The distance between the tips of the hands is changing at a rate of 55 inches per minute at 9 o'clock.
To find the distance between the tips of the hands, we can use the Pythagorean theorem:
distance = $\sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$
As the clock moves, the minute hand will rotate 360 degrees in 60 minutes, or 6 degrees per minute, and the hour hand will rotate 360 degrees in 12 hours or 0.5 degrees per minute.
To find the rate at which the distance between the tips of the hands is changing, we need to find the rate at which the angle between the hands is changing.
We can use the fact that the angle between the hands is equal to the difference in the angular velocities of the hands.
Angular velocity of the minute hand = 6 degrees/minute
Angular velocity of the hour hand = 0.5 degrees/minute
Angular velocity of the distance between the tips of the hands = 6 - 0.5 = 5.5 degrees/minute
To convert this to distance per minute, we can use the fact that the distance between the tips of the hands is equal to the length of the hour and minute hand multiplied by the sine of the angle between them.
Distance per minute = 10 * 5.5 degrees/minute = 55 inches/minute
So, the distance between the tips of the hands is changing at a rate of 55 inches per minute at 9 o'clock.
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a 2x2x2 cube is made of 8 small cubes of which 4 are blue and 4 are white. the surface of the cube is formed from 6 2x2 squares. the small cubes are arranged in such a a way that the surface has as many fully white faces (faces white no black color anywhere) as possible. how many fully white faces does the 2x2x2 cube have?
The 2x2x2 cube has 6 fully white faces.
A cube is a solid shape with six square faces. Each square face has the same side length and thus all the faces have the same size. A cube has 12 edges and 8 vertices. Each vertex refers to a corner where three edges of a cube meet.
from given conditions, a 2x2x2 cube is made of 8 small cubes of which 4 are blue and 4 are white. the surface of the cube is formed from 6 2x2 squares.
and have to arranged in such a a way that the surface has as many fully white faces (faces white no black color anywhere) as possible.
So, A 2x2x2 cube has a total of 6 faces, and since the goal is to have as many fully white faces as possible, there must be at least 1 fully white face on each of the 6 sides. hence, the 2x2x2 cube has 6 fully white faces.
Therefore, the 2x2x2 cube has 6 fully white faces.
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What is the measure of angle R?
A. 30°
B. 50°
C. 100°
D. 180°
(Second image is a different question)
a hand of 14 cards is dealt from a well-shuffled standard 52-card deck of cards. what is the probability that the hand contains 4 jacks?
The probability that the hand contains 4 jacks is solved to be
0.003697
How to solve the probabilityProbability is solved using the formula
= required outcome / possible outcome
The required outcome
= number of ways of picking 4 jacks * number of ways of 10 cards from 48
= ⁴C₄ * ⁴⁸C₁₀
= 1 * 6540715896
= 6540715896
The possible outcome
= number of ways of picking 14 card from possible 52 cards
= ⁵²C₁₄
= 1.768966345 * 10¹²
The probability
= required outcome / possible outcome
= 6540715896 / 1.768966345 * 10¹²
= 11 / 2975
= 0.00369747
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Please help meeee this is due soon and I need help. It’s math :((((
The exact value of the trigonometric expression sin(x - y) is given as follows:
[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]
How to obtain the exact value of the trigonometric expression?The trigonometric expression in the context of this problem is defined as follows:
sin(x - y).
The identity used to obtain the sine of the subtraction of two angles is given as follows:
[tex]sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]
Considering the sine of x, the cosine of x is obtained as follows:
[tex]\sin^2{x} + \cos^2{x} = 1[/tex]
[tex]\left(\frac{\sqrt{28}}{6}\right)^2 + \cos^2{x} = 1[/tex]
[tex]\frac{28}{36} + \cos^2{x} = 1[/tex]
[tex]\cos^{2}{x} = \frac{7}{9}[/tex]
[tex]\cos{x} = \frac{\sqrt{7}}{3}[/tex]
The angle y, with a tangent of [tex]\frac{1}{\sqrt{3}}[/tex], is the angle of 30º, hence the sine and cosine are given as follows:
[tex]\sin{y} = \frac{1}{2}[/tex][tex]\cos{y} = \frac{\sqrt{3}}{2}[/tex]Hence the trigonometric expression is given as follows:
[tex]\sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]
[tex]\sin{(x - y)} = \left(\frac{\sqrt{28}}{6}\right) \times \frac{\sqrt{3}}{2} - \frac{\sqrt{7}}{3} \times \frac{1}{2}[/tex]
[tex]\sin{(x - y)} = \frac{\sqrt{84}}{12} - \frac{2\sqrt{7}}{12}[/tex]
[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]
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David has a Collection of nine gray fingerboards 4 white fingerboards and 3 yellow fingerboards. He chooses one at random locate the probability of the following events on the number line.
Answer:
B
Step-by-step explanation:
There are a total of 16 fingerboards. 4 of these are white. The probability that he will select a white fingerboard is 1/4. B represent 1/4.
The the probability of finding a white finger board is 0.25.
What is probability?Probability is the measure of how likely are the chance for any event to happen.
Given is that David has a Collection of nine gray fingerboards 4 white fingerboards and 3 yellow fingerboards.
We can write the probability of finding a white finger board as -
P{white} = 4/16
P{white} = 1/4
P{white} = 0.25
Therefore, the the probability of finding a white finger board is 0.25.
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What is the largest 3-digit number that is divisible by both 9 and 7?
The largest 3 digit number that is divisible by 9 and 7 is 945.
What are factors of a number?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.
If a number is divisible by 7 and 9 it shows that 7 and 9 are factors of the number. Since the number is a three digit number, the product of 7and 9 which is 63 will also be a factor.
the highest three digit multiple of 63 is 945.
This means that 945 can be divided by 7 and 9. i.e 945/7 = 135 and 945/9 = 105
Therefore the largest three digit number that can be divisible by both 9 and 7 is 945
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Find area of the rectangle
Answer:
[tex]6 {x}^{2} + 10x[/tex]
David is ordering tea from an online store. black tea costs $0.80 per ounce and green tea costs $1.20 per ounce. he plans to spend a total of $12 on the town types of tea combined. write an equation that represents the different situation and write what the variables represent
Answer: A good equation would be 1.20/12 and then 0.80/12.
Step-by-step explanation: after getting the answers from both equations you can determine how much to spend on each tea to evenly spend your money on both
750=1000*(1-(1/(1.01^139)))+(R/(1.01^140)
The value of R for the given expression will be 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰). The expression for the R will be solved as below,
750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰)
1000(1 - 1 / 4 + R / 4 ) = 750
1000(4 -1 + R ) / 4 = 750
1000 ( 3 + R ) = 3000
3 + R = 3
R = 3 - 3
R - 0
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a set of $16$ positive integers has mean, median, and unique mode all equal to $16.$ what is the largest possible value of one of the numbers in the set?
For a set of 16 positive integers to have a mean, median, and mode all equal to 16, the numbers in the set must all be equal to 16. Therefore, the largest possible value of one of the numbers in the set is 16.
The mean, median and mode of a set of numbers are all measures of the "typical" or "central" value of the set.
The mean is the sum of all the numbers divided by the number of elements in the set, the median is the middle value when a set of numbers is arranged in order of magnitude, and the mode is the number that appears most frequently in the set.
In this case, if all the 16 integers in the set are equal to 16, then the mean, median, and mode will all be 16 as well. Since the question states that the median, mode, and mean are all equal to 16, the only way for this to be true is if all the 16 integers in the set are equal to 16. So the largest possible value of one of the numbers in the set would be 16.
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y=x^{2}-2x-3 in vertex from
The vertex form is
y = (x - 1)^2 - 4.
What is vertex form?Generally, The equation of a parabola, which is a kind of quadratic function, may be written in a particular format known as the vertex form. The equation of the parabola may be written out in vertex form as follows:
y = a(x - h)^2 + k
If the vertex of the parabola is located at (h, k), and the leading coefficient is denoted by a. If an is positive, the parabola will have its lowest point at the vertex, and if an is negative, the vertex will have its highest point.
The vertex form is important because it makes it simple to determine where the vertex of a parabola is located, and it may also be used to establish the direction in which the parabola is pointing.
The vertex form of the equation y = x^2 - 2x - 3 is
y = (x - 1)^2 - 4.
The vertex of this parabola is at the point (1, -4).
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The value of a gold coin picturing the head of the Roman Emperor Marcus Aurelius is increasing at the rate of 11% per year. If the coin is worth $115 now, what will it be worth in 11 years?
$299.23
$236.00
$362.45
$254.15
The coin will be worth $299.23 in 11 years when increasing at the rate of 11% Option A is the correct answer.
What is exponential growth?A steady rate of expansion that is proportionate to the quantity's current size is referred to as exponential growth. In other words, a quantity expands more quickly the larger it is. The exponential function, which has the formula y = ab raised to x, can be used to mathematically represent exponential growth. Here, "a" stands for the beginning quantity or value, "b" is the growth factor or base, and "x" stands for the duration or number of growth periods. Population expansion, compound interest, and the spread of infectious illnesses are a few examples of real-world processes that show exponential growth.
