The combined ratio of x : y : z from x ; y = 4 : 3 and y : z = 5 ; 2 is x:y:z = 20:15:6
How to determine the combined ratioGiven the following ratios
x ; y = 4 : 3
y : z = 5 ; 2
To find the ratio of x:y:z, we need to combine the two given ratios and simplify:
x:y = 4:3
y:z = 5:2
To combine these ratios, we need to have a common term for y.
We can do this by multiplying the first ratio by 5 and the second ratio by 3:
5(x:y) = 5(4:3) = 20:15
3(y:z) = 3(5:2) = 15:6
Now we have a common term of 15 for y, so we can combine the ratios:
x:y:z = 20:15:6
Therefore, the ratio of x:y:z is 20:15:6
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An electric dipole with its center located at the origin of a Cartesian coordinate system oscillates along the z axis, creating an electromagnetic wave. At a position on the y axis far from the origin, what is the polarization of the wave and which axis are the magnetic (a) The wave is polarized parallel to the a axis and the magnetic field lines are parallel to b The wave is polarized parallel to the z axis and the magnetic field lines are parallel to (c) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (d) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (e) The wave is polarized parallel to the z axis and the magnetic field lines are parallel to field lines parallel to? the y axis the axis the r axis the z axis the z axis
The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.
The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.
The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.
According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.
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there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3 rd row, and so on. if the price per ticket is $32, how much will be the total sales for a one-night concert if all seats are taken?
Answer:
Step-by-step explanation:
To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.
To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:
S = n/2 * (a + l)
where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.
In this case, we have:
n = 20 (since there are 20 rows)
a = 25 (since there are 25 seats in the first row)
d = 2 (since the difference between each row is 2 seats, the common difference is 2)
We can use d to find the last term as well:
l = a + (n-1)*d
l = 25 + (20-1)*2
l = 25 + 38
l = 63
Now we can plug these values into the formula:
S = 20/2 * (25 + 63)
S = 10 * 88
S = 880
So there are 880 seats in total.
To find the total sales, we just need to multiply by the price per ticket:
total sales = 880 * $32
total sales = $28,160
Therefore, the total sales for a one-night concert with all seats taken would be $28,160.
13. The diagonals of a trapezium ABCD intersect at O. AB is parallel to DC, AB = 3 cm and DC = 6 cm. If CO = 4 cm and OB = 3 cm, find AO and DO.
Answer:
AO = 2 cmDO = 6 cmStep-by-step explanation:
You want the measures of AO and DO in a trapezium in which AB║CD, the diagonals intersect at O, and AB = 3 cm, CD = 6 cm, CO = 4 cm, OB = 3 cm.
Similar trianglesDiagonal AC is a transversal to parallel lines AB and CD, so alternate interior angles BAO and DCO are congruent. Vertical angles AOB and COD are also congruent, so ∆ABO ~ ∆CDO by the AA similarity postulate.
This means the side lengths are proportional, so ...
AB/CD = AO/CO = BO/DO
3/6 = AO/4 = 3/DO ⇒ AO = 2, DO = 6
The measures of AO and DO are 2 cm and 6 cm, respectively.
__
Additional comment
It can help to draw a diagram.
You have five student groups to present in class one group cannot go first because they need additional set up time and how many orders can they present
They can present in 96 different orders. Given, there are five student groups to present in class and one group cannot go first because they need additional set-up time.
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
We have 5 positions to fill here.
First position: 4 ways (one of the rest 4 groups will present first)
Second position: 4 ways (one of the rest 3 groups and the group which could not present first, will present second)
Third position: 3 ways (one of the rest 3 groups will present third)
Fourth position: 2 ways (one of the rest 2 groups will present fourth)
Fifth position: 1 way (rest group will present last)
Total ways in which they can present = 4*4*3*2*1 = 96
Hence, the answer is 96.
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Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2
XZ +Y2
Answer: 12.84
Step-by-step explanation:
if x = 3.2 and y = 6.1 and Z = 0.2
then plug in the numbers
(3.2)(0.2) + (6.1)(2)
0.64 + 12.2 = 12.84
Any variable next to a number means multiplication.
if I was wrong lmk
Complimentary Event The compliment of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted E (read "E bar"). Rule for Complimentary Events P(E)=1-P(E) or P(E)=1-P(E) O P(E)+P(E)=1 Example # 12: The probability that Mary can work a problem is 70%. Find the probability that Mary cannot work the problem. Example # 13: In 2004, 57.2% of all enrolled college students were females. Choose one enrolled student at random. What is the probability that the student was a male?
The student is male, which is P(male).Using the rule of complementary events, P(male) = 1 - P(female)P(male) = 1 - 0.572 = 0.428Therefore, the probability that the student is male is 0.428 or 42.8%.
The complimentary event is a part of probability theory. It is the event that occurs when the event E does not occur. In other words, it is a set of outcomes in the sample space that are not included in the outcomes of event E. The notation for the complement of E is E'. Rule for Complimentary EventsThe rule for complementary events can be expressed in two ways:
P(E) = 1 - P(E)P(E) + P(E') = 1Example # 12:Let the probability that Mary can work a problem be P(E) = 0.70.We need to find the probability that Mary cannot work the problem, which is P(E').Using the rule of complementary events,P(E') = 1 - P(E)P(E') = 1 - 0.70 = 0.30Therefore, the probability that Mary cannot work the problem is 0.30 or 30%.Example # 13:Let P(female) be the probability that the student is female. We are given that P(female) = 0.572.
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refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
Confidence interval = (y ± t∗s/√n)g1 = y - t*s/√ng2 = y + t*s/√n Substituting the values, g1 = 26.22 - 1.860*(0.11)/√9 = 25.84g2 = 26.22 + 1.860*(0.11)/√9 = 26.59Therefore, the statistics g1 and g2 that will satisfy the required inequality are 25.84 and 26.59 respectively.
The formula for finding the confidence interval is as follows: n − 1, where t is the value of the t-distribution corresponding to the specified confidence level and the sample size minus one.
As per the given exercise 7.11, suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample.
If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p(g1 ≤ (y - u) ≤ g2) = 90
To find the statistics g1 and g2 that will satisfy the required inequality
the following formula can be used: Confidence interval = [tex](y ± t∗s/√n)[/tex]
From the formula, we can see that the confidence interval depends on the values of y, s, t and n.
The value of y is the sample mean
the value of s is the sample standard deviation
And the value of n is the sample size.
The value of t depends on the confidence level desired and the degrees of freedom for the t-distribution. In this case, the confidence level is 90%, which means that we want to find the value of t that will give us a total area of 0.90 under the t-distribution curve with 8 degrees of freedom .Using the t-table, the value of t can be found to be 1.860, where the value for 90% and 8 degrees of freedom is 1.860.t = 1.860Now, we need to calculate the value of s, which is the sample standard deviation.
Since we do not have any information about the population standard deviation, we will use the sample standard deviation as an estimate of the population standard deviations = σ/√nσ = s*√nσ = 0.11*√9σ = 0.33Substituting the values in the confidence interval formula
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PLEASE Answer before 3/12/2023
6, 14, 22, 30, 38, … Use the expression below to determine the value of the 15th term. 6 + 8n, where n is equal to 0, 1, 2, 3, … answers: 112 118 120 126
Answer: 118
Step-by-step explanation: 38 is the highest value, which is the fifth number in the pattern, and we need to find out what the 15th number is. We simply need to add (8x10) to 38.
Answer: 118
Step-by-step explanation:
you just keep going up at the rate of 8
Ted is five times as old as Rosie was when Ted was Rosie's age. When Rosie
reaches Ted's current age, the sum of their ages will be 72. Find Ted's current age.
Answer:
45 yo
Step-by-step explanation:
Let's start by defining some variables to represent the ages of Ted and Rosie:
- Let's call Ted's current age "T"
- Let's call Rosie's current age "R"
From the problem statement, we know that:
- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:
T = 5(R - (T - R))
Simplifying this equation, we get:
T = 5(R - T + R)
T = 10R - 5T
- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:
R + T = 72 - T
We now have two equations with two variables. We can use substitution to solve for T.
Substitute the second equation into the first equation to eliminate R:
T = 10R - 5T
T = 10(72 - T) - 5T
T = 720 - 15T
16T = 720
T = 45
Therefore, Ted's current age is 45.
Elmer is on a Ferris wheel which has a diameter of 180 ft and whose center is 120 ft off the ground. Find all of the angles θ such that 0≤θ≤3π and such that Elmer's carriage is at a height of 165 ft when it makes an angle of θ with the horizontal. Leave your answers in exact form
The angles θ at which Elmer's carriage is at a height of 165 ft are θ = π/6, 13π/6 and 25π/6
The center of the Ferris wheel is represented by the point at the top of the triangle, and Elmer's carriage is represented by the lower point on the right-hand side of the triangle. We are given that the diameter of the Ferris wheel is 180 ft and that its center is 120 ft off the ground. This means that the radius of the Ferris wheel is 90 ft (half of the diameter), and that the distance from the center of the Ferris wheel to Elmer's carriage is also 90 ft.
We are also given that Elmer's carriage is at a height of 165 ft when it makes an angle of θ with the horizontal. Using trigonometry function , we can find the sine of θ as follows:
sin(θ) = (165 - 120) / 90
= 45 / 90
= 1/2
Therefore, we have:
θ = sin^(-1)(1/2)
= π/6
Since we are looking for all angles θ such that 0≤θ≤3π, we need to add multiples of 2π to our answer. The multiples of 2π that satisfy this inequality are 0, 2π, and 4π. Therefore, the solutions to the problem are:
θ = π/6, 13π/6, 25π/6
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A bag contains 8 green cubes, 12 black cubes and 16 white cubes. What is the ratio of green to black to white cubes in its simplest form?
Answer:
Total number bags is 36
green cubes is 8white cubes is 16Black cubes is 121:2:3 the answer
Suppose we create a box model for the outcome of a game of darts. The player has a 1/3 chance of throwing a dart in the inner ring, and a 2/3 chance of the dart landing in the outer ring. In our model, we have two unique tickets marked "inner" and "outer." We put in 1 ticket marked "inner." How many tickets do we put in that are marked "outer?"
a. 0
b. 1
c. 2
d. 3
As per the combination method, the number of tickets that we put in that are marked "outer" is 3 (option d).
In this case, we want to choose the number of tickets marked "outer." Let's call this number k. We know that we already put one ticket marked "inner" in the box, so the total number of tickets in the box is 2. Therefore, n = 2.
Now we need to determine k. We want to know how many tickets we need to put in that are marked "outer." We can represent this as a. So we have:
ᵃC₁ = a! / ((1!)(a-1)!) = a
We want to find the value of a that satisfies the condition that the probability of choosing an "inner" ticket is 1/3 and the probability of choosing an "outer" ticket is 3/2.
Since we already put in 1 ticket marked "inner," the probability of choosing an "inner" ticket is 1/2, which means the probability of choosing an "outer" ticket is also 1/2.
We know that the probability of choosing an "outer" ticket is 3/2, so we can set up the following equation:
ᵃC₁ / 2 = 3/2
Solving for a, we get:
a = 3
In conclusion, the answer is (d) 3.
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I need the answer to this question(PLEASE IM BEGGING YOU)
Answer:
B & D
Step-by-step explanation:
For future reference, you can just a site called desmos. It has a graphing tool where you can just write the function and then check where the lines meet.
firm produces output (y) using two inputs, labor (L) and capital (K), according to the following Cobb-Douglas production function: y = f(L, K) = 0.25 K0.75. Assuming that we draw the isoquant map with labor on the horizontal axis and capital on the vertical axis, what is the slope of this firm's isoquant when L = 100 and K = 50? Give your answer to two decimal places and remember that the sign matters when describing the slope of an isoquant.
The slope of this firm's isoquant when L = 100 and K = 50 is -0.50.
When the firm produces output (y) using two inputs, labor (L) and capital (K), according to the following Cobb-Douglas production function: y = f(L, K) = 0.25 K0.75, the slope of this firm's isoquant when L = 100 and K = 50 is equal to -0.50.What is an isoquant?An isoquant, also known as an equal product curve, is a graph that shows the various combinations of two inputs, say labor and capital, that produce the same level of output. It's a contour map that shows the different levels of output that can be produced using various combinations of inputs at the same cost. The slope of an isoquant is known as the marginal rate of technical substitution (MRTS) and represents the rate at which one input can be substituted for another while holding the level of output constant.How to determine the slope of an isoquant?The slope of an isoquant can be calculated by taking the ratio of the marginal product of the two inputs, which is the change in output resulting from a unit change in one input when the other is held constant, and is given by the following formula:Slope of isoquant = MP_L / MP_Kwhere MP_L and MP_K are the marginal products of labor and capital, respectively.Now, to determine the slope of this firm's isoquant when L = 100 and K = 50, we must first compute the marginal products of labor and capital as follows:MP_L = ∂f / ∂L = 0MP_K = ∂f / ∂K = 0.75 * 0.25 * K^-0.25 = 0.0469Then we can plug these values into the slope of isoquant formula:Slope of isoquant = MP_L / MP_K = 0 / 0.0469 = 0The slope of the isoquant when L = 100 and K = 50 is zero, indicating that labor and capital cannot be substituted for one another to produce the same level of output. However, since the question asks for the sign of the slope, we must take into account the standard convention for labeling isoquants. When labor is measured on the horizontal axis and capital on the vertical axis, the slope of the isoquant is negative. Therefore, the slope of this firm's isoquant when L = 100 and K = 50 is -0.50.
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In data analytics, a _____ refers to all possible data values in a certain dataset
In data analytics, a population refers to all possible data values in a certain dataset.
What is data analytics?Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.
The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.
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a ladder leans against the side of a house. the top of the ladder 8ft is from the ground. the bottom of the ladder is from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth.
The length of the ladder is c = √(x^2 + 64) ft.
The question is asking to find the length of the ladder. We can use the Pythagorean Theorem to solve this problem. Let x be the length of the ladder.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Pythagoras theorem is useful to find the sides of a right-angled triangle. If we know the two sides of a right triangle, then we can find the third side.
The Pythagorean Theorem states that a^2 + b^2 = c^2.
Therefore, x^2 + 8^2 = c^2
Solving for c: x^2 + 64 = c^2
Taking the square root of both sides: √(x^2 + 64) = c
Therefore, the length of the ladder is c = √(x^2 + 64).
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19. Assertion(A): The graph of the linear equation 7x - 2y = 6 cuts the Y-axis at the point (0, -3). Reason(R): The coordinates of any point on the Y-axis is (a, 0), where a is any real number. pls help
get the answer
Answer:
Pretty sure its C
Step-by-step explanation:
To cut through y axis, x axis is always 0, So it would be (0, a) where a is any real number, not (a,0) as is given in reason.
PLEASE HELP !!!! QUICK
the wholesale price for a pair of shoes is $4.50 a certain department store marks up the wholesale price by 40%. find the price of the pair of shoes in the department store.
round your answer to the nearest cent, as necessary
Using percentages we know that the markup price of the pair of shoes will be $6.3.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A% is a number that has neither dimensions nor a defined unit of measurement.
When expressing a proportionate share of a total, percentages are frequently utilized.
(Similarly, the term "per mille" or the sign "%" can be used to denote a number as a fraction of 1,000.)
So, the market price of the store would be:
= 4.50/100 * 40
= 0.045 * 40
= 1.8
Markup price: 1.8 + 4.5 = $6.3
Therefore, using percentages we know that the markup price of the pair of shoes will be $6.3.
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Each of these measures is rounded to nearest whole: a=5cm and b=3cm Calculate the upper bound of a +b
The upper bound of a + b can be found by adding the upper bounds of a and b.
For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.
For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.
So the upper bound of a + b is:
5.5 + 3.5 = 9
Therefore, the upper bound of a + b is 9cm.
I need the answer for number 3 step by step, please help!
Answer:
[tex]\frac{-1}{3}[/tex]
Step-by-step explanation:
Look at the red slope triangle that is drawn. If you start at the point on the left, you go down 1 unit and then to the right 3 units. This would be represented by -1/3. Down would be negative and going right would be positive. The slope is the rise over the run.
Helping in the name of Jesus.
Suppose that 30 students take a quiz worth 30 points. The SD of the scores is 1 point. Which of the following gives the most reasonable description of the distribution of quiz scores?
A) All of the individual scores are one point apart.
B) The difference between the highest and lowest score is 1.
C) The difference between the 1st and 3rd quartile marks is 1.
D) A typical score is within 1 point of the mean.
The statement that gives the most reasonable description of the distribution of quiz scores is "A typical score is within 1 point of the mean." The correct answer is Option D.
What is Standard deviation?The standard deviation (SD) is a measure of the variability of data in a population. Standard deviation is a measure of how much each value differs from the mean (average) value of the data set.
What is the range?The difference between the highest and lowest values in a dataset is known as the range. It's a quick way to see the data's spread. If the range is big, it implies that the data is more diverse, while if it's small, it implies that the data is more consistent.
What is the first quartile?The first quartile (Q1) is the value that splits the lowest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the first quartile is the value at the 25th percentile.
What is the third quartile?The third quartile (Q3) is the value that splits the highest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the third quartile is the value at the 75th percentile.
What is the mean?The sum of all values in a dataset divided by the total number of values in the dataset is known as the mean. The mean, often known as the arithmetic mean, is one of the most basic measures of central tendency in statistics.
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Will a 12.5-inch x 17-inch rectangular tray fit in
the box shown? Explain.
Please help!!!
Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.
what is rectangle ?A rectangle is a geometric shape with four edges and four angles that exists in two dimensions. Because it is a sort of quadrilateral, it has four sides that are parallel to one another. Rectangles are a form of parallelogram because they have opposite sides that are the same length and opposite angles that are the same size. A rectangle's two adjacent sides make right angles, so all four of the angles, which each measure 90 degrees, are right angles.
given
The tray has a breadth of 17 inches and a length of 12.5, according to the measurements given. The package is 13 inches by 11 inches by 11 inches in size.
The platter can fit inside the box because its length is less than the box's length, which is 13 inches. But we also need to think about the box's breadth and height.
The tray cannot fit inside the box in that dimension because its width, which is 17 inches, is larger than the box's, which is 11 inches. The tray cannot fit inside the box because the height of the box is also 11 inches, which is shorter than the length of the tray neither in that realm.
Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.
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Find the mean, median, mode, and range for the data set given.
112, 122, 132, 142, 152
what proportion of values for a standard normal distribution are less than 2.98?
Regardless of the appearance of the normal distribution or the size of the standard deviation, approximately less than 2.98% of observations consistently fall within two deviations types (one high and one low).
The normal distribution, also known as the Gaussian distribution, is a probability distribution symmetrical about the mean, indicating that data near the mean occurs more frequently than data far from the mean. In graphical form, the normal distribution is represented by a "bell curve".
The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the mean of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases. Therefore, physical quantities assumed to be the sum of many independent processes, such as measurement errors, tend to have a near-normal distribution.
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16^(3x-1) = 32. pls help
Answer:x=33/4096=0.008
Step-by-step explanation: 1.1 16 = 24
(16)3 = (24)3 = 212
Equation at the end of step
1
:
((212 • x) - 1) - 32 = 0
STEP
2
:
Equation at the end of step 2
4096x - 33 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : 4096x-33 = 0
Add 33 to both sides of the equation :
4096x = 33
Divide both sides of the equation by 4096:
x = 33/4096 = 0.008
#1 Brainlist!
Answer and show steps and I will make you brainlist.
Answer:
Multiplying the second equation by 5, we get:
15x + 20y = 180
Now, we can add this equation to the first equation:
26x = 208
x = 8
Substituting x = 8 in the second equation:
3(8) + 4y = 36
4y = 12
y = 3
Therefore, the solution to the system is (8, 3).
WHAT IS THE CENTRAL ATOM OF NITRIC OXIDE (NO)
Answer:
The answer is Nitrogen
Hope this helps :)
Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
D. A population of rabbits is doubling every 3 months. If there were 2 rabbits to begin
with, how many will there be after 5 years?
There will be a population of 2,097,152 rabbits after 5 years.
What is exponential growth?A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.
Given that, population of rabbits is doubling every 3 months.
That is,
5 years = 5 x 12 = 60 months
Number of doublings = 60 / 3 = 20
For every doubling, the population will be twice as large.
Thus,
P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits
Therefore, there will be approximately 2,097,152 rabbits after 5 years.
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josh borrowed $250 from his mother to buy an electric scooter. josh will pay her back in 1 year with 3% simple annual interest. how much interest will josh pay?
The interest which josh will pay on the electric scooter with a simple annual interest of 3% is 7.50.
What is interest rate?Interest rate can be defined as the amount of interest which is due per period, as a proportion of the amount lent, deposited, or borrowed by someone.
The interest rate formula is:
Interest Rate = {(Simple Interest × 100)}/{ (Principal × Time)}
Here,
Josh borrowed 250 from his mother to buy an electric scooter and will pay her back in one year with three simple annual interest.
The amount of interest that Josh will pay is calculated as:
Interest = Principal Amount × Rate of Interest × Time
Interest = 250 × 3
Therefore, Josh will pay his mother $7.50 in interest for the loan.
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