How to solve probability?

In the triangle ABC, the value of x, y and z is obtained as 21, 7 and 48 units respectively.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 16 + z units.

The measure of AD is given as 16 units.

The measure of DB is given as z - 16 units.

The measure of BE is given as 21 units.

The measure of BC is given as x units.

The measure of AC is given as 14 units.

According to the midpoint theorem, the length of DE is -

DE = 1/2 (AC)

y = 1/2 (14)

y = 7 units

Therefore, the value of y is obtained as 7 units.

Now according to indirect measurement -

AB / AC = BD / DE

Substitute the values in the equation -

16 + z / 14 = z - 16 / 7

7(16 + z) = 14(z - 16)

112 + 7z = 14z - 224

7z - 14z = -224 - 112

-7z = -336

z = 48

Therefore, the value of z is obtained as 48 units.

Now according to indirect measurement -

BC / AC = BE / DE

Substitute the values in the equation -

21 + x / 14 = 21 / 7

7(21 + x) = 14 × 21

147 + 7x = 294

7x = 294 - 147

7x = 147

x = 21

Therefore, the value of x is obtained as 21 units.

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Answer:

x = 21

y = 7

z = 32

Step-by-step explanation:

DE = 1/2 (AC)

y = 1/2 (14)

y = 7

AB / AC = BD / DE

Substitute values

16 + z / 14 = z - 16 / 7

7(16 + z) = 14(z - 16)

112 + 7z = 14z - 224

7z - 14z = -224 - 112

-7z = -336

z = 32

BC / AC = BE / DE

Substitute values

21 + x / 14 = 21 / 7

7(21 + x) = 14 × 21

147 + 7x = 294

7x = 294 - 147

7x = 147

x = 21

Answer:

Step-by-step explanation:

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Answer:

1

Step-by-step explanation:

3 - 2 = 1

Answer:

To compare Arthur's long jump to the record, we need to convert both measurements to the same unit. Let's convert both measurements to inches:

Record: 22 ft 6 3/4 in = (22 x 12) + 6 + 3/4 = 270 + 6 + 0.75 = 276.75 in

Arthur's jump: 22 ft 5 1/2 in = (22 x 12) + 5 + 1/2 = 270 + 5 + 0.5 = 275.5 in

To determine how much farther Arthur needs to jump to break the record, we subtract Arthur's jump distance from the record distance:

Record distance - Arthur's jump distance = 276.75 in - 275.5 in = 1.25 in

However, we are told that long jumps are measured to the nearest quarter inch. Therefore, we need to round the difference to the nearest quarter inch. Since 1.25 inches is closer to 1.25 than it is to 1.5, we round down to the nearest quarter inch. This gives us:

1.25 in ≈ 1.25/4 = 0.3125 quarters ≈ 0.25 quarters

Therefore, Arthur needs to jump an additional 0.25 quarters (or 1/16 of an inch) to break the record.

The cost of admission for a group of 5 people is $200 dollars.

The cost of admission for a group of 5 people is given by the function C(p) = 40p, where p is the number of people in the group. To find the cost for a group of 5 people, we simply plug in 5 for p and solve for C:

C(5) = 40(5)
C(5) = 200

Therefore, the cost of admission for a group of 5 people is $200 dollars.

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The area of the circle is 63.62 square meters

To work out the area of a circle, we need to use the formula A = πr^2, where A is the area of the circle, π is a mathematical constant approximately equal to 3.142, and r is the radius of the circle.

In this problem, we are given the diameter of the circle, which is the distance across the circle passing through its center. The radius is half of the diameter, so we can find it by dividing the diameter by 2.

In this case, the diameter is 9 meters, so the radius is 9/2 = 4.5 meters. We then substitute this value into the formula:

A = πr^2

A = 3.142 x (4.5)^2

A = 3.142 x 20.25

A = 63.6175

A ≈ 63.62 square meters

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The given question is incomplete, the complete question is:

Work out the area of the circle where diameter is 9 meter

Take π it to be 3.142 and give your answer to 2 decimal places.

