Answer:
After 1st Dose:As Sophie has just taken the medicine, the quantity of drug present in her body is 500mg
After 2nd Dose:
Amount left from 1st dose = 4.5/100 × 500 = 22.5mg
Amount of Drug after 2nd dose = Amount left from 1st dose + 2nd dose taken.
Amount of Drug after 2nd dose = 22.5mg + 500mg
Amount of Drug after 2nd dose = 522.5mg
After 3rd Dose:
Amount left from 2nd dose = 4.5/100 × 522.5 = 23.513 mg
Amount of Drug after 3rd dose = Amount left from 2nd dose + 3rd dose taken.
Amount of Drug after 3rd dose = 23.513mg + 500mg
Amount of Drug after 3rd dose = 523.513 mg
After 4rth Dose:
Amount left from 3rd dose = 4.5/100 × 523.513 = 23.558mg
Amount of Drug after 4rth dose = Amount left from 3rd dose + 4rth dose taken.
Amount of Drug after 4rth dose = 23.558mg + 500mg
Amount of Drug after 4rth dose = 523.558 mg
Highest Amount:
The pattern formed above can be written in the form of sum of finite geometric series:
Sₙ = 500 + 500(0.045) +500(0.045)² + ........................500(0.045)ⁿ
Sₙ = 500(1 + 0.045 + 0.045² ........................0.045ⁿ)
Where
Sₙ = Sum till nth term
a = 500
r = 0.045
As Sophia takes medicines 2 times a day, she takes medicine 20 times in 10 days. So substitute n=20 in the formula for the sum of finite geometric series
[tex]S_n=a\frac{(1-r^n)}{1-r}\\S_{20}=500(\frac{1-0.045^{20}}{1-0.045})\\S_{20}=523.5602~\text{mg}[/tex]
Greatest amount of antibiotic present = 523.5602 mg
This amount is almost constant after 3rd dose, so it will occur after every dose after 3rd dose
Drug present in body at different points:
After 1st dose = 500mg
After 2nd dose = 522,5mg
After 3rd dose = 523.513 mg
After the the amount left in the body almost remains constant.
Which means that after each dose, the amount in body is maximum, at the end of the 12 hours, the amount reduces to 4.5%, which reaches almost the same maximum after taking another dose.
What value represents the horizontal translation from the graph of the parent function f(x)2 to the graph of the function g(x)=
(x-4)²+2?
-4
-2.
2
04
Answer:
4
Step-by-step explanation:
I graphed the functions on the graph below so you can see that the horizontal translation is represented by 4.
12x+7< -11 AND 5x−8≥40 need help asap
Answer:
B
Step-by-step explanation:
Let's solve 12x + 7 < -11.
12x < -18
x < -3/2
Solving 5x − 8 ≥ 40 we get:
5x ≥ 48
x ≥ 48 / 5
Since it says AND, the answer is no solution.
Describe the graph of y > mx, where m > 0. Plz wright it in your own words I do not want a "Sample Response" if it is I will not thank you and I will report you
Answer:
that graph will feature an area delimited by a line of slope m passing through the origin (0,0). Since m>0 the slope is positive, meaning the line goes up. Since the equation is y > mx, the inequality sign being >, that means the area represented will be ABOVE the line drawn.
Arya spins both spinners. What is the probability that Arya gets blue on both spinners? Give your answer as a fraction.
Answer:
2/16
Step-by-step explanation:
Since the total number on a spinner is 8 and there are 2 of them we get 8 + 8=16 and the blue one has 1 and they are 2 we get 1+1=2.
probability=desired chances/total chances
=2/16
The probability that Arya gets blue on both spinners is 2/16.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Since the total number on a spinner is 8 and there are 2 of them we get 8 + 8 = 16 and the blue one has 1 .
we get 1 + 1 = 2.
The probability that Arya gets blue on both spinners
= desired chances/total chances
=2/16
Learn more about probability here;
https://brainly.com/question/11234923
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Jane sold a radio costing sh.3800 at a profit of 20%.She earned a commission of 22 1/2% on the profit.Find the amount he earned
Answer:
20%=3800 => all of it is 19000
i didn't undrestand what do you want
sorry:)
Applying the recursive rule aₙ; a ₙ ₋ ₁ + 3, write the first seven (7) terms of the sequence when a = 10.
