Write the equation of the line that is parallel to the line y=3x+7 and passes through the
point (-4,-14).

Use L'Hopital's rule twice:

[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \lim_{x\to0^+} \frac1{\sin^2(x)} \left(\int_0^x \sin^{-1}(t) \, dt - \int_0^{\frac x2} \sin^{-1}(t) \, dt\right) \\\\ = \lim_{x\to0^+} \frac{\sin^{-1}(x) - \frac12 \sin^{-1}\left(\frac x2\right)}{2\sin(x)\cos(x)} ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{2\sin^{-1}(x) - \sin^{-1}\left(\frac x2\right)}{2\sin(2x)} \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{2\sqrt{1-\frac{x^2}4}}}{4\cos(2x)}  ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{\sqrt{4-x^2}}}{4\cos(2x)}[/tex]

The remaining limand is continuous at x = 0, and the limit is

[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \frac{2-\frac12}4 = \boxed{\frac38}[/tex]

Presumably, both δ and ρ represent density of some object. Considering the context, ρ is likely a function of 3 variables, ρ = ρ(x, y, z). Then the mass of the sphere with the prescribed density δ(x, y, z) = k ρ(x, y, z) is

[tex]\displaystyle \iiint_B k \rho(x,y,z) \, dx\, dy\, dz[/tex]

where B is the set

[tex]B = \left\{(x,y,z) ~ : ~ x^2+y^2+z^2 \le 7^2\right\}[/tex]

If you have all the details at hand, you can compute the integral by converting to spherical coordinates, substituting

[tex]\begin{cases}x = u \cos(v) \sin(w) \\ y = u \sin(v) \sin(w) \\ z = u \cos(w)\end{cases} \text{ and } dx\,dy\,dz = u^2 \sin(w) \, du \, dv \, dw[/tex]

The integral then transforms to

[tex]\displaystyle k \int_0^{2\pi} \int_0^\pi \int_0^7 \rho(u\cos(v)\sin(w),u\sin(v)\sin(w),u\cos(w)) \, u^2 \sin(w) \, du \, dw \, dv[/tex]

Without any additional information, there's not much more to say...

Answer:

239.8 feet to the nearest tenth.

Step-by-step explanation:

We have 2 right triangles one inside the other.

Let the height of the builing be x ft and the distance from foot of thebuiding to the closest point be y feet.

So we have the system:

tan 28.8 = x/(y + 100)

tan 35.5 = x/y

From second equation:

x =  tan35.5 y

Sustituting in the first equation:

tan 28.8 = tan35.5 y / (y + 100)

tan35.5 y = tan 28.8 y + 100 tan 28.8

y(tan35.5 - tan28.8) = 100 tan 28.8

y =  100 tan 28.2 / (tan35.5 - tan28.8)

y =  336.16 ft

So x = height of the buiding =   tan35.5 *  336.16

= 239.78 ft.

Answer:

Step-by-step explanation:

Answer:

  1

Step-by-step explanation:

Translation of a function h units to the right is accomplished by replacing x in the function definition with (x-h).

Here, x has been replaced by x-4, so we expect to see the graph look like the original function graph shifted 4 units to the right.

That matches Graph 1.

Answer:

using of fractional exponents give us the value 6(x^2y^3)^1/2 or 6xy^3/2.

Multiplication of a positive number and negative number

   ⇒ is like any other multiplication

      30 * -20 = 30 * ((-1) * 20) = 30 * -1 * 20 = (-1) * 600 = -600

Hope that helped!

24/8 = 3

the 24 to 8 gear = 3:1 ratio which is greater than 2:1

Answer:

3/13

Step-by-step explanation:

P(Choosing a Face card) =

12/52= 3/13

pls mark as brainliest

Answer:

1 tsp of oil = 4 g

Step-by-step explanation:

1 Tbsp of syrup = 5 tsp of oil

2 tsp of oil = 1 Tbsp of syrup - 12 g

2 tsp of oil = 5 tsp of oil - 12 g

-3 tsp of oil = -12 g

1 tsp of oil = 4 g

The amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

Let we take:

X = The balance of a person’s bank account in Superior, WI

Then, by the given data, we have:

[tex]X \sim N(\mu = 580, \sigma = 125)[/tex]

Let the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents be X = x dollars. This is the money, below which lie 80% of Superior, WI residents, and so as their income, or values of X.

Symbolically, we have:

[tex]P(X < x) = 80\% = 0.8[/tex]

Converting X to standard normal variate Z, we have:

[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - 580}{125}\\[/tex]

Thus, the probability statement can be rewritten as:

[tex]P(X < x) =0.8\\P\left( Z < z = \dfrac{x -580}{125} \right) = 0.8[/tex]

From the z-tables, the value of Z for which the p-value comes out as between 0.84 and 0.85, let it be their average 0.845.

Thus, we get:

[tex]P(Z < z = 0.845) \approx 0.8[/tex]

Thus, we get:

[tex]z = \dfrac{x - 580}{125} \approx 0.8\\\\x \approx 0.8 \times 125 + 580 = 680[/tex]

Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx.

Now, for second question, we need:

The probability a random person from Superior has less than $400 or more than $1000 in their bank account.

So, income of a random person from Superior is a random value of X.

So, this probability is written as:

[tex]P(400 < X < 1000)[/tex]

Rewritting it, we get:

[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)[/tex]

Converting X to Z (standard normal variate), we get:

[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)\\\\P(400 < X < 1000) = P\left(Z < \dfrac{1000-580}{125} \right) - P\left(Z \leq \dfrac{400-580}{125} \right)\\\\P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)[/tex]

The p-value for Z = 3.36 is 0.9996

The p-value for Z = -1.44 is 0.0749

Thus, we get:

[tex]P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)\\\\P(400 < X < 1000) = 0.9996 - 0.0749 = 0.9247[/tex]

Thus, the probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

Learn more about z-score here:

https://brainly.com/question/21262765

#SPJ1

Answer:

tan 70 times thirty gives you -1.70

Answer:

A.

Step-by-step explanation:

B and C seem to stray away from what the question originally asked.

Answer:

the answer is B ( offer proof by example in answering interview questions)

Step-by-step explanation:

hope this helps:)

ed 2023

Answer:

40 percent of 46 is 18.4.

Answer:

It should be called A decic polynomial

Step-by-step explanation:

Answer:

O = 15

Step-by-step explanation:

.mean ' is the average

(12 + 16 + O + 14 + 8) / 5 = 13

50 + O = 65

O = 15

Answer:

Is shifted downwards

Step-by-step explanation:

K determines where the parabola is on the y axis basically. If the k value was positive it would be shifted upwards and if it was negative it would be shifted downwards.

Answer:

D

Step-by-step explanation:

Here's why I think it's D.

y = x + 44 is the equation the car wash owner uses

x represents the number of days

y represents the number of cars (washed)

so if we plug in one of the given numbers (from the chart)

example:

Day 2 Numbers of Cars Washed 44

2 will represent the "number of days" also known as x

44 will represent the "number of cars" also known as y

so if we plug in those values to the equation the car wash owner uses

y = x + 44, it doesn't match

__________________________________

(44) = 2 + (44)

44 [tex]\neq[/tex] 46

Therefore, I believe the answer is D

Answer:

D

Step-by-step explanation:

Answer:

34 degrees

Step-by-step explanation:

Assuming that ADJ is a right angle, we can add 4x and 3x-8 and set equal to 90 degrees to simply to get get x.

7x-8=90

Add 8

7x = 98

 x= 14

Now that we know x, we can plug in the value to find angle CDJ.

3x-8

3(14)-8

34 degrees

A graph that shows a function must pass the vertical line test

The true statement is (b) No; the graph fails the vertical line test.

For a graph to show a function, the graph must pass the vertical line test

The given graph do not pass the vertical line test;

This is so because, a line drawn from the x-axis would touch the graph at at least two different points

Hence, the true statement is (b) No; the graph fails the vertical line test.

Read more about the vertical line tests at:

https://brainly.com/question/1821791

The f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain, and range

Linear equations are equations that has a degree of 1 while polynomial equations are equations that has a degree of 2 and above.

Given the following functions

f(x) = –4x + 5 and;

g(x) = x^3 + x^2 – 4x + 5

Since the f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain and range

Learn more on functions here: https://brainly.com/question/25638609

Answer:

The answer is (n – 2) (3n + 2)

Step-by-step explanation:

3n² – 4n – 4

3n² – 6n + 2n – 4

3n(n – 2) + 2(n – 2)

(n – 2) (3n + 2)

Thus, (n – 2) (3n + 2) is a factored of

3n² - 4n - 4

Answer:

Step-by-step explanation:

This is a counting problem. As with many counting problems, it is helpful to adopt a strategy that helps ensure you count everything only once.

__

There are two pentagonal faces and 5 rectangular faces for a total of ...

  7 faces

__

There are 5 edges around each of the pentagonal faces, and 5 edges connecting the top face to the bottom faces, for a total of ...

  15 edges

__

There are 5 vertices on the top face, and 5 on the bottom face, for a total of ...

  10 vertices

Step-by-step explanation:

589292 is the correct answer:-)

Answer:

I think its 40

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Got it right on the assignment.

Hope this helps!!