We want to find a recursive formula for f(n) = 64 + 6n
The recursive formula is f(n) = f(n - 1) + 6
First, a recursive formula is a formula that gives the value of f(n) in relation to the value of f(n - 1) or other previous terms on the sequence.
We know that:
f(n) = 64 + 6n
f(n - 1) = 64 + 6*(n - 1) = 64 + 6*n - 6
Then we can rewrite:
f(n) = 64 + 6n + 6 - 6
f(n) = ( 64 + 6n - 6) + 6
And the thing inside the parenthesis is equal to f(n - 1)
Then we have:
f(n) = f(n - 1) + 6
This is the recursive formula we wanted to get.
If you want to learn more, you can read:
https://brainly.com/question/11679190
Gary earned an average score of 77 on his first five quizzes. What score will he need on his next quiz to have an overall average of 79
Answer:
The next score he needs to have an overall average of 79 is 89.
Step-by-step explanation:
Gary earned an average score of 77 on his 5 quizzes . The number of score he needs to have an average of 79 can be calculated below.
average score = 77
number of quizzes = 5
sum of Garry score = a
a/5 = 77
cross multiply
a = 77 × 5
a = 385
let
the next score he needs be b to score an average of 79
average = 79
number of quizzes = 6
385 + b/6 = 79
cross multiply
385 + b = 474
b = 474 - 385
b = 89
The next score he needs to have an overall average of 79 is 89.
A hyperbola centered at the origin has vertices at (0,±\sqrt(54) and foci at (0,±\sqrt(89)
Write the equation of this hyperbola
The equation of the hyperbola with vertices at[tex](0,±\sqrt{54}) and foci at (0,±\sqrt{89}) is \(\frac{y^2}{54} - \frac{x^2}{35} = 1\).[/tex]
To write the equation of a hyperbola, you need to know the values of a (which determines the distance from the center to the vertices) and c (which determines the distance from the center to the foci). The general equation for a hyperbola centered at the origin (h, k) with a vertical transverse axis is:
[tex]\(\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1\)[/tex]
Since the hyperbola is centered at the origin (0,0), this simplifies the equation:
[tex]\(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)[/tex]
For this hyperbola, the vertices are at [tex](0,\(\pm\sqrt{54}\)), so a is \(\sqrt{54}\)[/tex]. The foci are at [tex](0,\(\pm\sqrt{89}\))[/tex], so c is [tex]\(\sqrt{89}\)[/tex]. To find b, we use the relationship [tex]c^2 = a^2 + b^2 (since e > 1)[/tex].
Calculating b, we have:
[tex]\(c^2 = a^2 + b^2\)[/tex]
[tex]\(89 = 54 + b^2\)[/tex]
[tex]\(b^2 = 35\)[/tex]
Thus, the equation of the hyperbola is:
[tex]\(\frac{y^2}{54} - \frac{x^2}{35} = 1\)[/tex]
The equation of the hyperbola is : [tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]
To write the equation of the hyperbola given its vertices and foci, we need to determine the major axis, minor axis, and eccentricity.
The vertices of the hyperbola are at [tex]\( (0, \pm \sqrt{54}) \)[/tex] and the foci are at [tex]\( (0, \pm \sqrt{89}) \).[/tex]
The distance from the center to a vertex is [tex]\( \sqrt{54} \)[/tex], which is the length of the semi-major axis, [tex]\( a \)[/tex]. The distance from the center to a focus is [tex]\( \sqrt{89} \),[/tex] which is the length of [tex]\( c \)[/tex], the distance from the center to a focus.
The relationship between [tex]\( a \), \( b \)[/tex] (the length of the semi-minor axis), and [tex]\( c \)[/tex] for a hyperbola is given by the equation [tex]\( c^2 = a^2 + b^2 \).[/tex]
Substituting the given values, we get:
[tex]\[ 89 = 54 + b^2 \][/tex]
[tex]\[ b^2 = 89 - 54 \][/tex]
[tex]\[ b^2 = 35 \][/tex]
So, [tex]\( b = \sqrt{35} \)[/tex].
