Using proportions, it is found that the original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
This question is solved by proportions, using a rule of three.The weight of 1 batch, in grams, is of [tex]6.9 \times 10^{-10}[/tex]. How much do the sample of 12 batches weigh?The rule of three is:
1 batch - [tex]6.9 \times 10^{-10}[/tex] grams.
12 batches - x grams
Applying cross multiplication:
[tex]x = 12 \times 6.9 \times 10^{-10} = 82.8 \times 10^{-10}[/tex]
Applying scientific notation:
[tex]8.28 \times 10^{-9}[/tex]
The original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
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Find the value of r in the isosceles triangle shown below.
8
8
6
Answer:
r = 6
.....................
What is the LCM of 8 and 10
Fill in the blanks with the answer to each question based on information provided.Two toy robots are having a race. Robot A can go 14 meter in 15 seconds. Robot B can go 1 meter in 50 seconds.1) If Robot A continues at that same speed, how long will it take to go 1 meter? Remember units! __________2) How long for Robot A to go 4 meters at that speed? Remember units! _________
Answer:
1 1/14 seconds4 2/7 secondsStep-by-step explanation:
We are being asked for times, so we can express the rate in terms of seconds per meter.
(15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter
__
1) It will take Robot A 1 1/14 seconds to go 1 meter.
2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)
Someone please help me with this I learned this in class of the day I don’t remember it
[tex]\boxed{\sf \lim_{n \to \infty} (\frac{1}{1-n^2}+\frac{2}{1-n^2} +...\: \frac{n}{1-n^2} }[/tex]
- Need a step-by-step answer!
- Thank you!
[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{1}{1-n^2}+\dfrac{2}{2-n^2}\dots \dfrac{n}{1-n^2}\right)[/tex]
Take LCM as 1-n^2[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{1+2+3\dots n}{1-n^2}\right)[/tex]
1+2..n=n(n+1)/2[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{\dfrac{n(n+1)}{2}}{1-n^2}\right)[/tex]
[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\dfrac{n(n+1)}{2(1-n^2)}[/tex]
[tex]\\ \sf\Rrightarrow \lim_{n\to infty}\dfrac{n(1+n)}{2(1-n)(1+n)}[/tex]
[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\dfrac{n}{2(1-n)}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{\infty}{2-\infty}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{-1}{2}[/tex]
[tex]{\sf \lim_{n \to \infty} (\frac{1}{1-n^2}+\frac{2}{1-n^2} +...\: \frac{n}{1-n^2}) } \\ = {\sf \lim_{n \to \infty} (\frac{1 + 2 + ..n}{1-n^2})} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2} \div 1 - {n}^{2} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2} \times \frac{1}{ 1 - {n}^{2}} )} \\ ={\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2(1 - {n}^{2} )} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2 (1 - n )(1 + n) } )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(1 + n)}{2 (1 - n )(1 + n) } )} \\ = {\sf \lim_{n \to \infty} ( \frac{n}{2 (1 - n )} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n}{2 - 2 n } )} \\ = \sf \frac{ \infty }{2 - \infty } \\ = \frac{ - 1}{2}
[/tex]
Answer:
[tex] \frac{ - 1}{2} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
a breakfast cereal advertizes that it has 5g of fibre in every 30g serving. How much fibre would someone receive if he or she ate a 50g serving of that cereal?
Answer:
8.33... grams of fiber
Step-by-step explanation:
The grams per serving is 5/30 or 1/6 or .166... or 16.66...%.
So Fiber = 16.66% * serving size or
F = 16.66 * 50 = 8.33...
a drilling team detected water 38 feet below the ground. if it took workers 8 days to be able to dig and pull up the water, how much did they dig each day on average? What do the x and y intercepts represent?
Answer:
On average, the workers dig 4.75ft each day. Also, what x and y questions?
Step-by-step explanation:
Take [tex]38/8=4.75[/tex]
I hope you have a great day and make me the brainliest.
The drilling team digs 4.75 feet every day, as per the given conditions, and y and x-intercept represent the depth and days respectively.
Given that,
A drilling team detected water 38 feet below the ground. if it took workers 8 days to be able to dig and pull up the water,
the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
The total depth of dig = 38 feet
Total time took to dig 38 feet = 8 days
For 1 day, the depth of the dig = 38 / 8 = 4.75
Now,
Let x is the number of days,
while y be the depth left to dig in feet,
y = 38 - 4.75x
The drilling team digs 4.75 feet every day, as per the given conditions, and y and x-intercept represent the depth and days respectively.
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Please show working out I will give out brainiest :)
enter an algebraic expression for the word expression.
2 decreased by n
Answer:
2 - n
Step-by-step explanation:
2 decreased by n means n less than 2.
Answer:
Write each phrase as an algebraic expression. Phrase, Expression. nine increased by a number x, 9 + x. fourteen decreased by a number p, 14
Step-by-step explanation:
2-n Plz mark brainliest if correct
If a dozen exercise books cost 144, what will 14 of the same books cost
what is the 5th multiple of 6
Answer:
30
Step-by-step explanation:
What is 6, 5 five times?
Or 5x6?
In IJK, i = 40 inches, j = 80 inches and ZK=92°. Find ZJ, to the nearest degree.
Answer:
61.9
Step-by-step explanation:
mark me as brainliest
Answer:
62°
Step-by-step explanation:
The law of cosines is used to find the length of side k:
k² = i² +j² -2i·j·cos(K)
k² = 40² +80² -2·40·80·cos(92°) ≈ 8223.3568
k ≈ 90.6827 . . . . . . . take the square root
Then the law of sines is used to find angle J.
sin(J)/j = sin(K)/k
J = arcsin(j/k·sin(K)) = arcsin(80/90.6827·sin(92°)) ≈ 61.84°
J ≈ 62°
PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls
Answer:
1. =
Step-by-step explanation:
1.
R.H.S
5.2 + 5.a
(now taking 5 common)
5(2+a)
64 divided by 1184 worked out
Answer: 18.5
Step-by-step explanation: 1184/64= 18.5
In a bag, the ratio of red to blue counters is 3:4.
If 3 red counters are removed the ratio of red to blue counters becomes 3:5.
How many blue counters are there in the bag?
What is the y intercept of the line y + 11=-2(x+1.5)
[tex]y +11 = -2(x+1.5)\\\\\implies y = -2x -3 -11\\\\\implies y = -2x - 14\\\\\text{The above equation is in a form of y = mx +b,}~\text{where}~~ b = -14~\text{ is the y-intercept.}[/tex]
If 2 caterpillars eat 6 leaves each day, how many leaves do 12 caterpillars need each day?
Answer:
72 Leafs
Step-by-step explanation:
Write 5.4 as a mixed number and as an improper fraction.
Write your answers in simplest form.
Answer:
5.4 as a fraction is 27/5.
Step-by-step explanation:
Learned in 5th grade
how to turn 18/48 into the power of 10 please tell the answer as soon as possible, it's for my semester
a calculus problem that i have no idea what to do please help
Answer:
-[tex]\sqrt{5}[/tex]/8
Step-by-step explanation:
so you are looking to find the second derivative of this function, given the derivative. that means that all you have to do is take the derivative of that function and then plug in 16 for h.
rewrite the function to be -(5h)^1/2
then take its derivative using power rule and chain rule
-(1/2)*(5)*(5h)^(-1/2) **the five comes from the chain rule and taking the derivative of the 5h
then plug in 16 for h to find -[tex]\sqrt{5}[/tex]/8 or about -0.2795
Need help quick !!!!!!!
write an equation for the nth term of the arithmetic sequence.then fine a10
Answer is attached.
Hope it helps :)
Triangle JKL is similar to triangle MNO. Find the measure of side MN. Round your answer to the nearest tenth if necessary.
Answer:
I believe the answer is 47. Forgive me if I'm wrong
Find the inverse function. f(x) = (x + 1
Answer:
( x + 1 ) ^ 3
Step-by-step explanation:
f(x) = 3√x - 1
replace x with y
x = 3√y - 1
solve for y,
x = 3√y - 1
x^3 + 3x^2 + 3x + 1 = (x+1)^3
HOPE THIS HELPS :)
16.11 ÷ 99
19.6 ÷ 20
0.9 ÷ 11
50.8 ÷ 45
0.1414 ÷ 2
0.213 ÷ 31
Ella brought 7 new Christmas cards to add to her card collection this year. the next day she mailed half of her entire collection to her elf family and friends. there are now only 21 cards left. how many cards did Ella start with?
Answer:
42
Step-by-step explanation:
the half of 42 is 21 so if she mailed the half of it then she just have 21 cards
In the equation = + , what does b represent?
Answer:
Although the equation is incomplete (b doesn't appear), I'll venture a guess that the correct equation looks something like this:
y = 2x + b [or y = mx+b]
b is the y-intercept.
Step-by-step explanation:
In the format of y = 2x + b, b represents the y-intercept (the value of y when x = 0).
if l||m, find the value of x.
Answer:
9
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
Step-by-step explanation:
11x - 47 = 6x - 2 Corresponding angle. Add 47 to both sides
11x = 6x + 47 - 2 Combine
11x = 6x + 45 Subtract 6x from both sides
11x - 6x = 45 Combine
5x = 45 Divide by 5
5x/5 = 45/5
x = 9
What two numbers multiplied together equal 42 but when added they equal -13
Answer: -7 and -6
Step-by-step explanation:
6. Line a: y - 3x = 4
Line b: y = 3x + 5
Line c: y - 4x = 3
Which lines are parallel
Answer:
Line a and b
Step-by-step explanation:
Pleas help me for B and C
Answer:
In no b 7 people has represented □
In no c 2 people referred giraffe than dogs
Answer:
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.