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kirill115 [55]
3 years ago
14

Sarah has a bag of jolly ranchers. There are 15 grape, 20 blue raspberry, 10 watermelon, 8 cherry, and 7 green apple jolly ranch

ers in a bag.
A) what is the probability that she will choose a grape jolly rancher?

B) what is the probability that she will choose either watermelon or cherry?

C) what is the probability that she will not choose green apple?

Explain your reasoning.
Mathematics
2 answers:
Anettt [7]3 years ago
3 0
A) 15/33 B) 18/33 C) 26/33 if you have to use words use most likely, probably, etc
dalvyx [7]3 years ago
3 0
Total J<span>olly Ranchers = 15 + 20 + 10 + 8 + 7 = 60

Grapes = 15
Raspberry = 20
Watermelon = 10
Cherry = 8
Green apple = 7
</span>
P(\text{Grapes}) =  \dfrac{\text{Grapes}}{\text{Total}}  =  \dfrac{15}{60} =  \dfrac{1}{4}


&#10;P(\text{Watermelon or Cherry}) =  \dfrac{\text{Watermelon or Cherry}}{\text{Total}}  =  \dfrac{10 + 8}{60} =  \dfrac{3}{10}


&#10;P(\text{Not green apple}) =  \dfrac{\text{Not green apple}}{\text{Total}}  =  \dfrac{15 + 20 + 10 + 8}{60} =  \dfrac{53}{60} 


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In a single growing season at the smith family orchard, the average yield per apple tree is 150 apples when the number of trees
Mariana [72]

Answer:

100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

Step-by-step explanation:

<u>Functions </u>

Expressing some quantities in terms of other(s) comes in handy to understand the behavior of the situations often modeled by those functions.

Our problem tells us about the smith family orchard, where the average yield per apple tree is 150 apples when the number of trees per acre is 100 (or less). But the average yield per tree decreases when more than 100 trees are planted. The rate of decrease is 1 for each additional tree is planted

Let's call x the number of trees planted per acre in a single growing season. We have two conditions when modeling:  when x is less than 100, the average yield per apple tree (Ay) is (fixed) 150.

Ay(x)=150\ ,\ x\leqslant 100

When x is more than 100:

Ay(x)=150-x\ ,\ 100< x\leqslant 150

The upper limit is 150 because it would mean the Average yield is zero and no apples are to be harvested

Part 1

We are asked what happens if the number of trees per acre was doubled, but we don't know what the original number was. Let's make it x=60

If x=60, then we must use the first function, and

Ay(60)=150

The yield per acre will be 150*60=9000 apples

If we doubled x to 120, we would have to use the second function

Ay(120)=150-x=30

The yield per acre will be 30*120=3600 apples

Note that doubling the number of trees would make the production decrease

If we started with x=30, then  

Ay(30)=150, and we would have 150*30=4500 apples per acre

We already know that for x=60 (the double of 30), our production will be 9000 apples per acre

This shows us that in some cases, increasing the number of trees is beneficial and in other cases, it is not

Part 2

The total yield is computed as

Y(x)=x.Ay(x)

This function will be different depending on the value of x

Y(x)=150x\ ,\ x\leqslant 100

Y(x)=150x-x^2\ ,\ 100< x\leqslant 150

To find the maximum total yield we take the first derivative

Y'(x)=150\ ,\ x\leqslant 100

Y'(x)=150-2x\ ,\ 100< x\leqslant 150

The first expression has no variable, so the total yield must be evaluated in the endpoints

Y(0)=0

Y(100)=15000

Now, the second expression contains variable, it will be set to 0 to find the critical point

150-2x=0

x=75

x is outside of the boundaries, we cannot find the maximum in this interval

Answer: 100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

7 0
3 years ago
If arc EF = 151°, find mEDF.
user100 [1]
There is a theorem that says that this angle (formed by thre points on the circumference) is half such arc called EF.

We can deduct it as well.

1) Call O the center of the circle. The central angle (EOF) = arc EF = 151°

2) Draw a chord from F to D and other chord from D to E.

You have constructed two triangles, FOD and DOE.

3) Triangle FOD has two sides equals (because both are the radius of the circcle). Then, this is an isosceles triangle and it has two angles of the same measure. Call this measure a.

4) Triangle DOE is also isosceles, for the same reason explained in the poiint 3. Call the measure of its equal angles b.

5) The sum of the angles of the two triangles is 180° + 180 ° = 360°.

This is a + a + b + b + (360 - central angle) = 360°

=> 2a + 2b = central angle
=> 2(a+b) = cantral angle
=> (a+b) = central angle / 2 = 151° / 2 =71.5°

(a+b) is the angle that you are looking for.

Then the answer is 71.5°

 
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Answer:

x = 12

Step-by-step explanation:

3x + 9 = 5x - 15

2x = 24

x = 12

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