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Komok [63]
2 years ago
5

Graph the function f(x) = -42-4+ 5 on the axes below. You must plot the

Mathematics
1 answer:
valentina_108 [34]2 years ago
7 0

Answer:

- attached graph

- Horizontal Asymptote: y = 5

- twon whole number points are (4,4) and (5,1)

Step-by-step explanation:

- Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote

y = -4^(x-4) + 5

  = -4^(4-4) + 5

  = -4^(0) + 5

  = -1 + 5

  = 4

y = -4^(x-4) + 5

  = -4^(5-4) + 5

  = -4^(1) + 5

  = -4 + 5

  = 1

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Sergio [31]

A=2800,B=120,C=140,D=6

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3 years ago
Olivia wants to walk 8000 steps today. She walked 45% of this total before lunch? How many steps did Olivia walk before lunch?
LiRa [457]

Answer:

3600 steps

Step-by-step explanation:

Step 1: Multiply 45 by 8000.

  • 45 * 8000
  • 360000

Step 2: Move the decimal point two places to the left.

  • 36000.0
  • 3600.00

Therefore, the answer is 3600 steps.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

4 0
3 years ago
What is the value of
jasenka [17]

Answer

My answer is in the photo above

7 0
3 years ago
A small lawnmower company produced 1,500 lawnmowers in 2008. In an effort to determine how maintenance-free these units were, th
ikadub [295]

Answer:

The 95% confidence interval for the average number of years until the first major repair is (3.1, 3.5).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the average using the finite correction factor is:

CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\cdot\sqrt{\frac{N-n}{N-1}}

The information provided is:

N=1500\\n=183\\\sigma=1.47\\\bar x=3.3

The critical value of <em>z</em> for 95% confidence level is,

<em>z</em> = 1.96

Compute the 95% confidence interval for the average number of years until the first major repair as follows:

CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\cdot\sqrt{\frac{N-n}{N-1}}

     =3.3\pm 1.96\times\frac{1.47}{\sqrt{183}}\times\sqrt{\frac{1500-183}{1500-1}}\\\\=3.3\pm 0.19964\\\\=(3.10036, 3.49964)\\\\\approx (3.1, 3.5)

Thus, the 95% confidence interval for the average number of years until the first major repair is (3.1, 3.5).

7 0
3 years ago
For 0 ≤ ϴ &lt; 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va
Black_prince [1.1K]

Answer:

3 solutions:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is tan(\frac{\theta}{2}) so let's focus on that part of the equation first.

We know that:

tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}

therefore:

cos(\frac{\theta}{2})\neq0

so we need to find the angles that will make the cos function equal to zero. So we get:

cos(\frac{\theta}{2})=0

\frac{\theta}{2}=cos^{-1}(0)

\frac{\theta}{2}=\frac{\pi}{2}+\pi n

or

\theta=\pi+2\pi n

we can now start plugging values in for n:

\theta=\pi+2\pi (0)=\pi

if we plugged any value greater than 0, we would end up with an angle that is greater than 2\pi so,  that's the only angle we cannot include in our answer set, so:

\theta\neq \pi

having said this, we can now start solving the equation:

tan(\frac{\theta}{2})=sin(\theta)

we can start solving this equation by using the half angle formula, such a formula tells us the following:

tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}

so we can substitute it into our equation:

\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)

we can now multiply both sides of the equation by sin(\theta)

so we get:

1-cos(\theta)=sin^{2}(\theta)

we can use the pythagorean identity to rewrite sin^{2}(\theta) in terms of cos:

sin^{2}(\theta)=1-cos^{2}(\theta)

so we get:

1-cos(\theta)=1-cos^{2}(\theta)

we can subtract a 1 from both sides of the equation so we end up with:

-cos(\theta)=-cos^{2}(\theta)

and we can now add cos^{2}(\theta)

to both sides of the equation so we get:

cos^{2}(\theta)-cos(\theta)=0

and we can solve this equation by factoring. We can factor cos(\theta) to get:

cos(\theta)(cos(\theta)-1)=0

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

cos(\theta)=0

\theta=cos^{-1}(0)

\theta={\frac{\pi}{2}, \frac{3\pi}{2}}

Equation 2:

cos(\theta)-1=0

we add a 1 to both sides of the equation so we get:

cos(\theta)=1

\theta=cos^{-1}(1)

\theta=0

so we end up with three answers to this equation:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

7 0
3 years ago
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