800 students were surveyed to find out their favorite subject. 35% chose Math. How many students chose Math?

Answer:24

Step-by-step explanation:

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The particle moves in a circular path with a radius of 1/π. The speed of the particle is increasing when t = 1 and t = 2.

(a) The graph of r(t) for 0 ≤ t ≤ 3 is a circle with a radius of 1/π. The particle starts at the point (1/π, 0) and moves counterclockwise.

(b) The vectors r(1), r(2), a(1), and a(2) are shown on the graph. The vector r(1) points to the right, the vector r(2) points up, the vector a(1) points to the left, and the vector a(2) points down.

(c) The acceleration of the particle is ar = -aπsin(at) and ay = aπcos(at). When t = 1, ar = -π and ay = π. When t = 2, ar = 2π and ay = -2π.

(d) The speed of the particle is v = |r'(t)| = a√(sin^2(at) + cos^2(at)) = a. When t = 1 and t = 2, the speed of the particle is increasing because the acceleration is in the opposite direction of the velocity.

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Answer:

1 3/8

Step-by-step explanation:

Subtract the fractions, but you need to find common denominators first. Since 4 can go into 8, 8 is the common denominator. Multiply 2 3/4 by 2/2

2 3/4 × 2/2 = 2 6/8

Now subtract.

2 6/8 - 1 3/8 = 1 3/8

Answer:

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Answer:

Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f   brainliest ?

Answer:

I can help!

In point form: (5,10)

In equation form: x=5 y=10

Explanation

Solve for the first variable in one of the equations (y=x+5), then substitute the result in the other equation.

Answer:

5

Step-by-step explanation:

Because of pythagorean theorem the answer is 5

Let us consider the black paint in the mixture = 7x

and white paint in the mixture = 12x

total quantity of mixture = 600ml

according to the question , black : white paint = 7 : 12

quantity of black paint = \(\frac{7}{19}\) × 600= 221.052

quantity of white paint =  \(\frac{12}{19}\) × 600 = 378.94

{ 221.052ml black paint + 378.94 ml white paint = 599.99 ml grey paint }

Ans :- It would be 221.052 ml of black paint

Answer:

A

Step-by-step explanation:

We know that 8+3x= x

solve for x

8= -2x

-4 =x

The only answer that has -4 is A

Answer:

Let x be the measure of the angle we are trying to find, in degrees.

The complementary angle to x is 90° - x, since the sum of complementary angles is 90 degrees.

The problem tells us that x is 3.4 degrees less than its complementary angle, so we can set up the following equation:

x = (90 - x) - 3.4

Simplifying and solving for x, we get:

x = 86.6/2

x = 43.3

Therefore, the angle we are trying to find has a measure of 43.3 degrees, and its complementary angle has a measure of 90 - 43.3 = 46.7 degrees.

Answer:

7 \(\frac{1}{8}\)

Step-by-step explanation:

The reciprocal of a number n is \(\frac{1}{n}\)

The reciprocal of 8 is \(\frac{1}{8}\)

The reciprocal of \(\frac{1}{7}\) is \(\frac{1}{\frac{1}{7} }\)  = 7

sum = 7 + \(\frac{1}{8}\) = 7 \(\frac{1}{8}\)

Confidence coefficient or confidence level for the interval is 0.95.

What is confidence coefficient?

The proportion of samples of a given size that may be anticipated to contain the true mean is all that the confidence coefficient is.

Confidence level:

Confidence level means the proportion or frequency of acceptable confidence intervals that contain the true value of the unknown parameter.

For example,

A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results.

Main Body :

Confidence Interval = 95%

Hence the confidence interval would be 0.95.

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33 square yards is equal to 297 square feet.

To convert from square yards to square feet, you need to know that 1 yard is equal to 3 feet. Since the area is a two-dimensional measure, the conversion factor for square units is the square of the linear conversion factor. In this case, since 1 yard is equal to 3 feet, we square both sides to find that 1 square yard is equal to 9 square feet.

Now, let's calculate the conversion of 33 square yards to square feet. We multiply 33 square yards by the conversion factor of 9 square feet per square yard.

33 square yards * 9 square feet/square yard = 297 square feet

Therefore, 33 square yards is equal to 297 square feet.