The standard form equation of a hyperbola centered at the origin with vertices on the y-axis is:
[tex]\[ \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \][/tex]
Substituting [tex]\( a = \sqrt{54} \) and \( b = \sqrt{35} \),[/tex] we get:
[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]
Therefore, the equation of the hyperbola is:
[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]
This equation represents a hyperbola centered at the origin with vertices at [tex]\( (0, \pm \sqrt{54}) \) and foci at \( (0, \pm \sqrt{89}) \).[/tex]
A newspaper reported the results of a poll concerning topics that teenagers most want to discuss with their parents. In the the poll 37% of teenagers said they would like to talk with their parents about school. These and other percentages were based on a national sampling of 536 teenagers. Estimate the proportion of all teenagers that want more discussions with their parents about school. Use a 99% confidence level. Right-click this Excel file to open a worksheet template.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 536
p = 37/100 = 0.37
q = 1 - 0.37 = 0.63
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.005 = 0.995
The z score corresponding to the area on the z table is 2.53. Thus, confidence level of 99% is 2.58
Therefore, the 99% confidence interval is
0.37 ± 2.58 × √(0.37)(0.63)/536
= 0.37 ± 0.054
The lower limit of the confidence interval is
0.37 - 0.054 = 0.316
The upper limit of the confidence interval is
0.37 + 0.054 = 0.424
Therefore, with 99% confidence interval, the proportion of all teenagers that want more discussions with their parents about school is between 0.316 and 0.424
Jimmy has 14 apples and 6 bananas. If he gives half of his fruit to Lisa, how many bananas did he give away? Please help
Answer:
3
Step-by-step explanation:
14/2=7 6/2=3 7+3=10 which is also half of 20 (20 is how many fruits he has) He gave away 3 bananas
1. The midpoint of GH is (-2,3), and its endpoints are G (g,4) and H (-2,h). What are the values of g and h
Answer:[tex](g,h)=(-2,2)[/tex]
Step-by-step explanation:
Given
Midpoint is [tex](-2,3)[/tex]
Endpoints are [tex]G(g,4)[/tex] and [tex]H(-2,h)[/tex]
Mid point of any two point is given by
[tex]x=\frac{x_1+x_2}{2}[/tex]
and [tex]y=\frac{y_1+y_2}{2}[/tex]
So,[tex]-2=\frac{g+(-2)}{2}[/tex]
[tex]-4=g-2[/tex]
[tex]g=-2[/tex]
Also
[tex]3=\frac{4+h}{2}[/tex]
[tex]6=4+h[/tex]
[tex]h=2[/tex]
Therefore [tex](g,h)=(-2,2)[/tex]
An office supply company manufactures paper clips, and even tolerates a small proportion of those paper clips being ‘defective’ (or incorrectly shaped and/or twisted) in its outgoing product. (The company reasons that paper clips are so cheap, users will simply discard the occasional defective paper clip they might find in a box.) The average proportion of ‘defective’ paper clips is known to be 2% when the paper clip manufacturing process is ‘in control’. To monitor this issue, what should be the value of the upper control limit of a p-chart if the company plans to include 25 paper clips in each of its samples and use z-value of 3.0 to construct the chart? g
Answer:
0.104 (10.4%)
Step-by-step explanation:
[tex]UCL = \bar{p}+z(\sigma)[/tex]
[tex]\sigma = p(1-)) Vn = 1.02(1-202)) 5[/tex] = 0.028
[tex]\thereforeUCL = .02+(3x0.028)[/tex] = 0.104
[tex]\thereforeUCL[/tex]= 10.4%
In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the relationship between gender and participation in the last election. The results were: Men Women Voted 2744 3733 Didn't Vote 1599 1924 If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance level? Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)]
Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.
P-value=0.0036 (two tailed test).
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of women that vote is differs from the proportion of men that vote.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
Being π1: proportion of men that vote, and π2: proportion of women that vote.
The significance level is 0.05.
The sample 1 (men), of size n1=(2744+1599)=4343 has a proportion of p1=0.6318.
[tex]p_1=X_1/n_1=2744/4343=0.6318[/tex]
The sample 2 (women), of size n2=(3733+1924)=5657 has a proportion of p2=0.6599.
[tex]p_2=X_2/n_2=3733/5657=0.6599[/tex]
The difference between proportions is (p1-p2)=-0.0281.
[tex]p_d=p_1-p_2=0.6318-0.6599=-0.0281[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{2744+3733}{4343+5657}=\dfrac{6477}{10000}=0.6477[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.6477*0.3523}{4343}+\dfrac{0.6477*0.3523}{5657}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00004}=\sqrt{0.00009}=0.0096[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0281-0}{0.0096}=\dfrac{-0.0281}{0.0096}=-2.913[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(t<-2.913)=0.0036[/tex]
As the P-value (0.0036) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. Find the probability that a given class period runs between 50.75 and 51.25 minutes. Find the probability of selecting a class that runs between 50.75 and 51.25 minutes.
Answer:
The probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.
Step-by-step explanation:
Let the random variable X represent the lengths of the classes.
The random variable X is uniformly distributed within the interval 49.0 and 54.0 minutes.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
Compute the probability that a given class period runs between 50.75 and 51.25 minutes as follows:
[tex]P(50.75<X<51.25)=\int\limits^{51.25}_{50.75}{\frac{1}{54-49}}\, dx\\\\=\frac{1}{5}\times [x]^{51.25}_{50.75}\\\\=\frac{51.25-50.75}{5}\\\\=0.10[/tex]
Thus, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.
Answer: 0.050
I just did it and i got it right.
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $140 of the population mean, and the population standard deviation is known to be $569.
A minimum sample size of 64 business students must be randomly selected to estimate the mean monthly earnings with 95% confidence within $140 of the true population mean, given the population standard deviation of $569.
Explanation:To find the minimum sample size required to estimate an unknown population mean μ with a certain level of confidence, we can use the formula:
n = (Z*σ/E)^2
Where:
n is the sample sizeZ is the Z-score corresponding to the desired confidence levelσ (sigma) is the population standard deviationE is the margin of errorFor a 95% confidence level, the Z-score is approximately 1.96. The population standard deviation σ is given as $569. The margin of error E is $140.
Plugging these values into the formula, we get:
n = (1.96*569/140)^2
n = (1114.44/140)^2
n = (7.96)^2
n = 63.4
Since the sample size must be a whole number, we would round up to the next whole number which gives us a minimum sample size of 64 business students that must be randomly selected to estimate the mean monthly earnings of business students at one college with the desired precision and confidence level.
Final answer:
To estimate the population mean with a 95% confidence level and a margin of error of $140, we use the formula n = (Z*σ/E)^2 with σ = $569. Using the z-score for 95% confidence (1.96), the calculation yields 119.44, which we round up to 120 business students needed for the sample.
Explanation:
Calculating Minimum Sample Size for Estimating a Population Mean
To determine the minimum sample size needed to estimate the mean monthly earnings of business students at one college with 95% confidence and a margin of error of $140, we use the formula for the sample size (n). The formula is derived from the properties of a normal distribution and the central limit theorem and is as follows:
n = (Z*σ/E)^2
where:
Z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence),
σ (sigma) is the population standard deviation, and
E is the desired margin of error.
Plugging in the given values of σ = $569 and E = $140, we find:
n = (1.96 * 569 / 140)^2
n ≈ (10.924)^2
n ≈ 119.44
Since we cannot survey a fraction of a person, we round up to the nearest whole number. Therefore, 120 business students must be randomly selected to achieve the desired precision.
Round 506.57915 to the nearest hundredth.
Answer:
506.58
Step-by-step explanation:
Your welcome ;w;
1. 3 (x + 1)2 - 3
a. What is the "a" value?
b. What is the "h" value?
c. What is the "K" value?
Peter measures the angles in a triangle.
He finds that the angles are 95°, 10° and 75º.
a)
Could he be correct?
b)
Explain your answer.
Can someone please help?
Answer:
x=±√7 -2
Step-by-step explanation:
In Bangladesh, approximately 50.6% of the population is male and 49.4% of the population is female. By the Law of Large Numbers, we can take this to mean that the probability that a randomly selected birth is that of a male child is 0.506 and the probability that a randomly selected birth is that of a female child is 0.494. In a randomly selected family with six children, what is the probability that at most 2 of the children are boys? What is the expected number of boys in a randomly selected family with six children?
Answer:
A) 0.015
B) 4 bous6
Step-by-step explanation:
That at most 2 of the selected children are male means that number of male must be less than or equal to 2
Pr (male) = 0.506
Pr (female) = 0.494
Pr (at most 2 males) = 0.506 x 0.506 x 0.494 x 0.494 x 0.494 x 0.494 = 0.015
Expected number of boys in a randomly selected number of 6 is
0.506 x 6 = 3.03
We round off to 4 boys
What is the mean 9, 8, 12, 6, 10
Answer:
Mean = sum of elements/number of elements = (9 + 8 + 12 + 6 + 10)/5 = 9
Hope this helps!
:)
Answer:
9
Step-by-step explanation:
The mean is also called the average
Add up all the number
(9+8+ 12+ 6+ 10)
45
Then divide by the number of numbers
45/5 = 9
A school has two kindergarten classes. There are 21 children in Ms. Toodle's kindergarten class. Of these, 17 are "pre-readers" children on the verge of reading. There are 19 children in Mr. Grimace's kindergarten class. Of these, 13 are pre-readers. Using the plus four confidence interval method, a 90% confidence interval for the difference in proportions of children in these classes that are pre-readers is -0.104 to 0.336.
1. Which of the following statements is correct?
a. This confidence interval is not reliable because the samples are so small.
b. This confidence interval is of no use because it contains 0, the value of no difference between classes.
c. This confidence interal is reasonable because the sample sizes are both at least 5.
d. This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population
Answer:
The correct answer is option (d).
Step-by-step explanation:
From the given example, the statement that is correct is, this confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.
This is because, In this scenario or setup, all the students are already part of the data. This is not a sample from a l population that is larger, but probably, the population itself.
An aquarium at a pet store contains six fish; three yellow goldfish and three black goldfish. On Sunday, a customer came to the store and randomly selected three fish to purchase. Suppose you know the customer purchased a black goldfish. What is the probability that two yellow goldfish and a black goldfish remain in the tank after the customer has left? Please simplify your answer to a decimal value and circle your answer. Ensure you show your work.
Answer:
[tex]P=0.4737[/tex]
Step-by-step explanation:
First, we need to know that nCx give as the number of ways in which we can select x elements from a group of n. It is calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
Then, to select 3 fish in which at least one a them is a black goldfish we can:
1. Select one black goldfish and 2 yellow goldfish: There are 9 different ways to do this. it is calculated as:
[tex]3C1*3C2 =\frac{3!}{1!(3-1)!}* \frac{3!}{2!(3-2)!}=9[/tex]
Because we select 1 black goldfish from the 3 in aquarium and select 2 yellow goldfish from the 3 in the aquarium.
2. Select 2 black goldfish and 1 yellow goldfish: There are 9 different ways. it is calculated as:
[tex]3C2*3C1 =\frac{3!}{2!(3-2)!}* \frac{3!}{1!(3-1)!}=9[/tex]
3. Select 3 black goldfish and 0 yellow goldfish: There is 1 way. it is calculated as:
[tex]3C3*3C0 =\frac{3!}{3!(3-3)!}* \frac{3!}{0!(3-0)!}=1[/tex]
Now, we identify that just in part 2 (Select 2 black goldfish and 1 yellow goldfish), two yellow goldfish and a black goldfish remain in the tank after the customer has left.
So, the probability that two yellow goldfish and a black goldfish remain in the tank after the customer has left given that the customer purchased a black goldfish is equal to:
[tex]P=\frac{9}{9+9+1} =0.4737[/tex]
Because there are 19 ways in which the customer can select a black fish and from that 19 ways, there are 9 ways in which two yellow goldfish and a black goldfish remain in the tank.
There are two spinners containing only black and purple slices.
Spinner A has 3 black slices and 12 purple slices.
All the slices are the same size.
Spinner B has 2 black slices and 6 purple slices.
All the slices are the same size.
Each spinner is spun.
List theseſevents from least likely to most likely.
Event 1: Spinner B lands on a black slice.
Event 2: Spinner A lands on a black slice.
Event 3: Spinner B lands on a black or purple slice.
Event 4: Spinner A lands on a green slice.
Least likely
Most likely
Event |
Event |
Event |
Event []
Answer:
Event 4, Event 2, Event 1, Event 3 (least to most likely)
Step-by-step explanation:
Let's take a look at each event:
Event 1- Spinner B lands on a black slice.
2 black slices, 8 total slices
2/8=1/4=25% probability
Event 2- Spinner A lands on a black slice.
3 black slices, 15 total slices
3/15=1/5=20%
Event 3- Spinner B lands on a black or purple slice.
8 black or purple slices, 8 total slices
8/8=1=100%
Event 4- Spinner A lands on a green slice.
0 green slices, 15 total slices
0/15=0=0%
So, in order of least to most likely, we have Event 4 (0%), Event 2 (20%), Event 1 (25%), and event 3 (100%).
A computer company shipped two new computers to a customer. These two computers were randomly selected from the 15 computers in stock. Unfortunately, the inventory clerk by mistake mixed up new computers with refurbished computers. As a result, the 15 computers in stock consisted of 11 new computers and 4 refurbished computers. If the customer received one refurbished computer, the company will incur a shipping and handling expense of $100 to replace that computer with a new computer. However, if both computers were refurbished, the customer would cancel the order and the company will incur a total loss of $1,000. If the customer received both computers as new, then there is no extra cost involved (i.e., zero loss). Find the expected value and standard deviation of the computer company's loss.
Answer:
Expected value of company loss = $99.01
Standard deviation = $226.91
Step-by-step explanation:
We first obtain the probability mass function of the company's losses based on the chances of the possible various number of refurbished computers in the customers order.
There are 15 total computers in stock.
There are 4 refurbished computers in stock.
There are 11 new computers in stock
The customer orders 2 computers. If there are no refurbished computers in the order, there are no losses on the company's part.
Probability of no refurbished computers in the order = (11/15) × (10/14) = 0.5238
The customer orders 2 computers. If there is only 1 refurbished computer in the order, there is a loss of $100 on the company's part.
Probability of 1 refurbished computers in the order = [(11/15) × (4/14)] + [(4/15) × (11/14)]
= 0.4191
The customer orders 2 computers. If there are 2 refurbished computer in the order, there is a loss of $1000 on the company's part.
Probability of 2 refurbished computers in the order = [(4/15) × (3/14)] = 0.0571
So, the Probabilty function of random variable X which represents the possible losses that the company can take on is given as
X | P(X)
0 | 0.5238
100 | 0.4191
1000 | 0.0571
Expected value of company loss is given as
E(X) = Σ xᵢpᵢ
xᵢ = each variable or sample space
pᵢ = probability of each variable
E(X) = (0 × 0.5238) + (100 × 0.4191) + (1000 × 0.0571) = $99.01
Standard deviation is obtained as the square root of variance.
Variance = Var(X) = Σx²p − μ²
where μ = E(X) = 99.01
Σx²p = (0² × 0.5238) + (100² × 0.4191) + (1000² × 0.0571) = 0 + 4191 + 57,100 = 61,291
Var(X) = Σx²p − μ²
Var(X) = 61291 − 99.01² = 51,488.0199
Standard deviation = √(51,488.0199) = $226.91
Hope this Helps!!!
The magnitude, M, of an earthquake is defined to be M=log l/s, where l is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?
Answer:
M = Log (10S/S)
Step-by-step explanation:
We are told that the magnitude, M, of an earthquake is defined to be;
M = Log l/S
Where I is intensity and S is standard earthquake.
Now, we want to find the magnitude of an earthquake that is 10 times more intense than a standard earthquake
Since 10 times more intense than standard earthquake, it means that;
I = 10S
So plugging in 10S for I in the original equation for magnitude gives;
M = Log (10S/S)
Answer:It’s C on edge
Step-by-step explanation:
What is the value of the expression: 4.6+(-3.2)
Answer:
1.4
Step-by-step explanation:
4.6 + (- 3.2)
A plus sign and a minus sign results in a minus sign
Re-write the expression without the parenthesis
4.6 - 3.2
Subtract
1.4
Hope this helps :)
Answer:
the answer is attached to the picture
) You want to rent an unfurnished one-bedroom apartment after you graduate from high school. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $940. The margin of error for a 95% confidence interval is $160. Find the 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community. Write your answer in this format: x to y
Answer:
$780 to $1100
Step-by-step explanation:
A confidence interval has two bounds. A lower bound and an upper bound. They are dependent of the sample mean and of the margin of error M.
In this problem:
Sample mean: $940
Margin of error: $160
The lower end of the interval is the sample mean subtracted by M. So it is 940 - 160 = $780
The upper end of the interval is the sample mean added to M. So it is 940 + 160 = $1100
So the answer is
$780 to $1100
Answer:
[tex]940-160=780[/tex]
[tex]940+160=1100[/tex]
So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100
Step-by-step explanation:
For this case we can define the following random variable X as the monthly rent and we know the following properties given:
[tex]\bar X= 940 [/tex] represent the sample mean
[tex] ME = 160[/tex] represent the margin of error
n = 10 represent the sample size
The confidence interval for the true mean is given by:
[tex] \bar X \pm z_{\alpha/2} \sqrt{\frac{\sigma}{\sqrt{n}}}[/tex]
And is equivalent to:
[tex]\bar X \pm ME[/tex]
And for this case if we replace the info given we got:
[tex]940-160=780[/tex]
[tex]940+160=1100[/tex]
So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100
which of the following is the inverse of f(x)=3-14x
Answer:
f(x)=-3+14x
Step-by-step explanation:
its the opposite
The inverse of the following function f(x)=3-14x will be [tex]f^-(x)[/tex] = [3 -f(x)]/14.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
A function is basically a relationship between which one variable will be dependent and another will be independent.
For example, let's say y = sinx then here x will be independent but y will be dependent.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +9 like that.
Given that the function
f(x)=3-14x
⇒ f(x) + 14x =3
⇒ 14x = 3 -f(x)
⇒ x = [3 -f(x)]/14 hence, it will be the correct answer.
For more about the function
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Suppose SAT Writing scores are normally distributed with a mean of 488488 and a standard deviation of 111111. A university plans to award scholarships to students whose scores are in the top 8%8%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for the scholarship is 644.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 488, \sigma = 111[/tex]
What is the minimum score required for the scholarship?
Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 488}{111}[/tex]
[tex]X - 488 = 1.405*111[/tex]
[tex]X = 644[/tex]
The minimum score required for the scholarship is 644.
Use the Ratio Test to determine whether the series is convergent or divergent.
Σ[infinity] n = 1 (-1)^n - 1 3^n/2^nn^3
Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
6 friends share 3 apples. How much each friend receive?
Answer:
Each friend would receive Half (1/2) of an apple.
Each friend receives 1/2 apple.
What is the unitary method?The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Total number of friends = 6
Total number of apples = 3
The apple gets each friend is determined in the following steps given below.
[tex]\rm Each \ friend =\dfrac{Total \ Apple}{Total \ frineds}\\\\Each \ friend = \dfrac{3}{6}\\\\Each \ friend =\dfrac{1}{2}[/tex]
Hence, each friend receives 1/2 apple.
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Kate has 48 softballs. She wants to divide them evenly among b softball bags. Which expression represents how many softballs she should put into each bag? a. 48/b, b. 48b, c. b/48, d. 48-b.
Answer:
A
Step-by-step explanation:
48 softballs
Divided among b bags
Divide 48 by b
48 ÷ b
Division expressions can also be written as fractions
Rewrite
48/b
The correct answer is A, 48/b
Hope this helps :)
Final answer:
Kate should use the expression 48/b to determine how many softballs go into each bag, which means dividing 48 softballs by the number of bags she has.
Explanation:
The expression that represents how many softballs Kate should put into each bag is 48/b. This expression shows that Kate will divide her total number of 48 softballs by the variable b, which represents the number of softball bags she has. The correct choice is therefore a. 48/b, which suggests that each bag will receive an equal share of the total softballs.
Researchers collected two different samples, X and Y, of temperatures, in degrees Celsius, of the habitat for Florida scrub lizards. The confidence interval 36±1.66 was constructed from sample X, and the confidence interval 36±1.08 was constructed from sample Y. Assume both samples had the same standard deviation.
Which of the following statements could explain why the width of the confidence interval constructed from X is greater than the width of the confidence interval constructed from Y?
A. The sample size of X is greater than the sample size of Y, and the confidence level is the same for both intervals.
B. The sample size of X is greater than the sample size of Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.
C. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.
D. The sample size is the same for X and Y, and the confidence level is the same for both intervals.
E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y
Answer:
E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y
Step-by-step explanation:
Confidence interval formula is given as
CI = \bar{x} \pm z*(\sigma/\sqrt{n})
Here, we can see that the width of confidence interval is z*(\sigma/\sqrt{n}) , which is dependent only on z critical value, standard deviation (sigma) and sample size (n)
This simply entails that either z or n or both are greater for x as compared to y.
Option E is correct answer because x and y can have sample sizes, but if the z critical is greater for x, then the width will be larger.
The confidence interval tells about the probability where a value falls between a range. The interval constructed from X is greater than that of Y because the z value for X is greater than Y.
The confidence interval:[tex]CI = \bar{x} \pm z\times (\dfrac {\sigma}{\sqrt{n}})[/tex]
Where,
[tex]CI[/tex] = confidence interval
[tex]\bar{x}[/tex] = sample mean
[tex]z[/tex] = confidence level value
[tex]{s}[/tex] = sample standard deviation
[tex]{n}[/tex] = sample size
From the formula, confidence interval is the the directly proportional to the confidence level value, standard deviation, and population.
Since the standard deviation, and the population is constant,
Therefore, the interval constructed from X is greater than that of Y because the z value for X is greater than Y.
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If p=2(a+b), then b=
Solving the equation p = 2(a + b) for b involves two steps: first dividing each side by 2, then subtracting 'a' from each side. This results in the final equation 'b = (p/2) - a'.
Explanation:To solve the equation p = 2(a + b) for b, you would first divide each side by 2 to isolate 'a + b'.
This gives you p/2 = a + b. Next, to isolate 'b', you would subtract 'a' from each side of the equation.
This gives you b = (p/2) - a, which is your final, simplified expression for 'b' in terms of 'p' and 'a'.
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Use the spinner to find the theoretical probability of spinning an even number.
25
Step-by-step explanation:
25