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What is the slope of a line that contains the points (-8,7) and (-4,-5)?

Pani-rosa [81]

Answer:

-3

Step-by-step explanation:

To find the slope given two points

m = (y2-y1)/(x2-x1)

= (-5-7)/(-4- -8)

= (-12)/(-4+8)

=-12/4

= -3

7 0

2 years ago

Six identical squares are cut from the corners and edges of an 80 cm by 50 cm cardboard rectangle. the remaining piece is folded

Anna11 [10]

Check the picture.

let the length of a side of each of the squares removed be x.

The box formed will have dimensions: 80-2x, 50-2x, x(the height)

So the volume can be expressed as a function of x as follows:

f(x)=(80-2x)(50-2x)x= $[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x$

so $f(x)=4 x^{3}-260x^{2}+4000x$

the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,

$f'(x)=12x^{2}-520 x +4000=0$

solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions

x=10 and x=33.333

plug in f(x) these values to see which greater:

$f(10)=(80-20)(50-20)10=60*30*10=18000$ cm cubed

$f(33.333)=(80-66.666)(50-66.666)33.333=$ which is negative because (50-66.666)<0

Answer: 18000 cm cubed

5 0

3 years ago

Read 2 more answers

3. Factory farming funk - The US Environmental Protection Agency (EPA) recently reported that confined animal feeding operations

Vikentia [17]

Answer:

Step-by-step explanation:

Hello!

There was a survey made in Michigan asking the residents if they were in favor of or against the creation of standards to limit pollution by CAFOs.

Using the results of the survey the student that conducted it estimated the population proportion of Michigan residents that are in favor of the creation of standards to limit pollution by CAFOs.

The calculated 95% CI is [0,7752; 0,8248]

Interpretation: With a 95% confidence level you'd expect that the interval [0,7752; 0,8248] will include the true population proportion of Michigan residents that are in favor of the creation of standards to limit pollution by CAFOs.

i.e. If you were to construct 100 confidence intervals, you'd expect 95 of them to contain the true value of the proportion of Michigan residents that are in favor of the creation of standards to limit pollution by CAFOs.

With this in mind:

Consider all of the following statements and determine which among them is incorrect

1) There is a 95% probability that the actual percent of Michigan residents in favor of pollution standards is between 77.52% and 82.48%. INCORRECT

2) Approximately 95% of MSU students favor pollution standards at a rate of 77.52% and 82.48%. INCORRECT

The confidence level is the probability that the interval will contain the true value of the parameter of interest and the bonds of the interval indicate the possible range of that parameter.

Also in 1) The parameter is not defined correctly, and in 2) the population of interest is incorrect.

3) If this study were repeated many times, we'd expect approximately 95% of future confidence intervals to contain the true rate at which Michigan residents favor the creation of pollution standards. CORRECT

4) With 95% confidence, we estimate the true rate at which Michigan residents favor the creation of pollution standards to be between 77.52% and 82.48%. CORRECT

I hope it helps!

6 0

3 years ago

Write <br> 2/9 as a repeating decimal.

grigory [225]

Answer:

.2 repeating

Step-by-step explanation:

if you are allowed to use calculators, then do so, if not, you're going to have to do a lot of division

8 0

3 years ago

Read 2 more answers

A baseball is thrown into the air from a height of 5 feet. The ball reaches a maximum height of 43.5 feet and spends a total of

xeze [42]

Answer:

h(t) = -16t^2 + 49.64t + 5

Step-by-step explanation:

The above choice is the only one that makes the height function be a downward-opening parabola and gives h(0) = 5, the initial height of the baseball.

___

Any function starting with 16t^2 will not have any positive x-intercepts.

8 0

3 years ago