Answer:
D) 263
Step-by-step explanation:
Step 1: Define
10m³ - |n|
m = 3
n = -7
Step 2: Substitute and Evaluate
10(3)³ - |-7|
10(27) - 7
270 - 7
263
Answer:
263
Step-by-step explanation:
10(33)− l 7 I
=(10)(27)− I 7 I
=270− I 7 I
=263
I WILL GIVE YOU BRAINLIEST!!!
what is the greatest common factor of the term in the expression 73/ ab - 7/ 6 b?
Answer:
I tried solving it and I got an answer of 86c
Hope I helped!! :)
Step-by-step explanation:
Is scale factor of 1 a dilation?
If the scale factor is 1, then there is no change -- all measurements remain the same.
So the image and the pre-image would be congruent.
What is the use of a Scalar Factor of Dilation?
The Scalar factor of the dilation determines how larger or smaller the image is when compared to the original object.
we can find a scalar factor of dilation by finding and measuring the center point of dillution and distance from centre point to point on the preimage and also the distance from the center point to the image point.
Expansion occurs when the absolute value of a scalar factor is greater than another one.
comparison occurs when the absolute value of the scale factor is less than another one.
The scale factor can be obtained by dividing the dimension of the new shape by the dimension of the original shape.
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Marjane wants to create a set of data with 6 values. She wants the mode to be as good as the median to represent the data set. Which set of data best represents what Marjane could create?
24, 24, 25, 29, 29, 29
24, 25, 26, 27, 30, 30
24, 25, 25, 25, 26, 26
24, 24, 25, 26, 26, 27
As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).
In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.
The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.
The third set of data is 24, 25, 25, 25, 26, 26.
The median is the middle value, which is also (25+25)/2 = 25.
The mode is the value that appears most frequently, which is 25.
Therefore, the mode and median are the same, fulfilling Marjane's requirement.
Therefore, the correct option is (c).
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A conceptual model that helps strategists choose between seeking internal development, entering into an alliance, or acquiring new resources, capabilities, and competencies is called the " framework. a) build-borrow-or-buy b) organic growth c) internal-versus-external growth d) capability development
Build-borrow-or-buy.
The build-borrow-or-buy framework is a conceptual model used by strategists to help them decide whether to build capabilities internally, borrow them through partnerships and alliances, or buy them through mergers and acquisitions. The framework helps organizations identify the most efficient and effective way to acquire the resources, capabilities, and competencies they need to achieve their strategic goals. It is a useful tool for decision-making when considering growth strategies, and can help managers evaluate the costs, risks, and benefits of each option.
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(a) build-borrow-or-buy. This framework helps strategists decide whether to pursue internal development, enter into an alliance, or acquire new resources, capabilities, and competencies.
the build-borrow-or-buy framework suggests that companies have three options when it comes to acquiring new resources and capabilities. First, they can build or develop these resources and capabilities internally through investments in research and development or employee training. Second, they can borrow or enter into strategic alliances with other companies to gain access to new resources and capabilities. Finally, they can buy or acquire companies that already possess the desired resources and capabilities.
the build-borrow-or-buy framework provides a structured approach for companies to evaluate their options when it comes to acquiring new resources and capabilities. By considering the pros and cons of each option, companies can make more informed decisions that align with their strategic goals and objectives.
The build-borrow-or-buy framework is a conceptual model that helps strategists decide whether to seek internal development (build), enter into an alliance (borrow), or acquire new resources, capabilities, and competencies (buy). This model assists organizations in evaluating their options for growth and resource allocation based on their strategic goals and objectives.
the build-borrow-or-buy framework is a valuable tool for strategists when choosing between internal development, alliances, or acquisitions to achieve their organization's growth and resource needs.
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∣
2
2
1
−3
1
4
3
3
−1
∣
∣
Compute the determinant using a cofactor expansion across the first row. Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) A. Using this expansion, the determinant is (2)(−13)−(−3)(−5)+(3)(7)= B. Using this expansion, the determinant is (−3)(−5)−(1)(−5)+(4)(0)= C. Using this expansion, the determinant is −(−3)(−5)+(1)(−5)−(4)(0)= D. Using this expansion, the determinant is −(2)(−13)+(−3)(−5)−(3)(7)=
The correct choice is A. Using the cofactor expansion across the first row, the determinant of the given matrix is (2)(-13) - (-3)(-5) + (3)(7) = -26 + 15 + 21 = 10.
To compute the determinant using the cofactor expansion across the first row, we multiply each element of the first row by its cofactor and sum them up. The cofactor of an element is determined by taking the determinant of the submatrix obtained by removing the row and column containing that element, and then multiplying it by (-1) raised to the power of the sum of the row and column indices.
For the given matrix:
2 2 1
-3 1 4
3 3 -1
Expanding along the first row, we have:
Det = (2)(cofactor of 2) + (2)(cofactor of 2) + (1)(cofactor of 1)
= (2)(-13) - (-3)(-5) + (3)(7)
= -26 + 15 + 21
= 10.
Therefore, the correct choice is A. The determinant of the matrix, using the cofactor expansion across the first row, is 10.
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Amazon Math Flow Questions • You have 30 associates who all work an 8 hour day, 5 days a week. 2 need to be indirect-they are not on the floor producing. Your direct rate is 150 units per hour but you have two 15 minute breaks during the day. How many units can your department produce in a 40 hour week? . If you need to produce an extra 10,000 units in a given week how many extra people will it require? Question: Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a... Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a total of 60 sandwiches. The deli wants an efficient way to increase the sandwich output using the same five workers and 10 hour shift (Don't Factor Break in) to produce 75 because of the 25% increase due to the expansion of the deli. What would you do to make the the process more efficient? Where each sandwich would take 8 minutes to make instead of 10 minutes. Please answer the question throughly.
Extra people required is 50.
Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Question 1 :
Number of associates = 30
Number of direct workers = 30 - 2 = 28
You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.
Direct rate = 150 units per hour
Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week
= 37.5 hours per week
Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units
28 people produce 5625 units in a week
Let x people produce 10,000 + 5625 = 15,625 units in a week
Using proportion,
28 : 5625 = x : 15,625
28 / 5625 = x / 15,625
x = (28 × 15,625) / 5625 = 77.78 ≈ 78
Extra people required = 78 - 28 = 50
Question 2 :
Number of sandwiches made in 10 minutes = 1
Number of sandwiches made in 10 hours = 60
5 workers are there. one worker makes 60/5 = 12 sandwiches
But Deli want number of sandwiches in 10 hours = 75
One worker should make 75/5 = 15 sandwiches instead of 12.
Number of sandwiches made in 8 minutes should be 1.
So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.
Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.
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How can you change the dimensions of the rectangle so that the ratio of the length to the width stays the same, but the perimeter is 185 centimeters? l=25cm h=12cm
Answer:
Width= 30
Length= 62.5
Step-by-step explanation:
First we simplify the length to width ratio
25/12=
2 1/12 ratio of length to width
width=x
length=2 1/12x
Make the equation for this ratio's perimeter being equal to 185
2(2 1/12x) + 2(x)=185
Solve for x
4 1/6x +2x=185
6 1/6x=185
x=30
Substitute the answer in for x to find the length and width
Width= 30
Length= 2 1/12(30)
Length= 62.5
A line passes through the points (–4, –1) and (8, 2). What is its equation in slope-intercept form?
I always get it wrong when I write it out
\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{2 +1}{8 +4} \implies \cfrac{ 3 }{ 12 } \implies \cfrac{1 }{ 4 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y +1 = \cfrac{1 }{ 4 } ( x +4) \\\\\\ y+1=\cfrac{1 }{ 4 }x+1\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 4 }x \end{array}}\)
What is the slope of the line that passes through
the points (2,
-4) and (5, 2)? Write your
answer in simplest form.
Answer:
2
Step-by-step explanation:
slope : ( The amount y increases , when x is increased by 1 )
slope : { y2 - y1 / x2 - x1 }
slope : y2 = 2
y1 = -4
x2 = 5
x1 = 2
You must minus the values in the formula to find the slope line that passes through the points:
slope : { y2 - y1 / x2 - x1 }
slope : (2) - (-4) / (5) - (2)
=> 2 + 3 / 3
=> 6/3
=> 2
Text explanation:
Difference between both y-coordinates. = 6
Difference between both x-coordinates. = 3
Divide the difference between y and x. =
y/x =2
Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.
Hope this helps! Sorry it took so long! ⸜(。˃ ᵕ ˂ )⸝ xx
The slope of the line that passes through the points (2, -4) and (5, 2) is 2.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,
Slope = (y₂-y₁)/(x₂-x₁) = [2 - (-4)] / (5 - 2)= 6/3 = 2
Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.
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Write the equation in Slope Intercept form for the line that passes through (-2,-11) and is perpendicular to the x-axis. m= _______ Equation: ________________________________
Answer:
x = -2Step-by-step explanation:
Line perpendicular to x-axis is going to be parallel to y-axis
The formula for this line is
x = bConsidering the given point (-2, -11)
x = -2Valentina has $$ batteries for her remote controlled helicopter. The helicopter will run for $$ hours with regular batteries, but $$ hours with PowerCharge batteries. Write an expression for the number of hours Valentina will be able to use her helicopter if all of her batteries are PowerCharge batteries.
Find the measure of each numbered angle
Answer:
m<1 = 40°
m<2 = 118°
m<3 = 71°
Step-by-step explanation:
✔️m<2 = 180° - 62° (angles in a straight line/supplementary angles)
m<2 = 118°
✔️m<1 = 180° - (118° + 22°) (sum of ∆)
m<1 = 40°
✔️m<3 = 180 - (47 + 62) (sum of ∆)
m<3 = 71°
Consider the function f(x)=10^x and function g.
g(x) = f(x + 4)
How will the graph of function g differ from the graph of function f?
Α. The graph of function g is the graph of function f shifted 4 units down.
B. The graph of function g is the graph of function fshifted 4 units up.
C. The graph of function g is the graph of function f shifted 4 units to the left.
D. The graph of function g is the graph of function fshifted 4 units to the right.
I believe A and C are part of the answer but I am unsure of the rest
Please find attached the image of the enlargement of the shape X by a scale factor of -1 created using MS Word, which is a drawing equivalent to option B. The correct option is therefore;
B.
What is an enlargement transformation?An enlargement transformation is one in which the pri-image object size is scaled about a center of enlargement, using a scale factor, with the sign of the scale factor indicating the direction of the enlargement, which for a +ve sign is on the same side, and for a -ve sign is on the other side of the center of enlargement.
An enlargement by a scale factor of -1, can be obtained by producing the image on the alternate side of the center of enlargement, which with a scale factor of -1, is the same size as the size of the image.
Therefore, the dilation by a scale factor of -1, with the center at the origin, produces an image which is equivalent to a reflection of the original object (pre-image), across the y-axis followed by a reflection across the y-axis.
The image of the object following the dilation will therefore be the mirror image of the mirror image of the object reflected across the y-axis, which takes the shape of a vertically flipped, left flipped F, which is option B
Please find attached a drawing of the shape of the image of the enlargement of shape X by a scale factor of -1, created with MS Word
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what is the answer for -40= -50 + x ?
Answer:10
Step-by-step explanation: Because negative 40 equals -50 + x equals 10
A seagull is flying at a height of 10 feet above ocean. The seagull dives into the water to catch a fish that is at a depth of 6 feet. What is the change in elevation of the seagull?
Answer:
The change in elevation of the seagull is -16 ft
Step-by-step explanation:
Displacement
The displacement, unlike distance, considers the direction of the lengths occurring in the systems.
To solve the problem, we need to set a zero-level reference. Let's assume the sea level as zero height, any position above this reference as positive, and any position below this reference as negative.
The seagull is flying at a height of 10 ft above the ocean. Thus, its position is positive +10 feet.
The seagull then dives into the water to catch a fish at a depth of 6 feet. This position is negative: -6 ft.
The change in elevation is found by subtracting the final elevation and the initial elevation:
change = -6 ft - 10 ft = -16 ft
The change in elevation of the seagull is -16 ft
a company had 80 employees whose salaries are summarized in the frequency distribution below. find the standard deviation.
The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.
The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).
By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.
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Find the perimeter of a rectangular lot if the length is 2x-5 meters while the width is 3x+6 meters.
A. 10x + 2 meters
B. 10x + 22 meters
C. 10x meters
D. 12x meters
A strain of bacteria takes 30 minutes to undergo fission. Starting with 500 bacteria, how many would there be after 7 hours?
There would be approximately \(1.79 \times 10^{135\) bacteria after 7 hours. This
number is extremely large and is beyond the capacity of most calculators
to handle.
After 30 minutes (0.5 hours), each bacterium will undergo fission and
become two bacteria. Therefore, the number of bacteria will double after
every 30 minutes.
In 7 hours, there are 7 x 2 x 2 x 2 x 2 x 2 x 2 = 7 x 2^6 = 448 bacterial
cycles.
So, the final number of bacteria would be:
\(500 \times 2^{448} = 1.79 \times 10^{135\)
Therefore, there would be approximately 1.79 x 10^135 bacteria after 7
hours.
This number is extremely large and is beyond the capacity of most
calculators to handle.
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518. Coin Change 2
You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.
If we have coins = [1, 2, 5] and amount = 5, then the function should return 4, because there are four combinations of coins that make up an amount of 5: [1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], and [5].
This problem can be solved using dynamic programming. Let's define dp[i][j] as the number of combinations of coins using the first i coins to make up an amount j. Then we can use the following recurrence relation:
dp[i][j] = dp[i-1][j] + dp[i][j-coins[i]]
The first term on the right-hand side of the equation corresponds to the case where we don't use the i-th coin, while the second term corresponds to the case where we use the i-th coin at least once. Note that we only need to consider cases where j >= coins[i], because it's impossible to make up an amount less than the value of the i-th coin using that coin.
We can initialize dp[0][0] = 1, because there is exactly one way to make up an amount of zero using no coins. Finally, the answer to the problem is dp[n][amount], where n is the total number of coins.
Here's the Python code:
def change(amount, coins):
n = len(coins)
dp = [[0] * (amount+1) for _ in range(n+1)]
dp[0][0] = 1
for i in range(1, n+1):
dp[i][0] = 1
for j in range(1, amount+1):
dp[i][j] = dp[i-1][j]
if j >= coins[i-1]:
dp[i][j] += dp[i][j-coins[i-1]]
return dp[n][amount]
For example, if we have coins = [1, 2, 5] and amount = 5, then the function should return 4, because there are four combinations of coins that make up an amount of 5: [1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], and [5].
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deer ticks can be carriers of either lyme disease or human granulocytic ehrlichiosis (hge). based on a recent study, suppose that 18% of all ticks in a certain location carry lyme disease, 7% carry hge, and 7% of the ticks that carry at least one of these diseases in fact carry both of them. if a randomly selected tick is found to have carried hge, what is the probability that the selected tick is also a carrier of lyme disease?
Therefore, the probability that the selected tick is also a carrier of Lyme disease, given that it carries HGE, is approximately 0.999 or 99.9%.
To find the probability that the selected tick is also a carrier of Lyme disease given that it carries HGE, we can use the concept of conditional probability.
Let's define the following events:
A: The tick carries Lyme disease
B: The tick carries HGE
We are given:
P(A) = 0.18 (probability of a tick carrying Lyme disease)
P(B) = 0.07 (probability of a tick carrying HGE)
P(A ∩ B) = 0.07 (probability of a tick carrying both Lyme disease and HGE)
The probability we want to find is P(A|B), the probability of the tick carrying Lyme disease given that it carries HGE.
We can use Bayes' theorem to calculate this:
P(A|B) = (P(B|A) * P(A)) / P(B)
P(B|A) represents the probability of a tick carrying HGE given that it carries Lyme disease. We are not given this information directly, so we need to calculate it.
P(B|A) = P(A ∩ B) / P(A)
= 0.07 / 0.18
= 0.3889
Now we can substitute this value into Bayes' theorem:
P(A|B) = (0.3889 * 0.18) / 0.07
= 0.999
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5. Juanita traveled at an average speed of 50 miles per hour for 2.5 hours and then
traveled at an average speed of 65 miles per hour for 3 hours. What was the total
distance in miles that Juanita traveled during this time?
The total distance in miles that Juanita traveled is 320.
How to find distance with velocity and time ?Use the formula d = st to determine speed, distance, or time. Distance is equal to speed multiplied by time. Given two known numbers, the Speed Distance Time Calculator can solve for the unknown sdt value.Units of seconds (s), minutes (min), hours (hr), or hours, minutes, and seconds can be used to input or solve for time (hh:mm:ss). Time format shortcuts are shown below.Distance = speed x timeSince both reflect a certain amount of distance per unit of time, such as miles per hour or kilometers per hour, rate and speed are comparable. If speed s and rate r are equal, then r = s = d/t. You may substitute d = rt, which stands for "distance equals rate times time," in place of this calculation.Given data :
S1 = 50 miles
S2 = 65 miles
T1 = 2.5 hours
T2 = 3 hours
therefore : distance d = speed x time
d1 = 50 x 2.5 = 125 miles
d2 = 65 x 3 = 195 miles
So, the total distance = d1 + d2 = 195 + 125 = 320
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Answer:
The total distance in miles that Juanita traveled is 320.
identify the random variable in each distribution, and classify it as discrete or continuous. 1. the number of bytes in the memory of a computer 2. the world population 3. the mass of a banana 4. the speed of a car
The following parts can be answered by the concept from Statistics.
The random variable in the first distribution is the number of bytes in the memory of a computer, and it is a discrete variable.
The random variable in the second distribution is the world population, and it is a continuous variable.
The random variable in the third distribution is the mass of a banana, and it is a continuous variable.
The random variable in the fourth distribution is the speed of a car, and it is a continuous variable.
1. The number of bytes in the memory of a computer is a discrete variable, as it can only take on certain specific values. For example, a computer's memory may have 4 gigabytes (GB) of RAM or 8 GB of RAM, but it cannot have 6.5 GB of RAM.
2.The world population is a continuous variable, as it can take on any value within a certain range. For example, the world population may be 7.8 billion people, but it could also be 7.801 billion people or 7.799 billion people.
3. The mass of a banana is also a continuous variable, as it can take on any value within a certain range. For example, a banana may have a mass of 120 grams, but it could also have a mass of 120.5 grams or 119.8 grams.
4. The speed of a car is also a continuous variable, as it can take on any value within a certain range. For example, a car may be traveling at a speed of 50 kilometers per hour, but it could also be traveling at a speed of 50.5 kilometers per hour or 49.8 kilometers per hour.
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The Walker family and the James family each used their sprinklers last summer. The water output rate for the Walker family’s sprinkler was 20L per hour. The water output rate for the James family’s sprinkler was 35L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1300L. How long was each sprinkler used?Walker family’s sprinkler:James family’s sprinkler:
we have
Walker family= 20 L/H
James family = 35 L/H
Total time= 50h
total water= 1300L
let's x be the time walker family use the sprinkler
let's y be the time James family use the sprinkler
then the total time is given by
First equation
\(x+y=50\)second equation
then the flow of water of is
Walker family = x*20
James Family = y*35
since the total flow is 1300L
then
\((x\ast20)+(y\ast35)=1300\)\(20x+35y=1300\)now with the 2 system equation we can solve x and y
\(x=50-y\)then
\(20(50-y)+35y=1300\)\(1000-20y+35y=1300\)\(15y=300\)\(y=\frac{300}{15}=20\)then
x+20=50
x=50-20=30
wich means
the walker family use the sprinkler for 30h
and
the James family use the sprinkler for 20h
Change the following fraction to a decimal. (Carry the division for three places as indicated. Do not round your answer.)
1/64 =
1/64 fraction is equal to 0.015625 in decimal form.
To change the fraction 1/64 to a decimal, we need to perform division.
1 divided by 64 can be written as:
0.015625
----------
64 | 1.000000
0
10
0
The result of the division is 0.015625. This means that 1/64 is equal to 0.015625 in decimal form.
Note that in this case, we carried the division out to six decimal places, but the question specified that we should carry it out to three decimal places. In that case, we would round the answer to 0.016.
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Solve the compound inequality 8 < 3 - 5x < 18
Answer:
−1 > x > −3
Step-by-step explanation:
Let's solve your inequality step-by-step.
8<3−5x<18
Answer:
aaaaaaaaa
Step-by-step explanation:
Drag a company name into each box to show the total cost from least to greatest.
Answer:
Company A:
$3 each6% for shipping150*3*1.06 = $477 total costCompany B:
$3.10 each4% for shipping150*3.1*1.04 = $483.60 total costCompany C:
$3.20 eachNo shipping charge150*3.2 = $480 total costLeast cost | Medium cost | Greatest cost
Company A | Company C | Company B
You pick a card at random. Without putting the first card back, you pick a second card at random.What is the probability of picking a 2 and then picking a number less than 4?
The probability of picking a 2 and then picking a number less than 4will be 0.56%
What is prοbability?By simply dividing the favοrable number οf pοssibilities by the entire number οf pοssible οutcοmes, the prοbability οf an οccurrence can be determined using the prοbability fοrmula. Because the favοrable number οf οutcοmes can never exceed the entire number οf οutcοmes, the chance οf an event οccurring might range frοm 0 tο 1.
The number οf favοurable οutcοmes tο all pοssible οutcοmes οf an event is the ratiο, which is knοwn as prοbability. The number οf gοοd οutcοmes can be represented by the symbοl x fοr an experiment with 'n' number οf οutcοmes. The fοllοwing equatiοn can be used tο determine an event's prοbability.
Yοu pick a card at randοm. Withοut putting the first card back, yοu pick a secοnd card at randοm.
1/13 chance οf picking a 5.
4/51 chance οf picking a 3 οn secοnd draw.
4/(13*51) οf dοing these sequentially = 0.56%
Hence the prοbability will be 0.56%
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Even and Odd Functions. (a) Are the following expressions even or odd? Sums and products of even functions and of odd functions. Products of even times odd functions. Absolute values of odd functions. f(x) + f(-x) and f(x) - f(-x) for arbitrary f(x).
Let's analyze the properties of the given expressions:
Sums and products of even functions:
An even function is defined as f(x) = f(-x) for all x in the domain.
The sum of two even functions, f(x) + g(x), will also be even because (f+g)(x) = f(x) + g(x) = f(-x) + g(-x) = (f+g)(-x).
The product of two even functions, f(x) * g(x), will also be even because (fg)(x) = f(x) * g(x) = f(-x) * g(-x) = (fg)(-x).
Sums and products of odd functions:
An odd function is defined as f(x) = -f(-x) for all x in the domain.
The sum of two odd functions, f(x) + g(x), will also be odd because (f+g)(x) = f(x) + g(x) = -f(-x) - g(-x) = -(f+g)(-x).
The product of two odd functions, f(x) * g(x), will be even because (fg)(x) = f(x) * g(x) = -f(-x) * -g(-x) = (fg)(-x).
Products of even times odd functions:
When an even function is multiplied by an odd function, the resulting function will be odd because (even * odd)(x) = even(x) * odd(x) = even(-x) * -odd(-x) = -(even * odd)(-x).
Absolute values of odd functions:
The absolute value of an odd function will be an even function because |f(x)| = |f(-x)|.
f(x) + f(-x) and f(x) - f(-x) for arbitrary f(x):
If f(x) is an even function, then f(x) + f(-x) will also be an even function because (even + even)(x) = even(x) + even(-x) = even(x) + even(x) = 2 * even(x).
If f(x) is an odd function, then f(x) + f(-x) will be an even function because (odd + odd)(x) = odd(x) + odd(-x) = odd(x) - odd(x) = 0.
If f(x) is an even function, then f(x) - f(-x) will be an even function because (even - even)(x) = even(x) - even(-x) = even(x) - even(x) = 0.
If f(x) is an odd function, then f(x) - f(-x) will also be an odd function because (odd - odd)(x) = odd(x) - odd(-x) = odd(x) + odd(x) = 2 * odd(x).
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If the frequency of a fm wave is 8.85 × 107 hertz, what is the period of the fm wave? a. 2.58 × 10–8 seconds b. 1.13 × 10–8 seconds c. 1.25 × 10–7 seconds d. 5.82 × 10–7 seconds
The time period of fm wave is found to be 1.13 x 10⁻⁸ sec.
Define the term frequency of the wave?The quantity of waves that pass a fixed point in a unit of time is referred to as frequency in physics.
A body in periodic motion undergoes how many cycles or vibrations in one unit of time, according to this definition.The rate at which current changes direction each second is known as frequency. It is expressed in hertz (Hz), a unit of measurement that is used internationally. One hertz is equal to one cycle per second. One hertz (Hz) is equivalent to one cycle per second. A complete alternating current or voltage wave is referred to as a "cycle.".For the given frequency of a fm wave = 8.85 × 10⁷ hertz.
Time period = 1 / frequency
T = 1 / 8.85 × 10⁷
T = 0.112 x 10⁻⁷ sec
T = 1.13 x 10⁻⁸ sec
Thus, the period of the fm wave is found to be 1.13 x 10⁻⁸ sec.
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