Making an inference usingig a two-way frequency tableA group of 150 college students who took math fost term were interviewed. They were asked whether they passed their math course and whether they live oncampus. Their responses are summarized in the following tablePassed math Failed mathve on campus2466Live off campus392152(a) What percentage of the students passed moth? []%(b) What percentage of the students live off campus? []%(c) What percentage of the students who live off campus passed math? []%(d) Is there evidence that students who live off campus tend to pass math more often than average?Yes, because the percentage found in part (e) is much greater than the percentage found in part (0)Yes, because the percentage found in part() is much greater than the percentage found in part (b)No, because the percentage found in part(e) is about the same as the percentage found in part (a).No, because the percentage found in part (5) is about the same as the percentage found in part (b).

2. q and v are parallel. YES

3. r and s are parallel. NO

4. r and t are parallel. NO

5. s and u are parallel. YES

6. q and s are perpendicular. NO

7. q and v are perpendicular. NO

8. r and s are perpendicular. YES

9. t and v are perpendicular. YES

In order to write an inequality we can read the original statement in small parts.

In this case, the statement is:

"the product of c and 9 is greater than 16"

We have that "the product" is a multiplication

Then, "the product of c and 9" is the multiplication between c and 9:

9 · c

And, "the product of c and 9 is greater than 16" means that 9 · c is greater than 16:

9 · c > 16

Answer:

x ≥ -6

Option C

Step-by-step explanation:

Hello!

We can solve the inequality by isolating x. Remember, flip the sign when you divide or multiply both sides by a negative number in an inequality.

The answer is option c, all values greater than -6.

Answer:

4

Explanation:

Given the below;

To simplify the above, we have to note that any number or variable raised to the power of 0 is 1.

So, we'll have;

I would loan my money to the one who pays the compound interest.

This is because more money would be generated from the compound interest as it is based on the principal (Amount loaned) and also the interest generated from the loan. Unlike simple interest that is only based on the principal.

When a stone is dropped in a body of water, ripples are created and move outward in concentric rings. The least-squares regression line has the equation Area = 0.010 + 3.141 (Time2).

The least squares regression equation is the equation y=1x+0 that specifies the least squares regression line.

the least squares regression line's y=1x+0 equation.

Time (t = d/v) or, alternatively, time = speed/distance (v = d/t).

Concentric circles are those that share a common center but have differing radii. It is described as two or more circles with the same center, in other words. An annulus is the space between two concentric circles with dissimilar radii.

Concentric circles are two or more circles with the same center but various radii. Congruent circles are any two or more circles that have the same radius but different centers.

Concentric circles are those that share a common center but have differing radii. It is described as two or more circles with the same center, in other words.

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The company’s equivalent markup on selling price is 26%.

The markup is the gap between the selling price and the cost of a good or service. It is frequently represented as a percentage of the total cost. To cover the costs of doing business and generate a profit, a markup is added to the overall cost borne by the manufacturer of a good or service.

The following can be deduced based on the information:

Markup on cost = 35%

Cost = 100%

Selling price = 135%

Markup on selling price will be:

= (0.35/1.35 x 100)

= 26%

Therefore, the value is 26%.

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In order to simplify this equation, we are going to start by simplifying the radicals.

Now we have the radicals simplified and we are going to replace them on the equation that we already have.

ANSWER

30°, 30° and 120°

EXPLANATION

We want to find the measures of the angles of the triangle if the ratio of the angles is x : x : 4x

In other words, the ratio is 1 : 1 : 4

The total angle in a triangle is 180°.

Therefore, we have to find the value of x. To do this, we first find the total ratio:

Now, find x by apply ratios. x is equal to 1/6 of the total angle of the triangle:

Now, find 4x:

Therefore, the ratio of angles is:

In other words, the angles are 30°, 30° and 120°.

So we have to graph the function:

First is important to note that the cotangent can be defined by the quotient between the cosine and the sine:

By looking at this new expression we can infer a few things about the graph. First of all, we have a sine in the denominator which means that the denominator can be equal to 0. Let's assume that the denominator is 0 at x=a. Then the graph has a vertical asymptote at x=a. What's more, the sine is a periodic funtion that is equal to zero for an infinite amount of x values so the graph of the cotangent has infinite vertical asymptotes. The good part is that we just need to graph one full period and in the case of the cotangent one full period is completed between two consecutive vertical asymptote. So basically we have to find two consecutive vertical asymptote and graph the function between them.

So let's begin by finding two x values that makes the denominator equal to 0. The sine is equal to 0 when its argument is equal to 0 and the next value at which the sine is equal to zero is pi so:

Then we can construct two equations:

The equations are:

We can substract π/6 from both sides of both equations:

So we have a vertical asymptote at x=-π/6 and another one at x=5π/6. This means that we just need to graph f(x) between these two vertical lines. It is also important to note that f(x) reaches positive or negative values when the value of x approaches to -π/6 or 5π/6.

Now that we have the asymptotes let's find the x-intercept i.e. the point where f(x) meets with the x-axis. This happens when f(x)=0 which happens when the numerator is equal to 0. Then we get:

The cosine is equal to zero at π/2 so we have:

We can substract π/6 from both sides:

So the x-intercept is located at x=π/3. So for now we have the x-intercept and two vertical asymptotes so at the moment we have the following:

The black dot is the x-intercept at (π/3,0) and the dashed lines are the asymptotes. Our function passes through the black dot and is limited by the asymptotes.

We still need to find if it reaches positive or negative infinite values when approaching to the asymptotes. As we saw the function is equal to zero at x=π/3. This means that between the first asymptote and x=π/3 the function is either entirely positive or entirely negative. The same happens with the interval between x=π/3 and the second asymptote. So we have two intervals where the function mantains its sign: (-π/6,π/3) and (π/3,5π/6). Let's evaluate f(x) in one value of each interval and see if it's positive or negative there. For example, x=0 is inside the first interval and x=2 is inside the second interval:

So f(x) is positive at (-π/6,π/3) which means that as x approaches to -π/6 from the right it reaches positive infinite values. We also have that f(x) is negative at (π/3,5π/6) so as x approaches 5π/6 from the left the function reaches negative infinite values.

Using this information and the fact that the graph must pass throug the x-intercept we can graph the function. It should look like this:

And that's the graph of f(x).

Given:

The value of a collectible coin can be represented by the equation

Required:

We need to find the original purchased value

Explanation:

To find the orginal value we just put

Final answer:

The original value is $9.74

By forming equations, we know that the garden is 37.5 yards long, and 37.5 yards wide, and it has an opening that is 12.5 yards wide.

So, the dimensions and area of the garden:

There are 150 yards of fencing available, so:

The garden's area (A) is given as follows:

At A' = 0, the area is largest.

Garden opening: 1/3 × 37.5 = 12.5 yards

Therefore, by forming equations, we know that the garden is 37.5 yards long, and 37.5 yards wide, and it has an opening that is 12.5 yards wide.

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The correct question is given below:
A farmer has 150 yards of fencing to place around a rectangular garden. The fence will have an opening that is 1/3 of the garden's length. Write a function A(x) that describes the area of the garden, where x is the length of the garden. Find the dimensions if that has a maximum area, and find the maximum area

Answer:

The length is 45 yards.

The width is 37.5 yards.

The area is 1,687.5 yards

Step-by-step explanation:

I go to RSM too lolol

The other answer posted here was incorrect. Since the length and width DID have a relatively equal factor without the -12.5 yard opening taken into account, you'd usually get 37.5 yards.

BUT, if we use the width and subtract it from the total (which we'd get 75 yards left), we can see that in the total length, a sixth (it is 1/6th since we are taking both sides) is taken from that. 75 is easily dividable by 5, so we can take 15, and multiply it by 3. We'd then get 45 yards in total for each side (minus the 12.5 yard opening).

All you need to do now is multiply the length and width to get 1,687.5 yards.

Now get a 100 on that RSM assignment and get the bragging rights for your class. You can thank me later. Your homework is more important.

The equation can be given as B=64+5x

And the cost of phone bill if he uses 23GB will $104

What is an linear equation is one variable?

An linear equation is an equation of degree one. the highest exponent is 1 and one variable is number of variable is 1 in the equation

We are given that, Simba pays $15 per month for the phone he bought. His cell phone plan costs $49 per month.

He pay additional $5 for 1 gb data after 15gb data limit got over

Let the number of gb's used be x

Hence the total bill will be given by the equation

B= 15+49+5x

B= 64+5x

If he uses 23 gb of data the first 15 Gb are covered in his phone plan

And he has to pay $5 for each gb

The total cost is 8*5=$40

Hence the total phone bill is B=64+40

B=$104

Hence the equation can be given as B=64+5x

And the cost of phone bill if he uses 23GB will $104

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-3)}}} \implies \cfrac{-8 +2}{5 +3} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{ 3 }{ 4 }[/tex]

Given:

City A is due east of city B.

City C is located 35° west of north from city B.

Distance between city C and city A is 100 miles.

Distance between city C and city B is 70 miles.

The objective is to find the distance between city A and city B.

The above situation can be represented as,

Thus the total angle of ∠B = 90°+35° = 125°.

Now the measure of angle A can be calculated by law of sines.

By the angle sum property of triangle the value of angle C can be calculated as,

Now, the distance between A and B can be calculated by,

Thus, the distance of city A is 42 miles due east of city B.

Hence, option (C) is the correct answer.

To find the slope of the line that passes through points (0, 3) and (4, -2), we can use the formula for the slope of a line:

We have then:

(0, 3) ---> x1 = 0, y1 = 3

(4, -2) --->x2 = 4, y2 = -2

Therefore:

Then, the slope of the line that passes through points (0, 3) and (4, -2) is m = -5/4.

SOLUTION

A company's logo was designed using circles of 3 different sizes. The diameters of two of the circles are shown:

6 cm

12 cm

Which measurement is closest to the area of the largest circle in square centimeters?

