let f:{1,2,3,4} -> {a,b,c,d} be a function. how many possible such functions can be defined? and what is the principle that this counting is based on? \
Answers
If f:{1,2,3,4} -> {a,b,c,d} be a function, then the number of possible such functions can be defined is 256. The principle that this counting is based on multiplication principle.
To find the number of possible functions that can be defined from a set of 4 elements {1,2,3,4} to a set of 4 elements {a,b,c,d}, we need to calculate the number of ways we can map each element of the first set to an element of the second set.
For the first element of the first set, we have 4 choices of elements from the second set to map it to. Similarly, for each of the 4 elements in the first set, we have 4 choices of elements in the second set to map them to. Therefore, the total number of possible functions that can be defined is:
4 X 4 X 4 X 4 = 256
This Principle of counting is based on the multiplication principle, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things. In this case, we have 4 choices for each of the 4 elements in the first set, so by the multiplication principle, we have a total of 4 X 4 X 4 X 4 = 256 possible functions.
Learn more about Principle of counting :
https://brainly.com/question/22598222
#SPJ4
Related Questions
A clay specimen, 25 mm thick, has been tested in an oedometer apparatus with two way rainage, and it is observed that 50% of the consolidation settlement occurs in 1 hour. A ayer of the same clay is observed to settle 10 mm in 10 years and after many years to settle (total primary consolidation) by 35 mm. Determine the thickness of the clay layer if it drains only from upper surface
Answers
The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.
The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.
Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.
Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.
To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.
To learn more about thickness click here: brainly.com/question/23622259
#SPJ11
Which measure of central tendency is not resistant to extreme values in a numeric data set? A. Parameters B. Mean C. Median D. Mode
Answers
B. Mean is not resistant to extreme values in a numeric data set. The mean is affected by outliers or extreme values in a dataset because it takes into account all the values in the dataset, including the extreme values.
Central tendency is a measure that is used to find the central or typical value of a set of data. The most common measures of central tendency are mean, median, and mode. These measures provide different ways of summarizing the data, depending on the nature of the dataset and the research question.
The mean is calculated by adding up all the values in a dataset and dividing by the number of values. The mean is often considered to be the most common measure of central tendency because it takes into account all the values in the dataset. However, the mean is not resistant to extreme values or outliers. An outlier is an observation that is significantly different from other observations in the dataset.
When a dataset contains extreme values or outliers, the mean is often affected, resulting in a value that does not represent the central tendency of the dataset. This is because the mean is influenced by every value in the dataset, including the outliers, and is not a robust measure of central tendency. In contrast, the median and mode are resistant to extreme values and provide better estimates of central tendency when a dataset contains outliers.
To learn more about central tendency refer below
https://brainly.com/question/2018505
#SPJ11
If h(t) = 161-4 and g(t) = 3-2t, what is the value of g(-1)-h(1)? Pls help me
Answers
Answer:
-152
Step-by-step explanation:
Given that h(t) = 161-4t and g(t) = 3-2t,
g(-1) = 3-2(-1) = 3+2 = 5
h(1) = 161-4(1) = 161-4 = 157
Therefore, g(-1)-h(1) = 5 - 157 = -152
So the value of g(-1)-h(1) is -152
solve 2x+6=7x-14
help
Answers
Answer:
x = 4
Step-by-step explanation:
2x + 6 = 7x - 14
+ 14 +14
2x + 20 = 7x
-2x -2x
20 = 5x
/5 /5
4 = x
Answer:
\(x=4\)
Step-by-step explanation:
\(\textbf{Hi there!}\)
\(2x + 6=7x-14\)
\(\textnormal{\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}}\)
\(2x+6-6=7x-14-6\)
\(2x=7x-20\)
\(\textnormal{\mathrm{Subtract\:}7x\mathrm{\:from\:both\:sides}}\)
\(2x-7x=7x-20-7x\)
\(-5x=-20\)
\(\textnormal{\mathrm{Divide\:both\:sides\:by\:}-5}\)
\(\frac{-5x}{-5}=\frac{-20}{-5}\)
\(x=4\)
\(\textbf{OAmalOHopeO}\)
Use Trigonometric substitution to eliminate the roots 1.1. 164+2 + 1 Use Trigonometric substitution to eliminate the roots 1.1. V64+2 + 1 1.2. V4z2 – 49
Answers
To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.
1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:
V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49
We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:
V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)
Here is a more detailed explanation of the substitution:
In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.
When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3
In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.
When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)
To know more about root click here
brainly.com/question/16880173
#SPJ11
15 points Need ASAP- Use the table to write a proportion ~ (table on pic)
Answers
Answer:
m=24
Step-by-step explanation:
Answer:
m/3 = 32/4 using columns
or
m/32 = 3/4 using rows
Step-by-step explanation: You can use columns or rows to write a proportion when using tables.
-Using columns numerators would have the same units and denominators would have the same units.
-Using rows units are the same on each side of the proportion.
what is the rules for multiplying pairs of numbers with the same signs?
Answers
Answer:
When you multiply two integers with the same signs, the result is always positive. Just multiply the absolute values and make the answer positive. When you multiply two integers with different signs, the result is always negative. Just multiply the absolute values and make the answer negative.
Hope this helps
Step-by-step explanation:
what information do you need to know to write an equation relating two quantities that have a proportional relationship
Answers
Answer:Two quantities have a proportional relationship if they can be expressed in the general form y = kx, where k is the constant of proportionality. In other words, these quantities always maintain the same ratio. That is, when you divide any pair of the two values, you always get the same number k.
Step-by-step explanation:
The function f(x) has a vertical asymptote at x= [blank].
![The function f(x) has a vertical asymptote at x= [blank].](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/6xxxaZb2ICWVfiXxmeiop4OmBPoIYA53.png)
Answers
Answer:
The vertical assymptote is at x = 0
Step-by-step explanation:
Vertical assymptote are simply defined as lines that correspond to the points where the denominator of a rational function is zero.
From the graph, we can see that the curve remains on the y - axis at x = 0
Thus, the vertical assymptote is x = 0
Cards numbered 500 through 799 are placed into a box. How many of the cards satisfy both of the conditions shown below?
• The first digit of the three-digit number on the card is odd.
• The three-digit number on the card is divisible by 6.
Answers
Answer:A
Step-by-step explanation:
It’s really the only answer that make sure sense. The firs time step Is to figure which have the odd number as their first number and that’s would be everything but the 600-699 scale which leaves about 200 more numbers and it wouldn’t make sense for it to be that low due to all of the number s being quite big and 6 being an even number that is easier to divide by when you have the divisor as a bigger number
A consumer watchdog organization estimates the mean weight of 1-ounce "Fun-Size"
candy bars to see if customers are getting full value for their money. A random sample
of 25 bars is selected and weighted, and the organization reports that a 95% confidence
interval for the true mean weight of the candy bars is 0.982 to 0.988 ounces.
a) What is the point estimate (=sample mean) from this sample?
b) What is the margin of error?
(Hint: find the distance between the sample mean and the upper limit).
c) Interpret the confidence level of 90% in the context of the problem?
Answers
Point estimate from the sample is 0.985, margin error is 0.003.
What is Confidence Interval?Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.
(a) To calculate point estimate or sample mean :
Point estimate is the mid point of the confidence interval.
Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.
Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985
(b) Margin error is the one half of the total width of the interval.
Margin error = (0.988 - 0.982) / 2 = 0.003
(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.
Hence the point estimate and margin error are 0.985 and 0.003 respectively.
Learn more about Confidence Interval here :
https://brainly.com/question/18914334
#SPJ1
Harry wants to download some songs to his mp3 player. He received a $20 giftcard for his birthday. It costs $0.90 to download a song. At most, how many songs can he download?
Answers
Step-by-step explanation:
vvvvvec7oecyoeciiiv7oric7oriivsbshshshshshshsJ
At most, Harry can download 22 songs.
22 • $0.90= $19.80
find the value of "x" in the following
Answers
(a) 60° (b) 125°
Step-by-step explanation:-
a)Given are three \(x\)'s, so,
\(3x = 180\)(As all sides of triangle add upto 180°)
\( = > x = \frac{180}{3} \)
\( = > x = 60\)
Hence, value of x is 60°
b)Given two interior angles(55°,70°) & one exterior angle(\(x\)°)
\( = > x° = (55 + 70)°\)
\( = > x° = 125°\)
Hence, value of x is 125°
The weights of boxes of a certain brand of pasta follow an approximately normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounces.
What percentage of boxes have weights that are more than 2 standard deviations below the mean? (Use the Empirical Rule 68, 95, 99.7) ?
Answers
Answer:
2.5%
Step-by-step explanation:
According to the Empirical Rule:
68% of the data in a normal distribution are \(\pm1\sigma\) from the mean \(\mu\)95% of the data in a normal distribution are \(\pm2\sigma\) from the mean \(\mu\)99.7% of the data in a normal distribution are \(\pm3\sigma\) from the mean \(\mu\)Hence, the percentage of boxes that have weights of more than 2 standard deviations below the mean is \(\frac{100\%-95\%}{2}=\frac{5\%}{2}=2.5\%\)
7. If (2,- 1) is the solution to the following linear system, what are the values of a and b?
ax +by = -7
2ax – 3by = 1
Answers
Answer:
• Considering ax + by = -7
\({ \tt{ax + by = - 7}} \\ \\ { \tt{(a \times 2) + (b \times - 1) = - 7}} \\ \\ { \boxed{ \tt{2a - b = - 7 \: - - - eqn \{1 \}}}}\)
• make b the subject of eqn{1}
\({ \tt{b = 2a + 7 - - - eqn \{2 \}}}\)
• considering 2ax - 3by = 1
\({ \tt{2ax - 3by = 1}} \\ \\ { \tt{(2a \times 2) - (3b \times - 1) = 1}} \\ \\ { \boxed{ \tt{4a + 3b = 1 - - - eqn \{3 \}}}}\)
• substitute b in eqn{3} with b from eqn{2}
\({ \tt{4a + 3(2a + 7) = 1}} \\ \\ { \tt{4a + 6a + 21 = 1}} \\ \\ { \tt{10a = - 20}} \\ \\ { \boxed{ \boxed{ \tt{ \: \: a = - 2 \: \: }}}}\)
• find b using eqn{2}
\({ \tt{b = 2a + 7}} \\ \\ { \tt{b = (2 \times - 2) + 7}} \\ \\ { \tt{b = - 4 + 7}} \\ \\ { \boxed{ \boxed{ \tt{ \: \: b = 3 \: \: }}}}\)
A farmer owns chickens and sheep. In total, his animals have 54 eyes and 74 legs. (All of his animals have the expected number
of body parts.) How many of each animal does he have?
Answers
The farmer have 17 chickens and 10 sheep.
What is word problem?A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario.
Given that, a farmer has chickens and sheep, his animals have 54 eyes and 74 legs.
Let the number of the chicken be x and that of sheep be y
Since, all the animal will have 2 eyes therefore,
2x+2y = 54
x+y = 27
x = 27-y...(i)
Also, a sheep have 4 legs whereas a chicken has 2,
2x+4y = 74
x+2y = 37......(ii)
Solving eq(i) and (ii)
27-y+2y = 37
y = 10
Put y = 10 in equation (i)
x = 27-10
x = 17
Hence, the farmer have 17 chickens and 10 sheep.
Learn more about word problems, click;
https://brainly.com/question/2610134
#SPJ1
Solve the problem below, inputting your answer in decimal form.
421.06+212.9
Answers
Please answer quick ill give brainliest to the best
Jerome parked his car for 4½ hours each day for two days at two different parking lots. The cost of parking at each parking lot is shown below. Day 1 - $5.00 for the first hour plus $1.50 for every additional hour. Day 2 - $2.50 for the first hour plus $1.50 for every additional hour. How much more money did Jerome pay on Day 1 compared to Day 2?
A) $19.00
B)$3.50
C) $18.00
D) $2.50
Answers
hope this helped you out!!
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY
Answers
Answer:
25
Step-by-step explanation:
20^2 + 15^ = c^2
400 + 225 = c^2
625 = c^2
25 = c
Answer: The length of the ladder is 25 feet.
It is geometry the question is on the paper can you please help me I’m desperate
Answers
Given:
The lines l and m are parallel lines and x=40 degrees.
To find the angle:
\(\angle\text{DEF}\)We know that alternate angles are equal.
So that,
\(\begin{gathered} \angle EDG=x \\ =40^{\circ} \end{gathered}\)And then, using the angle sum property of a triangle,
\(\begin{gathered} \angle EDG+\angle DFE+\angle DEF=180^{\circ} \\ 40^{\circ}+40^{\circ}+\angle DEF=180^{\circ} \\ \angle DEF=180^{\circ}-40^{\circ}-40^{\circ} \\ \angle DEF=100^{\circ} \end{gathered}\)Thus, the measure of angle DEF is 100 degrees.
What is 32/48 in simplest form?
A.2/3
B.3/4
C.4/6
Answers
--------------------------------
32/48
Divide the numerator and denominator by 16:2/3
<3
Answer:
A. 2/3
Step-by-step explanation:
32 = 2 x 16
48 = 3 x 16
32 / 48
= ( 2 x 16 ) / ( 3 x 16 )
= 2 / 3
The spinner shown has congruent sections. The spinner is spun 63 times. What is a reasonable prediction for the number of times the spinner will land on a section that is shaded red?
Answers
Answer:
36 times
Step-by-step explanation:
Given
\(Red = 4\)
\(Total = 7\)
\(n = 63\)
See attachment
Required
Predicted number of times to land on red
First, we calculate the probability of landing on red
\(Pr = \frac{Red}{Total}\)
\(Pr = \frac{4}{7}\)
The predicted number of red is the =n calculated as:
\(Red = Pr * n\)
\(Red = \frac{4}{7}*63\)
\(Red = 4 * 9\)
\(Red = 36\)
Solve for the red variable
Answers
Answer:
1/3 Bh = V
Step-by-step explanation:
B = 3 V / h
Multiply each side by h
Bh = 3 V / h *h
Bh = 3V
Divide each side by 3
1/3 Bh = 3V/3
1/3 Bh = V
Please help need by tomorrow it would be very very very appreciated
Answers
The linear inequality for the graph in this problem is given as follows:
y ≥ 2x/3 + 1.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:
b = 1.
When x increases by 3, y increases by 2, hence the slope m is given as follows:
m = 2/3.
Then the linear function is given as follows:
y = 2x/3 + 1.
Numbers above the solid line are graphed, hence the inequality is given as follows:
y ≥ 2x/3 + 1.
More can be learned about linear functions at https://brainly.com/question/15602982
#SPJ1
PLEASE HELP MIDDLE SCHOOL MATH
Answers
Answer:
x>=5
Step-by-step explanation:
If x is less than five, then there will be a negative in the square root, which will yield x an imaginary number.
mount everest begins on a plain that is 14,000 feet high, then the summit sits at 29,028 feet. the difference between the height of these two areas is called the .
Answers
The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world.
The difference between the height at the base of Mount Everest, which is 14,000 feet and the summit, which is 29,028 feet is 15,028 feet. This is also known as the elevation gain. It can be calculated using the following formula:
Elevation Gain = Summit Height - Base Height
So in this case, Elevation Gain = 29,028 ft - 14,000 ft
Which gives us: Elevation Gain = 15,028 ft
The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world. It is also the highest mountain in the world, with the summit standing at an impressive 29,028 feet. This is a testament to the power of nature and the sheer scale of Mount Everest.
Learn more about elevation gain here:
https://brainly.com/question/13005580
#SPJ4
answer this guys.....
Answers
9514 1404 393
Answer:
(b) 25 cm²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
ar(ΔABC)/ar(ΔDEF) = (AB/DE)² = (1/2)² = 1/4
Then ...
ar(ΔABC) = (1/4)(100 cm²) = 25 cm² . . . . . multiply by ar(ΔDEF)
The area of ΔABC is 25 cm².
Which table has a constant of proportionality between y and az of 0.6?
Choose 1 answer:
(G
z
Y
47
6
8
-8
4
9
14
H
10
13
y
2.4
5.4
8.4
y
3
2
9 6
15 10
Answers
Answer:
C
Step-by-step explanation:
if you divide the y by x, the answer it will give you will be 2/3 or .6
find the perimeter and area of the parallelogram
Answers
Hi there! your perimeter would be 40+40+48+48 (cuz you add all sides together) which would be 176. Your area would be 40 multiplied by 48 which is 1920. I’m sorry if I’m wrong. Hope this helps!
What is the value of the rational expression 6-x/x+5 when x=2
Answers
Answer:
4/7
Step-by-step explanation:
6-2/2+5=4/7=.57142857142 but usually you can just keep it as a fraction
Hope this helped!!!!!