Answer:
First seven terms apart from 10 are
13, 16, 19, 22, 25, 28, 31
Step-by-step explanation:
Given recursive rule aₙ = a ₙ ₋ ₁ + 3
a1 = 10
[tex]x_{1} = 10\\x_{2} = x_{2-1} + 3= x_{1} + 3 = 10 + 3 = 13\\x_{3} = x_{3-1} + 3= x_{2} + 3 = 13 + 3 = 16\\x_{4} = x_{4-1} + 3= x_{3} + 3 = 16 + 3 = 19\\x_{5} = x_{5-1} + 3= x_{4} + 3 = 19 + 3 = 22\\x_{6} = x_{6-1} + 3= x_{5} + 3 = 22 + 3 = 25\\\x_{7} = x_{7-1} + 3= x_{6} + 3 = 25 + 3 = 28\\x_{8} = x_{8-1} + 3= x_{7} + 3 = 28 + 3 = 31[/tex]
Thus, first seven terms apart from 10 are
13, 16, 19, 22, 25, 28, 31
Using the quadratic formula, which of the following are the zeros of the quadratic equation below
Answer:
the answer for this question is D
Answer:
Correct answer is actually B
Step-by-step explanation:
I used someone’s answer with their work shown for my test
This is my last one please help you need to explain it just tell me the right answer thank you
Answer:
i might be 25
Step-by-step explanation:
Charge q is one unit of distance away from the source charge s. Charge p is two times further away. The force exerted between S and q is ? The force exerted between S and p.
Charge q is 1 unit of distance away from the source charge S. Charge p is two times further away. The force exerted between S and q is _____ the force exerted between S and p
a. 1/2
b. 2 times
c. 1/4
d. 4 times
Answer:
4 times
Step-by-step explanation:
Given the following :
Distance between q and S (r) = 1 unit
Distance between P and S (r) = 2 × 1 unit = 2
According to coliumbs law:
F = Ke(q1q2) /r^2
Where F = electrostatic force, Ke = coloumbs constant
q1,q2 = charges, r = distance between two charges
For q and S :
Fsq = Ke(q1q2) / 1^2
Fsq = Ke(q1q2) - - - - - equation 1
For P and S :
Fsp = Ke(q1q2) / 2^2
Fsp = Ke(q1q2) / 4 - - - - - equation 2
Dibiding equation 1 by equation 2
Fsq/Fsp = Ke(q1q2) / Ke(q1q2)/4
Fsq / Fsp = Ke(q1q2) × 4 / Ke(q1q2)
Fsq / Fsp = 4 / 1
Using cross multiplication
Therefore, Fsq = 4 × Fsp
Select the polynomial that is a perfect square trinomial. A. 49x^2 - 8x + 16 B. 4a^2 - 10a + 25 C. 25b^2 - 5b + 10 D. 16x^2 - 8x + 1
Answer:
(4x - 1)^2 = 16x^ - 8x + 1. This is a perfect square trinomial.
Step-by-step explanation:
Take a look at B: 4a^2 - 10 a + 25. The square roots of 4a^2 and 25 are 2a and 5 respectively. Does (2a - 5)^2 come out to 4a^2 - 10a + 25? No.
Take a look at C: 25b^2 - 5b + 10 We know this is not a perfect square trinomial because 10 is not a square.
D: 16x^2 - 8x + 1: both 16x^2 and 1 are perfect squares, so we have:
(4x - 1)^2 = 16x^ - 8x + 1. This is a perfect square trinomial.
N
(7x5 – 2x3 + 6) – (3x” – 4x3 – 2)
+
Answer:
67
Step-by-step explanation:
67 bcz
Answer:
67
Step-by-step explanation:
What is the nth term of the following sequence……… 8, 3, -2, -7………..explain clearly aswell
8, 3, -2, -7
basically
you have to figure how to get from one term to the other. so in this case, to get from 8 to 3, you have to minus 5. and same again to get from 3 to -2, you again have to -5.
so the first past of the answer is -5n.
then after that, you have to figure out how to get from -5, to the first term of your sequence. so you have to add 13, in this case.
your answer would then be
-5n + 13Answer:
-5x + 13
Step-by-step explanation:
to find the nth term, you must find the difference between each consecutive given terms.
So,
8 and 3 = -5
3 and -2 = -5
-2 and -7 = -5
This is the m in the equation mn+c
c is the value you must add to -5n when n is 1
Hope this helps
Work out m and c for the line: y = x + 4
Answer:
Step-by-step explanation:
When [(a2bc4)(ab3c2)]2(b2c5)3 is simplified, the exponent of b is Answer
all the numbers are roots and powers
Answer:
14
Step-by-step explanation:
We want to simplify [tex][(a^2bc^4)(ab^3c^2)]^2 (b^2c^5)^3[/tex] so as to find the exponent of b.
