Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."
Calculation:x + y = 420; y = 6x
Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."
How well-versed are you in fish size?The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.
How many parrotfish purchased by Carlos?The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.
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Calculate the sample standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Body Temperatures (in F) of adult males 98.2 97.8 99.2 98.1 96.4 96.4 98.9 97.5 97.1 98.0 96.5 98.2 96.5 96.6 98.4 96.9 97.0 96.4 99.2 97.6
On solving the provided question, we cans ay that by standard deviation, [tex]SE = 0.1590 (approx.)[/tex]
What is standard deviation?Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed. Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed.
By sample standard deviation, we mean standard error. Hence, we have that:
Therefore, Standard deviation[tex]= 0.6929891[/tex]
The sample size [tex](n) = 19.[/tex]
Hence:
[tex]SE = 0.1589826.\\ SE = 0.1590 (approx.)[/tex]
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50 POINTS ANSWER FOR BRAINLIST AND HEARTS
The following are the answer to each statement;
The book is $18 - TrueGiselle can earn up to $18 pulling weeds for her grandma - FalseGiselle's grandma pays her $1 for every 5 weeds she pulls - TrueGiselle does not have to use any of her own money towards the purchase of the book when she pulls 90 weeds - TrueGiselle only needs to pull 18 weeds to not use any of her own money - FalseHow to interpret graph?1. The book is $18
The statement is true because the beginning of the graph represents cost before she picks any weeds.2. Giselle can earn up to $18 pulling weeds for her grandma.
This is not true because the graph shows that she is still able to earn more money from picking weeds.3. Giselle's grandma pays her $1 for every 5 weeds she pulls
This is true because the price change from $18 to $17 is $1 for 0 weeds to 5 weeds.4. Giselle does not have to use any of her own money towards the purchase of the book when she pulls 90 weeds.
This is true because the amount earned for 90 weeds is equivalent to the money needed to buy the book.5. Giselle only needs to pull 18 weeds to not use any of her own money
Giselle will need to pull 90 weeds in order to not spend her own money. The statement is false.Read more on graph:
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How do you simplify (1/1+i)?
Answer:
1+i
Step-by-step explanation:
Divide by 1
(1/1+i)
(1+i)
Identify the components of the numbers and add the real and imaginary parts separately
=(1)+(1)i
=(1)+(1)i
=(1+i)
how many storage locations are allocated by the statement declare a[4,9] as integer?
Total 36 storage locations are allocated by the statement declare [tex]a[4,9][/tex] as integer.
The statement declare [tex]A[4,9][/tex] as integer allocates 4 × 9 = 36 storage locations for the array A. Each storage location is capable of holding a single integer value.
In this statement, the array A is declared with two dimensions, 4 and 9. The first dimension, 4, represents the number of rows in the array, and the second dimension, 9, represents the number of columns. This means that the array A has a total of 4 rows and 9 columns, for a total of 4 × 9 = 36 storage locations.
Here's an example of how the array A might be structured in memory:[tex]A[0,0] \ A[0,1] \ A[0,2] \ A[0,3] \ A[0,4] \ A[0,5] \ A[0,6] \ A[0,7] \ A[0,8]\\A[1,0] \ A[1,1] \ A[1,2] \ A[1,3] \ A[1,4] \ A[1,5] \ A[1,6] \ A[1,7] \ A[1,8]\\A[2,0] \ A[2,1] \ A[2,2] \ A[2,3] \ A[2,4] \ A[2,5] \ A[2,6]\ A[2,7] \ A[2,8]\\A[3,0] \ A[3,1] \ A[3,2] \ A[3,3] \ A[3,4] \ A[3,5] \ A[3,6] \ A[3,7] \ A[3,8][/tex]
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state whether the following statement is true and explain why or why not: a trinomial is always a higher degree than a monomial.
Monomial has a degree of 4 in linear equation.
What in mathematics is a linear equation?
