This is a one step equation

The value of x in the triangle is given by x = 33.7°

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of hypotenuse = AC = 18 cm

The measure of the opposite side = AB = 10 cm

From the trigonometric relations ,

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin x = 10 / 18

On simplifying the equation , we get

sin x = 0.555556

Taking inverse on both sides of the equation , we get

x = sin⁻¹ ( 0.555556 )

On further simplification , we get

x = 33.7°

Hence , the value of x is 33.7°

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Answer:

5 students out of each of the 4 homeroom classes

Step-by-step explanation:

The most random sample is 5 students out of each of the 4 homeroom classes.

Thus, option (C) is correct.

Selecting 5 students from each of the 4 homeroom classes ensures that the sample represents a diverse range of students from different classes.

This approach helps to minimize bias and increase the randomness of the sample.

The other options, such as selecting the first 20 students who arrive at school or the last 20 people in line for breakfast, may introduce some bias based on the specific circumstances or characteristics of those groups. Selecting all 20 boys on the swim team would also not provide a representative sample of the overall student population.

Thus, option (C) is correct.

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The coordinate plane is missing, so i have attached it.

Answer:

Perimeter of room = 140 ft

Area of room = 1200 sq.ft

Step-by-step explanation:

From the cordinate plane attached, we can see the polygon QRST which represents the floor plan of the roo.

Thus;

The length of the sides of the room are;

ST = RQ = 30

QT = RS = 40

Perimeter of a rectangle is the sum of all sides of the rectangle.

Thus, perimeter of the room = (30 × 2) + (40 × 2) = 140 ft

Now, area of a rectangle is the product of two perpendicular sides.

Thus area of room = 40 x 30 = 1200 sq.ft

Thus, CDF of X for the log-normal distribution with parameters μ and σ, is Var(X) = E[X^2] - (E[X])^2 = e^(2μ+2σ^2) - e^(2μ+σ^2).

a. To find the CDF of X, we first note that X is a transformation of the standard normal variable Z, and so we have:
F_X(x) = P(X ≤ x) = P(e^(σZ+μ) ≤ x)

Taking the natural logarithm of both sides gives:
ln(e^(σZ+μ)) ≤ ln(x)
σZ+μ ≤ ln(x)
Z ≤ (ln(x) - μ)/σ

Since Z has a standard normal distribution, we have:
F_X(x) = P(Z ≤ (ln(x) - μ)/σ) = Φ((ln(x) - μ)/σ)

where Φ is the standard normal CDF. Therefore, the CDF of X is given by:
F_X(x) = Φ((ln(x) - μ)/σ)

b. To find the PDF of X, we differentiate the CDF with respect to x:
f_X(x) = d/dx F_X(x) = (1/x) * Φ'((ln(x) - μ)/σ) * (1/σ)

where Φ' is the standard normal PDF. Simplifying, we have:
f_X(x) = (1/xσ) * φ((ln(x) - μ)/σ)

where φ is the standard normal PDF. Therefore, the PDF of X is given by:
f_X(x) = (1/xσ) * φ((ln(x) - μ)/σ)

To find the expected value of X, we use the fact that the log-normal distribution has the property that if Y ~ N(μ,σ^2), then X = e^Y has mean e^(μ+σ^2/2).

Therefore, we have:
E[X] = E[e^(σZ+μ)] = e^(μ+σ^2/2)

To find the variance of X, we use the formula Var(X) = E[X^2] - (E[X])^2. Since X = e^(σZ+μ), we have:
E[X^2] = E[e^(2σZ+2μ)] = e^(2μ+2σ^2)

Therefore, we have:
Var(X) = E[X^2] - (E[X])^2 = e^(2μ+2σ^2) - e^(2μ+σ^2)

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Answer:

mag try sa chrome

Step-by-step explanation:

thank you

hope it's help

Answer:

See below

Step-by-step explanation:

(a+c)^2 = t

(a+c) = sqrt t

c = sqrt(t) - a

Answer:

Step-by-step explanation:

Answer:

33.33%

Step-by-step explanation:

75*100=7500

7500/225=33.3333333

Using the z-distribution, the sample sizes required are given as follows:

a) 822.

b) 1068.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Then, the margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

We have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

Item a:

The estimate is of \(\pi = 0.26\), hence we solve for n when M = 0.03.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}\)

\(0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2\)

n = 821.2

Rounding up, a sample of 822 is needed.

Item b:

No prior estimate, hence \(\pi = 0.5\), which is when the largest sample size is needed.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2\)

n = 1067.11

Rounding up, a sample of 1068 is needed.

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Step-by-step explanation:

it is the right answer you have to learn inverse function . if f:A to B and is a function then new function from B to A is said to be inverse function in which each element of set a maps unique element of b

Answer:

length = 75 ft and width = 25 ft

Step-by-step explanation:

Let W = width of rectangle

Let L = length of rectangle

Area of a rectangle = L x W

Perimeter of a rectangle = 2L + 2W

Therefore, if the perimeter is 200 ft then:

2L + 2W = 200

2(L + W) = 200

    L + W = 100

           L = 100 - W

If the Area is 1875 ft² then:                             1875 = L x W

Substitute the equation for L found above:  1875 = (100 - W) x W

Expand the brackets:                                    1875 = 100W - W²

Subtract 1875 from both sides:  100W - W² - 1875 = 0

Swap signs:                                W² - 100W + 1875 = 0

Factorize:                                       (W - 25)(W - 75) = 0

Therefore, W = 25 or 75

If W = 25, then L = 100 - 25 = 75

If W = 75, then L = 100 - 75 = 25

Therefore, as length > width, length = 75 ft and width = 25 ft

Answer:

The second one is right

Step-by-step explanation:

Hope it helpssss

The answer choices which are solutions to the given equation as required are Choice D; 6 and Choice E; -4.

