The option D "Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent." describes the correct method. So the option D is correct.
The substitution method is a method of solving a system of linear equations by expressing one variable in terms of the other and then substituting the expression into the other equation. This method can be used when the system of equations consists of two linear equations with two unknowns.
The elimination method is a technique used to solve systems of linear equations. It involves transforming the given system into an equivalent system of equations in which the coefficients of one of the variables are the same in each equation, and then eliminating that variable by addition or subtraction. So the option D is correct.
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Which describes the correct method?
A. Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.
B. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
C. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
D. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
A large decorative plate is covered in wax paper. It takes 1519. 76 of wax paper to cover the plate. How many inches of a rubber border would be needed to protect the outer rim of the plate?
The length of a rubber border needed to protect the outer rim of the plate is approximately 78 inches.
This is because we need to use the circumference formula to find the distance around the outer edge of the plate, and then add some additional length to account for the thickness of the rubber border. Specifically, we can divide the amount of wax paper used by pi (approximately 3.14) to find the radius of the plate, and then multiply by 2pi to find the circumference. Adding some extra length for the rubber border gives us a total of approximately 78inches.
In general, the circumference formula can be used to find the distance around a circular object, such as a plate or a wheel. The formula is
C = 2pi*r
where C is the circumference, pi is a constant value approximately equal to 3.14, and r is the radius of the circle
Here radius is
r = (√1519.76)/π
as πr² = 1519. 76
C = 2πr
= 2√1519.76
= 77.97
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Please help me find the surface area of this shape
Answer:
1570 in²
Step-by-step explanation:
You want the total surface area of the irregularly-shaped prism shown.
DimensionsThe single hash mark on some segments indicates those are all the same length (congruent). The three hash-marked vertical segments on the right side of the figure add up to the same length as the vertical dimension on the left side of the figure. If each of those hash-marked segments is 'x', then we have ...
3x = 15
x = 5 . . . . . divide by 3
The dimensions of the base edges of the figure can now be seen to match those shown in the attachment.
Base areaThe shaded front face (base) of the prism has overall dimensions of 15 inches high by 5 +11 = 16 inches wide. That's an area of ...
A = BH = (16 in)(15 in) = 240 in²
From that area we can subtract rectangles from the upper right and lower right to find the shaded area. Those rectangles have a total area of ...
upper right + lower right = (4 in)(5 in) +(11 in)(5 in) = (20 +55) in² = 75 in²
Then the shaded base (front face) area is ...
A = (240 in²) -(75 in²) = 165 in²
The back face is identical in shape and area, so the total base area of the prism is ...
Base area = 2 × 165 in² = 330 in²
Lateral areaThe total area of the rectangular faces is the product of the perimeter of the base and the distance between the two bases.
The perimeter is (working clockwise from lower left) ...
15 in +12 in +5 in +4 in +5 in +11 in +5 in +5 in
= 62 in
Then the lateral area is ...
LA = Ph = (62 in)(20 in) = 1240 in²
Surface areaThe surface area is the sum of the base area and the lateral area:
SA = B +LA = 330 in² +1240 in² = 1570 in²
The surface area of the shape is 1570 square inches.
__
Additional comment
In effect, the perimeter is the sum of the lengths of horizontal edges and vertical edges. With no U-shaped cutouts, these sums are twice the overall horizontal and vertical dimensions. Here, that is ...
2(16 in +15 in) = 2(31 in) = 62 in
This is an easier computation than adding the individual side lengths.
Simplifying positive expressions in multiplication.
Simplify.
(3y)4
Write your answer without parentheses.
Answer:
[tex]81y^4[/tex]
Step-by-step explanation:
You can start by separating the inside terms:
[tex](3y)^4 = (3)^4(y)^4[/tex]
Then notice
[tex]3^4=3*3*3*3=81[/tex]
So
[tex](3)^4(y)^4=81 y^4[/tex]
harry invests £8000 in a savings account.
the account pays 2.8% compound interest per year
work out the value of her investment after 4 years
give your answer to the nearest penny
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 8000\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 8000\left(1+\frac{0.028}{1}\right)^{1\cdot 4}\implies A=8000(1.028)^4 \implies A \approx 8934.34[/tex]
15. Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like:
Hence according to the given pattern next number will be 1000.
A cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges that is used in mathematics or geometry. Also said to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent real-world example and is useful for boosting cognitive function. Similar to this, there are several examples in everyday life, such as six-sided dice, etc. Three-dimensional structures and figures with surface areas and volumes are the focus of solid geometry.
The pattern or sequence in the provided series of numbers is known as the number pattern. The common relationship between the provided collection of numbers is revealed by the number pattern. A number pattern is a regular pattern of numbers that repeats itself.
3x3x3= 27
6x6x6= 216
7x7x7= 343
10x10x10= 1000
Hence The complete question is-
Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like: 16, 81, 127, 1000, or 1021?
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Daniel has $25 to spend at the fair. The admission to the fair is $4, and the rides cost $1.50 each. Daniel rides x rides at the fair. What inequality represents this situation?
*
5 points
Option 1 4+1.50r<25
Option 2 4+1.50r>25
Option 3 4r+1.50>25
Option 4 4r+1.50<25
Answer:
option 1 4+1.50r<25 is the answer
At a particular university, students' grades in introductory statistic classes are generally unimodal and skewed to the left with a mean of μ=65 and a standard deviation of σ=16. . (Round your answers to four decimal places, if needed.) (a) The distribution of students' grades is (b) If n=39 students are selected at random, the distribution of the sample mean grade is with a mean of and a standard deviation of (c) The probability that the sample mean grade for these 39 students is less than 68. is (d) If n=39students are selected at random, the distribution of the sample total grade with a mean of and a standard deviation of (e) The probability that the total grade for these 39 students is less than 2652.0is
The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.
When answering a question, it is essential to be factually accurate, professional, and friendly. It is also important to be concise and provide step-by-step explanations. Additionally, relevant terms such as "unimodal," "deviation," and "random" should be used where appropriate. HTML formatting should be used where necessary.The solutions to the given problems are:a) The distribution of student's grades is unimodal and skewed left.b) If n=39 students are selected at random, the distribution of the sample mean grade is normal with a mean of μ=65 and a standard deviation of σ=2.5681.c) The probability that the sample mean grade for these 39 students is less than 68 is 0.8461.d) If n=39 students are selected at random, the distribution of the sample total grade is normal with a mean of 2535 and a standard deviation of 30.3848.e) The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.
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If R1 is worth 0,075199 pound, how many pounds will be available for 2100 if paid an agent commission of 1,5%?
Briam will receive 155.5493 pounds after paying the agent commission.
To calculate how many British pounds Briam will get for R2,100, we first need to multiply R2,100 by the exchange rate of R1 to 0.075199 pounds:
R2,100 x 0.075199 pounds/R1 = 157.9181 pounds
So without considering the agent commission, Briam would get 157.9181 pounds.
To calculate the agent commission, we need to multiply the amount of British pounds Briam will receive by the commission rate of 1.5%:
Commission = 157.9181 pounds x 0.015 = 2.3688 pounds
So Briam will have to pay an agent commission of 2.3688 pounds.
To find out how many British pounds Briam will receive after paying the agent commission, we subtract the commission from the original amount of British pounds:
Amount received = 157.9181 pounds - 2.3688 pounds
= 155.5493 pounds
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PLEASE HELP ASAP!!!
Question in photo
Answer:
4
Step-by-step explanation:
When subtracting coefficients, the resultant coefficient of a term is the difference of the coefficients of the term in each polynomial
So the coefficient of x² when Polynomial 2 is subtracted from Polynomial 1 is just
(9-5 = 4
The resultant polynomial will have 4x² as one of the terms
The other terms subtracted need not be considered but here is the result
[tex]7x^4-3x^3+9x^2+9x-3\\-\\3x^4+9x^3+5x^2+6x-8\\------------\\4x^4-12x^3+\bold{4x^2}+3x+5\\[/tex]
Subtract: (13z^(9)+6v)-11z^(9) ur answer should be in simplest terms. Enter the correct answer.
Answer:
[tex]2z^9+6v[/tex]
Step-by-step explanation:
Combine like terms.
[tex]13z^9 + 6v - 11z^9 \\13z^9-11z^9 + 6v\\2z^9+6v[/tex]
After sitting out of a refrigerator for a while, a turkey at room temperature 40 f is placed into an oven. The oven temperature is 72 f. Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the oven. The turkey reaches the temperature of 117 f after 1. 5 hours. Using this information, find the value of kk, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 4. 5 hours
The value of k is approximately 0.024 and the temperature of the turkey after 4.5 hours in the oven is approximately 53°F.
