Answer:
a) The interest is compounded monthly, so should use the compound interest formula.
b) [tex]A(t) = 3000(1.0067)^{12t}[/tex]
c) Linda would have $14898.33 in her account after 20 years.
Step-by-step explanation:
Compound Interest Formula:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years for which the money is invested.
Continuous Interest Formula:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial amount invested and r is the interest rate, as a decimal.
For Linda: a. State which formula should be used to solve this problem.
The interest is compounded monthly, so should use the compound interest formula.
b. Write the function for Linda.
Invests 3000, so [tex]P = 3000[/tex]
8% interest, so [tex]r = 0.08[/tex]
Compounded monthly. An year has 12 months, so [tex]n = 12[/tex]
Then
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A = 3000(1 + \frac{0.08}{12})^{12t}[/tex]
[tex]A = 3000(1.0067)^{12t}[/tex]
c. Determine how much Linda would have in her account after 20 years
This is A(20)
[tex]A = 3000(1.0067)^{12*20} = 14898.33[/tex]
Linda would have $14898.33 in her account after 20 years.
For Linda the formula that would be used to solve this problem is: FV = A (1 + r)^nm
For Linda, the function is: $3000(1.0067)^12n.
The amount Linda would have in her account after 20 years is $14,780.41.
The formula for determining the future value of an amount of money is: FV = A (1 + r)^nm
Where:
FV = Future value A = Amount deposited R = interest rate = 8%/12 = 0.067 m = number of compounding = 12 N = number of years = 20Value after 20 years $3000(1.0067)^(12 x 20) = $14,780.41.
A similar question was answered here: https://brainly.com/question/16035671
The average speed of a baseball line drive is 83 miles per hour. Josiah practiced a new technique to improve his hitting speed. His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour. Part A: State the correct hypotheses Josiah is trying to prove the new technique is an improvement over the old technique. (4 points) Part B: Identify the correct test and check the appropriate conditions. (6 points)
Answer:
We conclude that the new technique is not an improvement over the old technique at 5% level of significance.
Step-by-step explanation:
We are given that the average speed of a baseball line drive is 83 miles per hour.
His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour.
Let [tex]\mu[/tex] = true average speed using the new technique.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 83 miles per hour {means that the new technique is not an improvement over the old technique}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 83 miles per hour {means that the new technique is an improvement over the old technique}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed using the new technique = 84.2 mph
s = sample standard deviation = 4.7 mph
n = sample of hits = 42
So, the test statistics = [tex]\frac{84.2-83}{\frac{4.7}{\sqrt{42} } }[/tex] ~ [tex]t_4_1[/tex]
= 1.655
The value of t test statistics is 1.655.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of 1.6832 at 41 degree of freedom for right-tailed test.
Since our test statistic is less than the critical value of t as 1.655 < 1.6832, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the new technique is not an improvement over the old technique.
What is the factorization of 121b^4-49
The factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).
Explanation:The given expression is 121b^4 - 49. We can recognize that it is a difference of squares, which can be factored using the formula (a^2 - b^2) = (a + b)(a - b). In this case, a is 11b^2 and b is 7.
Therefore, the factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).
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A survey of 76 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.55 minutes. The population standard deviation was 12 minutes. Construct a 95% confidence interval for the average time that a commercial flight of under 2 hours is late. What is the point estimate? What does the interval tell about whether the average flight is late?
Answer:
The best point of estimate for the true mean is:
[tex]\hat \mu = \bar X = 2.55[/tex]
[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]
[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]
Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.
Step-by-step explanation:
Information given
[tex]\bar X=2.55[/tex] represent the sample mean for the late time for a flight
[tex]\mu[/tex] population mean
[tex]\sigma=12[/tex] represent the population deviation
n=76 represent the sample size
Confidence interval
The best point of estimate for the true mean is:
[tex]\hat \mu = \bar X = 2.55[/tex]
The confidence interval for the true mean is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level given is 0.95 or 95%, th significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got [tex]z_{\alpha/2}=1.96[/tex]
Replacing we got:
[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]
[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]
Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.
A mountain climber starts a climb at an elevation of 453 feet above sea level. At his first rest stop he has climbed 162 feet, and by his second rest stop he has climbed another 207 feet. It's getting late in the day, so the climber starts his way down. If the climber descends 285 feet, how much does he need to ascend or descend to return to the original starting point?
