Ask question

Ask question

All categories

2 years ago

5

The given function k is a composition of two functions m and n so that k(x) = (m ∘ n)(x). k (x) = StartFraction 2 Over RootIndex

4 StartRoot 4 x minus 7 EndRoot EndFraction If n(x) = 4x – 7, m(x) must be equal to which expression?

1 answer:

kotykmax [81]2 years ago

6 0

Answer:

$\frac{2}{\sqrt[4]{x} }$

Step-by-step explanation:

You might be interested in

Suppose pieces of chocolate pie served at a restaurant average 350 calories with a standard deviation of 20 calories. Calories h

Over [174]

Answer:

Step-by-step explanation:

Suppose pieces of chocolate pie served at a restaurant average 350 calories with a standard deviation of 20 calories. Calories have a Normal distribution due to inexact cutting of the pies. Which graph represents the proportion of pieces of pie that have more than 375 calories.

Answer: The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and for a negative z score means the raw score is below the mean. The z score is given as:

$z=\frac{x-\mu}{\sigma}$

Given that: μ = 350 calories, σ = 20 calories, x > 375

$z=\frac{x-\mu}{\sigma}\\\\z=\frac{375-350}{20}=1.25$

From the graph, The shaded area represents the proportion of pieces of pie that have more than 375 calories

From the normal distribution table, P(x > 375) = P(z > 1.25) = 1 - P(z < 1.25)

= 1 - 0.8944 = 0.1056 = 10.56%

3 0

2 years ago

A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th

icang [17]

Answer:

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

$D = \sqrt{l^2+w^2}$ ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

$l = 2 \times w$ = 2w

Now, substitute these in [1] we have;

$\sqrt{(2w)^2+w^2} = w+5$

Squaring both the sides we get;

$4w^2+w^2 = (w+2)^2$

$5w^2 = w^2 + 4 + 4w$

or

$5w^2 -w^2 = 4w + 4$ or

$4w^2= 4w + 4$

Simplify:

$w^2-w-1 =0$ ......[2]

The quadratic equation is in the form of $ax^2+bx+c = 0$

the solution is given by: $x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}$

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

$w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}$

Simplify:

$w \approx 1.62$ and $w \approx -0.62$

Then, the diagonal D = w+2

For $w \approx 1.62$

$D = 1.62 +2 \approx 3.62$

For $w \approx -0.62$

$D =-0.62 +2 \approx 1.38$

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

5 0

2 years ago

Consider circle O below. The length of arc BA is 8.4 cm and the length of the radius is 8 cm. The measure of angle AOC is 45°. C

denis23 [38]

Answer:

i) 60°

ii) 14.7 cm

Step-by-step explanation:

length of Arc BA = 8.4 cm

length of radius = 8 cm

angle AOC = 45°

BO = AO = CO = 8 cm

<u>i) What is the measure of Angle BOA </u>

= length of Arc BA / Radius

= 8.4 / 8 = 1.05 radians = 60.16° ≈ 60°

<u>ii) what is the length of arc BAC</u>

= radius * angle BAC * $\pi /180$

angle BAC = angle AOC + angle BOA

= 45° + 60° = 105°

hence length of arc BAC

= 8 * 105 * $\pi /180$

≈ 14.7 cm

3 0

2 years ago

Read 2 more answers

Estimate the unit rate to the nearest hundredth.<br><br> $1.19 per 12fl oz price of 1 fl oz

Korvikt [17]

To find the unit rate you need to divide the 1.19 by 12 so that the ounces would be the price per 1 ounce.
1.19/12 = .099 per ounce
Since we are talking about money your answer needs to be rounded to TWO decimals unless told otherwise.
Rounding .099 would be $ 0.10 per ounce

7 0

2 years ago

Read 2 more answers

By how many factors of 10 did you multiply 0.008? Why?

Tamiku [17]

Answer: 3

Step-by-step explanation:

Move the decimal back to its point of origin

7 0

2 years ago