Answer:
Child's dosage=60 milligram
Step-by-step explanation:
The correct formula is below
C= a/(a+12) ∙ A
Where,
C = child’s dosage in milligrams
a = age of the child
A = adult dosage in milligrams
a=6 year old
A=180 milligrams
C= a/(a+12) ∙ A
=6/(6+12)*180
=6/18*180
=1/3*180
=60
Child's dosage in milligram=60 milligram
Lapid.
(ii) Find the remainder when f(x) is
divided by (x - 1)(x + 2).
14) The remainder when the expression
ax' + bx + 2x + c is divided by x-1
is twice of that when it is divided by
x + 1. Show that c = 3a - b + 6.
ii) When a polynomial f(x) is divided by (x-1) and (x+2) it leaves remainder 5 and 17 respectively. find the remainder when f(x) is divided by (x-1) (x+2)
14) The remainder when the expression ax³ + bx² + 2x + c is divided by x-1
is twice of that when it is divided by x + 1. Show that c = 3a - b + 6.
Answer:
ii) R(x) = -4x + 9
14) c = 3a - b + 6 ( Proved)
Step-by-step explanation:
14) The correct expression is [tex]ax^3 + bx^2 + 2x + c[/tex]
To get the remainder when the expression [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by
x - 1, let x - 1 = 0; x = 1
Remainder:
[tex]R_1(x) = a(1)^3 + b(1)^2 + 2(1) + c\\R_1(x) = a + b + 2 + c[/tex]
When [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by x + 1
Let x + 1 = 0; x = -1
Remainder:
[tex]R_2(x) = a(-1)^3 + b(-1)^2 + 2(-1) + c\\R_1(x) = -a + b - 2 + c[/tex]
According to the question, R₁(x) = 2R₂(x)
a + b + 2 + c = 2(-a + b - 2 + c)
a + 2a +b - 2b + 2 + 4 = 2c - c
c = 3a - b + 6 ( Proved)
ii)
The dividend is f(x)
(x - 1)(x + 2) is the divisor, i.e. D(x) = (x - 1)(x + 2)
Let the quotient = A(x)
Let the Remainder, R(x) = ax + b..............(1)
Therefore, f(x) = A(x)D(x) + R(x)
f(x) = A(x)(x - 1)(x + 2) + R(x)...................(2)
When f(x) is divided by x - 1, x = 1
Put x = 1 into equation (2) knowing that R(1) = 5
f(1) = R(1) = 5
R(1) = a(1) + b = 5
a + b = 5....................(3)
When f(x) is divided by x + 2, x = -2
Put x = -2 into equation (2) knowing that R(-2) = 17
f(-2) = R(-2) = 17
R(-2) = a(-2) + b = 17
-2a + b = 17..................(4)
Subtracting equation (1) from (2)
-3a = 12
a = -12/3
a = -4
Substitute the value of "a" into equation (4)
-2(-4) + b = 17
8 + b = 17
b = 9
Since R(x) = ax + b
R(x) = -4x + 9
What's the difference?
Answer:
first one is the right one
Step-by-step explanation:
1+1(I want to give points back so i am doing this).Pay it Forward
Answer:
2
Step-by-step explanation:
thanks! i will do it too!
Select the equivalent expression. Thanks :)
Answer:
b
Step-by-step explanation:
(y^3 * 2^5)^2
3x2=6
5x2=10
y6x2^10
****PLEASE HELP BRAINLIEST IF ANSWERED****
What is the sum of the measures of the interior angles of a 9-gon? *
1800 degrees
360 degrees
1260 degrees
720 degrees
Answer:
its 1260°.
as by the formulae,
(n-2)×180°
we get,
sum of interior angle =(9-2)×180°
=1260°.....is anwer.
Work out the area of this circle.
Take it to be 3.142 and give your answer to 1 decimal place.
4 cm
→Answer:
[tex]50.3cm^2[/tex]
→Step-by-step explanation:
Well the formula for the area of a circle is [tex]\pi r^2[/tex].
