Answers
Therefore , the solution of the given problem of function comes out to be he function's average rate of change over the range 3 x 4 is 4.
Describe function.There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.
Here,
Calculate the difference between the function values at
=> x = 4 and x = 3, then split by the difference in x-values,
which is 4 - 3 = 1, to determine the average rate of change of the function over the range 3 x 4.
We can see from the table that f(4) = -5 and f(3) = -9. As a result, the following function numbers are different:
=> f(4) - f(3) = (-5) - (-9) = 4
=> 4 - 3 = 1 represents the x-value disparity.
Therefore, the function's average rate of change over the period 3 x 4 is:
Average rate of change is equal to
=> (f(4)-f(3))/(4-3) = 4/1 = 4.
Consequently, the function's average rate of change over the range 3 x 4 is 4.
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Related Questions
If Karel starts at Street 1 and Avenue 1, facing East, where will Karel be, and what direction will Karel be facing after running the following code? (Assume the world is 10x10 in size)move();turnLeft();putBall();turnLeft();turnLeft();turnLeft();move();turnLeft();
Answers
After running the given code, Karel will be at Street 2 and Avenue 2, facing North.
Here is a step-by-step explanation of what the code does:
move(); - Karel moves one block east, to Street 1 and Avenue 2.
turnLeft(); - Karel turns left to face north.
putBall(); - Karel puts a ball at Street 1 and Avenue 2.
turnLeft(); turnLeft(); turnLeft(); - Karel turns left three times to face south.
move(); - Karel moves one block south to Street 2 and Avenue 2.
turnLeft(); - Karel turns left to face east.
So after executing this code, Karel will be at Street 2 and Avenue 2, facing North.
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I need help asap I just need atleast one of these explained and I can do the rest
Answers
Answer:
To factor 30b³-54b², we can factor out the greatest common factor of 6b² to get:
30b³-54b² = 6b²(5b-9)
To factor 35-48y³, we can notice that it is a difference of cubes:
35-48y³ = (5)³ - (4y)³ = (5-4y)(25+20y+16y²)
To factor x³+8, we can use the sum of cubes formula:
x³+8 = (x+2)(x²-2x+4)
To factor 3-64, we can use the difference of squares formula:
3-64 = (1)² - (8)² = (1+8)(1-8) = -7(-9) = 63
To factor 8c³+343, we can use the sum of cubes formula:
8c³+343 = (2c)^3 + 7³ = (2c+7)(4c²-14c+49)
To add or subtract complex polynomials, we simply combine like terms. For example:
(3x²+2x-5) + (4x²-3x+7) = 7x²-x+2
To multiply complex polynomials, we can use the distributive property and FOIL method. For example:
(2x+1)(3x-4) = 6x²-5x-4
To factor complex polynomials, we can use various methods such as factoring out the greatest common factor, using the difference of squares formula, using the sum or difference of cubes formula, or factoring by grouping.
The formulas provided are for factoring the sum or difference of cubes:
(a + b³) = (a + b)(a² - ab + b²)(a - b³) = (a - b)(a² + ab + b²)These formulas can be useful for factoring complex polynomials that have a cube term or a constant term in addition to the quadratic and linear terms.
23 people attend a party. each person shakes hands with at most 22 other people. what is the maximum possible number of handshakes, assuming that any two people can shake hands at most once?
Answers
The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.
What is the maximum possible number of handshakes?Twenty-three people attend a party. each person shakes hands with at most 22 other people.
To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.
nCr (combination) to find the number of unique pairs of people.
Therefore,[tex]^nC_r = \frac{n!}{(n-r)! r!}[/tex]
where n is the total number of people and r is the number of people in a handshake at a time.
Therefore, the number of unique pairs of people that can shake hands at most once is:
[tex]^{23}C_2 = \frac{23!}{(23-2)! (2!)}[/tex] [tex]=\frac{23 X22}{2} = 253[/tex]
Hence, the maximum possible number of handshakes that can happen at the party is 253.
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when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)
Answers
The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.
What is the probability of randomly selected component?We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.
We need to find the probability that a randomly selected component is shorter than 7 inches long.
We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:
z = (7 - 8) / 1.5 = -0.67
Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:
P(z < -0.67) = 0.2514
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Six more than the quotient of a number and 8 is equal to 4
use the variable x for the unknown number
!!!TRANSLATE INTO A EQUATION!!!
Answers
Answer:
x/8 + 6 = 4
Step-by-step explanation:
x / 8 + 6 = 4
x/8 = -2
x = 8*-2 = -16.
A friend is building a garden with two side lengths 16 ft and exactly one right angle. What geometric figures could describe how the garden might look?
SELECT ALL THAT APPLY:
A. Kite.
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
(Remember it is multiple choice)
Answers
Answer:
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
Step-by-step explanation:
Answer:
The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.
which sampling approach was used in the following statement?kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in wisconsin to study their attitudes toward evidence-based practice.
Answers
The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.
What is Stratified random sampling?Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.
Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.
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At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?
Answers
Answer:
Step-by-step explanation:
Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:
999n = 727272
To solve for "n", we divide both sides by 999:
n = 727272/999
Using a calculator or long division, we get:
n ≈ 728.56
Therefore, each pizza has approximately 728 slices.
The mayor of a town sees an article that claims the national unemployment rate is
8%. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate. Let p represent the proportion of residents that are unemployed.
Which of the following is an appropriate set of hypotheses for the mayor's significance test?
Choose 1 answer:
Answers
The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].
What is Hypothesis test?Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.
Using the appropriate notation, the hypotheses can be expressed as:
$H_0: p = 0.08$
$H_a: p < 0.08$
Therefore, the appropriate set of hypotheses for the mayor's significance test are:
[tex]$$H_0: p = 0.08$$[/tex]
[tex]$$H_a: p < 0.08$$[/tex]
Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate
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could someone help out?
Answers
Answer:
27.18
Step-by-step explanation:
Firstly, you must label the triangle.
r- opposite
13.85- adjacent
We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.
tan (63) = r/13.85
Then, times 13.85 on both sides so we only have our unknown on one side.
(x13.85) tan(63)= r/13.85 (x13.85)
r= tan (63) x 13.85
r=27.18
:)
if belongs to the interval , at which values of does the curve have a tangent line parallel to the line ?
Answers
Answer:
you need to show the numbers
Step-by-step explanation:
Please help me with my math
Answers
Answer:
[tex]\textsf{$\boxed{\checkmark}\;\;y$-value\;of\;vertex\;is\;$-1$}[/tex]
[tex]\textsf{$\boxed{\checkmark}$\;\;Minimum\;value\;occurs\;at\;$y = -1$}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=x^2+8x+15[/tex]
As the given equation is quadratic with a positive leading coefficient, it is a parabola that opens upwards. Therefore, its vertex is its minimum point. This means that the minimum value of the range is the y-value of the vertex.
The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a. Therefore, the x-value of the vertex of the given equation is:
[tex]\implies x=\dfrac{-8}{2(1)}=-4[/tex]
To find the y-value of the vertex, substitute x = -4 into the equation:
[tex]\begin{aligned}\implies y&=(-4)^2+8(-4)+15\\&=16-32+15\\&=-16+15\\&=-1\end{aligned}[/tex]
Therefore, the minimum y-value of the function is y = -1, so the range is y ≥ -1.
Therefore, the following are true statement about the given equation:
y-value of vertex is -1Minimum value occurs at y = -1Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.W = {[\begin{array}{ccc}a\\b\\c\\\d\end{array}\right] : 3a+b=c, a+b+2c=2d}
Answers
An appropriate theorem to show that the given set, W, is a vector space. A specific example can be
[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s and 3p = -2s - 3r
Sets represent values that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.
The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.
The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.
The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.
Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is
S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties
u +v =y+ u and (u + v)+w=u + (v +W).
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b) The nearest-known exoplanet from earth is 4.25 light-years away.
About how many miles is this?
Give your answer in standard form.
Answers
The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
Hence, The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
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In the diagram below what is the measure in angel x
Answers
Answer:
143°
When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.
What is the image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the
origin?
Answers
The image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the origin is given as follows:
(-1, 3).
What is a dilation?A dilation is a transformation that changes the size of a figure, but not its shape. Specifically, a dilation is a type of similarity transformation that involves multiplying the coordinates of each point in a figure by a scale factor. This causes the figure to either enlarge or reduce in size.
The scale factor in the context of this problem is given as follows:
1/2.
The coordinates of the original point are given as follows:
(-2, 6).
Multiplying the coordinates of the original point by the scale factor, the coordinates of the image are given as follows:
(-1,3).
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I’m a bit stuck please help me out
Answers
On solving the question we can say that Therefore, the solutions to the inequality given inequality are: x < 4 or x > 6.
What is inequality?An inequality in mathematics is a relationship between two expressions or values that are not equal. Imbalance therefore leads to inequality. An inequality establishes a connection between two values that are not equal in mathematics. Equality is different from inequality. The inequality sign () is most commonly used when two values are not equal. Various inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be solved by changing both sides until only variables remain. But many things contribute to inequality.
two inequalities
4x - 6 < 10
4x < 16
x < 4
2x - 4 > 8
2x > 12
x > 6
Therefore, the solutions to the given inequality are:
x < 4 or x > 6.
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Which of the following subsets of M3(R) are subspaces of M3(R)? (Note: M3(R) is the vector space of all real 3 x 3 matrices)
A. The 3×3 matrices in reduced row-echelon form
B. The 3×3 matrices with all zeros in the third row
C. The diagonal 3×3 matrices
D. The invertible 3×3 matrices
E. The non-invertible 3×3 matrices
F. The symmetric 3×3 matrices
Answers
The subsets B. The 3×3 matrices with all zeros in the third row. C. The diagonal 3×3 matrices, and F. The symmetric 3×3 matrices are subspaces of M3(R).
What is a subspace?A subspace of a vector space is a portion of that space that meets the three criteria of closure under addition, closure under scalar multiplication, and the presence of the zero vector. If two vectors from the subspace are added, the resultant vector will still be in the subspace because of closure under addition. If a vector from the subspace is multiplied by any scalar, the resultant vector will still be in the subspace, according to the concept of closure under scalar multiplication.
The conditions of a subspace are: closure under addition, closure under scalar multiplication, and contains the zero vector.
For all the options we have:
A: The 3 x 3 matrices in reduced row-echelon form (A): As this subset is not closed under addition, M3(R), it is not a subspace of M3(R).
B. The 3 x 3 matrices with all zeros in the third row: Due to its closure under addition and scalar multiplication as well as the presence of the zero vector, this subset is a subspace of M3(R).
C. The diagonal 3 x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).
D. The invertible 33 matrices: Because this subset is not closed under addition, M3(R), it is not a subspace of M3(R).
E. The 3 x 3 matrices that are not invertible Due to the fact that it is not closed under scalar multiplication, this subset is not a subspace of M3(R).
F. The symmetric 3x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).
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Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour
(mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 + 0.541 In(Speed), what is the predicted fuel
efficiency for a speed of 30 mph?
17.67 mpg
26.50 mpg
30.00 mpg
37.74 mpg
Answers
The predicted fuel efficiency for a speed of 30 miles per hour is given as follows:
26.50 mpg.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is defined as follows:
In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).
The speed is of 30 miles per hour, hence the predicted fuel efficiency is given as follows:
In(Fuel Efficiency) = 1.437 + 0.541 x In(30).
In(Fuel Efficiency) = 3.277.
The exponential is the inverse of the ln, hence:
Fuel Efficiency = e^3.277
Fuel Efficiency = 26.50 mpg.
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Graph the system of equations {y=−12x+4y=−12x−2
Answers
Answer:
Step-by-step explanation: i hope this help if not let me know so i can fix it
Scientists determined that the cause of death in many prawns off the coast of Chile was a nutrient deficiency. So, they set out to determine if the distribution of plants in the ocean near the coast was out of proportion when compared to the ideal environment: 40% Kelp, 25% Phytoplankton, 25% Coral and 10% Other (mostly nutrient-low seaweed). In randomly chosen areas along the coast, they sampled 240 plants.
KELP PHYTOPLANKTON CORAL OTHER
84 67 57 32
In an ideal environment how many of the 240 plants would you expect to be Kelp?
If a goodness of fit test is conducted, what is the null Hypothesis?
If a goodness of fit test is conducted, what is the alternative Hypothesis?
What is the probability of getting the observed values or values as extreme from the ideal?
Is there enough evidence to conclude that the environment for prawns is not ideal? Base this conclusion on p-value and a level of significance of 0.05 or 5%.
Answers
Answer:
Step-by-step explanation:
#Brainlist! Help! Will! Make! You! Brainlist!
Show all steps and how you got the answer
Answers
Answer:
x = 8500
y = 15000
Step-by-step explanation:
small vans: x
large vans: y
A: 5x + 2y = 72500
B: 2x + 6y = 107000
5x + 2y = 72500 => y = (72500 - 5x)/2
2x + 6(72500 - 5x)/2 = 107000
2x + 217500 - 15x = 107000
15x - 2x = 217500 - 107000
13x = 110500
x = 110500/13 = 8500
y = (72500 - 5x)/2 = y = (72500 - 5x8500)/2 = 15000
The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−[infinity], [infinity]); y'' − y = 0, y(0) = 0, y'(0) = 5
Answers
The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).
Now, we are required to find a member of the family that is a solution to the initial-value problem which is
y(0) = 0 and y′(0) = 5.
The differential equation is y'' − y = 0
The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1
The general solution of the differential equation is y = c1ex + c2e−x
Let us solve for the constants by using the given initial conditions:
At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0
means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2
Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2
The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.
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Which of the following are key ingredients of a confidence interval based on the Central Limit Theorem?
(1) A summary statistic (e.g. a mean) from your sample
(2) A multiple z, based on a tail area from the normal distribution.
(3) A formula for the standard error of your summary statistic.
a. All of the above (1, 2, and 3)
b. (1) and (2)
c. (1) and (3)
d. (2) and (3)
Answers
Option a. (All of the above (1, 2, and 3)) is the right answer to the question regarding the key ingredients of a confidence interval based on the Central Limit Theorem.
A confidence interval is a statistical estimate of a population parameter with a level of confidence or certainty.
The Central Limit Theorem states that the distribution of the means of a sufficiently large sample size from a population with a finite variance will be approximately normal, regardless of the population's actual distribution.
A confidence interval based on the Central Limit Theorem, there are three key ingredients:
1. A summary statistic (e.g. a mean) from your sample
2. A multiple z, based on a tail area from the normal distribution.
3. A formula for the standard error of your summary statistic.
For a given level of confidence, the z-score corresponds to the number of standard deviations from the mean. The standard error of a summary statistic is a measure of the variability of the estimate that is dependent on the size of the sample, the variability of the population, and the type of summary statistic. The standard error of a sample mean is given by the formula σ/√n, where σ is the population standard deviation and n is the sample size.
Thus, all the above points (1, 2, and 3) are the key ingredients of a confidence interval based on the Central Limit Theorem.
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out of total student 3/5 are girls .On a particular day one third boys and 2/5 girls were absent. If total absentees was 280 find total number of students
Answers
Answer:
Step-by-step explanation:
Calculate fraction of boys
If girls =3/5, then boys = 1 - 3/5 = 2/5.
Calculate fraction of students absent
Girls - 2/5 of 3/5 = 6/25
Boys - 1/3 of 2/5 = 2/15
6/25+2/15=28/75
Calculate total number of students
If 28/75 = 280
280/28=10
10x75=750
Total number of students = 750
The spinner above is used in a game. What is the theoretical probability of the given event with one spin?
P (5)
Answers
Answer:
B
Step-by-step explanation
so there is 8 numbers so when you spin you have a 1/8 chance of spinning the numberMaria purchased 1,000 shares of stock for $35. 50 per share in 2014. She sold them in 2016 for $55. 10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent
Answers
Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.
To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.
The purchase price for 1,000 shares of stock was:
$35.50 x 1,000 = $35,500
The selling price for 1,000 shares of stock was:
$55.10 x 1,000 = $55,100
The capital gain is the difference between the selling price and the purchase price:
$55,100 - $35,500 = $19,600
To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:
($19,600 / $35,500) x 100 = 55.21%
In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.
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What is the value of (sine 30 + cos 30 ) - (sin 60 + cos 60 )
Answers
The value of ( sin 30° + cos 30° ) - ( sin 60° + cos 60° ) is 0.
(sine 30 + cos 30 ) - (sin 60 + cos 60 )
= ([tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{3} }{2}[/tex]) - ([tex]\frac{\sqrt{3} }{2}[/tex] + [tex]\frac{1}{2}[/tex])
= [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{1}{2}[/tex]
= [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex]
= 0
Trigonometry is a branch of mathematics that focuses on the relationships between angles and the sides of triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, and their various properties and applications. These functions relate the angles of a right triangle to the lengths of its sides, and they can be used to solve a wide range of problems in fields such as engineering, physics, astronomy, and navigation.
Trigonometry also includes the study of trigonometric identities, which are mathematical expressions that are true for all values of the variables involved. These identities can be used to simplify complex trigonometric expressions and to prove other mathematical theorems.
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find the long leg: b =
Answers
Answer:
b ≈ 12.1
Step-by-step explanation:
using the tangent ratio in the right triangle
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )
7 × tan60° = b , then
b ≈ 12.1 ( to the nearest tenth )
Make up a sequences that have (a) 3,3,3,3,... as its second differences. (b) 1, 2,3,4,5,... as its third differences (c) 1, 2, 4,8,16,... as its 100th differences.
Answers
The nth term of the sequence is 2^n.
(a) 3, 3, 3, 3, ... is a sequence that has 0 for both its first and second differences. That is, every term in the sequence is the same.(b) The sequence is the series of natural numbers. It has 0 for its first and second differences, and 6 for its third differences. The nth term of the sequence is n.(c) The sequence has 0 for its first 99 differences and 100! for its 100th difference. The nth term of the sequence is 2^n.
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