The area of the garden is 135 square yards.
Let's imagine you have a rectangular garden measuring 15 yards in length and 9 yards in width.
You want to find the area of this garden, which represents the amount of space inside the garden.
To find the area of a rectangle, you multiply the length by the width.
In this case, the length is 15 yards and the width is 9 yards.
Area = Length × Width
Area = 15 yards × 9 yards
Area = 135 square yards
This means that the garden can hold 135 square yards of grass, flowers, or any other objects you place inside it.
It's worth noting that the unit of measurement for area is always squared, such as square yards in this example.
This is because area is a two-dimensional measurement, representing the space within a flat surface.
By using the formula to calculate the area of a rectangle, you can easily determine the amount of space enclosed by any rectangular area when given the length and width.
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If f(x) = 16x2, what is the value of f(2.5)?
Answer:
f(2.5) = 100
Step-by-step explanation:
to evaluate f(2.5) substitute x = 2.5 into f(x)
f(2.5) = 16(2.5)² = 16 × 6.25 = 100
what is e^0? and e^infinity?
e^0 equals 1. e^infinity is undefined.
In mathematics, e^0 is equal to 1. This is because any number raised to the power of 0 is always equal to 1. The number e, which is approximately equal to 2.71828, follows this rule as well. So, when e is raised to the power of 0, the result is 1.
On the other hand, e^infinity is undefined. As the exponent approaches infinity, the value of e^infinity increases without bound. It does not converge to a specific number or approach any finite value.
In calculus and mathematical analysis, this is expressed by saying that the limit of e^x as x approaches infinity is equal to infinity.
The exponential function e^x is a fundamental mathematical concept with many applications in various fields such as physics, engineering, and finance.
Understanding the behavior of this function at different values of x, including 0 and infinity, is important for solving equations, modeling growth and decay processes, and studying the properties of exponential functions.
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determine the surface area and volume
The surface area and the volume of the rectangular prism are 280 and 300
How to determine the surface area and volumeFrom the question, we have the following parameters that can be used in our computation:
The rectangular prism
The surface area is caculated as
Surface area = 2 * (10 * 5 + 10 * 6 + 5 * 6)
Evaluate
Surface area = 280
For the volume, we have
Volume = 10 * 5 * 6
Evaluate
Volume = 300
Hence, the surface area and the volume are 280 and 300
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i need help!!!! does anyone know this..!!???
The period of oscillation is 3 seconds
What is period of oscillation?A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.
The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds
Oscillation can also be vibration or revolution or cycle.
Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.
This means that the period of the particle is 3 seconds.
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A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 24 feet long, 13 feet wide, and 6 inches deep.
a) Determine the volume, in cubic feet, of mulch the contractor will need.
b) If mulch costs 9$ per cubic foot, what will the cost of mulch be?
Answer:
A= 220.5ft
B= $2425.5
Step-by-step explanation:
A= 220.5ft
B= $2425.5
1. A student determines that one solution to a system of quadratic-quadratic equations is (2.1).
Determine the value of n if the equations are:
4x² - my=10
mx² + ny=20
Answer: -4
The value of n is approximately -0.327.
To determine the value of n, we can substitute the given solution (x = 2.1) into the system of equations:
4x² - my = 10 ...(1)
mx² + ny = 20 ...(2)
Substituting x = 2.1 into equation (1), we get:
4(2.1)² - my = 10
8.4 - my = 10
-my = 10 - 8.4
-my = 1.6
Now, substituting x = 2.1 into equation (2), we get:
m(2.1)² + ny = 20
4.41m + ny = 20
Since we already have an expression for -my from equation (1), we can substitute it into equation (2):
4.41m + (-1.6) = 20
4.41m - 1.6 = 20
4.41m = 20 + 1.6
4.41m = 21.6
To solve for m, we divide both sides by 4.41:
m = 21.6 / 4.41
m ≈ 4.9
Now that we have the value of m, we can substitute it back into equation (1) to solve for n:
4(2.1)² - 4.9y = 10
8.4 - 4.9y = 10
-4.9y = 10 - 8.4
-4.9y = 1.6
Finally, to solve for y, we divide both sides by -4.9:
y = 1.6 / -4.9
y ≈ -0.327
Consequently, n has a value of roughly -0.327.
