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4 years ago

10 POINTS !

Mathematics

2 answers:

satela [25.4K]4 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - $\frac{3}{2}$ , thus

y = - $\frac{3}{2}$ x + c ← is the partial equation

To find c substitute (8, 2) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y = - $\frac{3}{2}$ x + 14 ← equation in point- slope form

sesenic [268]4 years ago

5 0

Gradient= -3/2 Equation: Y=mx+c Y=2 , X=8

So you substitute the numbers in

2=(-3/2) x 2 + c (then you backtrack to solve for c which is the y intercept)

2=-3+c

5=c So the equation should be Y=-3/2x+5

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Consider the probability that at least 88 out of 158 software users will not call technical support. Assume the probability that

Nookie1986 [14]

Answer:

$E(X) = 158*0.57 =90.06$

And the standard deviation for the random variable is given by:

$\sigma= \sqrt{158*0.57*(1-0.57)} = 6.223$

And the distribution for the approximation is given by:

$X \sim N (\mu = 90.06, \sigma = 6.223)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And using the complement rule we got:

$P(X \geq 88) = 1-P(X$

And using the standard normal table we got:

$P(X \geq 88) = 1-P(X$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Bin (n = 158, p =0.57)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

We want this probability:

$P(X\geq 88)$

Normal approximation

We need to check if we can use the normal approximation , the conditions are:

$np =158*0.57 = 90.06>10$

$n(1-p) = 158*(1-0.57) = 67.94>10$

Since we satisfy both conditions the normal approximation makes sense

The expected value is given by this formula:

$E(X) = 158*0.57 =90.06$

And the standard deviation for the random variable is given by:

$\sigma= \sqrt{158*0.57*(1-0.57)} = 6.223$

And the distribution for the approximation is given by:

$X \sim N (\mu = 90.06, \sigma = 6.223)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And using the complement rule we got:

$P(X \geq 88) = 1-P(X$

And using the standard normal table we got:

$P(X \geq 88) = 1-P(X$

4 0

3 years ago

PLEASE HELP!! A culture started with 1000 bacteria. After 6 hours, it grew to be 1100 bacteria. Predict how many bacteria will b

Viktor [21]

1000 to 1100 is an increase of 100 bacteria per 6 hours
100/6 = 16.67 bacteria per hour
16.67 * 15 hours = 250
Total bacteria should be 1100+250= 1350

6 0

3 years ago

Read 2 more answers

Colleen is 15 years from retiring. She opens an account at the Savings Bank. She plans to deposit

gulaghasi [49]

9514 1404 393

Answer:

a) $169,234.59

b) $19,234.59

Step-by-step explanation:

The first question you must answer is whether Colleen will earn interest on her first deposit in the first year. That is, does she deposit the money at the first of the year or the end of the year?

The usual "annuity" formula assumes the deposit is at the end of the year, so no interest at all is earned on the last deposit made. If the deposit is at the first of the year, an "annuity due" formula is used, that multiplies the entire ending account value by the annual multiplier, 1.017 in this case.

a) Assuming an "annuity", the formula is ...

A = P((1 +r)^t -1)/r . . . . . for annual compounding at rate r for t years

A = $10,000(1.017^15 -1)/0.017 = $169,234.59 . . . . ending balance

b) Colleen has made 15 deposits of $10,000, for a total of $150,000, so the amount of interest earned is ...

$169,234.59 -150,000 = $19,234.59 . . . . interest earned

8 0

3 years ago

How dose this input and output table work?

alexandr402 [8]

Aswer:I am sure of the answer it is 6 and 42

Step-by-step explanation:

5+30=35
12+30=42
30+30=60
36+30=66
40+30=60

6 0

3 years ago

What is the measure of angley to the nearest whole degree? 58° 64° 68° 73°

dalvyx [7]

Applying the law of cosines, the measure of angle Y in the image below, to the nearest whole degree, is: B. 64°

<h3>What is the Law of Cosine:</h3>

Law of cosines is given as: y² = x² + z² – 2xz(cosY)

Given the following:

x = 12

y = 16

z = 17

Y = ?

Apply the law of cosines:

16² = 12² + 17² – 2(12)(17)(cosY)

256 = 433 - 408(cos Y)

256 - 433 = -408(cos Y)

-177 = -408(cos Y)

-177/-408 = cos Y

Y = cos^(-1)(177/408)

Y ≈ 64°

Learn more about law of cosines on:

brainly.com/question/7872492

7 0

2 years ago