Using exponential functions, it is found that:
a) Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.
b) The patient could have ingest 231 milligrams of caffeine.
A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
Caffeine metabolize at a rate of 13% per hour, hence [tex]r = 0.13[/tex].Then:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = A(0)(1 - 0.13)^t[/tex]
[tex]A(t) = A(0)(0.87)^t[/tex]
Item a:
The coffee cup contains 150 milligrams of caffeine, hence [tex]A(0) = 150[/tex].
At 6 a.m., it is 8 hours after drinking the coffee, hence we have to find A(8).
[tex]A(t) = A(0)(0.87)^t[/tex]
[tex]A(8) = 150(0.87)^8[/tex]
[tex]A(8) = 49.2[/tex]
Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.
Item b:
This A(0), considering A(11) = 50, hence:
[tex]50 = A(0)(0.87)^{11}[/tex]
[tex]A(0) = \frac{50}{(0.87)^{11}}[/tex]
[tex]A(0) = 231[/tex]
The patient could have ingest 231 milligrams of caffeine.
A similar problem is given at https://brainly.com/question/25537936
The difference between interior angle in centesimal measurement and sexagesimal measurement is 15° of a regular polygon. Find the number of sides of the polygon.
Answer:
8
Step-by-step explanation:
x = centesimal angle (100 degrees in a right angle)
y = sexagesimal angle (90 degrees in a right angle)
x - y = 15
x×90/100 = y
x×9/10 = y
x - x×9/10 = 15
10x/10 - 9x/10 = 15
x/10 = 15
x = 150
y = 150×9/10 = 15×9 = 135
using centesimal system :
the sum of all external angles in a polygon is 400 degrees (a full circle).
one external angle is the complement of one internal angle to 200 degrees = 200-150=50 degrees.
to find the number of sides of the polygon we need to find the number of angles or corners. and that is how many external angles fit into the full circle.
n = 400/50 = 8
the polygon has 8 sides
complete the square x^2+45=-14x
What is the surface area of the cylinder?
•9377 ft2
•5787 ft2
•1,156 ft2
•2891 ft2
Answer:
3631.681108 ft^2
Step-by-step explanation:
The surface area of a cylinder is
SA = 2pi r^2 + 2pi r h where r is the radius and h is the height
= 2pi (17)^2 + 2 pi (17)(17)
= 578pi +578pi
= 1156pi
Approximate pi with the pi button
3631.681108 ft^2
I need help to find y=
Answer:
I know but I will not tell you have to do by self
State the slope of the line shown below (help ASAP)
Is it a, b, c or d?
Answer:
D
Step-by-step explanation:
(the above graph depicts a horizontal line that intersects the y axis at -2)
(so, y = -2)
Answer:
0
Step-by-step explanation:
Horizontal line x axis is 0 while the vertical y axis is undefined.
Here are the ages (in years) of 8 professors at a college.
61, 42, 61, 34, 49, 44, 36, 47
What is the percentage of these professors who are younger than 47?
Answer:
50%
Step-by-step explanation:
There are 8 professors. 4 of them are younger than 47 (not equal to 47, YOUNGER)
1. 42
2. 34
3. 44
4. 36
To find percentage we have to do 4/8 x 100
this equals to 50%
Evaluate the expression when b=4.
b^2-7b+3
Answer:
16-28+3 do it now ok!!!!!!
Answer:
If b=4,
b^2-7b+3
=4^2-7(4)+3
=16-28+3
=-9
Which inequality is represented by this graph?
Answer:
x> 0
Step-by-step explanation:
There is an open circle at 0 so this means it is not equal to
The line goes to the right so x is greater than
x> 0
Also the same as the other problem
Answer:
30-60-90
Step-by-step explanation:
A 30-60-90 triangle is a right angled triangle
Please mark it as brainliest if it helped
Answered by Gauthmath
Answer:
A (30 - 60 - 90) right triangle has the side ratios: [tex]x, x\sqrt{3}, 2x[/tex].
Step-by-step explanation:
A right triangle with the angle measures (30 - 60 - 90) is often referred to as a special right triangle becaase its sides follow the following ratio,
The side; Angle it's opposite to;
[tex]x[/tex] 30
[tex]x\sqrt{3}[/tex] 60
[tex]2x[/tex] 90
please help! look at picture!
Answer:
[tex]\frac{9}{8} = 1 \frac{1}{8}[/tex]
Step-by-step explanation:
2 [tex]\frac{7}{8}[/tex] = [tex]\frac{23}{8}[/tex]
1[tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex] = [tex]\frac{14}{8}[/tex]
[tex]\frac{23}{8}[/tex] -[tex]\frac{14}{8}[/tex] = [tex]\frac{9}{8} = 1 \frac{1}{8}[/tex]
Hey there! For this you will need to use the rule of subtracting fractions. 4 (the denominator) x 2 (to make it them equal) is 8. 3 x 2 is 6. The new fraction is 1 and 6/8. Now, subtract these to get your final answer, 1 and 1/8.
