Answer:
Step-by-step explanation:
The value of Domain should appear once.
Relation 1 is a function
Domain: t, j, v, s
Relation 2 is a function
Domain: -2, 4, 3 - 9, - 1
Relation 3 is not a function
Domain: 5, -2, -2, 5
Relation 4 is not a function
Domain: b, v, m, m
6,075 / 450=
I need an answer pls
Answer:
13.5
Step-by-step explanation:
Answer: 13.5
Step-by-step explanation:
just use the calculator
Can someone help me with number 5 or 6. ( find the perimeter and area)
Answer:
5. [tex]P = 11.2 cm[/tex], [tex]A=7.8cm^2[/tex]
6.[tex]P = (4x -28) yds[/tex], [tex]A= (x-7)yds^2[/tex]
Step-by-step explanation:
5) Because the figure is a square then the diagonal splits the shape into two isosceles right triangles then the triangles are 45° 45° 90° triangles and the rule for such triangle is that the hypotenuse(in this case 4) is equal to a leg ·√2 so to find the leg we divide the hypotenuse by √2 so
4/√2 which is approximately 2.83 which when rounded to the nearest tenth is 2.8
so x = 2.8 cm
And because the figure is a square the perimeter is the length if a side times four so
P= 2.8(4)
P = 11.2 cm
A= 2.8(2.8)
A = 7.84cm^2 which when rounded to the nearest tenth is 7.8cm^2
6) This figure is also a square so the same rules apply for finding perimeter and area so
P = 4(x-7)
P = 4x - 28
P = (4x -28) yds
A = (x - 7)(x-7) which would just be A=(x-7)yds^2 or we could expand our answer
Use the FOIL method
x^2 -7x -7x + 49
Combine like terms
x^2 -14x +49
In your music collection, 75% are "burned" discs while 25% are CDs you purchased from a store. The CD player in your car is very particular...if there is the slightest irregularity in the disc it will not play. You have realized your car CD player will play 95% of the store purchased discs, but only 20% of the burned discs.
Let event B occur if the CD is burned and event P occur if the disc will play. Create a tree diagram starting with P(B) and P (-B)
on the far left.
a) What is the probability that a CD will not play in your car? Round to 4 decimal places.
b) What is the probability, given that the CD does not play, that it is store bought? Round to 4 decimal places.
ewdf
The probability that a CD will not play in your car is 0.76 and given that the CD does not play, the probability that it is store bought is 0.1053.
What is Probability?Probability is the study of the chances of particular outcomes in a set of given circumstances. It is used to measure the likelihood of an event occurring, and it is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can also be expressed as percentages, fractions, or decimals. Probability is used in many fields, including mathematics, finance, engineering, and science.
P(B) = 0.20
P(-B) = 0.80
P(No Play | B) = 0.20
P(No Play | -B) = 0.95
a) P(No Play) = P(No Play | B)*P(B) + P(No Play | -B)*P(-B)
= 0.20*0.20 + 0.95*0.80 = 0.76
b) P(Store Bought | No Play) = P(No Play | B)*P(B) / P(No Play)
= 0.20*0.20 / 0.76 = 0.1053
From the tree diagram, the probability that a CD will not play in your car is 0.76 and given that the CD does not play, the probability that it is store bought is 0.1053.
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Compute the compound amount and the interest on a loan of $10800 compounded annually for four years at 10%. Use the $1.00 future value table or the future value and compound interest formula.
Answer:
$5,149.44
Step-by-step explanation:
To calculate the compound amount and interest on a loan of $10800 compounded annually for four years at 10%, we can use the formula:
A = P(1 + r)^t
where A is the compound amount, P is the principal (the initial loan amount), r is the interest rate (as a decimal), and t is the number of years.
In this case, P = $10800, r = 0.10 (10% as a decimal), and t = 4. Substituting these values into the formula, we get:
A = $10800(1 + 0.10)^4
A = $10800(1.10)^4
A = $15,949.44
Therefore, the compound amount after four years is $15,949.44.
