A biologist is trying to determine the average age of a local forest. She cuts down 18 randomly selected trees and counts the number of tree rings, which can be used to estimate the age of the tree. What critical value should she use to construct a 99% confidence interval
Answers
Answer:
The critical value of t for 99% confidence interval is 2.898.
Step-by-step explanation:
The complete question is:
A biologist is trying to determine the average age of a local forest. She cuts down 18 randomly selected trees and counts the tree rings. They find the average number of tree rings to be 83 with a variance of 320. What is the critical value for the 99% confidence interval?
The population variance is not known and the sample size is too small. So a t-confidence interval will be used to estimate the population mean age of a local forest.
The (1 - α)% confidence interval for population mean is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
The information provided is:
n = 18
(1 - α)% = 99%
The degrees of freedom of the critical value of t is:
n - 1 = 18 - 1 = 17
Compute the critical value of t as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.01/2, (18-1)}=t_{0.005, 17}=2.898[/tex]
*Use a t-table.
Thus, the critical value of t for 99% confidence interval is 2.898.
Related Questions
A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to difference between the radius of the hole and the radius of the shaft. Let the random variable X denote the clearance, in millimeters. The probability density function of X is
F(x) =1.25(1 - x4) if 0 < x < 1
F(x) = 0 otherwise
A. Components with clearances larger than 0.8 mm must be scrapped. What proportion of components are scraped?
B. Find the cumulative distribution function F(x) and plot it.
C. Use the cumulative distribution to find the probability that the shaft clearance is less than 0.5 mm.
D. Find the mean clearance and the variance of the clearance.
Answers
Answer:
(A)
[tex]P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192[/tex]
(B)
Then the cumulative function would be
[tex]CF(x) = 1.25x - 0.25x^5[/tex] if 0<x<1
0 otherwise.
Step-by-step explanation:
(A)
We are looking for the probability that the random variable X is greater than 0.8.
[tex]P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192[/tex]
(B)
For any [tex]x[/tex] you are looking for the probability [tex]P(X \geq x)[/tex] which is
[tex]P(X \geq x) = \int\limits_{-\infty}^{x} 1.25(1-t^4) dt = \int\limits_{0}^{x} 1.25(1-t^4) dt = 1.25x - 0.25x^2[/tex]
Then the cumulative function would be
[tex]CF(x) = 1.25x - 0.25x^5[/tex] if 0<x<1
0 otherwise.
This response provides step-by-step instructions for calculating probability density functions, cumulative distribution functions, the mean, and the variance using calculus. The solution involves probability theory, calculus, and graphing techniques.
Explanation:A. To find the proportion of components that are scraped, we need to integrate the probability density function from 0.8 to 1. This can be done using calculus and you should get an answer around 0.41 if done correctly.
B. The cumulative distribution function is the integral of the probability density function. Integrating f(x) from 0 to x will give you a polynomial expression that represents F(x). You can plot this using any graphing software.
C. To find the probability that the clearance is less than 0.5 mm, evaluate the cumulative distribution function at x = 0.5. This will give you a decimal number which represents the probability.
D. The mean clearance is found by taking the expected value of the random variable, which is the integral of x * f(x) from 0 to 1. The variance is found by subtracting the square of the mean from the expected value of the square of the random variable, which is the integral of x^2 * f(x) from 0 to 1.
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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)
Answers
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
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.
Answers
Hope this helps
Find the arc length of the bolded arc in the picture A) 99.0 ft
C) 756.1 ft
B) 19.6 ft
D) 7.9 ft
Answers
Answer:
D) 7.9 ft
Step-by-step explanation:
To answer this, you only need to reject the nonsense answers.
The arc length will be more than 5 ft and less than the length of 2 sides of a 5 ft square (10 ft). Only one answer choice falls in that range.
7.9 ft
__
If you like, you can figure 1/4 of the circumference of a circle with radius 5 ft:
C/4 = (1/4)(2π)(5 ft) = 2.5π ft ≈ 7.854 ft ≈ 7.9 ft
Answer:
D 7.9ft
Step-by-step explanation:
What is the volume of a sphere with a radius of 6 mm?
