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4 years ago

X = -2y - 5 4x – 3y = 2 How to solve this linear system?

Mathematics

2 answers:

sweet [91]4 years ago

6 0

The answer is x=-1 and y=-2

cricket20 [7]4 years ago

4 0

Plug in the first equation(x) into another instead of x. If x equals -2y-5. Then we get 4(-2y-5)-3y=2. -8y-20-3y=2. Group like terms on different sides. -11y=22. y=22/-11. y=-2.

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A fitness center currently has 320 members. Monthly membership fees are $45. The manager of the fitness center has determined th

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3 years ago

A magazine provided results from a poll of 500500 adults who were asked to identify their favorite pie. Among the 500500 respon

Komok [63]

Answer:

99% confidence interval is wider as compared to the 80% confidence interval.

Step-by-step explanation:

We are given that a magazine provided results from a poll of 500 adults who were asked to identify their favorite pie.

Among the 500 respondents, 14% chose chocolate pie, and the margin of error was given as plus or minus ±3 percentage points.

The pivotal quantity for the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who chose chocolate pie = 14%

n = sample of adults = 500

p = true proportion

Now, the 99% confidence interval for p = $\hat p \pm Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

Here, $\alpha$ = 1% so $(\frac{\alpha}{2})$ = 0.5%. So, the critical value of z at 0.5% significance level is 2.5758.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.03 for 99% interval.

So, 99% confidence interval for p = $0.14 \pm2.5758 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

= [0.14 - 0.03 , 0.14 + 0.03]

= [0.11 , 0.17]

Similarly, 80% confidence interval for p = $0.14 \pm 1.2816 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

Here, $\alpha$ = 20% so $(\frac{\alpha}{2})$ = 10%. So, the critical value of z at 10% significance level is 1.2816.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.02 for 80% interval.

So, 80% confidence interval for p = [0.14 - 0.02 , 0.14 + 0.02]

= [0.12 , 0.16]

Now, as we can clearly see that 99% confidence interval is wider as compared to 80% confidence interval. This is because more the confidence level wider is the confidence interval and we are more confident about true population parameter.

5 0

4 years ago

Radius = 16 in ; height = 27 in

nataly862011 [7]

Assuming that this problem is asking about a cylinder, the volume can be found using the formula (pi)(r)^2 * h (area of the circle * height) and the surface area can be found using the formula (2)(pi)(r)h (circumference of the circle * height).

Volume = (pi)(16)^2 * 27 = 21,714.688 in^3
Surface Area = (2)(pi)(16) * 27 = 2,714.336 in^2

8 0

2 years ago

The midpoint of UV is (5, -10). The coordinates of one endpoint are U(3,6). Find the coordinates of endpoint V.

Grace [21]

The answer is (7, -26) for The second endpoint.

We'll call the midpoint M. In order to find this, we must first note that to find a midpoint we need to take the average of the endpoints. To do this we add them together and then divide by 2. So, using that, we can write a formula and solve for each part of the k coordinates. We'll start with just x values.

(Ux + Vx)/2 = Mx

(Vx + 3)/2 = 5

Vx + 3 = 10

Vx = 7

And now we do the same thing for y values

(Uy + Vy)/2 = My

(Vy + 6)/2 = -10

Vy + 6 = -20

Vy = -26

This gives us the final point of (7, -26)

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3 years ago

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