Based on the number of tablets to be taken per day, the days supply for 30 tablets would be 10 days.
The patient is to take a tablet 3 times a day which means that they are to take:
= 1 x 3
= 3 tablets daily
If they have 30 tablets, this will last:
= Number of tablets / Tablets per day
= 30 / 3
= 10 days
In conclusion, it will take 10 days for the tablets to run out.
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The position of an object at any time t is given by
s(t)=3t4−40t3+126t2−9
.
1 Determine the velocity of the object at any time t.
2 Does the object ever stop changing?
3 when is the object moving to the right and when is the object moving to the left
Answer:
Step-by-step explanation:
I will ASSUME that your equation is
s(t) = 3t⁴ - 40t³ + 126t² - 9
1) velocity is the derivative of position
v(t) = s'(t) = 12t³ - 120t² + 252t
2) changing what? position? velocity? acceleration? gender? color?
position No the plot is continuous
velocity Yes both magnitude and direction. Zeros at t = 0, 3, and 7 s
acceleration Yes, both magnitude and direction. Zeros at approx. t = 1.306 and 5.361 s
gender? who knows
color? probably.
3) velocity is positive (moving to the right on a standard number line) for
0 < t < 3 and t > 7
Moves to the left for
t < 0 and 3 < t < 7
1. the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.
2. the object stops changing at t = 6 and t = 3.5.
3. the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.
To determine the velocity of the object at any time "t," we need to find the derivative of the position function "s(t)" with respect to "t."
1. Velocity of the object at any time "t":
The velocity is the rate of change of position with respect to time, which is given by the derivative of the position function, s(t).
s(t) = 3t⁴ - 40t³ + 126t² - 9
To find the velocity function, we take the derivative of s(t) with respect to t:
v(t) = d/dt (3t⁴ - 40t³ + 126t²- 9)
v(t) = 12t³ - 120t² + 252t
So, the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.
2. Does the object ever stop changing?
The object stops changing when its velocity becomes zero. To find when the velocity is zero, we need to solve the equation v(t) = 0.
12t³ - 120t² + 252t = 0
Now, we can factor out common terms:
t(12t² - 120t + 252) = 0
Now, set each factor equal to zero and solve for "t":
1st factor: t = 0
2nd factor: 12t² - 120t + 252 = 0
To solve the quadratic equation, we can either factor it further or use the quadratic formula. Factoring the quadratic equation gives us:
(t - 6)(12t - 42) = 0
Setting each factor to zero:
1. t - 6 = 0
t = 6
2. 12t - 42 = 0
12t = 42
t = 3.5
So, the object stops changing at t = 6 and t = 3.5.
3. When is the object moving to the right and when is the object moving to the left?
The object is moving to the right when its velocity (v(t)) is positive, and it is moving to the left when its velocity (v(t)) is negative.
Let's analyze the velocity function
v(t) = 12t³ - 120t² + 252t
To find the intervals where the object is moving to the right or left, we need to determine when v(t) is positive or negative.
1. Find critical points by setting v(t) = 0 and solving for "t":
12t³ - 120t² + 252t = 0
As we already found earlier, the critical points are t = 6 and t = 3.5.
2. Test each interval created by these critical points using test points to determine the sign of v(t) in those intervals.
Pick a value of "t" in each of these intervals:
- When t < 3.5 (e.g., t = 0),
- When 3.5 < t < 6 (e.g., t = 4),
- When t > 6 (e.g., t = 7).
Now, substitute these test values into the velocity function v(t):
- v(0) = 12(0)³ - 120(0)² + 252(0) = 0
- v(4) = 12(4)³ - 120(4)² + 252(4) = 192
- v(7) = 12(7)³ - 120(7)² + 252(7) = -588
Based on the test points, we can conclude:
- The object is moving to the right when 0 < t < 3.5 (positive velocity).
- The object is moving to the left when t > 6 (negative velocity).
Therefore, the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.
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y + y + y + y + ytytyty
Collect like terms
6. Suppose that a password for a computer system must have at least 6, but no more than 9 characters, where each character in the password is a lowercase English letter, or an uppercase English letter, or a digit, or one of the five special characters *, <, >,!, and #.
(a) How many different passwords are available for this computer system?
(b) How many of these passwords contain at least one occurrence of at least one of the five special characters?
(c) Using your answer to part (b), determine how long it takes a hacker to try ev ery possible password, assuming that it takes one microsecond for a hacker to check each possible password.
a. There are 26 letters in the English alphabet, with two cases for each letter; 10 numerical characters in the range 0-9; and 5 special characters; thus a total of 26•2 + 10 + 5 = 67 characters.
