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3 years ago

The area of triangle ABC is 24 square centimeters. If B = 30° and a = 6 cm, what is the measure of side c? 4 cm 8 cm 16 cm 32 cm

Mathematics

1 answer:

disa [49]3 years ago

4 0

Answer:

16 cm

Step-by-step explanation:

Given : The area of triangle ABC is 24 square centimeters.

To Find: If B = 30° and a = 6 cm, what is the measure of side c?

Solution:

Formula : $Area = \frac{1}{2} \times a \times c \times sin B$

a = 6

Area = 24

B = 30°

Substitute the values in the formula

$24 = \frac{1}{2} \times 6 \times c \times sin 30$

$24 = \frac{1}{2} \times 6 \times c \times \frac{1}{2}$

$24 =3 \times c \times \frac{1}{2}$

$\frac{24 \times 2}{3} =c$

$16=c$

Hence the measure of side c is 16 cm

So, Option c is correct.

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Here are summary statistics for randomly selected weights of newborn girls: nequals=174174, x overbarxequals=30.930.9 hg, seq

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Answer:

The 95% confidence interval would be given by (29.780;32.020)

Step-by-step explanation:

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".

$\bar X=30.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=174-1=173$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that $t_{\alpha/2}=1.97$ , this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.