Form an equation in u and show it simplifies to 2u^2-20u+36=0

The PMF of X+Y is given byP(X + Y = k) = P(X = 0,Y = k) + P(X = 1,Y = k-1) + P(X = 1,Y = k) = (1/2)(1/3)^k + (1/2)(1/3)^(k-1) + (1/2)(1/3)^(k-1)for k = 0, 1, 2.

The CDF of X+Y can be determined as below:P(X + Y = 0) = (1/2)(1/3)^0 = 1/2P(X + Y ≤ 1) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) = 1/2 + (1/2)(1/3) + (1/2)(1/3) = 5/6P(X + Y ≤ 2) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) + P(X = 1,Y = 1) + P(X = 0,Y = 2) = 1/2 + (1/2)(1/3) + (1/2)(1/3) + (1/2)(1/3)(2/3) + (1/2)(1/3)^2 = 11/18P(X + Y ≤ 3) = 1, as the range of X+Y is 0, 1, 2.

The expectation of X+Y can be determined asE(X + Y) = E(X) + E(Y) = 1/2 + 1/3 = 5/6

The variance of X+Y can be determined asVar(X + Y) = Var(X) + Var(Y) = (1/2)(1/2) + (1/3)(2/3) = 7/18

The expectation of X⋅Y can be determined as below: E(X⋅Y) = P(X = 1,Y = 1) = (1/2)(1/3) = 1/6

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Answer:

The perimeter of the portrait is $2\times(1+2)=6$ yards.

To find the cost of the frame, we need to calculate the length of the frame needed, which is the same as the perimeter of the portrait. So, the length of the frame needed is 6 yards.

The cost of the frame will be the cost per yard multiplied by the length of the frame:

$6~\text{yards} \times $10.17/\text{yard} = $61.02$

Therefore, the frame will cost $61.02.

Answer:

429

Step-by-step explanation:

using graph f(x) is concave down on (-1,0), (1,∞).

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

f(x) is concave up where f'(x) is increasing and concave down where f'(x) is decreasing

So, using graph f(x) is concave down on (-1,0), (1,∞).

Hence, using graph f(x) is concave down on (-1,0), (1,∞).

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Answer:

35 Degrees

Step-by-step explanation:

Given in figure.

Happy to help :)

The solution is, the value of the angle ADF = 35° .

Here, we have,

from the given diagram, we get,

ABCD is a trapezium.

EBC is a straight line.

F is the point on AB so that DFE is a straight line.

Angle BEF = 45°

Angle FBC = 100°

now, we have,

angle FBE = 180 - 100

                 = 80 degrees

now, from triangle BEF , we get,

Angle EFB = 55 degrees

again, as AFB is vertically opposite angle,

so, angle AFB = Angle EFB = 55 degrees

finally from triangle ADF , we get,

Angle ADF = 180 - 90 - 55

                  = 90 - 55

                  = 35 degrees

so, the value of the angle ADF = 35° .

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Answer:

e = - 10

Step-by-step explanation:

4e - 6e - 5 = 15

- 2e - 5 = 15 ( add 5 to both sides )

- 2e = 20 ( divide both sides by - 2 )

e = - 10

Answer: e = -10

Step-by-step explanation:

4e-6e-5=15

-2e-5=15

add 5 on both sides

-2e=20

divide 20 on both sides

e=-10

There is no significant evidence that more than two-thirds (67%) of authors support continuing this system.

This hypothesis is either rejected or accepted, depending on whether the population or sample under investigation is viable.

In other words, the null hypothesis is an assertion that the sample observations are the result of chance. It is asserted that surveyors who are interested in the data have made this allegation. It has the prefix H0.

Let p be the proportion of authors who support continuing the system.

Then hypotheses are:

H0: p=0.67

Ha: p>0.67

For calculating the test statistic:

z = p(s)-p/√ [p0(1-p)/N]

where, p(s) = 72/104 ≈ 0.692, p is 0.67 and N is the sample size =104

Then Z ≈ 0.477

The test statistic's p-value is 0.317.

Since 0.317>0.05 and we're assuming a significance level of 0.05, we are unable to reject the null hypothesis.

p-value 0.317 is the likelihood that the sample is chosen from the distribution assumed under null hypothesis, that is where the fraction of authors favouring the new publication scheme is at most 0.67.

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We can be 95% confident that the true mean concentration of THMs in your drinking water lies within the range [2.9584 ppb, 3.0416 ppb]. This was calculated using a confidence interval formula for the mean.

The confidence interval for the mean concentration of THMs can be calculated using the formula x ± z * (s/√n), where x is the sample mean, z is the z-score for a given confidence level, s is the sample standard deviation and n is the sample size.

In this case, we have x = 3 ppb, s = 0.3 ppb, and n = 200. To calculate the confidence interval at a certain confidence level (e.g. 95%), we need to find the corresponding z-score. For a 95% confidence level, the z-score is approximately 1.96.

Substituting these values into the formula above gives us:

3 ± 1.96 * (0.3/√200) = [2.9584, 3.0416]

So we can be 95% confident that the true mean concentration of THMs in your drinking water lies within the range [2.9584 ppb, 3.0416 ppb].

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Peter will receive R134,417.50 of the profit.

Investment refers to the purchase of goods that are not consumed today but are used in the future to create wealth. In financial terms, investment typically involves buying assets such as stocks, bonds, real estate or other financial instruments with the expectation of earning a profit or income from them.

Khomo paid R245,000 for the house, so his investment ratio is:

245,000 / 575,000 = 0.426

Peter's investment ratio is:

1 - 0.426 = 0.574

If they share the profit in the same ratio as their respective investment, then Peter will receive:

0.574 x 234,500 = 134,417.5

Therefore, Peter will receive R134,417.50 of the profit.

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We can say that after answering the offered question The terms in the equation given equation can be streamlined and rearranged to produce the following equation: 23p – 101 = 64p – 40

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

Using the equality properties, we can rewrite the preceding equation as follows:

2.3p – 10.1 = 6.5p – 4 – 0.01p

2.3p – 10.1 = 6.49p – 4

We can alter the equations using the equality characteristics to look for equations that have the same solution. The answers to the next two equations are the same as those for the previous one:

2.3p – 10.1 = 6.4p – 4

The following equation can be created by adding 0.09p to both sides of the given equation:

2.3p - 10.1 + 0.09p = 6.5p - 4 - 0.01p + 0.09p

2.39p – 10.1 = 6.4p – 4

23p – 101 = 65p – 40 – p

The terms in the given equation can be streamlined and rearranged to produce the following equation:

23p – 101 = 64p – 40

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The expression 1÷2+2 3÷4-3÷8​ when simplified is 9/4

From the question, we have the following parameters that can be used in our computation:

1÷2+2 3÷4-3÷8​

Express the terms properly as fractions

So, we have the following

1/2 + 2 3/4 - 3/8

Express each term as proper/improper fraction

So, we have the following representation

1/2 + 11/4 - 3/8

Express the denominator as the same

So, we have

4/8 + 22/8 - 3/8

Evaluate the like terms

18/8

So, we have

9/4

Hence, the solution is 9/4

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A. Differently organized; B. Different rates; C. Inconvenient access; D. Limited membership.

To calculate the interest rate on a loan, you will need to figure out the amount of interest you will need to pay over the life of the loan. First, you will need to determine the loan amount, the interest rate, and the loan term. Then, you will need to calculate the total interest by multiplying the loan amount by the interest rate and the loan term. Finally, you will need to divide the total interest by the loan amount and then multiply that by 100 to get the annual percentage rate (APR). This will give you the interest rate you will need to pay over the life of the loan.

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Answer:0.27 miles

Step-by-step explanation:

Answer:

The answer to your question is 7040

Step-by-step explanation:

How many yards are in 1 mile:

So 1 mile = 1760 yards

Speed = 1760 yard per minute

= 1760 yd/min

Since we have 4 miles, we are gonna multiply 4 multiplied by 1760.

So 4 miles x 1760 = 7040

I hope this helps and have a wonderful day!

Answer:

The two teachers are approximately 4.1 meters apart.

Step-by-step explanation:

Let's use the following variables:

d = distance between the two teachers

Using the Pythagorean theorem:

d^2 = 4^2 + 1^2

d^2 = 16 + 1

d^2 = 17

d = sqrt(17)

d ≈ 4.1

Answer: 4.1

Step-by-step explanation:

[tex]\sqrt{1^2+4^2}[/tex]

evaluate the equation / expression

4.12311

round

4.12311 to the required place

4.1

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

dudjeisosidheis9sjdhxisjdgskkjehud

Answer:

a. from A to B, a rotation by 90 degrees anti-clockwise about (0,0).

b. from B to C, a translation by vector (-3/4, -1/4).

c. from A to C, a rotation by 60 degrees, anti-clockwise about (0,0).

Hope this helps, I'm sorry if it doesn't. If you need more help, ask me! :]

Answer: -1

Step-by-step explanation:

An easy way to figure out the slop of a linear graph is the formula:

(y1-y2)/(x1-x2)

In order to use this, find two spots on the line that run exactly through a point, in this example (0,20) and (20,0).

Plug in the xs and ys into the formula, which gets you  

(20-0) / (0-20)

When simplified, the result is -1 and that is your slope

the distance from point C to line AB, you must find the length of the segment from C perpendicular to AB

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.

When the angle of inclination between two line segments is exactly equal, those two segments are said to be perpendicular.

The plus symbol is formed when two perpendicular line segments cross one other.

To find the distance from point C to line AB, you must find the length of the segment from C_______ to AB

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The missing measurements of the triangle given include:

The value of angle B can be found thanks to the knowledge that the interior angles of a triangle add up to 180 degrees and we have two of the angle measurements :

= 180 - angles measurements

= 180 - 27 - 90

= 63 degrees

The value of AB can be found by using the Sin theta operation such that:

Sin theta = Opposite / hypotenuse

Sin ( 27 degrees ) = 12 / hypotenuse which is AB

hypotenuse = 12 / ( Sin ( 27 degrees ))

= 26 .4 units

The value of AC measurement is:

Tan ( 27 degrees ) = 12 / AC

AC = 12 / Tan ( 27 degrees )

AC = 23. 6 units

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The derivative for each of the definite integrals using the fundamental theorem of calculus is

a) d/dx ∫ 4x(2(6cos(t)+7)⁴)dt is 4(2(6cos(b)+7)⁴) - 4(2(6cos(a)+7)⁴)

b)  d/dx ∫ x³(4sin(t³−3))dt is 12(b²sin(b³-3) - a²sin(a³-3))

The fundamental theorem of calculus tells us that the derivative of the definite integral of a function f(x) with respect to x is equal to the function evaluated at the upper limit of integration minus the function evaluated at the lower limit of integration. In other words, if we have an integral of the form ∫f(x)dx evaluated from a to b, then

d/dx ∫f(x)dx = f(b) - f(a)

Let's apply this to the first integral, A).

A) d/dx ∫ 4x(2(6cos(t)+7)⁴)dt

We begin by recognizing that the function inside the integral is a function of t, not x. However, we want to take the derivative with respect to x. This means that we need to use the chain rule to differentiate the integrand with respect to x.

Using the chain rule, we have

d/dx [4x(2(6cos(t)+7)⁴)] = 4(2(6cos(t)+7)⁴)(d/dx [4x])

= 4(2(6cos(t)+7)⁴)(4)

= 32(2(6cos(t)+7)⁴)

Now, we can apply the fundamental theorem of calculus. Let's say we are evaluating the integral from a to b. Then,

d/dx ∫ 4x(2(6cos(t)+7)⁴)dt = [4b(2(6cos(t)+7)⁴)] - [4a(2(6cos(t)+7)⁴)]

= 4(2(6cos(b)+7)⁴) - 4(2(6cos(a)+7)⁴)

This is the final answer for A).

Now, let's move on to integral B).

B) d/dx ∫ x³(4sin(t³−3))dt

Again, we need to use the chain rule to differentiate the integrand with respect to x.

d/dx [x³(4sin(t³−3))] = (d/dx [x³])(4sin(t³−3))

= 3x²(4sin(t³−3))

Now, we apply the fundamental theorem of calculus. Let's say we are evaluating the integral from a to b. Then,

d/dx ∫ x³(4sin(t³−3))dt = [3b²(4sin(t³−3))] - [3a²(4sin(t³−3))]

= 12(b²sin(b³-3) - a²sin(a³-3))

This is the final answer for B).

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Answer:

-5 is your answer

Step-by-step explanation:

What do you mean leading coefficient of the following polynomial.

Look at the x^n and see who has the biggest values.

-5x^7 is the leading coefficient.

(15) The value of x is -588 (option A).

(16) The value of x makes the expression equal to 0 is -2i. (option B).

The value of x is calculated by solving the equation as follows;

(15) We have the equation:

√x = 14i√3

Squaring both sides, we get:

x = (14i√3)^2

x = -588

(16) Factoring the expression, we get:

x(x⁴ + 6x² + 8)

Setting each factor equal to 0, we get:

x = 0 or x⁴ + 6x² + 8 = 0

Let's solve for the second equation:

Let y = x²

Then we have:

y² + 6y + 8 = 0

Factorizing, we get:

(y + 2)(y + 4) = 0

So y = -2 or y = -4

Since y = x², this means:

x² = -2 or x² = -4

Taking the square root of both sides, we get:

x = ±√(-2) or x = ±√(-4)

Simplifying using imaginary numbers, we get:

x = ±i√(2) or x = ±2i

Thus, for the expression √x is equivalent to 14i√3,  the value of x is -588. And for the expression x⁵ + 6x³ + 8x, x = -2i.

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After answering the presented question, we can conclude that The point of intersection of these two equations is (2, 0), which is the spot on the graph where the parabola and line intersect.

An equation is a mathematical statement that validates the equivalent of two expressions linked by the equal symbol '='. For example, 2x - 5 = 13. 2x-5 and 13 are two phrases. The character '=' is used to connect the two expressions. An equation is a mathematical formula that has two algebras on either side of an assignment operator (=). It illustrates the equivalency relationship between the left and middle formulas. In any formula, L.H.S. = R.H.S. (left side = right side).

The graph represents the following equation system:

[tex]y = x^2 + 3x + 2 x + y = 2[/tex]

This is due to the fact that the graph of a quadratic function intersecting a linear function at point (2, 0) is represented by a parabola and a straight line intersecting at that point (2, 0).

The equation [tex]y = x^2 + 3x + 2[/tex] represents an upward-opening parabola that goes through the point (-2, 0).

The equation x + y = 2 denotes a straight line that connects the locations (0, 2) and (2, 0).

The point of intersection of these two equations is (2, 0), which is the spot on the graph where the parabola and line intersect.

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Answer:x=5/4

Step-by-step explanation:

you can take numbers with same variable(i mean x or y or other) in the same side:

2+3x=12-5x

2-12=-5x-3x

-10=-8x

x=10/8=5/4

Answer:

x = 5/ 4

Step-by-step explanation:

2 + 3x =12- 5x

3x + 5x = 12 - 2

8x = 10

x = 10/8

x = 5/4

Answer:

Step-by-step explanation:

angle

Answer:10ft

Step-by-step explanation:

we must use pythagorean theorem

[tex]which \ is \ a^{2} +b^{2} =c^{2} \\6^{2} + 8^{2} =36+64=100=10^{2}\\c=10--- > hypotenuse[/tex]

The probability that the second person chosen will also be a boy is roughly 0.872, or 87.2%.

Since the first person chosen is a boy, there are now 12 boys and 15 girls left in the class. We want to find the probability that the second person chosen is also a boy.

The probability of choosing a boy for the first selection is 13/28. Then, for the second selection, there are now 12 boys and 27 students left, so the probability of choosing a boy is 12/27.

Using conditional probability, we can calculate the probability that the second person chosen is also a boy given that the first person chosen is a boy:

P(Second person is a boy | First person is a boy) = P(Both are boys) / P(First person is a boy)

P(Second person is a boy | First person is a boy) = (12/27) / (13/28)

P(Second person is a boy | First person is a boy) ≈ 0.872

Therefore, the probability that the second person chosen is also a boy given that the first person chosen is a boy is approximately 0.872 or 87.2%.

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Answer: We know that the area of the base of a cylinder is given by the formula:

A = πr²

where A is the area of the base, π is the mathematical constant pi (approximately equal to 3.14), and r is the radius of the base.

To find the perimeter of the base, we need to know the circumference of the circle that forms the base of the cylinder. The formula for the circumference is:

C = 2πr

where C is the circumference and r is the radius.

To find the radius of the base, we can rearrange the formula for the area:

A = πr²

r² = A/π

r = √(A/π)

Substituting the given value for the area of the base, we get:

r = √(38.5/π) ≈ 3.5 m

Now, we can use the formula for the circumference to find the perimeter of the base:

C = 2πr = 2π(3.5) ≈ 22 m

Therefore, the perimeter of the base is approximately 22 meters.

Step-by-step explanation:

The prime factorization of 6 is the expression of 6 as a product of its prime factors.

A prime factor is a prime number that is a factor of the given number. To find the prime factorization of 6, we need to express 6 as a product of its prime factors. Since 6 can be evenly divided by 2 and 3, which are both prime numbers, the prime factorization of 6 is 2 x 3. We can also write this as 2^1 x 3^1, using exponents to show that there is only one 2 and one 3 in the prime factorization of 6. Finally, since 2 and 3 are both prime, we order the factors from least to greatest as 2 x 3.

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98 Degrees and 82 degrees  are  the measurements of the numbered angles of this circle.

What is a circle?

With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.

                           The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The symmetry line of reflection is formed by each line that traverses the circle. Moreover, it possesses rotational symmetry around the center for each angle.

Measure of angle 1 = (33 + 131)/2

                         = 82 degrees

Measure of angle 2 = 180 - 82

                         = 98 Degrees

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