Answer:
a. Assuming we are starting out with the same mass or number of both cells, definitely there would be more cells of sample 2 after three hours
b. If there are equal number of both cells initially, there would be 8 times more of cell 2 than cell 1
Step-by-step explanation:
a.The first part of the question asks if there would be more cells of sample 1 or 2 after three hours.
Now, the first assumption we shall be making is that we have equal numbers or let’s say mass of both cells initially.
Okay, let’s say we have x g of both cells initially.
Now sample 1 cell divides every 20 minutes.
How many times will have divided in 3 hours? The correct way to tackle this is by knowing the number of two minutes in 3 hours.
In an hour, we have 3 20 minutes. So in 3 hours, we will have 9 20 minutes
Let’s take a look at the sample 2 cell.
it divides every 30 minutes.
Now, in an hour, we have 2 30 minutes. In 3 hours, we will be having 6 30 minutes
Since cell 2 underwent 6 divisions while cell 1 underwent 9 divisions within the same 3 hours and they both have the same mass initially, then we will have more of cell 2 after three hours.
b. We want to know by how many more.
Now, for cell 1 since the division is 9 times, and it is definitely an exponential division, the mass or amount of the original left after 9 half divisions would be;
(1/2)^9 = 1/512
So 1/512 of x would be left and that would be x/512 left
For cell 2, we have the same approach. There are six divisions.
The amount left after the 6th division would be;
(1/2)^6 = 1/64
So the amount left after the sixth division would be x * 1/64 = x/64
Now, we want to know by which amount is the division of cell 2 greater.
That would be x/64 divided by x/512 = x/64 * 512/x = 8
Which step can you use to solve the equation m+9=-2?
please help !!
Answer:
Subtract 9 from each side of the equation.
m = – 11
Step-by-step explanation:
m + 9 = – 2
To solve the above equation, we simply subtract 9 from each side of the equation.
This is illustrated below:
m + 9 = – 2
Subtract 9 from each side of the equation
m + 9 – 9 = – 2 – 9
m + 0 = – 11
m = – 11
Therefore, the value of m is – 11
Multiply the number by 4. Add 10 to the product. Divide this sum by 2. Subtract 5 from the quotient.
The first number is 1 and the result is 2
The second number is 5 and the result is 10
the third number is 9 and the result is 18
the fourth number is 10 and the result is 20
Write a conjecture that relates the result of the process to the original number selected. part a)
Represent the original number as n.
Answer is 2n
part b Represent the original number as n, and use deductive reasoning to prove the conjecture in part (a). Multiply the number by 4.
Help with part b please.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following instructions :
It can be deduced from part a that the final result will be twice the original number 'n'
The number 'n' multiplied by 4 = (4 * n) = 4n
10 added to 4n = 4n + 10
The result of the sum divide by 2 = (4n + 10) / 2
= 2n + 5
5 subtracted from the result of the quotient obtained : 2n +5 - 5 = 2n
Where n is the original number.
2n = twice the original number.
What is the product of (x+1) (x+4)
Answer:
x² + 5x + 4
Step-by-step explanation:
(x + 1) (x + 4)
apply the FOIL method
xx + (x * 4) + (1 * x) + (1 * 4)
xx + 4x + (1 * x) + (1 * 4)
xx + 4x + 1x + 4
x² + 5x + 4
how many solution this equation have 3r-5=3r-5
Answer:
infinite solutions
Step-by-step explanation:
Hello!
Since 3r - 5 is on both sides of the equation we can put any number in for r and it would still be true so the answer is infinite solutions
The answer is infinite solutions
Hope this helps!
x & y intercept for 4x+6y=12
Answer:
x- intercept at (3, 0)
y- intercept at (0, 2)
Step-by-step explanation:
x-intercept occurs at y=0.
4x +6y= 12
when y=0,
4x +6(0)= 12
4x= 12
x= 12 ÷4
x= 3
Thus, x-intercept occurs at x=3, at the point (3, 0).
y- intercept occurs at x=0.
4x +6y= 12
when x=0,
4(0) +6y= 12
6y= 12
y= 12 ÷6
y= 2
Thus, y- intercept occurs at the point (0, 2).
Miranda brought a square frame that has an area of 30 inches.what is the approximate side length of the frame?
Answer:In this question , the area of square frame is given which is 30 square inches .
And we have to find the length of the square frame .
Here we use the area of square, which is
Substituting the value of given area and solving for length, we will get
TO get rid of square , we have to take square root to both sides.
THerefore the length of the square frame is approximately 5.48 inches .
Step-by-step explanation:
Find the value of x. A. 20 B. 22–√ C. 163 D. 30−−√
Answer: Choice D. sqrt(30)
sqrt is shorthand for "square root"
======================================================
Explanation:
We'll use the intersecting chords theorem here
We multiply the pieces of each chord together and set the products equal to one another to help solve for x
TW*WU = CW*WV
x*2x = 6*10
2x^2 = 60
x^2 = 60/2
x^2 = 30
x = sqrt(30)
The value of x is √30. The correct option is D.
What is an intersecting chords theorem?The measure of the angle created when two chords collide inside a circle is one-half the sum of the arcs intercepted by the angle and its vertical angle.
Use the intersecting chords theorem here. Multiply the pieces of each chord together and set the products equal to one another to help solve for x
TW*WU = CW*WV
x*2x = 6*10
2x² = 60
x² = 60/2
x² = 30
x = √(30)
Therefore, the value of x is √30. The correct option is D.
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PDF attached below All questions are related to each other
1. The first option is represented by a linear function, ∴ y = 50x + 150. The y intercept here is 150, as the first week is 200 dollars, not the 0th week. 200 - 50 = 150.
Given the domain here is 1 - 6 (6 weeks) we can plug in x as 1,2,3 etc and solve for y, completing the table.
Option A :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 250 | 300 | 350 | 400 | 450 |
And for option b we have an exponential function. 1 + 10% = 1 + 0.1 = 1.1. Therefore we have the function ∴ y = 200( 1.1 )^x-1 that models this situation. Remember that we have " x - 1 " as the exponent rather than x, as the first week begins with 200 dollars, not the 0th week.
That gives us the following table,
Option B :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 220 | 242 | 266.2 | 292.82 | 322.102 |
2. (a) We already calculated the " iterative rules " for each sequence in the first part. For your explanation on that behalf, just include the explanation above. Rule of Option A : y = 50x + 150. Rule of Option B : [tex]y = 200( 1.1 )^{x-1}[/tex].
(b) Let's take an example week and substitute into our equations to help clarify our friend's doubt. Say week 2...
y = 50(2) + 150 = 100 + 150 = 250 ✓
y = 200( 1.1 )^2-1 = 200( 1.1 )^1 = 200( 1.1 ) = 220 ✓
3. (a) A function is an equation that represents the relation between x and y, which is exactly the purpose of the rules y = 50x + 150, and y = 200( 1.1 )^x-1.
(b) I disagree with my friend. These particular examples do have y - intercepts, but just because a rule is a function, doesn't make it have a y - intercept. There are some exceptions, such as y = 1 / x.
(c) An input such as 18.5 is meaningless, as x represents the weeks. An employer doesn't provide the payments at half weeks.
4. Let's substitute 20 as x,
y = 50 * 20 + 150 = 1,000 + 150 = $1,150
y = 200( 1.1 )^x-1 = 200( 1.1 )^20-1 = 200( 1.1 )^19 = $1,223.1818
The first payment option will provide the greatest total income.
Find the length of BC¯¯¯¯¯¯¯¯ A. 53.68 B. 48.21 C. 66.35 D. 28.34
Answer:
A 53.68
Step-by-step explanation:
tan54° = BC/39
BC = tan 54° x 39
BC = 53.68
Answer:
A. 53.68
Step-by-step explanation:
If f(x) = -3x2 - 4x + 8, find f(-6)
Answer:
-76
Step-by-step explanation:
[tex]f(x) = - 3 {x}^{2} - 4x + 8 \\ f( - 6) = - 3 {( - 6)}^{2} - 4( - 6) + 8 \\ f( - 6) = - 3 {( 36)} + 24+ 8\\ f( - 6) = - 108 + 32\\ f( - 6) = - 76[/tex]
Answer:
-3 × 2- 4x + 8 = -3 × 2 + -4 × -6 + 8 = -6 + 24 + 8 = 10
The discriminant is a quick way to determine the quantity and type of the possible solutions of a quadratic equation. If the discriminant has a value of -28, what can we conclude about the solution(s) to the equation? There are two real solutions to the quadratic equation. There is only one real solution to the quadratic equation. There are three real solutions to the quadratic equation. There are no real solutions to the quadratic equation.
Step-by-step explanation:
3x2 -5x+1=0
Quadratic eq ax2 +bx+c=0
Discriminant=b2 -4ac
=(-5)2 -4*3*1
=25-12
=13>0 so 2 solutions.
a parallelogram has sides lengths of 7inches and 11inches find the perimeter
Answer:
36 inches
Step-by-step explanation:
7 * 2 = 14
11 * 2 = 22
14 + 22 = 36
Answer: 36
Step-by-step explanation: Perimeter is the outside of a shape, so you double each number and add them since a parallelogram has 4 sides. 11+11=22. 7+7=14. 14+22=36
Solve for d when t = 0, t = 3, t = 5 d = t2 asap
Answer:
see below
Step-by-step explanation:
d = t^2
t =0
d = 0^2 = 0
t =3
d = 3^2 = 9
t =5
d = 5^2 = 25
Answer:
Step-by-step explanation:
If you are using
t =0
d = 0
t =3
d = 3^2 = 9
t =5
d = 5^2 = 25
∠5 is a supplement of ∠6, and m∠5=78°. Find m∠6.
Answer:
[tex]102^\circ[/tex]
Step-by-step explanation:
Given that:
[tex]\angle 5[/tex] is a supplement of [tex]\angle 6[/tex].
m[tex]\angle 5[/tex] = 78°
To find:
m[tex]\angle 6[/tex] = ?
Solution:
First of all, let us learn about the concept of an angle being a supplement of the other angle.
[tex]\angle B[/tex] is known as supplement of [tex]\angle A[/tex], if sum of the two angles is equal to 180°.
[tex]i.e. \angle A +\angle B=180^\circ[/tex].
For example, angle made on one side by a line intersecting the other line are supplement of each other.
Here, we are given that [tex]\angle 5[/tex] is a supplement of [tex]\angle 6[/tex].
In other words:
[tex]\angle 5+\angle 6=180^\circ[/tex]
Putting value of [tex]\angle 5[/tex]:
[tex]\Rightarrow 78^\circ+\angle 6=180^\circ\\\Rightarrow \angle 6 =180^\circ-78^\circ\\\Rightarrow \bold{\angle 6 =102^\circ\\}[/tex]
So, the answer is: [tex]102^\circ[/tex]
If the sales tax on $150 is $7.50
Answer:
$157.50
Step-by-step explanation:
150
+7.50
______
157.50
The diagram is a straightedge and compass construction. C is the center of both circles.
Which of the following statements must be TRUE by construction?
Answer:
The correct option is;
AC and CD have the same length
Step-by-step explanation:
Given that the circle with center C, we have;
The length of AC extending from C to A being from the center to the circumference is the radial length of the smaller circle of center C.
Similarly, the length of the segment that extends from the center of the circle with center C to the circumference of the circle is the also the radial length of the smaller circle of center C.
Whereby the radial length of a circle is constant, then two radial lengths of the same circle are congruent and and circle radius AC is congruent to radius CD, which gives;
Length of AC = Length of CD or AC and CD have the same length.
Find the value of x in the triangle shown below.
4
5
Choose 1 answer
Answer:
x=3
Step-by-step explanation:
using the pythagorean theorem, c^2=a^2+b^2
5^2=x^2+4^2, x=3
Answer:Three is the right answer I just finished
Step-by-step explanation:
If you were to round 897.234 to the hundredths place, what would be the
number?
Your answer
This is a required question
Answer:
897.23
Step-by-step explanation:
The decimal places start at the tenths:
00.tenths, hundredths, thousandths
So you would need to end up with only two numbers after the decimal.
To round, if a number is 4 or less, leave the next number as it is.
Ex: 2.32 → 2.3 Rounding to the tenths
78.614 → 78.6 Rounding to the tenths
If the number is 5 or higher, round up one number
EX: 37.76 → 37.8 Rounding to the tenths
6.389 → 6.4 Rounding to the tenths
Our number, 897.234, needs to be rounded to the hundredths place, so use the number to its right to determine the rounded value. The number 4 means that the hundredths place will remain the same, so the new value is:
897.23
:Done
Given the equation 5 + x -12 = 2x - 7. Part A. Solve the equation 5 + x - 12 = 2x - 7. In your final answer, be sure to state the solution and include all of your work. Part B. Use the values x = -0.5,0,1 to prove your solution to the equation 5 + x - 12 = 2x - 7 . In your final answer, include all of your calculations.
Answer:Solving for 5 + x - 12 = 2x - 7
Standard form:
−x = 0
Factorization:
−x = 0
Solutions:
x = 0
The solution is x = 0
The value of x in the equation 5 + x -12 = 2x - 7 is x = 0
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
5 + x -12 = 2x - 7 be equation (1)
On simplifying the equation , we get
Subtracting x on both sides of the equation , we get
5 - 12 = x - 7
Adding 7 on both sides of the equation , we get
x = 5 - 12 + 7
On simplifying the equation , we get
The value of x = - 7 + 7
The value of x = 0
Therefore , the value of x = 0
Hence , the value x of the equation is x = 0
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The sum of a number and six is two less than half the same number.
Answer:
-16
Step-by-step explanation:
x+6=x/2-2
solve the equation, x=-16
check:
-16+6=-10
-16/2=-8
-10-(-8)=-2
If the sum of a number and six is two less than half the same number then the number is -16.
Given,
The sum of a number and six is two less than half the same number
We will find the unknown number.
We have,
The sum of a number and six is two less than half the same number.
Let the unknown number be M.
Let us separate the given statement into parts:
- Sum of a number and six
This can be written as M + 6.
- is means equal sign "=".
- Two less than half the same number.
This can be written as (1/2)M - 2.
Now,
We can write as:
M + 6 = (1/2)M - 2
M - (1/2)M = -2 - 6
(1/2)M = -8
M = -8 x 2
M = -16
Thus the unknown number is -16.
We can also crosscheck:
M + 6 = (1/2)M - 2
-16 + 6 = (1/2)(-16) - 2
-10 = -8 -2
-10 = -10
Hence proved.
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A student has a rectangular block.It is 2 cm wide 3 cm tall and 25 cm long.It has a mass of 600 g.
Options for first blank: V=PR V=(PR)^(1/2) V=P^2R Options for second blank 16 5 4
Answer:
The formula to find the voltage is:
[tex]v=\sqrt{P*R}[/tex]
And the voltage is 4 volts
Step-by-step explanation:
To get the equation of voltage you need to isolate v in one side of the equation. In order to do that, you need to remove the divisor/denominator and its square. How will you do that?
First, multiply both sides with R:
[tex]P*R=\frac{v^{2} }{R} *R[/tex]
That would result into removing the divisor R from the right side of the equation:
[tex]P*R=v^{2}[/tex]
Next, square-root both sides:
[tex]\sqrt{P*R} =\sqrt{v^{2} }[/tex]
That would result in removing the square of v from the right side of the equation:
[tex]\sqrt{P*R} =v[/tex]
Thus we get the equation, [tex]v=\sqrt{P*R}[/tex].
To find out the voltage, simply replace R with 32 and P with 0.5
[tex]v=\sqrt{0.5*32}[/tex]
[tex]r=\sqrt{16}[/tex]
[tex]r=4[/tex]
Thus, the voltage is 4 volts.
Question 4 of 10
Which of the following is the inverse of the statement "If I do my homework,
then it will snow"?
A. If it snows, then I will do my homework.
B. If I do not do my homework, then it will snow.
Ο Ο Ο
C. If it does not snow, then I will not do my homework.
D. If I do not do my homework, then it will not snow.
Answer:
A
Step-by-step explanation:
The inverse of the statement "if a, then b" will always be "if b, then a". In this case, a = I do my homework and b = it will snow so the inverse is if it snows, then I will do my homework.
I need the answer ASAP !
Answer: A
Step-by-step explanation:
7[tex]\pi[/tex] pi is an irrational number and multiply it by 7 which is an rational number makes it irrational.
List three ordered pairs that represent solutions to the equation x - y = 5.
Answer:
2x-y=3
Step-by-step explanation:
Please Help. Most helpful answer and explanation would be very appreciated. I don't understand this.......Write each of the following equations in slope-intercept form.
1.) y − 1 = 4x − 4
2.) 3x = 2 − y
Answer:
1.) y = 4x - 3
2.) y = -3x + 2
Step-by-step explanation:
I'm not really sure how to explain it super well, but I do know the answers
2. 8- X6 + 9x2 - 2x
polynomial i need help
Answer:
26-8x
Step-by-step explanation:
factor the expression
simplify the expression
how many plants of each variety were planted?
Answer: u didnt give us the full problem
Step-by-step explanation:
whats 2 ( 4 + 7 ) =
Answer:
22. first multiply two with the digits and signs then add
So using order of operations (parentheses, exponents, multiplication & division, addition & subtraction), you have to do 4+7 inside the parentheses first, then multiply that by 2.
4+7=11
11×2=22
2(4+7)=22
♡ Hope this helps! ♡
❀ 0ranges ❀
i need help with 5 please
Answer:
28
Step-by-step explanation:
When x is equal to 4, j(x) = 28.