Find the given trigonometric ratio in the problem below.

Answer:

y intercept: (0,4)

Step-by-step explanation:

Answer:

8+k2-6>8(k+2)-4k

Step-by-step explanation:

8+7×2-6 and 8(7+2)-4×7

8+14-16 and (56+16)-28

6 and 44

Answer:

Acct A      $96.80

Acct B      $48.40

Step-by-step explanation:

I = PRT

Acct A      I = 1000(.0242)(4)

                  = $96.80

Acct B      I = 1000(.0242)2)

                  = $48.40

Answer:

x=y=-2

Step-by-step explanation:

Comparing these ordered pairs, we will get

4^(1/x)=1/2 and 9^(1/y)=1/3

x=-2 and y=-2

Answer:

x = y = - 2

Step-by-step explanation:

Using the rule of radicals/ exponents

\(a^{\frac{m}{n} }\) = \(\sqrt[n]{a^{m} }\) , \(a^{-m}\) = \(\frac{1}{a^{m} }\) , \((a^m)^{n}\) = \(a^{mn}\)

Given

\(\sqrt[x]{4}\) = \(\frac{1}{2}\) , then

\(\sqrt[x]{2^{2} }\) = \(\frac{1}{2}\)

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

Since the bases on both sides are equal, both 2 , then equate exponents

\(\frac{2}{x}\) = - 1 ( multiply both sides by x )

2 = - x , that is

x = - 2

Similarly

\(\sqrt[y]{9}\) = \(\frac{1}{3}\) , then

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

\(3^{\frac{2}{y} }\) = \(3^{-1}\)

Equating the exponents gives

\(\frac{2}{y}\) = - 1 ⇒ - y = 2 ⇒ y = - 2

We can write\(:∫0¹(1-x^q)^1/pdx = ∫1⁰(1-v)^1/pv^(1/q - 1) dv.\)

To prove that \(∫0¹(1-x^p)^1/qdx=∫0¹(1-x^q)^1/pdx,\) we use the substitution u = x^p and u = x^q respectively.

Using the substitution method, we have the following:  Let\(u = x^p,\) then \(du/dx = px^(p-1)\)and \(dx = (1/p)u^(1/p - 1) du.\)

Hence we can write\(:∫0¹(1-x^p)^1/qdx = ∫0¹(1-u)^1/qu^(1/p - 1) duLet v = (1 - u), then dv/dx = -du and dx = -dv.\)

Therefore, we can write:\(∫0¹(1-u)^1/qu^(1/p - 1) du = ∫1⁰(1-v)^1/qv^(1/p - 1) dvS\)

Since p and q are both positive, 1/p and 1/q are positive, which implies that the integrals are convergent. Now let us apply the same technique to the other integral. I\(f v = x^q, then dv/dx = qx^(q-1) and dx = (1/q)v^(1/q - 1) dv.\)

Hence we can write:∫\(0¹(1-x^q)^1/pdx = ∫1⁰(1-v)^1/pv^(1/q - 1) dv.\)

Using the identity\((1 - u)^1/q = (1 - u^q)^(1/p),\)

we can write:\(∫0¹(1-x^p)^1/qdx = ∫0¹(1 - (x^p)^q)^(1/p)dx = ∫0¹(1 - x^q)^(1/p)dx∫0¹(1-x^q)^1/pdx = ∫0¹(1 - (x^q)^p)^(1/q)dx = ∫0¹(1 - x^p)^(1/q)dx.\)

Hence, we have shown that \(∫0¹(1-x^p)^1/qdx = ∫0¹(1 - x^q)^(1/p)dx.\)

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The first differential equation has two stationary points, y = 0 and y = 1, with y = 0 being stable and y = 1 being unstable. The second differential equation has no stationary points, and therefore, no equilibrium points to analyze.

To draw the phase line for the first differential equation dy/dt = y^3(y - 1), we can locate the critical points by setting dy/dt = 0. This gives us two stationary points: y = 0 and y = 1. We can now analyze the dynamic stability of these points. For y = 0, we observe that when y < 0, dy/dt < 0, indicating that y = 0 is a stable equilibrium point. When y > 0, dy/dt > 0, indicating that y = 0 is an unstable equilibrium point. For y = 1, we find that dy/dt < 0 when y < 1 and dy/dt > 0 when y > 1, meaning that y = 1 is an unstable equilibrium point.

