Answer:
the number of caffeine still in his system by 9:00 am is 192 mg.
Step-by-step explanation:
given information
the mass of initial caffein, m₁ = 300 mg
time, t = 9 - 6 = 2 hours
metabolised = 18%/hour = 0.18/h = 0.18 x 300 mg = 54 mg/h
the student metabolised the caffeine 54 mg/h. thus from 6 am to 9 am the caffeine metabolised is
metabolised in 2 hr = 2 x 54
= 108 mg
the remaining caffeine = initial caffeine - metabolised caffeine
= 300 - 108
= 192 mg
Answer:
The correct answer is 138 mg.
Step-by-step explanation:
To understand this problem we must first analyze it.
We know that the student's body metabolizes 18% of the caffeine ingested every hour.
Therefore we can solve that percentage to already have the number of metabolized caffeine per hour:
(300. 18): 100 =
5400: 100 = 54 mg
We now know that the student's body will metabolize 54 mg of caffeine per hour.
The question is much caffeine is still in his system by 9:00 am?
From 6:00 am to 9:00 am we have 3 hours of difference: 3 . 54 = 162
In three hours 162 mg of caffeine were already processed by his body, therefore, it still needs to be metabolized: 300 - 162 = 138 mg.
Answer these questions about the steps of simplifying this rational expression: 4x-8/x^2+3x-10 Part A What is the greatest common factor (GCF) of the terms in the numerator and in the denominator? Rewrite the expression by factoring out the GCF.
Answer:
GCF: (x - 2)
4 / (x + 5)
Step-by-step explanation:
The expression given is:
(4x - 8) / (x² + 3x - 10)
To find the greatest common factor, we have to factorise the numerator and denominator individually.
NUMERATOR:
4x - 8 = 4(x - 2)
DENOMINATOR:
x² + 3x - 10 = x² + 5x - 2x - 10
x² + 3x - 10 = x(x + 5) - 2(x + 5)
x² + 3x - 10 = (x - 2) ( x + 5)
So, the expression becomes:
4(x - 2) / [(x - 2) ( x + 5)]
We observe that the common factor in both numerator ad denominator is (x - 2).
This is the greatest common factor (GCF).
Factoring out (x - 2), the expression can be rewritten as:
4 / (x + 5)
Answer:
The terms in the denominator have a GCF of 1, so nothing gets pulled out in the denominator. The GCF of the terms in the numerator is 4.
Step-by-step explanation:
I need help with this please. I don’t understand how to do this
Answer:
i can help!
Step-by-step explanation:
all you have to do is first add all the # after you should be left with 2 # multiply them together and there you have your answer!
Maten forgot some of her 12 facts. She wants to find 6x12 , but all she can remember is 5x12=60 . How could she use the fact 5x12=60 to find 6x12? Explain
Answer:
5 times 12 = 12 times 5
Step-by-step explanation:
You flipped the factors since they were the same. 5 times 12 = 60 when you flip the factors 12 times 5 = 60
a movie theater charges $10.50 per ticket and $5 per bucket le popcorn. you never buy the popcorn because you think it's too expensive
Answer:
any other info pls tell me
Step-by-step explanation:
Answer:the answer is yes
Step-by-step explanation:
What is the value of the expression when a = 4, b = 3 ,and c = 10?
3a4b−c
1
4
6
12
Step-by-step explanation:
hope it will help you....
List the following numbers in order from least to greatest.
4.2 x 10-2, 0.088, 8.9 x 10-3, 0.01
Answer:
0.01 , 0.088 , 4.2 x 10-2 , 8.9 x 10-3
Step-by-step explanation:
4.2 x (10.2).
4.2 x 8
=33.6
8.9 x (10-3)
8.9 x 7
=62.3
0.01 , 0.088 , 4.2 x 10-2 , 8.9 x 10-3
Complete the following table with the properties used to solve 4(x + 3) =20
Statements Proof:
4(x + 3) = 20:
4x + 12 = 20:
4x = 8:
x =2:
Answer:
distributive property, subtraction, division
Step-by-step explanation:
i don't know the exact name of the last two but that's what i'm assuming they're called lol
The properties used to solve the equation 4(x + 3) = 20 are the distributive property, subtraction property of equality, and division property of equality. First, the distributive property is used to expand the left-hand side, then subtraction is used to isolate 4x. Finally, division is used to find x = 2.
