Ask question

Ask question

All categories

3 years ago

12

\begin{aligned} &-x+4y=-9 \\\\ &y=-2x +6 \end{aligned} −x+4y=−9 y=−2x+6 Is (2,3)(2,3)left parenthesis, 2, comma, 3,

right parenthesis a solution of the system?

1 answer:

zheka24 [161]3 years ago

5 0

Answer:

NO

Step-by-step explanation:

Given the system of equation

-x+4y = -9,... 1

y = -2x+6.... 2

To find the solution to the equation

Substitute equation 2 into 1

-x+4(-2x+6) = -9

-x-8x+24 = -9

-9x= -9-24

-9x = -33

x = 33/9

Find y

y = -2x+6

y = -2(33/9)+6

y = -66/9 + 6

y = -66+54/9

y = -12/9

y = -4/3

Hence (2,3) is not the solution to the system of equation

You might be interested in

Four times a number add to 9 times the number is 65. What is the number?

Westkost [7]

Answer:

5

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production

Ghella [55]

Answer:

a) 0.3174 = 31.74% probability of a defect. The number of defects for a 1,000-unit production run is 317.

b) 0.0026 = 0.26% probability of a defect. The expected number of defects for a 1,000-unit production run is 26.

c) Less variation means that the values are closer to the mean, and farther from the limits, which means that more pieces will be within specifications.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Assume a production process produces items with a mean weight of 10 ounces.

This means that $\mu = 10$ .

Question a:

Process standard deviation of 0.15 means that $\sigma = 0.15$

Calculate the probability of a defect.

Less than 9.85 or more than 10.15. Since they are the same distance from the mean, these probabilities is the same, which means that we find 1 and multiply the result by 2.

Probability of less than 9.85.

pvalue of Z when X = 9.85. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{9.85 - 10}{0.15}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

2*0.1587 = 0.3174

0.3174 = 31.74% probability of a defect.

Calculate the expected number of defects for a 1,000-unit production run.

Multiplication of 1000 by the probability of a defect.

1000*0.3174 = 317.4

Rounding to the nearest integer,

The number of defects for a 1,000-unit production run is 317.

Question b:

Now we have that $\sigma = 0.05$

Probability of a defect:

Same logic as question a.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{9.85 - 10}{0.05}$

$Z = -3$

$Z = -3$ has a pvalue of 0.0013

2*0.0013 = 0.0026

0.0026 = 0.26% probability of a defect.

Expected number of defects:

1000*0.0026 = 26

The expected number of defects for a 1,000-unit production run is 26.

(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

Less variation means that the values are closer to the mean, and farther from the limits, which means that more pieces will be within specifications.

3 0

3 years ago

Select the three ratios that are equuvalent to 3/5

Viefleur [7K]

Answer:

0.60 0.6 and .60 are all ratios hope this helps.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A car ride is drawn on a coordinate plane so that the first card is located at the point by (5,10) what are the coordinates of t

Rudiy27

Answer:

There are two possible solutions:

Clockwise rotation

$P'(x,y) = (-10,5)$

Counterclockwise rotation

$P'(x,y) = (10, -5)$

Step-by-step explanation:

There are two possible answers: (i) Clockwise rotation, (ii) Counterclockwise rotation. Vectorially speaking, rotation of point of rotation of a point about another point of reference is defined by:

$P'(x,y) = O(x,y) + r_{OP}\cdot (\cos (\theta_{OP}\pm \theta'),\sin (\theta_{OP}\pm \theta'))$ (1)

Where:

$O(x,y)$ - Point of reference.

$r_{OP}$ - Length of the segment OP.

$\theta_{OP}$ - Direction of segment OP, measured in sexagesimal degrees.

$\theta '$ - Angle of rotation, measured in sexagesimal degrees.

Please notice that clockiwise rotation occurs when $\theta = \theta_{OP}-\theta'$ and counterclockwise rotation when $\theta = \theta_{OP}+\theta'$ . In addition, we define length and direction of the segment below:

$r_{OP} = \sqrt{(x_{P}-x_{O})^{2}+(y_{P}-y_{O})^{2}}$ (1)

$\theta_{OP} = \tan^{-1} \frac{y_{P}-y_{O}}{x_{P}-x_{O}}$

If we know that $x_{O} = y_{O} = 0$ , $x_{P} = 5$ , $y_{P} = 10$ and $\theta' = 270^{\circ}$ , then the coordinates of the first car after rotation is:

$r_{OP} = \sqrt{(5-0)^{2}+(10-0)^{2}}$

$r_{OP} \approx 11.180$

Please notice that original point is located at first quadrant of the Cartesian plane centered at origin, then the direction of the segment OP is:

$\theta_{OP} = \tan^{-1} \frac{10-0}{5-0}$

$\theta_{OP} \approx 63.435^{\circ}$

The two solutions are finally presented:

Clockwise rotation

$P'(x,y) = (0,0) + 11.180\cdot (\cos (-206.565^{\circ}),\sin (-206.565^{\circ}))$

$P'(x,y) = (-10,5)$

Counterclockwise rotation

$P'(x,y) = (0,0) + 11.180\cdot (\cos (333.435^{\circ}),\sin (333.435^{\circ}))$

$P'(x,y) = (10, -5)$

5 0

3 years ago

Carlotta has 2/3 of a bag of dog food. She gives her dog 2/9 of the bag at each feeding. How many times can she feed her dog wit

77julia77 [94]

Hope you get it right

6 0

3 years ago

Read 2 more answers