Answers
I REALLY NEED HELP WITH THIS!! I'VE BEEN TRYING TO SOLVE IT FOR SO LONG!!
THANK YOU AND STAY SAFE!!
Answers
Answer:
44
Step-by-step explanation:
In this example, a is 5
B is 2
C is -2
2^2-4*5*-2
So the discriminant is 44
An article presents measures of penetration resistance for a certain fine-grained soil. Fifteen measurements, expressed as a multiple of a standard quantity, had a mean of 2.62 and a standard deviation of 1.02. Can you conclude that the mean penetration resistance is greater than 2.5? Find the P-value and state a conclusion.
Answers
Answer:
[tex]t=\frac{2.62-2.5}{\frac{1.02}{\sqrt{15}}}=0.456[/tex]
[tex]df=n-1=15-1=14[/tex]
[tex]p_v =P(t_{(14)}>0.456)=0.328[/tex]
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is higher than 2.5 at 5% of significance
Step-by-step explanation:
Data given and notation
[tex]\bar X=2.62[/tex] represent the sample mean
[tex]s=1.02[/tex] represent the sample deviation
[tex]n=15[/tex] sample size
[tex]\mu_o =2.5[/tex] 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 true mean is higher than 2.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 2.5[/tex]
Alternative hypothesis:[tex]\mu > 2.5[/tex]
If we analyze the size for the sample is <30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-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]t=\frac{2.62-2.5}{\frac{1.02}{\sqrt{15}}}=0.456[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=15-1=14[/tex]
Since is a right tailed test the p value would be:
[tex]p_v =P(t_{(14)}>0.456)=0.328[/tex]
Conclusion
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is higher than 2.5 at 5% of significance
Six pounds of grapefruit costs 3 dollars 5 pound of apples cost 2.65. What is the cost per pound for each fruit ?
Answers
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
At the Kansas City Airport, a group of pilots for Skyways and Yellow Jet airlines were asked whether their flights were flying east or west. The two-way table shows their answers. Which joint frequency has the most flights?
A) Skyways, going east
B) Skyways, going west
C) Yellow jet, going east
D) Yellow jet, going west
Answers
The frequency has the most flights from the airlines is C. Yellow jet, going east.
What is a frequency table?The frequency table is a table that's used to illustrate the data that's given.
In this case, the frequency has the most flights from the airlines will be Yellow jet, going east. This is because most people are going in that direction.
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The joint frequency with the most flights is yellow jets going east.
Option C is the correct answer.
What is a joint frequency?Joint frequency refers to the number of observations that fall in each category when we have two categorical variables.
We have,
To determine which joint frequency has the most flights, we need to look for the highest value in the table.
From the table,
We can see that the highest value is 35, which represents the number of yellow jets going east.
Therefore,
The joint frequency with the most flights is yellow jets going east.
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Among a banks 214 customers with checking or savingsaccounts, 189 have checking accounts, 73 have regular savingsaccounts, 114 have money market savings accounts, and 69 have bothchecking and regular savings accounts. No customer is allowed tohave both savings and money market savings accounts.
a.) How many customers have both checking and money marketsavings accounts?
b.) How many customers have a checking account but no savingsaccount?
Answers
Answer:
a) 93 customers
b) 27 customers
Step-by-step explanation:
Total number of customers (n) = 214
Checking (C) = 189
Regular Savings (R) = 73
Market Savings (M) = 114
Checking and Regular (C&R) = 69
a) The total number of customers is given by:
[tex]n = C+R+M-C\cap R-C\cap M\\214=189+73+114-69-C\cap M\\C\cap M = 93[/tex]
93 customers have both checking and money market savings accounts
b) The number of customers with savings accounts is given by:
[tex]C = C_{only} +C\cap R+C\cap M\\189=C_{only} +69+93\\C_{only} = 27[/tex]
27 customers have a checking account but no savings account.
Change each mixed number into an equal improper fraction.
a. 1 7⁄16
b. 11 5⁄9
c. 30 5⁄7
d. 10 10⁄13
e. 24 3⁄5
f. 129 1⁄2
Answers
Answer:
In converting a mixed number to an improper fraction, you would have to multiply the denominator to the whole number, once you do that you have to add the product to the numerator. The denominator would still stay the same.
