Given:
15 mL of a solution contains 75 mg of medication.
To find:
How many mg of medication are in 60 mL of solution?
Solution:
We have,
Medication in 15 mL of a solution = 75 mg
Medication in 1 mL of a solution = [tex]\dfrac{75}{15}[/tex] mg
= [tex]5[/tex] mg
Medication in 60 mL of a solution = [tex]60\times 5[/tex] mg
= [tex]300[/tex] mg
Therefore, 60 mL of a solution contains 300 mg of medication.
Determined the perimeter and area of the following figure. Use 3.14 for pi
Step-by-step explanation:
first you will put a line in the missing part of the inside of the figure.Once you do you will see that there are two figures.
to find the diagonal of the half-circle : 7cm-2cm-1cm=4cm
Now use the area formulas for each figure.The area of the semicircle is pi×d/2.The area of the rectangle is a×b.
A of semicircle =3.14×4cm/2=6.28cm²
A of rectangle =7×3=21cm²
to find the perimeter of them:
P of semicircle = 3.14×4=12.56cm
P of rectangle =2(7+3)=14+6=20cm
PLEASE HELP 100 POINTS!!! PLEASE DON'T ANSWER IF YOU DON'T KNOW!!
Alana and Kelsa are training for a marathon. To prepare for this marathon they have been training and tracking their progress periodically.
In the first week of training Alana ran an average of 20 minutes per mile. Later, in week seven of training she ran an average of 14 minutes per mile.
In the first week of training Kelsa ran an average of 15 minutes per mile. Later, in week five of training she ran an average of 13 minutes per mile.
Assuming that Alana and Kelsa continue to train and improve their times at the same rate your task is to determine which week they will have the same average minutes per mile. We will assume that the relationship is linear as they will be training for a maximum of 43 weeks. To complete this task follow the steps below.
1. Determine the equation of a line in standard form that represents Alana’s training progress. Her progress corresponds to the points (1, 20) and (7,14).
2. Determine the equation of a line in standard form that represents Kelsa’s training progress. Her progress corresponds to the points (1, 15) and (5,13)
3. Solve the system of equations (you must show all your work to receive full credit).
4. In which week will Alana and Kelsa have the same average minutes per mile?
5. If Alana and Kelsa continue to train until week 30, what will their times be?
6. Do you believe a linear model best represents the relationship of the time of the runners and the weeks that passed?(Hint: look at question 5). What do you think this says about problems in the real world? Justify your thoughts in 3-4 sentences.
Answer: Alana's training experience in (weeks, minutes per mile) is (1, 12) and (5, 6).
Kelsa's training experience is (1, 10), (11, 5).
Find:
A linear equation in standard form that describes Alana's experience
A linear equation in standard form that describes Kelsa's experience
A solution to the pair of linear equations
The week in which the number of minutes per mile is the same
Minutes per mile for Alana and Kelsa at week 25
Comment on the use of a linear model in this context
Solution:
Please note that in parts 1 and 2 a "standard form" linear equation has a positive leading coefficient and the numbers have no common factor.
1. A linear equation can be written from two points (x1, y1) and (x2, y2) as ...
... (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
Using the given points in order, this becomes
... (6-12)(x -1) -(5 -1)(y -12) = 0 . . . . above equation with values filled in
... -6x +6 -4y +48 = 0 . . . . . . . . . . eliminate parentheses
... 3x +2y -27 = 0 . . . . . . . . . . . . . divide by -2 to make x-coefficient positive
... 3x +2y = 27 . . . . . . . . . . . . . . . . Alana's training experience
2. In similar fashion, we can write the equation for Kelsa's experience.
... (5 -10)(x -1) -(11 -1)(y -10) = 0
... -5x +5 -10y +100 = 0 . . . . . . eliminate parentheses
... x +2y -21 = 0 . . . . . . . . . . . . . divide by -5
... x +2y = 21 . . . . . . . . . . . . . . . . Kelsa's training experience
3. We note that both equations have the term 2y, so we can subtract the second equation from the first to eliminate that term:
... (3x +2y) -(x +2y) = (27) -(21)
... 2x = 6 . . . . . . . simplify
... x = 3 . . . . . . . . divide by 2
... 3·3 +2y = 27 . . . substitute x=3 into Alana's equation
... 2y = 18 . . . . . . . . subtract 9
... y = 9 . . . . . . . . . . divide by 2
The solution is (weeks, minutes) = (x, y) = (3, 9).
