Final answer:
The expected time between successive mosquito bites is calculated using the probabilities of landing and biting, resulting in an average time of 10 seconds between bites.
Explanation:
The expected time between successive mosquito bites can be calculated by considering the probabilities of two independent events: a mosquito landing on your neck and a mosquito bite, given that it has landed. As per the data provided, a mosquito lands with a probability of 0.5 per second, and out of those, it will bite with a probability of 0.2. The probability of getting bitten by a mosquito that has landed is then 0.5 (probability of landing) × 0.2 (probability of biting) = 0.1 per second.
To find the expected time between successive bites, we need to consider the inverse of this probability, which tells us that on average, you can expect to get bitten every 1/0.1 or 10 seconds.
The expected time between bites is 10 seconds.
To find the expected time between successive mosquito bites, we need to consider the probability of a mosquito biting you at any given second.
Given the probabilities:
Probability that a mosquito lands on your neck in a second: 0.5 = P(land)Probability that a mosquito bites you if it lands: 0.2 = P(bite | land)Probability that a mosquito doesn't bite you if it lands: 0.8 = [tex]P(not\ bite |\ land)[/tex]The combined probability that a mosquito both lands and bites in any given second is the product of the two probabilities:
[tex]P(bite) = P(land) * P(bite\ |\ land) = 0.5 * 0.2 = 0.1.[/tex]
To find the expected time between successive bites, we take the reciprocal of the probability of being bitten in a given second:
[tex]Expected time = \frac{1}{P(bite)} = \frac{1}{0.1} = 10\ seconds[/tex].
The expected time between successive mosquito bites is approximately 10 seconds.
A study was done by a social media company to determine the rate at which users used its website. A graph of the data that was collected is shown
What can be interpreted from the range of this graph?
The range represents the 24-month time period of the study
The range represents the number of users each month for 24 months
The range represents the 20-month time period of the study
The range represents the number of users each month for 20 months
Answer:
The range represents the number of users each month for 24 months
Step-by-step explanation:
The range depends on the y axis. Looking at the y axis we see the number of users for each month. Looking at the x axis we see that it's 24 months not 20 months
From the graph, we can interpret the range represents the number of users each month for 24 months. Therefore, option B is the correct answer.
We need to find what can be interpreted from the range of the given graph.
What is the range?The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest.
From the given graph, we can see the x-axis represents the number of months and the y-axis represents the number of users.
So, the range represents the number of users each month for 24 months
20-15.8=4.2
Therefore, option B is the correct answer.
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Determine,in each of the following cases, whether the described system is or not a group. Explain your answers. Determine what is an Abelian group.
a) G = {set of integers , a ∗ b = a − b}
b) G = {set of matrices of size 2 × 2, A ∗ B = A · B}
c) G = {a0, a1, a2, a3, a4ai ∗aj = aIi+jI , if i+j < 5, ai ∗aj = aIi+j-5I , if i+j ≥ 5}
Answer:
(a) Not a group
(b) Not a group
(c) Abelian group
Step-by-step explanation:
In order for a system <G,*> to be a group, the following must be satisfied
(1) The binary operation is associative, i.e., (a*b)*c = a*(b*c) for all a,b,c in G
(2) There is an identity element, i.e., there is an element e such that a*e = e*a = a for all a in G
(3) For each a in G, there is an inverse, i.e, another element a' in G such that a*a' = a'*a = e (the identity)
If in addition the operation * is commutative (a*b = b*a for every a,b in G), then the group is said to be Abelian
(a)
The system <G,*> is not a group since there are no identity.
To see this, suppose there is an element e such that
a*e = a
then
a-e = a which implies e=0
It is easy to see that 0 cannot be an identity.
For example
2*0 = 2-0 = 2
Whereas
0*2 = 0-2 = -2
So 2*0 is not equal to 0*2
(b)
The system <G,*> is not a group either.
If A is a matrix 2x2 and the determinant of A det(A)=0, then the inverse of A does not exist.
(c)
The table of the operation G is showed in the attachment.
It is evident that this system is isomorphic under the identity map, to the cyclic group
[tex]\mathbb{Z}_{5}[/tex]
the system formed by the subset of Z, {0,1,2,3,4} with the operation of addition module 5, which is an Abelian cyclic group
We conclude that the system <G,*> is Abelian.