Moving to the second differential equation dy/dt = y^2 - 5x + 6, we notice that it is not in the standard form for a phase line analysis. We need to express it as dy/dt = f(y), where f(y) is a function of y only. By rearranging the equation, we have dy/dt = y^2 - 5x + 6 = y^2 + 6 - 5x. Since the term -5x is not a function of y, it does not affect the analysis of the equilibrium points. Thus, we can focus on the function f(y) = y^2 + 6. In this case, there are no stationary points since f(y) = y^2 + 6 is always positive. Hence, there are no equilibrium points to analyze for this differential equation.

In summary, the first differential equation has two stationary points, y = 0 and y = 1, with y = 0 being stable and y = 1 being unstable. The second differential equation has no stationary points, and therefore, no equilibrium points to analyze.

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Answer:

b

Step-by-step explanation:

took the test i got bj : fz wf

The value of m in the inequality 28 > 4+1.5m is 16

A relationship between two expressions or values that are not equal to each other is called 'inequality.

To solve for m, we need to isolate it on one side of the inequality.

We can start by subtracting 4 from both sides:

28 - 4 > 1.5m

Simplifying:

24 > 1.5m

Next, we can divide both sides by 1.5:

16 > m

So Kate can travel at most 16 miles in the cab if she wants to spend no more than $28 on cab fare.

Therefore, the value of m in the inequality 28 > 4+1.5m is 16

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Answer:

look at the photo.............

There are six possible interactions in a 2 × 3 factorial ANOVA. The correct option is (d) 6.

In a 2 × 3 factorial ANOVA, there are two factors, each with two levels and three levels, respectively. The number of interactions that can be observed in a factorial ANOVA is determined by the product of the number of levels of each factor.

In this case, the first factor has two levels, and the second factor has three levels.

Therefore, the number of possible interactions is given by multiplying the number of levels of the first factor by the number of levels of the second factor: 2 × 3 = 6.

Each interaction represents a unique combination of the levels of the two factors.

For example, one interaction might represent the effect of the first factor at the first level interacting with the second factor at the first level, while another interaction might represent the effect of the first factor at the second level interacting with the second factor at the third level, and so on.

Therefore, the correct answer is d. 6, as there are six possible interactions in a 2 × 3 factorial ANOVA.

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The price of a restaurant meal for the family is $1,978.75.

let's assume the price of a restaurant meal is x dollars.

if the family buys 4 restaurant meals, the total cost would be 4x dollars.

we are given that the family has a budget of $7,915 for sit-down restaurant meals and fast food. this means that the total cost of the meals (including both restaurant meals and fast food) is $7,915.

if the family chooses to spend the entire budget on restaurant meals, without buying any fast food, the cost would be 4x dollars.

so, we can set up the equation:

4x = 7,915

apologies for the brief response. here's a more detailed explanation:

let's assume the price of a restaurant meal for the family is x dollars.

if the family buys 4 restaurant meals, the total cost would be 4 times the price of a restaurant meal, which is 4x dollars.

we are given that the family has a budget of $7,915 for sit-down restaurant meals and fast food.

if the family decides not to buy any fast food and spends the entire budget on restaurant meals, the total cost of the meals would be $7,915.

so, we can set up the equation:

4x = 7,915

to find the price of a restaurant meal (x), we need to solve this equation.

dividing both sides of the equation by 4, we get:

x = 7,915 / 4

x = 1,978.75 75.

this means that if the family decides to buy 4 restaurant meals without purchasing any fast food, each meal would cost $1,978.75.

to find the price of a restaurant meal (x), we divide both sides of the equation by 4:

x = 7,915 / 4

x = 1,978.75

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Answer:

I think it's c all real number

Answer:

B. Positive real numbers (y > 0)

Step-by-step explanation:

Just took the quiz

Answer:

He is 2 years old.