The initial population is 4001 and the maximum population is 4000

The given population growth model is [tex]12000/3+e^{-0.02(t)}.[/tex]

To find the initial population, we need to plug in t=0 into the equation.

[tex]12000/3+e^{-0.02(0)}[/tex]

= [tex]12000/3+1[/tex]

= [tex]4000+1[/tex]

= [tex]4001[/tex]

So the initial population is 4001.

To find the maximum population, we need to find the limit of the equation as t approaches infinity.


= [tex]12000/3+0[/tex]

= [tex]4000[/tex]

So the maximum population is 4000.

In conclusion, the initial population is 4001 and the maximum population is 4000.

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[tex]\stackrel{ \textit{Partial Variation} }{V=aD+bD^2}\qquad \impliedby \begin{array}{llll} \textit{V\textit{ varies partly}}\\ \textit{with D and partly with }D^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} V=5\\ D=2\\[-0.5em] \hrulefill\\ V=9\\ D=3 \end{cases}\implies \begin{array}{llll} 5=a2+b2^2&\qquad &5=2a+4b\\\\ 9=a3+b3^2&&9=3a+9b \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{5=2a+4b}\implies 5-2a=4b\implies \cfrac{5-2a}{4}=b \\\\\\ \stackrel{\textit{using the 2nd equation}}{9=3a+9b}\implies \stackrel{\textit{substituting from above}}{9=3a+9\left( \cfrac{5-2a}{4} \right)}\implies 9=3a+\cfrac{45-18a}{4} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(9)=4\left( 3a+\cfrac{45-18a}{4} \right)}\implies 36=12a+45-18a\implies -9=-6a[/tex]

[tex]\cfrac{-9}{-6}=a\implies \boxed{\cfrac{3}{2}=a}\hspace{5em}b=\cfrac{5-2\left( \frac{3}{2} \right)}{4}\implies \boxed{b=\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill V=\cfrac{3}{2}D+\cfrac{1}{2}D^2~\hfill[/tex]

The solution to the equation -(2)/(7)u=-14 is u = 49.

Knowledge of inverse operations tells us that we need to multiply both sides of the equation by the reciprocal of -(2)/(7) to cancel out the fraction on the left side of the equation. The reciprocal of -(2)/(7) is -(7)/(2).

Multiply both sides of the equation by -(7)/(2):
u = -(7)/(2) * -(2)/(7)u = -(7)/(2) * -14

Simplify the left side of the equation:
u = 49

Solve for u:
u = 49

Therefore, the solution to the equation -(2)/(7)u=-14 is u = 49.

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Fοr the inequality 12 + 11/6x ≤ 5 + 3x, the cοrrect οptiοns are -

E. 6 ≤ x

F. The sοlutiοn set is (x l x∈R, x ≥ 6].

In Algebra, an inequality is a mathematical statement that uses the inequality symbοl tο illustrate the relatiοnship between twο expressiοns. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the phrase οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa.

Tο sοlve the inequality 12 + 11/6x ≤ 5 + 3x, we can fοllοw these steps -

Mοve all the terms cοntaining x tο οne side -

12 + 11/6x - 3x ≤ 5

Simplify the left-hand side -

72/6 + 11/6x - 18/6x ≤ 5

(72 + 11x - 18x)/6 ≤ 5

(72 - 7x)/6 ≤ 5

Multiply bοth sides by 6 tο eliminate the fractiοn -

72 - 7x ≤ 30

Mοve all the terms cοntaining x tο οne side -

72 - 30 ≤ 7x

42 ≤ 7x

Divide bοth sides by 7 (since 7 is pοsitive, we dοn't need tο flip the inequality) -

6 ≤ x

Therefοre, the cοrrect statement(s) and number line(s) that can represent the inequality are -

E. 6 ≤ x

F. The sοlutiοn set is (x ∈ R, x ≥ 6].

This means that the sοlutiοn set includes all real numbers greater than οr equal tο 6.

