Given a discount rate of 0.15, the NPV of these financial movements is therefore $378.73.
What is cash flow, and how does it work?Spending that occurs in the normal run of business is included in cash flow from activities. Payroll, the cost of products sold, rent, and utility bills are a few examples of these cash withdrawals. When company activities are extremely seasonal, cash outflows can differ greatly.
Here's how to do the calculation:
We need to determine how many days passed between the first monetary influx of $-1000, which was received on 12/15/2021, and the present day (2/21/2023). It's been 432 days. Using the equation PV = FV / (1 + r)n, we can determine the current value (PV), the future value (FV), the discount rate (r), and the number of times (n). When the numbers are plugged in, we get PV = -1000 / (1 + 0.15)(432/365) = -845.67.
We must determine how many days passed between the second monetary influx of $300, which was received on January 11, 2022. It's been 406 days. We obtain PV = 300 / (1 + 0.15)(406/365) = 246.87 using the same method.
In order to determine the third financial movement, which is a $600 payment received on 4/7/2023, we must determine how many days have passed since that date. It's been 410 days. Using the same method, we get PV = 600 / (1 + 0.15)^(410/365) = 427.81.
We need to figure out how many days passed between the fourth financial transfer, which was $925 and was received on July 15, 2024. It has been 875 days. We obtain PV = 925 / (1 + 0.15)(875/365) = 548.72 using the same method.
Now we can add up the present values of all the cash flows to obtain the NPV:
NPV = -845.67 + 246.87 + 427.81 + 548.72 = 378.73
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ASAP!! Please help!!
If on the scale of a map, 3/4 inch equals 72 miles, what is the actual distance between two cities that are 3 7/8 inches apart on the map?
Answer:
The actual distance between two cities that are 3 7/8 inches apart on the map is 279 miles.
Step-by-step explanation:
To find the actual distance between two cities, we need to convert the distance on the map to miles. The scale of the map is 3/4 inch equals 72 miles, which means 1 inch on the map is equal to 72/3=24 miles.
So, the actual distance between two cities on the map that are 3 7/8 inches apart is 24 * 3 7/8 = 279 miles.
Write the slope-intercept form of the equation of the line described.
2) through: (4, 3), parallel to x=0
quick caveat, there's no slope-intercept form per se for a vertical line, Check the picture below.
A car can be rented for $80 per week plus $0.25 per mile. How many miles can be driven if you have at most $110 to spend for weekly transportation?
Answer: Let x be the number of miles driven.
The cost of renting the car and driving x miles is 80 + 0.25x.
We want to find the maximum number of miles that can be driven given a budget of $110, so we set 80 + 0.25x = 110 and solve for x:
80 + 0.25x = 110
0.25x = 110 - 80
0.25x = 30
x = 120
So the maximum number of miles that can be driven is 120.
Step-by-step explanation:
round 107.06 one decimal place
Answer: 107.1
Step-by-step explanation:
4 or less down
5 or more up
In this case, we round to 1 decimal place, so we look at the hundredths column.
It is 6, so we round up.
h(x)=-x+3 complete the function table
Answer:
Here is the function table for the given equation:
x H(x)
1 2
2 1
3 0
4 -1
5 -2
Note: The table shows the result of the equation H(x) = -x + 3 for different values of x.
Step-by-step explanation:
Use a table to find the solution of each equation.
38.2+-1= 11
Answer:
Here is a table that can be used to solve the equation:
Operation Result
38.2 38.2
+ (-1) 37.2
= 11 False
The equation 38.2 + (-1) = 11 is not true for any value of x. There is no solution for this equation.
Oh, hello there! Let's work on this equation together.
38.2 + -1 = 11
Let's create a table to keep track of our work.
-1 38.2 11
+1 37.2 12
As you can see, we added 1 to both sides to cancel out the negative 1.
So now, our equation is 37.2 = 12.
Let's subtract 12 from both sides.
-12 37.2 11
-12 25.2 -1
And there you have it! The solution is 25.2.
