The point P = (-2, -6) on the circle x² + y² = r² is also on the terminal side of an angle θ in standart position find sinθ, cosθ, tanθ, cscθ, secθ, and cotθ

Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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The probability of getting 1 on two of the dice, given that the sum of the numbers on the three dice is 7, is:

P(A|B) = P(A and B) / P(B) = 3/3 = 1

To solve this problem, we need to use conditional probability.

We are given that the sum of the numbers on the three dice is 7, so let's first find the number of ways that we can obtain a sum of 7.

There are six possible outcomes when rolling a single die, so the total number of outcomes when rolling three dice is 6 x 6 x 6 = 216.

To get a sum of 7, we can have the following combinations:

- 1, 2, 4
- 1, 3, 3
- 2, 2, 3

So there are three possible outcomes that give us a sum of 7.

Now let's find the number of ways that we can obtain 1 on two of the dice.

There are three ways that this can happen:
- 1, 1, x
- 1, x, 1
- x, 1, 1

where x represents any number other than 1.

We need to find the probability of getting 1 on two of the dice, given that the sum of the numbers on the three dice is 7. This is a conditional probability, which is given by:
P(A|B) = P(A and B) / P(B)

where A is the event of getting 1 on two of the dice, and B is the event of getting a sum of 7.

The probability of getting 1 on two of the dice and a sum of 7 is the number of outcomes that satisfy both conditions divided by the total number of outcomes:

- 1, 1, 5
- 1, 5, 1
- 5, 1, 1

So there are three outcomes that satisfy both conditions.

Therefore, the probability of getting 1 on two of the dice, given that the sum of the numbers on the three dice is 7, is:
P(A|B) = P(A and B) / P(B) = 3/3 = 1

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Answer:

well instead of being the value of 50 it would be the value of 5.

Step-by-step explanation:

It's being moved to the ones place

Answer:

it would be 5, if it moves to the right it takes the place of the 6

Answer:

i think the answer is C. 1/2

The expression of linear inequalities that represents Tami's earnings is as follows: 6x + 12y ≥ 150.

A linear inequality is a mathematical expression that involves a linear function and a relational operator such as <, >, ≤, ≥, or ≠ and it can be used to compare two expressions or values. It defines a range of values that satisfy inequality.

For the scenario painted above, we see that Tani is meant to earn a minimum of $150 Thus, the greater than or equal to symbol  ≥ should be used for the expression. $6 per hour and $12 per hour are also well represented in the equation.

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Answer:

go to khan academy

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

y=3x+1; 6x-2y=5

6x-2(3x+1)=5    replacing y with 3x+1 because y is equal that equation

6x -6x-2=5

0=7-->no solution

Answer:

The exact form is 161/12 but the mixed number is 13 5/12

Step-by-step explanation:

You need to find a common donominator for all of the fractions 2,3,4 all go into 12 so I multiplied 1/2x6 (multiply both 1 and 2 by 6 same with all the others) then 2/3x4 and 1/4x3. That should get you 6/12 8/12 and 3/12. Add all of those and then add all of the whole numbers.

Answer/Step-by-step explanation:

In order, from least to greatest, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Answer:

\(3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}\)

Step-by-step explanation:

Given

\(3\sqrt{5}\:-\:3\sqrt{11}+2\sqrt{121}-3\sqrt{90}\)

Required

Simplify the expression

\(3\sqrt{5}\:-\:3\sqrt{11}+2\sqrt{121}-3\sqrt{90}\)

Express the square root of 121 as 11

\(3\sqrt{5}\:-\:3\sqrt{11}+2 * 11-3\sqrt{90}\)

\(3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{90}\)

Express 90 as 9 * 10

\(3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{9 * 10}\)

Split the surd to 2

\(3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{9} * \sqrt10}\)

Express the square root of 9 as 3

\(3\sqrt{5}\:-\:3\sqrt{11}+22-3 * 3 * \sqrt10}\)

\(3\sqrt{5}\:-\:3\sqrt{11}+22-9 * \sqrt10}\)

\(3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}\)

Hence, the result of the expression is

\(3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}\)

Answer: GCF = 9

Step-by-step explanation: 45/9 = 5 and 81/9 = 9. 5/9 is as much as you can simplify. Brainliest please?

Greatest common factor is 9

Step-by-step explanation:

The biggest factor that matches 45 and 81 is 9.

45: 1,3,5,9,15,45

81: 1,3,9,27,81

Answer:

53361

Step-by-step explanation:

All you need to do is sub in 225 for x.

