Ax+16=b−3x what is a= and what does b= ?

Answer:

(a) P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) P(X ≥ 13.01) = 0.3075

Step-by-step explanation:

To address this problem, one needs to grasp the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems involving normally distributed samples are resolved through the application of the z-score formula.

In a data set with a mean and standard deviation , the z-score for a measurement X is defined as:

The Z-score indicates how many standard deviations the measurement deviates from the mean. After determining the Z-score, one can consult the z-score table to find the relevant p-value for that score. This p-value represents the probability that the measure's value is less than X, which indicates the percentile of X. By subtracting this p-value from 1, we obtain the likelihood that the measure's value exceeds X.

Central Limit Theorem

According to the Central Limit Theorem, for a normally distributed random variable X with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated by a normal distribution, characterized by mean and standard deviation .

The Central Limit Theorem can also be applicable to a skewed variable, provided that n is 30 or more.

In this case, we are given that:

(a) Compute P(12.99 ≤ X ≤ 13.01) when n = 16.

In this scenario, we find

This probability equates to the p-value of Z at X = 13.01 minus the p-value of Z at X = 12.99.

X = 13.01

According to the Central Limit Theorem

has a p-value of 0.6915

X = 12.99

yields a p-value of 0.3075

0.6915 - 0.3075 = 0.3840

P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) What is the probability that the sample mean diameter is greater than 13.01 when n = 25?

P(X ≥ 13.01) =

This is obtained by subtracting the p-value of Z when X = 13.01 from 1. Hence

has a p-value of 0.6915

1 - 0.6915 = 0.3075

P(X ≥ 13.01) = 0.3075

Response:

b

Detailed explanation:

The equation of the line through the point (5,4) with a slope of 6/5 is y = 6/5x - 2. This is determined using the linear equation format y = mx + b. By substituting in the values, you can simplify to find the y-intercept.

Answer:

y

y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction y = StartFraction 3 menos 6 StartRoot 2 EndRoot Over 4 EndFraction

Explicación paso a paso:

La ecuación cuadrática que tenemos es (4y - 3)² = 72

Debemos encontrar el valor de y.

Ahora, 4y - 3 = ± 6√2

⇒ 4y = 3 ± 6√2

⇒ y

Por lo tanto, las soluciones son y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction y y = StartFraction 3 menos 6 StartRoot 2 EndRoot Over 4 EndFraction (Respuesta)

An even function can be reflected over the y-axis and still remain unchanged.
Example: y=x^2
On the other hand, an odd function can be reflected around the origin and also remains unchanged.
Example: y=x^3


A straightforward method to determine this is:

if f(x) is even, then f(-x)=f(x)
if f(x) is odd, then f(-x)=-f(x)


Hence, for an even function
substitute -x in for each and check for equivalence
make sure to fully expand the expressions
g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original expression
g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
Not the same, as the original contains -2x
Therefore, it is not even
g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
It matches, hence it is even
g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
Not equivalent, thus not even
g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
Not equal, therefore not even



g(x)=2x²+1 is the confirmed even function.