write the standard form of the line that passes through the given points. (1, 5) and (-2, 3)

The Engel curve for good q2​, given Sally's utility function U=6(q1​)0.5+q2​, is Y= (6(q1​)0.5) / p2​.

To derive the Engel curve, we need to find the relationship between income (Y) and the quantity consumed of good q2​. In Sally's utility function, the first term represents the utility she receives from consuming q1​, and the second term represents the utility she receives from consuming q2​.

To find the Engel curve for q2​, we need to hold q1​ constant and vary Y. We can do this by solving the utility function for q1​ and substituting it into the income equation.

Rearranging the utility function, we have (q1​)0.5 = (U - q2​) / 6. Substituting this into the income equation Y = p1​q1​ + p2​q2​, we get Y = p1​(U - q2​) / 6 + p2​q2​.

Simplifying further, we have Y = (p1​U - p1​q2​) / 6 + p2​q2​.

Rearranging the terms, we get Y = (p1​U + 6p2​q2​ - p1​q2​) / 6. Finally, we can factor out q2​ from the numerator to obtain Y = (6(q1​)0.5) / p2​.

Therefore, the Engel curve for good q2​ is Y = (6(q1​)0.5) / p2​, where Y represents income, q1​ is the quantity consumed of good q1​, and p2​ is the price of good q2​.

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Answer:

6400

Step-by-step explanation:

To find the number that makes the perfect square of 80, multiply 80 times 80 (square 80).

80 squared equals 6400, which means the square root of 6400 would be the perfect square 0f 80.

Approximately 6.25% of the average difference in wages can be attributed to differences in work experience.

Regression estimates the return to experience for men, denoted as 'b,' to be 0.25. To understand the portion of the average difference in wages attributable to differences in work experience, we need to consider the data for both men and women. Let's assume that the average difference in wages between men and women is denoted as 'D.'

The average difference in wages between men and women can be decomposed into two components: one due to differences in work experience and another due to factors other than work experience (such as discrimination, education, industry, etc.). Let's denote the portion attributable to differences in work experience as 'P.'

We can express the average difference in wages as follows:

D = P + Q

where P represents the portion attributable to differences in work experience, and Q represents the portion due to other factors.

Given that the regression estimates the return to experience for men (b) as 0.25, we can calculate P by multiplying the average difference in work experience between men and women (W) by 'b':

P = b * W

The portion attributable to differences in work experience can be expressed as a percentage of the average difference in wages (D):

P% = (P / D) * 100

Substituting the value of P from the equation above, we get:

P% = (b * W / D) * 100

In this case, since the value of b is given as 0.25, we can calculate the percentage as:

P% = (0.25 * W / D) * 100

Therefore, the estimated portion of the average difference in wages attributable to differences in work experience is 6.25% when b = 0.25.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Shelter A has 500 beds and is 90% occupied.

Number of occupied beds:

The ratio of beds occupied in Shelter A to Shelter B is 15:16

Number of occupied beds in Shelter B is 480 which is 60% of total. Total number of beds is:

Answer:

Answer:there are 900 beds in shelter B

Step-by-step explanation:

Shelter A has a capacity of 300 beds and is 80% occupied. This means that the number of beds in Shelter A that would be

80/100 × 300 = 0.8 × 300 = 240 beds.

Let x represent the capacity of Shelter B. Shelter B is 45% occupied. It means that number of beds in Shelter B that would be occupied is

45/100 × x = 0.45 × x = 0.45x beds.

Total occupancy of shelter A and shelter B would be

240 + 0.45x

The ratio of the occupancy of shelter A to shelter B is 16:27

Total ratio of occupancy = 16 + 27 = 43

Therefore

27/43 × (240 + 0.45x) = 0.45x

27(240 + 0.45x) = 0.45x × 43 = 19.35x

6480 + 12.15x = 19.35x

6480 = 19.35x - 12.15x = 7.2x

x = 6480/7.2 = 900

Step-by-step explanation:

\(11 \times {10}^{11} \times 12 \times {10}^{12} = \)

\(132 \times {10}^{11 + 12} = 132 \times {10}^{23} \)

\(1.32 \times {10}^{2} \times {10}^{23} =1.32 \times {10}^{25} \\ \)

_________________________________

And we're done.

Thanks for watching buddy good luck.

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The product in scientific notation is 1.32 × 10²⁵.

Scientific notation is a method for expressing numbers that are too large or too small to be easily written in decimal form (usually resulting in a long string of digits). It is known as standard form, scientific form, or standard index form. Scientists, mathematicians, and engineers all use this base ten notation because it can simplify some arithmetic operations. It is typically referred to as "SCI" display mode on scientific calculators.

Non-zero numbers are written in the form (m x n¹⁰) in scientific notation.

Given (11 x 10¹¹)(12 x 10¹²)

11 x 10¹¹ x 12 x 10¹²

132 x 10¹¹⁺¹² (base same add powers)

132 x 10²³ (132 can be written as 1.32 x 100)

1.32 x 100 x 10²³

1.32 x  10²³⁺²

1.32 x 10²⁵

Therefore the scientific notation is 1.32 x 10²⁵.

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The correct answer is 12:16 P.M.

According to the problem,

∴ Time at which Dev finishes her lunch =

                  9:52 A.M.  + ( 1 hour and 48 minutes +  36 minutes )

                =   11:40 A.M. +  36 minutes = 12 : 16 P.M.

∴ Deb finish eating lunch at 12:16 P.M.

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Answer:

3x^4 + 4 / x - 2

Step-by-step explanation:

(3x³x+4) /(x − 2)

3(x ⋅ x^3) + 4 / x - 2

3x^4  + 4 / x - 2

We can't simplify anymore, so the answer is 3x^4 + 4 / x - 2

the probability that an American man is 69.8 inches or taller is 0.5 (or 50%).

To solve this problem, we can use the properties of the normal distribution and the standard normal distribution.

First, we need to standardize the variable (the height of men) to a standard normal variable (with a mean of 0 and a standard deviation of 1). We can do this using the formula:

\(z = (x - mu) / sigma\)

where z is the standard normal variable, x is the original variable, mu is the mean of the original variable, and sigma is the standard deviation of the original variable.

In this case, we want to find the probability that an American man is 69.8 inches or taller. So we need to calculate the z-score for x = 69.8:

\(z = (69.8 - 69.8) / 3.5 = 0\)

The z-score is 0 because 69.8 is equal to the mean of the distribution.

Next, we can use a standard normal distribution table (or a calculator with a normal distribution function) to find the probability that a standard normal variable is less than or equal to 0. We can also use the fact that the area under the standard normal curve is 1.

Using a standard normal distribution table, we find that the probability that a standard normal variable is less than or equal to 0 is 0.5.

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Answer: 3 weeks and $40

Step-by-step explanation:

Let the number or weeks taken for them to have same amount be represented by x.

The information given in the question can be presented as an equation as:

Stephanie = 25 + 5x

Jose = 16 + 8x

We then equate them together

25 + 5x = 16 + 8x

25 - 16 = 8x - 5x

3x = 9

x = 9/3 = 3

The number of weeks is 3

The amount of money that they'll have will be:

= 25 + 5x

= 25 + 5(3)

= 25 + 15 = $40

Answer:

No

Step-by-step explanation:

4x+5 is not equivalent to 4(x+5) because when you solve for 4(x+5) using distributive property it equals 4x+20 which is not the same as 4x+5.

Answer:

Step-by-step explanation:

No, 4x+5 does not equal 4(x+5), because the operations are different for each expression.

4x+5 is an addition expression and 4(x+5) operation is multiplication.

You must using the distributive property to find the product: 4(x+5) = 4(x) + 4(5) = 4x +20

Therefore, 4x+5 is not equivalent to 4(x+5).

4x+5 is not equivalent to 4x+20.

Answer:

b. m∠KML + m∠MLK = m∠JKM

Step-by-step explanation:

right on edge

The statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have a triangle shown in the picture:

As we know, triangle is a polygon with three sides and three interior angles.

From the definition of the triangle, The triangle's interior angles add up to 180°

m∠MKL + m∠MLK + m∠KML = 180

Also, the sum of the two interior angles is equal to the exterior angle.

m∠KML + m∠MLK = m∠JKM

Thus, the statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.

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Answer:

The second one. it's the only one that has a pattern for both sides. for every x value that goes up, the y-values goes down one. that function has a slope of -1

Step-by-step explanation:

I hope this helps :)

The given sequence, [(-1)^n] * (7n + 6), diverges.

To determine the limit or divergence of the sequence, let's analyze its behavior. The sequence is defined as [\((-1)^n\)] * (7n + 6), where n represents the position of the term in the sequence. The term (-1)^n alternates between -1 and 1 as n increases.

When n is even, \((-1)^n\) becomes 1, and the term in the sequence becomes 7n + 6. As n increases, the value of 7n + 6 grows without bound.

When n is odd, \((-1)^n\) becomes -1, and the term in the sequence becomes -(7n + 6). Again, as n increases, the absolute value of -(7n + 6) also grows without bound.

Since the terms of the sequence do not approach a specific value as n increases, we can conclude that the sequence diverges. In other words, the sequence does not have a finite limit.

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Answer:

See below

Step-by-step explanation:

Domain: negative infinity, positive infinity

Range: -392, positive infinity

Y-intercept: (0, -150)

X-intercepts: (25, 0) (-3, 0)

Axis of symmetry: x = 11

Answer:

Reflexive Property

The dimensions of the screen are:

length = L = 12 inches

width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches

a. The area of the browser window is given by:

area = length * width

24 = x(x-2)

Simplifying and solving for x, we get:

\(x^2\) - 2x - 24 = 0

(x - 6)(x + 4) = 0

Since the length cannot be negative, we take x = 6. Therefore, the length of the browser window is x = 6 inches.

b. Let L and W be the length and width of the computer screen, respectively. We are given that:

length of browser = x inches = L - 7 inches

width of browser = x - 2 inches

The area of the browser is:

area of browser = x(x-2) = (L-7)(L-9)

We are also given that the browser covers 3/13 of the screen, so:

area of browser = (3/13) * area of screen

x(x-2) = (3/13) * L * W

Substituting x = L - 7 and simplifying, we get:

(L-7)(L-9) = (3/13) * L * W

Expanding and simplifying, we get:

13L\(^2\) - 182L + 546 = 3LW

Since L and W are positive, we can divide both sides by 3L to get:

W = (13L - 182) / 3

We also know that the browser covers 3/13 of the screen, so:

area of browser = (3/13) * area of screen

x(x-2) = (3/13) * L * W

6(4) = (3/13) * L * ((13L-182)/3)

24 = (L/3) * (13L-182)

8 = L(13L-182)/3

24 = L(13L-182)

13L^2 - 182L - 24 = 0

(L - 12)(13L + 2) = 0

Since the length cannot be negative, we take L = 12. Therefore, the dimensions of the screen are:

length = L = 12 inches

width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches

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Answer:

Graph B is not a function, because the graph intersects the vertical  line more than one.

Step-by-step explanation:

The transverse line is: Line t

The parallel lines are: m and n

From the transverse and parallel line theorem of geometry, we know that:

If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, from the given image, we see that the transverse line is clearly the line t.

However we see that the lines m and n are parallel to each other and as such we will refer to them as our parallel lines in the given image.

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The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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Answer:

a. p= 36/(m + 1)

b. p = 3

Step-by-step explanation:

If p varies inversely as (m + 1)

then p = k × 1/(m + 1). {Where k is the constant}

when p = 4, m = 8, that means 4 = k/(8 + 1)

4 × 9 = k and k = 36

a. Therefore the equation is p= 36/(m + 1)

b. When m = 11,

p = 36/(11 + 1)

p = 36/12

p = 3

The point (8, 0) doesn't make the given equation y = x + 8 true which is determined by substituting the values of x = 8 and y = 0 in the equation.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have to determine the point (8, 0) makes the equation y = x + 8 true or not.

If we substitute the values of x = 8 and y = 0 the equation should be satisfying.

The given equation is:

y = x + 8

Here the x-coordinate is 8 and the y-coordinate is 0.

Substitute the values of x = 8 and y = 0 in the above equation,

⇒ 0 = 8 + 8

⇒ 0 = 16

This is not true.

Therefore, the point (8, 0) doesn't make the given equation true.

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Answer:

$1500

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 20%/100 = 0.2 per year,

then, solving our equation

I = 500 × 0.2 × 10 = 1000

I = $ 1,000.00

The simple interest accumulated

on a principal of $ 500.00

at a rate of 20% per year

for 10 years is $ 1,000.00.

Answer:

400 boys

Step-by-step explanation:

First use the fraction along with the given information (240 girls)

If 5/8 of the school are boys, then that means 3/8 of the school's students are girls. 3/8 happen to be equal to 240, which means we can conclude that 1/8 is equivilant to 240/3 = 80

80 multiplied by 5 = 400

There are 400 boys in the school. (640 total students in school)

Tip: Easy way to check answer is by putting the boys over the total students to find the ratio, and if it matches, your answer is correct. 400/640 = 0.625, which equals 5/8

Hope this helps :)

Answer:

(3,60)

Step-by-step explanation:

Marc is walking at a rate of 20 minutes per 1 mile; therefore, at that rate he can walk 3 miles in 60 minutes.

Answer:

13.20 or 1.5%.

Step-by-step explanation:

Since Emily borrowed 880, you need to subtract 893.20 from 880. That equals 13.20. The percentage of interest is 1.5 because 6 months is half of a year and the annual interest rate is 3 percent.

Answer:

M = 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

it rose 3 and ran 1

3/1=3

Answer:

x=3-3y

Step-by-step explanation:

Step-by-step explanation:

123456 less then 7

unlimited greater then 7

The numbers from negative infinity to 7, excluding 7."are less than 7 and "all numbers from 7 to positive infinity, excluding 7" are more than 7.

The combination of positive, negative numbers including 0  are called as integers.

The numbers less than 7 are:

This set includes all real numbers that are strictly less than 7.

It can be denoted as (-∞, 7), which means "all numbers from negative infinity to 7, excluding 7."

The numbers greater than 7 are:

This set includes all real numbers that are strictly greater than 7. It can be denoted as (7, +∞), which means "all numbers from 7 to positive infinity, excluding 7."

Thus, there are infinite numbers which are less than 7 and more than 7.

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