Give the domain and range.

I don't know what to do I'm very confused

finlep [7]

Answer:

x = 33.8°

Step-by-step explanation:

The resulting diagram we have is a right triangle. To find x, apply trigonometric function.

Reference angle = x

Opposite = 116

Adjacent = 173

Apply TOA:

Tan x = Opp/Adj

$tan (x) = \frac{116}{173}$

$x = tan^{-1}(\frac{116}{173})$

x = 33.8° (nearest tenth)

7 0

3 years ago

Need help with this math question

anastassius [24]

Answer:

The vertex is: $(6, 8)$

Step-by-step explanation:

First solve the equation for the variable y

$x^2-4y-12x+68=0$

Add 4y on both sides of the equation

$4y=x^2-4y+4y-12x+68$

$4y=x^2-12x+68$

Notice that now the equation has the general form of a parabola

$ax^2 +bx +c$

In this case

$a=1\\b=-12\\c=68$

Add $(\frac{b}{2}) ^ 2$ and subtract $(\frac{b}{2}) ^ 2$ on the right side of the equation

$(\frac{b}{2}) ^ 2=(\frac{-12}{2}) ^ 2\\\\(\frac{b}{2}) ^ 2=(-6) ^ 2\\\\(\frac{b}{2}) ^ 2=36$

$4y=(x^2-12x+36)-36+68$

Factor the expression that is inside the parentheses

$4y=(x-6)^2+32$

Divide both sides of the equality between 4

$\frac{4}{4}y=\frac{1}{4}(x-6)^2+\frac{32}{4}$

$y=\frac{1}{4}(x-6)^2+8$

For an equation of the form

$y=a(x-h)^2 +k$

the vertex is: (h, k)

In this case

$h=6\\k =8$

the vertex is: $(6, 8)$

5 0

3 years ago

18 ÷ -3 - -12 x -1 x -11 (the x is times, please solve)

Elena L [17]

126
Explanation
18/-3-(-12)•(-1)•(-11)
divide 18 by -3 and change signs on the 12
(-6)+12•(-1)•(-11)
multiply 12 and -1
(-6)+(-12)•(-11) then multiply -11 and -12
-6+132
126

5 0

3 years ago

The equation (-2, 3) (3, 0) point slope form is

yulyashka [42]

<span>(a) y - 0 = -3/5(x - 3) . . . . . . the 1st selection

(b) </span><span>y = -3/5x + 9/5 . . . . . . . . the 3rd selection</span>

5 0

4 years ago

. The time required for a technician to machine a specific component is normally distributed with a mean of 2 hours and a standa

erma4kov [3.2K]

Answer:

a) There is a 3.84% probability that the technician can machine one component in 1.5 hours or less.

b) There is a 0.42% probability that the technician will require at least 2.75 hours to complete one component

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.

In this problem, we have to be careful. The mean is in hours, while the standard deviation is in minutes. I am going to work with both in hours, as the problem states. 17 minutes is 0.283 hours, so:

$\mu = 2, \sigma = 0.283$

(a.) What is the probability that the technician can machine one component in 1.5 hours or less?

This probability is the pvalue of the Zscore when $X = 1.5$ . So:

$Z = \frac{1.5 - 2}{0.283}$

$Z = \frac{-0.5}{0.283}$

$Z = -1.77$

$Z = -1.77$ has a pvalue of 0.0384.

This means that there is a 3.84% probability that the technician can machine one component in 1.5 hours or less.

(b.) What is the probability that the technician will require at least 2.75 hours to complete one component?

The pvalue of the score of $X = 2.75$ is the probability that the technican will require less than 2.75 hours to complete one component. The probability that he will require at least 2.75 hours to complete one component is 1 subtracted by this pvalue. So:

$Z = \frac{2.75 - 2}{0.283}$

$Z = \frac{0.75}{0.283}$

$Z = 2.65$

$Z = 2.65$ has a pvalue of 0.99598.

This means that the probability that the technican will require at least 2.75 hours to complete one component is 1 - 0.99598 = 0.0042 = 0.42%.

4 0

4 years ago