I hope this helps!
Identify the hypothesis and the conclusion for each of the following conditional statements. (a) If n is a prime number, then n2 has three positive factors.
(b) If a is an irrational number and b is an irrational number, then a⋅b is an irrational number.
(c) If p is a prime number, then p=2 or p is an odd number.
(d) If p is a prime number and p≠2 or p is an odd number.
(e) p≠2 or p is a even number, then p is not prime.
The hypothesis and conclusion are -
(a) Hypothesis : n is a prime number.
Conclusion : n² has three positive factors.
(b) Hypothesis : a and b are irrational numbers.
Conclusion : a · b is an irrational number .
(c) Hypothesis : p is a prime number.
Conclusion : p = 2 or p is an odd number .
(d) Hypothesis : ap is a prime number and p≠2 .
Conclusion : p≠2, p is an odd number .
(e) Hypothesis : p≠2 and p is a even number.
Conclusion : p is not a prime number .
What is irrational number?
A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio.
The hypothesis of a conditional statement is the phrase immediately following the word if.
The conclusion of a conditional statement is the phrase immediately following the word then.
(a) If n is a prime number, then n² has three positive factors.
Hypothesis : n is a prime number.
Conclusion : n² has three positive factors.
(b) If a is an irrational number and b is an irrational number, then a⋅b is an irrational number.
Hypothesis : a and b are irrational numbers.
Conclusion : a · b is an irrational number .
(c) If p is a prime number, then p=2 or p is an odd number.
Hypothesis : p is a prime number.
Conclusion : p = 2 or p is an odd number .
(d) If p is a prime number and p≠2 or p is an odd number.
Hypothesis : ap is a prime number and p≠2 .
Conclusion : p≠2, p is an odd number .
(e) p≠2 or p is a even number, then p is not prime.
Hypothesis : p≠2 and p is a even number.
Conclusion : p is not a prime number .
Therefore, the hypothesis and conclusions are made.
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please tell me what i need to do to solve this problem
The standard form of the equation of the sphere with center (0, -1, 3) and a radius of square root of 5 is given as follows:
x² + (y + 1)² + (z - 3)² = 5.
How to obtain the equation of a sphere?The two parameters for the equation of a sphere are given as follows:
Center (x*, y*, z*).Radius r.Then the equation for the sphere is given as follows:
(x - x*)² + (y - y*)² + (z - z*)² = r².
The parameters for this problem are given as follows:
Center (0, -1, 3).Radius: square root of 5.Hence the equation of the sphere is defined as follows:
x² + (y + 1)² + (z - 3)² = 5.
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can someone tell me how to do this problem? please
Hi there, here's your answer:
The general formula of a circle:
[tex](x-h)^{2} +(y-k)^{2}=r^2\\[/tex]
Where the ordered pair (h, k) is the center of the circle.
Given (h, k) = (-6, -2)
We also have that the circle passes through a point (7, 12)
Which means that (7, 12) lies on the circumference of the circle.
Let this be labelled as [tex](x_{1}, y_{1})[/tex]
Since this point lies on the circumference of the circle, it must satisfy the equation when substituted in for (x, y).
Thus, we substitute [tex]x_{1}[/tex] for x and [tex]y_{1}[/tex] for y.
We get the final equation to be:
[tex](7+6)^2 + (12+2)^2 = r^2[/tex]
Or
[tex]169 + 196 = r^2[/tex]
[tex]r^2 = 365[/tex]
Thus, we get the final equation of the circle to be [tex](x+6)^2 + (y+2)^2 = 365[/tex]
Hope it helps!
A bag contains 8 green candies and 4 red candies. You randomly select one candy at a time to eat. If you eat five candies, there are relatively prime positive integers m and n so that m n is the probability that you do not eat a
green candy after you eat a red candy. Find m + n.
If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.
