A store has a pair of pants marked $39.99 with a 40% off tag. What is the sale price of the pants?

Determine whether the quantitative variable is discrete or continuous. Weight of a rock

NemiM [27]

Answer:

Continuous.

Step-by-step explanation:

In Mathematics, a random variable can be defined as any variable whose values are determined by the outcome of a random experiment.

Basically, random variables are classified into two (2) main categories and these are;

1. Discrete random variable: a discrete random variable is a data set in which the number of possible values are either finite or countable. For instance, the value of a fair die, number of sweets in a jar, number of eggs in a crate etc.

2. Continuous random variable: a continuous random variable is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable. Any quantity such as height, volume, weight, density, length, pressure, temperature, speed, distance, time are generally a continuous random variable.

Hence, the weight of a rock is continuous random variable because it has an infinite number of possible values such as 1kg, 20kg, 10kg, 50kg etc.

5 0

3 years ago

A cooler at a picnic contains 100 cans of soda covered by ice. There are 34 cans of cola, 50 cans of orange soda, 12 cans of g

andriy [413]

Answer:

P = 1/2 = 0.5

Step-by-step explanation:

Total amount of cans = 100

Cans of cola = 34

Cans of orange soda = 50

Cans of ginger ale = 12

Cans of root beer = 4

Probability of selecting

- a can of cola = 34/100 = 0.34

- a can of orange soda = 50/100 = 0.5

- a can of ginger ale = 12/100 = 0.12

- a can of root beer = 4/100 = 0.04

Since we are asked the probability that the can selected is a root beer, cola, or ginger ale, we need to add together the probabilities of each.

P = 0.04 + 0.34 + 0.12 = 0.5 = 1/2

6 0

3 years ago

Test for convergence

Elan Coil [88]

You've established that

$\displaystyle\sum_{n\ge1}\frac1{2^n}\le\int_1^\infty\frac{\mathrm dx}{2^x}$

so all you need to do is compute the integral. Rewrite the integrand as

$\dfrac1{2^x}=2^{-x}=e^{\ln2^{-x}}=e^{-x\ln2}$

and replace $y=-x\ln2$ , so that $\mathrm dy=-\ln2\,\mathrm dx$ . Then

$\displaystyle\int_{x=1}^{x\to\infty}\frac{\mathrm dx}{2^x}=\int_{y=-\ln2}^{y\to-\infty}e^y\,\frac{\mathrm dy}{-\ln 2}=\frac1{\ln2}\int_{-\infty}^{-\ln2}e^y\,\mathrm dy$

By the fundamental theorem of calculus, this evaluates to

$\dfrac1{\ln2}e^y\bigg|_{y\to-\infty}^{y=-\ln2}=\dfrac1{\ln2}\left(e^{-\ln2}-\lim_{y\to-\infty}e^y\right)=\dfrac{e^{-\ln2}}{\ln2}=\dfrac{\frac12}{\ln2}=-\dfrac1{2\ln2}=\dfrac1{\ln4}$

and so the series converges.

You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.

4 0

3 years ago

9.20 Divide it by 100 and write the product in expanded form

DedPeter [7]

565666666765665657557 is the answer or maybe it’s 6 sorry if it’s wrong

4 0

3 years ago

Please help and explain it would be very helpful

iris [78.8K]

So for the first one think of it as decimals so it’s easier: 9.20-7.35, subtract and it would be 1.85 so since we use decimals to make it easier it isn’t actually a decimal so it would be 2 hours and 25 minutes. And for the second one you just add 50 minutes to that and you would get 3 hours and 15 minutes.

6 0

3 years ago