At which step did Fatu make an error, if at all?

Half of a number when added to 42 becomes 50. What is the original number?

aev [14]

Answer:

16

Step-by-step explanation:

50-42=8

8 times 2 is 16

3 0

2 years ago

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A thin metal plate, located in the xy-plane, has temperature T(x, y) at the point (x, y). Sketch some level curves (isothermals)

Sophie [7]

Answer:

Step-by-step explanation:

Given that:

$T(x,y) = \dfrac{100}{1+x^2+y^2}$

This implies that the level curves of a function(f) of two variables relates with the curves with equation f(x,y) = c

here c is the constant.

$c = \dfrac{100}{1+x^2+2y^2} \ \ \--- (1)$

By cross multiply

$c({1+x^2+2y^2}) = 100$

$1+x^2+2y^2 = \dfrac{100}{c}$

$x^2+2y^2 = \dfrac{100}{c} - 1 \ \ -- (2)$

From (2); let assume that the values of c > 0 likewise c < 100, then the interval can be expressed as 0 < c <100.

Now,

$\dfrac{(x)^2}{\dfrac{100}{c}-1 } + \dfrac{(y)^2}{\dfrac{50}{c}-\dfrac{1}{2} }=1$

This is the equation for the family of the eclipses centred at (0,0) is :

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

$a^2 = \dfrac{100}{c} -1 \ \ and \ \ b^2 = \dfrac{50}{c}- \dfrac{1}{2}$

Therefore; the level of the curves are all the eclipses with the major axis:

$a = \sqrt{\dfrac{100 }{c}-1}$ and a minor axis $b = \sqrt{\dfrac{50 }{c}-\dfrac{1}{2}}$ which satisfies the values for which 0< c < 100.

The sketch of the level curves can be see in the attached image below.

7 0

3 years ago

As discussed in Exercise 6.10, the General Social Survey reported a sample where about 61% of US residents thought marijuana sho

Maslowich

Answer: 2285

Step-by-step explanation:

Formula to find the sample size is given by :-

$n=p(1-p)(\dfrac{z_c}{E})^2$

, where p = prior estimate of population proportion.

E= Margin of error.

$z_c$ = z-value for confidence interval of c.

Given : Confidence interval : 95%

From the z-value table , the z-value for 95% confidence interval = $z_c=1.96$

The General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal.

i.e. the prior estimate of population proportion of US residents thought marijuana should be made legal : p=0.61

[∵ sample proportion is the best estimate for population proportion.]

Margin of error : E= 2%=0.02

Now, the required minimum sample size would be :-

$n=0.61(1-0.61)(\dfrac{1.96}{0.02})^2$

Simplify ,

$n=0.2379\times9604=2284.7916\approx2285$

Thus , we need to survey <u>2285</u> Americans .

4 0

3 years ago

Will give brainiest if correct

amm1812

If a=c and b=c then a=c this is transitive property

4 0

3 years ago

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The bill for Dino's lunch was $19.45. He wanted to leave 20% of the total bill as a tip. How much should the tip be?

Salsk061 [2.6K]

You could multiply 19.45 by 0.2 to solve for it, but if you're not using a calculator, then 19.45/5 would be much more convenient and easier.

0.2 is 1/5 in fraction form, which is why we can do that.

19.45/5 = 3.89

Dino should leave $3.89 as a tip.

7 0

3 years ago

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