Answer:
b = 28
Step-by-step explanation:
8*21 then 168/6 = 28
Answer:
b = 28
Step-by-step explanation:
[tex] \frac{6}{8} = \frac{21}{b} \\ \\ b = \frac{21 \times 8}{6} \\ \\ b = \frac{7\times 8}{2} \\ \\ b = 7 \times 4 \\ \\ \huge \red{ \boxed{ b = 28}}[/tex]
This is for google classroom
The subject of this question is Science in Middle School. The student is learning about scientific models by making a model of air flow in their classroom or room in their house.
Explanation:The subject of this question is Science and the grade level is Middle School. In this question, the student is learning about scientific models by making a model of how air flows through their classroom or a room in their house. The student can use this activity to gain a better understanding of how air moves in closed spaces and the factors that affect its flow.
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Suppose that a manager is interested in estimating the average amount of money customers spend in her store. After sampling 36 transactions at random, she found that the average amount spent was $ 41.15 . She then computed a 90 % confidence interval to be between $ 38.01 and $ 44.29 .
Answer:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The 90% confidence interval for this case would be (38.01, 44.29) and is given.
The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .
And the best option would be:
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
Step-by-step explanation:
Assuming this complete question: Which statement gives a valid interpretation of the interval?
The store manager is 90% confident that the average amount spent by the 36 sampled customers is between S38.01 and $44.29.
There is a 90% chance that the mean amount spent by all customers is between S38.01 and $44.29.
There is a 90% chance that a randomly selected customer will spend between S38.01 and $44.29.
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The 90% confidence interval for this case would be (38.01, 44.29) and is given.
The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .
And the best option would be:
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 9 minutes. We want our 90 percent confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size that we should consider
Answer:
The minimum sample size required is 25 so that margin of error is no more than 3 minutes.
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 42 minutes
Standard Deviation, σ = 9 minutes.
We want to build a 90% confidence interval such that margin of error is no more than 3 minutes.
Formula for margin of error:
[tex]z_{critical}\times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.64[/tex]
Putting values, we get.
[tex]z_{critical}\times \dfrac{\sigma}{\sqrt{n}}\leq 3\\\\1.64\times \dfrac{9}{\sqrt{n}}\leq 3\\\\\dfrac{1.64\times 9}{3}\leq \sqrt{n}\\\\4.92\leq \sqrt{n}\\\Rightarrow n\geq 24.2064\approx 25[/tex]
Thus, the minimum sample size required is 25 so that margin of error is no more than 3 minutes.
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central district. The city plans to pay for the structure through parking fees. During a two-week period (14 days), daily fees collected average $126 with standard deviation $15. We want to construct a confidence interval for the true mean daily fees collected at this parking garage.
(a) To construct the confidence interval, should you use the normal distribution orat distribution?
(b) Construct a 90% confidence interval.
(c) The consultant who advised the city on this project predicted that parking revenues would average $130 per day. Based on your confidence interval, do you think the consultant could have been correct? Why or why not?
Final answer:
To construct a confidence interval for the true mean daily fees collected at the parking garage, the normal distribution should be used. Using a 90% confidence level, the confidence interval is calculated as $116 to $136. Based on the confidence interval, it is possible that the consultant's prediction of $130 per day could be correct.
Explanation:
(a) To construct the confidence interval, we should use the normal distribution. This is because the sample size is large enough (14 days) and the Central Limit Theorem applies, which states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
(b) To construct a 90% confidence interval, we need to find the critical value corresponding to a 90% confidence level. The critical value for a 90% confidence level can be found using a z-table. From the z-table, we find that the critical value is approximately 1.645. The margin of error is calculated as the critical value multiplied by the standard deviation of the sample mean, which is the standard deviation divided by the square root of the sample size. In this case, the margin of error is (1.645 x 15) / √14. We can then construct the confidence interval by subtracting and adding the margin of error to the sample mean. The 90% confidence interval for the true mean daily fees collected at this parking garage is approximately $116 to $136.
(c) Based on the confidence interval, we can see that the range of $116 to $136 includes the predicted average of $130 per day by the consultant. Therefore, it is possible that the consultant could have been correct.
what is 2/3 plus 1/6
Answer:
5/6
Step-by-step explanation:
2/3=4/6
4/6+1/6=5/6
Answer:
That would be 5/6
Step-by-step explanation:
You multiply the denominator and the numerator by 2 to get a common denominator of 6. You add the 4 to the 1 to get 5/6
An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line at their site. A consumer group is suspicious of the claim and thinks that the proportion is lower than 60%. A random sample of 80 graduate students show that only 44 students have ever done so. Is there enough evidence to show that the true proportion is lower than 60%
Answer:
[tex]z=\frac{0.55 -0.6}{\sqrt{\frac{0.6(1-0.6)}{80}}}=-0.913[/tex]
[tex]p_v =P(z<-0.913)=0.181[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6
Step-by-step explanation:
Data given and notation
n=80 represent the random sample taken
X=44 represent the students that have bought merchandise on-line at their site
[tex]\hat p=\frac{44}{80}=0.55[/tex] estimated proportion of graduate students show that only 44 students have ever done so
[tex]p_o=0.6[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion of interest is lower than 0.6 or 60%, so then the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.6[/tex]
Alternative hypothesis:[tex]p < 0.6[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.55 -0.6}{\sqrt{\frac{0.6(1-0.6)}{80}}}=-0.913[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed for this case is [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
[tex]p_v =P(z<-0.913)=0.181[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6
Calculate the area of the shaded region in each figure. Use 3.14 and round to the nearest tenth, if necessary.
Given:
Given that the length of the side of the square is 12 cm.
The given figure consists of two circles with radius of 3 cm each.
We need to determine the area of the shaded region.
Area of the square:
The area of the square can be determined using the formula,
[tex]A=s^2[/tex]
Substituting s = 12, we get;
[tex]A=12^2[/tex]
[tex]A=144 \ cm^2[/tex]
Thus, the area of the square is 144 square cm.
Area of the two circles:
The area of the circle can be determined using the formula,
[tex]A=\pi r^2[/tex]
Substituting r = 3, we get;
[tex]A=(3.14)(3)^2[/tex]
[tex]A=(3.14)(9)[/tex]
[tex]A=28.26 \ cm^2[/tex]
The area of 2 circles is given by
[tex]A=2(28.26)[/tex]
[tex]A=56.52 \ cm^2[/tex]
Thus, the area of the two circles is 56.52 square cm.
Area of the shaded region:
The area of the shaded region can be determined by subtracting the area of the two circles from the area of the square.
Thus, we have;
Area = Area of square - Area of two circles.
Substituting the values, we get;
[tex]Area = 144- 56.52[/tex]
[tex]Area=87.5 \ cm^2[/tex]
Thus, the area of the shaded region is 87.5 square cm.
What is the solution to the following system?
3x+10y-12z=40
x-5y=0
x-4z=0
9514 1404 393
Answer:
(x, y, z) = (20, 4, 5)
Step-by-step explanation:
The last two equations allow y and z to be expressed in terms of x, so we have ...
3x +2(5y) -3(4z) = 40
3x +2(x) -3(x) = 40
x = 20 . . . . . . . . . . . . divide by the coefficient of x
y = 20/5 = 4
z = 20/4 = 5
The solution is (x, y, z) = (20, 4, 5).
Subtract 6 from me. Then multiply by 2. If you subtract 40 and then divide by 4 you get 8. What number am I?
Answer:
42
Step-by-step explanation:
work backwards And use the opposite operation
start with 8 x 4 = 32 + 40 = 72/2 = 36 + 6 = 42
what is y?
2y + 3 = 19
Answer:
y = 8
Step-by-step explanation:
2y + 3 = 19
2y = 19 - 3
2y = 16
y = 16/2
y = 8
Hopefully this help u
Answer: y = 8
Step-by-step explanation: To solve for y, we must first isolate the term containing y which in this problem is 2y.
Since 3 is being added to 2y, we subtract 3 from
both sides of the equation to isolate the 2y.
On the left, the +3 and -3 cancel
out and on the right, 19 - 3 is 16.
So we have 2y = 16.
Now we can finish things off by just dividing
both sides of the equation by 2.
On the left the 2's cancel and on
the right, 16 divided by 2 is 8.
So y = 8.
Why does the margin of error increase as the level of confidence increases? Choose the correct answer below. A. The margin of error increases as the level of confidence increases because of the law of large numbers. B. The margin of error increases as the level of confidence increases because, as the level of confidence increases, the sample size n decreases. C. The margin of error increases as the level of confidence increases because the smaller the expected proportion of intervals that will contain the parameter, the larger the margin of error. D. The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter, the larger th
Answer:
The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter, the larger the margin error.
Step-by-step explanation:
Margin of Error is a statistical measure of random sampling error insurvey results.
Level of confidence reflects percentage range around sample mean, that can be expected to contain population actual parameter.
High level of confidence means larger range band of confidence interval, supposed to contain the population parameter. This further implies high expected variation between sample statistic & actual parameter i.e Margin Error increases.
The margin of error increases as the level of confidence increases because the smaller the expected proportion of intervals that will contain the parameter, the larger the margin of error (C).
Explanation:The correct answer is C. The margin of error increases as the level of confidence increases because the smaller the expected proportion of intervals that will contain the parameter, the larger the margin of error. When we calculate a confidence interval, we need to balance our desire for a higher level of confidence with the need for a smaller margin of error.
For example, let's say we want to estimate the proportion of students at a school who prefer chocolate ice cream. If we want to be extremely confident in our estimate, let's say 99% confident, there will be a larger margin of error since we need to consider a smaller proportion of intervals that will contain the true proportion.
On the other hand, if we were only interested in being 90% confident, there would be a smaller margin of error since we can include a larger proportion of intervals that will contain the true proportion.
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50,866(underlined digits "66")
What is the relationship between
the underlined digits?
Answer:
6 at tens place is 10 times 6 at unit place.
Step-by-step explanation:
We are given that a number
50,866
Underlined digits are 66.
We have to find the relationship between underlined digits.
Unit place =6
Tens place=
Tens place value=[tex]6\times 10=60[/tex]
Unit pace value=6
6 at tens place is 10 times 6 at unit place.
This is required relation relation between underlined digits 66.
I need help with this, please
Given:
Given that the pie chart shows the relative frequency distribution resulting from a survey of 6000 US rural households with internet connections in a certain year.
We need to determine the total number of households with each type of internet in the survey.
Cable modem:
Since, the relative frequency distribution for cable modem is 0.142
The total number of households that use cable modem is given by
[tex]0.142 \times 6000=852[/tex]
Thus, 852 households use cable modem.
DSL:
Since, the relative frequency distribution for DSL is 0.092
The total number of households that use DSL is given by
[tex]0.092 \times 6000=552[/tex]
Thus, 552 households use DSL.
Dialup:
Since, the relative frequency distribution for dialup is 0.747
The total number of households that use dialup is given by
[tex]0.747 \times 6000=4482[/tex]
Thus, 4482 households use dialup.
Others:
Since, the relative frequency distribution for others is 0.019
The total number of households that use others is given by
[tex]0.019 \times 6000=114[/tex]
Thus, 114 households use others.
You wish to test the claim that mugreater than21 at a level of significance of alphaequals0.05 and are given sample statistics n equals 50 and x overbar equals 21.3. Assume the population standard deviation is 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places.
Answer:
[tex]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]
Step-by-step explanation:
Data given and notation
[tex]\bar X=21.3[/tex] represent the sample mean
[tex]\sigma=1.2[/tex] represent the population standard deviation
[tex]n=50[/tex] sample size represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 21, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 21[/tex]
Alternative hypothesis:[tex]\mu > 21[/tex]
If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]
You are looking at the number of multi-million dollar companies in each state. Based on data from last year, you have found a mean of 37 and a standard deviation of 8. Use this information to answer the following question. What is the probability of a randomly selected state having between 21 and 53 multi-million dollars
Answer:
By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars
Step-by-step explanation:
We have no information about the distribution, so we use the Chebyshev's theorem to solve this question.
Chebyshev Theorem:
75% of the data within 2 standard deviations of the mean.
89% of the data within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 37
Standard deviation = 8
What is the probability of a randomly selected state having between 21 and 53 multi-million dollars
21 = 37 - 2*8
So 21 is 2 standard deviations below the mean.
53 = 37 + 2*8
So 52 is 2 standard deviations above the mean.
By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars
What is the midpoint of EC ?
A: (t + p, r)
B: (p – t, r)
C: (p, r)
Given:
Given that the graph OACE.
The coordinates of the vertices OACE are O(0,0), A(2m, 2n), C(2p, 2r) and E(2t, 0)
We need to determine the midpoint of EC.
Midpoint of EC:
The midpoint of EC can be determined using the formula,
[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
Substituting the coordinates E(2t,0) and C(2p, 2r), we get;
[tex]Midpoint=(\frac{2t+2p}{2},\frac{0+2r}{2})[/tex]
Simplifying, we get;
[tex]Midpoint=(\frac{2(t+p)}{2},\frac{2r}{2})[/tex]
Dividing, we get;
[tex]Midpoint=(t+p,r)[/tex]
Thus, the midpoint of EC is (t + p, r)
Hence, Option A is the correct answer.
4. Find the Area of the trapezoid.
Answer:
40 in^2
Step-by-step explanation:
The area of the trapezoid is found by
A = 1/2 (b1+b2)h where b1 and b2 are the lengths of the bases and h is the height
= 1/2 (7+3)*8
= 1/2 (10)*8
= 40 in^2
Answer:
ok the answer is 40
Step-by-step explanation:
a+b/2*h
7+3/2*8
7+3=10
10/2=5
5*8=40
if the slope is 2 and the line goes through (3,-3) what is the equation?
Answer:
[tex]y = 2x -9[/tex]
Step-by-step explanation:
To find the equation of a line using slope and a point, first use the slope to create the basic line using the slope and work from there.
For instance, the base equation here is
[tex]y = 2x[/tex]
This line passes through the point (0, 0).
You can then plug in a value for x. In this case, use the value of 3, as it corresponds with your question.
[tex]y = 2 * 3[/tex]
A point on the line of y = 2x would thus be (3, 6).
To make the y-value equal -3, you must then subtract from the original equation. There are 9 units between 6 and -3, so you must subtract nine units in the equation. You should get this at the end:
[tex]y = 2x -9[/tex]
ucsd reddit A watermelon is thrown down from the 7th floor of Urey Hall at UCSD. If the initial height of the watermelon is 21.0 meters, and it is thrown straight downward with an initial downward velocity of 3.00 m/s. How far will the watermelon have fallen from its starting height after 1.50 seconds?
Answer:
15.525 feet
Step-by-step explanation:
GIVEN: A watermelon is thrown down from the [tex]7th[/tex] floor of Urey Hall at UCSD. If the initial height of the watermelon is [tex]21.0\text{ meters}[/tex], and it is thrown straight downward with an initial downward velocity of [tex]3.00\text{ m/s}[/tex].
TO FIND: How far will the watermelon have fallen from its starting height after [tex]1.5[/tex] seconds.
SOLUTION:
initial height of watermelon [tex]=21\text{ meter}[/tex]
initial velocity of watermelon[tex]=3\text{ m/s}[/tex]
acceleration due to gravity [tex]=9.8\text{m/s}^2[/tex]
According to newton's law of motion
[tex]S=ut+\frac{1}{2}at^2[/tex]
when [tex]t=1.5[/tex] seconds
[tex]S=3\times1.5+\frac{1}{2}\times9.8\times1.5^2[/tex]
[tex]S=4.5+11.025[/tex]
[tex]S=15.525\text{ feet}[/tex]
Hence watermelon will have fallen 15.525 feet from its starting height after 1.5 seconds
The data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique.
{5,3,5, 30, 4,5,4,3,4,5)
The best measure of center for this data set is _______
, and its value is _______
Answer:
Average
6.8
Step-by-step explanation:
[tex]\frac{5+3+5+30+4+5+4+3+4+5}{10}=6.8[/tex]
- 5 + 2y > 5 (y-2) - 3y
Diet cola was on sale last week. It cost $10 for every four pack of diet cola. How much do two packs of diet cola cost?
Answer:
The answer is $5.
Step-by-step explanation:
$10 divided by 2 packs = $5
OR
$10 divided by 4 to get the per pack price which is $2.50 each
Then multiply $2.50 times 2 packs = $5
Hope this helps!!
What’s the diagonal of a tv whose length is 44 inches and height is 38 inches
Answer:
58.1377674149945 inches. (Round to whatever you need)
Step-by-step explanation:
Here we turn to Pythagoras theorem.
Because there is a right angled triangle,
Let the two shorter sides (length and width) be a and b and the longer side (diagonal) be c
A² + B² = C²
38² + 44² = 3380inches² (this is not the area. It's how Pythagoras theorem works)
Then the square root of this is 58.1377674149945 inches. (Round to whatever you need)
So that is the length of the diagonal
Which theorem would show that the two right triangles are congruent?
Answer:
D.
Step-by-step explanation:
AAS triangle congruence theorem. These triangle have the same side, angle and other angle
The theorem that would determine if two right triangles are congruent or not are AAS Triangle Congruence Theorem.
What is a congruent right-angled triangle?If two right triangles have similar sizes and shapes, they are considered to be congruent triangles. In other terms, two right triangles are described to be congruent if the lengths of their respective sides and angles are the same.
The angle-angle-side (AAS) theorem posits that when two angles and any side of a triangle are equivalent to two angles and any side of some other triangle, then the triangles are considered to be congruent triangles.
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Find the quotient of 2/5 and 4/5
Give your answer as a fraction in its simplest form.
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
What is the quotient?
The quotient is the number which is generated when we perform division operations on two numbers.
The quotient of 2/5 and 4/5.
The quotient of 2/5 and 4/5 is determined in the following steps given below.
[tex]\rm Quotient =\dfrac{\dfrac{2}{5}}{\dfrac{4}{5}}\\\\Quotient =\dfrac{2}{5}\times \dfrac{5}{4}\\\\ Quotient =\dfrac{2}{4}\\\\Quotient =\dfrac{1}{2}[/tex]
Hence, the quotient of 2/5 and 4/5 is 1/2.
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You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provide housing for most of these women. After recording data for a whole year, you find that the mean number of women in shelters each night is 250, with a standard deviation of 75. Fortunately, the distribution of the number of women in the shelters each night is normal, so you can answer the following question posed by the city council.
If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights? If not, what number of shelter openings will be needed?
Answer:
Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.
274 shelters will be needed.
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 = 250, \sigma = 75[/tex]
If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?
What is the percentile of 350?
This is the pvalue of Z when X = 350.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{250 - 150}{75}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a pvalue of 0.9082.
Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.
If not, what number of shelter openings will be needed?
The 95th percentile, which is X when Z = 1.645. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 150}{75}[/tex]
[tex]X - 150 = 1.645*75[/tex]
[tex]X = 274[/tex]
274 shelters will be needed.
The current shelter capacity of 350 will not be sufficient for 95% of nights according to the normal distribution of the number of women in shelters each night. To have enough capacity for 95% of the nights, the city's shelter would need approximately 397 bed openings.
Explanation:The subject of this question relates to a discipline in statistics called normal distribution. Essentially, we have the mean number of women in shelters each night (250) and the standard deviation (75). Since the council wants the capacity to be enough for 95% of nights, we need to find the number corresponding to the 95th percentile in this normal distribution.
In a normal distribution, 95% of the data falls within 1.96 standard deviations of the mean. So, we will calculate the upper limit of the capacity using the following formula: Upper Limit = Mean + (1.96 * Standard Deviation)
By substituting the given mean and standard deviation (250 and 75 respectively), we get: Upper Limit = 250 + (1.96 * 75) = 397.
So, a shelter capacity of 350 will not be sufficient to house most abused women on 95% of all nights. The city's shelters would need 397 openings to meet this requirement.
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which equations are equivalent to -1/4(x)+3/4=12 select all that apply
1.(-4x/1)+3/4=12
2.-1(x/4)+3/4=12
3.-x+3/4=12
4.1/4(x+3)=12
5.(-x/4)+3/4=12
Answer:
B C E are the answers
Step-by-step explanation:
hope it helps
Only the equations -1(x/4) + 3/4 = 12 and (-x/4) + 3/4 = 12 are equivalent to the original equation. The other equations provided do not hold the same properties of distribution and are not equivalent to the original equation.
Explanation:When comparing these equations to the original, we must take into consideration the properties of distribution, a crucial component of algebra. The original equation is -1/4(x) + 3/4 = 12. Let's go through the options one by one:
Equation 1: (-4x/1)+3/4=12. This one is not equivalent to the original equation because the coefficient of x in the original equation is -1/4, not -4.Equation 2: -1(x/4)+3/4=12. This equation is the same as the original one because -1/4 times x is the same as -1 times x/4.Equation 3: -x+3/4=12. This equation is not equivalent because the coefficient of x in the original equation is -1/4, not -1.Equation 4: 1/4(x+3)=12. This equation is not equivalent because the original equation does not have a term x+3 in it.Equation 5: (-x/4)+3/4=12. This equation is the same as the original one because dividing -x by 4 is the same as multiplying -1/4 times x.Learn more about Equivalent Equations here:https://brainly.com/question/34191741
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What does (-3/4)(-4/7)(-2/3 equal to please show work!?
Answer:
-2/7 0r 2/-7 or the negative sign is in the middle
Step-by-step explanation:
(-3/4)(-4/7)= 3/7
3/7 x -2/3= -2/7
A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years with a sample standard deviation of 1.5 years. What is the 99% confidence interval for the population mean?
A. [0.44,3.80]
B. [14.23,23.98]
C. [17.42,20.78]
D. [17.48,20.72]
Answer:
[tex]19.1-3.355\frac{1.5}{\sqrt{9}}=17.42[/tex]
[tex]19.1+3.355\frac{1.5}{\sqrt{9}}=20.78[/tex]
And the best option would be:
C. [17.42,20.78]
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=19.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=1.5 represent the sample standard deviation
n=9 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=9-1=8[/tex]
Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that [tex]t_{\alpha/2}=[/tex]
Now we have everything in order to replace into formula (1):
[tex]19.1-3.355\frac{1.5}{\sqrt{9}}=17.42[/tex]
[tex]19.1+3.355\frac{1.5}{\sqrt{9}}=20.78[/tex]
And the best option would be:
C. [17.42,20.78]
A) A club is considering changing its bylaws. In an initial straw vote on the issue, 24 of the 40 members of the club favored the change and 16 did not. A committee of six is to be chosen from the 40 club members to devote further study to the issue. a) How many committees of six can be formed from the club membership
Answer:
38,38,380
Step-by-step explanation:
GIVEN: A club is considering changing its laws. In an initial straw vote on the issue, [tex]24[/tex] of the [tex]40[/tex] members of the club favored the change and [tex]16[/tex] did not. A committee of six is to be chosen from the [tex]40[/tex] club members to devote further study to the issue.
TO FIND: How many committees of six can be formed from the club membership.
SOLUTION:
Total number of members [tex]=40[/tex]
Total members to be chosen [tex]=6[/tex]
To select committee of [tex]6[/tex] members from [tex]40[/tex] [tex]=^{40}C_6[/tex]
[tex]=\frac{40!}{34!6!}[/tex]
[tex]=38,38,380[/tex]
Hence 38,38,380 different committee can be formed.