Given:
[tex]f(x)=12(0.82)^x[/tex]
where, f(x) is the amount of a 12-mg dose of antibiotic left in her bloodstream after x hours.
To find:
The remaining mg in her bloodstream after 2 hours.
Solution:
The amount of a 12-mg dose of antibiotic left in her bloodstream after x hours is represented by the function
[tex]f(x)=12(0.82)^x[/tex]
Putting x=2, we get the remaining mg in her bloodstream after 2 hours.
[tex]f(2)=12(0.82)^2[/tex]
[tex]f(2)=12(0.6724)[/tex]
[tex]f(2)=8.0688[/tex]
Therefore, the remaining mg in her bloodstream after 2 hours is 8.0688 mg.
Answer:
8.07
Step-by-step explanation:
...
How many different committees can be formed from 10 teachers and 37 students of the committee consist of three teachers and two students? how many ways can the committee of five members be selected?
Answer:
79,920 different ways
Step-by-step explanation:
Combination has to do with selection:
If we are to select 3 teachers from a pool of 10 teachers to form a committee, this can be done in 10C3 number of ways.
10C3 = 10!/(10-3)!3!
10C3 = 10!/7!3!
10C3 = 10*9*8*7!/7!3!
10C3 = 10*9*8/3*2
10C3 = 720/6
10C3 = 120 ways
Similarly, selecting five 2 students from a pool of 37 students to form a committee, this can be done in 37C2 difference ways;
37C2 = 37!/(37-2)!2!
37C2 = 37!/35!2!
37C2 = 37*36*35!/35!*2
37C2 = 37*36/2
37C2 = 37 * 18
37C2 = 666 ways
Hence the total number of ways that the 5 committees can be selected is expressed as 10C3 * 37C3 = 120 * 666
120 * 666 = 79,920 ways
what is the answer to this equation
Step-by-step explanation:
Let's see
Firstly produce the line to Q such that it passes through and dives Q into two.
The interior angle of the Pentagon at the point Q=sum of its interior angle/5
The angle=540°/5=108°
That would make the exterior angle there=180°-108°=72°
Again,find the interior angle of the heptagon at the point Q=(sum of its interior angles)/7
Angle=900°/7=128.57°≈129°
That would make the exterior angle there=180°-129°=51°
Since Q was divided into the two exterior angles,we sum them up to obtain the angle value of Q
That is 51°+72°=123°
A restaurant sold tacos and burritos. Tacos cost $2.00 and burritos cost $1.00. The restaurant sold 48 items for a total of $86.00. Write a system of equations.
Answer:
blank 1-2x+y1=86
Blank 2- x+y=48
Step-by-step explanation:
Someone answer all 1-10 please
the tempature rises 36° F. each hour the tempature rises 6°F. write an equation that models the tempature y, in degrees Fahrenheit, after x hours
Before the holidays Apple wants to raise the price of the new iPhones. If the new iPhone 12 is
$839, and they want to markup the price by 15%. What is the new total cost?
Answer:
$964.85
Step-by-step explanation:
$839 x 1.15 = $964.85
The answer is 964.85. 964.85 would be the new total cost.
If the water level in a lake drops by 14 feet, the water level will still be higher than the 20-foot mark that triggers restricted water use. If L is the water level, which inequality and solution represents this situation?
A. L - 14 > 20; L > 34
B. L - 14 20; L > 6
D. L + 14 < 20; L < 6
Answer:
A is correct
Step-by-step explanation:
Here, we want to write an inequality
If the water level drops by 14 feet
what this mean is that we are subtracting 14 from the original level L
Thus, we have
L-14
Higher than 20 means that we have;
L-14 > 20
L > 20 + 14
L > 34
1st correcct will get brainliest
Answer:
it s A
Step-by-step explanation:
if the two to the power of ten is on the outside, you will always need to add that to the other powers of ten
Brianliest plz thanks
Sara works 40 hours per week and earns $660. Which graph shows the unit rate for this situation?
