An Olympic-distance triathlon includes a 1. 5 km swim. To determine the swim course of an Olympic-distance triathlon in Shoe Lake, the planners need to first find the distance between points A and B on opposite sides of a lake in order to determine where to place the buoys that will mark the swim course. You have been called in to help with determining the distances. From a point C on the shore, you find that CA = 259 m, CB = 423 m, and angle ACB measures 1320.


A. Determine the distance across the lake

B. Is the lake long enough to simply have an "out-and-back" swim course for this triathlon (that is: swimming from point A to point B and then back to point A)? If not, what additional distance will need to be set off of the straight-line distance between A and B in order to meet the distance requirements for this triathlon?

The required equation is x × 3 = 528.75 - 60.

The cost of the labor per hour is $156.25

How do equations work?

The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.

Let x be the cost of the labor per hour.

We know that

x × 3 = labor cost

60 + x × 3 = total cost

We also know that the total cost is $528.75

So we can write the equation:

60 + x × 3 = 528.75

Solving for x:

x × 3 = 528.75 - 60

x × 3 = 468.75

x = 468.75/3

x = 156.25

Therefore, the cost of the labor per hour is $156.25

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Answer:

- 14

Step-by-step explanation:

the bars around 2t , indicate the absolute value of 2t

the absolute value function always gives a positive value , that is

| - a | = | a | = a

so for example

| - 4 | = | 4 | = 4

given

[tex]\frac{2}{3}[/tex] p - | 2t | - s² ( substitute values for p, t and s into the expression )

= [tex]\frac{2}{3}[/tex] × 12 - | 2(- 3) | - (- 4)²

= 2 × 4 - | - 6 | - 16

= 8 - 6 - 16

= 2 - 16

= - 14

Answer:

The correct answer is C. 1

Answer:

12ft  x 9ft

Step-by-step explanation:

1/6" equals 1' actual ==> 1"=6'actual.

1.5" = 9'

2" = 12'

By utilizing the given scale of 1/6 inch equals 1 foot, the actual length of the bathroom is calculated to be 9 feet and width is 12 feet, from the given measurements of the drawing.

The mentioned math problem is based on scale conversion, specifically in the realm of measurement. Given that every 1/6 inch on the scale drawing equals 1 foot in reality, the first step to solving this problem is to convert the measurements of the drawing into scale inches. To convert the length of 1 1/2 inches to the actual length, multiply 1.5 by 6 (as 1 inch is 6 times of 1/6 inch). This equals to 9 feet. Similarly, for the width of 2 inches, multiply 2 by 6 to get 12 feet.

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These two lines intercept on a graph on the coordinate X(0, 1) Y(9, 7).

The term "intercept" refers to the location where a line or curve intersects an axis on a graph. An object's x-intercept is defined as where a point crosses the x-axis. The term "y-intercept" refers to a point that crosses the y-axis. The intersection of the x-axis and the y-axis is what is meant by a line's intercept.

step1

y=-2x+9

graph the line using the slope and y intercept or two points

y=-2x+9

X(0,1) Y(9,7)

step2

y=3x-6

slope 3 y intercept (0,-6)

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The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.

(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)

This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.

The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.

The result is 4x².

Then, subtract 4x² from 8x²³ to get the remainder of 4x³.

Next, divide 4x² into 21².

The result is 33x.

Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.

Finally, divide 4x²-33x into 67x.

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The value of 21•15 equals (20+1)•15. This is true.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of 21•15 will be:

= 21 × 15

= 315

Also (20+1)•15 will be:

= 21 × 15

= 315

Therefore, they're equal.

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Complete question

The value of 21•15 equals (20+1)•15. True or false?

Answer:

no.................,.............

The final balace in Tracy's bank account is $ 361.80.

In this question we must pay attention to every movement in a bank account and determine final balance within. The hint is having an active reading in the meaning of translating every Tracy's movement in additions and subtractions, First, we translate very sentence into numbers and signs:

Tracy's checking account: + $ 300.00

Tracy bought new sneakers: - $ 63.00

Tracy deposited a paycheck: + $ 43.25

Tracy wrote a check: - $ 17.75

Tracy wrote a check: - $ 9.45

Tracy made a withdrawal at her bank: - $ 20.00

Tracy deposited a paycheck: + $ 43.25

Tracy wrote a check: - $ 18.00

Tracy made a withdrawal at another bank: - $ 20.00 - $ 1.50

Tracy deposited her birthday money: + $ 125.00

Second, calculate the final balance in Tracy's account:

x = 300.00 - 63.00 + 43.25 - 17.75 - 9.45 - 20.00 + 43.25 - 18.00 - 20.00 - 1.50 + 125.00

x = 361.80

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Answer: The answer is 5x-8.

Step-by-step explanation: The equation we have is (8x-9)-(3x-1). The first step is to write the equation as shown:

8x-9-(3x-1)

After that step, next is to apply the distributive law:

8x-9-3x+1

Then, group/combine like terms:

8x-3x-9+1

Then adding similar elements:

5x-9+1

And finally, solving:

5x-8

Answer:

x = p(m-n)

Step-by-step explanation:

we can eliminate the 'p' in the denominator by multiplying each side of the equation by 'p' to get:

mp = np + x

now we can subtract 'np' from each side to get:

mp - np = x

we can further simplify it as:

p(m-n) = x

Answer:

X=n-p×m

Step-by-step explanation:

m=n-x/p

p×m=n-x

n-p×m=n+x-n

X=n-p×m

Answer:

Step-by-step explanation:

a)
0.5 x (a + b) x h
0.5 x (5 + 30) x 30
Area = 525

b) Overestimate

The marginal column total for the given data is option D: 39; 16.

What is marginal total?

A set of marginal totals is produced when the cell frequencies of a (multidimensional) contingency table are added over one or more of the classifying variables. The row and column totals are the marginal totals for a two-dimensional table.

The sum of the row entries or the sum of the column entries are called the marginal totals. Marginal distributions are computed by dividing the row or column totals by the overall total.

The number of men who prefer to eat fish = 11

The number of women who prefer to eat fish = 6

The number of men who prefer to eat red meat = 28

The number of women who prefer to eat red meat = 10

So, the marginal column total for the number of men who prefer to eat fish and red meat collectively is -

11 + 28 = 39

The marginal column total for the number of women who prefer to eat fish and red meat collectively is -

6 + 10 = 16

Therefore, the marginal total is 39, 16.

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Answer:

170 miles

Step-by-step explanation:

Use 80 miles and 150 miles as the legs of a right triangle, and find the length of the hypotenuse using the Pythagorean theorem.

a² + b² = c²

80² + 150² = c²

6400 + 22500 = c²

c = √28900

x = 170

Answer: 170 miles

If 12 out of every 15 people prefer eating at a restaurant, then 12/15 of the people who took the survey chose that option. We know that 12/15 of the total number of people who took the survey is equal to 400 people, so we can set up the equation:

(12/15)x = 400

To find the total number of people who took the survey, we can solve for x by multiplying both sides of the equation by 15/12:

x = (400)(15/12)

x = 500

So, 500 people took the survey.

Each of the given statements are interpreted in context below.

What is the quadratic equation?

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants. The solutions of the equation are the values of x that make the equation true.

a. N(1) = 11: This statement represents that 1 hour after the food truck opens, there are 11 people in line.

b. N(0) = N(3): This statement represents that at the time the food truck opens, the number of people in line is the same as 3 hours after the food truck opens.

c. N(4) > N(6): This statement represents that at 4 hours after the food truck opens, the number of people in line is greater than at 6 hours after the food truck opens.

d. N(R) = 34: This statement represents that the number of people in line at an unspecified time R is 34. The letter "R" can be any value for time, it is only a placeholder for any arbitrary value.

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y = 32 home runs will Mario hit during his ninth season.

Now, According to the question:

Linear models describe a continuous response variable as a function of one or more predictor variables. They can help you understand and predict the behavior of complex systems or analyze experimental, financial, and biological data. Linear regression is a statistical method used to create a linear model.

According to the graph, we have

The equation is:

y = 3x + 5

Put the value of x = 9

We get:

y = 3 × 9 + 5

y = 32

(Figure out the function of the image, and then bring the value of 'x' into it.)

Hence, y = 32 home runs will Mario hit during his ninth season.

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The model to solve t + 4 = 5 is that John hast number of oranges and got 4 more making 5 oranges.

A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modeling is the process of creating a mathematical model.

To make a prediction or offer insight, mathematical modeling is the process of creating a mathematical representation of a real-world scenario.

The equation t + 4 = 5 can be solved by subtracting 4 from both sides of the equation:

t + 4 = 5

t = 5 - 4

t = 1

So t = 1 is the solution to the equation

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Answer: C

Step-by-step explanation:

The length of the PR would be 82.

Option (A) is correct.

What is an expression?

An expression is a combination of numbers, variables, and mathematical operations that represents a value or a computation. Expressions can be simple or complex and can include constants, variables, and various mathematical operations such as addition, subtraction, multiplication, and division. Expressions are often used to represent mathematical operations in algebraic, trigonometric, and calculus problems. They can be evaluated to find a numerical value or simplified to reveal underlying mathematical relationships.

In the given figure, the length of both line segments is equal, hence

PR = 10x + 842

PQ + QR = 10x + 842

8x + 678 + 12 = 10x + 842

First we can subtract 12 from both sides of the equation:

8x + 678 = 10x + 830

Then we can subtract 8x from both sides of the equation:

678 = 2x + 830

Then we can subtract 830 from both sides of the equation:

-152 = 2x

Then we can divide both sides of the equation by 2:

x = -76

So PR = 8x + 678 + 12

PR = 8(-76) + 678 + 12

PR = -608 + 678 + 12

PR = -608 + 690

PR = 82

Hence, the length of the PR would be 82.

Option (A) is correct.

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The time taken by both the workers working together, which is 2 days.

The time taken to build a house by two workers working together can be calculated using the formula T = (1/W1 + 1/W2)^-1, where W1 and W2 are the working speeds of each worker. In this case, W1 = 2 days and W2 = 3 days. So, the time taken to build a house by both workers together is calculated as follows:

T = (1/2 + 1/3)^-1 = (3/6)^-1 = 6/3 = 2 days

Therefore, both the workers working together will take 2 days to build a house. This is because when two workers work together, the total work done in a given time is equal to the sum of the work done by each worker separately in that given time. In this case, both the workers will take 2 days and 3 days respectively to build the house when working separately, so when they work together the total work done in a given time will be 5 days. This is equal to the time taken by both the workers working together, which is 2 days.

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Answer:

Since Marshall gives away 13 buttons out of b buttons, it means that b is an expression of a number which is greater than 13. Therefore,the answer is b - 13.

The height of the bullet after 3 second is 640m

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is gravity. In fact, gravity works towards the centre of the Earth.

When an object is thrown up, the height of the object is calculated as h = v²/2g

where v is the velocity and g is the acceleration due to gravity.

v = -16t²+ 256(t)

when t = 3s

v = -16( 3)²+ 256

v = -144+256

v = 112m/s

therefore the height attained by the bullet =

h = 112²/2×9.8

h = 640m

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

Explanation:

I appreciate you showing your work so far, and your thought process.

Your steps are correct because the events [tex]A \cup B[/tex] and [tex](A \cup B)'[/tex] are complementary, aka opposite. One or the other must happen. It's like a coin flip heads vs tails.

The last thing you need to do really is simplify 1-0.5-0.5+0.25 to get the final answer 0.25

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

This is what I would do as an approach.

P(A u B) = P(A) + P(B) - P(A n B)

P(A u B) = 0.5 + 0.5 - 0.25

P(A u B) = 0.75

So,

P( (A u B)' ) = 1 - P(A u B)

P( (A u B)' ) = 1 - 0.75

P( (A u B)' ) = 0.25

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

Another approach:

Imagine we had 100 people.

50 are in set A to give P(A) = 50/100 = 0.50

50 are in set B to give P(B) = 0.50

25 are in both A and B to get P(A n B) = 25/100 = 0.25

50+50-25 = 75 people are in either A, or B, or both

That leaves 100-75 = 25 in neither set

25/100 = 0.25

I recommend to draw out the Venn Diagram.

Range, because it measures the distinction between the highest and lowest values in a dataset, providing a clear estimate of variability for both sets of data. It is unaffected by skewness or symmetry, making it a useful measure of variability for comparing the temperature consistency of Desert Landing and Flower Town.

A histogram is a rough illustration of how numerical values are distributed. Karl Pearson coined the phrase at the beginning.

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.

A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.

Therefore, the correct answer is both option c) and d) Range, because Flower Town is skewed and symmetric.

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Answer:

The correct answer is:

Range, because Flower Town is symmetric

The surface area of the pyramid is 1702.8 ft².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Rectangular pyramid has a rectangular base and four triangular faces.

Net of the pyramid is shown below.

Area of the rectangular base = 25 × 22 = 550 ft²

Now we have to find the area of four triangular faces.

Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

Heights of the triangle BCX and ADZ can be found as below :

Combined height of both triangles = 74.8 - 25 = 49.8

Height of each triangle = 49.8 / 2 = 24.9 ft

Area of triangles BCX and ADZ = 2 × ( [tex]\frac{1}{2}[/tex] × base × height)

                                                    = Base × height

                                                    = 22 × 24.9

                                                    = 547.8 ft²

Similarly,

Combined height of triangles ABW and CDY = 70.4 - 22 = 48.4

Height of each triangle = 48.4 / 2 = 24.2 ft

Area of triangles ABW and CDY = Base × height

                                                      = 25 × 24.2

                                                      = 605 ft²

Total surface area of the pyramid = 550 ft² + 547.8 ft² + 605 ft²

                                                        = 1702.8 ft²

Hence 1702.8 ft² is the total surface area of the pyramid.

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Answer: Please see explanation column for answer.

x= -36

Step-by-step explanation:

Step 1

from the attachment, Carlo solving is given as

1/3 (1/2x- 9) = 1/2 (x+18)

1/6x-3= 1/2x+9

1/4x-3=9

1/4x=12

x=48

Carlos error started when he subtracted wrongly 1/2 x from 1/6x which gave him 1/4 x instead of - 1/3 x.

Solving correctly, we have that

1/3(1/2x-9) = 1/2(x+18)

1/6x -3= 1/2x+ 9

taking like terms to like terms

1/6x-1/2x= 9+3

(1-3)/6x= 12

-2/6x= 12

-1/3x= 12

multiplying both sides by -3

-1/3x X -3 = 12 X -3

x= -36

Answer:

2.50x + 1.25y ≤ 30

x + y ≥ 14

x ≤ 10 and y ≤ 24

Step-by-step explanation:

we can by elimination if we multiply the second inequality by -2.5, we get:

-2.50x - 2.5y ≥ -35

if we add the first inequality to the above we get:

   2.50x + 1.25y ≤ 30

+  -2.50x - 2.5y ≥ -35

-1.25y = -5

divide each side by -1.25 to get:

y = 4

therefore, x = 10

if you graph each system you must look for the area where the shading of each inequality overlaps

upon graphing, the solution is x ≥ 10 and y ≤ 24

Answer:

Always start with the first number. The one in 1.47 is less than the 4 in 4.01, so 1.47 is less than 4.01.

Least to greatest is 1.4, 1.47, 4.01, and 4.1

Total number of  a customer uses his phone each day in hour 0.25t + 1.75

Total number of  a customer uses his phone each day in hour (e) =  the customer spend time in hour on calls +  the customer spend time in hour on texts.

total number of  a customer uses his phone each day in hour (e) =  the customer spend time in hour on calls +  the customer spend time in hour on texts.

the customer spend time in hour on calls = the number of calls the customer made per day (t) times the average time spent by customers per day per hour (0.25 hours)

The number of hours the customer spend on texts is given as 1.75 hours each day.

Therefore required equation is:

e = 0.25t + 1.75

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Answer: I believe it is A