What is the value of x?
X+67°
U
W
75⁰
X+66°

The total accumulated amount needed to support your son's education is approximately $128,019.22.


Let's solve the problem step by step.

⇒ Calculate the future value of the funds needed for four years of university expenses.

PV1 = $40,000 (amount needed each year)

r1 = 5% (annual interest rate)

n1 = 1 (compounded once a year)

t1 = 4 (number of years)

Using the formula for future value (FV = PV × (1 + r/n)^(n × t)), we can calculate the accumulated amount for these four years:

FV1 = $40,000 × (1 + 0.05/1)^(1 × 4)

FV1 = $40,000 × (1.05)^4

FV1 ≈ $46,620.25

⇒ Calculate the future value of the $50,000 gift upon graduation.

PV2 = $50,000 (amount of the gift)

r2 = 5% (annual interest rate)

n2 = 1 (compounded once a year)

t2 = 9 (number of years from your son's 19th birthday to his graduation at age 28)

Using the same formula, we can calculate the accumulated amount for this gift:

FV2 = $50,000 × (1 + 0.05/1)^(1 × 9)

FV2 = $50,000 × (1.05)^9

FV2 ≈ $81,398.97

⇒ Calculate the total accumulated amount by summing up FV1 and FV2.

FV = FV1 + FV2

FV ≈ $46,620.25 + $81,398.97

FV ≈ $128,019.22

Therefore, the total accumulated amount needed to support your son's education is approximately $128,019.22.

Please keep in mind that these calculations assume a constant interest rate of 5% throughout the investment period and do not consider any additional contributions or fluctuations in the interest rate.

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Answer:

y = 20

x = 120

Step-by-step explanation:

2x + 3y = 300

3x + 5y = 460

mutliply eqn 1 by 3 and 2 by 2

6x + 9y = 900

6x + 10y = 920

y = 20

x =

Answer:

132 chocolates

Step-by-step explanation:

We know that after Ramesh arranges his chocolates in rows, the number of rows multiplied by the number of chocolates in each row will give us the total number of chocolates, 17424.

Let the number of rows be x.

From the question, the number of chocolates in each row will also be x.

\(=> x * x = 17424\\\\x^2 = 17424\\\\=> \sqrt{x^2} = \sqrt{17424} \\\\x = 132\)

Therefore, he placed 132 chocolates in each row.

The symmetric difference, denoted by the symbol ⊕, between two sets A and B is defined as the set of elements that are in either A or B, but not in both.

a) If a is a subset of u, then a⊕a will contain all elements that are in a and not in a, which is an empty set (∅). Therefore, a⊕a=∅.
b) The symmetric difference between a and an empty set (∅) is simply a, because there are no elements in ∅ that are not in a. Thus, a⊕∅=a.
c) The symmetric difference between a and the universal set u will contain all elements that are in either a or u, but not in both. Since a is already a subset of u, a⊕u will simply be all elements in u that are not in a, which is just a. Therefore, a⊕u=a.
d) The symmetric difference between a and itself (a⊕a) will contain all elements that are in either a or a, but not in both. This is equivalent to the set of elements that are not in a, which is the complement of a in u. Therefore, a⊕a is equal to u-a, or simply the universal set u. Hence, a⊕a=u.
In conclusion, if a is a subset of a universal set u, then a) a⊕a=∅, b) a⊕∅=a, c) a⊕u=a, and d) a⊕a=u.

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The area of the figure given below is 56.6 units² .

In the question ,

a figure is given

where there is one rectangle and two semicircles .

the length of the rectangle is given as 11 units

and the breadth of the rectangle is = 4 units

we know that the area of the rectangle is = length × breadth

on substituting the values ,

we get

area = 11 × 4

area = 44 units²

the radius of the semicircle = 2 units

the are of the semi circle = (1/2)*π*r²

since there are two semicircle , the area of the two semi circle will be

= 2 * (1/2)πr²

= π*r²

On substituting , the value of radius = 2 ,

we get the area is = 3.14*(2)² = 12.56       using π = 3.14

so the area of the complex figure is = 44 + 12.56 = 56.56

≈ 56.6

Therefore , The area of the figure given below is 56.6 units²  .

