find the value of x. show process please!

Answer:

  see attached

Step-by-step explanation:

You want the boxes of the pyramid shown filled with mixed numbers such that each box is the sum of the two numbers below it.

As the example shows, each box is filled with the difference between the box above and the one adjacent. Work must necessarily proceed from the top down.

As you know, the difference of fractions can be computed as ...

  [tex]\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}[/tex]

Of course the number 1 can be written in terms of denominator d as ...

  1 = d/d

This can be used to adjust the integer and fractional parts so both are positive.

We will use subscripts rc to indicate the row and column of a box, counting rows from the top down.

  [tex]X_{22}=12\dfrac{3}{4}-8\dfrac{2}{3}=(12-8)+\left(\dfrac{3}{4}-\dfrac{2}{3}\right)=4\dfrac{9-8}{12}=\boxed{4\dfrac{1}{12}}\\\\\\X_{31}=8\dfrac{2}{3}-2\dfrac{4}{5}=(8-2)+\left(\dfrac{2}{3}-\dfrac{4}{5}\right)=6\dfrac{10-12}{15}=\boxed{5\dfrac{13}{15}}\\\\\\X_{33}=4\dfrac{1}{12}-2\dfrac{4}{5}=(4-2)+\left(\dfrac{1}{12}-\dfrac{4}{5}\right)=2\dfrac{5-48}{60}=\boxed{1\dfrac{17}{60}}[/tex]

  [tex]X_{41}=5\dfrac{13}{15}-1\dfrac{5}{9}=(5-1)+\left(\dfrac{13}{15}-\dfrac{5}{9}\right)=4\dfrac{39-25}{45}=\boxed{4\dfrac{14}{45}}\\\\\\X_{43}=2\dfrac{4}{5}-1\dfrac{5}{9}=(2-1)+\left(\dfrac{4}{5}-\dfrac{5}{9}\right)=1\dfrac{36-25}{45}=\boxed{1\dfrac{11}{45}}\\\\\\X_{44}=1\dfrac{17}{60}-1\dfrac{11}{45}=(1-1)+\left(\dfrac{17}{60}-\dfrac{11}{45}\right)=\dfrac{51-44}{180}=\boxed{\dfrac{7}{180}}[/tex]

__

Additional comment

In a couple of places the denominators have a common factor.

For example, 13/15 and 5/9 have denominators that have a common factor of 3: 15=3·5 and 9=3·3. When we did the cross multiplication to find the difference, we divided the cross products by that common factor so the resulting fraction would be in lowest terms.

That is, we used 13·9/3 = 39 and 15·5/3 = 25 for the numerator values, and 15·9/3 = 45 for the denominator value.

You will also recognize that 6+(-2/15) became 5+13/15 by using 6 = 5+15/15.

Many calculators and spreadsheets can perform arithmetic on mixed numbers and give a mixed number result. (That is how we checked our work.)

The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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Therefore , the solution of the given problem of expression comes out to be 10⁸ One hundred million.

In arithmetic, addition, algebra, and division are necessary. They result in the following when combined: An equation, some statistics, and a mathematical function Values, parameters, and arithmetic processes like additions, subtractions, matrix multiplication, and divisions can all be found in a declaration of fact. Different phrases and terms can be compared and evaluated.

Here,

Given :

Expression : 100000000

To convert into short expression

So,

=> 10⁸

Thus ,One hundred million.

Therefore , the solution of the given problem of expression comes out to be 10⁸ One hundred million.

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Answer: Let's call the increase from 15 to 20 as "z".

So, 20 is (z / 15) * 100% greater than 15, or x = (z / 15) * 100.

And, 15 is (z / 20) * 100% less than 20, or y = (z / 20) * 100.

Since z is the same in both equations, we can set the two equations equal to each other:

x = (z / 15) * 100

y = (z / 20) * 100

Step-by-step explanation:

Hopefully you pass but without seeing the boxes i cant see! but the answer should be D or E

The increase in the price of crude oil was 10% in March, and then again by 10% in September. Let the original price be $x, then after the first 10% increase in March, the new price is 1.1x. After the 10% increase in September, the new price is 1.1(1.1x) = 1.21x.

So, the price increased from $x to $1.21x, which is an increase of $0.21x. Since the final price is $72.60, we can set up the equation:

$1.21x = $72.60

Solving for x, we get:

x = $60

Therefore, the original price was $60 and the increase was $12.60. The percent increase is then:

(12.60/60) x 100% ≈ 21%

So the total percent increase in the price of crude oil in 2018 was approximately 21%, which is option D.

Using the compound interest formula, we can calculate that the original price was around $65.04 and the total increase in price across 2018 was about 11.6%. Therefore, none of the options provided are correct.

