Answer:
It's 8.3
Step-by-step explanation:
Answer:
8.3
Step-by-step explanation:
Find the first six partial sums S1, S2, S3, S4, S5, S6 of the sequence whose nth term is given. 1 2 , 1 22 , 1 23 , 1 24 , . .
Answer:
the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Step-by-step explanation:
The term of the sequence are given as : [tex]\dfrac{1}{2}[/tex], [tex]\dfrac{1}{2^2}[/tex], [tex]\dfrac{1}{2^3}[/tex], [tex]\dfrac{1}{2^4 }[/tex] , . . .
The nth term for this sequence is , [tex]\mathtt{a_n =( \dfrac{1}{2})^n}[/tex]
The nth partial sum of the sequence for [tex]\mathtt{a_1,a_2,a_3.... a_n}[/tex] is [tex]\mathtt{S_n}[/tex]
where;
[tex]\mathtt{S_n = a_1 +a_2+a_3+ ...+a_n}[/tex]
The first partial sum is: [tex]\mathtt{S_1= a_1}[/tex]
[tex]\mathtt{S_1= (\dfrac{1}{2})^1}[/tex]
[tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
Therefore, the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
The second partial sum is: [tex]\mathtt{S_2= a_1+a_2}[/tex]
[tex]\mathtt{S_2= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2}[/tex]
[tex]\mathtt{S_2= \dfrac{1}{2} + \dfrac{1}{4}}[/tex]
[tex]\mathtt{S_2= \dfrac{2+1}{4} }[/tex]
[tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
Therefore, the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
The third partial sum is : [tex]\mathtt{S_3= a_1+a_2+a_3}[/tex]
[tex]\mathtt{S_3= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3 }[/tex]
[tex]\mathtt{S_3= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}}[/tex]
[tex]\mathtt{S_3= \dfrac{4+2+1}{8}}[/tex]
[tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
Therefore, the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
The fourth partial sum : [tex]\mathtt{S_4= a_1+a_2+a_3+a_4}[/tex]
[tex]\mathtt{S_4= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 }[/tex]
[tex]\mathtt{S_4= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}}[/tex]
[tex]\mathtt{S_4= \dfrac{8+4+2+1}{16}}[/tex]
[tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
Therefore, the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
The fifth partial sum : [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5}[/tex]
[tex]\mathtt{S_5= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 }[/tex]
[tex]\mathtt{S_5= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}}[/tex]
[tex]\mathtt{S_5= \dfrac{16+8+4+2+1}{32}}[/tex]
[tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
Therefore, the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
The sixth partial sum: [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5+a_6}[/tex]
[tex]\mathtt{S_6= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 +(\dfrac{1}{2})^6 }[/tex]
[tex]\mathtt{S_6= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64} }[/tex]
[tex]\mathtt{S_6= \dfrac{32+16+8+4+2+1}{64}}[/tex]
[tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Therefore, the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
will mark brainliest. PROMISE!! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
Lori wants to buy a radio for 60 dollars.
She can pay $60 now, or she can pay $12
a month for 6 months. How much more will
she pay for the radio if she makes monthly
payments?
Answer:
Lori will pay $12 more if she makes monthly payments
Step-by-step explanation:
to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72
subtracting the amount she would pay as a down payment
$72 - $60 is $12
Lori will pay $12 more if she makes monthly payments
Tina's age is 4 years less than 3 times her niece's age. If her niece's age is x years, which of the following expressions best shows Tina's age? x − 4 4x − 3 3x − 4 4 − 3x
Answer:
3x - 4
Step-by-step explanation:
As Tina's age is 3 into x ( 3 x x= 3x)but 4years less (-4)
Therefore Tina's age is 3x - 4
Answer:
3x - 4
Step-by-step explanation:
Use these representations: niece's age: x
We triple x and then subract 4 years from the result, obtaining:
Tina's age: 3x - 4
The length of a rectangle is three times its width. If the perimeter of the rectangle is 160 cm, what are the dimensions of this rectangle?
Answer:
The dimensions or Area of the rectangle is 1200cm².
Tessa’s employee benefits include family health care coverage. She contributes 18% of the cost. Tessa gets paid biweekly and $108.00 is taken out of each paycheck for family health care coverage. How much does her employer contribute annually for the family coverage? Clearly show your work.
The answer is $12792
Explanation:
It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:
1. Write the values you know and use x to represent the value you need to find
108 = 18
x = 82
3. Cross multiply
x 18 = 8856
4. Find the value of x by solving this simple equation
x = 8856 ÷ 18
x = 492 - Amount the employer pays every two weeks for Tessa's family coverage
Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.
1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks
52 ÷ 2 = 26
2. Finally, multiply the money paid by the employer every two weeks by 26
26 weeks x $492 = $12792- This is the total the employer pays annually
Suppose that the neighboring cities of Tweed and Ledee are long-term rivals. Neal, who was born and raised in Tweed, is confident that Tweed residents are more concerned about the environment than the residents of Ledee. He knows that the average electricity consumption of Tweed households last February was 854.11 kWh and decides to test if Ledee residents used more electricity that month, on average. He collects data from 65 Ledee households and calculates the average electricity consumption to be 879.28 kWh with a standard deviation of 133.29 kWh. There are no outliers in his sample data. Neal does not know the population standard deviation nor the population distribution. He uses a one-sample t-test with a significance level of α = 0.05 to test the null hypothesis, H0:µ=854.11, against the alternative hypothesis, H1:μ>854.11 , where μ is the average electricity consumption of Ledee households last February. Neal calculates a t‑statistic of 1.522 and a P-value of 0.066.
Based on these results, complete the following sentences to state the decision and conclusion of the test.
Neal's decision is to__________ the __________ (p 0.066). There is_________ evidence to _________ the claim that the average electricity consumption of ____________ is _________ , ________
Complete Question
The option to the blank space are shown on the first uploaded image
Answer:
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 854.11[/tex]
The sample size is [tex]n = 65[/tex]
The sample mean is [tex]\= x = 879.28 \ kWh[/tex]
The standard deviation is [tex]\sigma = 133.29 \ kWh[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o: \mu = 854.11[/tex]
The alternative hypothesis is [tex]H_a : \mu > 854.11[/tex]
The t-statistics is [tex]t = 1.522[/tex]
The p-value is [tex]p-value = 0.066[/tex]
Now from the given data we can see that
[tex]p-value < \alpha[/tex]
Generally when this is the case , we fail to reject the null hypothesis
So
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
Simplify 70 +(-30)+2+(-9)+0.3+(-0.1)=[70+(-30)] +[2+(-9)]+[0.3+(-0.1)]
Answer:
Step-by-step explanation:
When you add the left side of the equation, you get 33.2 because 70-30 is 40, 40+2 is 42, 42-9 is 33, 33+0.3 is 33.03, 33.3-0.1 is 33.2.
When you add the right side of the equation, you get 33.2, because they are the same problem but on side has brackets.
Hope this helps you.
Find the product. (7x+2)(x−1) A 8x+1 B 6x+3 C 7x2−5x−2 D 7x2−2
Answer:
7x^2 -5x-2
Step-by-step explanation:
(7x+2)(x−1)
FOIL
first 7x*x = 7x^2
outer 7x*-1 = -7x
inner 2x
last 2*-1 = -2
Add them together
7x^2 -7x+2x -2
7x^2 -5x-2
Answer:
[tex] \boxed{\red{7 {x}^{2} - 5x - 2}}[/tex]
Answer C is correct
Step-by-step explanation:
[tex](7x + 2)(x - 1) \\ 7x(x - 1) + 2(x -1 ) \\ 7 {x}^{2} - 7x + 2x - 2 \\ = 7 {x}^{2} - 5x - 2[/tex]
Sebastian studies from 3:15 - 4:45 p.m his sister,Sara studies from 4:30 -6:15 p.m who studies longer and by how,much?
Answer:
Sara studies longer by 15 minutes.
Step-by-step explanation:
Let's calculate how long Sebastian studies for. From 3:15 - 4:15, there is 1 hour and from 4:15 to 4:45, there are 30 minutes so Sebastian studies for 1 hour and 30 minutes. Now, let's calculate how long Sara studies for. From 4:30 - 5:30, there is 1 hour, from 5:30 - 6:00, there are 30 minutes and from 6:00 - 6:15, there are 15 minutes so Sara studies for 1 hour 45 minutes. This means that Sara studies longer by 45 - 30 = 15 minutes.
The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school? A. $16.13 B. $5.37 C. $16.34 D. $16.63
Answer: A. $16.13
Step-by-step explanation:
Total students = 82+74+96+99 =351
Sum of earnings of 82 seniors = $26.75 x 82= $2193.5
Sum of earnings of 74 juniors = $12.25 x 74 = $906.5
Sum of earnings of 96 sophomores = $15.50 x 96 = $1488
Sum of earnings of 99 freshmen = $10.85 x 99 = $1074.15
Total earnings = $2193.5 + $906.5+ $1488 +$1074.15
= $5662.15
(Total earnings) ÷ (Total students )
= $5662.15÷ 351
= $16.13
A line passes through the point ( 10,3 ) and has a slope of 1/2. write an equation in slope-intercept form for this line.
Answer:
[tex]\displaystyle y=\frac{1}{2}x-2[/tex]
Solve
The point-slope form is represented with the formula:
[tex]y-y_1=m(x-x_1)[/tex]
We are given a point [tex](x_1, y_1)[/tex] and a slope: [tex]\displaystyle \frac{1}{2}[/tex].
We are asked to solve this equation in slope-intercept form, which is:
[tex]y=mx+b[/tex]
Givens
[tex]x_1: 10\\\\y_1: 3\\\\\displaystyle m: \frac{1}{2}[/tex]
To solve:
1. Substitute the givens into the point-slope form equation:
[tex]y-y_1=m(x-x_1)\\\\\displaystyle y-3=\frac{1}{2}(x-10)[/tex]
2. Simplify by using the distributive property, which states:
[tex]a(b+c)=ab+ac[/tex]
[tex]\displaystyle y-3=\frac{1}{2}x-5[/tex]
3. Simplify further by combining like terms:
[tex]\displaystyle y-3+3=\frac{1}{2}x-5+3\\\\\displaystyle y=\frac{1}{2}x-2[/tex]
The final answer in slope-intercept form is:
[tex]\large \boxed{\displaystyle y=\frac{1}{2}x-2}[/tex]
Answer:
y = 1/2x - 2
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
y = 1/2x + b Equation
Step 3:
3 = 1/2 ( 10 ) + b Input x and y
Step 4:
3 = 5 + b Multiply
Step 5:
3 - 5 = b Subtract 5 on both sides
Step 6:
b = - 2
Answer:
y = 1/2x - 2
Hope This Helps :)
Take thus quote, and embed (introduce) it into a complete sentence: "TV plots
and characters tended to be simple" The author is Ostergaard.
What is the area, in square meters, of the shaded part of the rectangle shown below?
Answer:
C) 100 cm²
Step-by-step explanation:
(14*6)/2*10
20/2*10
10*10
100
The area of the given shaded part of the rectangle is 100 square meters as shown.
What is the area of a triangle?The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area.
The fundamental formula for calculating the area of a triangle is A = 1/2 b h.
The area of the shaded part = area of the rectangle - area of the triangle
The area of the shaded part = 14 × 10 - (1/2) × 8 × 10
The area of the shaded part = 140 - 80/2
The area of the shaded part = 140 - 40
Apply the subtraction operation, and we get
The area of the shaded part = 100 meters²
Thus, the area of the given shaded part of the rectangle is 100 square meters.
Learn more about the triangles here:
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The value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2, find the value of y when x = 3 and z = 336. I will rate you brainliest
Answer:
18
Step-by-step explanation:
Given that:
y∞ xz
y=kxz. Where k is constant
When z=196 and x= 2 then y= 7
7=(196)(2)k
7=392k
k=1/56
There fore y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
if value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2 then the value of y when x = 3 and z = 336 is 18.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Value of y varies jointly with x and z.
y ∞ xz
y=kxz.
Where k is constant
When z=196 and x= 2 then y= 7
Let us find the value of k
7=(196)(2)k
7=392k
Divide both sides by 7
k=1/56
y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
Hence, the value of y when x = 3 and z = 336 is 18.
To learn more on Ratios click:
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State the correct polar coordinate for the graph shown.
It is not the option selected.
One way to write this polar coordinate is to say (2.5, pi/2) meaning we move 2.5 units away from the origin toward the pi/2 direction
pi/2 radians = 90 degrees
An alternative is to write (-2.5, 3pi/2) which is where we aim at the 3pi/2 direction (270 degrees) and walk backward while still facing directly south, and we'll arrive at the same location.
What does the tape measure say Measurement # 2 is?
Answer:
Measure number 2 of the tape is for the pinus
Step-by-step explanation:
To measure, kindly place pinus next to ruler and pinus will be in line with measurement #2
Call and ask for pinus step by step
Answer:
7 and one sixteenths of an inch.
A point (x,y) is a distance of 6 units from the x-axis. It is a distance of 5 units from the point (8,3). It is a distance [tex]\sqrt{n}[/tex] from the origin. Given that x<8, what is n?
Answer: n = 52
Step-by-step explanation:
when we have two vectors (x,y) and (a,b) the distance between the vectors is:
D = √( (x - a)^2 + (y - b)^2)
now, we know that:
1) the distance between (x, y ) and the x-axis is 6 units.
The nearest point to (x, y) in the x-axis is the point (x, 0) so we have:
D = 6 = √( (x - x)^2 + (y - 0)^2) = √y^2
so y can be 6 or -6.
So we know that y = 6, and now we can write our point as (x, +-6)
2) The distance between our point and (8, 3) is 5 units:
D = √( (x - 8)^2 + (y - 3)^2) = 5.
And we know that the distance from the origin, (n, n) is:
D = √n = √(x^2 + y^2}
n = x^2 + y^2
Now, we should start with:
√( (x - 8)^2 + (y - 3)^2) = 5
first suppose that y = -6, then:
√( (x - 8)^2 + (-6 - 3)^2) = √( (x - 8)^2 + (-9)^2) = 5.
√( (x - 8)^2 + 81) = 5.
Then we must have that:
and we know that √25 = 5
so (x-8)^2 + 81 = 25
this can never happen, so we can discard y = -6
Now the second case, if y = 6,
√( (x - 8)^2 + (6 - 3)^2) = 5.
√( (x - 8)^2 + (3)^2) = 5.
√( (x - 8)^2 + 9) = 5.
here:
(x - 8)^2 + 9 = 25
(x - 8)^2 = 16
(x - 8) = √16 = +-4
So again we have two cases:
if x - 8 = 4, then:
x = 4 + 8 = 12
but we must have x < 8, so this can be discarded.
now, if x - 8 = -4 then:
x = -4 + 8 = 4, this is an acceptable answer, then our point is (4, 6)
And we have:
n = 4^2 + 6^2 = 16 + 36 = 52
Which is one of the transformations applied to the graph of f(x) = X^2 to change it into the graph of g(x) = -x^2 +16x - 44
Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
Step-by-step explanation:
Let's construct g(x) in baby steps.
Ok, we start with f(x) = x^2
The first thing we have is a horizontal translation of A units (where A is not known)
A vertical translation of N units to the right, is written as:
g(x) = f(x - N)
Then we have:
g(x) = (x - A)^2 = x^2 - 2*A*x + A^2
Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.
Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)
Then if we apply also a reflection over the x-axis, we have:
g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44
Then:
2*A = 16
A*A = 44.
The first equation says that A = 16/2 = 8
But 8^2 is not equal to 44.
Then we need another constant coefficient, which is related to a vertical translation.
If we have a relation y = f(x), a vertical translation of N units up, will be
y = f(x) + N.
Then:
g(x) = -f(x - A) + B
-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44
Now we have:
2*A = 16
-A^2 + B = - 44
From the first equation we have A = 8, now we replace it in the second equation and get:
-8^2 + B = -44
B = -44 + 64 = 20
Then we have:
The transformation is:
First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
(-2×3)+(3×2) how do we solve it
Answer:
0
Step-by-step explanation:
- 2×3= - 6
2×3=6
-6+6=0
Answer:
0
Step-by-step explanation:
first
(-2x3)+(3x2)
-6+6=0
Question:
A school's band members raised money by selling magazine subscriptions and shirts. Their profit from selling shirts was per shirt minus a one-time set-up fee. Their profit from selling magazine subscriptions was per subscription. They made exactly the same profit from shirts as they did from magazines. They also sold the same number of shirts as magazine subscriptions. How many shirts did they sell?
Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
The gasoline gauge on a van initially read ⅛ full. When 15 gallons of gasoline were added to the tank, the gauge then read ¾ full. How many more gallons would be needed to fill the tank?
Answer:
Question 1: 40 shirts and 40 magizines
Question 2: $4.4
Question 3: 6 gallons
Answer:
hello
Step-by-step explanation:
find the perimeter of a square of sides 10.5cm
Answer:
Perimeter = 42 cm
Step-by-step explanation:
A square has all equal sides so you would just add 10.5 + 10.5 + 10.5 + 10.5 to get 42 cm.
Answer:
42 cm
Step-by-step explanation:
Side of square = 10.5 cm (given)
Perimeter of square = Side X 4
= 10.5 X 4
= 42 cm
HOPE THIS HELPED YOU !
:)
Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
sam ran 63,756 feet in 70 minutes what is sam rate in miles per hour there are 5,280 feet in one mile
Answer:
simply convert first feets into miles
Given is 5280 feets=1 miles
63756 /5280=12.075 miles
70 minutes = 1.16666= 1.17 hrs
rate is 12.075 miles/1.17 hrs
Step-by-step explanation:
What is the difference between a consistent and inconsistent system of equations?
Answer:
A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.
Answer: see below
Step-by-step explanation:
Consider the standard form of a linear equation in Slope-Intercept form:
y = mx + b where
m is the slopeb is the y-interceptA CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.
This results in the lines crossing so they have at least one solution.
An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.
This results in parallel lines so they have no solutions.
In a regression class, a student suggested the following: If extremely influential outlying cases are detected in a data set, simply discard these cases from the data set. Provide your comments as the validity of this statement.
Answer:
Discarding the influential outlying cases when detected is also known as flagging outliers in a data set, and this is because outliers do not follow the rest of the dataset's pattern. if this outliers are not discarded they would have a negative effect on any model attached to the dataset
Step-by-step explanation:
In a regression class ; If extremely influential outlying cases are detected in a Data set, discarding this influential outlying cases is the right way to go about it
Discarding the influential outlying cases when detected is also known as flagging outliers in a data set, and this is because outliers do not follow the rest of the dataset's pattern. if this outliers are not discarded they would have a negative effect on any model attached to the dataset
A square has a side length that is decreasing at a rate of 8 cm per second. What is the rate of change of the area of the square when the side length is 7 cm
Answer:
112cm²/secStep-by-step explanation:
Area of a square is expressed as A = L² where L is the length of one side of the square.
The rate of change of area will be expressed using chain rule as;
dA/dt = dA/dL * dL/dt where;
dL/dt is the rate at which the side length of the square is decreasing.
Given L = 7cm, dL/dt = 8cm/sec and dA/dL = 2L
dA/dL = 2(7)
dA/dL = 14cm
Substituting the given value into the chain rule expression above to get the rate of change of the area of the square, we will have;
dA/dt = dA/dL * dL/dt
dA/dt = 14cm * 8cm/sec
dA/dt = 112cm²/sec
Hence, the rate of change of the area of the square when the side length is 7 cm is 112cm²/sec
If 75% of a number 60, what is the number?
Answer:
80
Step-by-step explanation:
75 60
------ = ------
100 x
100 x 60 = 6000
75x = 6000
x = 80
Using the power series methods solve the 1st order Lane-Emden Equation:
xy = 2y + xy = 0
You may only use a power series solution to find both linearly independent functions. This means you may not use Abel’s theorem, variation of parameters or reduction of order.
Answer:
Step-by-step explanation:
xy = 2y + xy = 0
Hence, 2y + xy = 0 ---------(1)
Differentiating equation (1) n times by Leibnitz theorem, gives:
2y(n) + xy(n) + ny(n - 1) = 0
Let x = 0: 2y(n) + ny(n - 1) = 0
2y(n) = -ny(n - 1)
∴ y(n) = -ny(n - 1)/2 for n ≥ 1
For n = 1: y = 0
For n = 2: y(1) = -y
For n = 3: -3y(2)/2
For n = 4: -2y(3)
