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4 years ago

7. PHOTOGRAPHY Francine has a camera in which the distance from the lens to the film

Mathematics

1 answer:

Len [333]4 years ago

5 0

Answer:

a) The height of the image = 11.2 millimeters

b) The distance between the camera and her friend = 2.24 meters

Step-by-step explanation:

<u>Part A: find the height of the image:</u>

distance from the lens to the film = 24 millimeters

distance from the lens to the her friend = 3 meters = 3000 millimeters

height of her friend = 140 centimeters = 1400 mm

the height of the image = x

Using the similarity :

$\frac{x}{140} = \frac{24}{3000} \\x= \frac{140*24}{3000} = 1.12 cm = 11.2 mm.$

<u>Part B: find the distance between the camera and her friend</u>

If the height of the image on the film of her friend is 15 millimeters.

Let the the distance between the camera and her friend = y

$\frac{y}{24} = \frac{1400}{15} \\y = \frac{24 * 1400}{15} = 2,240 mm = 2.24 meters$

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A self proclaimed psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the c

swat32

Answer:

The 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

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".

Description in words of the parameter p

$p$ represent the probability that the psychic correctly identifies the symbol on the card in a random trial

$\hat p$ represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

n=200 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the cases successful

$\hat p=\frac{46}{200}=0.23$ represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

Confidence interval

The confidence interval for a proportion is given by this formula:

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.23 - 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.172$

$0.23 + 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.288$

And the 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).

6 0

4 years ago

Izzie recently took a math test where each correct answer (a) on the main part of the test was worth 8.3 points. She also correc

Temka [501]

Answer:

12 correct answers

Step-by-step explanation:

Since in the main part she scores 8.3 points for each question she answers correctly, we can assume that the number of questions she answers correctly=a

Therefor, the total number of points she achieved in the math test in the main part alone can be expressed as:

Total score(main part)=8.3×a=8.3a points

She also solved a bonus question worth=11 points

Consider expression 1 below

The total score in the whole test=Total score in the main part+Bonus points, where;

Total score in the whole test=110.6 points

Total score in the main part=8.3a points

Bonus points=11 points

Substituting the values in expression 1:

8.3a+11=110.6

8.3a=110.6-11

8.3a/8.3=99.6/8.3

a=12

Number of correct answers in the main part=a=12

4 0

4 years ago

A matatu carries 14 passengers per trip. In

PilotLPTM [1.2K]

Answer:

"23,520"

Step-by-step explanation:

one trip: 14 passengers

one day: 3 trips

passengers: 80

80x14= 1,120

1,120x3= 3,360

3,360x7= 23,520

6 0

3 years ago

Sboob wohs dna ten.esaelpemetaD ot og FG evah i naC

emmainna [20.7K]

Answer:

Ummmm no thanks. I am not going there.

Step-by-step explanation:

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3 years ago

A line has a slope of 9/5 and the point (-10, -16). which of the following could be another point on the line?

Allisa [31]

Answer: C

Step-by-step explanation:

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3 years ago