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NO LINKS!! URGENT HELP PLEASE!!
Answer:
a. 5π cm
b. 144π in²
c. 6 ft
Step-by-step explanation:
a.
The circumference of a circle is given by:
Circumference pf circle= πd
where d is the diameter.
In this case, d = 5 cm,
Therefore, Circumference of circle = π*5=5π cm
b.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, the diameter is d = 24 in,
so, the radius is r = d/2 = 24/2=12in
Therefore, Area of circle=π*12²=144π in²
c.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, Area is 36π ft²
Now substituting value
36π=πr²
dividing both side by π, we get
36=r²
[tex]r=\sqrt{36}=6[/tex]
r=6 ft.
Therefore, Radius is 6 ft.
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is (x with a line over it), while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.
The 90% confidence interval for the population variance (σ^2) is approximately [7.19, 20.19].
To construct a 90% confidence interval for the population variance (σ^2), given a sample size of 20 and a sample variance (s^2) of 12.5, we need to utilize the chi-square distribution.
The formula for constructing a confidence interval for the population variance is:
[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]
Where n is the sample size, s^2 is the sample variance, χ^2_upper is the upper critical value from the chi-square distribution, and χ^2_lower is the lower critical value from the chi-square distribution.
For a 90% confidence interval, we need to find the critical values from the chi-square distribution that correspond to the upper and lower tails of 5% each (since the confidence level is divided equally into two tails).
(a) Degrees of freedom:
The degrees of freedom (df) for the chi-square distribution is equal to n - 1. In this case, n = 20, so df = 20 - 1 = 19.
(b) Chi-square critical values:
We need to find the upper and lower critical values from the chi-square distribution table for df = 19 and a significance level of 0.05/2 = 0.025 (for each tail).
From the chi-square distribution table or using a statistical software, the upper critical value for a significance level of 0.025 and df = 19 is approximately 32.852. Similarly, the lower critical value is also approximately 8.907.
(c) Confidence interval calculation:
Substituting the values into the formula, we can construct the confidence interval:
[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]
[ (20 - 1) * 12.5 / 32.852, (20 - 1) * 12.5 / 8.907 ]
[ 19 * 12.5 / 32.852, 19 * 12.5 / 8.907 ]
[ 7.19, 20.19 ]
Therefore, the [7.19, 20.19] is roughly inside the 90% confidence interval for the population variance (2).
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Question
A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample variance, s^2, is determined to be 12.5.Complete parts (a) through (c).Construct a 90% confidence interval for
σ2 if the sample size, n, is 20.
Answer:
B :3
Step-by-step explanation:
good luck <3
Joint probability of independent events J and K is equal to
Select one:
a. P(J) * P(K) - P(J * K)
b. P(J)- P(K)
c. P(J) * P(K)
d. P(J) * P(K) + P(J-K)
e. P(J) + P(K)
Note: Answer A is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
The joint probability is found by multiplying the probability of event J by the probability of event K P(J and K) = P(J) * P(K) Option C.
When two events J and K are independent, it means that the occurrence or non-occurrence of one event does not affect the probability of the other event. In other words, the probability of event J happening is completely unrelated to the probability of event K happening.
The joint probability of two independent events J and K is the probability that both events J and K occur simultaneously. Since the events are independent, the probability of their intersection is equal to the product of their individual probabilities.
The joint probability is found by multiplying the probability of event J by the probability of event K.
This formula holds true for independent events because there is no interaction or dependency between the events. Each event has its own probability, and when they occur together, the joint probability is simply the product of their individual probabilities. Option C is correct.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are options 1 (x < 5) and 3 (–6x + 15 < 10 – 5x).
To determine the correct representations of the inequality –3(2x – 5) < 5(2 – x), let's simplify the expression and analyze the options:
First, we simplify the inequality:
–3(2x – 5) < 5(2 – x)
–6x + 15 < 10 – 5x
Now let's analyze the options:
x < 5: This option represents the solution to the inequality. It indicates that x must be less than 5 for the inequality to hold true.