A) ascend 84 feet
B) ascend 78 feet
Eliminate
C) descend 84 feet
D) descend 78 feet
Answer:
C) Descend 84 feet
Step-by-step explanation:
162+207=369
369-285=84ft above starting point, this means that he must descend 84 feet to reach the starting point.
how is adding 6+3 like adding 60+30
Answer:
because your just adding a zero at the end.
Step-by-step explanation:
Adding 6+3 is like adding 60+30 because both utilize the place value system and the commutative property of addition where units are added to units and tens to tens, respectively.
The question of adding 6+3 is similar to adding 60+30 due to the property of place value and the commutative property of addition. In both cases, you are adding units that are consistent within their respective places. In single-digit addition, such as 6+3, you are adding units to units. Similarly, in the addition of multi-digit numbers like 60+30, you are adding tens to tens. This is much like the property A+B=B+A, which holds true for ordinary numbers, meaning you'll get the same result regardless of the order in which you add them.
Which equation is equivalent to
equivalent to ( 1/3)^x=27^x+2
Answer:
x=\frac{-3}{2}
Step-by-step explanation:
We have been given with the expression (1/3)^x=(27)^x+2
Now, to solve the equation firstly we have to make the base same on both sides
(1/3)^x=3^{-x}
27 can be written as 3^3
27^x=(3^3)^x=3^{3x}
Hence, given expression can be rewritten as
3^{-x}=3^{3(x+2)}
Now since, base is same we can equate the powers on both sides
-x=3(x+2)\\ \Rightarrow-x= 3x+6\\ \Rightarrow -x-3x=6\\-4x=6\Rightarrow x=\frac{-3}{2}
Therefore given expression (1/3)^x=(27)^x+2 is equivalent to x=\frac{-3}{2}
Equivalent means the simplified form of any given expression
The equation is equivalent to [tex]\(\boxed{3^x = 3^{-3x+2}}\)[/tex]
To solve the equation [tex]\((\frac{1}{3})^x = 27^{(x+2)}\)[/tex], we first need to express [tex]\(27\)[/tex] as a power of [tex]\(3\)[/tex], as [tex]\(27 = 3^3\)[/tex]. Then, we rewrite the equation as:
[tex]\[\left(\frac{1}{3}\right)^x = (3^3)^{(x+2)}\][/tex]
Now, we apply the properties of exponents, specifically the power of a power rule which states [tex]\((a^m)^n = a^{m \times n}\)[/tex], to simplify the expression:
[tex]\[\left(\frac{1}{3}\right)^x = 3^{3(x+2)}\][/tex]
Now, we have the same base on both sides of the equation. We can set the exponents equal to each other:
[tex]\[x = 3(x+2)\][/tex]
Now, let's solve for [tex]\(x\)[/tex]:
[tex]\[x = 3x + 6\][/tex]
[tex]\[x - 3x = 6\][/tex]
[tex]\[-2x = 6\][/tex]
[tex]\[x = \frac{6}{-2}\][/tex]
[tex]\[x = -3\][/tex]
Complete correct question:
Which equation is equivalent to [tex]( 1/3 )^x=27^{x+2}[/tex] ?
[tex]3^x=3^{-3x+2}[/tex]
[tex]3^x=3^{3x+6}[/tex]
[tex]3^{-x} =3^{3x+2}[/tex]
[tex]3^{-x} =3^{3x+6}[/tex]
How is a net useful when finding the surface area or prisms and pyramids?
Answer:oh yeah I remember that
Step-by-step explanation:
That’s tuff
Each student in a statistics class had a randomly assigned bag of candies and counted the number of each color (Blue, Red, Orange, Green, Brown, Yellow). The bags were all the same size. The investigators claimed to use a randomized block design, with Bag as the blocking factor. They counted the number of candies of each color in each bag. Their results are reproduced in the given ANOVA output. Complete parts (a) through (c).
Source Degrees Sum of Mean F-ratio P-value
of Freedom Squares Square
Bag 13 4.726 0.364 0.10 1.000
Color 6 350.679 70.136 18.72 <0.001
Error 65 243.488 3.746
Total 83 598.893
(a) Was this an observational or experimental study?
(b) What was the treatment? What factors were manipulated?
