Answer:
The mass of Element X will reach 62 grams in 7.0 years.
Step-by-step explanation:
We can find the time of decay of Element X by using the exponential decay equation:
[tex] \frac{dm}{dt} = -\lambda t [/tex]
The solution of the above equation is:
[tex]m_{(t)} = m_{0}e^{-\lambda t}[/tex] (1)
Where:
t: is the time =?
λ: is the decay constant
[tex]m_{(t)}[/tex]: is the mass at time t = 62 grams
[tex]m_{0}[/tex]: is the initial mass = 90 grams
First, we need to calculate λ
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex] (2)
Where [tex]t_{1/2}[/tex] is the half-life = 13 years
By entering equation (2) into (1) and solving for "t" we have:
[tex]\frac{m_{(t)}}{m_{0}} = e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]
[tex]ln(\frac{m_{(t)}}{m_{0}}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]
[tex]t = -ln(\frac{m_{(t)}}{m_{0}})(\frac{t_{1/2}}{ln(2)}) = -ln(\frac{62}{90})(\frac{13}{ln(2)}) = 7.0 y[/tex]
Therefore, the mass of Element X will reach 62 grams in 7.0 years.
I hope it helps you!
Write each expression using exponents.
3/8 * 3/8 * 3/8=
Answer:
3/8^3
Step-by-step explanation:
the exponent is 3
Answer:
(3/8)^3
3^3 * 2^-9
Step-by-step explanation:
3/8 * 3/8 * 3/8 = (3/8)^3
= 3^3 * (1/8)^3 = 3^3 * (2^-3)^3 = 3^3 * 2^-9
Can you help me with these questions
Answer:
7) Unfilled dot at 5 with a line going right
8) A filled dot at 8 with a line going right
9) Unfilled dot at 22 with a line going left
10) A filled dot 13 with a line going left
11) x < 9
12) x > 14
13) x ≤ 11
14) x ≥ 7
Step-by-step explanation:
> means greater than
≥ means greater than or equal to
< means less than
≤ means less than or equal to
If something is greater than the given number then the variable increases in value and will be on the right side of the number line
If something is less than the given number then the variable decreases in value and will be on the left side of the number line
If a variable is < or > the dot is unfilled because it does not include that number
If a variable is ≤ or ≥ the dot is filled because it includes the given number
I need help
An amount of $16,000 is borrowed for 8 years at 7.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Answer:
$28009.05
Step-by-step explanation:
Let us use the formula A = P(1 + r/n)^(nt)
Step 1: Convert 7.25 to decimal
[tex]7.25\% = 0.0725[/tex] in decimal form
Step 1: Percent means 'per 100'. So, 7.25% means 7.25 per 100 or simply 7.25 over 100. [tex]7.25 \div 100\\\\= \frac{7.25}{100}\\\\= 0.0725[/tex] If you divide 7.25 by 100, you'll get 0.0725 (a decimal number).Step 2: Solve with the formula
[tex]A = 16000(1 + 0.0725)^8\\\\A= 28009.05[/tex]
Step 1: Add the numbers: [tex]1+0.0725=1.0725[/tex][tex]=16000\cdot \:1.0725^8[/tex][tex]=16000\cdot \:1.75056[/tex]Step2: Multiply[tex]=28009.05068[/tex]the sum of three consecutive natural number is 30 find the numbers
Answer:
9 + 10 + 11
Step-by-step explanation:
guess and check
Answer:
9,10,and 11
Step-by-step explanation:
The triangles have a scale of 3: 5. What is the value of a? *
Answer:
Step-by-step explanation:
multiply the ratio by 24/5 and you have
72/5 : 24
or
14.4:24
Y/3+y/4=5/6
Find the LCD that would eliminate the fractions
Answer:
the answer is in the picture
Which values are equivalent to the fraction below? Check all that apply
4 5/4 7
Answer:
the answer is the 4/-2
Step-by-step explanation:
you can understand from the answer
how is 2/5 + 3/5 = 1
Answer:
Hey mate......
Step-by-step explanation:
This is ur answer.....
= 2/5 + 3/5 = 5/5 = 1(When you simplify both numbers, you get 1)
Hope it helps!
Brainliest pls!
Follow me! :)
Imagine cutting up a pizza into 5 slices
If you take 2 slices, then you take 2 out of the 5, so the fractional amount you took is 2/5 of the full pizza.
If your friend takes 3 slices, then she or he takes 3/5 of the full pizza
Adding the two fractional amounts should get us back to 1 full pizza, which is why 2/5+3/5 = 1.
-----------
We could say this:
2/5 + 3/5 = (2+3)/5 = 5/5 = 1
Dividing any number over itself, as long it's not zero, always leads to 1.
So that's why 5/5 = 1.
Write the standard equation of each circle below
Order these numbers from least to greatest.
7.13, 7.013, 7.2, 7.1371
Answer:
7.013, 7.13, 7.1371, 7.2
Step-by-step explanation:
i will give brainliest!! please help me, i appreciate it !!
Answer:
-4050
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
6x²y³ - 2x + 10
x = 5
y = -3
Step 2: Evaluate
Substitute in variables: 6(5)²(-3)³ - 2(5) + 10Exponents: 6(25)(-27) - 2(5) + 10Multiply: -4050 - 10 + 10Add: -4050Please help with this
help fast please lol
Answer:
Between 0 and 3: decreasing
Between 3 and 4: constant (stays the same)
Between 4 and 8: decreasing
Step-by-step explanation:
Find a.
Write your answer in simplest radical form.
Answer:
[tex]a=10[/tex]
Step-by-step explanation:
This problem can be solved in a ridiculous number of ways. However, it is likely introduced as a special-triangle problem in this question, because 4 pieces of information are given opposed to the necessary 3 to solve the triangle.
Special Right Triangles:
In any 30-60-90 triangle, all sides are in the proportion [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse and [tex]x[/tex] is the side opposite to the 30 degree angle. Since we notice that the side we're solving for is directly opposite to the 30 degree angle, we know that the side marked [tex]10\sqrt{3}[/tex] must be [tex]x\sqrt{3}[/tex] and therefore we have [tex]a=\boxed{10}[/tex]
Four coins are tossed in succession. What is the probability of getting all heads?
1/4
1/2
1/16
Answer:
1/16
Step-by-step explanation:
There is a 1/2 chance to flip a heads.
So, in this case, we would multiply 1/2 four times in reference to the coins being flipped a total of 4 times to find its probability.
1/2 x 1/2 x 1/2 x 1/2 = 1/16
Thus, there is a 1/16 chance that you'd get heads four times in a row.
Through: (-3,1), slope = 2
Answer:
y = 2x + 7
Stepy by-step explanation:
y = 2x + b
1 = 2(-3) + b
1 = -6 + b
7 = b
Please help me out with this problem :)
Find the maximum value of P= x + 6y subject to the following constraints
Answer:
I cant tell what the answer is cause X and Y dont have a value
Step-by-step explanation:
Answer:
p=9
Step-by-step explanation:
Solve for x. Round to the nearest tenth, if necessary.
P
29°
х
Q
-6.6
R
Answer:
The x in this question is 151 degrees
Answer:
13.6
Step-by-step explanation:
find the area of the figure with coordinates A (-6,1), B (2,1), C(-3,4), D(5,4)
Answer: The area of the figure is 24 units.
Step-by-step explanation:
After plotting, the given points on the graph, we can observe that it is a parallelogram(opposite sides are equal and parallel)
Height = 4-1 = 3 units
Base = 2-(-6) = 8 units
Area of parallelogram = Base x height
= 8 x 3 square units.
= 24 square units.
Hence, the area of the figure is 24 units.
