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3 years ago

What is the slope of any line perpendicular to y=-1/3x+22

1 answer:

5 0

Answer:
The slope of any line perpendicular to the given line is 3

Explanation:
The general form of the linear line is:
y = mx + c where m is the slope
The given line is:
y = -1/3 x + 22
Comparing the given line with the general form, we will find that:
slope of the given line (m1) is -1/3

Now, for any two lines to be perpendicular, the product of their slopes should be equal to -1.
This means that:
m1 * m2 = -1
We have m1 = -1/3
Therefore:
-1/3 * m2 = -1
m2 = 3*1
m2 = 3

Hope this helps :)

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A local animal rescue organization receives an average of 0.55 rescue calls per hour. Use the Poisson distribution to find the p

andreyandreev [35.5K]

Answer:

B) 0.894

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

A local animal rescue organization receives an average of 0.55 rescue calls per hour.

This means that $\mu = 0.55$

Probability that during a randomly selected hour, the organization will receive fewer than two calls.

$P(X < 2) = P(X = 0) + P(X = 1)$

In which

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.55}*(0.55)^{0}}{(0)!} = 0.577$

$P(X = 1) = \frac{e^{-0.55}*(0.55)^{1}}{(1)!} = 0.317$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.577 + 0.317 = 0.894$

5 0

3 years ago

The curved surface area of a right circular cylinder of height 14 cm is 88 cm².

Slav-nsk [51]

Answer:

The diameter of the base of the cylinder is 2 cm.

Step-by-step explanation:

GIVEN :

As per given question we have provided that :

➣ Height of cylinder = 14 cm
➣ Curved surface area = 88 cm²

$\begin{gathered}\end{gathered}$

TO FIND :

in the provided question we need to find :

➠ Radius of cylinder
➠ Diameter of cylinder

$\begin{gathered}\end{gathered}$

USING FORMULAS :

$\star{\underline{\boxed{\sf{\purple{Csa = 2 \pi rh}}}}}$

$\star{\underline{\boxed{\sf{\purple{d = 2r}}}}}$

➛ Csa = Curved surface area
➛ π = 22/7
➛ r = radius
➛ h = height
➛ d = diameter

$\begin{gathered}\end{gathered}$

SOLUTION :

Firstly, finding the radius of cylinder by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{Csa = 2 \pi rh}}} \\ \\ \qquad{\longrightarrow{\sf{88 = 2 \times \dfrac{22}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{\cancel{7}}\times r \times \cancel{ 14}}}} \\ \\ \qquad{\longrightarrow{\sf{88 =44 \times r \times 2}}} \\ \\ \qquad{\longrightarrow{\sf{88 =88 \times r}}} \\ \\ \qquad{\longrightarrow{\sf{r = \frac{88}{88}}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\pink{r = 1 \: cm}}}}}} \end{gathered}$

Hence, the radius of cylinder is 1 cm.

———————————————————————

Now, finding the diameter of cylinder by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{d = 2r}}} \\ \\ \qquad{\longrightarrow{\sf{d = 2 \times 1}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\red{r = 2 \: cm}}}}}}\end{gathered}$