10/12 divided by ?/? = 5/6

Answer:

a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Step-by-step explanation:

To solve this question, we need to understand the normal and the binomial probability distributions.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Proportion repaired below 6 hours:

Mean 5 hours and standard deviation 1 hour, which means that [tex]\mu = 5, \sigma = 1[/tex]

This proportion is the p-value of Z when X = 6. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{6 - 5}{1}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

0.8413 repaired below 6 hours.

For the binomial distribution, this means that [tex]p = 0.8413[/tex]

5 are chosen:

This means that [tex]n = 5[/tex]

a) Probability that all are repaired in less than 6 hours

This is P(X = 5). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.8413)^{5}.(0.1587)^{0} = 0.4215[/tex]

0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) Probability that exactly 3 of them repaired below 6 hours

This is P(X = 3). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{5,3}.(0.8413)^{3}.(0.1587)^{2} = 0.15[/tex]

0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Answer:

q^2

Step-by-step explanation:

Answer:

q^2

Step-by-step explanation:

4q^2 – 3q^2

Factor out the q^2

q^2 ( 4-3)

q^2(1)

1q^2

q^2

Answer:

y = - 2x + 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute (4, 5) into the partial equation

5 = - 8 + c ⇒ c = 5 + 8 = 13

y = - 2x + 13 ← equation of line

Answer:

Step-by-step explanation:

slope=-2

now using slope intercet formof equation of straight line,we get

y=mx+b

or, y=-2x + b

y + 2x =b

2x + y=b ......................   eq(i)

since the line passes through the point (4,5) it satisfies the equation (i)

y=5 and x=4 so,

equation is 2x +y =b

2*4 + 5=b

8+5=b

13=b

substituting the value of b in eq(i)

2x + y=b

2x + y=13

2x + y-13=0  is the required equation of the line.

Answer:

If x is the one vertically opposite to 40, then x will be 40, due to vertically opposite angles.

Step-by-step explanation:

[tex] - 2 {x}^{2} - 9 = - 107 \\ - {2x}^{2} = - 98 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ { \boxed{lesser : \: - 7}} \\ { \boxed{greater : \: + 7}}[/tex]

create your own scale, it could be 2cm=40mm, so 3cm=60mm and 2.5cm=50mm.

then draw your trapezium in the given space using your scale

Answer: 2

Step-by-step explanation:

3x+4y=10

3x+4(x-1)=10

3x+4x-4=10

7x-4=10

Add 4 to both sides

7x=14

x=2

Answer:(2,1)

Step-by-step explanation:ap3x beans

Answer:

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Trust me

Answer: a. x=4 b. x=17.5

Step-by-step explanation:

a. 5x/2+1=11

subtract 1 from both sides : 5x/2=10

multiply both sides by 2 : 5x=20

divide both sides by 4 : x=4

b. 2x/7-3=2

add 3 to both sides : 2x/7=5

multiply both sides by 7 : 2x=35

divide both sides by 2 : x=17.5

========================================================

Explanation:

Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.

The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.

The area of the second larger square is 114*114 = 12,996 square inches.

Now divide the two areas: (12,996)/(9) = 1444

It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.

In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.

Or put another way:

large area = 1444*(small area)

------------------

Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.

Answer:

8 x 5 x 2

Step-by-step explanation:

total number of windows seen = total number of cars x total number of windows a car has

total number of windows a car has = number of windows a car has x total number of sides  = 5 x 2

total number of windows seen = 8 x 5 x 2

Answer:

1. 452.39

2. 615.75

Step-by-step explanation:

area of a circle = A=πr2

Answer:

x =  [tex]\sqrt{14}[/tex]

Step-by-step explanation:

[tex]\sqrt{7}[/tex] / sin(45) = x / sin(90)  (Cause its a square, the edges are 90 degrees)

[tex]\sqrt{14}[/tex] = x / 1

x = [tex]\sqrt{14}[/tex]

Answer:

The y intercepts is -2

y = 1x-2

Step-by-step explanation:

The y intercept is where it crosses the y axis

The y intercepts is -2

We need to determine the slope, by using to points on the line

(0,-2) and (2,0)

m = (y2-y1)/(x2-x1)

   = (0 --2)/(2-0)

   = (0+2)/(2-0)

   = 2/2

  = 1

The equation for the line is

y = mx+b where m is the slope and b is the y intercept

y = 1x-2

Answer: To me it (Zero) or (Undefined)

Answer:

no

Step-by-step explanation:

so in order for it to be a right triangle this would have to be true:

a^2 + b^2 = c^2

since c represents the hypoteneuse, it will be the longest side. so:

60^2 + 63^2 = 88^2

3600 + 3969 = 7744

7569 = 7744

since that statement is not true, the answer is no.

it is not a right triangle  

the square root of 7569 is 87, so the triple would have to be : {60,63,87}

Answer:

1.26 years

Step-by-step explanation:

Answer:

2. (x+2)²+(y+3)²=49

Step-by-step explanation:

it is possible to re-write the given equation:

x²+4x+4+y²+6y+9-49=0;

(x+2)²+(y+3)²-49=0;

(x+2)²+(y+3)²=7².

Answer:

D. 4000 per month

Step-by-step explanation:

If they make 48000 per year, to find how mmuch s/he makes in a month, we have to divide it by 12 because there are 12 months in a year.

$48,000/12= $4000 per month

Answer:

49N

Step-by-step explanation:

Below is the calculation for the force applied:

It is given that the mass of stone is 5 kg and it falls from the height of 100 meters. Therefore, a force can be determined by multiplying the mass will a constant value of "a".

Force = Mass x a

Force = 5 x 9.8

Force = 49 N

Since the action-reaction are equal and opposite so the each will apply the same force.

Step-by-step explanation:

The left side represent the tens place of the number, and the right side represent the one sides of the number. So the numbers are

12,12,13,14,18,19,19, 20,23,26,27,31,31,31,32,34,41,44,45,48.

a. There are 20 terms so this equation 20/2=10 means the 10th term will be the median. make sure to also include the number 11th term becuase the number of terms is even. The 10th and 11th term are 26,27 so the median is the midpoint.

[tex] \frac{26 + 27}{2} = 26.5[/tex]

The median is 26.5

b. The range is maximum value minus minimum value.

[tex]48 - 12 = 36[/tex]

c. The mode is the number that appear the most

That number is 31.

d. 20 students took apart of this survey.

Answer: [tex]15\ ft,6\ ft[/tex]

Step-by-step explanation:

Given

The area of a rectangular wall of a barn is [tex]135\ ft^2[/tex]

Suppose the width of the wall is [tex]x[/tex]

So, the length of the wall is [tex]6+x[/tex]

Area can be written as the product of length and width

[tex]\Rightarrow (6+x)x=135\\\Rightarrow 6x+x^2=135\\\Rightarrow x^2+6x-135=0\\\Rightarrow x=\dfrac{-6\pm \sqrt{6^2-4(1)(-135)}}{2(1)}\\\\\Rightarrow x=\dfrac{-6\pm 24}{2}\\\\\Rightarrow x=-15,9[/tex]

neglecting the negative value, width of the wall is [tex]9\ ft[/tex]

So, the length of the wall is [tex]9+6=15\ ft[/tex]

Answer:

47 and now I'm just typing so it lets me answer

Step-by-step explanation:

calculator

Answer:

1). Does Not

2). Ratio

Step-by-step explanation:

According to the Question,

Given that, Luis has saved $15. He doubles the amount he saves each week.