So: 225^2+12(225)+36

= 53361

(11+21)-(3-101)=(11+21-3-10=(11-3)+(21-101=8-18=53

Answer:

Plural of Axis. Pronounced "ak-seez". Axes often means the "x" and "y" lines that cross at right angles to make a graph. See: Axis (graph) Cartesian Coordinates.

Step-by-step explanation:

The prime factors of 87 are 3 and 39. This can be found out by using prime factorisation method.

An integer that evenly splits a number, leaving no remainder, is referred to as a factor. Using division principles and divisibility rules, one can identify a number's factors.

The numbers that divide 87 without leaving a remainder are known as the factors of 87. In other terms, we can say that it will be completely divided by the factors of 87.

Although 87 can be divided into positive and negative components, it cannot be divided into decimals or fractions. The result of splitting 87 by its factor yields a quotient that is also a factor of 87.

A factor tree can be used to find out the prime factors of 87. It can be written as,

87 = 3 × 29

Consequently, 3 and 29 are the prime factors of 87.

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9514 1404 393

Answer:

  54/(-6) = -9

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

  6·9 = 54

From your knowledge of signed arithmetic, you know that ...

  54/(-6) = -(54/6) = -(6·9)/6 = -9

The expression is not undefined. The quotient is -9.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The equation of the line is y = x + 5

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line y = mx + c

Now,

The equation of the line passes through the points:

(-2, 3) and (2, 7).

This means,

(-2, 3) = (a, b)

(2, 7) = (c, d)

The slope is given as:

Slope:

= (d - b) / (c - a)

= (7 - 3) / (2 + 2)

= 4 / 4

= 1

Now,

The line passes through point (-2, 3) = (x, y) so,

3 = (-2) x 1 + c

3 = -2 + c

c = 3 + 2

c = 5

Now,

m = 1

c = 5

The equation of the line is y = x + 5

Thus,

The equation of the line is y = x + 5

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Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{(m-n)}\)

\(\frac{2^{5} }{8}\)

= \(\frac{2^{5} }{2^{3} }\)

= \(2^{(5-3)}\)

= 2²

We need to know about the concept of dilation to understand the question.

The coordinate of C' will be 1/2 times it's original coordinate.

Dilation is a form of transforming an object by changing it's size or shape by either increasing or decreasing it's dimensions with the use of scaling factors.For example if a shape is said to have been dilated by a factor of 2 it simply means that the object has been doubled it's size.The coordinates of the new object will be twice of the original coordinates. So if one of the coordinate was (1,1) then the coordinates of that point will be (2,2) after dilation.

Here in the question it is said that ABCD has been dilated by a factor of 1/2, so to find the new coordinates of the point C' we will have to multiply the original coordinates at C by 1/2.

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Answer:

729

Step-by-step explanation:

The equation for the plane that passes through the point (3, 6, −7) and is perpendicular to the line v = (0, −6, 5) t(1, −2, 3) is given by: Ax + By + Cz + D = 0, where A, B and C are the components of the normal vector to the plane and (x, y, z) are the coordinates of a point on the plane and D is the constant.

To calculate A, B, C and D we need to take the dot product of the normal vector and the position vector.  Since the line is perpendicular to the plane, any vector parallel to the line can be a normal vector to the plane. Hence, the direction vector of the line, i.e. (1, -2, 3), is a normal vector to the plane.

Substituting the coordinates of the given point (3, 6, -7) and the components of the normal vector (1, -2, 3) into the equation of the plane, we get: 1(3) - 2(6) + 3(-7) = d => d = -24. Therefore, the equation of the plane is: x - 2y + 3z = -24

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Answer: 1/13

Step-by-step explanation:

1/13 is the simplest form of 4/52, which is the number of king cards to the number of cards total.

Answer:

yes they are because they have matching sides

The distance of the point P(5,7,5) to the plane through the three points Q(4,2,3), R(5,-1,2), and S(8,7,8) is 16 / sqrt(26) units.

We have to find the distance between the point P(5,7,5) and the plane through the three points Q(4,2,3), R(5,-1,2), and S(8,7,8).

Using the equation of a plane ax + by + cz + d = 0, we can find the equation of the plane that passes through Q, R, and S.