Attachment: Table for the operation * in (c)
Suppose a certain computer virus can enter a system through an email or through a webpage. There is a 40% chance of receiving this virus through the email. There is a 35% chance of receiving it through the webpage. These are not mutually exclusive: the virus enters the system simultaneously by both email and webpage with a probability of 0.17. What is the probability that the virus does not enter the system at all? Enter your answer in decimal form
Answer:
P = 0.42
Step-by-step explanation:
This probability problem can be solved by building a Venn like diagram for each probability.
I say that we have two sets:
-Set A, that is the probability of receiving this virus through the email.
-Set B, that is the probability of receiving it through the webpage.
The most important information in these kind of problems is the intersection. That is, that he virus enters the system simultaneously by both email and webpage with a probability of 0.17. It means that [tex]A \cap B[/tex] = 0.17.
By email only
The problem states that there is a 40 chance of receiving it through the email. It means that we have the following equation:
[tex]A + (A \cap B) = 0.40[/tex]
[tex]A + 0.17 = 0.40[/tex]
[tex]A = 0.23[/tex]
where A is the probability that the system receives the virus just through the email.
The problem states that there is a 40% chance of receiving it through the email. 23% just through email and 17% by both the email and the webpage.
By webpage only
There is a 35% chance of receiving it through the webpage. With this information, we have the following equation:
[tex]B + (A \cap B) = 0.35[/tex]
[tex]B + 0.17 = 0.35[/tex]
[tex]B = 0.18[/tex]
where B is the probability that the system receives the virus just through the webpage.
The problem states that there is a 35% chance of receiving it through the webpage. 18% just through the webpage and 17% by both the email and the webpage.
What is the probability that the virus does not enter the system at all?
So, we have the following probabilities.
- The virus does not enter the system: P
- The virus enters the system just by email: 23% = 0.23
- The virus enters the system just by webpage: 18% = 0.18
- The virus enters the system both by email and by the webpage: 17% = 0.17.
The sum of the probabilities is 100% = 1. So:
P + 0.23 + 0.18 + 0.17 = 1
P = 1 - 0.58
P = 0.42
There is a probability of 42% that the virus does not enter the system at all.
A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 25 minutes. The owner has randomly selected 21 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 25 minutes. Suppose the p-value for the test was found to be .0284. State the correct conclusion.
Question 22 options:
At ? = .025, we fail to reject H0.
At ? = .05, we fail to reject H0.
At ? = .03, we fail to reject H0.
At ? = .02, we reject H0.
Answer:
Claim : The average time spent on a delivery does not exceed 25 minutes.
n = 21
We are given that p-value for the test was found to be .0284.
Now we are supposed to state the conclusions
a) At α = .025, we fail to reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value > α
So, we accept the null hypothesis i.e. we fail to reject null hypothesis.
b)At α = .05, we fail to reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value < α
So, we reject the null hypothesis
c)At α =.03, we fail to reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value < α
So, we reject the null hypothesis
d)At α =.02, we reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value > α
So, we accept the null hypothesis i.e. we fail to reject null hypothesis.
A company that manufactures small canoes has a fixed cost of $24,000. It costs $100 to prod canoes produced and sold.) a. Write the cost function. C(x) = 24,000 + 100x (Type an expression using x as the variable.) b. Write the revenue function. R(x) = 200x (Type an expression using x as the variable.) c. Determine the break-even point. (Type an ordered pair. Do not use commas in large numbers.)
Answer:
240
Step-by-step explanation:
Given:
The cost function for canoes, c(x) = 24,000 + 100x
Revenue function for canoes, R(x) = 200x
here, x is the number of canoes sold
Fixed cost = $24,000
Cost of production = $100
now at break even point, Revenue = cost
thus,
200x = 24,000 + 100x
or
100x = 24,000
or
x = 240 canoes
Hence, at breakeven, the number of canoes sold is 240
If you roll one die and flip one coin, does the occurrence of a particular outcome on the die affect the probability of a particular outcome on the coin? Why or why not?
Answer:
No, because these events are independent.
Step-by-step explanation:
When we roll one die (a fair die), we will have outcomes in the numbers from 1 to 6.
And when we flip a coin, we will have either a heads or a tails.
Now these two events are independent events as the occurrence of any result in one event is not affecting the result of second event,
Hence, these two are independent events. So, the answer is no, the occurrence of a particular outcome on the die will not affect the probability of a particular outcome on the coin.
Final answer:
The outcomes of a die roll and a coin toss are independent events, meaning the result of the die does not affect the result of the coin toss.
Explanation:
The occurrence of a particular outcome on the die does not affect the probability of a particular outcome on the coin because each event is independent of the other.
For example, if you roll a die and flip a coin, the result of the die does not influence the result of the coin toss as they are separate events.
Additionally, the concept of independence in probability states that the outcomes of the coin toss and die roll do not impact each other.
TRUE OR FALSE. The carrying capacity of Earth can be determined accurately without any ambiguity.
Answer:
false
Step-by-step explanation:
Matrices A and B are square matrices of the same size. Prove Tr(c(A + B)) = C (Tr(A) + Tr(B)).
Answer with Step-by-step explanation:
We are given that two matrices A and B are square matrices of the same size.
We have to prove that
Tr(C(A+B)=C(Tr(A)+Tr(B))
Where C is constant
We know that tr A=Sum of diagonal elements of A
Therefore,
Tr(A)=Sum of diagonal elements of A
Tr(B)=Sum of diagonal elements of B
C(Tr(A))=[tex]C\cdot[/tex] Sum of diagonal elements of A
C(Tr(B))=[tex]C\cdot[/tex] Sum of diagonal elements of B
[tex]C(A+B)=C\cdot (A+B)[/tex]
Tr(C(A+B)=Sum of diagonal elements of (C(A+B))
Suppose ,A=[tex]\left[\begin{array}{ccc}1&0\\1&1\end{array}\right][/tex]
B=[tex]\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex]
Tr(A)=1+1=2
Tr(B)=1+1=2
C(Tr(A)+Tr(B))=C(2+2)=4C
A+B=[tex]\left[\begin{array}{ccc}1&0\\1&1\end{array}\right]+\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex]
A+B=[tex]\left[\begin{array}{ccc}2&1\\2&2\end{array}\right][/tex]
C(A+B)=[tex]\left[\begin{array}{ccc}2C&C\\2C&2C\end{array}\right][/tex]
Tr(C(A+B))=2C+2C=4C
Hence, Tr(C(A+B)=C(Tr(A)+Tr(B))
Hence, proved.
what‘s -x if x is -4? is it 4 or -4?
Answer:
If x = -4, then -x = 4.
Step-by-step explanation:
The procedure for answering this question is straightforward, you just have to substitute the value of x, when you write -x:
If x = -4, then -x = -(-4) = 4 (remember the law of signs)
Therefore: -x = 4.
It actually holds for any real number.
The square matrix A is called orthogonal provided
thatAT=A-1. Show that the determinant of such
amatrix must be either +1 or -1.
Answer: The proof is done below.
Step-by-step explanation: Given that the square matrix A is called orthogonal provided that [tex]A^T=A^{-1}.[/tex]
We are to show that the determinant of such a matrix is either +1 or -1.
We will be using the following result :
[tex]|A^{-1}|=\dfrac{1}{|A|}.[/tex]
Given that, for matrix A,
[tex]A^T=A^{-1}.[/tex]
Taking determinant of the matrices on both sides of the above equation, we get
[tex]|A^T|=|A^{-1}|\\\\\Rightarrow |A|=\dfrac{1}{|A|}~~~~~~~~~~~~~~~~~~~~[\textup{since A and its transpose have same determinant}]\\\\\\\Rightarrow |A|^2=1\\\\\Rightarrow |A|=\pm1~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}][/tex]
Thus, the determinant of matrix A is either +1 or -1.
Hence showed.
Convert the following to rational numbers: (a) 0.12345, (b) 5.4321.
Answer:
A) [tex]\frac{2469}{20000}[/tex]
B) [tex]\frac{54321}{100000}[/tex]
Step-by-step explanation:
To answer this question first we define what are rational numbers.
A rational number is a number that can be expressed in the form of a fraction [tex]\frac{x}{y}[/tex], where x and y are integers and y ≠ 0.
a) 0.12345
This can be written in fraction form as
[tex]\frac{12345}{100000}[/tex]
Now, we simplify this fraction to lowest form. Simplified form of the above fraction is [tex]\frac{2469}{20000}[/tex]. This simplified form was obtained by dividing both numerator an denominator by 5.
b) This number can be written in fraction form as [tex]\frac{54321}{100000}[/tex]
Now, we simplify this fraction.
The simplified form of the above fraction is [tex]\frac{54321}{100000}[/tex] as the numerator and denominator have no common factor.