The exponential growth is given by the formula:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
For the given situation we have: (P) = $115, the interest rate (r) = 11% or 0.11, and the number of years (t) = 11.
Thus,
[tex]A = $115(1 + 0.11/1)^{(1*11)}\\A = $115(1.11)^{11}[/tex]
A = $299.23
Hence, the coin will be worth $299.23 in 11 years. Option A is the correct answer.
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Right triangles 1,2, and 3 are given with all their angle measures and approximate side
lengths.
One of the right triangles that are given which can be used to approximate PQ of the given triangle above is triangle labelled 3 and it's value = 9.5.
What is a right triangle?A right triangle is defined as the triangle that is has one of its angle equal to 90 degrees.
Therefore, the value of the side of the triangle PQ can be obtained using the Pythagorean formula;
c² = a² + b²
c² = PR = 7²
a² = 6.4²
b² = PQ = ?
b² = c² - a²
b² = 49+40.96
b² = 89.96
b= √ 89.96
b = 9.5.
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A mirror should be centered on a wall. The mirror is 36 inches wide and the wall is 18 feet wide. Which equation helps determine the distance x on each side of the mirror O X =18 +3 O 3 + x + 3 = 18O X + 36 + x = 18O X + 3 + x = 18
The equation helps determine the distance x on each side of the mirror O is X + 36 + x = 18 (Option 3)
This equation helps determine the distance x on each side of the mirror. The mirror is 36 inches wide, so the distance on each side of the mirror should be equal. The wall is 18 feet wide, so we add the distance on each side and the width of the mirror to find the total width of the wall.
X + 36 inches (width of the mirror) + x = 18 feet (width of the wall)
So the equation is X + 36 inches + x = 18 feet
We can convert the inches to feet by dividing it by 12, so the equation becomes X + 36/12 + x = 18
X + 3 + x = 18
This is the equation that helps determine the distance x on each side of the mirror.
Therefore, The equation helps determine the distance x on each side of the mirror O is X + 36 + x = 18 (Option 3)
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describe and correct the error a student made in determining the relationship between the domain and range of f(x)
On solving the provided question, we can say that the relationship between the domain and range of f(x) = [tex]y = 9x + 1 = 10 + (x-1)(9)[/tex]
what is domain?Domain of a function is the set of possible values that it can accept. X-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. Set the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.
[tex]f(x) = y = 9x + 1 = 10 + (x-1)(9)\\f(1) = 9+1 = 10\\f(2) = 9(2)+1 = 19\\f(3) = 9(3)+1 = 28\\f(4) = 9(4)+1 = 37[/tex]
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529 students stand in the assembly hall so that there are as many students in a row as there are rows in the hall. How many students are standing in each row?
Answer:
Step-by-step explanation:
There are 529 students standing in the assembly hall, and since there are as many students in a row as there are rows in the hall, there must be an equal number of students in each row. Therefore, each row must have 529/rows = 529/rows students in it.
A drawing of a monster has an eye to head ratio of 5:1 and a head to tailratioof 2:6 if a monster has 20 eyes
The monster has 4 heads and 12 tails.
What is the ratio of the number?
A ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six .
We know that the ratio of the number of eyes to the number of heads is 5:1. If a monster has 20 eyes, we can set up the equation:
20 eyes = x heads
Where x is the number of heads.
We also know that the ratio of the number of heads to the number of tails is 2:6. We can set up the equation:
x heads = 2y tails
Where y is the number of tails.
We know the number of eyes is 20, therefore x = 20/5 = 4 heads
We also know the number of heads is 4, therefore y = 4*6/2 = 12 tails
Hence, the monster has 4 heads and 12 tails.
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Given the data set 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, which of the mean, median or mode would you use to describe the typical or central value in this date set? Why? O None of these as this data set is qualitative.O The mode as this data set is dominated by a single value. O The median as there are outliers at the high end of the data set causing the mean to be skewed high. O The mean as this data set has no outliers causing the mean to be skewed.
The mean as this data set has no outliers causing the mean to be skewed. option ( D )
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
The mode is the number that occurs most often in a data set.
Mean - Add all numbers and divide by the total number of numbers
-> 5.5
Median - When all the numbers are put in order least to greatest, the middle value (if there are two numbers, find the average of the two numbers)
-> 5.5
Mode - Number that shows up most often
-> None
I would use the mean or median to describe the typical central value because they are the same value.