→Given information
Pi is 3.142
radius is 4 cm
answer must be rounded to the nearest tenth
____________________________________________________________
So now we have to plug in the given information into the following formula [tex]\pi r^2[/tex].
(3.142)(4)^2
So now we have to solve this formula using PEMDAS.
So 4 squared is 16 and 16*3.142 is 50.272cm^2.
The question clearly states the given answer must be rounded into the nearest tenth so 50.272 is 50.3 cm^2.
__________________I do hope this helps!__________________________
factorising can someone plz helpw itht the last one than you
Answer:
3x^2(3+x)
Step-by-step explanation:
Answer: 3x^2(3+1)
Because it is divisible by 3 and x^2
What is the difference of the polynomials? (m^2n^2-7)-(mn+4)
━━━━━━━☆☆━━━━━━━
▹ Answer
m²n² - 11 - mn
▹ Step-by-Step Explanation
(m²n² - 7) - (mn + 4)
Remove the parentheses
m²n² - 7 - (mn + 4)
Calculate the difference
m²n² - 11 - mn
Final Answer
m²n² - 11 - mn
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
mn -11
Step-by-step explanation:
john asked 60 people there favourite fruit
Answer:
45
Step-by-step explanation:
it only has 15 people as liking pears so if you already have a angle of 60 for apples that is you solution
A ladder is used to scale a 13 foot wall. If the angle of elevation from the ground to the top of the wall has
to be 36 degrees, how tall must the ladder be?
Answer:
22.12feet
Step-by-step explanation:
the ladder becomes your hypotenuse,the wall is the height,this forms a right angled triangle and the angle of elevation forms at the base,use sine which is opposite over hypotenuse to get your answer
the value of x is: 12. 6. 2. None of the choices are correct.
Answer:
x=6
Step-by-step explanation:
The triangle is an equilateral triangle since all angles are 60 degrees
That means all sides are equal
3x-13 = x-1
Subtract x from each side
3x-13-x = x-1-x
2x-13 =-1
Add 13 to each side
2x= -1+13
2x = 12
Divide by 2
2x/2 =12/2
x = 6
Answer:
B. 6
Step-by-step explanation:
Two angles are 60 degrees, the other is also 60 degrees.
The triangle is an equilateral triangle.
All sides are equal.
3x - 13 = x - 1
3x - x = -1 + 13
2x = 12
x = 6
What is the value of
P(X = 2 or X = 0)
Enter your answer in the box
Answer:
0.4
Step-by-step explanation:
Answer: 0.4
Step-by-step explanation:
Study the diagram of circle K, where JL¯¯¯¯¯¯¯ and LM¯¯¯¯¯¯¯¯¯ are tangent to circle K at points J and M, respectively. Also, JL=3x+10 and ML=7x−6. What is the length of LM¯¯¯¯¯¯¯¯¯?
22
17.6
16
4
Answer:
22
Step-by-step explanation:
The answer is 22. You solve the equation 3x+10=7x-6 like so
3x+10=7x-6
-3 = -3
10= 4x-6
+6 = +6
16=4x
x=4
You then plug in the value of x to the equation for LM.
7x-6 becomes 7*4-6 which is 22.
Solve for x. Please help
Answer:
x = 37/45
Step-by-step explanation:
Here's how similar triangles work. We set up an equation as SIDE 1A/ SIDE 1B = SIDE 2A/ SIDE 2B
Ok, so these 2 triangles are similar, so we can set up a butterfly equation:
Side 1a would be 8x
Side 1b would be 5x +3
Side 2a would be 10x - 2
Side 2b would be 7x
----------------------------------------------------
Our equation would be
8x/(5x+3) = (10x-2)/7x
We cross multiply to get 8x(10x-2) = 7x(5x+3)
Instead of solving and getting squares, we can x on both sides and we get:
8(10x - 2) = 7(5x+3) ----> we simplify to get
80x - 16 = 35x + 21 ----> it's easy sailing from here.