A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:
GRRRR : [tex]\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}[/tex]
GGRRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}[/tex]
GGGRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}[/tex]
GGGGR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
GGGGG : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
The sum is [tex]\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}[/tex]
Probability that you do not eat green candy after you eat a red candy =[tex]\frac{1}{5}[/tex]
so m = 1 and n = 5
m + n =6
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Decide whether Rolle's Theorem can be applied to f(x) = x2 - 3 on the interval [-2, 2]. If Rolle's Theorem can be applied, find all value(s) of c in the interval such that f '(c) = 0. Rolle's theorem can be applied; c = 0
Rolle's theorem can be applied; c = -2, 2
Rolle's theorem cannot be applied because f '(c) ≠ 0
Rolle's theorem cannot be applied because f(-2) ≠ f(2)
Therefore , the solution of the given problem of function comes out to be the value of c for which f'(c) = 0 in the interval [-2, 2] is c = 0.
Explain Function.The study of numbers and their variable, as well as in out environment, architecture, and both real and imagined places, are all covered in the mathematics curriculum. A function range illustrates visually how the amounts of the inputs and the corresponding outputs for each are related. Simply stated, a function is a set of inputs that, when combined, produce specific outputs for each input. Each position is given a locale, region, or range.
Here,
Rolle's Theorem can be applied to $f(x) = x^2 - 3$ on the interval [-2, 2]. This is because f(x) satisfies the following conditions of Rolle's Theorem:
1 ) f(x) is continuous on the interval [-2, 2]
2 ) f(x) is differentiable on the interval (-2, 2)
3) f(-2) = 1 and f(2) = 1
Since f(-2) = f(2), there must exist at least one point c in the interval (-2, 2) such that f'(c) = 0.
Taking the derivative of f(x) with respect to x, we get f'(x) = 2x. Setting f'(c) = 0, we have:
2c = 0
Solving for c, we get c = 0.
Therefore, the value of c for which f'(c) = 0 in the interval [-2, 2] is c = 0.
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concerning the relationship between the chi squared test and two proportion z test with a two sided alternative hypothesis, which of the following statements is true?The x^2 test statistic is equal to the z test statistic. The x^2 test statistic is equal to the z test statistic squared. The x^2 test statistic is not equal to the z test statistic squared. The x^2 test statistic is not equal to the alternative hypotheses value squared.
The concept is the Chi-square test, a statistical test for comparing observed results to expected results. The answer is option A.
The test statistic x^2 is equivalent to the test statistic Z. Homogeneity 2x2 The chi-square statistic (and the test) is equivalent to a two proportion test.
The chi-square test is a statistical test used to compare observed results to expected results.The purpose of this test is to determine whether the difference between the observed and expected data is due to chance or to the relationship between the variables being studied. The
Two Ratio Z-Test is a statistical hypothesis test used to determine whether two ratios are different from each other. When you run the test, the z-statistic is calculated from two independent samples, and the null hypothesis is that the two proportions are equal.
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The length of a rectangle is 2 ft longer than it’s width if the perimeter of the rectangle is 36ft find it’s area
Answer:
two of the sides are x and the other two sides are x+2
x+x+x+2+x+2 = 36
4x = 32
x = 8
the sides are 8, 8, 10, 10
area is length x width
8 x 10 = 80
answer: 80ft
Step-by-step explanation:
explain why A*B*C and (A*B)*C are not same
Which of the following lists of properties contains only those that are characteristic properties of a substance? Odensity, solubility, melting point O boiling point, mass, density O volume, density, temperature O solubility, mass, volume
Of the lists of properties you provided, only the list of "identity, solubility, melting point" contains only those that are characteristic properties of a substance.
Identity refers to the name or chemical formula of the substance, which is unique to that substance and can be used to identify it.
Solubility refers to the ability of a substance to dissolve in a solvent, such as water. The solubility of a substance can also be used to identify it, as different substances have different solubility's.
Melting point refers to the temperature at which a solid substance will change into a liquid. Like solubility, the melting point of a substance is also a characteristic property that can be used to identify it.
On the other hand, boiling point, mass, and density are not always characteristic properties of a substance. While they can give us information about a substance, they are not unique to that substance and cannot be used to identify it.
