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3 years ago

Josh and Richard each earn tips at their part-time jobs. This table shows their earnings from tips for five days.

Mathematics

1 answer:

maxonik [38]3 years ago

3 0

Answer:

a) Richard had the greater median earnings from tips

b) $10

c) $1

Step-by-step explanation:

Median is the middle number when arranged from least to greatest.

Josh's Tips (smallest to greatest): 20, 28, 31, 36, 40

Richard's Tips (smallest to greatest): 28, 40, 41, 45, 53

The middle number (median) for Josh is the 3rd number, which is 31

The middle number (median) for Richard is the 3rd number, which is 41

Richard had the greater median earnings from tips

Josh's median is 31 and Richard's median is 41. The difference is:

41 - 31 = $10

Interquartile range is Third Quartile - First Quartile

For 5 number series, the third quartile is the average of 4th and 5th number. The first quartile is the average of the 1st and 2nd number.

For Josh:

Average of 4th and 5th number: (36+40)/2 = 38

Average of 1st and 2nd number: (20+28)/2 = 24

Interquartile Range = 38 - 24 = 14

For richard:

Average of 4th and 5th number: (45+53)/2 = 49

Average of 1st and 2nd number: (28+40)/2 = 34

Interquartile Range = 49 - 34 = 15

Thus, difference in IQR (interquartile range) between Josh and Richard is 15 - 14 = 1

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What is the domain of this exponential function?

Pavlova-9 [17]

Answer:

Domain = x E R

Step-by-step explanation:

Since an exponential function has no restriction on the "x" value, its domain can range from anywhere on the plane of "x."

3 0

3 years ago

Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
$V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;$
$V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.$

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$