Tell whether the lines for y

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

2 years ago

Jill sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin?

Alex777 [14]

Answer:

$\frac{1}{2}x + 16 = 36$

40 comic books

Step-by-step explanation:

Let x be the Jill comic books.

Given:

Jill sold half of her comic books and then bought sixteen more. She now has 36.

$\frac{1}{2}\ (Jill\ books) + 16\ more\ books = 36$

$\frac{1}{2}\ (x) + 16 = 36$

$\frac{1}{2}x + 16 = 36$

Therefore the algebraic equation of the given statement.

$\frac{1}{2}x + 16 = 36$ --------(1)

Now we solve above equation for x.

Subtract by 16 both side of the equation 1.

$\frac{1}{2}x + 16 -16 = 36 -16$

$\frac{1}{2}x = 20$

Multiply by 2 both side of the above equation.

$2\times \frac{1}{2}x =2\times 20$

$x = 40$

Therefore, Jill had 40 comic books.

8 0

2 years ago

What does the Principle of Superposition tell us about relative ages of the strata in the cross-sections you were looking at? Ol

iogann1982 [59]

Answer:

1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.

2. The intrusion of the younger rock by the principle of cross-cutting relationship

3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.

Step-by-step explanation:

In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.

The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.

The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.

6 0

3 years ago

Araceli had 61 pennies and then lost 12. Now she wants to buy a treat that costs 4 sevenths of the pennies she has left. How man

igor_vitrenko [27]

The treat would cost 7 cents of your 49

8 0

3 years ago

Can somebody please show me how to do this problem

tia_tia [17]

Answer:

g(20) > f(20)
g(x) exceeds f(x) for any x > 4

Step-by-step explanation:

As with most graphing problems not involving straight lines, it works well to start with a table of values. Pick a few values of x and compute f(x) and g(x) for those values. Plot the points and draw a smooth curve through them.

As in the attached, your table will show that there are two points of intersection between f(x) and g(x), and that for values of x more than 4, g(x) becomes much greater very quickly. Both curves rapidly reach the top of your graph space.

To find whether f(20) or g(20) is greater, you can evaluate the functions for that value of x.

f(20) = 20² = 400

g(20) = 2²⁰ = 1,048,576

Clearly, g(20) has a greater value.

8 0

3 years ago

Tell whether the lines for y - 3x = 5 and