Triangle HOP has coordinates H (2, 1), O (-3, 4), and P (5, 7). Determine the coordinates of the
image of AHOP after each rotation.
a A rotation 90° clockwise about the origin
b) A rotation 90° counterclockwise about the origin
A rotation 180° about the origin

Answer:

divide -4 from 20 so t is -5

Step-by-step explanation:

Answer:

t=-5

Step-by-step explanation:

divide both sides by -4 now we have t=-5

Answer:The domain of the function A(x) = -220x + 4180 represents the valid inputs or values of x in the context of the problem. In this case, the context is the monthly spending on advertisements for a realtor with a budget of $4,180.

Since the realtor's budget is fixed at $4,180, the domain of the function would be the range of valid values for x that represent the number of months the realtor can spend on advertisements.

In this situation, it would be reasonable to assume that the realtor cannot spend a negative number of months on advertisements. Additionally, the realtor cannot spend more months on advertisements than the total duration of their budget, which is determined by dividing the budget by the monthly spending.

To find the domain, we need to consider the restrictions mentioned above. Therefore, the domain would be:

x ≥ 0 and x ≤ 4180 / 220

Simplifying the inequality:

x ≥ 0 and x ≤ 19

So, the domain of the function A(x) would be the set of non-negative integers less than or equal to 19.

The parametric equation for the line segment from (−4, 14, 32) to (10, −9, 46), using the parameter t is r(t) = (-4+14t, 14-23t, 32+14t), for 0<= t <=1.

The given points are (-4,14,32) and (10,-9,46).

To find the parametric equations for the line segment we need to follow the below steps.

Step 1: Calculate the direction vector of the line segment. We use the difference of the given points for this purpose.  Let d= direction vector = (10,-9,46)-(-4,14,32)  = (14,-23,14)

Step 2: Choose the initial point on the line segment. We can choose (-4,14,32).

Step 3:  Since there are infinite choices for parameter t, choose any parameter t. We choose t in the range 0<= t <=1, to get the parametric equation for the line segment.

Let the parametric equation for the line segment be r(t).

Then,  r(t) = (-4,14,32) + t(14,-23,14)    

= (-4+14t, 14-23t, 32+14t), for 0<= t <=1.

Thus, the parametric equation for the line segment is r(t) = (-4+14t, 14-23t, 32+14t), for 0<= t <=1.

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Answer:

Both can be true irrespective of the common difference.

Answer: The standard answer would be 4.612258099 × 10.

Step-by-step explanation: Pls give me brainliest. It might help w/ my depression. :\

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

36 different salads can be ordered

Step-by-step explanation:

Write the highlighted digit's place and value.

3. 567; ones place                4. 6,327; thousandth place

5. 9,325; hundredth place    6. 8,281; tenth place

Write each number in standard form.

7. 5,000 + 500 + 3; 5,503     8. 2,000 + 300 + 20 + 9; 2,329

9. 4,000 + 600 + 8; 4,608     9. 9,000 + 300 + 70 + 2; 9,372

11. 1,221

We know Sierra has the same numbers in the thousandth and ones place, so keep does numbers: 1,?2?

It also has two more hundreds and 3 fewer ones place: Take the original number; 1,024 (Make sure you keep the numbers) into a equation; (1024+200)-3. First Add as it's in the ( ), then subtract, 1,221

I hope I've helped!

Answer:

#3. ones place. #4. thousands place.#5. hundreds place. #6. tens place. #7. 5,503. #8. 2,329. #9. 4,608. #10. 9,372.

Step-by-step explanation:

#11.sierras seat number 1,221

We need to determine the score a student must achieve to place in the top 5% of all students taking the SAT Verbal test with an N(\(515, 109\)) distribution, which came out to be \(695\) marks.

Identify the mean (μ) and standard deviation (σ) of the distribution: In this case, µ \(= 515\) and σ\(= 109\).

Determine the percentile rank: To place in the top \(5%\)% of students, we need to find the score corresponding to the \(95th\) percentile, as this represents the point where \(95\)% of students have a lower score.

Use a standard normal (Z) table or calculator to find the Z-score corresponding to the \(95th\) percentile: A Z-score represents the number of standard deviations a data point is from the mean.

For the \(95th\) percentile, the Z-score is approximate \(1.645\).

Apply the Z-score formula to find the required SAT score: \(X =\) µ \(+ Z*\) σ. In this case, \(X = 515 + (1.645 *109)\).Calculate the result: \(X = 515 + (1.645 *109)\)

\(=515 + 179.305 = 694.305\).

Round up to the nearest whole number: Since a student's SAT score must be a whole number, round up to \(695\). A student must score \(695\) or higher on the SAT Verbal test to place in the top \(5\)% of all students taking the test, given the N(\(515, 109\)) distribution.

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Answer: The probability that the teacher randomly selects 3 female students is 0.0556.

Explanation :Given ,In an algebra class there are 18 male students and 12 female students. Each day, the teacher randomly selects 3 students from the class to present their work on a problem, If no one student can be selected twice To find :The probability that the teacher randomly selects 3 female students

Formula used: Probability of event =  \(\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\)Number of total students = 18 + 12 = 30Number of ways to select 3 students from 30 students =  \(_{30}C_3 = \frac{30!}{3!(30-3)!} = \frac{30!}{3!27!} = \frac{30*29*28}{3*2*1} = 4060\)Number of ways to select 3 female students out of 12 female students = \(_{12}C_3 = \frac{12!}{3!(12-3)!} = \frac{12!}{3!9!} = \frac{12*11*10}{3*2*1} = 220\)Therefore, the probability that the teacher randomly selects 3 female students is \(\frac{220}{4060}\) = 0.0556.

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Answer:

rectangle only has 4 sides , a rectangular prism has 6 sides

Answer:

160+65%=264

Step-by-step explanation:

i think

Answer:

264 inches

Step-by-step explanation:

160/ 0.65 = 104

104 + 160 = 264

Answer:

I think its d

isn't the inverse the opposite of the original?

Answer:

Explanation:

Generally, the slope-intercept form of the equation of a line is given as;

where m = the slope of the line

b = y-intercept of the line

From the question, we're told that the required line will pass through the origin and (3, 2), so we can find our slope(m) of the line using the given coordinates x1 = 0, y1 = 0, x2 = 3, and y2 = 2;

So the slope(m) of the line is 2/3.

Since we're told that the line will pass through the origin, it means that the y-intercept (b) = 0.

Since the gragh will be shaded above the dashed line, it means that the inequality will have a greater than sign(>).

We're told that the line will be dashed, it means that the function have only the greater than sign(>) without the equal to sign(=).

Combining all the information above, the function for the line can be

The average value of the function f(x) = 6x over the interval [0, 9] is 27.

To find the average value of a function over a given interval, you need to take the definite integral of the function over that interval, and divide by the length of the interval. In this case, the function is f(x) = 6x, and the interval is [0, 9].

So first, we need to find the definite integral of 6x over [0, 9]:

∫[0,9] 6x dx = 3x^2 |[0,9] = 243

Next, we need to find the length of the interval, which is simply 9 - 0 = 9.

Finally, we divide the definite integral by the length of the interval:

Average value of f(x) = (1/9) * 243 = 27

So the average value of the function f(x) = 6x over the interval [0, 9] is 27.

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A useful technique in controlling multicollinearity involves the use of variance inflation factors. Thus, option A is the correct answer.

Multicollinearity is a state that occurs when there is a high correlation between two or more predictor variables. In other words, when one predictor variable can be linearly predicted from the other predictor variable. Multicollinearity causes unstable regression estimates and makes it hard to evaluate the role of each predictor variable in the model.

Variance inflation factor (VIF) is one of the useful techniques used in controlling multicollinearity. VIF measures the degree to which the variance of the coefficient estimates is inflated due to multicollinearity. When VIF is greater than 1, multicollinearity is present.

Therefore, a is correct.

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Answer:

=4x2+12x+9

hope it helps you!

Step-by-step explanation:

Answer:

4x2−12x+9

Step-by-step explanation:

expand using the foil method

Simplify and combine like terms

and you get the answer

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

2,303

Step-by-step explanation:

First, we have to realize that 6 times as many miles in May as he did in April, means that we have to multiply 329 by 6, giving us 1,974.

But we're not done as we then need to add this total, to 329 as they want the total number of miles.

So, we add 1,974 to 329 giving us our answer of 2,303.

The probability that a randomly selected member of Congress who favours corporate tax reform is a Democrat is 0.4444, rounded to four decimal places.

To solve this problem, we can use Bayes' theorem. Let D represent the event that the selected member is a Democrat, and R represent the event that the selected member is a Republican, and I represent the event that the selected member is an Independent. Let F represent the event that the selected member favors some type of corporate tax reform. We are given the following probabilities:

P(R) = 0.28, P(D) = 0.50, P(I) = 0.22

P(F|R) = 0.34, P(F|D) = 0.35, P(F|I) = 0.31

We want to find P(D|F), the probability that the selected member is a Democrat given that they favor corporate tax reform. We can use Bayes' theorem:

P(D|F) = P(F|D)P(D) / [P(F|D)P(D) + P(F|R)P(R) + P(F|I)P(I)]

Plugging in the values we know, we get:

P(D|F) = 0.35 * 0.50 / [0.35 * 0.50 + 0.34 * 0.28 + 0.31 * 0.22]

P(D|F) = 0.4444 (rounded to four decimal places)

Therefore, the probability that the selected member is a Democrat given that they favour corporate tax reform is 0.4444.

