Help pls all shaded parts need answers

Lindsey earns $15 per hour for the first 40 hours she works in a week and 50% more for every hour over 40. How many hours did Li

solmaris [256]

Answer:

E. 55 hours.

Step by step:

Multiple $15x40, equals $600

Subtract $600 from $937.50, equals $337.50

50% more over 40 hours is $22.50

Divide $337.50 by $22.50, equals 15

Add 15 to 40, equals 45

So she worked 55 hours to get paid $937.50

7 0

3 years ago

When we make inferences about the difference of two independent population proportions, what assumptions do we need to make? mar

Elis [28]

When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

The datasets must represent a random sample
Each dataset must contain at least 15 successes and failures

Hence, the above highlights are the assumptions of two independent population proportions.

To learn more about independent populations from the given link

brainly.com/question/23989150

#SPJ4

4 0

10 months ago

Six identical squares are cut from the corners and edges of an 80 cm by 50 cm cardboard rectangle. the remaining piece is folded

Anna11 [10]

Check the picture.

let the length of a side of each of the squares removed be x.

The box formed will have dimensions: 80-2x, 50-2x, x(the height)

So the volume can be expressed as a function of x as follows:

f(x)=(80-2x)(50-2x)x= $[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x$

so $f(x)=4 x^{3}-260x^{2}+4000x$

the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,

$f'(x)=12x^{2}-520 x +4000=0$

solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions

x=10 and x=33.333

plug in f(x) these values to see which greater:

$f(10)=(80-20)(50-20)10=60*30*10=18000$ cm cubed

$f(33.333)=(80-66.666)(50-66.666)33.333=$ which is negative because (50-66.666)<0

Answer: 18000 cm cubed

5 0

2 years ago

Read 2 more answers

Natalie consumes only apples and tomatoes. Her utility function is U(x, y) = x 2y 8 , where x is the number of apples consumed a

Kamila [148]

Answer:

16 apples.

Step-by-step explanation:

$U(x, y) = x^2y^8$

$MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\$

Price of apples, Px=$4

Price of tomatoes, Py=$3

Ratio of their Marginal Utilities

$\frac{MU_x}{MU_y} = \frac{Px}{Py}$

$\frac{y}{4x} = \frac{4}{3}$

$y=\frac{16x}{3}$

Since Natalie’s income is $320

320 = xPx+yPy

$320=4x + 3*\frac{16x}{3} \\320= 4x+16x = 20x\\x=\frac{320}{20} = 16\\Also\\y=\frac{16x}{3}=\frac{16X16}{3}=\$85.33$

Since x=16, Natalie will consume 16 apples.

6 0

2 years ago

Let $f(x)$ be the real-valued function defined for all real $x$ except for $x = 0$ and $x = 1$ and satisfying the functional equ

Mademuasel [1]

We have to find the values of F.
In this case. F is unlikely to be a polynomial.
But the problem is, we can’t calculate the values of F directly.
There is no real value of x for which x = x−1 x because F isn’t defined at 0 or 1. so,
substituting x = 2.
F(2) + F(1/2) = 3.

Substitute, x = 1/2
F(1/2) + F(−1) = −1/2.
We still are not getting the required value,
therefore,
Substitute x = −1

As, F(2) +F(−1) = 0.
now we have three equations in three unknowns, which we can solve.
It turns out that:
F(2) = 3/4
F(3) = 17/12
F(4) = 47/24
and
F(5) = 99/40

Setting
g(x) = 1 − 1/x
and using
2 → 1/2
to denote
g(2) = 1/2
we see that :
x → 1 - 1/x → 1/(1-x) →x

so that:
g(g(g(x))) = x.

Therefore, whatever x 6= 0, 1 we start with, we will always get three equations in the three “unknowns” F(x), F(g(x)) and F(g(g(x))).
Now solve these equations to get a formula for F(x)

As,
h(x) = (1+x)/(1−x)
which satisfies h(h(h(h(x)))) = x

Now, mapping x to h(x) corresponds to rotating the circle by ninety degrees.

7 0

2 years ago