Answer:
Area covered by the fences will be 16.1 unit²
Step-by-step explanation:
Let the first parabola is represented by the function f(x) = 6x²
and second parabola by g(x) = x² + 9
point of intersection of the graphs will be determined when f(x) = g(x)
6x² = x² + 9
5x² = 9
x² = 1.8
x = ± 1.34
Now we will find the area between these curves drawn on the graph.
Area = ![\int_{-1.34}^{1.34}[f(x)-g(x)]dx=\int_{-1.34}^{1.34}[6x^{2}-(x^{2}+9)]dx](https://tex.z-dn.net/?f=%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5Bf%28x%29-g%28x%29%5Ddx%3D%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5B6x%5E%7B2%7D-%28x%5E%7B2%7D%2B9%29%5Ddx)
= 
= ![[\frac{5}{3}x^{3}-9x]_{-1.34}^{1.34}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7Dx%5E%7B3%7D-9x%5D_%7B-1.34%7D%5E%7B1.34%7D)
= ![[\frac{5}{3}(-1.34)^{3}-9(-1.34)-\frac{5}{3}(1.34)^{3}+9(1.34)]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7D%28-1.34%29%5E%7B3%7D-9%28-1.34%29-%5Cfrac%7B5%7D%7B3%7D%281.34%29%5E%7B3%7D%2B9%281.34%29%5D)
= ![[-4.01+12.06-4.01+12.06]](https://tex.z-dn.net/?f=%5B-4.01%2B12.06-4.01%2B12.06%5D)
= 16.1 unit²
The dimensions of the rectangular cross section will be<u> 10 centimeters by 18 centimeters</u>
<u></u>
Step-by-step explanation:
As ,we know
<u>The rectangular cross section is parallel to the front face</u>
Which clearly states that
The dimensions of the rectangular cross section is congruent with the dimensions of the front face
Lets assume that dimensions of the front face are 10 centimeters by 18 centimeters
<u>Then ,The dimensions of the cross section will also be 10 centimeters by 18 centimeters</u>
<u></u>
<u>Hence we can say that the</u> dimensions of the rectangular cross section will be<u> 10 centimeters by 18 centimeters</u>
The question asks for the rate of toys per hour.
So we shall divide the total toys assembled by the total hours.
Its a five day week.
The number of hours allotted per day are 8.
So total allotted during the week are 8 × 5 = 40 hours.
Number of toys made during the week are 400.
Hence the number of toys assembled per hour per person
= number of toys / number of hours
= 400 / 40
= 10 toys per hour per person.
The average number of toys assembled per hour per person is 10.
Answer:
Mia scored 6 baskets Last Saturday.
Step-by-step explanation:
Let:
Mia made score of baskets on Last Saturday = x
Mia made score of baskets yesterday = 3x (Mia made three times as many baskets in yesterday’s basketball game as she did last Saturday. three times means multiply 3 with score of Last Saturday baskets, i.e. x)
Total score of baskets = 24
We need to find How many baskets did Mia score last Saturday?
We can write:
<em>Total Score = Score on Last Saturday + Score yester</em>day

Solving this equation we can find value of x:

So, we get value of x = 6
Mia made score of baskets on Last Saturday = x = 6
Mia scored 6 baskets Last Saturday.
Answer: a) 0.9961, b) 0.9886
Step-by-step explanation:
Since we have given that
Probability that does not show up = 0.10
Probability that show up = 0.90
Here, we use "Binomial distribution":
n = 125 and p = 0.90
Number of passengers that hold in a flight = 120
a) What is the probability that every passenger who shows up can take the flight?

(b) What is the probability that the flight departs with empty seats?

Hence, a) 0.9961, b) 0.9886