A. 1 7/16 = 23/16
B. 11 5/9 = 104/9
C. 30 5/7 = 215/7
D. 10 10/13 = 140/13
E. 24 3/5 = 123/5
F. 129 1/2 = 259/2
~hope this helps~
To convert mixed numbers to improper fractions, multiply the whole number part by the denominator of the fraction, add the numerator, and keep the denominator the same. Examples include converting 1 7/16 to 23/16 and 11 5/9 to 104/9.
To change each mixed number into an equal improper fraction, you should follow a consistent method. This involves multiplying the whole number by the denominator of the fraction part and then adding the numerator of the fraction part. The resulting sum becomes the numerator of the improper fraction, with the denominator remaining the same as in the original fraction.
a. 1 7⁄16: Multiply 1 by 16 (the denominator) = 16, then add 7 (the numerator) = 23. Thus, 1 7⁄16 equals 23/16.
b. 11 5⁄9: Multiply 11 by 9 = 99, then add 5 = 104. So, 11 5⁄9 equals 104/9.
c. 30 5⁄7: Multiply 30 by 7 = 210, then add 5 = 215. Therefore, 30 5⁄7 equals 215/7.
d. 10 10⁄13: Multiply 10 by 13 = 130, add 10 = 140. Hence, 10 10⁄13 is 140/13.
e. 24 3⁄5: Multiply 24 by 5 = 120, add 3 = 123. Thus, 24 3⁄5 equals 123/5.
f. 129 1⁄2: Multiply 129 by 2 = 258, add 1 = 259. Therefore, 129 1⁄2 is 259/2.
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:
Answers
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)
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Natalie is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 6 inches x 13 1/2 inches. She needs to cut another rectangle that is 10 1/3 inches by 10 1/2 inches. How many total square inches of construction paper does Natalie need for her project?
Answers
To find the total area of the construction paper needed for Natalie's project, multiply the length by the width of each rectangle and add them together.
Explanation:To find the total area of the construction paper needed for Natalie's project, we need to find the area of each rectangle and then add them together.
Rectangle 1:
Length = 6 inches and width = 13 1/2 inches.
To find the area, multiply the length by the width: 6 inches x 13 1/2 inches = 81 square inches.
Rectangle 2:
Length = 10 1/3 inches and width = 10 1/2 inches.
To find the area, multiply the length by the width: 10 1/3 inches x 10 1/2 inches = 108 1/3 square inches.
Total area:
Add the areas of both rectangles: 81 square inches + 108 1/3 square inches = 189 1/3 square inches.
Therefore, Natalie needs a total of 189 1/3 square inches of construction paper for her project.
Natalie needs a total of 149 square inches of construction paper for her project.
To find the total square inches of construction paper needed for Natalie's project, we calculate the area of each rectangle and then add them together.
1. Area of the first rectangle:
[tex]\( \text{Area}_1 = \text{length} \times \text{width} = 6 \times 13\frac{1}{2} \) square inches.[/tex]
2. Area of the second rectangle:
[tex]\( \text{Area}_2 = \text{length} \times \text{width} = 10\frac{1}{3} \times 10\frac{1}{2} \) square inches.[/tex]
3. Calculate the total area:
Total area = Area of first rectangle + Area of second rectangle.
Let's compute:
1. [tex]\( \text{Area}_1 = 6 \times 13\frac{1}{2} = 6 \times \frac{27}{2} = \frac{81}{2} = 40.5 \) square inches.[/tex]
2. [tex]\( \text{Area}_2 = 10\frac{1}{3} \times 10\frac{1}{2} = \frac{31}{3} \times \frac{21}{2} = \frac{651}{6} = 108.5 \) square inches.[/tex]
3. Total area = 40.5 + 108.5 = 149 square inches.
So, Natalie needs a total of 149 square inches of construction paper for her project.
what is the measure of BFD?
Answers
Answer:
BFD
Step-by-step explanation:
The measure of BFD refers to the angle measurement in a geometric figure formed by points B, F, and D. It's impossible to provide a definitive answer without further context or a diagram. The measure of an angle depends on point positions in a geometrical shape and information provided.
Explanation:Inquiring about the measure of BFD likely refers to the measure of an angle in a geometric shape with points labeled as B, F, and D. However, without additional information or context such as a diagram displaying details of the geometrical figure involved, it is impossible to definitively provide the exact measure of angle BFD. It's crucial to understand that the measure of an angle depends upon the positions of the points and any information given in an accompanying diagram or problem. For a closer grasp of the concept, remember that in a triangle, for instance, the sum of all angles is always 180 degrees. Thus, if two angles are given, you can determine the measure of the third angle.
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Harry has 20 sweets. He gives 7 of the sweets to Nadia. What fraction of the 20 sweets does Harry have now?
Answers
Answer: 13
Step-by-step explanation:
1. Harry has 20/20 sweets
2. Nadia takes 7/20 sweets
3. Your left with 13/20
The fraction of the 20 sweets Harry has now is 13/20.
What is fraction?A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fraction," which means "to break," is the source of the English term "fraction." The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.
Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions are first written in India with one number above the other but without a line. The line used to divide the numerator and the denominator were only added by Arabs.
Given:
The total no of sweets Harry has is 20,
The no of sweets given to Nadia is 7,
So the no of sweets left = 20 -7 = 13
Hence, the faction will be,
F = No of sweets left / total no of sweets harry has
F = 13 / 20
Therefore, the 13 / 20 parts of sweets Harry has now.
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Lorne subtracted 6x3 - 2x + 3 from -3x3 + 5x2 + 4x - 7. Use the drop-down menus to identify the steps Lome used
to find the difference.
1.(-3x3 + 5x2 + 4x – 7) + (-6x3 + 2x - 3)
2.(-3x3) + 5x2 + 4x + (-7) + (-6X2}) + 2x + (-3)
3.[(-38°) + (-6x3)] + [4x + 2x] + [(-7) + (-3)] + [5x?]
4.-9x3 + 6x + (-10) + 5x?
5.-9x3 + 5x2 + 6x - 10
Answers
Answer:
✔ wrote as addition of the additive inverse
✔ wrote terms as addition of opposite
✔ grouped like terms
✔ combined like terms
The expression is subtracted and the equivalent value is -9x³ + 6x + (-10).
Given data:
To find the difference between -3x³ + 5x² + 4x - 7 and 6x³ - 2x + 3, Lorne would follow these steps:
(-3x³) + 5x² + 4x + (-7) + (-6x³) + 2x + (-3)
Here, Lorne is combining like terms by grouping the variables and constants separately.
[(-3x³ + (-6x³))] + [(5x² + 2x)] + [(-7 + (-3))]
This step involves simplifying the expressions within each set of parentheses.
On simplifying the equation:
A = -9x³ + 6x + (-10)
Hence , the equation is A = -9x³ + 6x + (-10).
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give an equation of the form f(x)=a^x to define the exponential function whose graph contains the point (3,8)
Answers
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]
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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
Answers
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 certain chemical pollutant in the Arkansas River has been constant for several years with mean μ = 34 ppm (parts per million). A group of factory representatives whose companies discharge liquids into the river is now claiming they have lowered the average with improved filtration devices. A group of environmentalists will test to see if this is true. Find the rejection region appropriate for this test if we are using a significance level of 0.05 and have a sample size of 25.
A) Reject H0 if t < -1.960
B) Reject H0 if t < -2.064
C) Reject H0 if t < -1.711
D) Reject H0 if t < -1.708
E) Reject H0 if t < -2.064 or t > 2.064
Answers
Answer:
C) Reject [tex]H_0[/tex] if t < -1.711
Step-by-step explanation:
We are given that a certain chemical pollutant in the Arkansas River has been constant for several years with mean μ = 34 ppm (parts per million).
Also, it is given that the level of significance is 0.05 and a sample size of 25 is taken.
Let [tex]\mu[/tex] = average chemical pollutant in the Arkansas River
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 ppm {means that the average is same as before with improved filtration devices}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 24 ppm {means that they have lowered the average with improved filtration devices}
Now, t test statistics is given by; T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, n = sample size = 25
n - 1 = degree of freedom = 25 - 1 = 24
Now, at 0.05 significance level in the t table, the critical value at 24 degree of freedom is given as - 1.711 for left tailed test.
So, we will reject our null hypothesis when the t test statistics is less than the critical value of t which means reject null hypothesis if t < -1.711.
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?
Answers
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 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)?
Answers
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 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?
Answers
Answer: Four Curricula
Step-by-step explanation:
Business
Mathematics
History
Social Science
Answer:
Four Curricula
Express as a single natural logarithm.
ln 16 - ln 8
ln 2
ln 8
ln 128
Answers
Answer:
ln 2, ln 4
Step-by-step explanation:
edge 2021
Using natural logarithm properties, we will see that we can write this expression as:
Ln(2).
How to express the difference of logarithms as a single logarithm?
Here we start with the expression:
Ln(16) - Ln(8).
Here you need to remember the properties for the natural logarithm:
Ln(a) + Ln(b) = Ln(a*b)Ln(a) - Ln(b) = Ln(a/b).Then, if we apply the second property to the given expression, we can get:
Ln(16) - Ln(8) = Ln(16/8) = Ln(2).
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Austin bought 7 pounds of rice for $3.
How many pounds of rice did he get per dollar?
At Cheng's Bike Rentals, it costs 36 to rent a bike for 9 hours.
How many hours of bike use does a customer get per dollar?
Answers
Final answer:
Austin receives roughly 2.33 pounds of rice for every dollar spent. At Cheng's Bike Rentals, a customer gets 0.25 hours (or 15 minutes) of bike use for every dollar spent.
Explanation:
To solve the questions about how many pounds of rice Austin gets per dollar and how many hours of bike use a customer gets per dollar at Cheng's Bike Rentals, we need to perform a simple division.
Calculate Rice per Dollar:
Austin bought 7 pounds of rice for $3. To find out how many pounds of rice he gets per dollar, you divide the total pounds of rice by the total cost in dollars:
7 pounds ÷ 3 dollars = 2.33 pounds of rice per dollar.
Calculate Bike Rental Time per Dollar:
At Cheng's Bike Rentals, it costs $36 to rent a bike for 9 hours. To find how many hours of bike use a customer gets per dollar, divide the total hours by the total cost in dollars:
9 hours ÷ 36 dollars = 0.25 hours of bike use per dollar, or 15 minutes per dollar.
Final answer:
Explanation of pounds of rice and hours of bike use per dollar
Explanation:
The ratio of pounds of rice to dollars:
7 pounds of rice for $3
7/3 pounds per dollar
The ratio of hours of bike use to dollars:
36 to rent a bike for 9 hours
9/36 hours per dollar
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
Answers
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.
through: (-3, 5) and (-3,-1)
Answers
Answer:
x=-3
Step-by-step explanation:
The x values repeat and the y values are different that means its a vertical line
so it must be x=something the x value in both is -3 so
x=-3
Answer:
x=.3
Step-by-step explanation:
the x is same and y is not meaning a vertical line
An experiment consists of 8 independent trials where the probability of success on each trial is 3 8 . Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 13. Exactly 3 successes. 14. Exactly 6 successes. 15. Exactly 1 success. 16. Exactly 5 successes. 17. At least 1 success. 18. At least 2 successes. 19. At least 6 successes. 20. At least 7 successes. 21. At most 7 successes. 22. At most 6 successes
Answers
Answer:
Step-by-step explanation:
This is a binomial distribution because the probabilities are either that of success or failure.
If probability of success, p = 3/8 = 0.375, then probability of failure, q = 1 - p = 1 - 0.375 = 0.625
The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = represents the probability of failure.
n represents the number of trials or sample.
n = 8
13) P(x = 3) = 8C3 × 0.375^3 × 0.625^(8 - 3) = 0.28
14) P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03
15) P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11
16) P(x = 5) = 8C5 × 0.375^5 × 0.625^(8 - 5) = 0.1
17) P(x ≥ 1) = 1 - P(x < 1)
P(x < 1) = P(x = 0)
P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023
P(x ≥ 1) = 1 - 0.023 = 0.977
18) P(x ≥2) = 1 - P(x < 2)
P(x < 2) = P(x = 0) + P(x = 1)
P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023
P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11
P(x ≥ 2) = 1 - (0.023 + 0.11) = 0.867
19) P(x ≥ 6) = P(x = 6) + P(x = 7) + P(x = 8)
P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03
P(x = 7) = 8C7 × 0.375^7 × 0.625^(8 - 7) = 0.005
P(x = 8) = 8C8 × 0.375^8 × 0.625^(8 - 8) = 0.0004
P(x ≥ 6) = 0.03 + 0.005 + 0.0004 = 0.0354
20) P(x ≥ 7) = P(x = 7) + P(x = 8)
P(x ≥ 7) = 0.005 + 0.0004 = 0.0054
21) P(x ≤ 6) = 1 - P(x = 8)
P(x ≤ 6) = 1 - 0.0004 = 0.9996
22) P(x ≤ 6) = 1 - [P(x = 7) + P(x = 8)]
P(x ≤ 6) = 1 - (0.005 + 0.0004) = 0.9946
The probabilities are listed below:
The probability of success of exactly 3 successes is 5.27 %.The probability of success of exactly 6 successes is 0.28 %.The probablity of success of exactly 1 success is 37.5 %.The probablity of success of exactly 5 successes is 0.74 %.The probability of success of at least 1 success is at most 37.5 %.The probability of success of at least 2 successes is at most 14.1 %.The probablity of success of at least 6 successes is at most 0.28 %.The probability of success of at least 7 successes is at most 0.10 %. The probability of success of at most 7 successes is at least 0.10 %.The probability of success of at most 6 successes is at least 0.28 %.If each trial represents an independent event, then the probability of success of a given number of consecutive trials ([tex]p_{T}[/tex]) in defined by the following formula:
[tex]p_{T} = p^{n}[/tex] (1)
Where:
[tex]p[/tex] - Success probability for a sole event.[tex]n[/tex] - Number of consecutive events.If we know that [tex]p = \frac{3}{8}[/tex], then the probabilities associated to a given number of trials:
1) 3 successes
[tex]p_{3} = \left(\frac{3}{8} \right)^{3}[/tex]
[tex]p_{3} = \frac{27}{512}[/tex]
The probability of success of exactly 3 successes is 5.27 %.
2) 6 successes
[tex]p_{6} = \left(\frac{3}{8} \right)^{6}[/tex]
[tex]p_{6} = \frac{729}{262144}[/tex]
The probability of success of exactly 6 successes is 0.28 %.
3) 1 success
[tex]p_{1} = \frac{3}{8}[/tex]
The probablity of success of exactly 1 success is 37.5 %.
4) 5 successes
[tex]p_{5} = \left(\frac{3}{8} \right)^{5}[/tex]
[tex]p_{5} = \frac{243}{32768}[/tex]
The probablity of success of exactly 5 successes is 0.74 %.
5) At least 1 success
The probability of success of at least 1 success is at most 37.5 %.
6) At least 2 successes
The probability of success of at least 2 successes is at most 14.1 %.
7) At least 6 successes
The probablity of success of at least 6 successes is at most 0.28 %.
8) At least 7 successes
The probability of success of at least 7 successes is at most 0.10 %.
9) At most 7 successes
The probability of success of at most 7 successes is at least 0.10 %.
10) At most 6 successes
The probability of success of at most 6 successes is at least 0.28 %.
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i’m almost done with my problems can someone answer this
Answers
Step-by-step explanation:
8p + 5 = 6p + 1
8p - 6p = 1 - 5
2p = - 4
p = - 4/2
p = -2
Hope it will help :)
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
Answers
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
whats the ratio of 14,10 and 4
Answers
Step-by-step explanation:
14 : 10 : 4
Divide it by 2
7 : 5 : 2
This is the simplest form because it cannot be divided further