Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 460 miles o. 20 gallons of gas. How far could you drive on 70 gallons of gas.

Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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Answer:

The probability that the selected number is an odd number or a multiple of 3 is 6/9, or 2/3. This is because there are 6 numbers that meet the criteria out of the 9 numbers in the set: 1, 3, 5, 7, 9, and 3.

Answer:

B. $5.99

Step-by-step explanation:

Let's start by finding the total cost of the sodas. We know that there were 5 sodas and each cost $0.75, so the total cost of the sodas is:

5 * $0.75 = $3.75

Next, we need to subtract the cost of the sodas from the total cost before tax to find the cost of the pizzas:

$33.70 - $3.75 = $29.95

Finally, we can divide the cost of the pizzas by the number of pizzas to find the cost of each pizza:

$29.95 ÷ 5 = $5.99

Therefore, the cost of each pizza pie was $5.99. Answer choice B is correct.

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

The distance between any coordinate (x,y) and the origin is given by the equation presented as follows:

D = square root of (x² + y²).

The angle between these coordinates and the positive x-axis is given as follows:

Angle = arctan(y/x).

The distance between two points on a coordinate line is equivalent to the hypotenuse of a right triangle.

The sides of the triangle are represented by the differences of the x-coordinates and the y-coordinates of each point.

For the origin, the coordinates are (0,0), hence the distance of any point from the origin is given by the equation presented as follows:

D = square root of (x² + y²).

For the angle, we have that:

Hence the tangent is applied, as follows:

tan(Angle) = y/x

Angle = arctan(y/x).

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Scale factor of 1/2, means shrink lines to half

Then

A'B'= AB/2

Trace the 2 diagonals

Find point of intersection of AC ,and BD

DRAWING

Find distance from point (-1,2) to A,B,C and D

and reduce to half

A= (-10,2)

Distance to A =

X'= (-10-1)/ 2 = -5.5

Y' = (2--2) /2= 4/2 = 2

Then

A'= (-5.5,2)

Distance to B

B= (7,8)

Distance to B=

X'= (7-1)/2= 3

Y'= (8--2) /2= 10/2= 5

Therefore

B'= (3, 5)

Distance to C

C= (5,-8)

X'= (5-1)/2= 4/2= 2

Y'=(-8--2)/2 = -6/2= -3

Then

C'= (2,-3)

Distance to D

D= (-3,-10)

X'=(-3-1)/2= -4/2=-2

Y'=(-10--2)/2 = -8/2= -4

Then also

D'= (-2,-4)

Now we have the 4 coordinates of new figure A'B'C'D'

Answer:

Step-by-step explanation:

Step 1: Convert
8 3/7= 43/5
7 2/15= 10/15

Step 2: Multiply
43×107=4601
----------
5×15=75

\(\frac{4601}{75}\)

Step 3: Convert to an improper fraction

\(\frac{4601}{15}= 61\frac{26}{75}\)

Hence, our answer is 61 26/75

The intersection points are (6, 6) and (-6, -6).

What is Intersection points?

The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.

The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.

6 sin(Ф) = 6 cos(Ф)

Dividing both sides by 6 and rearranging terms, we get:

tan(Ф) = 1

This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].

Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.

Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).

Therefore, the intersection points are (6, 6) and (-6, -6).

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Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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The equation in slope-point form is:

A. The change in "y" is represented by "y - y1". The function shifts "y1" units down.

B. The change in "x" is represented by "x -x1". The function shifts "x1" units right.

Answer:

The answer is 56°. Angle B is an exterior angle of triangle ABC, which means it is equal to the sum of the two remote interior angles (angles A and C). Angle A is 35°, angle C is 121°, so angle B is 56°.

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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Answer:

y=50+45x.

Step-by-step explanation:

It says  $50 plus $45 So add them and x represents the hour so y=50+45x

Answer:

2 feet 3 inches

Step-by-step explanation:

So we know there are 12 inches in one foot. so 27/3= 2 remainder 3. So the answer is 2 feet 3 inches

The solution for the linear system will be , x(t) = 4 c₁e^t +  4 c₂e^t and

y(t) = -c₂e^t + c₂(1 - t)e^t .

The solution is given by ,

matrix | x y | = c₁ .v . e^λt  + c₂( w + v.t ) e^λt

Given that the matrix has repeated eigenvalue with eigenvector  generalized  vectors ,

λ = 1 with eigenvector v = [ 4 , -1 ] and  generalized  vectors w =[ 0,1 ].

then the solution will be,

c₁ [ 4 , 1 ] e^t +  c₂[ 0 , 1] + [ 4 , -1 ] )e^t

therefore,

x(t) = 4 c₁e^t +  4 c₂e^t

y(t) = -c₂e^t + c₂(1 - t)e^t

Matrixes represent linear maps and allow for explicit linear algebra operations. As a result, matrices play an important role in linear algebra, and most characteristics and operations in abstract linear algebra may be represented in terms of matrices.

