Answer:
Step-by-step explanation:
It helps immensely if you understand how place value works in a decimal number system. It also helps if you understand the rules of exponents.
Around the decimal point, the place values are ...
(hundreds) (tens) (ones) . (tenths) (hundredths) (thousandths)
Each location to the right of any given place has a place value that is 1/10 of the one to its left. When there get to be many factors of 10, it is useful to use exponents to represent the repeated multiplication.
1/10 = 1/10^1
1/100 = 1/10^2
1/1000 = 1/10^3
If you count carefully, you find the the digit 1 in your number is in the 9th place to the right of the decimal point, so its multiplier is 1/10^9. That is ...
0.000000001 = 1/10^9
By the rules of exponents, a positive exponent in the denominator is the same as its opposite exponent in the numerator, so this number can also be written as ...
0.000000001 = 1×10^-9 . . . . scientific notation
Answer:
Step-by-step explanation:
Given that minimum is 8 and maximum equals 82
Range =
No of classes =6
Class width = 76/6 ~13
But not given whether variable is discrete or continuous.
If discrete, we have classes as
8-20, 21-33, 34-46, 47-59, 60-72, 73-85
If continuous, we have classes as
8 to <21
21 to <34
and ... ending 73-<86
Answer:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that: where c is the total amount in the glass. This means that:
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: and that:
.
So if we're going to add the two glasses, we simply add the two sides, and get: . Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get:
Now we can add like terms to get the equation:
. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
Answer:
which agrees with option"B" of the possible answers listed
Step-by-step explanation:
Notice that in order to solve this problem (find angle JLF) , we need to find the value of the angle defined by JLG and subtract it from , since they are supplementary angles. So we focus on such, and start by drawing the radii that connects the center of the circle (point "O") to points G and H, in order to observe the central angles that are given to us as
and
. (see attached image)
We put our efforts into solving the right angle triangle denoted with green borders.
Notice as well, that the triangle JOH that is formed with the two radii and the segment that joins point J to point G, is an isosceles triangle, and therefore the two angles opposite to these equal radius sides, must be equal. We see that angle JOH can be calculated by :
Therefore, the two equal acute angles in the triangle JOH should add to:
resulting then in each small acute angle of measure
.
Now referring to the green sided right angle triangle we can find find angle JLG, using:
Finally, the requested measure of angle JLF is obtained via:
