Find the particular solution of the first-order linear differential equation for x > 0 that satisfies the initial condition. Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) = 9 y = sin x + 9x cos x +9
Previous question

Answer:

  A)  2C

Step-by-step explanation:

The relevant rule of logarithms is ...

  log(x²) = 2·log(x)

__

We know that 64 = 8². So, ...

  log(64) = log(8²) = 2·log(8)

We are given that log(8) = C, so 2·log(8) = 2C

__

Here, all logarithms are to the base 9. That does not change the relations shown.

Answer:

The discount is $3.40. The total price is $13.60.

Step-by-step explanation:

Answer:

MN ;K ;K ;K ;K

Step-by-step explanation:

The triangle ABC is equal to triangle ADE by Angle-Angle-Side theorem.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In triangle ABC and ADE -

It can be seen that ∠B = ∠E.

Also the line segment AB is equal to line segment AE.

AB = AE

The angles ∠BAC and ∠DAE are vertically opposite to each other.

So, they are also equal.

∠BAC = ∠DAE

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, Δ ABC ≅ Δ ADE according to AAS theorem.

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Answer and explanation:

1. pop. 418, sample:link to diet

Determin.

1. statistic, because a specific percentage s given.

2. Parameter, because there is no number given

3. Statistic, because  a specific percentage in a specific population has been given.

2652 blue macaws are there if 2,730 red macaws are living in Brazil.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that the ratio between blue macaws and red macaws that live in Brazil is 272 : 208

We need to find the number of  blue macaws are there if 2,730 red macaws are living in Brazil.

Let x be the number of  blue macaws for 2,730 red macaws are living in Brazil.

Let us form a proportional equation

272/208=x/2730

Apply cross multiplication

272×2730=208x

742560=208x

Divide both sides by 208

2652=x

Hence, 2652 blue macaws are there if 2,730 red macaws are living in Brazil.

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Answer:

Slope = 5/2

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

In this case the two points are (6,7) and (4,2)
Using the formula we find that the slope is:
slope = (2-7)/(4-6)
slope = -5/-2
The negatives cancel out and therefore the final answer or slope is 5/2.

Since both sides are equal, we have shown that ∑(i=1 to 6) (dx_i + e) = d(∑\((i=1 to 6) x_i\)) + 6e. This represents the summation of the terms \((5x_3 + i)\) for i = 1 to 6.

To show that ∑(i=1 to 6) \((dx_i + e)\)= d(∑(i=1  \(x_i\)) + 6e, we can expand both sides and compare.

Left-hand side:

∑\((i=1 to 6) (dx_i + e) = (dx_1 + e) + (dx_2 + e) + (dx_3 + e) + (dx_4 + e) +\)(dx_5 + \(e) + (dx_6 + e)\)

                        = \(dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6 + e + e + e + e\)+ e + e

                        = \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6) + 6e\)

Right-hand side:

d(∑\((i=1 to 6) x_i)\)+ 6e = d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\)+ 6e

Now, let's compare the two sides:

Left-hand side: \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6)\) + 6e

Right-hand side: d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\) + 6e

Since both sides are equal, we have shown that ∑\((i=1 to 6) (dx_i + e)\) = d(∑(i=1 to 6)\(x_i)\) + 6e.

To represent the equation\((5x_3 + 4) + (5x_3 + 5) + (5x_3 + 6) + (5x_3 +\)7) + \((5x_3 + 8) + (5x_3 + 9)\) using a Sigma operator notation, we can write it as:

∑\((i=1 to 6) (5x_3 + i)\)

This represents the summation of the terms \((5x_3 + i)\)for i = 1 to 6.

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The null hypothesis (H_0) and alternative hypothesis (H_1) for the given statement are: A. H_0: μ < 15, H_1: μ ≥ 15.

In the given statement, the claim is about the standard deviation of IQ scores of statistics students. The null hypothesis (H_0) represents the claim being tested, while the alternative hypothesis (H_1) represents the opposite or alternative claim.

