Answer:
Yes
Step-by-step explanation:
18 × 200 = 3600
120 × 25 = 3000
270 × 5 = 1350
in total 7950
tickets = 10 × 1000 = 10000
7950 < 10000
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 vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Their data is given below α = 0.01.
Row Machine A Machine B Machine C
1 11.5 10.3 11.1
2 12.1 9.7 11.3
3 11.6 10.4 11.9
4 12.0 10.7 11.5
5 11.1 9.9 11.7
6 12.2 10.1 11.3
H0: μA = μB = μC
Ha: Not all means are equal
One-way ANOVA: Machine A, Machine B, Machine C
Source DF SS MS F P
Factor 2 8.363 4.182 31.73 0.000
Error 15 1.977 0.132
Total 17 10.340
P-value: _____
Decision: _____
Is there a significant difference between the vending machines A, B, and C? Use α=0.05.
A. No, there is no significant difference between the means.
B. Yes, there is a significant difference between the means.
C. The F-test cannot be used to answer whether or not there is a significant difference between the means.
Answer:
The correct option is B.
Step-by-step explanation:
The hypothesis to determine whether the vending machines are properly dispensing 12 ounces of coffee is:
H₀: [tex]\mu_{A}=\mu_{B}=\mu_{C}[/tex]
Hₐ: Not all means are equal.
The ANOVA output is as follows:
One-way ANOVA: Machine A, Machine B, Machine C
Source DF SS MS F P
Factor 2 8.363 4.182 31.73 0.000
Error 15 1.977 0.132
Total 17 10.340
The significance level is α = 0.05.
The p-value of the model is:
p-value = 0.000
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
p-value = 0.000 < α = 0.05
The null hypothesis will be rejected.
Conclusion:
There is a significant difference between the means.
Thus, the correct option is B.
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
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)
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.
The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $100,000 per year: "Do you believe that it is morally wrong for unwed women to have children?" Of the individuals who earned in excess of $100,000 per year, said yes; of the individuals who earned less than $100,000 per year, said yes. Construct a 95% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The lower bound is [tex]0.0234[/tex]
The upper bound is [tex]0.100[/tex]
So from the value obtained the solution to the question are
1 Does not include
2 sufficient
3 not different
Step-by-step explanation:
From the question we are told that
The sample size of individuals who earned in excess of $100,000 per year is [tex]n_ 1 = 1205[/tex]
The number of individuals who earned in excess of $100,000 per year that said yes is
[tex]w = 712[/tex]
The sample size individuals who earned less than $100,000 per year is [tex]n_2 = 1310[/tex]
The number of individuals who earned less than $100,000 per year that said yes is
[tex]v= 693[/tex]
The sample proportion of individuals who earned in excess of $100,000 per year that said yes is
[tex]\r p _ 1 = \frac{w}{n_1 }[/tex]
substituting values
[tex]\r p _ 1 = \frac{712}{1205}[/tex]
[tex]\r p _ 1 =0.5909[/tex]
The sample proportion of individuals who earned less than $100,000 per year that said yes is
[tex]\r p _ 1 = \frac{v}{n_2 }[/tex]
substituting values
[tex]\r p _ 1 = \frac{693 }{1310}[/tex]
[tex]\r p _ 1 = 0.529[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 1 -0.95[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p _1 (1- \r p_1 )}{n_1} + \frac{ \r p _2 (1- \r p_2 )}{n_2} } }[/tex]
substituting values
[tex]E = 1.96 * \sqrt{ \frac{ 0.5909 (1- 0.5909 )}{1205} + \frac{ 0.592 (1- 0.6592 )}{1310} } }[/tex]
[tex]E =0.03846[/tex]
Generally the 95% confidence interval is
[tex](\r p_1 - \r p_2) - E < p_1 - p_2 <( \r p_1 - \r p_2 ) + E[/tex]
substituting values
[tex](0.5909 - 0.529 ) - 0.03846 < p_1 - p_2 < (0.5909 - 0.529 ) + 0.03846[/tex]
[tex]0.02344 < p_1 - p_2 < 0.10036[/tex]
The lower bound is [tex]0.0234[/tex]
The upper bound is [tex]0.100[/tex]
So from the value obtained the solution to the question are
1 Does not include
2 sufficient
3 not different
The lower bound is 0.0234 and the upper bound is 0.100. Then the 95% confidence interval is (0.0234, 0.100)
What is the margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $100,000 per year.
The sample size of individuals who earned in excess of $100,000 per year will be
[tex]\rm n_1 =1205[/tex]
The sample size of individuals who earned less than $100,000 per year will be
[tex]\rm n_1 =1205[/tex]
The number of individuals who earn an excess of $100,000 per year that said yes will be
[tex]\rm w = 712[/tex]
The number of individuals who earn less than $100,000 per year that said yes will be
[tex]\rm v= 693[/tex]
Then the sample proportion of individuals who earned in excess of $100,000 per year that said yes will be
[tex]\rm \hat{p}_1=\dfrac{w}{n_1}\\\\\hat{p}_1=\dfrac{712}{1205}\\\\\hat{p}_1= 0.5909[/tex]
Then the sample proportion of individuals who earned less than $100,000 per year that said yes will be
[tex]\rm \hat{p}_2=\dfrac{v}{n_2}\\\\\hat{p}_2=\dfrac{693}{1310}\\\\\hat{p}_2= 0.529[/tex]
The confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha =1-0.95\\\\\alpha =0.05[/tex]
Then the critical value of α/2 from the normal distribution table. Then the value of z is 1.96, then the error of margin will be
[tex]E = z_{\alpha /2} \times \sqrt{\dfrac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \dfrac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\E = 1.96 \times \sqrt{\dfrac{05909(1-0.5909)}{1205} + \dfrac{0.529(1-0529)}{1310}}\\\\E = 0.03846[/tex]
The 95% confidence interval will be
[tex]\begin{aligned} (\hat{p}_1-\hat{p}_2)-E & < p_1-p_2 < (\hat{p}_1-\hat{p}_2) + E\\\\(0.5909 - 0.529) - 0.03846 & < p_1-p_2 < (0.5909 - 0.529) + 0.03846\\\\0.02344 & < p_1-p_2 < 0.10036 \end{aligned}[/tex]
More about the margin of error link is given below.
https://brainly.com/question/6979326
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
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
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.
PLEASE HELP ASAP THANKS IN ADVANCE
Answer:
the answer to the question is "C"
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
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.
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 !
:)
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
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
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.
(-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
convert the following measurements 13 miles to a yard
Answer:
22,880 yard
Step-by-step explanation:
1 mile - 1760 yard
therefore 13 miles x 1760 yard/mile = 22,880 yard
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.
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
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:
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.
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
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:
https://brainly.com/question/17997149
#SPJ3
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]
Please answer this correctly without making mistakes
Answer:
6 1/6 pounds
Step-by-step explanation:
since 2/3 coverted into sixths is 4/6, and 14-6 is 8, and 1/2 into sixths is 3/6, 4/6-3/6 is 1/6. You put the whole in the front and you have 6 1/6
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 :)
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.
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]
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.
