Find the missing length indicated

Find The Missing Length Indicated

Answers

Answer 1

The value of the missing length indicated is 128 units.

What are similar triangles?

Two or more triangles are said to be similar when on comparing their properties, they have some common relations. But similarity is not congruency.

Let the missing length indicated be represented by x. So that comparing the triangles, we have;

21/ 77 = 48/ (48 + x)

21(48 + x) = 48*77

1008 + 21x = 3696

21x = 3696 - 1008

      = 2688

x = 2688/ 21

  = 128

x = 128

The missing length indicated is 128 units.

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Related Questions


Draw a graph of two linear equations whose associated system has the solution (-1,-3).
Choose the correct graph.

Answers

Answer:

Step-by-step explanation:

first you sit on the tolit then think and you'll get your anwser

Determine what fraction of the figure is shaded.

Answers

Answer:

I would say that it would be 1/3 because there are 3 parts

Answer:

3/7

Step-by-step explanation:

There are 4 small squares inside the figure.

The partial squares are all half squares, so each two triangles have the same are as 1 small square. There are 6 small triangles which add to 3 squares.

4 + 3 = 7

Total area = 7 squares

Shaded area = 2 squares + 2 half squares = 3 squares

Fraction of shaded area = 3/7

g is a trigonometric function of the form � ( � ) = � cos ⁡ ( � � + � ) + � g(x)=acos(bx+c)+dg, left parenthesis, x, right parenthesis, equals, a, cosine, left parenthesis, b, x, plus, c, right parenthesis, plus, d. Below is the graph of � ( � ) g(x)g, left parenthesis, x, right parenthesis. The function has a maximum point at ( 3.5 , − 4 ) (3.5,−4)left parenthesis, 3, point, 5, comma, minus, 4, right parenthesis and a minimum point at ( − 1 , − 5 ) (−1,−5)left parenthesis, minus, 1, comma, minus, 5, right parenthesis. Find a formula for � ( � ) g(x)g, left parenthesis, x, right parenthesis. Give an exact expression. � ( � ) = g(x)=g, left parenthesis, x, right parenthesis, equals A graph of a trigonometric wave on an x y coordinate plane. The x axis scales by two and the y axis scales by one. There is a point on the graph at the minimum at (negative one, negative five) and a point on the maximum next to the mentioned point at (three and one half, negative four).

Answers

The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.

Describe Function?

A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.

From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).

The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.

Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.

To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.

To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.

Substituting these values into the equation for g(x), we have:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4

Therefore, the exact expression for g(x) is:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.

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Please try to explain it

Answers

The table of value of the function and it's graph are attached below

What is the table of value

Here's the table of values for the function m(x) = 0.5x^2 with x ranging from -5 to 5

All we need to do is simply substitute the corresponding value of x into the function to get the value of y.

m(x) = 0.5x^2

m(-5) = 0.5(-5)^2

m(-5) = 12.5

Doing this for all other values, we will have our table below

x m(x)

-5 12.5

-4 8.0

-3 4.5

-2 2.0

-1 0.5

0 0.0

1 0.5

2 2.0

3 4.5

4 8.0

5 12.5

You can use this table to plot the function using a graphing calculator.

Kindly find the attached graph below;

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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS!!!!

Answers

1,2,4 are all linear

A new water park, Tony’s Tidal Takeover, just opened. You have not heard anything specific about how much it costs to go to this park, but some of your friends have told you what they spent. The information is organized in the table below.

Answers

Since we can go on the same number of rides at both parks with $14, we would choose the park with the lower admission fee, which is Park A.

What is percent?

Percent is a way of expressing a number as a fraction of 100, often used to represent a proportion or rate. It is denoted by the symbol "%". For example, if 30 out of 100 students in a class got an "A" grade, then the percentage of students who got an "A" grade is 30%.

Here,

To determine which park to attend with only $14 to spend, we need to find out how many rides we can go on at each park with that amount of money.

For Park A, we can divide the $14 by the cost per ride, which is $2.50:

$15 - $12 = $3 for 4 rides,

$3 ÷ 4 = $0.75 per ride;

$0.75 x 2 rides = $1.50.

Thus, we can go on 2 rides at Park A.