Therefore, The mean as this data set has no outliers causing the mean to be skewed. option ( D )
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Andre came up with the following puzzle. “I am three years younger than my brother, and I am 2 years older than my sister. My mom’s age is one less than three times my brother’s age. When you add all our ages, you get 87. What are our ages?”
Jada writes this equation for the sum of the ages: (x)+(x+3)+(x−2)+3(x+3)−1=87 . Match each term of the equation with its meaning.
Answer:
Step-by-step explanation:
x: Andre's Age
(x+3): Andre's Brother's Age
(x−2): Andre's Sister's Age
3(x+3): Andre's Mom's Age
87: The Sum of All Four Ages
what is the area, in square inches, of a right triangle with a 24-inch leg and a 25-inch hypotenuse?
The area, in square inches, of a right triangle with a 24-inch leg and a 25-inch hypotenuse is 84 cm.
The area of a right triangle of base b and height h can be calculated using the formula 1/2 × b × h and its perimeter is obtained by just adding all the sides.
Length of one side of the right triangle (p) = 24-inch
Length of the hypotenuse of the right triangle (h) = 25-inch
Therefore, we can calculate the third side (b) of the triangle by applying the Pythagorean theorem
p² + b² = h²
24² + b² = 25²
b² = 625 - 576
b² = 49
b = 7 inch
Now, the area of the right triangle will be
= 1/2 × b × h
= 1/2 × 7 × 24
= 84 inch²
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Help me please thank you
Answer: 20 + x = y.
Step-by-step explanation:
When you deposit, you are adding onto something. Because there is no real value for x, the expression would be 20 + x = y. Also, it would be = y because it says clearly the total amount would be equal to y. and also since why has no value in this context, it would still be y.
What is 1/2 equal to as a number?
Two fractions are equivalent if they represent the same decimal number. For example, the three previous fractions represent the same decimal: 0.5. 1/2 is 1 between 2, which is 0.5
The converse is:
If a number is a whole number, then it is a natural number.
The following information should be considered:
Considering the conditional:
In the case when the number is a natural number, then it is a whole number.
>If a number is not a whole number, then it is not a rational number. The converse is false. ( converse must be true)
>If a number is a rational number, then it is a whole number. The converse is false. (converse must be true)
>If a number is not a rational number, then it is a whole number. The converse is false. (hypothesis should've been "then it is not a whole number")
In the Law of Detachment, if both conditional and hypothesis are true, then the conclusion is true.
All whole numbers are rational numbers.
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The circumference of a circle, in terms of π, is 13π m. Find the length of the radius.
Answer: The length of the radius is 13/2 m.
Step-by-step explanation:
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is pi (approximately 3.14159).
Given that C = 13πm. To find the length of the radius, we can divide both sides of the equation by 2π:
C = 2πr
13πm = 2πr
r = 13πm/2π
r=13/2 m.
The length of the radius of the circle is 6.5 m
If the circumference of the circle is C and the radius is r
Therefore, C= 2πr
According to the sum, the circumference of the circle is 13π m
Substituting that value in the equation,
13π= 2πr
=> r= 13π/ 2π
=> r= 6.5 m
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TRUE OR FALSE
The margin of error of a confidence interval is the error from using volunteer sampling methods.
True or False
False. The margin of error of a confidence interval is a measure of the amount of random sampling error in a survey's results.
What is error?Error in math is defined as an incorrect result or procedure in mathematical calculations or reasoning. It can be caused by a miscalculation, a wrong formula or equation, or a misinterpreted concept or instruction. It can also be caused by a misreading or misunderstanding of data, a misapplication of a theorem or rule, or a mistake in logic. Error in math can lead to incorrect or misleading results, and can have serious implications for applications relying on mathematics, such as engineering and financial analysis.
It reflects the amount by which an estimate from a sample might differ from the true population value. The margin of error does not reflect errors from using volunteer sampling methods. Volunteer sampling is a type of non-probability sampling in which individuals volunteer to participate in the survey. The margin of error is not affected by the type of sampling method used; it is affected by the sample size, confidence level, and variability of the population.
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Solve the system of linear equations by elimination.
3x+4y=-1
-2x-5y=10
Answer:
x = 5
y = -4
Step-by-step explanation:
3x+4y = -1
-2x-5y = 10
We time the first equation by 2 and the second equation by 3
6x + 8y = -2
-6x -15y = 30
-7y = 28
y = -4
Now put -4 back in for y and solve for x
3x+4(-4) = -1
3x - 16 = -1
3x = 15
x = 5
Let's check
3(5) + 4(-4) = -1
15 - 16 = -1
-1 = -1
So, x = 5 & y = -4 is the correct answer.