Answer: $16.5/hour
Step-by-step explanation:
The unit rate is the relationship between y and x if x = 1
660/40 = 16.5
That means, if x = 1, y = 16.5
Therefore, $16.5/hour
Can someone plz help me it is timed ill give Brainliest if it is correct
Answer:
b
Step-by-step explanation:
I had this exactl question a while ago
what was the average speed of the winner in miles per hour? Explain
Answer:
my mom
OOOO
Step-by-step explanation:
huh 12x*5
SCHOOL LUNCH In 2015, Ed spent $800 buying lunches. In 2017, he spent $300 buying lunches. What was the rate of change from 2015 to
2017? Plz help asap plz
The rate of change from 2015 to 2017 is -$250 per year.
Given that,
In 2015, Ed spent $800In 2017, Ed spent $300We need to find the rate of change.According to the scenario, computation of the given data are as follows,
Total change = $300 - $800
= -$500
Total years from 2015 to 2017 = 2 years
So rate of change = -$500 [tex]\div[/tex] 2
= - $250
Learn more : https://brainly.com/question/11833462
4 6/7 + 3 5/7 please help me
Answer: The answer is 60/7 or in mixed number form it is 8 4/7...
to make it easier, all you do is make the fractions improper and then add... If they didn't have the same denominator then you would make them have the same denominator. But they already have the same denominator... Or in other words convert the fractions into improper fractions, then find the LCD and combine... 34/7+26/7
34+26/7
60/7
decimal form: 8.571428
mixed number form: 8 4/7
Hope this helps... Stay safe and have a great day/night!! :D
Answer:
about 8.6, or 8.57142857143
Step-by-step explanation:
4 6/7 + 3 5/7
= 28+6/7 + 21+5/7
= 34/7 +26/7
= 60/7
= about 8.6
Write an equation in slope intercept form for the line that passes through the points (6,-3) and (0,2)
Answer: 14/6
Step-by-step explanation:
A line passes through point A(14,21). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.
Hey! I was wondering if you could give me some help with math?
[tex]1\frac{1}{9}*4\frac{1}{2}+(3\frac{1}{5}-\frac{1}{3} )[/tex]
Answer:
118/15 or 7.8666666666666666666666666666666666666666666666666666666666666666... decimal
Step-by-step explanation:
Simplify the following:
(1 + 1/9) (4 + 1/2) + 3 + 1/5 - 1/3
Put 1 + 1/9 over the common denominator 9. 1 + 1/9 = 9/9 + 1/9:
9/9 + 1/9 (4 + 1/2) + 3 + 1/5 - 1/3
9/9 + 1/9 = (9 + 1)/9:
(9 + 1)/9 (4 + 1/2) + 3 + 1/5 - 1/3
9 + 1 = 10:
10/9 (4 + 1/2) + 3 + 1/5 - 1/3
Put 4 + 1/2 over the common denominator 2. 4 + 1/2 = (2×4)/2 + 1/2:
10/9 (2×4)/2 + 1/2 + 3 + 1/5 - 1/3
2×4 = 8:
10/9 (8/2 + 1/2) + 3 + 1/5 - 1/3
8/2 + 1/2 = (8 + 1)/2:
10/9 (8 + 1)/2 + 3 + 1/5 - 1/3
8 + 1 = 9:
10/9×9/2 + 3 + 1/5 - 1/3
10/9×9/2 = (10×9)/(9×2):
(10×9)/(9×2) + 3 + 1/5 - 1/3
(10×9)/(9×2) = 9/9×10/2 = 10/2:
10/2 + 3 + 1/5 - 1/3
The gcd of 10 and 2 is 2, so 10/2 = (2×5)/(2×1) = 2/2×5 = 5:
5 + 3 + 1/5 - 1/3
Put 5 + 3 + 1/5 - 1/3 over the common denominator 15. 5 + 3 + 1/5 - 1/3 = (15×5)/15 + (15×3)/15 + 3/15 - 5/15:
(15×5)/15 + (15×3)/15 + 3/15 - 5/15
15×5 = 75:
75/15 + (15×3)/15 + 3/15 - 5/15
15×3 = 45:
75/15 + 45/15 + 3/15 - 5/15
75/15 + 45/15 + 3/15 - 5/15 = (75 + 45 + 3 - 5)/15:
(75 + 45 + 3 - 5)/15
| 1 |
| 7 | 5
| 4 | 5
+ | | 3
1 | 2 | 3:
(123 - 5)/15
| | 1 | 13
| 1 | 2 | 3
- | | | 5
| 1 | 1 | 8:
Answer: 118/15
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[tex]1 \frac{1}{9} \times 4 \frac{1}{2} + (3 \frac{1}{5} - \frac{1}{3} ) = \\ [/tex]
[tex] \frac{9 + 1}{9} \times \frac{8 + 1}{2} + ( \frac{15 + 1}{5} - \frac{1}{3} ) = \\ [/tex]
[tex] \frac{10}{9} \times \frac{9}{2} + ( \frac{16 \times 3}{5 \times 3} - \frac{1 \times 5}{3 \times 5} ) = \\ [/tex]
[tex] \frac{9 \times 10}{9 \times 2} + ( \frac{48}{15} - \frac{5}{15} ) = \\ [/tex]
[tex] \frac{10}{2} +( \frac{48 - 5}{15} ) = \\ [/tex]
[tex]5 + ( \frac{43}{15} ) = \\ [/tex]
[tex] \frac{75}{15} + \frac{43}{15} = \frac{118}{15} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
PLEASE I NEED HELP, ILY ILL GIVE 30 POINTS
Answer:
Question 1:
The angles are presented here using Autocad desktop application
The two column proof is given as follows;
Statement [tex]{}[/tex] Reason
S1. Line m is parallel to line n [tex]{}[/tex] R1. Given
S2. ∠1 ≅ ∠2 [tex]{}[/tex] R2. Vertically opposite angles
S3. m∠1 ≅ m∠2 [tex]{}[/tex] R3. Definition of congruency
S4. ∠2 and ∠3 form a linear pear [tex]{}[/tex] R4. Definition of a linear pair
S5. ∠2 is supplementary to ∠3 [tex]{}[/tex] R5. Linear pair angles are supplementary
S6. m∠2 + m∠3 = 180° [tex]{}[/tex] Definition of supplementary angles
S7. m∠1 + m∠3 = 180° [tex]{}[/tex] Substitution Property of Equality
S8. ∠1 is supplementary to ∠3 [tex]{}[/tex] Definition of supplementary angles
Question 2:
(a) The property of a square that is also a property of a rectangle is that all the interior angles of both a square and a rectangle equal
(b) The property of a square that is not necessarily a property of all rectangles is that the sides of a square are all equal, while only the length of the opposite sides of a rectangle are equal
(c) The property of a rhombi that is also a property of a square is that all the sides of a rhombi are equal
(d) A property of a rhombi that is not necessarily a property of all parallelogram is that the diagonals of a rhombi are perpendicular
(e) A property that applies to all parallelogram is that the opposite sides of all parallelogram are equal
Step-by-step explanation:
what is the value of x?
Answer:c
Step-by-step explanation:
Answer:
48
Step-by-step explanation:
[tex]x \degree = 180 \degree - (90 \degree + 42\degree) \\ \\ x \degree = 180 \degree - 132\degree\\ \\ x \degree = 48\degree \\ \\ x = 48[/tex]
What is
of 1 of 10?
5
Answer:
Pretty sure it's 2
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
7
y
450
X
Find the value of x and the value of y.
A. x = 16, y = 9V2
B. x = 7, y = 16 V2
C. x= 16V/, y = 7.12
D. x= 7/3, y = 16
Answer:
[tex]A.\ ~~x=16,~ y=9\sqrt{2}[/tex]
Step-by-step explanation:
We have completed the diagram with some lengths that come directly from the figure's symmetry.
Note the triangle formed at the left side of the trapezium is isosceles because it has an angle of 90° and another angle of 45°.
This means the base of the triangle has the same length as the height of 9.
