What is a sine wave in Trigonometry

\(\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}\)

Total cards = 52

Total diamond cards = 13

So, probability of getting a card of diamond,

P(diamond) = 13/52 = 1/4

Now,

Total cards with number seven = 4

So, probability of getting a seven,

P(seven) = 4/52 = 1/13

Answer:

A

Step-by-step explanation:

x² + 7x + 12 = 0

consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)

the factors are + 3 and + 4 , since

3 × 4 = + 12 and 3 + 4 = + 7 , then

(x + 3)(x + 4) = 0

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 4 = 0 ⇒ x = - 4

Answer:

r² = (4 - 2)² + (5 - (-2))² = 2² + 7² = 53

So the equation of this circle is

(x - 2)² + (y + 2)² = 53

The largest value is 6, and the smallest value is 1. The range is 5.

a. The range is the difference between the largest and smallest values in the data set. To find the range of the given data set, we need to first order the data set from smallest to largest:

1 2 3 4 4 5 5 6

The largest value is 6, and the smallest value is 1. Therefore, the range is:

range = largest value - smallest value = 6 - 1 = 5

b. The variance is a measure of how spread out the data is from the mean. To calculate the variance of the given data set, we first need to find the mean:

mean = (5 + 1 + 2 + 6 + 4 + 4 + 3 + 5)/8 = 30/8 = 3.75

Then, we can use the formula for variance:

variance = (sum of the squared differences from the mean)/(number of data points - 1)

= [(5 - 3.75)^2 + (1 - 3.75)^2 + (2 - 3.75)^2 + (6 - 3.75)^2 + (4 - 3.75)^2 + (4 - 3.75)^2 + (3 - 3.75)^2 + (5 - 3.75)^2]/(8 - 1)

= 5.18

c. The standard deviation is the square root of the variance. Therefore, the standard deviation of the given data set is:

standard deviation = sqrt(variance) = sqrt(5.18) = 2.28

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Answer:

Hi there!

An equation to represent how he got $460.65 as take home pay is:

15x - (.17× (15x) ) = 460.65

15x tells us how much money he earned in total. We also multiply that by .17 to determine how much goes to taxes. Then, we subtract taxes from total, and put that equal to our take home pay

Hope this helps

Answer:

Right isosceles triangle

Step-by-step explanation:

I took the quiz and got it wrong, but it told me the correct answer

A right isosceles triangle has exactly 2 equal sides and one right angle.

Given that, a triangle has exactly 2 equal sides and one right angle.

Isosceles triangle: An isosceles triangle is a triangle that has two sides of equal length.

Right isosceles triangle: An isosceles right triangle is defined as a right-angled triangle with an equal base and height which are also known as the legs of the triangle.

Obtuse isosceles: An isosceles obtuse triangle is a triangle in which one of the three angles is obtuse (lies between 90° and 180°), and the other two acute angles are equal in measurement.

Right triangle: A right triangle is a triangle in which one angle is 90°.

Hence, right isosceles triangle has exactly 2 equal sides and one right angle.

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Answer:

(2⁵/x²)⁴

(32/X²)

32⁴+x⁶

1,048,576 + X⁶

Step-by-step explanation:

i don't know if this is right. this is all I know

Another way to write that is:

\(\sqrt{2} =2^{\frac{1}{2} }\\\sqrt[3]{2} =2^{\frac{1}{3} }\\\\\\\\2^{\frac{1}{2} }*2^{\frac{1}{3} }\\ = 2^{\frac{1}{6} } \\\)

So the correct answer is A.

#Team Trees #Team Seas #PAW #Spread_Positivity

I hope this helps,

-Oceanbreeze24

Answer:

4.5%

Step-by-step explanation:

a. To simplify the integral ∫[(4x²-2)^(3/2)] dx, we can make the trigonometric substitution x = (sqrt(2/4))sec(t).

Let's solve for dx in terms of dt:

x = (sqrt(2/4))sec(t),

dx = (sqrt(2/4))sec(t)tan(t) dt.

Substituting these expressions into the integral, we have:

∫[(4x²-2)^(3/2)] dx = ∫(4(sqrt(2/4))sec(t)²-2)^(3/2)sec(t)tan(t) dt.

Simplifying the expression inside the integral:

(4(sqrt(2/4))sec(t)²-2) = 4(2/4)sec(t)² - 2 = 2sec(t)² - 2 = 2(tan²(t) + 1) - 2 = 2tan²(t).

Now, we can rewrite the integral as:

∫2tan²(t)sec(t)tan(t) dt.

Simplifying further:

∫2tan³(t)sec(t) dt = ∫(sqrt(2)tan³(t)sec(t)) dt.

At this point, we can use a trigonometric identity: tan³(t)sec(t) = sin(t).

Therefore, the integral becomes:

∫(sqrt(2)sin(t)) dt.

This integral is now simpler to evaluate. Once you find the antiderivative, you can convert back to the original variable x.

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Answer:

all you have to do is substitute the given x into the equations then graph it!

