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3 years ago

Consider the equation, -2x + 3y = 6. Identify the slope.

Mathematics

1 answer:

Lerok [7]3 years ago

7 0

Answer: 2/3

Step-by-step explanation: To identify the slope of this line, we first need to convert this equation to slope-intercept form.

In slope-intercept or y = mx + b form, the y

is by itself on the left side of the equation.

So our first task in this problem is to get y by itself

on the left side of the equation and we do that by

first adding 2x to both sides to get 3y = 2x + 6.

Notice that I put the x term first on the right side of the equation and then the number because in y = mx + b form, the x term comes first on the right side of the equation.

Continuing on, to get y by itself we would

divide both sides by 3 to get y = 2/3x + 2.

Now in y = mx + b form, the slope is coefficient of the x term.

So we can see that the slope of this line is 2/3.

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Division of two quantities is expressed as the ____ of those two quantities.

andreev551 [17]

Division of two quantities is expressed as the quotient of those two quantities.

The word quotient is derived from the Latin language. It is from the Latin word "quotiens" which means "how many times." A quotient is the answer to a divisional problem. A divisional problem describes how many times a number will go into another. The first time that this word was known to have been used in mathematics was around 1400 - 1500 AD in England.

There are two different ways to find the quotient of two numbers. One of them is through Fractions. The quotient of a fraction is the number obtained when the fraction is simplified. The other way to find a quotient is by employing the long division method where the quotient value is positioned above the divisor and dividend.

6 0

3 years ago

1. Find the LCM of 12 and 9 NEED HELP ASAP

kondaur [170]

Answer:

its 36

Step-by-step explanation:

7 0

3 years ago

The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar busi

eimsori [14]

Answer:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=4.2$ represent the sample mean

$s=1.4$ represent the sample standard deviation

n=16 represent the sample selected

$\alpha=0.05$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 3.6, the system of hypothesis would be:

Null hypothesis: $\mu = 3.6$

Alternative hypothesis: $\mu \neq 3.6$

If we analyze the size for the sample is < 30 and we know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Critical values

On this case since we have a bilateral test we need to critical values. We need to use the t distribution with $df=n-1=16-1=15$ degrees of freedom. The value for $\alpha=0.05$ and $\alpha/2=0.025$ so we need to find on the t distribution with 15 degrees of freedom two values that accumulates 0.025 of the ara on each tail. We can use the following excel codes:

"=T.INV(0.025,15)" "=T.INV(1-0.025,15)"

And we got $t_{crit}=\pm 2.131$

So the decision on this case would be:

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

Conclusion

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

3 0

3 years ago

Write as a decimal. If a repeating decimal, round to the nearest hundredth.

Mamont248 [21]

Given:

$\frac{475}{80}$

Let's evaluate and find the quotient.

We have:

$\frac{475}{80}=5.9375$

SInce it is not a repeating decimal, we are asked to leave to answer as it is.

A repeating decimal is a decimal with digits or group of digits that repeats endlessly.

The decimal 5.937

ANSWER:

5.9375

6 0

1 year ago

High in the rocky mountains, a biology research team has drained a lake to get rid of all fish. After the lake was refilled, the

nadya68 [22]

Answer:

Step-by-step explanation:

High in the Rocky Mountains, a biology research team has drained a lake to get rid of all fish. After the lake was refilled, they stocked it with an endangered species of Greenback trout. Of the 2000 Greenback trout put into the lake 400 were tagged for later study. An electroshock method is used on individual fish to get a study sample. However, this method is hard on the fish. The research team wants to know the smallest number of fish that must be electroshocked to be at least 50% sure of getting a sample of two or more tagged trout.

we have to find out smallest number fish (n) that must be electroshoked to be atleast 50% &

species of Greenback trout of the 2000 greenback trout put into the lake 400

6 0

3 years ago