Determine the number of terms n :

a 1 = 15, a n = 79, S n = 423

Using the concept of probability, the likelihood of the given events using the two-way table are :

0.233

0.775

0.575

The events are not independent

Here, we have,

From the two-way table :

P(English IV) = 0.233

Part B :

P(11th grader takes English 11 or English 111)

=0.755

Part C:

P(English 3 | 11th grade) = 0.575

Part D :

Let :

A = student takes English 1

B = student ls a 10th grader

The events are independent if :

P(AnB) = p(A) × p(B)

P(AnB) = 0.082

P(A) × P(B) = 0.0512

Hence, (AnB) ≠ p(A) × p(B)

Therefore, the events are not independent.

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Answer:

The translation vector can be drawn on the coordinate grid or written as

\vec{v}=\langle a,b\rangle

v

=⟨a,b⟩

. For example, a translation vector that moves a figure

3

3

units right and

2

2

units down can be represented mathematically as

\vec{v}=\langle3,-2\rangle

v

=⟨3,−2⟩

, or graphically as

It doesn’t matter where the vector is positioned in the plane. In this figure, the vector starts at

(1,1)

(1,1)

and ends at

(4,-1)

(4,−1)

. But the initial point and terminal point of the vector are irrelevant. What matters is the length of the vector and the direction in which it points, so all you have to look at is how many units the vector moves in the

y

y

-direction and how many units the vector moves in the

x

x

-direction.

Answer:

See picture for explanation.

Step-by-step explanation:

Thus,  the proof of the identity cos^2(5x) - sin^2(5x) = cos(10x) involves the use of the double angle formula for cosine. This identity is useful in solving various problems related to trigonometry.

To prove the trigonometric identity cos^2(5x) - sin^2(5x) = cos(10x), we will use the double angle formula for cosine.

This formula states that cos(2θ) = cos^2(θ) - sin^2(θ). We can rewrite our identity as:
cos^2(5x) - sin^2(5x) = cos(2 * 5x)

Using the double angle formula, we get:
cos^2(5x) - sin^2(5x) = cos(10x)

This proves the given trigonometric identity.

To understand this identity better, let's break it down.

The left-hand side of the identity consists of two terms, cos^2(5x) and sin^2(5x).

These terms are known as the Pythagorean identity and state that cos^2(θ) + sin^2(θ) = 1.

We can rewrite cos^2(5x) as 1 - sin^2(5x) using this identity.

Substituting this value in the given identity, we get:
1 - sin^2(5x) - sin^2(5x) = cos(10x)

Simplifying this equation, we get:
cos^2(5x) - sin^2(5x) = cos(10x)

Therefore, we have successfully proven the given trigonometric identity.

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For the function y = 5x³ + 3x² - 4x + 7, the third derivative, d³y/dx³, is equal to 60x.

For the function f(x) = (x³ + 4x² - 5) /√x, the derivative can be found using the quotient rule, resulting in f'(x) = (3x² + 8x - 5) / (2√x) - (x³ + 4x² - 5) / (2x√x).

For the function y = 3x² cot(x), the derivative can be found using the product rule, resulting in y' = 6xcot(x) - 3x²csc²(x).

To find the third derivative of y = 5x³ + 3x² - 4x + 7, we differentiate the function three times. The derivative of 5x³ is 15x², the derivative of 3x² is 6x, and the derivative of -4x is -4. Since these are constants, their derivatives are zero. Therefore, the third derivative, d³y/dx³, is equal to 60x.

For the function f(x) = (x³ + 4x² - 5) / √x, we can differentiate using the quotient rule. The quotient rule states that the derivative of f(x) = (g(x) / h(x)) is given by f'(x) = (g'(x)h(x) - g(x)h'(x)) / (h(x))^2. Applying the quotient rule, we find that f'(x) = (3x² + 8x - 5) / (2√x) - (x³ + 4x² - 5) / (2x√x).

For the function y = 3x² cot(x), we can differentiate using the product rule. The product rule states that the derivative of y = u(x)v(x) is given by y' = u'(x)v(x) + u(x)v'(x). Applying the product rule, we find that y' = 6xcot(x) - 3x²csc²(x), where the derivative of cot(x) is -csc²(x) and the derivative of 3x² is 6x.

