Finding the Decay constant(λ):
λ = 0.693 / (half-life)
we are given that the half-life is 36 hours
λ = 0.693 / (36)
λ = 0.01925 /hour
Time taken for 87% decay:
Since decay is first-order, we will use the formula:
[tex]t = \frac{2.303}{decay constant}log(\frac{A_0}{A} )[/tex]
Where A₀ is the initial amount and A is the final amount
Let the initial amount be 100 mg,
the final amount will be 87% of 100
Final amount = 100*87/100 = 87 mg
Replacing the values in the equation:
[tex]t = \frac{2.303}{0.01925}log(\frac{100}{87} )[/tex]
[tex]t = \frac{2.303}{0.01925}*0.06[/tex]
t = 7.18 hours
We used 'hours' as the unit because the unit of the decay constant is '/hour'
Therefore, the drug will decay to 87% of initial dosage after 7.18 hours
At a summer camp, there are 15 counselors, 5 cooks, and 120 campers. 5 points
What is the ratio between the number of counselors and the number of campers for this summer camp?*
1:4
1:6
1:8
1:12
Pls answer asap!!
Please help me out here
Answer:
your answer is C) A negative radius does not make sense.
Step-by-step explanation:
hope it helps ^_^
Find ∠B in ABC if ∠A = 85° and ∠C = 11°
Answer:
a
Step-by-step explanation:
A.3(f) The line graphed on the grid represents the first of two equations in a system of linear equations.
20
-16
12
-8
-20 -16 -12
-
-4
48
12
16 2024
-8
-12
16
If the graph of the second equation in the system passes through (-12, 20) and (4,12), which statement is true?
I need help finding
sin B=
?
the options to choose from are
b/a
a/c
b/c
Answer:
the correct answer will be b/c
Gabrielle is 13 years older than Mikhail. the sum of their ages is 113. what is mikhails age?
Step-by-step explanation:
g=m+13
g+m=113
use substitution
Answer:
50 years old
Step-by-step explanation:
Let's say that Mikhail's age is x.
If so, Gabrielle's age would be 13 years older, therefore x + 13
We know that the sum of their ages is 113, so we can form this equation:
x + x + 13 = 113
Solving this equation, we get:
x + x = 100
2x = 100
x = 50
50 is Mikhail's age, so Gabrielle's age is 63
A bookstore costs $78 a day to keep open, and it spends $14 for each book
that it sells. If each book sells for $20, what is the break-even point for this
bookstore?
O A. n= 14
O B. n= 13
O C. n = 22
O D. n = 20
Answer:
13
Step-by-step explanation:
13
The break even point for this bookstore is n = 13.
What is Break-even Point?Break even point is the point where the total revenue and total cost are equal to each other. That is, person does not suffer from loss or does not acquire profit.
Given that,
Cost for the bookstore for a day to keep open = $78
Cost for each book = $14
Let n denote the number of books made or sold in a day.
Then total cost for n books = 78 + 14n
Selling price for each book = $20
Revenue from n books = 20n
Break even point is the point when,
Total revenue = total cost
20n = 78 + 14n
6n = 78
n = 13
Hence the break even point for the store is n = 13.
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THE amusement park won't allow kids to ride roller-coasters until they are a minimum of 48 inches tall. Michael is now 42 inches tall, and grows about 1/2 inch every month. How many months will it be until Michael can read a roller coaster? Please show me the individual steps?
Answer: It will one year (or 12 months) before Michael is able to ride the roller coaster.
Step-by-step explanation: Because he grows a half inch every month, this means that It takes him two months to grow one full inch. Because he has to grow six inches, you just multiply 2 by 6 to get 12 months or one year.
Answer:
48-42=6, which is how much Michael needs to grow.
1/2x=6, where x is the number of months
x = 12 months.
1 year = 12 months so the answer is one year.
How many pairs of intersecting lines are shown?
D
a. 24
b. 16
c. 8
d. 4.
Need help please confused
Answer:
a. 11.6 (rounded to nearest tenth)
b. Yes
Step-by-step explanation:
a²+b² = c²
6²+10² = c²
36²+100 = c²
136 = c²
√136 = √c²
11.6 = c
b. because 11.6 is the hypotenuse (longest side length) and there is 6 and 10 as the shorter leg lengths.
A ramp slopes upward
from the sidewalk to the entrance of a
building at a constant incline. If the
ramp is 2 feet high when it is 5 feet
from the sidewalk, how high is the
ramp when it is 7 feet from the
sidewalk
Answer:
4 feet
Step-by-step explanation:
hope this helps!!
Answer:
4ft
Step-by-step explanation:
Find the exact values of the solutions in the interval 0 <= x < 2pi of the following equations without using a calculator. a) 3sec(x) + 2 = 8
Answer:
a) [tex]x_{1} = \frac{\pi}{3}\,rad[/tex], [tex]x_{2} = \frac{5\pi}{3}\,rad[/tex], b) [tex]x_{1} = \frac{\pi}{4}\,rad[/tex], [tex]x_{2} = \frac{3\pi}{4}\,rad[/tex], [tex]x_{3} = \frac{5\pi}{4}\,rad[/tex], [tex]x_{4} = \frac{7\pi}{4} \,rad[/tex]
Step-by-step explanation:
a) We proceed to solve the expression by algebraic and trigonometrical means:
1) [tex]3\cdot \sec x + 2 = 8[/tex]
2) [tex]3\cdot \sec x = 6[/tex]
3) [tex]\sec x = 2[/tex]
4) [tex]\frac{1}{\cos x} = 2[/tex]
5) [tex]\cos x = \frac{1}{2}[/tex]
6) [tex]x = \cos^{-1} \frac{1}{2}[/tex]
Cosine has positive values in first and fourth quadrants. Then, we have the following two solutions:
[tex]x_{1} = \frac{\pi}{3}\,rad[/tex], [tex]x_{2} = \frac{5\pi}{3}\,rad[/tex]
b) We proceed to solve the expression by algebraic and trigonometrical means:
1) [tex]6\cdot \cos^{2} x = 3[/tex]
2) [tex]\cos^{2} x = \frac{1}{2}[/tex]
3) [tex]\cos x = \pm\frac{\sqrt{2}}{2}[/tex]
4) [tex]x = \cos^{-1} \left(\pm \frac{\sqrt {2}}{2} \right)[/tex]
There is one solution for each quadrant. That is to say:
[tex]x_{1} = \frac{\pi}{4}\,rad[/tex], [tex]x_{2} = \frac{3\pi}{4}\,rad[/tex], [tex]x_{3} = \frac{5\pi}{4}\,rad[/tex], [tex]x_{4} = \frac{7\pi}{4} \,rad[/tex]
HELLLP I WILL MARK YOU BRILLLLL
Answer:
5.6x=30
We move all terms to the left:
Step-by-step explanation:
5.6x-(30)=0
We move all terms containing x to the left, all other terms to the right
5.6x=30
x=30/5.6
x=5+2/5.6
A) 1080°
C) 720°
B) 1800°
D) 1620
Answer:
D- I hope I helped you. Good luck.
HELP ME PLEASE I WILL MARK BRAINLIEST
a) 50
b)12/6
.......................
HELP PLEASE ASAP What is the length of the diagonal of the square shown below?
Answer:
C) diagonal = 5√2
Step-by-step explanation:
diagonal² = 5² + 5²
diagonal² = 50
diagonal = √50
diagonal = √25x2
diagonal = 5√2
Answer:
C) diagonal = 5√2
Step-by-step explanation:
diagonal² = 5² + 5²
diagonal² = 50
diagonal = √50
diagonal = √25x2
diagonal = 5√2
what is the value of the underlined digit ? write your answers as as fraction
Answer: one place
Step-by-step explanation:
Write the Whole Number as a Fraction Over One.
Choose A New Denominator.
Multiply Both Numerator and Denominator.
I NEED HELP NOW PLZ!!!
Answer:
c
Step-by-step explanation:
x=-8
y= -5
therefore y=-5
and c is the answer
A store has clearance items that have been marked down by 35%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
in how many ways can a family of four be seated at a round table if two brothers must sit together a)1 b)8 c)2 d)4
Answer:
8
Step-by-step explanation:
i think this is right if not it would be 2
Answer plz!!! if you put a not so nice or relevent answer i will do the same...
Answer:
The answer should be B) T = 4.5n
Step-by-step explanation:
Answer:
B. T = 4.5n
Step-by-step explanation:
4.5 * n (the number of tickets sold) = T (Total money the school makes from the ticket money)
Which graph represents the relationship?
Answer:
option 3 is the answer of this
3x+4y = 12
Can you help solve please?
Answer: y = -3/4x+3
Step-by-step explanation:
3x+4y=12
4y=-3x+12
y = -3/4x+3
Solve this equation for a: 6a + 3 = 45
A.6
B.7
C.8
D.9
Answer: 7
Step-by-step explanation:
6 x 7 = 42
42+3 =45
Therefore 7 is the answer
Answer:
B. 7
Step-by-step explanation:
Answer to A. 6 = 6(6) + 3 = 39 (wrong answer)
Answer to B. 7 = 6(7) + 3 = 45 (correct answer)
Answer to C. 8 = 6(8) + 3 = 51 (wrong answer)
Answer to D. 9 = 6(9) + 3 = 57 (wrong answer)
I hope this helps :)
Help pls show work if needed!
Answer:
d = 50h
Step-by-step explanation:
We are using the linear property y = mx.
We know that distance = rate × time, so if we subsitute this, we get that the distance is d, the rate is 50 mph, and the time is h.
Therefore, we can form the equation d = 50h.
PLEASE HELP ON THIS QUESTION IVE BEEN STUCK ON IT FOR HOURS! WILL MARK BRAINLIEST ASAP!!
Your realized income from your primary job is $2,034.24/month. Your fixed expenses are 30% of your primary job’s realized income. You have a 2nd job that pays $9.50/hr with deductions of FICA (7.65%), federal tax withholding (11.5%), and state tax withholding (7.75%). If you want to save enough in the next 10 months to have an emergency fund that will cover 5 months using only 20% of your discretionary monies from your primary job, how many hours per month do you need to work at your 2nd job to meet your monthly savings goals?
The answer would be 3 hours.
Out of 4,000 colleges surveyed, 60% reported that SAT scores were not used as a high consideration in viewing their applications. How many schools view the SAT as important in screening applicants?
Answer:
Hi.
The first thing you want to know is how many schools 60% is.
To find 60%: 4,000 x 0.6 (b/c 0.6 = 60%)
so, 60% of 4,000 = 2,400
To find the number of schools that consider SAT scores:
Subtract 2,400 from 4,000 which, equals 1,600
or
Find the remaining percentage; 40%:
4,000 x 0.4 = 1,600
Answer: 1,600 colleges
I hope this helps a little bit.
tanx cscx= 1/f(x)
simplify and write the trigonometric expression in terms of sine and cosine
Answer:
f(x) = cos(x)
Step-by-step explanation:
tanx cscx = (sinx/cosx) * (1/sinx) = 1/cosx
1/f(x) = 1/cosx
f(x) = cos(x)
The given trigonometric equation in terms of sine and cosine is f(x)=cosx.
The given trigonometric function is tanx·cscx= 1/f(x).
What is the trigonometric equation?A trigonometric equation is one that involves one or more of the sixs sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.
We know that, tanx = sinx/cosx and cscx=1/sinx
Now, 1/f(x) = tanx·cscx
= sinx/cosx × 1/sinx
= 1/cosx
So, 1/f(x) = 1/cosx
Take inverse on both the side of equation, we get
f(x)=cosx
Hence, the given trigonometric equation in terms of sine and cosine is f(x)=cosx.
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9. Use the formula A=bh to find the area of the
rectangle below. Substitute' the appropriate
numbers for each variable and solve to find A,
the area.
10. L
of th
appr
solv
7 ft
4.5 ft
Answer:
31.5 ft²
Step-by-step explanation:
7x4.5=31.5 ft²
what is the first step to solve the equation 2x - 8 = 14