[tex] \times 2 \: y \: - 2xy = \times 4 + 3 = \times - \frac{3}{4} \: y \: e \: r[/tex]
The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated
coffee in the morning. How long will it take for only 60% of the caffeine to remain in his body?
We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.
We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.
So we can define the proportion of coffee that Jeremiah has in his body as:
P(t) = 1*e^{k*t}
Such that:
P(4.8 h) = 0.5 = 1*e^{k*4.8}
Then, if we apply the natural logarithm we get:
Ln(0.5) = Ln(e^{k*4.8})
Ln(0.5) = k*4.8
Ln(0.5)/4.8 = k = -0.144
Then the equation is:
P(t) = 1*e^{-0.144*t}
Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:
P(t) = 0.6 = 1*e^{-0.144*t}
Again, we use the natural logarithm:
Ln(0.6) = Ln(e^{-0.144*t})
Ln(0.6) = -0.144*t
Ln(0.6)/-0.144 = t = 3.55
So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.
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The two numbers are in the ratio of 4:5 and the sum of these numbers in981 find the numbers
Answer:
Step-by-step explanation:
let x be the larger number
x + (4/5)x = 981
(9/5)x = 981
x = 981(5/9)
x = 545
(4/5)(545) = 436
Find the equation of the line passing through the points 7,2 and 9,1
9514 1404 393
Answer:
y = -1/2x +11/2
Step-by-step explanation:
The slope of the line is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -2)/(9 -7) = -1/2
The y-intercept is ...
b = y -mx
b = 2 -(-1/2)(7) = 11/2
Then the slope-intercept equation is ...
y = -1/2x +11/2
_____
Alternative solution
A general form equation for the line can be ...
(y1 -y2)(x -x1) -(x1 -x2)(y -y1) = 0
(2 -1)(x -7) -(7 -9)(y -2) = 0
x-7 +2y -4 = 0
x +2y -11 = 0 . . . . . general form equation
x +2y = 11 . . . . . . . standard form equation
Note that we want the x-coefficient to be positive, so we chose the order of the points to make that be the case.
Exercise #14: The mile and the kilometer are relatively close in size. Can you convert 1 mile into an equivalent
in kilometers? Here's what I'll give you. There are 2.54 centimeters in an inch, 5,280 feet in a mile, 100
centimeters in a meter, and 1000 meters in a kilometer. All else you should be able to do for yourself. Round
your answer to the nearest tenth of a kilometer. This takes quite a string of multiplications, but you can do it!
The equivalent of 1 mile to kilometres is approximately 1.6 km.
2.54 cm = 1 inch
5280 ft = 1 mile
100 cm = 1 m
1000 m = 1 km
Using the information let's convert 1 mile to kilometre.
1000 m = 1 km
Therefore,
1 m = 0.000621371 miles
1000 m(1 km) = ?
cross multiply
length = 1000 × 0.000621371 = 0.621371 miles
Therefore,
0.621371 miles = 1 km(1000 m)
1 miles = ?
length in km = 1.60934449789 km
Therefore,
1 miles = 1.6 km
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Lord...... Help me god pleas I will be giving u guy's credit.
Answer:
a. 36
b. 8.5 (8 1/2)
c. 2/5
d. 6
e. 9
f. 8
Step-by-step explanation:
a. 36
b. 8.5 (8 1/2)
c. 2/5
d. 6
e. 9
f. 8
write an indirect proof that a triangle cannot have 2 right angles
Solve 12x- 6y = 18 for y.
The given equation solved for y as y=2x-3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 12x-6y=18.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The equation can be solved as follows
6(2x-y)=18
⇒ 2x-y=3
⇒ y=2x-3
Therefore, the given equation solved for y as y=2x-3.
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What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that apply. In addition to the Privileges and Immunities Clause, Article IV, Section 2 includes the
Hello!
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2x+5y=10
We want to turn this equation into y=mx+b form:
5y=-2x+10
Divide both sides by 5:
y=-2/5x+2
Now, the equation of the line parallel to it:
Remember, parallel lines have the same slope.
So these two lines have the same slope (-2/5)
Now, use Point-Slope form:
y-y1=m(x-x1)
y=1=-2/5(x-(-5)
y-1=-2/5(x+5)
y-1=-2/5x-2
y=-2/5x-2+1
y=-2/5-1
Hence, this is the required solution. I hope you find it helpful!
~SparklingFlower
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Write the equation of the line with a slope of 10 that goes through the point (8,-2) in slope intercept and point slope form?
Answer:
y=10x-2
Step-by-step explanation:
What is the answer to
2 3/8 - 1 5/8 =
Answer:
6/8
Step-by-step explanation:
you have to convert each fraction into an improper. because the denominators are already the same, you dont have to worry. once you have it as an impropper, you can now subtract it. 19/8 - 13/8 = 6/8
reduce if you can
- A small waffle cone has a height of 6 inches and a diameter of 2.5 inches. Two scoops of
sorbet are placed on the wide end of the cone. The scoops are spheres with a diameter
of 2.5 inches. If all the sorbet melts into the cone, will the cone overflow?
Answer:
NO
Step-by-step explanation:
What is the unit rate of km per hour in the example below?
You can walk 7/10 km in 1/4 hours.
Maybe 28kms in 1 hour
Or 2,8kms because 7/10 is 0,7km
Simplify 10^9 ÷ 10^7
Answer:
10^2
Step-by-step explanation:
10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2
Answer:
100
Step-by-step explanation:
Hope it helps
(b) Express the number 17
(i) in base 2
(ii) in base 5
Answer:
Step-by-step explanation:
IF 17 is in base 10
THEN
17₁₀ = 1 x 10¹ + 7 x 10⁰
10001₂ = 1 x 2⁴ + 0 x 2³ + 0 x 2² + 0 x 2¹ + 1 x 2⁰
32₅ = 3 x 5¹ + 2 x 5⁰
A driver driving a business trip of 240 miles would have reached his destination if he'd been able to drive 12 mph faster than he made the trip. Find the average speed of his trip.
The average speed of his trip is = 12 mile/ hour
The total distance covered by the driver = 240 miles
The rate at which he traveled = 12 miles per hour
Therefore, the time he used to cover his distance
= 240/12
= 20 hrs
But average speed = distance/ time
= 240/ 20
= 12 miles/ hour
Therefore, the average speed of his trip is = 12 mile/ hour
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Line a passes through points (3, 1) and (5, 10). Line b is parallel to line a. What is the slope of line b?
Answer:
9/2
Step-by-step explanation:
Answer:2.8
Step-by-step explanation: casue yeas.
will give brainliest to whoever helps
Answer:
x=4y
Step-by-step explanation:
Solving for x means you need to get it in the form x=?.
1. let's isolate the variable.
-2x-7y=y-4x
Add 4x to both sides to isolate:
2x-7y=y
Add 7y to both sides to isolate the x term:
2x=8y
Now we divide both sides by 2 (as we are solving for x):
x=4y
Hope this helps!
plsssss helpppppp i’ll give brainliest
Answer:
[tex]-6\leq x\leq 6[/tex]
Step-by-step explanation:
This is answer for the last question.
A shipment contains 9 igneous, 7 sedimentary, and 7 metamorphic rocks. If 7 rocks are selected at random, find the probability that exactly 5 are sedimentary.
Answer:
75 percent
Step-by-step explanation:
see the thing is
The probability that exactly 5 are sedimentary is from a shipment which contains 9 igneous, 7 sedimentary, and 7 metamorphic rocks is 21/33649.
What is combination?Combination is the way of arrangement or the collection of items in the particular order. The order of this group of items does not matter in the combination type of arrangement.
A shipment contains 9 igneous, 7 sedimentary, and 7 metamorphic rocks. If 7 rocks are selected at random, find the probability that exactly 5 are sedimentary.
Number of ways to choose 5 sedimentary from 7 sedimentary is,
[tex]^7C_5=\dfrac{7!}{(7-5)!5!}\\^7C_5=\dfrac{7\times6\times5!}{2!5!}\\^7C_5=\dfrac{7\times6}{2\times1}\\^7C_5=21[/tex]
There are total 23 rocks (9+7+7). Number of ways to choose 7 rocks from 23 rocks is,
[tex]^{23}C_5=\dfrac{23!}{(23-5)!5!}\\^{23}C_5=\dfrac{23!}{18!5!}\\^{23}C_5=33649[/tex]
Thus, the probability that exactly 5 are sedimentary is,
[tex]P=\dfrac{21}{33649}[/tex]
Hence, the probability that exactly 5 are sedimentary is from a shipment which contains 9 igneous, 7 sedimentary, and 7 metamorphic rocks is 21/33649.
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phone company offers to monthly plans. Plan a cost $11 plus an additional $.19 for each minute of calls. Plan B cost $16 plus an additional $.15 for each minute of calls
Answer:
whats the question I can't help without a question
Explain how you would use mental math to solve this
proportion.
How do you round 245.456456 to the nearest hundredth?
Answer: 245.46
Step-by-step explanation:
Hundredth is the 2nd number after the decimal so in this, it would be 245.456456. I'd assume you already know how to round.
A company that manufactures small canoes has a fixed cost of $24,000. It costs $80 to produce each canoe. The selling price is $160 per canoe. (In solving this exercise, let x represent the number of
canoes produced and sold.)
a. Write the cost function.
C(x) = 150 (Type an expression using x as the variable.)
Answer:
C(x)=2400 - 80x
Step-by-step explanation:
since 24000 is a fixed cost, lets put it was the y-intercept (the cost when no canoes are produced and sold). next subtract 160 from 80 to get the amount of cost gained for every canoe produced and sold. this value is -80, it is negative since the company is earning a profit for every canoe produced and sold. now you have your equation: C(x) = 2400 - 80x
What is 2+100009 it for my homework and I need it done today
Answer:
100011
Step-by-step explanation:
A bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents the first bus stop. The location of each stop after that is determined using the same relationships as those between the coordinates of the bus station and the first bus stop. A coordinate plane is titled Which point represents the fourth bus stop? A. (11, 8) B. (13, 12) C. (15, 10) D. (19, 12)
Answer:
D. (19,12)
Step-by-step explanation:
For each bus stop, the X coordinate increases 4, and the Y coordinate increases 2.
Name x y Point
bus station: 3 4 (3,4)
1st bus stop: 7 6 (7,6)
2nd bus stop: 11 8 (11,8)
3rd bus stop: 15 10 (15,10)
4th bus top: 19 12 (19,12)
Answer:
Step-by-step explanation:
19,12
If 14 out of 20 students in a college classroom are make, what percentage of the class is composed of men?
Answer:
70% of the class is composed of men.
Step-by-step explanation:
14: 20*100 =
(14*100): 20 =
1400: 20 = 70
math help please :) thxx
Answer: 15 inches
Step-by-step explanation:
15 × 1 ÷ 12 = 1.25 ft
1.25 ft = 1.25 × 12 = 15 in
Evan swims 321 laps in a month. He swims for 22 days in the month, How
many laps does he swim each day? Write your answer as a mixed number,
14 laps
14 13/22 laps
15 5/22 laps
14 7/22 laps
Answer:
Step-by-step explanation:
321
find the radius of a circle with an area of 100 in^2
I will give brainliest and 25 points!
Answer:
The answer is the following:
r≈5.64in
Answer:
5.641
Step-by-step explanation:
If you think about it, the formula for getting the area of a circle is:
[tex]a = \pi r^2[/tex]
So to rearrange and make r the subject, divide both sides of the equation by pi:
[tex]\frac{a}{\pi} = \frac{\pi r^2}{\pi}[/tex]
[tex]\frac{a}{\pi} = r^2[/tex]
Now square root both sides to find r:
[tex]\sqrt{\frac{a}{\pi} } = \sqrt{r^{2} }\\\sqrt{\frac{a}{\pi} } = r[/tex]
Plug the known area value in:
[tex]\sqrt{\frac{100}{\pi} } = r[/tex]
= 5.641
Hope this helps!
the value of 3 1/5 - 1 2/3 is?
please write the answer with sums and explanations
anyone with the correct answer will be given 10-20 points and will be marked as Brainliest
note: it's not 31 or 12 it's seperated
QUESTION :-
The value of 3 1/5 - 1 2/3ANSWER :-
[tex] = > \: \frac{16}{5} \times \frac{5}{3} \\ [/tex]Take Lcm by the denominator ( check the pic )
[tex] = > \: ( \frac{16 \times3 }{5 \times 3} ) \: = \: \frac{48}{15} [/tex][tex] = > \: ( \frac{5 \times 5}{3 \times 5} ) \: = \: \frac{25}{15} [/tex]Now subtract this
[tex] \frac{48}{15} - \frac{25}{15} = \: \frac{23}{15} [/tex]So , now ur ans is :-[tex] \frac{23}{15} [/tex]
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Answer:[tex] \large\rightarrow \tt 1 \frac{8}{15}[/tex]
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Explanation/Solution:To solve the problem, let's find the LCM or Latest Common Multiple.
[tex]\tt5 \underline{ | \tt5, \: 3} \\ \tt3 \underline{ \tt |1, \: 3} \\ \: \: \: \: \tt1, \: 1[/tex]
[tex] \rightarrow [/tex] LCM = 5 x 3 = 15
[tex] \\ [/tex]
Since the LCM is already finished let's solve for the both numerator and denominator.
[tex]\rightarrow \: \tt3 \frac{1 \times 3}{5 \times 3} = 3 \frac{3}{15} \\ \\ \rightarrow \: \tt1 \frac{2 \times 5}{3 \times 5} = 1 \frac{10}{15} [/tex]
Since both of the fractions cannot be subtracted from each other, then let's make it to a improper fraction.
[tex] \rightarrow \: \tt3 \frac{3}{15} = 3 \times 15 + 3 = \frac{48}{15} \\ \\ \rightarrow \: \tt1 \frac{10}{15} = 1 \times 15 + 10 = \frac{25}{15} [/tex]
Now its time to subtract.
[tex]\rightarrow \: \tt \frac{48}{15} - \frac{25}{15} = \frac{23}{15} \: \: or \: \: 1 \frac{8}{15} [/tex]
Therefore, the answer is 1 8/15.
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