The question has to do with the concept of compound interest in Mathematics. In this case, the price of crude oil increased by 10% twice in the year. The compounded increase, however, is not just the sum of these two increases, which would be 20%. It's actually slightly more, because the second 10% increase is applied not to the initial price, but to the price that already had been increased by 10% in March.

To calculate the total increase, we can use the formula for compound interest, which is A =[tex]P(1 + r/n)^(^n^t^)[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Considering the given scenario, and setting P as the unknown initial price of oil, r as 0.1 (10% expressed in decimal), t as 1 (since the increment happened twice within the same year), and n as 2 (since the increment happened twice). From the compound interest formula, we know that the final price $72.60 =[tex]P(1 + 0.10/2)^(^2^*^1^)[/tex]. Solving this equation for P, we find that P approximately equals $65.04, indicating the price at the start of the year.

Expressed in percentage terms, the total increase during 2018 is approximately (($72.60 - $65.04)/$65.04) * 100% = 11.6%. So, from the options given in your question, none is the correct answer.

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Answer: One way to check Abby's solution using a number line and counting on is as follows:

Start at 5 2/5 on the number line.

Subtract 2 1/2 by counting left 2 and a half units.

Check if the result is 2 9/10.

If the result of the subtraction is 2 9/10, then Abby's solution is correct. If not, then the solution is incorrect and needs to be re-evaluated.

Using this method, we can visually see the subtraction and verify the result.

Step-by-step explanation:

Answer:

Step-by-step explanation:

haha I won’t delete it nerdyyy

Answer:

frequency

Step-by-step explanation:

For the right prism having volume of 360 cm², the total surface area is 408 cm².

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

The right prism has measurements (6 , 8, 10).

The perpendicular is 6 cm, the base is 8 cm.

The area of base is -

Area = 1/2 × base × height

Substitute the values into the equation -

Area = 1/2 × 8 × 6

Area = 24 cm²

The volume of the prism is 360 cm³.

Volume = Area of base × height

Substitute the values into the equation -

360 = 24 × height

height = 260 / 24

height = 15 cm

The lateral surface area of the prism is -

Lateral Surface area = Perimeter of base × height

Substitute the values into the equation -

LSA = (8+6+10) × 15

LSA = 24 × 15

LSA = 360 cm²

The total surface area of the prism is -

Total Surface Area  = Lateral Surface Area + 2(Area of base)

Substitute the values into the equation -

TSA = 360 + 2(24)

TSA = 360 + 48

TSA = 408 cm²

Therefore, the total surface area is 408 cm².

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Find the total surface area of the right prism if it's sides are 6cm , 8cm and 10 cm. The volume of the prism is 360 cm².

The correct statement representing the function f(x) = 8x³ is given as follows:

The function is odd because f(-x) = -f(x).

To classify a function as even or odd, we must observe the relation between f(x) and f(-x), as follows:

For any ax³ function, we have that f(-x) = -f(x), hence the function is odd and the fourth statement is correct.

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the real vector space of all continuous real-valued functions on the interval [0,1] is infinite-dimensional.

A vector space, also known as a linear space, is a collection of vectors that have been put together and multiplied ("scaled") by integers known as scalars. Real numbers are frequently seen as being scalars. Scalar multiplication by rational numbers, complex numbers, etc., on the other hand, seldom occurs. The term "subspace" refers to a vector space that is enclosed within another vector space. Each subspace is a vector space in and of itself, but it also has a definition in relation to another (bigger) vector space. We'll soon find out that there are a lot of different subspaces from earlier parts that we already know about.

We prove this theorem by contradiction.

(i.e. Suppose the vector space has finite dimension and we show that contradiction)

Suppose dimension vector space with finite dimension

Let, dim v = N, then N vector is linearly independent.

And Any (N + 1) vectors 1, x, x²,......, xⁿ cannot to be linearly independent, for we know that any linearly independent elements in a vector space with dimension N has size ≤ N.

Such that (N + 1) vectors 1, x, x²,......, xⁿ must be linearly independent.

The there elements exists Scalars a(j) ∈ R (0 ≤ i ≤ N), Not all Zero,

so that, a₁ + a₂²x + a₃x²+.......+ a^(N)x^(N) = 0; x ∈ [0,1]

∑a(i) x^(i) = 0 , x ∈ [0,1]

This is contradiction because any non-zero polynomial of degree N cannot be equal zero for all x ∈ [0,1].

Hence the real vector space for all continuous real-valued functions on the interval [0,1] which is infinite dimensional.