To calculate the interest, we can subtract the principal from the compound amount:
Interest = $15,949.44 - $10,800
Interest = $5,149.44
Therefore, the interest on the loan is $5,149.44.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10800\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A = 10800\left(1+\frac{0.10}{1}\right)^{1\cdot 4} \implies \boxed{A = 15812.28} ~\hfill \underset{ earned~interest }{\stackrel{ 15812~~ - ~~10800 }{\boxed{5012}}}[/tex]
Which expressions are equivalent to -8x + 4? Mark all that
apply.
A. -4 (2x - 1)
B. 4(2x - 1)
C. 4x (2 - 1)
D. 4x (2x + 1)
E. 4(-2x + 1)
F. 4(2x + 1)
Answer:
A and E
Step-by-step explanation:
A. -4 (2x - 1) = -8x + 4
B. 4 (2x - 1) = 8x - 4
C. 4x (2 - 1) = 8x - 4
D. 4x (2x + 1) = 8x² + 4x
E. 4 (-2x + 1) = -8x +4
F. 4 (2x + 1) = 8x + 4
(a) Consider a t distribution with 15 degrees of freedom. Compute P(t2-1.34). Round your answer to at least three
decimal places.
P(t≥-1.34) =
(b) Consider a t distribution with 13 degrees of freedom. Find the value of c such that P(-c
answer to at least three decimal places.
=0
C=
The probability from the t distribution is 0.8999 and the value of c is 1.77
Calculating the probability from the t distributionFrom the question, we have the following parameters that can be used in our computation:
Degrees of freedom = 15
Using a graphing calculator, we have
P(t ≥ -1.34) = 1 - 0.1001
So, we have
P(t ≥ -1.34) = 0.8999
Calculating the value of c, we have
P(-c < t < c) = 0.95
At a degree of freedom of 13, we have
c = 1.77
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HELP ASAP OVERDUE!!!!!!!
R(3, 2), S(5, -2), and T(6, 0) are the coordinates of a triangle's vertices. If the triangle is reflected over the y-axis, what are the coordinates of the image?
R'(-3, 2), S'(-5, -2), T'(6, 0)
R'(-3, -2), S'(-5, 2), T'(-6, 0)
R'(3, -2), S'(5, 2), T'(6, 0)
R'(-3, 2), S'(-5, -2), T'(-6, 0)
R'(-3, 2), S'(-5, -2), T'(-6, 0) is the correct answer for the given problem.
To reflect a point over the y-axis, we negate its x-coordinate.
Using this rule, the coordinates of the image of R, S, and T after reflecting the triangle over the y-axis are:
R'(-3, 2) (negate the x-coordinate of R)
S'(-5, -2) (negate the x-coordinate of S)
T'(-6, 0) (negate the x-coordinate of T)
Therefore, the correct answer is: R'(-3, 2), S'(-5, -2), T'(-6, 0).
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The taxes on a house assed at 110,000 are 2970
Answer:
$3267
Step-by-step explanation:
$121000 × $2970/$110000
= 11 × 297
= $3267
The taxes on the house with an assessment of $121000 are $3267
Answer:
$3267
Step-by-step explanation:
You want to know the taxes on a house assessed at $121000 if the taxes on a house assessed at $110000 are $2970.
ProportionThe taxes are proportional to the house value, so if the house value goes up by a factor of 121000/110000, so do the taxes. The taxes will be ...
(121000/110000)·$2970 = $3267
The taxes on the house with an assessment of $121,000 are $3267.
__
Additional comment
You could go to the trouble to find the tax rate, which is ...
rate = $2970/$110000 = 0.027
This can be described as 27 mils, 27‰, or $27 per thousand.
Multiplying this rate by the higher assessed value shows the taxes are ...
0.027 × $121000 = $3267
We don't really need to know the tax rate. All we need to know is that the house with the 10% higher value will have 10% higher taxes.
Student Name:.
Module 10 Test
Date:.
19) Grace competes on her school's archery team. On average she hits a bullseye 2 out of every 3
arrows. She shoots 5 arrows during each round of competition. Describe a simulation that you
could run to estimate the number of bullseyes Grace will hit during her next round. Explain
In order to simulate the amount of bullseyes that Grace will strike during her upcoming turn, we can carry out the following steps:
What are the steps?Set up a loop which will execute the simulation for a predetermined number of rounds. Let's say that we wish to conduct 10,000 rounds as an example.
Within each cycle of the loop, mimic every round by generating 5 random numbers between 0 and 1 – signifying the likelihood of hitting a bullseye with each projectile.
For each round, accumulate the total number of bullseyes achieved by summing together the resultant quantity of times when the generated figure is less than or equivalent to 2/3.
Subsequent to the successful running of the simulation through the 10,000 rounds, calculate the average number of bullseyes struck in per round basis by dividing the complete amount of bullseyes hit with 10,000.
Finally, express the projected amount of bullseyes that Grace is anticipated to hit within her successive turn, by stating the average attained from step 4.
Consequently, with judicious repeating of multiple rounds, our calculation can factor in the differential element instinctive within this process and finally acquire a more precise tally of the estimated number of bullseyes Grace could potentially hit during her impending turn.
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please help me wih the answer
Volume of pyramid = lwh/3
V = (7/3) x (15/2) x (24/5) / 3
V = (2520/30) / 3
V = 28cm^3
ABC Insurance offers an annuity with a minimum interest rate of 3.5% APR for the *
next 5 years. You decide to invest $2000 into this account. What type of annuity is
this?
OSingle-payment fixed annuity
OSingle-payment variable annuity
ORecurring-payment fixed annuity
O Recurring-payment recurring annuity
Answer:
Single payment Variable annuity
Need help now with this problem please! If your not going to help, kindly don’t comment.
The value of θ for the given equation is θ = 54.74°.
What is inverse cosine function?The inverse cosine function (arccos) has a range of 0 to arccos(x), where x is a real number in the range of -1 to 1. An angle in radians between 0 and, which measures the angle between the x-axis and the terminal side of a unit circle that crosses the line between the origin and the point (x, y), is the result of the inverse cosine function. To put it another way, the inverse cosine function returns the angle whose cosine is equal to a specified value x.
The given equation is 4sec(θ) - 7 = 0:
Now, isolating the value of sec(θ) we have:
4sec(θ) = 7
sec(θ) = 7/4
Now, converting into cos we have:
cos(θ) = 4/7
θ = arccos(4/7)
θ = 54.74°
Hence, the value of theta for the given equation is θ = 54.74°.
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Graph 2 4/5, -2/5, -1 1/7, and 7/6 on a number line.
Answer:
trying not to get too much
Step-by-step explanation:
j and
In the diagram below, P is a point inside square ABCD. Find x.
The length of AB, x is 2.414 units.
Let's call the length of the square's side x. Then, the hypotenuse of each triangle is the diagonal of the square, which has length x√2.
Let's consider one of these triangles, say triangle APC. We can use the Pythagorean theorem to find the length of PC:
PC² = AP² + AC²
PC² = 1² + x²
PC = √(1+x²)
Since triangle APC is isosceles, we know that angle APC is 45 degrees. Therefore, angle CPB is also 45 degrees, since it is the supplement of angle APC. Similarly, angle BPC is 90 degrees, since it is the sum of angles CPB and BPA.
We can now use the sine rule in triangle BPC to find the length of BP:
sin(BPC) / BP = sin(CPB) / x√2
sin(90°) / BP = sin(45°) / x√2
BP = x / √2
Since AP = BP = CP = 1, we have:
1 + x / √2 + √(1+x²) = x
Solving this equation for x gives:
x ≈ 2.414
Therefore, the length of AB is approximately 2.414 units.
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What meaning of the statement this?
The statement proposes that for any subset X of a group G, there exists a unique smallest subgroup H of G that contains X.
How do we explain this?We must take into consideration the collection of all subgroups of G that contain X in order to get the smallest subgroup of G that contains X.
Given that G is included in the collection, it is not empty.
The smallest subgroup of G that contains X is then obtained by taking the intersection of all the subgroups in the said collection.
The subgroup contains X and is contained in every other subgroup of G that contains X because the intersection of subgroups may not be immediately apparent or simple to compute.
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Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
The p value is: 13.1578
P-value:P-value is calculated as P (Z> Test statistics) in a right-tailed test. P-value is generally compared with 5% but it is a misconception that if p is less than 0.05, then there is sufficient evidence to reject the null hypothesis whereas it is always considered with the significance level.
We have the information:
[tex]H_0:p=0.4\\\\H_1:p > 0.4[/tex]
n = 100
[tex]\alpha =0.05[/tex]
x = 45
The sample proportion is given as:
[tex]p_0=\frac{x}{n}\\ \\p_0=\frac{45}{100}\\ \\p_0=0.45[/tex]
[tex]np_0(1-p_0)= 100(0.45)(0.55)[/tex]
= 24.75 > 10
The test statistics value is calculated as:
[tex]z=\frac{p_0-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
= [tex]\frac{0.45-0.4}{\sqrt{\frac{0.4(1-0.4)}{100} } }[/tex]
= 0.05/0.0038
= 13.1578
The p value is: 13.1578
Now, Put z value in bracket and p value will be found.
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An urn contains five red and three blue balls. Suppose that four of these balls are selected at random and transferred to a second urn, which is originally empty. If a random chosen ball from this second urn is blue, what is the probability that two red and two blue balls were transferred from the first urn to the second urn.
The probability that two red and two blue balls were transferred from the first urn to the second urn is 0.27 (approx).
What is probability ?
Probability is a measure of the likelihood or chance of an event occurring. It is a mathematical concept that ranges from 0 (indicating an impossible event) to 1 (indicating a certain event).
Let R1 be the event that the first ball drawn from the first urn is red, and let B1 be the event that the first ball drawn from the first urn is blue. Similarly, let R2 and B2 be the events that the second and third balls drawn from the first urn are red and blue, respectively. Finally, let B be the event that a blue ball is drawn from the second urn.
We want to find P(R2=2, B2=2 | B), the probability that two red and two blue balls were transferred from the first urn to the second urn, given that a blue ball was drawn from the second urn.
By Bayes' theorem, we have:
P(R2=2, B2=2 | B) = P(B | R2=2, B2=2) * P(R2=2, B2=2) / P(B)
To find each of these probabilities, we can use the following:
P(R2=2, B2=2) = (5 choose 2) * (3 choose 2) / (8 choose 4) = 15/56, which is the probability of selecting 2 red and 2 blue balls from the first urn.
P(B | R2=2, B2=2) = 2/4 = 1/2, which is the probability of drawing a blue ball from the second urn, given that 2 red and 2 blue balls were transferred from the first urn.
P(B) = P(B | R2=0, B2=4) * P(R2=0, B2=4) + P(B | R2=1, B2=3) * P(R2=1, B2=3) + P(B | R2=2, B2=2) * P(R2=2, B2=2), which is the total probability of drawing a blue ball from the second urn.
To find P(R2=0, B2=4), we need to use the complement rule:
P(R2=0, B2=4) = 1 - P(R2=1, B2=3) - P(R2=2, B2=2)
To find P(R2=1, B2=3), we can use:
P(R2=1, B2=3) = (5 choose 1) * (3 choose 3) / (8 choose 4) = 5/56
Substituting all these values into Bayes' theorem, we get:
P(R2=2, B2=2 | B) = (1/2) * (15/56) / P(B)
To find P(B), we can use the law of total probability:
P(B) = P(B | R2=0, B2=4) * P(R2=0, B2=4) + P(B | R2=1, B2=3) * P(R2=1, B2=3) + P(B | R2=2, B2=2) * P(R2=2, B2=2)
Substituting the values we found earlier, we get:
P(B) = (0/4) * (1 - 5/56 - 15/56) + (1/4) * 5/56 + (2/4) * 1/2 = 0.27 (approx)
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I'm confused need help
Check the picture below.
Below is the graph of equation y = -|x − 2 | +2. Use this graph to find all values of x
for the given values of y
If y = 3, we can see that there are again two values of x that satisfy the equation: x = 0 and x = 4. This is because the graph intersects the horizontal line at y = 3 at two points.
What is equation of graph?A mathematical statement used to describe the relationship between the variables that make up a graph is called an equation.
To put it another way, a graph equation is a formula that can be applied to either build the graph or identify certain points on the graph.
Using the graph of the equation y = -|x - 2| + 2, we can find all the values of x for a given value of y by looking at where the graph intersects the horizontal line at y.
For example, if y = 1, we can see from the graph that there are two values of x that satisfy the equation: x = 3 and x = 1. This is because the graph intersects the horizontal line at y = 1 at two points.
If y = 2, we can see that there is only one value of x that satisfies the equation: x = 2. This is because the vertex of the absolute value function is at (2, 2), and the graph is reflected below the x-axis, so it only intersects the horizontal line at y = 2 at one point.
We can repeat this process for any value of y to find the corresponding values of x that satisfy the equation.
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Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of the original square to make a new figure.
How does the area of her new figure compare with that of the original square?
Answer:
Step-by-step explanation:
When the mortgage is completely paid off for Mark and Lynne’s house, it will be 4 times as old as it is now. If they have 18 years left on the mortgage, how old is the house right now?
h = how old the house is right now
so right now Mark and Lynne are paying the house off, the house as we speak is "h" years old, it happens that Mark and Lynne are going to be paying the whole house in 18 years from now, so by then the house will be whatever years is now, or "h", plus 18 years, so when Mark and Lynne are done paying for it, the house will be "h + 18" years old.
Now, if the house in 18 years is going to be 4 times as old as it's right now, well, hell right now is "h" years old, 4 times that much is just "4h" years, so we can say
[tex]\stackrel{\textit{18 years from now}}{h+18}~~ = ~~\stackrel{\textit{18 years from now}}{4h}\implies 18=3h\implies \cfrac{18}{3}=h\implies 6=h[/tex]
3x^2+16x+20 vertex form
Answer:
the vertex form of the given quadratic expression is:
y = 3(x + 8/3)^2 - 4/3
Step-by-step explanation:
To write the given quadratic expression 3x^2+16x+20 in vertex form, we need to complete the square.
Step 1: Factor out the coefficient of x^2:
3(x^2 + (16/3)x) + 20
Step 2: Take half of the coefficient of x and square it:
(16/3)/2 = 8/3
(8/3)^2 = 64/9
Step 3: Add and subtract the result from step 2 inside the parentheses:
3(x^2 + (16/3)x + 64/9 - 64/9) + 20
Step 4: Simplify inside the parentheses and factor:
3[(x + 8/3)^2 - 64/9] + 20
Step 5: Simplify the constant term:
3(x + 8/3)^2 - 4/3
Therefore, the vertex form of the given quadratic expression is:
y = 3(x + 8/3)^2 - 4/3
PLEASE HELP, TURNING IN LATE AND IM CONFUSED
Answer:
The answer should be P'(-3,-7), Q(-9,3), and R'(-4,1) which is D.
Step-by-step explanation:
Data set:115 127 119 113 121 123 113 111 118 115 119 129 111 115 117 112; data value:121
The percentile for the data value 121 in the given data set is 75th percentile.
To find the percentile for the data value 121 in the given data set, we need to follow these steps:
Step 1, Sort the data set in ascending order.
111 111 112 113 113 115 115 115 117 118 119 119 121 123 127 129
Step 2, Calculate the rank of the data value 121 in the sorted data set.
The rank of 121 is the position of 121 in the sorted data set. Counting from left to right, we see that 121 is the 12th value in the sorted data set.
Step 3, Calculate the percentile rank.
Percentile rank = (Rank of the data value / Total number of data values) x 100
In this case, the total number of data values is 16. Therefore,
Percentile rank = (12/16) x 100 = 75
This means that 75% of the data values in the set are less than or equal to 121.
Correct Question :
Find the percentile for the data values. Data set:115 127 119 113 121 123 113 111 118 115 119 129 111 115 117 112; data value:121
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A train track through a mountain is 1600 feet long and makes an angle of 1.1 with the horizontal. What is the change in elevation from one end of the tunnel to the other?
Answer:
Please mark me the brainliest. It took me a lot of time to answer this question.
Step-by-step explanation:
To solve this problem, we can use trigonometry. We know that the length of the train track through the mountain is 1600 feet and that the angle it makes with the horizontal is 1.1. Let's call the change in elevation from one end of the tunnel to the other "h".
We can use the tangent function to find "h", which is defined as the opposite side (the change in elevation) divided by the adjacent side (the length of the train track through the mountain). In this case, the tangent of the angle 1.1 is equal to h divided by 1600:
tan(1.1) = h/1600
To solve for "h", we can multiply both sides by 1600:
h = 1600 * tan(1.1)
Using a calculator, we can find that tan(1.1) is approximately 0.0192. Therefore:
h = 1600 * 0.0192
h = 30.72 feet
So the change in elevation from one end of the tunnel to the other is approximately 30.72 feet.
2s +3≤7 OR 3s +5> 26
Number 10
The solutions of the inequalities are s≤2 and s>7 respectively
The given inequalities are 2s +3≤7 OR 3s +5> 26
We have to find the solutions
2s +3≤7
Subtract 3 from both sides
2s≤4
Divide both sides by 2
s≤2
Now inequality 3s +5> 26
Subtract 5 from both sides
3s>21
s>7
Hence, the solutions of the inequalities are s≤2 and s>7 respectively.
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If you had the following scores in your math quizzes (80,85,90,95,100). What would be the average of all your quiz scores which is also called the mean? 50 points
The average of all your quiz scores which is also called the mean would be 90.
Since we know that average or mean can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
We are given that the following scores in your math quizzes (80,85,90,95,100).
Therefore,
Average = Sum of observations/the number of observations
Average = 80 + 85 + 90 + 95 + 100 / 5
Average = 450/5
Average = 90
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A university health services physician is concerned about how much sleep freshman are getting. she asks a simple random sample of 50 students if they got at least 8 hours of sleep the previous night. then she constructs a 95% confidence interval for the true proportion of all freshman college students who got at least 8 hours of sleep the previous night.
(a) Explain what would happen to the width of the interval if the confidence level were decreased to 90%.
(b) Explain what you would expect to happen to the width of the interval if the sample size was increased to 200 students.
(c) After calculating the interval, the physician realizes that the sample was drawn from only the 70% of freshman who had turned in their health forms by the time they arrived on campus. can she adjust the confidence interval to take this undercoverage into account? if so, how? if not, why not?
Decreasing confidence level or increasing sample size decreases width of confidence interval. Undercoverage cannot be adjusted after sampling.
Define sampling ?
Sampling is the process of selecting a subset of individuals or units from a larger population to estimate characteristics of the population.
(a) If the confidence level were decreased from 95% to 90%, the width of the interval would decrease. This is because a lower confidence level requires a smaller margin of error, which is the product of the critical value and the standard error of the proportion.
(b) If the sample size were increased from 50 to 200 students, the width of the interval would decrease. This is because as the sample size increases, the standard error of the proportion decreases, resulting in a smaller margin of error and a narrower confidence interval.
(c) The physician cannot adjust the confidence interval to take undercoverage into account after the sample has been collected. Undercoverage is a type of sampling bias that occurs when some members of the population are less likely to be included in the sample than others. Adjusting the confidence interval would require information about the characteristics of the missing 30% of freshmen, which is unknown. The best way to address undercoverage is to try to improve the sampling method in future studies, such as by using stratified sampling to ensure that all subgroups of the population are represented in the sample.
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Determine the 12th term in the following geometric sequence
7, 14, 28, 56, 112...
d
14,336
28,672
7,168
29
Answer:
14336
Step-by-step explanation:
the general term is:
s(n) = 7*(2)^(n-1)
you can check it by plugging in some number:
s(3) = 7*2^(3-1) = 7*4 = 28
s(4) = 7*2^(4-1) = 7*8 = 56
The 12th term is:
s(12) = 7*2^(12-1) = 7*2^11 = 7*2048 = 14336
_ + 46 =231 what is the answer
Answer: 185
Step-by-step explanation:
231-46=185
Answer: 185
Step-by-step explanation:
231-46