A person is standing 24 feet away from a street light that is 25 feet tall. How tall is he if his shadow is 6 feet long?

Mathematics

1 answer:

SVEN [57.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

The triangle formed by the lamp post and the (24+6)foot side on the ground is similar to the right triangle formed by the person of height h and his 6 foot shadow.

H/25=6/36

H=5

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sally has 20 coins in her piggy bank,all dimes and quarters. The total amount of money is $3.05. How many of each coin does she

Dafna11 [192]

Let d = number of dimes, q = number of quarters

Sally has 20 coins in her piggy bank, so 
d + q = 20 

The total amount of money is $3.05. 
Use the value of each coin multiplied by its number to get total value 
.10d + .25q = 3.05 
multiply everything by 100 to clear the decimal places 
10d + 25q = 305 and 
d + q = 20 

solve the second equation above in terms of either d or q - lets do d 
d = 20 - q 
sub that into the first equation 
10d + 25q = 305 
10(20 - q) + 25q = 305 
200 - 10q + 25q = 305 
15q = 105 
q = 105/15 = 7 
and from above 
d = 20 - q = 20 - 7 = 13 

so, there are 13 dimes and 7 quarters 
verify with orig problem 
13 + 7 = 20, OK, and $1.30 + $1.75 = $3.05

5 0

3 years ago

Read 2 more answers

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

VMariaS [17]

Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

Step-by-step explanation:

Previous concepts

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".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size

Solution to the problem

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:

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$