A frequency polygon having a peak in the center of its distribution is:
symmetric
skewed
kurtosis
a histogram
Which of the following is a true statement regarding the mode?
The mean, median, and mode may be the same value.
The mode is equal to the second quartile, Q2.
A dataset cannot have more than one mode.
The mode is the tallest bar in a histogram.
A measure of spread which magnifies the effect of values far from the mean is the:
median
interquartile range
variance
mode
In Chap4 Practice Exercise Prob #5, the histogram interval width is:
20 units
400
6 classes
Answer:
(a) symmetric
(b) The mean, median, and mode may be the same value.
and, The mode is the tallest bar in a histogram.
(c) variance
Step-by-step explanation:
Data is said to be symmetric if it is not skewed. i.e. if it has peaked at the center of the distribution.
Skewness gives us an idea about the shape of the curve.
Kurtosis enables us to have an idea about the flatness and peakedness of the frequency.
Mode represents the highest repetition of the observation.
The mean, median, and mode can have the same value.
The histogram represents the frequency of observation by the length of the bar this is the same as Mode. Thus, the mode is the tallest bar in a histogram.
Variance is the square of standard deviation and it is defined as, the sum of the square of the distance of an observation from the mean.
So, Variance is the correct option.
Linear Algebra Question
The general equation for a circle is
a(x2+y2)+bx+cy+d=0.
There is exactly one circle passing through the points (2,3),(−3,2), and (0,0). Find an equation for this circle.
To find the specific circle passing through points (2,3), (-3,2), and (0,0), we started by substituting these coordinates in the general circle equation. This gave us a system of equations, which when solved, resulted in the coefficients for the circle equation. The equation of the circle we were seeking is (x^2 + y^2)/13 - (3x/32) + (15y/32) = 0.
Explanation:In order to find the equation for a specific circle we need to plugin the coordinates for (x, y) in the general equation a(x^2+ y^2) + bx + cy + d = 0 which represent three points on the circle. Let's start to solve this system using the points (2,3), (−3,2), and (0,0).
First, let's plug in (2,3) in general equation: 13a + 2b + 3c + d = 0Second, we will plugin (−3,2): 13a - 3b + 2c + d = 0Lastly, we will use the point (0,0): 0 = dNow, we have a system of three equations with three variables that we can solve. By subtracting the second from the first to eliminate d and simplifying, we obtain 5b + c = 0. Substituting d = 0 into the first and second equations, we get 13a + 2b + 3c = 0 and 13a - 3b + 2c = 0. Solving this system gives a = 1/13, b = -3/32 and c = 15/32.
Therefore, the equation of the circle is (x^2 + y^2)/13 - (3x/32) + (15y/32) = 0.
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Set P = {x, 4, 6, 10, -2, x, 6, 1, x} In set P, if the value of x is 4 greater than the largest numerical value present, what is the range of the set?
Answer:
16.
Step-by-step explanation:
The largest numerical value present in the set P is 10, then x is 4+10 = 14. Then the set P is
P = {14, 4, 6, 10, -2, 14, 6, 1, 14}.
Now, the range is the difference between the greatest and the smallest element in the set. The greatest number is 14 and the smallest is -2, then the range is
14-(-2) = 14+2 = 16.
Then the range of the set P is 16.
in the following ordinary annuity interest is compounded with each payment and the payment is made at the end of the compounding period. find the accumulated amount of the annuity. 4,500 annually at 6% for 10 years
Answer: $59313.58
Step-by-step explanation:
Formula to find the accumulated amount of the annuity is given by :-
[tex]FV=A(\frac{(1+\frac{r}{m})^{mt})-1}{\frac{r}{m}})[/tex]
, where A is the annuity payment deposit, r is annual interest rate , t is time in years and m is number of periods.
Given : m= $2000 ; m= 1 [∵ its annual] ; t= 10 years ; r= 0.06
Now substitute all these value in the formula , we get
[tex]FV=(4500)(\frac{(1+\frac{0.06}{1})^{1\times10})-1}{\frac{0.06}{1}})[/tex]
⇒ [tex]FV=(4500)(\frac{(1.06)^{10})-1}{0.06})[/tex]
⇒ [tex]FV=(4500)(\frac{0.79084769654}{0.06})[/tex]
⇒ [tex]FV=(4500)(13.1807949423)[/tex]
⇒ [tex]FV=59313.5772407\approx59313.58 \ \ \text{ [Rounded to the nearest cent]}[/tex]
Hence, the accumulated amount of the annuity= $59313.58
Baytown Village Stone Creations is making a custom stone bench. the recommended height for the bench is 18 in. the depth of the stone bench is 3 3/8 in. Each of the two supporting legs is made up of three stacked stones. Two of the stones measure 3 1/2in. and 5 1/4 in. how much must the third stone measure?
Answer:
x = tex]5\frac{\textup{7}}{\textup{8}}\ in[/tex]
Step-by-step explanation:
Given:
Total height of the bench = 18 in
Depth of the stone bench = [tex]3\frac{\textup{3}}{\textup{8}}\ in[/tex] = [tex]\frac{\textup{27}}{\textup{8}}\ in[/tex] = 3.375 in
Measure of stones = [tex]3\frac{\textup{1}}{\textup{2}}\ in[/tex] = [tex]\frac{\textup{7}}{\textup{2}}\ in[/tex] = 3.5 in
measure of another stone = [tex]5\frac{\textup{1}}{\textup{4}}\ in[/tex] = [tex]\frac{\textup{21}}{\textup{4}}\ in[/tex] = 5.25 in
let the height of the third stone be 'x'
Now,
The total height of the bench = depth of bench + Measure of two stones + x
18 = 3.375 + 3.5 + 5.25 + x
or
x = 18 - 12.125
or
x = 5.875 in
or
x = tex]5\frac{\textup{7}}{\textup{8}}\ in[/tex]
Sketch the Cartesian product on the x-y plane R^2: Zx Z.
Answer:
[tex]\mathbb{Z}\times \mathbb{Z}=\{(a,b)\lvert a, b\in \mathbb{Z}\}[/tex]
Step-by-step explanation:
In general, the Cartesian product of two sets [tex]A,B[/tex] is a new set defined by
[tex]A\times B=\{(a,b)\lvert a\in A,b\in B\}[/tex]
The pair [tex](a,b)[/tex] is ordered pair because the order is important, that is to say, in general [tex](a,b)\neq (b,a)[/tex].
One of the most important Cartesian products in mathematics is [tex]\mathbb{R}\times \mathbb{R}=\{(x,y) \lvert x,y \in \mathbb{R}\}[/tex] which is precisely the Cartesian Plane xy. The set [tex]\mathbb{Z}\times \mathbb{Z}[/tex] is a subset of [tex]\mathbb{R}\times \mathbb{R}[/tex] which is the set of all the points in the Cartesian plane whose coordinates are integers numbers. So, sketching the set [tex]\mathbb{Z}\times \mathbb{Z}[/tex] we have a picture as the shown below.
Find the distance between the origin and the point R = (9,7,8). The distance is: Ensure that you use at least 4 decimal place accuracy or exact values
Answer:
The distance between the origin and the given point is 13.9283 units.
Step-by-step explanation:
The coordinates of origin are (0,0,0)
We are given a point R(9,7,80
The distance formula:
[tex]\sqrt{(y_1 -x_1)^2 + (y_2 -x_2)^2 + (y_3 -x_3)^2}[/tex], where [tex](x_1, x_2, x_3)[/tex] are coordinates of one point and [tex](y_1, y_2, y_3)[/tex] are coordinates of other point.
Putting the values as:
[tex]y_1 = 9, y_2 = 7, y_3 = 8\\x_1 =0, x_2 = 0, x_3 = 0[/tex]
We get d = [tex]\sqrt{81 + 64 + 49}[/tex]
d = [tex]\sqrt{194}[/tex]
d = 13.9283
Thus, the distance between the origin and the given point is 13.9283 units.
A jar of marbles contains the following: two red marbles, three white marbles, five blue marbles, and seven green marbles.
What is the probability of selecting a red marble from a jar of marbles?
5/17
2/15
2/17
17/2
The probability of selecting a red marble from the jar of marbles is 2/17.
To calculate the probability of selecting a red marble from the jar, we need to determine the total number of marbles in the jar and the number of red marbles.
Total number of marbles = 2 (red) + 3 (white) + 5 (blue) + 7 (green) = 17
Number of red marbles = 2
Now, the probability of selecting a red marble is given by:
Probability = (Number of red marbles) / (Total number of marbles) = 2 / 17
So, the correct probability of selecting a red marble from the jar is 2/17.
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Final answer:
The probability of selecting a red marble from the jar is [tex]\frac{2}{17}[/tex] since there are 2 red marbles out of a total of 17 marbles.
Explanation:
The probability of selecting a red marble from a jar of marbles containing two red marbles, three white marbles, five blue marbles, and seven green marbles can be calculated by dividing the number of red marbles by the total number of marbles in the jar. First, we determine the total number of marbles: 2 (red) + 3 (white) + 5 (blue) + 7 (green) = 17 marbles. Next, we calculate the probability of selecting a red marble by dividing the number of red marbles (2) by the total (17).
Therefore, the probability of selecting a red marble is [tex]\frac{2}{17}[/tex].
If a is an integer, prove that (14a + 3, 21a + 4) = 1.
Answer:
(14a+3, 21+4) = 1
Step-by-step explanation:
We are going to use the Euclidean Algorithm to prove that these two integers have a gcd of 1.
gcd (14a + 3, 21a + 4) = gcd (14a+3, 7a + 1) = gcd (1, 7a+1) = 1
Therefore,
(14a + 3, 21a + 4) = 1
An article reports "attendance increased 5% this year, to 4948." What was the attendance before the increase? (Round your answer to the nearest whole number.)
Answer: The attendance before the increase was 4712.
Step-by-step explanation:
Let the attendance before the increase be 'x'.
Rate of increment = 5%
so, Attendance after increment becomes
[tex]\dfrac{100+5}{100}\times x = 4948\\\\\dfrac{105}{100}\times x=4948\\\\1.05\times x=4948\\\\x=\dfrac{4948}{1.05}\\\\x=4712.38\\\\x=4712[/tex]
Hence, the attendance before the increase was 4712.
Final answer:
To find the original attendance, an equation was formulated where the original attendance (x) increased by 5% equals 4,948. By solving for x, the original attendance before the increase was determined to be approximately 4,712 when rounded to the nearest whole number.
Explanation:
The question asks to find the original attendance before a 5% increase that resulted in a final attendance of 4,948. To calculate the initial attendance, you can set up an equation where the original attendance (which we will call 'x') plus 5% of the original attendance equals the final attendance (4,948).
This can be expressed algebraically as:
x + 0.05x = 4948
Solving for x gives you:
1.05x = 4948
x = 4948 / 1.05
x = 4,712 (rounded to the nearest whole number)
Therefore, the attendance before the increase was approximately 4,712.
A bird flies from its nest (528 1/5) to the bottom of the canyon (-89 3/5). How far did the bird fly?
same as before here, the bird is up above and from there goes down, so we sum up both amounts.
[tex]\bf \stackrel{mixed}{528\frac{1}{5}}\implies \cfrac{528\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{2641}{5}}~\hfill \stackrel{mixed}{89\frac{3}{5}}\implies \cfrac{89\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{448}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2641}{5}+\cfrac{448}{5}\implies \stackrel{\textit{using an LCD of 5}}{\cfrac{(1)2641+(1)448}{5}}\implies \cfrac{3089}{5}\implies 617\frac{4}{5}[/tex]
Answer:
[tex]617\frac{4}{5}[/tex]
Step-by-step explanation:
We have been given that a bird flies from its nest [tex]528\frac{1}{5}[/tex] to the bottom of the canyon [tex]-89\frac{3}{5}[/tex].
First of all, we will convert both mixed fractions into improper fraction.
[tex]528\frac{1}{5}\Rightarrow \frac{2640+1}{5}=\frac{2641}{5}[/tex]
[tex]89\frac{3}{5}\Rightarrow \frac{445+3}{5}=\frac{448}{5}[/tex]
To solve our given problem, we will find difference of both elevations as:
[tex]\frac{2641}{5}-(-\frac{448}{5})[/tex]
[tex]\frac{2641}{5}+\frac{448}{5}[/tex]
[tex]\frac{2641+448}{5}[/tex]
[tex]\frac{3089}{5}[/tex]
[tex]617\frac{4}{5}[/tex]
Therefore, the bird flown [tex]617\frac{4}{5}[/tex] units.
Suppose that A, B, and C are invertible matrices of the same
size,Show that the product ABC is invertible and that
(ABC)-1= C-1B-1A-1.
Answer:
Step-by-step explanation:
Given that t A, B, and C are invertible matrices of the same
size.
To pr that [tex](ABC)^{-1} = C^{-1}B^{-1}A^{-1}.[/tex]
to pr that [tex]( ABC) (C^{-1}B^{-1}A^{-1})=e[/tex]
LS=[tex]( AB(C (C^{-1})B^{-1}A^{-1})\\=ABIB^{-1}A^{-1})\\=A(BB^{-1})A^{-1})\\=AA^{-1})\\=I[/tex]
Thus proved
To show that the product of invertible matrices A, B, and C (ABC) is invertible and that its inverse is (ABC)-1 = C-1B-1A-1, we use the property that the inverse of a product is the product of inverses in reverse order, and the associativity of matrix multiplication.
Explanation:A student asked to show that if A, B, and C are invertible matrices of the same size, the product ABC is invertible, and that the inverse of this product is (ABC)-1 = C-1B-1A-1.
To prove this, we can use the properties of matrix multiplication and inverses:
First, we confirm that the product of two invertible matrices is itself invertible, and the inverse is given by the product of their inverses in reverse order. This is due to the property that (AB)-1 = B-1A-1.Using associativity, we have the combined product (AB)C. Since AB is invertible, by the first point, we can consider (AB)C as a product of two invertible matrices, (AB) and C.Therefore, ((AB)C)-1 = C-1(AB)-1 = C-1B-1A-1, as required.This completes the proof that the product ABC is invertible and its inverse is C-1B-1A-1
Mr Cosgrove is comparing movie rentals deals. Netflix charge a flat rate of $8.50 Blockbuster charge $4.50 plus a $0.50 per movie after how many movie rental with the cost of two stores be the same
Answer:
8 rental movies will make the costs of the two stores be the same
Step-by-step explanation:
- Mr Cosgrove is comparing movie rentals deals
- Netflix charge a flat rate of $8.50
- Blockbuster charge $4.50 plus a $0.50 per movie
- We need to find how many movie rental make the costs of the two
stores will be the same
- Assume that the number of rental movies is m
∵ Blockbuster charge $4.50 plus a $0.50 per movie
∴ Blockbuster cost = 4.50 + 0.50 m
∵ The cost of Netflix = 8.50
- Equate the two costs to find the number of the rental movies
∵ 4.50 + 0.50 m = 8.50
- Subtract 4.50 from both sides
∴ 0.50 m = 4
- Divide both sides by 0.50
∴ m = 8 movies
8 rental movies will make the costs of the two stores be the same
I need help with how to "Create a column vector from 15 to -25 with a step size of 5"
Answer:
Your column vector is:
[tex]\left[\begin{array}{c}15&10&5&0&-5&-10&-15&-20&-25\end{array}\right][/tex]
Step-by-step explanation:
The first step to solve your problem is knowing what is a column vector:
A column vector is a matrix that only has one column, and multiple rows.
The problem wants the vector to range from 15 to -25.
It means that the biggest value in the vector is 15, and the smallest is -25. Since it is from 15 to -25, the first element of your column vector is 15, and the last element is -25.
With a step size of 5
At each element, you decrease 5. So you have: 15,10,..,-20,-25.
The vector is:
[tex]\left[\begin{array}{c}15&10&5&0&-5&-10&-15&-20&-25\end{array}\right][/tex]
A survey was conducted among 78 patients admitted to a hospital cardiac unit during a two-week period. The data of the survey are shown below. Let B equals the set of patients with high blood pressure. Let C equals the set of patients with high cholesterol levels. Let S equals the set of patients who smoke cigarettes.n(B) equals 36 n(B intersect S) equals 10 n(C) equals 34 n(B intersect C) equals 12 n(S) equals 30 n(B intersect C intersectS) equals 5 n[(B intersect C) union (B intersect S) union (C intersect S)] equals 21
Sets and set operations are ways of organizing, classifying and obtaining information about objects according to the characteristics they possess, as objects generally have several characteristics, the same object can belong to several sets, an example is the subjects of a school , where students (objects) are classified according to the subject they study (set).
The intersection of sets is a new set consisting of those objects that simultaneously possess the characteristics of each intersected set, the intersection of two subjects will be those students who have both subjects enrolled.
The union of sets is a new set consisting of all the objects belonging to the united sets, the union of two subjects will be all students of both courses.
In this case there are three sets B, C and S of which we are given the following information:
Answer
n(BꓵSꓵC)=5
n(BꓵS)=10 – 5 = 5
n(BꓵC)=12 – 5 = 7
n[(BꓵC)ꓴ(BꓵS)ꓴ(CꓵS)]=21 – 5 – 5 – 7 = 4
n(B)=36 – 5 – 5 – 7 = 19
n(S)=30 – 5 – 5 – 4 = 16
n(C)=34 – 5 – 7 – 4 = 18
The demand equation for kitchen ovens is given by the equation
D(q) = –338q + 4,634
where D(q) is the price in dollars and q is the number of kitchen ovens demanded per week. The supply equation for kitchen ovens is
S(q) = 400q^2 + 20
where q is the quantity the supplier will make available per week in the market when the price is p dollars. Find the equilibrium point (q, p) rounded to the nearest hundredth.
Answer:
The equilibrium point is (3, 3620)
Step-by-step explanation:
We set the supply and the demand equation equal to each other and solve:
[tex]-338q+4634=400q^2+20\\400q^2+338q-4614=0[/tex]
We can solve by factoring:
[tex]2(q-3)(200q+769)=0[/tex]
Setting each factor equal to zero we get:
[tex]q=3\text{ or }q=\displaystyle-\frac{769}{200}[/tex]
Only a positive quantity makes sense, so q=3 is the equilibrium quantity.
To get the equilibrium price we just plug 3 in place of q in any of the functions. Let us use the demand function which is easier to handle:
[tex]D(3)=-338(3)+4634=3620[/tex]
Therefore the equilibrium price is p=3620
In ordered pair form the equilibrium point is (3, 3620)
You have a plate of 50 cookies. Ten have chocolate chips and 14 have pecans. On the cookies mentioned in the preceding sentence, 6 have both chocolate chips and pecans. You select a cookie at random. What is the probability that your cookie has chocolate chips or pecans
The probability of selecting a cookie with either chocolate chips or pecans from a plate of 50 cookies is 36%.
The question asks about the probability of selecting a cookie with either chocolate chips or pecans from a plate of 50 cookies, with some overlapping flavors. Given the information:
Total cookies: 50
Chocolate chip cookies: 10
Pecan cookies: 14
Cookies with both flavors: 6
To calculate the probability of choosing a cookie with either chocolate chips or pecans (or both), we can use the formula:
P(C OR N) = P(C) + P(N) \'u2013 P(C AND N)
where:
P(C) is the probability of choosing a chocolate chip cookie,
P(N) is the probability of choosing a pecan cookie, and
P(C AND N) is the probability of choosing a cookie with both flavors.
Thus:
P(C) = 10/50 = 0.20,
P(N) = 14/50 = 0.28, and
P(C AND N) = 6/50 = 0.12.
Therefore:
P(C OR N) = 0.20 + 0.28 - 0.12 = 0.36 or 36%.
This is the probability that a randomly selected cookie from the plate will have either chocolate chips, pecans, or both.
Gary buys a 31/2 pound bag of cat food every 3 weeks.Gary feeds his cat the same amount of food each day.Write a numeric expression and solve to determine the number of pounds of cat food his cat eats each year?(year=52weeks)
Answer:
[tex]52\times \frac{7}{6}[/tex]
[tex]60\frac{2}{3}\text{ pounds}[/tex]
Step-by-step explanation:
Given,
The total pounds eaten by cat in 3 weeks = [tex]3\frac{1}{2}[/tex]= [tex]\frac{7}{2}[/tex]
∵ Each day the pounds of eaten is same,
⇒ Total pounds eaten in each week = [tex]\frac{7}{6}[/tex]
∵ 1 year = 52 weeks,
So, the pounds eaten in 52 weeks or 1 year = 52 × pounds eaten in each week
= 52 × [tex]\frac{7}{6}[/tex]
Which is the required expression,
By solving it,
The number of pounds eaten by cat in a year
[tex]=\frac{364}{6}[/tex]
[tex]=60\frac{2}{3}[/tex]
Two percent of all seniors in a class of 50 have scored above 96% on an ext exam, which of the following is the number of seniors who scored above 96%? O 10
Answer:
The number of seniors who scored above 96% is 1.
Step-by-step explanation:
Consider the provided information.
Two percent of all seniors in a class of 50 have scored above 96% on an ext exam.
Now we need to find the number of seniors who scored above 96%
For this we need to find the two percent of 50.
2% of 50 can be calculated as:
[tex]\frac{2}{100}\times50[/tex]
[tex]\frac{100}{100}[/tex]
[tex]1[/tex]
Hence, the number of seniors who scored above 96% is 1.