Answer:
193 mg
Step-by-step explanation:
Exponential decay formula:
[tex]A_t = A_0e^r^t[/tex]where Aₜ = mass at time t, A₀ = mass at time 0, r = decay constant (rate), t = timeOur known variables are:
1998 to the year 2004 is a total of t = 6 years.The sample of radioactive isotope has an initial mass of A₀ = 360 mg at time 0 and a mass of Aₜ = 270 mg at time t.Let's solve for the decay constant of this sample.
[tex]270=360e^-^r^(^6^)[/tex][tex]270=360e^-^6^r[/tex] [tex]\frac{3}{4} =e^-^6^r[/tex][tex]\text{ln} (\frac{3}{4} )= \text{ln}(e^-^6^r)[/tex] [tex]\text{ln} (\frac{3}{4} )=-6r[/tex] [tex]r=-\frac{\text{ln}\frac{3}{4} }{6}[/tex] [tex]r=0.04794701[/tex]Using our new variables, we can now solve for Aₜ at t = 7 years, since we go from 2004 to 2011.
Our new initial mass is A₀ = 270 mg. We solved for the decay constant, r = 0.04794701.
[tex]A_t=270e^-^(^0^.^0^4^7^9^4^8^0^1^)^(^7^)[/tex] [tex]A_t=270e^-^0^.^3^3^5^6^2^9^0^7[/tex][tex]A_t=193.01982213[/tex]The expected mass of the sample in the year 2011 would be 193 mg.
(c)x(c)x(c)x(c)x(c)x(c)?
Help please
for the equation below y=2.5^x-6
what is the y intercept of the graph
a) -6
b) -5
c) -3.5
d) 2.5
Answer:
kvh
Step-by-step explanation:
m
What is 200×300?
A. 60,000
B. 5,000
C. 50,000
D. 6,000
Answer:
A. 60,000
Step-by-step explanation:
The answer is A because 2 × 3 is 6 then you add the 4 0's. So it would be 60,000
Help me find out it.
Answer: The answer is 36
PLEASE HELP ME WILL MARK BRAINLIEST!!
Answer:
A line segment
Step-by-step explanation:
(3 x 10-7) x (8 x 10 )
Answer:
1840
Step-by-step explanation:
Answer:
2160
to solve this
(3*10-7) * (8*10)
(30 - 7) * (80)
27 * 80
= 2160
Please help find the volume in inches
Answer:
504 inches^3
Step-by-step explanation:
you multiple the height x length x width
May i get some help with a step by step concept of the first question please
9514 1404 393
Answer:
J 3/4 cup
Step-by-step explanation:
Step 1: read and understand the question.
The question is giving you amounts of flour and 2 types of sugar.
The question is asking for a difference between two quantities:
the amount of flour (2 1/4 cups)the combined amount of sugar (3/4 cup white, 3/4 cup brown)Step 2: determine the relations you need to use to solve the problem
You need the combined amount of sugar, which you find by adding the quantities of each of the kinds.
3/4 cup white + 3/4 cup brown = 6/4 cup sugar combined
You need the difference of that quantity from the quantity of flour, which you find by performing subtraction:
flour - sugar = (2 1/4) - (6/4) . . . . cups
Step 3: Use your knowledge of arithmetic.
(2 1/4) -(6/4) = 9/4 -6/4 = (9 -6)/4 = 3/4
Step 4: Answer the question that was asked.
The difference between the flour and sugar amounts is 3/4 cup.
Here is the list of ingredients for making 30 biscuits.
Lucas has the following ingredients.
900 g butter
1000 g caster sugar
1000 g plain flour
225 g chocolate chips
What is the greatest number of biscuits Lucas can make?
You must show your working.
Ingredients for 30 biscuits
225 g butter
110g caster sugar
275 g plain flour
75 g chocolate chips
Answer:
90 biscuits
Step-by-step explanation:
900÷225=4
1000÷110=9
1000÷275=3
225÷75=3
Which of the following is represented by the expression below?
