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3 years ago

Today only a sofa is being sold at a 29% discount. The sale price is $639. What was the price yesterday?

1 answer:

7 0

What we need to do is find out what 29% of 639 is and add it to 639 to find the total. The easiest way to find a percentage of a number, if you don't know how to calculate it, is by taking 10%. So 10% of 639 is 63.9. Now since there is 29%, we need to multiply 63.9 x 2, to get 127.8. However, we only have 20% out of the 29%. So we need to find the other 9%. If 10% is 63.9, then 1% is 6.39. So we need to multiply 6.39 x 9, and that equals 57.51. Now, we need to add 127.80 and 57.51 together. That will give us 185.31. Add that to the 639, and you have your answer. Hope this helped!

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An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

nirvana33 [79]

Answer:

The 80% confidence interval for the mean number of words a third grader can read per minute is between 40.4 wpm and 40.8 wpm.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.1 = 0.99$ , so $z = 1.28$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.28*\frac{4.1}{\sqrt{840}} = 0.2$

The lower end of the interval is the sample mean subtracted by M. So it is 40.6 - 0.2 = 40.4 words per minute.

The upper end of the interval is the sample mean added to M. So it is 40.6 + 0.2 = 40.8 words per minute.

The 80% confidence interval for the mean number of words a third grader can read per minute is between 40.4 wpm and 40.8 wpm.

3 0

3 years ago

Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5

zmey [24]

Differentiate both sides of the equation of the circle with respect to $x$ , treating $y=y(x)$ as a function of $x$ :

$x^2+y^2=5\implies2x+2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac xy$

This gives the slope of any line tangent to the circle at the point $(x,y)$ .

Rewriting the given line in slope-intercept form tells us its slope is

$x=2y+5\implies y=\dfrac12x-\dfrac52\implies\mathrm{slope}=\dfrac12$

In order for this line to be tangent to the circle, it must intersect the circle at the point $(x,y)$ such that

$-\dfrac xy=\dfrac12\implies y=-2x$

In the equation of the circle, we have

$x^2+(-2x)^2=5x^2=5\implies x=\pm1\implies y=\mp2$

If $x=-1$ , then $-1=2y+5\implies y=-3\neq2$ , so we omit this case.

If $x=1$ , then $1=2y+5\implies y=-2$ , as expected. Therefore $x=2y+5$ is a tangent line to the circle $x^2+y^2=5$ at the point (1, -2).

7 0

3 years ago

Read 2 more answers

4) Find the missing term.

BartSMP [9]

I think it’s 14,35,16,80

7 0

3 years ago

It would be great if i can get some help. Thank you. Include explanation please

NISA [10]

We're given two sides and the included angle and asked to find the third side. That's the Law of Cosines.

$c^2 = a^2 + b^2 - 2 a b \cos C$

$c = \sqrt{15^2 + 20^2 - 2 (15)(20) \cos 50^\circ} \approx 15.5 \textrm{ feet}$

7 0

3 years ago

Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below: 6E+10

BabaBlast [244]

Answer:

Step-by-step explanation:

Because it shows 6 with the 10 therefore there are going to be 10 zeros so thag would mean that its c

6 0

3 years ago