Angle ψ
is in standard position with its terminus in the second quadrant. You are given that sin(ψ) = x/9 assume 0 < x < 9. (a) Is arcsin (sin ψ)=ψ
? Why/why not? (b) Find cos ψ
, using rational and/or radical expressions of x. (c) Evaluate tan(ψ
). Express your answer in terms of rational and/or radical expressions of x. (d) Express cos(2ψ) in terms of rational and/or radical expressions of x.

Answer:

58.3°

Step-by-step explanation:

Missing Information:

In this question the diagram is missing Following are the attachment of diagram of the given question.

As we seen that the vertex c is making the right angle i,e 90°  also there is an acute angle the Hypotenuse: 20 cm and the perpendicular is 10.5 cm

Now we have find the best approximation of the angle ABC used the cosx  trigonometric function.

\(cos\ x\ =\ \frac{perpendicular}{Hypotenuse} \\\)

Putting the value of perpendicular and hypotenuse in the previous formula we get

\(cos\ x\ =\ \frac{10.5\ cm}{20\ cm} \\\)

\(x\ =cos^{-1}\ 0.525\\x \ = \ 58.33\)

Answer:

58.3

Step-by-step explanation:

jus did the test review on EDGE! :)

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Therefore, the standard error of the mean, σ= 2.53 (approx).

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

Given: A simple random sample of 10 items resulted in a sample mean of 25.

The population standard deviation is = 8.

We have to find out the standard error of the mean, σ/Sample Size n,

so we will first calculate σ as;

σ = Population standard deviation = 8

Sample Size n = 10

Substituting values in the formula to find the standard error of the mean, we get;σ/√n = 8/√10 = 2.53 (Round off the value to two decimal places)

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Answer:

(2,4)

Step-by-step explanation:

The solution for the system is where the two lines intersect.

The two lines intersect at x = 2 and y =4

(2,4)

Answer:

(2, 4)

Step-by-step explanation:

Solutions on graphs are where 2 lines meet on a point.

For this graph, both lines (equations) have a solution of (x=2, y=4).

Picture is included for more detail.

The solution to the initial value problem is y(t) = 9 - 9e^(-t/7)

To solve the initial value problem, we can use the integrating factor method.

First, we find the integrating factor, which is given by e^(int P(t) dt), where P(t) is the coefficient of y in the differential equation.

In this case, P(t) = 1/7, so the integrating factor is e^(t/7).

Next, we multiply both sides of the differential equation by the integrating factor and simplify to get:

d/dt [e^(t/7) * y] = 9e^(t/7)

We can then integrate both sides with respect to t to get:

e^(t/7) * y = 63e^(t/7) + C

where C is a constant of integration.

Using the initial condition y(0) = 0, we can solve for C to get C = -54.

Substituting this value of C back into the equation and solving for y, we get:

y(t) = 9 - 9e^(-t/7)

Therefore, the solution to the given initial value problem is y(t) = 9 - 9e^(-t/7), which we obtained using the integrating factor method and the given initial condition.

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The time to complete 15 bricklayers is 3.5 hours

How to calculate time taken?

The ratio of an object's traveled distance to its constant speed is known as the time formula. Time describes how things happen in time. The order of this movement is such that it moves from the past to the present and then into the future.

The first step is to calculate the constant proportionality

t ∝ 1/n

t = k/n  

Where t = time, K= constant and n = number of people

t = k/n

k =tn

 = 5×7 = 35

∴t = 35/n

for n = 10,

t = 35/10

t = 3.5 hours.

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For the function transformation form of f(x), \(g(x) = a f(\frac{1}{b} x - h) + k \), we are replacing variable a by 2, result will in the transformation displayed in the above graph. So, option(d) is right one.

A transformation is an another way to a parent function's graph. There are serval formulas for distinct rules of transformation. If consider transformation function of f(x) is g(x) = f(x - h) + k,

We have a function f(x) = 2cos(x), that is cosine function and g(x) is it's transform function. Here, \(g(x) = a f(\frac{1}{b} x - h) + k \), now see the graph carefully.

Thus, for g(x) in above graph, there are no horizontal and vertical translation. So, h = k = 0. Also, the graphs are not reflected on both axes. However, notice that the graph of g(x) is just the vertical stretched version of f(x). The values of g(x) are twice that of f(x). Therefore, the factor a must be twice, a = 2. Hence, we replace a by 2.

