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Find the sum of each pair of rational numbers. plelz help

Answer:

dimensions are 2.19 inches by 9.14 inches

Step-by-step explanation:

Here, we are interested in knowing the dimensions of the rectangle

Now, let the width of the rectangle be x, from the question, we can write;

6x-4 as the length

Area of rectangle = l * b

x(6x-4) = 20

6x^2 - 4x = 20

divide through by 2

3x^2-2x = 10

3x^2 -2x -10 = 0

using quadratic formula;

x = -b ± √(b^2 - 4ac)/2a

From the quadratic equation, a = 3, b = -2 and c = -10

substituting these values, we have

x = 2 ± √(-2)^2 -4(3)(-10))/6

x = 2 ± √(124)/6

x = 2 + √(124)/6 or 2 - √(124)/6

x = (2+11.14)/6 or (2-11.14)/6

x = 2.19 or -1.52

Since width cannot be negative, we choose 2.19 alone

So the length is 6(2.19) -4 = 9.14

Answer:I think it’s b too

Step-by-step explanation:

Maka should plan to spend $13.10 + $7.10 = $20.20.

Based on the given menu, the price of a combo meal is the same as purchasing each item separately.

Maka wants 2 burritos and 1 enchilada, so let's calculate the cost.

From combo meal 1, the price of one burrito is $6.55.
From combo meal 2, the price of one enchilada is $7.10.

Since Maka wants 2 burritos, she will spend $6.55 x 2 = $13.10 on burritos.
She also wants 1 enchilada, so she will spend $7.10 on the enchilada.

Adding the two amounts together, Maka should plan to spend $13.10 + $7.10 = $20.20.

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Given the fraction of each colored chalk, Andrea is right that less than 1/2 the chalk in the bucket is blue.

Total = 2/6 + 5/12 + 3/12

= (4+5+3) / 12

= 12/12

= 1

Fraction of blue : Total chalk

= 5/12 : 1

Blue = 5/12 ÷ 1

= 5/12 × 1/1

= 5/12

= 0.42

So,

1/2 = 0.5

Therefore, Andrea is right that less than 1/2 the chalk in the bucket is blue.

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Answer:

25 computers per hour

Step-by-step explanation:

look ate the point 2 hours corresponding to 50 computers

50/2 = 25/1 or 25 computers per hour

Answer:

Choice D.

Step-by-step explanation:

5.2

Answer:

2.8 years

Step-by-step explanation:

The distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector.

To find the distance between the point P(2, 6, -4) and the line defined by the parametric equations r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩, we can use the formula for the distance between a point and a line in three-dimensional space.

The formula for the distance between a point and a line is given by:

d = ||PQ||/||v||

where PQ is the vector connecting the point P to any point Q on the line, v is the direction vector of the line, and || || represents the magnitude of a vector.

Let's first find the direction vector of the line. By examining the parametric equations, we can see that the direction vector of the line is v = ⟨1, 4, -2⟩.

Now, we need to find the vector PQ connecting the point P(2, 6, -4) to any point Q on the line. We can represent PQ as the difference between the coordinates of P and Q:

PQ = ⟨2 - 1, 6 - 3t, -4 - 1, 4t, -4 - 3, -2t⟩ = ⟨1, 6 - 3t, -5, 4t, -7, -2t⟩

Next, we calculate the magnitude of PQ:

||PQ|| = √(1^2 + (6 - 3t)^2 + (-5)^2 + (4t)^2 + (-7)^2 + (-2t)^2)

= √(1 + 36 - 36t + 9t^2 + 25 + 16t^2 + 49 + 4t^2)

= √(29t^2 - 36t + 111)

Finally, we calculate the magnitude of the direction vector v:

||v|| = √(1^2 + 4^2 + (-2)^2) = √(1 + 16 + 4) = √21

Now we can substitute these values into the formula for the distance:

d = ||PQ||/||v|| = (√(29t^2 - 36t + 111))/√21

To find the minimum distance between the point P and the line, we need to minimize the function d with respect to t. We can accomplish this by finding the critical points of the function and determining the value of t that gives the minimum distance.

Taking the derivative of d with respect to t and setting it equal to zero, we have:

d' = (29t - 18)/(√21(√(29t^2 - 36t + 111))) = 0

Solving for t, we get:

29t - 18 = 0

29t = 18

t = 18/29

By substituting this value of t into the formula for d, we can find the minimum distance between the point P and the line.

d = (√(29(18/29)^2 - 36(18/29) + 111))/√21

Simplifying this expression will give us the final value of the distance.

In summary, the distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector

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Answer:

try 12

Step-by-step explanation:

could be wrong, but i hope it helps :)

Answer:

I think it’s 12

Step-by-step explanation:

Uff desperate

Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

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Answer:

d) 5

Step-by-step explanation:

we can observe that the x-value 5 appears twice in the relation. However, in a function or a relation, each x-value should only have one corresponding y-value. Therefore, the repetition of (5, 1) and (5, 2) indicates an inconsistency or ambiguity in the relation. As a result, 5 is not a valid x-value in the domain.