The interval nοtatiοn (6, ∞) cοuld alsο be used tο represent this sοlutiοn set.

Optiοn A is incοrrect because it οnly includes natural numbers (pοsitive integers), but the sοlutiοn set includes all real numbers greater than οr equal tο 6.

Optiοn B is incοrrect because it shοws a number line frοm -7 tο 7, which is nοt relevant tο the sοlutiοn set.

Optiοn C is incοrrect because it shοws an arrοw with a filled circle mοving tοwards pοsitive infinity, which implies that the sοlutiοn set is all pοsitive numbers, but the inequality οnly requires x tο be greater than οr equal tο 6.

Optiοn D is incοrrect because it is tοο limited in scοpe - it οnly tells us that the number substituted fοr x is greater than 6, but dοesn't give us the full sοlutiοn set.

Therefοre, οptiοn E and F are cοrrect.

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Suppose 2022 balls are randomly distributed into 100 boxes. Let X be the total number of balls in the first 20 boxes.  P(X = 90) ≈ 0.  VarX = 323.52.

a) To find P(X = 90), we can use the binomial probability formula:

P(X = k) = C(n,k) * p^k * (1-p)^(n-k)

where C(n,k) = n! / (k! * (n-k)!)

In this case, n = 2022, k = 90, p = 20/100 = 0.2

P(X = 90) = C(2022,90) * 0.2^90 * 0.8^(2022-90)

P(X = 90) = 1.19 * 10^(-37)

Therefore, P(X = 90) ≈ 0.


b) To find VarX, we can use the formula for the variance of a binomial distribution:

VarX = n * p * (1-p)

In this case, n = 2022, p = 0.2

VarX = 2022 * 0.2 * 0.8

VarX = 323.52

Therefore, VarX = 323.52.

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Answer:

-12?

Step-by-step explanation:

Answer: A

Step-by-step explanation:

A best represents the graph

Answer

10 is the answer

Please mark as brainliest HOPE IT HELPS!

To write an equation in standard form using integers, we need to eliminate any fractions by multiplying both sides of the equation by the least common multiple of the denominators.

In this case, the denominator is 5. So we can multiply both sides of the equation by 5 to get:-

5Y = X

Now, we can rearrange the equation so that the variables are on the left-hand side and the constants are on the right-hand side, in the form of Ax + By = C.

X - 5Y = 0 (subtracted X from both sides)

Therefore, the equation in standard form using integers is -X - 5Y = 0.

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Step-by-step explanation:

For solving this problem, we will use √ab=√a√b. Therefore, the value of 3√27 is 9√3. Note: In the above solution, we factored 27 which is inside the root.

Answer: 600

Step-by-step explanation:150=.25*X Divide both sides by .25 to get rid of it on the right and move it to the left so now 150/.25=X  600=X

Using the statements given for congruency the proof is -

TC ≅ TM                      Given

AT bisects ∠CTM        Given

∠ATC ≅ ∠ATM            Definition of bisect

AT ≅ AT                       Reflexive property

Δ ATC ≅ Δ ATM          SAS theorem

CA ≅ MA                      ≅ Δs → ≅ parts

What is congruency?

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

A diagram of a diamond ACTM is given.

The line segment TC is equal and congruent to line segment TM.

This statement is already given in the question.

The line segment AT bisects angle CTM.

This statement is already given in the question.

The angle ATC is equal and congruent to angle ATM.

This statement is the definition of bisect.

The line segment AT is equal and congruent to line segment AT.

This statement is true by the reflexive property of the triangles.

Triangle ATC is equal and congruent to triangle ATM.

This statement is true by Side-Angle-Side (SAS) theorem of the triangles.

The line segment CA is equal and congruent to line segment MA.

This statement is true as the triangles are congruent to each other and congruent triangles have congruent parts.

Therefore, the proof is complete.

