All categories

3 years ago

A line goes through the point (6,-2) and has a slope of

Mathematics

1 answer:

svetoff [14.1K]3 years ago

4 0

Answer:

Step-by-step explanation:

eq. of line is y-(-2)=-3(x-6)

y+2=-3x+18

y=-3x+18-2

y=-3x+16

∵(a,7) lies on it.

7=-a+16

a=16-7=9

a=9

You might be interested in

There are two games involving flipping a coin. In the first game you win a prize if you can throw between 45% and 55% heads. In

Nina [5.8K]

Answer:

d) 300 times for the first game and 30 times for the second

Step-by-step explanation:

We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.

As the coin is flipped more than one time and calculated the proportion, we have to use the sampling distribution of the sampling proportions.

The mean and standard deviation of this sampling distribution is:

$\mu_p=p\\\\ \sigma_p=\sqrt{\dfrac{p(1-p)}{N}}$

We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.

The probability of getting a proportion within this interval can be calculated as:

$P(0.45$

referring the z values to the z-score of the standard normal distirbution.

We can calculate this values of z as:

$z_H=\dfrac{p_H-\mu_p}{\sigma_p}=\dfrac{(p_H-p)}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_H-p)>0\\\\\\z_L=\dfrac{p_L-\mu_p}{\sigma_p}=\dfrac{p_L-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_L-p)$

If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.

With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.

For the second game, we win if we get a proportion over 80%.

The probability of winning is:

$P(p>0.8)=P(z>z^*)$

The z value is calculated as before:

$z^*=\dfrac{p^*-\mu_p}{\sigma_p}=\dfrac{p^*-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p^*-p)>0$

As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).

If our chances of winnings depend on P(z>z*), they become lower as z* increases.

Then, we can conclude that our chances of winning decrease with the increase of the number of trials.

We prefer the option of 30 trials for this game.

8 0

3 years ago

5 2/5 as a mixed number

valentina_108 [34]

Answer:

Mixed numbers have a whole number followed by the fraction (2 1/2). You would say "two and one half." The other format is an improper fraction where the numerator is greater than the denominator (5/2). Mathematicians would say that is five halves.

7 0

3 years ago

Read 2 more answers

500 increased by 30%

fgiga [73]

500 + 30% equals 650. 30% of 500 equals 150.

4 0

3 years ago

LOOK AT PICTURE. VOLUME OF CAN PROBLEM

adoni [48]

Answer:

The correct answer is third option. 994

Step-by-step explanation:

Points to remember

Volume of cylinder = πr²h

Where 'r' is the radius and 'h' is the height of cylinder

From the given question we get the cylinder height and radius

The height h = 3 times the diameter of one ball

= 3 * 7.5 = 22.5 cm

Radius = half of the diameter of a ball

= 7.5/2 = 3.75 cm

To find the volume of cylinder

Volume of cylinder = πr²h

= 3.14 * 3.75² * 22.5

= 993.515 ≈ 994

The correct answer is third option. 994

8 0

3 years ago

Tom and Martin both worked 9 hours this week and sold $360 worth of meals. Their hourly wages are $2.15 and $2.50, respectively.

serious [3.7K]

Tom and Martin worked 9 hours this week.

These are their hourly wages:

Tom: $2.15

Martin: $2.50

This means that:

Tom earned 9 x $2.15 in wages, which is equal to $19.35.

Martin earned 9 x $2.50 in wages, which is equal to $22.50.

--------------------

Now, we've been told that Tom and Martin sold $360 worth
of meals but we were not told how much they received in tips.

For all intents and purposes, let's say that they received $n
in tips. 15% of $n in tips would be less than 20% of $n
in tips. Now, Martin is already going to be receiving a higher
wage, and the fact that he is going to be receiving 20% of
$n in tips compounds the logical conclusion that at the end
of the week, he'd be leaving work with more money than Tom.

Answer:

Martin made more money than Tom.

3 0

3 years ago