Answer:
[tex]a_{n} = -64(-\frac{1}{4})^{n-1}[/tex]
it seems like the first term is -64, so lets write the formula accordingly:
a_n = a1(r)^(n-1)
where 'n' is the number of terms
a1 is the first term of the sequence
'r' is the ratio
the ratio is [tex]-\frac{1}{4}[/tex] because -64 * [tex]-\frac{1}{4}[/tex] = 16 and so on...
the explicit formula is :
[tex]a_{n}[/tex] = [tex]-64(-\frac{1}{4} )^{n-1}[/tex]
8.113 as a fraction PLEASE HELPP
Answer:
8 113/1000(as a mixed number) 8113/1000(as an improper fraction)
Step-by-step explanation:
1. Convert 0.113 to a fraction...113/1000
2. As there is no further simplification needed, add 8 to 113/1000....8 113/1000
3. To convert 8 113/1000 from a mixed number to an improper fraction, multiply 8 (the whole number) and 1,000(the denominator)...8,000. Then add 113 (the numerator) to 8,000...8113. After that, you put 8113 over the denominator of the previous mixed number, getting 8113/1000 as the improper fraction.
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
What are 3 ratios that are equivalent to 8 :5
Answer:
Step-by-step explanation:
8/5 = 16/10 = 24/15
8:5 = 16:10 = 24:15
If a $6 per unit tax is introduced in this market, then the new equilibrium quantity will be
Answer:
soory i dont know just report me if you angry
Lesson 1 Skills Practice
Lines For Exercises 1-12, use the figure at the right. In that figure, line m is parallel.
Classify each pair of angles as alternate interior, alternate exterior, or corresponding.
Pictures Below.
9514 1404 393
Answer:
alternate interior: (2, 4), (3, 5)alternate exterior: (1, 7), (43°, 6)corresponding: (1, 5), (2, 6), (3, 7), alternate interior: (2, 4), (3, 5)corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)4)
Step-by-step explanation:
In this geometry, "corresponding" angles are in the same direction from the point of intersection of the transversal with the parallel line.
"Alternate" refers to angles on opposite sides of the transversal. "Interior" and "exterior" refer to angles between and outside of the parallel lines, respectively.
Here, we list all angle pairs in each classification, so you can answer questions 1-12 based on this list.
alternate interior: (2, 4), (3, 5)
alternate exterior: (1, 7), (43°, 6)
corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)
__
Additional classifications are also used:
consecutive (same-side) interior: (2, 5), (3, 4)
consecutive (same-side) exterior: (1, 6), (43°, 7)
vertical: (1, 3), (2, 43°), (4, 6), (5, 7)
linear pairs: (1, 2), (1, 43°), (2, 3), (3, 43°), (4, 5), (4, 7), (5, 6), (6, 7)
у
х
9
3
Find the value of y.
9514 1404 393
Answer:
(d) 6√3
Step-by-step explanation:
There are several ways to work multiple-choice problems. One of the simplest is to choose the only answer that makes any sense. Here, that is 6√3.
y is the hypotenuse of the medium-sized right triangle, so will be longer than that triangle's longest leg. y > 9
The only answer choice that meets this requirement is ...
y = 6√3
__
In this geometry, all of the right triangles are similar. This means corresponding sides have the same ratio. For y, we're interested in the ratio of long leg to hypotenuse.
long leg/hypotenuse = y/(9+3) = 9/y
y² = 9(9+3) = 9·4·3
y = 3·2·√3 . . . . . . take the square root
y = 6√3
__
Additional comments
You may notice that y is the root of the product of the longer hypotenuse segment (9) and the whole hypotenuse (9+3 = 12). We can say that y is the "geometric mean" of these segment lengths. Similarly (pun only partially intended), x will be the root of the product of the short segment (3) and the whole hypotenuse (12)
x = √(3·12) = 6
This is another "geometric mean" relation.
Further, the altitude will be the geometric mean of the two segments of the hypotenuse:
h = √(9·3) = 3√3
A way to summarize all of these relations is to say that the legs of the right triangle that are not the hypotenuse are equal to the geometric mean of the segments of the hypotenuse that the leg intercepts.
x = √(3·12)
y = √(9·12)
h = √(3·9)
Suppose that a local TV station conducts a survey of a random sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
Required:
a. Construct and interpret a 99% CI for the true proportion of voters who prefer the Republican candidate.
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
Answer:
a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
So 120 - 62 = 58 favored the Republican candidate, so:
[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]
The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
II. Round to the nearest hundred.
11. 582
12. 1,234
13. 640
14. 770
15. 1,104 can you please tell what the answer?
