Eight plus the quotient of a number and 3 is -2

Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given freque

maw [93]

Answer:

The number of individuals included in the summary is 146.

Step-by-step explanation:

The frequency distribution table provided is as follows:

Class Intervals Frequency

100 - 199 24

200 - 299 90

300 - 399 27

400 - 499 1

500 - 599 4

The lower class limit it the smallest value of each class interval.

Lower class limit = {100, 200, 300, 400, 500}

The upper class limit it the highest value of each class interval.

Upper class limit = {199, 299, 399, 499, 599}

The lower class boundaries are the lower class limits decreased by 0.5 and the upper class boundaries are the upper class limits increased by 0.5.

Class boundaries:

99.5 - 199.5

199.5 - 299.5

299.5 - 399.5

399.5 - 499.5

499.5 - 599.5

The class width is the difference between the class boundaries of each class.

Class width = 199.5 - 99.5 = 100

So, the class width is 100.

The midpoints of a class is the average value of the boundaries of a class.

$\text{Midpoint}_{100-199}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{99.5+199.5}{2}\\\\=149.5$

$\text{Midpoint}_{200-299}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{199.5+299.5}{2}\\\\=249.5$

$\text{Midpoint}_{300-399}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{299.5+399.5}{2}\\\\=349.5$

$\text{Midpoint}_{400-499}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{399.5+499.5}{2}\\\\=449.5$

$\text{Midpoint}_{500-599}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{499.5+599.5}{2}\\\\=549.5$

The number of individuals included in the summary is the sum of all frequencies.

$\text{Number of Individuals}=24 + 90 + 27 + 1 + 4=146$

Thus, the number of individuals included in the summary is 146.

3 0

3 years ago

Read 2 more answers

One serving of rice has 44.9 grams of carbohydrates how many grams of carbohydrates de 2.5 servings of rice have

Fofino [41]

Answer:

$112.25\ grams\ of\ carbohydrates$

Step-by-step explanation:

we know that

using proportion

$\frac{1}{44.9}\frac{serving\ of\ rice}{grams\ of\ carbohydrates} =\frac{2.5}{x}\frac{serving\ of\ rice}{grams\ of\ carbohydrates} \\ \\x=44.9*2.5\\ \\x=112.25\ grams\ of\ carbohydrates$

4 0

3 years ago

What is the percent decline, to the nearest whole number, of rusty patched bumble bees from 20 years ago to today?

Andrej [43]

Sasuke is pretty cool

6 0

3 years ago

Read 2 more answers

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

3 years ago

What is the measure of angle z in this figure?

ASHA 777 [7]

Answer:

z = 137°

Step-by-step explanation:

$z^{o} =(180-43)^{o} =137^{o}$

Hope this helps

7 0

2 years ago