A rectangular hockey field is 50m long and 35m wide calculate the length of it's diagonal

Examine this system of linear equations. y – 3x=-2, y = 4

Verdich [7]

Answer:

2, 4

Step-by-step explanation:

Ok so for this you have to substitute. y=4 so you put a 4 where the y is. This becomes

4 - 3x = -2 We can already rule out (2,2) and (4,2) Why? Because the y is not a 4. So it’s gonna be either (0,4) or (2,4). Now, we have to find x. We have to isolate it. You do this by subtracting 4 from both sides.

4 - 4 - 3x = -2 - 4 Now Simplify

-3x = -6 Why -6? Because you can’t subtract a positive from a negative so it becomes -2 + -4. Since they are both negatives, you just add them together, then put the negative sign.

Now divide -3 from both sides. Which becomes

x = 2

4 0

3 years ago

Read 2 more answers

preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found tha

VladimirAG [237]

Answer:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

n=369

Step-by-step explanation:

1) Notation and definitions

$X=40$ number of the selected labourers opt for a new incentive scheme.

$n=100$ random sample taken

$\hat p=\frac{40}{100}=0.4$ estimated proportion of the selected labourers opt for a new incentive scheme.

$p$ true population proportion of the selected labourers opt for a new incentive scheme.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

2) Solution tot he problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

And rounded up we have that n=369

8 0

3 years ago

What is 0.003 is 1/10 of

Svetach [21]

.003 is 1/10 of .03. To find it divide by 1/10

4 0

3 years ago

What expression shows the relationship between the value term n

ruslelena [56]

-5n + 15 is the answer I think
I understand if it's not

4 0

3 years ago

Rocio leaves point A traveling due east at 40 miles per hour. At the same moment, Li leaves point A traveling due west at 50 mil

Afina-wow [57]

Their speed of separation will be equal to the sum of their speeds because they are in opposite directions.
Speed of separation = 40 + 50 = 90 miles per hour

Time = distance / speed
Time = 405 / 90
Time = 4.5 hours

3 0

3 years ago

A rectangular hockey field is 50m long and 35m wide calculate the length of it's diagonal​

A rectangular hockey field is 50m long and 35m wide calculate the length of it's diagonal