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The digit that occurs the least frequently in the numbers between 1 and 1,000 is 9, which appears only 271 times.

To answer this question, we need to analyze the numbers between 1 and 1,000 and determine which digit occurs the least frequently. We can start by looking at each individual digit (0-9) and counting how many times it appears in each of the numbers in this range.
For example, the digit 0 appears 192 times in this range, while the digit 1 appears 301 times. We can continue this process for all of the digits and find that the digit that occurs the least frequently is 9, which appears only 271 times.
We can also note that this is not surprising since 9 is the largest single-digit number, and thus, it is less likely to appear in numbers between 1 and 1,000. Additionally, we can observe that the digits 0-8 all appear relatively evenly throughout this range, with each digit appearing between 271-305 times.
In conclusion, the digit that occurs the least frequently in the numbers between 1 and 1,000 is 9, which appears only 271 times.

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The derivative of y with respect to x, or dy/dx, is \(-2xy - 7/2 y^2.\)

To use implicit differentiation to find dy/dx, we'll take the derivative of both sides of the equation with respect to x, using the chain rule for the left-hand side:

\((7xy+4)^2 = 28y\)

2(7xy+4)(7y dx/dx + 7x dy/dx) = 28 dy/dx

Simplifying and solving for dy/dx, we get:

(7xy+4)(14y + 14x dy/dx) = 28 dy/dx

\(98xy^2 + 56xy + 56x dy/dx = 28 dy/dx\)

\(98xy^2 + 28 dy/dx = -56xy\)

\(dy/dx = (-56xy - 98xy^2) / 28\)

Simplifying further, we get:

\(dy/dx = -2xy - 7/2 y^2\)

Therefore, the derivative of y with respect to x, or dy/dx, is \(-2xy - 7/2 y^2.\)

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The derivative of y with respect to x, or dy/dx, is \(-2xy - 7/2 y^2.\)

To use implicit differentiation to find dy/dx, we'll take the derivative of both sides of the equation with respect to x, using the chain rule for the left-hand side:

\((7xy+4)^2 = 28y\)

2(7xy+4)(7y dx/dx + 7x dy/dx) = 28 dy/dx

Simplifying and solving for dy/dx, we get:

(7xy+4)(14y + 14x dy/dx) = 28 dy/dx

\(98xy^2 + 56xy + 56x dy/dx = 28 dy/dx\)

\(98xy^2 + 28 dy/dx = -56xy\)

\(dy/dx = (-56xy - 98xy^2) / 28\)

Simplifying further, we get:

\(dy/dx = -2xy - 7/2 y^2\)

Therefore, the derivative of y with respect to x, or dy/dx, is \(-2xy - 7/2 y^2.\)

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Since the player makes 95 out of 140 free throws, the probability that he makes the next free throw is:

Answer: 67.86%

Answer:

it is a relation and a function

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

When multiplying those fractions, you multiply the top (numerators) by each other and you'll get 60

Then when you divide the denominators you'll get 15.

60 divided by 15 is 4.

10/3 x 6/5 = 4

Step-by-step explanation:

You multiply the numerators together, same with the denominator. You get 60/15. You divide those numbers so you get 4 as your answer. Hope this helps!

Solution

1) The volume of a cone.

The volume of a cylinder = 36

What is the relationship between the volume of the cone and the volume of the cylinder? (Answer: The cone takes up one-third of the volume of the cylinder.)

2) Volume of a sphere

The relation between the volume of sphere and the volume of cylinder is that the volume of the sphere is two-third of the volume of the cylinder with a height equal to the diameter of the sphere and the same radius.

Final answer

Answer:

Step-by-step explanation:

Area is equal to the product of the length and the width

The length is 10 inches and the width is 5 inches.

Thus the Area = 10in * 5in = 50\(in^{2}\)

Let g be the integral function defined by g(x) = ∫x-1 (-1/2 * cos (t³ / 2t)) dt for x = 0, g is g(x) = -1/2(x-1 * sin(t³/2t) - x-1 * cos(t³/2t)).

To solve this integral, we need to use the substitution method. We will let u = t/2t, du = 3t/2 dt.

Thus, the integral becomes:

g(x) = -1/2 * ∫x-1 cos(u) du

Using integration by parts, we get:

g(x) = -1/2(x-1 * sin(u) + ∫x-1 sin(u) du).

After integrating the second part, we obtain the final result:

g(x) = -1/2(x-1 * sin(u) - x-1 * cos(u))./2t

we subtitute the value of u to get:

g(x) = -1/2(x-1 * sin(t³/2t) - x-1 * cos(t³/2t)).

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The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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