The statement states that the standard deviation is at most 15. This implies that the population mean (μ) could be less than 15. Hence, the null hypothesis (H_0) is μ < 15, indicating that the mean is less than 15.

The alternative hypothesis (H_1) would then be the opposite claim, stating that the mean is greater than or equal to 15. Therefore, the alternative hypothesis (H_1) is μ ≥ 15, indicating that the mean is greater than or equal to 15.

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The t-value for 90% confidence and nu=9 is 1.833.

To find the t-value using the t-table, we need to know the degrees of freedom (nu) and the desired confidence level. In this case, nu=9 and the confidence level is 90%.

Using a two-tailed t-table, we find the critical value of t for a 90% confidence interval and 9 degrees of freedom to be 1.833. This means that there is a 90% probability that the true population mean falls within 1.833 standard errors of the sample mean.

This value is important when constructing confidence intervals or conducting hypothesis tests with small sample sizes. A t-value is used to assess whether the difference between sample means is significant or due to chance.

A larger t-value indicates a larger difference between the sample means and a higher likelihood of statistical significance.

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Eukaryotic cells have a true membrane-bound nucleus and prokaryotes do not.

Eukaryotic cells are larger than prokaryotic cells and have a “true” nucleus, membrane-bound organelles, and rod-shaped chromosomes. The nucleus houses the cell's DNA and directs the synthesis of proteins and ribosomes.

All cells have a plasma membrane, ribosomes, cytoplasm, and DNA. Prokaryotic cells lack a nucleus and membrane-bound structures. Eukaryotic cells have a nucleus and membrane-bound structures called organelles.

So..the answer should be Eukaryotic cells have a true membrane-bound nucleus and prokaryotes do not.

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Answer:

Prokaryotes

✔ do not have

a nucleus surrounding their chromosome of DNA.

Prokaryotes are

✔ more

simple cells than eukaryotes.

Prokaryotes have a

✔ cell wall

outside their cell membrane that gives protection and support.

Prokaryotes will often move by a tail-like

✔ flagellum

.

Step-by-step explanation:

The actual distance between the two cities is 288 miles.

A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio.  This means that the scale drawing of the two cities would be smaller than the actual cities.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.

The actual distance between the two cities = (3 x 24) ÷ 1/4

= 3 x 24 x 4 = 288 miles

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The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

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Answer:

Below

Step-by-step explanation:

Interest = p r t    p = principle = 300   r = decimal interest = .14    t = years = 4

 Interest = 300 * .15 * 4 = 180 dollars

D) being specific about the coefficient or coefficients of interest.

What is a Variable?

A variable is a quantity that can change in the context of a mathematical problem or experiment. We usually use one letter to represent a variable. The letters x, y, and z are common general symbols used for variables.

The guideline for whether or not to include an additional variable includes all of the following, except:

A) providing "full disclosure" representative tabulations of the results.

B) testing whether additional questionable variables have nonzero coefficients.

C) determining whether it can be measured in the population of interest.

D) being specific about the coefficient or coefficients of interest.

So, the answer is: D) being specific about the coefficient or coefficients of interest.

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The expression that represents the relationship between the step number n and the total number of small squares in the pattern is this: (n-1)^2.

From the given information, we can see that the pattern starts with 0 squares at step 1, and each subsequent step adds a square to the pattern. However, the lower right square is always missing. Therefore, the total number of small squares in the pattern at step n can be represented by the expression: (n-1)^2

The reason we subtract 1 from n is that we started counting from step 1, whereas the expression (n-1)^2 assumes that we start counting from 0. Then we square (n-1) to account for the number of squares in the pattern, excluding the missing square in the lower right corner.

Complete Question:

Which expression represents the relationship between the step number n and the total number of small squares in the pattern?

A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.

