The system does not have a periodic solution in each of 10 and 11.
A solution of the period depends on the independent variable t is called Periodic Solution. For a periodic solution x(t)( in the case of a system, x is a vector), there is a number T≠0 such that
x(t+T)=x(t) for t∈R.
The given equations are:
[tex]\frac{dx}{dt} =-2x-3y-xy^2\\\\\frac{dx}{dt} =y+x^3+x^2y[/tex]
F is the derivative of dx/dt and Gis the derivative of dy/dt:
[tex]F(x,y)=-2x-3y-xy^2\\G(x,y)=y+x^3+x^2y[/tex]
When Fx+Gx has the same sign on the entire domain D, then there are no periodic solutions on the domain D.
Fx+Gx=-2-y^2+1-x^2
=-1-y^2-x^2
<for all real numbers x,y[tex]\neq[/tex]0
Fx+Gx have the same sign for all pairs of real numbers with x[tex]\neq[/tex]0 and y[tex]\neq[/tex]0
Thus, there are no periodic solutions in the system(excluding contact solutions)
Hence proved.
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Lines that intersect at 90º are skew lines.
False
True
Answer:
False
Step-by-step explanation:
Lines that intersect at 90 degrees are called perpendicular lines.
Skew lines do not intercept.
Customers depart from a bookstore according to a Poisson process with rate A per hour Each customer buys a book with probability p, independent of everything else. Find the distribution of the time until the first sale of a book. Find the probability that no books are sold during a particular hour. Find the expected number of customers who buy a book during a particular hour.
The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].
The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]
As per the details share in the above question are as follow,
Poisson process with a rate λ per hour
While customer buys a book with probability p
First we have to find the distribution of the time until the first sale of a book.
Second to find the probability that no books are sold during a particular hour.
Third to find the expected number of customers who buy a book during a particular hour.
Giving the duration till a book sells its first copy
Consider,
Following are some instances of waiting times,
[tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
Now, to calculate the likelihood that no books will be sold at a specific time.
[tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex]
The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].
Consider the Poisson distribution to determine the anticipated number of book purchases during a specific hour.
[tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]
The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex].
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If the distance between points P(3.a) and Q(3, 1) is 4 units then find the value of a.)
Answer:
a = -3
Step-by-step explanation:
The explanation is in the image
what is the answer. a b c or d
all can be the answer I guess
kari is thinking about buying a laptop that cost $750 on sale if the sales tax is 7.5% how much money will she need in total to buy the computer
Answer: 806.25
Step-by-step explanation: First, we need to find how much the sales tax is worth in dollars. Recall the formula:
Worth = Wole number x part percent / 100
Now, plug in the numbers:
Worth = 750 x 7.5 / 100
So, 750 x 7.5 = 5625
So, 5625 / 10 = 56.25
But remember, $56.25 is the amount of the SALES TAX. To find the total, we need to add 56.25 to 750. So,
750 + 56.25 = 806.25
Therefore, $806.25 is the TOTAL AMOUNT she needs to pay.
Which inequality is true when z = 9
When x = 9, the inequality - 4 + x ≤ 9 has the necessary value.
What is meant by inequality?In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Mathematics that contains at least two terms with variables or integers that are not equal is referred to as being unequal.
Inequality, two integers or algebraic expressions with a declared order link (greater than, greater than, or equal to, less than, or less than or equal to).
As per option (B),
When substituting the values the equation -4 + 9 is less than or equal to 5.
-4 + 9 is 5 so this equation is true
The required value of inequality - 4 + x ≤ 9 is true when x = 9,
Therefore, the correct answer is option (B) -4 + x ≤ 5.
The complete question is:
Which inequality is true when x = 9?
A) 4 - x ≥ 5
B) -4 + x ≤ 5
C) 4 + x ≤ 5
D) -4 - x ≥ 5
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Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
What is the probability that a randomly selected bike is green given that the bike has bike tires?
Simplify any fractions.
The probability that a randomly selected bike is green given that the bike has road bike tires is 0.66
Given :
Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event .
From the table given :
Total number of 6 road bikes = 4
Total road bikes = 2 + 4 = 6
Probability = 4 / 6
= 2 / 3
= 0.66
Hence the probability that a randomly selected bike is green given that the bike has road bike tires is 0.66 .