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The complete question is:

Find d³y/dx³ given y = 5x³ + 3x² - 4x + 7

Differentiate f(x) = x³+4x²-5 /√x

Differentiate y = 3x² cot x

Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

The expression is x+2-2y

It is given to us that logp5=x and logp7=y

Now we are required to find logp(5p^2)/49 in terms of x and y

we know that in logarithmic formulas

loga^b=b loga

logab = log a+log b

log a/b= log a- log b

Now using these formulas to find the solution,

logp 5p^2/49

= logp5+ logp p^2 -log 49

=logp5+2 logpp-2log7

we know that logpp=1,hence

= logp5+2 -2 logp7

=x+2-2y

Hence the expression is x+2-2y

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Answer:

True

Step-by-step explanation:

Solutions to quadratic equations are often called

roots / zeros / x- intercepts

The given problem involves a related rates problem that incorporates distance and angle of elevation. The distance from the rocket is 40 ft, and the rocket takes off vertically at a rate of 20 ft/sec. Let y be the height of the rocket, and we know that the height of the rocket increases at a rate of 20 ft/sec.

Therefore, the equation dy/dt = 20 ft/sec is obtained. Using the Pythagorean theorem, we can calculate the distance x between the rocket and the person. By differentiating both sides of the equation with respect to time, we obtain dx/dt = y/√(1600 - y²) * 20 ft/sec. We can find x by using x² + y² = 40² => x = √(1600 - y²).

When the rocket is 30 ft in the air, the rate at which the angle of elevation changes is 3/4 rad/sec (approximately 1.17 rad/sec).

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When comparing hash values, if the provided hash value matches the one you calculated, it means that the file you have received is identical to the original file used to calculate the hash. This implies that the file has not been modified or tampered with since the hash was generated.

However, it is important to note that a matching hash value does not guarantee that the file is completely safe or trustworthy. Hash functions are designed to generate a unique hash value for each unique input, but it is still theoretically possible for two different files to have the same hash value (known as a collision). Although the chances of a collision are extremely low with well-designed hash functions, it is not entirely impossible.

Therefore, while a matching hash value provides some level of confidence that the file has not been altered, it does not guarantee the integrity or security of the file. Other factors should be considered, such as the source and reputation of the file, the context in which it was obtained, and the presence of any additional security measures or verification methods.

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The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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Answer:

the statement that is true is: A and B are not independent because P(AIB) + P(B) is not equal to P(BIA) + P(A)

Step-by-step explanation:

ur welcome

The points at which the curve has a horizontal tangent are (x, y) = (-3/2, 0) and (x, y) = (3/2, 0).

To find the points at which the curve has a horizontal tangent, we need to determine the values of t that satisfy the condition dy/dt = 0, where dy/dt is the derivative of y with respect to t.

1. Start with the parametric equations x(t) = 3cos(t) and y(t) = 3sin(2t).

2. Differentiate y(t) with respect to t to find dy/dt:

3. Apply the chain rule:

4. Set dy/dt equal to 0 and solve for t to find the values of t at which the curve has a horizontal tangent:

5. Solve for t by considering the values of cos(2t) that are equal to 0:

a. When 2t = π/2, t = π/4.

b. When 2t = 3π/2, t = 3π/4.

6. Substitute the values of t into the parametric equations x(t) and y(t) to find the corresponding points (x, y):

Therefore, the point is (x, y) = (3√2/2, 3).

Therefore, the point is (x, y) = (-3√2/2, -3).

Hence, the points at which the curve has a horizontal tangent are (x, y) = (-3/2, 0) and (x, y) = (3/2, 0).

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Point (-3, 0) is required solution to the inequality. Hence option B. is correct.

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

As from graph,
The inequality can be define as -\(y > \frac{4}{3}x+4\)
And the point(-3, 0) lies on the boundary line.
Which gives the solution to the given inequality.

Thus, point (-3, 0) is required solution to the inequality.

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Answer:

  f'(x) = -2/√(x³)

Step-by-step explanation:

You want the derivative of f(x) = 4/√x.

The power rule for derivatives is ...

  \(\dfrac{d}{dx}(x^n)=nx^{(n-1)}\)

Applied to the given function, we have ...

  \(f(x)=\dfrac{4}{\sqrt{x}}=4x^{-\frac{1}{2}}\\\\f'(x)=4(-\frac{1}{2}x^{-\frac{3}{2}})\\\\\boxed{f'(x)=-\dfrac{2}{\sqrt{x^3}}}\)

__

Additional comment

The first attachment shows a calculator gives the same result.

The second attachment shows the derivative curve matches the one described by the function we found.

Answer:

-4W-6k would be the answer

Answer:

i think its c

Step-by-step explanation:

Answer:

I think it would be the second answer.

Here is sufficient evidence that revenue and the number of downloads are linearly related.