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Complete question:

The above graph of shows f(x) = 2cos(x) and transform g(x). For the transformation rule in the form , g(x) = a f( 1/b x - h) + k

replacing which variable with what number will result in the transformation displayed in the graph?

a) b is replacing by 1/2

b) k is replacing by -1/2

c) h is replacing by -2

d) a is replacing by 2

Answer:

5

Step-by-step explanation:

41 - 32 = 9

5/9 x 9 = 5

Answer:

3445!

Step-by-step explanation:

hI swear i rember tis question!

The linear programming model would include equation for profit will be Z = 0.85X + 0.9Y and production constraints are 0.3X <= Y <= 0.6X; demand constraints are X <= (5000 + 3A) and Y <= (4000 + 5B); and cost constraint are 0.6X + 0.85Y + A + B <= 16,000.

Optimal values of X, Y, A, and B that maximize profit (Z) can be determined by using Excel Solver.

The linear programming model for the given problem is shown below:

Let X be the number of jars of applesauce produced. Y be the number of bottles of apple juice produced.

The objective function will be to maximize profit, which can be calculated by the following equation:

Profit = revenue - cost

Revenue can be calculated by multiplying the number of units produced by their respective selling prices. Cost can be calculated by multiplying the number of units produced by their respective production costs. The equation for profit will be:

Z = 1.45X + 1.75Y - (0.6X + 0.85Y)

Z = 0.85X + 0.9Y

The marketing manager estimates that the demand for applesauce is a maximum of 5,000 jars, plus an additional 3 jars for each $1 spent on advertising. The maximum demand for apple juice is estimated to be 4,000 bottles, plus an additional 5 bottles for every $1 spent on promoting apple juice. The maximum amount of money that can be spent on production and advertising is $16,000.

Therefore, we can write the constraints as follows:

Production constraints:

0.3X <= Y <= 0.6X

Demand constraints:

X <= (5000 + 3A)

Y <= (4000 + 5B)

Cost constraint:

0.6X + 0.85Y + A + B <= 16,000

Where A and B are the amounts spent on advertising for applesauce and apple juice, respectively.

To solve the model by using the computer, we can use any software that solves linear programming problems.

One such software is Microsoft Excel Solver. We can set up the problem in Excel as follows:

Cell C9: 0.85X + 0.9Y

Cell C12: 0.6X + 0.85Y + A + B

Cell C13: $16,000

Cell C15: 0.3X

Cell C16: XCell C17: 0.6X

Cell C18: 5000 + 3A (for applesauce)

Cell C19: Y

Cell C20: 4000 + 5B (for apple juice)

Cell C21: A

Cell C22: B

We then use Excel Solver to find the optimal values of X, Y, A, and B that maximize profit (Z).

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Answer:

p = 308

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

trrsygg. vbbkkmmk. jk. k

Scores range from 80 to 99, with scores exceeding 99 and scores falling below 60 points.

In the given range of scores, which spans from 80 to 99, it encompasses a range of values that are considered satisfactory and relatively high. These scores reflect a level of achievement or performance within a specific context, such as academic grading or test results. Additionally, it is important to note that there are scores that exceed 99, indicating exceptional performance or outstanding results. On the other hand, there are also scores below 60, which indicate lower levels of achievement or performance. These scores may require further attention or improvement in order to reach a more desirable outcome. The varying range of scores allows for a comprehensive evaluation of individuals or entities based on their performance, highlighting both strengths and areas that may need improvement.

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The Laplace transform of f2(t) is, L{f2(t)} = 216/(s^3(s^2+36)) - 6s/(s^2+36)^2

To find the Laplace transform of f2(t), we use the definition of the Laplace transform:

L{f(t)} = \(\int_0^{\infty} e^{-st} f(t) dt\)

where L{f(t)} denotes the Laplace transform of f(t), s is a complex number, and u(t) is the unit step function.

Substituting f2(t) into this formula, we get:

L{f2(t)} = \(\int_0^{\infty} e^{-st} (27t^2sin(6t-60)u(t)) dt\)

Using the properties of the Laplace transform, we can simplify this expression. First, we can factor out the constant 27:

L{f2(t)} = \(27 \int_0^{\infty} e^{-st} (t^2sin(6t-60)u(t)) dt\)

Next, we use the identity sin(a-b) = sin(a)cos(b) - cos(a)sin(b) to write the sin function as a sum of exponential functions:

L{f2(t)} = \(27 \int_0^{\infty} e^{-st} (t^2(sin(6t)cos(60) - cos(6t)sin(60))u(t)) dt\)