5x+2
aTwo more than five times a number
bFive more than 12 of a number
cFive more than twice a number
dTwo more than 15 of a number
ps its not c
Answer:
2 more than 5 times a number
Step-by-step explanation:
Problem #2: Ethan bought plates and cups for his upcoming birthday party. He
bought twice as many plates as cup. Altogether, he bought 102 items. How many
of each item did he buy?
If cost of 15 eggs is ? 75, then find out the cost of 4 dozens eggs.
Answer:
Each egg is $5 so 4 dozen(48) is $240
Step-by-step explanation:
the way to do this is 75/15= 5
and then you multiply 12 x 4 to get 48 eggs
and then multiply 48 x 5 to get $240
15:75
divide each by 5
3:15
(4 dozen is 48 -> 48/3 = 16)
multiply each by 16
48: 240
240Solve the system by graphing.
y = −x + 2
y = −4x − 1
The solution of the system is
Answer:
(-1,3)
Step-by-step explanation:
Answer the question below
Answer:
Well I know the formula but im not sure which option it matches to.
Step-by-step explanation:
3 x 3.5 times 1/2
+
11.4 x 10.5 times 1/2
4x+a=4x+3. How do you get to 6? Please explain and write down like you would write on paper.
Answer:
a=3 x= all reals
Step-by-step explanation:
I actually did not get 6 for an answer
4x+a=4x+3
cancel equal terms on both sides of the equation
a=3
which means the x would be all reals cause it is true.
Use the diagram to solve for x.
Answer:
8
Step-by-step explanation:
You know that the horizontal lines are parallel to each other.
The 8 and x is both on that diagonal right there. Since the horizontal lines are parallel, that means the angle of 8 should have the same angle as x.
*I forgot what this thing was called but please trust me i learned this before*
1.The gradient of a straight line is the measure of the ratio of the
change to the
change.
Answer:
The gradient of a straight line is the measure of the ratio of the vertical change to horizontal change
Step-by-step explanation:
Required
Fill in the gap
Gradient is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
or
[tex]m = \frac{\triangle y}{\triangle x}[/tex]
Where [tex]\triangle[/tex] means change; y and x are vertical and horizontal change respectively
find the measure of the arc or angle indicated. please help and i need work shown... brainliest answer for work shown
Answer:32
Step-by-step explanation:
Answer:
190°Step-by-step explanation:
Inscribed angle is half the measure of the intercepted arc:
m∠EFG = 1/2mEG1/2mEG = 95°mEG = 2*95° = 190°What number is 16% of 46? Which equation and solution represents each situation?
Answer:
the answer to this question is 7.36....its equation is 16/100*46
Answer:
7. 36 is the answer.
Step-by-step explanation:
but, what equation, and what situations?
which is the distance between the point with the coordinates (-2,3) and the line with the equation 6x-y=-3
Answer:
I think it is 6x+3=y (y=6x+3)
A. 20 mph
B. 35 mph
C. 70 mph
D. 100 mph
The answer is B. 35 mph
Speed is shown as distance/time
If you pick a point, for example 70 miles and divide it by the time which is 2 hours, then you get 35 miles per hour
(4-9-8)÷3×3please help AFAP
Answer:
I am not really sure but try this -13/9 or -13 divided by 9
Step-by-step explanation:
Answer:
-13
Step-by-step explanation:
So, we're gonna use PEMDAS here. First, we have to subtract what's in the parentheses.
4-9 is -5. -5 - 8 is -13. We can rewrite the equation now.
-13/3*3
The answer is -13
-3x + y = 1 4x + y = 8
-3x+y=1
/-3 /-3
x+y=-1/3
4x+y=8
/4 /4
x+y=8
---
hope it helps
Answer:
x=-1y-9
Step-by-step explanation:
find the solution of given expression
[tex] \sqrt{36 \times 36 \times 4} [/tex]
Answer:
√(36×36×4)=√(36²×2²)=±(36×2)=±72
[tex]\sqrt{36 \times 36 \times 4} = 72[/tex]
Show whether or not the points with coordinates (1,3) (4,2) (-2,6) are vertices of a right triangle
Answer:
No
Step-by-step explanation:
See attached
what is the area of a trapezoid that has a height of 12 and it’s parallel sides measure 15 and 20? Show the steps in your work.