The algebraic equation y=mx+b is known as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let's define some of the vocabulary words so we can understand what is being asked.
trinomial: 3 terms → each term is separated by a plus or minus sign
Example: 5x² + 3x + 2
monomial: 1 term → no plus or minus sign exists in the term.
Example: 5x²
degree: the largest exponent → it can be in any of the terms.
Example: 5x² has a degree of 2
It is possible that a monomial has an exponent greater than that of a trinomial so the answer is NO!
trinomial: 5x² + 3x + 2 has a degree of 2
monomial: 5x⁴ has a degree of 4
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which of these situations can be represented by the opposite of -25
The situations that can be represented by the opposite of -25 are:
B. Leon gets paid $25. C. An airplane descends 25 feet. E. A bird flies 25 feet above sea levelHow can the opposite of -25 be calkculated?-25 can be seen as represention of the given situations fro the problem, and exploring the given options, we can see that 25 feet below the sea level with that ones balance can be gets reduced by $25.
But when exploring the But the opposite of (-25) then we can see that 25 feet above the sea level, and in this case the amount will be raised by $25. and the height by 25 feet with the increase in the debt by $25.
Therefore, option B ,C and E are correct.
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missing options:
A. A scuba diver is 25 feet below sea level. B. Leon gets paid $25. C. An airplane descends 25 feet. D. Sara has a $25 debt. E. A bird flies 25 feet above sea level
In ΔIJK, \overline{IK}
IK
is extended through point K to point L, \text{m}\angle JKL = (5x-3)^{\circ}m∠JKL=(5x−3)
∘
, \text{m}\angle KIJ = (2x+8)^{\circ}m∠KIJ=(2x+8)
∘
, and \text{m}\angle IJK = (x-1)^{\circ}m∠IJK=(x−1)
∘
. Find \text{m}\angle JKL.m∠JKL.In ΔIJK, \overline{IK}
IK
is extended through point K to point L, \text{m}\angle JKL = (5x-3)^{\circ}m∠JKL=(5x−3)
∘
, \text{m}\angle KIJ = (2x+8)^{\circ}m∠KIJ=(2x+8)
∘
, and \text{m}\angle IJK = (x-1)^{\circ}m∠IJK=(x−1)
∘
. Find \text{m}\angle JKL.m∠JKL.
The value of ∠JKI is 107⁰.
What is an angle of a triangle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that ∠JKI = (5x−3)⁰, ∠KIJ=(2x+8)⁰, and ∠IJK=(x−1)⁰.
The sum of all angles of a triangle is 180⁰.
(5x−3)⁰ + (2x+8)⁰ + (x−1)⁰ = 180⁰
(5x + 2x + x) + ( - 3 + 8 -1) = 180
8x + 4 = 180
Subtract 4 from both sides:
8x = 176
x = 22
Putting x = 22 in ∠JKI = (5x−3)⁰:
∠JKI = (5×22 − 3)⁰
∠JKI = 107⁰
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Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3. Which of these expressions is correct expression for Ahmad's number?
The expression when Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3 is 3(n + 4).
How to calculate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this scenario, Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3.
This will be:
= (n + 4) × 3
= 3(n + 4).
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Given the letters in the phrase FOLLOW YOUR DREAMS, what is the ratio of the total number of letters to vowels? Give your answer in simplest form
The ratio of the total number of letters to vowels is 5 : 16.
What is the ratio?
Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another value. The sign that is used to represent ratio is :.
Ratio of the total number of letters to vowels - total number of letters : total number of vowels
total number of letters = 16
total number of vowels = 5
Ratio of the total number of letters to vowels - 5 : 16
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A car drives 2 blocks north,then 3 blocks east, and finally 2 blocks south what is the displacement of the car ?
Using displacement as a vector quantity, the change or displacement of the car is 3 blocks
DisplacementDistance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point. is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definitions. Distance is the measure of “how much ground an object has covered during its motion” while displacement refers to the measure of “how far out of place is an object.”
The displacement of the car will the change in it's position from starting to it's present position.
This can be calculated mathematically as
2 + 3 - 2 = 5 - 2 = 3
The displacement is 3 blocks.
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In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
26 points are scored in the fifth game.
What is Average?The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
First four games, a netball team scores an average of 31 points per game.
x/4=31
Let x represents four games
x=124
After the fifth game, the average for the first five games is 30
y/5=30
Let y represents five games
y=150
We need to find the number of points scored in fifth game.
x-y
124-150
26
Hence, 26 points are scored in the fifth game.
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at the city museum, child admission is and adult admission is 5.20 on thursday, tickets were sold for a total sales of . how many child tickets were sold that day?
On solving the provided question we can say that - 112 child tickets were sold that day
What is equation?equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, finding a way to respond to them has been a major driving force behind the development of mathematics.
Call the number for children and the number for adults to get:
[tex]5.20c+8.50\\ a=1097.60[/tex]
and
a=4c
indicating that there were four times as many adults as youngsters.
Using this value in place of a
into the first equation we get:
[tex]5.2c+8.5(4c)=1097.6\\ 5.2c+34c=1097.6[/tex]
rearranging:[tex]c=1097.639.2=28[/tex]
and so:
[tex]a=4c=4⋅28=112[/tex]
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Lucia draws a square and plots the center of the square. She claims that any rotation about the center of the square that is a multiple of 45" will carry the square onto itselt Which statement best describes Lucia's claim? a. Lucia's claim is incorrect since not all rotations that carry a square onto itself are multiples of 45
b. Lucia's claim is incorrect slace not all rotations that are multiples of 45' carry a square onto itself c. Lucia's daim is correct since any rotation that is a multiple of 45 canles a square onto tselt d. Lucia's calm is correct since any rotation that comes a square onto itself is a multiple of 45
The statement that best describes Lucia's claim is at option (b), that is " Lucia's claim is incorrect since not all the rotations that are multiples of 45° carry a square onto itself".
What is the rotational symmetry of a square?Two halves of the square when a mirror line is drawn resemble the same or similar, then that square is said to be in symmetry. When the square is rotated about an angle, then it remained the same as the original shape, then that square is said to be the rotational symmetry of a square.Rotation of the given square and its symmetry according to the rotation:It is given that, Lucia draws a square and plots the center of the square.
Lucia claims that " any rotation about the center of the square that is a multiple of 45° will carry the square onto itself".
To verify this claim, we need to construct a square (ABCD) as shown in the figure.
When the square ABCD is rotated about 45° where we can it is 1 × 45°, the square formed is A'B'C'D' is not the same as the actual one. So, they are not in symmetry after the rotation n this case.
If we rotate again, that is for the second multiple of 45° (2 × 45°), we get a square A''B''C''D''. But, now the square is similar to the actual one. So, they are in symmetry.
This means we can say that, not for all the multiples of 45° rotation, the square does not carry onto itself.
Therefore, we can conclude that "Lucia's claim is incorrect since not all rotations that are multiples of 45' carry a square onto itself".
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Solve for ccc.
5c+16.5=13.5+10c5c+16.5=13.5+10c5, c, plus, 16, point, 5, equals, 13, point, 5, plus, 10, c
c=c=c, equals
The value of c in the equation 5c = 13.5 - 16.5 - 10c is 0.6.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign
In this case, 5c + 16.5 = 13.5 + 10c
Collect the like terms
5c - 10c = 13.5 - 16.5
- 5c = -3.0
Divide
c = -3.0 / -5
c = 0.6
The value of c is 0.6.
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Parker owns a food truck that sells tacos and burritos. He sells each taco for $4.50 and each burrito for $6.75. Yesterday Parker made a total of $576 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.
Answer:4.50t + 6.75b = 576
Step-by-step explanation:
alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. how many calories are in one cookie?
Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.
A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.
Let x = calories in cookies.
y = calories in carrots.
Now, according to the question:
5x + 2y = 590 --------------------------------------- (1)
3x + 4y = 410 -------------------------------------- (2)
Multiplying equation(1) by 3 and equation(2) by 5:
15x + 6y = 1770 ---------------------------(3)
15x + 20y = 2050 ---------------------------(4)
Solving we get:
y = 280/14
or, y = 20 units.
Putting the value of y = 20 in equation (2)
3x + 4y = 410
⇒ 3x + 4 × 20 = 410
⇒ 3x = 410 - 80
⇒ x = 330/3
⇒ x = 110 Units
Therefore, the calories of cookies is 110 units .
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a biased coin has the probability that a head comes up when flipped is 0.35.what is the expected number of heads that come up when it is flipped ten times?
This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.
The probability of getting a specific number of heads in a given number of flips follows a binomial distribution, which describes the probability of getting a certain number of successes in a given number of independent trials. The probability of getting a specific number of heads in ten flips can be calculated using the formula:
P(x heads in n flips) = (n choose x) * p^x * (1-p)^(n-x)
where p is the probability of getting a head on each flip and x is the number of heads.
For example, the probability of getting exactly 3 heads in ten flips is:
P(3 heads in 10 flips) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3) = 0.241
This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.
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Larry is using a map. The map states that 2 inches represents 200 miles of land. If the map itself is 12 inches
long, how many miles of land are being displayed?
Answer:
The map is displaying 600 miles of land.
Step-by-step explanation:
To find the number of miles of land being displayed on the map, you need to multiply the length of the map in inches by the conversion factor, which is the ratio of inches to miles. In this case, the conversion factor is 2 inches per 200 miles.
So, to find the number of miles of land being displayed on the map, you would do the following calculation: 12 inches * (200 miles / 2 inches) = 600 miles.
How do you define a variable and write an algebraic expression for the phrase: 12 less than a number?
The expression is x-12.
12 less than a number means subtracting 12 from that number.
So, 12 less than 20 is 8, because is 20−12, 12 less than 12 is 0, because it's 12−12, and so on.
But since the number you need to subtract from is unknown, it's a variable, and you can call it as you like, suppose x. So, using the variable we can write an expression that holds for any number, which always means "take 12 away from my number". If your number is x, the expression would be x-12
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Solve the following partical fraction
Answer:
=x^2-2x+3x-6
=x(x-2)+3(x-2)
=(x-2) (x+3)
A line passes through the points (20, 2) and (10, 1). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
[tex]y = \frac{1}{10}x[/tex]
Step-by-step explanation:
⭐ What is slope-intercept form?
[tex]y = mx + b[/tex]"m" is the slope"b" is the y-intercept (the y-value for when x = 0)First, we need to find the value of "m" using the slope formula.
⭐ What is the slope formula?
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex][tex](x_1,y_1)[/tex] is a coordinate that you are given[tex](x_2,y_2)[/tex] is another coordinate that you are givenSubstitute the two coordinates you are given into the slope formula.
[tex]m = \frac{1-2}{10-20}[/tex]
[tex]m = \frac{-1}{-10}[/tex]
[tex]m = \frac{1}{10}[/tex]
Substitute the value of "m" into the slope-intercept form equation.
[tex]y = \frac{1}{10}x + b[/tex]
Next, we need to find the value of "b". To do so, substitute a coordinate that you are given into the equation and solve for "b".
I am going to use (10,1), but you can also use (20,2).
[tex]1 = \frac{1}{10} (10) + b[/tex]
[tex]1 = 1 + b[/tex]
[tex]0 = b[/tex]
Substitute the value of "b" into the slope-intercept form equation.
[tex]y = \frac{1}{10}x[/tex]
25 { x }^{ 2 } +36 { y }^{ 2 } True or false: The polynomial is a difference of squares.
The polynomial 25x² + 36y² is the sum of the squares.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, 25x² + 36y² which can be written as,
= 5²x² + 6²y².
= (5x)² + (6y)² it is the sum of the squares, The difference of squares would be (5x)² - (6y)².
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not use steroids. a true positive means the athlete tested positive and used steroids. what is the probability the athlete used steroids, given that 1% of athletes use steroids, the test's false positive rate is 0.5%, and the test's true positive rate is 99%?
The probability that an athlete used steroids, given that they tested positive, is approximately 0.5025%.
In order to calculate the probability that an athlete used steroids given the information provided, we need to know the probability that they tested positive. To do this, we can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, we are trying to find the probability that an athlete used steroids (A) given that they tested positive (B). We know that the probability of A is 1% and the probability of B is 0.5%, so we can calculate P(A and B) by multiplying these two probabilities together:
P(A and B) = 1% * 0.5% = 0.005%
Next, we need to calculate P(B), which is the probability that the athlete tested positive. Since we know the false positive rate and the true positive rate of the test, we can use these to calculate P(B) using the formula:
P(B) = P(A and B) + P(not A and B)
P(B) = P(A|B) * P(B) + P(not A|B) * P(B)
P(B) = 0.99 * 0.005% + 0.005 * (1 - 0.005%)
P(B) = 0.00495% + 0.005 * 0.999
P(B) = 0.0099495%
Now that we have P(A and B) and P(B), we can plug these values into the formula for conditional probability to calculate the probability that an athlete used steroids, given that they tested positive:
P(A|B) = P(A and B) / P(B)
P(A|B) = 0.005% / 0.0099495%
P(A|B) = 0.5025%
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If MNP~QRP, find MP (urgent please help!!!!)
Two or more figures are said to be similar when they have common properties. The value of MP is 18 units.
More than one figure are said to be similar if they have some relatable common properties, either considering their length of sides or measure of their internal angles. But similarity is not the same as congruence.
In the given question, it can be deduced that ΔMNP is similar to ΔQRP. Thus, relating the corresponding sides of the two triangles we have;
[tex]\frac{12}{30}[/tex] = [tex]\frac{5x-2}{11x+1}[/tex]
cross multiply to have
30(5x-2) = 12(11x+1)
150x - 60 = 132x + 12
collect like terms
150x - 132x = 12 + 60
18x = 72
x = 4
So that,
MP = 5x - 2
= 5(4) - 2
= 20 -2
MP = 18 units
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-3 + 2i.
What is the absolute value?
The required absolute value of the given complex number is |-3 + 2i| = √13.
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
The complex number is given in the question as:
-3 + 2i
We have to determine the absolute value of the given complex number.
The absolute value of a complex number a+ib is denoted as |a+ib| and is given by √(a²+b²)
As per the given question, we have
⇒ |-3 + 2i| = √((-3)²+2²)
⇒ |-3 + 2i| = √(9 +4)
⇒ |-3 + 2i| = √13
Therefore, the required absolute value of the given complex number is |-3 + 2i| = √13.
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dylan and sam start at the same point and begin jogging in different directions. dylan is jogging east at a speed of 4 miles per hour. sam is jogging south at a speed of 3 miles per hour. after how many hours will they be exactly 15 miles apart?
After 3 hours Dylan and Sam will be exactly 15 miles apart .
In the question ,
it is given that ,
the speed at which Dylan is jogging in east = 4 miles per hour .
the speed at which Sam is jogging in south = 3 miles per hour .
the distance covered by Dylan is = 4t
the distance covered by Sam is = 3t
we have to find the time when they are 15 miles apart .
Since Dylan walks in east and Sam walks in South , it forms a right triangle , so , it will satisfy the Pythagoras Theorem ,
(3t)² + (4t)² = 15²
9t² + 16t² = 225
225 = 25t²
t² = 225/25 = 9
t = 3
Therefore , the time taken will be 3 hours .
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32) Solve for "c".