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Answer:

Two quantities are in direct proportion if an increase in one quantity leads to a proportional increase in the other quantity. In this case, the number of melons and the cost of melons are in direct proportion if an increase in the number of melons leads to a proportional increase in the cost of melons.

To check if the given statement is true, we can use the concept of unit rate. Unit rate is the rate for one unit of a given quantity. In this case, the unit rate for melons would be the cost of one melon.

If 7 melons cost £5, then the cost of one melon can be calculated by dividing the total cost by the number of melons:

Cost of one melon = Total cost / Number of melons

= £5 / 7

= £0.714 (rounded to 3 decimal places)

Now, let's calculate the cost of different numbers of melons and see if they are in direct proportion:

For 1 melon, the cost would be £0.714

For 2 melons, the cost would be £1.429

For 3 melons, the cost would be £2.143

For 4 melons, the cost would be £2.857

For 5 melons, the cost would be £3.571

For 6 melons, the cost would be £4.286

For 7 melons, the cost would be £5.000

As we can see, the cost of melons increases proportionally with the number of melons. Therefore, we can conclude that the number of melons and the cost of melons are in direct proportion

Answer:

Yes

What is horizontal distance ?

The distance between two points is understood to mean the horizontal distance, regardless of the relative elevation of the two points.

How to calculate horizontal distance?

Horizontal distance can be expressed as x = Vtx = Vtx=Vt. Vertical distance from the ground is described by the formula y = – 1 2 g t 2 y = – \frac{1}{2}g t^2 y=–21gt2, where g is the gravity acceleration, and h is an elevation.

Step by step explanation:

As long as the ramp is no more than .9965 feet high, then yes

If the ramp is .9965 feet high then its horizontal distance is 12 X .9965 feet or 11.958 feet

Using Pythagoras’ Theorem, the actual length of the ramp would be the square root of (11.958 X 11.958 + .9965 X .9965)

Or the square root of (142.9934 + .9930)

Or SQRT (143.987)

= 11.999 feet

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The answer is approximately 2.2198, which is option (b).

To evaluate log13(297) using the change-of-base formula, we can express it in terms of a logarithm with a base that we can easily calculate, such as the common logarithm (base 10) or the natural logarithm (base e).

Let's use the common logarithm:

log13(297) = log10(297) / log10(13)

We can use a calculator to find the decimal approximations of log10(297) and log10(13), and then divide them to get the final answer:

log13(297) ≈ 2.2198 (rounded to 4 decimal places)

Therefore, the answer is approximately 2.2198, which is option (b).

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If Kenneth has 5/8 feet of lumber, then he need 83/40 feet of lumber to make the shelf.

First we convert the length of lumber in improper fraction form,

So, we convert 2(7/10) feet to an improper fraction,

⇒ 2(7/10) = (2×10 + 7)/10 = 27/10,

To find the length of lumber required we need to subtract the amount of lumber Kenneth has from the total length required,

Kenneth has a total of 5/8 feet of lumber,

Length of lumber required is = 27/10 - 5/8,

Taking LCM of 10 and 8 as 40 , and simplifying further,

We get,

⇒ 108/40 - 25/40

⇒ 83/40

Therefore, Kenneth needs 83/40 feet more lumber to make the shelf.

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Answer:

Step-by-step explanation:multiply x by y to the power of 67000 and then you will get 730000000.

Answer: Your welcome!

Step-by-step explanation:

The students can decorate the circles for placemats in a variety of ways. They can use paint, markers, fabric, or any other creative material of their choice. They can also add images, shapes, and words to the circles. They could even attach ribbons or other decorations to the circles to create a unique design. The possibilities are endless!

The multiplied the binomials of

Multiplying binomials involves using the distributive property to multiply each term in one binomial by each term in the other binomial.

