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3 years ago

-3x+5y=-9 and 4x+8y=12

Mathematics

2 answers:

liq [111]3 years ago

7 0

Let's solve your system by substitution.

−3x+5y=−9;4x+8y=12

Step: Solve−3x+5y=−9for x:

−3x+5y=−9

−3x+5y+−5y=−9+−5y(Add -5y to both sides)

−3x=−5y−9

−3x

−3 = −5y−9 −3

(Divide both sides by -3)

y+3

Step: Substitute

y+3forxin4x+8y=12:

4x+8y=12

y+3)+8y=12

y+12=12(Simplify both sides of the equation)

y+12+−12=12+−12(Add -12 to both sides)

y=0

(Divide both sides by 44/3)

y=0

Step:

3 y+3:

x= 5

3 y+3

x= 5

3 (0)+3

x=3(Simplify both sides of the equation)

Answer:

x=3 and y=0

insens350 [35]3 years ago

4 0

-3x + 5y = -9

4x + 8y = 12

Simplify the second,

x + 2y = 3

Times three,

3x + 6y = 9

Add to the first equation,

11y = 0

y = 0

-3x + 5(0) = -9

x = 3

Answer: x=3, y=0

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3 years ago

A company that teaches self-improvement seminars is holding one of its seminars in Middletown. The company pays a flat fee of $1

Nutka1998 [239]

Answers:

To reach the breakeven point, how many attendees will that take? 117

What will be the company's total expenses and revenues? $1755 for each

=============================================================

Explanation:

x = number of attendees

C(x) = cost function for the company

C(x) = 14x+117

This is because the company pays $14 per person, so x of them accounts for 14x dollars. Then we add on the flat fee of $117 to get 14x+117 dollars overall.

In contrast, the revenue is

R(x) = 15x

because each attendee brings in $15 for the company

The breakeven point is when the cost and revenue are the same. This produces a profit of $0.

R(x) = C(x)

15x = 14x+117

15x-14x = 117

x = 117

If 117 people attend the seminar, then the company breaks even.

To check this, we'll compute the cost and revenue

C(x) = 14x+117

C(117) = 14*117+117

C(117) = 1755

R(x) = 15x

R(117) = 15*117

R(117) = 1755

The cost and revenue is $1755 for each. Because we get the same value, this confirms the correct x value.

Since 117 people is the breakeven point, the company should aim for an attendee count above this, so they can get a positive profit. At some point, there is a max capacity so x can't go up forever.

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2 years ago

What is the height of this triangular prism?

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3 years ago

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

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Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

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3 years ago

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stellarik [79]

Answer:

Graph D is correct

Step-by-step explanation:

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3 years ago