4. The solution of part 3 tells us both have an average time of 9 minutes per mile in week 3 of training.
5. Substituting x=25 into the equations of parts 1 and 2, we get ...
... 3·25 +2y = 27
... y = (27 -75)/2 = -24 . . . . Alana's time per mile at week 25
... 25 + 2y = 21
... y = (21 -25)/2 = -2 . . . . . Kelsa's time per mile at week 25
6. A linear model makes no sense in this context. At some point a linear equation for minutes per mile will always have a value of 0. We know that marathon runners will never have a time of zero minutes per mile. Under the best of conditions, we expect training to improve time toward some asymptotic limit determined by body mechanics. A linear model is completely inappropriate for describing such training effects. Not every real-world problem is appropriately represented by a linear equation.
Step-by-step explanation:
36= W/4 what does w equal ???????????///
Answer:
W=144
Step-by-step explanation:
36=w/4
36 times 4=w/4 times 4
144=W
Answer:
144
Step-by-step explanation:
144/4=36 36x4=144
(4) + (14 – 4i) =
Express your answer in the form (a + bi).
Answer:
I would recommend using photomath and math away for stuff like this :D
Step-by-step explanation:
use these apps save you lot of time
PLEASE Help mE wiTh the two QUESTIONS
Answer:
the coefficient 2 is the slope (each coordinate is 2 units up and 1 unit right from the previous unit)
the constant 3 is the y-intercept (0, 3)
Step-by-step explanation:
i need urgent help
this is my maths work
Answer:
A. only inequality 1.
Step-by-step explanation:
The inequality 1 can be written as
- 5 = 1 - 3d
- 5 - 1 = - 3d
- 3d = - 6
d = 2
Now the inequality 2 can be written as
- 1 =( 1 - d) / 3
- 3 = 1 - d
d = 1 + 3
d = 4
So the answer is A only inequality 1.
Hope it will help :)
can someone please help
Answer:
x=3, y= - 2
Step-by-step explanation:
4x + 3y = 6
x-3y= 9
x=9+3y
4.(9+3y)+3y=6
36+12y+3y=6
15y = - 30
y = - 2
=> x= 9+3y
x= 9+ 3.(- 2)
x= 3
can someone actually help?
Answer:
[tex]5\sqrt{2} =7.07106781187[/tex]
Step-by-step explanation:
i hope this was what you were looking for
The art club had an election to select a president. 79 members voted in the election and 21
did not vote. What percentage of the members voted?
Answer:
79%
Step-by-step explanation:
Solve for Y
13= 4y+5
y=?
Please help this is my last question and it’s due by 10 PM
sorry there’s only 11 points •.•
Help me please...........
Answer:
6/19
Step-by-step explanation:
Answer:
6/19 subtracting 3 each time form the numerator
Step-by-step explanation:
Given the function g(x) = -3x + 4, compare and contrast g(-2) and g(4). Choose the statement that is true concerning these two values.
Answer: D
Step-by-step explanation:
Fill in the x's with -2 for the first time to get one answer then go back and fill in 4 for the second answer.
g(-2)= 10
g(4)=-8
Proving g(-2) is greater than g(4).
Solve the system of equations using elimination. SHOW WORK!!!!!!!!!!!!!
15q – 4r = 62
5q + 8r = 86
q= 6
r= 7
work--
Multiply 1st column by -2:
-30q+8r=-124
5q+8r=86
Subtract 2nd column from the first column:
-35q= -210
Solve for q:
q=6
Subtract q=6 by any of the two equations, so:
-30q+8r=-124
-30*6+8r=-124
Solve for r:
r=7
394.6 divided by 2 plssss help
Answer: 197.3 ok bye
Step-by-step explanation:
Answer:
197.3
Step-by-step explanation:
HELP PLS MY MOM WILL BEAT ME HELP THXS
Answer:
Solution is the missing word.
