the scores on a mathematics exam have a mean of 69 and a standard deviation of 7. find the x-value that corresponds to the z-score . round the answer to the nearest tenth.

The value of ∫ (x + 1)/(9x² + 6x + 5) dx by partial fractions is 1/18ln(9x² + 6x + 5) + 1/9 (tan^-1 (3x+1)/2)

Given ∫ (x + 1)/(9x² + 6x + 5) dx

Discriminant of is 9x² + 6x + 5 is

                                 D = 6² - 4 x 9 x 5 = - 144 < 0

So, 9x² + 6x + 5 cannot be factorized in rational factors

Observing that differential of 9x² + 6x + 5, let us split (x + 1)/(9x² + 6x + 5) as (18x + 18)/18(9x² + 6x + 5)

or (18x + 6)/18(9x² + 6x + 5) + (12)/18(9x² + 6x + 5)

So, (x + 1)/(9x² + 6x + 5) = (18x + 6)/18(9x² + 6x + 5) + (12)/18(9x² + 6x + 5)

∫ (x + 1)/(9x² + 6x + 5) dx = ∫ (18x + 6)/18(9x² + 6x + 5) dx + ∫ (12)/18(9x² + 6x + 5) dx

= 1/18∫ (18x + 6)/(9x² + 6x + 5) dx + 2/3∫ 1/(9x² + 6x + 5) dx

Let us integrate the first part and assume u = 9x² + 6x + 5

then, du = (18x + 6) dx

So, 1/18∫ (18x + 6)/(9x² + 6x + 5) dx = 1/18∫ 1/u du

                                                         = 1/18 lnu

                                                         = 1/18ln(9x² + 6x + 5)

For second part, 2/3∫ 1/(9x² + 6x + 5) dx, we will use

                     ∫ dx/(x² + a²) = 1/a tan^-1(x/a) +c

For this converting denominator into the sum of two squares, we get

    2/3∫ 1/(9x² + 6x + 5) dx = 2/27∫ 1 / ((x + 1/3)²+(2/3)²) dx

Let us now substitute u = x + 1/3 and as du = dx

so, 2/27∫ 1 / ((u)²+(2/3)²) dx = 2/27 (3/2 tan^-1 (3u/2))

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

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

Hence,∫ (x + 1)/(9x² + 6x + 5) dx = 1/18ln(9x² + 6x + 5) + 1/9 (tan^-1 (3x+1)/2)

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Answer: The correct answer is Credit Freeze

Step-by-step explanation:

According to the question , laplace transformation  y(0) = 1 = -1 + e^t + 3, so e^t = -1, which is impossible. Therefore, there is no solution that satisfies the initial conditions.

To find the Laplace transformation of y''-2y'-y=e^2t-e^t, we first need to take the Laplace transform of both sides. Let Y(s) be the Laplace transform of y(t).

Taking the Laplace transform of y''-2y'-y, we get:

s^2 Y(s) - s y(0) - y'(0) - 2s Y(s) + 2y(0) - Y(s) = (1/(s-2^2)) - (1/(s-1))

Simplifying this equation, we get:

Y(s) = (1/(s-2)^2) - (1/(s-2)) + (1/(s-1)) + (s+3)/(s^2-2s+1)

Now, we need to solve for the inverse Laplace transform of Y(s) to get the solution y(t).

Using partial fraction decomposition, we can write:

Y(s) = (1/(s-2)^2) - (1/(s-2)) + (1/(s-1)) + (s+3)/(s-1)^2

Taking the inverse Laplace transform of each term, we get:

y(t) = t*e^2t - e^2t + e^t + (3+2t)e^t

Using the initial conditions y(0)=1 and y'(0)=3, we can solve for the constants in the solution.

y(0) = 1 = -1 + e^t + 3, so e^t = -1, which is impossible. Therefore, there is no solution that satisfies the initial conditions.

In conclusion, the Laplace transformation of y''-2y'-y=e^2t-e^t is Y(s) = (1/(s-2)^2) - (1/(s-2)) + (1/(s-1)) + (s+3)/(s^2-2s+1), but there is no solution that satisfies the given initial conditions.

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a. ln 7 = y in exponential equation is e^y = 7

b. e² = x in logarithm function is log x base e = 2

What is exponential and logarithmic function?

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

The logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as. For x > 0 , a > 0, and a ≠1, y= loga x if and only if x = a^y

Therefore,

ln 7 = y

using inverse of ln

7 = e^y

and;

e² = x

using logarithm function as inverse

log x base e = 2.

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When the first ball is red, there is a 0.57 percent chance that the second ball will also be red.

