The radioactive isotope of phosphorus P-32 is used as a tracer in the liver. If 3.5 mg is left in a sample after 288 hrs then the initial amount of P-32 administered was 7 mg.
What is radioactive isotope?A radioactive isotope is a form of an element that has an unstable nucleus and undergoes radioactive decay, emitting radiation in the form of particles and/or energy.
These isotopes can be used for various purposes in medicine, industry, and research.
We can use the radioactive decay formula to solve this problem:
N = N0 * (1/2)^(t/T)
where:
- N is the final amount of P-32 remaining after 288 hours (3.5 mg)
- N0 is the initial amount of P-32
- t is the time elapsed (288 hours)
- T is the half-life of P-32 (14.3 days converted to hours is approximately 343.2 hours)
Substituting the given values into the formula, we get:
3.5 mg = N0 * (1/2)^(288/343.2)
Simplifying and solving for N0:
N0 = 3.5 mg / (1/2)^(288/343.2) = 7 mg
Therefore, the initial amount of P-32 administered was 7 mg.
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If
f(x) = 2x² - 5
and
g(x) = 5x + 7
Find
f(g(x)) = [?]x² + [?]x + [?]
Answer:
f(g(x)) = 50x² + 140x + 93
Step-by-step explanation:
f(g(x)) means that within the f(x) equation, you want to replace all of the x variables with the g(x) equation.
So,
f(g(x)) = 2 (5x+7)² -5
= 2 ( 25x²+ 70x + 49) - 5
= 50x² + 140x + 93
:)
Determine the amount needed such that when it comes time for retirement, an individual can make semiannual
withdrawals in the amount of $15,265 for 35 years from an account paying 4.5% compounded semiannually. Round
your answer to the nearest cent.
$938,272.00
b. $941,790.00
$535,528.03
0
$547,577.41
Answer:
the correct answer is 0 54,577.41
Step-by-step explanation:
you needed to take the withdrawal amount divide it by 35 and divide that answer by the 4.5 percentage rate
Answer:
C. $535,528.03
Step-by-step explanation:
Trust me
For the sequence a n =a n−1 +a n−2 and a 1 =2,a 2 =3 its first term is its second term is its third term is its fourth term is its fifth term is quence a n =a n−1 +a n−2 and a 1 =2,a 2 =3 its first term is its second term is its third term is its fourth term is its fifth term is
A function assigns the value of each element of one set to the other specific element of another set. The third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively
A function assigns the value of each element of one set to the other specific element of another set.
Given the nth term of the sequence is given by the formula,
[tex]a_n = a_{(n-1)}+a_{(n-2)}[/tex]
Also, the first term and the second term of the sequence are 2 and 3 respectively, therefore, the other terms of the sequence are,
[tex]a_3 = a_{(3-1)}+a_{(3-2)}\\\\a_3 = a_2 + a_1\\\\a_3 = 3 + 2\\\\a_3 = 5[/tex]
[tex]a_4 = a_{(4-1)}+a_{(4-2)}\\\\a_4 = a_3 + a_2\\\\a_4 = 5 + 3\\\\a_4 = 8[/tex]
[tex]a_5 = a_{(5-1)}+a_{(5-2)}\\\\a_5 = a_4 + a_3\\\\a_5 = 8 + 5\\\\a_5 = 13[/tex]
Hence, the third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively.
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Richard wants to purchase a Jeep. The purchase price of the Jeep is $ 42 , 000. The dealership will allow him to pay cash or finance the Jeep with a down payment of $ 4 , 000. and 72 monthly payments of $ 680. Richard chose to finance the jeep.
Answer:
Good for him for buying a Jeep
Step-by-step explanation:
How can you tell if 3 given angles form a triangle?
Answer:
You can tell if the sum of the degrees of all the angles adds up to 180.
Aisha has a health insurance policy with an 80/20 coinsurance and deductible of $3,200. She has met 45% of her deductible before having
some tests done. Given the cost of her tests below, how much will she pay?
