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Anuta_ua [19.1K]

2 years ago

14

A bridge builder wants to know the width of a river. He stands at point A along the river. He picks a point C directly across th

e river. He then walks downstream 90 feet from point A to point B. From point B, he sites C and determines the angle between the bank and point C (θ), to be 43º. What is the width of the river?

1 answer:

Maurinko [17]2 years ago

8 0

<span>width = 90 tan43 degrees = about 84 feet </span>

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a company makes a profit of $50 per software program and $35 per video game. The company can produce at most 200 software progra

Lynna [10]

Answer:

In order to maximize the profit, should be produced 200 software program and 235 video games per week

Step-by-step explanation:

Let

x ------> the number of software program

y -----> the number of video games

we know that

$x \leq 200$ -----> inequality A

$y \leq 300$ -----> inequality B

$x+y \leq 435$ -----> inequality C

Using a graphing tool

The solution is the shaded area between the positive values fo x and y

see the attached figure

The vertices of the shaded area are

(0,0),(0,300),(135,300),(200,235),(200,0)

The profit function is equal to

$P=50x+35y$

Substitute the value of x and the value of y of each vertices in the profit function

For (0,300) ----- $P=50(0)+35(300)=\$10,500$

For (135,300) ----- $P=50(135)+35(300)=\$17,250$

For (200,235) ----- $P=50(200)+35(235)=\$18,225$

For (200,0) ----- $P=50(200)+35(0)=\$10,000$

therefore

In order to maximize the profit, should be produced 200 software program and 235 video games per week

4 0

2 years ago

Read 2 more answers

A store manager records the total visitors and sales, in dollars, for 10 days. The data is shown in the scatter plot. What concl

pickupchik [31]

Answer:An increase in visitors is correlated with an increase in sales.

Step-by-step explanation:

From the given scatter plot we can see that variables are positively correlated because they are moving in the same direction.

Since we know that the positive correlation is a relationship between two variables such that they increase or decrease together.

Since, the two variables given her is " number of visitors" and "Total sales"

Therefore, based on the given data it can be observed that "An increase in visitors is correlated with an increase in sales."

3 0

2 years ago

The equations below represent the numbers y of tickets sold after x weeks for two different local music festivals

Anton [14]

Assuming you mean y=10x+150 and y=20x+115, you need to use a simultaneous equation, because you have two equations with two unknowns (x and y)

rearrange so
10x-y=-150
20x-y=-115

multiply the top by -1, so that if we add the two lines together, the y will cancel out
-10x+y=150
20x-y=-115

add the two lines together
10x=35
x=3.5

so the time is 3 and a half weeks

then we can sub in x to find y
20x-y=-115
20(3.5)-y=-115
70-y=-115
-y=-185
y=185

so 185 tickets were sold !
you can sub these values into your original equations to check your answer :)

5 0

2 years ago

Read 2 more answers

The formula for the volume V of a cylinder is V = πr2h, where r is the radius of the base and h is the height of the cylinder. S

lana [24]

Answer:

Part A) $h=V/(\pi r^{2})$

Part B) $h=4\ cm$

Step-by-step explanation:

Part A)

we have the formula of the volume of a cylinder

$V=\pi r^{2}h$

Solve for h

That means ----> isolate the variable h

Divide both side by πr²

$V/(\pi r^{2})=\pi r^{2}h/(\pi r^{2})$

Simplify

$V/(\pi r^{2})=h$

Rewrite

$h=V/(\pi r^{2})$

Part B) Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm

we have

$V=36\pi\ cm^3$

$r=3\ cm$

substitute in the formula and solve for h

$h=36\pi/(\pi 3^{2})$

$h=4\ cm$

8 0

2 years ago

Carmen's golf score is 6 strokes less than Linda's. Their two scores total 156. What is each girls score?

DochEvi [55]

Answer:

Carmen's score is 75 strokes.

Linda's score is 81 strokes.

Step-by-step explanation:

Let the score of Linda be "x".

<em>It is given that Carmen's golf score is 6 strokes less than Linda's.</em>

Thus, Carmen's score is (x-6).

The total score of the girls is

= $x + (x-6) = 2x-6$

The total score is given to be 156.

Thus, the equation becomes,

$2x-6 = 156$

$2x= 162$

$x = 81$

<em>Thus Linda's score is 81 and Carmen's score is (156-81) 75.</em>

5 0

2 years ago