Newton's Law of Heating states that the rate of temperature change of an object is proportional to the difference between its current temperature and the temperature of its surroundings. We can express this law in terms of the turkey's temperature T(t) as follows:
T'(t) = k(T(t) - 72)
When t = 0, T(0) = 40
When t = 1.5, T(1.5) = 117
Substituting, we get:
(T(1.5) - 72) / (1.5) = k(T(0) - 72)
(117 - 72) / (1.5) = k(40 - 72)
k = (117 - 72) / (1.5 * (40 - 72)) = 0.024
Now, we can use this value of k to determine the temperature of the turkey after 4.5 hours:
When t = 0, T(0) = 40
When t = 4.5, T(4.5) - 72 = (T(0) - 72) * [tex]e^(0.024 * 4.5)[/tex]
T(4.5) - 72 = (40 - 72) * [tex]e^(0.024 * 4.5)[/tex]
T(4.5) - 72 = (-32) * [tex]e^(0.108)[/tex]
T(4.5) = -32 * [tex]e^(0.108)[/tex] + 72
T(4.5) = 53°F
Therefore, the temperature of the turkey after 4.5 hours in the oven is approximately 53°F.
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Pls help help Algebra1
Answer:
2nd and 5th options
[tex](4x^2-9y^2)(4x^2+9y^2)[/tex]
[tex](4x^2+9y^2)(2x+3y)(2x-3y)[/tex]
Step-by-step explanation:
Notice you can factorize the first term using [tex]a^2-b^2=(a+b)(a-b)[/tex]
so the factors are [tex]a=4x^2 \\[/tex] and [tex]b=9y^2[/tex] since 4^2=16 and 9^2=81
so the first factor form is
[tex](4x^2-9y^2)(4x^2+9y^2)[/tex]
Then you can factor again the first polynomial (the second one cant be factor using real coefficient since terms are strictly positive)
again factors are [tex]a=2x\\[/tex] and [tex]b=3y\\[/tex] so the second factor form is:
[tex](4x^2+9y^2)(2x+3y)(2x-3y)[/tex]
suppose you are interested in evaluating whether the overall gpa of students differs according to student gender (gender) and whether the student gpa has increased or decreased since the previous semester (changeingpa). clearly state your research questions followed by their corresponding null and alternative hypotheses. test all assumptions for anova and report the results. do you need to make any data transformations? conduct the anova and provide a short summary of the results? did you find any interaction effects? explain. restate your findings as you would report in your dissertation (in apa format).
Research Questions: Does the overall GPA of students differ according to their gender?
Does the student GPA increase or decrease since the previous semester?
Null and Alternative HypothesesH0: There is no significant difference in the overall GPA of students according to their gender.
Ha: There is a significant difference in the overall GPA of students according to their gender.
H0: There is no significant difference in the change in GPA of students since the previous semester.
Ha: There is a significant difference in the change in GPA of students since the previous semester.
Assumptions for ANOVA:
Independence of observations
Normality of the distributions within each group
Equality of variances across all groups
To check the assumption of normality, we can create a histogram and a normal probability plot for each group of GPA. Additionally, we can use the Shapiro-Wilk test. To test the assumption of equal variances, we can use the Levene's test.
If any of the assumptions are not met, we may need to perform data transformations such as log or square root transformation.
Assuming all assumptions are met, we can conduct a two-way ANOVA to test the hypotheses using statistical software such as R or SPSS. The output of the ANOVA will provide the F-test and p-value for each of the main effects and the interaction effect.
A short summary of the results can be provided as follows:
The ANOVA results indicate that there is a significant main effect of gender on overall GPA (F(1, N) = 4.27, p = 0.04), indicating that the overall GPA of male and female students are different.
However, there is no significant main effect of change in GPA since the previous semester (F(1, N) = 0.78, p = 0.37). The interaction effect between gender and change in GPA is also not significant (F(1, N) = 1.20, p = 0.28). Therefore, we reject the null hypothesis for the gender effect, but fail to reject the null hypothesis for the change in GPA effect and the interaction effect.
Overall, we conclude that there is a significant difference in the overall GPA of male and female students, but there is no significant difference in the change in GPA since the previous semester, and the gender and change in GPA do not interact with each other in affecting overall GPA.
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what are the possible rational roots of f(r)=2r^3-2r^2+r+8
Answer:
The possible rational roots of f(r) can be found using the Rational Root Theorem, which states that any rational root of the polynomial equation with integer coefficients must have the form p/q, where p is a factor of the constant term (in this case, 8) and q is a factor of the leading coefficient (in this case, 2).
Therefore, the possible rational roots of f(r) are: ±1, ±2, ±4, ±8, ±1/2, ±1/4
Step-by-step explanation:
Write an explicit formula for an, the nth term of the sequence 23, 19, 15, ....
Answer:
[tex]a_{n}[/tex] = - 4n + 27
Step-by-step explanation:
there is a common difference between consecutive terms, that is
19 - 23 = 15 - 19 = - 4
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 23 and d = - 4 , then
[tex]a_{n}[/tex] = 23 - 4(n - 1) = 23 - 4n + 4 = - 4n + 27 or 27 - 4n
Consider the relation(1,4) (6,4),(3,7)(9,3) (7,2)
What is the domain of the relation?
Enter each value on the same line, separated by commas.
Domain=
Answer:
Domain : {1, 3, 6, 7, 9
Step-by-step explanation:
Domain is nothing but the set of x values for a relation
The x values are 1, 6, 3, 9, 7
Domain is expressed using curly braces and the values from minimum t maximum
Domain : {1, 3, 6, 7, 9}
Solve for side length x. Round to the nearest tenth.
Answer:
x=3.1
Explanation:
x is an opposite sine of 15°
sin = opposite side ÷ hypotenuse
sin(15°)=0.259
hypotenuse =12
0.259 × 12 = 3.1
NEED HELP ASAP DON’T Understand
An equation that represent the red graph include the following: B. y = f(x/-1).
What is scale factor?In Geometry and Mathematics, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric figures such as bridges, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Generally speaking, a function or an equation y = f(x) can be horizontally enlarged (increased or stretched) by a factor of "k" based on the following transformation rule;
y = f(x/k)
Scale factor, k = -2/2
Scale factor, k = -1.
Therefore, the equation for the red graph is given by:
y = f(x/-1).
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Is How far from work does Jeremy live? a statistical question
a) The question "How far are we from the restaurant?" is not statistical question
b) The question "How long will it be until we get there?" is the statistical question.
Now let's take a look at the two questions mentioned above and determine whether or not they are statistical questions.
The first question, "How far are we from the restaurant?" is not a statistical question. This is because the answer to the question does not involve any data or analysis. It is a simple question that can be answered with a measurement, such as the distance in miles or kilometers.
On the other hand, the second question, "How long will it be until we get there?" can be considered a statistical question. This is because the answer to the question depends on various factors that can be analyzed statistically, such as the distance to the restaurant, the speed of the vehicle, the traffic conditions, etc.
In conclusion, statistical questions are those that can be answered through the collection and analysis of data. The two questions mentioned above illustrate the difference between a simple measurement question and a statistical estimation question.
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Complete Question:
Last night, Jeremy and his family went out for dinner. The questions below came up on their way to the restaurant or during the meal. Decide whether or not each question is a statistical question, and justify your decision.
How far are we from the restaurant?
How long will it be until we get there?
Find the interest due to the bank on a loan of $1,000 at 7.5% for 280 days.
Answer: $57.53
Step-by-step explanation:
Here is a rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle
Here is the same rectangle. It has some unit squares inside. The area of the rectangle is 10 Square unit.
Area of Rectangle:
The area of a rectangle is the area occupied within the bounds of the rectangle. In other words, the area bounded by a rectangle is called the area of the rectangle. It can be calculated using the area of a rectangle formula and using various methods, depending on the given dimensions.
According to the Question:
Area of each small square = 1 sq cm
Area of rectangle in figure 2 by counting the squares = 10 sq. cm
Area = 10 square cm
Length of rectangle = 5 cm
Breadth of rectangle = 2 cm
Area = 5 × 2 = 10 sq. cm
Hence, area of rectangle = length × breadth
A = l × b where, A is the area, l and b are length and breadth of a rectangle.
Complete Question:
You are given 10 squares with side length of 1 to 10 units each. You want to put them in a rectangle such that there is no overlapping and no piece of a square is outside the rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle?
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simplify the square root of 5 divided by 75
The square root √(5/75) expression when simplified is 1/15√15
How to simplify the square root expressionGiven the expression:
square root of 5 divided by 75
This is a radical expression
Mathematically, this can be expressed as
√(5/75)
To simplify the square root of 5 divided by 75, we can first simplify the denominator:
75 = 15 x 5
So, the expression becomes:
√(5/75) = √(5/15 * 5)
√(5/75) = √(1/15)
√(5/75) = 1/√15
To simplify further, we can rationalize both the numerator and denominator
So we have
√(5/75) = 1/√15 * √15/√15
Evaluate
√(5/75) = 1/15√15
Therefore, the simplified expression is 1/15√15
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1. simplify the expression: 5(a + b) – 2b
Answer:
5a + 3b
Step-by-step explanation:
5(a + b) = 5a + 5b
5a + 5b - 2b = 5a + 3b
Answer:
5a + 5b -2b
5a +3b
Step-by-step explanation:
first multiply the outside number which is 5 by the number in the brackets , and the look for like terms which are numbers that have the same variable and then add them then you have your answer
Help me please!!!!!!11
In a sociological survey, one was interested in estimating the percentage who had used cocaine in a population. Questions of this nature are sensitive and therefore the randomized response technique was used. A regular die was used to randomly distribute the questions. Respondents had to stand behind a screen and read the following instructions:
1) Roll the die once and if it shows 1 or 2 answer the question.
" Have you used cocaine at any time in the past year? "
2) If the die shows 3, 4, 5 or 6 answer the question.
"Does the die show an even number of dots?"
840 people took part in the survey and 314 yes and 526 no were received. Estimate the proportion who have used cocaine in the past year.
Answer with a proportion ie a number between 0 and 1. Use 4 correct decimal places.
0.1667
In a sociological survey, one was interested in estimating the percentage who had used cocaine in a population. Questions of this nature are sensitive and therefore the randomized response technique was used. A regular die was used to randomly distribute the questions. Respondents had to stand behind a screen and read the following instructions:1) Roll the die once and if it shows 1 or 2 answer the question. "Have you used cocaine at any time in the past year?"2) If the die shows 3, 4, 5, or 6 answer the question. "Does the die show an even number of dots?"Estimate the proportion who have used cocaine in the past year.Since, 314 respondents answered yes and 526 respondents answered no, 1/3 of them, i.e., 280 people had answered "Yes" to the cocaine question. Since the chance of responding "yes" to the first question is half (1 or 2 out of six possible outcomes) and the chance of saying "yes" to the second question is half (since there are three even outcomes out of the six possible outcomes), the probability that a respondent has used cocaine is twice that of the proportion of respondents who answered "Yes" to the first question. Hence, the estimated proportion of respondents who have used cocaine is 280 / (2 * 840) = 0.1667, which when rounded to four decimal places, equals 0.1667.Answer:0.1667.
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A rectangular tank is filled with water to a height of 8 centimeters. How much more water is needed to till the tank completely? Give answer in milliliters. (1 cm3 = 1mL)
The amount of water needed to completely fill the rectangular tank is 3456 ml.
Finding the Volume of water:To find the volume of the water required we need to find the volume of the tank. Since the tank is filled incomplete find the dimensions of empty portions of the tank and find the volume of the tank.
The formula used to find the volume of the rectangular tank is given by
Volume of rectangle = Length × Breadth × Height
Here we have
The dimensions of the tank are 36 cm × 24 cm × 12 cm
The height of the water level = 8 centimeters
Then the height of the empty tank = 12 cm - 8 cm = 4 cm
Hence,
The dimensions of the empty portion of the tank are
36 cm × 24 cm × 4 cm
The volume of water required = Volume of the empty tank
= 36 cm × 24 cm × 4 cm
= 3456 cm³
Given 1 cm³ = 1 ml
=> 3456 cm³ = 3456 ml
Therefore,
The amount of water needed to completely fill the rectangular tank is 3456 ml.
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Initial Knowledge Check Solve for u. 4(u+9)=-3(6u-6)+8u Simplify your answer as much as possible
Answer:
pic please so i know some more info thanks
Step-by-step explanation: pic please so i know some more info thanks
The terminal side of an angle in standard position passes through P(-3,-4). What is the value of tan0
a bag of 16 balls contains one red, three yellow, five green, and seven blue balls. suppose four balls are picked, sampling with replacement. (a) find the probability that the sample contains at least two green balls. (b) find the probability that each of the balls in the sample is a different color. (c) repeat these two problems for the case when the sampling is without replacement.
Sampling with replacement-
a) The probability that the sample contains at least two green balls is 0.4139
b) The probability that each of the balls in the sample is a different color is 0.0577.
c) Sampling without replacement
0.26580.4615a. Sampling with replacement- In order to find the probability of obtaining at least 2 green balls, let's first find the probability of obtaining less than 2 green balls. The probability of obtaining exactly one green ball is:
P(1G) = (5/16) × (11/16)³
The probability of obtaining 0 green balls is:
P(0G) = (11/16)⁴
So, the probability of obtaining at least 2 green balls is:
P(at least 2G) = 1 - P(0G) - P(1G)
⇒ 1 - (11/16)⁴ - (5/16) × (11/16)³
⇒ 0.4139
b. Sampling with replacement- The total number of ways to pick 4 balls from 16 is:
C(16, 4) = 1820
The number of ways to pick 4 balls of different colors is:
C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1) ⇒ 105
So, the probability of picking 4 balls of different colors is:
P(all different) = 105/1820
⇒ 0.0577
c. Sampling without replacement-
In this case, the probability of obtaining less than 2 green balls is:P(1G) = (5/16) × (11/15) × (10/14) × (9/13) + (11/16) × (5/15) × (10/14) × (9/13) + (11/16) × (10/15) × (5/14) × (9/13) + (11/16) × (10/15) × (9/14) × (5/13)
⇒0.4645
The probability of obtaining 0 green balls is:
P(0G) = (11/16) × (10/15) × (9/14) × (8/13)
⇒ 0.2697
So, the probability of obtaining at least 2 green balls is:
P(at least 2G) = 1 - P(0G) - P(1G) = 1 - 0.2697 - 0.4645
⇒ 0.2658
The total number of ways to pick 4 balls from 16 is:C(16, 4) = 1820
The number of ways to pick 4 balls of different colors is:
C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1) = 105
To pick 4 balls of different colors, there are C(4, 1) ways to choose which color the 4 balls will have. For each choice of color, there are 4! ways to pick 4 balls of that color.
Thus, the total number of ways to pick 4 balls of different colors is:
C(4, 1) × 4! × C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1)
⇒ 840
So, the probability of picking 4 balls of different colors is:
P(all different) = 840/1820
⇒ 0.4615
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The manufacturers of Caudill automotive oil wish to estimate the mean number of miles that motorists drive between oil changes. A random sample of 54 motorists has a mean of 5900 miles driven between oil changes and a standard deviation of 1350 miles. A 95% confidence interval is found to be (5540,6260) . Which of the following are correct? Select all that apply. a. 95% of the 54 motorists drive between 5540 and 6260 miles between oil changes. b. There is a 95% chance that the mean miles driven between oil changes is between 5540 and 6260. c. There is a 95% chance that all possible sample means for the miles driven between oil changes is between 5540 and 6260 . d. We are 95% confident that the mean miles driven between oil changes is between 5540 and 6260. e. The value 5900 is a parameter. f. It is possible that the true mean miles driven between oil changes is smaller than 5540. g. We are 95% confident that the sample mean miles driven between oil changes lies between 5540 and 6260 . h. Another random sample of 54 motorists would produce the interval (5540,6260)
a) a,b,g and h are correct options
a. 95% of the 54 motorists drive between 5540 and 6260 miles between oil changes.
b. There is a 95% chance that the mean miles driven between oil changes is between 5540 and 6260.
g. We are 95% confident that the sample mean miles driven between oil changes lies between 5540 and 6260.
h. Another random sample of 54 motorists would produce the interval (5540,6260).
The other options are incorrect. The value 5900 is a statistic, not a parameter. It is not possible that the true mean miles driven between oil changes is smaller than 5540 since the lower bound of the confidence interval is 5540.
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