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4 years ago

Three times a number minus another number is -3. The sum of the numbers is 11. Find the numbers

Mathematics

1 answer:

MatroZZZ [7]4 years ago

8 0

The first equation is

$3x-y=-3$

The second equation is

$x+y=11$

If you sum the two equations you'll cancel y:

$4x=8 \iff x=2$

And since the sum must be 11, we have y=9.

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A quality analyst of a tennis racquet manufacturing plant investigates if the length of a junior's tennis racquet conforms to th

Burka [1]

Answer:

Confidence interval : $21.506$ to $24.493$

Step-by-step explanation:

A quality analyst selects twenty racquets and obtains the following lengths:

21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

So, sample size = n =20

Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.

Since n < 30

So we will use t-distribution

Confidence level = 99.9%

Significance level = α = 0.001

Now calculate the sample mean

X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

Sample mean = $\bar{x}=\frac{\sum x}{n}$

Sample mean = $\bar{x}=\frac{21+25+23+22+24+21+25+21+23+ 26+ 21+24+22+ 24+23+21+ 21+ 26+23+ 24}{20}$

Sample mean = $\bar{x}=23$

Sample standard deviation = $\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Sample standard deviation = $\sqrt{\frac{(21-23)^2+(25-23)^2+(23-23)^2+(22-23)^2+(24-23)^2+(21-23)^2+(25-23)^2+(21-23)^2+(23-23)^2+(26-23)^2+(21-23)^2+(24-23)^2+(22-23)^2+(24-23)^2+(23-23)^2+(21-23)^2+(21-23)^2+(26-23)^2+(23-23)^2+(24-23)^2}{20-1}}$

Sample standard deviation= s = $1.72$

Degree of freedom = n-1 = 20-1 -19

Critical value of t using the t-distribution table $t_{\frac{\alpha}{2}$ = 3.883

Formula of confidence interval : $\bar{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}$

Substitute the values in the formula

Confidence interval : $23 \pm 1.73 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $23 -3.883 \times \frac{1.72}{\sqrt{20}}$ to $23 + 3.883 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $21.506$ to $24.493$

Hence Confidence interval : $21.506$ to $24.493$

3 0

4 years ago

Read 2 more answers

Which equations represent the line shown in the graph?

zaharov [31]

The given graph is a straight line passing through points (-4, -3) and (1, 5)
Equation in point slope form is y + 3 = (5 - (-3))/(1 - (-4)) (x - (-4))
y + 3 = 8/5(x + 4)
y + 3 = 8/5x + 32/5
y = 8/5x + 32/5 - 3
y = 8/5x + 17/5

Multiplying through by 5 gives
5y = 8x + 17
-8x + 5y = 17
Options B and C are the correct answers.

6 0

3 years ago

Find the exact solution of -x2 +7x + 5 = 0 by using the Quadratic Formula.

jonny [76]

Answer:

The answer to your question is:

x 1 = -0.65

x2 = 7.65

Step-by-step explanation:

Equation -x² + 7x + 5 = 0

a = -1

b = 7

c = 5

Quadratic formula x = -b ±√(b² -4ac) / 2a

x = - 7 ± √(7² -4(-1)(5) / 2(-1)

x = -7 ± √(49 + 20) / -2

x = -7 ± √69 / -2

x = - 7 ± 8.3 / -2

x1 = -7 + 8.3 / -2 x2 = -7 -8.3 / -2

x 1 = -0.65 x2 = 7.65

7 0

3 years ago

If their food and beverages cost 25.30 and there is an 8% meals tax, how much is the bill?

pentagon [3]

25.3 × 1.08
27.324

The total bill is $27.32

7 0

3 years ago

Describe what a graph with infinitely solutions look like

never [62]

A graph with y = 2x + 1 is an example of one

8 0

3 years ago