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Answer:

-3(2x-5)<5(2-x)

Step-by-step explanation:

hope this helps

Answer:

x ≥ -3/4

Step-by-step explanation:

3(2x + 5) ≥ 2(x + 6)

Distribute

6x+15 ≥ 2x + 12

Subtract 2x from each side

6x-2x+15 ≥ 2x-2x + 12

4x+15 ≥ 12

Subtract 15 from each side

4x+15-15 ≥ 12-15

4x ≥ -3

Divide each side by 4

4x/4 ≥ -3/4

x ≥ -3/4

In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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the diameter of the circumscribed circle is approximately 24. Here's how we calculate it: diameter = 12/sin(30) = 12/(1/2) = 24.

The diameter of the circumscribed circle in a triangle can be found using the formula: diameter = a/sin(A), where "a" is the length of one side and "A" is the opposite angle. In this case, if one side of the triangle is 12 and the opposite angle is 30 degrees, we can plug these values into the formula to find the diameter.

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Answer:

∠ B = 69°

Step-by-step explanation:

complementary angle sum to 90° , that is

∠ A + ∠ B = 90°

x + 13 + 7x + 13 = 90

8x + 26 = 90 ( subtract 26 from both sides )

8x = 64 ( divide both sides by 8 )

x = 8

Then

∠ B = 7x + 13 = 7(8) + 13 = 56 + 13 = 69°

Answer:

add all the sides up

Step-by-step explanation:

yw

Answer:

10%

Step-by-step expla

loss percent = 100 - x

-------------- × 300= 270

100

multiply both sides by 100

100 - x

100 × -------------- × 300 = 270× 100

100

300( 100 - x) = 27000

30000 - 300x = 27000

30000 - 27000 = 300x

3000 = 300x

divide both sides of the equation by 300

3000 = 300x

-------- ----------

300 300

x = 10

Note that the   results show sthat the pair of vectors (5, -2) and (3, 4) is not normal  or perpendicular to each   other.

To determine  whether two vectors are normal (perpendicular) to each other,we can check if their dot product is equal to zero.

Let's calculate the dot product of the given vectors  -

(5, - 2) ·(3, 4)

  = (5 * 3) + ( -2 * 4)

=15 - 8

= 7

Since the dot product is NOT zero (it is 7), hence, it is right to state or indicate that the pair of vectors (5, -2) and (3, 4) is not normal (perpendicular) to each other.

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Answer:

Step-by-step explanation:

its 212123s\

Answer: Rolling a six-sided number cube 24 times and recording if a 5 comes up

Thank you for being so generous with the points!! <3

The number of eigenvalues possible for the covariance matrix of a data matrix X with n rows and p columns is equal to the smaller of n and p.

1. Start with a data matrix X with n rows and p columns.

2. Compute the covariance matrix of X. The covariance matrix is a symmetric matrix that measures the covariance between pairs of variables in X.

3. The covariance matrix of X will be a square matrix with dimensions p x p.

4. The number of eigenvalues of a matrix is equal to its dimension, counting multiplicities. Since the covariance matrix of X is p x p, it will have p eigenvalues.

5. However, the number of eigenvalues for the covariance matrix is also constrained by the number of observations (n) and the number of variables (p) in X.

6. If n < p, it means that there are more variables than observations. In this case, the maximum number of eigenvalues possible for the covariance matrix is n.

7. On the other hand, if p ≤ n, it means that there are more observations than variables. In this case, the maximum number of eigenvalues possible for the covariance matrix is p.

8. Therefore, the number of eigenvalues possible for the covariance matrix of X is equal to the smaller of n and p.

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Answer:

(0, 10 )

Step-by-step explanation:

5 units up means add 5 to the y- coordinate

3 units left means subtract 3 from the x- coordinate

Translation rule is

(x, y ) → (x - 3, y + 5 ) , thus

(3, 5 ) → (3 - 3, 5 + 5 ) → (0, 10 )

The output obtained after executing the java code snippet,

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

will be 4.

As per the question statement, we are provided with a java code snippet, which goes as:

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We are required to determine the output, that we will obtain on executing the above mentioned code.

That is, on executing the code

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We will obtain an output of 4, as "++" is the post increment function.

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