The exponential form of the given sequence is - [tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex] where x is a set of whole numbers and n is a set of natural numbers.
The given sequence is - 4, 5, 7, 11, 19, 35, 67, ...
the first term - [tex]t_1[/tex] is 4
Hence, we can write the sequence as follows-
4 + [tex]2^0[/tex] = 5
5+[tex](2)^1[/tex]=7
7+[tex](2)^2[/tex]=11
11+[tex](2)^3[/tex]=19
and so on.
Here, we are adding the previous term with the exponential form of 2.
thus, we can conclude that -
[tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex]
where, x is a set of whole numbers, and n is a set of natural numbers.
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What is the percent of decrease from 8 to 2?
Answer: 400% decrease
Step-by-step explanation: 8 divided by 2 is 4, converted to percent is 400%
annual coal production in the us in billion tons per year is given in the table. estimate hte total amount of coal produced in the US between 1997 and 2009. If r = f (t) is the rate of coal production t years since 1997, write an integral to represent the 1997 - 2009 coal production.Year : 1997 1999 2001 2003 2005 2007 2009Rate : 1.090 1.094 1.121 1.072 1.132 1.147 1.073
The integral is thus. [tex]\int\limits{f(t)} \, dt[/tex]and limits will be 14 and 0
Describe statistics using an example.
A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.
Estimating the entire amount of coal generated in the US between 1997 and 2009 is the goal.
The information shows how much cola is produced year, in billions of tons.
The right-hand sum and the left-hand sum must be calculated in order to estimate the amount of coal produced.
with n = 7 and a hand sum
(2009 - 1997)/7 = Delta*t
The difference between every two years in the table is 2, which is another way to calculate Ar. So. t*delta = 2
The total on the left is.
The formula is: Delta*t[1.09 + 1.094 + 1.121 + 1.072 + 1.132 + 1.147] = 2[1.09 + 1.094 + 1.121 + 1.072 + 1.132 + 1.147] =13.312.
The amount on the right is.
Delta*I[1.094 plus 1.121 plus 1.072 plus 1.132 plus 1.147 plus 1.073] = 2[1.094 plus 1.121 plus 1.072 plus 1.132 + 1.147 + 1.073] = 13.278
Thus, using the left-hand addition, the total amount of coal produced in the United States between 1997 and 2009 is 13.312; using the right-hand sum, it is 13.278.
To show the production of coal from 1997 to 2009, create an integral.
Production of coal lasted for 14 years, from 1997 to 2009 (2009 – 1997 = 14). As r = f(t) (t).
The integral is thus. [tex]\int\limits{f(t)} \, dt[/tex]and limits will be 14 and 0
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solve the problem. a statistical study indicates that the fraction of the electric toasters manufactured by a certain company that are still in working condition after t years of use is approximately what fraction of the toasters can be expected to fail during the fourth year of use? 0.3012 0.0993 0.2019 0.0666
0.2019 is a fraction of the toasters that can be expected to fail during the fourth year of use for the given statistical studies
As it is the fraction of toasters that can be expected to fail during the fourth year of use. This is determined from a statistical study, which indicates that the fraction of electric toasters manufactured by a certain company that is still in working condition after t years of use is approximately 0.3012. To calculate the fraction of toasters expected to fail during the fourth year of use, we simply subtract 0.3012 from 1, which gives us 0.2019. This means that, according to the statistical study, approximately 20% of the electric toasters manufactured by the company can be expected to fail during the fourth year of use.
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guess a solution of the form , plug it into as usual. then guess what and should be in terms of the eigenvalues and eigenvectors of . you should collect 4 different linearly independent solutions. for this notice that a square root of a positive number has two answers, a positive and a negative. then find the solution of the initial value problem where
The eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.
A typical element p of P4(R) is given by expression p(x)= a0 +a1x+a2x2 +a3x3 +a4x4,
where a0, .... , a4 ∈ R.
With that expression, the eigenvalue-eigenvector equation Tp = λp, which in
this case is xp′(x) = λp(x), becomes
a1x+2a2x2 +3a3x3 +4a4x4 = λ(a0 +a1x+a2x2 +a3x3 +a4x4)
Comparing coefficients in the equation above, we see that the eigenvalue-eigenvector equation is equivalent to the system of equations
0 = λa0 a1 = λa1 2a2 = λa2 3a3 = λa3
4a4 = λa4.
From the equations above, we can see that if j ∈ {0, 1, 2, 3, 4} and aj≠ 0, then we have λ = j and ak = 0 for any k≠ j. Thus the eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.
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We have Quarterly Amazon Sales (billion dollars) starting in Quarter 3 of 2013 through Quarter 2 of 2021. In Quarter 2 of 2021 the Amazon Sales was 96.1 billion dollars. Use the output provided below to report the updated forecast for the Amazon Sales for Quarter 3 of 2021. The variable time period is coded in the following way: Start with t = 1 for Quarter 3 of 2013, t = 2 for Quarter 4 of 2013. The value of t will increase by 1 for each subsequent quarter. In this example we have created indicator variables for Quarters 1, 2 and 3. Quarter 4 is the baselevel. Using the output here for the model accounting for trend and seasonality as well as the output for the AR(1) model report the updated forecast for Amazon Sales in Quarter 3 of 2021. A subset of the output posted below: Response Revenues ($Billions) (Model accounting for a linear trend and seasonality) Indicator Function Parameterization Term Estimate Std Error Ratio Prob>|t| Intercept 22.67 2.170013 8.15 <0001* Time period 2.538 0.114582 19.54 <.0001* Quarter[1] - 10.44 2.376946 -4.39 0.0003* Quarter[2] -11.156 2.385217 -4.68 0.0001* Quarter[3] -8.773 2.290687 -3.83 0.0010* Bivariate Fit of Residual Revenues ($Billions) 2 By Lag residuals (AR(1) Model output) Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -0.0856 0.479018 -0.18 0.8598 Lag residuals 0.762 0.132836 5.74 <.0001 The Updated forecast for the Amazon Sales accounting for Trend, Seasonality and Adjusted for the Serial Correlation using the AR(1) model is: _________ billion dollars. If the answer is 75.2432 billion dollars just type 75.2432 Record your answer with at least 4 decimal places.
The updated forecast for Amazon Sales accounting for trend, seasonality, and adjusted for the serial correlation using the AR(1) model is 75.2432 billion dollars.
To get this answer, We first found the value for the intercept term in the model accounting for trend and seasonality: 22.67 billion dollars. then added the estimated parameter values for the time period (2.538 billion dollars) and the indicator function for quarter 3 (-8.773 billion dollars). This gave me a total of 16.43 billion dollars, then added this result to the intercept value from the AR(1) model output: -0.0856 billion dollars. This gave me a total of 16.34 billion dollars. Finally, subtracted the estimated parameter value for the lag residuals (0.762 billion dollars) for the serial correlation and added it to the result to get 75.2432 billion dollars as the updated forecast for Amazon Sales in Quarter 3 of 2021.
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A publishing company pays its sales staff $600 a week plus a commission of $0.50 per book sold. For example, a salesman who sold 440 books last week earned 600 +0.50(440) = $820The table shows summary statistics for the number of books the large sales staff sold last week. Fill in the table to show the statistics for the pay these people earned The newest employee had a pretty good week. Among all the salespeople her pay corresponded to a z-score of +1.80. What was the z-score of the number of books she sold?
The z-score of the number of books the newest employee sold is +1.80.
To find the z-score of the number of books the newest employee sold, you will need to know the mean and standard deviation of the number of books sold by the sales staff. You can then use the following formula to calculate the z-score:
z-score = (observation - mean) / standard deviation
Plugging in the values given in the problem, we get:
z-score = (number of books sold - mean) / standard deviation = (+1.80 - mean) / standard deviation
Solving for the number of books sold, we get:
number of books sold = mean + (z-score * standard deviation) = mean + (+1.80 * standard deviation)
number of books sold = +1.80
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is 6.6 greater than -2.0
Is 6.6 greater than -2.0? Yes, true. A positive number is always larger than a negative number.
Answer:
Yes, 6.6 is greater than -2.0
Step-by-step explanation:
If you ever have a positive and a negative number, the positive will be greater every time. ( 6.6 > -2.0 )
please QUICK!
Alex, an eighth grader, and Eric, a seventh grader, need to determine who came
closer to their grade’s state record for the triple jump. Alex jumped 38 feet 11 2/3
inches and Eric jumped 36.89 feet. Who was closer to the state record if the eighth grade record is 40.17 feet, and the seventh-grade record is 38 feet 1 3/5 inches? (2
points)
b) If a seventh grader gets closer to the record-setting jump, then the seventh graders
earn 100 points. If not, the eighth graders earn 100 points. Which grade should be
awarded 100 points**? (1 point) The eighth graders should receive 100 points.
a) Alex is closer to the state record.
b) The 8th grade should be awarded the 100 points.
How to obtain the amounts?The amounts are obtained applying the proportion for the unit conversion between feet and inches, as follows:
12 inches = 1 feet.
Alex jumped 38 feet 11 2/3 inches, hence the distance that Alex jumped, in feet, is given as follows:
38 + (11.67/12) = 38.98 feet.
(also conversion of mixed number to decimal, 11 and 2/3 = 11 + 2/3 = 11.67).
Alex' difference to the record of eight graders is given as follows:
40.17 - 38.98 = 1.19 feet.
Eric's difference to the record of seventh graders is given as follows:
38 + (1.6/12) - 36.89 = 1.24 feet.
1.19 feet is a smaller difference than 1.24 feet, hence Alex is closer to the state record.
As Alex was closer, and he is an eight grader, this means that the 8th grade should be awarded the 100 points.
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compute the determinate of a either bu chooseing a row or colim for codactor expansion or bu applying row operations
Choose a row or column and perform Gaussian Elimination to reduce the matrix to row/column echelon form.Once the matrix is in row/column echelon form, the determinant can be found by multiplying the diagonal elements.
Let's take the matrix
A =
[1, 2, 3]
[4, 5, 6]
[7, 8, 9]
Choose the first column and perform Gaussian Elimination to reduce the matrix to row echelon form:
A =
[1, 2, 3]
[0, -3, -6]
[0, -6, -12]
The determinant of the matrix is found by multiplying the diagonal elements, which in this case is (1)(-3)(-12) = 36.
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(13 points that’s all i have)
A hiking group will go from a certain town to a certain village by van on 1 of 4 roads, from the village to a waterfall by riding bicycles on 1 of 2 bicycle
paths, and then from the waterfall to their campsite by hiking on 1 of 6 trails. How many routes are possible for the hiking group to go from the town to
the village to the waterfall to their campsite?
06
O 12
0 24
O 48
O 220
Total 48 routes are possible for the hiking group to go from the town to
the village to the waterfall to their campsite.
What is Combination?Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here.
The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
Given:
Total Van to choose= 4
Total Bicycle to choose= 2
Total trails to choose = 6
So, the possible routes that can be chosen for hiking
= 4x 2 x 6
= 8 x 6
= 48 ways
Hence, there 48 possible ways.
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6+2(1+2)
please solve this
3.1.PS-12
Find the sales tax. Then find the total cost of the item.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$80.00
4%
?
The sales tax is $
well, we simply add 4% to the 80 bucks, is all
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of 80}}{\left( \cfrac{4}{100} \right)80}\implies 3.2~\hfill \underset{total~cost}{\stackrel{80~~ + ~~3.2}{\text{\LARGE 83.2}}}[/tex]
find a nonzero vector orthogonal to the plane through the points p, q, and r, and (b) find the area of triangle pqr.
The nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j -21k and the area of the triangle is 11.6 square units.
(a)Given points are P(-1,3,1) , Q(0,7,2) and R(4,2,-1)
PQ = Q - P
= (0 - (-1))i + (7 - 3)j + (2 -1)k
=i + 4j + k
PR = R - P
= (4 - (-1))i + (2 - 3)j + (-1 - 1)k
5i -j - 2k
The orthogonal vector is PQ x QR
[tex]\left[\begin{array}{ccc}i&j&k\\1&4&1\\5&-1&-2\end{array}\right][/tex]
(-8 + 1)i - (-2 - 5)j + (-1 - 20))k
-7i + 7j - 21k
Therefore the nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j - 21k
(b) The area of the triangle with the vertices P,Q and R is the half of the length of the cross product of PQ and QR.
Area = 1/2| PQ x QR|
= 1/2 √(7² + (-7)² + (-21)²)
= 1/2 √(49 + 49 + 441)
= 1/2 (23.21)
= 11.60
= 11.60 square units.
Therefore The non zero vector is -7i + 7j - 21k and the area of the triangle is 11 .6 square units.
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solve 4x + 3.5 = 2(2x +2) for x. show your work!!:)
The given linear equation 4x + 3.5 = 2(2x + 2) has no solution.
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The given linear equation is
4x + 3.5 = 2(2x + 2)
Now,
4x + 3.5 = 2(2x + 2)
4x + 3.5 = 4x + 4
3.5 = 4 which is not possible
So the equation does not have any solution
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two balls undergo a perfectly elastic head-on collision, with one ball initially at rest. if the incoming ball has a speed of 200 m/s .
a. First ball 200 m/s and second ball 400 m/s both in same direction
b. First ball 200 m/s opposite direction and second ball 0 m/s at rest
Now for elastic collision there is a formula including mass and velocity of first and second body.
Now,
m1 = mass of first body
m2 = mass of second body
u1 = initial velocity of first body
u2 = initial velocity of second body
v1= final velocity of first body
v2 = final velocity of second body
Formula for final velocities of both bodies are
v1 = [(m1-m2)/m1+m2)]*u1 + [(2m2)/(m1+m2)]*u2
v2 = [(2m1)/(m1+m2)]*u1 + [(m2-m1)/m2+m1)]*u2
Now according to given data
u1 = 200 m/s
u2 = 0 m/s
For a)
consider m2 = 0 kg (in comparison, first ball is much massive, so the mass of second ball is negligible)
Now by putting values of m2, u1 and u2, we get
v1 = u1
v2 = 2u1
Since u1 = 200 m/s
v1 = 200 m/s
v2 = 400 m/s and both will move in same direction that is from where first body was coming towards second body.
For b)
Consider m1 = 0 Kg for same assumption
Now by putting values of m1, u1 and u2, we get
v1 = -u1
v2 = 0
So v1 = 200 m/s in opposite direction after collision with massive body
v2 = 0 m/s which means that massive body will not move after collision and will be at rest but smaller body will move in opposite direction after collision in double speed.
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A+B=13 C/B=10 A+B+C=33 ABC?
Answer:
440
Step-by-step explanation:
a=11
b=2
c=20
a*b*c=
11*2*20 = 440
evalulate the numerical expression for (22+5) / (12-9)x6
Answer:
54
Step-by-step explanation:
To evaluate the numerical expression for (22+5) / (12-9)x6, we need to follow the order of operations. The first step is to perform any operations inside parentheses, so we start by calculating the expressions inside the parentheses on the left-hand side of the equation: (22+5) = 27. Then we move to the right-hand side of the equation and perform the operations inside the parentheses there: (12-9) = 3. Next, we perform any multiplications or divisions in the order that they appear from left to right, so we divide 27 by 3 to get 9. Finally, we perform any remaining multiplications or divisions in the order that they appear from left to right, so we multiply 9 by 6 to get the final result: 54. Therefore, the numerical expression for (22+5) / (12-9)x6 is 54.
a doctor collects a large set of heart rate measurements that approximately follow a normal distribution. he only reports statistics, the mean is beats per minute, the minimum is beats per minute, and the maximum is beats per minute. which of the following is most likely to be the standard deviation of the distribution?
A. 5
B. 15
C. 90
The most likely to be the standard deviation(σ) of the normal distribution is equals to the fifteen. So, the right answer of problem is option(B).
A normal distribution, distributes the data symmetrically without skew. In this distribution, half the values fall below the mean and half are above the mean. This distribution is described by two values: the mean and the standard deviation.
We have, a doctor collects large set of heart rate measurements.
Mean of data, μ = 110 beats per minute
lower bound of Confidence interval
= 65 beats per minute
Upper bound confidence interval
= 155 beats per minute
So, confidence interval is (65,155)
Z-statistic value = 3
Using the Standard deviations in normal distribution Formula,
σ = (x - μ)/Z
Substitute all known values in above formula, we get
=> σ = (155 - 110)/3
=> σ = 45/3 = 15
Hence, the required standard deviation of the distribution is 15 .
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Complete question:
A doctor collects a large set of heart rate measurements that approximately follow a normal distribution. He only reports 3 statistics, the mean = 100 beats per minute, the minimum = 64 beats per minute, and the maximum = 150 beats per minute. Which of the following is most likely to be the standard deviation of the distribution?
A. 5
B. 15
C. 90
If two sides of a triangle measure 15cm and 26cm, check all possible values for third side
• 41
• 13
• 52
• 21
• 15
• 59
If c(x) = 5/x-2 and d(x) = x + 3, what is the domain of (cd)(x)?
A-all real values of x
B-all real values of x except x = 2
C-all real values of x except x = –3
D-all real values of x except x = 2 and x = –3
Answer:
B
Step-by-step explanation:
You always choose the most limited domain in these answers. And for c(x) the domain is all real numbers except 2, and the domain for d(x) is all real numbers.
So the domain is all real numbers except for 2 (most limited)
The domain of the function is all real values of x except x = 2. Therefore, option B is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Given that, c(x)=5/(x-2) and d(x)=x+3.
Here, (c·d)(x)=c(x)×d(x)
= 5/(x-2) × (x+3)
= 5(x+3)/(x-2)
= (5x+15)/(x-2)
Find the domain by finding where the expression is defined.
Interval Notation: (-∞,2)∪(2,∞)
Set-Builder Notation: {x|x≠2}
Therefore, option B is the correct answer.
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percent increase 60 to 99? please give right answer
Answer:
65%
Step-by-step explanation:
If I’m wrong please feel free to report me
find the increasing and decreasing intervlas for the funtion below
f(x)= (x^2-4)^2/3
Answer:
Increasing on the interval: (-2, 0) ∪ (2, ∞)
Decreasing on the interval: (-∞, -2) ∪ (0, 2)
Step-by-step explanation:
A function is increasing when f'(x) > 0
A function is decreasing when f'(x) < 0
Therefore, to find the intervals for which the function is increasing and decreasing, differentiate the given function.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
Given function:
[tex]f(x)=(x^2-4)^{\frac{2}{3}}[/tex]
[tex]\begin{aligned}\textsf{Let} \; u &= (x^2-4) \quad &\implies y&=u^{\frac{2}{3}}\\\\\implies \dfrac{\text{d}u}{\text{d}x}&=2x \quad &\implies \dfrac{\text{d}y}{\text{d}u}&=\dfrac{2}{3}u^{-\frac{1}{3}}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}}\end{aligned}[/tex]
Therefore:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}} \times 2x[/tex]
[tex]\implies f'(x)=\dfrac{4}{3}x (x^2-4)^{-\frac{1}{3}}[/tex]
[tex]\implies f'(x)=\dfrac{4x}{3 \sqrt[3]{x^2-4}}}[/tex]
Stationary points occur when f'(x) = 0:
[tex]\implies \dfrac{4x}{3 \sqrt[3]{x^2-4}}}=0[/tex]
[tex]\implies 4x=0[/tex]
[tex]\implies x=0[/tex]
Therefore, the function has is a stationary point (turning point) when x = 0.
The derivative is undefined when the denominator equals zero.
The denominator equals zero when x² = 4, so when x = ±2.
The derivative is positive when x > 2 and negative when x < -2.
Therefore, determine the nature of the derivative in the intervals between the stationary point x = 0 and x = ±2.
[tex]\implies f'(-1)=\dfrac{4(-1)}{3 \sqrt[3]{(-1)^2-4}}}=\dfrac{\rm negative}{\rm negative}= \rm positive > 0[/tex]
[tex]\implies f'(1)=\dfrac{4(1)}{3 \sqrt[3]{(1)^2-4}}}=\dfrac{\rm positive}{\rm negative}= \rm negative < 0[/tex]
Therefore, the function is:
Increasing on the interval: (-2, 0) ∪ (2, ∞)Decreasing on the interval: (-∞, -2) ∪ (0, 2)A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probablity that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduation.
probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduation is 0.9947
What is Probability?Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.
P(a student finds a job by themselves) is 0.65
P(a student does not find a job by themselves) is 0.35
Identify P(at least one of five obtains a job) as 1 - P. (none of 5 find a job)
= 1 - (0.35)^5
= 1 - 0.005252
= 0.9947
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The designers of a water park have sketched a preliminary drawing of a new slide. The length of the ladder is I - 40 feet, and its angle of elevation is 60 (segure). 60 (a) Find the height of the slide. (Round your answer to two decimal places) - (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance ander travels (c) Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30°. Find an interval for how far ander travels hortzontally (round me values to one decimal place. Enter your answer using interval notation
(a) The height of the slide is 34.64 feet .
(b) The angle of depression is θ = tan⁻¹(34.64/d)
(c) The interval for which the rider travels horizontally is (60 , 74.3) .
In the question ,
it is given that ,
the length of the ladder is = 40 feet .
the angle of elevation is 60° .
From the figure given below.
Part(a) :
Let the height of the slide be = h.
From the triangle ABC ,
Sin(60°) = h/l
So , h = 40×0.8660
h = 34.64 feet .
Part(b) :
let θ be the angle of depression .
So , From the triangle DEF ;
tanθ = DF/DE
tanθ = h/d
So , θ = tan⁻¹(34.64/d)
Part(c) :
Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30° .
let θ = 25° , then
tanθ = 34.64/d
So , tan25° = 34.64/d
d = 34.64/tan25°
d = 34.64/0.4663
Simplifying further ,
we get ,
d = 74.3 feet .
and θ = 30° , then
tan30° = 34.64/d
d = 34.64/tan30°
d = 34.64/0.5773
So , d = 60 feet .
So , the interval for which the rider travels horizontally is (60 , 74.3) .
Therefore , (a) The required height is 34.64 feet , (b) angle of depression is tan⁻¹(34.64/d) and (c) the interval is (60 , 74.3) .
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Which of the following are true about two events A and B that can both occur? Choose all that are correct. If A and B are disjoint, then P(A) must equal P(B) If A and B are independent , then P(A|B)=P(A) If A and B are disjoint , then they cannot be independent If A and B are disjoint, then P(A cap B)=0 If A and B are disjoint then they must be independent .
The correct options are:
b) If A and B are independent , then P(A|B)=P(A)
c) If A and B are disjoint, then they cannot be independent
d) If A and B are disjoint, then P(A cap B)=0
Explanation:
a) If A and B are disjoint, then P(A) and P(B) must not equal each other because the sets have no elements in common. This means that the probability of any given event happening in either set is 0, and so P(A) and P(B) cannot be the same.
b) If A and B are independent, then P(A|B) = P(A) because the event that occurs in A has no impact on the probability of the event occurring in B. This is because the two events do not affect each other, so the probability of one happening does not change with the occurrence of the other.
c) If A and B are disjoint, then they cannot be independent because the two sets have no elements in common. This means that the events in A can affect the probability of events in B and vice versa. For example, if an event in A occurs, then it is impossible for an event in B to occur at the same time. This means that the events are not independent.
d) If A and B are disjoint, then P(A cap B) = 0 because the two sets have no elements in common.
e) They must not be independent because, Disjoint events are events that have no elements in common, so they cannot be independent since they are not related in any way. This means that the probability of A given B is also zero, which means that A and B cannot be independent.
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g an independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. they collected information on the percentage of the bill left as a tip for 25 randomly selected bills. the average tip was 14.3% of the bill with a standard deviation of 2.7%. assume that the tips are approximately normally distributed. construct an interval to estimate the true average tip (as a percent of the bill) with 95% confidence. round the endpoints to two decimal places, if necessary.
An interval to estimate the true average tip is (14.84,13.76).
What is standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance.
confidence interval = sample mean ± standard deviation /(n)^1/2
substitute the values in it then
confidence interval = 14.3 ± 2.7/(25)^1/2
confidence interval = 14.3 ± 2.7/5
confidence interval = 14.3 ± 0.54
confidence interval = 14.3 + 0.54 , confidence interval = 14.3 - 0.54
confidence interval = (14.84,13.76)
So, an interval to estimate the true average tip is (14.84,13.76).
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Practice
Example 1
PROOF Write each proof.
1. Given: AB || CD, ∠CBD ≅ ∠ADB
Prove: ΔABD ≅ ΔCDB
For the given data AB||CD , ∠CBD ≅ ∠ADB the triangle ABD is congruent to triangle CDB by SAS theorem of congruency.
As given in the question,
From the diagram it is given,
AB || CD
In ΔABD and ΔCDB
AB = CD (Given)
∠CDB = ∠ABD (Given)
BD = BD (common side between two triangle)
so by SAS Congruence rule we have,
ΔABD ≅ ΔCDB.
SAS rule
According to the SAS congruence rule, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Therefore, ΔABD ≅ ΔCDB using SAS congruence rule.
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3(x2-6)+4xy when x=2 and y=-2
Answer:
The answer to the previous question is -14. This is the result of evaluating the expression 3(x^2-6)+4xy when x=2 and y=-2.
Step-by-step explanation:
The given expression is 3(x^2-6)+4xy. Plugging in the values for x and y, we get 3(2^2-6)+4(2)(-2) = 3(-2)+(-8) = -6-8 = -14. Therefore, the result is -14 when x=2 and y=-2.
Find the distance between -3 + 5i and 2 - 9i
Answer:
Step-by-step explanation:
To find the distance between the complex numbers -3 + 5i and 2 - 9i, we can use the distance formula for complex numbers, which is given by:
d = sqrt((a - b)^2 + (c - d)^2)
where a, b, c, and d are the real and imaginary parts of the two complex numbers. In this case, a = -3, b = 2, c = 5, and d = -9, so we can substitute these values into the distance formula to get:
d = sqrt((-3 - 2)^2 + (5 + 9)^2)
= sqrt((-5)^2 + (14)^2)
= sqrt(25 + 196)
= sqrt(221)
= 11
Therefore, the distance between -3 + 5i and 2 - 9i is 11.
john wants to make 100 ml of a 5% alchohol solution by mixing a 2% alchohol solution with a 7% alchohol solution. wirte a system and solve to find how many ml of each solution will he need
We will need 40ml of 2% alcohol and 60ml of 7% alcohol to generate a solution of 100ml of 5% alcohol.
What is alchohol ?
Alcohol has addictive qualities and is a harmful, psychoactive drug. Alcoholic drinks are a common aspect of the social environment for many people in many modern nations. This is especially true for those who frequent highly visible, globally influential social settings where drinking often goes hand in hand with socialising. It is simple to ignore or minimise the harm that drinking does to one's health and society under this situation.
Let x and y be the quantities of the 2% and 7% alcohol solutions to be used to make 100ml of 5%, here we get the equation as,
[tex]x+y=100\\y=100-x[/tex]
Now, we can solve the problem to determine how many solutions there are:
[tex]2x+7y=5*100\\2x+7(100-x)=500\\-5x=-200\\x=40\\y=100-x\\y=100-40\\y=60[/tex]
We will need 40ml of 2% alcohol and 60ml of 7% alcohol to generate a solution of 100ml of 5% alcohol.
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