Three solutions of the equation Ax + By = Cz

Consider this story problem: "Priscilla bought cheese that weighs ¾ pounds. If she divides it into portions that are each 1/8 po

Katena32 [7]

Answer:

4

Step-by-step explanation:

8 0

2 years ago

A recent poll of 1500 new home buyers found that 60% hired a moving company to help them move to their new home. Find the margin

Mrac [35]

Answer:

The margin of error M.O.E = 2.5%

Step-by-step explanation:

Given that;

The sample size = 1500

The sample proportion $\hat p$ = 0.60

Confidencce interval = 0.95

The level of significance ∝ = 1 - C.I

= 1 - 0.95

= 0.05

The critical value:

$Z_{\alpha/2} = Z_{0.05/2} \\ \\ Z_{0.025} = 1.96$ (From the z tables)

The margin of error is calculated by using the formula:

$M.O.E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1 -\hat p)}{n}}$

$M.O.E = 1.96 \times \sqrt{\dfrac{\hat 0.60(1 -0.60)}{1500}}$

$M.O.E = 1.96 \times \sqrt{\dfrac{0.24}{1500}}$

$M.O.E = 1.96 \times \sqrt{1.6 \times 10^{-4}}$

M.O.E = 0.02479

M.O.E ≅ 0.025

The margin of error M.O.E = 2.5%

8 0

2 years ago

The graph above is a linear equation that includes the points (-3,-2) and (-1,2). Find the slope of the line. Explain how you ar

omeli [17]

Answer:

The slope is 2 and the equation would be m(x)=2x+4.

Step-by-step explanation:

y/x so by looking at the graph you would go up to units and over l unit, therefore giving you the slope of 2.

8 0

2 years ago

Mrs.Johnson just purchased a total of 12 books and magazines for her office. The total bill was $112. She spent $18 on magazines

SCORPION-xisa [38]

She bought 154 books

3 0

2 years ago

If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

6 0

2 years ago

Three solutions of the equation Ax + By = Cz - 14 are