45x = 37
x = 37/45
gosh i hope it's right...
An auditorium has its length, breadth, and height equal to 18m. How much air does it contain? An average adult person requires approximately 0.3 cu.M air per hour. The owner of auditorium organizes a concert there. But he limits the duration of concert 3 hours and allows only 6480 tickets to be sold. Why has the owner taken this decision?
Answer:
The volume of air in the auditorium = 5832 cubic meter
Step-by-step explanation:
Length, breadth, and height of the auditorium = 18m
Therefore, the volume of air in the auditorium
[tex]=18 \times 18 \times 18\\=5832 $ cubic meter[/tex]
An average adult person requires approximately 0.3 cu.M air per hour.
Therefore:
6480 adult person will require: 0.3 X 6480 = 1944 cu.M air per hour.
For three hours:
6480 adult person will require: = 1944 X 3 =5832 cubic meter of air
We notice that the volume of air in the room will be exhausted exactly after 3 hours when 6480 persons attend.
Therefore, the owner has taken this decision to avoid suffocation as an increase in the number of tickets or hours will cause such.
PLZ HELP This is due today and if I don’t finish I fail
Answer:
The solution ( 12,6) is correct, Lizette's solution
Answer:
[tex]x=12,\:y=6[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}\frac{2}{3}x+3y=26\\ 2x+\frac{1}{2}y=27\end{bmatrix}[/tex]
[tex]\frac{2}{3}x+3y=26[/tex]
[tex]\frac{2}{3}x+3y-3y=26-3y[/tex]
[tex]\frac{2}{3}x=26-3y[/tex]
[tex]3\cdot \frac{2}{3}x=3\cdot \:26-3\cdot \:3y[/tex]
[tex]2x=78-9y[/tex]
[tex]\frac{2x}{2}=\frac{78}{2}-\frac{9y}{2}[/tex]
[tex]x=\frac{78-9y}{2}[/tex]
[tex]\begin{bmatrix}2\cdot \frac{78-9y}{2}+\frac{1}{2}y=27\end{bmatrix}[/tex]
[tex]\begin{bmatrix}78-\frac{17}{2}y=27\end{bmatrix}[/tex]
[tex]78-\frac{17}{2}y=27[/tex]
[tex]78-\frac{17}{2}y-78=27-78[/tex]
[tex]-\frac{17}{2}y=-51[/tex]
[tex]2\left(-\frac{17}{2}y\right)=2\left(-51\right)[/tex]
[tex]-17y=-102[/tex]
[tex]\frac{-17y}{-17}=\frac{-102}{-17}[/tex]
[tex]y=6[/tex]
[tex]x=\frac{78-9\cdot \:6}{2}[/tex]
[tex]x=12[/tex]
[tex]x=12,\:y=6[/tex]
Korey is planning to open a comic book store. In his first year of operation, Korey expects to average $1,000 of profit each month. He then expects profits to increase by 6% each year for the next 4 years. How much does Korey expect to make in profits in his fifth year of operation? A = P (1 + r) superscript t
Answer:
Korey expects to make in profits in his fifth year of operation : 15149.73 dollars
Step-by-step explanation:
the first year : 1000 *12=12000
for the nest four years :12000(1+0.06)^4 = 15149.73
Korey expects to make in profits in his fifth year of operation : 15149.73
John used digits from 0 to 6 to create a three-digit PIN code. He forgot his PIN code. He remembers that his code contains different ascending digits. What is the maximum number of combinations John has to check to find his PIN code.
Answer:
35 combinations
Step-by-step explanation:
The first digit cannot be 5 or 6 (Since the digits could not be in ascending order if that was the case).
If the first digit is 4, there is 1 possibility:
(4, 5, 6)
If the first digit is 3, there are 3 possibilities:
(3, 4, 5) (3, 4, 6) (3, 5, 6)
If the first digit is 2, there are 6 possibilities:
(2, 3, 4) (2, 3, 5) (2, 3, 6) (2, 4, 5) (2, 4, 6) (2, 5, 6)
If the first digit is 1, there are 10 possibilities :
(1, 2, 3) (1, 2, 4) (1, 2, 5) (1, 2, 6) (1, 3, 4) (1, 3, 5) (1, 3, 6) (1, 4, 5) (1, 4, 6) (1, 5, 6)
If the first digit is 0, there are 15 possibilities:
(0, 1, 2) (0, 1, 3) (0, 1, 4) (0, 1, 5) (0, 1, 6) (0, 2, 3) (0, 2, 4) (0, 2, 5) (0, 2, 6) (0, 3, 4) (0, 3, 5) (0, 3, 6) (0, 4, 5) (0, 4, 6) (0, 5, 6)
Therefore, he would need to try at most 35 combinations.
LINEAR Equations HELP ASAP
Answer: D) -4/3
Step-by-step explanation:
Slop can be represented as [tex]\frac{rise}{run}[/tex]. This equation rises -24 units then runs 18. Thus, the slope is -24/18, or -4/3.
Hope it helps <3
Answer:
-4/3.
Step-by-step explanation:
To get the slope, you do the rise over the run.
In this case, the rise is going to be -24, since the track is falling. The run will be 18.
-24 / 18 = -12 / 9 = -4/3
Hope this helps!
please simplify this
Using this distribution, find the probability
that a teenager has 4 or more pairs of shoes
in their closet.
Answer:
P = 0.3
Step-by-step explanation:
Here, we are to use the probability distribution in the table to calculate the probability that a children has 4 or more shoes in his or her closet
When we say 4 or more, what we mean by this is that the teenager has 4 shoes or 5 shoes
In probability expressions, when we use the term ‘or’ we are simply talking about adding the terms involved
So what we can do here is to add the probability that the teenager has 4 shoes to the probability that the teenager has five shoes
From the table that would be; 0.1 + 0.2 = 0.3
Claim: Most adults would not erase all of their personal information online if they could. A software firm survey of 665 randomly selected adults showed that 49.5% of them would erase all of their personal information online if they could. Make a subjective estimate to decide whether the results are significantly low or significantly high, then state a conclusion about the original claim.
Answer:
State the null and alternate hypothesis which shows a probability value of 0.5 and greater than 0.5 on the one-tailed test to the right respectively. The sample proportion which gives a value of 0.5050. The standard error can then be calculated which gives a value of 0.01925. The Z statistic is then calculated as 0.2598. When compared to a P value of 0.3975, it can be concluded that the null hypothesis is not rejected given the p-value is greater than 0.5.
Therefore, given the not so significant values, there is no sufficient evidence that most adults will not erase their personal information online.
Step-by-step explanation:
With a 0.5 P value as null hypothesis and a an alternative hypothesis greater that 0.5 on a one tailed test. The sample proportion which gives a value of 0.5050. The standard error can then be calculated which gives a value of 0.01925. The Z statistic is then calculated as 0.2598. When compared to a P value of 0.3975, it can be concluded that the null hypothesis is not rejected given the p-value is greater than 0.5.
Therefore, given the not so significant values, there is no sufficient evidence that most adults will not erase their personal information online.
please help me answer this
Answer:
Train was late by 13 minutes.
Step-by-step explanation:
Time train took to travel = 290 miles / 50 mph
= 5.8 h
= 5h 48 min.
Time train left = 10:10 am
Time of arrival
= 10:10 + 5:48
= 15:58 pm
= 3:58 pm
Scheduled time of arrival
= 3:45 pm
Train arrived late by
3:58 - 3:45
= 0:13
= 13 minutes.
The diagram shows two straight lines. Work out the value of x
Answer:
136
Step-by-step explanation:
Answer:
136°
Step-by-step explanation:
The angle opposite of x and x are a pair of vertically opposite angles.