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Answer:

1696 m^2

Step-by-step explanation:

Using the area of the larger circle to minus the area of smaller one, so A = 2*pi*r^2. 24^2*pi - 6^2*pi = 540 pi = 1696 m^2

Percentage of data within 2 population standard deviations of the mean is 68%.

To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.

The mean can be found by summing all the values and dividing by the total number of values:

Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68

To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98

Standard Deviation = sqrt(139.98) = 11.83

Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.

Range = 2*11.83 = 23.66

The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:

Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34

Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:

Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).

Therefore, approximately 68% of the data falls within two population standard deviations of the mean.

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Answer:

bro I can’t do it TvT

Answer:

x= 28 and y=21

Step-by-step explanation:

x - y = 7

x + y = 49

add the two equation and the y's will cancel out

2x = 56  divide by 2

x = 28

replace 28 for x in the first equation and solve for y

28 - y = 7

y = 21

Answer:

The correct answer is not rational.

Step-by-step explanation:

Answer:

Need a Picture please repost so I can help you :)

Step-by-step explanation:

Jorge has a ticket has a probability of 0.3 of winning a prize. after seven days, probability that jorge has won at least one prize is 0.9176

Let the probability of Jorge winning be 0.3 so ,

Probability of not winning be (1-0.3)⁷

(0.7)⁷

= 0.0823

Therefore, Jorge not winning is 0.0823.

If he wins at least one prize is,

1 - P(win nothing)

1 - 0.0823

= 0.9176

Therefore, the probability that the Jorge wins at least one prize is 0.9176.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

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The antiderivative of 7ex is 7ex, and the antiderivative of 6 sec2(x) is 6 tan(x). Thus, the most general antiderivative is F(x) = 7ex + 6 tan(x) + C, where C represents the constant of integration.

To find the antiderivative of the given function f(x) = 7ex 6 sec2(x), we integrate each term separately. The antiderivative of 7ex is simply 7ex, as the exponential function ex is its own antiderivative.

Next, we consider the antiderivative of 6 sec2(x). The derivative of the tangent function tan(x) is sec2(x), so the antiderivative of sec2(x) is tan(x). However, there is a coefficient of 6 in front of sec2(x), so the antiderivative becomes 6 tan(x).

Combining these results, we have F(x) = 7ex + 6 tan(x) as the antiderivative of the original function f(x) = 7ex 6 sec2(x). The "+ C" at the end represents the constant of integration, as any constant added to the antiderivative remains undetermined. Therefore, the most general antiderivative of f(x) is F(x) = 7ex + 6 tan(x) + C, where C is a constant.

To verify this result, we can differentiate F(x) and confirm that it indeed yields the original function f(x). Taking the derivative of F(x) with respect to x will give us back 7ex 6 sec2(x), thus confirming the correctness of the antiderivative.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Answer:

y = -1

Step-by-step explanation:

Right away, you should notice that the y-coordinate is the same between both points. If it's a straight line (which you can assume), that means it's a horizontal line at y = that y-coord, or y = -1 in this case.

Answer:

w ≤ 19

Step-by-step explanation:

4w−16≤60

Add 16 to both sides.

4w−16+16≤60+16

4w≤76

Divide both sides by 4.

4w/4 ≤ 76/4

w≤19

Answer:

w<=19

Step-by-step explanation:

4w<=60+16

w<=76/4

Answer:

x = -3.25

Step-by-step explanation:

2/5 = 0.4

0.4x - 0.2 = -2(3/4)

-2(3/4) = -2/1 * 3/4 = -6/4

0.4x - 0.2 = -6/4

Convert to fraction

2/5x - 1/5 = -6/4

Add 1/5 to both sides

-6/4 + 1/5 = -30/20 + 4/20 = -26/20

2/5x = -26/20

Convert to decimal

0.4x = -1.3

-1.3/0.4 = -3.25

x = -3.25

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Answer:

7

Step-by-step explanation:

It is 7:

31 - 7 = 24

15 - 7 = 8

8/24 = 1/3 = 33%

It is not 12:

31 - 12 = 19

15 - 12 = 3

3/19 = 15%

It is not 6:

31 - 6 = 25

15 - 6 = 9

9/25 = 36%

It is not 9:

31  - 9 = 22

15 - 9 = 7

7/22 = 31%

It is not 11:

31 - 11 = 20

15 - 11 = 4

4/20 = 20%

I subtracted the option from 31 (the new total of marbles) and from 15 (the new total of blue marbles). Then, I divided the new total by the new total of the blue marbles. I converted the decimal into a percentage. If the percentage was not 33%, then it was not the answer.

The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Answer:

the gcf of 16, 20, and 14 is 4

Answer:4

Step-by-step explanation:

16: 1,2,4,16

20:1,2,4,5,10,20

24: 1,2,3,4,6,8,12,24

The greatest common factor is four

Viola needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m

On average, she has jumped 3.80 m so far. Therefore, the sum of distances jumped so far by her is:

3.80 m × the total number of jumps taken so far.

On the next jump, she reaches 3.99 m. Therefore, after the next jump, the total distance jumped so far by her will be 3.80 m × total number of jumps taken so far + 3.99 m. The new mean is 3.81 m.

Therefore, (3.80 m × total number of jumps taken so far + 3.99 m)/(total number of jumps taken so far + 1) = 3.81.

The above equation can be simplified as 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × (total number of jumps taken so far + 1).

This simplifies to 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m. Now, we need to solve the above equation to find out the distance she needs to jump on her next attempt to increase her mean to 3.82 m.

3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m.

0.01 m = 0.01 m × total number of jumps taken so far.

1 = total number of jumps taken so far. Now, she needs to jump a distance of (3.82 m × (total number of jumps taken so far + 1)) - (3.80 m × total number of jumps taken so far)

= (3.82 m × (1 + 1)) - (3.80 m × 1)

= 3.82 m × 2 - 3.80 m

= 0.04 m

Therefore, she needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m.

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Answer:

A. {(0, 3), (1, 6), (2, 9)}

Step-by-step explanation:

All you have to do is substitute them

A.

y − 3 = 3x

3 - 3 = 3 (0)

0 = 0

y − 3 = 3x

6 - 3 = 3 (1)

3 = 3

y - 3 = 3x

9 - 3 = 3 (2)

6 = 6

__________________________________________________________

B.

y - 3 = 3x

0 - 3 = 3(3)

-3 = 6

You can tell that this one can't be one of the answer which means that B wont be the answer, so you don't have to do anymore work for this one.

__________________________________________________________

C.

y - 3 = 3x

3 - 3 = 3(1)

0 = 3

This one can't be an answer either

__________________________________________________________

D.

y - 3 = 3x

1 - 3 = 3(1)

-2 = 3

And this one can't be an answer either

__________________________________________________________

This concludes, that A will be the answer here since all of the ordered pair can be x and y when you use the inputs and outputs that were given.

Hope this helped!

Answer:

A

Step-by-step explanation:

If a random variable "z" follows a standard normal distribution and the probability of "z" being greater than "k" is 0.39, then the value of "k" such that satisfies the equation [p(z > k) = 0.39] will be 0.28

As per the question statement, a random variable "z" follows a standard normal distribution.

We are required to determine the value of "k" such that the equation   [p(z > k) = 0.39] is satisfied.

To solve this question, first we will have to calculate the probability of "z" being greater than "k" and then from the Z-table, we will determine the z-score corresponding the above calculated probability value. This z-score will be our desired answer, i.e.,

Given, P(Z > k)  = 0.39

Or, P(Z < k) = (1 - 0.39)

Or, P(Z < k) = 0.61

Now, from the Z table, we get the z-score corresponding to probability value of 0.61 is 0.28

Hence, (k = 0.28)

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The ability to order items in a sequence, such as longest to shortest, is known as Seriation.

Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.

Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.

Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.

Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.

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Test the hypothesis step of the scientific method is he performing.

Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

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