Answer:
Area of trapezoid = 210 unit²
Step-by-step explanation:
Given:
Height = 12 unit
Parallel side a = 15
Parallel side b = 20
Find:
Area of trapezoid
Computation:
Area of trapezoid = [(a+b)/2]h
Area of trapezoid = [(15+20)/2]12
Area of trapezoid = 210 unit²
Ryan and Taylor are both saving money to buy new video game
equipment. Ryan's savings plan can be modeled by the function
s= 15m + 50 where m represents the number of months since Ryan
started his plan, and s represents the amount of money saved in
dollars. The table shown represents Taylor's savings plan.
Taylor's Savings Plan
Number of
Month Amount Saved ($)
0 25
1 45
2 65
3 85
Select the options that correctly complete the sentences.
greather or less than -----answer
Ryan's rate of change is ________ Taylor's rate of change .
Ryan'sstaring balanced is_______ Taylor's starting balanced.
We want to compare the rates of change and starting balances of Ryan and Taylor, the correct answers are:
"Ryan's rate of change is _less than_ Taylor's rate of change.""Ryan's starting balance is greater than Taylor's starting balance."So we know that Ryan's savings plan can be modeled by:
S(m) = 15*m + 50.
This means that he starts with 50, and saves 15 per month, then:
Ryan's rate of change = 15 per monthRyan's initial balance = 50For Taylor we have a table:
month amount saved:
0 25
1 45
2 65
3 85
So, in month 0 he has 25, thus, his initial balance is 25.
And each month the amount saved increases by 20, then the equation is:
T(m) = 20*m + 25
Then we have:
Taylor's rate of change = 20 per month.Taylor's initial balance = 25Now we can see that:
"Ryan's rate of change is _less than_ Taylor's rate of change."
"Ryan's starting balance is greater than Taylor's starting balanced."
If you want to learn more about rates of change, you can read:
https://brainly.com/question/18904995
Mrs. Crosland asked students to factor the expression 28x - 8. The students offered the answers shown
Carlos: 2(14x - 4)
Danny: 7(4x - 1)
Irene: 4(7x - 2)
Which student(s) offered answer(s) equivalent to the original expression?
Equivalent expression for the given expression is
4(7x-2)
Irene offered answer equivalent to the original expression
Given :
Mrs. Crosland asked students to factor the expression 28x - 8
The student are given some expression . To find correct expression , we need to factor the given expression
[tex]28x-8[/tex]
Both 28 and 8 are divisible by 4
Lets factor out 4 from the given expression.
When we factor out 4, then we divide each term by 4
[tex]28x-8\\4(\frac{28}{4} -\frac{8}{4} )\\4(7x-2)[/tex]
The students offered the answers shown
Carlos: 2(14x - 4)
Danny: 7(4x - 1)
Irene: 4(7x - 2)
so , from the answer we can say that Irene offered answer equivalent to the original expression
Learn more : brainly.com/question/22345708
Which equation can be used to answer the question below?
Christopher made 12 of the 40 recipes he downloaded from the Internet. What percent of the recipes did he make?
A X=12(40)
B 12x=40
C 12=x/40
D 12=40x
Christopher made 30% of the recipe downloaded
He made 12 of the 40 recipes he downloaded from the internet.
He downloaded a total of 40 recipes.
PercentagePercentage is is a number or ratio that can be expressed as a fraction of 100. Therefore,
The percentage of the recipe he made can be calculated as follows;
percentage of recipe made = 12 / 40 × 100percentage = 1200 / 40 = 30%
Therefore, he made 30% of the recipe downloaded
learn more on equation here: https://brainly.com/question/4345896
Ivan has $50,000 in a savings account that earns 4% interest per year. The interest is not compounded. To the nearest dollar, how much interest will he earn in 5 years?
Answer:
$2,000
Step-by-step explanation:
4% of $50,000 is $2,000 so 2,000 X 5 =10,000