Answer:
x=14
Step-by-step explanation:
you should set up your problem like this:
5x=3x+28
use order of operations aka PEMDAS to solve
you're answer is 14
Answer:
see the attachment
Step-by-step explanation:
We assume that the question is interested in the probability that a randomly chosen class is a Friday class with a lab experiment (2/15). That is somewhat different from the probability that a lab experiment is conducted on a Friday (2/3).
Based on our assumption, we want to create a simulation that includes a 1/5 chance of the day being a Friday, along with a 2/3 chance that the class has a lab experiment on whatever day it is.
That simulation can consist of choosing 1 of 5 differently-colored marbles, and rolling a 6-sided die with 2/3 of the numbers being designated as representing a lab-experiment day. (The marble must be replaced and the marbles stirred for the next trial.) For our purpose, we can designate the yellow marble as "Friday", and numbers greater than 2 as "lab-experiment".
The simulation of 70 different choices of a random class is shown in the attachment.
_____
<em>Comment on the question</em>
IMO, the use of <em>70 trials</em> is coincidentally the same number as the first <em>70 days</em> of school. The calendar is deterministic, so there will be exactly 14 Fridays in that period. If, in 70 draws, you get 16 yellow marbles, you cannot say, "the probability of a Friday is 16/70." You need to be very careful to properly state the question you're trying to answer.
Answer:
She uses 200 milliliters of solution B
Step-by-step explanation:
Notice that there are two unknowns in this problem: 1) the amount of solution A that is being used, and 2) the amount of solution B being used. We can name such unknowns with letters to facilitate our work:
Amount of solution A to be used = A
Amount of solution B to be used = B
So, since we need to find two unknowns, we need to create a system of two equations to solve them.
Our first equation can be obtained from the sentence: "She uses twice as much Solution A as Solution B," which written in mathematical form is:
A = 2 B
The second equation we can build from the information of the amount of alcohol in each solution that combined will add up to 104 milliliters of alcohol in the mixture. Knowing the percent of alcohol in each solution, we can write an equation for the amount of alcohol:
0.19 A + 0.14 B = 104
Now we can use our first equation to substitute A in terms of B in the second equation:
0.19 (2 B) + 0.14 B = 104
0.38 B + 0.14 B = 104
0.52 B = 104
B = 104 / 0.52
B = 200 milliliters
Step-by-step explanation:
last week there were
62 + 60 + 2 = 124 customers.
that means that the fraction of the customers, who paid by credit card, was
2/124 = 1/62
in situations like that, when we use history data and try to predict future behavior, we use that past experience and extrapolate to a predicted result.
we simply say that we expect the same fraction, 1/62, if customers to use credit cards.
for the absolute number of predicted credit card customers we multiply the predicted number of customers by the expected fraction
1000 × 1/62 = 500/31 = 16.12903226... ≈ 16
so, he expects 16 credit card customers.
Answer:
Using trigonometric ratio:
From the given statement:
and sin < 0
⇒
lies in the 3rd quadrant.
then;
Using trigonometry identities:
Substitute the given values we have;
Since, sin < 0
⇒
now, find 
:
Substitute the given values we have;
Therefore, the exact value of:
(a)
(b)