Bill #1- Blood Test = $345.25
Bill #2 - Allergy Test = $175.00
Bill #3- MRI = $920.65
Select one:
O a. $319.10
O b. $1,440.90
O c. $3,200.00
O d. $1,760.00
The payment for the test based on the information about the insurance will be B. $1440.90.
How to compute the value?The cost for the payment will be:
= Blood test expenses + Allergy test - MRI expenses
= $345.25 + $175.00 + $920.65
= $1440.90
Therefore, the payment for the test based on the information about the insurance will be $1440.90
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Simplify: √36x² if x is less than or equal to 0
Answer:
[tex]-6x[/tex]
Step-by-step explanation:
[tex]\sqrt{36x^2} = 6\times\sqrt{x^2}\\\\=6\times-x\\\\=-6x[/tex]
A company received a shipment of 8 boxes of metal brackets.
. There are 20 metal brackets in each box.
The total weight of the shipment is 48 pounds.
What is the weight, in pounds, of each metal bracket?
Answer:
160 boxes = 384 pounds
Step-by-step explanation:
sgshshdhdjd
Solve the system of equations.
y+4z=0
4x+y-2z=2
-3x-3z=-9
Step-by-step explanation:
y+4z=0
4x+y-2z=2
-3x-3z=-9
Answer:
x = 7/3y = - 8/3z = 2/3Step-by-step explanation:
y + 4z = 0
4x + y - 2z = 2
____________ -
- 4x + 6z = - 2
- 4x + 6z = - 2 → times 3 → - 12x + 18z = - 6
- 3x - 3z = - 9 → times 4 → - 12x - 12z = - 36
- 12x + 18z = - 16
- 12x - 12z = - 36
______________ -
30z = 20
z = 20/30
z = 2/3
y + 4(2/3) = 0
y + 8/3 = 0
y = - 8/3
- 3x - 3z = - 9
- 3x - 3(2/3) = - 9
- 3x - 6/3 = - 9
- 3x - 2 = - 9
- 3x = - 9 + 2
- 3x = - 7
x = - 7/- 3
x = 7/3
Select the correct answer.
Consider the graph of function f below.
Y
-8 -4
8+
O
A
O
4
-4-
-8
The function g is a transformation of f. If g has a y-intercept at 4, which of the following functions could represent g?
4 8
O g(x)=f(x) + 4
g(x) = f(x-4)
g(x) = f(x) - 2
Og(x)=f(x + 2)
Answer:
742
Step-by-step explanation:
4x203
Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6
What is function ?A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input.
Here, we have,
Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).
Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).
The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).
Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).
=> f(x) = (x-h)² + k
The outcome of translating a unit to the right with b unit up is
=>f'(x) = (x-h-a)² + k + b
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WHAT IS THE CORRECT ANSWER ANSWER ASAP
Answer:
d
Step-by-step explanation:
Which of the following expressions is equivalent to ab² + 6ab + 7a³-14a?
a. (b + 7)(b + 6)(a²-2)
b. b(b + 6)+7(a2-2)
c. a[b(b + 6)+7(a²-2)]
d. a[(b + 7)(b + 6)(a²-2)]
Answer:
c. a[b(b + 6)+7(a²-2)]
Step-by-step explanation:
look at the pic
The equivalent expression of the expression ab² + 6ab + 7a³ - 14a is
C. a [b (b + 6) + 7 (a² - 2)]
Option C is the correct answer.
We have,
To find the expression that is equivalent to ab² + 6ab + 7a³ - 14a, we can factor out common terms from the given expression.
The common terms in the expression are "a" and "(b + 7)".
