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kirza4 [7]
3 years ago
9

Question

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
8 0
Answer: y= -14/27

Explanation: Calculator
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A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian
SOVA2 [1]

Answer:

(b) 4,445

Step-by-step explanation:

If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U.S. adults), what sample size should be used?

Given a=0.05, |Z(0.025)|=1.96 (check standard normal table)

So n=(Z/E)^2*p*(1-p)

=(1.96/0.015)^2*0.5*0.5

=4268.444

Take n=4269

Answer:(b) 4,445

3 0
2 years ago
F=(2xy +z³)i + x³j + 3xz²k find a scalar potential and work done in moving an object in the field from (1,-2,1) to (3,1,4)​
Alex73 [517]

Step-by-step explanation:

Given:

\textbf{F} = (2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}

This field will have a scalar potential \varphi if it satisfies the condition \nabla \times \textbf{F}=0. While the first x- and y- components of \nabla \times \textbf{F} are satisfied, the z-component doesn't.

(\nabla \times \textbf{F})_z = \left(\dfrac{\partial F_y}{\partial x} - \dfrac{\partial F_x}{\partial y} \right)

\:\:\:\:\:\:\:\:\: = 3x^2 - 2x \ne 0

Therefore the field is nonconservative so it has no scalar potential. We can still calculate the work done by defining the position vector \vec{\textbf{r}} as

\vec{\textbf{r}} = x \hat{\textbf{i}} + y \hat{\textbf{j}} + z \hat{\textbf{k}}

and its differential is

\textbf{d} \vec{\textbf{r}} = dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}}

The work done then is given by

\displaystyle \oint_c \vec{\textbf{F}} • \textbf{d} \vec{\textbf{r}} = \int ((2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}) • (dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}})

\displaystyle = (x^2y + xz^3) + x^3y + xz^3|_{(1, -2, 1)}^{(3, 1, 4)}

= 422

5 0
3 years ago
Identify √169/64 as rational or irrational and explain your reasoning.
Alex_Xolod [135]

Answer:

Rational

Step-by-step explanation:

This is rational because the square root of 169/64 would be 13/8 and any rational number could be put into a fraction

4 0
2 years ago
Write an equation in slope intercept form that is perpendicular to 3x + 2y equals 12 and passes through the point (1,2)​
Zigmanuir [339]

Answer:

The equation is y = (2/3)x + (4/3).

Step-by-step explanation:

First, you have to change the equation into slope-intecept formula to find its gradient (slope) :

3x + 2y = 12

2y =  - 3x + 12

y =   - \frac{3}{2}x  + 6

Given that when a line is perpendicular to the other line, their slope value multiplied, will form -1. Next, we have to find the slope for line :

m1 \times m2 =  - 1

-  \frac{3}{2}  \times m2 =  - 1

m2 =  - 1 \div  -  \frac{3}{2}

m2 =  \frac{2}{3}

Lastly, we have to subatitute the x and y values into the equation, to find its intercept value :

y =  \frac{2}{3}x  + b

let \: x = 1,y = 2

2 =  \frac{2}{3} (1) + b

b = 2 -  \frac{2}{3}

b =  \frac{4}{3}

y =  \frac{2}{3} x +  \frac{4}{3}

5 0
3 years ago
Is it possible for two numbers to have a difference of 5, and a sum of 12?
frozen [14]
Uhhh that doesn’t seem possible but then again i forgot simple math lol
4 0
2 years ago
Read 2 more answers
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