Find the image of the given point
under the given translation.
P(3, -4)
T(x, y) = (x-6, y + 5)
P' = ([?], [])
27

Answer:

13 and 15

Step-by-step explanation:

x + (x+1) + (x+2) > 40

3x + 3 > 40

3x > 37

x > 12.34

Therfore x= 13,15 satisfy the equation

The value of h for which b is in the plane spanned by a1 and a2 is -17

If the plane is spanned by a1 and a2 and if y is in the plane, then y is a linear combination of a1 and a2.

y = x(a1) +  y(a2), where x and y are constants.

[4, 1, h] = x[1, 4, -2] + y[-2, -3, 7]

[4, 1, h] = [x - 2y, 4x -3y, -2x+ 7y] .

Vectors are equal if their corresponding components are equal:

So, x - 2y = 4, 4x - 3y = 1 and -2x + 7y = h

We can solve for x and y from the first two equations to find h:

                                                 x = -2

                                                 y = -3

                                                 h = -17

The question is incomplete, the complete question is

"For what value(s) of h is b in the plane spanned by a1 and a2?

a1 = [1, 4, -2] a2 = [-2, -3, 7] b = [4, 1, h]"

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(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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The median of the data set is 5.35.

To find the median, we need to first arrange the data set in order from smallest to largest. In this case, the data set is:

0.53, 5.2, 5.3, 5.35, 5.5, 53.

The median is the middle value of the data set. In this case, there are 6 values, so the median is the average of the 3rd and 4th values. In this case, 5.35 is the average of 5.3 and 5.35, so 5.35 is the median.

Therefore, the answer is 5.35 (Option d).

Median is a measure of central tendency and is used to describe a set of numerical values. It is the middle value when the values are arranged in ascending or descending order. It is the midpoint of a distribution and is often used as a measure of central tendency when the data is skewed or has outliers. The median is less affected by extreme values than the mean, making it a more accurate measure of the central location of the data.

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Answer: Below :p

Step-by-step explanation:

-10 - (-3) is -7.

The opposite of -3 is 3 since there were parentheses around -3.

Tom might have added the negatives wrong to get -13 or he thought the subtraction symbol was an addition symbol.

Answer:

A. Because he doesn’t like to eat Chinese food too much in a short period of time, p is not really the same for each trial and so we cannot use the binomial distribution to calculate the desired probability.

Step-by-step explanation:

As it is mentioned in the question that he doesn't like the Chinese too much in a very short interval so he prefers various other foods for dinner

So now we have to determine the probability for the next 7 days

So based on the options mentioned, we prefer option A as we do not use the binomial distribution here as it shows only success results that are not confirmed in the given case

Therefore, the correct option is A.

Answer:

Step-by-step explanation:

4x4=16

16x4=64

its easy

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Answer:

26

Step-by-step explanation:

26

Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.

To find the difference in time between Kyle's normal time and yesterday's time, we need to subtract his normal time from yesterday's time:

(21 minutes 38seconds)−(23 minutes 26 seconds)

(21 minutes 38 seconds)−(23 minutes 26 seconds)

We can first convert both times to seconds to make the subtraction easier:

=(21×60+38)seconds

−(23×60+26)seconds

=(21×60+38) seconds−(23×60+26) seconds

=(1298 seconds)−(1406 seconds)

=(1298 seconds)−(1406 seconds)

=−108 seconds

=−108 seconds

The result is negative because Kyle's yesterday's time is faster than his normal time. To find the positive difference, we can multiply by -1:

∣−108∣ =108seconds

∣−108∣= 108 seconds

Therefore, Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.

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In testing the hypotheses the p-value is 0.0071.

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

To find the p-value, we need to determine the probability of getting a z-score of 2.45 or higher if the null hypothesis is true (i.e. if the population mean is really 34).

Since this is a one-tailed test (Ha: μ > 34), we look up the area to the right of z = 2.45 in the standard normal distribution table.

Using a standard normal distribution table, the area to the right of z = 2.45 is approximately 0.0071.

Therefore, the p-value is 0.0071.