Express y in terms of x. 0.5y - 2 = 0.25x
Answer:
y = 0.5x + 4
Step-by-step explanation:
1. Move terms to one side of the equation
0.5y - 2= 0.25x +0
+2 +2
__________________
0.5y = 0.25x + 2
2. Divide the coefficient of y (0.5) to both sides of the equation
[tex]\frac{0.5y}{0.5} = \frac{0.25x}{0.5} + \frac{2}{0.5}[/tex]
3. Solve and simifpy
[tex]y = 0.5x +4[/tex]
53% of 2343 american adults surveyed said, they have watched digitally streamed tv programming on some type of device. what sample size would be required for the width of a 99% ci to be at most 0.05 irrespective of the value of at 99%
The sample size that would be required for the width of 99% is 2653.
What is sample size?The number of subjects involved in a sample size is referred to as the sample size in market research. A set of people chosen from the general community who are thought to be a representative sample size for that particular study is referred to as the sample size.
The following details are given:
Margin of error, E = 0.025; Significance Level, = 0.01
The proportion p is estimated to be p = 0.53.
The significance level with a critical value of 0.01 is 2.58.
The smallest sample size needed to estimate the population proportion p within the necessary margin of error is determined using the formula shown below:
n >= p*(1-p)*(zc/E)2 n = 0.53 *(1 - 0.53*)2 n = 2652.97 *(1-p)*(2.58/0.025)2
As a result, we determine that n = 2653 is the minimal sample size needed to satisfy the criteria that
n >= 2652.97 and that it must be an integer value.
Sample size is 2653.
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Anna has $274.00 in her account on sunday. over the next week, she makes the following changes to her balance via deposits and purchases: day debit ($) credit ($) monday 194.62 35.45 tuesday --- 11.20 wednesday 145.86 24.75 thursday 53.35 33.80 friday 31.60 45.77 saturday 12.90 61.63 on which day or days does anna get charged an overdraft fee? i. wednesday ii. thursday iii. fridaya. i onlyb. i and iic. ii and iiid. iii only
Thursday and Friday show a negative balance, then the answer is option c: II and II.
Overdrafts are charged when your balance is negative because it means the bank made a loan (an unexpected one) to you.
An overdraft occurs when a bank account holder withdraws more money than they have in their account. Banks typically allow account holders to spend more money than they have in their accounts, but they charge a fee or interest for doing so.
Overdraft protection is a service offered by many banks that automatically covers a certain amount of overdrafts, usually up to a certain limit, by transferring funds from a savings account or a line of credit. Banks will also charge a fee for this service.
Initial balance: $274
Day Debit ($) Credit ($) Balance($)
Monday 194.62 35.45 274.00 - 194.62 + 35.45 = 114.83
Tuesday --- 11.20 114.83 - 0 + 11.2 = 126.03
Wednesday 145.86 24.75 126.03 - 145.86 + 24.75 = 4.92
Thursday 53.35 33.80 4.92 - 53.35 + 33.8 = - 14.63
Friday 31.60 45.77 -14.63 - 31.60 + 45.77 = -0.46
Saturday 12.90 61.63 -0.46 - 12.90 + 61.63 =48.27
Thursday and Friday show a negative balance, then the answer is option c: II and II.
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Cells were infected with approximately 1,000 copies of either virus A or virus B at the 0 time point. At five-minute intervals, a sample of the virus and cell mixture was removed. The intact cells were removed from the sample, and the number of viruses per milliliter of culture was determined.
The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.
This graph will show the rate of infection for each virus and the total amount of virus present in the culture at any given time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.
The experimenters infected cells with either virus A or virus B and then sampled the mixture at five-minute intervals. After removing the intact cells, the number of viruses per milliliter of culture was determined and plotted on a graph over time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.
The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.
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Graph h(x)=7sinx . Use 3.14 for π . Use the sine tool to graph the function. Graph the function by plotting two points. The first point must be on the midline and closest to the origin. The second point must be a maximum or minimum value on the graph closest to the first point.
The graph of the function h(x) = 7sin(x) is given by the image presented at the end of the answer.
How to define the sine function?The sine function is given as follows:
y = Asin(Bx) + C.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.From this problem, the amplitude is given as follows:
A = 7.
Hence:
The midline is at y = 0.The minimum value is of -7, as there is no vertical shift.The maximum value is of 7, as there is no vertical shift.As there is no phase shift, the minimum and maximum values have the x-coordinate given as follows:
Minimum: x = -π/2.Maximum: x = π/2.As the function has no phase shift, the period is given as follows:
2π.
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