Explanation:The question provides an algebraic equation and uses properties to solve for the variable 'x'. The steps taken demonstrate the following properties:
Distributive property: The equation starts as 4(x + 3) = 20. Through the distributive property (a*(b + c) = a*b + a*c), this is expanded to 4x + 12 = 20.Subtraction property of equality: Next, 12 is subtracted on both the sides giving 4x = 8. This property states that we can subtract the same value from both sides of the equation and it will still hold true.Division property of equality: Finally, the equation is divided by 4 on both sides, which results in x = 2. This property tells us that if we divide both sides of the equation by the same non-zero number, the equation will still be equal.Learn more about Algebraic Properties here:https://brainly.com/question/32858114
#SPJ3
Find the volume of a cylinder with a diameter of 10 inches and a height that is three times
the radius. Use 3.14 for pi and round your answer to the nearest tenth. (Hint: You may only
enter numerals, decimal points, and negative signs in the answer blank) (4 points)
Answer:
1177.5 in^3
Step-by-step explanation:
Volume of a cylinder=π*r^2*h
3.14*radius^2*height=
3.14*5*5*15=1177.5
6x^2=726
[tex]6x^2 = 726[/tex]
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
Step 1: Divide both sides by 6
[tex]6x^2 / 6 = 726 / 6[/tex]
[tex]x^2 = 121[/tex]
Step 2: Square root both sides
[tex]\sqrt{x^2} = \sqrt{121}[/tex]
[tex]x = 11[/tex]
Answer: [tex]x=11[/tex]
Answer:
[tex]6 {x}^{2} = 726 \\ \frac{6 {x}^{2} }{6} = \frac{726}{6} \\ {x}^{2} = 121 \\ x = \sqrt{121} \\ x = 11[/tex]
What does it mean when we write √100 = 10 in terms of squares and side lengths? Explain. *
Step-by-step explanation:
[tex]\sqrt{100}=10[/tex] because [tex]10^{2}=100[/tex]. 10 is the square root of 100, which means that 10 multiplied by itself (10×10=[tex]10^2[/tex]) is equal to 100. So, when you are trying to find the square root of a number, the square root is itself multiplied by itself.
How would you classify number 125?
A perfect square
B perfect cube
C both a perfect cube and a perfect square
D neither a perfect square nor a perfect cube
Answer:B (perfect cube)
Step-by-step explanation: 125 is the cube of 5
Write an equation for the line shown
A coin is tossed two times, then a month of the year is randomly selected. What is the probability of getting tails each time, and a month that starts with the letter J? I got 1/8 is that correct if not what’s the answer
Answer:
1/16
Step-by-step explanation:
1/2 getting tails
1/4 getting tails twice
3/12 getting a J month =1/4
1/4 x 1/4 =1/16
Answer:
1/16
Step-by-step explanation:
Given a fair coin, the probability of getting tails on any one toss =
P(tails) = 1/2
if a coin is tossed twice and we get tails both times,
P( 2 tails on 2 consecutive tosses) = (1/2)(1/2) = 1/4
Total number of months = 12 months
Months that start with J = January, June, July = 3 months
P(selecting months that start with J) = 3/12 = 1/4
Hence the probability of tossing 2 consecutive tails then selecting a month that starts with J
= (1/4) x (1/4)
= 1/16
What is the distance between the points (-3,-5) and (3, 3)?
A. 14
B. 2
C. 10
D. -2
Answer:
-2
Step-by-step explanation:
Answer: IT IS NOT -2 IT IS 10
Step-by-step explanation:
At a raffle, 250 tickets are sold at $1 each for 3 prizes of $100, $50, and $10. You buy 1 ticket. What is the expected value of your gain? Should you play this game? 1. Explain HOW to determine the expected value. (one paragraph) 2. Interpret the meaning of the expected value for this scenario. (one paragraph)
Answer:
enervsorry it glitched, but the expected value would be 50
Step-by-step explanation:
A circle with area 36 π has a central angle of 11/6 π radians
Answer:
33pi or 103.62 square units
Step-by-step explanation:
central \: angle \: ( \theta) \\ = \frac{11}{6} {\pi}^{c} = \frac{11}{6} \times 180 \degree = 330 \degree \\ \\ area \: of \: sector \\ = \frac{ \theta}{360 \degree} \times area \: of \: circle \\ \\ = \frac{ 330 \degree}{360 \degree} \times 36 \: \pi \\ \\ = \frac{ 330 }{10 } \pi \\ \\ = \red{ \bold{33\pi}} \: {units}^{2} \\ = 33 \times 3.14 \\ = 103.62 \: {units}^{2} \\
don't mind this question, there's gonna be another one thats actually relevent
Answer:
oke
Step-by-step explanation:
If the volume of the pyramid shown is 360 inches cubed, what is its height?
