The histogram summarises a health score for a group of people. Estimate the fraction of the group who had a score of 45 or more

Which expression is equivalent to [4mn/m⁻2n⁻6}⁻2? Assume m and n do not equal zero

leva [86]

The answer would be {(n^5)^2}/{(4*m^3)^2} = { n^{10} }/{16*m^6}

8 0

2 years ago

A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his

Karolina [17]

Answer:

a) The ratio of passenger cars to pickup trucks is $\frac{5}{7}$

The ratio of pickup trucks to passenger cars is $\frac{7}{5}$

The ratio of passenger cars to total vehicles is $\frac{5}{12}$

The ratio of pickup trucks to total vehicles is $\frac{7}{12}$

b) The tape diagram is shown in the attached picture.

c) The tape diagram has 12 equal-sized parts.

d) The total quantity that the tape diagram represent is 192.

e) The value of each individual part of the tape is 16.

f) There were registered 80 passenger cars and 112 pickup trucks.

Step-by-step explanation:

a) According to the information in the problem, that for every 5 passenger cars registered, there were 7 pickup trucks registered.

So the ratios are:

Passenger cars to pickup trucks: $\frac{5}{7}$

Pickup trucks to passenger cars: $\frac{7}{5}$

If we calculate the total vehicles: 5+7=12

So, we can get two ratios more:

Passenger cars to total vehicles is $\frac{5}{12}$

Pickup trucks to total vehicles is $\frac{7}{12}$

b) We make a tape diagram where each box represents a vehicle so we draw 5 boxes for cars and 7 boxes for pickup trucks.

c) If we count the total quantity of boxes, there are 12.

d) This diagram represents the total quantity of registrations in August which is 192.

e) To get the representation of each part of the tape diagram we have to divide 192 by 12. 192÷12=16

f) Finally, we multiply 16 by the number of boxes of each type of vehicle:

Cars: 16×5=80

Pickup trucks: 16×7=112

6 0

2 years ago

The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit in

Marina86 [1]

Answer:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

Step-by-step explanation:

Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"

We have the following formula in order to find the sum of cubes:

$\lim_{n\to\infty} \sum_{n=1}^{\infty} i^3$

We can express this formula like this:

$\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2

$\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

If we operate and we take out the 1/4 as a factor we got this:

$\lim_{n\to\infty} \frac{n^2(n+1)^2}{n^4}$

We can cancel $n^2$ and we got

$\lim_{n\to\infty} \frac{(n+1)^2}{n^2}$

We can reorder the terms like this:

$\lim_{n\to\infty} (\frac{n+1}{n})^2$

We can do some algebra and we got:

$\lim_{n\to\infty} (1+\frac{1}{n})^2$

We can solve the square and we got:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

3 0

2 years ago

A triangular prism has an equilateral base with each side of the triangle measuring 8.4 centimeters. The height of the prism is

qaws [65]

Answer:

It is 20.4 and 16.8

Step-by-step explanation:

This is similar to 8.4 (because its doubled) and it is similar to 10.2 (because its doubled)

5 0

2 years ago

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Janet makes 67% of free throws in her basketball games. Her coach wants to know the probability that she will make 7 out of the

8_murik_8 [283]

The probability that Janet makes a free throw is given by:
P(f)=0.67
The simulation that will be used to design the possibility of her making 7 out of 8 free throws will be:

<span>D) Roll a die letting 1-4 represent Janet making a free throw and 5-6 represent Janet not falling. Roll the die eight times.
This is is because the probability of obtaining 1,2,3 or 4 from rolling a dice is
4/6=0.67 </span>

3 0

2 years ago

Read 2 more answers