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3 years ago

The value of n. 3n = (3^2)8

Mathematics

1 answer:

nika2105 [10]3 years ago

4 0

Answer:

Step-by-step explanation:

3n = 3² × 8 3² = 3 × 3

n × 3 = 3 × 3 × 8 notice a times 3 on both sides of the equation

divide both sides by 3

n = 3 × 8

n = 24 <---------------- FINAL ANSWER

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Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)

Shtirlitz [24]

Answer:

The endpoints of the latus rectum are $(12, -7)$ and $(-8, -7)$ .

Step-by-step explanation:

A parabola with vertex at point $C(x, y) = (h,k)$ and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

$(x-h)^{2} = 4\cdot p \cdot (y-k)$ (1)

Where:

$y$ - Independent variable.

$x$ - Dependent variable.

$p$ - Distance from vertex to the focus.

$h$ , $k$ - Coordinates of the vertex.

The coordinates of the focus are represented by:

$F(x,y) = (h, k+p)$ (2)

The latus rectum is a line segment parallel to the x-axis which contains the focus. If we know that $h = 2$ , $k = -2$ and $p = -5$ , then the latus rectum is between the following endpoints:

By (2):

$F(x,y) = (2, -2-5)$

$F(x,y) = (2,-7)$

By (1):

$(x-2)^{2} = -20\cdot (-7+2)$

$(x-2)^{2} = 100$

$x - 2 = \pm 10$

There are two solutions:

$x_{1} = 2 + 10$

$x_{1} = 12$

$x_{2} = 2-10$

$x_{2} = -8$

Hence, the endpoints of the latus rectum are $(12, -7)$ and $(-8, -7)$ .

4 0

3 years ago

An electronic product contains 48 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the

BigorU [14]

Answer:

0.6173 = 61.73% probability that the product operates.

Step-by-step explanation:

For each integrated circuit, there are only two possible outcomes. Either they are defective, or they are not. The integrated circuits 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.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

An electronic product contains 48 integrated circuits.

This means that $n = 48$

The probability that any integrated circuit is defective is 0.01.

This means that $p = 0.01$

The product operates only if there are no defective integrated circuits. What is the probability that the product operates?

This is P(X = 0). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{48,0}.(0.01)^{0}.(0.99)^{48} = 0.6173$

0.6173 = 61.73% probability that the product operates.

5 0

3 years ago

Find the distance between ( - 10 , - 7 ) and ( - 8 , 1 ).

nevsk [136]

Answer:

The distance point between (-10, -7) and (-8, 1) is 6

Step-by-step explanation:

8 0

3 years ago

Al and Bill each have two bullets. They fire alternately at a glass bottle. Al has hitting probability 1/3 and Bill 1/4. What is

enot [183]

P(Al hits bottle first time) = 1/3
P(Al misses the first shot but hits on his second shot) =
P( Al misses and bill misses and Al hits) = 2/3 * 3/4 * 1/3 = 1/6

So required probability = 1/3 + 1/6 = 1/2

8 0

4 years ago

Find two numbers that multiply to make the first number and add to make the second number. (I understand how to do it, I’m just

oee [108]

Let
x-----------> the first number
y-----------> the second number

we know that
x*y=x-----------> y=x/x----------> y=1
and x+y=y------> x=y-y---------> x=0

the answer is
 the first number is 0
the second number is 1

6 0

4 years ago