Find the slope of GH: G(-11, -3) and H(-6,7)

Mathematics

1 answer:

Phantasy [73]3 years ago

7 0

-5/-10=1/2. you can cancel the negative and the gcf of 5 and 10 is 2. so after you divide you get 1/2.

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Suppose the life span of a calculator has a normal distribution with a mean of 60 months and a standard deviation of 8 months. W

rusak2 [61]

Answer:

Probability that the calculator works properly for 74 months or more is 0.04 or 4%.

Step-by-step explanation:

We are given that the life span of a calculator has a normal distribution with a mean of 60 months and a standard deviation of 8 months.

Firstly, Let X = life span of a calculator

The z score probability distribution for is given by;

Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 60 months

$\sigma$ = standard deviation = 8 months

Probability that the calculator works properly for 74 months or more is given by = P(X $\geq$ 74 months)

P(X $\geq$ 74) = P( $\frac{ X - \mu}{\sigma}$ $\geq$ $\frac{74-60}{8}$ ) = P(Z $\geq$ 1.75) = 1 - P(Z < 1.75)

= 1 - 0.95994 = 0.04

Therefore, probability that the calculator works properly for 74 months or more is 0.04 or 4%.

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3 years ago

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3 years ago

If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.

alexgriva [62]

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

$\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]$

The inverse of the matrix is

$\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]$

So, the Inverse Transformation is given by

$T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$