Volume and temperature are not considered characteristic properties of a substance, as they are dependent on external factors, such as the pressure and the amount of the substance being measured.
In conclusion, the list of "identity, solubility, melting point" contains only those properties that are characteristic of a substance and can be used to identify it.
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2.
A house that costs $200,000 will appreciate in value by 3% each year.
Write a function that models the cost of the house over time. Use x for years and y for
the value of the house, in dollars.
Find the value of the house at the end of ten years.
Answer: The function that models the cost of the house over time can be written as y = 200,000 * (1 + 0.03)^x, where x is the number of years and y is the value of the house.
To find the value of the house at the end of ten years, we need to plug in x = 10 into the function:
y = 200,000 * (1 + 0.03)^10 = 200,000 * 1.33489 = 266,978.8
So the value of the house at the end of ten years is $266,978.8.
Step-by-step explanation:
4. Write a word problem for 3/4 X 1/2! Please help me!!
A word problem for the given expression is the division of 3/4 cups of juice among two friends equally.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given is an expression [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex].
Suppose that there are 3/4 cups of juice available.
There are two friends who are in need of this.
The total amount of juice has to be divided equally among these two friends.
Amount of cups of juice each friend gets = [tex]\frac{3}{4}[/tex] ÷ 2.
[tex]\frac{3}{4}[/tex] ÷ 2 = [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]
So each friend gets 3/8 cups of juice.
Hence the division of a total of 3/4 cups of juice among two friends equally is a word problem for the given expression.
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Pre-calc. WIll give brainliest
Answer:
[tex]S_{18}=-792[/tex]
Step-by-step explanation:
The given arithmetic series is:
24 + 16 + 8 + ...From inspection of the given series, the first term is 24.
The common difference is the difference between consecutive terms.
Therefore, the common difference of the given series is -8 as each term is 8 less than the previous term.
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
To find the sum of the first 18 terms of the given series, substitute a = 24, d = -8 and n = 18 into the sum formula.
[tex]\implies S_{18}=\dfrac{1}{2}(18)\left[2(24)+(18-1)(-8)\right][/tex]
[tex]\implies S_{18}=9\left[48+(17)(-8)\right][/tex]
[tex]\implies S_{18}=9\left[48-136\right][/tex]
[tex]\implies S_{18}=9\left[-88\right][/tex]
[tex]\implies S_{18}=-792[/tex]
Therefore, the sum of the first 18 terms of the given arithmetic series is -792.
The graph below shows the relationship between the number of money spent and the amount of cans bought. For the data in the graph, which of the following equations can be used to calculate c, the amount of cans, bought for m money spent ?
c = 2m
c = 5m
c = 10m
c = 1/10m
Answer:
C = 10m
Step-by-step explanation:
when c=20, m=2
when c=40, m=4
we can see that c is equals to 10 times the value of m
Therefore c = 10m
There are 12 inches in 1 ft. what fact family would you use to find the number of inches in 2 ft.
The offered statement states that there's 12 inches throughout 1 foot and 24 inches in 2 feet.
What does inch serve?In the United States, Quebec, and the United Kingdom, the inch is a widely used conventional measure of length. In Japan, particularly for display screens, it is utilized for electrical components as well. The inch is also a commonly-used informal unit of measurement for display screens throughout most of continental Europe. Half, quarter, eighth, and sixteenths are the minor fractions that make up an inch. The size of both the line indicating each lowers as the sum or length does. Millimeters are used to divide centimeters (10 per centimeter).
In 1 feet there are 12 Inches.
12 inches/foot * 2 feet = 24 inches
So, 2 feet is equal to 24 inches.
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Shayla created two patterns. Pattern X increases by 7 each time. Pattern Y increases by 5 each time. Shayla used the corresponding values in each pattern to make coordinate pairs. She graphed the coordinate pairs on a coordinate plane.
The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
Then the equation of the line is given as,
(y - 5) = [(10 - 5) / (14 - 7)](x - 7)
y - 5 = (5/7)x - 1
y = (5/7)x + 4
At x = 63, the value of 'y' is given as,
y = (5/7)63 + 4
y = 45 + 4
y = 49
The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.
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Two ordinary fair dice are thrown. The resulting score is found as follows.
• If the two dice show different numbers, the score is the smaller of the two numbers.
• If the two dice show equal numbers, the score is 0.
(i) Draw up the probability distribution table for the score.
The probability distribution table is shown below
How to determine the probability distribution tableFrom the question, we have the following parameters that can be used in our computation:
Dice = 2
This means that
Sample size = 6 * 6
Sample size = 36
So, the number of outcomes is 36
To determine the distribution table, we need to identify that the dice are distinct.
This means that (1, 2) and (2, 1) are not the same outcomes
We can create a probability distribution table for the score by listing all possible outcomes and their probabilities, and then determining the score for each outcome based on the rules given.
So, we have
Outcomes Probability
(1, 1) 1/36
(1, 2) 1/36
(1, 3) 1/36
(1, 4) 1/36
(1, 5) 1/36
(1, 6) 1/36
........
(6, 1) 1/36
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Can you help me in this problem algebra
Answer:
2^4*2^5=2^(4+5)=2^9
Step-by-step explanation:
When dealing with operations with exponents and multiplication, the exponent operations always come first. So while the exponent 9 is correct for the answer, 4 is incorrect.
For example, if you were to solve each operation and eliminate every exponent, you would have
2^4*2^5=16*32=512 which is the same as 2^9=512.
As you can see, the exponent operation must come before the multiplication.
The area of the circle is 4pix^2+12pix+9pi what is the least possible integer value of x for the circle to exist
The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The area of the circle is 4π x² + 12πx + 9π. Then the radius is given as,
A = 4π x² + 12πx + 9π
πr² = π [(2x)² + 2 · 2x · 3 + 3²]
r² = (2x + 3)²
r = 2x + 3
The value of the radius should be more than zero. Then we have
r > 0
2x + 3 > 0
x > - 3/2
The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.
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The complete question is given below.
The area of a circle is 4π x 2 + 12πx + 9π.
a. What is an expression for the radius of the circle?
b. What is the least possible integer value of x for the circle to exist? Explain.
The ratio of boys to girls on a softball team was 5:3. For every 35 girls how many ratio of boys will be there?
Answer:
let the boys and girls be 5x and 3x
the ratio of boys to girls= 5:3
the total girls = 35
the ratio of boys to girls = the total girls
5 =35
3 x
5x = 105
x= 105÷5
x= 25
5x= 5×25= 125
3x= 3× 25 = 75
In exercises 17-20, approximate the logarithm using the properties of logarithms, given the values logb2 = 0.3562, logb3 = 0.5646, and logb = 0.8271. Round your result to four decimal places.
I only need 19 and 20!
19. logb 16/25
20. logb [tex]\sqrt{3}[/tex]
The solution of the logarithmic expressions will be:-
19) 2logb4 - 2logb5
20) (1/2)logb (3)
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 two expressions are logb 16/25 and logb √3.
The expressions will be solved as:-
E = logb 16/25
E = logb 16 - logb 25
E = logb 4² - logb 5²
E = 2logb 4 - 2logb 5
The second expression will be solved as:-
E = logb √3.
E = ( 1 / 2 ) logb 3
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A child is flying a kite. If the kite is "h" feet above the child's hand level and the wind is blowing it on a horizontal course at "v" feet per second, the child is paying out cord at _____ feet per second when "s" feet of cord are out. Assume that the cord remains straight from hand to kite.
The child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The distance between the kite and the child's hand level "d".
By using the Pythagorean theorem, we can write:
d² + h² = s²
Simplifying and solving for d, we get:
d² = s²-h²
d = √(s²-h² )
Let's call the length of the cord "L". Then, we can write:
d² + L² = s²
Differentiating both sides with respect to time (t), we get:
2d (dd/dt) + 2L (dL/dt) = 2s (ds/dt)
We want to find (dL/dt) when L = s and d = √(s²-h² )
(dd/dt) = 0 as the height of the kite above the child's hand level is constant.