–6x – 5 < 10 – x: This is not a correct representation of the inequality. The sign of the x-term on the right side of the inequality is incorrect.
–6x + 15 < 10 – 5x: This option represents the solution to the inequality. It correctly represents the simplified inequality we obtained earlier.
A number line from negative 3 to 3 in increments of 1, with an open circle at 5 and a bold line starting at 5 and pointing to the right: This representation does not accurately represent the solution to the inequality. The inequality is not satisfied at x = 5, so the circle should be closed.
A number line from negative 3 to 3 in increments of 1, with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left: This representation is not correct as it does not represent the solution to the inequality.
Therefore, choices 1 (x 5) and 3 (-6x + 15 10 - 5x) are the proper expressions of the inequality -3(2x - 5) 5(2 - x).
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Can some please help me I don’t understand this?
Please due tmr morning thanks!
The numbers to complete the pythagorean triple in the equation (n² - 1)² + k² = (n² + 1)² are B. 35 and 37
What is the pythagorean triple?A pythagorean triple is a set of 3 numbers that obey the pythagorean theorem.
Given the equation
(n² - 1)² + k² = (n² + 1)², we need to find the remaining numbers generated by the equation when k = 12. So, we proceed as follows/
Since we have the equation
(n² - 1)² + k² = (n² + 1)²
Subtracting (n² + 1)², from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = (n² + 1)² - (n² + 1)²
(n² - 1)² - (n² + 1)² + k² = 0
Now, subtracting k from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = 0
(n² - 1)² - (n² + 1)² + k² - k² = 0 - k²
(n² - 1)² - (n² + 1)² + 0 = - k²
(n² - 1)² - (n² + 1)² = - k²
Using the difference of two squares a² - b² = (a + b)(a - b)
(n² - 1)² - (n² + 1)² = - k²
(n² - 1 + n² + 1)[n² - 1 - (n² + 1)] = - k²
(n² + n² - 1 + 1)[n² - n² - 1 - 1)] = - k²
(2n² + 0)[0 - 2)] = - k²
(2n²)(- 2) = - k²
-4n² = - k²
4n² = k²
n² = k²/4
Taking square root of both sides, we have that
n = √(k²/4)
n = k/2
Since k = 12, we have that
n = 12/2
n = 6
So, the first number is (n² - 1) = (6² - 1)
= 36 - 1
= 35
The second number is (n² + 1) = (6² + 1)
= 36 + 1
= 37
So, the numbers are B. 35 and 37
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which of the following is equivalent to x^2 -5x +6
Hello!
x² - 5x + 6
= (x² - 2x) + (-3x + 6)
= x(x - 2) - 3(x - 2)
= (x - 2)(x - 3)
me movement o
Which choice shows (3+9) + 13 correctly rewritten using the associative property and then
correctly simplified?
O 13+(3+9) = 13 + 12 = 25
13+(9+ 3) = 13 + 12 = 25
O 3+ (91+3) = 3 +94 = 97
O 3+ (9+13) = 3 +22= 25
(3+9) + 13 correctly rewritten using the associative property and then correctly simplified is 13+(9+3) = 13 + 12 = 25.
1. Start with the expression (3+9) + 13.
2. According to the associative property of addition, we can group the numbers in any order without changing the result.
3. Rearrange the expression by grouping the numbers differently: (9+3) + 13.
4. Now simplify the grouped numbers: 9+3 = 12.
5. The expression becomes 12 + 13.
6. Finally, simplify the addition: 12 + 13 = 25.
Therefore, the correct rewritten expression using the associative property and the simplified result is 13+(9+3) = 13 + 12 = 25.
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This example using cluster sampling, how do we know whether these estimates are considered valid?
The estimates are not correct because we are to find the proportion and sample error of the given values. The proportion expresses the number of opposing votes to the total number of voters. Also, the sampling error follows the formula of [tex]SE = Z\sqrt{P(1 - P/n)}[/tex]
The right estimate to use
The exact formula used in the expression is quite different from the standard formula for calculating the standard error. We are supposed to find the root of the standard deviation but that is not the case as can be seen in the formula above.
So, the main issue with this formula is that the square root is not considered in the proportion formula used by the council, so it is not a valid estimate.
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a 4-foot length of ribbon costs $1.32. how much will it cost to buy 10 yards of ribbon?
Answer:
$3.3
Step-by-step explanation:
4x = 1.32
x = 0.33$ / ft
10x = 10 * 0.33 = 3.3$
Find x intercepts y=(x+3) (6x-2)
Answer:
x = - 3 , x = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
to find the x- intercepts let y = 0 , that is
(x + 3)(6x - 2) = 0
equate each factor to zero and solve for x
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
6x - 2 = 0 ( add 2 to both sides )
6x = 2 ( divide both sides by 6 )
x = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
the x- intercepts are then x = - 2 and x = [tex]\frac{1}{3}[/tex]
(-14)+x=14[/tex] what is the answer
The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.
To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:
Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.
(-14) + x + 14 = 14 + 14
x = 28
The solution to the equation (-14) + x = 14 is x = 28.
In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.
Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:
(-14) + 28 = 14
14 = 14
The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.
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complete the table of values for y=3/x
The table of values for the equation y = 3/x can be completed as follows:
x | y
1 | 3/1 = 3
2 | 3/2 = 1.5
3 | 3/3 = 1
4 | 3/4 = 0.75
5 | 3/5 = 0.6
To complete the table of values for the equation y = 3/x, we substitute different values of x into the equation and calculate the corresponding values of y.
When x = 1:
Substitute x = 1 into the equation: y = 3/1 = 3
So, when x = 1, y = 3.
When x = 2:
Substitute x = 2 into the equation: y = 3/2 = 1.5
So, when x = 2, y = 1.5.
When x = 3:
Substitute x = 3 into the equation: y = 3/3 = 1
So, when x = 3, y = 1.
When x = 4:
Substitute x = 4 into the equation: y = 3/4 = 0.75
So, when x = 4, y = 0.75.
When x = 5:
Substitute x = 5 into the equation: y = 3/5 = 0.6
So, when x = 5, y = 0.6.
By substituting different values of x into the equation y = 3/x, we can complete the table of values as shown above.
Hence, the completed table of values for y = 3/x is:
x | y
1 | 3
2 | 1.5
3 | 1
4 | 0.75
5 | 0.6
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Pls help I need this answer now
Answer:
The correct answer is A. As x increases, the rate of change of f(x) exceeds the rate of change of g(x)
Step-by-step explanation:
The cost to produce a bag of golf tees is modeled by the function that is graphed below.
Production Costs for Bags of Golf Tees
A graph has number of tees on the x-axis, and cost in dollars on the y-axis. A line goes through (0, 4) and (2, 5).
Which table shows this same function?
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries negative 8, negative 4, 0, 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 0, 4, 0, 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 8, 12, 16.
The table that shows the same function as the given graph is: A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.
To determine which table shows the same function as the given graph, we need to find the values of y corresponding to the given values of x on the graph.
Point A: (0, 4)
Point B: (2, 5)
Let's check each table:
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries negative 8, negative 4, 0, 4.
In this table, the corresponding y-values for x = 0 and x = 2 are incorrect. The correct values should be 4 and 5, respectively. Therefore, this table does not represent the same function as the given graph.A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 0, 4, 0, 4.
In this table, the corresponding y-values for x = 2 and x = 6 are incorrect. The correct values should be 5 and 7, respectively. Therefore, this table does not represent the same function as the given graph.A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.
In this table, the corresponding y-values for x = 0 and x = 2 match the given points on the graph. Therefore, this table represents the same function as the given graph.A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 8, 12, 16.
In this table, the corresponding y-values for x = 2 and x = 4 do not match the given points on the graph. Therefore, this table does not represent the same function as the given graph.For such more question on function:
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According to the Committee for the Study of the American Electorate, the voter turnout in the 2004 presidential election was higher in all but four states than it was in the 2000 election. The four states with lower voter turnout are listed below.
According to the Committee for the Study of the American Electorate, the four states with lower voter turnout in the 2004 presidential election compared to the 2000 election were Arkansas, Hawaii, Maryland, and Tennessee.
In the 2004 presidential election, voter turnout increased in most states compared to the 2000 election. However, Arkansas, Hawaii, Maryland, and Tennessee experienced a decrease in voter participation. This means that fewer eligible voters in these states cast their ballots in the 2004 election compared to the previous one.
The reasons behind the lower voter turnout in these states could vary and might be influenced by factors such as changes in voter registration laws, campaign strategies, voter demographics, or the overall political climate in each state during that particular election cycle.
It is worth noting that while voter turnout increased in most states, overall voter participation in the United States has been historically lower compared to some other democracies.
Efforts to increase voter engagement and turnout, such as expanding access to voting and improving voter education, continue to be important in ensuring that more eligible citizens exercise their right to vote and have their voices heard in the democratic process.
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when 24/5and another number are added together the answer is 9. what is the number
The number we're looking for, which when added to 24/5 results in 9, is 21/5 or 4.2 in decimal form.
Let's solve the equation: 24/5 + x = 9, where x represents the unknown number we're trying to find.
To isolate x, we'll start by subtracting 24/5 from both sides of the equation:
x = 9 - 24/5
To add these two fractions, we need a common denominator. The denominator of 9 is 1, and the denominator of 24/5 is 5. To find a common denominator, we multiply 1 by 5:
x = (9 * 5)/5 - 24/5
This gives us:
x = 45/5 - 24/5
Now we can combine the fractions with the same denominator:
x = (45 - 24)/5
Simplifying the numerator:
x = 21/5
Therefore, the number we're looking for is 21/5. In decimal form, it can be written as 4.2.
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Gabby is going on holiday and needs to exchange some pounds (£) for euros (€)
. How many euros can she get for £21? Give your answer to 2 decimal places.
£1
Exchange rate
= €1.13
Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.
To calculate how many euros Gabby can get for £21, we need to use the exchange rate of £1 = €1.13.
To find the number of euros, we multiply the amount in pounds (£21) by the exchange rate (€1.13):
£21 * €1.13 = €23.73
Therefore, Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.
This means that for every pound exchanged, Gabby will receive €1.13. So, by multiplying the amount in pounds (£21) by the exchange rate (£1 = €1.13), we can determine the equivalent amount in euros.
It's important to note that exchange rates can fluctuate, and the rate provided here is just an example. When exchanging currency, it's always advisable to check the current exchange rates as they may vary. Additionally, some currency exchange services may charge fees or have different rates, so it's essential to consider those factors as well.
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A bacteria culture triples every 5 minutes. At 4:27 P.M. the population is . Determine what the population was 27 minutes earlier, at 4:00 P.M.
The population at 4:00 P.M., 27 minutes earlier, is[tex]3^3[/tex] times the initial population P.
To determine the population of a bacteria culture 27 minutes earlier, we need to calculate the population growth from 4:00 P.M. to 4:27 P.M. given that the bacteria culture triples every 5 minutes.
Let's break down the time period into intervals of 5 minutes:
From 4:00 P.M. to 4:05 P.M., the population triples once.
From 4:05 P.M. to 4:10 P.M., the population triples again.
From 4:10 P.M. to 4:15 P.M., the population triples for the third time.
From 4:15 P.M. to 4:20 P.M., the population triples for the fourth time.
From 4:20 P.M. to 4:25 P.M., the population triples for the fifth time.
From 4:25 P.M. to 4:27 P.M., the population undergoes partial growth.
Since the population triples every 5 minutes, we can express the population at 4:27 P.M. as 3^5 times the initial population at 4:00 P.M.
Let's denote the initial population at 4:00 P.M. as P. Then, the population at 4:27 P.M. is [tex]3^5[/tex] * P.
To find the population 27 minutes earlier, we need to reverse the growth from 4:27 P.M. to 4:00 P.M. Since the population triples every 5 minutes, we need to divide the population at 4:27 P.M. by [tex]3^{(27/5).[/tex]
Therefore, the population at 4:00 P.M., 27 minutes earlier, can be calculated as:
Population at 4:00 P.M. = (Population at 4:27 P.M.) / [tex]3^{(27/5)[/tex]
[tex]= (3^{5} * P) / 3^{(27/5)\\\\\\\\= 3^{(25/5)} * P\\= 3^5 * P / 3^2\\= 3^3 * P[/tex]
Hence, the population at 4:00 P.M., 27 minutes earlier, is 3^3 times the initial population P.
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Han make sparkling juice by mixing 1. 5 liter of juice and 500 milliliter of sparkling water
Han will have 2 liters (or 2000 milliliters) of sparkling juice after combining 1.5 liters of juice and 500 milliliters of sparkling water.
To make sparkling juice, Han mixes 1.5 liters of juice and 500 milliliters of sparkling water.
To add the quantities together, we need to convert the units to the same measurement. We can convert the liters to milliliters since 1 liter is equal to 1000 milliliters.
1.5 liters is equal to 1.5 x 1000 = 1500 milliliters.
Now we have 1500 milliliters of juice and 500 milliliters of sparkling water.
To find the total quantity of the sparkling juice, we add the volumes of juice and sparkling water together:
1500 milliliters + 500 milliliters = 2000 milliliters
Therefore, Han will have a total of 2000 milliliters (or 2 liters) of sparkling juice by mixing 1.5 liters of juice and 500 milliliters of sparkling water.
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Find the surface area of the prism.
A. 78 in2
B. 158 in2
C. 120 in2
D. 119 in2
Answer:
119in^2
Step-by-step explanation:
formula= 2(width×length+hight×length+hight×5
2×(5×8+3×8+3×5) = 119in^2
If the mass of a proton is 1.67 × 10-24 gram, what is the mass of 2,000 protons?
Answer:
3.34 * 10^-21 g
Step-by-step explanation:
1.67*10^-24 * 2000 = 1.67 * 10^-24 * 2 *10^3 = 3.34 * 10^-21 g
Can you use the ASA postulate or the AAS theorem to prove the triangles are congruent
In square $ABCD,$ $P$ is on $\overline{BC}$ such that $BP = 4$ and $PC = 1,$ and $Q$ is on $\overline{CD}$ such that $DQ = 4$ and $QC = 1.$ Find $\sin \angle PAQ.$
In triangle PAD, using the Pythagorean theorem, we find AD = 5√2. Given that ∠PAQ's opposite side is PQ, which equals 3, we have sin∠PAQ = PQ/AQ = √2/10.
Explanation:In square ABCD, we are given that points P and Q are on lines BC and CD respectively such that BP=4 and PC=1, DQ=4 and QC=1. Considering triangle PAD, it is a right triangle in the given square, and, using the Pythagorean theorem, we can find the hypotenuse AD as AD = √(5² + 5²) = 5√2. The same reasoning, AD = AQ.
Because ∠PAQ is the angle we are interested in finding the sine of, we know that sin∠PAQ = opposite/hypotenuse. In this case, the opposite side is PQ which we determine is 3 using the given distances (PC+QC). So, sin∠PAQ = PQ/AQ = 3/(5√2) = √2/10. Thus, the sine of angle PAQ is √2/10.
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Find a function of the form or whose graph matches this one:
The function that matches the graph is of the form:
4cos((pi x)/7) + 1
Graphs of trigonometric functionsGraphs of trigonometric functions are graphs used in representing trigonometric functions.
From these graphs, some basic properties such as Amplitude, phase difference, period and vertical shift can be deduced.
From the given graph in the question, it can be seen that the graph crosses the y-axis at it's amplitude (highest point), so its easier to use the cosine relation.
To calculate the midline M:
Use the formula,
M = (maximum + minimum)/2
= (5 + -3)/2 = 2/2 = 1
Vertical shift: It can be seen from the graph that there is a vertical upward shift of 1 unit. C = 1
Amplitude: Maximum value - vertical shift is:
A = 5 - 1 = 4
Period = spacing between repeating patterns. There are 14 units between each peak (peak when x = -14, next peak when x = 0).
k = 2pi/Period;
So: k = 2pi/14 = pi/7
Therefore y = 4cos(pix/7) + 1 is the function that matches the given graph.
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