Which of the following functions is graphed below?

Exactly 240 years ago students planted a tree in front of their school since did the tree has grown 30 beers taller and the dist

alexandr1967 [171]

Ok so the units will be taller if u mix it with water

5 0

1 year ago

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

1 year ago

Alan has to pay Robin $48, but he has only $36 with him. Alan overdraws the remaining amount from the bank to pay Robin. After p

Rashid [163]

I assume his account balance will become negative. With no overdraft fees in the question, then his account balance should be $-12.

6 0

1 year ago

Read 2 more answers

An aquarium has a base in the shape of a trapezoid. The base is 90 cm long at the front, 60 cm long at the back, and 30 cm wide

Nonamiya [84]

Answer:

Step-by-step explanation:

First calculate for the area of the trapezoid (the formula is (base + base / 2) x height):

60 cm + 90 cm = 150 cm

150 cm / 2 = 75 cm

75 cm x 30 cm = 2250 cm²

Now 1 cm² = 1 mL and 1000 mL = 1 L

2250 cm² = 2250 mL

2250 mL = 2.25 L

5 0

2 years ago

In △XYZ, m∠Z = 34, x = 61 cm, and z = 42 cm. Find m∠X. Round your answer to the nearest tenth of a degree.

Elza [17]

M∠X = 54.3°.

Using the Law of Sines, we have:
$\frac{\sin{Z}}{z}=\frac{\sin{X}}{x}
\\
\\\frac{\sin{34}}{42}=\frac{\sin{X}}{61}$

Cross multiplying gives us
61(sin 34) = 42(sin X)

Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X

Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X

8 0

1 year ago