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The solution to the initial value problem can be written in the form:

y(x) = (1/K)∫|sin(5x)|⁵ (3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

To solve the initial value problem and find the solution y(x), we can use the method of integrating factors.

Given: dy/dx + 5cot(5x)y = 3x³ - csc(5x), y = 0

Step 1: Recognize the linear first-order differential equation form

The given equation is in the form dy/dx + P(x)y = Q(x), where P(x) = 5cot(5x) and Q(x) = 3x³ - csc(5x).

Step 2: Determine the integrating factor

To find the integrating factor, we multiply the entire equation by the integrating factor, which is the exponential of the integral of P(x):

Integrating factor (IF) = e^{(∫ P(x) dx)}

In this case, P(x) = 5cot(5x), so we have:

IF = e^{(∫ 5cot(5x) dx)}

Step 3: Evaluate the integral in the integrating factor

∫ 5cot(5x) dx = 5∫cot(5x) dx = 5ln|sin(5x)| + C

Therefore, the integrating factor becomes:

IF = \(e^{(5ln|sin(5x)| + C)}\)

= \(e^C * e^{(5ln|sin(5x)|)}\)

= K|sin(5x)|⁵

where K =\(e^C\) is a constant.

Step 4: Multiply the original equation by the integrating factor

Multiplying the original equation by the integrating factor (K|sin(5x)|⁵), we have:

K|sin(5x)|⁵(dy/dx) + 5K|sin(5x)|⁵cot(5x)y = K|sin(5x)|⁵(3x³ - csc(5x))

Step 5: Simplify and integrate both sides

Using the product rule, the left side simplifies to:

(d/dx)(K|sin(5x)|⁵y) = K|sin(5x)|⁵(3x³ - csc(5x))

Integrating both sides with respect to x, we get:

∫(d/dx)(K|sin(5x)|⁵y) dx = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

Integrating the left side:

K|sin(5x)|⁵y = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

y = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

Step 6: Evaluate the integral

Evaluating the integral on the right side is a challenging task as it involves the integration of absolute values. The result will involve piecewise functions depending on the range of x. It is not possible to provide a simple explicit formula for y(x) in this case.

Therefore, the solution to the initial value problem can be written in the form: y(x) = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

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The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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The radius of convergence R for the power series representation of f(x) is R = 1.

The radius of convergence of a power series can be determined using the ratio test. For the power series representation of f(x) = Σ(10x^n)/(11^n+9), we need to apply the ratio test to find the radius of convergence.

Using the ratio test, we compute the limit as n approaches infinity of the absolute value of the ratio of consecutive terms:

lim(n→∞) |(10x^(n+1))/(11^(n+1)+9)| / |(10x^n)/(11^n+9)|

Simplifying the expression, we have:

lim(n→∞) |10x^(n+1)(11^n+9)| / |10x^n(11^(n+1)+9)|

Canceling out the common terms, we get:

lim(n→∞) |x(11^n+9)| / |(11^(n+1)+9)|

Taking the absolute value of x outside the limit, we have:

|x| * lim(n→∞) |(11^n+9)| / |(11^(n+1)+9)|

Now, as n approaches infinity, the terms (11^n+9) and (11^(n+1)+9) both grow exponentially, and their ratio approaches 11/11 = 1.

Thus, the limit simplifies to:

|x| * 1 = |x|

Therefore, the radius of convergence R for the power series representation of f(x) is R = 1.

Regarding the statement "The interval of convergence of the power series Σ xn+1 n=0 n^2/4 is (-4,4]," it is false. The interval of convergence cannot be determined solely based on the given series. Further information or calculations are needed to determine the actual interval of convergence.

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The statements that are a result of corresponding parts of congruent triangles being congruent are:

An isosceles triangle is a type of triangle with two equal sides and angles. The other types of triangle includes;

From the figure;

Sides EFGH are congruent, that is, equal

Since Sides EFGH are congruent, it can not be a rectangle, it is a square.

Triangle FGH and FEH are both isosceles triangle.

Diagonal FH bisects triangle FGH and FEH

So therefore, the isosceles triangle FGH and FEH are congruent and bisected by diagonal FH.

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Answer:

x=u/k

Step-by-step explanation:

To get x, you would divide by k. Because its x times k. The oppisite is division. This gets you u/k=x

x is equal to u divided by k.

x=u/k

An acute triangle

Step-by-step explanation:

Using a calculator, these measurements fit an acute scalene triangle.