Step-by-step explanation:
Answer:
Solution
Step-by-step explanation:
8 cm
4 cm
18 cm
16 cm
please hurry
Answer:
288
Step-by-step explanation:
11) Elsa took out a $2,200 loan with a 2-year term to buy a car at a 6% simple interest rate. How much will she have to pay IN INTEREST? *
Answer:
$264
Step-by-step explanation:
A 6% interest means that you have to pay 6% of the loan every period (which in this case is a year because it isn't stated anywhere). 6% of $2.200 is equal to $132, so for a loan of 2 years Elsa has to pay [tex]\$132 \cdot 2 = \$264[/tex], which is exactly what the question was asking for.
IF 2 + 2 = 4 AND 4 + 4 = 8 WHY AM I STILL BROKE !!!!!
Answer:
You are still broke because you forgot that you have no money to add with
Step-by-step explanation:
helppp meeee pleaseeee
Answer:
0.3907 I think hope this helps
PLEASE HELP QUICKLY!!!
x^2 + (x+9)^2 = 45^2
Step-by-step explanation:
x^2+(x+9)^2=90
x^2+(x+9)^2-90=0
x^2+x^2+9^2+2*x*9-90=0
x^2+x^2+81+18x-90=0
2x^2+18x-9=0
16 ÷ 22 + (6 x 2) - 8
Write these numbers in order of size, start with the
smallest number
60% 1/2 0.3 3/4 0.4
6TH GRADE MATH!!
A store makes 20% profit on the total price of all the items they sell.
let t represent the total price of all items sold in dollars, and let p represent the profit in dollars.
1) WRITE AN EQUATION TO REPRESENT THE RELATIONSHIP BETWEEN THESE VARIABLES:
Pls help! I don’t understand!! :/
Answer:
p=1/5t
Step-by-step explanation:
Since t is 100% of the items sold and p is 20% of that, the profit, p is 20% of t, or 1/5t.
Answer:
p = t(0.2)
Step-by-step explanation:
The profit is 20% of the total price. So if you multiply the total price by 0.2, you will get 20% of the total price which is the profit.
can someone pls pls help me with this
Answer:
-41
Step-by-step explanation:
f(3) = -13x - 2
f(3) = -13(3) - 2
f(3) = -39 -2
f(3) = -41
Answer:
should be -41
Step-by-step explanation:
just did it
Determine which function has a greater change of rate.
Be sure to show work as well.
how to write a fraction in interval notation
Answer:
So it's all real numbers except for that value okay now I want to show you guys how to write that in interval. Form because it we wrote all real numbers as negative infinity to infinity
Step-by-step explanation:
Find the missing angle? *
80 + 35 = 115
180 - 115 = 65
the answer is 65
Subtract. 225.37−41.46
Answer:
183.91
Step-by-step explanation:
In the triangle below, x= cm round to the nearest tenth
9514 1404 393
Answer:
8.6 cm
Step-by-step explanation:
We notice the hypotenuse is given, and the desired length is of the side opposite the given angle.
The mnemonic SOH CAH TOA reminds you of the relevant relationship:
Sin = Opposite/Hypotenuse
sin(35°) = x/(15 cm) . . . . . . fill in the given information
We can multiply by 15 cm to find the value of x.
x = (15 cm)sin(35°)
x ≈ 8.6
_____
For those inclined to copy this answer to a different question, we suggest ...
y = (15 cm)cos(35°) ≈ 12.3 cm
Answer: 8.603646545 or rounded to the nearest tenth 8.6
Step-by-step explanation:
you are going to have to use (sin). so,
(15)sin(35)
8.603646545 or 8.6
this is correct.
if you haue 189*123 cats what isthe ansr
Answer:
23247 cats
Step-by-step explanation: