GOD GIVE ME STRENGTH MATH REALLY BE TESTING ME

Answer:

a) 0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

b) 0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

Mean of 12 potholes per mile, which means that in a quarter-mile stretch, the mean is [tex]\mu = \frac{12}{4} = 3[/tex]

This probability is:

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

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*(3)^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*(3)^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0498 + 0.1494 = 0.1992[/tex]

0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

b. Find the probability of finding more than one pothole in a quarter-mile stretch of the highway.

This is

[tex]P(X > 1) = 1 - P(X < 2)[/tex]

We have that [tex]P(X < 2) = 0.1992[/tex]

So

[tex]P(X > 1) = 1 - P(X < 2) = 1 - 0.1992 = 0.8008[/tex]

0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.

Answer:0=−6

Step-by-step explanation:

Answer:

Here you go. Check the answer in book too.

Answer:

10m ( p - q )

Step-by-step explanation:

[tex] \frac{15lm \times 2 {cp}^{2} {q}^{2} }{3l(p + q)}[/tex]

[tex] \frac{30lm \: (p - q)(p + q)}{3l(p + q)} [/tex]

[tex] \frac{10lm(p - q)}{l} [/tex]

[tex]10m(p - q)[/tex]

Hope it is helpful....

Step-by-step explanation:

you just do 180 - 90 = 90 degree is x value

Answer:

x should equal 90.

Step-by-step explanation:

x is the sum of those two interior angles. 50 + 40 equals 90.

Answer:

204

Step-by-step explanation:

17x12=204

Answer:

36.1

Step-by-step explanation:

Answer:

the equivalent expression is 0.88(x)

Step-by-step explanation:

Given that

There is 12% off on the total purchase price

Based on the above information

The expression that used the given terms i.e.

b - 0.12b

i.e.

1 - 0.12

= 0.88(x)

Hence, the equivalent expression is 0.88(x)

Answer:

63c^5

Step-by-step explanation:

Answer:

AB is the diameter,,,,,,,,,

Answer:

Use Trigonometric formulae to simplify expressions

Step-by-step explanation:

Re-order to group the x and y,

Sin(y) / Sin(a+y) = x

to differentiate apply d/dx to both sides

[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x

use division rule on left side which will give

[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1

Group them so dy/dx is on the left hand side:

[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)

Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),

[tex]\frac{dy}{dx}[/tex] =  Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]

Simplify it

[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))

[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))

Answer:

This is a rectangle

Step-by-step explanation:

2D shape with 4 right angles would be a rectangle because 2 sides are equal and the other 2 would be equal to give you 4 right angles

Answer:

a I think please be right

Answer:If you draw a graph or look it up on Desmos, it curves down around y = 10. It only hits the second and third quadrant. B is the only situation that describes this.

Step-by-step explanation:g

Answer:

x(the number)=3

Step-by-step explanation:

3×3+3squared = 18

Answer:

3x + x^2 = 18

x^2 + 3x - 18 = 0

(x + 6)(x - 3) = 0

x + 6 = 0

x = -6

x - 3 = 0

x = 3

Answer:

(5x3m) + (5x2) = 15m + 10

Step-by-step explanation:

multiply 5 to 3m plus 5 to 2 which is equivalent to 15m + 10

Answer:

y = -1/2 is the answer to 125=(1/25)^(y-1)

Answer:

$1,344.00

Step-by-step explanation:

A=P(1+rt)

A=1,200(1+(0.04)(0.03))

Answer:

5000 * (e^((1 /4) * ln(55 / 50) * (13))) = 6,815.47 from My text book

Step-by-step explanation:

Answer:

B.   128

Step-by-step explanation:

Answer:

by using Pythagoras law

hypotenuse ²=perpendicular ²+base²

h²=100²+80²

h²=10000+6400

h=√16400=128.06m

128m is the required answer.

Answer:

94 / π = 29.9211293...

Step-by-step explanation:

brainliest plz

Answer:

the sum of all even number from 0 to 420 is 175980

Answer:

To be complement sum of angle must be 90°

But to be supplement sum of angle must be 180°

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

divided 7200 by 45 to get 160

Answer:

The step-by-step procedure to solve this question is given, using the normal approximation to the binomial distribution.

Step-by-step explanation:

We use the normal approximation to the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

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]

Normal probability distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study.

This means that [tex]p = 0.45[/tex]

Mean and standard deviation for the approximation, for a sample of n:

[tex]\mu = E(X) = np = 0.45n[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{0.45*0.55n}[/tex]

Calculate the probability that fewer than 320 out of the n

Using continuity correction, this is [tex]P(X < 320 - 0.5) = P(X < 319.5)[/tex], which is the pvalue of Z when X = 319.5. So

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

[tex]Z = \frac{319.5 - 0.45n}{\sqrt{0.45*0.55n}}[/tex]

Just have to replace the value of n, find Z, and then find its pvalue.

Answer:

a. 42

b. 122

a. 57

b. 130

Step-by-step explanation:

For problem A:

because both of these values have positive numbers, just use normal subtraction

82 - 40 = 42 degrees warmer

For problem B:

because we are subtracting a negative number from a positive number, we add both of these numbers because 82 - -40 can also be equal to 82 + 40

82 - -40 = 122

For problem A:

the sentences 30m up a cliff and 87m up a cliff are describing positive values.

87 - 30 = 57

For problem B:

Now in this problem, the sentence 100m above the surface is describing a positive value, but the sentence 30m below the surface describes a negative value

how do I know this?

if the sentences above the surface and below the surface are describing positive and negative values, then there has to be a neutral value ( which is 0)

0 meters = the surface, because they are using both positive and negative values, meaning that the surface is the neutral value

by using a number line, you can draw it out like this

below the surface-------------------------the surface----------------------------above the surface

-30--------------------------------------------0--------------------------------------------100

therefore, 100 - - 30 = 100 + 30 = 130