Step-by-step explanation:

no answer needed just explanation?

Answer:

there is a website called math.w.a.y (take out the dots) aand this is what i use to help me with equations like this

Step-by-step explanation:

This integral cannot be easily solved analytically. We would need to use numerical methods such as numerical integration or approximation techniques to find the length.

A parametric equation models a set of quantities as functions of one or more parameters, which are independent variables.

To find the length of the loop represented by the curve with parametric equations:

x = 9t − 3t³

y = 9t²

We can use the arc length formula for parametric curves:

L = ∫[a,b] √((dx/dt)² + (dy/dt)²) dt

where a and b are the parameter values that correspond to the start and end points of the loop.

First, let's find the derivative of x and y with respect to t:

dx/dt = 9 - 9t²

dy/dt = 18t

Next, let's calculate the integrand:

√((dx/dt)² + (dy/dt)²) = √((9 - 9t²)² + (18t)²)

                     = √(81 - 162t² + 81t⁴ + 324t²)

                     = √(405t⁴ - 162t² + 81)

Now we can integrate the expression above from the start to end values of t for the loop.

To find the start and end points, we set x = 0 and solve for t:

9t - 3t³ = 0

t(9 - 3t²) = 0

This equation gives us t = 0 and t = ±√3 as possible values for the start and end points of the loop. However, since we are looking for the length of the loop, we consider only the positive values of t.

So, the length of the loop is given by:

L = ∫[0,√3] √(405t⁴ - 162t² + 81) dt

Unfortunately, this integral cannot be easily solved analytically. We would need to use numerical methods such as numerical integration or approximation techniques to find the length.

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What are the term associated with set?

Now, According to the question:

Let's know:

What are Sets?

A set is a well-defined collection of objects. Sets are named and represented using a capital letter. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.

Any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.

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Answer:y=124

x=67

Step-by-step explanation:

y=180-56

y=124

x=67

The empirical rule may be used to determine the percentage of data values that must be within only one, two, and three standard deviations of the mean for data having a bell-shaped distribution.

The 68 95 99 rule, commonly referred to as the empirical rule in statistics, asserts that given normal distributions, 68% of observed data points will fall within one standard deviation from the mean, 95% will fall between two standard deviations, and 99.7% will happen within three standard deviations.

Fairly anticipate that your data will resemble a normal distribution, the empirical rule, the mean, as well as the standard deviation become even more beneficial. Determine probabilities and percentages for many events just by knowing these two statistics.

The term "empirical rule" derives from empirical research, which relies on measurements and observations of actual results rather than theory. In other words, the term "empirical" denotes a foundation in actuality.

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Answer:70

Step-by-step explanation:

70 divided by 5 equals 14

Option A. If the alternative hypothesis of the test had been lower-tailed instead of two-tailed, the conclusion of the test would be different.

Recall that a two-tailed test is used when the alternative hypothesis is that the population parameter is different from the null hypothesis value in any direction, while a lower-tailed test is used when the alternative hypothesis is that the population parameter is less than the null hypothesis value.

In the given scenario, if the alternative hypothesis of the test had been lower-tailed instead of two-tailed, we would have tested the following null and alternative hypotheses:

H0: Pharaoh's translation is not worse than the other software's translation.

Ha: Pharaoh's translation is better than the other software's translation.

In this case, we would have calculated the p-value for the lower tail of the sampling distribution, and compared it to the significance level alpha. If the p-value is less than alpha, we would reject the null hypothesis and conclude that Pharaoh's translation is better than the other software's translation. If the p-value is greater than alpha, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that Pharaoh's translation is better than the other software's translation.

Therefore, the correct answer to the question is option A: Unlike the two-tailed test, we would conclude that there is a difference between Pharaoh's translation and the translation of the other software.

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The correct option among the given choices is $4,918.16.

To calculate the future value, we can use the formula for compound interest:

FV = P * (1 + r/n)^(n*t)

Where:

FV is the future value

P is the principal amount (initial investment)

r is the interest rate (in decimal form)

n is the number of compounding periods per year

t is the number of years

In this case, the principal amount is $300, the interest rate is 12 percent (0.12), the compounding is semiannual (n = 2), and the time period is 24 years. Plugging these values into the formula, we get:

FV = $300 * \((1 + 0.12/2)^(2*24)\)

  ≈ $300 * \(1.06^{48}\)

  ≈ $300 * 4.91816

  ≈ $1,475.45

Therefore, the future value of $300 after 24 years, compounded semiannually at an interest rate of 12 percent, is approximately $4,918.16. Among the given options, the closest match is $4,918.16.

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9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

Maybe you want to find x such that ...

  2/7 = x/(x +10)

  2(x +10) = 7x . . . . . . multiply by 7(x+10)

  20 = 5x . . . . . . . . . . subtract 2x, simplify

  4 = x . . . . . . . . . . . . divide by 5

_____

Additional comment

You can almost solve this "by inspection" if you recognize the difference of the denominator and numerator is 5 on the left and 10 on the right. If you multiply the fraction on the left by 2/2, you get 4/14, the values in x/(x+10) in the fraction on the right.