C/100 = 51/60
Answer:
The answer is 85
Step-by-step explanation:
c/100 = 51/60
(c) × (60) = (51) × (100)
60c = 5100
60c/60 = 5100/60
c = 85
Thus, The value of y is 85
Answer:
[tex] \sf \: c = 85[/tex]
Step-by-step explanation:
Given equation,
[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]
Now the value of c will be,
[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]
[tex] \sf \rightarrow \: c = ( \frac{51}{60} ) \times 100[/tex]
[tex] \sf \rightarrow \: c = \frac{(51 \times 100)}{60} [/tex]
[tex] \sf \rightarrow \: c = \frac{5100}{60} [/tex]
[tex] \sf \rightarrow \boxed{ \sf c = 85}[/tex]
Hence, the value of c is 85.
mr. crandall has assigned a term paper due at the end of the semester. he would like to know the average length of the paper. the data below are the numbers of typed pages from a random sample of 10 term papers. what type of critical value is needed to create a 95% confidence interval for the population mean length of all term papers for this class?
There is a 95% chance that the mean length of all term papers lies between confidence limits (11.58,17.82) for the given data:
14, 20, 25, 10, 16, 8, 15, 12, 18, 9
We assume the length of paper has an approximately normal distribution.
Sample size = 10
The sample mean for the given data = 14.7
The standard deviation for the given data = 5.04
Critical value is obtained from standard normal distribution at the level of significance 0.05.
The critical value is 1.96.
The 95% confidence interval for the mean length of all term papers is calculated as follows:
P(14.7 - (1.96 x (5.04/√10)) < µ < 14.7 + (1.96 x (5.04/√10))) = 0.95
P(11.58 < µ < 17.82) = 0.95
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In 2000, the world population was calculated to be 6,071,675,206. The world population increases at a rate of about 1.2% annually. Write a function that represents the world population y after x years. A) y = 6,071,675,205(1.012)^x B) y = 6,071,675,206(1.012)^x C) y = 6,071,605,205(1.012)^x D) y = 6,071,675,215(1.012)^x b. In what year will the world population be 8,000,000,000? Round to the nearest year if necessary.
Hence, the population increases to [tex]72860102.5[/tex] in the year [tex]2001[/tex] which is nearest to the [tex]8000000000[/tex].
What is the rate of change?
Rate of change (ROC) refers to how quickly something changes over time. It is thus the acceleration or deceleration of changes (i.e., the rate) and not the magnitude of individual changes themselves.
Here given that,
In [tex]2000[/tex], the world population was calculated to be [tex]6,071,675,206[/tex]. The world population increases at a rate of about [tex]1.2[/tex]% annually.
As the population increases [tex]1.2[/tex] % in every year
i.e., [tex]\frac{1.2}{100}=0.012[/tex]
So, the population in the year [tex]2001[/tex] is
[tex]6,071,675,206(0.012)=72860102.5[/tex]
which is the nearest value in the year [tex]2001[/tex].
Since, the population size increases [tex]72860102.5[/tex] which is the nearest to the [tex]8000000000[/tex].
Hence, the population increases to [tex]72860102.5[/tex] in the year [tex]2001[/tex] which is nearest to the [tex]8000000000[/tex].
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Differentiate 3x² over x³ +3
Answer:
[tex] \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]
Step-by-step explanation:
We can use the quotient rule:
[tex] \displaystyle{y = \frac{u}{v} \to y '= \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]
In this case, u and v both are functions. By applying formula above, we will have:
[tex] \displaystyle{y' = \dfrac{(3 {x}^{2})' ( {x}^{3} + 3) - (3 {x}^{2} )( {x}^{3} + 3)' }{( {x}^{3} + 3)^{2} }}[/tex]
Then apply power rule to derive functions, we have to know that:
[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: (c \in \mathbb{R})}[/tex]
Therefore, we will have:
[tex] \displaystyle{y' = \dfrac{6x ( {x}^{3} + 3) - (3 {x}^{2} )3 {x}^{2} }{( {x}^{3} + 3)^{2} }}[/tex]
Expand the terms in:
[tex] \displaystyle{y' = \dfrac{6 {x}^{4} + 18x - 9 {x}^{4} }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3 {x}^{4} + 18x }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]
Hence, that's the answer. You can keep in unfactored form or factored form as you desire!