Find the sum of the first 40 terms of the arithmetic sequence: 16,24,32,40
Answer:
320 is the answer
Step-by-step explanation:
8x40=320
[tex]2x - 4 = 30[/tex]
Answer:
x=17
Step-by-step explanation:
2x-4=302x=30+42x=34x=34/2x=17stay safe healthy and happy.Answer:
x = 12
Step-by-step explanation:
2x - 4 = 30
2x = 30 + 4
2x = 34
x = 34/2
◆ x = 17
This is a Right answer
If f(y) = e^(9y) + e^(-9y), find f'(y). Use exact values.
Given:
[tex]f(y)=e^{9y}+e^{-9y}[/tex]
To find:
The f'(y).
Solution:
Chain rule of differentiation:
[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]
Differentiation of exponential:
[tex]\dfrac{d}{dx}e^x=e^x[/tex]
We have,
[tex]f(y)=e^{9y}+e^{-9y}[/tex]
Differentiate with respect to y.
[tex]f'(y)=e^{9y}\dfrac{d}{dx}(9y)+e^{-9y}\dfrac{d}{dx}(-9y)[/tex]
[tex]f'(y)=e^{9y}\cdot 9(1)+e^{-9y}\cdot (-9)(1)[/tex]
[tex]f'(y)=9e^{9y}-9e^{-9y}[/tex]
Therefore, the differentiation of the given function is [tex]f'(y)=9e^{9y}-9e^{-9y}[/tex].
i need help!! im struggling with this question
Answer:
1 gallon : 25.6 miles
Step-by-step explanation:
So, the way we can find the rate, or ratio between 2 units is to divide one unit by the other unit.
So basically, we see the first set of units is:
2 gallons - 51.2 miles
So basically, for every 2 gallons, there are 51.2 miles.
To find the ratio, or rate, we must find the miles per gallon.
We can do that by dividing both sides by 2:(g=gallons, m=miles)
2g/2=51.2/2m
=
g=25.6
So for every gallon, there is 25.6 miles.
We can write this as:
1 : 25.6
Hope this helps!
Answer:
25.6
Step-by-step explanation:
51.2/2=25.6
Determine the value of x in the diagram.
−12 = 2 + 5v + 2v
help me plzzzzzzzzzzzz
Answer:
v = - 2
Step-by-step explanation:
Given
- 12 = 2 + 5v + 2v ( subtract 2 from both sides )
- 14 = 7v ( divide both sides by 7 )
- 2 = v
अब पछताए होत कया जब चिडिया चुग गई खेत अनुचछेद लिखिए
Step-by-step explanation:
Go to the Indian Brainly.
I am Indian.
This question is worth 20 points and I will mark brainliest
which expressions are equivalent to 2 (3h + 7) choose "equivalent" or "Not equivalent" for each expression.
6h+7
2+3h+7
6h+7+7
3h+3h+14
(3h+7) + (3h+7)
Answer:
2(3h+7)
=6h+14
6h+7+7 (True)
3h+3h+14 (True)
Jack can program an app in 3 hours. Chris can program the same app in 8 hours. How long would it take them to program the same app working together?
Answer:
2 2/11 hours
Step-by-step explanation:
Let the number of hours
Jack spent programming his app = J
Chris spent programming his app = C
Total hours if they worked together = T
Hence,
1/T = 1/3 + 1/8
Lowest Common Denominator = 34
1/T = 8 + 3/24
1/T = 11/24
Cross Multiply
T × 11 = 1 × 24
T = 24/11
T = 2 2/11 hours
Therefore, it would take them to program 2 2/11 hours to program the same app working together
help please help me please
Answer:
B
Step-by-step explanation:
Only 1 because
1/1 = 1
2/1 = 2
The answer can't be 0 because we can't divide by zero.
The answer can't be 2 because you can't divide 1 by 2 without having a number with decimal places
Same thing for the 4
Find the measure of angle C
Answer:
ajnasnnanananandbabbabbansbansbz svabsvsb