Lesson 8 Practice Problems
1. A number line can represent positions that are north and south of a truck stop on a
highway. Decide whether you want positive positions to be north or south of the
truck stop. Then plot the following positions on a number line.
a. The truck stop
b. 5 miles north of the truck stop
c. 3.5 miles south of the truck stop

Answer:

B

Step-by-step explanation:

I cannot see option D but regardless, C is a function for the following reasons

A function y = f(x) is a relationship in x such that f(x)  has only 1 value for a value of x.

In A, we see that for x = -1 we have y = 2 and y = 4 for a single value of x = -1

That alone is sufficient to dismiss this as a function. If that wasn't bad enough you see that y = -3 and -4 for x = 2

In C we see the same problem
For x = 5 there are two value of y = -3 and -2
So we can disregard C

In B we can see a definite pattern
Between x = -2 and x = 0 we see that y increases by 1 unit for every increase of 1 unit in x. This is a linear relationship with a slope of + 1

Between x = 0 and x = +2, for every increase of 1 unit in the x-value, the y-value decreases by 1 unit. This is also a linear relationship but with a slope of -1

In particular this is what is known as a piecewise function. Its function expression is different for different intervals of x value

It can be expressed as follows
f(x) =    x + 2 for -2 ≤ x ≤ 0
     =   -x + 2  for 0 ≤ x ≤ 2

The probability that Julian will roll a 3 on the next roll is approximately 16.67%. The probability of rolling a 3 on a normal 6-sided die is independent of the previous rolls. This means that regardless of the outcomes of Julian's previous rolls, the probability remains the same.

Explanation

On a 6-sided die, there is 1 favorable outcome for rolling a 3 (the number 3 itself) out of 6 possible outcomes (1, 2, 3, 4, 5, and 6).

To find the probability, you can use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

In this case:

Probability of rolling a 3 = 1 (favorable outcome) / 6 (total outcomes)

Probability of rolling a 3 = 1/6 ≈ 0.1667 or 16.67%

So, the probability that Julian will roll a 3 on the next roll is approximately 16.67%.

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Answer:

720 words

Step-by-step explanation:

From the question, we are given the function

f(x)=1.5x + 20

When f(x) = Cost function or the cost

From the question, f(x) = $1100

1100 = 1.5x + 20

1100 - 20 = 1.5x

1080 = 1.5x

x = 1080/1.5

x = 720

Therefore, Filipa has to write 720 words

Therefore , the solution of the given problem of angles comes out to be x has a value of 55 degrees.

Lines that curve together to form a skew's ends are divided into its largest and lowest walls using cartesian measurements. At a junction, there is a possibility that two wires will meet. Angle is another outcome of two things interacting. They are most comparable to dihedral shapes. A two-dimensional curve can be created by arranging two line beams in various configurations between their ends.

Here,

We can commence by utilizing the parallelogram's equal opposite angles. We know that angle x equals angle y because segment j and segment m are parallel. As a result, we can construct the solution shown below:

=> x + 90 + 35 = 180

When we simplify this solution, we obtain:

=> x + 125 = 180

The result of deducting 125 from both parts is:

=> x = 55

Consequently, x has a value of 55 degrees.

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\u gotta ask ur question

Step-by-step explanation:

240 is the answer you're looking for!

Step-by-step explanation:

To find the area, spilt the trapezoid into 3 shapes.

2 triangles (at the ends) and 1 rectangle (the center).

Let's start with the rectangle, the formula for rectangle area is:

\(l*w=A\)

The length of the rectangle is 12, the width is 20. Add the numbers in:

\(12*20=A\)

Solve:

\(12*20=240\)

The area of the rectangle is 240. Now solve for the Triangles.

The formula for finding the area of triangles are is:

\((L*W)/2\)

The length of the triangle is 12. To find the width subtract 20 from 30.

L = 12, W = 10. Add in the numbers.

\((12*10)/2 = A\)

Use order of operations to solve, start with parenthesis:

\(120/2=A\)

Rember to divide it by 2 because a triangle is half of a rectangle.

\(60 =A\)

Since there are two identical triangles, you don't need to solve for the other

Now, add the areas together:

\(60 + 120+60=A\)

Then solve:

\(180+60=A\)

\(240=A\)

The correct answer is 240.

Answer:

b = 70 degrees

c= 110 degrees

Step-by-step explanation:

10 hours ago — Find the length of the arc in terms of pi. A 60° В С C 12 AB = [?] T T Hint: The arc is only part of the circle. Enter Corporation. All Rights Reserued..

O Zeema gets paid £1870 per month in equal monthly payments.

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.

Now when the total amount earned in a month is given then the monthly payment is calculated by dividing the total amount by 12 as there are 12 months in a year.

Annual amount earned by O Zeema=£22,440

Therefore monthly amount earned=£22,440 ÷12=£1870

Hence O Zeema earns £1870 per month

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Answer:

It would be the third option, because the square root of 85 is 9.22, and 28/3 is 9.33 repeated.

Hope this helps, have a great day! :D

Step-by-step explanation:

According to the question The critical value for a two-tailed test with a significance level of 0.05 is approximately ±1.96.

Let's denote the proportion of mail carriers bitten in Cleveland as \(\(p_1\)\) and the proportion in Philadelphia as \(\(p_2\)\).

The null hypothesis \((\(H_0\))\) assumes that there is no significant difference between the proportions: \(\(p_1 = p_2\)\) . The alternative hypothesis \((\(H_1\))\)assumes that there is a significant difference: \(\(p_1 \neq p_2\)\).

The test statistic for the two-proportion z-test is calculated as:

\(\[z = \frac{{(p_1 - p_2) - 0}}{{\sqrt{\frac{{p_1(1-p_1)}}{n_1} + \frac{{p_2(1-p_2)}}{n_2}}}}\]\)

where \(\(n_1\) and \(n_2\)\) are the sample sizes for Cleveland and Philadelphia, respectively.

In this case, \(\(n_1 = 73\), \(n_2 = 80\), \(p_1 = \frac{{10}}{{73}}\), and \(p_2 = \frac{{16}}{{80}}\).\)

Calculating the test statistic:

\(\[z = \frac{{\left(\frac{{10}}{{73}} - \frac{{16}}{{80}}\right) - 0}}{{\sqrt{\frac{{\frac{{10}}{{73}}(1-\frac{{10}}{{73}})}}{73} + \frac{{\frac{{16}}{{80}}(1-\frac{{16}}{{80}})}}{80}}}}\]\)

The critical value for a two-tailed test with a significance level of 0.05 is approximately ±1.96.

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So the values of n that make each equation true are 9, 15, 48, 12, 81, and 18, respectively.

To find the value of n that makes each equation true, we need to isolate the variable n on one side of the equation by using inverse operations.

Divide both sides by 3 to get n by itself:
n = 27/3
n = 9

Add 3 to both sides to isolate the variable:
2n = 30

Divide both sides by 2 to get n by itself:
n = 15

Subtract 3 from both sides to isolate the variable:
n/2 = 24

Multiply both sides by 2 to get n by itself:
n = 48

Subtract 3 from both sides to isolate the variable:
2n = 24

Divide both sides by 2 to get n by itself:
n = 12

Multiply both sides by 3 to get n by itself:
n = 81

Multiply both sides by 2 to get rid of the fraction:
3n = 54

Divide both sides by 3 to get n by itself:
n = 18

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Answer:

cost price = $262.57

selling price = $302.48

Explanation:

The selling price is

Selling price = cost + markup

We know that markup is 15.2% of the cost price. Since the markup is $39.91,

dividing both sides by 0.152 gives

The selling price is

cost price + 15.2% of the cost price

= (100% + 15.2%) cost price

=115.2% cost price

Now, 115.2% of the cost price is

Hence the selling price is $302.48.

Therefore, to summerise,

cost price = $262.57

selling price = $302.48

9514 1404 393

Answer:

  86.6 inches

Step-by-step explanation:

The side length of an equilateral triangle is 2/√3 times the altitude. So, the perimeter is ...

  P = 3s = 3(25)(2/√3) = 50√3 ≈ 86.6 . . . . inches

The factored form of the equation are as follows;

Converting a quadratic function to factored form is called factoring.

Therefore,

let's factor the equation,

a.

d² - 7d + 6 = 0

d² - d - 6d + 6 = 0

d(d - 1) - 6(d - 1) = 0

(d - 6)(d - 1) = 0

b.

x² + 18x + 81 = 0

x² + 9x + 9x + 81 = 0

x(x + 9) + 9(x + 9) = 0

(x + 9)(x + 9) = 0

c.

u² + 7u - 60 = 0

u² - 5u + 12u - 60 = 0

u(u - 5) 12(u - 5) = 0

(u + 12)(u - 5) = 0

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A structural break occurs when we see A. an unexpected shift in time-series data.

It is the change in a time series's data-generating mechanism, it is a phenomenon that occurs when a significant event or structural shift in the economy alters the underlying data-generating mechanism. A structural break can happen for several reasons, including natural catastrophes, changes in economic policy, new inventions, and other reasons that alter the way the data is generated.

In the presence of a structural break, we can't assume that the relationships between variables before and after the break are the same. The primary objective of identifying structural breaks in the time-series is to detect changes in the behavior of the series over time, such as changes in the variance of the series, changes in the mean of the series, and changes in the covariance of the series. So therefore the correct answer is A. an unexpected shift in time-series data, the structural break occurs.

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Answer:

x = 1/2 and

x = -15/2

Step-by-step explanation:

First, get the absolute value alone on one side if the equation.

2 |2x + 7 | = 16

Divide both sides by 2.

| 2x + 7 | = 8

Once the absolute value sign is by itself, you will separate the equation into two separate equations.

2x+7=8 and 2x+7=-8

Solve these two equations separately and get two solutions.

2x + 7 = 8

Subtract 7.

2x = 1

Divide by 2.

x = 1/2 Here is one solution.

2x + 7 = -8

Subtract 7.

2x = -15

Divide by 2.

x = -15/2 Here is a second solution.

Answer:

x = - \(\frac{15}{2}\) , x = \(\frac{1}{2}\)

Step-by-step explanation:

2 | 2x + 7 | = 16 ( divide both sides by 2 )

| 2x + 7 | = 8

the absolute value function always gives a positive result, but the expression inside can be positive or negative , that is

2x + 7 = 8 ( subtract 7 from both sides )

2x = 1 ( divide both sides by 2 )

x = \(\frac{1}{2}\)

or

- (2x + 7) = 8

- 2x - 7 = 8 ( add 7 to both sides )

- 2x = 15 ( divide both sides by - 2 )

x = - \(\frac{15}{2}\)

As a check

substitute these values into the left side and if equal to the right side then they are a solution

x = \(\frac{1}{2}\)

2 | 2(\(\frac{1}{2}\) ) + 7 | = 2 | 1 + 7 | = 2 | 8 | = 16 = right side

x = - \(\frac{15}{2}\)

2 | 2(- \(\frac{15}{2}\) ) + 7 | = 2 | - 15 + 7 | = 2 | - 8 | = 2 | 8 | = 16 = right side

then x = - \(\frac{15}{2}\) and x = \(\frac{1}{2}\) are the solutions

Answer:

-2

you take two away every time

The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000

formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

I bedroom = x

2 bedroom = y

3 bedroom = z

All the condition s gjvbbs'

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

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Answer:

A) 210 B) 0.18

Step-by-step explanation:

got it right

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet

Answer:

y = 70x

Step-by-step explanation:

The correct steps he could use to solve the quadratic equation are;

Steps 2, 3, 5

We are told that Sergey is solving the quadratic equation given as;

5x² + 20x – 7 = 0.

Now, when solving a quadratic equation, we can employ factorization, completing the square of via the use of quadratic formula.

Now, one step that can be taken is to add 7 to both sides to get;

5x² + 20x = 7

Another step is to factorize the left to get;

x + 2 = ±√(27/5)

Another step that can be taken is to complete the square on the left to get; 5(x² + 4x + 4) = 7 + 20

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The options are;

5(x² + 4x + 4) = –7 + 20 x + 2

x + 2 = ±√(27/5)

5(x² + 4x) = 7

5(x² + 4x + 4) = 7 + 20

5(x² + 4x) = -7

Answer:

3rd quadrant

Step-by-step explanation:

Step-by-step explanation:

Answer:17

Step-by-step explanation: you’re welcome

Answer: 10

Step-by-step explanation:

The point 7.4 on the number line is 3/5 of the way from the point -7 to the point 17. This is solved by calculating the distance between -7 and 17, multiplying that by 3/5, and adding the result to -7.

The subject of this question is Mathematics, and it is typically dealt with at the Middle School level. To solve this you need to find the distance between the two points (-7 and 17) on the number line. The distance can be calculated with subtraction, so 17 - (-7) = 24. Now, to find a point that is 3/5 of the way from -7 to 17, you multiply this distance by 3/5, hence 24 * 3/5 = 14.4. Add this to the starting point (-7), results -7 + 14.4 = 7.4. So, point 7.4 on the number line is 3/5 of the way from point -7 to point 17.

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Answer:

slice priced $1.50 is better value

Step-by-step explanation:

Angles around a point add up to 360°

Area of a circle = πr²

360° ÷ 60° = 6

⇒ This slice is 1/6 of the whole pizza

⇒ area of the slice = (1/6)π × 6² = 6π in²

⇒ $1.50 ÷ 6π = $0.079577... per in²

360° ÷ 45° = 8

⇒ This slice is 1/8 of the whole pizza

⇒ area of the slice = (1/8)π × 7² = (49/8)π in²

⇒ $1.70 ÷ (49/8)π = $0.088347.. per in²

Therefore, the slice priced $1.50 is cheaper per in²

hypotenuse of a right triangle is always the side opposite the right angle.

In geometry, a right triangle is a type of triangle that contains one angle measuring 90 degrees, known as the right angle. Right triangles have several distinguishing properties, and one of the fundamental concepts associated with them is the identification of the sides relative to the right angle. In this detailed explanation, we will explore the term that describes the specific side of a right triangle that is always opposite the right angle.

In a right triangle, there are three sides: the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the side opposite the right angle and is the longest side of the triangle. The adjacent side is the side that forms the right angle with the hypotenuse, while the opposite side is the side that is opposite the right angle. The term that refers to the side of a right triangle that is always opposite the right angle is the "hypotenuse."

To better understand the concept, let's consider the Pythagorean theorem, which is a fundamental relationship in right triangles. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as:

\(c^2 = a^2 + b^2\)

In this equation, "c" represents the length of the hypotenuse, while "a" and "b" represent the lengths of the other two sides (adjacent and opposite). By rearranging the equation, we can solve for the hypotenuse (c):

\(c = \sqrt(a^2 + b^2)\)

From this equation, we can see that the hypotenuse is determined by the lengths of the other two sides of the right triangle. The relationship expressed by the Pythagorean theorem highlights the importance of the hypotenuse in determining the overall shape and size of the right triangle.

Furthermore, the hypotenuse is significant because it provides the longest side of the right triangle. Its length directly influences the triangle's shape and can be used to calculate various properties, such as the triangle's area or the lengths of the other sides.

In trigonometry, the hypotenuse is also crucial for defining trigonometric ratios, such as sine, cosine, and tangent, which are used to establish relationships between the sides and angles of a right triangle.

In conclusion, the side of a right triangle that is always opposite the right angle is called the "hypotenuse." It is the longest side of the triangle and is directly related to the lengths of the other two sides through the Pythagorean theorem. Understanding the concept of the hypotenuse is essential for working with right triangles, as it plays a fundamental role in determining the triangle's properties, shape, and trigonometric relationships.

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