ADDITIONAL TOPICS IN TRIGONOMETRY De Moivre's Theorem: Answers in standard form Use De Moivre's Theorem to find (-5√3+51)³. Put your answer in standard form. 0 2 0/0 X 5 ?

The probability of Stephen Curry making exactly three of his next five free throws is 0.3264 or 32.64%.

\(p(x) = nCx * p^x * q^(n-x)\)

where:

n = total number of attempts (5 in this case)

x = desired number of successes (3 in this case)

p = probability of success (0.92 in this case)

q = probability of failure (1 - p, or 0.08 in this case)

Plugging these numbers into the equation gives us:

p(3) = 5C3 * 0.92^3 * 0.08^2 = 0.3264

Stephen Curry is a professional basketball player in the NBA who is known for his incredibly accurate shooting ability. He made 92% of his free throws during the 2018-2019 regular season with the Golden State Warriors. We can calculate the probability of Curry making exactly three of his next five free throws using the binomial probability formula. This formula takes into account the probability of the event (Curry making the free throw) and the number of attempts (five). In this case, the probability of success (Curry making the free throw) is 0.92 and the number of attempts is five. Plugging these numbers into the equation gives us a probability of 0.3264 or 32.64%. This means that Curry has a 32.64% chance of making exactly three of his next five free throws.

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The hypothesis in a hypothesis test is an alternative hypothesis a statement about a parameter.

An alternative hypothesis in a hypothesis test is a statement about a parameter, not a statistic. The null hypothesis is typically a statement about a parameter that assumes there is no significant difference or relationship, while the alternative hypothesis is a statement that contradicts the null hypothesis and suggests there is a significant difference or relationship.

The alternative hypothesis can take one of three forms: it can be a one-tailed hypothesis (either greater than or less than the null hypothesis), or a two-tailed hypothesis (not equal to the null hypothesis). In all cases, the alternative hypothesis is a statement about the population parameter, which is typically denoted by a Greek letter such as μ (mean) or σ (standard deviation).

Therefore, the alternative hypothesis is a statement about the parameter being tested.

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The probability sampling method in which you randomly select one of the first k elements and then select every k element thereafter is known as c. systematic sampling. Therefore, option c. systematic sampling is correct.

Systematic sampling is a probability sampling technique where the sample is chosen by selecting every kth element from the population, where k is a constant. This method is often used when the population is large and the complete list of elements is not easily available.

Stratified random sampling is a technique where the population is divided into strata or subgroups based on certain characteristics and a random sample is chosen from each stratum.

Cluster sampling involves dividing the population into clusters or groups and then selecting a random sample of clusters. The elements within each selected cluster are then included in the sample.

Convenience sampling is a non-probability sampling method where the sample is chosen based on convenience and availability. This method is often used in situations where it is difficult or expensive to obtain a random sample.

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Answer:

3rd option

Step-by-step explanation:

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through

The only equation in this form is option 3

3x - 2 = 0 , as

3x = 2 and

x = \(\frac{2}{3}\) ← equation of vertical line

The required answer is  \(m^{(-z)} = V\) . In other words, the exponential equation of logarithmic equation \(log_m V = -z\)  is \(m^{(-z)} = V\)

To convert the logarithmic equation \(log_m V = -z\) into an exponential equation, we can rewrite it using the definition of logarithms. In exponential form, the base m is raised to the power of the logarithm's result, which is -z in this case.

\(m^{(-z)} = V\)

In this equation, m is the base, -z is the exponent, and V is the result.

Converting a logarithmic equation to its exponential form helps us express the relationship between the base, exponent, and result differently, which can be useful in solving equations or simplifying expressions involving logarithms.

Therefore, the exponential equation of logarithmic equation \(log_m V = -z\)  is \(m^{(-z)} = V\)

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The  measure of each exterior angle of a regular polygon of 12 sides is equal to 30° option D.

A polygon's exterior angles are generated by extending one of its sides and extending the other side. The sum of a polygon's outside angles equals 360 degrees. You've probably heard of the phrase polygon. A polygon is an enclosed flat shape made up of three or more line segments. The line segments are referred to as sides, and the location where two sides intersect is referred to as the polygon's vertex.

Adjacent sides are a pair of sides that meet at the same vertex. The inner angle is the angle formed by one of the vertices. For all polygons, the interior and external angles at each vertex vary.

We know that the sum of a polygon's outer angles is 360.

As a result, the exterior angle of a regular polygon with 12 sides Equals 360/ 12 = 30.

So, The  measure of each exterior angle of a regular polygon of 12 sides is equal to 30°.

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To solve this problem, we need to use some basic geometry concepts. First, we know that the diagonal of a unit square is the square root of 2, since the sides are of length 1.  The side length of the smaller square inscribed within a circle inscribed in a unit square is 1.

Next, we know that the circle inscribed in the square will have a diameter equal to the diagonal of the square, which is the square root of 2. The radius of the circle will therefore be half of the diameter, which is sqrt(2)/2.
Now we can use the radius of the circle to find the side length of the smaller square inscribed within it. If we draw the diagonal of the smaller square, it will be twice the radius of the circle, or sqrt(2). This is because the diagonal of the square passes through the center of the circle and therefore has a length equal to twice the radius.
We can then use the Pythagorean theorem to find the length of each side of the smaller square. If we let x be the side length of the smaller square, then we have:
x^2 + x^2 = 2
2x^2 = 2
x^2 = 1
x = 1
Therefore, the side length of the smaller square is 1, which makes sense since it is inscribed within a unit square.

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A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Triangles are similar ,

Thus :

\( \frac{9}{3} = \frac{6}{x} \\ \)

\(3 = \frac{6}{x} \\ \)

\( \frac{6}{x} = 3 \\ \)

Inverse both sides

\( \frac{x}{6} = \frac{1}{3} \\ \)

Multiply sides by 6

\(6 \times \frac{x}{6} = 6 \times \frac{1}{3} \\ \)

\(x = 2 \times 3 \times \frac{1}{3} \\ \)

\(x = 2\)

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Answer:

x=4.8

Step-by-step explanation:

9.6 is the diameter, and x is the radius. The radius is half of the diameter, so 9.6/2.

x=4.8

Step-by-step explanation:

Let's call the number of girls in the school "g". We know that there are 1000 boys, so the total number of students is 1000 + g.

The problem states that 48% of the total number of students were successful in the examination. Therefore, we can write an equation:

0.48(1000 + g) = 0.5(1000) + 0.4(g)

Simplifying and solving for g:

480 + 0.48g = 500 + 0.4g

0.08g = 20

g = 250

Therefore, the number of girls in the school is 250.

Answer:

250

Step-by-step explanation:

Hi dear,

Firstly, let the girls be G

1000 + G = Total number of students

50% of boy = 1000 × 0.5 = 500

40% of girls = G × 0.4 = 0.4G

0.48 • (1000 + G) = 480 + 0.48G

480 + 0.48G = 500 + 0.4G

Collect Like Terms

0.48G - 0.4G = 500 - 480

0.08G = 20

G = 20/0.08

G = 250

Therefore, the girls are 250( two hundred and fifty)in the school

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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Answer:

C. 2x^4; E. -5x

Step-by-step explanation:

P(x) = x^3 − x − 2 and Q(x) = x^2 + 2x + 1

P(x) * Q(x) = (x^3 − x − 2)(x^2 + 2x + 1) =

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

= x^5 + 2x^4 - 4x^2 - 5x - 2

Answer: C. 2x^4; E. -5x

\(\frac{10}{3}\) liters of water are necessary to water all the plants in the house.

The multiplication equation for the situation is \(\frac{4}{3} \times \frac{5}{2}$\)

The division equation for the situation is \(\frac{4}{3} \div \frac{2}{5}$\)

As per the given data in the question

\($\frac{2}{5}$\) plants required \(\frac{4}{3}$\) liters of water to water them.

We have to determine the water which is necessary to water all the plants in the house

We will solve this question using the unitary method.

Unitary method: This method generally involves finding the value of a unit in the given terms, using which the value of the given quantity of units can be calculated.

1 plant \($\rightarrow \frac{4}{3} \div \frac{2}{5}$\) liters (the division equation for the situation)

1 plant \($\rightarrow \frac{4}{3} \times \frac{5}{2}$\) liters (the multiplication equation for the situation)

1 Plant \($=\frac{20}{6}=\frac{10}{3}$\) liters

The total number of plants in the house are 5.

The water required to water the 5 plants:

\($=\frac{10}{3} \times 5$\)

\($=\frac{50}{3}$\) liters

Therefore the water which is necessary to water the plants in the house are \(\frac{50}{3}$\) liters.

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The price of the meal before the tax is applied is $22.

The current sales tax rate in Wisconsin is 5%, which means that if the price of your meal was $20, you would have to pay an additional $1 as sales tax.

Now, when it comes to leaving a tip, it is customary in Wisconsin to leave a tip of 5% of the meal's price before the sales tax is applied. So, let's say your meal cost $20 before the sales tax, your tip would be calculated as follows:

Tip = 5% of $20 = 0.05 x $20 = $1

It's important to note that sales tax is not calculated on the tip amount. So, the total cost of your meal including sales tax and tip would be:

Total cost = Price of meal + Sales tax + Tip

Total cost = $20 + $1 + $1 = $22

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Answer:  B

Step-by-step explanation:

I am a trained tutor and professional trust me you'll get this right.

Answer:

4 would be 36

Step-by-step explanation:

PEMDAS! <3

Answer:

50

36

0

Step-by-step explanation:

Answer:

a and b shows a solution all you have to do is place the numbers in x value and see if it makes sense for example 8>9 is not a solution but 9> 8 that is a solution so c cannot be a solution

Step-by-step explanation:

Answer:

its a and b

Step-by-step explanation:

Answer:

10 in³

Step-by-step explanation:

Length = 10/3 inches

Width = 8/4 inches = 2 inches

Height = 3/2 inches

Volume = Length * width * height

Volume = 10/3 * 2/1 * 3/2

Volume = (10*2*3) / (3*1*2)

Volume = 60/6

Volume = 10 in³

The value of the Arrow-Debreu security is calculated as the present value of its expected payoff, discounted at the risk-neutral rate. As a result, the premium of the Arrow-Debreu security can be computed using the following formula: \($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$,\)

where π=0.4, R=1.05, n=6, and t=2 (expiry node).

By substituting the values, we obtain:

\($P_{2}=\frac{1}{(1+1.05)^{6-2}}\times 0.4 = \frac{0.4}{(1.05)^4} \approx 0.3058$.\)

Therefore, the premium of the Arrow-Debreu security is approximately $0.3058.

Arrow-Debreu securities are typically utilized in financial modeling to simplify the pricing of complex securities. They are named after Kenneth Arrow and Gerard Debreu, who invented them in the 1950s. An Arrow-Debreu security pays $1 if a particular state of the world is realized and $0 otherwise.

They are generally utilized to price derivatives on numerous assets that can be broken down into a set of Arrow-Debreu securities. The value of an Arrow-Debreu security is calculated as the present value of its expected payoff, discounted at the risk-neutral rate. In other words, the expected value of the security is computed using the risk-neutral probability, which is used to discount the value back to the present value.

The formula is expressed as:

\($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$\),

where P_t is the price of the Arrow-Debreu security at time t, π is the risk-neutral probability of the security’s payoff, R is the risk-free rate, and n is the total number of time periods.However, Arrow-Debreu securities are not traded in real life. They are used to determine the prices of complex securities, such as options, futures, and swaps, which are constructed from a set of Arrow-Debreu securities.

This process is known as constructing a complete financial market, which allows for a more straightforward pricing of complex securities.

The premium of the Arrow-Debreu security is calculated by multiplying the risk-neutral probability of the security’s payoff by the present value of its expected payoff, discounted at the risk-neutral rate.

The formula is expressed as

\($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$,\)

where P_t is the price of the Arrow-Debreu security at time t, π is the risk-neutral probability of the security’s payoff, R is the risk-free rate, and n is the total number of time periods. Arrow-Debreu securities are not traded in real life but are used to price complex securities, such as options, futures, and swaps, by constructing a complete financial market.

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Answer:

34.54cm

Step-by-step explanation:

Perimeter of a semicircle is

\(\pi \: d \div 2\)

\(p = 3.14 \times 22 \div 2\)

\(p = 3.14 \times 11 \\ p = 34.54cm\)

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The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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The sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function\(f(x) = 0\) on the interval \(I = [0, \infty)\).

To examine the uniform convergence of the sequence\(f_n(x) = e^{-nx}\) on the interval\(I = [0, \infty)\), we need to check if the sequence converges uniformly to a limit function on that interval.

For uniform convergence, we need the following condition to hold:

Given any\(\(\epsilon > 0\\)), there exists an \(\(N \in \mathbb{N}\\)) such that for all \(n > N\) and for all \(x \in I\), we have\(\(\left| f_n(x) - f(x) \right| < \epsilon\)\), where \(\(f(x)\)\) is the limit function.

Let's find the limit function\(\(f(x)\\)) of the sequence \(f_n(x) = e^{-nx}\) as \(n\) approaches infinity. Taking the limit as \(\(n\)\)goes to infinity

\(\[f(x) = \lim_{n \to \infty} e^{-nx}\]\)

We can rewrite this limit using the exponential function property:

\(\[f(x) = \exp\left(\lim_{n \to \infty} -nx\right)\]\)

Since the limit inside the exponential is\(\(-\infty\)\) as \(\(n\)\) goes to infinity, we have:

\[f(x) = \exp(-\infty) = 0\]

Therefore, the limit function \(f(x)\) is the constant function\(\(f(x) = 0\\)) on the interval \(I = [0, \infty)\).

To check for uniform convergence, we need to evaluate the difference \(\left| f_n(x) - f(x) \right|\) and see if it is less than any given \(\epsilon > 0\) for all \(n > N\) and for all \(x \in I\).

\(\[\left| e^{-nx} - 0 \right| = e^{-nx}\]\)

To make this expression less than\(\(\epsilon\),\) we need to find an \(N\) such that \(e^{-nx} \(< \epsilon\)\) for all\(n > N\) and for all\(\(x \in I\).\)

However, as \(\(x\)\) approaches infinity, \(e^{-nx}\) approaches 0. But for any finite \\((x\)\) in the interval \([0, \infty)\), \(e^{-nx}\)  will always be positive and never exactly equal to 0. This means we cannot find an\(\(N\)\)that satisfies the condition for uniform convergence.

Therefore, the sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function \(f(x) = 0\) on the interval \(I = [0, \infty)\).

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Answer: C. Zula can write 4 articles in 10 hours is the best interpretation of the slope of this linear model.

The slope of a linear equation in the form y = mx + b represents the rate of change of y with respect to x. It tells us how much y changes for a one-unit change in x. In this case, the slope of the equation y = 0.4x is 0.

Step-by-step explanation:

Answer:

I can't understand the picture...

Step-by-step explanation:

Sorry...

Answer:

simple interest=371.25

Step-by-step explanation:

1500×8.25%×3

=123.75×3

=371.25

Answer:

371.25

Step-by-step explanation:

interest = principal x rate (expressed as a decimal, annual) x time (years)

our principal is 1500, and 8.25% as a decimal is 0.0825, and then its 3 years, multiply that all up and that equals 371.25

She needs to get her interest rate at will 5.592 %/year.

What is Compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.

\(A = P(1 + \frac{r}{n})^{nt}\)

Where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest is applied per time period

t = number of time periods elapsed

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 12 × [(2,500.00/2,000.00)1/(12)(4) - 1]

r = 0.0559158

Then convert r to R as a percentage

R = r * 100

R = 0.0559158 * 100

R = 5.592%/year

Hence, she needs to get her interest rate at will 5.592 %/year.

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A factor in an experiment that changes from the manipulation of the independent variable is the dependent variable.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.

The variable being measured or tested in an experiment is known as the dependent variable. 1 The results of the participants' tests, for instance, since that is what is being measured, would be the dependent variable in a study looking at how tutoring affects test scores.

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