i will mark brainliest

Answer:

21 cm

Step-by-step explanation:

We can start by using the formula for the area of a triangle:

Area = (1/2) * base * height

Where the base is b = 24 cm and the height by side a is h = 12 root 3 cm.

Area = (1/2) * 24 cm * 12 root 3 cm = 144 cm^2

We can also use the formula for the area of a triangle in terms of its sides and circumradius:

Area = (abc) / (4R)

Where a, b, and c are the sides of the triangle and R is the radius of its circumcircle.

Plugging in the values we know, we get:

144 cm^2 = (24 cm * a * c) / (4 * 7 root 3 cm)

Simplifying, we get:

9 root 3 cm = a * c / 7

Multiplying both sides by 7 and dividing by a, we get:

c = (63 root 3 cm^2) / a

Substituting the value we know for a, we get:

c = (63 root 3 cm^2) / (12 root 3 cm) = 21 cm

Therefore, the length of side c is 21 cm.

Hopes this helps

Angle R is 125.5 degrees.

To find ∠R, we can use the fact that the sum of the angles in a triangle is 180°:

∠Q + ∠R + ∠S = 180°

We know that ∠S = 154° and q = QS, so we can use the Law of Cosines to find ∠Q:

q² = r² + s² - 2rs cos ∠Q

5.5² = 7.9² + s² - 2(7.9)(s) cos ∠Q

30.25 = 62.41 + s² - 15.8s cos ∠Q

s² - 15.8s cos ∠Q + 32.16 = 0

Using the quadratic formula, we get:

s = (15.8 cos ∠Q ± √((15.8 cos ∠Q)² - 4(1)(32.16))) / 2

Since s is the length of a side of a triangle, it must be positive, so we take the positive square root:

s = (15.8 cos ∠Q + √((15.8 cos ∠Q)² - 4(1)(32.16))) / 2

We also know that r = 7.9 cm, so we can use the Law of Cosines to find ∠R:

r² = s² + q² - 2sq cos ∠R

7.9² = s² + 5.5² - 2(7.9)(5.5) cos ∠R

62.41 = s² - 85.9 cos ∠R

Substituting for s, we get:

62.41 = ((15.8 cos ∠Q + √((15.8 cos ∠Q)² - 4(1)(32.16))) / 2)² - 85.9 cos ∠R

Simplifying, we get:

62.41 = 12.5 cos² ∠Q - 39.5 cos ∠Q + 32.16 - 85.9 cos ∠R

Rearranging, we get:

85.9 cos ∠R = 12.5 cos² ∠Q - 39.5 cos ∠Q - 30.25

cos ∠R = (12.5 cos² ∠Q - 39.5 cos ∠Q - 30.25) / 85.9

Using the value of ∠S, we get:

∠Q + ∠R + 154° = 180°

∠Q + ∠R = 26°

Substituting into the previous equation, we get:

cos ∠R = (12.5 cos² (26°) - 39.5 cos (26°) - 30.25) / 85.9

cos ∠R ≈ -0.547

Taking the inverse cosine, we get:

∠R ≈ 125.5°

Therefore, ∠R is approximately 125.5 degrees.

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we know that the cos(θ) is -(3/5), however θ is in the II Quadrant, where the cosine is negative whilst the sine is positive, meaning the fraction is really (-3)/5, so

\(cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{5}}\qquad \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\)

\(\pm\sqrt{5^2-(-3)^2}=b\implies \pm\sqrt{25-9}=b\implies \pm 4=b\implies \stackrel{II~Quadrant}{+4=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}~\hfill\)

The distance between point M and point N is 12 units.

Coordinates are a set of numbers or vaIues that describe the position or Iocation of a point in space. In two-dimensionaI space (aIso known as the Cartesian pIane), coordinates are typicaIIy represented by two vaIues, usuaIIy denoted as (x, y), that describe the horizontaI and verticaI position of a point reIative to a set of axes.

The distance formuIa is a mathematicaI formuIa used to find the distance between two points in a two- or three-dimensionaI space.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

The distance formuIa is based on the Pythagorean theorem, which states that in a right triangIe, the square of the Iength of the hypotenuse (the side opposite the right angIe) is equaI to the sum of the squares of the Iengths of the other two sides.

In the given question,

We can use the distance formuIa to find the distance between point M and point N:

d = √[(x₂ - x₁)²+ (y₂ - y₁)²]

where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.

PIugging in the given vaIues, we have:

d = √[(-8 - 4)² + (-8 - (-8))²]

d = √[(-12)² + 0²]d = √[144]

d = 12

Therefore, the distance between point M and point N is 12 units.

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Answer: 20,225  

Step-by-step explanation:

If the margin of error is 4.6, the interval estimate would be the point estimate plus or minus 4.6.

In statistical estimation, the margin of error represents the maximum amount by which the point estimate may deviate from the true population parameter. It provides a measure of the precision or uncertainty associated with the estimate. When constructing a confidence interval, the margin of error is used to determine the range within which the true parameter is likely to fall.