The chances that an occurrence will take place or a claim will be true is measured by statistical mechanics, a discipline of mathematics. The probability of an action is a numeric value and 1, where about 0 represents how likely the action is to occur and value of 1 indicates certainty. A probability is a quantifiable illustration of the odds that a specific occurrence will actually happen. Probabilities can also be expressed using percentages ranging from 0% and 100% or from 0 to 1. the ratio of the number of outcomes to the proportion all occurrences in a whole set o equally likely options that lead to a specific occurrence.

There are seven balls in total.

The sample space is

7! / 2!5!

=21 ways

P(red ball and a green ball) =12/21

=4/7

When the first ball is red, there is a 0.57 percent chance that the second ball will also be red.

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Answer:

students in the drama club: 57

students in the yearbook club: 44

Step-by-step explanation:

101 - 13 = 88

88 / 2 = 44

101 - 44 = 57

44 in the drama club and 57 in the yearbook club

The solution of the separable differential equation 5ydx = 3xdy is ln |y| = ln |x| + C, where C is the constant of integration.

To solve the given separable differential equation, we start by separating the variables by writing it as 5ydx - 3xdy = 0. Next, we integrate both sides with respect to their respective variables.

∫5ydx = ∫3xdy

Integrating the left side with respect to x gives 5xy + g(y), where g(y) is the constant of integration with respect to x. Similarly, integrating the right side with respect to y gives 3xy + f(x), where f(x) is the constant of integration with respect to y.

Therefore, we have 5xy + g(y) = 3xy + f(x).

To simplify the equation, we can rearrange it as 5xy - 3xy = f(x) - g(y), which gives us 2xy = f(x) - g(y).

Now, we can equate the constant term on both sides, f(x) - g(y) = C, where C is the constant of integration.

Simplifying further, we have f(x) = g(y) + C.

Since f(x) and g(y) are arbitrary functions, we can express them as ln |x| and ln |y| respectively, leading to ln |x| = ln |y| + C.

Therefore, the solution to the separable differential equation 5ydx = 3xdy is ln |y| = ln |x| + C, where C is the constant of integration.

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In the sentence 52 = 15∙3 + 7, 7 is equal to 36.7

In mathematics, equality is a relationship that states that two quantities have the same value or that two mathematical expressions represent the same mathematical object.

Someone or something that is equal to another has the same quantity, value, or rights as that other thing. One cup and eight ounces are equivalent, for instance. Equal pay for equal work performed by men and women is an illustration of equality.

If both operands have the same value, the equal-to operator (==) returns true; otherwise, it returns false. If the operands do not have the same value, the not-equal-to operator (!=) returns true; otherwise, it returns false.

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Answer:

26.411

Step-by-step explanation:

3a+bc-c

3(8.6)+(2.3*0.47)-0.47

25.8+1.081-0.47

26.881-0.47

26.411

Answer:

3*8.6+2.3*0.47-0.47

25.8+1.081-0.47

26.411

Answer:

7-(-3)

Step-by-step explanation:

-(-3)=3

Answer:

The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Step-by-step explanation:

The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2

Which gives;

3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0

3.1·x³ - 6.4·x²+ 3·x  - 5 = 0

Factorizing online, we get;

3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0

Therefore, the possible solutions are;

x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0

The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;

x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.

Answer:

72

Step-by-step explanation:

you is correct good job

The range of the graph shown is

range { y | y < 0 }

When a figure is transported from one place to another without changing its size, shape, or orientation, a translation takes place.

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The graph's entire range, from lower to upper numbers vertically, represents the range.

The translation downwards, means that the graph moved down and considering the image of the attached graph, the effect of the translation means that the range to be numbers less than zero

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75% is percentage of undergraduate students are between 36 and 52 years old.

What is percentage and example?

This would be true if k=3, but k=2

because (36-44)/4 = -2 and (52-44)/4 = 2

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Answer:

Congress. would equal 80 due to x being worth 1/4 of y's total.

Step-by-step explanation:

Given Function

f(x) = 2.5x + 150

f^-1(x) = ?

Let y = f(x)

y = 2.5x + 150

Interchanging the role of x and y we get,

x = 2.5y + 150

x - 150 = 2.5y

y = (x - 150) / 2.5

So therefore

f^ -1(x) = (x - 150) / 2.5

Hope it will help :)

A function is a function that represents the area under a curve. In this case, f is the curve being considered. The function a(x) represents the area under the curve of f from x=0 up to x.

So, if we want to find the area under the curve of f from x=0 up to x=3, we would evaluate a(3) - a(0). This would give us the total area under the curve of f from x=0 to x=3. Similarly, if we have another area function, say b(x), that represents the area under the curve of f from some other starting point (e.g. from x=1), we would use b(x) to find the area under the curve of f from x=1 up to some other x value.
The graph of f, displayed in the figure to the right, represents a function that can be analyzed using various mathematical concepts. In this case, we can consider two area functions for f, denoted as A(x) and B(x), which would allow us to evaluate the areas under the curve of the graph with respect to the x-axis. These area functions can be used to understand properties and behaviors of the function f in different regions of the graph.

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Answer: 168.7 degrees

Step-by-step explanation:

Supplementary angles have measures that add to 180 deg, so 180-11.3=168.7

The probability that a part chosen at random from the 160 parts is from the first factory is 0.625 or 62.5%.

The probability that a part chosen at random from the 160 is from the first factory can be calculated using the concept of conditional probability.

Given that 100 parts were obtained from the first factory and 60 from the second factory, the probability of selecting a part from the first factory can be found by dividing the number of parts from the first factory by the total number of parts.

To calculate the probability that a part chosen at random is from the first factory, we divide the number of parts from the first factory by the total number of parts.

In this case, 100 parts were obtained from the first factory, and there are 160 parts in total.

Therefore, the probability can be calculated as:

Probability of selecting a part from the first factory = (Number of parts from the first factory) / (Total number of parts)

= 100 / 160

= 0.625

So, the probability that a part chosen at random from the 160 parts is from the first factory is 0.625 or 62.5%.

This probability calculation assumes that each part is chosen at random without any bias or specific conditions.

It provides an estimate based on the given information and assumes that the factories' defect rates do not impact the selection process.

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Answer:

22 is the number

Step-by-step explanation:

When ratio  

         88:22

Is divided with 11 it gives 8:2

Answer:

6:12=1:2

Step-by-step explanation:

as we will cut 6:12 by 6 . please mark me as brainliest and follow me

Answer:

1:2

Step-by-step explanation:

6 and 12 are divisible by 6

6 ÷ 6 = 1

12 ÷ 6 = 2

Answer:

45

Step-by-step explanation: i know what im talking about :)

The double integral of 4x + xydA over the region [0, 4] × [0, 1] is equal to 8.5. This can be computed by integrating x + xy with respect to x from 0 to 4 and then integrating with respect to y from 0 to 1.

The double integral of 4x + xydA over the region [0, 4] × [0, 1] is equal to 8.5. This can be computed by:

1. Integrate 4x with respect to x from 0 to 4:

∫04x dx = [x2/2]04

= (42/2) - (02/2)

= 16/2

2. Integrate xy with respect to x from 0 to 4:

∫04xydx = [x2/2]41

= (41/2) - (01/2)

= 1/2

3. Add the two integrals together to get the final answer:

16/2 + 1/2

= 8 + 1/2

= 8.5

The double integral of 4x + xydA over the region [0, 4] × [0, 1] is equal to 8.5. This can be computed by first integrating 4x with respect to x from 0 to 4, which gives 16/2, and then integrating xy with respect to x from 0 to 4, which gives 1/2. Adding these two integrals together yields 8 + 1/2, or 8.5.

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Answer:

$126

Step-by-step explanation:

100 * 0.08 = 8

100 * 0.18 = 18

100 + 8 + 18 = 126

The equation of the circle is x² - 24x + y² + 14y + 144 = 0

We have,

The center of the circle is at (12, -7), so the coordinates of the center give us the values of h and k in the equation of the circle:

(x - h)² + (y - k)² = r²

where (h,k) is the center and r is the radius.

Substituting the given values, we get:

(x - 12)² + (y + 7)² = r²

The diameter of the circle is 14, so the radius is half of that, or 7.

Substituting this value into the equation above, we get:

(x - 12)² + (y + 7)² = 7²

Expanding the left side and simplifying, we get:

x² - 24x + 144 + y² + 14y + 49 = 49

Combining like terms, we get:

x² - 24x + y² + 14y + 144 = 0

Therefore,

The equation of the circle is x² - 24x + y² + 14y + 144 = 0

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Answer:

6400

Step-by-step explanation:

We have 1 + 3 + 5 + ... + 155 + 157 + 159.

We can use Gauss's strategy.

Since we are adding 80 numbers, there are 40 pairs. Each pair adds up to 1 + 159 = 160. (Notice that 3 + 157, 5 + 155 = 160)

Thus, because there are 40 pairs and each pair adds up to 160, we have 160 * 40 = 6400.

I hope this helps!

Answer:

-12x^2+15x

Step-by-step explanation:

-3x(4x-5)

Distributive property:

-3x*4x-(-3x)*5

-3*4x^2+3*5x

Simplify:

-12x^2+15x

Answer:

Step-by-step explanation: