Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
The factors of 15 are numbers that can divide even through 15 without any remainders.
These numbers are 1, 3, 5 and 15;
When we roll two fair dice once, there are about 36 possible out comes and this is the sample space of rolling this fair dice.
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
The total that will give a factor of 15;
(1, 2) (2, 3) (1, 4) (2, 1) (3, 2) (4, 1)
Out of the 36 possible outcomes, we have 6 whose sum will give a factor of 15;
Probability of this = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex]
The difference between 12 and 1/3 of a number is 18.
Answer:
90
Step-by-step explanation:
work backwards, (18+12)3= 90
Plz brainliest :)
Answer:
90Step-by-step explanation:
work backwards (18+12)3=90hope it helps to you
please mark it as brainlist
Find the domain for f(x)=x^2+3x+2
Answer:
all real numbers: -∞ < x < ∞
Step-by-step explanation:
Any polynomial function is defined for all real numbers. This one is, too.
The domain is ...
-∞ < x < ∞
_____
Additional comment
Polynomial functions are often used to model things in the real world. One common application is the use of a quadratic function to model ballistic motion (height versus time). Such functions are defined for all values of the independent variable (time), but only have practical application over a smaller domain (time and height ≥ 0). Any question of domain might need to consider the practical domain, where the function is useful.
Question Help Explain the difference between statistical significance and practical significance. Choose the correct answer below. A. Statistical significance means that the hypothesis test being performed is useful for building theoretical foundations for other statistical work. Practical significance means that the particular application of the hypothesis test is of great importance to the real world. B. Statistical significance refers to the type of hypothesis test needed to analyze a population, with some tests being more important than Z tests. Practical significance refers to how difficult a desired hypothesis test is to perform in an application, with some tests being easier to perform than others. C. Statistical significance refers to how an unusual event is unlikely to actually appear in a real world application, such as every entry in a sample of size 50 having the same value. Practical significance refers to how an unusual event is likely to actually appear in a real world application, such as a rejection of a null hypothesis using data that looks feasible. D. Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. Practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application.
Answer:
Option D is the correct answer.
Step-by-step explanation:
The possibility that a relationship between two or more variables is caused by something other than chance is known as statistical significance. Statistical hypothesis testing is used to ascertain whether the result of a data set is statistically significant. This test provides a P-value, which represents the probability that random chance could explain the result.
Generally, a P-value of 5% or lower is regarded to be statistically significant.
Statistical significance relates to whether an effect exists, whereas practical significance indicates the magnitude of the effect.
Thus, by the definitions of Statistical significance and practical significance provided, only option D is correct, the other options are wrong.
The correct option is D- “Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. Practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application”.
The difference between statistical and practical significance involves whether findings are unlikely due to chance (statistical significance) or if the differences observed are large enough to matter in real applications (practical significance), correctly identified as option D.
The question asks to explain the difference between statistical significance and practical significance. The correct answer is option D. Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. This involves probability estimates and is often indicated by p-values like p < 0.05, which means the data is very unlikely to have been caused by chance factors alone, and therefore, there might be a real relationship. On the other hand, practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application. This considers if the findings have a real-world impact or importance beyond just being statistically unlikely due to chance.
Conceptual Set 1. The same researcher wants to then compare the final (time 2) levels of anger in this experimental group to a control group that just had the water balloons thrown at them. He compares the group from the previous questions to a group who did not do pushups. Which t-test should he use?
QUESTION 55-Conceptual Set 1. Why should the researcher from question 54 use that test?
A.Because single sample t-tests compare a sample mean to a population mean, which is what the researcher is attempting to do
B. Because single sample t-tests compare scores before and after an event, which is what the researcher isattempting to do
C. Because single sample t-tests compare two completely different groups in a sample, which is what the researcher is attempting to do
D. Because paired samples t-tests compare a sample mean to a population mean, which is what the researcher is attempting to do
E. Because paired samples t-tests compare scores before and after an event, which is what the researcher is attempting to do
F. Because paired samples t-tests compare two completely different groups in a sample, which is what the researcher is attempting to do
G. Because independent sample t-tests compare a sample mean to a population mean, which is what the researcher is attempting to do
H. Because independent sample t-tests compare scores before and after an event, which is what the researcher is attempting to do
I. Because independent sample t-tests compare two completely different groups in a sample, which is what the researcher is attempting to doA
Answer:
I
Step-by-step explanation:
Because independent sample t-tests compare two completely different groups in a sample, which is what the researcher is attempting to do.
A survey is being conducted in a county where 62% of the voters are Democrats and 38% are Republican. (a) What is the probability that two independently surveyed voters would both be Democrats?
Answer:
0.3844 = 38.44% probability that two independently surveyed voters would both be Democrats
Step-by-step explanation:
For each voter, there are only two possible outcomes. Either the voter is a Democrat, or he is not. The probability of the voter being a Democrat is independent of other voters. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
62% of the voters are Democrats
This means that [tex]p = 0.62[/tex]
(a) What is the probability that two independently surveyed voters would both be Democrats?
This is P(X = 2) when n = 2. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.62)^{2}.(0.38)^{0} = 0.3844[/tex]
0.3844 = 38.44% probability that two independently surveyed voters would both be Democrats
A quality-control inspector rejects any shipment of printed circuit boards whenever 3 or more defectives are found in a sample of 50 boards tested. Find the (1) expected number defective and (2) the probability of rejecting the shipment when the proportion of defectives in the entire shipment is
(a) Proportion of Defectives=0.01
Expected Number Defective=
Probability of Rejecting the Shipment=
(b) Proportion of Defectives=0.05
Expected Number Defective=
Probability of Rejecting the Shipment=
(c) Proportion of Defectives=0.1
Expected Number Defective=
Probability of Rejecting the Shipment=
Expert
Answer:
(a) Proportion of Defectives = 0.01
Expected Number Defective = 0.5
Probability of Rejecting the Shipment = 0.0138
(b) Proportion of Defectives = 0.05
Expected Number Defective = 2.5
Probability of Rejecting the Shipment = 0.459
(c) Proportion of Defectives = 0.1
Expected Number Defective = 5
Probability of Rejecting the Shipment = 0.888
Step-by-step explanation:
This is a binomial distribution problem due to the unchanging probability of getting a defective board, no matter the number of trials ran.
The expected number for binomial distribution is given as E(X) = np
The probability mass funaction for binomial distribution is given as
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 50
x = Number of successes required = ≥3
p = probability of success = changing from question to question
q = probability of failure = 1 - p
Total number of boards tested = 50
Note that probability of rejecting the shipment for each of the sub-question is the probability that 3 or more boards are defective. That is, P(X ≥ 3)
P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]
a) Proportion of Defectives=0.01
Expected Number Defective = np = 0.01 × 50 = 0.5
Probability of Rejecting the Shipment = P(X ≥ 3)
n = total number of sample spaces = 50
p = probability of success = probability of a detective board = 0.01
q = probability of failure = 1 - 0.01 = 0.99
P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)] = 0.01381727083 = 0.0138
b) Proportion of Defectives = 0.05
Expected Number Defective = np = 0.05 × 50 = 2.5
Probability of Rejecting the Shipment = P(X ≥ 3)
n = total number of sample spaces = 50
p = probability of success = probability of a detective board = 0.05
q = probability of failure = 1 - 0.05 = 0.95
P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)] = 0.45946687728 = 0.459
c) Proportion of Defectives = 0.1
Expected Number Defective = np = 0.1 × 50 = 5
Probability of Rejecting the Shipment = P(X ≥ 3)
n = total number of sample spaces = 50
p = probability of success = probability of a detective board = 0.1
q = probability of failure = 1 - 0.1 = 0.90
P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)] = 0.88827124366 = 0.888
Hope this Helps!!!
what is a numerators characteristics
9 of the 13 participants in a triathlon are men and the rest are women. What is the ratio of the number of women participating to the total number of participants?
The ratio of the number of women to the total number of participants in the triathlon is 4:13.
Explanation:The question is asking for the ratio of the number of women to the total number of participants in a triathlon. We know that there are 13 total participants and 9 of them are men. We can determine that there are 4 ladies by taking 9 out of 13. Therefore, the ratio of the number of women to the total number of participants is 4:13. This indicates that 4 women make up each of the 13 participants, according to our calculations.
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Which simplified fraction is equal to 0.53?
Answer:
53/100?
Step-by-step explanation:
I mean you can't really simplify it any more. There's no LCD, GCD. Can't divide it evenly.
To solve it I just looked at the number of places, (3 which mean 100.)
Then I looked at the numbers, (53.)
So you just turn that into a fraction...
Answer:
well there are many ways to but id say 8/15
Step-by-step explanation:
What is the volume of a sphere with a radius of 6 mm?
A certain bowler can bowl a strike 85 % of the time. What is the probability that she a) goes three consecutive frames without a strike? b) makes her first strike in the third frame? c) has at least one strike in the first three frames? d) bowls a perfect game (12 consecutive strikes)?
The probability calculations for the bowler indicate that she has a 0.33% chance of not getting a strike for three consecutive frames, a 1.9% chance of getting her first strike in the third frame, a 99.66% chance of getting at least one strike in the first three frames, and a 3.4% chance of bowling a perfect game.
Explanation:The subject here is probability, with the scenario provided being that a bowler can strike 85% of the time. We assume that all strikes are independent events, meaning one strike does not affect the probability of the next strike.
a) Probability of no strike in three consecutive frames:
The probability of her not getting a strike in one turn is 1 - 0.85 = 0.15 (the complement of her strike rate). For three consecutive frames without a strike, we multiply these probabilities because of their independence: 0.15 * 0.15 * 0.15 = 0.003375 or 0.33%.
b) Probability of first strike in the third frame:
This means not striking in the first two frames and getting a strike in the third. Calculate this by multiplying the probabilities: 0.15 * 0.15 * 0.85 = 0.01912 or 1.9%.
c) Probability of at least one strike in three frames:
This is best calculated by subtracting the probability of no strikes in 3 frames (found in part a) from 1, as it is the complement: 1 - 0.003375 = 0.996625 or 99.66%.
d) Probability of a perfect game:
A perfect game requires 12 consecutive strikes. Multiply the probability of a strike (0.85) by itself 12 times : 0.85^12 = 0.034 (3.4% chance of a perfect game).
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The step-by-step probabilities for varying scenarios in a bowling game are: a) 0.003375 for no strikes in three frames, b) 0.019125 for the first strike in the third frame, c) 0.996625 for at least one strike in three frames, and d) 0.1489 for a perfect game.
Probability Calculations for a Bowler
A certain bowler has an 85% chance of bowling a strike. Let's break down each part of the question:
a) Probability of three consecutive frames without a strike
The probability of not getting a strike in one frame is 1 - 0.85 = 0.15. Therefore, the probability of not getting a strike in three consecutive frames is:
(0.15) × (0.15) × (0.15) = 0.003375
b) Probability of making the first strike in the third frame
The probability of not getting a strike in the first two frames but getting a strike in the third frame is:
(0.15) × (0.15) × (0.85) = 0.019125
c) Probability of at least one strike in the first three frames
First, find the probability of no strikes in three frames, which we've already calculated as 0.003375. Therefore, the probability of at least one strike is:
1 - 0.003375 = 0.996625
d) Probability of a perfect game (12 consecutive strikes)
The probability of getting a strike in each of the 12 frames is:
(0.85)¹² = 0.1489
A washer and dryer cost $584 combined. The washer costs $66 less than the dryer. What is the cost of the dryer?
Final answer:
By creating equations representing the cost relationship between the washer and dryer, and solving for the unknown, we find that the cost of the dryer is $325.
Explanation:
To calculate the cost of the dryer when the combined cost of a washer and dryer is $584 and the washer costs $66 less than the dryer, we can set up an equation. Let's denote the cost of the dryer as D and the cost of the washer as W.
1. The first step is to express the washer's cost in terms of the dryer's cost:
W = D - 66
2. Then, use the combined cost to create an equation:
W + D = 584
3. Substitute the expression for W into the second equation:
(D - 66) + D = 584
4. Solve for D:
2D - 66 = 584
2D = 584 + 66
2D = 650
D = 650 / 2
D = 325
Therefore, the cost of the dryer is $325.
If Serena painted all the faces of the piece of the model, including the base, what area did she paint?
Answer:
is there any measurements included?
Step-by-step explanation:
The question mainly discusses the artistic attributes and historical aspects of a sculpture, including descriptions of paint used, rather than providing information needed to calculate the area painted.
Explanation:The question provided does not directly relate to computing the area painted as it mostly describes the artistic characteristics and historical context of a sculpture. It talks about the sculpture's features, color schemes used for painting such as black hair, red and blue dress with a yellow belt, and the use of paint on the sculpture's body and face.
To calculate the area painted, one would ideally need the dimensions of each face of the model or sculpture to sum up their areas if it were a geometric problem in Mathematics. However, the question mainly focuses on the art critique, interpretation, and visual description of the sculpture, highlighting its historical significance and the artistic techniques employed.
what is the slope of the line that is parallel ^
Given:
Given that the equation of the line is [tex]y=2x-4[/tex]
We need to determine the slope of the line.
Slope:
The general form of the equation of the line is [tex]y=mx+c[/tex] where m is the slope of the line.
Comparing the equation [tex]y=2x-4[/tex] with the general form of the equation of the line, we get;
Slope = m = 2.
Hence, the slope is 2.
Since, we need to determine the slope of the parallel lines and we know that the slope of the parallel lines are equal.
Thus, the slope of the parallel line is 2.
Hence, Option B is the correct answer.
Insert the greater than, less than, or equal sign (>, <, or =) to make each statement true.
a. 45⁄45 ____1
b. 1____ 6⁄3
c. 2⁄7 ____1
d. 64⁄23 ____1
You borrow $2250 at 4.8% compounded weekly for tuition. While you do not have to make payments for the 5 years that you are in school, the interest is compounding. What is your loan balance after the 5-year grace period (if you've made no payments)?
Final Answer:
The balance of the loan after the 5-year grace period, with no payments made and interest compounding weekly at an annual rate of 4.8%, would be approximately $2884.50.
Explanation:
To solve this problem, we want to calculate the future value of the loan after 5 years of weekly compounding interest. The formula for the future value of an investment compounded more frequently than once a year is
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt}, \][/tex]
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Given:
- P = $2250 (the initial loan amount)
- r = 4.8\% = 0.048 (the annual interest rate converted to a decimal)
- n = 52 (the loan is compounded weekly)
- t = 5 (the loan is for a period of 5 years)
Now we will plug these values into the formula to calculate the future value of the loan.
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \\\\\\\[ A = 2250 \left(1 + \frac{0.048}{52}\right)^{52 \times 5} \][/tex]
Calculating the term inside the parentheses first:
[tex]\[ \frac{0.048}{52} = 0.00092307692 \] (approximately)[/tex]
Adding 1 to this result:
[tex]\[ 1 + 0.00092307692 = 1.00092307692 \] (approximately)[/tex]
Now we need to raise this to the power of 260 (which is [tex]\( 52 \times 5 \)[/tex]):
[tex]\[ \left(1.00092307692\right)^{260} \] (use a calculator for this step)[/tex]
After doing this calculation, you should get a value of approximately 1.282002. (Remember, the exact result might vary slightly depending on the precision of your calculator.)
Finally, we can calculate the future value A:
[tex]\[ A = 2250 \times 1.282002 \\\\\[ A \approx 2884.505 \][/tex]
Therefore, the balance of the loan after the 5-year grace period, with no payments made and interest compounding weekly at an annual rate of 4.8%, would be approximately $2884.50.
As part of a fundraiser, a local charity has sold 6 raffle tickets,
with a goal of selling 140 tickets. What percentage of the goal has been sold? (Round to the nearest tenth of a percent, if necessary).
Answer:
4.3%
Step-by-step explanation:
[tex]selling \: percent \\ = \frac{6}{140} \times 100 \\ \\ = \frac{60}{14} \\ \\ = 4.28 \\ = 4.3\% \\ [/tex]
As per linear equation, 4.3% of tickets are sold of the goal.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Given, a local charity has sold 6 raffle tickets.
The goal of selling tickets is 140.
Therefore, the percentage of sold tickets is
[tex]= \frac{6}{140}[/tex] ×100%
[tex]= 4.3[/tex]%
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Write a quadratic function f whose zeros are 3 and -6.
Answer:
(x+3) (x-6) = 0
Step-by-step explanation:
A quadratic equation is in the form of ax²+bx+c. The quadratic function whose zeros are 3 and -6 is (x² + 3x - 18).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Given that the quadratic function whose zeros are 3 and -6. Therefore, the quadratic function can be written as,
(x-3)(x+6)
= x² + 6x - 3x -18
= x² + 3x - 18
Hence, the quadratic function whose zeros are 3 and -6 is (x² + 3x - 18).
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I REALLY NEED HELP WITH THIS!! I'VE BEEN TRYING TO SOLVE IT FOR SO LONG!!
THANK YOU AND STAY SAFE!!
Answer:
44
Step-by-step explanation:
A student planning her curriculum for the upcoming year must select one of six business courses, one of three mathematics courses, two of eight elective courses, and either one of three history courses or one of two social science courses. How many different curricula are available for her consideration?
Answer: Four Curricula
Step-by-step explanation:
Business
Mathematics
History
Social Science
Answer:
Four Curricula
Six pounds of grapefruit costs 3 dollars 5 pound of apples cost 2.65. What is the cost per pound for each fruit ?
Answer:
We need to find the unit rates for the fruit. To do this, divide the cost by the number of pounds
Grapefruit:
cost/pounds
$3/6 pounds
3/6=0.5
0.5 per pound
Apples:
cost/pounds
$2.65/5 pounds
2.65/5=0.53
0.53 per pound
The starting salary of business students in a university is known to be normally distributed. A random sample of 18 business students results in a mean salary of $46,500 with a standard deviation of $10,200. Construct the 90% confidence interval for the mean starting salary of business students in this university.
Problem 2.2 (20 points)Black and yellow pigment cells (melanophores and xanthophores) are responsible for patterns onthe skin of Zebra Fish. We denote the number of melanophores at timetbyM(t) and the numberof xanthophores at timetbyX(t). Suppose that 10% of melanophores become (differentiate into)xanthophores per unit time. Conversely, 40% of xanthophores become melanophores per unit time,and 10% of xanthophores die per unit time. Finally, 10 melanophores and 20 xanthophores areborn per unit time.1. DefineP(t)
Your question is not complete as you have not provided some details.
Please let me assume this to complete your question;
P(t) = M(t) ÷ X(t)
ANSWER:
P(t) is the ratio of the number of melanophores to the number of xanthophores per unit time.
Therefore P(t) = 1.55
Step-by-step explanation:
KEY NOTE:
I) 10% of melanophore converts to Xanthophore per unit time.
II) 40% of Xanthophore converts to melanophore per unit time.
III) 10 melanophore and 20 Xanthophore are born per unit time
IV) 10% of Xanthophore die per unit time.
STEP 1: Conversion rate to number of birth per unit time.
For M(t) 10% of 10 = 1
For X(t) 40% of 20 = 8
Therefore;
M(t) = 10 + 8 - 1 = 17
X(t) = 20 + 1 - 8 = 13
STEP 2:
10% of Xanthophore die per unit time.
10% of 20 = 2
Therefore X(t) is;
13 - 2 = 11
The total X(t) = 11
The total M(t) = 17
P(t) = M(t)/X(t) = 17÷ 11 = 1.55
Which of the following statements is true?
A. A tangent is never a secant.
B. A secant is always a chord.
C. A chord is always a radius.
D. A diameter is never a chord.
Please select the best answer from the choices provided
Answer:
a tangent is never a secant
Step-by-step explanation:
the secant is in the circle
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The correct statement is A: 'A tangent is never a secant.' because it accurately describes that a tangent only touches the circle at one point and does not cross the circle's interior unlike a secant.
Explanation:The question you've asked pertains to the geometric definitions of a tangent, secant, chord, and diameter in relation to a circle. Reviewing the options provided:
A tangent is a line that touches a circle at exactly one point and never enters the circle's interior, so it's distinct from a secant, which does enter the interior. Therefore, option A ('A tangent is never a secant.') is true.A secant is a line that intersects a circle at two points and always includes a chord, the segment between these two points, which makes option B ('A secant is always a chord.') incorrect as a secant is not a chord, it includes a chord.A chord is a segment whose endpoints lie on a circle, and it could be any length up to the length of the diameter; hence, option C ('A chord is always a radius.') is incorrect.A diameter is a special type of chord that passes through the center of the circle and its longest possible chord. So, option D ('A diameter is never a chord.') is incorrect.Given these explanations, the best answer from the choices provided is in fact option A.
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A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.
The value to use for the standard error of the mean is:
1.13.5
2.9
3.2.26
4.1.5
Answer:
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(60,13.5)[/tex]
Where [tex]\mu=60[/tex] and [tex]\sigma=13.5[/tex]
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard error of the mean would be:
[tex]\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5[/tex]
4.1.5
Step-by-step explanation:
Previous concepts
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".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(60,13.5)[/tex]
Where [tex]\mu=60[/tex] and [tex]\sigma=13.5[/tex]
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard error of the mean would be:
[tex]\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5[/tex]
4.1.5
The standard error of the mean for the sample of automobiles is 1.5 mph ,i.e, option 4, which is found by dividing the standard deviation, 13.5 mph, by the square root of the sample size, 9, because the sample size is 81 vehicles.
The standard error of the mean (SEM) is the standard deviation ()divided by the square root of the sample size (n). For the given data, with a sample size of 81 automobiles and a standard deviation of 13.5 mph, the standard error of the mean can be calculated as follows:
SEM = 13.5 / 81 = 13.5 / 9 = 1.5 mph
Therefore, the value for the standard error of the mean is 1.5.
give an equation of the form f(x)=a^x to define the exponential function whose graph contains the point (3,8)
Answer:
f(x) = 2^x
Step-by-step explanation:
Solve for a. At point (3,8), x = 3, f(x) = 8
Plugging into the equation it becomes 8 = a^3
a = [tex]\sqrt[3]{8}[/tex]
a = 2
The exponential function is [tex]\boldsymbol{f(x)=2^x}[/tex].
Exponential FunctionA mathematical function of the form [tex]\boldsymbol{f(x)=a^x}[/tex] is an exponential function. where [tex]x[/tex] is a variable and [tex]a[/tex] is a constant known as the function's base.
Put [tex](x,f(x))=(3,8)[/tex] in the given exponential function.
[tex]8=a^3\\2^3=a^3\\a=2[/tex]
So, the exponential function is [tex]\boldsymbol{f(x)=2^x}[/tex]
Find out more information about exponential function here:
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A triangular pyramid. The triangular base has a height of 8 units and base of 12 units. 2 sides have a base of 10 and height of 14. 1 side has a base of 12 and height of 13.6. Find the surface area of the pyramid. The triangular base has a height of 8 units and a base of 12 units. What is the base area? What is the lateral area? What is the surface area?
Base area of the triangular pyramid is 96 square units.
Lateral surface area of the triangular pyramid is 221.6 square units.
Surface area of the triangular pyramid is 317.6 square units.
Step-by-step explanation:
Base area = 8 x 12
= 96 square units
Base area of the triangular pyramid is 96 square units.
Lateral surface area = 2[(1/2) 10x 14] + (1/2) (12 x 13.6)
= 2(70) +81.6
= 140 + 81.6
= 221.6 square units
Lateral surface area = 221.6 square units
Lateral surface area of the triangular pyramid is 221.6 square units.
Surface area= 221.6 + 96
= 317.6 square units
Surface area of the triangular pyramid is 317.6 square units.
Answer:
the right answer is 48,221.6,269.6
Step-by-step explanation:
A simple random sample of 100 bags of tortilla chips produced by Company X is selected every hour for quality control. In the current sample, 18 bags had more chips (measured in weight) than the labeled quantity. The quality control inspector wishes to use this information to calculate a 90% confidence interval for the true proportion of bags of tortilla chips that contain more than the label states.
1. What is the value of the standard error of the sample proportion?
a. 0.038
b. 384
c. 0.0015
d. 0.063
Answer:
Option A) 0.038
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 100
Number of of bags of tortilla chips that contain more than the label states, x = 18
Sample proportion:
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{18}{100} = 0.18[/tex]
Formula for standard of error:
[tex]\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
Putting the values, we get:
[tex]\sqrt{\dfrac{0.18(1-0.18)}{100}} =0.038[/tex]
Thus, the correct answer is
Option A) 0.038
A company estimates that it will sell ????(x) units of a product after spending x thousand dollars on advertising, as given by ????(x)=−5x3+235x2−3400x+20000,10≤x≤40. (A) Use interval notation to indicate when the rate of change of sales ????′(x) is increasing. Note: When using interval notation in WeBWorK, remember that: You use 'I' for [infinity] and '-I' for −[infinity], and 'U' for the union symbol. If you have extra boxes, fill each in with an 'x'. ????′(x) increasing:
Answer:
[tex](11\frac{1}{3},20)[/tex]
Step-by-step explanation:
If the Number of Sales of x units, N(x) is defined by the function:
[tex]N(x)=-5x^3+235x^2-3400x+20000,10\leq x\leq 40[/tex]
[tex]N'(x)=-15x^2+470x-3400\\When -15x^2+470x-3400=0\\x=20, x=11\frac{1}{3}[/tex]
Next, we text the critical points and the end points of the interval to see where the derivative is increasing.
[tex]N'(10)=-200\\N'(11\frac{1}{3})=0\\N'(19)=115\\N'(20)=0\\N'(40)=-8600[/tex]
Thus, the rate of change of sales [tex]N'(x)[/tex] is increasing in the interval [tex](11\frac{1}{3},20)[/tex] on 10≤x≤40.
The rate of change is how much the company sales changes after spending
The rate of change increases at: (10, 20)
The function is given as:
[tex]\mathbf{f(x) = -5x^3 +235x^2 - 3400x + 20000}[/tex]
Differentiate, to calculate the rate of change
[tex]\mathbf{f'(x) = -15x^2 +470x- 3400}[/tex]
Set to 0
[tex]\mathbf{ -15x^2 +470x- 3400 = 0}[/tex]
Divide through by 5
[tex]\mathbf{ -3x^2 +94x- 680 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{x = \{20,11.3\}}[/tex]
The domain is given as: [tex]\mathbf{10 \le x \le 40}[/tex]
When x = 10, we have:
[tex]\mathbf{f'(10) = -15(10)^2 +470(10)- 3400 = -200}[/tex]
When x = 11.3, we have:
[tex]\mathbf{f'(11.3) = -15(11.3)^2 +470(11.3)- 3400 = -4.35}[/tex]
When x = 20, we have:
[tex]\mathbf{f'(20) = -15(20)^2 +470(20)- 3400 = 0}[/tex]
When x = 40, we have:
[tex]\mathbf{f'(40) = -15(40)^2 +470(40)- 3400 = -8600}[/tex]
The value of f'(x) increases at x = 10 to 20.
Hence, the rate of change increases at: (10, 20)
Read more about rates at:
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Find the period, range, and amplitude of the cosine function y= 3/2cos t/2
Answer:
[tex]Amplitude = /\frac{3}{2}/[/tex]
[tex]Range = [\frac{-3}{2} , \frac{3}{2}][/tex]
[tex]Period = \pi[/tex]
Step-by-step explanation:
Given: [tex]y = \frac{3}{2}cos\frac{t}{2}[/tex]
Comparing the equation with the standard form of cosine function :
[tex]y = A cos(Bx- C)[/tex]
where:
[tex]A = Amplitude[/tex]
Formula for calculating Amplitude is given as:
[tex]Amplitude = /A/[/tex]
The formula for calculating Period is given as :
[tex]Period =\frac{2\pi }{B}[/tex]
[tex]B = \frac{1}{2}[/tex]
Therefore , with the comparison
[tex]A = /\frac{3}{2}/[/tex]
which means that:
[tex]Range = \frac{-3}{2} , \frac{3}{2}[/tex]
[tex]Period = \frac{2\pi }{2}[/tex]
[tex]Period = \pi[/tex]