This means the total base of the trapezium is x = 9 + 7 = 16
The right triangle must satisfy Pythagora's Theorem:
[tex]y^2=9^2+9^2[/tex]
[tex]y^2=2*9^2[/tex]
[tex]y=\sqrt{2*9^2}[/tex]
Simplifying the radical:
[tex]y=9\sqrt{2}[/tex]
The correct answer is: [tex]\mathbf{A.\ ~~x=16,~ y=9\sqrt{2}}[/tex]
Which expression uses the associative property to make it easier to evaluate
8(1.3)
A. 8(3
B. 43
C. (8)
D. (8)
Answer:
The answer to this question is A. 8(3/5*1/4).
Answer:
b
Step-by-step explanation
i think
Plz help me I’m behindddd
Answer: A; r = square root (S/4pi)
Step-by-step explanation:
1. Divide 4pi on both sides to get r^2 by itself so the left side becomes S/4pi (you do this because 4, pi, and r^2 are being multiplied together on the right side in the original equation so to cancel that out and get r by itself you do the opposite of multiplication)
The equation should now look like r^2 = S/4pi
2. Square root both sides including r to get rid of the r^2 so it becomes just r (also when you square root both sides, you square root all of S/4pi not just S or 4pi but the whole thing)
After you do that, you get r = square root (S/4pi) which is answer A
Hope this helps! :)
Anna can buy 3 sweatshirts for a total of $45.00. How much would it cost if she were to buy 5 sweatshirts at the same price. a.$15 b.$45 c.$60 d.$75 ?
I need help finding the slope
Answer:
slope=0.5
equation of the line= y=.5x+5
Step-by-step explanation:
[tex]x_{2}[/tex]-[tex]y_{2}[/tex]/[tex]x_{1}[/tex]-[tex]y_{1}[/tex] substitute your x and y values in
5.5-5/1-0=.5
5.5 is [tex]x_{2}[/tex] and 5 is [tex]y_{2}[/tex]
1 is [tex]x_{1}[/tex] and0 is [tex]y_{1}[/tex]
Hope this helps!
WILL NAME BRAINLEST ONGGG
Answer:
yes
Step-by-step explanation:
because they are all faced up and not touching each other
raul drove 80 miles.this represent 50% of the entire trip what is the total number of miles on raul trip
Answer:
its 160 miles
Pls helpp me ASAP!!!!!
Answer:
28,42,56, And 70..
Step-by-step explanation:
Its because after 14 count by 14 then get 70 4 more times.✌
Jordan has traveled 255 miles out of 340 miles on a trip. What percent of the total distance has he traveled?
A. 73%
B. 82%
C.75%
D. 70%
Solve for x.
14x + 18 + x = −112(x + 36) + 13
A
x = −6
B
x = −3
C
x = 3
D
x = 6
Answer:
x = -4037/127
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Step-by-step explanation:
Step 1: Define
14x + 18 + x = -112(x + 36) + 13
Step 2: Solve for x
Distribute -112: 14x + 18 + x = -112x - 4032 + 13Combine like terms: 15x + 18 = -112x - 4019Add 112x on both sides; 127x + 18 = -4019Isolate x term: 127x = -4037Isolate x: x = -4037/127Answer:
The correct answer is a.) x=-6
Step-by-step explanation:
what is the (gcf) of 18 and 72?
Answer:
18
Step-by-step explanation:
The GCF is also known as the greatest common factor. Every number can be written as the product of at least 2 numbers, and almost every number has at least one factor that is a prime number (or a number that is only divisible by 1 and itself).
Let's find the prime factorization of 18 and 72; in other words, let's find what prime numbers make these numbers up.
18 = 2 * 9 = 2 * 3 * 3 ⇒ notice that while 9 isn't a prime number, 2 and 3 are
72 = 2 * 36 = 2 * 2 * 18 = 2 * 2 * 2 * 3 * 3 ⇒ again, 2 and 3 are primes
In finding the GCF, we want to find the largest value of the prime numbers that the two numbers share.
Here, we see that both 18 and 72 have at least one factor of 2 and at least two factors of 3. So, that's the greatest common factor: 2 * 3 * 3 = 18.