For instance, we might simply show the following conditional statement:
1. Return true if the array's size is zero or one.
2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.
In the given question, we have to state true or false for the given statement.
In our programs, we frequently want to be able to "conditionally" execute certain actions, i.e., "if this is true, then do X, but if this other thing is true, then do Y." It's similar to how we dress when we get out of bed: "If it's sunny, I wear sunglasses, but if it's raining, I take an umbrella." In our programs, we can use if statements, if/else statements, and conditional expressions to do things conditionally.
If a condition is true, an if statement instructs the computer to run a certain piece of code. Only if x is bigger than 0 do we output a message in the following code:
We would be able to see the message on the canvas since x is 5, which is bigger than 0. If we modified x to -1, the message wouldn't appear at all because x wouldn't be greater than 0.
A conditional expression is one that can only be evaluated as either true or false, and the x > 0 qualifies as one. A boolean value is one that can only be either true or false (as opposed to a number or a string). For instance, we might simply show the following conditional statement:
1. Return true if the array's size is zero or one.
2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.
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The right question is:
State in predicate calculus that an array of int, say a, is sorted. You may use the Java expression syntax (e.g., a.length, a[i], ==, and <) and logical operators (&&).
Simplify the expression.
fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 as the denominator
ten fourths
negative ten fourths
8
−8
The simplified form of the given expression as required in the task content is; 8.
What is the simplified form of the expression as described?It follows from the task content that the simplified form of the given expression; -4 ( 2 - (³√8 × 6) ) / 5 is to be determined.
Therefore, By solving the innermost parentheses; we have;
-4 ( 2 - (2 × 6) ) / 5
= -4 ( 2 - 12 ) / 5
= -4 ( -10 ) / 5
= 40 / 5
= 8.
Therefore, the simplified form of the expression is; 8.
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If 60% of the population supports massive federal budget cuts, what is the probability in that a survey of 250 people ,at most 155 people support such cuts
Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
If 60% of the population supports massive federal budget cuts.
We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.
So, the probability is, 155 / 250 = 0.62
Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.
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What are 2 examples of geometric sequence?
Two examples of geometric sequence are {2, 6, 18, 54, 162, 486, 1458, ...} and {1, 2, 4, 8, 16, 32, 64, 128, 256, …}.
In mathematics, a geometric sequence or geometric progression refers to a sequence of non-zero numbers where the ratio between consecutive terms is constant. In such a sequence, each term (after the initial term) is determined by multiplying the previous one by a fixed, non-zero number called the common ratio. An example of geometric sequence is {2, 6, 18, 54, 162, 486, 1458, ..} where each term is 3 times the previous term i.e., the common ratio is 3. Another example is {1, 2, 4, 8, 16, 32, 64, 128, 256, .. } where each term is 2 times the previous term i.e., the common ratio is 2.
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Can someone pls help me on question 8) plss thank you!! I will give a brainstar Question 8!!
Answer:
$226
Step-by-step explanation:
1. define the variable x
x = # of days to rent the carpet cleaner
2. substitute x for 7 days
c(7) = 30(7) + 16
3. solve
c(7) = 210 + 16
c(7) = 226
For 7 days, Rhonda will have to rent the carpet cleaner for $226.
Which overlapping triangles are congruent by AAS?
A. ΔADC = ΔEBC
B. ΔABE = ΔCDA
C. ΔΑΒΕ = ΔDEA
D. ΔΑDC = ΔEDA
By Angle-Angle-Side (AAS) triangle congruence theorem we know that two triangles are congruent if they have two sets of congruent angles and a set of non-included congruent sides.
Since no figure is given in the question we employ the reflexive characteristic to demonstrate that the overlapping sections are congruent in order to demonstrate that overlapping triangles are congruent.
If two triangles are precisely the same size and shape—that is, if they have the same side lengths and angle measurements—they are said to be congruent. If we are aware that two triangles have all the same sides and angles, we can conclude that the triangles are congruent.
To demonstrate that two triangles are congruent, however, we don't necessarily need to know that all of their sides and angles are congruent.
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If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic? The two samples both have n 15, with sample variances of 20 and 25. The two samples both have n 15, with variances of 120 and 125. The two samples both have n 30, with sample variances of 20 and 25. The two samples both have n 30. with variances of 120 and 125 Save Question 15 (1 point) For the repeated measures t statistic. df n1 + n2 2 n1 -1)+ (n2 1) Save Question 16 (1 point
If other factors are held constant, sets of data that would produce the largest value for an independent-measures t statistic is the two samples both have n =30, with sample variances of 20 and 25
In a T test, the T statistic is used to help you decide whether to accept or reject the null hypothesis.
You utilize it in a manner that is quite similar to using a Z-score. When you don't know the population standard deviation or have a limited sample size, you use the t statistic.
You employ the T statistic with a p value while performing a hypothesis test. Your results' likelihood of being the result of chance is indicated by the p-value. Typically, in statistics, you use a T Test with a T Statistic rather than a Z score because you don't know much about the population.
To have larger t value , Combined standard deviation should be less
Therefore, n should be large and standard deviation should be less
Hence , The two samples both have n=30, with sample variances of 20 and 25 will provide us larger t-statistics
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Solve the following equation over the real number set
Answer:
x = (π/2 +2nπ) ± π/3
Step-by-step explanation:
You want the solutions to the radical equation involving sin(x).
Solution[tex]\sqrt{\sin^2{x}-4\sin{x}+4}+\sqrt{\sin^2{x}+4\sin{x}+4}=\sqrt{\sin^2{x}+7\sin{x}+12.25}\\\\\sqrt{(\sin{x}-2)^2}+\sqrt{(\sin{x}+2)^2}=\sqrt{(\sin{x}+3.5)^2}\\\\|\sin{x}-2|+|\sin{x}+2|=|\sin{x}+3.5|\\\\(2-\sin{x})+(\sin{x}+2)=\sin{x}+3.5\\\\0.5=\sin{x}[/tex]
The values of x that make this true are ...
x = {π/6, 5π/6} +2πn . . . . . for any integer n
__
Additional comments
√(x²) = |x|
sin(x) -2 is always less than zero, so its absolute value is 2-sin(x).
The attachment shows the equation written so the x-intercepts give the desired solutions.
The real number solution set for the trigonometric equation is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer
What is a trigonometric equation?A trigonometric equation is an equation that contains the trigonometric ratios.
How to solve the trigonometric equation for the set of real numbers?Given the trigonometric equation
√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)
We know that sin²x - 4sinx + 4 = (sinx - 2)².
Also, sin²x + 4sinx + 4 = (sinx + 2)².
Also, sin²x + 7sinx + 12.25 = (sinx + 3.5)².
So, substituting these into the equation, we have that
√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)
√(sinx - 2)² + √(sinx + 2)² = √(sinx + 3.5)²
|sinx - 2| + |sinx + 2| = |sinx + 3.5|
(2 - sinx) + (sinx + 2) = (sinx + 3.5)
2 - sinx + sinx + 2 = sinx + 3.5
Colecting like terms, we have that
-sinx + sinx + 2 + 2 = sinx + 3.5
0 + 4 = sinx + 3.5
4 = sinx + 3.5
Subtracting 3.5 from both sides, we have that
sinx = 4 - 3.5
sinx = 0.5
Taking inverse sin, we have that
x = sin⁻¹(0.5)
x = π/6 or 5π/6
So, the real number solution set is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer
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Ticket sales for Six Flags White Water totaled $94,520 this summer. Tickets for the water park cost $17 each. How many tickets were sold?
The number of tickets that will be sold is 5,560.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Ticket sales for Six Flags White Water totaled $94,520 this summer.
Tickets for the water park cost $17 each.
The number of tickets that will be sold is = $94,520/17 = 5,560.
Hence the number of tickets that will be sold is 5,560.
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Is 1 is a root of f/x Which of the following must be true?
According to Polynomial System, the correct answer is that the roots of f(x) are (x+1).
A polynomial system (sometimes just a polynomial system) is a set of simultaneous equations f₁ = 0,..., fₙ = 0. where fi is a polynomial in multiple variables such as x₁,..., xₙ over the fields. k.
This is due to the zero product property that when two binomials are multiplied by 0, one of their factors must be 0.
A simple example of a system of polynomial equations is
x²+y²- 5 = 0
xy-2 = 0.
Its solutions are the four pairs (x, y) = (1, 2), (2, 1), (-1, -2), (-2, -1). These solutions are easily verified by substitution, but proving that there are no other solutions requires more work.
Based on above description, we can say that:
(x+1) must be 0.
(x+1)=0
x=-1
Thus, If (x-1)=0 then x is 1 instead of -1 in question.
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Over the last 50 years the population has doubled. Today the world population is 7 billion people. What is the average rate of change of the worlds population?
Answer:
70000000 (70 million people per year)------------------------------------
Average rate of change for this case is:
r = difference in the population / time ranger = (7 000000000 - 3 500000000)/50 = 70000000an = r·(an-1)
determine the recrusive function to model the geometric sequence.
24, 6, 1.5
show work
On solving the provided question, we got to know that - recursive function to model the geometric sequence is 0.25
What is recursive function?In order to create a sequence of terms, a recursive function either repeats itself or uses a previous term to compute a new term. An arithmetic-geometric series with terms that differ from each other frequently is used to explain this function.
Given, geometric sequence
24, 6, 1.5
First term of this sequence = 6
a1 = 6
Recursive formula geometric sequence
[tex]a_{n} = a_{(n-1)}r[/tex]
[tex]Here r = common. ratio .of .successive. and previous term\\From .the given .sequence\\[/tex]
r = a2/a1
r = 6/24
r = 0.25
[tex]Recursive formula of the given sequence will be,[/tex]
[tex]a_{n} = a_{(n-1)}(0.25)[/tex]
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Find the following
I need help with this 2 questions
The value of x is 15. The measurement of m∠M = 20°
What is an equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60° and congruent with the others.
The length each side of △ABC is 9 units.
Thus it is an equilateral triangle. The measurement of each angle is 60°.
Given that, ∠ABC = 4x°.
Therefore, 4x° = 60°
Divide both sides by 4:
x = 15
43)
Given that, △LMN and △QRS are congruent triangle.
∠MNL = ∠QRS = 90°.
∠MLN = ∠QSR = 70°
and ∠NML = ∠RQS = x° (say)
The sum of all three angles of a triangle is 180°.
∠MNL + ∠MLN + ∠NML = 180°
90° + 70° + x° = 180°
Add like terms:
160° + x° =180°
Subtract 160° from both sides:
x° = 20°
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Refer to the SENIC data set in Appendix C.1. Length of stay (Y) is to be predicted, and the pool of potential predictor variables includes all other variables in the data set except medical school affiliation and region. It is believed that a model with logio Y as the response variable and the predictor variables in first-order terms with no interaction terms will be appropriate. Consider cases 57–113 to constitute the model-building data set to be used for the following analyses. a Prepare separate dot plots for each of the predictor variables. Are there any noteworthy features in these plots? Comment b. Obtain the scatter plot matrix. Also obtain the correlation matrix of the X varjables. Is there evidence of strong linear pairwise associations among the predictor variables here? c. Obtain the three best subsets according to the Cp criterion, Which of these subset models appears to have the smallest bias?
We make distinct dot plots for every predictor variable.
x₂=6.3368+0.7604×x₄
x₂=6.67+0.04×x₆
x₂=7.718+0.04×x₁₂
Given that,
Refer to Appendix C.1's SENIC data collection. All additional variables in the data set, with the exception of medical school affiliation and area, are included in the list of potential predictor variables for length of stay (Y). It is anticipated that the best model will have logio Y as the response variable, first-order terms for the predictor variables, and no interaction terms. Take examples 57–113 into consideration as the model-building data set for the subsequent studies.
We have to make distinct dot plots for every predictor variable. Do these storylines have any significant elements.
We know that,
Average length of stay = x₂
Infection risk = x₄
X-ray ratio = x₆
Available Services = x₁₂
57–113 into consideration as the model-building data set for the subsequent studies.
By using, regression equation for x₂ as dependent variable and regression equation for x₄ as independent variable..
Then,
x₂=6.3368+0.7604×x₄
x₂=6.67+0.04×x₆
x₂=7.718+0.04×x₁₂
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a grocery store is interested in determining whether or not a difference exists between the shelf life of two different brands of doughnuts. a random sample of 100 boxes of each brand was selected and the shelf life in days was determined for each box. the sample results are given below. brand a brand b mean
Therefore ,Based on this sample, of 90% confidence interval that Hot'n Now doughnuts will remain fresher for an additional 1.1 to 2.4 days than Sugar Yum doughnuts.
What is confidence interval ?An estimation range for an unknowable parameter is referred to as a confidence interval in frequentist statistics. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals.
Here,
Given: random sample of 100 boxes of each brand
The difference of the means,μhn−μsy had a 90% confidence interval that was calculated as follows: (1.1,2.4).
Therefore,
Based on this sample, we are 90% confidence interval that Hot'n Now doughnuts will remain fresher for an additional 1.1 to 2.4 days than Sugar Yum doughnuts.
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The population of bears on a nature preserve was 95 last year.This year , the population increased by 20% . what is the new bear population on the preserve
Answer: 19 new bears
Step-by-step explanation: To find the percentage of something, let's recall the formula:
Whole number x part % / 100
So, let's plug in the numbers to the formula:
95 x 20 / 100
95 x 20 = 1900
So, 1900 / 100 = 19; our answer
I hope this helped!
A national businessman magazine reports that the mean age of retirement for women executives is 61.0. A women’s rights organization believes that this value does not accurately depict the current trend in retirement. to test this the group pulled a simple random sample of 95 recently retired will make executives and found that they have a mean age of retirement at 61.5 and the standard deviation is 2.5 years. is there is sufficient evidence of support the organization belief at the a=0.05 significance level?
P-value >= 0.05 and adequate evidence supporting the organization's opinion at the a=0.05 significance level prevent the null hypothesis from being rejected.
What is null hypothesis ?A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.
The alternative and null hypotheses are listed below. μ = 61
61 Alternative Hypothesis
Rejection Area
For = 0.05, this test has two tails.
Z has a critical value between -1.96 and 1.96.
Reject H0 thus if z -1.96 or z > 1.96
The test statistic is z = (xbar - mu)/(sigma/sqrt(n)) z = (61.5 - 61)/(2.5/sqrt(95)) z = 1.95.
P-value P-value for the method is 0.0512.
Failure to reject the null hypothesis because P-value >= 0.05.
Approach to the Rejection Zone
Failure to reject the null hypothesis because the test statistic z is within the crucial value range.
P-value >= 0.05 and adequate evidence supporting the organization's opinion at the a=0.05 significance level prevent the null hypothesis from being rejected.
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rewrite the sentence adding a nonrestrictive element. using commas Mr. Powel told us we have a geometry test next week
Mr. Powel, who is our geometry teacher, told us we have a geometry test next week.
What is non-restrictive element?A nonrestrictive element is an element of a sentence that is not necessary for understanding the basic meaning of the sentence, but instead provides additional information. Nonrestrictive elements are usually set off with commas, while restrictive elements are not. For example, “My brother, who is an engineer, works in Chicago” is a sentence with a nonrestrictive element. The nonrestrictive element (“who is an engineer”) provides additional information about the brother, but does not provide any information about which brother is being referred to. The restrictive element “My brother who works in Chicago” does provide information about which brother is being referred to.
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Solve for h when they are similar triangles and 2 sides are given
The value of h is 70/17 if they are similar triangles and two sides are given in the figure.
What is a triangle?Three edges and three vertices make up a triangle, which is a polygon.
In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and that triangle is contained in just one plane. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however in higher-dimensional Euclidean spaces, this is no longer the case. Except as specifically stated, this article is about triangles in the Euclidean plane and general Euclidean geometry.
Given,
The figure has two similar triangles.
Here in the question the two sides are given,
We have the condition,
1/AB +1/PC=1/MN
From the figure,
(1/7)+(1/10)=(1/h)
17/70=1/h
h=70/17
Therefore, the value of h is 70/17 if they are similar triangles and two sides are given in the figure.
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Starting salaries of 150 college graduates who have taken a statistics course have a mean of $42,991. Suppose the distribution of this population is approximately normal and has a standard deviation of $9,166.
Using an 99% confidence level, find both of the following:
(NOTE: Do not use commas or dollar signs in your answers.)(a) The margin of error: (b) The confidence interval for the mean
At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.
Define margin of error.The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error. In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.
Given,
Starting salaries of 150 college graduates who have taken a statistics course have a mean of $42,991. Suppose the distribution of this population is approximately normal and has a standard deviation of $9,166.
Margin of error:
At 85% confidence level
α = 1 - 85%
α = 1 - 0.85 = 0.15
Zα/2 = 0.075
α/2 = Z0.075
Zα/2 = 1.44
At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.
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The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $944/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 100) for the cruise, then each fare is reduced by $8 for each additional passenger. Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht? What is the maximum revenue?
69 Passengers (20 plus additional 49) will result in maximum revenue for the owner of the yacht. Maximum Revenue will be $38,088.
current: 20 passengers at $944 each
let the number of additional passengers be x
cost per passenger = 944 - 8x
revenue (R) = (20+x)(944-8x)
= 18880 - 160x + 944x -8 x^2
dR/dx = -160 + 944 - 16x = 0 for a max of R
16x = 784
x = 49
There should be an additional 49 or a total of 69 passengers
The cost per passenger would be 944-8(49) or $552 per day
Maximum revenue for the yacht:
revenue (R) = (20+x)(944-8x)
revenue (R) = (20+49)(944-8(49))
revenue (R) = (69)(944-392)
revenue (R) = $38,088
Hence , 69 Passengers (20 plus additional 49) will result in maximum revenue for the owner of the yacht. Maximum Revenue will be $38,088.
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Alice makes porridge from milk and oats.
The ratio of milk to oats is 1:2
What proportion of Alice's porridge is milk?
Anyone can help ASAP
Answer:
1 milk and 2 oats
Step-by-step explanation:
milk to oats show that milk is first followed by oats and since 1 is first it is 1 milk and 2 oats
A baker sells boxes of cookies for $5 each. She has a total of 20 boxes of cookies to sell, and each box contains 12 cookies. The bakers total sales, in dollars, is a function of the number of boxes of cookies she sells, as shown by the
graph below
The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A pastry specialist sells boxes of treats for $5 each. She has a sum of 20 boxes of treats to sell, and each crate contains 12 treats.
Let 'x' be the number of boxes of cookies and 'y' be the total cost. Then the equation is given as,
y = 5x
The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.
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97 patients spent time with therapy dogs, and 101
patients did not. What percent of the total patients spent time
with a therapy dog, rounded to the nearest percent? Record
your work and answer on our Numbers in the News answer
sheet.
Answer:
94%
Step-by-step explanation:
How much potential energy does a 40 kg rock have if it was on a 10m cliff?
How much potential energy does the same 40 kg rock have if it was on a 5 m cliff?
If you shorten the height of an object, how does this affect its potential energy?
A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby has a mass of 1.5 kg.
A cinder block is sitting on a platform 20 m high. It weighs 7.9 kg. What is the PE?
There is a bell at the top of a tower. The bell weighs 19 kg. If the PE is 8550 J, how high is the tower?
The potential energy of an rock of 40 kg and at a height of 10m is 4000 kgm^2s^2
What is potential energy and its formula?
An object possesses potential energy as a result of its position in relation to other objects. Potential energy is so named because it has the ability to transform into other types of energy, such kinetic energy. the formula for potential energy is mgh where m is the mass, g is the acceleration due to gravity and h is the height of the object.
We are given a rock of mass 40 kg which is at a height of 10m
We substitute the values in the formula to find the potential energy of the rock
Potential energy = m*g*h
Potential energy = [tex]40*10*10[/tex]
Potential energy = 4000 kgm^2s^2
Hence the potential energy of the rock is 4000 kgm^2s^2
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Assume that a normal distribution of data has a mean of 19 and a standard deviation of 5. Use the 68-95-99. 7 rule to find the percentage of values that lie about 29.What percentage of values lie above 29?___% (Type an integer or a decimal.)
2.5% of values will lie above 29.
What is normal distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
The 68-95-99.7 rule is an illustration of how those many percentage of values lie in between mean +/- 1, 2, and 3 standard deviations respectively.
For values to lie above 29, their z value comes out to be
(29-19) / 5 = 10/5 = 2
(Note: z value means how many standard deviations above the mean)
Thus for a z value = 2 (which 29 is in this problem) the percentage of values that lie between mean +/- 2*(standard deviation) is 95 (as stated by the 68-95-99.7 rule).
Thus only 5% values wont lie between mean +/-2 standard deviations.
So 5% values wont lie between 29 (z value=2) and 9 (z value=-2).
Since normal curve is symmetric, half of the values of the 5% will lie above 29 and the rest half will lie below 9.
So 50% of 5 % which is 2.5% of values will lie above 29.
Hence, 2.5% of values will lie above 29.
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For the functions f(t) = 5t and g(t) = sin(t) defined on 0≤t<[infinity], compute f * g in two different ways.a. By directly evaluating the integral in the definition of f * g.b. By computing L−1{F(s)G(s)} where F(s)=L{f(t)} and G(s)=L{g(t)}.
The laplace inverse transformation L−1{F(s)G(s)} = 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]
If L{f(t)} = F(s), then the inverse Laplace transform of F(s) is
L−1{F(s)} = f(t). (1)
The inverse transform L−1is a linear operator:
L−1{F(s) + G(s)} = L−1{F(s)} + L−1{G(s)}, (2)
andL−1{cF(s)} = cL−1{F(s)}, (3)
for any constant c
given functions are
f(t) =5t ,g(t) = sin(t)
L(f(t)) = F(s)
L{F(s)*G(s)} = L^-1{5tsin(t)}
=5L^-1{tsin(t)}
=5L^-1{[tex]\frac{d}{ds}[/tex] tsin(t)}
= 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]
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Anyone know how to get this? I dont understand
The value of x in the diagram is 80°
What is an isosceles triangle?
Isosceles triangles are those triangles that have at least two sides of equal measure. We know that triangles are three-sided enclosed polygons and they are classified as equilateral, isosceles, and scalene, based on the length of their sides. In this article, we will learn about the definition of an isosceles triangle and its properties.
The body of the calculation is attached in a document.
In conclusion the value of x is 80°
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Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that P(E) = 0.24, P(B) = 0.16, and P(E and B) = 0.13. Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.0.530.130.60.27
The probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
We have to find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.
Since,
P(E or B) = P(E) + P(B) - P(E and B)
Given,
P(E) = 0.24
P(B) = 0.16
P(E and B) = 0.13
Hence,
P(E or B) = 0.24 + 0.16 - 013
P(E or B) = 0.27
Option D is correct.
Hence, the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.
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Find the area of the triangle. [?] units² Round to the nearest hundredth.
The area of the triangle is 48 square units.
To calculate the length of each side of the triangle ACB, the radii of the circles should be added respectively.
Length of side BC = 9+3 = 12 units
Length of side CA = 3+5 = 8 units
Length of side BA = 9+5 = 14 units
Area of triangle = (1/2 × Base × Height) square units
Area of triangle ACB = 1/2 × CA× BC sq units
Area = 1/2 × 8 × 12 = 48 sq units
Hence, the area of triangle ACB is 48 square units.
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Answer:
47.91 units²
Step-by-step explanation:
The radius of each circle is:
Circle A: radius = 5Circle B: radius = 9Circle C: radius = 3Therefore, the side lengths of the triangle are:
AB = 5 + 9 = 14BC = 9 + 3 = 12AC = 3 + 5 = 8Heron's Formula allows us to find the area of a triangle in terms of its side lengths.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, half the perimeter of the triangle is:
[tex]\implies s=\dfrac{14+12+8}{2}=17[/tex]
To calculate the area of the triangle, substitute the sides lengths and the value of s into Heron's formula and solve for A:
[tex]\implies A=\sqrt{17(17-14)(17-12)(17-8)}[/tex]
[tex]\implies A=\sqrt{17(3)(5)(9)}[/tex]
[tex]\implies A=\sqrt{2295}[/tex]
[tex]\implies A=47.906158268...[/tex]
[tex]\implies A=47.91\; \sf units^2\;\;(nearest\;hundredth)[/tex]
This is so confusing could anyone help me with this
Answer:
I am not exactly sure what they want you to put in the boxes, but hopefully the explanation below will shed some light on what is going on with this problem.
Step-by-step explanation:
The equation would be
y = 3x
It looks like your question wants you to write the equation in the form
r(x) = 3x
y would be the student's score on the test.
x would be the number of questions that the student got right.
The x is the independent variable. It tells us how many questions the student got right.
The y is the dependent variable. It is the student's score. The student's score depends on how many questions the student got right.
R(25) is saying what would be the score if the student got 25 answer correct?
3(25) = 75. The student would get a score of 75