For Park B, we can divide the $14 by the cost per ride, which is $1.50:

$16.50 - $12 = $4.50 for 6 rides,

$4.50 ÷ 6 = $0.75 per ride;

$0.75 x 2 rides = $1.50

Thus, we can go on 2 rides at Park B.

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Need help fill in the box please

Answers

The value of function f(x) will be 2,-1/2,-1,5/2,4 when x is equal to 0,1,2,-1,-2 respectively.

The given function is f(x) = (-3/2)x + 2

We want to find the value of f(x) for all values of x, we simply substitute different values of x in the given function and evaluate it. For example:

If x = 0, then [tex]$f(0)=-{\frac{3}{2}}\times(0)+2=2$[/tex]

If x = 1, then  [tex]$f(1)=-{\frac{3}{2}}\times(1)+2=-{\frac{1}{2}}$[/tex]

If x = 2, then [tex]$f(2)={\frac{-3}{2}}\times(2)+2=-1$[/tex]

If x = -1, then [tex]$f(-1)=-{\frac{3}{2}}\times(-1)+2={\frac{5}{2}}$[/tex]

If x = -2, then [tex]$f(-2)=-{\frac{3}{2}}\times(-2)+2=4$[/tex]

So, the value of f(x) for all values of x is given by f(x) = (-3/2)x + 2

Similarly, we can find the value of f(x) for any value of x.

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The value of function f(x) will be 2,[tex]\frac{1}{2}[/tex],-1,[tex]\frac{7}{2}[/tex],5 when x is 0,1,2,-1,-2 respectively.

What is the function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function of s domain and co domain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

What Does a Function's Table of Values Mean?

In mathematics ,The list of numbers used to replace the variable is defined by the table of values. The   value of function at a solution is determined by the optimization problem of value function, which only depends on the problem's parameters.

The given function is f(x) =[tex]\frac{-3}{2} x[/tex] + 2

We find the value of f(x) ∀ x,

we substitute different values of x in the given function and evaluate it. For example:

If x = 0, then

f(x) =[tex]\frac{-3}{2} *0+2[/tex] ⇒f(x)=2

If x = 1, then  

f(x)

[tex]=(\frac{-3}{2} *1)+2\\=\frac{-3}{2} +2\\=\frac{-3+4}{2}\\=\frac{1}{2}\\[/tex]

If x = 2, then f(x)=

[tex]=(\frac{-3}{2} *2)+2\\=\frac{-6}{2} +2\\=\frac{-6+4}{2}\\=\frac{-2}{2}\\=-1[/tex]

If x = -1, then

[tex]f(x)=(\frac{-3}{2} *(-1))+2\\=\frac{3}{2} +2\\=\frac{3+4}{2}\\=\frac{7}{2}\\[/tex]

If x = -2, then

[tex]f(x)=(\frac{-3}{2} *(-2))+2\\=\frac{6}{2} +2\\=\frac{6+4}{2}\\=\frac{10}{2}\\=5[/tex]

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What would the area of this shape be?

Answers

Answer:

3,081.6 square feet

Step-by-step explanation:

Draw the diagonal that divides this figure into two right triangles. We then have:

[tex] \frac{1}{2} (24)(76.8) + \frac{1}{2} (60)(72) = 921.6 + 2160 = 3081.6[/tex]

What is statistical​ inference? Why is it​ important?

(In your own words, please! ) Thanks!

Answers

Statistical inference is the process of using data from a sample to make generalizations or draw conclusions about a larger population.

What is statistical Inference?

Based on the sample data, assumptions are made about the fundamental traits of the population, and the uncertainty in those assumptions is quantified using statistical techniques.

Because it enables us to forecast the future and make judgements based on incomplete data, statistical inference is crucial. For instance, with a sample of data, it enables us to confidently estimate population parameters such as averages and proportions. This can be helpful in a variety of contexts, including marketing analysis, surveys of public opinion, clinical trials, and manufacturing quality control.

By comparing the results of several groups or treatments, statistical inference also enables us to assess the efficacy of interventions or treatments.This can inform decisions about which treatments are most effective or which interventions should be implemented.

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I really need help pls!​

Answers

The integer that should be added to y² + 7y to make it factorable is 49/4.

What integer should be added?

To factor y² + 7y, we need to find two numbers that multiply to give us the coefficient of y (which is 7) and add up to give us the coefficient of y² (which is 1).

We can use the technique of completing the square to find the missing number.

To complete the square, we add the square of half of the coefficient of y (which is (7/2)² = 49/4) to both sides of the equation.

So, we have:

y² + 7y + 49/4 = y² + 7y + 49/4 + 49/4

= (y + 7/2)²

Therefore, to factor y² + 7y, we need to add 49/4 to it.

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The sum of three consecutive odd numbers is 39. What is the value of the least number?

Answers

Answer: 11

Step-by-step explanation:

The three integers are 11, 13, and 15.

Explanation:We shall consider the integers as x, 

(x+2), and (x+4).

The sum of these is 39, so we can write:

x+(x+2)+(x+4)=39

Open the brackets and simplify.

x+x+2+x+4=393x+6=39

Subtract 6 from each side.

3x=33

Divide both sides by 3.

x=11

Therefore: 

(x+2)=13 

and

(x+4)=15

O 400
560
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460
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Grace needs to make 35 pounds of turkey for dinner. The turkey packaging at the grocery store indicates how many
ounces each turkey weighs. How many ounces of turkey does Grace need in order to have enough turkey for dinner?
O 500
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The answer of the given question based on the  ounces of turkey does Grace need in order to have enough turkey for dinner is , Grace needs 560 ounces of turkey for dinner.

What is Weight unit?

A weight unit is a standard of measurement used to express the mass or weight of an object. The most commonly used weight unit is the kilogram, which is the base unit of mass in the International System of Units (SI). Other common weight units include pounds, ounces, grams, and tons. Weight units are used in a variety of applications, including commerce, industry, and science. They are also used in everyday life to describe the weight of objects such as food, people, and animals. Accurate measurement of weight is important in many areas, including manufacturing, transportation, and health care. Weight units can be converted from one system to another using conversion factors.

There are 16 ounces in 1 pound. To convert 35 pounds to ounces, you need to multiply by 16:

35 pounds * 16 ounces/pound = 560 ounces

Therefore, Grace needs 560 ounces of turkey for dinner.

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The answer to the question is that Grace requires 560 ounces of turkey for dinner, or the amount of turkey she needs to have enough for dinner.

What is Weight unit?

A weight unit is a unit of measurement that is used to describe an object's mass or weight. The kilogram, the base measure of mass in the International System of Units, is the most widely used weight unit. (SI). The weights in pounds, ounces, grams, and tons are other popular weight units. Numerous fields, including business, industry, and research, use weight units.

In daily living, they are also used to describe the weight of things like food, people, and animals. In a variety of contexts, including production, transportation, and health care, accurate weight measurement is crucial. Conversion factors can be used to translate weight measures between different systems.

There are 16 ounces in 1 pound. To convert 35 pounds to ounces, you need to multiply by 16:

35 pounds * 16 ounces/pound = 560 ounces

Therefore, Grace needs 560 ounces of turkey for dinner.

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The complete question is,

Grace needs to make 35 pounds of turkey for dinner. The turkey packaging at the grocery store indicates how many ounces each turkey weighs. How many ounces of turkey does Grace need in order to have enough turkey for dinner?

DUE TODAY, I WILL MARK BRAINLIEST
screenshot provided!!

Answers

Answer:

6% for open side up

14% for closed side up

80% for landing on side

Please help!!! WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!

Golf Skydiving Fishing 100-yard dash
Drag racing

1. Brainstorm: Which of the above sports do you think the graph could represent? Why?

2. Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?

(Photo of graph is added)
Please!!!!! 30 points added!

Answers

Answer:The graph represent skydiving, Because when you jump out of the plane you have a bunch of speed and when you pull your parachute the speed will drop exceedingly.

Step-by-step explanation:

help pls show ur work

Answers

The height of the telephone pole is approximately 12.5 ft.

And the ladder will reach approximately 6 ft up the building.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It focuses on the study of the functions of angles, such as sine, cosine, tangent, cosecant, secant, and cotangent, and how they are used to solve problems involving triangles.

Part 9:-To solve the problem, we can use trigonometry. Let's draw a right triangle where the height of the pole is the opposite side, the distance from the top of the pole to the attachment point of the guy wire is the adjacent side, and the guy wire itself is the hypotenuse. We know the length of the hypotenuse is 12 ft, and the length of the adjacent side is 9.5 ft. The angle between the hypotenuse and the ground is given as 51°.

Using the trigonometric function tangent, we can calculate the height of the pole as follows:

tan(51°) = height of pole / 9.5 ft

height of pole = tan(51°) × 9.5 ft

height of pole ≈ 12.5 ft

Therefore, the height of the telephone pole is approximately 12.5 ft.

Part 10:-Again, we can use trigonometry to solve the problem. Let's draw a right triangle where the height of the building is the opposite side, the distance from the base of the building to the ladder is the adjacent side, and the ladder itself is the hypotenuse. We know the length of the hypotenuse is 8 ft, and the angle between the hypotenuse and the ground is given as 46°.

Using the trigonometric function sine, we can calculate the height of the building as follows:

sin(46°) = height of building / 8 ft

height of building = sin(46°) × 8 ft

height of building ≈ 6 ft

Therefore, the ladder will reach approximately 6 ft up the building. Rounded to the nearest whole number, the answer is 6 ft.

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Keisha is playing a game using a wheel divided into 8 equal sectors, as shown in the diagram below. Each time the spinner lands on blue, she will win a prize.

If Keisha spins this wheel twice, what is the probability that she will win a prize on both spins?

show step bye step

Answers

On solving the provided question we can say that As a result, Keisha's probability chances of winning a reward on both spins are 1/64, or around 0.0156.

What is probability?

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Because the results of the two spins are independent of each other, we need to multiply the chance of winning a prize on the first spin by the likelihood of winning a prize on the second spin to obtain the probability that She will win a prize on both spins.

Because there are 8 equal sectors on the wheel and only one of them is blue, the likelihood of winning a reward on any given spin is 1/8.

Hence the odds of winning a reward on both spins are:

(1/8) x (1/8) = 1/64

As a result, Keisha's chances of winning a reward on both spins are 1/64, or around 0.0156.

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Suppose you conduct an experiment with 24 subjects and your t-obt turns out to be 2.92, which is statistically significant. Which of the following is the correct way to report your results?
A. t-obt=2.92, p<0.05
B. t(24)=2.92, p<0.05
C. t(23)=2.92, p>0.05
D. t(23)=2.92, p<0.05

Answers

The correct way to report the results of this experiment is t(23)=2.92, p<0.05.

Therefore answer is D.

The notation 't(24)=2.92, p<0.05' indicates the degrees of freedom (24), the value of the test statistic (2.92), and the level of significance (p<0.05).

The notation "t(23)" indicates that the t-value was calculated with 24 degrees of freedom, which is the number of subjects minus 1. The level of significance (p<0.05) means that the probability of obtaining a t-value of 2.92 or greater by chance alone is less than 5%. This indicates that the results are statistically significant and unlikely to be due to random chance.

Option A is incomplete because it does not indicate the degrees of freedom. Option B is incorrect because it states that the degrees of freedom is 24. Option C is incorrect because it incorrectly states that the probability is greater than 0.05, which would mean that the results are not statistically significant. Therefore the correct answer is option D.

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University car wash purchased new soap

Answers

Answer: University Car Wash purchased new soap dispensing equipment that cost $258,000 including installation. The company estimates that the equipment will have a residual value of $28,500. University Car Wash also estimates it will use the machine for six years or about 12,500 total hours.

Step-by-step explanation:

What is the measure of each numbered angle?

Answers

We can use various parallel line properties to solve this problem like corresponding angles, alternate interior-exterior angle, Vertically opposite angle, etc.

What is the measure of each of the numbered angles?

Here are the measure of each angle -

Angle 1 = 76 degrees (By using verically opposite angle property)

Angle 2 = 32 degrees (By using linear property)

Angle 3 = 72 degrees (By using verically opposite angle property)

Angle 4 = 32 degrees (By using linear property)

Angle 5 = 72 degrees (By using alternate interior property)

Angle 6 = 108 degrees

Angle 7 = 72 degrees

Angle 8 = 72 degrees

Angle 9 = 76 degrees

Angle 10 = 76 degrees

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Adalia spent 1/6 of her money on food, 3/5 of the remaining on transport and 1/12 of what still remained on sweets. If she still had $22.00 left, how much was her money?

Answers

Answer:

$132

Step-by-step explanation:

Hope this helps!

A bag contains 3 blue, 9 green, and 8 red
marbles. Find the probability of picking 3 red
marbles if each marble is NOT returned to the
bag before the next marble is picked.
P(red and red and red)

1/6840

1/8000

8/125

14/285

Answers

the probability of picking 3 red marbles if each marble is NOT returned to the bag before the next marble is picked is14/285.

Define probability

Probability is a measure of the likelihood or chance that a particular event will occur, expressed as a number between 0 and 1. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

After the first red marble is drawn, there will be 19 marbles left in the bag, of which 7 are red.

So, the probability of picking a red marble on the second draw, given that the first marble was red and not returned to the bag, is 7/19.

Similarly, after the second red marble is drawn, there will be 18 marbles left in the bag, of which 6 are red.

So, the probability of picking a red marble on the third draw, given that the first two marbles were red and not returned to the bag, is 6/18 or 1/3.

Therefore, the probability of picking 3 red marbles in a row is:

(8/20) x (7/19) x (6/18) = 14/285

So, the answer is 14/285.

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negative five and one seven divided by negative two and two fifths

Answers

Answer:

Step-by-step explanation:

[tex]-5\frac{1}{7} \div 2\frac{2}{5} =-\frac{36}{7}\div \frac{12}{5}[/tex]

                [tex]=-\frac{36}{7} \times \frac{5}{12}[/tex]

                [tex]=-\frac{3}{7} \times \frac{5}{1}[/tex]           (÷ top and bottom by 12)

                [tex]=-\frac{15}{7}[/tex]

                [tex]=-2\frac{1}{7}[/tex]

the circumference of a circle is 20 π centimeters what is the area in square centimeters express your answer in terms of Pi​

Answers

Answer:

A = 100π cm²

Step-by-step explanation:

the area (A)  of a circle is calculated as

A = πr² ( r is the radius )

we require to find r

the circumference (C) of a circle is calculated as

C = 2πr

given

C = 20π , then

2πr = 20π ( divide both sides by 2π )

r = 10

Then

A = π × 10² = 100π cm²

How do I make x the subject of y= a√x-b

Answers

Divide both sides by y

The bill at a restaurant comes to $40. The sales tax is 6% and you will leave a 15% tip. What is the total cost?

Answers

40+6%+15%

=$ 42.55

I hope this helps!

Which statement is true?

Answers

The correct answer is (D) It is between 0.00007 and 0.0007 square miles

What is exponent ?

An exponent, also known as a power, is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript to the right of the quantity being raised to a power. For example, in the expression 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, or 2 x 2 x 2 = 8. Exponents are commonly used in mathematics, physics, engineering, and other sciences to represent very large or very small numbers, as well as to simplify calculations involving repeated multiplication.

According to the question:
To convert 7.4E-4 to a standard decimal, we move the decimal point four places to the left since the exponent is negative. This gives us:

7.4E-4 = 0.00074

Therefore, the area of the piece of land is 0.00074 square miles.

The correct answer is (D) It is between 0.00007 and 0.0007 square miles.

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Out of 160 workers surveyed at a​ company, 23 walk to work.
a.
What is the experimental probability that a randomly selected worker at that company walks to​ work?
b.
Predict about how many of the 2600 workers at the company walk to work.

Answers

A. The experimental probability of a randomly selected worker walking to work is approximately 0.144. B. We can predict that about 374 workers walk to work out of the 2600 workers at the company.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

According to the given information:

a. The experimental probability of a randomly selected worker walking to work can be calculated as:

Experimental probability = Number of workers who walk to work / Total number of workers surveyed

Experimental probability = 23/160

Experimental probability ≈ 0.144

Therefore, the experimental probability that a randomly selected worker at that company walks to work is approximately 0.144.

b. To predict how many of the 2600 workers at the company walk to work, we can use the experimental probability found in part (a) and multiply it by the total number of workers:

Number of workers who walk to work = Experimental probability x Total number of workers

Number of workers who walk to work = 0.144 x 2600

Number of workers who walk to work ≈ 374.4

Therefore, we can predict that about 374 workers walk to work out of the 2600 workers at the company.

Therefore,a. The experimental probability of a randomly selected worker walking to work is approximately 0.144.b. We can predict that about 374 workers walk to work out of the 2600 workers at the company.

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Core concept
EXAMPLE 4
Using the Distance Formula
Your school is 4 miles east and 1 mile south of your apartment. A recycling center,
where your class is going on a field trip, is 2 miles east and 3 miles north of your
apartment. Estimate the distance between the recycling center and your school.

Answers

The estimated distance between the recycling center and your school is approximately 4.47 miles.  

WHAT IS DISTANCE?

Distance is a numerical measurement of the amount of space between two points. In physics, distance is often described as the length of a path traveled by an object from one point to another. Distance is a scalar quantity, which means it has magnitude but not direction. It is typically measured in units such as meters (m), kilometers (km), feet (ft), or miles (mi).
Distance is an important concept in many fields, including physics, mathematics, geography, and engineering. It is used to describe the separation between two objects or locations, and to calculate various quantities such as speed, velocity, and acceleration.

To estimate the distance between the recycling center and your school, we can use the distance formula:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y) represents the coordinates of your school, (x₂, y₂) represents the coordinates of the recycling center, and the √ symbol denotes the square root.

From the problem statement, we know that:

Your school is 4 miles east and 1 mile south of your apartment. Therefore, the coordinates of your school are (4, -1).

The recycling center is 2 miles east and 3 miles north of your apartment. Therefore, the coordinates of the recycling center are (2, 3).

Substituting these values into the distance formula, we get:

distance = √((2 - 4)²+ (3 - (-1))²)

= √((-2)² + (4)²)

= √(4 + 16)

= √20

≈ 4.47 miles

Therefore, the estimated distance between the recycling center and your school is approximately 4.47 miles.

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Brianna goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Brianna decides to leave a tip of 19% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Brianna paid.

Answers

Brianna left a tip οf 19% οn the entire bill, which includes the tax. Therefοre, the tοtal amοunt Brianna paid is 1.2495(xx), so the expressiοn in terms οf xx that represents the tοtal amοunt Brianna paid is 1.2495(xx).

What is the equivalent expressiοn?

Equivalent expressiοns are expressiοns that perfοrm the same functiοn despite their appearance. If twο algebraic expressiοns are equivalent, they have the same value when we use the same variable value.

The tax οn the bill is 5% οf xx, which can be expressed as 0.05(xx). Therefοre, the tοtal bill including tax is:

xx + 0.05(xx) = 1.05(xx)

Brianna left a tip οf 19% οn the entire bill, which includes the tax. Therefοre, the tοtal amοunt Brianna paid is:

1.05(xx) + 0.19(1.05(xx)) = 1.05(xx) + 0.1995(xx)

Simplifying the expressiοn, we get:

Tοtal amοunt Brianna paid = 1.2495(xx)

Therefοre, the expressiοn in terms οf xx that represents the tοtal amοunt Brianna paid is 1.2495(xx).

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Question 5(Multiple Choice Worth 1 points)
(08.02 LC)

Complete the square to transform the expression x2 − 2x − 2 into the form a(x − h)2 + k.

(x − 1)2 + 3
(x − 1)2 − 3
(x − 2)2 − 3
(x − 2)2 + 3

Answers

The expression  x2 − 2x − 2 can be transformed into the form (x − 1)2 +-3.

Completing the square is a technique used to convert a quadratic expression of the form ax^2 + bx + c into the form a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex of the quadratic function.

To complete the square, we need to add and subtract the square of half of the coefficient of x from the expression.

Starting with x2 − 2x − 2:

x2 − 2x − 2 = x2 - 2x + (-2)

We take half of the coefficient of x, which is -1, and square it to get 1.

x2 - 2x + 1 - 1 - 2 = (x - 1)2 - 3

Therefore, the expression x2 − 2x − 2 can be transformed into the form (x − 1)2 − 3, which is an option (B).

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