Let us expand all brackets:
[tex][(a^2bc^4)(ab^3c^2)]^2 (b^2c^5)^3\\\\= [a^3b^4c^6]^2 (b^{2*3}c^{5*3})\\\\= [a^6b^8c^{12}] (b^{6}c^{15})\\\\= a^6b^{8+6}c^{12 + 15}\\\\= a^6b^{14}c^{27}[/tex]
The exponent of b is 14.
Hi. Can somebody help me with this problem
Answer:
draw a table and calculate the x axis and find the x intercept
Step-by-step explanation:
Answer:
The correct answer is ..
(-1,-2)
Step-by-step explanation:
First, you reflect over the x-axis and get (1,-2) then reflect over the y- axis and the point will be on (-1,-2)
Hope this helps!
- Quinn <3
Help a chick out only if u know what u doing
Answer:
for 12:00 1 for 1:00 2
Step-by-step explanation:
this is a pattern where each number multiplies itself by 2 making 12:00 and 1:00 pm 1 and 2
edit: is it right? if it is, may I have brainliest?
Rectangle ABCD has vertices A(–6, –2), B(–3, –2), C(–3. –6), and D(–6, –6). The rectangle is translated so that the coordinates of the image are A’(–10, 1), B’(–7,1), C’(–7, –3), and D’(–10, –3). Which rule was used to translate the image? T–4, 3(x, y) T–4, 1(x, y) T4, –1(x, y) T4, –3(x, y)'
Answer:
T₋₄, ₃ (x, y)
Step-by-step explanation:
The coordinates of rectangle ABCD are;
A = (-6, -2)
B = (-3, -2)
C = (-3, -6)
D = (-6, -6)
The coordinates of the image are;
A' = (-10, 1)
B' = (-7, 1)
C' = (-7, -3)
D' = (-10, -3)
We note that for A and A', x - x' = -6 + 10 = 4 and y - y' = -2 - 1 = -3
For B and B', x - x' = -3 + 7 = 4 and y - y' = -2 - 1 = -3
For C and C', x - x' = -3 + 7 = 4 and y - y' = -6 + 3 = -3
For D and D', x - x' = -6 + 10 = 4 and y - y' = -6 + 3 = -3
Therefore, the transformation rule used to translate the image of rectangle ABCD is T₋₄, ₃ (x, y)
Answer:
T₋₄, ₃ (x, y)
Step-by-step explanation:
oblems
Congruency Pront
Name: Jarol
Comments
Statements
AC bisects BCD
Reasons
Given
Given
DCIAD
Given
BC AB
Given:
AC bisects BCD
DC I AD
BC AB
Right angles are =
Prove:
AC AC
BC DC
Bc z oo
Answer:
[tex]\overline{BC} \cong \overline{DC}[/tex] because corresponding parts of congruent triangles ΔACD and ΔACB are Congruent
Step-by-step explanation:
Statements, Reason
[tex]\overline{AC}[/tex] bisects ∠BCD, Given
[tex]\overline{DC} \perp \overline{AD}[/tex] Given
∠CDA ≅ ∠CBA Right angles are ≅
[tex]\overline{AC} \cong \overline{AC}[/tex] Reflexive property
ΔACD ≅ ΔACB Hypotenuse Leg (HL) congrurency
[tex]\overline{BC} \cong \overline{DC}[/tex] CPCTC
Where:
CPCTC = Corresponding parts of Congruent Triangles are Congruent
⊥ = Perpendicular to
≅ = Congruent
∠ = Angle
Δ = Triangle.
You don’t have to explain this just tell me the tight answer
Answer:
The triangles are similar by the AA similarity postulate
Step-by-step explanation:
The only thing we know is that the three angles are the same
70+30 +80 = 180 so the missing angle in each triangle is 80 in the first and 70 in the second
The triangles are similar by the AA similarity postulate
OKAY HELP so Raegan has a rectangular breadspread that is 238 cm by 435 cm. She wants to sew a fringe around the bread spread. what is the perimiter of the bed spread??? figured that out its 1346 but then it says raegan gets a new breadspread that is 27 cm longer. whats the perimiter now?
Answer:
The new perimeter is 1400 cm
Step-by-step explanation:
The perimeter of the bedspread is the perimeter of a rectangle, whose formula is:
Perimeter = 2 * width + 2 * length
Then the perimeter of the initial bed spread is:
Perimeter = 2 * (238 cm) + 2 * (435 cm) = 1346 cm
as you calculated.
Now, she gets a new bedspread that is 27 cm longer. So the new dimensions are 238 cm width, and (435 + 27) cm length, then the perimeter becomes:
Perimeter = 2 * (238 cm) + 2 * (462cm) = 1400 cm
A wedding ring costs £13000. Work out the price after a 11% price increase.
