We are given the Geometric Series:
[tex]2 + \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \frac{2}{243} + \frac{2}{729}[/tex]
which can be rewritten as:
[tex]2 + \frac{2}{3} + \frac{2}{3^{2} } + \frac{2}{3^{3}} + \frac{2}{3^{4}} + \frac{2}{3^{5}} + \frac{2}{3^{6}}[/tex]
here, we can see that every term is (1/3) times the last term
Hence, we can say that the common ratio of this Geometric Series is 1/3
Finding the Sum:
We know that the sum of a Geometric Series is:
[tex]S_{n} = \frac{a(r^{n}-1)}{r-1}[/tex]
(where r is the common ratio, a is the first term, and n is the number of terms)
another look at the given Geometric Series tells us that the first term is 2 and the number of terms is 7
plugging these values in the formula, we get:
[tex]S_{n} = \frac{2((1/3)^{7}-1)}{(1/3)-1}[/tex]
[tex]S_{n} = \frac{-1.99}{-0.67}[/tex]
Sₙ = 2.97
Step-by-step explanation:
[tex] \tt2 + \frac{2}{3} + \frac{2}{ {3}^{2} } + \frac{2}{ {3}^{3} } + \frac{2}{ {3}^{4} } + \frac{2}{ {3}^{5} } + \frac{2}{ {3}^{6} } [/tex]
r = [tex]\tt{a_2 \div a_1}[/tex]
r = [tex]\tt{\frac{2}{3} \div 2}[/tex]
r = [tex]\tt{\bold{\frac{1}{3}}}[/tex]
Soo :
[tex] \sf s_n = \frac{a( {r}^{n} - 1) }{r - 1} [/tex]
[tex] \sf s_7 = \frac{2(( \frac{1}{3} ) {}^{7 - 1} - 1) }{( \frac{1}{3} - 1) } [/tex]
[tex] \sf s_7 \approx \bold{ \underline{2.97}}[/tex]
Select the correct answer.
What is the corresponding point on the unit circle for the given radian measure?
Answer: A. -sqrt (3)/2, 1/2
To get from radians to degrees, you replace the pi symbol with 180° and solve
So, (5 • 180) / 6 = 150°
150° makes a 30° angle, as the nearest x axis is the negative x axis at 180°.
As we know, a 30°, 60°, 90° triangle has sides sqrt(3)/2 and 1/2.
Since the 30° angle is on the x axis, sqrt(3)/2 will be the x value and 1/2 will be the y value. And since the triangle is in the negative x, positive y quadrant, 1/2 will be positive and sqrt(3)/2 will be negative. Giving you (-sqrt(3)/2, 1/2)
Find the equation of a line Passing through the
origin so that the tangent of the angle between the
Line in Quadrant I and the positive x-axis is square root of 3 over 3. Also find the angle.
Please also find the Augle.
Answer:
Step-by-step explanation:
y = 1/2x
the angle is 30° or in radians [tex]\pi[/tex]/6
Find an equation for the line below.
Answer:
Slope = ⅓
Step-by-step explanation:
Slope (m) = change in y/change in x
Using two points on the line, (-5, 1) and (1, 3),
Change in y = 3 - 1 = 2
Change in x = 1 - (-5) = 6
Slope (m) = change in y/change in x = 2/6
Slope = 1/3
Students in a representative sample of 69 second-year students selected from a large university in England participated in a study of academic procrastination. Each student in the sample completed the Tuckman Procrastination Scale, which measures procrastination tendencies. Scores on this scale can range from 16 to 64, with scores over 40 indicating higher levels of procrastination. For the 69 second-year students in the study at the university, the sample mean procrastination score was 41.00 and the sample standard deviation was 6.85.
Required:
a. Construct a 95% confidence interval estimate of μ, the population mean procrastination scale for second-year students at this college.
b. How does the confidence interval for the population mean score for second-year students compare to the confidence interval for first-year students of (35.447, 38.633)?
Answer:
a) The 95% confidence interval estimate of μ is (39.35, 42.5).
b) Second-year students tend to procrastinate more than first-year students
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 69 - 1 = 68
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 68 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9955
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.9955\frac{6.85}{\sqrt{69}} = 1.65[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 41 - 1.65 = 39.35
The upper end of the interval is the sample mean added to M. So it is 41 + 1.65 = 42.65
The 95% confidence interval estimate of μ is (39.35, 42.5).
b. How does the confidence interval for the population mean score for second-year students compare to the confidence interval for first-year students of (35.447, 38.633)?
The confidence interval for second-year students had higher values both at the lower and the upper end of the interval, which means that they tend to procrastinate more than first-year students
[tex]8 \div \frac{2}{3} [/tex]
I need this is an improper fraction
Answer:
you could just do 12/1 or let 8 turn into 24/3
Step-by-step explanation:
on step 1 we should do reciprocal
on step 2 we should multiply
on third step 3 we should divide
so the answer is 12
The value of a specific piece of machinery depreciates at a rate of 10% per year. The initial value of the machinery is $400. Write a formula that models the value of the machine after "t" years.
Please answer fast thank you
Answer: Y= 400 (1-0.1t)
Step-by-step explanation:
Y the value after depreciation period
400 initial value
0.1 dep rate
T time
A ski company in Vail owns two ski shops, one on the west side and one on the east side of Vail. Ski hat sales data (in dollars) for a random sample of 5 Saturdays during the 2004 season showed the following results. Is there a significant difference in sales dollars of hats between the west side and east side stores at the 10 percent level of significance?
Saturday Sales Data ($) for Ski Hats
Saturday East Side Shop West Side Shop
1 548 523
2 493 721
3 609 695
4 567 510
5 432 532
Required:
a. State the decision rule for 5 percent level of significance.
b. Find the test statistic tcalc.
Answer:
At 10 percent significance level, there is not enough statistical evidence to suggest that there is a difference between mean
a. The decision rule for 5% level of confidence is;
For test statistic is less than 2.306 we fail to reject the null hypothesis
For a test statistic larger than 2.306 we reject the null hypothesis
b. The test statistic is approximately -1.2008
Step-by-step explanation:
The given data are;
No; 1, 2, 3, 4, 5
East Side Shop; 548, 493, 609, 567, 432
West Side Shop; 523, 721, 695, 510, 532
Therefore, we have;
The mean for the East Side Shop, [tex]\overline x_1[/tex] = 529.8
The standard deviation for the East Side Shop, s₁ = 68.751
The mean for the West Side Shop, [tex]\overline x_2[/tex] = 596.2
The standard deviation for the West Side Shop, s₂ = 102.7701
[tex]t_0=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_1^{2} }{n_{1}}+\dfrac{s{2}^{2}}{n_{2}}}}[/tex]
Therefore, we have;
The null hypothesis is H₀; μ₂ - μ₁ = 0
The alternative hypothesis is Hₐ; μ₂ - μ₁ ≠ 0
[tex]t_0=\dfrac{(529.8-596.2)}{\sqrt{\dfrac{68.751^{2} }{5}+\dfrac{102.7701^{2}}{5}}} \approx -1.2008[/tex]
At degrees of freedom, df = n₁ + n₂ - 2 = 8, we have the critical-t = 1.895
Given that the critical-t is more than test statistic, we do not reject the null hypothesis, therefore, there is not enough statistical evidence to suggest that there is a difference between mean
Required;
a. At 5% level, we have critical-t = 2.306
Therefore, the decision rule for 5% level of confidence is that we fail to reject the null hypothesis when the magnitude of the test statistic is less than 2.306 and we reject the null hypothesis for a test statistic larger than 2.306
b. The test statistic is given as follows;
[tex]t_0=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_1^{2} }{n_{1}}+\dfrac{s{2}^{2}}{n_{2}}}}[/tex]
[tex]t_0=\dfrac{(529.8-596.2)}{\sqrt{\dfrac{68.751^{2} }{5}+\dfrac{102.7701^{2}}{5}}} \approx -1.2008[/tex]
For the function f(x)=2^x the y intercept is (0,1). What is the y intercept of the function y=a•2^x?
A. (0,1)
B. (0,-a)
C. (0,a)
D. (0, 1/a)
Answer:a
Step-by-step explanation:
In the decimal number 147.529, the 5 is in the
place.
Answer:
the TENTHS place
Step-by-step explanation:
hundreds tens ones.tenths hundredths thousandths
helpp i'll give you brainlyest
Answer:
D
Step-by-step explanation:
a b and c are not correct by looking at the first value
Answer:
Im guessing its D because i cant see all the options.
Step-by-step explanation:
its the graph that has two dots on 1, three dots on 2, one dot on 3, and four dots on 4.
A cashier in a bank counts the total money as 450000 in denomination of ₹100 ₹500 and ₹100 notes the number of notes are in the ratio 1:2:5 find the number of notes of each denomination
Answer:
1x+2x+5x=4,50,000
8x=450000
x=450000/8
x=56,250
put the value of x
100 rupee note = 56,250
500 rupee note =2*56250=112500
1000 rupee note =5*56250=281250
total value =56250+112500+281250=450,000
Hope this helps you!
A line that passes through the point (-4,6) with a slope of 2. The equation of that line in slope is y=......... X+?
Answer:
y=2x-2
Step-by-step explanation:
For the diagram below ,The Value of q , r is
Answer:
angle r= 45°
angle r+angle q=180°
45°+ angle q=180°[linear pair]
angle q=180°- 45°
angle q= 135°
Which of the following tables shows that y is a function of x?
Answer:
Table B
Step-by-step explanation:
Recall: a table of values can only represent a function if and only if every x-value has exactly only one y-value.
The only table that satisfies this condition is the table in option B.
In table B, every x-value is related to only exactly one y-value.
Which point best approximates 45? A B В C D 0 1 2 3 4. 5 6 7. 8 9 Ο Α OB С OD
Answer:
b or c???
Step-by-step explanation:
The point that best approximates √45 is C.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
√45
This can be written as,
= 6.7082
Now,
6.7082 is near 7 so,
The point that best approximates √45 is C.
Thus,
The point that best approximates √45 is C.
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solve
8=56
7=42
6=30
5=20
3=??
Answer:
3 = 6
Step-by-step explanation:
Every number is being multiplied by one lower than the number being used:
8 x 7 = 56
7 x 6 = 42
6 x 5 = 30
and so on.
Therefore 3 will be multiplied by 2, resultng in the number 6.
11 x m when m=3
PLSS help
Answer:
33
Step-by-step explanation:
11 times 3 =33
Are the following expressions equivalent?
A. 3x - 2x + 0.5x3x−2x+0.5x.
a. 1.5x1.5x
Answer:
1.5 x
Step-by-step explanation:
3x - 2x + 0.5x = 1.5 x
X and Y are center of circles which intersect at A and C. XA and XC are produced to meet at B and D. Prove AB = CD.
Answer:
On the diagram, construct lines BY, XY and DY.
Now, consider triangles ΔXBY and ΔXDY. We can say that these triangles are congruent by the SAS postulate (they share side XY, XY bisects ∠BYD so ∠BYX=∠DYX, and BY=DY=radius). If they're congruent, their sides are the same so BX=DX.
BX=DX
AB+radius = CD +radius
AB=CD
I NEED HELP ASAP HELP HELP HELP....
According to the line plot, what is the total amount of time spent studying by the students who studied for 1/2 of an hour each?
Answer:
2.5hrs
Step-by-step explanation:
Plz help well mark brainliest if you are correct!
Answer:
12 centimenters.
Step-by-step explanation:
Answer:
6 cm
Step-by-step explanation:
We need to find the distance from R to s which is basically the radius, we know radius is r=d/2 to 12/2 (since 12 is diameter) is 6.
Consider the inequality: y < -x + 4 So, the slope m= -1 and
Y-intercept b =4
true
or
false
helpe meee plz
Answer:true
Step-by-step explanation:
Because your slope is -x or -1 and your y intercept is 4 or b=4
The given condition is true, the inequality: y < -x + 4 So, the slope m= -1 and Y-intercept is b =4.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that the inequality is,y < -x + 4
A straight line is a combination of endless points joined on both sides of the point.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0. The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Compare the given inequality with the standard equation.
We get the slope m= -1 and Y-intercept b =4.
Thus, the given condition is true, the inequality: y < -x + 4 So, the slope m= -1 and y-intercept is b =4.
Learn more about inequality here:
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PLEASE HELP!
I AM IN A HURRY
Answer:
Honestly I have no idea what is going on in this passage or whatever it is.
Step-by-step explanation:
Compare y= -3x + 2 and x - 3y = 9.
You stop for lunch at a local pizza shop where each pizza is cut into 8
equal slices. If you ate 3 slices of pizzas, what is the approximate area of
the remaining pizza if the diameter of the pizza is 14 inches?
Answer:
11 slices
Step-by-step explanation:
If ∆HCN~∆BMD, solve for x.
Answer options:
A.11
B.12
C.13
D.14
PLEASE HELP ASAP THANK YOU!
Answer:
13
Step-by-step explanation:
GIVING EVERYTHING IF CORRECT. NO fake answers, you will be reported. And it hurts my grades so please don't.
Answer is C, hopefully I helped. :)
Find x in each triangle 4 cm 3 cm
Answer:
5cm
Step-by-step explanation:
What exactly do you mean by x?
The value of x is 5 cm.
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
example:
The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.
Given : Hypotenuse = 16 units
Let us consider the given side of a triangle as the perpendicular height = 8 units
On substituting the given dimensions to the Pythagoras theorem formula
Hypotenuse2 = Base2 + Height2
162 = B2 + 82
B2 = 256 - 64
B = √192 = 13.856 units
Given:
Two sides are 4 cm and 3 cm
Using Pythagoras theorem
x² = 4² + 3²
x² = 16+ 9
x² = 25
x=√25
x= 5 cm
Also, the range of x is in between 1 cm and 7 cm.
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Tim spent $8.16 on 12 pounds
of Sweet-smarts. How much is one
pound of Sweet-smarts?
Answer:
1.47058823529
Step-by-step explanation:
Round if needed
Answer:
Tim is gonna get diabetes >:(
Step-by-step explanation:
but your answer is .68 cents lol
What is the value of the expression below when x=1? 4x ^2 5x
Answer: 80
Step-by-step explanation:
Just substitute 1 for x in your expression and solve