Given; x² - 2x -24 = 0.

By factorisation;

x² - 6x + 4x - 24 = 0

(x - 6) (x + 4) = 0

x - 6 = 0 or x + 4 = 0

Consequently, x = 6 or x = -4

Therefore, the solutions to the given equation are; Choice D; 6 and Choice E; -4.

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No, Josiane's statement is incorrect. The number 12 has 6 divisors, but only one prime factor, which is 2. The other prime factor of 12 is 3, which is not counted in the number of divisors.

Josiane is not correct. The number 12 has a total of 6 divisors, which are 1, 2, 3, 4, 6, and 12. However, only one of its factors is prime, which is the number 2. The other prime factor of 12 is 3. Therefore, 12 has only one prime factor and not two.

To find the number of divisors of a given number, we can factorize the number into its prime factors and then use the formula (a+1)(b+1)(c+1)... where a, b, c, etc. are the exponents of the prime factors.

In the case of 12, its prime factorization is 2² x 3, which gives us (2+1)(1+1) = 6, the correct number of divisors.

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Answer:

9 days

Step-by-step explanation:

13 1/4 / 1 1/2 = 8 5/6 so 9 days

Answer:

uhhugvtrctreex

Step-by-step explanation:

Answer: The item is $42 off.

Step-by-step explanation:

Whenever you have a percentage of a number you simply turn the percentage into a fraction by dividing it by 100. Here 60% would become 0.6. Then you multiply the regular price of $70 by 0.6 to get 60 percent of 70 which is 42. That means that $42 is discounted from the original.

Answer:

Isn't it 18?

Step-by-step explanation:

Because you need to add 4 and 2 then multiply it with 3?

\(y = \begin{cases}- 2x + 1& x > 1 \\- x + 2&x\leqslant1\end{cases}\)

from the figure

\((x_1,y_1) \: (x_2,y_2) = >y = \frac{y_2 - y_1}{x_2 - x_1} \: x + a \\ a = y_1 - \frac{y_2 - y_1}{x_2 - x_1} \: x_1\)

235 millimeters is approximately 9.25 inches. To convert the millimeter measurement to inches, divide the given number of millimeters by 25.4.

The conversion of millimeters to inches is quite simple. To convert the millimeter measurement to inches, divide the given number of millimeters by 25.4. The result of this calculation is the number of inches. In this example, 235 millimeters is equal to 9.25 inches. This is because when you divide 235 by 25.4, you get 9.25 as the result. Therefore, 235 millimeters is equal to 9.25 inches.

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Answer:

I believe its 990

Step-by-step explanation:

you would multiply 9 times 10 times 11 and it equals 990

Answer:

Step-by-step explanation:

This is a parallelogram

base = 11 in

Height = 9 in

Area of parallelogram = base * height

                                    = 11 * 9

                                    = 99 square inches

Answer:

your answer would be the second option.

Step-by-step explanation:

How this is is because it is in simple y=mx+b formation

the b is +1 and you go down one and over to the  three which is decreasing so it would be -1/3

The propositions among the given options are: \( \exists x P(x) \) and \( (\exists x S(x)) \vee R(x) \). A proposition is a declarative statement that can be either true or false.

In the first option, \( \exists x(S(x) \vee R(x)) \), the statement is not a proposition because it contains a quantifier (\( \exists \)) without specifying the domain of discourse. This makes it unclear whether the statement is true or false.

The second option, \( \exists x P(x) \), is a proposition. It states that there exists an \( x \) for which \( P(x) \) is true. This statement can be evaluated as either true or false, depending on the specific meaning and truth value of \( P(x) \).

The third option, \( P(x) \vee(\forall x Q(x)) \), is not a proposition because it contains a mixture of a universal quantifier (\( \forall \)) and an existential quantifier (\( \exists \)) without a clear domain of discourse.

The fourth option, \( (\exists x S(x)) \vee R(x) \), is a proposition. It states that either there exists an \( x \) such that \( S(x) \) is true, or \( R(x) \) is true. This statement can be evaluated as either true or false, depending on the specific meanings and truth values of \( S(x) \) and \( R(x) \).

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Answer:

x = 3 +√43, x = 3 - √43

Step-by-step explanation:

x^2 - 6x - 34 = 0

move the 34 across

x^2 - 6x = 34

take -6 and divide by two, then square it

(-6/2)^2 = 9

add the product to your equation

x^2 - 6 + 9 = 34 + 9

solve

(x - 3)^2 = 43

x - 3 = ± √43

x = 3 ± √43

Answer:

the answer is x ≥ 6

Step-by-step explanation:

x ≥ 8 - 2

x ≥ 6

Answer:

The translation rule is;

Explanation:

Given the graph attached;

Let us pick a corresponding edge(point) on the preimage and image respectively;

The change on the x and y axis is;

Therefore, the translation rule is;

Answer:

Your Domain Will be (6,-12,-6,20)

Your Range will Be 36

Sorry i dont have work shown i just remember doing this problem and just gave answers glad to help and stay safe

Answer:

Domain: {6, -12, -6, 20}

Range: {0, -16 , 10 , -7}

Step-by-step explanation:

Domain and Range:

Domain: In the set of ordered pairs, domain is all the x-values.

Range: In the set of ordered pairs, range is all the y-values

Domain: {6, -12, -6, 20}

Range: {0, -16 , 10 , -7}

Its 0

0x2=0

0+4=4

0x7=0

4-4=0