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2 years ago

If point A is located at (0,-8) and B is located at (4,-5) what is the distance between them

1 answer:

6 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{-8})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{[4-0]^2+[-5-(-8)]^2}\implies AB=\sqrt{(4-0)^2+(-5+8)^2} \\\\\\ AB=\sqrt{4^2+3^2}\implies AB=\sqrt{25}\implies AB=5$

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2 years ago

A chemist is using 336 milliliters of a solution of acid and water. If 19.4 % of the solution is acid, how many milliliters of a

denpristay [2]

Answer:

65.2 milliliters

Step-by-step explanation:

The quantity 336 milliliters is the 100% of the solution. We can represent this information on a table:

Milliliters Percentage of solution

336 ⇔ 100%

we are told that 19.4% of this solution is acid, and we need to know how many milliliters represents this percentage. I will call the number of milliliters of acid on the solution 'x', and updating the last table:

Milliliters Percentage of solution

336 ⇔ 100

x ⇔ 19.4%

We can solve this problem for 'x' using the<u> rule of three</u> which is to multiply the cross quantities on the table (336 by 19.4) and then divide by the remaining amount (100):

x = 336(19.4)/100

x = 6,518.4/100

x = 65.184

which rounding to the nearest tenth is: 65.2 milliliters

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2 years ago

The domain of y = cot x is all real numbers such that _______.

Artyom0805 [142]

Answer:

Step-by-step explanation:

x≠ n*π, where n is an integer

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2 years ago

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2 years ago

A newsletter publisher believes that above 78 % of their readers own a personal computer. Is there sufficient evidence at the 0.

GalinKa [24]

Answer:

$h_{0}$ : p= .78

$h_{a}$ : p > .78

Step-by-step explanation:

Determining the null and alternate hypotheses of a scenario require several components. The first is if one should use p or mu. This depends on if they are assessing a proportion or a mean, since the publisher states a percentage, you know that they are asking for a proportion, and therefore should use p. Next, they will need to assess what value to use for the hypothesis statements, here only .78 is provided and therefore should be used in both. Finally, it is time to add in the comparison symbols, the null hypothesis always uses an equals sign so it therefore becomes:

$h_{0}$ : p= .78

The alternate hypothesis then needs to consider if the researchers claim that the new proportion is greater, fewer, or different. In this case it is greater as they think that the ownership is above 78%, so a greater than sign would be used and the final statement would be:

$h_{a}$ : p > .78

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2 years ago