Michael is looking up at an object. Michael points one arm at the object and

Write an equation in point-slope then convert into slope-intercept for a line that passes through (-4,1) with a slope of 3/2

Alexandra [31]

Answer:

y = 3/2x + 7

Step-by-step explanation:

y - 1 = 3/2 (x + 4)

y = 3/2x + b

1 = 3/2(-4) + b

1 = -6 + b

7 = b

8 0

2 years ago

Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9?

Sphinxa [80]

Answer:

Step-by-step explanation:

a. The vertex is (1, -9). False. The vertex is (-1, -9).

b. The graph opens upward. True. That coefficient '6' is positive.

c. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. False. It's DOWN 9 units.

d. The graph is steeper than the graph of f(x) = x^2. True. The given function increases 6 times faster than does x^2.

e. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

Let's put f(x) = 6(x + 1)^2 -9 into standard form. Expanding the first term, we get f(x) = 6(x^2 + 2x + 1) - 9, or f(x) = 6x^2 + 12x + 6 - 9. YES, TRUE

3 0

2 years ago

Find f-1(x), if f(x) = 3x – 6. Justify your

Sergio039 [100]

Answer: 1/3 (x + 6)

Explanation: given f(x) = 3x - 6.
Let y = f(x) and so y = 3x - 6.
Trade places between x and y.
x = 3y - 6
Solve for y
x + 6 = 3y
y = x + 6/3
Now the new y is the inverse and so y = f-1(x)
f-1(x) = 1/3(x + 6)

4 0

2 years ago

Find a polynomial that describes the area of the lawn which kevin has to mow in his front yard 6x+5,4x-9

Likurg_2 [28]

Answer:

$Area=24x^2-34x-45$

Step-by-step explanation:

Length and width of the yard are $(6x+5)$ and $(4x-9)$ .

$Area=length\times width\\\\Area=(6x+5)\times (4x-9)\\\\Area=24x^2+20x-54x-45\\\\Area=24x^2-34x-45$

7 0

3 years ago

A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = <u><em>probability of obtaining head.</em></u>

So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

$1-\beta$ = $\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}$

$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

3 0

3 years ago