Step 1:
Factor out "a" from the expression:
ab² + 6ab + 7a³ - 14a = a(b² + 6b + 7a² - 14)
Step 2:
Factor the quadratic expression inside the parenthesis:
b² + 6b can be factored as b(b + 6)
7a² - 14 can be factored as 7(a² - 2)
Step 3:
Putting it all together, the equivalent expression is:
a [b (b + 6) + 7 (a² - 2)]
Now let's check which option matches this expression:
a. (b + 7)(b + 6)(a² - 2) - Not equivalent
b. b(b + 6) + 7(a^2 - 2) - Not equivalent
c. a[b(b + 6) + 7(a² - 2)] - Equivalent
d. a[(b + 6)(b + 7a² - 14)] -Not equivalent
Thus,
The equivalent expression is
C. a [b (b + 6) + 7 (a² - 2)]
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Solve 10x=3
how do i take logarithms on both sides?
Answer:
x ≅ 0.477.
Step-by-step explanation:
You probably meant:
[tex]10^x = 3.[/tex]
If that is the case, then let's solve it:
[tex]10^x = 3\\\\log\,10^x=log\,3\\\\x = log\,3\\\\x = (approx.)\,\,0.477.[/tex]
Slope is given by the formula
Answer:
A
Step-by-step explanation:
Answer
You never add or subtract to get the slope. That makes C and D incorrect. B is the upside down of the answer.
Answer: the answer is A slope = rise / run
Equation P: a + b = 6
Equation Q: 4a + 2b = 19
Which of the following steps can be used to eliminate the a term?
−1(4a + 2b = 19)
−4(4a + 2b = 19)
−4(a + b = 6)
4(a + b = 6)
Answer:
-4(a + b = 6)
Step-by-step explanation:
When you multiply equation P by -4, you obtain -4a - 4b = -24. You can then add this equation to equation Q to eliminate the a term.
modal mark of 1,2,3,4,5,6,7,8
Answer:
1
Step-by-step explanation:
the mode is the number that is repeated more often than any other numbers. the given numbers are 1,2,3,4,5,6,7,8 firstly, the numbers should be counted accordingly.
the number 1 is counted as 1.
the number 2 is counted as 1.
the number 3 is counted as 1.
the number 4 is counted as 1.
the number 5 is counted as 1.
the number 6 is counted as 1.
the number 7 is counted as 1.
the number 8 is counted as 1.
after counting the numbers, the maximum number counted (or) repeated most is 1 as 1 times.
the mode of the given values is 1.
Ten copper pennies having a total mass of 25 grams warm up from 23oC to 38oC as you hold in your hand. If the specific heat capacity of copper is 0.39 J/(g *oC), how much energy is absorbed by the pennies?
The amount of energy absorbed by the pennies made up of copper is 146.25J
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Amount of energy absorbed = mass * temperature change * specific heat capacity
Amount of energy absorbed = 25 * (38 - 23) * 0.39 = 146.25J
The amount of energy absorbed by the pennies made up of copper is 146.25J
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3. What is the measure of angle HEK in this figure?
95
55
85
150
Answer:
95 is the correct answer
Step-by-step explanation:
The initial or beginning side is H. Look on the protractor and you will see the top number is 55 degrees. That is where we start. Now, go to line E, that is where we end. The top number is 150. To find <HEK, we need to subtract 55 from 150 to get 95.
Solve the system.
{3x+ 2y=8
{3x+3=y
Let's take this problem step-by-step:
Note:
'-- (1), -- (2), etc.' are equation markers used to show steps
First step, isolate all the variables to one side and constant to the other
[tex]3x + 2y = 8--(1)\\3x-y=-3--(2)[/tex]
Second step: (1) - (2)
[tex](1) - (2)\\3x + 2y-(3x-y)=8-(-3)\\2y + y=11\\3y = 11\\y = \frac{11}{3} --(3)[/tex]
Third step: Plug (3)'s value of y into (2)
[tex](3)_.into_.(2)\\3x -\frac{11}{3} = -3\\3x = \frac{11}{3}-3\\ 3x = \frac{11-9}{3} \\3x = \frac{2}{3} \\x=\frac{2}{9}[/tex]
Answer: x = 2/9, y = 11/3
Hope that helps!
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Answer:
3x+ 2y=8 ⇒ ( 1 )
3x+3=y ⇒ ( 2 )
First, let us take the equation (1).
We can replace y with ( 3x + 3 ).
Solving the below expression let us find the value of x.
[tex]3x + 2y = 8\\3x + 2 ( 3x + 3 ) = 8\\3x + 6x + 6 = 8\\9x + 6 = 8\\9x = 8 - 6\\9x = 2\\x = \frac{2}{9}[/tex]
And now let us take equation ( 2) to find the value of y.
For that let us replace x with 2/9.
Let us find it now.
[tex]3x+3=y\\\\3*\frac{2}{9} +3=y\\ \\\frac{6}{9} +3=y\\ \\\frac{6}{9} +\frac{3}{1} =y\\\\\frac{6}{9} +\frac{3*9}{1*9} =y\\\\\frac{6}{9} +\frac{3*9}{1*9} =y\\\\\frac{6}{9} +\frac{27}{9} =y\\\\\frac{33}{9} =y\\\\\frac{11}{3} = y[/tex]
The product of a number and the sum of six and five is equal to the sum of the number and thirteen. What is the number?
The number is 13 / 10
How to solve words problem using equation?The product of a number and the sum of six and five is equal to the sum of the number and thirteen.
Therefore,
let the number = x
x(6 + 5) = x + 13
Hence,
x(6 + 5) = x + 13
11x = x + 13
11x - x = 13
10x = 13
x = 13 / 10
Therefore, the number is 13 / 10
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the eastern alberta DC transmission like is a project that began construction in 2012. It includes a 500km, 500kv power line from the brooks area to the edmonton area. (the V stands for volts, and SI unit for the electrical potential)
The number of the required towers based on the information given is 3334.
How to calculate the number?From the information given, it should be noted that the length of power line is 500km
The towers supporting the line are 1.5hm apart. It should be be noted that 1km = 10hm. Therefore, the require towers will be:
= (500 × 10)/1.5
= 3334
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How many positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1?
Using the Fundamental Counting Theorem, it is found that there are 10 positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The number of options for each selection are given as follows, considering there are 10 possible digits, and that the last two are fixed at 7 and 1, respectively:
[tex]n_1 = 10, n_2 = n_3 = 1[/tex]
Hence, the number of integers is given by:
N = 10 x 1 x 1 = 10.
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Write an equation that represents the line
Answer:
y=2/3x±3
Step-by-step explanation:
use the formula y=MX+b m being alive b being the y intercept
Hello,
f(x) = ax + b
We know f(0) = 3 = b
a = ∆y/∆x = 3/2
equation that represents the line → y = 3/2x + 3
translate the sentence into an equation rhoda's score decreased by 10 is 51 use r to represent rhoda's score
Answer: r - 10 = 51
Step-by-step explanation:
A beekeeper’s hives are making honey at a constant rate. The profit from honey can be represented by the equation
P(t) = -16t2 + 2050t + 150, where t is the time in days and P(t) is the profit the beekeeper receives. After how many days should she harvest her honey to maximize profit?
Using the vertex of a quadratic function, she should harvest her honey after 64 days to maximize profit.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.The profit function is given as follows:
P(t) = -16t² + 2050t + 150.
The coefficients are a = -16 < 0, b = 2050, c = 150, hence the t-value of the vertex is:
[tex]t_v = -\frac{b}{2a} = -\frac{2050}{-32} = 64[/tex]
Hence she should harvest her honey after 64 days to maximize profit.
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1. a. Determine the equation of a parent function for the parabola that has zeros 1,-5.
Determine the member equation that passes through the point (-2,-36)
The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .
What is a Parabola ?Parabola is a U shaped figure , whose all points are at a fixed distanced from a point called as focus and a line called as Directrix.
It is given that
The zeroes of the parabola is 1,-5.
The equation of the parabola is given by
y = a( x - x')(x-x'')
y = a( x-1)( x+5)
This is the equation for the parent function for the parabola
The parabola passes through the point ( -2 , -36 )
-36 = a( -2 -1)(-2+5)
-36 = (-3) * (3) a
-36 = -9 a
a = 4
y = 4 ( x-1)(x+5)
The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .
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Suppose 20 cars start at a car race. In how many ways can the top 3 cars finish the race?
The number of different top three finishes possible for this race of 20 cars is
There are 6,840 different top 3 finishes.
In how many ways can the top 3 cars finish the race?We need to count the number of options for each position.
For the first position there are 20 possible options (20 cars).For the second position, there are 19 options (because one car is already on the first position).For the third position, there are 18 options.The number of different top 3 finishes is given by the product between the numbers of options, so we have:
20*19*18 = 6,840
There are 6,840 different top 3 finishes.
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need help with this question
The Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).
What is a conic section?It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (circle is a special of type of ellipse).
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the graph:
a) The domain: all values of x
The range: all values of y
Except: Values at asymptotes are excluded.
Domain = (-∞, -2) U (-2, 2) U (2, ∞)
Range = (-∞, -2) U [-1, ∞)
b)
x-intercept = (-1.5, 0), (1.5, 0)
y-intercept = (0, -1)
c) Horiznotal asymptotes: y = -2
d)Vetical asymptotes: x = -2, x = 2
e) Oblique asymptotes: There is no oblique asymptotes
Thus, the Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).
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Which of the following is a solution to the equation ¾x-12=-18?
4.5
-22.5
-40
-8
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
We have the equation [tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x-12=-18}}[/tex].
First we should add 12 to both sides of the equation.
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x=-18+12}}[/tex]. Simplify
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x=-6}}[/tex].
This done, let's multiply the equation by 4. You'll see why
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{\not4}x\times\not4=-6\times4}}[/tex]
Did you see how on the left, the 4's cancelled? That's
because dividing by 4 and then multiplying the same
number, or the result, by 4, are operations that undo each
other.
This being said, let's finish solving this equation in terms of x
[tex]\large\boldsymbol{\sf{3x=-24}}[/tex]. See how this works?
Now, remember that we ought to use inverse operations
to solve for x. These are operations that undo each other.
So if x is multiplied by 3, we should... divide by 3!
Also, please keep in mind that we can only divide the left side
by 3 if we divide the right side by 3.
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3x}{3}=\displaystyle\frac{-24}{3}}}[/tex]. Once again the 3s on the left cancel, leaving
x. Wait! Isn't that what we wanted? Yepp, sure!
The right side is now -8. Thus,
[tex]\large\boldsymbol{\sf{x=-8}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
Using a supply and demand graph for gasoline starting at an equilibrium price of $5.00 per gallon and a quantity of 20
gallons, show the effect of a government price ceiling on gasoline of $2.50 a gallon. Is this a binding price ceiling? Why
or wy not? Please explain.
Yes, to some extent President Biden is right in telling them to lower the price rate because due to the war, a lot of gas companies a using it as a yardstick to inflate their prices and sell above the normal rate they bought it and the oil firms needs to consider the times that people are too.
2. The effect of a government price ceiling on gasoline of $2.50 a gallon is shown in the image attached. There is a binding at $2.00.
3. As price increases, demand also increases in times of gasoline because due to the war, Russia have refuse selling their oil and as such, this has lead to increase demand on the gasolines on ground.
What is Binding Price Ceiling?
A binding price ceiling is one that often takes place if the government are known to have set up a standard price on a good or goods at a specific price that is below equilibrium.
Therefore, to the number one question, we respond Yes, to some extent President Biden is right in telling them to lower the price rate because due to the war, a lot of gas companies a using it as a yardstick to inflate their prices and sell above the normal rate they bought it and the oil firms needs to consider the times that people are too.
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