Step-by-step explanation:
The volume of the rectangular fish tank is:
V = l x w x h = 60 cm x 15 cm x 34 cm = 30,600 cm³
Since the tank is 1/3 full, the volume of water in the tank is:
V_water = (1/3) x V = (1/3) x 30,600 cm³ = 10,200 cm³
To find the volume of water needed to fill the tank completely, we can subtract the volume of water already in the tank from the total volume of the tank:
V_needed = V - V_water = 30,600 cm³ - 10,200 cm³ = 20,400 cm³
Therefore, 20,400 cm³ of water is needed to fill the tank completely.
find the closed formula for 3,6,11,18 by relating them to a well known sequence. assume the first term given is
The closed formula for this particular sequence is an = n² + 2.
Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².
As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.
So, the closed formula for this particular sequence is an = n² + 2.
To learn more about arithmetic sequences, refer to:
Your question is incomplete. The complete question is:
Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.
Between 11pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
A. Find the probability that at least 3 minutes will elapse before the next telephone order
B. Find the probability that less then 15 minutes will elapse
C. Find the probability that between 15 and 30 minutes will elapse
Answer all please URGENT
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
The probability that less than 15 minutes will elapse between orders is 0.677.
The probability that between 15 and 30 minutes will elapse between orders is 0.2275
Using Poisson distribution:To solve the following problem, we need to use the Poisson distribution, which is a probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average rate of occurrence of those events.
The Poisson distribution has the following formula:
[tex]P(X = k) = (\lambda\times ex^{-\lambda}) / k![/tex]
Where:
P(X = k) is the probability that there are exactly k events in the interval
λ is the average rate of occurrence of events in the interval
e is the mathematical constant e (approximately 2.71828)
k! is the factorial of k (i.e., k * (k-1) * (k-2) * ... * 2 * 1)
Here we have
Between 11 pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
A. The probability that at least 3 minutes will elapse before the next telephone order, using the complement rule:
=> P(at least 3 minutes) = 1 - P(less than 3 minutes)
Assume that the time between telephone orders follows an exponential distribution with a mean of 1/4.2 = 0.2381 hours (or 14.28 minutes).
Therefore, the Poisson distribution is λ = 1/0.2381 = 4.2/1.0 = 4.2.
Using the exponential distribution, we can find the probability of less than 3 minutes elapsing between orders as follows:
P(less than 3 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]
Where t = 3/60 = 0.05 hours
P(less than 3 minutes) = [tex]1 - e^{(-4.2\times 0.05) } = 0.203[/tex]
Therefore,
P(at least 3 minutes) = 1 - 0.203 = 0.797
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
B. To find the probability that less than 15 minutes will elapse between orders, we can use the same exponential distribution as before and set t = 15/60 = 0.25 hours:
P(less than 15 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]
P(less than 15 minutes) = [tex]1 - e^{(-4.2 \times 0.25)} = 0.677[/tex]
Hence, The probability that less than 15 minutes will elapse between orders is 0.677.
C. To find the probability that between 15 and 30 minutes will elapse between orders, we can subtract the probabilities found in less than 15 minutes and less than 30 minutes.
P(15 to 30 minutes) = P(less than 15 minutes) - P(less than 30 minutes) -
P(15 to 30 minutes) = [tex]e^{ (-\lambda0.5)} - e^{ (-\lambda 0.25)}[/tex]
= 0.3499 - 0.1224 = 0.2275
Therefore,
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
The probability that less than 15 minutes will elapse between orders is 0.677.
The probability that between 15 and 30 minutes will elapse between orders is 0.2275
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Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
He has 2 pens. His friend gives him 2 more pens. How many pens he has?
Step-by-step explanation:
4 i guess... sry i m not good at maths
1) Pendant la période des soldes, tous les manteaux d'un magasin sont soldés à 15%.
a. Marjorie a repéré un manteau qui coûtait initialement 78€.
Quel est son prix après réduction ?
b. Mélanie veut acheter un manteau dont le prix après réduction est de 55,25€.
Quel était son prix initial ?
2) Manu affirme que sur les étiquettes suivantes, le pourcentage de réduction appliqué au prix
de la montre est supérieur à celui appliqué aux lunettes. A-t-il raison ?