Hope this helps!
Please help, easy geometry work
Step-by-step explanation:
Find the slope of AB
: The slope is
[tex] \frac{7 - 0}{3 - 8} = - \frac{7}{5} [/tex]
Find the y intercept by plugging coordinates in
[tex]0 = - \frac{ 7}{5} (8) + b[/tex]
[tex]0 = \frac{ - 56}{5} + b[/tex]
[tex]b = \frac{56}{5} [/tex]
Find CD: We know that AB and CD are parallel to each other so this means they both have the same slope.
We can find the next point by subtracting 7 from the y coordinate of Point D, Adding 5 to the x coordinate of Point D.
Point C=(10,-2).
Find the y intercept by a plugging coordinates in
[tex] 5 = - \frac{7}{5} (5) + b[/tex]
[tex]5 = - 7 + b[/tex]
[tex]12 = b[/tex]
So the Equation of Line CD is
[tex] - \frac{7}{5} x + 12[/tex]
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x + 6)(x + 4)
B.
f(x) = (x + 6)(x − 4)
C.
f(x) = (x − 6)(x + 4)
D.
f(x) = (x − 6)(x − 4)
Answer:
C
Step-by-step explanation:
If x = a is a zero of f(x) then (x - a) is a factor of f(x)
Here the zeros are x = 6 and x = - 4 then the corresponding factors are
(x - 6) and (x - (- 4) ) , that is (x - 6) and (x + 4)
Then f(x) is the product of the factors
f(x) = a(x - 6)(x + 4) ( a is a multiplier )
If a = 1 , then
f(x) = (x - 6)(x + 4) ← is a possible choice → C
Answer:
С.
Step-by-step explanation:
f(x) = (x − 6)(x + 4)
x-6=0
x1=6
x+4=0
x2=-4
Find the area of the triangle.
Answer:
B
Step-by-step explanation:
area=1/2×32×6.1=16×6.1=97.6 yd²
Answer:
Choice B. 97.6 yd^2
Step-by-step explanation:
B×W×.5= A
Please help
Solve for x
Answer:
X=15 since it the same
Step-by-step explanation:
X is simply equal to 15 because it an equilateral triangle
Two numbers have a sum of 35 and an
LCM of 42. What are the two numbers?
HELP PLEASE <3
Answer:
14, 21
Step-by-step explanation:
LCM : least common multiplier.
x + y = 35
LCM = 42
means that there is a combination of 2 of the following divisors of 42 :
2, 3, 6, 7, 14, 21
so, which two of these numbers can create the sum of 35 ?
only 14 and 21
Suppose f(x) = x^2. what is the graph of g(x)
Answer: g(x) = (1/16)*x^2
========================================================
Explanation:
Plug x = 4 into f(x) to find that f(4) = 16.
The output y = 16 drops to y = 1. We've multiplied by 1/16 to get this to happen.
In other words,
g(x) = (1/16)*f(x)
g(4) = (1/16)*f(4)
g(4) = (1/16)*16
g(4) = 1
So we can say that,
g(x) = (1/16)*f(x)
g(x) = (1/16)*x^2
and furthermore, we can say f(x) has been vertically compressed by a factor of 16.
3. In a primary election, 35% of voters voted for Goron, 15% voted for Smith, 40% voted for Fishman, and 10% voted for other candidates. (a) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work. (b) Forty people voted for "Other." Was the estimate of total voters from Part (a) accurate? Explain.
Answer:
98 ppl voted for Gordan
Step-by-step explanation:
a) 35% of 280=98
b) 15% of 280=42
40% of 280=112
10% of 280=28
Add 98, 42, 112, and 28 and you get 280! Hope this helps :)
Can someone help me
Answer:
G' (-2,-1) F' (-5,0) E' (-4,3)
Step-by-step explanation:
This is because R90(x,y)=(-y,x)
G(-1,2)=G'(-2,-1)
F(0,5)=F'(-5,0)
E(3,4)= E'(-4,3)
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answer:
Value of tan( π/3 ):
[tex]{ \tt{ \frac{\pi}{3} = \frac{180}{3} = 60 \degree }}[/tex]
60° lies within the first quadrant.
[tex]{ \sf{ \tan( \frac{ \pi}{3} ) = ( \frac{1}{2} , \: \frac{ \sqrt{3} }{2}) }}[/tex]
Since it's a half:
[tex]{ \boxed{ \sf{ \tan( \frac{\pi}{3} ) = \sqrt{3} }}}[/tex]
Length of hypotenuse:
[tex]{ \bf{ \sin(31 \degree) = \frac{16.5}{h} }} \\ { \sf{h = 32.04}}[/tex]
Hypotenuse = 32.0
Four thousand runners began the marathon. Eighty-nine percent of them completed the run. What percentage of the runner finished the marathon?
Answer:
3560 people.
Step-by-step explanation:
You have to do 89% × 4000.
Or 0.89×4000=3560.
So 3560 is the answer.
A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. To test this claim, he selects random samples of each type of car, and records the prices. The standard deviation of 16 convertibles is $6800 and the standard deviation of 24 station wagons is $3900. For , what is the p-value? Group of answer choices
Answer:
Hence the critical value for the right-tailed test is [tex]F_{15,23,0.05}=2.1282[/tex]. Since the test value is greater than the critical value so we reject the null hypothesis.
Step-by-step explanation:
Hypotheses are:
[tex]H_{0}:\sigma_{1}^{2}=\sigma_{2}^{2}\\H_{a}:\sigma_{1}^{2}>\sigma_{2}^{2}[/tex]
Here we have s_{1}=6800 and s_{2}=3900. Here we will use F -test. The Value of test statistics is
[tex]F=\frac{s_{1}^{2}}{s_{2}^{2}}\\\\F=\frac{6800^{2}}{3900^{2}}\\\\F=3.0401[/tex]
Here the degree of freedom of the numerator is [tex]df_{1}=n_{1}-1=16-1=15[/tex] and The degree of the denominator is
[tex]df_{2}=n_{2}-1 \\\\=24-1=23 .[/tex]
The critical value for the right-tailed test is [tex]F_{15,23,0.05}=2.1282[/tex]. Since the test value is greater than the critical value so we reject the null hypothesis.
Answer:
Step-by-step explanation:
the perimeter of equilateral triangle is 21m. Find the area. Using Heron's Formula
plzzz answer fast i will mark brainliest.
Answer:
A ≈ 21.22 m²
Step-by-step explanation:
The area (A) of a triangle using Heron's formula is
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s is the semi perimeter and a, b, c the sides of the triangle.
Here the perimeter of the equilateral triangle is 21 m , then
a = b = c = 21 ÷ 3 = 7 m
s = 21 ÷ 2 = 10.5
Then
A = [tex]\sqrt{10.5(10.5-7)(10.5-7)(10.5-7)}[/tex]
= [tex]\sqrt{10.5(3.5)(3.5)(3.5)}[/tex]
= [tex]\sqrt{450.1875}[/tex]
≈ 21.22 m² ( to 2 dec. places )
14. Peter needs to buy a package of pencils to write his final exam. The store offers two packages.
Package 1: pack of 6 pencils for $1.68
Package 2: pack of 9 pencils for $2.34
Determine the cost per pencil. Which is the better deal? Round to 2 decimal places. Show all your work for full marks. (3 marks)
Please help me solve this I’ve been trying all day it’s impossible for me
Answer:
36; 18; -35; 0
Step-by-step explanation:
They break even again when their profit is zero, i.e. at the x-intercept (36).
The worst case scenario is when their profit is the lowest, i.e. at the minimum vertex where they produce 18 items for a profit (in this case loss) of -35 dollars.
The first root tells us that the profit will be zero when zero products are produced.
Alaina wants to decide whether her current cell phone plan is better than a package that another company offers. To compare the two plans, she plotted two lines on a graph, where y represented the total cost of one month’s service and x represented the megabytes of data that she used in a month. Which part of the graph will represent the cost per megabyte of data used in each plan?
Answer:
The y-intercepts of the two lines will represent the cost per megabyte of data used in each plan.
Step-by-step explanation:
i also took the test
Answer:
The y intercept forms the two lines.
Step-by-step explanation:
I just took the test
The number of pairs of corresponding angles formed by a transversal of two
lines is
Answer:
When a transversal intersects with two parallel lines eight angles are produced. The eight angles will together form four pairs of corresponding angles.
URGENT!!! ABCD is parallelogram. If m
Answer:
angle BAD= angle BCD = 100
then,
angle BCD + angle ECD = 180
100+ angle ECD = 180
angle ECD= 180-100 = 80
angle ECD =80
Solve the equation by finding square roots. x2-1/4=0
Answer:
x = ±1/2
Step-by-step explanation:
x^2-1/4=0
Add 1/4 to each side
x^2 -1/4+1/4 = 0+1/4
x^2 = 1/4
Take the square root of each side
sqrt(x^2) = sqrt(1/4)
x = ±1/2
What is the value of x?
Answer:
x=5
Step-by-step explanation:
Since both of these length are equal, 6x+4=8x-6, 2x=10, x=5
Câu 2. Cho hình thang cân ABCD (AB // CD, AB CD). Gọi O là giao điểm của AD và BC, E là giao điểm của AC và BD. Chứng minh rằng: | a) Tam giác AOB cân ở O.
b) Các tam giác ABD và BAC bằng nhau. C) EC = ED
d) OE là trung trực của AB và CD.
Answer:
Step-by-step explanation:
