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2 years ago

Mr. Lee asks a student to solve the following system of linear equations. Which ordered pair (p, q) is a solution to the system?

Mathematics

2 answers:

zalisa [80]2 years ago

8 0

The system of equations is:
-28 = -40(q) - 14p (1)
10q+4 = 2p (2)

There are a number of ways to solve this problem. I personally, when it can be done easily, like to get one of the variables by itself and substitute it into the other equation. For example, let's get p by itself in equation (2):
2p = 10q + 4 Divide both sides by 2:
p = 5q + 2
Now we have an easy way to plug p into equation (1) and solve for q:
-28 = -40q - 14p Divide both sides by -2 to simplify:
14 = 20q + 7p Plug in (5q+2) for p
14 = 20q + 7(5q + 2) Distribute
14 = 20q + 35q + 14 Subtract 14 from both sides
0 = 55q
q = 0

We lucked out, and q= 0, so now we can easily plug q into either of our equations. Let's go with equation (1)
-28= -40q - 14p
-28 = 0 - 14p
-28 = -14 p Divide both sides by -14
p = 2

Our ordered pair (p,q), therefore, is (2,0)
Answer is D

svp [43]2 years ago

8 0

Answer:

The correct answer is D .

Step-by-step explanation:

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A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to dif

VashaNatasha [74]

Answer:

(A)

$P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192$

(B)

Then the cumulative function would be

$CF(x) = 1.25x - 0.25x^5$ if 0<x<1

0 otherwise.

Step-by-step explanation:

(A)

We are looking for the probability that the random variable X is greater than 0.8.

$P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192$

(B)

For any $x$ you are looking for the probability $P(X \geq x)$ which is

$P(X \geq x) = \int\limits_{-\infty}^{x} 1.25(1-t^4) dt = \int\limits_{0}^{x} 1.25(1-t^4) dt = 1.25x - 0.25x^2$

Then the cumulative function would be

$CF(x) = 1.25x - 0.25x^5$ if 0<x<1

0 otherwise.

5 0

2 years ago

A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 10 of th

Digiron [165]

Answer:

f(x) = -5x + 250

Step-by-step explanation:

* Lets explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

the line which represent the equation and c is the y-intercept

- The slope of the line m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

the linear equation between the cars' numbers and the weeks

numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴ $m=\frac{175-200}{15-10}=\frac{-25}{5}=-5$

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

7 0

2 years ago

Read 2 more answers

Marks age, X is six times his age 2 years ago. which equation represents the statement

FinnZ [79.3K]

x=6x-2 This would be your answer, hope this helps if you need any further explanation feel free to let me know and I would be happy to help you out.

6 0

2 years ago

Read 2 more answers

The parallel dotplots below display the girths (belly

liraira [26]

Answer:

The standard deviation for the distribution of girths is

about the same for both male and female pigs.

Step-by-step explanation:

Step 1

We will interprete the dotplots

For the Male pigs

24, 26, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32

Range

Maximum value - Minimum value

= 32 - 24

= 8

IQR = Interquartile range = Q3 - Q1

Q1 formula = 1/4(n + 1)th

=n = 25

= 1/4(25 + 1)

= 1/4(26)

= 26/4

= 6.5

This mean the value is between the 6th and 7th value

6th value = 26

7th value = 26

Q1 = 26 + 26/2

Q1 = 26

Q3 formula = 3/4(n + 1)th

=n = 25

= 3/4(25 + 1)

= 3/4(26)

= 78/4

= 19.5

This mean the value is between the 19th and 20th value

19th value = 30

20th value = 30

Q3= 30+ 30/2

= 30

IQR = 30 - 26

= 4

Standard deviation

Mean

First we find the mean

= 24+ 26+26+ 26+ 26+ 26+26+28+ 28+ 28+ 28+28+ 28+ 28+28+ 28+28+28+30+ 30+30+ 30+30+30+32/28

= 700/25

= 28

Standard deviation Formula = √(x - mean)²/n - 1

= √[(24-28)² + (26- 28)² + (26 -28)² + (26 - 28)² +................ (32 - 28)²]/25 - 1

= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1

= √80/25 - 1

=√3.333333333

1.825741858

Female Pigs

21, 23, 23, 23,23,23,23,25, 25, 25, 25, 25, 25, 25, 25, 25, 25,25, 27, 27, 27, 27,27, 27, 29

Range:

Maximum value - Minimum value

= 29 - 21

IQR

IQR = Interquartile range = Q3 - Q1

Q1 formula = 1/4(n + 1)th

=n = 25

= 1/4(25 + 1)

= 1/4(26)

= 26/4

= 6.5

This mean the value is between the 6th and 7th value

6th value = 23

7th value = 23

Q1 = 23 + 23/2

Q1 = 23

Q3 formula = 3/4(n + 1)th

=n = 25

= 3/4(25 + 1)

= 3/4(26)

= 78/4

= 19.5

This mean the value is between the 19th and 20th value

19th value = 27

20th value = 27

Q3= 27+ 27/2

Q3 = 27

IQR = 27 - 23

= 4

First we find the Mean

=(21+23+23+23+23+23+23+25+ 25+ 25+ 25+25+ 25+ 25+ 25+25+25+25+27+27+ 27+27+27+ 27+29)/25

= 625/25

= 25

Standard deviation Formula = √(x - mean)²/n - 1

= √[(21-25)² + (23- 25)² + (23 -25)² + (23 - 25)² +................ (29 - 25)²]/25 - 1

= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1

= √80/25 - 1

=√3.333333333

1.825741858

Looking at the calculation above and comparing both the girths from the male and female

We can conclude that: The standard deviation for the distribution of girths is

about the same for both male and female pigs which is 1.825741858

5 0

2 years ago

Which expression is equivalent to StartFraction 3 x Superscript negative 6 Baseline y Superscript negative 3 Baseline Over 15 x

arsen [322]

Answer:

<h3>The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction</h3>

Step-by-step explanation:

Given the expression $\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }$ for x ≠ 0, y ≠ 0 to get the equivalent expression we will have to simplify the given expression.

$\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }\\= \frac{3}{15} x^{-6-2}y^{-3-10}\\ = \frac{3}{15}x^{-8}y^{-13} \\ =\frac{1}{5}x^{-8}y^{-13} \\$

The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction

6 0

2 years ago