Answer:

acute

Step-by-step explanation:

The process of making coffee grounds involves sourcing, roasting, grinding, and packaging high-quality beans.

The process of making coffee grounds starts with sourcing and selecting high-quality beans, which sets the foundation for a superior product. These beans are then carefully roasted to unlock their unique flavors and aromas, enhancing the overall coffee experience.

The roasted beans are ground to the desired consistency, catering to different brewing methods and preferences. Finally, the freshly ground coffee is meticulously packaged to preserve its freshness, ensuring that customers can enjoy the full flavor profile.

Through value-added analysis, each step is evaluated to identify activities that directly contribute to the product's value, allowing for optimization and efficiency in the production process.

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In a two-factor experiment, the expected value of the mean square for the major factor

(a) can differ depending on whether the minor factor

(b) is fixed or random.

Both parts are briefly discussed belwo.

If the minor factor (b) is fixed, it means that the levels of the minor factor are chosen by the experimenter, and they are held constant throughout the experiment.

In this case, the expected value of the mean square for the major factor (a) is calculated by dividing the sum of squares for the major factor by the degrees of freedom for the major factor.

The degrees of freedom for the major factor are equal to the number of levels of the major factor minus one.

On the other hand, if the minor factor (b) is random, it means that the levels of the minor factor are chosen randomly from a population of possible levels, and they are not held constant throughout the experiment.

In this case, the expected value of the mean square for the major factor (a) is calculated by dividing the sum of squares for the major factor by the degrees of freedom for the major factor and the degrees of freedom for the interaction between the major and minor factors.

The degrees of freedom for the interaction are equal to the product of the degrees of freedom for the major and minor factors.

The reason why the expected value of the mean square for the major factor (a) differs depending on whether the minor factor (b) is fixed or random is that in the fixed case.

The variability due to the minor factor is accounted for in the error term, while in the random case, the variability due to the minor factor is accounted for in the interaction term.

Therefore, the degrees of freedom for the major factor are different in the two cases, and this affects the expected value of the mean square for the major factor.

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Answer:

x=35

Step-by-step explanation:

3x+15=2x+50 (opposite angles are equal)

3x=2x+35

x=35

Answer:

x=6

Step-by-step explanation:

You can reach this answer by doing the equation

4+(x-3) = 2x-5

doing the math you will get that 6 is your x.

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None of the options is correct

To find the number of distinct memorable telephone numbers, we need to consider the possibilities for the prefix sequence. Since each digit can be any of the ten decimal digits, there are 10 options for each digit in the prefix sequence.

Now, we need to consider the two possibilities:
1) The prefix sequence is the same as the first sequence.
2) The prefix sequence is the same as the second sequence.

For the first sequence, there are 10 options for each of the 3 digits in the prefix sequence. Therefore, there are 10^3 = 1000 possible numbers.

For the second sequence, there are also 10 options for each of the 4 digits in the prefix sequence. Therefore, there are 10^4 = 10000 possible numbers.

Since the telephone number can be memorable if the prefix sequence is exactly the same as either of the sequences or both, we need to consider the union of these two sets of possible numbers.

The total number of distinct memorable telephone numbers is 1000 + 10000 = 11000.

Therefore, the correct answer is not among the options provided.

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The central metaphor which is presented in six degrees of separation is:

This refers to the figure of speech which makes use of comparison to show the similarity between two different things.

With this in mind and from the concept of six degrees of separation, we can see that it is based on the theory that people are about six or fewer connections away from each other.

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Answer: A) the number of CDs Ahmed has.

Step-by-step explanation:

Answer:

a = 3.6

Step-by-step explanation:

\( \frac{2}{3} (6a + 9) = 20.4 \\ \\ \bigg( \frac{2}{3} . \boxed{6a} \bigg) + \bigg(\boxed{ \frac{2}{3}} . {9} \bigg) = \boxed{ 20.4} \\ \\ (2.2a) + (2.3) = 20.4 \\ \\ 4a + 6 = 20.4 \\ \\ 4a = 20.4 - 6 \\ \\ 4a = 14.4 \\ \\ a = \frac{14.4}{4} \\ \\ a = \boxed{3.6}\)