(i) 2a-9 and 3a+4
(2a-9)(3a+4) = 2a(3a) + 2a(4) - 9(3a) - 9(4) = 6a²+ 8a - 27a - 36 = 6a² - 19a - 36

(ii) x-2y and 2x-y
(x-2y)(2x-y) = x(2x) + x(-y) - 2y(2x) - 2y(-y) = 2x² - xy - 4xy + 2y² = 2x^(2) - 5xy + 2y²

(iii) kl+lm and k-l
(kl+lm)(k-l) = kl(k) + kl(-l) + lm(k) + lm(-l) = k^(2)l - kl²+ lmk - l²m = k²l - l²m - kl² + lmk

(iv) m²-n² and m+n
(m²-n²)(m+n) = m²(m) + m²(n) - n²(m) - n²(n) = m³ + m²n - mn² - n²

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The vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).

To find the vertex, axis of symmetry, x-intercept, y-intercept, range, and domain of the function f(x) = x² + 6x - 11, we can use the following formulas:

- Vertex: (-b/2a, f(-b/2a))

- Axis of symmetry: x = -b/2a

- X-intercept: Solve f(x) = 0

- Y-intercept: f(0)

- Range: All real numbers for a parabola that opens up or down

- Domain: All real numbers


Using these formulas, we can find the following:

- Vertex: (-3, -20)

- Axis of symmetry: x = -3

- X-intercept: (-8.44, 0) and (1.44, 0)

- Y-intercept: (-11)

- Range: (-∞, -20]

- Domain: (-∞, ∞)


Therefore, the vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).

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4x^(2)+2x+2 with a remainder of -8.

The quotient and remainder of the given expression can be found by performing polynomial long division.

First, divide the leading term of the dividend, 8x^(3), by the leading term of the divisor, 2x. This gives a quotient of 4x^(2).

Next, multiply the divisor, (2x+5), by the quotient, 4x^(2), to get 8x^(3)+20x^(2).

Then, subtract this product from the dividend to get a new dividend of 4x^(2)+14x+2.

Repeat this process by dividing the leading term of the new dividend, 4x^(2), by the leading term of the divisor, 2x, to get a new quotient of 2x.

Multiply the divisor, (2x+5), by the new quotient, 2x, to get 4x^(2)+10x.

Subtract this product from the new dividend to get a new dividend of 4x+2.

Finally, divide the leading term of the new dividend, 4x, by the leading term of the divisor, 2x, to get a new quotient of 2.

Multiply the divisor, (2x+5), by the new quotient, 2, to get 4x+10.

Subtract this product from the new dividend to get a remainder of -8.

So, the final quotient is 4x^(2)+2x+2 and the final remainder is -8.

Therefore, the answer is: (8x^(3)+24x^(2)+14x+2)-:(2x+5) = 4x^(2)+2x+2 with a remainder of -8.

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The solution for x is 1/(3^16).

To solve for x, we need to convert the logarithmic equation to exponential form. The general formula for converting a logarithmic equation to an exponential equation is:

log_b(x) = y => b^y = x

In this case, the base is 3, the exponent is -2 - 6 - 8 + (1/9) - (1/9), and x is the value we are trying to find. So, we can write the exponential equation as:

3^(-2 - 6 - 8 + (1/9) - (1/9)) = x

Simplifying the exponent gives us:

3^(-16) = x

Now, we can solve for x by taking the inverse of both sides:

x = 1/(3^16)

Therefore, the solution for x is 1/(3^16).

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Answer:

4700=πr²×31

4700/31=πr²

151.6.../π=r²

√151.6.../π=

6.946933566=r

r=6.95mm

Explain:

Volume of cylinder=

πr²×height

The solution of the given quadratic system above would be = 6 , -10 for X and y respectively. That is option B.

To calculate the value of x and y substitution method should be used.

3x + y= 8 ---> equation 1

y=-x² + 3x + 8 ---> equation 2

Make y the subject of formula in equation 1;

y = 8 - 3x

Substitute y = 8 - 3x into equation 2;

8 - 3x = -x² + 3x + 8

x² = 3x +3x +8 -8

x² = 6x

X = 6

Substitute X = 6 into equation 1;

3(6) + y = 8

Make y the subject of formula;

y = 8-18

y = -10

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