Any character can be used more than once, so there are
67⁶ + 67⁷ + 67⁸ + 67⁹
or 27,618,753,243,839,080 total possible passwords.
b. If we require at least 1 special character, then there are 62 choices for each ordinary character we use and 5 for each special character.
Suppose we use a password of length 6. Then there are
62⁵•5¹ + 62⁴•5² + 62³•5³ + 62²•5⁴ + 62¹•5⁵ + 62⁰•5⁶
or
[tex]\displaystyle \sum_{k=1}^6 62^{6-k}\cdot5^k[/tex]
We count the longer passwords in a similar fashion:
[tex]\displaystyle \sum_{m=6}^9 \left(\sum_{k=1}^m 62^{m-k}\cdot5^k\right)[/tex]
or 1,206,930,268,794,100 total passwords
c. 1 second (s) is equal to 10⁶ microseconds (μs). If it takes 1 μs to try 1 password, then it would take
(1,206,930,268,794,100 passwords) • (1 μs / password) • (1 s / 10⁶ μs)
= 1,206,930,268.7941 s
= (1,206,930,268.7941 s) • (1 min / 60 s)
≈ 20,115,504.4799 min
≈ (20,115,504.4799 min) • (1 h / 60 min)
≈ 335,258.408 h
≈ (335,258.408 h) • (1 day / 24 h)
≈ 13,969.1003 days
≈ (13,969.1003 days) • (1 year / 365 days)
≈ 38.2715 years
Please help! I'm confused
The solution to the equation f(x) = g(x) is any x-value that makes the equation true. In terms of using graphs, the solutions are the x-coordinates of any point of intersection.
So if the graphs intersect at (1,5), then the solution is x=1.
This checks, because f(1) = 5 and g(1) = 5, so f(1) = g(1).
11.2+X=-24.7. what is X
After doing some quick calculations, we can determine that X = −35.9
I hope this helps! :)
Answer:
x = -35.9
Step-by-step explanation:
Subtract both sides by 11.2 11.2 - 11.2 equals zero leaving x on one side.
x = - 24.7 - 11.2
A negative minus another negative number is a larger negative number.
x= -24.7 - 11.2 = -35.9
x = -35.9
which equation is the inverse of y=7x^2-10
Answer:
d
Step-by-step explanation:
Answer:
Step-by-step explanation:
Identify the figure and denote it by its appropriate symbol
ОА.
Half Line, AB
OB.
Ray
AB
O C. Line, AB
OD
Line Segment AB
What is the property used and the solution 4.(-3).5
Answer:
60
Step-by-step explanation:
using the bodmas
multiply 4 by -3
then multiply with 5
Quadrilateral ABCD has the following angle measures. Find the Measure of angle A.
B: 59°
C: 103°
D: 100°
Answer:
∠A = 98
Step-by-step explanation:
total sum of angles in a quadrilateral is 360
∠A + ∠B + ∠C +∠D = 360
∠A + 59 + 103 + 100 = 360
∠A + 262 = 360
∠A = 360- 262
∠A = 98
I need help , how do we know if the graph are positive or negative
Answer:
The negatives are at the bottom and the positives are at the top, if you need help with the (x,y) let me know!!!
Step-by-step explanation:
Answer:
right and above side of graph are positive
and
left and bottom side of graph are negative
BRINLEST WIL BE GIVIN
Answer:
[tex]\huge\boxed{-0.001a^{n+1}}[/tex]
Step-by-step explanation:
[tex]-0.001a^{3n+3}=-0.001a^{3(n+1)}=(-0.001a^{n+1})^3\\\\\text{Used}\\\\a(b+c)=ab+ac\qquad\text{distributive property}\\\\(a^n)^m=a^{n\cdot m}[/tex]
Warm-Up
Abena invited 40 people to a party.
How many came if 25% of those invited didn't come?
Answer: 30
Step-by-step explanation:
25% of forty is 10 so we minus 40 by 10 to see the remaining 75% which is our answer.
40 - 10 = 30
30 people came
The number of people attend the party is 30.
Given that, Abena invited 40 people to a party.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, 25% of 40
= 25/100 × 40
= 0.25 × 40
= 10
Number of people didn't come = 10
So, number of people came = 40-10=30
Therefore, the number of people attend the party is 30.
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The two tables below show the amount of tip, y, included on a bill charging x dollars.
A 2-column table with 3 rows titled Restaurant A. Column 1 is labeled x with entries 10, 20, 30. Column 2 is labeled y with entries 1, 2, 3.
A 2-column table with 3 rows titled Restaurant B. Column 1 is labeled x with entries 25, 50, 75. Column 2 is labeled y with entries 5, 10, 15.
Which compares the slopes of the lines created by the tables?
The slope of the line for Restaurant B is One-fifth times greater than the slope of the line for Restaurant A.
The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.
The slope of the line for Restaurant B is 5 times greater than the slope of the line for Restaurant A.
The slope of the line for Restaurant B is 10 times greater than the slope of the line for Restaurant A.
9514 1404 393
Answer:
(b) The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.
Step-by-step explanation:
The slope of the relation for Restaurant A is ...
y/x = 1/10
The slope of the relation for Restaurant B is ...
y/x = 5/25 = 1/5 = 2×1/10
The slope of the line for Restaurant B is 2 times as great as the slope of the line for Restaurant A.
Senna was having a party for 15 friends. She bought 3 jars of
pickles for $4.50. What is the cost per jar?
Answer:
it is 1.5
Step-by-step explanation:
if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5
The admission fee at a local zoo is $1.50 for children and $3.00 for adults. On a certain day, 2400 people enter the zoo and $4,800.00 is collected. How many children and how many adults?
Answer:
Step-by-step explanation:
c = children
a = adults
2200 people enter the zoo mean :
c + a = 2200
$4,550.00 is collected mean :
1.5 c + 4 a = 4550
Now you must solve system:
c + a = 2200
1.5 c + 4 a = 4550
c + a = 2200 Subtract c to both sides
c + a - c = 2200 - c
a = 2200 - c
1.5 c + 4 a = 4550
1.5 c + 4 ( 2200 - c ) = 4550
1.5 * c + 4 * 2200 - 4 c = 4550
1.5 * c + 8800 - 4 c = 4550
- 2.5 c + 8800 = 4550 Subtract 8800 to both sides
- 2.5 c + 8800 - 8800 = 4550 - 8800
- 2.5 c = - 4250 Divide both sides by - 2.5
c = - 4250 / - 2.5
c = 1700
a = 2200 - c = 2200 - 1700 = 500
1700 children and 500 adults
Proof :
c + a = 1700 = 2200
$ 1.5 * c + $ 4 * a =
$ 1.5 * 1700 + $ 4 * 500 =
$ 2550 + $ 2000 = $ 4550
The number of children and the number of adults are 1600 and 800, respectively.
What is the solution to the equation?The allocation of weights to the relevant variables that produce the calculation's optimum is referred to as a direct consequence.
A nearby zoo charges $1.50 for kids and $3.00 for adults to enter. 2400 persons visit the zoo on a certain day, and $4,800.00 is gathered.
Let x be the number of children and y be the number of adults. Then the equation is written as,
x + y = 2400 ...1
1.5x + 3y = 4800
x + 2y = 3200 ...2
Subtract equation 1 from equation 1, then
2y - y = 3200 - 2400
y = 800
Then the value of x is calculated as,
x + 800 = 2400
x = 2400 - 800
x = 1600
The number of children and the number of adults are 1600 and 800, respectively.
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50 pencils cost £3. How much would 8 pencils
cost
What is the answer
Answer:
0.48£
Step-by-step explanation:
(3x8)/50=0.48£
A dog park is divided into sections for large and small dogs. The ratio of the perimeter of the small dog section to the perimeter of the entire dog park is 7 : 12. Find the area of each section.
Answer:
58
Step-by-step explanation:
Sequences
3, 7, 11, 15, ____, _____
4, 8, 16, 32, ____, _____
9, 16, 25, 36, ____, _____
256, 64, 16, 4, ____, _____
50, 45, 34, 26, ____, _____
[] 3, 7, 11, 15, 19, 23
4 is being added
[] 4, 8, 16, 32, 64, 128
They are being multipled by 2
[] 9, 16, 25, 36, 49, 64
It is increasing the addition by 2s, first one is adding 7, then 9, then 11, etc
[] 256, 64, 16, 4, 1, 1/4
It is being divided by 4
[] 50, 45, 34, 26, ____, _____
I am currently unsure on this one, if I figure it out I will edit my answer to reflect that!
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Evaluate : X + 2 ( x -20) (4)
for x = 10
Answer:
x + 2 ( x - 20 )( 4 ) = -70
Step-by-step explanation:
hope this helps. . .<3
Find the 91st term of the arithmetic sequence 5, -14, -33, ...5,−14,−33,...
Answer:
1724
Step-by-step explanation:
first find the nth term = -19n+5
then do -19×91+5= 1724
A new yo-yo factory is operating at 80%
of capacity and produces 4,000 yo-yos
daily. When the factory reaches 100%
of capacity, how many yo-yos should be
produced each day?
Answer:
5,000 yoyos per day
Step-by-step explanation:
80 x 1.25 = 100
4,000 x 1.25 = 5,000
The length of a rectangle is 6 in less than 3 times the width. If the perimeter is 36 in, what is the width of the rectangle?
Answer:
width = 6
Step-by-step explanation:
We can think of the width as x and the height as 3x-6. the perimeter formula is (width + height)*2, since we have x as width and 3x-6 as height, we can put it in the formula, which will get you (x + 3x-6)*2 = 36, if we devide both sides by 2, we'll get (x + 3x - 6) = 18, when we simplify it, we will get 4x-6 = 18, which can then be simplified into 4x = 24, which will get you that x = 6
Hope it helped :)
WILL MARK BRAINLIEST IF CORRECT PLS HELP
Select the interval where h(x)< 0.
Choose 1 answer:
(А) -3.5
(в) -2 < x < -1
(C) 2.5
Answer:
Step-by-step explanation:
C
Where does -3/7 belong on the Venn diagram
A) integers
B) natural numbers
C)rational numbers
D) irrational numbers
Answer:
rational
Step-by-step explanation:
Answers:
A.113 cm^3
B.141 cm^3
C.565 cm^3
D.126 cm^3
Answer:
D. 126 cm³
Step-by-step explanation:
The formula for the volume of a cylinder in terms of its diameter can be written as ...
V = (π/4)d²h
The difference between the volume of the overall cylinder and the volume of the hole is ...
V = V2 -V1 = (π/4)(d2²)h -(π/4)d1²)h = (π/4)(d2² -d1²)h
V = (π/4)((6 cm)² -(2 cm)²)(5 cm) = (π/4)(36 -4)(5) cm³ = 40π cm³ ≈ 126 cm³
The volume of the solid cylinder with a hole in it is about 126 cm³.
C – 4 = 10 I need help with this question
Answer:
The answer is 14
Step-by-step explanation:
c - 4 = 10
c = 10 + 4
c = 14
Answer: c = 14
Step-by-step explanation:
14 - 4 = 10
Determine the x-intercept for 3x + 2y = 14,
A)
(7,0)
B)
(0,7)
C)
2,0)
D)
(0,14
Answer:
X-intercept: [tex](\frac{14}{3}, 0)[/tex].
Y-intercept: (0, 7) ⇒ Option B.
Step-by-step explanation:
I'm not certain whether the question asks for either the x-intercept or the y-intercept, but I will provide the answers for both since none of the given options matches the coordinates of the x-intercept.
X-intercept:The x-intercept is the point on the graph where it crosses the x-axis, with coordinates of (a, 0). The x-intercept is the value of x when y = 0.
Given the linear equation in standard form, 3x + 2y = 14, set y = 0 to solve for the x-intercept:
3x + 2y = 14
3x + 2(0) = 14
3x + 0 = 14
3x = 14
Divide both sides by 3 to solve for x:
[tex]\frac{3x}{3} = \frac{14}{3}[/tex]
[tex]x = \frac{14}{3}[/tex]
Therefore, the x-intercept is [tex](\frac{14}{3}, 0)[/tex]. None of the given option matches the value of the x-intercept.
Y-intercept:The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). It is the value of y when x = 0.
Set x = 0, and substitute into the given equation.
3x + 2y = 14
3(0) + 2y = 14
0 + 2y = 14
2y = 14
Divide both sides by 2 to solve for y:
[tex]\frac{2y}{2} = \frac{14}{2}[/tex]
y = 7
Therefore, the y-intercept is (0, 7), which matches Option B.
How do you evaluate (-12)3
Step-by-step explanation:
-1728 y'all i do by using calculator and it is correct
Answer:
its -1728
Step-by-step explanation:
i worked it out right.
Drag the descriptions of each investment in order from which will earn the least simple interest to which will earn the most simple interest.
Answer:
Hello! I know I am a bit late but for those who come here in the future,
This is the order (Least to Greatest)
1) 1,500 at 8% simple interest for 6 years
2) 1,500 at 6% simple interest for 10 years
3) 1,500 at 8% simple interest for 10 years
Hope this helps!
In situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
It is given for the three cases as,
P =$1500, R=8% , T = 10 years
P =$1500, R=8% , T = 6 years
P =$1500, R=6% , T = 10 years
The formula for the simple interest is,
Case 1,
SI = (P×R×T) / 100
SI = (1500×8×10)/100
SI = $ 1200
Case 2,
SI = (P×R×T) / 100
SI = (1500×6×10)/100
SI = $ 900
Case 3,
SI = (P×R×T) / 100
SI = (1500×8×6)/100
SI = $ 720
The simple interest for cases 1, 2, and 3 will be $ 1200, $ 900, and $ 720.
Thus, in situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.
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