Find the exact value of each of the following under the given conditions below.
(1) sin a (alpha) = 5/13 , -3pi/2 a) sin (alpha + beta)
b) cos (alpha + beta)
c) sin (alpha - beta)
d) tan (alpha - beta)

Answer:

92

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

What is the product of 4 x 23? Type in the answer?

=> 23 × 4

=> 92 answer

hope that helps...

Using the Integral Test, infinite series is converges. the correct answer is A.

We can use the Integral Test to determine the convergence of the given series.

The Integral Test states that if f(x) is a positive, continuous, and decreasing function on the interval [n, ∞) and if the infinite series ∑f(n) converges or diverges, then the improper integral ∫n  to ∞ f(x) dx also converges or diverges, respectively.

Let's check if the conditions of the Integral Test are satisfied for the given series:

f(n) = (n³ + 5)/(n²) = n + 5/n² is a positive function for n ≥ 1.

f(n) is a decreasing function for n ≥ 1 because as n increases, the denominator (n²) increases faster than the numerator (n³ + 5).

Now, we can use the Integral Test to determine the convergence of the series:

\(\int\limits^{\infty}_24 f(x) dx = \int\limits^{\infty}_24 (x + 5/x^2) dx\)

= [1/2 x² + (-5)/x]24 to ∞

= lim as b → ∞ [1/2 b² + (-5)/b - (1/2 (24)² + (-5)/24)]

The limit exists, so the improper integral converges if and only if the series converges.

Since the integral converges, the series converges by the Integral Test.

Therefore, the answer is A. The infinite series converges.

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Segregation and recombination are best represented by the diagram.

In molecular biology, segregation and recombination are key processes. Segregation is the process of dividing two separate alleles present in a single organism so they can each reproduce on their own. The two alleles split and then have individual copies in the daughter cells during cellular division.

On the other hand, recombination entails joining two distinct alleles to create a new allele that is distinct from both of them. Meiosis, when genes exchange parts between chromosomes, causes this to happen. This procedure causes variation in a population, which aids in the evolution of species. Recombination and segregation are necessary for organisms to live and adapt to their environment.

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The complete question is:

Which two processes are best represented by the diagram above?

Answer:

y = 6.5

Step-by-step explanation:

Using a ratio

10           13

-----    = -----------

10+5      13+y

10           13

-----    = -----------

15        13+y

Using cross products

10(13+y) = 13*15

10(13+y) = 195

130+10y = 195

Subtract 130 from each side

10y = 65

Divide by 10

y = 65/10

y = 6.5

To fit a quadratic function of the form f(t) = c₀ + c₁t + c₂t² to the given data points, we can use the method of least squares. The goal is to find the coefficients c₀, c₁, and c₂ that minimize the sum of the squared differences between the observed y-values and the predicted y-values.

Using the given data points: (0, 7), (1, 8), (2, -3), and (3, -6), we can set up a system of equations to solve for the coefficients c₀, c₁, and c₂.

Using the general form of the quadratic function, we have the following equations:

7 = c₀ + c₁(0) + c₂(0)²

8 = c₀ + c₁(1) + c₂(1)²

-3 = c₀ + c₁(2) + c₂(2)²

-6 = c₀ + c₁(3) + c₂(3)²

Simplifying these equations, we get:

c₀ = 7

c₀ + c₁ + c₂ = 8

c₀ + 2c₁ + 4c₂ = -3

c₀ + 3c₁ + 9c₂ = -6

Solving this system of equations will give us the coefficients c₀, c₁, and c₂ that represent the quadratic function that best fits the given data points using the least squares method.

By solving the system of equations, we can determine the specific values of c₀, c₁, and c₂, and substitute them back into the quadratic function f(t) = c₀ + c₁t + c₂t² to obtain the final fitted quadratic function.

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Answer:

\(y=\frac{1}{2}(x+6)^2-1\)

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

\(y=a(x-h)^2+k\)

Where (h, k) is the vertex of the parabola that graphically represents the function, and a is a coefficient different from zero.

The vertex of the required equation is located at (-6,-1)

The parabola passes through (-12,17)

Substituting the coordinates of the vertex, the equation of the function is:

\(y=a(x+6)^2-1\)

The value of a will be determined by using the given point:

\(17=a(-12+6)^2-1\)

Operating:

\(17=a(36)-1\)

\(36a=18\Rightarrow a=18/36=1/2\)

Solving:

\(a=1/2\)

The equation of the parabola is:

\(\boxed{y=\frac{1}{2}(x+6)^2-1}\)

The standard deviation of the thickness of layer 1 = 15.81 x 10⁻⁵ m

                                                                       layer 2 = 20 x 10⁻⁵m

                                                                       layer 3 = 17.32 x 10⁻⁵ m

The variance of the thickness of the three layers is 25,40 and 30 in nanometers

Let v₁, v₂, v₃ be the variance of the three layers of thickness.

Then, the standard deviation of the thickness of these layers can be found using the formula

                             v = σ²

Let us re-write this equation in order to find the standard deviation,

                             σ = √v

where v is the variance and

          σ is the standard deviation

The standard deviation of layer 1 is

                          σ₁ = √v₁

                              = √(25 x 10⁻⁹)

                              = √(250 x 10⁻¹⁰)

                              = 15.81 x 10⁻⁵

The standard deviation of layer 2 is

                            σ₂ = √v₂

                                 = √(40 x 10⁻⁹)

                                 = √(400 x  10⁻¹⁰)

                                 = 20 x 10⁻⁵

The standard deviation of layer 3 is

                             σ₃ = √v₃

                                  = √(30 x  10⁻⁹)

                                  = √(300 x 10⁻¹⁰)

                                  = 17.32 x 10⁻⁵

Therefore, the standard deviation is 15.81 x 10⁻⁵m , 20 x 10⁻⁵ m, 17.32 x 10⁻⁵m

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The percentage of 322 out of 450 using the percentage formula was found out to be approximately 71.56%.

To find the percentage of 322 out of 450, we can use the following formula:

percentage = (part/whole) x 100

where, "part" is the value we want to express as a percentage (in this case, 322), "whole" is the total value (in this case, 450), and "x" means "multiply".

Using the formula mentioned above, we get:

percentage = (322/450) x 100

percentage = 0.7156 x 100

percentage = 71.56%

Therefore, percentage of 322 out of 450 is approximately 71.56%.

A percentage is a way to express a number as a fraction of 100. It is often denoted using the "%" symbol.

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Answer:

He did not take anything

Step-by-step explanation:

Answer:

Hi there!

Your answer is;

A) her bravery

Explanation:

Using background knowledge of the bravery & courage that Harriet Tubman had to have will help us answer this

Step-by-step explanation:

Answer:

The answer must be B because the rest are not possible.

Step-by-step explanation:

Answer:

They are both the same.

Step-by-step explanation:

The closet has 3 tiles, and the bathroom has 3 tiles as well (add up the 2 half tiles) thus they both cost the same to tile.

Answer: The first step would be to subtract 32 from both sides.

Step-by-step explanation:

The answer to the whole equation is -44.

To get -44 you need to get rid of the 32 to get the x to be alone.

Answer:

1,4,9,25,36,49,64,81,100,121,144

Question: What numbers make up the perfect squares

Answer:  

A perfect square is a number that can be expressed as the product of two equal integers.

Step-by-step explanation:

9 9 is a perfect square because it can be expressed as 3 * 3 (the product of two equal integers) 16 16 is a perfect square because it can be expressed as 4 * 4 (the product of two equal integers)

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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Answer:

1.8

2.12

3. 30

Step-by-step explanation:

the answer is base to what I learned so if im wrong please correct me..

Answer: The critical value is a value used in hypothesis testing to determine the rejection or acceptance of a null hypothesis. The critical value is determined based on the significance level of the test and the degrees of freedom. The critical value is usually determined from a table or calculated using statistical software.

Here are the general steps to calculate the critical value:

Determine the significance level, denoted by α. This is the probability of making a Type I error, which is the probability of rejecting a true null hypothesis.

Determine the degrees of freedom, which depend on the specific test and sample size.

Look up the critical value in a table of critical values for the appropriate significance level and degrees of freedom. These tables are available in most statistics textbooks or can be found online.

If a table is not available, the critical value can be calculated using statistical software or a calculator that provides a cumulative distribution function for the appropriate distribution. For example, the critical value for a two-tailed t-test can be calculated in R using the qt function. The syntax is qt(1-α/2, df), where α is the significance level and df is the degrees of freedom.

Note that the critical value will depend on the specific hypothesis test being performed and the null and alternative hypotheses. It is important to choose the correct test and use the appropriate critical value to ensure accurate results.

Step-by-step explanation:

For f(x + h) - f(x) = 4xh + 4h + 2h², the slope of the tangent line at x = 4 is 20. The correct answer is option OD) 20.

To find the slope of the tangent line at x = 4, we can use the definition of the derivative.

The given equation can be rewritten as:

f(x + h) - f(x) = 4xh + 4h + 2h².

Let's rewrite it in a form that resembles the definition of the derivative:

(f(x + h) - f(x)) / h = (4xh + 4h + 2h²) / h.

Canceling out the common factor of h in the numerator and denominator, we have:

(f(x + h) - f(x)) / h = 4x + 4 + 2h.

Now, let's take the limit as h approaches 0 on both sides of the equation:

lim(h->0) [(f(x + h) - f(x)) / h] = lim(h->0) (4x + 4 + 2h).

The left side of the equation is the definition of the derivative of f(x) with respect to x. So, we have:

f'(x) = 4x + 4.

To find the slope of the tangent line at x = 4, we substitute x = 4 into the derivative:

f'(4) = 4(4) + 4 = 16 + 4 = 20.

Therefore, the slope of the tangent line at x = 4 is 20.

The correct answer is OD) 20.

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Using the Binomial probability distribution,

the probability that sheer guesswork will yield exactly 18 correct answers is ²⁷C₁₈(0.2)¹⁸(0.8)⁹

We have given that,

total number of multiple choice questions= 27

each question has number of possible answer

= 5

but only one is correct .

we have to find out the probability that sheer guesswork will yield 18 correct answer.

P(C) = probability of answering any question correctly = (1 / 5) = 0.2

P(W) = probability of answering any question wrongly = (4/ 5) = 0.8

Using the Binomial probability distribution,

P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Probability of answering exactly 18 questions correctly = P(X=18) = ²⁷C₁₈(0.2)²⁸(0.8)⁹

Hence, the probability value is ²⁷C₁₈(0.2)²⁸(0.8)⁹

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Answer:

11165

Step-by-step explanation:

77*145= 11165

Hope this helps. :D

the least buckling load for the strut is determined by Euler's formula, which predicts a larger buckling load than the Rankine formula for the same boundary conditions and material properties. Therefore, for this situation, Euler's formula is preferable as it gives a more conservative estimate.

According to the Euler formula, the least buckling load (Pcr) of a column can be computed as

\(Pcr = π²EI / L²\)

where Pcr is the critical or least buckling load, E is the modulus of elasticity, I is the moment of inertia of the column cross-section about its axis of buckling, and L is the length of the column.

The strut's I cross-section has cross-sectional values of 610 x 229 x 113 (mm x mm x kg/mm).

Its weaker axis is its Z axis (i.e., the axis perpendicular to the 610 mm face) and its stronger axis is its Y axis (i.e., the axis perpendicular to the 229 mm face).

As a result, the moment of inertia of the strut about its weaker axis can be computed as

IZ = (610 x 229³) / 12 - (533 x 113³) / 12 = 6.47 x 10¹⁰ mm⁴

And the moment of inertia of the strut about its stronger axis isIY = (229 x 610³) / 12 = 9.35 x 10⁸ mm⁴

When the strut is pinned on both ends and buckles about its stronger axis, it has a buckling factor of 1/2 (as opposed to 1 for a fixed-fixed end strut).

As a result, the Rankine constant for a column that is fixed at both ends is 1/6400, so the Rankine constant for a column that is pinned at both ends is 1/4 of that, or 1/25600.

Using the same values as before and the Rankine formula, the least buckling load for the strut when buckling about its weaker axis is:

Pcr,z = (π² x 210 x 6.47 x 10¹⁰) / (10²)² x (1/25600) = 0.357 MN (to three significant figures)

And the least buckling load for the strut when buckling about its stronger axis is

:Pcr,y = (π² x 210 x 9.35 x 10⁸) / (10²)² x (1/25600) = 25.5 kN (to three significant figures)

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4a - 5b = 7

substract 4a from both sides

4a - 5b - 4a = 7 - 4a

positive 4a with negative 4a

5b = 7 - 4a

devide both sides by 5

\( \frac{5b}{5} = \frac{7 - 4a}{5} \)

\(b = \frac{7 - 4a}{5} \)

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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The probability that a student is both a sophomore and a business major is 12/61.

The probability that a student is both a sophomore and a business major can be calculated by dividing the number of students who are both into the total number of students.

Let's denote the event of a student being a sophomore as A and the event of a student being a business major as B. We want to find the probability of both events occurring, denoted as P(A and B).

From the given information, we know that there are 61 students in total, with 37 being sophomores and 26 being business majors. We are also given that 10 students are neither sophomores nor business majors.

To find the probability of a student being both a sophomore and a business major, we need to determine the number of students who satisfy both conditions.

Since there are 61 students in total and 10 of them are neither sophomores nor business majors, the number of students who are both sophomores and business majors is 37 + 26 - 61 + 10 = 12.

Therefore, the probability of a student being both a sophomore and a business major is:

P(A and B) = Number of students who are both sophomores and business majors / Total number of students = 12 / 61.

Thus, the probability that a student is both a sophomore and a business major is 12/61.

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The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Answer:

25m

Step-by-step explanation:

A square is a parallelogram having all sides equal. Hence, if Casey walked diagonally, she should have gone 25m as the rules of square states.

please mark brainliest

Answer:

-15

Step-by-step explanation:

if its just asking for what number would represent a loss of 15 it would be negative 15

i dont know if there's more to the problem or not

Answer:

-15

Step-by-step explanation:

This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,

hope this helps!