A computer software developer would like to use the number of downloads for the trial version of his new shareware to predict the amount of revenue.

The Null hypothesis is the common statistical theory that asserts that no statistical relationship or significance exist between two sets of observed data and measure phenomena based on a single observed variable.

Therefore the null hypothesis become,

H₀ : ρ₁ = 0

and the adjacent hypothesis will become,

H₁ : ρ ≠ 0

Now we will calculate test statistic,

t = r × \(\sqrt{\frac{n-2}{1-r^{2} } }\)

 = (0.8691) × \(\sqrt{\frac{30 - 2}{0.1309^{2} } }\)

t = 9.2974

we know that degree of freedom = n - 2 = 28

p-value at t = 9.2974 is 0.00

α = 0.05

since p-value < α

so null hypothesis will be rejected.

Hence we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.

If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:

C(n + k - 1, k - 1)

where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:

C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)

There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:

C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55

Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars

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amount he earned for selling all of the oranges =

$0.5 x 100 = $50

% profit = ((50 - 40)/40) x 100% = 25%

Therefore, he made a 25% profit

Step-by-step explanation:

Substitute the given value of x into the expression;

\(4(10)-5\)

Multiply;

\(40-5\)

Subtract;

\(35\)

The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(-3,-5) and B(-2,5)

The distance between them is

\( |AB| = \sqrt{ ({ - 3 + 2})^{2} + ({ - 5 - 5})^{2} } \\ = \sqrt{ {1}^{2} + ( { - 10})^{2} } \\ = \sqrt{1 + 100} \: \: \: \: \: \: \: \: \: \\ = \sqrt{101} \\ = 10.04987562...\)

We have the final answer as

Hope this helps you

Answer:

i think it is 10 but .-.

Step-by-step explanation:

i graphed it o.o

Answer:

The perimeter is 4√81 = 4 × 9 = 36 meters.

Answer:

42

Step-by-step explanation:

3 is equal to 42 degrees because when you have two parallel lines that have another line pass through both parallel lines the values of degrees are the same as the opposite side so:

42 = 3

2 = 4

and another way you could find the value of 3 is since there is a perpendicular line going through line p we know that since it is perpendicular that the angle between them is 90 so angle 3 is:

90 - (angle 4) = angle 3

You may use this method if you first solved for angle 4 or angle 2 and we can get angle 2 from:

180 - 42 = 138

we can do this because 42 + angle two should be 180 degrees since they are along line n.

Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

The equation holds for k, it also holds for k + 1. we have proven that (1 2 3 ··· n)² = 1 3 2 3 3 3 ··· n³ for every n ∈ ℕ.

To prove that (1 2 3 ··· n)² = 1 3 2 3 3 3 ··· n³ for every n ∈ ℕ, we will use mathematical induction.

Base case:

Let's start by verifying the equation for the base case when n = 1:

(1)² = 1³

The base case holds true.

Inductive step:

Next, we assume that the equation holds for some positive integer k, where k ≥ 1. That is, we assume that (1 2 3 ··· k)² = 1 3 2 3 3 3 ··· k³.

Now, we need to show that the equation holds for k + 1, i.e., we need to prove that ((1 2 3 ··· k) (k+1))² = 1 3 2 3 3 3 ··· k³ (k+1)³.

Expanding the left-hand side of the equation:

((1 2 3 ··· k) (k+1))² = (1 2 3 ··· k)² (k+1)²

Using the assumption that (1 2 3 ··· k)² = 1 3 2 3 3 3 ··· k³, we can rewrite the left-hand side as:

(1 3 2 3 3 3 ··· k³) (k+1)²

Now, let's analyze the right-hand side of the equation:

1 3 2 3 3 3 ··· k³ (k+1)³ = 1 3 2 3 3 3 ··· k³ (k³ + 3k² + 3k + 1)

We can see that the right-hand side consists of the terms from 1³ to k³, followed by (k+1)³, which is equivalent to (k³ + 3k² + 3k + 1).

Comparing the expanded left-hand side and the right-hand side, we notice that they are equivalent:

(1 3 2 3 3 3 ··· k³) (k+1)² = 1 3 2 3 3 3 ··· k³ (k³ + 3k² + 3k + 1)

Therefore, we have shown that if the equation holds for k, it also holds for k + 1.

Since the base case holds true and we have shown that if the equation holds for k, it also holds for k + 1, we can conclude that the equation holds for all positive integers n.

Hence, we have proven that (1 2 3 ··· n)² = 1 3 2 3 3 3 ··· n³ for every n ∈ ℕ.

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