To obtain the interval estimate, we add and subtract the margin of error from the point estimate. Let's denote the point estimate as x bar. Therefore, the interval estimate can be expressed as X bar ± 4.6, where ± denotes the range above and below the point estimate.

In summary, if the margin of error in an interval estimate of μ is 4.6, the interval estimate is given by the point estimate plus or minus 4.6. This range captures the likely range of values for the true population parameter μ.

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The probability that at least 1 ell phone of 8 randomly selected phones is defective will be 0.5577.

We have,

The probability that a cell phone manufactured at Electronics Unlimited is defective i.e. p = 0.11

And,

Total number of phones i.e. n = 8,

Now,

Using the Binomial Probability Distribution,

i.e.

P(X = x) = Cₙ, ₓ * pˣ * (1 - p)ⁿ⁻ˣ,

Here,

x = number of successes

n = number of trials

p = probability of a success on a single trial,

And,

Cₙ, ₓ =  \(\frac{n!}{x!(n-x)!}\)

Now,

According to the question,

The probability that at least 1 is defective,

i.e.

P(X ≥ 1) = 1 - P(X = 0)

And,

We have,

P(X = x) = Cₙ, ₓ * pˣ * (1 - p)ⁿ⁻ˣ,

Now,

Substituting values in above equation,

P(X = 0) = C₈,₀ * (0.11)⁰ * (1 - 0.11)⁸⁻⁰,

On solving we get,

P(X = 0) = \(\frac{8!}{0!(8-0)!}\) * (0.11)⁰ * (1 - 0.11)⁸⁻⁰,

We get,

P(X = 0) = 1 × 1 × (1 - 0.11)⁸

i.e.

P(X = 0) = 0.4423

So,

Now,

The probability that at least 1 is defective,

i.e.

P(X ≥ 1) = 1 - 0.4423

i.e.

P(X ≥ 1) = 0.5577

So,

The probability that at least 1 is defective is 0.5577.

Hence we can say that the probability that at least 1 ell phone of 8 randomly selected phones is defective will be 0.5577.

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Answer:

56.4 is your answer

Correct me if I'm wrong.

Answer:

56.368

Step-by-step explanation:

Answer:

\(x = 9\)

Step-by-step explanation:

\(7x + 49 = 2x + 94 \\ 7x - 2x = 94 - 49 \\ 5x = 45 \\ \\ x = \frac{45}{5} \\ \\ x = 9\)

I hope I helped you^_^

Answer:

2

Step-by-step explanation:

3(6+x) = 24

18 + 3x = 24

3x = 24 - 18

3x = 6

x = 6/3

= 2

The converse statement involves switching the hypothesis and the conclusion of a conditional statement.

The correct statement is (d) If B is the midpoint of AC, then AB = BC.

The converse of the given conditional statements are:

From the above statements, (a), (b) and (c) are not the same as the conditional statement, because:

For option (d):

For B to be a midpoint of AC, it means that sides AB and BC are congruent.

Hence, the correct statement is (d)

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Answer:

EF = 32

Step-by-step explanation:

DE + EF = DF

5x - 9 + 2x + 10 = 78

5x + 2x + 10 - 9= 78

7x + 1 = 78

7x = 78 - 1

7x = 77

x = 77/7

x = 11

\(EF=2x+10 = 2 \times 11 + 10 \\ EF=22 + 10 \\ \huge \red { \boxed{EF=32}}\)

In order to compute the impulse response of the single filter that corresponds to the cascade of the two filters given above, we need to use the convolution sum.

This is because the output of the first filter is the input to the second filter and the overall output is the output of the second filter. The convolution sum for an LTI filter is given by y[n] = sum(i=0 to infinity){h[i] * x[n-i]}.This formula tells us that the output of a filter at time n is the weighted sum of all the input values and past outputs. The weights are given by the impulse response of the filter. For example, if the input is x[n] = {1,2,3} and the impulse response is h[n] = {1,1,1}, then the output is y[n] = {1,3,6,5}.

To find the impulse response of the cascade of the two filters given above, we need to convolve the impulse responses of the two individual filters. Since the first filter has length 3 and the second filter has length 2, the resulting filter will have length 4. We can compute the convolution sum as follows:h[n] = sum(i=0 to infinity){h1[i] * h2[n-i]}Note that the limits of the summation are not the same as for the convolution of two sequences.

This is because we are summing over the impulse response of one filter and indexing the other filter with a variable. The result is a sequence that tells us the response of the cascade to an impulse. The values of h[n] can be computed as follows:n = 0: h[0] = h1[0] * h2[0] = 1 * 2 = 2n = 1: h[1] = h1[0] * h2[1] + h1[1] * h2[0] = 1 * 1 + 0 * 2 = 1n = 2: h[2] = h1[0] * h2[2] + h1[1] * h2[1] + h1[2] * h2[0] = 2 * 1 + 1 * 2 = 4n = 3: h[3] = h1[1] * h2[2] + h1[2] * h2[1] = 0 * 1 + 2 * 2 = 4The impulse response of the cascade of the two filters is h[n] = {2, 1, 4, 4}.