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If each calculation stays the same, at 0.0000000009 seconds every calculation, you can use this equation:

Therefore, for the computer to perform 41,000,000,000,000 calculations with each calculation taking 0.0000000009 seconds, it will take the computer 36900 seconds, or 10 hours, 8 minutes and 20 seconds to complete.

Solving a system of equations we will see that the two integers are 3 and 7.

Let's define the two positive integers as x and y.

With the given information, we can write a system of equations to get:

x = 4y - 5

x*y = 21

Now we can replace the first equation intothe second one to get:

(4y - 5)*y = 21

4y^2 - 5y = 21

4y^2 - 5y - 21 = 0

Now we have a little quadratic equation, we can use the quadratic formula to solve this.

[tex]y = \frac{5 \pm \sqrt{(5)^2 - 4*4*-21} }{2*4} \\\\y = \frac{5 \pm 19 }{8}[/tex]

We know that the integers are positive, so we need to take the positive solution:

y = (5 + 19)/8 = 24/8 = 3

And the other number is:

x = 4*3 - 5

x = 12 - 5 = 7

These are the two integers.

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The remaining portion of the sheet from the overall length is 10.16 units.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

Given that the overall length of the sheet is 18 5/ 8 = 149 / 8.

The two pieces removed are:

8 1/2 =17/ 2 and

7 9/16 = 121 / 16 inches.

The sawcut removed 1/16.

For two pieces we have two saw cuts thus, 2(1/16) = 1/8 inches.

The remaining portion is:

R = 149 / 8 - 17/2 - 121/6 - 1/8

R = 447 - 204 - 484 - 3 / 24

R = 10.16

Hence, the remaining portion of the sheet is 10.16 units.

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Answer:

h - 3

See explanation below

Step-by-step explanation:

This is not too difficult

We have (- 2h + 1) + (3h - 4) and we are asked to simplify

Expand the brackets:
(- 2h + 1) = - 2h + 1

(3h - 4) = 3h - 4

Add the two:
(- 2h + 1) + (3h - 4)  = - 2h + 1 + 3h - 4

Group like terms

- 2h + 3h + 1 - 4

-2h + 3h = h

+1 - 4 = -3

- 2h + 1 + 3h - 4 = h - 3

and therefore

(- 2h + 1) + (3h - 4)  = h - 3

Answer:

Step-by-step explanation:

The synthetic division process involves dividing the polynomial by a linear factor in a compact manner. In this case, we are dividing the polynomial 4x^4 - 9x^3 + 14x^2 - 12x - 1 by x - 1.

To perform synthetic division, we first write the coefficients of the polynomial in a row and add a zero at the end. Then, we divide the first coefficient (4) by the leading coefficient of the divisor (x - 1), and write the result (4) above the next coefficient (-9). Next, we multiply the divisor (x - 1) by the first quotient (4) and subtract the result from the row. The new row of coefficients is the result of this subtraction. Repeat this process until all coefficients have been processed or a remainder is left.

Here is the process:

4 -9  14 -12 -1 | 0

+------------------

-4  4  14 -12 -1

-4  4  14 -12 -1

-4 -4  10  12  1

So the result of the division is 4x³ + 10x² + 12x + 1, with a remainder of -4.

Thus, the final answer is 4x³ + 10x² + 12x + 1 + (-4) = 4x³ + 10x² + 12x - 3.

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The total length of cable needed is given as follows:

358.875 inches.

The total length of cable needed is obtained applying the proportions in the context of this problem.

The separate lengths are given as follows:

Then the total length is obtained adding these lengths as follows:

7 x 6.5 + 4 x 34.75 + 9 x 19.375 = 358.875 inches.

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The inverse of the function is [tex]g^{-1} (x)= 3x + 12[/tex]

when plotted on the same set of axes, exhibit symmetry. Keep in mind that (3, 2) is a point on its inverse and that (2, 3) is a point on f. In other words, all you have to do to graph the opposite is change the coordinates of each ordered pair.

If the picture with regard to the line y = x is the same or f (x) = y is solved, we get the same function x = f 1 (y) = f (y), then the inverse function can be the same as the original function.

Given the function is g(x) = [tex]\frac{1}{3}x - 4[/tex]

⇒ let [tex]y = \frac{1}{3}x - 4[/tex]'

Re-arranging the equation -

⇒ [tex]y + 4 = \frac{1x}{3}[/tex]

⇒ [tex]x = 3y + 12[/tex]

⇒ [tex]g^{-1} (x)= 3x + 12[/tex]

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Step-by-step explanation:

total ratio= 2+3

5

Grace= 3/5 × 120

Grace= 72 stamps

Answer: grace has 72 stamps

Step-by-step explanation:

120/5 is 24, 24 x 3 is 72

A ray will always have one starting point before it may or may not diverge to produce other rays.

A ray is a geometric figure that consists of a part of a line that starts from a starting point and extends infinitely in one direction. It is represented by an arrow and has only one endpoint, with the other end extending without bounds. In mathematical terms, a ray can be described as half-line.

In geometry, there are two types of rays:

Opposite Rays: These are two rays that have the same endpoint and extend in opposite directions from that endpoint.

Same-side Rays: These are two rays that have the same endpoint and extend in the same direction from that endpoint, but do not overlap.

In optics, a third type of ray is often considered, which is:

Light Ray: This is a type of ray that travels in a straight line and carries energy, including electromagnetic radiation in the form of light.

Generally, all rays have one starting point and may or may not diverge to produce other rays.

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The triangles are congruent by the AAS property.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Given a parallelogram ABCD,

with diagonal BD

to prove ΔABD ≅ ΔCDB

so AD ║ BC (because ABCD is a parallelogram)

so BD works as the transverse line between AD and BC,

similarly, AB and DC

so ∠ADB = ∠CBD (alternate interior angles are congruent)

AB ║ CD (because ABCD is a parallelogram)

so ∠ABD = ∠CDB (alternate interior angles are congruent)

DB = DB (common side)

ΔABD ≅ ΔCDB by AAS property

Hence triangles are congruent by AAS property.

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3(t+4).

[tex]t+4[/tex]

[tex](t+4)[/tex]

For this, just write a 3 infront of the parenthesis to express the multiplicaition of the sum (t+4) by 3.

[tex]3(t+4)[/tex]

Final answer: [tex]3(t+4)[/tex].

Answer:

35%

Step-by-step explanation:

The most accurate statement is "Speed is decreasing." This means that the object is moving at a decreasing velocity over the 10 seconds.

What is the Speed is constant?

When we say that the speed of an object is constant, it means that the magnitude of the velocity of the object remains unchanged over time. In other words, the object is moving at a steady pace and its speed does not vary.

The statement "Speed is not constant; Object is at rest" is not accurate.

From the position-time graph, it is clear that the object is moving in one direction and its position is changing with time. Hence, the object is not at rest.

Furthermore, the slope of the position-time graph gives us the velocity of the object, and from the graph, it appears that the slope is changing with time, which means that the speed is not constant. Hence, the statement that "Speed is constant" is also not accurate.

Hence, the most accurate statement is "Speed is decreasing." This means that the object is moving at a decreasing velocity over the 10 seconds.

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Complete question:

Solving for x gives the axis of symmetry of quadratic equation, where the quadratic equation is given as: y = ax² + bx + c.

How is this determined?

The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The line on the graph that separates the graph into two symmetrical sides and runs through the vertex of the parabola is known as the axis of symmetry of the parabola.

It is written as:

x = -b /2a.

Hence, for x = -b /2a. Solving for x gives the axis of symmetry of quadratic equation, where the quadratic equation is given as: y = ax² + bx + c.

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The coordinates of the other endpoint, Q is (5, -8).

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x₁+x₂)/2, (y₁+y₂)/2].

Given that, the midpoint of PQ is M =(1,-5). One endpoint is P= (-3, -2).

Let the coordinates of the other endpoint, Q be (a, b).

Here, (1, -5) = [(-3+a)/2, (-2+b)/2]

1= (-3+a)/2

2=-3+a

a=5

-5=(-2+b)/2

-10=-2+b

b=-8

Therefore, the coordinates of the other endpoint, Q is (5, -8).

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The amount of carbon present after 2000 years is 7.85 grams.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 5 is an equation.

We have,

The equation for half-life.

y = m [tex](1/2)^{t/f}[/tex] _____(1)

Where y = quantity remaining

m = initial quantity

t = time

f = half-life of the substance

Now,

f = 5730 years

m = 10 grams

t = 2000 years

Substituting in (1)

y = m [tex](1/2)^{t/f}[/tex] _____(1)

y = 10 [tex](1/2)^{2000/5730}[/tex]

y = 10 x [tex](1/2)^{0.35}[/tex]

y = 10 x 0.785

y = 7.85

Thus,

7.85 grams of carbon will be present after 2000 years.

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Answer: Sure! To simplify the expression -3y + 4 - 2 + 6y, we'll follow these steps:

Start by combining like terms:

-3y + 6y = 3y

Next, add the constant terms:

3y + 4 - 2 = 3y + 2

Finally, simplify the expression by substituting the values:

3y + 2 = 3y + 2

So the simplified expression is 3y + 2.

Step-by-step explanation: