mx-2mx+my + 2ny
I have to factorize this

The dimensions of the scale model of your room would be 3/4 inch represents 1 foot. To determine the dimensions of the scale model, we need to apply the scale ratio of 3/4 inch represents 1 foot.

Let's assume the length and width of your actual room are L feet and W feet, respectively. To find the dimensions of the scale model, we can multiply the actual dimensions by the scale ratio.

The length of the scale model would be L * (3/4) inch, and the width would be W * (3/4) inch.

For example, if your actual room is 12 feet long and 10 feet wide, the dimensions of the scale model would be:

Length of the scale model = 12 feet * (3/4) inch = 9 inches

Width of the scale model = 10 feet * (3/4) inch = 7.5 inches

Therefore, the scale model would have a length of 9 inches and a width of 7.5 inches, based on the given scale ratio.

It's important to note that when creating a scale model, maintaining the proportionality between the actual dimensions and the model dimensions is crucial to accurately represent the physical space in a smaller scale.

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Answer:

42 snow cones

Step-by-step explanation:

57.12/1.36= 42

Answer:

5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.

Step-by-step explanation:

First find the length of the 2 missing sides. Remember that the picture is WAY out of proportion, so the sides won't be what they look like.

Since the left side is 4 and the right side is 8 cm, the missing left side is 4 cm.

Since the top side is 5 and the bottom side is 10 cm, the missing top piece is 5 cm.

So the sides starting at the bottom right and going clockwise are 10, 4, 5, 4, 5, 8 cm. Multiply each of these * 0.5 and call them meters.

5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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Answer:

15:35

Step-by-step explanation:

There will be $21,935.05 in retirement account on the day of retirement.

To calculate the amount of money you will have in your retirement account on the day you retire:

The annual contribution to your retirement account is $4,500.

The interest rate is 9.5% per year.

You plan to retire in 43 years.

To calculate the amount of money in your retirement account, we can use the following formula:

retirement fund = annual contribution * (1 + interest rate)**number of years

Plugging in the values for the annual contribution, interest rate, and number of years, we get:

retirement fund = 4500 * (1 + 0.095)**43 = 21935.05

Therefore, you will have $21,935.05 in your retirement account on the day you retire.

Correct Question:

You are trying to decide how much to save for retirement. Assume you plan to save $4,500 per year with the first investment made one year from now. You think you can earn 9.5​% per year on your investments and you plan to retire in 43 ​years, immediately after making your last $4,500 investment. How much will you have in your retirement account on the day you​ retire?

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Answer:

no, x=-3 is not a solution

Step-by-step explanation:

Plug in -3 as x.

5-(-3)<8

Distribute the -1 to the -3.

5+3<8

Add the 5 and 3.

8<8

8 is not less than 8, so -3 is not a solution to the inequality.

HTH :)

Answer:

y = -6

Step-by-step explanation:

-6y + -7 = 29

       +7    +7

      -6y = 36  

       -6      -6

          y = -6

Here's our original equation. We're trying to get y by itself, so we first subtract seven. (What you do to one side, you do to the other). That leaves us with -6y = 36. Next, let's divide both sides by -6. This leaves us with our final equation, y = -6. I really hope this helps!

Yes, these data support the scientist's belief that large islands are more effective at protecting at-risk species than small islands. To provide statistical justification, we can compare the probability of extinction for each island size: For large islands, the probability of extinction is 19/208, or approximately 0.091. For small islands, the probability of extinction is 66/299, or approximately 0.221.

The data provided can support the scientist's belief that large islands are more effective than small islands for protecting at-risk species. We can use the concept of probability to calculate the likelihood of extinction for both large and small islands.

For the large island, the probability of extinction for any given species is 19/208 or approximately 0.091. For the small island, the probability of extinction for any given species is 66/299 or approximately 0.221.

Comparing these probabilities, we see that the probability of extinction is higher for at-risk species on small islands than on large islands. This supports the scientist's belief that large islands are more effective for protecting at-risk species.

Additionally, we can use statistical tests such as a chi-square test or a two-sample t-test to confirm whether the difference in extinction rates between large and small islands is statistically significant.

These tests would require more information such as sample size and variance, but based on the provided data alone, the probability calculations suggest that the scientist's belief is supported.

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Answer:

a.20

Step-by-step explanation:

20 is standing out from the rest of the numbers

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

cccccccccccccccccccc

Step-by-step explanation:

cccccccccccccccccccccccc

I will do that soon okay I will

Answer:

I think its c but just so you know I'm not really smart so I might be wrong

Probability of getting all of the answers correct is (1/3)^8 = 1/6561 ≈ 0.0001524 or 0.0152% , the probability of getting all of the answers wrong is (2/3)^8 ≈ 0.00285 or 0.285% (rounded to four decimal places),the probability is (1/3) x (1/3) x (2/3)^6 ≈ 0.00207 or 0.207%

(a) The number of different ways to answer all the questions on the exam can be determined using the Fundamental Counting Principle. Since there are 3 possible answers for each of the 8 questions, the total number of different ways to answer all the questions is calculated by multiplying the number of choices for each question: 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3^8 = 6561.

To find the probability that the student got all of the answers correct, we need to consider that the student randomly guessed on each question. Since there is only one correct answer for each question, the probability of guessing the correct answer for each question is 1/3. Therefore, the probability of getting all of the answers correct is (1/3)^8 = 1/6561 ≈ 0.0001524 or 0.0152% (rounded to four decimal places).

(b) Similarly, to find the probability that the student got all of the answers wrong, we need to consider that there is only one correct answer for each question and the student randomly guessed. Since there are 3 possible answers for each question, the probability of guessing the wrong answer for each question is 2/3. Therefore, the probability of getting all of the answers wrong is (2/3)^8 ≈ 0.00285 or 0.285% (rounded to four decimal places).

(c) To find the probability that the student got questions 2 and 3 correct and the rest of the answers wrong, we need to consider that there is only one correct answer for questions 2 and 3, and the student randomly guessed on all the other questions. The probability of guessing the correct answer for questions 2 and 3 is 1/3, and the probability of guessing the wrong answer for the remaining 6 questions is 2/3. Therefore, the probability is (1/3) x (1/3) x (2/3)^6 ≈ 0.00207 or 0.207% (rounded to four decimal places).

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There are 2 possible values for N.

To find the number of possible values for N, we must first find the common fraction representing people who value both color and smell. To do this, we need to find the LCM (Least Common Multiple) of the denominators 14 and 12. The LCM of 14 and 12 is 84.

Let x be the number of people who value both color and smell. Then, (9/14)N + (7/12)N - x = 753, which simplifies to (27/84)N + (14/84)N - x = 753. Combining the fractions gives (41/84)N - x = 753.

Now, we know that x is an integer, and (41/84)N must be an integer as well. Therefore, N must be a multiple of 84. Since 41 is a prime number, the only multiples of 84 that can satisfy this condition are 84 and 168, making 2 possible values for N.

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Answer:

For two triangles to be congruent, SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle. If the congruent angles are not between the corresponding congruent sides, then such triangles could be different.

hope that helps

Step-by-step explanation:

When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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Answer:

let me think abt it give me a few

Step-by-step explanation:

The value of an expression will be equal to -1.

The complete question is given below:-

If the value of w is -5 then find the value of the expression w² + 3w -11.

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

The given expression will be solved as follows:-

E = w² + 3w -11.

E = ( -5 )²  + ( 3 x -5 ) -11

E = 25 - -15 - 11

E = 25 - 26

E = -1

Therefore the value of an expression will be equal to -1.

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To prove the expression for Pₙ(x) using the Rodrigues formula and the Leibniz formula, we'll follow these steps:

Step 1: Rodrigues formula for Pₙ(x)

The Rodrigues formula for the Legendre polynomials states that:

\(P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} [(x^2 - 1)^n]\)

Step 2: Expand (x² - 1)ⁿ using the binomial theorem

We can expand (x² - 1)ⁿ using the binomial theorem as follows:

\((x^2 - 1)^n = \sum_{k=0}^n \binom{n}{k} (-1)^k x^{2n-2k}\)

Step 3: Substitute (x² - 1)ⁿ in the Rodrigues formula

Substituting the expansion of (x² - 1)ⁿ from Step 2 into the Rodrigues formula from Step 1, we have:

\(P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} \left[ \sum_{k=0}^n \binom{n}{k} (-1)^k x^{2n-2k} \right]\)

Step 4: Apply the Leibniz formula for derivatives

The Leibniz formula states that the nth derivative of a product of functions is given by:

\(\frac{d^n}{dx^n}(uv) = \sum_{k=0}^n \binom{n}{k} \left(\frac{d^{n-k}u}{dx^{n-k}}\right) \left(\frac{d^kv}{dx^k}\right)\)

In our case, we have the product u = (x²)ⁿ⁻ᵏ and v = (-1)ᵏ. Taking the nth derivative of the product, we get:

\(\frac{d^n}{dx^n}[(x^2)^{n-k}(-1)^k] = \sum_{k=0}^n \binom{n}{k} \left(\frac{d^{n-k}(x^2)^{n-k}}{dx^{n-k}}\right) \left(\frac{d^k(-1)^k}{dx^k}\right)\)

The derivative of (x²)ⁿ⁻ᵏ with respect to x is:

\(\frac{d^{n-k}(x^2)^{n-k}}{dx^{n-k}} = (n-k)(n-k-1)\cdots(1)(x^2)^{n-2}\)

The derivative of (-1)ᵏ with respect to x is zero since it is a constant.

Step 5: Simplify the expression

Substituting the derivatives of (x²)ⁿ⁻ᵏ and (-1)ᵏ into the Leibniz formula, we have:

\(P_n(x) = \frac{1}{2^n n!} \sum_{k=0}^n \binom{n}{k} (n-k)^k x^{n-2k} (-1)^k\)

Simplifying the expression further, we obtain:

\(P_n(x) = \frac{1}{2^n n!} \sum_{k=0}^n \binom{n}{k} (n-k)^k (x^2)^{n-2k} (-1)^k\)

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Answer:

110

Step-by-step explanation:

add each side together to get the whole

OPR+RPQ=OPQ

84+26=110

Answer:

110°

Step-by-step explanation:

Angle OPQ= angle OPR + angle OPQ

=84+26

=110°

i. c b a

ii. e d f

iii. h i g

hope this helps

now give me your brain lol

Answer:

1. (<A) > (<B) > (<C)

2. (<F) > (<D) > (<E)

3. (<H) > (<I) > (<G)

Step-by-step explanation:

The sides-angles theorem in a triangle states that the largest angle in a triangle will be opposite the largest side. One can apply this to the given set of triangles:

(1)

CB > AC > AB

4.4 > 3.1 > 2.7

(<A) > (<B) > (<C)

(2)

DE > FE > DF

(x) > (x-3) > (x-5)

(<F) > (<D) > (<E)

(3)

GI > GH > HI

(21x) > (14x) > (13x)

(<H) > (<I) > (<G)

Answer:

46$ in total

y=2r+20

If Isabella goes on 13 rides, she would have to pay a total of $46. If she rides 'r' times, the total cost would be expressed by the mathematical equation 20 + 2r.

This question relates to a linear relationship involving a fixed cost and a variable cost. In Isabella's case, the fixed cost is the admission fee, which is $20. The variable cost is the rides, where each ride costs $2.

So, if she goes on 13 rides, she will have to pay: $20 (for admission) + ($2 * 13 (rides)) = $20 + $26 = $46.

For r rides, the total cost would be: $20 (for admission) + ($2 * r (rides)). So the total cost for r rides can be expressed in a mathematical equation as: 20 + 2r.

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