L{f2(t)} = \(27 \int_0^{\infty} e^{-st} (t^2sin(6t)u(t)cos(60) - t^2cos(6t)u(t)sin(60)) dt\)

We can now apply the Laplace transform to each term separately. Using the formula L{t^n} = n!/s^(n+1), we get:

L{t^2sin(6t)u(t)cos(60)} = (2!/(s^3)) L{sin(6t)u(t)} = 12/(s^3(s^2+36))

L{t^2cos(6t)u(t)sin(60)} = (2!/(s^3)) L{cos(6t)u(t)} = (2s)/(s^2+36)^2

Substituting these expressions back into the original equation, we get:

L{f2(t)} = 27 (12/(s^3(s^2+36))cos(60) - (2s)/(s^2+36)^2sin(60))

Simplifying this expression, we get:

L{f2(t)} = 216/(s^3(s^2+36)) - 6s/(s^2+36)^2

Therefore, the Laplace transform of f2(t) is:

L{f2(t)} = 216/(s^3(s^2+36)) - 6s/(s^2+36)^2

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The expression of the statement is 9 + 21 + 6 and the value is 36

From the question, the mathematical statement is given as

Add 9 to the sum of 21 and 6.

To take the sum of numbers means that we add the numbers

So, we have

Add 9 to the sum of 21 and 6 ⇒ Add 9 to 21 + 6

Solving further, we have

Add 9 to the sum of 21 and 6 ⇒ 9 + 21 + 6

When the expression is solved, we have

9 + 21 + 6 = 36

Hence, the expression is 9 + 21 + 6

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In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. So , the correct option is C.

In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. The mean and median are both measures of the central tendency of a distribution and in a symmetrical distribution, they are the same value.

Option (a) is false because the range is the difference between the largest and smallest values in a distribution, whereas the interquartile range is the difference between the first quartile (25th percentile) and the third quartile (75th percentile), which are measures of variability.

Option (b) is false because the interquartile range is always smaller than the mean in any distribution, symmetrical or not.

Option (d) is false because in a symmetrical distribution, the variance and standard deviation may be equal, but this is not always the case.

So , the correct option is c.

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If a caterer can purchase 4 cartons of Sprite for $10, then the cost of a single carton is $ 2.50 per carton.

The cost of a single carton of Sprite which is also called the unit cost of the cartons of Sprite can be determined as follows.

1. You are given that the caterer can purchase 4 cartons of Sprite for $10.

2. Divide the total cost by the number of cartons to find the cost per carton.

The cost of a single carton of Sprite is $10 / 4 cartons = $2.50 per carton.

Hence, the cost of a single carton if four cartons of Sprite cost $10 is $2.50 per carton.

Note: The question is incomplete. The complete question probably is: A caterer can purchase 4 cartons of Sprite for $10, what is the cost of a single cartons.

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a₃ = a₇ = a₁₂ = 0.  To find the values of a3, a7, and a12 in the Taylor series of f(x) = x^3 ln(1 - x^2) about 0, we need to determine the coefficients of the corresponding terms in the series expansion.

The general formula for the coefficients in the Taylor series expansion of a function f(x) about 0 is given by:

an = f⁽ⁿ⁾(0) / n!

where f⁽ⁿ⁾(0) represents the nth derivative of f evaluated at 0.

Let's calculate the derivatives of f(x) and evaluate them at 0 to find the coefficients.

f(x) = x^3 ln(1 - x^2)

f'(x) = 3x^2 ln(1 - x^2) + x^3 * (1 - x^2)^(-1)

f''(x) = 6x ln(1 - x^2) + 3x^2 * (1 - x^2)^(-1) - 6x^4 * (1 - x^2)^(-2)

f⁽³⁾(x) = 6 ln(1 - x^2) + 6x * (1 - x^2)^(-1) - 12x^3 * (1 - x^2)^(-2) + 24x^5 * (1 - x^2)^(-3)

Now, let's evaluate these derivatives at 0:

f(0) = 0

f'(0) = 0

f''(0) = 6

f⁽³⁾(0) = 6

The coefficients of the terms in the Taylor series expansion are determined by these derivatives. Specifically, the nth coefficient aₙ is equal to f⁽ⁿ⁾(0) / n!.

Therefore, we have:

a₃ = f⁽³⁾(0) / 3! = 6 / 6 = 1

a₇ = f⁽⁷⁾(0) / 7! = 0 / 5040 = 0

a₁₂ = f⁽¹²⁾(0) / 12! = 0 / 479,001,600 = 0

Hence, a₃ = a₇ = a₁₂ = 0.

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Yes, your friend is correct. It is possible for a rational function to have two vertical asymptotes.

A rational function is defined as the ratio of two polynomial functions. The denominator of a rational function cannot be zero since division by zero is undefined. Therefore, the vertical asymptotes occur at the values of x for which the denominator of the rational function is equal to zero.

In some cases, a rational function may have more than one factor in the denominator, resulting in multiple values of x that make the denominator zero. This, in turn, leads to multiple vertical asymptotes. Each zero of the denominator represents a vertical asymptote of the rational function.

Hence, it is possible for a rational function to have two or more vertical asymptotes depending on the factors in the denominator.

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Answer:

derivative on r^2 with respect to r

one time derivative is 2r

second time derivative is 2

third time derivative is 0

Answer:

D. The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 41°.

Step-by-step explanation:

The correct description of the vector is that the magnitude is √(113) and therefore the direction angle is 41°.

The magnitude of the vector is the length of the vector which can be calculated from the coordinate of its endpoint.

Let (x1,y1) and (x2,y2) are the coordinate of the two endpoints of a vector V.

The magnitude of the vector= |V|= √(y2-y1)²+(x2-x1)²

We have,

Origin of vector = (0,0)

And,

Terminal point = (8, 7)

Here,

a = 8 and  b = 7

Now,

To find the magnitude of the vector, we are going to use;

Formula, |v| = √(a² + b² )

|v| = √(8² + 7² )

|v| = √(64 + 49)

|v| = √113

So, the magnitude of the vector is √113.

Now,

Direction angle is find out using ;

Θ = tan ⁻¹ (b / a)

So, Here,

Θ = Angle Direction

Now,

Θ = tan ⁻¹ (7 / 8)

Θ = 41°

Therefore, the proper description of the vector is that the magnitude is √(113) and also the direction angle is 41°.

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The parabola's equation is y = -x2 + 12x - 27.

A parabola is a point's location where the focus and a fixed point's distance from a fixed line, known as the directrix, are the same.

A parabola's equation is in quadratic form.

Thus, it is stated as:

Y = Ax2, Bx, and C

Located at (3, 0):

0 = a(3²) + b(3) + c

9a + 3b + c = 0 (1) (1)

Located at (9, 0):

0 = a(9²) + b(9) + c

81a + 9b + c = 0 (2) (2)

Located at (10, -7):

-7 = a(10²) + b(10) + c

100a + 10b + c = -7 (3) (3)

Equations 1, 2, and 3 are solved to yield: a = -1, b = 12, and c = -27.

Consequently, the parabola's equation is y = -x2 + 12x - 27.

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7^2/7^-2 and (7^2)^2

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 139}}{\left( \cfrac{6}{100} \right)139}\implies 8.34\)

Answer:The answer

Step-by-step explanation:

Answer below

Step-by-step explanation:

For the first 3x+7=-x-3 you will get 4x=-10 and the final answer is x=-5/2

The second is 3(x+7)=-x-3 which is different since it will equal 3x+21=-x-3 then 4x=-24 and you get x=-6

Solution

Hypotheses:

- The population mean is 132. In order to test the claim that the mean is 132, we should check for if the mean is not 132.

- Thus, the Hypotheses are:

Test statistic:

- The test statistic has to be a t-statistic because the sample size (n) is less than 30.

- The formula for finding the t-statistic is:

- Applying the formula, we have:

Critical value:

- The critical value t-critical, is gotten by reading off the t-distribution table.

- For this, we need the degrees of freedom (df) which is gotten by the formula:

- And then we also use the significance level of 0.1 and the fact that it is a two-tailed test to trace out the t-critical. (Note: significance level of 0.1 implies 10% significance level)

- This is done below:

- The critical value is 1.729

P-value:

- To find the p-value, we simply check the table for where the t-statistic falls.

- The t-statistic given is 1.5747. We simply check which values this falls between in the t-distribution table. It falls between 1.328 and 1.729. We can simply choose a value between 0.1 and 0.05 and multiply the result by 2 since it is a two-tailed test.

- However, we can also use a t-distribution calculator, we have:

- Thus, the p-value is 0.13183

Final Conclusion:

- The p-value is 0.13183, and comparing this to the significance level of 0.1, we can see that 0.13183 is outside the rejection region.

- Thus, the result is not significant and we fail to reject the null hypothesis

One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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