If if Spencer spent a total of $704.00 in the month of July, which is the best estimate for the amount of money he spent on clothing?

Answer:

a) 0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.

b) 0 is less than 2.5 standard deviations from the mean, so it would not be unusual.

Step-by-step explanation:

For each passenger, there are only two possible outcomes. Either they will have been stopped due to a change in the pocket, or not. Passengers are independent. This means that we use the binomial probability distribution to solve this question.

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.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

A measure is considered unusual if it is more than 2.5 standard deviations of the mean.

25% chance that the cause is change in the passenger's pocket.

This means that [tex]p = 0.25[/tex]

During a given hour, 15 passengers are stopped because of a signal from the metal detector.

This means that [tex]n = 15[/tex]

a) Find the probability that at least 3 passengers will have been stopped due to change in their pockets.

This is

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

So

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

[tex]P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134[/tex]

[tex]P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668[/tex]

[tex]P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.2361 = 0.7639[/tex]

0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.

b) If 15 passengers are stopped by the detector, would it be unusual for none of these to have been stopped due to change in the pocket

First we find the mean and the standard deviation:

[tex]E(X) = np = 15*0.25 = 3.75[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15*0.25*0.75} = 1.68[/tex]

3.75 - 2.5*1.68 = -0.45

0 is less than 2.5 standard deviations from the mean, so it would not be unusual.

Answer:

reduced traffic on the road

Step-by-step explanation:

just took the test :)

Answer: C) Reduced traffic on the road

Step-by-step explanation: Ive taken this test

Answer:

$756.00

Step-by-step explanation:

6.30 x 2 = 12.60/hour

12.60 x 60 = $756.00

Answer:

A, E, G

Step-by-step explanation:

Answer:

A

E

G

Step-by-step explanation:

When you divide A, E, and G with the common factor, they all equal 5 : 9

uhm... I’m sorry I don’t actually know the answer to your question but I’m trying to get some points...

Answer:

The perimeter is:

24

Step-by-step explanation:

Perimeter is the outside frame of the area. Add the dimensions together to get your answer. Adding:

7+7= 14

5+5= 10

10+14= 24

:) Hope this helps have a wonderful day!

Answer:

Answer in attachment photo

Answer:

Step-by-step explanation:

You should add the weights of each kitten and then divide by the number of kittens. Ex. There are 5 kittens weighing 2, 1, 3, 2, and 2. So you would add those to get 10 and divide by the number of kittens which is 5 to get an average of 2.

So in this case you would first add the weight of the kittens

Then divide that by the number of kittens

Then the quotient would be the average of the weight of the kittens in the shelter.

Answer:

11

Step-by-step explanation:

1/2 times 2³=4

+7=11

Answer:

Her monthly payment is approximately $4,611.65

Step-by-step explanation:

The monthly payment on the loan is given by the following formula;

[tex]A = P \cdot \dfrac{r\cdot (1 + r)^n}{(1 + r)^n - 1}[/tex]

A = The monthly payment

P = The principal amount = $423,000

r = 5.65%

The number of years = 10 years

[tex]A = 423,000 \cdot \dfrac{\dfrac{0.0565}{12} \cdot \left (1 + \dfrac{0.0565}{12} \right )^{180}}{\left (1 + \dfrac{0.0565}{12} \right )^{180} - 1} \approx 4611.65[/tex]

Her monthly payment, A ≈ $4,611.65

Answer:

260 cm^2

Step-by-step explanation:

Area of parallelogram: bh, so it is 20x13 which is 260cm^2

Answer:

Explained below.

Step-by-step explanation:

There are quite a few examples of this but I will go with what is common in physics which is "acceleration due to gravity".

Acceleration due to gravity is positive when an object is falling down in the direction of gravity but negative when it is thrown upwards and acting against gravity motion.

Thus;

g_downwards = 9.8 m/s²

g_upwards = -9.8 m/s²

If acceleration due to gravity is zero, it means that the object is at the centre of the earth because at that point g = 0.

Answer:

A miner digs 100ft underground. Then he went up to the surface and climbed all the way to the top of the mountain. The entrance of the underground cave represents 0.

Step-by-step explanation:

Answer:

4x-3y=-10 ans C

2x+3y=4

Step-by-step explanation:

4x-3y=-10--------eqn 1

2x+3y=4----------eqn 2

multiply eqn 1 by 2 and eqn 2 by 4

8x-6y=-20

8x+12y=16

subtract eqn 2 from 1

8x-8x ,12-(-6y)=16-(-20)

18y=36

divide both sides by 18

y=2

substitute y=2 in eqn 1

4x-3(2)=-10

4x-6=-10

4x=-10 + 6

4x= -4

divide both sides by 4

x= -1

Answer:

15.736

Step-by-step explanation:

Answer:

The first answer one is true

Answer:

yes, 29 is a monomial

Step-by-step explanation:

Answer:

here you go

Step-by-step explanation:

Answer:

21.4

Step-by-step explanation:

just trust me i come from DeltaMAth

Answer:

the angle of inclination of the hill is 46.56°

Step-by-step explanation:

  Given the data in the question;

Just as illustrated in the diagram below

so to find the angle of inclination of the hill;

sinA/30 = sinB/125

since angle BAC  is 8°

we substitute

sin8°/30 = sinB/125

sinB = ( sin8°/30 ) × 125

B = sin⁻¹ ( ( sin8°/30 ) × 125 )

B = sin⁻¹ ( 0.004639 × 125 )

B =  35.44°

so since the some of a the angles of a triangle is 180;

A + B + C = 180

8° + 35.44° + C = 180

C = 180 - ( 8° + 35.44° )

C = 136.56°  

Hence, Angle of inclination x will be;

x = 136.56° - 90°

x = 46.56°

Therefore, the angle of inclination of the hill is 46.56°

Answer:

180

Step-by-step explanation:

i had that question

Answer:

-8.45, 0.95, 8.25

Step-by-step explanation:

The easiest way to do this is to convert the fraction to a decimal, and then compare the values.

8 8/32 is equal to 8 and 1/4. Because 1/4 = 0.25, 8 and 8/32 equals 8.25.

Now, let's compare values.

Numbers we need to compare: -8.45, 0.95, 8.25

The smallest number is -8.45, then 0.95, and lastly, 8.25.

Thus the answer is

-8.45, 0.95, 8.25

Answer:

**********************868/14=62********************

Step-by-step explanation:

Answer:

+*~868 ÷ 14 = 62~*+

(Hope this helps! Btw, I answered first. Brainliest please! :D)

Answer:  6.5 ÷ 100 = 0.065

Answer:

y = 3/4x -2

Step-by-step explanation:

Points on the graph: (4, 1) and (0, -2)

Slope:

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

m= (-2-1)/0-4)

m=(-3)/(-4)

m = 3/4

Point-slope:

y - y1 = m(x - x1)

y - 1 = 3/4(x - 4)

y - 1 = 3/4x - 3

y = 3/4x -2