Select all values of x that make the inequality -x + 8 ≥11 true.

University dean is interested in determining the proportion of students who receive some sort offinancial aid. rather than exami

vladimir2022 [97]

The confidence interval is
$0.59\pm0.081$

We first find p, our sample proportion. 118/200 = 0.59.

Next we find the z-score associated with this level of confidence:
Convert 98% to a decimal: 98% = 98/100 = 0.98
Subtract from 1: 1-0.98 = 0.02
Divide by 2: 0.02/2 = 0.01
Subtract from 1: 1-0.01 = 0.99

Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 2.33.

The margin of error (ME) is given by
$ME=z\sqrt{\frac{p(1-p)}{n}}
\\
\\=2.33\sqrt{\frac{0.59(1-0.59)}{200}}=2.33\sqrt{\frac{0.2419}{200}}\approx0.081$

This gives us the confidence interval
$0.59\pm0.081$

8 0

3 years ago

What is the equation of the line, in general form, that passes through the point (-1, -1) and is parallel to the line whose equa

Ksenya-84 [330]

Answer:

Step-by-step explanation:

y = -x + 3

y + 1 = -(x + 1)

y + 1 = -x - 1

y = -x - 2

x + y + 2 = 0 is the solution

5 0

3 years ago

For their wedding, Rajai and Carly received $1000. Their financial advisor laid out 4 different options for them to invest in. A

dolphi86 [110]

Answer:

Their best investment when they retire in 40 years would be option B.

Step-by-step explanation:

Ragai and Carly invest the $1000 received for their wedding for 40 years.

From the diagram,

In option A, the initial investment do not increase at a constant rate yearly.

In option B, the amount invested increase by $75 yearly.

In option C, the yearly increase does not have a steady value.

In option D, the amount invested increases by a n + consecutive odd values yearly. Where n is the increase of the previous year.

Their best investment when they retire in 40 years would be option B because it would yield the highest profit.

8 0

3 years ago

F(x)=(x+1)(x-3)(x-4)

denis23 [38]

Answer:

x=-1, x=3, x=4

Step-by-step explanation:

1. Substitute 0 for f(x)

0=(x+1)(x-3)(x-4)

2. Set each set of parenthesis equal to 0

0=x+1, 0=x-3, 0=x-4

3. Solve for x

x=-1, x=3, x=4

5 0

3 years ago

1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

german

Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

$\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}$

2.

Using partial fraction decomposition to find the definite integral of:

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx$

By using the long division method; we have:

$x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }$

$- 2x^3 -16x^2-40x$

$x+ 20$

So;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}$

By using partial fraction decomposition:

$\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}$

$= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}$

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now; we have to relate like terms on both sides; we have:

A + B = 1 ; 2A - 10 B = 20

By solvong the expressions above; we have:

$A = \dfrac{5}{2}$ $B = \dfrac{3}{2}$

Now;

$\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}$

Thus;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}$

Now; the integral is:

$\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx$

$\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}$

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

4 0

3 years ago