For the given function f(t) = (2t + 1) using definition of Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
As given in the question,
Given function is equal to :
f(t) = 2t + 1
Simplify the given function using definition of Laplace transform we have,
L(f(t))s = [tex]\int\limits^\infty_0 {f(t)e^{-st} } \, dt[/tex]
= [tex]\int\limits^\infty_0[2t +1] e^{-st} dt[/tex]
= [tex]2\int\limits^\infty_0 te^{-st} + \int\limits^\infty_0e^{-st} dt[/tex]
= 2 L(t) + L(1)
L(1) = [tex]\int\limits^\infty_0e^{-st} dt[/tex]
= (-1/s) ( 0 -1 )
= 1/s , ( s > 0)
2L ( t ) = [tex]2\int\limits^\infty_0 te^{-st}[/tex]
= [tex]2[t\int\limits^\infty_0 e^{-st} - \int\limits^\infty_0 ({(d/dt)(t) \int\limits^\infty_0e^{-st} \, dt )dt][/tex]
= 2/ s²
Now ,
L(f(t))s = 2 L(t) + L(1)
= 2/ s² + 1/s
Therefore, the solution of the given function using Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
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Which statement describes 0.34? Select all that apply.
A It is a repeating decimal.
B It is a non-terminating decimal.
C It is a non-repeating decimal.
D It is a terminating decimal.
E It is a rational number.
F It is not a rational number.
The correct statements are A, B and E
SOLUTION:
Given, number is
We have to choose the statements that correctly describes the above number.
Now, we know that, a bar on a number represents it is repeating decimal. So let us check options now.
A. It is a repeating decimal.
As the number has it is repeating decimal. So this option is correct.
B. It is a non-terminating decimal.
As the number is repeating, it will not terminate, so this option is correct.
C. It is a non-repeating decimal.
No, it is repeating. So this is wrong statement.
D. It is a terminating decimal.
It is non – terminating, so this is wrong.
E. It is a rational number.
As it is repeating, we can represent it in fraction, so this is correct.
F. It is not a rational number.
It is rational number so, this is wrong option.
Answer:
The answers are
A.
B.
E.
What is the value of log 1 by 3?.
-0.477 is the value of log 1 by 3 .
A logarithm is defined simply?
The logarithm represents the power to which a number must be raised to obtain another number (see Section 3 of this Math Review for more about exponents).
For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.
log (1/3)
= log1 - log3
= 0 - 0.477
= -0.477
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the total probability rule is used when an analyst is interested in: a. all potential outcomes. b. a set of events. c. a single outcome.
The total probability rule is used when an an analyst is interested in a)all potential outcomes. So, correct option is a.
Probability is the branch of the mathematics concerning numerical descriptions of how likely an event is going to occur, or how likely it is that a proposition is true. The probability of an event is the number between 0 and 1, where, roughly speaking, 0 indicates that impossibility of the event and 1 indicates certainty. If probability of an event is higher then, the more likely it is that the event will occur.
Probability can be defined as the proportion of the number of favorable outcomes to the total number of outcomes of an event..
Hence, option a is correct.
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What is the constant variation of Y 8 when X 16?.
The constant variation of Y 8 when X 16 is 2.
What is Direct Proportion?
"When the relationship between two quantities is such that if we increase one, the other will also rise, and if we decrease one, the other quantity will also drop, then the two quantities are in a direct proportion," according to the definition of direct proportion. For instance, suppose there are two numbers, x and y, where x is the number of candies and y is the total amount of money spent. If we purchase more candy, we will be required to pay more, and if we purchase fewer candies, we will be required to pay less. This means that x and y are directly proportional to one another in this situation. The symbol for it is x y. Direct variation is another name for direct proportion.
So,
In the given question, we have:
y as 8 and x as 16;
So,
In order to find the proportional value, we have to divide the x quantity by the y quantity.
So, after dividing we get:
[tex]\frac{X}{Y} = \frac{16}{8}[/tex]
[tex]\frac{X}{Y} = 2[/tex]
So,
The constant proportion will be 2.
Hence,
The constant proportion will be 2.
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Which is true of the measures of the sides of the original square? each side of the original square is one-fourth the length of each side of the scale model. Each side of the original square is 4 times the length of each side of the scale model. Each side of the original square is the same length as each side of the scale model. Each side of the original square is 4 feet less than the scale model.
For the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.
It is known to us that -
The value of the scale factor = 4
We also know that -
Each side of the scale model = Scale factor * Side of the original square
=> Each side of the scale model = 4 * Side of the original square
=> Side of the original square = (1/4) * Each side of the scale model
Thus, for the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.
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please answer asap (20 points)
only write down what I gotta put in the box and explanation
The value b is 8 if m=1 and the line is passing through the point P(-4,4).
What is a slope-intercept form?The line's equation is expressed in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept. The slope of the line is 3 in our equation, y = 3 x + 5.
Consider the slope-intercept form equation y = 6 x + 9 y=6x+9 y=6x+9. We can find the x and y intercepts. The x-intercept occurs when y = 0, whereas the y-intercept happens when x equals 0. By setting the value of y to zero, we may find the x-intercept.
When an equation is not in the y = mx + b form, we can solve for the intercepts by substituting 0 and solving for the remaining variable.
Let, the slope-intercept form is,
y= mx +b
Given, m=1
And the line passes through the point P(-4,4)
Then,
4=1(-4)+b
b=4+4=8
b=8
Therefore, the value of b is 8
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50 POINTS!! Triangle ABC with vertices A(4, −6), B(2, −8), and C(−10, 4) is dilated by a scale factor of 2 to obtain triangle A′B′C′. Which statement best describes triangle A′B′C′?
A) It is similar to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
B) It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).
C) It is congruent to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
D) It is congruent to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20,
Answer:
B) It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).
Step-by-step explanation:
If the vertices of a triangle ABC are dilated by a scale factor of 2, the coordinates of the vertices of triangle A'B'C' can be found by multiplying each coordinate of ABC by the scale factor.
Therefore, the coordinates of the vertices of triangle A'B'C' are:
A' = (4 × 2, -6 × 2) = (8, -12)B' = (2 × 2, -8 × 2) = (4, -16)C' = (-10 × 2, 4 × 2) = (-20, 8)As the triangle has been dilated, its size has changed but its shape has not. Therefore, the triangles are similar.
What is the meaning of phenotype ratio?.
The alleles, or genes for a trait, are known as the genotype. A phenotypic ratio represents a relationship between the different physical characteristics and how often they occur. Ratios are typically done in relationship to a single trait among the individuals.
Phenotypic ratio pertains to the relative number of offspring manifesting a particular trait or combination of traits. It can be determined by doing a test cross and identifying the frequency of a trait or trait combinations that will be expressed based on the genotypes of the offspring.
For example: when a tall plant is crossed to a short plant, some of their offspring will be tall while others will be short. To determine the phenotypic ratio, the number of times the phenotypes (either tall or short) are expressed is counted. In this case, the phenotypic ratio shall indicate how many of the offspring will be tall and how many will be short based on the genotype.
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Select the correct answer. Victor solved this inequality as shown: Step 1: 3x − 5 > x + 5 Step 2: 2x − 5 > 5 Step 3: 2x > 10 Step 4: x > 5 What property justifies the work between step 3 and step 4? A. division property of inequality B. inverse property of multiplication C. subtraction property of inequality D. transitive property of inequality
The property that justifies the work between step 3 and step 4 is division of property of inequality (option A)
What is the division property of inequality?The division property of inequality states that if you divide one side of an inequality by a number, you can divide the other side of the inequality by the same number.
It can also be stated as if we divide both sides of an inequality by the same number, the inequality remains the same.
At step 3: 2x>10
2 is used to divide both sides
2x/2>10/2
x>5(step 4)
Therefore the property between step 3 and step 4 is division property of inequality.
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Trapezoid ABCD is congruent to trapezoid A′′B′′C′′D′′ . Which sequence of transformations could have been used to transform trapezoid ABCD to produce trapezoid A′′B′′C′′D′′ ? Responses Trapezoid ABCD was reflected across the y-axis and then across the x-axis. , , trapezoid A B C D, , , , was reflected across the y -axis and then across the x -axis. Trapezoid ABCD was reflected across the y-axis and then translated 7 units up. , , trapezoid A B C D, , , , was reflected across the y -axis and then translated 7 units up. Trapezoid ABCD was reflected across the x-axis and then across the y-axis. , , trapezoid A B C D, , , , was reflected across the x -axis and then across the y -axis. Trapezoid ABCD was translated 7 units up and then 12 units left. , , trapezoid A B C D, , , , was translated 7 units up and then 12 units left.
The sequence of transformations used to transform ABCD to A"B"C"D" is; Trapezoid ABCD was reflected across the y-axis and then translated 7 units up.
How to find the sequence of transformation?From the figure we have the pre image before transformation as Quadrilateral ABCD which is located at the bottom right of the graph.
Trapezoid ABCD and A"B"C"D" are equidistant from the x-axis
Trapezoid ABCD and A"B"C"D" are equidistant from the y-axis
Now, it is clear that Quadrilateral ABCD was first reflected across the y-axis.
Thereafter, when we look at the coordinates of the final transformed quadrilateral, it is clear that the second step of transformation was to translate the image by 7 units upwards.
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expert that helps you learn core concepts.
See Answer
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 23, 25, 16, 20, 13, 10, 28, 19. Use Table 2.
a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places. Round "Sample mean" to 3 decimal places and "Sample standard deviation" to 2 decimal places.)
Sample mean.
Sample standard deviation
b. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)
Confidence interval to
c. Construct the 99% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)
Confidence interval to
The sample mean of the observations is 19.25 and the standard deviation is 2.15
Sample mean is found by adding up all the individual values of the sample, then dividing by the total number of values in the sample.
Sample standard deviation is the square root of the variance
mean = (23 + 25 + 16 + 20 + 13 + 10 + 28 + 19)/8
mean = 19.25
variance = (x₁ - mean)²/n(n-1)
variance = ((23 - 19.25)² + (25 - 19.25)² + (16 - 19.25)² + (20 - 19.25)² + (13 - 19.25)² + (10 - 19.25)² + (28 - 19.25)² + (19 - 19.25)²)/(8(7))
variance = 259.5/56
variance = 4.63
Standard deviation = √variance = √4.63 = 2.15
Therefore, the sample mean of the observations is 19.25 and the standard deviation is 2.15
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
From a principal amount of $13000, the amount compounded at a rate of 3% quarterly over a time period of 5 years is $15,095.39
Compound InterestThe compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation. The compound interest formula is given below:
A = P(1 + r/n)^nt
Compound InterestP = principalr = rate n = number of times compoundedt = timePutting the values in the formula above
A = 13000(1 + 0.03/4)^4 * 5
A = 13000(1.0075)^20
A = $15,095.39
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please help
It's really important
How to answer: You divide the first number by the second number
a) 85.50/7=12.21
b) 76.00/6=12.67 or 12.6 repeating
c) 120/10= 12
d) 30/0.5= 60
e) 6/2.40= 2.5
f) 399/3= 133
g) 3/2.25= 1.33 or 1.3 repeating
h) 400/5= 80
i) 43.80/5.5=7.7182 or 7.718 (the 18 repeating)
I hope this helped
You are a researcher working with the General Social Survey (GSS) on a project focusing on income and health service utilization among men. The first part of your project involves collecting random samples from men. You collect a random sample of men (N = 1500) and determine that the average income for this group is $31,607. Based on research, you know that the average income for males in the population is $33,405 with a standard deviation of $8,432. Before you do any additional analyses, you need to determine whether the mean earnings of men in the General Social Survey is representative of the earnings of the entire U.S. male population. In essence, You want to understand your sample’s value is really different from the population’s. Please reflect on how you would engage in statistical hypothesis testing and then provide the responses to the following items. This is a two-tailed test. Please consider alpha = .05. Fill in the blank:
Compute the standard error of the mean(two decimal places) =
The Standard Error of mean is 217.71 .
The critical value , Z꜀= 1.96 < Z , it is then concluded that the null hypothesis is rejected.
Hence, we can say that the the mean earnings of men in the General Social Survey is not representative of the earnings of the entire U.S. male population.
We have given that
A researcher working with the General Social Survey (GSS) on a project focusing on income and health.
Sample size, N = 1500
Sample mean , X-bar =$31,607
male population mean , μ = $33,405
Standard deviations, σ = $8,432
Std. error of mean , S.E = σ /√N
= 8432/√1500
= 217.71
Consider null and alternative hypothesis as
H₀ : μ = 33405
Hₐ : μ not equal to 33,405
Rejection region: Based on information provided the significance level,alpha = 0.05 and the critical value for two tailed test , Z꜀ = 1.96.
The rejection region for two tailed test R is
{ z : |z|> 1.96}.
Test Statistic:
Z- statistic test formula,
Z = (X-bar - u)/std. error
=> Z = ( 31,607 - 33,405)/217.71
=> Z = - 8.259
Decision: Since, it is observed that |z| = 8.259 > Z꜀ = 1.96 , it is concluded that Null hypothesis is rejected .
Conclusion: It is concluded that Null hypothesis H₀ is rejected. So there is sufficient evidence to support the claim that the population mean ,u is different from 33,405 at α = 0.05 significance level.
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.
what are the coordinates of the point on the directed line segment from (-8, 5) to (-1, -2) that partitions the segment into a ratio of 5 to 2?
The coordinates of the point on the directed line segment from (-8, 5) to (-1, -2) that partitions the segment into a ratio of 5 to 2. Then the coordinates are (-3, 0).
How to determine the coordinatesComparison in Vector
If P divides AB by the ratio AP : PB = m : n, the position vector of the point P : [tex]\boxed{\vec {p} =\frac{m\vec b + n\vec a}{m + n}}[/tex]
Suppose
The position vector of the point A (-8, 5) = a
The position vector of the point B (-1, -2) = b
Look at the picture in the attachment
Point P that partitions the segment into a ratio of 5 to 2 so that AP : PB = 5 : 2. Since m = 5 and n = 2, then:
[tex]$\begin{align} \ \vec {p} & =\frac{5\vec b + 2\vec a}{5 + 2} \\ \vec {p}& = \frac{1}{7} (5\vec b + 2\vec a) \\ \vec {p}& = \frac{1}{7} \left (5\begin{array}{c} \left[\begin{array}{cc}-1\\-2\end{array}\right] +2 \left[\begin{array}{cc}-8\\5\end{array}\right] \end{array}\right) \\ \vec {p}& = \frac{1}{7} \left (\begin{array}{c} \left[\begin{array}{cc}-5\\-10\end{array}\right] + \left[\begin{array}{cc}-16\\10\end{array}\right] \end{array}\right) \end{align}[/tex]
[tex]$\begin{align} \ \vec {p} & = \frac{1}{7} \left (\begin{array}{c} -21\\0 \end{array}\right) \\ \vec {p} & = \left (\begin{array}{c} -3\\0 \end{array}\right) \end{align}[/tex]
The coordinates that partitions the segment into a ratio of 5 to 2 is (-3, 0).
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jessica does not notice when her father leaves the day care center and ignores him when he returns. jessica's behavior is characteristic of_______ attachment.
Jessica does not notice when her father leaves the day care center and ignores him when he returns. jessica's behavior is characteristic of Insecure-avoidant attachment.
Avoidant attachment:
Parents of children with avoidant attachments most often tend to be emotionally unavailable or unresponsive. These parents also discourage crying and encourage premature independence in their children, or learns early in life to suppress the natural urge to seek comfort from a parent when distressed.
Many people who avoid children have already become independent, precocious "little adults" as young children. As mentioned above, the primary defensive attachment strategy of children with avoidant attachment is to never outwardly demonstrate a desire for intimacy, warmth, affection, or love.
Insecure-Avoidant (aka Type A) is an attachment pattern identified by Ainsworth from an odd situation. This attachment type is ready for research but does not seek intimacy with their caregiver. They have low levels of fear of separation and fear of strangers and do not contact their mothers when reunited. Her 21% of children show this attachment pattern.
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Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of. 5. How many subscribers must they sample to obtain this interval?.
The number of subscribers they must sample to obtain this interval is: b) 385.
How to find the sample?
95% confidence interval for z-score is 1.96
Using this formula to find the number of subscribers they must sample to obtain this interval
n≥ (zσ/2 ÷ 2ME)²
Where:
n= Sample
zσ = Z-score
ME = margin of error
Let plug in the formula
n≥ [1.96 / 2(0.05)]²
n≥ [1.96 / 0.1]²
= (19.6)²
= 384.16
=385 (Rounded)
Therefore the correct option is B.
The complete question is:
Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of .05. How many subscribers must they sample to obtain this interval?
a) 1537
b) 385
c) 192
d) 10
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Find the arc length of the partial circle.
The arc length of the partial circle is 12,56 units.
How to find the length of an arc?The arc of a circle is defined as the part or segment of the circumference of a circle.
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleHence,
∅ = 90 degrees
r = 8 units
length of an arc = 90 / 360 × 2 × 3.14 × 8
length of an arc = 4521.6 / 360
length of an arc = 12.56 units.
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here are 100 balls in a hat. 10 of them are RED, and 90 are BLACK. 3 balls are drawn at random with replacement. The following is the discrete probability distribution where R is the number of red balls drawn from the hat described above. P(R) 0.729 0.243 0.027 .001 What is the standard deviation for this probability distribution? (Be sure to use many (floating) decimals in your calculations, but round your answer to 3 decimal places.)
The standard deviation for that probability distribution is 0.520.
How to calculate standard deviation?R = amount red ball drawn from the hat
P(R) = probability red ball drawn from the hat
σ = standard deviation
Standard deviation for probability distribution can be calculated by this formula,
σ = [tex]\sqrt{\sum R^2P(R)-(\sum RP(R))^2}[/tex]
First, we calculate [tex]\sum R^2P(R)[/tex]
[tex]\sum R^2P(R)[/tex] = [tex]0^2[/tex] × 0.729 + [tex]1^2[/tex] × 0.243 + [tex]2^2[/tex] × 0.027 + [tex]3^2[/tex] × 0.001
= 0 × 0.729 + 1 × 0.243 + 4 × 0.027 + 9 × 0.001
= 0 + 0.243 + 0.108 + 0.009
= 0.36
Next, we calculate [tex]\sum RP(R)[/tex]
[tex]\sum RP(R)[/tex] = 0 × 0.729 + 1 × 0.243 + 2 × 0.027 + 3 × 0.001
= 0 + 0.243 + 0.054 + 0.003
= 0.3
Now, we can calculate standard deviation,
σ = [tex]\sqrt{\sum R^2P(R)-(\sum RP(R))^2}[/tex]
= [tex]\sqrt{0.36-(0.3)^2}[/tex]
= [tex]\sqrt{0.27}[/tex]
= 0.51961524227
round to 3 decimal places
= 0.520
Thus, this probability distribution of red balls drawn from the hat has a standard deviation of 0.520.