Step-by-step explanation:

She is 22, in 8 years she will be 30. 30 is 3×10. At that time, her brother will be 10; that is 8 years from now. So now, the little brother is 10-8 = 2 years old.

If you must show algebra work:

x = brother's age now.

x+8=brother's age in 8 years.

YingYu's age in 8 years = 3 × brother's age in 8 years

22+8 = 3(x+8)

30 = 3x +24

6 = 3x

2 = x

Answer:

The answer is 4

Step-by-step explanation:

the general solution is; y = x²/4 + c1√(x²+y²)y = - x²/4 + c2√(x²+y²) where c1 and c2 are constants.  Thus, a general solution is;y = x²/4 ± c√(x²+y²) where c = √(c1² + c2²)

Given equation is 3xyy' = 3y² + 4x√(x²+y²)

For x, y>0The given differential equation is a first-order homogeneous differential equation.

To solve the differential equation we need to substitute y= vxThen y' = v + x v'

By substituting these values in the given equation,

we have;

3xvx(v+xv') = 3v²x + 4x√(x² + v²x²)3v(v+xv')

= 3v² + 4√(x² + v²x²)

⇒ 3v^2 + 3vxv' = 3v² + 4√(x² + v²x²) - 3v(v+xv')

⇒ 3vxv' + 3v² - 3vxv' = 4√(x² + v²x²) - 3v²

⇒ 3v² = 4√(x² + v²x²) - 3v²

⇒ 6v² = 4√(x² + v²x²)⇒ 9v⁴ = 16x²v² + 16x²v⁴

⇒ 9v⁴ - 16x²v² - 16x²v⁴ = 0

⇒ 9v⁴ - 16x²v² = 0 (1 - 16v²/x²) = 0⇒ 1 - 16v²/x² = 0

⇒ 16v² = x²⇒ v² = x²/16

For v = x/4, y = vx = x²/4 and y' = v + x v' = x/4 + x/4 v' = y/4x + √(x²+y²)For v = - x/4, y = vx = - x²/4 and

y' = v + x v' = - x/4 + x/4 v' = y/4x - √(x²+y²)

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Answer:

B, or -75

Step-by-step explanation:

f(x) is a function of x.

If f(x) = 50 when x = -10, you can rearrange this information.

f(-10) = 50

f = -5

If f = -5...

-5 ( 15) = -75

Answer:

Step-by-step explanation:

x = 4

=> y = 3

x = 8

=> y = -2

x = 12

=> y = -5

Answer: slope is 4, y intercept is ( 0,8) , x intercept is (-2,0)

Step-by-step explanation: graph the line using the slope and and y intercept.

Answer:

The amount of apples is the Xs and The cost is the Ys

Step-by-step explanation:

Theorem 5.5B is a helpful theorem that relates the measures of angles in a triangle to the lengths of the sides opposite those angles. Specifically, it states that if one angle in a triangle has a greater measure than another angle, then the side opposite the angle with the greater measure will be longer than the side opposite the angle with the smaller measure.

This theorem can be useful in a variety of situations, such as when solving for unknown side lengths or angles in a triangle.

To understand why this theorem works, it can be helpful to think about the relationship between the measures of angles and the lengths of sides in a triangle. For example, we know that in any triangle, the sum of the measures of the three angles is always 180 degrees. We also know that the length of one side of a triangle is related to the measures of the angles opposite that side, according to the Law of Sines or the Law of Cosines.

Using these relationships, we can see why Theorem 5.5B makes sense. If one angle in a triangle is larger than another angle, then the remaining angle must be smaller to ensure that the sum of the angles adds up to 180 degrees. This means that the side opposite the larger angle must be longer than the side opposite the smaller angle, since the length of a side is related to the measure of the angle opposite that side.

In summary, Theorem 5.5B provides a helpful way to relate the measures of angles and the lengths of sides in a triangle. By understanding this theorem, we can solve problems involving unknown side lengths or angles with greater ease and accuracy.

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The probability that the salesperson will make exactly two sales in a day is 0.1489, the probability that the salesperson will make at least two sales in a day is 0.1451, and the expected number of sales per day is 0.8.

Let X be the number of sales made per day by the salesperson.

Then X follows a binomial distribution with parameters n = 8 and p = 0.10.a. To find the probability that the salesperson will make exactly two sales in a day, we need to find P(X = 2).

P(X = 2) = nCx * p^x * q^(n-x) = 8C2 * (0.10)^2 * (0.90)^6 = 28 * 0.01 * 0.5314 = 0.1489

Therefore, the probability that the salesperson will make exactly two sales in a day is 0.1489.

b. To find the probability that the salesperson will make at least two sales in a day, we need to find P(X ≥ 2).

P(X ≥ 2) = 1 - P(X < 2) = 1 - [P(X = 0) + P(X = 1)] = 1 - [(8C0 * (0.10)^0 * (0.90)^8) + (8C1 * (0.10)^1 * (0.90)^7)] = 1 - [1 * 0.90^8 + 8 * 0.10 * 0.90^7] = 0.1451

Therefore, the probability that the salesperson will make at least two sales in a day is 0.1451.

c. Expected number of sales per day = E(X) = n * p = 8 * 0.10 = 0.8

Therefore, the expected number of sales per day is 0.8.

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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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The sine and cosine rule is typically used to find the measure of angles in trigonometry.

It should be noted that the sine rule is used when we are given:

The cosine rule is used when we are given:

The advantage is that it can help us understand the connections between the sides and their angles.

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Answer: hi! for the denominators (5, 9, 7) the least common multiple

Step-by-step explanation:

(LCM) is 315.

LCM(5, 9, 7)

Therefore, the least common denominator (LCD) is 315.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

3/5 = 3/5 × 63/63 = 189/315

4/9 = 4/9 × 35/35 = 140/315

6/7 = 6/7 × 45/45 = 270/315

Answer:

$1.73 per pint

Step-by-step explanation:

2 quarts is the equivalent of 4 pints. Therefore, in order to get the price per pint you must divide 6.92 by 4. This gives you $1.73 per pint.

Answer:

216 cm^2

Step-by-step explanation:

15^2 -3^2 = 225 -9

= 216

Based on the given information, we can conclude that tuition at Penn State has increased more rapidly than inflation.

The price index measures the average change in prices of a basket of goods and services over time. In this case, the price index increased from 207.34 in 2007 to 226 in 2012, indicating an overall inflation rate of approximately 9% over that period. On the other hand, tuition at Penn State increased from $6,142 to $7,562, representing an increase of approximately 23%.

When comparing the rates of increase, we can see that tuition has outpaced inflation. This implies that the cost of education at Penn State has been rising more rapidly than the general increase in prices for goods and services. It suggests that factors specific to the education industry, such as rising costs of resources, facilities, and personnel, have contributed to the higher tuition rates.

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The complete question is:

Assume tuition at Penn State cost $6,142 (per semester) in 2007 and $7,562 in 2012. If the price index was 207.34 in 2007 and 226 in 2012, then we could say:

By taking the average of the two middle numbers, Diane ensures that the median represents the central tendency of the dataset when there are an even number of values.

When there are two middle numbers in a set of scores, Diane can determine the value of the median by taking the average of the two middle numbers.

To find the median, Diane should follow these steps:

1. Arrange the scores in ascending order.

2. Identify the two middle numbers. If there is an even number of scores, there will be two middle numbers.

3. Take the average of the two middle numbers to determine the median value.

For example, let's say Diane has the following set of scores: 82, 75, 90, 86, 79, 88. To find the median, she would follow these steps:

1. Arrange the scores in ascending order: 75, 79, 82, 86, 88, 90.

2. Identify the two middle numbers: 82 and 86.

3. Take the average of the two middle numbers: (82 + 86) / 2 = 84.

Therefore, in this case, the median of the set of scores is 84.

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The width of each locker is 1 1/4 foot.

We have,

Length = 1 foot

Volume = 7 1/2 cubic feet

Height = 6 foot

So, Volume of Prism = l w h

7 1/2 = (1) w (6)

15/2 = 6w

w= 15/(2 x 6)

w = 5/4

w= 1 1/4 foot

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