10.25

What is the area of the figure

S_A_V [24]

Answer:

24 cm

Step-by-step explanation:

4 0

3 years ago

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Any one can help with this Venn Diagram question?.Please note that there is an another language, ignore except if you can unders

zloy xaker [14]

Answer:

(i) 30

(ii) 8

Step-by-step explanation:

Start by drawing 3 rings for the Venn diagram. Each ring represents either Audi, BMW, or Citroën.

Next, add the information provided in the problem statement. We know that 20 choose BMW only. Another 20 choose Citroën only.

We know the number who choose all 3 is the same as the number that choose BMW and Citroën, but not Audi. We'll call this number x.

Similarly, we know that the number who choose all 3 is half of those choose Audi and BMW, but not Citroën. So we'll say that number is 2x.

We know the total number of Audi votes is 48, the total number of BMW votes is 36, and the total number of Citroën votes is 34.

Finally, we know the total number of voters is 100, including those who voted for no favorites (we'll call that number n).

We know that BMW got 36 votes, so:

20 + x + x + 2x = 36

20 + 4x = 36

4x = 16

x = 4

We know that Citroën got 34 votes, so:

20 + x + x + z = 34

20 + 4 + 4 + z = 34

28 + z = 34

z = 6

We know that Audi got 48 votes:

y + 2x + x + z = 48

y + 2(4) + 4 + 6 = 48

y + 18 = 48

y = 30

Finally, we know that the total number of voters is 100.

20 + 20 + x + x + 2x + y + z + n = 100

20 + 20 + 4 + 4 + 2(4) + 30 + 6 + n = 100

92 + n = 100

n = 8

8 0

3 years ago

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the P

Oxana [17]

Answer:

<h2>Unknown side = 28</h2><h2>tan B = 7/24</h2>

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.

Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.

From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;

c² = a²+b²

100² = 96² +b²

b² = 100² - 96²

b² = 10,000 - 9216

b² = 784

b = √784

b = 28

Hence, the unknown length is 28.

To get tanB, we will use the SOH, CAH, TOA trigonometry identity

According to TOA, tan B = opposite/adjacent

tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)

Given b = 28 and a = 96

tan B = 28/96

tan B = 4*7/4*24

tan B = 7/24

8 0

3 years ago

A California grower has an 80-acre farm on which to plant strawberries and tomatoes. The grower has available 600 hours of labor

Makovka662 [10]

Answer:

a)

P=500s+300t

$s+t \leq 80$

$s\leq 60$

$T \leq 50$

$8s+4t \leq 600$

$5s+20t \leq 800$

$s \geq 0$

$t \geq 0$

b) See attached picture.

Possible extreme points:

(0,0), (0,40), (160/3, 80/3), (60,20), (60,0)

c) Optimal solution points:

(0,0), (0,40), (160/3, 80/3), (60,20), (60,0)

Optimal objective function value happens at (60,20) for a profit of $36,000.

Step-by-step Explanation:

a) In order to find the linear programming model, we need to start by setting our variables up.

s= number of acres of strawberries to plant.

t = number of acres of tomatos to plant.

With this we can start by setting our ojective function up, which is the profit function.

"The profit from an acre of strawberries is $500, and the profit from an acre of tomatoes is $300."

Our objective function is:

P=500s+300t

Next, we need to set our restrictions up, which come from the rest of the sentences of the problem:

"A California grower has an 80-acre farm on which to plant strawberries and tomatoes." This tells us that we can plant as much as 80 acres of strawberries and tomatoes, so our first restriction is:

$s+t \leq 80$

This sentence gives us the next two restrictions:

$s \leq 60$

$T \leq 50$

"The grower has available 600 hours of labor per week...", " An acre of strawberries requires 8 hours of labor..." and "...an acre of tomatoes requires 4 hours of labor...".

These sentences give us the next restriction:

$8s+4t \leq 600$

"The grower has available...800 tons of fertilizer...", "An acre of strawberries requires...5 tons of fertilizer", "...an acre of tomatoes requires...20 tons of fertilizer."

with this information we can build our next restriction:

$5s+20t \leq 800$

and finally, we also know that we cannot plant less than 0 acres of tomatos or strawberries since that would become a loss. So the final restrictions are:

$s \geq 0$

$t \geq 0$

So the linear programmin model is the following:

P=500s+300t

$s+t \leq 80$

$s \leq 60$

$T \leq 50$

$8s+4t \leq 600$

$5s+20t \leq 800$

$s \geq 0$

$t \geq 0$

b) Once we have the linear programming model, we can go ahead and graph each of the restrictions. All the restrictions are graphed the same so I will give a brief explanation on how to graph the first one.

So let's take the first restriction:

$s+t \leq 80$

we can start by turning it into an equation:

s+t=80

and pick any value we wish for s. We can pick s=0 since that will simplify the work:

0+t=80

therefore t=80

the first point to plot is (0,80)

in order to find the second point to plot we can set t=0 so we get:

s+0=80

s=80

therefore the second point to plot is (80,0)

We can plot these two points on our coordinate axis and connect them with a solid line.

Next, we know that the region to shade should be less than or equal to 80, so we pick a test point above and below the graph. Let's pick (100,60) and (0,0)

for (100,60) we get that:

$100+60 \leq 80$

$160 \leq 80$

this is false so that region should not be shaded. Let's take the other test point:

for (0,0) we get:

$0+0\leq 80$

$0 \leq 80$

is true, so we should shade the region below the graph.

The same procedure is done with the rest of the restrictions and we have as a result the graph in the attached picture.

The feasible area is the area all the shaded areas have in common.

The extreme points are the vertices of the polygon formed by the feasible area, we can find them graphically or algebraically.

If we were to find them algebraically we would solve the corresponding system of equations. The first point (0,0) is found at the intersection of the restrictions: $s \geq 0$ and $t \geq 0$ .

The second extreme point is at the intersection of the restrictions: $s \geq 0$ and $5s+20t \leq 800$ , which yields (0,40).

The next extreme point is at the intersection of the restrictions: $5s+20t \leq 800$ and $s+t \leq 80$ . When solving this system of equations we get the point: (160/3, 80/3).

The next extreme point is at the intersection of the restrictions: $s+t \leq 80$ and $s \leq 60$ which yields (60,20)

and the final extreme point is at the intersection of the restriction: $s \leq 60$ and $t \geq 0$ which yields (60,0)

so the possible extreme points are: (0,0), (0,40), (160/3, 80/3), (60,20), (60,0).

c) Now we solve the model, in order to solve the model we need to use the optimal solution points and evaluate them in the objective function:

P=500s+300t.

See attached table for the results of substituting the optimal points.

So the optimal point will happen at (60,20) with a profit of $36,000.

5 0

3 years ago

Ray paid $46.25 for 8.75 gallons of gas. What is the unit rate of gas in dollars, per gallon ?

hodyreva [135]

Answer:

$5.28571429 per gallon

Step-by-step explanation:

$46.25 divided by 8.75

You can round this 5.3 or 5.29.

7 0

3 years ago

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