This sequence tells us the response of the cascade to any input sequence. For example, if the input sequence is x[n] = {1,2,3,4}, then the output sequence is y[n] = {2, 4, 14, 24, 28}. This is obtained by convolving x[n] with h[n]. Note that the output sequence has length 5 because the impulse response has length 4 and the input sequence has length 4.

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Answer:

zxczxcz

Step-by-step explanation:

zxczxczxc

The sample mean of the given data is 24.

To find the mean:

Therefore, the sample mean of the given data is 24.

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When ab = 0, the zero-product property tells us that at least one of the factors (a or b) must be zero in order for the equation to hold true.

We are given that ab = 0, where a and b are variables or numbers.

According to the zero-product property, if the product of two factors is equal to zero, then at least one of the factors must be zero.

In our case, we have ab = 0. This means that the product of a and b is equal to zero.

To satisfy the condition ab = 0, at least one of the factors (a or b) must be zero. If either a or b is zero, then when multiplied with the other factor, the product will be zero.

It is also possible for both a and b to be zero, as anything multiplied by zero gives zero.

Therefore, based on the zero-product property, we can infer that either a = 0 or b = 0 when ab = 0.

In summary, when ab = 0, the zero-product property tells us that at least one of the factors (a or b) must be zero in order for the equation to hold true.

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A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.

B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.

To get the how much arrival rate must increase, we must get the expected waiting time for a customer.

Assuming;

X is the number of customers who arrive per hour

Y is the length of a phone call in minutes.

Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)

Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).

Total time is given as sum of waiting time and length of call;

T = W + Y

The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);

Then we have;

E(W) = 1/(2λ) = 1/8 hours

The expected total time T that a customer spends at the phone booth is:

E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours

For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.

E(W) ≥ 1/20

To get λ,

1/(2λ) ≥ 1/20

λ ≤ 10

This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.

b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,

we need to find the probability that a customer has to wait at all.

Let P(W > 0) be the probability that a customer has to wait.

P(W > 0) = 1 - P(W = 0)

The waiting time W follows a uniform distribution with mean 1/λ, so we have:

P(W = 0) = 1 - λ/4

The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:

P(Y > t) = e^(-μt) = e^(-t/12)

The probability that a customer has to wait is given as;

P(W > 0) = 1 - P(W = 0) = λ/4

To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;

P(W > 0) > 0.6

λ > 2.4

The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.

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Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

Answer:

Step-by-step explanation:

Here you go:

64 = 512x - 4

64 + 4 = 512x - 4 + 4

68 = 512x

Hope this helps

Answer:

.2 lbs

Step-by-step explanation:

4.5/22.5

0.2 pounds as 4.5 / 22.5 = 0.2

Answer:

The answer is D

Step-by-step explanation:

I just did this

The figure which has rotational symmetry is figure A.

It is the property of a shape that it looks same after some rotation by a partial turn.

In the figure given first shape has equal length of sides at each direction which means that if we rotates this figure then we will get same looking figure.

In the second figure when we rotates the figure vertically the it will look like a tower.

When we rotates the third figure they also look different.

In the graph figure are shown after some rotation.

Hence among all the figures given first figure has rotational symmetry.

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Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

To find sums, I would prefer to use the method of using compatible numbers and adjusting. The reason behind this is that it can help me to perform mental calculations and solve mathematical problems faster.What are compatible numbers?Compatible numbers are numbers that are close to the actual numbers, but are easier to work with mathematically. They are rounded numbers that make it easier to perform mental math. Once we have the answer, we can adjust it to get the correct answer.To solve an addition problem using compatible numbers, we choose numbers close to the actual numbers in the problem. For example, if we are adding 45 and 32, we can round the numbers to 50 and 30. Then we add 50 and 30 to get 80, which is the compatible number sum. But this is not the actual answer because we rounded the numbers, so we need to adjust. We subtract 5 from 50 and add 3 to 30 to get 45 and 33, respectively. Then we add the adjusted numbers (45 and 33) to get the correct answer, which is 78.Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

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The point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the points at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j, we need to find the gradient vector of the function and equate it to the given direction vector.

The gradient vector of the function f(x, y) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x - 2

∂f/∂y = 2y - 6

Setting the gradient vector equal to the given direction vector i + j:

[2x - 2, 2y - 6] = [1, 1]

Equating the corresponding components, we have:

2x - 2 = 1

2y - 6 = 1

Solving these equations, we get:

2x = 3  =>  x = 3/2

2y = 7  =>  y = 7/2

Therefore, the point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

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The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).

Answer:

branliest??

Step-by-step explanation:

h=height of pyramid

w=width of pyramid

l=lenght of pyramid

A=w×l

A=3×÷

A=9cm²

V=A×h/3

V=9×2/3

V=18/3

V=6

V=6cm³

I hope it helps

Answer:

c

Step-by-step explanation:

because the i just worked it out

Using function concepts, we have that:

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

For this problem, the volume is a function of time, hence Volume = f(Time) and:

The decay rate is constant, meaning that we have a decreasing linear function, and graph H fits this problem.

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