Your question is incomplete, but most probably your full question was (image attached)
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Write 52/11 decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
4.727273
Step-by-step explanation:
How do you know if a graph will cross or bounce?.
We know that the graph of a polynomial function will intersect the x-axis at its root values, and we know that if the multiplicity of that root is even, the graph will "bounce off"
If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero.
If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity.
If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity.
The sum of the multiplicities is n.
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Simplify 6(3x−5)5(2x−1). Write your anwer in factored form. Explain how you found your anwer. Input Field 1 of 1
Skip to input field
The given expression can be expressed in the form of factored form as (12x - 20)(12x - 6).
What is a quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in standard form as ax²+bx+c=0, where x is an unknown value and a, b, and c are known numbers.
It has two solutions.
The given equation is 6(3x−5)5(2x−1).
Then it can be expressed as
= 6(3x − 5)(10x − 5)
= (18x − 30)(10x − 5)
= (180x² − 90x - 300x + 150)
= 180x² − 390x + 150
Simplifying we get
= 60x² - 130x + 50
= (12x - 20)(12x - 6)
Hence, the given expression can be expressed in the form of factored form as (12x - 20)(12x - 6).
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Complete the square for the expression. Also, identify the resulting expression as a binomial squared. X2 + 15x + ____.
The completed square of the expression is x² + 15x + 225/4 and the expression as binomial squared is (x + 15/2)² .
In the question ,
it is given that ,
the expression s given as x² + 15x + 225/4 ,
we have to complete the expression,
Dividing 15 by 2 , = 15/2
writing 15/2 as a power of 2 , (15/2)² = 225/4
the completed equation is X2 + 15x + 225/4 .
and the binomial squared of the expression is (x + 15/2)²
Therefore , the expression is x² + 15x + 225/4 and binomial squared is (x + 15/2)² .
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How do you compare a poem?.
Answer:Step 1: Summarise the main idea of each poem in 1-2 sentences. ...
Step 2: Find similarities – thematic, stylistic, structural and formal. ...
Step 3: Find differences from similarities. ...
Step 4: Identify 3 key ideas for comparison.
Step-by-step explanation:
How do you compare two poem structures?
These are some points to think about:
use the introduction to explain which poems you are writing about.
try to balance out the detail you include for each poem.
compare the poems throughout the essay.
comment on content, themes, ideas and attitudes as well as form, structure and language.
How do you compare poems in a level essay?
try to balance out the detail you include for each poem. compare the poems throughout the essay. comment on content, themes, ideas and attitudes as well as form, structure and language. sum up your thoughts on ways in which the poems are similar and different in your conclusion.
in a call center the number of received calls in a day can be modeled by a poisson random variable. we know that on average about 0.5% of the time the call center receives no calls at all. what
The average number of calls per day that can be modeled by a Poisson random variable is denoted by λ is equal to 5.29832.
A Poisson distribution in statistics is a probability distribution that is used to demonstrate how frequently an event is likely to happen over a given period of time.
Let C denotes the number of calls per day.
Given:
On average about 0.5% of the time the call center receives no calls at all.
So, P(C = 0) = 0.5% = 0.005
The formula for Poisson distribution is:
=> e^-λ . λ^x / x!
where x = 0,1,2,3, ....
λ = mean number of occurrences in the interval
e = Euler's constant ≈ 2.71828
=> -λ = ln (0.005)
=> λ = 5.29832
Thus, the average number of calls per day is equal to λ = 5.29832.
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How do you prove that an equilateral triangle is similar?.
For equilateral triangles, each side is equal. Hence the ratio between two sides of different triangles will be constant. Hence, all equilateral triangles are similar.
What is the equilateral triangle?
An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal.
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Which of the following is true regarding the normal distribution?
a) It has two modes.
b) It is asymmetrical.
c) The mean, median, and mode are all equal.
d) The points of the curve meet the x-axis at z = -3 and z = 3.The correct option is c) The mean, median, and mode are all equal.
A normal distribution is a mathematical expression that defines the probability distribution of data. It is a unimodal concept, and it is symmetrical from both ends. Normal distribution emphasizes the equal mean, median, and mode of given data.
The correct option is C when the equal mean, median, and mode of the given data are highlighted by the normal distribution.
Given that,
We have to find the correct option for which of the following statements about the normal distribution is accurate.
The options are
a) It has two modes.
b) It is asymmetrical.
c) There is equality in the mean, median, and mode.
d) At z = -3 and z = 3, the curve's points intersect the x-axis.
We know that,
What is normal distribution?The most significant continuous probability distribution in probability theory and statistics is the normal distribution, also referred to as the gaussian distribution. On occasion, it is referred to as a bell curve.
The probability distribution of data is expressed mathematically as a normal distribution. It is symmetrical from both ends and has only one mode. The equal mean, median, and mode of the given data are highlighted by the normal distribution.
Therefore, The correct option is C when the equal mean, median, and mode of the given data are highlighted by the normal distribution.
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Given regular pentagon $ABCDE$, a circle can be drawn that is tangent to $\overline{DC}$ at $D$ and to $\overline{AB}$ at $A$. The number of degrees in minor arc $AD$ is
Define major arc DA as $DA$, and minor arc DA as $da$. Extending DC and AB to meet at F, we see that $\angle CFB=36=\frac{DA-da}{2}$. We now have two equations: $DA-da=72$, and $DA+da=360$. Solving, $DA=216$ and $da=144\Rightarrow \mathrm{(E)}$.
Let $O$ be the center of the circle. Since the sum of the interior angles in any $n$-gon is $(n-2)180^\circ$, the sum of the angles in $ABCDO$ is $540^\circ$.
Since $\angle ABC=\angle BCD=108^\circ$ and $\angle OAB=\angle ODC= 90^{\circ}$, it follows that the measure of $\angle AOD$, and thus the measure of minor arc $AD$, equals $540^\circ - 108^\circ-108^\circ-90^\circ-90^\circ=\boxed{\mathrm{(E)}144^\circ}$.
Number of degrees of minor arc is 108 degrees.
It is given that a regular pentagon ABCDE, a circle is drawn that is tangent to DC at D and to AB at A.
We need to find the number of degrees in the minor arc AD ie angle AED
A regular pentagon has all sides equal and all angles are equal.
The sum of all the angles of a pentagon is 540 degree
Each angle od a pentagon is 540/5 = 108 degree
Therefore, Number of degrees of minor arc is 108 degrees. or angle AED is 108 degrees.
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a coin is flipped eight times where each flip comes up either heads or tails. how many possible outcomes: 1). are there in total? 2). contain exactly three heads? 3). contain at least three heads? 4). contain the same number of heads and tails?
There are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.
Consider the provided information.
A coin is flipped eight times where each flip comes up either heads or tails.
Part (a) How many possible outcomes are there in total?
Each time we flip a coin it comes up either heads or tail.
Therefore the total number of ways are: 2⁸ = 256
Hence, there are 256 ways in total.
Part (b) contain exactly three heads?
We want exactly 3 heads, therefore,
n=8 and r=3
According to the definition of combination:
To get exactly 3 heads,
n=8 and r=3
(⁸C₃ ) = 8! / 3!(5!) = 56.
Therefore, there are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.
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An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, _____ the quantity demanded of the asset.
A) increases
B) decreases
C) has no effect on
D) erases
An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, (option a) increases the quantity demanded of the asset.
Given,
Asset's expected return;-
The weight of each asset is multiplied by its projected return to determine the expected return. The total predicted return for your portfolio may then be calculated by adding the figures for each investment. Hence, the equation Asset 1 Weight x Expected Return = Expected Portfolio Return Plus (Asset 2 Weight x Expected Return)
Hence,
An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, (option a) increases the quantity demanded of the asset.
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