Therefore, the annual annuity payment can be approximately $6,069,727.

To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:

PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]

Where:

PMT = Annual annuity payment

PV = Present value of the annuity

r = Annual interest rate

n = Number of periods

Given:

PV = $230 million

r = 8% = 0.08

n = 40 years

Using the formula, we can calculate the annual annuity payment:

PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]

PMT ≈ $6,069,727

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The building have to rent 14 offices with area 500 ft² each so that the total acquired space is  7000 ft².

What is division?

One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

The area of one office is 500 ft².

The total space acquired by the office building is 7000 ft².

To find the number of offices the building is renting, use the formula of division -

Number of office = Total space rented / Area of one office

Let the value of number of office rented be x.

Substituting the values in the equation -

x = 7000/500

x = 14

Therefore, the number of offices being rented is 14.

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To calculate the annualized rate of return, we can use the formula for compound interest. The correct answer is 11.66%.

The formula for compound interest is given by: A = P(1 + r)^t, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

In this case, the initial investment (P) is BD 14,000, the final amount (A) is BD 52,600, and the time (t) is 12 years. We need to solve for the annual interest rate (r).

\(BD 52,600 = BD 14,000(1 + r)^{12}\)

By rearranging the equation and solving for r, we find:

\((1 + r)^{12} = 52,600/14,000\)

Taking the twelfth root of both sides:

\(1 + r = (52,600/14,000)^{(1/12)}\\r = 0.1166 / 11.66 \%\)

Therefore, Areej has earned an annualized rate of approximately 11.66% on this investment.

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The domain of a function is the set of numbers that can go into a given function.

The set of input values (x) for which a function generates an output value is known as the domain of the function (y).

we can write \(y = f(x).\)

domain is the full set of x-values that can be plugged into a function to produce a y-value.

The most effective approach to finding a domain will depend on the type of function.

The domain is expressed using an open bracket or parenthesis, the domain's two endpoints separated by a comma, and then a closed bracket or parenthesis.

To find domain of function we should know the property of that function like what the function can take inside it.

Like if we consider square root function \(\sqrt{x}\) so inside root negative numbers are not allowed so value of x should be positive means x>=0

So domain of square root function [0, ∞).

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Answer:

Step-by-step explanation:

Initial price of both machines is $360

Price after 30% mark down:

Price after 10% and then 20% mark down:

The sale price of the first washing machine is lower:

Answer:

The sale price of the first washing machine is $252

Step-by-step explanation:

First washing machine

Given information:

If the washing machine is marked down by 30%, the sale price is 70% of the original selling price as 100% - 30% = 70%.

To find the sale price, calculate 70% of $360:

\(\begin{aligned}\implies \sf 70\% \:of\: 360 & = \sf 0.7 \times 360\\& = \sf 252 \end{aligned}\)

Therefore, the sale price of Washing Machine 1 is $252.

Second washing machine

Given information:

If the washing machine is marked down by 10%, then has an additional discount of 20% applied, the sale price can be calculated by first finding 90% of the selling price, then finding 80% of the reduced price:

\(\begin{aligned}\implies \sf 90\% \:of\: 360 & = \sf 0.9 \times 360\\& = \sf 324\end{aligned}\)

\(\begin{aligned}\implies \sf 80\% \:of\: 324 & = \sf 0.8 \times 324 \\& = \sf 259.2\end{aligned}\)

Therefore, the sale price of Washing Machine 2 is $259.50.

Joanne should buy the first washing machine rather than the second, as after the discounts are applied, the first washing machine is cheaper than the second by $7.50.

The farm for sale measures 1120 acres.  

How many acres are equivalent to one square mile?

1 square mile= 640 acres.

To convert square miles to acres, we need to know that there are 640 acres in one square mile.

Given that the farm for sale measures one and three-quarter square miles, we can calculate the number of acres as follows:

1 and 3/4 square miles = 1.75 square miles  

Number of acres = 1.75 square miles * 640 acres/square mile

Number of acres = 1120 acres

Therefore, the farm for sale measures 1120 acres.

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Answer: Yes

Step-by-step explanation:

If you plug in (0,0) to the equation you get: 0=4(0)

which is 0=0

Therefore, (0,0) is is a solution to y=4x

Answer:

Yes

Step-by-step explanation:

You can quickly test this by plugging (0, 0) into the equation. Remember that the first point in a coordinate is x, and the second is y.

y = 4x

0 = 4(0)

0 = 0

Answer:

Step-by-step explanation:

\(V=(4.5)(2)(2)=18 ft^3\\A=(4.5)(2)=9 ft^2\)

Answer:

the answer is 20% increase I used a calculator but you should be able to do that math by taking 40 dividing by five where that ends up being 8 that is 20 percent of 40 so adding that back to the original amount is a 20 percent increase hope this helps

Step-by-step explanation: