Answer:
[tex]20.25 \: m^2[/tex]
Step-by-step explanation:
Use the formula for the area of a square.
[tex]A=s^2[/tex]
Where [tex]s=4.5[/tex]
[tex]s^2\\(4.5)^2\\20.25[/tex]
The area of the square is 20.25 square meters as per the concept of the square.
To find the area of a square, we need to square the length of one of its sides. In this case, the side length is given as 4 1/2 meters.
First, we need to convert the mixed number 4 1/2 into an improper fraction. We can rewrite it as 9/2.
Next, we square the side length:
[tex]\frac{9}{2}^2 = \frac{81}{4}[/tex].
To simplify the fraction, we can divide the numerator by the denominator:
81 ÷ 4 = 20 remainders 1.
Therefore, the area of the square is 20 1/4 square meters.
However, we can simplify the mixed number further. Since 4 can be divided by 4 and 1 can be divided by 4, we have:
20 1/4
= 20 + 1/4
= 20 + 1/4
= 20 + 0.25
= 20.25.
Therefore, the area of the square is 20.25 square meters.
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The following is a Markov (migration) matrix for three locations
[1/5 1/5 2/5
2/5 2/5 1/5
2/5 2/5 2/5]
(a) Initially, there are 130 individuals in location 1, 300 in location 2, and 70 in location 3. How many are in each location after two time periods?
(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?
Answer:
(a) [tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
(b) After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
Step-by-step explanation:
The Markov Matrix can be interpret as :
[tex]M = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]
From (a) ; we see that the initial population are as follows: 130 individuals in location 1, 300 in location 2, and 70 in location 3.
Le P represent the Population; So ; [tex]P = \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]
The objective is to find How many are in each location after two time periods;
So, after two time period ; we have the population [tex]P_2 = [M]^2 [P][/tex]
where;
[tex][M]^ 2 = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right] \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]
[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc} 1+2+4 & 1+2+4 &1+2+4 \\ \\ 2+2+4&2+2+4&2+2+4\\ \\ 2+4+4&2+4+4& 2+4+4 \end{array}\right][/tex]
[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right][/tex]
Now; Over to after two time period ; when the population [tex]P_2 = [M]^2 [P][/tex]
[tex]P_2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right] \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]
[tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?
After a long time; that is referring to an infinite time (n)
So; [tex]P_n = [M]^n [P][/tex]
where ;
[tex][M]^n \ can \ be \ [M]^2 , [M]^3 , [M]^4 .... \infty[/tex]
; if we determine the respective values of [tex][M]^2 , [M]^3 , [M]^4 .... \infty[/tex] we will always result to the value for [tex][M]^n[/tex]; Now if [tex][M]^n[/tex] is said to be a positive integer; then :
After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
Which one of the following is always true?a. The coefficient of variation measures variability in a positively skewed data set relative to the size of the median.b. None of the suggested answers are correctc. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale.d. The interquartile range is very unique in the sense that it is a measure of central tendency as well as a measure of dispersion.e. The coefficient of variation should only be used to compare positive data on an interval scale.
Answer:
C. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale
Step-by-step explanation:
Th Coefficient of Variance is a measure of dispersion that can be calculated using the formula:
[tex]CV = \frac{\sigma_{x} }{\mu_{x} } * 100%[/tex]
Where [tex]\sigma{x}[/tex] is the Standard Deviation
and [tex]\mu_{x}[/tex] is the sample mean
From the formula written above, it is shown that the Coefficient of Variation expresses the Standard Deviation as a percentage of the mean.
Coefficient of variation can be used to compare positive as well as negative data on the ratio and interval scale, it is not only used for positive data.
The Interquartile Range is not a measure of central tendency, it is a measure of dispersion.
Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x= distance and t= time. Additionally, [speed x time= distance]. Won’t the van catch up when the distances are equal?
Please make it easy to understand your answer :)
Answer:
Time = X = 37.14 minutes
Distance they covered= 33.42 miles.
Step-by-step explanation:
Distance= speed * time
And the distance traveled by the two need to be equal.
Speed of storm = 33 mph
Speed of van = 54 mph
But storm is 13 miles away from van.
So
54*x = 33*x+ 13
54x-33x = 13
21x = 13
X= 0.62 hours
X = 37.14 minutes
54 *0.62= 33.42 miles.
A college job placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five. What is the sample space for the chance experiment of selecting two students at random
Answer:
Step-by-step explanation:
The following is the information provided
number of students is 5
The number of math major = 3
The number of statistic major = 2
Label math students as A, B, C
And statistic students as D, E
The total number of ways to select two students from 5 students is 10
The sample space is S = {AB,AC,BC,AD,AE,BD,BE,CD,CE,DE}
Yes , in the sample space the events are equally alike
What is the probability that both selected students are statistics majors
The selected students of statistic major are DE
the probability that both selected students are statistics majors is [tex]\frac{1}{10}[/tex]
= 1/10
What is the probability that both students are math majors
The selected students of statistic major are AC,AB,BC
the probability that both selected students are math majors is [tex]\frac{3}{10}[/tex]
= 3/10
What is the probability that at least one of the students selected is a statistics major
Number of ways to select at least one of the students selected is a statistic major is {AD,AE,BD,BE,CD,CE,DE}
the probability that at least one of the students selected is a statistics major is [tex]\frac{7}{10}[/tex]
7/10
What is the probability that the selected students have different majors
Number of ways to select students with different major is {AD,AE,BD,BE,CD,CE,}
the probability that the selected students have different majors is [tex]\frac{6}{10}[/tex]
6/10
Identify which of the following is NOT equivalent to 2 3/4
Answer:
Step-by-step explanation:
mabey its c
The equation which is equivalent to [tex]2^{\frac{2}{3} }[/tex] will be equal to [tex]\sqrt[4]{2^3}[/tex]. Hence, option C is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
[tex]2^{\frac{2}{3} }[/tex] = 1.68
Now, let's check the options,
A.
[tex](2^{\frac{1}{4} } )^{\frac{1}{2} }[/tex] = 1.09 ≠ 1.68, hence this is incorrect.
B.
[tex]2\frac{1}{4}*2\frac{1}{2}[/tex] = 9/4 × 5/2 = 5.625 ≠ 1.68, hence, this is incorrect.
C.
[tex]\sqrt[4]{2^3}[/tex] = 1.68 = 1.68, hence, this is correct.
D.
√8 = 2.82 ≠ 1.68, hence, this is incorrect.
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Last year at a certain high school, there were 96 boys on the honor roll and 85 girls on the honor roll. This year, the number of boys on the honor roll increased by 25% and the number of girls on the honor roll increased by 20%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
22.7
Step-by-step explanation:
ok so, First we need to find new values:
96( 1 + 0.25) =120
85( 1+0.2)= 102
Boys last year girls last year total this year
96 85 181
Boys this year girls this year total this year
120 102 222
Find the overall increase:
181( 1+r)= 1.226519
THEN U SUBTRACT 1
r=0.226519
Multiply by 100 and round to nearest 10th
22.7%
Final Answer: 22.7%
HOPED IT HELPED:)
What is the first step of the following division problem? (8x3 – x2 + 6x + 7) ÷ (2x – 1)
Answer:
The first step is to determine how many times 2x goes into 8x^3
Step-by-step explanation:
The first step is to determine how many times 2x goes into 8x^3
4x^2
--------------------------
2x-1 | (8x3 – x2 + 6x + 7
8x^3 -4x^2
Answer:
A
Step-by-step explanation:
i just took the test
What is the solution of the following linear system? y = 3x + 1 2y = 6x + 2
Answer:
y = 3x +1 (1)
2y = 6x +2 (2)
We can devide equation (2) by 2 and we got:
[tex] y =3x +1[/tex] (3)
And since equations (1) and (3) are equal we can do this:
[tex] 3x +1 = 3x+1[/tex]
And that implies:
[tex] 0=0[/tex]
And for this case we will have infinite solutions for the sytem given since we have two lines equal
Step-by-step explanation:
For this case we have the following system of equations given:
y = 3x +1 (1)
2y = 6x +2 (2)
We can devide equation (2) by 2 and we got:
[tex] y =3x +1[/tex] (3)
And since equations (1) and (3) are equal we can do this:
[tex] 3x +1 = 3x+1[/tex]
And that implies:
[tex] 0=0[/tex]
And for this case we will have infinite solutions for the sytem given since we have two lines equal
a large which has topics of Capsicum and onion in there in total there are 25 pieces of both on the pizza if there are four times as many onions pieces as capsicum pieces how many pieces of eat vegetable are there on the pizza
Step-by-step explanation:
I think there should be 5 capsicums because
4 times onions = 5 x 4 = 20
Then 5 capsicums = 20 + 5 = 25
Answer:
A large pizza has toppings of capsicum and onion. In total there are 36 pieces of both on the pizza .If there are 5 times as many onions pieces as capsicum pieces,how many of each vegetable are there on the pizza?
Step-by-step explanation:
Can you please help with this one
Whats the theorum called for working out the missing side of a triangle?
Answer:
The Pythagorean Theorum
Step-by-step explanation:
you can literally search it and see that it is right!
Three added to the product of -4 and a number X is less than 5 added to the product of -3 and the number. What is the number?
Answer:
x=-2
Step-by-step explanation:
3 + -4x = 5+ -3x
-4x = 2 - 3x
-x = 2
x = -2
Solve for x using the quadratic formula x^2-6x +9=0
Answer:
3 both ways x = 3
EXPLANATION:
plug in inputs and do a little simplifying we get
x = 6 ± √(36-36) all of that over 2
So we simplify and we get 6±sqrt(0) / 2
Then we get 6/2 = 3
x-0 = x+0
thats why there is only one answer
Answer:
The value of X is 3
Step-by-step explanation:
x²-6x+9=0
x²- 3x - 3x + 9= 0
X(x-3) -3(x-3)=0
(x-3) (x-3)=0
(x-3)²=0
(x-3)=0
x-3 = 0
X= 3
A cyclist travels at an average speed of 8 km/h over a distance of 32 km. How many hours does it take him?
Answer:
4 hours.
Step-by-step explanation:
Well we can simply divide 32 by 8 and we get 4 hours:
32 miles ÷ 8 miles = 4 hours
It takes the cyclist 4 hours.
Answer:
4 hours
Step-by-step explanation:
As every speed limit sign tells you, ...
speed = miles/hours
Solving for time and using generic distance units, we get ...
time = distance/speed
Filling in the given values, we have ...
time = 32 km/(8 km/h) = (32/8) h = 4 h
It takes the cyclist 4 hours to travel 32 km.
4x+6y=-10 8x+10y=-26 solve the system of the linear equation
Now by using equation 1 in equation 2 we get,
[tex]4x + 5y = - 13 \\ \\ 4( \frac{ - 5 - 3y}{2} ) + 5y = - 13 \\ \\ \frac{ - 20 - 12y}{2} + 5y = - 13 \\ \\ \frac{ - 20 - 12y + 10y}{2} = - 13 \\ \\ - 20 - 2y = - 26 \\ \\ - 2y = - 26 + 20 \\ \\ - 2y = - 6 \\ \\ y = 3[/tex]Now upon using the value of y in equation 1, we get
[tex]x = \frac{ - 5 - 3y}{2} \\ \\ x = \frac{ - 5 - 3 \times 3}{2} \\ \\ x = \frac{ - 5 - 9}{2} \\ \\ x = \frac{ - 14}{2} = - 7[/tex]PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
D (4,11)
Step-by-step explanation:
Answer: it’s d
x is just going up by 1 and y is going up by 2
In a video game an object represented by the point (2,7) is rotated counterclockwise 175 degrees around an origin. What are the new coordinates that represent the point?
Answer:
(-2.60, -6.80)
Step-by-step explanation:
The new coordinates can be found by multiplying by the rotation matrix:
[tex]\left[\begin{array}{c}x'&y'\end{array}\right]=\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right][/tex]
That is, ...
x' = x·cos(175°) -y·sin(175°) = 2(-0.9962) -7(0.0872) = -2.60
y' = x·sin(175°) +y·cos(175°) = 2(0.0872) +7(-0.9962) = -6.80
The new coordinates are ...
(x', y') = (-2.60, -6.80)
Ben bought 4 volleyballs and 5 footballs for $352.65 altogether. If Ben’s brother bought 2 volleyballs and 4 footballs for $249.12 altogether, what was the price of each football?
Answer:
$48.53
Step-by-step explanation:
The purchases can be written in equation form as ...
4v +5f = 352.65
2v +4f = 249.12
Doubling the second equation and subtracting the first gives ...
2(2v +4f) -(4v +5f) = 2(249.12) -(352.65)
3f = 145.59 . . . . simplify
f = 48.53 . . . . . . divide by 3
The price of each football was $48.53.
A goat is tied to a peg in the ground. The rope is 3m long. What area of grass can the goat eat? (use the value 3.14 for pie)
Answer:
28.26 (Please mark as brainiest if you find it helpful )
Step-by-step explanation:Area the goat will eat is equal to the are of circle having radius 3m.
Area of circle = pi * r ^ 2
⇒ 3.14 * (3) ^ 2 → 3.14 * 9
⇒ 28.26
If a number is added to the numerator of 7/9 and the same number is subtracted from the denominator, the result is 3. Find the number.
Answer:
5
Step-by-step explanation:
[tex]\frac{7+x}{9-x}=3\\ 7+x = 3(9-x)\\7+x=27-3x\\x+3x=27-7\\4x=20\\x=5[/tex]
An employee wants to invest $50,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.75% compounded continuously.
(a) Which investment will ear more interest in 5 yr?
(b) How much more will the better plan earn?
Answer:
a. 6% one is better
b. $12,285.95
Step-by-step explanation:
a. For determining which investment earn more first we have to calculate both the investment which are as follows
a. Based on compound quarterly, the amount is find out by using the following formula
[tex]Amount = {Present\ value\times (1 + interest\ rate)} ^{number\ of\ years}[/tex]
where,
Present value is $50,000
Interest rate is = [tex]\frac{0.06}{4}[/tex] = 0.015
And, the number of years is
= [tex]4\times4[/tex]
= 16
So, the amount is
[tex]= \$50,000 \times (1 + 0.015)^{16}[/tex]
= $63,449.28
And, based on compounded continuously, the amount is determined by using the following formula
[tex]Amount = Present\ value\times e^{rt}[/tex]
[tex]= \$50,000 \times e.^{0575(4)}[/tex]
= $51,163.33
Therefore, The the investment at 6% is better
b. Now the difference in earning is
= $63,449.28 - $51,163.33
= $12,285.95
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
Volume of cylinder = base area × height
25.5 = A × 4.8
A = 25.5/4.8
A = 5.3 inch ²
Write the ratio 70:80 in its simplest form
Answer:
7/8!
Step-by-step explanation:
They both can be divided by 10, so do just that. Then you are left with 7/8 which cannot be simplified.
The ratio 70:80 in its simplest form is equal to 7:8.
To simplify the ratio 70:80, we need to find the greatest common divisor (GCD) of the two numbers and then divide both numbers by the GCD.
Step 1: Find the GCD of 70 and 80:
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The common factors of 70 and 80 are 1, 2, 5, and 10. The greatest common divisor (GCD) is 10.
Step 2: Divide both numbers by the GCD (10):
70 ÷ 10 = 7,
80 ÷ 10 = 8.
In summary, the ratio 70:80 can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 10. After simplification, the ratio becomes 7:8. Simplifying ratios involves dividing both parts of the ratio by the greatest common factor to express the ratio in its simplest and most concise form.
This makes it easier to understand and work with the relationship between the quantities being compared. In this case, the simplified ratio tells us that for every 7 units of the first quantity, there are 8 units of the second quantity.
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Which table represents a function?
Think of the graph for the inequality y < 3x - 6
1. Would the line on the graph be dotted or solid? Why?
2. Would the shading be above the line or below the line? Why?
***Extra Credit
Name one point (x,y) that would be a solution to this inequality.
Answer:
1.dotted, because it is not less than or equal to, but just less than.
2.below, because Y is less than the equation.
3. 0, -6
Step-by-step explanation:
// have a great day //
What are the next two numbers in the pattern of numbers; 45, 15, 44, 17, 40, 20, 31, 25, ...
Answer:
15, 33
(if I'm not wrong, it should work this way)
how do I find the volume of a triangular prism?
Answer:
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h.
Step-by-step explanation:
plz answer this asap
Answer: 20
Step-by-step explanation: 5 times 4 is 20 times 2 is 40, but when you divide by 1/2 you drop down to 20.
PLEASE HELP ME!!! (WILL MARK BRAINLIEST!
Answer:
A) 13/20
Step-by-step explanation:
65% in simplest form,
65/100
= 13/20 (Divided by five)
Answer:
[tex]\frac{13}{20}[/tex].
Step-by-step explanation:
We can begin by converting 65% to a fraction over 100. 65% converts to 0.65, or [tex]\frac{65}{100}[/tex].
We can simplify this down. Both 65 and 100 share a common factor of 5, which allows us to produce a new fraction:
[tex]\frac{65}{100} = \frac{13}{20}[/tex]
Therefore, the simplified version is [tex]\frac{13}{20}[/tex].
y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a solution of the differential equation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter IMPOSSIBLE.) y(0) = 1, y'(π) = 9
Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
Explain why the sum of the angle measures in any
triangle is 180º.
Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360
hope this helped
