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defon
2 years ago
14

According to the table below, what is the probability that the grade of a student chosen at random will be a B or higher? Grade

A B с D F 4 Probability 2 35 3 35 17 35 9 35 35 3 OA. B. 7 Oc. VIN O D. / SUBMIT​

Mathematics
1 answer:
Nat2105 [25]2 years ago
5 0

Answer:

1 / 7

Step-by-step explanation:

Given the distribution above :

P(grade B or higher) can be defined explicitly as :

P(Grade A) + P(Grade B)

P(grade A) = 2/35

P(Grade B) = 3 / 35

Hence,

P(Grade B or higher) = 2/35 + 3/35 = 5/35 = 1/7

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Let c be the curve which is the union of two line segments, the first going from (0, 0) to (4, 4) and the second going from (4,
victus00 [196]
First of all we need to find a representation of C, so this is shown in the figure below.

So the integral we need to compute is this:

I=\int_c 4dy-4dx

So, as shown in the figure, C = C1 + C2, so:

I=\int_{c_{1}} (4dy-4dx)+\int_{c_{2}} (4dy-4dx)=I_{1}+I_{2}

Computing first integral:

c_{1}: y-y_{0}=m(x-x_{0}) \rightarrow y=x

Applying derivative:

dy=dx

Substituting this value into I_{1}

I_{1}=\int_{c_{1}} (4dx-4dx)=\int_{c_{1}} 0 \rightarrow \boxed{I_{1}=0}

Computing second integral:

c_{2}: y-y_{0}=m(x-x_{0}) \rightarrow y-0=-(x-8) \rightarrow y=-x+8

Applying derivative:

dy=-dx

Substituting this differential into I_{2}

I_{2}=\int_{c_{2}} 4(-dx)-4dx=\int_{c_{2}} -8dx=-8\int_{c_{2}}dx

We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:

 I_{2}= -8\int_{4}^{8}}dx=-8[x]\right|_4 ^{8}=-8(8-4) \rightarrow \boxed{I_{2}=-32}

Finally:

I=\int_c 4dy-4dx=0-32 \rightarrow \boxed{I=-32}
4 0
3 years ago
Solve the equation <br>5h +2 -h = 22​
astraxan [27]

Answer:

h=5

Step-by-step explanation:

5h +2 -h = 22​

4h+2=22

4h=20

h=5

4 0
3 years ago
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Using the following data, calculate the mean absolute deviation:
Bogdan [553]
First set of data:
Mean - 6.5
Absolute deviation - 2.4

Second set of data:
Mean - 4.475
Absolute deviation - 2.275
3 0
3 years ago
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The function f(x)=-(x-3)^2 +9 can be used to represent the area of a rectangle with the perimeter of 12 units, as a function of
Ivenika [448]

Maximum area of the rectangle is 9cm^{2}

<u>Explanation:</u>

<u></u>

Considering the dimensions to be in cm

f(x) = -(x-3)^{2} +9\\f(x) = -(x^{2} +9 - 6x)+9\\f(x) = -x^{2} +6x\\f'(x) = -2x+6\\-2x+6 = 0\\2x=6\\x=3cm\\\\

Putting the value of x = 3

Perimeter = 2(x+b)\\12 = 2(3+b)\\6 = 3+b\\b= 3cm

Area of rectangle = x X b\\                              = 3 X 3\\                              = 9cm^{2}

Therefore, maximum area of the rectangle is 9cm^{2}

7 0
3 years ago
Tell whether the two quantities vary directly. Explain your reasoning. The cafeteria provides three meals per day.
Dafna11 [192]

Answer:

The cafeteria provides three meals per day.

<u>Reason 1</u>

Yes, they vary directly  

As number of days increases ,Total number of meals i.e

1st day ⇒ 3

2nd day⇒6

3 rd day⇒9

4th day⇒12

......................

.........................

increases.

Total number of Meals = k×Number of days

But there is another possibility also

<u>Reason 2</u>

1 st day ⇒ 3

2nd day ⇒3

3rd day⇒ 3

.....................

.....................

As you can see from the above expression On each day number of meals is  

constant.

So we can say that ,

On each Day=Constant amount of meal=3

So, there is no Proportionality between Days and Meal.




3 0
3 years ago
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