A rectangular pyramid with base of 12 inches by 10 inches and a height of h.
1 in.
3 in.
6 in.
9 in.
Answer:
9 inches
Step-by-step explanation:
The formula for the volume of a rectangular pyramid is
Here we have volume (V), base (L), and width (W)
V = 360 in³, L = 12 in, W = 10 in
We need to manipulate the volume equation to solve for the height (H)
First we need to multiply both sides by 3 to get rid of the fraction: 3V = L×W×H
Then we need to divide both sides by (L×W) to get:
Now we can plug in the given values:
The height is 9 inches
Answer:
9
Step-by-step explanation:
edge
Which of the following is the correct solution to the linear inequality showin
V<1/2x-4
Answer:
Image attached.
Step-by-step explanation:
The given inequality is [tex]y<\frac{1}{2}x-4[/tex].
Let us make a table for [tex]y=\frac{1}{2}x-4[/tex]
x 0 2
y -4 -3
Then we draw the dotted line and shade below it because of the "<" sign.
Learn more: https://brainly.com/question/1594198
Evaluate the expression for m = –1.
–21m2 − 11m − 30 =
Hope this will help u....
Answer:
-40
Step-by-step explanation:
-21m^2 - 11m - 30
m = -1
Therefore
-21(-1)^2 - 11(-1) - 30
-21(-1 x -1) -11 x -1 -30
-21 x 1 +11 -30
-21 + 11 - 30
-10 - 30
-40
Simplify 9 to the 2nd over 9 to the 7th. (4 points)
Group of answer choices
95
1 over 9 to the 9th
1 over 9 to the negative 5th
1 over 9 to the 5th
Answer:
[tex]\frac{1}{9^{5} }[/tex]
Step-by-step explanation:
[tex]\frac{9^{2} }{9^{7} } \to 9^{2-7} \to 9^{-5} \to \frac{1}{9^{5} }[/tex]
Helper's Message:
Hi! I hope this helped you :)
I wouldn't mind a Brainliest or a five-star rating!
-ChocoChocoCho
PLEASE HELP!
Which function is represented by the graph?
Answer:
Step-by-step explanation:
b
Answer:b
Step-by-step explanation:
Matti built a greenhouse in his backyard as shown below.
How much cubic space is in Matti's greenhouse?
A. 191.1 ft 3
B. 367.5 ft
C. 382.2 ft3
D. 735.0 ft
Answer:
B) 367.5 ft
Step-by-step explanation:
BECAUSE ITS NOT A
Answer:
the answer is b
Step-by-step explanation:
Which number should each side of the equation 2/3x=10 be multiplied by to produce the equivalent equation of x = 15?
−2/3
1/3
3/2
3
Answer:
3/2
Step-by-step explanation:
If you want to get the coefficient of x to be 1, you multiply by the reciprocal of the coefficient. The reciprocal is 3/2, so you multiple by 3/2
help me plzzzzzzzzzz im begging youuuuu
Answer:
If the poster is enlarged by the scale factor 5/2 then,
length=12×5/2=30ft
And,
breadth=3×5/2=7ft
>>>>correct ans is 7.5 by 30
Answer:
7.5 feet by 30 feet
Step-by-step explanation:
i believe you would take 12 and divide it by 2 and then multiply it by 5=30. And then do the same for 3. 3 divided by 2 =1.5 and 1.5 multiplied by 5 =7.5
The answer would be 7.5 feet by 30 feet
Select the correct answer.
Cesar had a part-time job last year. He worked every week for the year and made $23 an hour. He worked 28 hours each week. Cesar saved
what was left of his earnings after paying all of his monthly expenses. At the end of the year, he had saved $3,360. What were Cesar's average
monthly expenses, rounded to the nearest dollar?
A
$1,288
B. $1,680
C. $2,403
D. $2,511
E. $2,791
Answer:
D. $2,511
Step-by-step explanation:
First off, we need to write down the facts we know.
There are about 52.177 weeks in a year
Cesar works 28 hours each week
Cesar makes $23 an hour
There are 12 months in a year
Cesar has $3,360 after his monthly expenses
To figure out how many hours are in a "work year," multiply the number of work hours in a week by the number of weeks in a year. In other words, multiply Cesar's 28 hour work week by about 52.177 weeks. That makes 1,456 hours in his work year. That means he makes $33,492 a year. If you multiply $2,511 by the months in a year (12), you get $30132. Finally, subtract his annual salary by $30132 to get $3,360, which is what was left of Cesar's earnings after paying all of his monthly expenses. This means that your answer is: D. $2,511.
Answer:
D. $2,511
Step-by-step explanation:
$23 x 28 x 52 = $33,488
$33,488 ÷ 12 = $2,790.66 = $2,791
12($2,791) - $3,360 = 30,132
$30,132 ÷ 12 = [$2,511]
Is the following number rational or irrational 0.5555?
Answer:
Simple.
The decimal 0.5555 is a rational number. It's a terminating decimal, since it doesn't end with an ellipsis.
How do you think inequalities are different from equations you have worked with before?
Answer:
The only difference is: If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses.
Hope this helps, and have a nice day
Step-by-step explanation:
Good luck! :)
Answer:yes they are different
Step-by-step explanation:
1. An equation is an equality of two mathematical expressions. That's why it has an equal(=) sign . For example:
12x=10x +2x
Or
3x+4y=5
2. While an inequation is an inequality of two expressions and here the greater than and lower than signs are used with equal sign i.e. >,< or=
For example
4y+5a > 5
Or
8a< 7b
........................................................................................
Answer:
[tex]125.9 ft^2[/tex]
Step-by-step explanation:
Missing question:
An artist is making a rectangular canvas for a custom painting. the canvas has a width of 9 1/2 feet and a length of 13 1/4 feet . what is the area of canvas in square feet?
The area of a rectangle is given by the formula
[tex]A=L\cdot w[/tex] (1)
where
A is the area
L is the length
w is the width
In this problem, we have a rectangular canvas, so we want to find its area.
We know that:
[tex]w=9\frac{1}{2}ft[/tex] is the width, converting into an improper fraction,
[tex]w=\frac{9\cdot 2+1}{2}=\frac{19}{2}[/tex] ft
[tex]L=13\frac{1}{4}ft[/tex] is the length, converting into improper fraction,
[tex]L=\frac{13\cdot 4+1}{4}=\frac{53}{4}[/tex] ft
Substituting into eq (1), we can find the area of the canvas:
[tex]A=\frac{19}{2}\cdot \frac{53}{4}=\frac{1007}{8}=125.9 ft^2[/tex]
A rectangle has a perimeter of (20x+12y). If one side of the rectangle is (3x-4y), write the expression for the other side
Answer:
(7x + 10y)
Step-by-step explanation:
To find this add (3x - 4y) to itself to calculate to lengths of the shorter sides.
(3x - 4y) + (3x - 4y) = 6x - 8y
Subtract this from (20x + 12y)
(20x + 12y) - (6x - 8y) = 14x + 20y Divide this by two to get the length of one side
14x + 20y / 2 = 7x + 10y
If this answer is correct, please make me Brainliest!
The expression for the other side of the rectangle, when one side is (3x-4y) and the perimeter is (20x+12y), is (7x + 10y).
To determine the expression for the other side of the rectangle with a perimeter of (20x+12y) and one side being (3x-4y), we must remember that the perimeter of a rectangle is calculated by adding together twice the length and twice the width (P = 2l + 2w). Since we have one length, we can solve for the width by dividing the perimeter by 2 and subtracting the length.
First, let's find half of the perimeter by dividing the given perimeter by 2:
(20x + 12y) / 2 = 10x + 6y
This represents the sum of one length and one width. We then subtract the given side (one length) from this to find the other side (one width):
(10x + 6y) - (3x - 4y) = 10x + 6y - 3x + 4y = 7x + 10y.