Matrix multiplication, for example, depicts the combination of linear maps.

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The formula for calculating the distance between two points is:

Therefore, for thr given points,

Answer:

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

Step-by-step explanation:

Given that the total cost of manufacturing by the company is $15000.

Let x be the number of gallons the company sells.

It is also mentioned that the company earns $10 on each gallon.

So the total profit will be the the difference of the selling cost of gallons and manufacturing cost

Mathematically,

\(10x-15000\)

Now it is mentioned that the profit should be at least 50000 dollars which means the profit can be minimally 50000 and also can be greater than it so

\(10x-15000 \geq 50000\)

The number of gallons can be found by solving the obtained inequality.

Hence,

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

Answer:

Answer: C. f(x) = 2x²+x+6

he needs to collect 40-26.50=13.50 dollars more

Answer:

b) all of the cupcakes in the bakery

Explanation:

in statistics, the population is a group of people/things that are in the same category for collecting data. c) and d) are thus wrong since no data is collected about the other goods or the employees, while a) is wrong because that is just a sample (which helps to test for a large population) and not the actual population.

i hope this helps! :D

Answer: B

Step-by-step explanation:

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

x-y=30

Step-by-step explanation:

-10(x-y)=20

x-y = 30

Answer:

23. Similar as well as congruent triangle

25. Conguent triangle

Step-by-step explanation:

Answers:

23. Not enough information

25. Congruent (by the HL theorem)

HL = hypotenuse leg

=============================================

Explanation for problem 23.

Check out figure 1 shown below.

I have marked the given diagram with light blue and light pink to show which angles are congruent.

Because lines UN and TC are parallel, we know the following alternate interior pairs are congruent.

Therefore, we can establish one link of paired congruent angles of the triangles LNU and TCH. However, we cannot determine any other angle pairings. Why not? Because we don't know if segment UL is parallel to segment TH. If they were parallel, then we could establish something like angle LUN = angle CHT as one alternate interior pairing.

But again, we don't know if UL is parallel to TH. The arrow markers aren't shown for these segments.

Therefore, we simply don't have enough information to determine if the triangles are similar or congruent.

----------------------------------------

Explanation for problem 25.

Luckily this problem will provide sufficient info to prove the triangles KSR and ISR are congruent.

We start with the given info that KR = SI due to the identical tickmarks. This represents one node in the flowchart (see figure 2).

Another node is angle RKS = angle RIS because both are right angles, aka 90 degree angles.

A third node is SR = SR because of the reflexive property.

Those three nodes then feed into the final conclusion node that triangle KSR = triangle ISR. The reasoning is "HL theorem" where HL = hypotenuse leg. This theorem works for right triangles only.

Take note how I structured the proof so that it flows from top to bottom. The three nodes side by side are related so they share the same row.

There are many other ways to make the flowchart, so don't feel obligated to use this format. Use whatever works best for you.

Answer:

Range is {3,-1, 15}

Step-by-step explanation:

Answer:

{3, -1, 15} is the range.

Step-by-step explanation:

the correct answer is negitive one hundred eighty (-180)

Answer:

t=12

Step-by-step explanation:

5t / 4 = 18 - 3

5t / 4 = 15

5t = 15 x 4

5t = 60

t = 12

Hope that helps!

Answer t is 12

Step by step explanantion

Answer:

20

Step-by-step explanation:

5 and 4 have no common factors until they are multiplied by each other. So if you were to convert your existing measurements, you would do the following.

(3/4) x (5/5)

(2/5) x (4/4)

Giving you 15/20 and 8/20

The sequence of transformations that maps circle B onto circle A is: Translate B by (4,2) to get B', Dilate B' by a factor of 3/2 with respect to the origin to get B'' and Translate B'' by (-4,-2) to get B''.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

To map circle B onto circle A, we can use the following sequence of transformations:

Translation: Move circle B to the origin by adding 4 to the x-coordinate and 2 to the y-coordinate. This gives us a new circle B' with center at (0,0) and radius of 4.

Dilation: Enlarge circle B' by a factor of 3/2 using the origin as the center of dilation.

This gives us a new circle B'' with center at (0,0) and radius of 6.

Translation: Move circle B'' to its final position by subtracting 4 from the x-coordinate and 2 from the y-coordinate.

This gives us the final circle B''' with center at (-4,-2) and radius of 6.

Therefore, the sequence of transformations that maps circle B onto circle A is: Translate B by (4,2) to get B', Dilate B' by a factor of 3/2 with respect to the origin to get B'' and Translate B'' by (-4,-2) to get B''.

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Answer:

The largest single disadvantage of geothermal energy is that it is location specific. Geothermal plants need to be built in places where the energy is accessible, which means that some areas are not able to exploit this resource.