Answer:
Number of bacteria at 11:53 for 53 min = [tex]2^{53}[/tex] = 9.007199 × [tex]10^{15}[/tex]
fraction that is full = [tex]2^{-7}[/tex]
Step-by-step explanation:
solution
Number of bacteria is express as here
Number of bacteria = [tex]2^t[/tex] ............1
so
bacteria at 1 min , 2 min and 3 min are
Number of bacteria at 1 min = [tex]2^1[/tex] = 2
Number of bacteria at 3 min = [tex]2^2[/tex] = 4
Number of bacteria at 3 min = [tex]2^3[/tex] = 8
and
as that Number of bacteria at 11:53 is for 53 min is
Number of bacteria at 11:53 for 53 min = [tex]2^{53}[/tex] = 9.007199 × [tex]10^{15}[/tex]
and
bottle is full at 12:00
so Number of bacteria at 12:00 for 60 min = [tex]2^{60}[/tex]
so fraction that is full = [tex]\frac{2^{53}}{2^{60}}[/tex]
fraction that is full = [tex]2^{-7}[/tex]
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Number of bacteria present in bottle at 11:53 are [tex]2^{53}[/tex].
At that time, fraction [tex]2^{-7}[/tex] or 0.00781 of bottle is full.
Since, single bacterium is placed in a bottle at 11:00am. It grows and at 11:01 divides into two bacteria. These two bacteria each grow and at 11:02 divide into four bacteria. Which grow and at 11:03 divide into eight bacteria.
So, a sequence is obtained 1, 2, 4, 8, 16, 32, 64, .........
We can also write as,
At 11:00 am, [tex]2^0[/tex] bacteria
At 11:01 am, [tex]2^1[/tex] bacteria
At 11:02 am, [tex]2^2[/tex] bacteria
Similarly, At 11:53 am, Number of bacteria present in bottle are [tex]2^{53}[/tex].
When the bottle will be full, that time number pf bacteria will be [tex]2^{60}[/tex].
S0, fraction of bottle is full at 11:53 is [tex]2^{53} /2^{60} = 2^{-7} = 0.00781[/tex]
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Please help me how do you recognize and complete a geometric sequence
Answer:
Step-by-step explanation:
If the sequence is being multiplied, for instance:
1, 2, 4 ,8 ,16
It is being multiplied by 2 every term.
Consider Brainliest.
Sir Dwayne is in charge of dragon designs at the King's Toy
Factory. He hopes that his new designs will please the king
*Your Highness," he says. "I have the plans for the toy
dragons. If it pleases you, every 3rd dragon shall billow
clouds of smoke through its nostrils. every 4th dragon shall
breathe fire, every 6th dragon shall have glowing eyes, and
every 8th dragon shall have a tail with spikes on it. i shail
make 100 dragons." The king asks. Sir Dwayne, how many
dragons shall have more than one of these
characteristics?" Sir Dwayne doesn't have the answer. Can
you help him answer the king before he is thrown into the
dungeon?
Answer:
24 dragonsExplanation:
Any multiple of 3 and 4 shall blow clouds of smoke through its nostrils and breathe fire. Those are:
the 12th, the 24th, the 36th, the 48th, the 60th, the 72nd, the 84th, and the 96th dragons.Hence, that is 8 dragons that shall have both characteristics.
Any multiple of 6 shall have glowing eyes. The common multiples of 6 and 3 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.
Then, that adds:
the 6th, 18th, 30th, 42nd, 54th, 66th, 78th, and the 90th dragons:Hence, add 8 more dragons.
And the common multiples of 6 and 4 are: 12, 24, 36, 48, 60, 72, 84, and 96, all of which are already included.
Any multiple of 8 shall have a tail with spikes on it. Then, you must find the common multiples of 8 and 3, 8 and 4, and 8 and 6.
Common multiples of 8 and 3 are: 24, 48, 72, and 96, which are already included.
Common multiples of 8 and 4 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96. Then, you must add:
the 8th, the 16th, the 32th, the 40th, the 56th, the 64th, the 80th, and the 88th.Those are other 8 dragons.
At the end the number of dragons that shall have more than one of these characteristics is:
8 + 8 + 8 = 24
Final answer:
By calculating the least common multiples (LCMs) of the intervals for the dragon's characteristics and considering the first 100 dragons, we find that there will be 12 dragons with overlapping features.
Explanation:
Sir Dwayne at the King's Toy Factory is tasked with creating dragons with characteristics that occur at different intervals. Specifically, every 3rd dragon billows smoke, every 4th breathes fire, every 6th has glowing eyes, and every 8th has a spiked tail. We are asked to calculate how many of the 100 dragons will have more than one of these features.
To solve this problem, we need to consider the least common multiples (LCMs) between the provided intervals: 3, 4, 6, and 8. The LCM of any two numbers is the smallest number that is a multiple of both numbers. We'll find the number of dragons that have characteristics occurring at multiple intervals (overlapping features).
LCM of 3 and 4 is 12, so every 12th dragon will both billow smoke and breathe fire.LCM of 3 and 6 is 6, so every 6th dragon will both billow smoke and have glowing eyes (this is not a new interval since 6 is a multiple of 3).LCM of 3 and 8 is 24, so every 24th dragon will billow smoke and have a spiked tail.LCM of 4 and 6 is 12, so every 12th dragon will breathe fire and have glowing eyes (also not new).LCM of 4 and 8 is 8, so every 8th dragon will breathe fire and have a spiked tail (this interval is covered by 8).LCM of 6 and 8 is 24, so every 24th dragon will have glowing eyes and a spiked tail (also not new).We must not forget to find the LCM for all three and four characteristics together, if any, to see if there is any dragon with three or all four features:
LCM of 3, 4, and 6 is 12.LCM of 3, 4, and 8 is 24.LCM of 3, 6, and 8 is 24.LCM of 4, 6, and 8 is 24.LCM of 3, 4, 6, and 8 is 24.Since the highest LCM (which covers all the characteristics) is 24, and we are making 100 dragons, we can divide 100 by 24 to find how many dragons would have all four characteristics. This results in 4 dragons with some remaining. Now, we'll consider all unique multiples of our LCMs up to 100 and sum them up, taking care not to double-count any dragons:
There are 8 multiples of 12 up to 100 (12, 24, ..., 96).There are 4 multiples of 24 up to 100 (24, 48, 72, 96).Note that every multiple of 24 is also a multiple of 12, which means these have already been counted. So, we only count the additional multiples of 12 that are not multiples of 24.
Counting all the unique multiples, we have: 8 (from LCM 12) + 4 (from LCM 24) = 12 dragons. Thus, Sir Dwayne will make 12 dragons having more than one of these characteristics.
Solve. 2x < -4 Find out for x!
Answer:
Step-by-step explanation:
2x < - 4
divide both sides by 2
[tex]\frac{2x}{2}<\frac{-4}{2}[/tex]
x < -2
x= {.........-5, -4 , - 3}
All values less than -2
at the grocery store, you bought 4 boxes of cereal and a carton of strawberries. The carton of strawberries costs $2.89. The bill came to a total of $12.25. How much was one box of cereal?
Answer:
$2.34
Step-by-step explanation:
Cost of 4 boxes
The cost of 4 boxes must be the difference between the total and the strawberries
total-strawberries
12.25-2.89=9.36
4 boxes costs $9.36
Cost of 1 box
You bought 4 boxes for $9.36, and each box costs the same, so we can divide the cost by the number of boxes
cost/boxes
9.36/4=2.34
Each box of cereal costs $2.34
Answer:
$2.34
Step-by-step explanation:
So first you have to subtract 2.89 from 12.25. then you should get 9.36. After you get that you have to divide 9.36 by 4 because there are 4 boxes of cereal and we need to know how much is the cost of one box of cereal. ONce you get that the answer would be $2.34.
Which graph models the function f(x) = -4(2)x? (2 points)
Answer:
pls mark me brainliest
Step-by-step explanation:
Answer:
Step-by-step explanation:
Refer to the image, please.
Answer:
7
Step-by-step explanation:
140*.60, 140*.55
=84 - 77 = 7
What is the rate of change in the equation?
y=8X+6
Answer:
the answer is -8
Step-by-step explanation:
Abdul is creating a cushion that is 1 foot by 2 feet by 3 feet. He wants to find the least amount of fabric he will need to cover the cushion. He starts by drawing the net shown here.
A net is formed by 2 rectangles. 1 rectangle has a base of 4 feet and height of 3 feet. The other rectangle has a base of 5 feet and height of 2 feet.
What is the least amount of fabric he will need to cover the cushion?
Answer:
22 ft²
Step-by-step explanation:
Surface area:
2×(1+3+1) + 3×(1+2+1)
2×5 + 3×4
10 + 12
22 ft²
Answer:
22
Step-by-step explanation:
im with you . i suck at math too
QR is tangent to circle P at point Q.
Circle P is shown. Line segment P Q is a radius. Line segment Q R is a tangent that intersects the circle at point Q. A line is drawn from point R to point P and goes through a point on the circle. Angle Q P R is 53 degrees.
What is the measure of angle R?
37°
53°
90°
97°
Answer:
A. 37 degrees
Step-by-step explanation:
Since QR is tangent to the circle, it means that is in a right angle. Meaning that angle Q is equal to 90 degrees.
Since you know what two angles are equal to, you can use the triangle angle sum theorem by setting them all up to 180.
53+90+x=180
Simplify the answer
143+x=180
Subtract 143 from both sides
X=37
:
The measure of angle ∠QRP = 37°.
What is a tangent to a circle ?Tangent to a circle is a straight line which touches the circle at only one point and the point of contact is perpendicular to the radius drawn from the center of the circle.
In the given question
Line segment PQ is radius, Line segment QR is is a tangent to the circle(P) at point Q.
Here QR is perpendicular to PQ because tangent to a circle is perpendicular to the point of contact and a line (PQ) drawn from the center of the circle (P).
∴ ∠PQR = 90° given ∠QPR = 53° We have to find ∠QRP .
We know the sum of all the interior angles in a triangle is = 180°
∠PQR + ∠QPR + ∠QRP = 180°
90° + 53° + ∠QRP = 180°
∠QRP = 180° - (90° + 53°)
∠QRP = 180° - 143°
∠QRP = 37°
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Which of the following is not equal to 63.7 mm?
6.37 x 10 4 µm
6.37 x 10 -5 km
637 cm
0.637 dm
The correct option is c. 637 cm is not equal to 63.7 mm.
To solve this problem, we need to convert each of the given units to millimeters (mm) and then compare them to 63.7 mm.
a. [tex]\(6.37 \times 10^4 \, \mu m\)[/tex] to mm:
Since 1 mm = \(1 \times 10^3 \, \mu m\), we have
\[6.37 \times 10^4 \, \mu m \times \frac{1 \, mm}{1 \times 10^3 \, \mu m} = 63.7 \, mm\]
This is equal to 63.7 mm.
b. [tex]\(6.37 \times 10^{-5} \, km\)[/tex] to mm:
Since 1 km = [tex]\(1 \times 10^6 \, mm\)[/tex], we have
[tex]\[6.37 \times 10^{-5} \, km \times \frac{1 \times 10^6 \, mm}{1 \, km} = 63.7 \, mm\][/tex]
This is also equal to 63.7 mm.
c. 637 cm to mm:
Since 1 cm = 10 mm, we have
[tex]\[637 \, cm \times \frac{10 \, mm}{1 \, cm} = 6370 \, mm\][/tex]
This is not equal to 63.7 mm.
d. 0.637 dm to mm:
Since 1 dm = 100 mm, we have
[tex]\[0.637 \, dm \times \frac{100 \, mm}{1 \, dm} = 63.7 \, mm\][/tex]
This is equal to 63.7 mm.
Therefore, the only option that is not equal to 63.7 mm is 637 cm.
What is the height of the prism if the surface area is 460 mm2?
A.) 13mm B.) 9.6mm C.) 7mm D.) 12mm
Answer:
C. 7mm
Step-by-step explanation:
the prism is rectangular so the answer is c
please help i’ll mark brainlest
Answer:i really dont know but i think it 27.5
Step-by-step explanation:
i think i've answered this before dont trust mee
Answer:
∠ A = 68°
Step-by-step explanation:
The sum of the interior angles of a kite = 360°
The opposite angles A and C are congruent
360° - (123 + 101)° = 360° - 224° = 136°
Thus since ∠ A = ∠ C, then
∠ A = [tex]\frac{136}{2}[/tex] = 68°
Given a 30-60-90 triangle with a long leg of 9 inches, determine the length of the hypotenuse
A Quick Guide to the 30-60-90 Degree Triangle
The 30-60-90 degree triangle is in the shape of half an equilateral triangle, cut straight down the middle along its altitude. It has angles of 30°, 60°, and 90°. In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, you can find the long leg by multiplying the short leg by the square root of 3.
Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. The long leg is the leg opposite the 60-degree angle.
Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles. All 30-60-90 triangles, have sides with the same basic ratio. If you look at the 30–60–90-degree triangle in radians, it translates to the following:
30, 60, and 90 degrees expressed in radians.
The figure illustrates the ratio of the sides for the 30-60-90-degree triangle.
A 30-60-90-degree right triangle.
A 30-60-90-degree right triangle.
If you know one side of a 30-60-90 triangle, you can find the other two by using shortcuts. Here are the three situations you come across when doing these calculations:
Type 1: You know the short leg (the side across from the 30-degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.
Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.
Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.
Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.
Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.
In the triangle TRI in this figure, the hypotenuse is 14 inches long; how long are the other sides?
Because you have the hypotenuse TR = 14, you can divide by 2 to get the short side: RI = 7. Now you multiply this length by the square root of 3 to get the long side:
The long side of a 30-60-90-degree triangle.
Use the table to write a linear function that relates y to x
Answer:
2/3x+5
Step-by-step explanation:
when x=0 your y-int is that y-coord.
the rest is just rise over run
What is the magnitude of the resultant of z-y?
x=9i-j-2k
y=-6i+2j-k
z=-i+5j+3k
Answer:
5sqrt(2)
Step-by-step explanation:
Z - Y
-i+5j+3k - (-6i+2j-k)
-i + 6i + 5j - 2j + 3k + k
5i + 3j + 4k
Magnitude:
sqrt(5² + 3² + 4²)
sqrt(50)
5sqrt(2)
Answer is
B = 5sqrt(2)
Lou started his savings account with 50$ he now only has 31$. What percent of change did his savings account have?
Answer:
Step-by-step explanation:
50 - 31 = 19
38%
How does -15/14 + 9/8 = 3/56
The point A(4, –1) is reflected over the x-axis. Use a mapping to find the coordinates of A’. A’(4, –1) A’(–4, –1) A’(4, 1) A’(–4, 1)
Answer:
(C) A'(4, 1)
Step-by-step explanation:
When a point is reflected across the x-axis, the following happens
The x-coordinate remains the sameThe y-coordinate is transformed into its opposite (its sign is changed).Given the Point A(4, –1)
When it is reflected, following the rules above
The x-coordinate remains 4The y-coordinate changes from -1 to 1.The coordinates of A' will therefore be: A'(4,1)
Answer:
c
Step-by-step explanation:
just did it on ed 2020
Please answer ASAP. What is the negative angle of rotation for the angle with positive angle
of rotation 270º?
Answer:
-90
Step-by-step explanation:
The full circle is 360 degrees, so is you turn one way say 10 degrees, then you would need to move 350 degrees in opposite direction.
So, in this case moving 270 one way would be equivalent to moving 360-270=90 degrees in the opposite direction
A farmer has $100,000 worth of cherries on the trees in his orchard. There is a 10% chance of the weather ruining his crop before harvest in
which case he would lose $40,000 worth of cherries. What would be the expected value of the crop?
??
Answer:
60,000 I think.
Step-by-step explanation:
the value (100,000) minus the damage (40,000) would equal 60,00
PLEASE HELP! Is my answer correct?
We know angle P is 90 degrees because of Thales Theorem, and angle N is 60 degrees. Because the angles in a triangle have to add up to 180 degrees, angle PMN has to be 30 degrees.
Angle QMO is half of angle PMN, so it's 15 degrees. Angle MQO is equal to angle QMO because the radii make Triangle OQM isosceles, so angle MQO is 15 degrees.
Answer:
yes this is right
Step-by-step explanation:
the triangle MOQ is icosceles and angle O is 150 degrees so that leaves 30/2... 15.
What ordered pair corresponds to point G?
Answer:
(-5,-2)
Step-by-step explanation:
g is on those coordinates.
Answer:
(-5,-2)
Step-by-step explanation:
You sell tires for $65 each at your automotive service shop. At this price, what does it cost to purchase a set of 4 tires, not including tax?
$69
$105
$260
$280
$325
Answer:
$260
Step-by-step explanation:
you multiply $65 by 4 for the set of four and the product is $260.
Answer:
A set of 4 tires cost $260.
Step-by-step explanation:
It is given that each tire is sold for $65. In order to find a set of 4 tires, you have to multiply it by 4 :
1 tire = $65
4 tires = $65×4
= $260
3/4 + 1/2=
7/8-3/8 =
5/6 1/4 =
4/6/1/4 =
178.96 - 25.78 =
10.25 - 110.25 + 1110.25 =
2.789 * 1.458 =
56.64/S =
Answer:
Okay so,
Step-by-step explanation:
the first one is
1.25 or 1 [tex]\frac{1}{4}[/tex]
second one is
0.5 or [tex]\frac{1}{2}[/tex]
the third one is
i'm not sure what the question is
the fourth one is
i'm not sure what the question is. Are you dividing?
the fifth one is
153.18
the sixth one is
1010.25
the seventh one is
4.066362
the eight one is
i'm not sure what the question is
Can you make me brainliest please
Divide.
12,360.1 ÷ 100,000
Enter your answer as a decimal in the box.
Answer:
0.123601
Step-by-step explanation:
Brian pays £180 per week in rent. His landlord decides to decrease the rent by 5%. How much rent does he pay now
Answer:
171
Step-by-step explanation:
180 - (5% × 180)
180 - 5% × 180
(1 - 5%) × 180
(100% - 5%) × 180
95% × 180
95 ÷ 100 × 180
95 × 180 ÷ 100
17,100 ÷ 100 = 171.
How many places do you need to move the decimal to the left to write the
number below in scientific notation?
6000000000000
Answer: 6 x 10^12
Step-by-step explanation:
Move the decimal to the left so there is one non-zero digit number left of the decimal point. This will be the exponent placed on 10
Milton has his money invested in a stock portfolio. The value, v(.r), of his
portfolio can be modeled with the function y(x) = 30,000(0.78)", where x is the
number of years since he made his investment. Which statement describes the rate
of change of the value of his portfolio?
A) It decreases 78% per year. B) It decreases 22% per year.
C) It increases 78% per year. D) It increases 22% per year.
Answer:
B) It decreases 22% per year.
Step-by-step explanation:
We are given that The value, v(.r), of his portfolio can be modeled with the function : [tex]y(x) = 30,000(0.78)^x[/tex]
Where x is the number of years since he made his investment.
Formula :[tex]P(1-r)^t=A[/tex]
Where P = Principal
r = rate of decrease
t = time
A = Amount after t years
So, On comparing
P = 30000
t=x
A=y(x)
[tex]1-r=0.78[/tex]
[tex]\Rightarrow 1-0.78=r[/tex]
[tex]\Rightarrow 0.22=r[/tex]
So, r = 0.22
r=22%
So, Rate of decrease is 22%
So, Option B is true,
It decreases 22% per year.
The solution (x, y) to a system of equations is the point where they...?
The solution (x, y) to a system of equations is the point where both equations intersect, meaning the coordinates (x, y) satisfy both equations simultaneously.
Explanation:In mathematics, specifically in algebra, the solution (x, y) to a system of equations is the point where they intersect. This means that the coordinates (x, y) satisfy both equations simultaneously.
For example, if you have the system of equations y = 2x + 1 and y = 4x - 3, their solution would be the point (x, y) that would make both equations true when substituted into these equations. This is an important concept in algebra and serves as the foundation for many subsequent topics.
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The solution to a system of equations is the point where their graphs intersect, representing values that satisfy both equations. This method is practical for two-variable systems.
The solution to a system of equations is the point where the graphs of the equations intersect. This point represents the values of x and y that satisfy both equations simultaneously.
For example, consider the system of equations:
Equation 1: 2x + y = 5
Equation 2: -x + 3y = 4
Graphing these equations, the point where the lines cross is the solution. If the lines intersect at (x, y) = (1, 3), then (1, 3) is the solution to the system. This graphical method is useful for two-variable systems but becomes impractical for systems with more variables.
Sophia invests $12,500 in an account that earns 4% annual simple interest. Assuming she makes no additional deposits or withdrawals, how much interest will Sophia earn after 3 years?
[tex]\text{Simple interest formula:}\\\\A=P(1+rt)\\\\\text{Plug in your given values:}\\\\A=12,500(1+0.04(3))\\\\\text{Solve:}\\\\A=12,500(1+0.04(3))\\\\A=12,500(1+0.12)\\\\A=12,500(1.12)\\\\A=14,000\\\\\boxed{\$14,000}[/tex]
Sophia will earn $14, 000 in interests after 3 years.
What is Interest?The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
We have,
Sophia invests $12,500 in an account.
R= 4%
Time= 3 years
So, Amount = P(1+ rt)
A = 12500 (1 + 0.04(3))
A = 12500 ( 1 + 0.12)
A = 12500 + 1.12
A = $14, 000
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