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2 years ago

4x - y = 6 and 2x - y/2 =4

1 answer:

5 0

4x - y = 6
2x - y/2 = 4 /multiply both sides by 2 to get rid of the fraction

4x - y = 6
4x - y = 8

This system has no solution because it contradicts itself.

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87432 divided by 24 need help

Julli [10]

Answer:

3643

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batterie

Fittoniya [83]

Answer:

The confidence interval is $25.16 < \mu < 26.85$

Step-by-step explanation:

From the question we are given a data set

25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is

$\= x = \frac{\sum x_i}{n}$

where is the sample size with values n = 10

$\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}$

$\= x = 26$

The standard deviation is evaluated as

$\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }$

substituting values

$= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }$

$\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }$

$\sigma = 1.625$

The confidence level is given as 90% hence the level of significance is calculated as

$\alpha = 100 -90$

$\alpha =10$ %

$\alpha = 0.10$

Now the critical values of $\frac{\alpha }{2}$ is obtained from the normal distribution table as

$Z_{\frac{\alpha }{2} } = 1.645$

The reason we are obtaining the critical values of $\frac{\alpha }{2}$ instead of $\alpha$ is because we are considering two tails of the area under the normal curve

The margin of error is evaluated as

$MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

substituting values

$MOE = 1.645 * \frac{1.625 }{\sqrt{10} }$

$MOE = 0.845$

The 90%, two sided confidence interval is mathematically evaluated as

$\= x - MOE < \mu < \= x + MOE$

$26 - 0.845 < \mu < 26 + 0.845$

$25.16 < \mu < 26.85$

Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours

5 0

3 years ago

What does the algebraic representation (x,y) → (-x, y) represent?

torisob [31]

Answer:

The given algebraic representation (x,y) → (-x, y) represents the reflection of a point (x, y) across the y-axis.

Step-by-step explanation:

We know that when a point P(x, y) is reflected across the y-axis, the x-coordinate changes/reverses its sign, but the y-coordinate stays the same.

Thus, the rule of reflection of a point P(x, y) across y-xis is:

P(x, y) → P'(-x, y)

For example, if a point A(1, 2) is reflected across the y-axis, the coordinates of the image A' of the point A(1, 2) will be:

A(1, 2) → A'(-1, y)

In our case, we are given the algebraic representation

(x,y) → (-x, y)

Here:

The x-coordinate changes/reverses its sign

The y-coordinate stays the same.

Thus, the given algebraic representation (x,y) → (-x, y) represents the reflection of a point (x, y) across the y-axis.

6 0

2 years ago

the three sides of an equilateral triangle measure x 12, 2x - 5 and 3x - 22 inches. the sides of the triangle measure:

Novay_Z [31]

27.... or whats the x12 ?

4 0

3 years ago

Which of the following ordered pairs, when graphed on a standard

mestny [16]

Answer:

Step-by-step explanation:

quadrants (that are labeled from first to fourth and are denoted by roman numerals). ▫. Students identify ... Some important aspects for students to remember include the following: ▫. The -axis ... Graph at least five points on the -axis, and label their coordinates. Points will vary. ... compare the standard symbols

4 0

2 years ago