what is the image point (0,2) after a rotation of 90 degree counterclockwise about the origin

Answer:

6.77 pounds or 6 7/9 pounds

Step-by-step explanation:

10 ≥ 4.99 + 0.74x

1. Swap sides

4.99 + 0.74x ≤ 10

2. Subtract 4.99 on both sides

(4.99 - 4.99) + 0.74x ≤ 10 - 4.99 = 0.74x ≤ 10 - 4.99

3. Subtract 4.99 from 10

0.74x ≤ 5.01

4. Divide both sides by 0.74

(0.74x/0.74) ≤ (5.01/0.74) = x ≤ 5.01/0.74

5. Solve

x ≤ 5.01/0.74 =

x ≤ 501/74 ≈

6.77

Applying the triangle proportionality theorem, the length of AD that will make DE║AB is: AD = 60.

According to the triangle proportionality theorem, the equation or proportion we can create to find x is expressed as:

(2x - 4) / 5x = 3x / 8x

Cross multiply:

8x(2x - 4) = (3x)(5x)

16x² - 32x = 15x²

x² - 32x = 0

Solve to find x by factoring:

The equation x² - 32x = 0 can be solved by factoring:

x(x - 32) = 0

So either x = 0 or x - 32 = 0, meaning x = 32.

The solutions to the equation are x = 0 and x = 32.

Using x = 32:

AD = 2x - 4 = 2(32) - 4

AD = 60

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Answer:

\(\huge\boxed{\sf p = -33}\)

Step-by-step explanation:

p - 15 = -48

p = -48 + 15

\(\rule[225]{225}{2}\)

Adding integer constraints to a linear programming model may or may not improve the optimal objective value.

When solving a linear programming problem, the standard approach is to relax the integer constraints and find an optimal solution in the continuous domain. This is known as linear programming (LP) relaxation. However, the optimal solution obtained from the LP relaxation may not satisfy the integer constraints. In such cases, if the integer constraints are added back to the problem, it becomes an integer programming (IP) problem.

The addition of integer constraints introduces discrete decisions into the problem, allowing for more precise control over the variables. In some cases, adding integer constraints can lead to a better optimal objective value because it forces the solution to select values that align with the discrete nature of the problem. This is especially true when the problem exhibits combinatorial or logical structures where discrete choices are crucial.

However, there are instances where adding integer constraints may not improve the optimal objective value. This can happen when the LP relaxation already provides an optimal solution that satisfies the problem's requirements. In such cases, the introduction of integer constraints may restrict the feasible solution space, making it harder to find a better solution.

In summary, while adding integer constraints to a linear programming model has the potential to improve the optimal objective value by incorporating discrete decisions, it is not guaranteed to do so. The impact of integer constraints depends on the problem structure and whether the LP relaxation already provides an optimal solution that meets the problem's criteria.

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Step-by-step explanation:

5x+2y=13

2x+6y=26

\(5x = 13 - 2y \\ x = \frac{13 - 2y}{5} \)

\(2( \frac{13 - 2y}{5} ) + 6y = 26\)

\( \frac{26}{5} - \frac{4y}{5} + 6y = 26\)

\(6y - \frac{4y}{5} = 26 - \frac{26}{5} \\ \)

\(5.2y = 20.8 \\ y = 4 \\ x = \frac{13 - 2 \times 4}{5} = \frac{13 - 8}{5} \\ x = 1\)

The Greek mathematicians started using the symbol pi (π) for as long as 4000 years in mathematical world.

A Short History of Pi

Even if we counted the number of seconds in those 4000 years and round the value of pi (π) to so many places, we would still only be estimating the true value of pi. Pi has been known for over 4000 years. Below is a quick summary of the discovery of.

By multiplying the radius of a circle by three, the ancient Babylonians determined its area, yielding the number pi = three. About 1900–1680 BC Babylonian tablets show a value of 3.125 for, which is a more accurate estimate.

The Rhind Papyrus, which dates to around 1650 BC, sheds light on ancient Egyptian mathematics. The calculation used by the Egyptians to determine a circle's area yielded a result that was around 3.1605 for.

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Answer: 102 Miles per Hour =

149.6 Feet per Second

Answer:

Its c

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The chi-squared analysis aims to check whether observed frequencies in one or more categories match up with expected frequencies. I don't see any answer choices, but hopefully this short explanation will help!

The F-test should only be used to test the joint significance of multiple variables or restrictions, and should not be used to reject all the hypotheses.

When testing joint hypothesis, you should use the F-statistics and reject at least one of the hypothesis if the statistic exceeds the critical value.

This is because the F-test is designed to test the joint significance of multiple variables or restrictions. In other words, it tests whether the combination of the hypotheses is statistically significant.

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Answer:

You have to find the mean of all of the numbers.

Step-by-step explanation:

You have to add 98, 82, 89, and 94 together and then divide it by 90 to find your answer.

Hope this helped

Answer:

The next 3 steps are:
#1: \(\sqrt{ (x+2)^{2}} =\sqrt{10}\) -- Using the square root method, we're going to find the square root of both sides.

#2: \(x+2 = \frac{+}{} \sqrt{ 10 }\) -- When finding the square root of 10 it has to be + and minus.

#3: \(x + 2 = \frac{+}{}\sqrt{10} \\ -2 \ \ \ \ \ \ \ -2\\\) -- Subtract 2 on both sides

#4 (solution): \(x = -2 \frac{+}{} \sqrt{10}\)

Answer:

1/5

Step-by-step explanation:

y = kx

k is the constant of proportionality

Pick any of the indicated points.

Using point (20, 4)

4 = k(20)

Divide both sides by 20

4/20 = k

reduce

1/5 = k

Answer:

4+2(n-1)+5(n-1)

Step-by-step explanation:

We know the pattern always has a +5 to the previous term then plus the lowest unrepeatded even number, such as +0, +2, +4, +6, and so on. The next erm will be 36+5+8, which is 49. The nth then will be the first term+2(n-1)+5(n-1).

That will result in

4+2(n-1)+5(n-1)

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a_e < a_d < a_c < a_b < a_a; due to air resistance, balls moving in the same direction experience a decreasing acceleration.

Let's begin by calculating the acceleration of each ball in the direction of its motion. First, the acceleration of ball aa is given by the equation of motion: aa = v2/r, where v is the speed and r is the radius of the circular path. For ball ab, the acceleration is given by the equation aab = v2/2r, as it is moving twice as fast as aa. Similarly, for ball ac, the acceleration is ac = v2/3r and for ball ad, the acceleration is ad = v2/4r. Finally, for ball ae, the acceleration is ae = v2/5r. Thus, the accelerations can be expressed in terms of the speed and radius of the circular path. We can then rank the accelerations from largest to smallest as a_e < a_d < a_c < a_b < a_a; due to air resistance, balls moving in the same direction experience a decreasing acceleration.

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Answer:

400%

Step-by-step explanation:

20 divided by 5 = 4

100 times 4 = 400

The answer is two base cases, using induction.

What is induction ?

Weak induction is when an inductive mathematical proof holds true for all integers in a set of countable proofs. Natural numbers typically use this. The base step and inductive step are used to prove a set, making it the simplest type of mathematical induction.

Two examples make up an induction proof. Without requiring any prior knowledge of other examples, the first, or base case, establishes the claim for n = 0. The induction process, which is used in the second case, demonstrates that if the assertion is true for any particular scenario where n = k, it must also be true for the subsequent case where n = k + 1.

If a statement true  for n= k, accordily to induction it have to hold good for n = k+1,

Hence, base cases does a proof by the weak form of the principle of mathematical induction requires 2 bases.

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Answer:

Option B = 108 cm

Step-by-step explanation:

Please refer the figure attached

As the given figure have four 90° angles,

AB = CH

BC = AH

So, AB = 30 cm , CH = 30 cm

BC = 15 cm, AH = 15 cm

Already given ED = FG = 5 cm, EF = 11 cm

Working note : As, AB = CH = 30 cm

CH = CD + 3cm + GH

30 = CD + 3cm + GH

CD + GH = 27 cm

Perimeter is the overall measure of the boundary of the given figure, ie

AB + BC + CD + DE + EF + FG + GH + AH

= 30 + 15 + CD + 5 + 11 + 5 + GH + 15

= CD + GH + 81

= 27 + 81

Perimeter = 108 cm

The equation of the tangent plane to the surface z = 1 + y at the point P(1, 3, 2) is z = y - 1 with coefficients accurate to at least 2 significant figures.

To find the tangent plane to the surface z = 1 + y at the point P(1, 3, 2), we need to calculate the partial derivatives with respect to x and y, and then use the equation of the plane.

Step 1: Find the partial derivatives.
∂z/∂x = 0 (since there's no x term in the equation)
∂z/∂y = 1 (the coefficient of y is 1)

Step 2: Use the point-slope form of the equation of the plane.
z - z0 = (∂z/∂x)(x - x0) + (∂z/∂y)(y - y0)

Step 3: Substitute the point P(1, 3, 2) and the partial derivatives into the equation.
z - 2 = (0)(x - 1) + (1)(y - 3)

Step 4: Simplify the equation.
z - 2 = y - 3

Step 5: Rearrange the equation to find the equation of the tangent plane.
z = y - 1

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The correct answer is D. The quadratic function has no real zeros if a > 0 and k>0 or a < 0 and k<0. This is because in the vertex form y=a(x- h2) + k, the value of k determines the vertical shift of the graph, and the value of a determines the direction of the graph. If a>0 and k>0, the graph will be shifted up and open upward, meaning it will not cross the x-axis and therefore have no real zeros.

Similarly, if a<0 and k<0, the graph will be shifted down and open downward, also not crossing the x-axis and having no real zeros.  The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. The value of a determines the shape of the parabola: if a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.

For a quadratic function to have no real zeros, it must not intersect the x-axis. This means that the vertex of the parabola must be above or below the x-axis, depending on the direction of the opening.

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A campsite is in the shape of a rectangle. The green region represents campsites with shade. The yellow region represents campsites without shade. The probability that your campsite has shade 1/2.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

A campsite is in the shape of a rectangle.

The green region represents campsites with shade.

The yellow region represents campsites without shade.

There are only two possibilities either shaded or not shaded So, the total number of outcomes would be 2.

The probability that your campsite has shade = 1/2

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The key difference between hypergeometric distribution and the binomial is which with the hypergeometric distribution,the probability of success changes from trial to trial.

The hypergeometric distribution is used when sampling without replacement whereas the binomial distribution is used when sampling with replacement.

We know in the hypergeometric distribution,

Each trial affects the probability of success for the remaining trials which is not the case in the binomial distribution where the trials are independent of each other.

The random variable in both distributions is discrete, not continuous.

There is no need for the probability of success to be less than 0.5 in either distribution.

Hence,

The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution, the probability of success changes from trial to trial.

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Answer:

y =  x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y =  x + 7 ← is in slope- intercept form

with slope m =

Parallel lines have equal slopes

line M crosses the y- axis at (0, 3) ⇒ c = 3

y =  x + 3 ← equation of line M

FOUND THIS ON THIS APP SO IM NOT 100% SURE THIS IS THE RIGHT ANSWER

Answer:50x-12

Step-by-step explanation:

We need to get rid of parentheses in this term.

All the negative factors will change sign.

In our example, we have 2 negative factors.

The sign of the term will not change, since there is an even number of negative factors.

Answer:

6 teachers and 10 tutors.

Step-by-step explanation:

if there are 120 student and they need 3 teachers per 63 students then there would be 6 teachers because 63x2=126 subtract the six and you get the number of students. 120 so 6 teachers and if they need 5 tutors per 60 student then double the students to get 120 and double the tutors to get 10.

Using cylindrical coordinates, integrate rho over Q to find the mass by evaluating the triple integral.

In cylindrical coordinates, the region Q can be described as 0 ≤ z ≤ 9 - r cos θ - 2r sin θ, and r ≤ 2. The density function becomes rho(r, θ, z) = k * sqrt(r^2). To find the mass of solid Q, we integrate the density function over the region Q:

M = ∫∫∫ rho(r, θ, z) * r dz dr dθ

Using the given density function and limits of integration, we have:

M = k * ∫∫∫ r * sqrt(r^2) * (9 - r cos θ - 2r sin θ) dz dr dθ

Solving this triple integral will yield the mass of the solid Q, given the constant k.

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Answer:x − x^{2} − 1.

Step-by-step explanation:

.

The correct answer is (b) The central limit theorem is applicable for the sample mean.

The condition that the population size be at least 10 times the sample size is necessary to ensure that the sample mean follows a normal distribution, as required by the central limit theorem. The central limit theorem states that the sample mean will be approximately normally distributed, regardless of the underlying population distribution, as long as the sample size is large enough. In this case, the condition is necessary to ensure that the sample size is sufficiently large for the central limit theorem to be applicable. Options (a), (c), (d), and (e) are not the correct answers because they do not directly relate to the condition that the population size be at least 10 times the sample size.

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Answer:

Step-by-step explanation:

Diameter = 28 cm

therefore, radius = 28 / 2 = 14 cm

Circumference = 2 π r

= 2 × 22 / 7 × 14

= 88 cm

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Answer:

88cm

Step-by-step explanation:

The formula is Diameter x pi (3.14)

Answer:

The federal government's "enumerated powers" are listed in Article I, Section 8 of the Constitution. Among other things, they include: the power to levy taxes, regulate commerce, create federal courts (underneath the Supreme Court), set up and maintain a military, and declare war. It is their job to carry out constitutional responsibilities for society.

Step-by-step explanation: