Jaime says that the value of -1 x n is always equal to the value of n = (-1) for all
values of n.
Explain whether Jaime is correct or incorrect.
Answers
Related Questions
Assume that lines which appear to be tangent are tangent.
Find the value of the?
Answers
Answer:
12
Step-by-step explanation:
Assume that lines which appear to be tangent are tangent.
Therefor this is a right triangle.
Use the pythagorean theorem
c^2 = a^2 + b^2
15^2 = ?^2 + 9^2
225 = ?^2 + 81
subtract 81 from both sides
144 = ?^2
Take the square root of both sides
12 = ?
9514 1404 393
Answer:
? = 12
Step-by-step explanation:
The tangent makes a right angle with the radius at the point of tangency. That means the Pythagorean theorem can be used to find the missing length.
?² +9² = 12²
?² = 225 -81 = 144
? = √144 = 12
The value of ? is 12.
__
Additional comment
When you see a right triangle with the ratio of hypotenuse to leg of 15:9 = 5:3, you know immediately that it is a multiple of a 3:4:5 right triangle. Here, the scale factor is 3, so the missing side is 3×4 = 12.
One Sunday, 120 days before Christmas, Aldsworth store publishes an advertisement saying ‘120 shopping days until Christmas'. Aldsworth subsequently publishes similar advertisements every Sunday until Christmas. a. How many times does Aldsworth advertise? b. Find the sum of the numbers of days published in all the advertisements. c. On which day of the week is Christmas?
Answers
Answer:
(a)18
(b)1089
(c)Sunday
Step-by-step explanation:
The problem presented is an arithmetic sequence where:
First Sunday, a=1Common Difference (Every subsequent Sunday), d=7We want to determine the number of Sundays in the 120 days before Christmas.
(a)In an arithmetic sequence:
\(\text{The nth term}, T_n=a+(n-1)d\\T_n \leq 120\\$Therefore:$\\1+7(n-1) \leq 120\\1+7n-7\leq 120\\7n-6\leq 120\\7n\leq 120+6\\7n\leq 126\\$Divide both sides by 7$\\n\leq 18\)
Since the result is a whole number, there are 18 Sundays in which Aldsworth advertises.
Therefore, Aldsworth advertised 18 times.
(b)Next, we want to determine the sum of the first 18 terms of the sequence
1,8,15,...
\(\text{Sum of a sequence}, S_n=\frac{n}{2}( 2a+(n-1)d)\\S_{18}=\frac{18}{2}( 2*1+(18-1)*7)\\=9(2+17*7)\\=9(2+119)\\=9*121\\S_{18}=1089\)
The sum of the numbers of days published in all the advertisements is 1089.
(c)SInce the 120th day is the 18th Sunday, Christmas is on Sunday.
Use an algebraic approach to solve the problem.
Abby has 37 coins, consisting only of dimes and quarters, worth $5.65. How many dimes and how many quarters does she have?
Answers
Answer:
13 quarters and 24 dimes
Step-by-step explanation:
13*.25=3.25
24*.1=2.4
3.25+2.4=5.65
Write the constraint described by each of the following statements. Variable terms should all be on the left side of the constraint followed by the correct inequality or equality symbol and the right side should be a numeric value. I recommend using the equation writer in Word under the Insert tab. To receive full credit the constraint should be written with variables on the left hand side and a single numeric value on the right hand side (e.g. 4x1-3x2≤0)
The total production of A and B must at least 100 units.
The quantity of Y must be at least two times as large as one-fifth the quantity of Z.
The ratio of x1 to x2 can be no more than the ratio of 13 to 23.
The quantity of M must be at least one-fourth as large as the sum of P and Q.
The production of D must be no more than 6 more than twice the production of C.
Answers
1) The total production of A and B must be at least 100 units: A + B ≥ 100.
2) Y ≥ 2/5 * Z. 3) x1 / x2 ≤ 13/23. 4) M ≥ 1/4 * (P + Q). 5) D ≤ 2C + 6.
1) The total production of A and B must be at least 100 units:
A + B ≥ 100.
2) The quantity of Y must be at least two times as large as one-fifth the quantity of Z:
Y ≥ 2/5 * Z.
3) The ratio of x1 to x2 can be no more than the ratio of 13 to 23:
x1 / x2 ≤ 13/23.
4) The quantity of M must be at least one-fourth as large as the sum of P and Q:
M ≥ 1/4 * (P + Q).
5) The production of D must be no more than 6 more than twice the production of C:
D ≤ 2C + 6.
In summary:
1) A + B ≥ 100.
2) Y ≥ 2/5 * Z.
3) x1 / x2 ≤ 13/23.
4) M ≥ 1/4 * (P + Q).
5) D ≤ 2C + 6.
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FILL THE BLANK. a ____ diagram is used to describe the wiring details of a specific piece of equipment.
Answers
A schematic diagram is used to describe the wiring details of a specific piece of equipment.
A schematic diagram is a graphical representation that depicts the electrical connections, components, and circuitry of a system or device.
It provides a simplified and standardized visual representation of the wiring and electrical connections, allowing engineers, technicians, or users to understand the internal workings of the equipment.
In a schematic diagram, different symbols and lines are used to represent various electrical components such as resistors, capacitors, switches, transformers, and wires.
The connections between these components are illustrated using lines that indicate the flow of electrical current.
Schematic diagrams are widely used in various fields, including electronics, electrical engineering, telecommunications, and industrial automation.
They are essential for designing, troubleshooting, and repairing equipment as they provide a clear and concise representation of the electrical connections and functionalities.
Overall, schematic diagrams serve as a vital tool for understanding the wiring details of a specific piece of equipment, enabling efficient analysis, troubleshooting, and communication of electrical systems.
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We just purchased some sweet tea concentrate (we're being adventurous). It's supplied as a 90% solution. We need 5 L of 40% sweet tea concentrate for the cookout later (it'll make some great tea). How would we make this solution (note: we'll need to add water to our concentrate to make the sweet tea)? 2. The molecular weight of anhydrous calcium chloride is 110.99grams/mol. How many grams do we need for 400ml of 790mM calcium chloride? 3. We have 10 mL of cells to treat with Hydrogen Peroxide (H
2
O
2
), such that the final concentration of H
2
O
2
is 20μM. How much of a 30mM stock solution of H
2
O
2
would we add to our cells? 4. We need to prepare a stock solution of medium for your culture cells, which usually includes liquid salt solution and bovine serum. Our liquid salt solution is supplied in a 50X concentration, and we need to dilute it to 1X for use. We also need to add 75% fetal bovine serum for a final concentration of 15%. How would we make up 0.80 liters of this culture media using water as our solvent?
Answers
1. To make 5 L of a 40% sweet tea concentrate, you need to mix approximately 2.22 L of the 90% sweet tea concentrate with 2.78 L of water.
2. For 400 ml of 790 mM calcium chloride, you would need approximately 34.97 grams of anhydrous calcium chloride.
3. To achieve a final concentration of 20 μM hydrogen peroxide in 10 ml of cells, you would need to add approximately 6.67 μL of a 30 mM stock solution of hydrogen peroxide.
4. To prepare 0.80 liters of culture media, you would need to mix 16 ml of the 50X liquid salt solution with 784 ml of water.
C1V1 = C2V2 where C1 is the initial concentration (90%), V1 is the initial volume (unknown), C2 is the desired concentration (40%), and V2 is the final volume (5 L). Rearranging the equation, we have:
V1 = (C2V2) / C1
Plugging in the values, we get:
V1 = (0.4 * 5 L) / 0.9
V1 ≈ 2.22 L
So, you'll need to mix approximately 2.22 L of the 90% sweet tea concentrate with 2.78 L of water to obtain 5 L of a 40% sweet tea concentrate for your cookout.
To calculate the amount of anhydrous calcium chloride needed for 400 ml of 790 mM calcium chloride, you can use the formula:
mass = molarity × volume × molecular weight
First, convert the molarity from mM to M (mol/L):
790 mM = 0.79 M
Then, calculate the mass using the formula:
mass = 0.79 M × 0.4 L × 110.99 g/mol
mass ≈ 34.97 g
Therefore, you would need approximately 34.97 grams of anhydrous calcium chloride for 400 ml of 790 mM calcium chloride solution.
To determine the amount of a 30 mM stock solution of hydrogen peroxide (H2O2) needed to achieve a final concentration of 20 μM in 10 ml of cells, you can use the formula:
C1V1 = C2V2
Where C1 is the initial concentration (30 mM), V1 is the initial volume (unknown), C2 is the desired concentration (20 μM), and V2 is the final volume (10 ml). Rearranging the equation, we have:
V1 = (C2V2) / C1
Plugging in the values, we get:
V1 = (20 μM × 10 ml) / 30 mM
V1 ≈ 6.67 μL
Therefore, you would need to add approximately 6.67 μL of the 30 mM stock solution of hydrogen peroxide to your 10 ml of cells to achieve a final concentration of 20 μM.
To prepare a stock solution of medium for your culture cells, you'll need to dilute the liquid salt solution and add the required amount of fetal bovine serum (FBS). Since the liquid salt solution is supplied at a 50X concentration and you need a 1X concentration, you'll need to dilute it 50-fold. For a final volume of 0.80 liters, you'll need to mix 0.016 liters (or 16 ml) of the 50X liquid salt solution with 0.784 liters (or 784 ml) of water.
Next, you'll need to calculate the volume of FBS required to achieve a final concentration of 15%. To calculate this, you can use the equation:
V_FBS = (C_FBS × V_total) / C_FBS%
Where V_FBS is the volume of FBS, C_FBS is the desired concentration (15%), V_total is the final volume (0.80 liters), and C_FBS% is the concentration of the supplied FBS (75%). Plugging in the values, we get:
V_FBS = (0.15 × 0.80 liters)
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2 or more angles are supplementary if their sum is 180°. An angle is 4 times the value of its supplement.
I really need help to set up and solve an equation in order to find the measures of the 2 of the angles immediately!!!
I give the Brainliest to whoever got the best correct answer with anyone’s best efforts of step-by-step explanation, so anyway guys, good luck with your answering and I will check to see if you understand my question or not in order to answer my mathematics question! :)
Answers
Answer:
Smaller Angle : 36 degrees
Bigger Angle : 144 degrees
Step-by-step explanation:
So we can name the smaller angle x and the larger one 4x. We can add them and make the answer 180. x+4x=180, 5x=180, x=36
Smaller angle : x=36
Bigger Angle : 4x=36*4=144
Answer:
Angle X = 36
Angle Y = 144
Please give me Branliest
Step-by-step explanation:
Ok, so
X + Y = 180
and
4X = Y
So we substitute
X+4X = 180
5X = 180
X = 36
Now
36 + Y = 180
-36 -36
Y = 144
Nadia constructed a figure with these views.
Bottom view: pentagon.
Side view: rectangle.
Front view: rectangle.
Which figure could Nadia have constructed?
a pentagonal pyramid
a hexagonal pyramid
a pentagonal prism
a hexagonal prism
Answers
Nadia has constructed a pentagonal prism
We know that, a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.
If we consider the bottom view of pentagonal prism then it would be pentagon in shape.
If we consider the side view of pentagonal prism then it would be rectangular in shape.
If we consider the front view of pentagonal prism then it would be rectangle.
Therefore, Nadia has constructed a pentagonal prism
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Find the area under the standard normal distribution curve to the right of z = 2. 13 ?.
Answers
The area under the standard normal distribution curve to the right of z = 2. 13 is 0.9896
what is standard normal distribution curve?
With a mean of 0 and a standard deviation of 1, the standard normal distribution is a normal distribution. The standard deviation, which indicates how much a given measurement deviates from the mean, is given by the standard normal distribution, which has zero as its center.
solution:
Here, P( z ≥ 2.13 ) = 0.9896 ( From the Area of standard normal distribution curve)
Hence the Area under the curve is 0.9896
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what is the maximum of the sinusoidal function? enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
B
What is the slope of the line that passes through the points (1, -1) and (-8, -7) Write your answer in simplest form
Answers
Answer:
2/3
Step-by-step explanation:
Compute the slope of the line through the following points:
p_1 = (1, -1) and p_2 = (-8, -7)
The slope of the line through (x_1, y_1) and (x_2, y_2) is:
(y_2 - y_1)/(x_2 - x_1)
Substitute (x_1, y_1) = (1, -1) and (x_2, y_2) = (-8, -7):
= (-7 - -1)/(-8 - 1)
-8 - 1 = -(8 + 1):
= (-7 - -1)/(-(8 + 1))
8 + 1 = 9:
= (-7 - -1)/(-9)
(-1)^2 = 1:
= (-7 + 1)/(-9)
-7 + 1 = -6:
= (-6)/(-9)
The gcd of -6 and -9 is -3, so (-6)/(-9) = (-3×2)/(-3×3) = (-3)/(-3)×2/3 = 2/3:
Answer: = 2/3
In space, how many planes can be perpendicular to a given line at a given point on that line in space?
A. 1
B.0
C. 3
D. infinitely many
Answers
In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.
The correct answer is Option D.
The key concept here is that a plane is defined by having at least three non-collinear points.
When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.
Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.
Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.
The correct answer is Option D.
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assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. xy
Answers
If the function is y=\(\sqrt{x}\), dx/dt=5 and x=9 then dy/dt is equal to 5/6.
Given that the function is y=\(\sqrt{x}\), dx/dt=5 and x=9.
We are required to find the value of dy/dt.
Function is relationship between two or more variables that are expressed in equal to form. The values that we enter in the function is known as part of domain and the values that we get in the function is known as part of codomain.
y=\(\sqrt{x}\)
differentiate both sides with respect to t.
dy/dt=1/2\(\sqrt{x}\) *dx/dt-------1
We have to use the value of x and dx/dt in 1.
dy/dt=1/2*\(\sqrt{9}\) *5
dy/dt=1/2*3 *5
dy/dt=5/6
Hence if the function is y=\(\sqrt{x}\), dx/dt=5 and x=9 then dy/dt is equal to 5/6.
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Question is incomplete. It should include the following function:
y=\(\sqrt{x}\)
Can someone tell me if this right or wrong
Answers
Answer:
Yes, it's right
Step-by-step explanation:
What is the area of the trapezoid above?
A. 188 cm²
B. 196 cm²
C. 392 cm²
D. 5,236 cm²
Answers
Answer:
B. 196cm²Step-by-step explanation:
Area = h/2 (b_1+b_2)
\(\sf\cfrac{7}{2}\:(22+34)\)
Add 22 and 34 = 56
\(\sf \cfrac{7}{2} \times 56\)
Let's express 7/2 * 56 as a single fraction:-
\(\sf \cfrac{7\times 56}{2}\)
Multiply 7 and 56 = 392
\(\sf \cfrac{392}{2}\)
Divide
\(\sf 196\)
Therefore, the area of the trapezoid is 196cm².
_______________________
A recipe for 20 cookies uses 2 1/2 cups of milk. How many cookies are
made from each cup of milk? *
Answers
Answer:
8 cookies are made per cup of milk.
Step-by-step explanation:
20 divided by 2 and 1/2 is 8.
8 + 8 + 4 (or half of 8) = 20
hope this helps. . .
have a good day. UwU
A ferris wheel has a radius of 80 feet. two particular cars are located such that the central angle between them is 165. to the nearest tenth, what is the length of the intercepted arc between those two cars on the ferris wheel?
Answers
Rounded to the nearest tenth, the length of the intercepted arc between the two cars on the ferris wheel is approximately 36.7 feet.
To find the length of the intercepted arc between the two cars on the ferris wheel, we can use the formula:
Arc length = r * θ
Where r is the radius of the ferris wheel and θ is the central angle between the two cars.
Given that the radius of the ferris wheel is 80 feet and the central angle is 165 degrees, we can plug these values into the formula:
Arc length = 80 * (165/360)
Simplifying this equation, we get:
Arc length ≈ 80 * 0.4583
Arc length ≈ 36.66 feet
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Find the measure of the arc or angle indicated
Answers
Answer:
b
Step-by-step explanation:
Hunter kicked a soccer ball. the ball went 33/2 yards in 3/8 second. at that rate, how far would the ball go in 1 second?
Answers
The ball would go 44 yards in 1 seconds
How to calculate the number of yards ?
Hunter kicked a soccer ball
It went 33/2 yards in 3/8 seconds
The distance it will travel in 1 second can be calculated as follows
33/2 = 3/8
x= 1
Cross multiply both sides
3/8x = 33/2
x= 33/2 ÷ 3/8
x= 33/2 × 8/3
x= 44
Hence the ball will move 44 yards in 1 second
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In a math test, there are 16 multiple-choice problems. Correct answer will get 6 points, and wrong answer will deduct 2 points, and leaving the question not answered will get 0 point. Stan has one question not answered, at least how many correct answer(s) should he get in order to get total score not less than 60
Answers
So if he has one question not answered that stays at 0 points+ however many points he already has. He has to get at least 10 questions right. 10x6= 60
Suppose that two cars are having a race. The distance traveled by one car after t seconds is 10t^2+50t meters, while the distance traveled by the other car after t seconds is meters. How far apart would the two cars be after t seconds?
Answers
For the given scenario, the distance traveled by the first car after t seconds is 10t^2+50t meters, while the distance traveled by the second car is not provided. Therefore, the exact distance between the two cars cannot be determined without additional information.
To find the distance between the two cars, we need to know the distance traveled by the second car after t seconds. Without this information, we cannot determine the distance between the two cars at any given time. However, we can make some general observations about the situation.
If the second car travels a greater distance than the first car, the distance between the two cars would increase over time. Conversely, if the second car travels a shorter distance than the first car, the distance between them would decrease over time. Additionally, if the second car travels the same distance as the first car, the distance between the two cars would remain constant.
In conclusion, without knowing the distance traveled by the second car, we cannot determine the exact distance between the two cars at any given time. However, we can make some general observations about the situation based on the relative distances traveled by the two cars.
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the volume of this cone is 1,884 cubic millimeters. What is the radius of this cone? Use 3.14 and round your answer to the nearest hundredth
Answers
18 mm is the height of the cone.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.
We can use the formula for the volume of a cone to solve for the height:
V = (1/3)πr²h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we have:
1884 = (1/3)π(10²)h
Simplifying, we get:
h = 1884 / [(1/3)π(10²)]
h ≈ 18
Therefore, the height of the cone is approximately 18 mm.
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Complete question:
the volume of this cone is 1,884 cubic millimeters. What is the height of this cone when the radius is 10 mm? Use 3.14 and round your answer to the nearest hundredth
An art teacher buys 9 bags of cotton balls there are 68 cotton balls in each bag whitch expression is best to estimate the number of cotton balls there teacher buys
Answers
Answer:
612
Step-by-step explanation:
9 x 68 = 612
By multiplying 5/3^4 by _________, we get 5^4
Answers
The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.
The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:
(5/3^4) * x = 5^4
To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:
5^4 = 5 * 5 * 5 * 5 = 625
Now, let's simplify the left side:
5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81
Now we have:
(5/81) * x = 625
To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:
(81/5) * (5/81) * x = (81/5) * 625
On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:
1 * x = (81/5) * 625
Simplifying the right side:
(81/5) * 625 = 13125
Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.
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William is thinking of 2 numbers. The larger number is four less than two times the smaller
number. The sum of the numbers is 104. What are William's numbers? Please write your
answer in a sentence.
Answers
Answer:
The numbers are 36 and 68.
Step-by-step explanation:
Let the smaller number be x.
"The larger number is four less than two times the smaller
number."
The larger number is
2x - 4
The sum of the numbers is x + 2x - 4, or 3x - 4.
"The sum of the numbers is 104."
3x - 4 = 104
3x = 108
x = 36
The smaller number is 36.
The larger number is 2x - 4, or
2x - 4 = 2(36) - 4 = 72 - 4 = 68
The larger number is 68.
Answer: The numbers are 36 and 68.
The high-low method: A.easily handles estimating the relationship between the dependent variable and two or more independent variables B.is more accurate than the regression method C.calculates the slope coefficient using only two observed values within the relevant range D.uses the residual term to measure goodness of fit
Answers
a balloon is released at ground level, and it rises into the air at a constant rate. after 12 seconds the balloon is 180 feet above the ground.
complete the table to describe the proportional situation. type your answers in the blanks.
Answers
Answer:
y = 15x
0=0, 1=15, 2=30, 3=45, 4=60, 5=75, 6=90
Step-by-step explanation:
180/12 = 15 ft/s
Therefore, every second, the balloon rises 15 feet.
Triangle T is enlarged with a scale factor of 4
and centre (0, 0).
a) What are the coordinates of A and A'?
b) What are the coordinates of B'?
Answers
1.823 radians are the coordinates of A and A, The coordinates of B' are; B' = (-3 * 4, -2 * 4) = (12, -8)
a) To enlarge a triangle with a scale factor of 4, we need to first enlarge the original triangle by a scale factor of 1, and then reflect it across the y-axis.
The coordinates of A can be found using the law of sines:
sin(A) = (a/2) / sin(c)
where a is the semi-perimeter of the original triangle, c is the semi-perimeter of the enlarged triangle, and sin(A) is the length of side A.
Substituting the given values, we get:
sin(A) = (4/2) / sin(6)
= 2 / 3 sin(6)
sin(6) = (a/2) / sin(A)
= (4/2) / 2 / sin(2)
= (4/2) / 2 * sin(2) / sin(A)
= (4/2) * sin(A) / sin(2)
= 4 * sin(A) / 3
Therefore, the length of side A is:
A = sin^-1(4 * sin(A) / 3)
= sin^-1(4) - sin^-1(sin(A) / 3)
= 1.823 radians
To find the coordinates of A', we can reflect the point A across the y-axis. The reflection is given by the equation:
(x, y) -> (-x, y)
Substituting the coordinates of A, we get:
A' = (-1.823, 1.823)
b) To find the coordinates of B', we need to find the coordinates of B first. We can do this by reflecting the point B across the y-axis using the equation:
(x, y) -> (-x, -y)
Substituting the coordinates of B, we get:
B = (-3, -2)
The coordinates of B' are:
B' = (-3, -2)
Since the triangle is enlarged with a scale factor of 4, the coordinates of B' will be multiplied by 4. Therefore, the coordinates of B' are:
B' = (-3 * 4, -2 * 4) = (12, -8)
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Hi pls help me ILL GIVE BRAINLIEST TO WHO ANSWERS CORRECTLY
Answers
Answer:
Linear pair
Step-by-step explanation:
∠6 and ∠7 are linear pair angles.
the count in a bacteria culture was 900 after 20 minutes and 1100 after 35 minutes. assuming the count grows exponentially,
What was the initial size of the culture?
Find the doubling period.
Find the population after 60 minutes.
When will the population reach 15000.
Answers
The population will reach 15,000 after approximately 156.24 minutes.
To find the initial size of the culture, we can use the exponential growth formula:
\(N = N0 * e^(rt)\)
Where:
N = final count after a certain time
N0 = initial count
r = growth rate
t = time in minutes
e = Euler's number (approximately 2.71828)
We are given two data points:
At 20 minutes: N = 900
At 35 minutes: N = 1100
Using these points, we can set up two equations:
\(900 = N0 * e^(20r) ---(1)\)
\(1100 = N0 * e^(35r) ---(2)\)
To solve this system of equations, we can divide equation (2) by equation (1):
\(1100 / 900 = (N0 * e^(35r)) / (N0 * e^(20r))\)
Simplifying:
\(1.2222 = e^(35r) / e^(20r)\)
\(e^(a - b) = e^a / e^b:\)
\(1.2222 = e^((35-20)r)\)
Taking the natural logarithm (ln) of both sides:
\(ln(1.2222) = ln(e^((35-20)r))\)
ln(1.2222) = (35-20)r
Now we can solve for r:
r = ln(1.2222) / 15
Using a calculator, we find:
r ≈ 0.0461
Now we can substitute the value of r into equation (1) to find N0:
\(900 = N0 * e^(20 * 0.0461)\)
\(N0 = 900 / e^(0.922)\)
N0 ≈ 697.86
Therefore, the initial size of the culture was approximately 697.86.
To find the doubling period, we can use the formula:
doubling period = ln(2) / r
doubling period = ln(2) / 0.0461
Using a calculator, we find:
doubling period ≈ 15.03 minutes
Therefore, the doubling period is approximately 15.03 minutes.To find the population after 60 minutes, we can use the formula:
\(N = N0 * e^(rt)\)
\(N = 697.86 * e^(0.0461 * 60)\)
Using a calculator, we find:
N ≈ 1579.83
Therefore, the population after 60 minutes is approximately 1579.83.
To find when the population will reach 15,000, we can rearrange the formula:
\(N = N0 * e^(rt)\)
15,000 = N0 \(* e^(0.0461 * t)\)
Dividing both sides by N0 and taking the natural logarithm:
ln(15,000/N0) = 0.0461 * t
Now we can solve for t:
t = ln(15,000/N0) / 0.0461
Substituting the value of N0 we found earlier:
t = ln(15,000/697.86) / 0.0461
Using a calculator, we find:
t ≈ 156.24 minutes
Therefore, the population will reach 15,000 after approximately 156.24 minutes.
Learn more about bacteria problem here:
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