A. The factors were color and bag and the treatments were all possible combinations of those two factors.
B. The factors were bag and student and the treatments were all possible combinations of those two factors.
C. The factors were color and student and the treatments were all possible combinations of those two factors
D. There is no treatment. No factors were manipulated.
(c) What was the response variable?
Answer:
Step-by-step explanation:
Hello!
a)
An observational study is one where the investigator has no control or intervenes on it. He just defines the variable of interest and merely collects and documents the information. These types of studies are usually made as precursors to a more formal experimental study, to have an idea of what's to be expected from the population.
An experimental study or experiment is one where the investigator intervenes by defining the variable of interest and artificially manipulates the study factor. It is also one of its characteristics the randomization of cases or subjects in groups (two or more, depending on what is the hypothesis of study).
In this example, the investigators used a randomized block design with "Bag" as the blocking factor and assigned the bags randomly to the students of the statistic class.
The researchers manipulated all confounding factors in this experiment leaving only "the number of candies per color per bag" as the only random variable. This is an experimental study.
b)
This is an ANOVA with two factors, "Bag" and "Colour" and the treatments are all possible combinations between these two factors.
Correct Option A.
c) The response variable is the "number of candies per color per bag"
Colors: Blue, Red, Orange, Green, Brown and Yellow.
I hope you have a nice day!
write a number with two decimal places, that is bigger than 4 wholes and 1/5 but smaller than 4.25
Answer :
11.45
step-by-step explantion :
4.25=17/4
when we add 41/5 and 17/4, we get
41×4+17×5/4×5
164+65/20
229/20
11.45 Ans
:
Matching angles are called
Answer:
Corresponding Angles.
Step-by-step explanation:
When two lines are crossed by another line (called the Transversal): The angles in matching corners are called Corresponding Angles.
A package has dimensions 10x10x6 inches mrs James wants to gift a wrap it for her grandson what is the total surface area to be wrapped?
Answer:
440 square inches
Step-by-step explanation:
10x10x2=200
10x6x4=240
240+200=440
a. The number 86,362,575 rounded to the nearest hundred is
Answer:
86362600
Step-by-step explanation:
We want to round to the hundreds place
We look at the 7 in the tens place. Since it is 5 or greater we round up
86,362,575 round to 86362600
Answer:
86,362,600
Step-by-step explanation
The weights of soy patties sold by a diner are normally distributed. A random sample of 25 patties yields a mean weight of 4.2 ounces with a sample standard deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 4 ounces. What is the correct calculated value of the test statistic?
Answer:
[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]
The degrees of freedom are given by:
[tex] df =n-1=25-1=24[/tex]
And the p value would be given by:
[tex] p_v = P(t_{24}>2) =0.0285[/tex]
And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate
Step-by-step explanation:
Data provided
[tex]\bar X=4.2[/tex] represent the sample mean for the weigths
[tex]s=0.5[/tex] represent the sample standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =4[/tex] represent the value that we want to analyze
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We want to conduct a hypothesis in order to check if the true mean weigth is less than 4 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 4[/tex]
Alternative hypothesis:[tex]\mu > 4[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]
The degrees of freedom are given by:
[tex] df =n-1=25-1=24[/tex]
And the p value would be given by:
[tex] p_v = P(t_{24}>2) =0.0285[/tex]
And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate
Similarities between inferential and descriptive statistics
Final answer:
Descriptive and inferential statistics both analyze research data and are used together in scientific studies to summarize, describe, and make predictions about a population based on sample data.
Explanation:
Understanding the similarities between descriptive statistics and inferential statistics is fundamental in scientific investigations. Although these two types of statistics serve different purposes, they share some common ground. Both are used to analyze data collected from a research study and help in making decisions or drawing conclusions about that data.
Descriptive statistics summarize and describe the main features of a dataset. Common descriptive measures include the mean, median, mode (measures of central tendency), and the range, standard deviation, and variance (measures of dispersion). On the other hand, inferential statistics use a random sample of data from a population to make inferences about the overall population. It includes various hypothesis tests and confidence intervals to determine the probability of the occurrence of a particular event.
Both descriptive and inferential statistics rely on the same underlying data collection principles and are often used in tandem. Descriptive statistics generally precede inferential statistics in the data analysis process, providing a foundation for further analysis. Moreover, they both employ graphical and numerical methods to present and summarize data, ensuring the findings are communicated in a clear and easily understood manner.
Ultimately, understanding both types of statistics allows researchers to accurately describe, summarize, and make predictions or generalizations regarding their data, which are crucial steps in any scientific study.
Product A requires 9 minutes of milling, 7 minutes for inspection, and 6 minutes of drilling per unit; product B requires 10 minutes of milling, 5 minutes for inspection, and 8 minutes of drilling per unit; product C requires 7 minutes of milling, 3 minutes for inspection, and 15 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $2.0 per unit to profit, product B contributes $2.3 per unit, and product C contributes $4.0 per unit. a. How many constraints are there in the Linear Programming Formulation of this problem
Answer:
The Linear programming problem has 3 constraints :- Milling time, Inspection time, Drilling time constraints.
Step-by-step explanation:
Product A : 9 minutes milling, 7 minutes inspection, 6 minutes drilling Product B : 10 minutes milling, 5 minutes inspection, 8 minutes drilling Product C : 7 minutes milling, 3 minutes inspection, 15 minutes drilling
Total milling time available = 20 hours = (20 x 60) i.e 1200 minutes Total inspection time available = 15 hours = (15 x 60) i.e 900 minutes Total drilling time available = 24 hours = (24 x 60) i.e 1440 minutes
Let QA, QB, QC be quantities of product A, B, C respectively
Milling time constraint : 9QA + 10QB + 7QC = 1200 Inspection time constraint : 7QA + 5QB + 3QC = 900Drilling time constraint : 6QA + 8QB + 15QC = 1440Labor statistics indicate that 77% of all U.S. cashiers and servers are women. A random sample of cashiers and servers in a particular metropolitan area found that 112 of 150 cashiers and 150 of 200 servers were women. At the 0.05 level of significance, is there sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population? What is the test statistic? Round to 2 decimal places.
Final Answer:
The test statistic for the difference in proportions between the metropolitan area and the U.S. population is approximately ( -0.11 ). Since this value does not exceed the critical value of [tex]\( \pm 1.96 \)[/tex] at the 0.05 significance level, there is insufficient evidence to conclude a significant difference. Therefore, we fail to reject the null hypothesis.
Step-by-step explanation:
To determine whether there is sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population, we can perform a hypothesis test for the difference in proportions.
Let:
[tex]\( p_1 \)[/tex] be the proportion of women in the metropolitan area.
[tex]\( p_2 \)[/tex] be the proportion of women in the larger U.S. population.
The null hypothesis [tex](\( H_0 \))[/tex] is that there is no difference between the proportions, and the alternative hypothesis [tex](\( H_1 \))[/tex] is that there is a significant difference.
The formula for the test statistic for the difference in proportions ( z ) is given by:
[tex]\[ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{p(1-p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} \][/tex]
Where:
[tex]\( \hat{p}_1 \)[/tex] and [tex]\( \hat{p}_2 \)[/tex] are the sample proportions of women in the metropolitan area and the U.S. population, respectively.
( p ) is the combined sample proportion.
[tex]\( n_1 \)[/tex] and [tex]\( n_2 \)[/tex] are the sample sizes for the metropolitan area and the U.S. population, respectively.
First, let's calculate [tex]\( \hat{p}_1 \)[/tex], [tex]\( \hat{p}_2 \)[/tex], ( p ), and then plug them into the formula to find the test statistic.
[tex]\[ \hat{p}_1 = \frac{112}{150} = 0.7467 \][/tex]
[tex]\[ \hat{p}_2 = \frac{150}{200} = 0.75 \][/tex]
[tex]\[ p = \frac{112 + 150}{150 + 200} = \frac{262}{350} = 0.7486 \][/tex]
Now, we can calculate the test statistic:
[tex]\[ z = \frac{(0.7467 - 0.75)}{\sqrt{0.7486(1-0.7486)\left(\frac{1}{150} + \frac{1}{200}\right)}} \][/tex]
Calculate the values and round the test statistic to two decimal places. If the absolute value of the test statistic is greater than the critical value for a two-tailed test at the 0.05 significance level, we reject the null hypothesis.
Note: The critical value for a two-tailed test at the 0.05 significance level is approximately [tex]\( \pm 1.96 \)[/tex].
Find the probability selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles when (a) you replace the first marble before drawing the second, and (b) you do not replace the first marble. Then, compare the probabilities. Round your answers to four decimal places.
Step-by-step explanation:
There are a total of 16 marbles, 8 of which are green.
(a) The probability the first marble is green is 8/16.
The marble is replaced, so there are still a total of 15 marbles, 8 of which are green. The probability the second marble is green is 8/16.
The probability of both events is (8/16) (8/16) = 1/4 = 0.2500.
(b) The probability the first marble is green is 8/16.
The marble is not replaced, so there are now a total of 15 marbles, 7 of which are green. The probability the second marble is green is 7/15.
The probability of both events is (8/16) (7/15) = 7/30 = 0.2333.
Final answer:
The probability of selecting a green marble, then another green marble from a bag of marbles is 0.25 when the first marble is replaced and 0.2333 when the first marble is not replaced.
Explanation:
To find the probability of selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles, we need to consider two scenarios: (a) replacing the first marble before drawing the second, and (b) not replacing the first marble.
a) If the first marble is replaced before drawing the second, the probability of selecting a green marble on the first draw is 8/16, and the probability of selecting a green marble on the second draw is also 8/16. We can multiply these probabilities together to get the overall probability: 8/16 × 8/16 = 16/64 = 0.25.
b) If the first marble is not replaced, the probability of selecting a green marble on the first draw is 8/16. However, since the first marble is not replaced, there are only 15 marbles left in the bag for the second draw, with 7 green marbles remaining. The probability of selecting a green marble on the second draw is 7/15. We can multiply these probabilities together to get the overall probability: 8/16 × 7/15 = 56/240 = 0.2333 (rounded to four decimal places).
Comparing the probabilities, we can see that the probability in scenario (a) when the first marble is replaced is higher than the probability in scenario (b) when the first marble is not replaced.
I=$54, P=$900, t=18 months
Answer:
about $982.20
Step-by-step explanation:
Formula = P(1+I)^T
T =18/12 because its in months not years, so 1.5 years
1+I = 1 + 54/900 or 1.03
P = 900
Plug those in and you get about 982.20
Answer:
4%
Step-by-step explanation:
For the simple interest rate,
I=P(i)t
54=900(i)(18/12)
i=54/900*(12/18)=4% annually
Which of the following is the inverse of y = 12 Superscript x? y = log Subscript one-twelfth Baseline x y = log Subscript 12 Baseline StartFraction 1 Over x EndFraction y = log Subscript x Baseline 12 y = log Subscript 12 Baseline
The inverse of the function is logx/log12
The inverse of a functionGiven the function expressed as:
y = 12^x
To find the inverse, switch the variables to have:
x = 12^y
Take the log of both sides
logx = y log 12
y = logx/log12
Hence the inverse of the function is logx/log12
Learn more on inverse of a function here: https://brainly.com/question/2873333
An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question.
Do you regularly recycle plastic bottles?
Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816)
How many students were in the sample selected by the environmental science teacher?
Answer:
60 students
Step-by-step explanation:
The confidence interval of a proportion is given by:
[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]
Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.
If the confidence interval is from 0.584 to 0.816, then:
[tex]p=\frac{0.584+0.816}{2}=0.7 \\0.816-0.584=2*(1.96*\sqrt{\frac{p*(1-p)}{n}}) \\0.116=1.96*\sqrt{\frac{0.7*(1-0.7)}{n}}\\n=16.8966^2*(0.7*0.3)\\n=60\ students[/tex]
60 students were in the sample.
Final answer:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher used a random sample and calculated a 95 percent confidence interval. Using the formula for the confidence interval for proportions, we can determine that the teacher selected approximately 223 students for the survey.
Explanation:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher selected a random sample of students and surveyed them one at a time, asking them if they regularly recycle plastic bottles. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816).
To find out how many students were in the sample selected by the teacher, we need to use the formula for the confidence interval for proportions:
n = (Z^2 * p * (1-p)) / (E^2)
Where:
n is the sample size,
Z is the Z-score corresponding to the desired level of confidence (in this case, 95 percent),
p is the estimated proportion of students who recycle plastic bottles (we can use the midpoint of the confidence interval, which is (0.584 + 0.816) / 2 = 0.7),
E is the margin of error (in this case, half the width of the confidence interval, which is (0.816 - 0.584) / 2 = 0.116).
Plugging in the values, we get:
n = (1.96^2 * 0.7 * (1-0.7)) / (0.116^2)
n = 2.992 / 0.013456
n ≈ 222.38
Since the sample size must be a whole number, we round up to the nearest whole number.
Therefore, the teacher selected approximately 223 students for the survey.
Which formula should be used to find the circumference of a circle?
C =πd
C=2πd
C=πr C=π/d
NEED HELP ASAP !
Answer:
C = πd or 2πr
Step-by-step explanation:
2r equals d
2r = d
Write the equation of a line that passes through the point (4,2) and has a
slope of 3.
Answer:
y = 3x - 4
Step-by-step explanation:
Start with your point-slope formula which is shown at the
top of the image that is provided below.
Then, plug in your appropriate values for the ordered pair (4, 2).
Now, simplify.
First distribute.
Then add 2 to both sides.
This leaves you with y = 3x - 10.
All my work is in the image attached.
42.23
Which inequality has -12 in its solution set?
A
B
C
D
Answer:
a
Step-by-step explanation:
Step-by-step explanation:
Simple
x + 6 < - 8
x < - 8 - 6
x < - 14
x + 4 > - 8
x > - 8 - 4
x > - 12
Option B is the correct answer
Write the equation in its equivalent exponential form: log5 25=2
Factor the expressions.
x2 + 25x + 24 =
Answer:
(x +1)(x +24)
Step-by-step explanation:
Factors of 24 that have a sum of 25 are 1 and 24. These are the constants you need in the binomial factors:
x^2 +25x +24 = (x +1)(x +24)
evaluate the expression
1. b ÷ 2.4; b = 16.8
Answer:
[tex]7[/tex]
Step-by-step explanation:
[tex] \frac{b}{2.4} \\ \frac{16.8}{2.4} \\ = 7[/tex]
f(1) = -16
f(n) = f(n-1) · (-1/2)
f(3) =
Answer:
-4
Step-by-step explanation:
Use the given value of f(1) to find f(2):
f(2) = f(1) · (-1/2) = (-16)(-1/2) = 8
Now, we can find f(3) using f(2):
f(3) = f(2) · (-1/2) = (8)(-1/2)
f(3) = -4
Classify the random variables below according to whether they are discrete or continuous.a. The time it takes for a light bulb to burn out.b. The number of fish caught during a fishing tournament.c. The number of statistics students now reading a book.d. The number of textbook authors now sitting at a computer.e. The height of a randomly selected giraffe.
Answer:
Discrete(b,c and d)
Continuous (a and e)
Step-by-step explanation:
Discrete
Discrete Random variables are variables that can only take on integer values. Therefore the following are discrete variables.
b. The number of fish caught during a fishing tournament. e.g. 6 fishes
c. The number of statistics students now reading a book. e.g. 12 Students
d. The number of textbook authors now sitting at a computer. e.g. 9 Authors
Continuous
Continuous random variables can take on an uncountable number of values.
a. The time it takes for a light bulb to burn out. e.g.178.897 seconds
e. The height of a randomly selected giraffe. e,g 16.67 feet
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Answer:
x=32, y=36, and z=25
Step-by-step explanation:
There are only two sums the equations can all add up to, 67 degrees and 113 degrees. I know that to the equation with x is equal to 67 degrees.
2x+3=67
2x=64 (subtract 3)
x=32 (divide by 2)
Now to find the measurement of the other angle, we subtract 180 and 67 since the measurement of a line is 180 degrees.
180-67=113
The equations of y and z are both equal to 113.
3y+5=113 4z+13=113
3y=108 (subtract 5) 4z=100 (subtract 13)
y=36 (divide by 3) z=25 (divide by 4)
A rectangular field is 0.3 kilometers long and 0.15 kilometers wide. What is the area of the field in square meters?
Final answer:
To find the area of the rectangular field in square meters, convert the dimensions from kilometers to meters and then multiply them together, resulting in 45,000 square meters.
Explanation:
To calculate the area of a rectangular field that is 0.3 kilometers long and 0.15 kilometers wide, use the following steps:
Convert the dimensions from kilometers to meters. Since there are 1,000 meters in a kilometer, the length in meters is 0.3 km × 1,000 = 300 meters and the width is 0.15 km × 1,000 = 150 meters.Multiply the length and width in meters to get the field's area in square meters. So the area is 300 m × 150 m = 45,000 square meters.