All categories

2 years ago

Write a function g whose graph represents the indicated transformation of the graph of f.

Mathematics

1 answer:

lozanna [386]2 years ago

6 0

Step-by-step explanation:

I guess this means a reflection across the x-axis.

what does that mean ?

imagine the line of the x-axis is a mirror.

everything that is originally above the x-axis, is now below the x-axis.

and everything that is originally below the x-axis, is now above it.

as with an actual mirror, the closer something is originality to the mirror the closer it also appears to be in the mirrored image.

how do we do this in math ?

well, a functional value of e.g. 1 turns into -1.

e.g. 2 turns into -2.

but also e.g. -3 turns into 3.

in other words, we only need to flip the sign of the functional result values.

how do we do this ?

by multiplying the whole original functional value by -1.

and therefore,

g(x) = f(x) × -1 = (1/2 × x - 3) × -1 = -x/2 + 3

You might be interested in

A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately

Genrish500 [490]

Answer:

a) 0.057

b) 0.5234

c) 0.4766

Step-by-step explanation:

To find the p-value if the sample average is 185, we first compute the z-score associated to this value, we use the formula

$z=\frac{\bar x-\mu}{\sigma/\sqrt N}$

where

$\bar x=mean\; of\;the \;sample$

$\mu=mean\; established\; in\; H_0$

$\sigma=standard \; deviation$

N = size of the sample.

So,

$z=\frac{185-175}{20/\sqrt {10}}=1.5811$

$\boxed {z=1.5811}$

As the sample suggests that the real mean could be greater than the established in the null hypothesis, then we are interested in the area under the normal curve to the right of 1.5811 and this would be your p-value.

We compute the area of the normal curve for values to the right of 1.5811 either with a table or with a computer and find that this area is equal to 0.0569 = 0.057 rounded to 3 decimals.

So the p-value is

$\boxed {p=0.057}$

Since the z-score associated to an α value of 0.05 is 1.64 and the z-score of the alternative hypothesis is 1.5811 which is less than 1.64 (z critical), we cannot reject the null, so we are making a Type II error since 175 is not the true mean.

We can compute the probability of such an error following the next steps:

Step 1

Compute $\bar x_{critical}$

$1.64=z_{critical}=\frac{\bar x_{critical}-\mu_0}{\sigma/\sqrt{n}}$

$\frac{\bar x_{critical}-\mu_0}{\sigma/\sqrt{n}}=\frac{\bar x_{critical}-175}{6.3245}=1.64\Rightarrow \bar x_{critical}=185.3721$

So we would make a Type II error if our sample mean is less than 185.3721.

Step 2

Compute the probability that your sample mean is less than 185.3711

$P(\bar x < 185.3711)=P(z< \frac{185.3711-185}{6.3245})=P(z$

So, the probability of making a Type II error is 0.5234 = 52.34%

The power of a hypothesis test is 1 minus the probability of a Type II error. So, the power of the test is

1 - 0.5234 = 0.4766

3 0

3 years ago

I NEED NUMBER 4 PLEEEEEASE

german

Find the area of the first dish: since it's a square multiply the side by the side: 8•8=64. Find the area of the second dish: 9•9=81. Now subtract the first one for the second one: 81-64=17 square inches :)

8 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + se

sertanlavr [38]

Answer:

The volume of the solid is: $\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

Step-by-step explanation:

GIven that :

$y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2$

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid can be calculated as follows:

$V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx$

$V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ]$

$\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

7 0

3 years ago

Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation? {–11, 3} {–3, 11} {–4, 4} {–7, 7}

HACTEHA [7]

ANSWER
$x = - 11\: or \: x = 3$

EXPLANATION

The quadratic equation given to us is

${x}^{2} + 8x = 33$

We add half the square of the coefficient of
$x$
to both sides of the equation to obtain,

${x}^{2} + 8x + {(4)}^{2} = 33 + {(4)}^{2}$

This implies that,
${x}^{2} + 8x + {(4)}^{2} = 33 + 16$

The right hand side simplifies to

${x}^{2} + 8x + {(4)}^{2} = 49$

The left hand side is a perfect square.

This gives us

${(x + 4)}^{2} = 49$

We take the square root of both sides

$x + 4 = \pm \sqrt{49}$

This evaluates to

$x + 4 = \pm 7$

We make x the subject.

$x = - 4\pm 7$

We now split the square root sign to get

.

$x = - 4 - 7 \: or \: x = - 4 + 7$

$x = - 11\: or \: x = 3$

The correct answer is A.

7 0

3 years ago

Help me please I need helped Answering this questions

a_sh-v [17]

Answer: 129 m^2

Step-by-step explanation

5 0

3 years ago

Read 2 more answers