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4 years ago

Look at picture. What is the solution WORTH 10 points. Show work.

Mathematics

2 answers:

lakkis [162]4 years ago

8 0

$\left\{\begin{array}{ccc}2x-y=6\\2x-2y=4&|\text{add 2y to both sides}\end{array}\right\\\left\{\begin{array}{ccc}2x-y=6\\2x=4+2y&|\text{divide both sides by 2}\end{array}\right\\\left\{\begin{array}{ccc}2x-y=6\\x=2+y\end{array}\right\\\\\text{Substitute x=2+y to the first equation}\\\\2(2+y)-y=6\ \ \ \ |\text{use distributive property}\\(2)(2)+(2)(y)-y=6\\4+2y-y=6\\4+y=6\ \ \ \ \ |\text{subtract 4 from both sides}\\\boxed{y=2}\\\\\text{Put the value of y to the second equation}\\\\x=2+2\\\boxed{x=4}$

$Answer:\ D.\ (4,\ 2)$

Hatshy [7]4 years ago

5 0

Hey there!!

The two equations we have :

2x - y = 6 ---------- ( 1 )

2x - 2y = 4 ----------- ( 2 )

Now subtract the second equation from the first equation :

2x - y = 6 ------ ( 1 )

- 2x + 2y = -4 ------ ( 2 )

y = 2

We have got the answer for y which is 2

Now we will have to substitute this value in place of y and find x

2x - y = 6

2x - 2 = 6

2x = 8

x = 4

For a ordered pair, the coordinates are written as ( x , y )

We got x = 4 and y = 2

Hence, the answer is ( 4 , 2 ) option d

Hope my answer helps!

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Answer:

30 students

Step-by-step explanation:

80% of N = 24 where N is the total number of students

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3 years ago

8+x/-9=9 Please solve this equation and show your work!

Oduvanchick [21]

8+(x/-9)=9 subtract 8

x/-9= 1 multiply by -9

x= -9

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3 years ago

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What is the value of the expression |a + b| + |c| when a = –3, b = 7, and c = 1

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3 years ago

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The county hospital is located at the center of a square whose sides are 3 miles wide. If an accident occurs within this square,

Dmitry_Shevchenko [17]

Answer:

Step-by-step explanation:

The x-coordinate of the accident is a random variable of uniform distribution with range [-1.5,1.5]. The same can be said for the y-coordinate. However, |x| and |y| are also uniform variables with range [0,1.5], since we still have the same probability on every pair of intervals with the same lenght.

Note that |X| and |Y| are independent with each other, therefore E(|x|+|y|) = E(|x|) + E(|y|) = 2*E(|x|). The last equality holds because both x and y are identically distributed, then so are |x| and |y|.

E(|x|) = $\int\limits^{1.5}_0 {\frac{x}{1.5} \, dx = \frac{2}{3}* ((1.5^2)/2 - 0^2/2) = \frac{3}{2}$

Therefore, E(|x| + |y|) = 2 * 3/2 = 3.

I hope that works for you!

4 0

3 years ago

An article presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new meth

Anna35 [415]

Answer:

With 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

Step-by-step explanation:

We are given that the effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 655.6 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.

A traffic engineer states that the mean improvement is between 583.1 and 728.1 vehicles per hour.

Let $\bar X$ = sample mean improvement

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = mean improvement = 655.6 vehicles per hour

$\sigma$ = standard deviation = 311.7 vehicles per hour

n = sample of simulations = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the mean improvement is between 583.1 and 728.1 vehicles per hour is given by = P(583.1 < $\bar X$ < 728.1) = P( $\bar X$ < 728.1) - P( $\bar X$ $\leq$ 583.1)

P( $\bar X$ < 728.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{728.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z < 1.64) = 0.9495

P( $\bar X$ $\leq$ 583.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{583.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z $\leq$ -1.64) = 1 - P(Z < 1.64)

= 1 - 0.9495 = 0.0505

So, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.64 in the z table which has an area of 0.9495.

Therefore, P(583.1 < $\bar X$ < 728.1) = 0.9495 - 0.0505 = 0.899 or 89.9%

Hence, with 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

6 0

3 years ago