Let the equation be ax + by + cz + d = 0.A plane that passes through three points has an equation given by| x - x1 y - y1 z - z1 || x2 - x1 y2 - y1 z2 - z1 || x3 - x1 y3 - y1 z3 - z1 | = 0

where the points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) are given.So, the equation of the plane passing through Q, R, and S is| x - 4 y - 2 z - 3 || 5 - 4 -1 - 2 2 - 3 || 8 - 4 7 - 2 8 - 3 | = 0

i.e.,| x - 4 y - 2 z - 3 || 1 -3 -1 || 4 5 5 | = 0or,| x - 4 y - 2 z - 3 || -12 -4 16 | = 0or, -12(x - 4) - 4(y - 2) + 16(z - 3) = 0or, -3x - y + 4z - 8 = 0.

The distance between the point (x1, y1, z1) and the plane ax + by + cz + d = 0 is given by| ax1 + by1 + cz1 + d | / sqrt(a² + b² + c²).

So, the distance between P and the plane is| (-3)·5 + (-1)·7 + 4·5 - 8 | / sqrt((-3)² + (-1)² + 4²)= 16 / sqrt(26) units (approx).

Therefore, the distance of the point P(5,7,5) to the plane through the three points Q(4,2,3), R(5,-1,2), and S(8,7,8) is 16 / sqrt(26) units.

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The amount needed for retirement, rounded to the nearest cent, is option b. $398,407.85.

To determine the amount needed for retirement, we can use the present value formula for an annuity. In this case, we want to calculate the present value of the monthly withdrawals of $2,154 for 30 years, with a monthly interest rate of 5.1%.

First, we need to convert the interest rate to a monthly decimal rate. We divide 5.1% by 100 to get 0.051, and then divide it by 12 to get 0.00425.

Next, we use the formula: PV = PMT * (1 - (1 + r)^(-n)) / r, where PV is the present value, PMT is the monthly withdrawal amount, r is the monthly interest rate, and n is the total number of withdrawals.

Plugging in the values, we have:

PV = $2,154 * (1 - (1 + 0.00425)^(-12*30)) / 0.00425

Using a calculator, we find that PV is approximately $398,407.85.

Therefore, the amount needed for retirement, rounded to the nearest cent, is option b. $398,407.85. This amount will allow the individual to make monthly withdrawals of $2,154 for 30 years from an account paying 5.1% compounded monthly.

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Let's say for example you wanted to graph the linear equation \(y = 2x+5\)

At minimum, we'll need 2 points to form this line.

To get any point of the form (x,y), we plug in a number for x to find a corresponding number for y.

For example, replace x with 0 to find that...

\(y = 2x+5\\\\y = 2(0)+5\\\\y = 0+5\\\\y = 5\\\\\)

Therefore, x = 0 leads to y = 5. So the point (0,5) is on the line.

Then we repeat this process for other x values. Let's try x = 1

\(y = 2x+5\\\\y = 2(1)+5\\\\y = 2+5\\\\y = 7\\\\\)

Telling us that (1,7) is also on this line. We have enough to graph this equation. Plot the two points (0,5) and (1,7). Then draw a straight line through them. Extend this line as far as you can to the left and right. The graph is shown below.

We can keep going to get other points like (2,9) and (3,11) and (4,13) and so on. A table is a way to keep track of the xy values.

\(\begin{array}{|c|c|}\cline{1-2}\text{x} & \text{y}\\ \cline{1-2}0 & 5\\ \cline{1-2}1 & 7\\ \cline{1-2}2 & 9\\ \cline{1-2}3 & 11\\ \cline{1-2}4 & 13\\ \cline{1-2}\end{array}\)

Each time x goes up by 1, y goes up by 2. This directly ties to the slope of 2/1 = 2.

The radius of the circular slice is 2.0 inches.

The diameter of the grapefruit is given as 6.0 inches, and since diameter is the distance from one end of the sphere to another end passing through the center, it means the radius is half of the diameter, which is 3.0 inches.

If an amateur fruit slicer misses its center by one inch, then it means the center is not cut off, and we are to find the radius of the circular slice.

From the diagram above, the distance between the point A (where the slicer missed) and the center is 1.0 inch.

herefore, the radius of the circular slice = radius of the grapefruit - distance between A and the center= 3.0 - 1.0= 2.0 inches.

Summary: The radius of the circular slice of the grapefruit is 2.0 inches.

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Answer:

y subtracted from 10 is

10 - y

Hope it will help :)

Answer: D: 10 - y

Step-by-step explanation:

we can rule out option B and C since there isn't a subtraction sign

so now we have A and D

The answer isn't A because thats 10 being subtracted from y

Answer:

Step-by-step explanation:

Solve for x by cross multiplying. Hope this helps! <3

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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