Vertically opposite angles are equal in size.
I will GIVE U Braniest! Which expressions can we use to describe the number of seconds it takes Mr. Golv to complete his jiu-jitsu drill 7 times? Choose 2 answers: (Choice A) 7(K+G) (Choice B) 2K+5G (Choice C) 7(5G-2K) (Choice D) 7(5G+2K) (Choice E) 14K+35G
Answer:
Option D and E
Step-by-step explanation:
Time for guard passes = 5G
Time for kimura arm locks = 2K
Altogether:
=> 5G+2K
If he does 7 times:
=> 7(5G+2K)
Simplified form:
=> 14K+35G
Answer:
Option D and E
Step-by-step explanation:
Time for guard passes = 5G
Time for kimura arm locks = 2K
Altogether:
=> 5G+2K
If he does 7 times:
=> 7(5G+2K)
Simplified form:
=> 14K+35G
Write the polynomial as a product: mn − mk + xk − xn
Answer:
m-x(n)+x-m(k)
Step-by-step explanation:
mn-mk+xk-xn
mn-xn+xk-mk
m-x(n)+x-m(k)
Hope it helps <3 :)
Answer:
m-x(n)+x-m(k)
Step-by-step explanation:
hope this helps :D
What is the area of the trapezoid below
Answer:
[tex]\boxed{Area = 130 units^2}[/tex]
Step-by-step explanation:
Area of trapezoid = [tex]\frac{a+b}{2} h[/tex]
Where a = 7, b = 19 and h = 10
Area = [tex]\frac{7+19}{2} (10)[/tex]
Area = (26)(5)
Area = 130 units²
Which functions have a vertex with a x-value of 0? Select three options.
f(x) = |x|
f(x) = |x|+ 3
f(x) = |x + 3|
f(x) = |xl - 6
f(x) = |x + 3|-6
Answer:
Hello!
________________________
(A) f(x) = |x|.
(B) f(x) = |x| + 3.
(D) f(x) = |x| - 6.
Would be correct!
Hope this helped you!
The functions that have a vertex with a x-value of 0 are:
f(x) = |x|
f(x) = |x|+ 3
f(x) = |xl - 6
An absolute value function is of the form:
f(x) = a|x - h| + k
where (h, k) represents the vertex
h is the x-coordinate of the vertex
k is the y-coordinate of the vertex
Comparing each of the options with f(x) = a|x - h| + k, the following absolute value functions have a vertex with x-value of 0.
f(x) = |x|
f(x) = |x| + 3
f(x) = |x| - 6
Learn more here: https://brainly.com/question/11212326
The midpoint of XY is M(0, 4). One endpoint is X(6, –2). Find the coordinate of the other endpoint Y. A.(–6, 10) B.(3, 1) C.(–6, 6) D.(12, 0)
Answer:
The answer is A.
Step-by-step explanation:
Given that the formula for midpoint is :
[tex]m = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
So you have to subtitute the coordinates into the formula :
[tex]let \: m = (0,4) \\ let \: (x1,y1) = (6, - 2)[/tex]
[tex](0,4) = ( \frac{6 + x2}{2} , \frac{ - 2 + y2}{2} )[/tex]
Next, you have to solve it by comparison :
[tex]x⇒ \\ \frac{6 + x}{2} = 0 \\ 6 + x = 0 \\ x = - 6[/tex]
[tex]y⇒ \\ \frac{ - 2 + y}{2} = 4 \\ - 2 + y = 8 \\ y = 10[/tex]
Use the Distributive Property to multiply. –5(2x – 5)\
Answer:
-10x +25
Step-by-step explanation:
–5(2x – 5)
Distribute
-5 * 2x - (-5) * 5
-10x +25
Answer:
-10x + 25
Step-by-step explanation:
-5(2x - 5)
Distribute the expression
-5(2x) + 5(5)
Multiply
-10x + 25
The expression cannot be simplified further
Hope this helps :)