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f=72°

d=153°

b=27°

a=64°

be careful i started with f

Answer:

a=64

b=27

d=153

f=72

Step-by-step explanation:

a+72+134+90=360(sum of the angles around a point is 360)

a+296=360

a=360-296

a=64

b=27(vertically opposite angles are equal in magnitude)

27+b+d+e=360(sum of the angles around a point is 360)

d=e (vertically opposite angles are equal in magnitude)

Therefore,

27+27+2d=360

54+2d=360

2d=360-54

2d= 306

d= 306÷2

d= 153

108+f=180(sum of the adjacent angles on a straight line is 180)

f=180-108

f=72

Answer:

Step-by-step explanation:

42

a) The probability that the score of a person more than 125 is 0.0478

b)  The probability that the score of a person between 90 and 110 is  0.4972

Let us assume that  X be a random variable that represents a random person's IQ

here the mean (μ) = 100 and standard deviation (σ) = 15

a) To find: the Probability that the score of a person more than 125

P(X > 125)

= 1 - P(X ≤ 125)

= 0.0478

b)  the probability that the score of a person between 90 and 110

P(90 ≤ X ≤ 110)

= P(X ≤ 110) - P(X ≤ 90)

= P(\(\frac{X-100}{15}\) ≤ \(\frac{110-100}{15}\)) - P(\(\frac{X-100}{15}\) ≤ \(\frac{90-100}{15}\))

= 0.4972

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The complete question is:

A randomly chosen IQ test taker obtains a score that is approximately a normal random variable with mean 100 and standard deviation 15. What is the probability that the score of such a person is (a) more than 125; (b) between 90 and 110?

The total number of cupcakes ordered, using proportions, is of:

5.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem to find the desired amounts in the same context of the problem.

These amounts are found using basic arithmetic operations, especially multiplication and division, with the unit rates in the context of the problem.

In this problem, the amounts are given as follows:

The total number of cupcakes that will be ordered is the sum of the amounts that will be needed for the family and for the friends, hence:

3.5 cupcakes + 1.5 cupcakes = 5 cupcakes.

The problem is:

I'd like to order 7 halves of cupcakes for my family plus an amount for six friends, considering that each of them wants a quarter. What is the total amount?

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Value of x is 66°.

Based on measurement, there are many kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees.

Given Data

A rectangular sheet of paper is folded at the corner.

Right triangles characterize both the folded-over region and its void. In the bottom left corner, there is a right angle that is marked at 33 degrees. Thus,

180-(33+90)

= 180-123

= 57° is what is left.

The angles in the triangle that has been folded over are the same.

To the left of x, there are two angles that meet at a straight angle. The sum of all right angles is 180 degrees. The 57° measure is shared by the two angles that make up the straight angle with x. This results in:

180-(57+57)

= 180-114

= 66°

Value of x is 66°.

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The pairings of equivalent expresions are:

To do it we just need to simplify the 3 expressions.

The first one is:

2(m + 3) + m - 2

2m + 6 + m - 2

3m + 4   this is equivalent to the first one.

5(m + 1) - 1 =

5m + 5 - 1

5m + 4   this is equivalent to the second one.

m + m + m + 1 + 3

= 3m + 4   this is equivalent to the first one.

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(A)The company should charge $300 per phone and produce 3000 phones to maximize weekly revenue

(B) The maximum weekly revenue is $900,000.

To find the price that maximizes weekly revenue, we need to find the quantity demanded at each price level and multiply it by the price. The weekly revenue equation is:
R(x) = x * p

Substituting the given price-demand equation p = 600 - 0.1x, we get:
R(x) = x(600 - 0.1x) = 600x - 0.1x^2

To maximize revenue, we need to find the critical point of this function by taking the derivative and setting it equal to zero:
R'(x) = 600 - 0.2x = 0
x = 3000

This means that the company should produce 3000 phones to maximize weekly revenue. To find the corresponding price, we substitute x = 3000 into the price-demand equation:
p = 600 - 0.1(3000) = 300

So the company should charge $300 per phone to maximize weekly revenue. The maximum weekly revenue can be found by substituting x = 3000 and p = 300 into the revenue equation:
R(3000) = 3000 * 300 = $900,000

Therefore, the company should charge $300 per phone and produce 3000 phones to maximize weekly revenue, which would be $900,000.

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Answer:

width of 3 units

Step-by-step explanation:

let 'w' = width

let '4+5w' = length

P = 2l + 2w

44 = 2(4+5w) + 2w

44 = 8 + 10w + 2w

36 = 12w

w = 36/12

w = 3

The image in the w-plane of the region in the z-plane bounded by the lines x = 1, y = 1, and x + y = 1 under the transformation w = z^2 consists of a single point (w = 1) and two curves (z = √w and z = -√w) in the w-plane.

To find the image in the w-plane of the region in the z-plane bounded by the lines x = 1, y = 1, and x + y = 1 under the transformation w = z^2, we need to substitute the equations of the lines into the transformation equation and observe how they transform.

Let's analyze each line one by one:

Line x = 1:

Substituting this equation into the transformation equation w = z^2, we get w = (1)^2, which simplifies to w = 1. So, the line x = 1 in the z-plane transforms into the point w = 1 in the w-plane.

Line y = 1:

Similarly, substituting y = 1 into the transformation equation gives us w = z^2, but we need to find the values of z that satisfy this equation. Taking the square root, we have z = ±√w. So, the line y = 1 in the z-plane transforms into two curves in the w-plane: z = √w and z = -√w.

Line x + y = 1:

For this line, we substitute x + y = 1 into the transformation equation w = z^2. Rearranging the equation, we get z^2 = w, which implies z = ±√w. So, the line x + y = 1 in the z-plane transforms into two curves in the w-plane: z = √w and z = -√w.

Combining the results, we have the following image in the w-plane:

The line x = 1 in the z-plane transforms into the point w = 1 in the w-plane.

The lines y = 1 and x + y = 1 in the z-plane transform into two curves: z = √w and z = -√w in the w-plane.

Therefore, the image in the w-plane of the region in the z-plane bounded by the lines x = 1, y = 1, and x + y = 1 under the transformation w = z^2 consists of a single point (w = 1) and two curves (z = √w and z = -√w) in the w-plane.

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Yes, you are correct. An equation in n variables is linear if it can be written in the form:

a1x1 + a2x2 + ... + an*xn = b

where a1, a2, ..., an are constants and x1, x2, ..., xn are variables. In this equation, each variable x appears with a coefficient a that is a constant multiplier.

Additionally, the variables can only appear to the first power; that is, there are no higher-order terms such as x^2 or x^3.

The equation is called linear because the relationship between the variables is linear; that is, the equation describes a straight line in n-dimensional space.

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Answer:

2/3

Step-by-step explanation:

Get it into slop-intercept form

2x - 3y = 4

3y = 2x - 4

y = 2/3x - 4/3

Answer:

Slope= 2/3

Step-by-step explanation:

-3y=-2x+4

y=2/3x-4/3

Answer:

Question 1 is x = 2, y = 2, z = 2

Question 2 is x = 1, y = 1, z = -3

Question 3 is x = 13, y = -10, z = -7

Question 4 is x = 5, y = -2, z = -3 (C)

Question 5 is x = 2, y = 0, z = -2

Step-by-step explanation:

I did not have time to do this...

Answer:

Step-by-step explanation:

5x+2x+7=7x+7

No it is not

5x+7+2x

5x + 7x are like terms add them

7x + 7 is the answer

Answer:

12

Step-by-step explanation:

Ratio of adults to children = 3 : 11

Let

x = number of adults at the party

32 + x = number of children at the party

Ratio of adults to children = x : (32 + x

Equate both ratios

3 : 11 = x : 32 + x

3/11 = x : (32 + x)

Cross product

3 * (32 + x) = 11 * x

96 + 3x = 11x

96 = 11x - 3x

96 = 8x

x = 96/8

x = 12

x = number of adults at the party = 12

Answer:

2035.75

Step-by-step explanation:

Vole of a cone is: V=πr^2h/3

18 squared is 324

V= π(324)(6/3)

That's

V= π(324)(2)

2035.75203953

Answer: True

Step-by-step explanation: