a. The expression of the amount of phosphorus-32 remaining as a function of time t is A(t) = [tex]6.6\left(\frac{1}{2}\right)^{t / 14}[/tex].
b. The time when 1 gram remaining is 38.1145 days.
What is the half-life?The half-life is the amount of time it takes for half of a unstable nuclei to decay. Each substance has its own half-life.
Now, as per the question;
Exponential growth is given by the formula;
[tex]A(t)=A_0(1+r)^t[/tex]
Where,
A(t) = amount at time t.
A₀ = Initial amount of the nuclei (= 6.6)
r = rate of increasing( = -1/2; as decay is always negative)
t = time (= t/14)
Part a. Calculate the expression for the amount of phosphorus-32 remaining as a function of time t as-
Substituting all the values in the equation;
[tex]\begin{aligned}&A(t)=6.6\left(1+\left(-\frac{1}{2}\right)\right)^{t / 14} \\&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
This is the requires expression.
Part b. Calculate the time there be 1 gram remaining as;
This time can be written as A(t) = 1.
Substitute the value in the equation.
[tex]\begin{aligned}&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14} \\&1=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
[tex]\left(\frac{1}{2}\right)^{t / 14}=\frac{10}{66}[/tex]
Further solving;
t = 38.1145 days.
Thus, the time taken by phosphorus-32 to remain as 1 gram is 38.1145 days.
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3/4x+8<41 graph it as well
Answer:
x<44
Step-by-step explanation:
After making several plates of empanadas, you are down to your last bag of shredded cheese. You realize that it’s not full; there is about / three-fourths of a bag left. If you want to make 4 plates with the remaining cheese, what fraction of a bag can you put on each plate?
The fraction of a bag that you can put on each plate is 3 /16.
What is the fraction you can put on each plate?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator and the denominator are divided by a line. An example of a fraction is 1 / 2.
The fraction of the cheese that you can put on each plate can be determined by dividing the amount of cheese left by the number of plates. Division is the process of grouping a number into equal parts using another number.
Amount that can be put on each plate = fraction left / number of plates
3 /4 ÷ 4
3/4 × 1/4 = 3 /16.
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What is 1/2x+1/2x=x+1
Answer: 2x..?
Not 100% sure but here's my reasoning
(1/2 + 1/2 + 1)x
1/2 + 1/2 = 1
1 + 1 = 2
then you add the x, making it 2x
i could be wrong im literally half asleep eating chicken wings and finishing my own homework so forgive me if this is completely wrong lol
An isotope with z > 83, which lies close to the band of stability, will generally decay through_______
An isotope with z > 83, which lies close to the band of stability, will generally decay through decay.
What do we mean by decay?The process by which an unstable atomic nucleus loses energy through radiation is known as radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, as well as nuclear disintegration). Radioactive material is one that contains unstable nuclei. Radioactive decay is the spontaneous transformation of one element into another. This can only happen by changing the number of protons in the nucleus (an element is defined by its number of protons). A radioactive procedure in which a nucleus spontaneously transforms into one or more different nuclei while emitting radiation, losing electrons, or fissioning. An isotope with z > 83, for example, which is close to the band of stability, will generally decay through decay.Therefore, an isotope with z > 83, which lies close to the band of stability, will generally decay through decay.
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140%of 138.6 is what
Hello, the answer is 194.04.
First, you would convert 140% to a decimal which is 1.4. Next, you would multiply 1.4 x 138.6 = 194.04.
So the steps to a percentage multiplied to a number are:
1. Convert the percentage to a decimal.
2. Multiply the decimal by the number.
3. You get the answer.
25. Communicate and Justify Ramon says that 4 1 can be rewritten as Jamal says that 12 124* it cannot because both the numerator and denominator need to be raised to the power of 4. Who is correct? Explain. Thinking For what values of x is
Answer:
Step-by-step explanation:
Ramon is correct to write the expression (1/12)⁴ that can be rewritten as 1/12⁴.
Use the concept of exponent defined as:
Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.
Given that,
Ramon says that (1/12)⁴ can be rewritten as 1/12⁴.
And, Jamal says that it cannot.
Here, the expression is,
(1/12)⁴
Apply the rule of exponent as
1⁴ / 12⁴
1 / 12⁴
Hence, Ramon is correct to write the expression.
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An instructor gives a short quiz involving 10 true-false questions. To test the hypothesis that the student is guessing the following decision rule is adopted :
176/2^10 = 0.171875.
n=10, p=1/2, q=1/2
probability of student passes the quiz only if he answers 7 or more than 7 questions correctly and let it be x
P(x)=10C7(0.5)^7(0.5)^3 + 10C8(0.5)^8(0.5)^2 + 10C9(0.5)^9(0.5)^1
+ 10C10(0.5)^10(0.5)^0
=120 /1024 + 45/1024 + 10/1024 + 1/1024
P(x)=176 / 1024
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(3.6 x 105) / (1.2 x 103) =
3.0582524271844
Step-by-step explanation:
1.multiply the numbers:3.6×105=378
2.multiply the numbers:1.2 ×103=123.6
3.Divide the numbers:378/123.6=3.0582524271844
Identify the property that justifies the statement. ∠LMN ≅ ∠LMN
Please Hurry!!
The property which justifies the statement, ∠LMN ≅ ∠LMN is: C. reflexive property of ≅.
Corresponding parts of two congruent figures.In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
What is the reflexive property of congruence?The reflexive property of congruence states that a line segment, an angle, or geometric shape (geometric figure) is always congruent to itself.
This ultimately implies that, for all angles M , ∠M ≅ ∠M. In this context, we can reasonably infer and logically deduce that the property which justifies the statement, ∠LMN ≅ ∠LMN is reflexive property of ≅.
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If the straight-line distance from her home to the university is 10. 3 km in a direction 25. 0° south of east, what was her average velocity in km/h?.
The average velocity in km/h is: 34.3km/hr
What is average velocity?Average velocity refers to speed at which the time intervals (t) change in position or displacement happens, divided by the change in position or displacement (x).
=> Average velocity = [tex]\frac{displacement}{time}[/tex]
Now,
The time taken is missing in the question; the time taken = 18 mins = [tex]\frac{18}{60}[/tex] hours.
The distance of her home to the university = 10.3 km
As, average velocity = [tex]\frac{displacement}{time}[/tex]
=> Velocity = [tex]\frac{10.3\times60}{18}[/tex] = 34.3 km/hr
Hence, the average velocity = 34.3 km/hr
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Your revenue (in dollars) for selling x bracelets is given by f(x) = 5x and your profit is $50 less than 80% of the revenue. What is your profit for 77 sales?
From the calculation carried out below, it can be observed that the profit for 77 sales is $258.
How do we calculate profit for sales?Given revenue as:
f(x) = 5x ............................ (1)
Where:
x = Number of bracelets sold or sales = 77
Total obtain the revenue, substitute x = 77 into equation (1), we have:
Revenue = f(77) = 5 * 77
Revenue = $385
Since profit is $50 less than 80% of the revenue, we have:
Profit = (Revenue * 80%) - 50
Profit = (385 * 80%) - 50
Profit = 308 - 50
Profit = $258
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At the beginning of the day, the temperature is -15oF. As the sun comes out, it warms to a high of 8oF. What is the difference in temperature throughout the day?
PLEASE ANSWER FAST IM TIMEDDDD!!!!
Answer:23
Step-by-step explanation: take -15 and negate it which will set you at 15 then add 8 will put you at 23degrees
latoya plots the integers -8, -5, and 2 on a number line. which of the following is the distance between one pair of integers that she plotted?
distance between one pair of integers that she plotted: 10 unit, 7 unit, 3 unit.
Number line :
the line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, in plotting a point.
The numbers on the left are smaller than the numbers on the right of the number line. A number line can also be used to carry out addition, subtraction, and multiplication. We always move right to add, move left to subtract, and skip count to multiply.
Distance formula :
D= right side integer of horizontal line - left side integer of the horizontal line
Distance between the points -8 and 2
d = 2-(-8)
d=10 unit
Distance between the points -5 and 2
d= 2-(-5)
d=2+5
d=7 unit
Distance between the points -5 and -8
d= -5-(-8)
d=-5+8
d=3
distance between one pair of integers that she plotted: 10 unit, 7 unit, 3 unit.
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Given f(-3) = -30 for some polynomial, what factor can f(x) be divided by that will result in a remainder of -30?
Answer:If you can spot a factor of
f(x)
then you can use synthetic division to divide by that factor to give a simpler polynomial to factor.
Step-by-step explanation:
What is the equation of the line that is perpendicular to and has the same y-intercept as the given line? y = one-fifthx 1 y = one-fifthx 5 y = 5x 1 y = 5x 5
For the following equation of the line: y = (1/5)x + 1, y = (1/5)x + 5, y = 5x + 1, and y = 5x + 5, the line that is perpendicular to it and has the same y - intercept is: y = -5x + 1, y = -5x + 5, y = (-1/5)x + 1, and y = (-1/5)x + 5, respectively.
If two equations of the line are perpendicular with each other, then their slopes are negative reciprocal of one another.
To generate the equation of the line perpendicular to the given lines, with the same y-intercept,
1. Get the slope of each line and determine its y-intercept
2. Take the negative reciprocal of the slope and use it and the same y-intercept to get the equation.
y = (1/5)x + 1
slope = 1/5
y-intercept = 1
perpendicular line :
slope = -5
y-intercept = 1
equation : y = -5x + 1
y = (1/5)x + 5
slope = 1/5
y-intercept = 5
perpendicular line :
slope = -5
y-intercept = 5
equation : y = -5x + 5
y = 5x + 1
slope = 5
y-intercept = 1
perpendicular line :
slope = -1/5
y-intercept = 1
equation : y = (-1/5)x + 1
y = 5x + 5
slope = 5
y-intercept = 5
perpendicular line :
slope = -1/5
y-intercept = 5
equation : y = (-1/5)x + 5
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Answer:
C y = 5x + 1
Step-by-step explanation:
Took the test on edu
19.6 is 24.5% of what number?
- For 11 points
Answer:
80
Step-by-step explanation:
[tex]\frac{24.5}{100} *x = 19.6\\x = 19.6 *\frac{100}{24.5} \\x = 80[/tex]
19.6 is 24.5% of 80
Answer:
24.5% of 80= 19.6
Step-by-step explanation:
24.5% of what number is equal to 19.6
24.5
____ x = 19.6
100 100
x = 19.6 x ____
24.5
= x =80
HOPE IT HELPS
If the volume of a cube increases at rate of 3 cm^3/sec what is the rate of increase of the length of its side ?
Greetings from Brasil...
We know that
V = L³ ⇒ L = ∛V
and
dV/dt = 3cm³/s (volume rate as a function of time)
Let
dL/dV = L' = 1/(3∛V²)
We need dL/dt (side rate as a function of time), so
(dV/dt) . (dL/dV) = dL/dt
then
dL/dt = 3 . [1/(3∛V²)]
dL/dt = 1/∛V²12. FIND THE ERROR A student is finding the
total cost c, including sales tax, of a book
that costs $9.95. The sales tax rate is 9%.
Find the student's mistake and correct it.
Here is what the student wrote (re-pasting for clarity)
C = 1.9 x 9.95
C = 18.91
C = $18.91
The error happens in the 1st line
Why? Because the 1.9 should be 1.09
The 1.9 represents a tax of 90% when we want a 9% tax instead
In other words, 9% = 9/100 = 0.09 while 90% = 90/100 = 0.9
-----------------
This is what the steps should look like
C = 1.09 x 9.95
C = 10.8455
C = 10.85
Don't forget to round to the nearest hundredth, aka nearest penny.
The total cost, after sales tax, is $10.85
When Betty painted her house, she used 3 gallons of white paint and 2 gallons of brown paint. How many gallons of paint did Betty use in all?
Answer:
5 gallons
Step-by-step explanation:
You just add 2 gallons and 3 gallons and you get
Find the value of
(8/125) -2/-3
The value of the exponent equation [tex]\frac{8}{125} ^{-2/3}[/tex] is 25/4 or 6.25.
According to the question the exponent equation that we have been given is :
[tex]\frac{8}{125} ^{-2/3}[/tex]
First, we will change the negative sign of the exponent and to change the negative sign of the exponent we will reciprocal the fraction that is
= [tex]\frac{125}{8} ^{2/3}[/tex]
Which is also equal to
= [tex]{125} ^{-2/3}/8^{2/3}[/tex]
Now we know that 5³ =125 and 2³ = 8. Thus replacing the numerator and denominator by it we get,
= [tex](5^{3}) ^{2/3}/(2^{3}) ^{2/3}[/tex]
= 5²/2²
= 25/4
= 6.25
Hence the value of the exponent equation is 25/4 or 6.25
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Given x = 1, y = 1, w = 1, and z = 1 and this expression: what is the evaluation of the logical expression?
The evaluation of the expression is 2, if the expression is x - y + z(x + w).
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that x = 1, y = 1, w = 1, and z = 1
We have been given expression
⇒ x - y + z(x + w)
Substitute the values of x = 1, y = 1, w = 1, and z = 1 in the above expression,
⇒ 1 - 1 + 1(1 + 1)
⇒ 0 + 1(2)
⇒ 2
Hence, the evaluation of the expression is 2.
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Your question is incomplete, probably the missing part is:
Given x = 1, y = 1, w = 1, and z = 1 and this expression x - y + z(x + w): what is the evaluation of the logical expression?
Question 12
4
Which of the following numbers is irrational?
-9
5
7
√√5. √9
3
Answer: square root of 5 and square root of 9
Step-by-step explanation:
Does each box at the fruit stand contain a different fruit? set all_different to true if each box contains a different fruit or to false if multiple boxes contain the same fruit.
No, multiple boxes contain the same fruit.
3 boxes contains the same fruit : strawberry
all different = False
From the given table,
box ID | fruit name | count
53686 | kiwi | 45
57181 | strawberry | 123
25274 | apple | 20
48800 | orange | 35
26187 | strawberry | 255
57930 | grape | 517
52357 | strawberry | 102
43566 | peach | 40
=> You can see that, each box have a unique box ID, and a fruit name for each box.
=> These 57181, 26187, 52357 boxes contains strawberry.
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Solve for u.
4u = 88
Simplify your answer as much as possible.
U=
X
3
Answer: u=22
Step-by-step explanation:
4u = 88
Divide by 4 on both sides
4u/4 = 88/4
Cancel out 4u
u = 22
Please help with photo below
Answer:
No
Step-by-step explanation:
like terms are terms which have the same variable , that is
10x and - 5x are like terms, they both have the same variable x
HELP PLS will mark brainliest
[tex](1-\frac{9x^2+4}{12x} )/(\frac{1}{3x}-\frac{1}{2} )+1[/tex]
Answer:
[tex] \frac{3x}{2} [/tex]
Use the expression -1/3-(-5/12) show an equivalent addition expression
The equivalent expression to -1/3-(-5/12) is 1/12.
How to calculate the expression?From the information, the expression given is -1/3-(-5/12).
Therefore, this will be computed thus:
= -1/3-(-5/12)
= - 1/3 + 5/12
= 5/12 - 1/3
= 5/12 - 4/12
= 1/12
Therefore, the equivalent expression to -1/3-(-5/12) is 1/12.
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simplify 3a x 5b x 5b x 6c
These numbers form an addition and subtraction fact family.
4, 2, 6
Choose the fact family formed by these numbers.
OA 2+6=8
8-6=2
2+2=4
4-2=2
OB. 2+4= 6
6-4=2
OC 4+2=6
6-2=4
OD. 4+2=6
6-2=4
2+4=6
6-4=2
The correct family is option D.
To understand this problem we must be aware of the concept of addition and subtraction and also BODMAS rules which applies in an linear equation.
The numbers given here are 4,2 and 6.
We can see here that on adding 4 and 2 we get 6;
4+2=6
And on subtracting 2 from 6 we get 4;
6-2=4
Also we can see here that on subtracting 4 from 6 we get 2;
6-4=2.
These three relations are true for the given numbers.
And we can see that option D clearly fits the answer.
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A random sample of 10 subjects have weights with a standard deviation of kg. What is the variance of their weights? be sure to include the appropriate units with the result.
The variance of their weights is 128.87270 kg².
It is required to find the variance of their weights.
What is standard deviation ?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Let n=sample size=10 subjects
Standard deviation=11.352211.3522 kg
Using this formula
Variance=(Standard deviation)²
By the formula we get,
Variance=(11.352211.3522 kg)²
Variance=128.87270 kg²
Therefore, the variance of their weights is 128.87270 kg².
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