

3600 + SA² = TA²

In ΔTAS,

TA² + AS² = TS²

TA² + AS² = 60²

TA² + AS² = 3600

In ΔASB,

AB² + BS² = AS²

AB² + 25² = AS²

AB² = AS² - 625

In ΔAST,

AS² + ST² = AT²

AS² + 54² = AT²

AS² + 2916 = AT²

From the above equations,

AS² - 625 + 2916 = AT²

AS² + 2291 = AT²

Substituting this value in ΔTAS:

TA² + AS² = 3600

TA² + (AT² - 2291) = 3600

TA² + AT² - 2291 = 36002

TA² = 5891TA² = 2945

TA = 54.23 ft (approx.)

Therefore, the length of SA is

From the above calculation, the length of SA is 43 ft.

In the given figure, two triangles are formed ΔASB and ΔTSC. We are to find the length of segment SA.

For that, we use the Pythagorean theorem to find the length of AT first.

The length of ST is 54 ft, SC is 18 ft and the length of TB is 25 ft. Applying the Pythagorean theorem, we get the length of TC as 60 ft.

Using this value, we apply the Pythagorean theorem again to find the length of AT, which comes out to be 54.23 ft (approx.).

Now that we have the length of AT, we apply the Pythagorean theorem in the triangle ΔTAS.

We find that the value of TA² is 2945. Substituting this value in the equation, we get that the length of SA is 43 ft.

Therefore, the length of line segment SA is 43 ft.

Therefore, from the above calculation, the length of line segment SA is 43 ft.

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The equation to plot in the complex Cartesian plane is 2Re(z) - |z²| ≥ -3Im(iz).

To plot the equation 2Re(z) - |z²| ≥ -3Im(iz) graphically, you can follow these steps:

1. Represent the complex number z in terms of its real and imaginary parts, z = x + yi, where x is the real part and y is the imaginary part.

2. Substitute the values of x and y into the equation and simplify it.

3. Separate the equation into real and imaginary parts.

4. For each part, plot the corresponding inequality on the Cartesian plane.

- For the real part, plot the inequality 2x - |(x + yi)²| ≥ -3y.

- For the imaginary part, plot the inequality 0 ≥ 0 (as -3Im(iz) = 0 for all values of x and y).

5. Determine the common region that satisfies both inequalities. This region represents the solution to the original equation.

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Answer:

35 multiplied by 12

Step-by-step explanation:

Because either you multiply it or you do sohcahtoa

Answer:

Bro u need to put in the graph or the chart or something

Step-by-step explanation:

Help

Help

Help

Help. Help help help help help help help help

The algebric expression "Twice the difference of a number z and 12" is equivalent to 2z - 24.

The phrase "Twice the difference of a number z and 12" represents a mathematical expression that can be written as 2(z - 12). Let's break down the meaning and interpretation of this expression.

First, we have the number z. This represents an unknown value or variable. It can be any real number.

Next, we have the difference of z and 12, which is obtained by subtracting 12 from z. So, z - 12 represents the numerical difference between z and 12.

Finally, we have "twice" this difference, which means multiplying the difference by 2. Therefore, we multiply z - 12 by 2, giving us the expression 2(z - 12).

To simplify this expression, we distribute the 2 to both terms inside the parentheses:

2(z - 12) = 2z - 24

The phrase represents an algebraic expression that calculates the result of doubling the difference between a given number z and 12. By substituting a specific value for z, you can evaluate the expression to obtain a numerical result.

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Answer:

x=15

Step-by-step explanation:

5x+17+36=128

5x+53=128

5x=75

x=15

Answer:

No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.  

Hence the correct option is option A.

Answer:

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

cosB = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{5}{13}\)

tanB = \(\frac{opposite}{adjacent}\) = \(\frac{AC}{BC}\) = \(\frac{12}{5}\)

sinB = \(\frac{opposite}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{12}{13}\)

The probability of randomly selecting someone who does not believe that some psychics can help solve murder cases is 46.4%. Hence, the answer is 46.4%.

Given the poll showed that 53.6% of Americans say they believe that some psychics can help solve murder cases.

We are to find the probability of randomly selecting someone who does not believe that some psychics can help solve murder cases.

Let us consider the following events:

Let A be the event that someone believes that some psychics can help solve murder cases and B be the event that someone does not believe that some psychics can help solve murder cases.

Then A and B are complementary events, that is A∩B=∅ (i.e., the events cannot happen at the same time) and A∪B = S (the event space).

Thus we can write P(A) = 53.6% and P(B) = 100% - 53.6% = 46.4%.

Therefore, the probability of randomly selecting someone who does not believe that some psychics can help solve murder cases is 46.4%. Hence, the answer is 46.4%.

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Answer:

120 males

Step-by-step explanation:

Well you need to set up your proportions which should look like this x/300 and 40%/100%.You need to cross multiply meaning you need to multiply 300 and 40 which equals to 12,000 then you will divide 12,000 by 100 and get 120