Find an equation of the plane. the plane through the point (3, 0, 7) and perpendicular to the line x = 5t, y = 2 − t, z = 8 + 4t

Answers

Answer 1

Answer: Let's write the parametric line

(x,y,z) = (0,2,8) + t(5,-1,4)

(5,-1,4) is called the direction vector of the line. It's normal to the plane

5x - y + 4z = constant

We get the constant by substituting the point (3,0,7),

5x - y +4z = 5(3) - 0 + 4(7) = 43

5x - y +4z = 43

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Scott is a software salesman. Let represent his total pay (in dollars). Let represent the number of copies of History is Fun he sells. Suppose that and are related by the equation 80x+2100=y Answer the questions below.

Note that a change can be an increase or a decrease.

For an increase, use a positive number. For a decrease, use a negative number.

What is the change in Scott's total pay for each copy of History is Fun he sells?

What is Scott's total pay if he doesn't sell any copies of History is Fun?

Answers

Answer:

A. $80

B. $2100

Step-by-step explanation:

Given:

80x+2100=y

Rewrite the equation

y = 80x + 2100

Where,

y = Scott's total pay (in dollars)

x = number of copies of History is Fun he sells

2100 = fixed pay

Since, x = number of copies of History is Fun he sells

If x = 0

y = 80x + 2100

= 80(0) + 2100

= 0 + 2100

= 2100

y = $2100

If x = 1

y = 80x + 2100

= 80(1) + 2100

= 80 + 2100

= 2180

y = $2180

change in Scott's total pay for each copy of History is Fun he sells = $2180 - $2100

= $80

B. What is Scott's total pay if he doesn't sell any copies of History is Fun?

That is, when x = 0

y = 80x + 2100

= 80(0) + 2100

= 0 + 2100

= 2100

y = $2100

Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.x-intercept 7; y-intercept -5

Answers

Answer:

The line with the x- and y-intercepts below has the following equation:

$f(x) = (5x)/(7) - 5$

Step-by-step explanation:

The equation of the line has the following format:

$f(x) = ax + b$

We are given two points, we are going to substitute them into the above equation, and find the equation of the line given the conditions.

Solution

Starting from the y-intercept makes the solution easier, since the term a is multiplied by 0

y-intercept -5

This means that when $x = 0, y = f(x) = -5$ , so:

$f(x) = ax + b$

$-5 = a(0) + b$

$b = -5$

For now, the line has the following equation:

$f(x) = ax - 5$

x-intercept 7

This means that when $y = f(x) = 0,x = 7$ , so:

$f(x) = ax - 5$

$0 = 7(a) - 5$

$7a = 5$

$a = (5)/(7)$

So, the line with the x- and y-intercepts below has the following equation:

$f(x) = (5x)/(7) - 5$

A random sample of 150recent donations at a certainblood bank reveals that
45 were type A blood.Does this suggest that the
actual percentage of type A
donations is less than40%, the percentage of the
population having type A
blood? Carry out a testof the appropriate
hypotheses using a significance
level of0.01.

Answers

Answer:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

$z=\frac{0.3 -0.4}{\sqrt{(0.4(1-0.4))/(150)}}=-2.5$

$p_v =2*P(Z<-2.5)=0.0124$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

Step-by-step explanation:

1) Data given and notation

n=150 represent the random sample taken

X=45 represent the people with type A blood

$\hat p=(45)/(150)=0.3$ estimated proportion of people with type A blood

$p_o=0.4$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of people type A blood is less than 0.4:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.3 -0.4}{\sqrt{(0.4(1-0.4))/(150)}}=-2.5$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z<-2.5)=0.0124$

Convert 51.7% to a fraction in simplest form and a decimal.

Answers

0.517 as a decimal 517/10 as a fraction

Making Connections: Selecting a CareerApply Your Knowledge I will double the points if you get this completely done (that means both documents completed with the correct answers)

Answers

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Full question "Making Connections: Selecting a Career. Apply Your Knowledge" Top Career Choice, Job Description, Personal Attributes, Education, Experience, Certification, Employment, Job Outlook, Earnings, Work Environment, Related Occupations