The measurement is closest to the area of the largest circle in square centimeters is

12 cm since it has a radius of 6 cm with 36 pi square centimetres; unlike the diameter

of 6 cm which has 3 cm radius and 9 pi square centimetres.

The correct answer is 12 cm.

We need to simplify the next given expression:

We can rewrite it as:

Solve each square root:

√2 =√2

√9 = 3

Then, the result is:

Hence, the correct answer is option A.

Answer:

f(11) = 9

Explanation:

The equation for f(x) is:

To know the value of f(11), we need to replace x by 11 and solve, so:

Therefore, the value of f(11) is 9.

Given the equation

4r=124

You have to clear the value of r, this is, that r ends up alone in one side of the equation and the rest of the terms of the equation stay in the other side.

As you can see r is being multiplied by 4, to nullify this multiplication you have to "reverse the operation" that is, divide it by four.

And for the equality to continue, every operation made in one side of the equation has to be done in the other side, this means that if you divide 4r by 4, you have to divide 12

The main difference between managerial accounting and financial accounting is who the statement is being prepared for.

There are several things that differentiate managerial accounting from financial accounting but the main one is the target of the financial statements.

Financial accounting is used for financial statements for those outside the company such as investors, customers, and the government. As such, it has to abide by certain standards.

Managerial accounting on the other hand, is for managers and decision makers in the company. It is less restrictive as the main goal is to provide information for managers and not those outside.

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Generic parabola equation:

y = a*x^2 + b*x + c

We have three points of the parabola:

(-5,8), (2,-3), (3,1)

For the point (-5, 8): x = -5, y = 8

8 = 25*a - 5*b + c

Point (2,-3): x = 2, y = -3

-3 = 4*a + 2*b + c

Point (3, 1): x = 3, y = 1

1 = 9*a + 3*b + c

Our system of equations:

8 = 25*a - 5*b + c

-3 = 4*a + 2*b + c

1 = 9*a + 3*b + c

The last option is the correct answer

Given:

The x-intercepts of the given polynomial are

Substitute x=0 in h(x) to find y-intercepts.

The graph of the given polynomial h(x) is

The degree of the polynomial is 6=even and the leading coefficient=1=positive.

Both ends of the graph point up.

End behaviour is

up/up.

In problem 3, we have a right triangle with:

• cathetus ,a = 7,,

• cathetus ,b = x,,

• and hypotenuse ,h = 9,.

Pigatoras Theorem states that:

Where a and b are cathetus and h the hypotenuse.

Replacing the data of the problem in the equation above, we have:

Solving for x the last equation, we get:

Answer

The value of x to the nearest tenth is 5.7.

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Scientific notation is a way of writing large or small numbers that have many digits in a simplified form. The index of the base 10 exponents indicates the number of digits there are after the decimal dot.

The table shows the population of 4 cities of Texas, Houston, San Antonio, El Paso, and Corpus Christi.

To determine the total population of all cities you have to add them together, the first step is to express each given population in standard form:

Houston:

This notation indicates that there are 6 digits after the decimal dot, the first one is 3 and the other five digits are zero. The positive index indicates that this number is greater than 1, so to write the number in the standard form you have to erase the decimal dot:

San Antonio:

The notation indicates that there are 6 digits after the decimal point, the first one is 5 and the other five digits are zero. The positive exponent indicates that this number is greater than 1, so you have to erase the decimal dot:

El Paso:

This population is already given in the standard form

Corpus Christi:

This notation indicates that there are 5 digits after the decimal dot, the first one is 5 and the next four are zero. The exponent is positive, so as mentioned before, this number is greater than one, and to write it in the standard form you have to erase the decimal dot:

Now that all values are expressed in the standard form you can add them:

In the standard form, the total population of the four cities is 4,800,000 people

To express this value using scientific notation you have to write the decimal dot after the first digit and then count the number of digits after the decimal dot.

When you use scientific notation you have to write only the digits that are different than zero.

There are 6 digits after the decimal dot, so the exponent of the base 10 number will be 6, and the result expressed in scientific notation is:

We can solve these values using the next triangle:

First, we need to label the sides using the angle of 30 degrees.

- The largest side is always the hypotenuse, h = 1.

- The opposite side is opposite to the angle, opp = 1/2.

- The adjacent side is between the angle of 30 degrees and the right angle,

adj = √3/2.

Now, we can solve the trigonometric expressions:

For sin:

sin θ = opposite side / hypotenuse

sin 30 = (1/2) / 1

sin 30 = 1/2

For cos:

cos θ = adjacent side / hypotenuse

cos 30 = (√3/2)/1

cos 30 =√3/2

For tan:

tan θ = opposite side / adjacent side

tan 30 =(1/2) / (√3/2)

Simplify the fractions:

tan 30 = 1/√3

Answer:

Detailed Explanation: The area of the figure provided is the sum of two areas, a rectangle, and a triangle:

The total area is calculated next, and the necessary steps are shown as follows