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3 years ago

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A family of four (two kids and two parents) spend the day at an amusement park. At the end of the day, the family adds up all of

the receipts from their meals: $16.25, $17.96, $3.58, $4.61, $5.23. What is the mean and median cost spent? What does the mean cost represent? Why is the mean cost significantly different from the median cost? Which measurement of central tendency is a better representation of the amount of money that the family spent at the amusement park?

1 answer:

Harrizon [31]3 years ago

5 0

A family of four spent the following for their meals $16.25, $17.96, $3.58, $4.61, $5.23.

Mean cost spent is calculated by:

Total Cost/Number of Meals

(16.25+17.96+3.58+4.61+5.23)/5

47.63/5

$9.53

Mean Cost represents the average amount per meal the family has spent.

Median cost is the cost that in the middle of the five costs which is $5.23.

<span>The mean cost is significantly different from the median cost because it is higher.</span>

Median cost is a better representation of the amount of money that the family spent because, with<span> regard to meal costs, this means that exactly half of the meals in the amusement park are above this price ($5.23) and exactly half are below. </span>

<span> </span>

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Find the surface area of the regular pyramid shown to the nearest whole number. plz help

Sav [38]

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3 years ago

Read 2 more answers

Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer

agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming: the function is $f(x)=x^{2}$ in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

$g'(0)=g'(1)$

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

$g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0$

$g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2$

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

$f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]$

This is what the Bilateral Theorem says:

$\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L$

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3 years ago

22. One kilometer is approximately 0.62 mile. What fraction represents this length?

bixtya [17]

<u><em>Answer:</em></u>

One kilometer is $\frac{31}{50}$ miles

<u><em>Explanation:</em></u>

<u>To convert a decimal to a fraction:</u>

1- Write the decimal as a fraction whose denominator is 1

2- Multiply both numerator and denominator by multiples of 10 to eliminate the decimal point

3- Simplify the fraction you have

<u>Now, for the given problem:</u>

<u>The given decimal is 0.62, following the above steps:</u>

<u>Step 1: </u>

$0.62 = \frac{0.62}{1}$

<u>Step 2:</u>

We have two digits after the decimal point, so to eliminate the decimal point, we will multiply the numerator and the denominator by 100

$0.62 = \frac{0.62}{1} * \frac{100}{100} = \frac{62}{100}$

<u>Step 3:</u>

We can note that, in the fraction obtained from step 2, both the numerator and the denominator are divisible by 2, so we simplify as follows:

$\frac{62}{100} = \frac{62/2}{100/2} =\frac{31}{50}$

Hope this helps :)

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3 years ago

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maksim [4K]

Answer:

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3 years ago

In a study of 100 new cars, 29 are white. Find and g, where

sleet_krkn [62]

Question

<em>In a study of 100 new cars, 29 are white. Find p and q , where p is the proportion of new cars that are white. </em>

Answer:

p = 0.29 and q = 0.71

Step-by-step explanation:

Given

Total new cars = 100

White new cars = 29

Required

Determine p and q

From the question;

<em>p represents white new cars</em>

Hence;

$p = 29$

Note that;

$p + q = 100$

Substitute 29 for p

$29 + q = 100$

$29 - 29 + q = 100 - 29$

$q = 100 - 29$

$q = 71$

The proportion of p is calculate by dividing p by the total number of new cars (Same process is done for q)

For proportion of p

$Proportion,\ p = \frac{p}{new\ cars}$

$Proportion,\ p = \frac{29}{100}$

$Proportion,\ p = 0.29$

For proportion of q

$Proportion,\ q = \frac{q}{new\ cars}$

$Proportion,\ q = \frac{71}{100}$

$Proportion,\ q = 0.71$

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3 years ago