The common ratio is -1/3 and the initial term is -4, then the formula is:
A(n) = -4*(-1/3)^(n - 1)
How to find the formula for the nth term?Remember that in a geometric sequence, to get the next term we need to multiply the previous term by the common ratio.
To get the common ratio, take the quotient between two consecutive terms.
We will get:
(4/3)/(-4) = -1/3
Then the n-th term of the geometric sequence is:
A(n) = -4*(-1/3)^(n - 1)
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Answer:
[tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]
Step-by-step explanation:
The common ratio between any two terms in a geometric sequence is constant. Let this ratio be denoted by r. Then, we have:
[tex]r = \frac{\frac{4}{3}}{-4} = \frac{-\frac{4}{9}}{\frac{4}{3}} = \frac{\frac{4}{27}}{-\frac{4}{9}} = \frac{1}{3}[/tex]
Using this value of r, we can write the formula for the nth term an as:
[tex]an=[/tex][tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]
show your work 3.37 times 9
Answer:
[tex]3.37 \times 9 \\ = 30.33[/tex]
hope it helps
Look at this table:
X
0
1
2
3
4
y
3
6
12
24
48
Write a linear function (y = mx + b) or an exponential function (y = a(b)*) that models the
data.
The exponential function that represents the data in the table is given as follows:
y = 3(2)^x.
How to define an exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which the parameters are given as follows:
a is the initial value, representing the value of y when x = 0.b is the rate of change.From the table, when x = 0, y = 3, hence the parameter a is given as follows:
a = 3.
When x is increased by one, y is multiplied by 2, hence this is an exponential function and the parameter b is given as follows:
b = 2.
Hence the function is defined as follows:
y = 3(2)^x.
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4. 1. 33% of 2406 adults surveyed said that skim milk is a good calcium source. Find the margin of error and explain the results
To find the margin of error, we use the formula:
Margin of Error (ME) = Z * [tex]\sqrt{(p * (1-p) / n)}[/tex]
Z = 1.96 (for a 95% confidence level)
p = 0.33 (proportion of adults who said skim milk is a good calcium source)
(1-p) = 1 - 0.33 = 0.67 (complement of the estimated proportion)
n = 2406 (sample size)
ME = 1.96 * [tex]\sqrt{(0.33 * 0.67 / 2406)}[/tex] = 0.0185 (rounded to four decimal places)
This means that we can estimate, with 95% confidence, that the true proportion of adults who believe skim milk is a good calcium source falls within a range that is 1.85% above or below the reported proportion of 33% based on the survey results.
In other words, the actual proportion of adults who believe skim milk is a good calcium source could be as low as 31.15% or as high as 34.85% based on the margin of error.
Cameron completed a 74 kilometer cycling race at an average speed of 11.84km/h.
How long did he take to complete the race? Give your answer in hours and minutes.
Mr. and Mrs. Johnson took their three children to the movies. If adult tickets cost $7 and children's tickets cost $4, what is the ratio of the total cost of the parents' tickets to the total cost of the children's tickets? Write your answer in the form aib, where a and b are whole numbers.
Let's assume that Mr. and Mrs. Johnson bought x adult tickets and y children's tickets.
Since there are three children, we know that:
y = 3x
The total cost of the parents' tickets is 7x, and the total cost of the children's tickets is 4y. Substituting y = 3x, we get:
total cost of parents' tickets = 7x
total cost of children's tickets = 4(3x) = 12x
Therefore, the ratio of the total cost of the parents' tickets to the total cost of the children's tickets is:
(7x) / (12x) = 7/12
So the answer is 7/12, which cannot be simplified further. Therefore, the ratio is 7/12, which can be written in the form aib as 0+7/12i.
Answer: 7:6
Step-by-step explanation:
1. There are two adults (Mr. and Mrs. Jonhson) and three children. So let's make adults = y and children = x
2. Adult tickets cost $7. So we are going to multiply 7 x 2y = $14
3. Children's tickets cost $4. So we are going to multiply 4 x 3x = $12
4. The last step is to fully reduce [tex]\frac{14}{12}[/tex] = [tex]\frac{7}{6}[/tex]
5. So the answer is 7:6
Tiffany’s mother bought a car for $9000 five years ago. She wants to sell it to Tiffany based on a 15% annual rate of depreciation.
Part A. Identify each feature of the problem as it relates to the context and the exponential growth formula: y=a(1−r)t
.
a=
r=
Part B. Which equation correctly models the context of the problem?
Choose : A. y=9000(0.15)t
or B. y=9000(0.85)t
Answer : The equation is
Part C.
Tiffany wants to buy the car from her mother now. (t = 5)
A fair price for the car will be about $
in 5 years.
A) The correct features is,
⇒ a = 9000
⇒ r = 15%
B) The equation correctly models the context of the problem is,
⇒ y = 9000 (0.85)ˣ
We have to given that;
Tiffany’s mother bought a car for $9000 five years ago.
And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.
Now, We have;
the exponential growth formula is,
⇒ y = a(1 − r)ˣ
Here, We have;
⇒ a = 9000
⇒ r = 15%
Thus, We get;
The equation correctly models the context of the problem is,
⇒ y = a(1 − r)ˣ
⇒ y = 9000 (1 - 0.15)ˣ
⇒ y = 9000 (0.85)ˣ
Therefore, We get;
A) The correct features is,
⇒ a = 9000
⇒ r = 15%
B) The equation correctly models the context of the problem is,
⇒ y = 9000 (0.85)ˣ
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write the ratio 5x10^-1 :2:3x10^-10 in its simplest form
Please answer asap
It would be helpful
The answer of the given question based on the cylinder is , the volume of the solid = 929.44 inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.
What is Volume?Volume is amount of three-dimensional space occupied by object or substance. It is a physical quantity that is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by measuring its dimensions and using a mathematical formula specific to its shape.
To find volume of solid, we need to subtract volume of inner cylinder from volume of outer cylinder.
Volume of the outer cylinder = πr²h
where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)
h = height of the outer cylinder = 23 inches
Volume of the outer cylinder = π(4)²(23) = 368π in³
Volume of the inner cylinder = πr²h
where r = radius of the inner cylinder = 2 inches
h = height of the inner cylinder = 18 inches
Volume of the inner cylinder = π(2)²(18) = 72π in³
So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder
= 368π - 72π
= 296π
= 929.44 inch³
The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.
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the sample size formula for estimating a proportion using a confidence interval with margin of error e involves the product p(1-p). this product is not known. a conservative approach is to use
A value of 0.25 for p(1-p) in the sample size formula when the true value of p is unknown.
This is because the value of p(1-p) is maximum when p=0.5, and since we do not have any information about the true value of p, assuming p=0.5 is the most conservative approach. Therefore, to calculate the sample size required to estimate a proportion using a confidence interval with a margin of error e, we can use the formula:
[tex]n = [z^2 * p(1-p)] / e^2[/tex]
where z is the z-score corresponding to the desired level of confidence (e.g., 1.96 for 95% confidence), and e is the desired margin of error. We can use p=0.5 and solve for n to get a conservative estimate of the sample size required for the given confidence level and margin of error.
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If prior knowledge or data suggests that the proportion is significantly different from 0.5, then a more accurate estimate of p should be used in the formula.
To calculate the sample size formula for estimating a proportion using a confidence interval with a margin of error e, we
use the following formula:
[tex]n = (Z^2 × p × (1-p)) / e^2[/tex]
where n is the required sample size, Z is the Z-score corresponding to the desired level of confidence,
p is the estimated proportion, and
e is the margin of error.
Since the product p(1-p) is not known, a conservative approach is to use p = 0.5, which is the value that maximizes the
product p(1-p) for any given proportion.
This approach ensures that the sample size will be large enough to obtain a reliable estimate of the proportion, even if
the true proportion is close to 0 or 1. However, if prior knowledge or data suggests that the proportion is significantly
different from 0.5, then a more accurate estimate of p should be used in the formula.
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Marilyn needs to buy two Series EE savings bonds as graduation gifts for her cousins. She has $75 to spend. What could be the face value on each bond? (Hint: The face values of the bonds she can buy are $50, $75, and $100. )
Marilyn has $75 to spend on two Series EE savings bonds as graduation gifts. The face values of the bonds she can buy are $50, $75, and $100. Therefore, she could buy two $50 bonds.
Since Marilyn has $75 to spend and she needs to buy two bonds, the total face value of the bonds she can purchase must be equal to $75.
Let x be the face value of the first bond, then the face value of the second bond must be 75 - x.
The face values of the bonds are $50, $75, and $100, so we can set up the following three equations
x + (75 - x) = 75 (since the total face value must be $75)
x = 50 (since the face value must be $50, $75, or $100)
x = 100 (since the face value must be $50, $75, or $100)
Solving these equations, we find that the possible face values for each bond are $50 and $25, $75 and $0, or $100 and $-25 (which is not a valid option).
Therefore, Marilyn could buy two bonds with face values of $50 each, or one bond with a face value of $75 and the other with a face value of $0 (which essentially means she would only be buying one bond).
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if you repeated a hypothesis test 1,900 times (in other words, 1,900 different samples from the same population), how many times would you expect to commit a type i error, assuming the null hypothesis were true, if
Answer: Assuming a significance level of 0.05 for each hypothesis test, the probability of committing a Type I error (rejecting the null hypothesis when it is actually true) in any given test is 0.05.
Therefore, the expected number of Type I errors in 1,900 hypothesis tests is:
Expected number of Type I errors = (0.05) x (1,900) = 95
So, we would expect to commit a Type I error about 95 times in 1,900 hypothesis tests, assuming the null hypothesis were true.
Step-by-step explanation:
In an instant lottery, your chances of winning are 0.1. If you play the lottery twice and outcomes are independent, the probability that you win at least once is
The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.
To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.
The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.
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Ok people. In the pdf are 2 questions. I literally just need to know what numbers go in them boxes. I am offering 30 points. Please Help soon.
Since the center of this semicircle is at the origin, O (0, 0), the radius of the semicircle is 5 units.
Since the center of this semicircle is at the point A (3, 4) and point B (-4, 5), the radius of the semicircle is 5√2 units.
How to calculate the distance between the two points?In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation (formula):
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
By substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(3 - 0)² + (4 - 0)²]
Distance = √[(3)² + (4)²]
Distance = √(9 + 16)
Distance = √25
Distance = 5 units.
At point A (3, 4) and point B (-4, 5), the radius is given by;
Distance = √[(-4 - 3)² + (5 - 4)²]
Distance = √[(-7)² + (1)²]
Distance = √(49 + 1)
Distance = √50 = 5√2 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
a hose fills hot tub at 4.6 gallons per minute. how many hours will it take to fill a 440-gallon hot tub?
It will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute
Assuming that the filling rate of the hose is constant, we can use the formula:
time = volume / rate
where time is the time taken to fill the hot tub, volume is the volume of the hot tub (440 gallons), and rate is the filling rate of the hose (4.6 gallons per minute).
Substituting the values, we get:
time = 440 / 4.6
which simplifies to:
time = 95.65 minutes
To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):
time = 95.65 / 60
which simplifies to:
time = 1.59 hours
Therefore, it will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute.
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It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.
To determine how many hours follow these steps:
First, we need to find out how many minutes it takes to fill the hot tub.
Divide the total volume of the hot tub (440 gallons) by the rate at which the hose fills (4.6 gallons per minute):
440 gallons ÷ 4.6 gallons/minute = 95.65 minutes
Now, we need to convert the minutes into hours.
Since there are 60 minutes in an hour, divide the minutes by 60:
95.65 minutes ÷ 60 minutes/hour = 1.594 hours
It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.
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Find the surface of each pyramid
The surface area of the given pyramid is 203 in²
Calculating the surface area of a square PyramidFrom the question, we are to calculate the surface area of the given square pyramid
From the given information, the base of the pyramid is 7 in
and
The slant height of the pyramid is 11 in
The surface area of a pyramid can be calculated by using the formula
A = a² + 2al
Where A is the area of the pyramid
a is the side base
and l is the slant height
From the given information,
a = 7 in
and
l = 11 in
Thus,
Surface area = 7² + 2(7)(11)
Surface area = 49 + 154
Surface area = 203 in²
Hence,
The surface area is 203 in²
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_____ is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero.
a. An F test b. A t test c. The least squares method d. Extrapolation
An F test is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero. So the correct option is A.
The F test is based on the ratio of the mean square of the regression to the mean square of the error, and it is used to test the overall significance of the regression model. It tests whether there is a linear relationship between the independent variables and the dependent variable, and whether the model is statistically significant. In contrast, a t test is used to test the significance of individual regression coefficients, and the least squares method is a technique used to estimate the parameters of a linear regression model. Extrapolation is the process of estimating values of a dependent variable outside the range of the independent variables based on the regression model.
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The F test is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero. therefore, option a. an F text is correct.
This test is commonly used in regression analysis to determine whether there is a significant relationship between the
dependent variable and the independent variables.
The F test compares the variance explained by the regression model to the residual variance, and the null hypothesis
assumes that all regression coefficients are equal to zero, indicating no relationship between the dependent variable
and the independent variables.
If the calculated F-statistic is larger than the critical value, we reject the null hypothesis and conclude that there is a
significant relationship between the dependent variable and the independent variables.
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If you make $15 per hour and work 20 hours per week, how much will you
make in 16 weeks?
Answer:
4800
Step-by-step explanation:
15 x 20 = 300 x 16 = 4800
if your degrees of freedom is 24, your sample size when conducting a t test for dependent means must be ______. a. 26 b. 23 c. 25 d. 24
If the degree of freedom is 24, your sample size when conducting a t-test for dependent means must be 25. Option C is the correct answer.
The sample size when conducting a t-test for dependent means depends on the specific study design and the level of significance desired, and cannot be determined solely based on the degrees of freedom.
However, if we assume that the sample size is equal for both groups, then the formula to calculate the degrees of freedom for a t-test for dependent means is:
df = n - 1
Where "n" is the number of pairs of observations in the sample.
Therefore, if the degree of freedom is 24, then the number of pairs of observations in the sample would be:
n = df + 1 = 24 + 1 = 25
Hence, the answer is 25.
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What is the relative minimum of the function?
Enter your answer in the box.
A grid with x axis increments of two increasing from negative ten to ten and y axis increments of two increasing from negative ten to ten. The grid contains a parabola opening up with a vertex at x equals negative three and y equals negative two.
The relative minimum of the function include the following: -2.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the relative minimum of the function with respect to the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that that its vertex is at x equals negative three and y equals negative two.;
Vertex (h, k) = (-3, -2)
Therefore, the relative minimum is equal to -2.
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Simplify. 5/12x1/12=
Answer:
Step-by-step explanation:
720
38 Mr. Liu buys 3 pizzas for a family dinner. He cuts each pizza into eighths.
How many pieces of pizza does Mr. Liu have for the family dinner?
(This is 5th grade)
Answer:
24 slices
Step-by-step explanation:
There are 3 whole pizzas. He cuts each of them into eighths. That means eight slices. 3 times 8 is 24. There are a total of 24 slices. This can also look like this: 24/8 or 24 over 8. Which also equals to 3.
suppose scores on the sat exam are normally distributed with mean 1100 and standard deviation 200. answer the following. (a) aaron scored 989 on the sat. what proportion of students performed worse than aaron? round to 2 decimal places.
Answer: To find the proportion of students who performed worse than Aaron, we need to find the area to the left of his score of 989 on the normal distribution curve.
First, we need to standardize Aaron's score using the formula:
z = (x - mu) / sigma
where x is the score, mu is the mean, and sigma is the standard deviation.
Plugging in the values, we get:
z = (989 - 1100) / 200 = -0.55
Next, we look up the area to the left of z = -0.55 on the standard normal distribution table, or use a calculator to find:
P(Z < -0.55) = 0.2912
Therefore, the proportion of students who performed worse than Aaron is approximately 0.2912, or 29.12% (rounded to 2 decimal places).
Step-by-step explanation:
create an equation that models the total amount that Madison spends on fruit
Answer:
2.15g + 0.75w = 20.35
Step-by-step explanation:
(no explanation needed)
Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4. 8 in. Each of the triangular faces has a base of 4. 8 in and a height of 4. 2 in. How much paper would it take to cover the entire pyramid?
To cover the entire area of pyramid, Serena would need approximately 63.36 square inches of paper.
The area of the square base is
4.8 in x 4.8 in = 23.04 sq in
The area of each triangular face is
(1/2) x base x height = (1/2) x 4.8 in x 4.2 in = 10.08 sq in
Since there are four triangular faces, the total area of the triangular faces is
4 x 10.08 sq in = 40.32 sq in
Therefore, the total surface area of the pyramid is
23.04 sq in + 40.32 sq in = 63.36 sq in
So, it would take 63.36 square inches of paper to cover the entire pyramid.
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Find all angle measures in the diagram.
The measure of ZKJL =
The measure of ZNJM =
The measure of ZMJL=
Answer: 1. 45%
2. 32%
3. 67%
For which distributions is the median the best measure of center?
Select each correct answer.
hurry pls
The 1st and the 3rd are the distributions where the median the best measure of center
What is meant by medianThe median represents the central value in a dataset that is organized in ascending or descending order. If there are an even number of data points, the median can be calculated as the mean of the two middle values.
This method is much less prone to influence by extreme values when compared to other methods such as the mean. Hence, it is considered a more reliable measure of center particularly for datasets with outliers.
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ey of the
1
11. The table shows the wages of a worker in
an office. Which equation can be used to
represent how much, y, the worker earns in x
hours?
Hours
2
CIT
4
10
6
10
A. y = 20x+ 5.50
B. y = 10x + 5.50
C. y = 20.5x
Dy = 10x
Wages
$25.50
$45.50
$65.50
$105.50
12. Carlisle is going to paint his living room
Answer:
To determine which equation represents how much the worker earns in x hours, we can use the table to find the rate of pay per hour, which is the change in wages divided by the change in hours:
Change in wages = $105.50 - $25.50 = $80
Change in hours = 6 - 2 = 4
Rate of pay per hour = Change in wages / Change in hours
= $80 / 4
= $20
Therefore, the worker earns $20 per hour. To find the total earnings, we can multiply the hourly rate by the number of hours worked:
y = $20x
Therefore, the correct equation is D) y = 10x, which represents how much the worker earns in x hours.
Step-by-step explanation:
Prisms that have 2400cm
Answer: A Rectangular prism
Gaulle Company began the year with a balance of $6,000 in Accounts Receivable and ended the year with $9,000 in the account. Revenues for the period amounted to $38,000. Under the direct method, Gaulle will report cash collected from customers of:A. $44,000B. $35,000C. $41,000D. $47,000
Under the direct method, Gaulle will report cash collected from customers of $35,000.cash collected from customers is determined by adding the changes in Accounts Receivable to the revenues recognized during the period.
Beginning Accounts Receivable was $6,000 and ending Accounts Receivable was $9,000, indicating that customers owed Gaulle an additional $3,000 during the year.
Revenue for the year was $38,000, which represents the total sales generated by the company during the period. To calculate the cash collected from customers, we need to subtract the change in Accounts Receivable from the revenue recognized during the period.
Therefore, the cash collected from customers for Gaulle is calculated as follows:
Cash collected from customers = Revenue - Decrease in Accounts Receivable
= $38,000 - ($9,000 - $6,000)
= $35,000
Therefore, the answer is B. $35,000.
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sam is a regular at joe's diner. according to the waitress, the probability that sam will order ham is 0.8 and the probability that he will order coffee is 0.65. what is the probability that he will order neither ham nor coffee?
For an event based on order by sam for ham and coffee with different probabilities, then the probability that he will order neither ham nor coffee is equals to the 0.07.
We have sam is a regular customer at joe's diner. Let us consider two events be defined as A: sam will order ham
B: sam will order coffee
Now, the probability that sam will order ham, P( A) = 0.8
The probability that sam will order coffee, P( B) = 0.65
We have to determine the probability that he will order neither ham nor coffee.
Probability is chances of occurrence of an event. It is calculated by dividing the favourable response to total possible outcomes. Probability value always lies between 0 to 1. Apply probability law P( will order ham ) + P( will not order ham) = 1
=> Probability that sam will not order ham
[tex]P( \bar A ) [/tex] = 1 - 0.8 = 0.2
Probability that sam will not order coffee,
[tex]P( \bar A ) [/tex]= 1 - 0.65 = 0.35
Now, as we see both events A and B are independent events so, there corresponding also independent. Therefore, Probability that he will order neither ham nor coffee, [tex] P( \bar A ∩ \bar B) [/tex]
[tex]= P( \bar A) P(\bar B) [/tex]
= 0.2 × 0.35 = 0.07
Hence, required probability is 0.07.
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