Using the Poisson distribution, it is found that there is a 0.8647 = 86.47% probability of at least one flaw appearing in 300 square feet.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

Flaws in a certain type of drapery material appear on the average of one in 150 square feet, hence, considering 300 square feet, the mean is of:

\(\mu = \frac{300}{150} \times 1 = 2\)

The probability of at least one flaw appearing in 300 square feet is given by:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1353\)

Then:

\(P(X \geq 1) = 1 - 0.1353 = 0.8647\)

0.8647 = 86.47% probability of at least one flaw appearing in 300 square feet.

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Answer:

£ 830

Step-by-step explanation:

       l = 70 cm

      w = 50 cm

      h = 40 cm

Find the Total surface area of the solid box and then multiply the area by 0.05. This will give us the painting cost of the box.

\(\sf \boxed{\text{Surface area of box = 2(lw+wh+hl)}}\)

                          =  2*(70*50 +50*40 + 40*70)

                          = 2* (3500 + 2000 + 2800)

                          = 2 * 8300

                           =  16600 cm²

Cost of painting = 16600 * 0.05

                          = £ 830

Answer:

182:242

Step-by-step explanation:

Reduce the ratio by its halves (50 percent) and simplify.

Although for this case, you could reduce it even further, because this is a ratio, not the true height.

If this is a test, I would not recommend that.

Answer:

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Step-by-step explanation:

75% more revenue in theaters than it did via streaming video.

The sum of the revenues is 100%.

So the theaters were responsible for the following percentage:

\(P = 50 + \frac{75}{2} = 50 + 37.5 = 87.5\)

How much money did Gray Widow make in theaters on opening weekend?

87.5% of the total revenue, that is, 0.875 out of $127,265,468.

0.875*127,265,468 = $111,357,284.5

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Answer:

If we are solving for x the answer would be

-1.5,-4 (fraction form is -3/2, -4)

Step-by-step explanation:

Yes, this is a binomial distribution because we are flipping the same coin ten times and the probability of a head is constant at 1/2 for each flip.

The number of heads, X, is a count of successes in a fixed number of trials, making it a binomial random variable.
Your question asks whether X is a binomial random variable or not. X represents the number of heads obtained from flipping the same coin ten times, with the probability of a head being ½.

Your answer: Yes, X is a binomial random variable. This is because there are a fixed number of trials (10 coin flips), each trial has only two outcomes (head or tail), the trials are independent, and the probability of success (a head) remains constant at ½.

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The correct code to swap elements 0 and 1 in the given array {7, 8, 10, 11, 4, 3} would be: int save = array[0];array[0] = array[1];array[1] = save;

The code above uses a temporary variable "save" to store the value of the first element of the array, then assigns the value of the second element to the first element, and finally assigns the value of "save" (which holds the original value of the first element) to the second element.

The other lines of code following this swap code would perform additional operations on the array, but they do not correctly swap the first two elements of the array.

For example, the line array[0] = array[1]; in the given code only assigns the value of the second element to the first element, effectively overwriting the original value of the first element before it can be saved. Similarly, the line array[1] = array[0]; then assigns the overwritten value of the first element to the second element, resulting in no swap at all.

Therefore, the correct code to swap the first two elements of the array is the code I mentioned at the beginning of this answer.

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Which of the following swaps elements 0 and 1 in array?

Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

The direction of the cross product is perpendicular to both of the vectors being multiplied. So, the answer to the question of what is the direction of the cross product could be any of the six options provided (x direction, -x direction, y direction, -y direction, z direction, -z direction), depending on the orientation of the vectors being multiplied.

The direction of the cross product is determined by the right-hand rule. When you have two vectors, A and B, the cross product (A x B) will be perpendicular to both A and B in a third direction. To find this direction, point your fingers in the direction of vector A, and then curl them towards vector B. Your thumb will point in the direction of the cross product. The options you provided (x, -x, y, -y, z, -z) depend on the specific vectors you are working with. In general, the cross product direction will be in the z direction or -z direction for vectors lying in the xy plane.

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Answer:

Here is the steps. 67.5 cm^3

Step-by-step explanation:

4.5 * 6 = 27

27 * 2.5 = 67.5

Answer:

67.5 cm

Step-by-step explanation:

\(4\frac{1}{2}\) × \(6\) ×\(2\frac{1}{2}\) = \(67\frac{1}{2}\) or \(67.5\)

Answer:

-74

Step-by-step explanation:

First: 5-2=3

-9*3=-27

111÷3=37

Then do -27-37=-74

Answer:

-9·3-111 ÷3

-27-111 ÷3

-27-37= -64

the answer is -64

(a-1) The value of the population mean is unknown.

(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.

(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).

(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.

(e-2) It would be reasonable to conclude that the population mean is 18 eggs.

(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.

(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.

(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.

Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.

In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.

(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.

(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.

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The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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There are four terms in the expression –2p³ – 3p² + 4p + 7. The first term is –2p³, the second term is –3p², the third term is 4p, and the fourth and final term is 7.

Terms in math are individual components of equations or expressions, which can consist of constants, variables, and operators. A term can also be a single number or variable, or several numbers or variables multiplied together. Terms are separated by addition or subtraction operators. Terms can also be used to describe an algebraic expression such as the sum of two terms, or the product of two terms.

The expression can be written as –2p³ – 3p² + 4p + 7 = 0. This expression is a polynomial equation with degree three, meaning the largest exponent of the variables is 3.

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