Answer:
582-600
1,234-1,200
640-600
770-800
1,104-1,100
What is the x intercept of the graph that is shown below? Please help me
Answer:
(-2,0)
Step-by-step explanation:
The x intercept is the value when it crosses the x axis ( the y value is zero)
x = -2 and y =0
(-2,0)
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school
year are given in the following table:
Grade Geometry Algebra II Pre-Calculus AP Statistics Total
10th
150
75
25
5
255
11th
50
100
75
20
245
12th
10
50
100
65
225
Total 210
225
200
90
725
Part A: What is the probability that a student will take AP Statistics? (2 points)
Part B: What is the probability that a 12th-grader will take either Pre-Calculus or AP Statistics? (2 points)
Part C: What is the probability that a student will take Algebra II given that he or she is in the 11th grade? (2 points)
Part D: Consider the events "A student takes Algebra II and "A student is a 10th-grader. Are these events independent? Justify your answer. (4 points)
A well formatted table of the distribution is attached below :
Answer:
0.124
0.733
0.408
Step-by-step explanation:
Using the table Given :
1.) P(AP Statistics) = 90 / 725 = 0.124
2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733
3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408
A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.96,1.81,1.97,1.83,1.87,1.84,1.85,1.94,1.96,1.81,1.86,1.95,1.89
===============================================
Explanation:
Add up the values to get
1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54
Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.
So the mean is approximately 1.8876923
---------------------
Now make a spreadsheet as shown below
We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.
After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.
That sum is approximately 0.04403076924
Next, we divide that over n-1 = 13-1 = 12
0.04403076924 /12 = 0.00366923077
That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.
sqrt(0.00366923077) = 0.06057417576822
This rounds to 0.061 which is the final answer.
A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs. If four eggs are selected at random, without replacement, what is the probability that all four are brown?
Answer:
The probability will 4.32%.
The probability that all four are brown is 35/8,64,501.
Given that, A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs.
What is the probability without replacement?Probability without replacement means once we draw an item, then we do not replace it back to the sample space before drawing a second item. In other words, an item cannot be drawn more than once.
If four eggs are selected at random, without replacement, the probability that all four are brown is 7/69 × 6/68 × 5/67 × 4/66
= 7/69 × 3/34 × 5/67 × 2/33
=7/23 × 1/17 × 5/67 × 1/33
=35/8,64,501
Therefore, the probability that all four are brown is 35/8,64,501.
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A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
look at the image below
Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6
Answer:
Step-by-step explanation:
I assume the sequence is 0, 2, 4, 6
nth term = 2(n-1)
The function f is defined by f(x) = 4x + 1. What is the value of f(3)?
O 13
O 17
O 65
O 82
Answer:
13
Step-by-step explanation:
f(x) = 4x + 1
Let x= 3
f(3) = 4*3+1
= 12+1
= 13
Can anyone please help me out?
look below for the image
Answer:
135.7 yd²
Step-by-step explanation:
Surface area of the cone,
πr²+πrl
= π×3²+π×11.4×3
= 43.2π
= 135.7 yd² (rounded to the nearest tenth)
Most brainiest for the right answer on this problem!
Answer:
82.8
Step-by-step explanation:
mean = sum of all points, over the total given number of points
84 * 26 = 2184
2184 + 69 + 66 = 2319
Now the total number of tests is 26 + 2 or 28
So divide 2319 by 28
2319/28 = 82.82142
rounded to the nearest tenth is 82.8
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
PLSSS HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
I believe its EG and NE but i might be wrong
Step-by-step explanation:
The expression y + y + 2y is equivalent to ??
because ??
Answer:
4y
They would have the same value if a number was substituted for y
Step-by-step explanation:
y+y+2y =
Combine like terms
4y
These are all like terms
They would have the same value if a number was substituted for y
Let y = 5
5+5+2(5) = 5+5+10 = 20
4(5) =20
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden. She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
What is the sample mean of the heights of the plants in Susan's garden?
Answer:
3.5 inches
Step-by-step explanation:
Sample mean basically means that we need to find the average of the samples.
So the formula for finding average is
Number of observations/ Number of Occurrences
So when we add the values together we get
42.
So there are 12 numbers
So, 42/12 =
3.5 inches
The sample mean of the heights of the plants in Susan's garden is
3.5 inches.
Here,
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.
She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
We have to find the sample mean of the heights of the plants in Susan's garden.
What is Average?
Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.
Now,
The recorded data is;
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.
Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]
Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]
Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.
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Find the missing side round to the nearest tenth
======================================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(29) = x/24
24*sin(29) = x
x = 24*sin(29) ..... exact value
x = 11.635430885912 .... approximate value
x = 11.6
To get the approximate value, you'll need a calculator. Make sure the calculator is in degree mode.
For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answer:
the probability of taking a clear picture of a California candor is .24
Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red then blue).
Answer:
4/27
Step-by-step explanation:
total number of marbles=9
probability of red=4/9
since you returned the first marble, the total number of marbles remains the same
prob(Blue)=(3/9)=1/3
P(red then blue)=(4/9)*(1/3)
=4/27
1. (02.01)
Solve -4(x + 10) - 6 = -3(x - 2). (1 point)
-40
-46
-52
52
Answer:
-52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Answer: -52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
How do you make 2.318181818 a mixed number
Please please help!! Quickly
Answer:
pretty sure its D
Answer:
I have to give 2 Ans for my question
Choose the system of inequalities that best matches the graph below. A. B. C. D.
The system of inequalities that is graphed is:
y ≤ - (2/3)*x
y < x - 3
So the correct option is B.
Which system of inequalities is the graphed one?First, we can see that for both of the inequalities the shaded part is below the lines.
You also can see that the solid line (correspondent to the symbol ≤) is the one with a negative slope, and the dashed line (correspondent with the line <) is the one with a positive slope.
Only with that, we conclude that the correct option is B.
y ≤ - (2/3)*x
y < x - 3
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