45€→ 35,55€
Réduction
de 20%
Answer: Zemāk
Step-by-step explanation:
1)
a. Le prix du manteau après la réduction de 15% est:
78€ - (15/100)*78€ = 66,30€
Le prix du manteau après la réduction est de 66,30€.
b. Soit x le prix initial du manteau.
Le prix du manteau après la réduction de 15% est:
x - (15/100)*x = 55,25€
Simplifions cette équation:
0,85x = 55,25€
x = 65€
Le prix initial du manteau était de 65€.
2)
Pour les lunettes, le prix initial est de 45€ et la réduction appliquée est de 20%:
45€ - (20/100)*45€ = 36€
Pour la montre, le prix initial est de 35,55€ et la réduction appliquée est également de 20%:
35,55€ - (20/100)*35,55€ = 28,44€
On constate que le pourcentage de réduction est le même pour les deux articles, donc Manu a tort.
Find the zeros of the function.
y = (x + 1)(x-2)(x - 5)
The zero(s) of the function are
(Use a comma to separate answers as needed.)
The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI
it is false. 0 is not a natural number. it is a whole number
f the random walk starts in the center, on average how many steps does it take to return to the center?
Total number of steps taken by an average man in a year while walking with 7192 steps a day is equals to 2,625,080 steps/year.
Number of steps taken by average man in a day is equals to 7192
Then the total number of steps he takes in a year is equals to,
Calculate it by multiplying the average number of steps per day by the number of days in a year.
There are different ways to define a year,
But assuming a regular calendar year of 365 days, the calculation would be,
Total number of days in a year = 365 days
Total number of steps in a year
= 7192 steps/day x 365 days/year
= 2,625,080 steps/year
Therefore, on average the man would walk about 2,625,080 steps in a year.
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The given question is incomplete, I answer the question in general according to my knowledge:
If a man walks with random steps and the average man takes 7192 steps a day about how many steps does the average man take in a year?
What is the slope of the line in the following graph?
Answer:
1/3
Step-by-step explanation:
using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3
Triangle ABC is similar to triangle DEF. What is AC?
Answer:
i think side AC is 14 because if you do subtract BC (18) from EF(12) you get 6, so u add 6 to DF(8) and get 14.
if its confusing ask me questions!!
Answer:
12
Step-by-step explanation:
When triangles are similar, their side ratios are the same. The ratio of EF to BC is 18/12, or 3/2. To find the side AC, we would multiply the corresponding part of DEF by 3/2, the same ratio. The corresponding part of DEF would be DF. DF = 8. 8 times 3/2 is 12. So AC is 12.
Let me know if this helped by hitting brainliest! If not, please comment and I'll get back ASAP.
PLEASE HELP MEEE
whoever answers right gets brainliest!!!
Answer:
[tex]30\leq x[/tex] AND [tex]x \leq 106[/tex]
Notice the valid answer is the one with the AND since need to be both at the same time.
Step-by-step explanation:
Is the one is market, you add 6 to each side and you obtain that answer
[tex]24 \leq x-6\leq 100[/tex]
[tex]24 +6\leq x\leq 100+6[/tex]
[tex]30\leq x\leq 106[/tex]
Calculate the following limits?
The answer of the given question based on the limits the answers are as follows, (a) lim f(x) = 1 , (b) lim f(x) = 3 , (c) lim f(x) = 3.
What is Graph?A graph is visual representation of data that shows the relationship between two or more variables. Graphs can be used to display wide variety of information, including numerical data, functions, and networks. The most common types of graphs like line graphs, bar graphs, scatter plots, and pie charts.
Graphs are widely used in many fields, like science, economics, engineering, and social sciences, to help people understand and analyze complex data. They are powerful tool for visualizing trends, patterns, and relationships, and are often used to communicate findings to wider audience.
a) The limit of f(x) as x approaches 2 from the left:
We can see from the graph that as x approaches 2 from the left, f(x) approaches 1. Therefore, we can write:
lim f(x) = 1
x→2-
b) The limit of f(x) as x approaches 2 from the right:
Similarly, as x approaches 2 from the right, f(x) approaches 3. Therefore:
lim f(x) = 3
x→2+
c) The limit of f(x) as x approaches 2:
Since the limit from the left and the limit from the right exist and are equal, we can say that the limit of f(x) as x approaches 2 exists and equals the common value of the left and right limits. Therefore:
lim f(x) = 3
x→2
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Mr. Chand is one of the landlords of his town. He buys a land for his daughter spanning over a
area of 480m². He fences the dimensions of the land measuring (x+12) mx (x+16) m. Now he
plans to erect a house with a beautiful garden in the ratio 5:3 respectively. A total of Rs. 5,00,000 is estimated as the budget for the expenses.
1)Give the area of the land purchased in linear polynomial form using algebraic expression
2)Mr. Chand's daughter is ready to share 3/5" of the expenses by her earnings. Express the
fraction in amount.
3)Can you solve the linear equation/polynomial of the area into different factors?
The required answers are 1) [tex]$$A = x^2 + 28x + 192$$[/tex] 2) 300000 3) [tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex].
How to deal with area and fractions?area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:
[tex]$$A = (x+12)(x+16)$$[/tex]
Expanding this expression, we get:
[tex]$$A = x^2 + 28x + 192$$[/tex]
Hence, the area of the land purchased is given by the polynomial expression [tex]$x^2 + 28x + 192$[/tex].
The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:
[tex]$\frac{3}{5}=\frac{x}{500000}$$[/tex]
Simplifying this expression, we get:
[tex]$x = \frac{3}{5}\times 500000 = 300000$$[/tex]
Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.
We can solve the polynomial [tex]$x^2 + 28x + 192$[/tex] into different factors by using the quadratic formula:
[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
Here, the coefficients of the polynomial are:
[tex]$$a = 1, \quad b = 28, \quad c = 192$$[/tex]
Substituting these values in the quadratic formula, we get:
[tex]$x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$[/tex]
Simplifying this expression, we get:
[tex]$$x = -14 \pm 2\sqrt{19}$$[/tex]
Therefore, the polynomial [tex]$x^2 + 28x + 192$[/tex] can be factored as:
[tex]$$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$[/tex]
or
[tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex]
So, we have factored the polynomial into two factors.
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An instructor is administering a final examination. She tells her class that she with give an A grade to the 10% of the students who earns the highest marks. Past experience with the same examination has yielded grades that are normally distributed with a mean of 70 and a standard deviation of 10. If present class runs true to form, what numerical score would a student need to earn an A grade?
To earn an A grade, a student needs to score at least 82.8 , calculated using the inverse normal cumulative distribution function with a mean of 70, a standard deviation of 10, and a 10th percentile of 0.10.
Given that the grades are normally distributed with a mean of 70 and a standard deviation of 10.
We need to find the score which is at the 10th percentile of the distribution.
Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile.
From the table, we can see that the z-score is approximately -1.28.
Using the formula for standardizing a normal distribution:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values, we have:
-1.28 = (x - 70) / 10
Solving for x, we get:
x = (-1.28 * 10) + 70
x = 82.8
Therefore, a student would need to earn a score of approximately 82.8 to receive an A grade.
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123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176
A bin size ofis most appropriate for the data shown above.
A. 69 B. 2 C. 10 D. 1
The answer of the given question based on statistics to find the most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.
What is Statistics?Statistics is the practice of collecting, analyzing, and interpreting the data. It involves use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.
It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.
To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.
To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.
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The answer of the given question based on statistics to find the most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.
What is Statistics?Statistics is the practice of collecting, analyzing, and interpreting the data. It involves use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.
It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.
To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.
To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.
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The complete question is as fpllows:
123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176
A bin size of is most appropriate for the data shown above.
A. 69
B. 2
C. 10
D. 1
If
f(x) = 2x² + 3x - 6, determine the value of f(2).
Answer:
8
Step-by-step explanation:
2x² + 3x - 6
plug in x with 2
2(2)^2+3(2)-6
2(4)+6-6
8+6-6
14-6
8
If 5 is increased to 9, the increase is what percentage of the original number
Answer: It's a 80% increase
Step-by-step explanation:
if the slope of the line joining the points (2,4) and (5,k) is 2. find the value of k
10 is the value of k of the slope of the line .
What are slopes called?
Slope, usually referred to as rise over run, is a line's perceived steepness. By dividing the difference between the y-values at two places by the difference between the x-values, we can determine slope.
You may determine a line's slope by looking at how steep it is or how much y grows as x grows. slope categories. When lines are inclined from left to right, they are said to have a positive slope, a negative slope, or a zero slope (when lines are horizontal).
the points (2,4) and (5,k)
formula from slope of two points
slope = y₂ - y₁/x₂ - x₁
substitute the values in formula
slope = 2
slope = k - 4/5- 2
2 =k - 4/3
6 = k - 4
k = 6 + 4
k = 10
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Suppose we want to choose 5 letters, without replacement, from 15 distinct letters
[tex]\text{order does not matter}[/tex]
[tex]\text{sample space}= \text{15 letters}[/tex]
[tex]\text{no repetition}[/tex]
[tex]\text{P(A)}= \text{15C5}= \text{3003 ways}[/tex]
PLEASE ASAP!!Graph the line 4x+5y=20
Step-by-step explanation:
Might be a little easier to visualize if yo re-arrange it into y = mx + b form:
4x+ 5y = 20
5y = -4x + 20
y = - 4/5 x + 4 y-axis intercept at y = 4
x axis intercept is found by:
0 = -4/5 x + 4
- 4 = -4/5 x
x = 5
So===> plot the two intercept points ( 0,4) and ( 5,0) and connect the dots
I will mark you brainiest!
Given the coordinates shown and given that SU = 10, what are the coordinates of U if STUV is a kite?
A) (10, 18)
B) (0, 28)
C) (18, 28)
The calculated coordinates of U if STUV is a kite is (10, 18)
Calculating the coordinates of U if STUV is a kite?From the question, we have the following parameters that can be used in our computation:
The figute of a kite
Also, we have
S = (0, 18)
And the distance SU to be
SU = 10
If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)
So, we have
U = (0 + 10, 18)
Evaluate
U = (10, 18)
Hence, the coordinates of U if STUV is a kite is (10, 18)
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What is the length of the distance between the two points of (6,-2)
and (3, 4)?
O √13
O √45
O √65
O √117
Answer:
[tex]\sqrt {45}[/tex]
Step-by-step explanation:
Distance between two points, (x1, y1) and (x2, y2) in a 2D cartesian coordinate is given by
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
here the points are (6, - 2) and (3, 4)
We get
[tex]d = \sqrt {(3 - 6)^2 + (4 - (-2))^2}\\\\d = \sqrt {(-3)^2 + (6)^2}\\\\d = \sqrt {{9} + {36}}\\\\d = \sqrt {45}[/tex]
What is the difference between the questionnaire and an interview?
Answer: Questionnaire refers to a research instrument, in which a series of question, is typed or printed along with the choice of answers, expected to be marked by the respondents, used for survey or statistical study. It consists of aformalisedd set of questions, in a definite order on a form, which are mailed to the respondents or manually delivered to them for answers. The respondents are supposed to read, comprehend and give their responses, in the space provided.
A ‘Pilot Study’ is advised to be conducted to test the questionnaire before using this method. A pilot survey is nothing but a preliminary study or say rehearsal to know the time, cost, efforts, reliability and so forth involved in it.
The interview is a data collection method wherein a direct, in-depth conversation between interviewer and respondent takes place. It is carried out with a purpose like a survey, research, and the like, where both the two parties participate in the one to one interaction. Under this method, oral-verbal stimuli are presented and replied by way of oral-verbal responses.
It is considered as one of the best methods for collecting data because it allows two way exchange of information, the interviewer gets to know about the respondent, and the respondent learns about the interviewer. There are two types of interview:
Personal Interview: A type of interview, wherein there is a face to face question-answer session between the interviewer and interviewee, is conducted.
Telephonic Interview: This method involves contacting the interviewee and asking questions to them on the telephone itself.
A invested Rs 4500 for 3 years at the rate of 8% annual compound interest and B invested the
same amount for same time at the rate of per month per rupee I paisa simple interest. Calculate
(i) The interest received by A. (ii) The interest received by B.
The calculation of the interest received by Investor A and Investor B is as follows:
Investor A = $1,168.70 (Compound)Investor B = $1,620 (Simple).What is the difference between compound and simple interest?Compound interest is based on the system of charging interest on accumulated interest and principal for each period.
Simple interest is charged on only the principal for each period.
A's Investment at 8% Annual Compound Interest:N (# of periods) = 3 years
I/Y (Interest per year) = 8%
PV (Present Value) = $4,500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $5,668.70
Total Interest = $1,168.70
B's Investment at Paisa 1 per R1.00 Monthly Simple Interest:N (# of periods) = 3 years
r = 1 paisa per rupee per month
= 1÷100*100 = 1%
Annually rate =1%*12 = 12%
PV (Present Value) = $4,500
Results:
Total Interest = $1,620 (R4,500 x 12% x 3)
Future Value (FV) = $6,120.
Thus, while Investor A receives $1,168.70 at the end of 3 years, Investor B receives $1,620.
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Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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how many one-to-one functions are there from a set with five elements to sets with the following number of ele- ments? a) 4 b) 5 c) 6 d) 7
a) Number of one-to-one functions are equal to the zero, because n< m.
b) Number of one-to-one functions are equal to the ⁵P₅ = 120.
c) Number of one-to-one functions are equal to the ⁶P₅ = 720.
c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.
One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then
Number of one-to-one functions from set A to Set B = P(n,m) or ⁿPₘ , n≥ m and number of one-to-one functions from set A to Set B = 0 , n< m.Now, we have a domain set with five elements, m = 5
a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.
b) number of elements in another set,n= 5
So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)
= 5!/0! = 120
c) Number of elements in another set, n= 6
So, Number of one-to-one functions= ⁶P₅
= 6!/(6 - 5)!
= 6!/1! = 720
d) Number of elements in another set, n
= 7
So, Number of one-to-one functions
= ⁷P₅ = 7!(7 - 5)!
= 7!/2! = 2250
Hence, required value is 2250.
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One side of the triangle is 4 cm, and the sum of the other two sides is equal to a whole number of cm. What is the smallest possible perimeter of the triangle?
F. 9 cm
G. 10 cm
H. 11 cm
J. 15 cm
K. 17 cm
Answer:
9 cm
Step-by-step explanation:
By the Triangle Inequality, any two sides of a triangle must be greater than the remaining side.
In order to minimize the perimeter, we will assume that 4 cm is the longest side.
Thus, the two remaining sides must be greater than 4.
Since we are given that the sum of the two remaining sides is a whole number, the smallest whole number value greater than 4 is 5.
Hence, the smallest perimeter possible 9 cm.
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Part 1
Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest.
R; % interest compounded semiannually for years.
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Part 1
The future value of the ordinary annuity is $
177,961.83.
(Round to the nearest cent as needed.)
Part 2
The amount from contributions is $
enter your response here and the amount from interest is
$
enter your response here. (Round to the nearest cent as needed.)
The Amount from contributions = R * n
Define the term future value?The future value refers to the value of an asset or investment at a specified time in the future, based on a specific interest rate or rate of return.
Without knowing the specific values of R, interest rate, and number of years, we cannot calculate the amounts from contributions and interest. However, we can provide the general formula for calculating the future value of an ordinary annuity:
FV = R * [(1 + i)ⁿ - 1] / i
where FV is the future value of the annuity, R is the periodic payment, i is the interest rate per period, and n is the number of periods.
To calculate the amount from contributions, we can multiply the periodic payment R by the number of periods n.
Amount from contributions = R * n
To calculate the amount from interest, we can subtract the amount from contributions from the future value of the annuity.
Amount from interest = FV - R * n
Once the specific values for R, interest rate, and number of years are provided, we can use these formulas to calculate the amounts from contributions and interest.
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12. What is the height of the trapezoid in yards? (Hint: Use the formula
A = 1/2h (b 1, + b2,) (Lesson 2)
Answer:
height = 7 yards
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the 2 parallel bases
here b₁ = 12 , b₂ = 9 and A = 73.5 , then
[tex]\frac{1}{2}[/tex] h(12 + 9) = 73.5 ( multiply both sides by 2 to clear the fraction )
h(21) = 147
21h = 147 ( divide both sides by 21 )
h = 7 yards
the value of the given test statistic lies between the given cutoffs -2.58 and 2.58. it falls in acceptance region.
Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.
The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.
Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.
a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.
b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.
So in both cases null hypothesis cannot be rejected.
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The complete question is :
f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:
a. z = −0.94
b. z = 2.12