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ANSWER PLEASE! DEADLINE 11:00 45+ POINTS
1.
The list represents the number of students who left school early in a 12-day period.
48, 62, 75, 43, 32, 52, 70, 63, 81, 40, 38, 67
Find the mean and interpret its meaning as it relates to the number of students who left school early.
2. The ages of a group of teachers are listed.
25, 32, 33, 35, 41, 43, 45, 48, 52, 55, 60, 62
If another teacher with an age of 45 is added to the data, how would the mean be impacted?
THANKS! ANSWER FAST!
Answer: To find the mean of the number of students who left school early, we must add all of the numbers together and then divide the sum by the number of days.
48 + 62 + 75 + 43 + 32 + 52 + 70 + 63 + 81 + 40 + 38 + 67 = 671
The mean of the number of students who left school early is 56.75 (671 / 12).
This mean represents the average number of students who left school early each day over the 12-day period. It tells us that on average, about 56.75 students left school early each day.
Step-by-step explanation: 2. The mean of the group of teachers' ages is currently (25+32+33+35+41+43+45+48+52+55+60+62)/12=45.5. If another teacher with an age of 45 is added to the data, the mean will be (25+32+33+35+41+43+45+45+48+52+55+60+62)/13=44.5. The mean will be slightly lower, as the additional value of 45 is being added to the sum, but the number of values being averaged is also increasing by 1.
3x-12=2x+7 subtract 7 from both sides and subtract 3x from both sides
x=19
According to question,
3x-12=2x+7
Subtracting 7 from both sides
3x-12-7=2x+7-7
⇒3x-19=2x
Subtracting 3x from both sides
3x-19-3x=2x-3x
⇒-19=-x
⇒x=19
∴The value of x is 19.
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The complete question is Find the value of x in the equation 3x-12=2x+7 when 7 and 3x is subtracted from both sides.
The functions f and g are defined by the following tables:
Function
Find the following composition of two functions: (f o g)(0) and (g o f)(1).
Write the appropriate formula(s). What is the domain of the function g(x) ? What is the range of the function f(x) ?
The following composition of two functions ( f o g ) ( 0 ) = 1 and ( g o f ) ( 1 ) = 1 .
Given :
The functions f and g are defined by the following tables:
Tables :
x -2 -1 0 1
f ( x ) 1 2 1 0
x 1 -3 0 -4
g ( x ) -2 0 1 5
( f o g ) ( 0 ) = ( f ( g ( 0 ) )
from the table g ( 0 ) = 1
= ( f ( 0 ) )
= 1
( g o f ) ( 1 ) = ( g ( f ( 1 ) )
= ( g ( 0 ) )
= 1
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enter the letters of the points that satisfy the inequalities \[y > -\frac{1}{2} x 2 \quad \text{and} \quad 2x y \le 8.\]
An inequality is a mathematical statement that compares two expressions using an inequality symbol. In this case, we have two inequalities that involve the variables \(x\) and \(y\): \(y > -\frac{1}{2} x 2\) and \(2x y \le 8\).
To find the points that satisfy these two inequalities, we must first solve for both \(x\) and \(y\).
To find the points that satisfy the first inequality, we can solve for \(y\) and substitute it into the second inequality:
\[y > -\frac{1}{2} x 2 \implies y = -\frac{1}{2} x 2 + k \quad \text{where} \quad k > 0\]
\[2x (-\frac{1}{2} x 2 + k) \le 8 \implies x^2 - 4x + 8 \le 0\]
Solving for \(x\) yields two solutions: \(x = 2 \pm \sqrt{2}\). To find the points that satisfy both inequalities, we must test both of these solutions in the original inequalities. For \(x = 2 + \sqrt{2}\), we have:
\[y > -\frac{1}{2} \cdot (2 + \sqrt{2}) \cdot 2 \implies y > 4 - 4\sqrt{2}\]
\[2 \cdot (2 + \sqrt{2}) \cdot y \le 8 \implies 8 + 8\sqrt{2} \le 8 \quad \text{which is true}\]
Therefore, the point \((2 + \sqrt{2}, 4 - 4\sqrt{2})\) satisfies both inequalities. For \(x = 2 - \sqrt{2}\), we have:
\[y > -\frac{1}{2} \cdot (2 - \sqrt{2}) \cdot 2 \implies y > 4 + 4\sqrt{2}\]
\[2 \cdot (2 - \sqrt{2}) \cdot y \le 8 \implies 8 - 8\sqrt{2} \le 8 \quad \text{which is true}\]
Therefore, the point \((2 - \sqrt{2}, 4 + 4\sqrt{2})\) also satisfies both inequalities.
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PLEASE HURRY PLEASE I WILL GIVE BRAINLYIST Your friend just returned to the United States from their trip to Nepal and wants to exchange their 9,576 Nepalese rupees for U.S. dollars.
How many dollars will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees?
$11.69
$85.50
$95.76
$107.25
There are $85.50 will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees.
What is convertibility of rupee?
Convertibility is the simplicity with which a national currency can be changed into gold or another asset through international exchanges. The rupee is a partially convertible currency in India; while smaller amounts can be exchanged at market rates, larger ones require permission.
Given:
Your friend just returned to the United States from their trip to Nepal and wants to exchange their 9,576 Nepalese rupees for U.S. dollars.
Since,
1 U.S dollar = 112 Nepalese rupees
Suppose x be the U.S dollars for 9576 Nepalese rupees.
So,
x = 9576/112 = 85.5
Hence, there are $85.50 will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees.
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ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of vegetables contains eight tomato and six carrots, the tomato-to-carrot ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of carrots to tomato is 6:8 (or 3:4), while the proportion of tomato to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive.
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
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hw11.3. projection onto a subspace consider the subspace of spanned by the orthogonal vectors let . compute the orthogonal projecti
The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
What is Projectile Motion ?An item or particle that is projected in a gravitational field, such as from the surface of the Earth, and moves along a curved route while solely being affected by gravity is said to be in projectile motion.
According to the given information
Given, [tex]$\quad b_1=\left[\begin{array}{c}2 \\ 2 \\ -2\end{array}\right], \quad b_2=\left[\begin{array}{l}2 \\ 0 \\ 2\end{array}\right], \quad w=\left[\begin{array}{c}-2 \\ 1 \\ -1\end{array}\right]$[/tex]
We know,
[tex]Proj_{v}(w)[/tex] = [tex]Proj_{b1}(w) + Proj_{b2}[/tex]
[tex]& =\left(\frac{w \cdot b_1}{b_1 \cdot b_1}\right) b_1+\left(\frac{w \cdot b_2}{b_2 \cdot b_2}\right) b_2[/tex]
[tex]w \cdot b_1 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{c}2 \\2 \\-2\end{array}\right][/tex][tex]=-4+2+2=0 \\[/tex]
[tex]w \cdot b_2 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]-4+0-2=-6 \\[/tex]
[tex]b_2 \cdot b_2 &[/tex] =[tex]\left[\begin{array}{c}2 \\0 \\2\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]4+0+4=8[/tex]
Therefore
[tex]Proj_{v}(w)[/tex] = [tex]\left(\frac{0}{b_1 \cdot b_1}\right) b_1+\left(\frac{-6}{8}\right)\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]
[tex]& =0+\frac{-3}{4}\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]
[tex]& =\left[\begin{array}{c}\frac{-3}{2} \\0 \\-3 \\2\end{array}\right] \\[/tex]
[tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
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Sarah budgeted $100 for new art supplies. When Sarah purchased the supplies, she
spend $75. What type of variance does this represent?
PLEASE HELP WILL MARK BARINLIEST
Answer:
Your answer is A.
Step-by-step explanation:
Using the following stem & leaf plot, find the five number summary for the data. View in full window so that you have 6 rows of data.
The five number summary of the data set that is represented in the stem and leaf plot is:
Min: 10.
Q1: 24.
Med: 47
Q3: 56.
Max: 68.
How to Find the Five Number Summary from a Stem and Leaf Plot?To find the five number summary, we need to write out each of the data points given in the stem and leaf plot from the least to the greatest.
Thus, the data set are:
10, 12, 23, 24, 24, 25, 29, 42, 42, 47, 49, 50, 54, 55, 56, 58, 59, 60, 68
Find the middle (median) of the data:
47 is the center of the data set, therefore it is the median of the data.
The minimum value is the least data point, which is 10.
The lower quartile is the center of the first part of the data that is divided by the median, which is 24.
The upper quartile is the center of the second part of the data that is divided by the median, which is 56.
The maximum data value is the largest data point which is, 68.
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The ratings for the ten leading passers in the league for 2009 regular season play are ranked in the table. Construct a box plot for the rating points data. Rank : 1, 2, 3, 4, 5, 6, 7, 8, 9. 10
NFL Passer : A, B, C, D, E, F, G, H, I, J
Rating Points : 93.5, 96.3, 97.9, 98.9, 99.3, 101.1, 103.9, 104.8, 105.1, 109.5 Choose the correct graph below ? A. Q1 -98.9, Q2-1011 Q3-105.1 B. Q1-96.3, Q2-98.9 Q3-101.1 C. Q1 -97.9, Q2-100.2, Q3-104.8
The minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value must all be calculated before we can create a box plot for the rating points data.
The median of the lower and upper halves of the data must be determined in order to determine the first and third quartiles, respectively. The numbers from the minimum to the median make up the lower half of the data, while the values from the median to the highest make up the upper half.
We must first organize the numbers in numerical order: 93.5, 96.3, 97.9, 98.9, 99.3, 101.1, 103.9, 104.8, 105.1, 109.5. This will help us determine the median of the lower half of the data. The lower half's mean, which is (99.3 + 101.1) / 2 = 100.2, is then the average of the fifth and sixth values.
Again, the numbers must be arranged in numerical order to determine the median of the upper half of the data: 93.5, 96.3, 97.9, 98.9, 99.3, 101.1, 103.9, 104.8, 105.1, and 109.5. The average of the sixth and seventh numbers, or (101.1 + 103.9) / 2, equals 102.5, which is the median of the top half.
Following that, Q1 = 100 indicates the first and third quartiles.
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How do you find the general solutions for tanx−3cotx=0?
The general solutions for tanx−3cotx=0 is [tex]\frac{\pi}{3} \text { and } \frac{2 \pi}{3}[/tex]
[tex]\begin{aligned}& \tan x-\frac{3}{\tan x}=0 \\& \tan ^2 x-3=0 \text { (condition } \tan \times \text { not zero) } \\& \tan ^2 x=3 \rightarrow \tan x=\pm \sqrt{3}\end{aligned}[/tex][tex]a. $\tan x=\sqrt{3} \rightarrow x=\frac{\pi}{3}$b. $\tan x=-\sqrt{3} \rightarrow x=\frac{2 \pi}{3}$Extended answers:$$\begin{aligned}& x=\frac{\pi}{3}+k \pi \\& x=\left(2 \frac{\pi}{3}\right)+k \pi\end{aligned}[/tex]
What is the general equation for tan's solution?
Tan + Tan Equals Tan
n Z (i.e., n = 0, 1, 2, 3, etc.), so n = n + n. Therefore, n Z (i.e., n = 0, 1, 2, 3, etc.) is the value for which the general solution of tan = tan is given as = n +. Because cot = 1/tan and cot = 1/tan, the expression cot = cot is identical to tan = tant
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Sophie kicks a football. It’s height in feet is given by h(t) = -16t^2 + 16t where t represents the time in seconds after kick. How many seconds have give by when the football is at it highest point?
Answer:
The time at which the football reaches its highest point is 0.5 seconds.
Step-by-step explanation:
The height of an object thrown into the air is determined by the formula h(t) = -16t^2 + vt + h, where t represents the time in seconds after the object is thrown, v is the initial velocity with which the object is thrown, and h is the initial height from which the object is thrown. In this case, the initial velocity of the object is 16 feet per second and the initial height is 0 feet.
To find the time at which the football reaches its highest point, we need to find the value of t that makes the value of h(t) maximum. This value of t can be found by taking the derivative of the equation h(t) and setting it equal to 0. The derivative of h(t) is given by h'(t) = -32t + 16. Setting h'(t) equal to 0, we get -32t + 16 = 0, which can be solved to get t = 0.5 seconds.
Therefore, the time at which the football reaches its highest point is 0.5 seconds.
the monthly salaries (in thousands of dollars) for a sample of 7 employees of a firm are: 9, 7, 8, 7, 10, 11 and 11. which of the following statements is true about the mean, median and mode?
For the given monthly salaries of the 7 employees of the firm , then the true statement is : (a) mean = median .
In statistics the Mean is defined as sum of a collection of numbers divided by count of numbers .
the given monthly salaries is 9, 7, 8, 7, 10, 11 and 11.
arranging the data in ascending order ,
we get ; 7 , 7 , 8 , 9 , 10 , 11 , 11 .
the sum of the salaries is = 63 ;
So , the mean is = 63/7 = 9 .
median is the middle term of the given data that is = 9 ;
the mode is the most times occurred frequency that is 7 and 11 .
On comparing the mean , mode and median ,
we get ; mean = median .
Therefore , the correct statement is (a) mean = median .
The given question is incomplete , the complete question is
The monthly salaries (in thousands of dollars) for a sample of 7 employees of a firm are: 9, 7, 8, 7, 10, 11 and 11.
Which of the following statements is true about the mean, median and mode ?
(a) mean = median
(b) mode < median < mean
(c) mode < mean < median
(d) mode = median = mode .
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consider two medical tests, a and b, for a virus. test a is 90% effective at recognizing the virus when it is present, but has a 5% false positive rate (indicating that the virus is present, when it is not). test b is 95% effective at recognizing the virus, but has a 10% false positive rate. the two tests use independent methods of identifying the virus. the virus is carried by 2% of all people.Say that a person is tested for the virus using only one of the tests, and that test comes back positive for carrying the virus.Which test returning positive is more indicative of someone really carrying the virus? Justify your answer mathematically (i.e. writing down your calculations).
P(V|B)>P(V|A)
P(V|B)>P(V|A), so Bob is more likely to have virus, however is is still very small probability (only 15%), so in order to confirm illness, he should make one more test.
P(A/V) = 0.95
From the text we can also conclude, that
P(A| V) = 0.1
P(B|V) = 0.9
P(B| V) = 0.5
P(V)= 0.1
What we need to calculate and compare is P( V |A) and P(V|B)
P(V∩A) = P(A) . P(V|A) => P(V|A)
P(V∩A) / P(A)
P(V∩A) means, that Joe has a virus and its detected so.,
P(V∩A) = P(A) . P(V|A) = 0.01 × 0.95
= 0.0095
P(A) is sum of two options: "Joe has virus and it is detected" and "Joe has no virus, but it was mistakenly detected", therefore:
P(A) = P(A) . P(V|A) + P(≈V)
P(A|≈V) = 0.01 . 0.95 + 0.99 . 0.1
= 0.1085
Dividing those 2 numbers we obtain
P(V|A) = 0.0095 / 0.1085
= 0.0875576036
Analogically,
P(V|B) = P(V∩B) / P(B)
= 0.01 . 0.9 / 0.01 . 0.9 + 0.99 . 0.1
= 0.1538461we observe that P(V|B) > P(V|A) ,
so Bob is more likely to have virus, however is is still very small probability (only 15%), so in order to confirm illness, he should make one more test.
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10. Spotify charges x dollars for individual songs and y dollars for entire albums. Person A pays $14.9 A to download 5 individual songs and 1 album. Person B pays $22.95 to download 3 individual songs and 2 albums. How much does Spotify charge to download a song? an entire album?
Spotify charges $0.98 for individual song and $10 for entire album
According to the question,
Spotify charges "x" dollars for individual songs and "y" for entire album
Also, Person A pays $14.9 to download 5 individual songs and 1 album
Which can be written as
=> 5x + y = 14.9 --------------(1)
Person B pays $22.95 to download 3 individual songs and 2 albums
=> 3x + 2y = 22.95 ---------(2)
Solving these two linear equations by elimination method
Multiplying equation (1) by 2
=> 10x + 2y = 29.8
Now, subtracting these equation
10x + 2y - 3x - 2y = 29.8 - 22.95
=> 7x = 6.85
=> x = 0.98
Replacing value of x in equation (1),
=> 5(0.98) + y = 14.9
=> 4.9 + y = 14.9
=> y = 10
Hence , Spotify charges $0.98 for individual song and $10 for entire album
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Hi i need help with this question.
The perimeter of the state of Wyoming, given the rectangle ABCD and the vertices, is 1, 282 miles
How to find the perimeter?The perimeter is the distance around the shape so to find the perimeter of the shape, you need to find the distance between the sides of the rectangle and then add them up.
The distance between vertices can be found by the formula :
= ((x2 – x1)² + (y2 – y1)²)
The distance between AB is therefore 3.65 miles.
The distance between BC is 2.76 miles
The distance between CD is 3.65 miles.
The distance between AD is 2.76 miles
The perimeter of Wyoming is therefore :
= ( 3.65 x 2) + ( 2.76 x 2 )
= 12.82 miles x 100
= 1, 282 miles
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Carlos is going to the amusement park, where he has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money
Carlos will spend is given by the equation y = 2x + 24, where y represents the total
amount of money, in dollars and cents, and a represents the number of rides Carlos goes on. What could the number 24 represent in the equation?
A) The total amount of money Carlos will spend if he goes on o rides.
B) The total amount of money Carlos will spend if he goes on 1 ride.
C) The change in the total amount of money he will spend for every additional ride he goes on.
D) The total amount of money Carlos will spend if he goes on 100 rides.
24 is represents the entry fee in the amusement park.
A. The total amount of money Carlos will spend $24 if he goes on o rides.
B. The total amount of money Carlos will spend $26 if he goes on 1 ride
C. The change in the total amount of money he will spend $2 for every additional ride he goes on.
D. The total amount of money Carlos will spend $224 if he goes on 100 rides.
What is a variable?
Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.
Given equation is y = 2x + 24
24 is represents the entry fee in the amusement park.
where y represents the total amount of money, in dollars and cents, and a represents the number of rides Carlos goes on.
Putting x = 0 in the equation to find the total amount of money Carlos will spend if he goes on o rides:
y = (2 × 0) + 24
y = 24
Putting x = 1 in the equation to find the total amount of money Carlos will spend if he goes on 1 rides:
y = (2 × 1) + 24
y = 2 + 24
y = 26
The change in the total amount of money he will spend for every additional ride he goes on is $26 - 24 = $2
Putting x = 100 in the equation to find the total amount of money Carlos will spend if he goes on 100 rides:
y = (2 × 100) + 24
y = 200 + 24
y = 224
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Find the inverse of y = 5x² - 6.
Answer:
The correct answer is the 3rd option
use the given information to complete the proof of the following theorem. the angles opposite the two congruent sides of an isosceles triangle are congruent.
The angle opposite to the two congruent sides of an isosceles triangle are congruent.
To prove that the angles opposite the two congruent sides of an isosceles triangle are congruent, we can use the following steps:
Draw a diagram of an isosceles triangle with two congruent sides and two corresponding angles opposite these sides. Label the vertices A, B, and C, with B being the vertex opposite the base of the triangle.Since the triangle is isosceles, AB = AC.Since the sides AB and AC are congruent, we can apply the SAS Congruence Theorem to triangles ABC and ACB. This states that if two sides of a triangle are congruent and the included angle is congruent, then the triangles are congruent.Therefore, triangles ABC and ACB are congruent.Since triangles ABC and ACB are congruent, the corresponding angles are congruent. In particular, ∠BAC is congruent to ∠CAB.Therefore, the angles opposite the two congruent sides of an isosceles triangle are congruent.This completes the proof of the theorem
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EXAMPLE 6 The Heaviside function H is defined by
H(t) = {(0 text( if ) t < 0,1 text( if ) t >= 0)
[This function is named after the electrical engineer Oliver Heaviside (1850-1925) and can be used to describe an electric current that is switched on at time t = 0.] Its graph is shown in the figure.
As t approaches 0 from the left, H(t) approaches
. As t approaches 0 from the right, H(t) approaches . Therefore the limit as t approaches 0 of H(t) does not exist.
H(t) = [tex]\left \{ {{0 if t < 0} \atop {1 if t \geq 0}} \right.[/tex]
As t→0 from the left, H(t) approaches 0, as t→0 from right H(t) approaches 1.
From Laplace transformation definition:
L{f(t)} = [tex]\int\limits^\alpha _0 {e^{-st} f(t)} \, dt[/tex]
Given, H(t) = [tex]\left \{ {{0 if t < 0} \atop {1 if t \geq 0}} \right.[/tex]
Then
L{H(t)} = [tex]\int\limits^1_0 {e^{-st} H(t) } \, dt+\int\limits^\alpha _1 {e^{-st} H(t) } \, dt[/tex]
[tex]=\int\limits^1_0 {e^{-st} (0) } \, dt+\int\limits^\alpha _1 {e^{-st} (1) } \, dt[/tex]
[tex]=[\frac{e^{-st} }{-s} ]^{\alpha }_{1}[/tex]
[tex]=\frac{e^{-st} }{s}[/tex]
L{H(t)} =[tex]\frac{e^{-st} }{s}[/tex]
As t→0 from the left, H(t) approaches 0, as t→0 from right H(t) approaches 1.
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a) 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 eighthgrade record is 40.17 feet, and the seventh-grade record is 38 feet 1 3/5 inches? (2
points)
The person that was closest to the state record after the jump is; Alex
How to solve Algebra word problems?We are told that Alex jumped 38 feet 11²/₃ inches or 38.9725 ft and that the eighth-grade record is 40.17 feet.
Let see how closer Alex jumped was;
40.17 feet - 38.9725 ft = 1.2425 ft
We are told that Eric jumped 36.89 feet and the state record of the eighthgrade record is 40.17 feet. Thus;
Let see how closer Eric jumped was;
40.17 feet - 36.89 ft = 3.28 ft
We conclude that 1.2425 ft is less than 3.28 ft and as such Alex was closer.
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Suppose five officials O1, O2, O3 , O4 , O5 are to be assigned five different city
cars: an Escort, a Lexus, a Nissan, a Taurus, and a Volvo. O1 will not drive an
Escort or a Nissan; O 2 will not drive a Taurus; O3 will not drive a Lexus or a
Volvo; O 4 will not drive a Lexus; and O5 will not drive an Escort or a Nissan. If
a feasible assignment of cars is chosen randomly, what is the probability that
(a) O1 gets the Volvo?
(b) O2 or O5 get the Volvo? (Hint: Model this constraint with an altered board.)
(a) The probability that O1 gets the Volvo is 3/10 .
(b) The probability that O2 or O5 will get the Volvo is 1/2 .
In the question ,
it is given that ,
the five officials : O1, O2, O3 , O4 , O5 are to be assigned five different city cars: a Escort, Lexus, Nissan, the Taurus, and the Volvo .
From the given data , the table formed is shown below .
From the table , we can observe that ,
O1 will not drive the Escort or a Nissan . So, he has chance of getting one car among Lexus, Taurus & Volvo = 3 possibilities
O2 will not drive the Taurus . So, he has chance of getting one car among Escort , Nissan ,Lexus, & Volvo = 4 possibilities
O3 will not drive the Lexus or Volvo . So, he has chance of getting one car among Escort , Nissan ,Taurus = 3 possibilities
O4 will not drive the Lexus so he has chance of getting one car among Escort , Nissan ,Taurus, Volvo = 4 possibilities
O5 will not drive the Escort or a Nissan . So, he has chance of getting one car among Lexus, Taurus & Volvo = 3 possibilities .
The 20 possible arrangements for E,L,N,T,V are :
{ (O2, O1, O3, O4, O5), (O2, O1, O3, O5, O4), (O2, O1, O4, O3, O5),
(O2, O5, O3, O1, O4), (O2, O5, O3, O4, O1),(O2, O5, O4, O3, O1),
(O3, O1, O2, O4, O5), (O3, O1, O2, O5, O4), (O3, O1, O4, O5, O2),
(O3, O2, O4, O1, O5), (O3, O2, O4, O5, O1), (O3, O5, O2, O1, O4),
(O3, O5, O2, O4, O1), (O3, O5, O4, O1, O2), (O4, O1, O2, O3, O5),
(O4, O1, O3, O5, O2), (O4, O2, O3, O1, O5), (O4, O2, O3, O5, O1),
(O4, O5, O2, O3, O1), (O4, O5, O3, O1, O2) }
Part(a) : The probability that O1 gets the Volvo is = 6/20 = 3/10 .
and
Part(b) :
Probability of O2 or O5 gets the Volvo = (Probability of O2 getting Volvo
) + (Probability of O5 getting Volvo) .
= 4/20 + 6/20
= 10/20 = 1/2 .
Therefore , the required probability for (a) is 3/10 and for (b) is 1/2 .
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