Answer:
£ 14430
Step-by-step explanation:
Costing price = £13000
Increase = 11% of 13000
=> 11/100 × 13000
=> 11 × 130
=> £ 1430
Increased Price = 13,000+1430
=> £ 14430
What value of x is in the solution set of 8x - 6 > 12 + 2x?
-1
e Of
3
5
Answer:
x > 3
Step-by-step explanation:
Step 1: Isolate x
6x -6 > 12
6x > 18
Step 2: Divide
x > 3
Find the value of each expression -7+12+15
Answer:
20
Step-by-step explanation:
Harun and Anis have m boys and n girls. How many children do they have?
Let f ( x ) = 5 x and g(x)=2x^2. (Need answer in less than 2 hours!)
Answer: (b) (g o g)(5)
Step-by-step explanation:
[tex]f(x)=\dfrac{5}{x}}\qquad g(x)=2x^2\\\\\\g(f(5)):\ f(5)=\dfrac{5}{5}=1\qquad g(1)=2(1)^2=2\\\\\\g(g(5)):\ g(5)=2(5)^2=50\qquad g(50)=2(50)^2=\large\boxed{5000}\\\\\\f(f(5)):\ f(5)=\dfrac{5}{5}=1\qquad f(1)=\dfrac{5}{1}=1\\\\\\f(g(5)):\ g(5)=2(5)^2=50\qquad f(50)=\dfrac{5}{50}=\dfrac{1}{10}[/tex]
What is the length, in units, of segment CD?
Answer:
The answet is C.
Step-by-step explanation:
First, you have to find the angle of ACB using Sine Rule, sinθ = opposite/hypotenuse :
[tex] \sin(θ ) = \frac{oppo.}{hypo.} [/tex]
[tex]let \: oppo. = 4 \\ let \: hypo. = 5[/tex]
[tex] \sin(θ) = \frac{4}{5} [/tex]
[tex]θ = {\sin( \frac{4}{5} ) }^{ - 1} [/tex]
[tex]θ = 53.1 \: (1d.p)[/tex]
Given that line AB is parallel to line CD so ∠C = 90°. Next, you have to find the angle of ACD :
[tex]ACD = 90 - 53.1 = 36.9[/tex]
Lastly, you can find the length of CD using Cosine rule, cosθ = adjacent/hypotenuse :
[tex] \cos(θ) = \frac{adj.}{hypo.} [/tex]
[tex]let \: θ = 36.9 \\ let \: adj. = 5 \\ let \: hypo. = CD[/tex]
[tex] \cos(36.9 ) = \frac{5}{CD} [/tex]
[tex]CD \cos(36.9) = 5[/tex]
[tex]CD = \frac{5}{ \cos(36.9) } [/tex]
[tex]CD = 6.25 units\: (3s.f)[/tex]
chameli has rupees 600 left after spending 75% of her money. how much did she have in the beginning
Answer:
Rs. 1050
Step-by-step explanation:
75/100×600= 7.5×60= 450+600= 1050
Hope this helps
can i have some help please?
Answer:
42°
Step-by-step explanation:
given OA and OC are perpendicular, the angle between the lines are 90°
this means that ∠AOB and ∠BOC add up to 90°, i.e.
(6x-6) + (5x+8) = 90
6x-6 + 5x+8 = 90
11x - 6 +8 = 90
11x + 2 = 90 (subtract 2 from both sides)
11x = 90- 2
11x = 88 (divide both sides by 11)
x = 8
Hence, m∠BOC
= 6x - 6
= 6(8) - 6
= 48 - 6
= 42°
A tram moved upward 18 meters in 6 seconds at a constant rate. what was the change in the trams elevation each second?
Answer:
3 meters per second.
Step-by-step explanation:
Change in elevation = distance / time
= 18/6
= 3 meters / second.
.
One fourth of a number is added to one fifth of the same number. If the result is 18, find the number
Answer:
[tex]40[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the number.
[tex]\frac{1}{4} x+\frac{1}{5} x=18[/tex]
[tex]\frac{9}{20} x=18[/tex]
[tex]x=18 \times \frac{20}{9}[/tex]
[tex]x=40[/tex]
If one fourth of a number is added to one fifth of the same number, and the result is 18, then the number = 40
Let the given number be represented by x
One-fourth of the number = x/4
One-fifth of the same number = x/5
One-fourth of the number is added to one fifth of the same number =
x/4 + x/5
The result is 18
This can be represented mathematically as:
x/4 + x/5 = 18
Simplifying the equation above
(5x + 4x)/20 = 18
Cross multiply
5x + 4x = 18(20)
9x = 360
x = 360/9
x = 40
The number = 40
Learn more on word problem here: https://brainly.com/question/21405634