(dL/dt) = (s(ds/dt) - d (dd/dt)) / L
Substituting in the values we found for d and L, we get:
(dL/dt) = s(ds/dt)) / √(s²-h² )
Therefore, the child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.
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The coordinate plane shown below is a graph of a relation.
What is the range of the graph?
The range of the function, given the graph of a relation, can be found to be −2 ≤ y ≤ 7 .
How to find the range of a graph ?Graphs can be used to determine a function's domain and range. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.
The range here would therefore be the y - values that the relations fall within. The lowest y - value is - 2 as no relation goes below this. The highest y - value is 7.
The range is therefore -2 ≤ y ≤ 7.
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Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U = 1, 2, 3, 4, 5, 6, 7, 8, 9
A = 1, 2, 5, 6
B = 2, 3, 4, 6, 7
C = 5, 6, 7, 8
Find ∪∩A′BC′.
The elements in C U (B' ∩ A') is {5, 6, 7, 8, 9}.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, and the complement of sets.
We have,
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 5, 6}
B = {2, 3, 4, 6, 7}
C = {5, 6, 7, 8}
Now,
A' = U - A = {3, 4, 7, 8, 9}
B' = U - B = {1, 5, 8, 9}
C' = U - C = {1, 2, 3, 4, 9}
Now,
(B' ∩ A')
= {1, 5, 8, 9} ∩ {3, 4, 7, 8, 9}
= {8, 9}
And,
C U (B' ∩ A')
= {5, 6, 7, 8} U {8, 9}
= {5, 6, 7, 8, 9}
Thus,
C U (B' ∩ A') = {5, 6, 7, 8, 9}
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The complete question:
Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U = 1, 2, 3, 4, 5, 6, 7, 8, 9
A = 1, 2, 5, 6
B = 2, 3, 4, 6, 7
C = 5, 6, 7, 8
Find C U (B' ∩ A').
2
Ghana Railways Co-operation has 20 trains for its operation. It is observed that x trains can
accommodate 2 passengers, y trains 3 passengers and z trains 5 passengers. However, the total
number of passengers always present at Ghana Railways is 64. During market day, 3 of x trains, 2
of y trains and 4 of 2 trains for a total of 10 trains were used. Determine the values of x, y and z.
The number of trains that can accommodate 2 passengers is x = 32, the number of trains that can accommodate 3 passengers is y = 1, and the number of trains that can accommodate 5 passengers is z = -11.
What do you mean by equation?It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.
Let x, y and z be the number of trains that can accommodate 2 passengers, 3 passengers and 5 passengers, respectively.
From the information given, we have:
x + y + z = 20 (the total number of trains)
2x + 3y + 5z = 64 (the total number of passengers)
We also know that 10 trains were used during market day:
3 of the x trains, 2 of the y trains and 4 of the z trains.
So, we have:
2x + y + 5z = 10
Solving these three equations simultaneously, we can find the values of x, y and z:
Subtracting the first equation from the third equation:
0 + y + 4z = -10
y + 4z = -10
Subtracting 2 times the first equation from the second equation:
-x + 3y + 4z = 32
y + 4z = 42
Subtracting the last two equations:
x = 32
Substituting the value of x back into the first equation:
32 + y + z = 20
y + z = -12
Substituting the value of y and z back into the third equation:
2x + y + 5z = 10
64 + y + 5z = 10
y + 5z = -54
Solving these two equations simultaneously, we can find the values of y and z:
Subtracting the second equation from the last equation:
4z = -44
z = -11
Substituting the value of z back into the second equation:
y + 5z = -54
y - 55 = -54
y = 1
Therefore, the number of trains that can accommodate 2 passengers is x = 32, the number of trains that can accommodate 3 passengers is y = 1, and the number of trains that can accommodate 5 passengers is z = -11.
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