Two conditions are not met, the AST cannot be used to determine the convergence or divergence of the series.
The Alternating Series Test (AST) is a tool that can be used to determine whether a series converges or not.
In order to apply the AST, the series must meet two conditions:
The terms of the series must alternate in sign. In other words, the terms should switch between positive and negative values.
Mathematically, this can be represented as [tex](-1)^n \times a_n or ( -1 ) ^(n+1) \times a_n[/tex] for some sequence a_n.
The terms of the series must be decreasing in magnitude, and the limit of the sequence a_n must be 0 as n approaches infinity.
In mathematical notation, this can be written as: [tex]a_(n+1) \leq a_n[/tex]for all n, and [tex]\lim_{n \to \infty} a_n = 0[/tex].
If a series meets both of these conditions, then the AST can be applied, and the series converges.
Either of these conditions is not met, the AST cannot be used to determine the convergence or divergence of the series.
To recap, the Alternating Series Test can be used to determine if a series converges if and only if:
The series alternates in sign (terms switch between positive and negative values).
The terms of the series are decreasing in magnitude, and the limit of the sequence [tex]a_n[/tex] is 0 as n approaches infinity.
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A paper distributor offers discounts to individuals who buy in quantity. They offer a 10 percent discount for orders of 50 -100 boxes of paper, a 20 percent discount for orders of 100 - 200, and a 30 percent discount for orders of 200 boxes or more. If Lee placed an order of 140 boxes (each box is $2.50), what would his discount and final price be?
His discount and final price be $280 for his order of 140 boxes.
What is Discount ?A discount is a drop in a product's or service's price.
It is frequently provided as a perk to customers to entice them to buy. Discounts are often stated as a percentage or dollar amount off the list price.
Depending on the sort of discount and the situation, discounts can be computed in a variety of ways.
For instance, a product that costs $100 would have a discounted price of $80 with a 20% discount applied. Similar to this, a product that costs $50 would have a discounted price of $40 if it received a $10 reduction.
In marketing and sales, discounts are frequently used to draw customers and boost sales volume.
What percentage is it?The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test.
In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage."
This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."
Exampe of Percentage :-
10% = 10/100 ( = 1/10 (or) 0.1)
25% = 25/100 ( = 1/4 (or) 0.25)
According to question
Lee qualifies for a 20% discount because his order of 140 boxes falls within the range of 100-200 boxes.
Since each box originally cost $2.50, the full price of 140 boxes, after any discounts, is:
140 * $2.50 = $350
The 20% Lee discount is determined as follows:
20% * $350 = $70
Lee's discount is therefore $70, and his adjusted price is as follows:
$350 - $70 = $280
Therefore, Lee will ultimately pay $280 for his order of 140 cartons.
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es meet at right angles.) 6 m 2 m 3 m 5 m grass cement 2 m 4 m square meters
The area of the cement part is 24 m².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the part with cement. we use the formula below
Formula:
Area of the part with cement = Area of the backyard-Area of the grassA = LW-lw....................... Equation 1Where:
A = Area of the part with cementL = Length of the backyardW = Width of the backyardl = Length of the cementw = Width of the cementFrom the question,
Given:
L = 5 mW = 6 ml = 3 mw = 2 mSubstitute these values into equation 1
A = (5×6)-(2×3)A = 30-6A = 24 m²Hence, the area is 24 m².
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Need help ASAP!!! It’s due today….
Thus, the value of y for the given linear function for the input value of x = 4 , is found as y = 5.
Explain about the linear function:Any function which it graphs as a straight line is said to be linear. Mathematically speaking, this indicates that the function contains one or two variables, but neither exponents nor powers.
If the function seems to have more variables, they must all be constants or well-known variables in order for the function to continue to be linear.A two-variable linear equation can be thought of as a linear relationship involving x and y, or two variables whose values rely on each other (often y and x) (usually x). Y is referred to as the dependent variable in this scenario since it depends on the independent variable, x.Given linear function:
y = 2x - 3 ; with x = 4
To get the value of y ,put x = 4 in the given function:
y = 2(4) - 3
y = 8 - 3
y = 5
Thus, the value of y for the given linear function for the input value of x = 4 , is found as y = 5.
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correct question:
Find the value of y for the given value of 'x'.
y = 2x - 3 ; x = 4
a random sample of 120 cast aluminum pots is taken from a production line once every day. the number of defective pots is counted. the proportion of defective pots has been closely examined in the past and is believed to be 0.05. what are the upper and lower control limits for the
The upper control limit for the p-chart is 0.111, and the lower control limit is 0.003.
To calculate the upper and lower control limits for a p-chart, we need to use the following formula:
UCL = p' + 3√(p'(1-p')/n)
LCL = p' - 3√(p'(1-p')/n)
Where p' is the mean proportion of defective pots, n is the sample size (in this case, 120), and UCL and LCL are the upper and lower control limits, respectively.
Given that the proportion of defective pots is believed to be 0.05, we can calculate the mean proportion of defective pots as:
p' = 0.05
Substituting this value in the above formula, we get:
UCL = 0.05 + 3√(0.05(1-0.05)/120) = 0.111
LCL = 0.05 - 3√(0.05(1-0.05)/120) = 0.003
Any sample proportion of defective pots falling outside these limits would be considered statistically significant and warrant further investigation to identify the root cause of the defects in the production process.
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Complete question is:
A random sample of 120 cast aluminum pots is taken from a production line once every day. the number of defective pots is counted. the proportion of defective pots has been closely examined in the past and is believed to be 0.05. what are the upper and lower control limits for the p' chart.
A counter in Adriana's kitchen is 1 meter wide and 3 meters long. Adriana wants to replace the counter with a granite countertop, which would cost $261.00 per square meter. How much would the granite countertop cost?
The granite countertop would cost $783.00.
Finding the cost of granite:
To find the cost of granite find the amount of granite that can be used for the entire kitchen.
Since the kitchen floor is in a rectangle shape find the area of the kitchen floor using the area of a rectangle. Which will equal the amount of granite used for the kitchen.
Use the formula for the cost of the countertop, which is the product of the area, and the cost per square meter, to determine the total cost.
Here we have
A counter in Adriana's kitchen is 1 m wide and 3 m long.
Hence, the area of the countertop can be found by multiplying the length and the width:
Area of kitchen = length x width = 3 m x 1 m = 3 m²
The cost of the granite is given by $ 261.00 per square meter
The cost of the granite countertop will equal the product of the area and the cost per square meter:
Total Cost = 3 m² x $261.00/m² = $783.00
Therefore,
The granite countertop would cost $783.00.
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a description of the distribution of the values of a random variable and their associated probabilities is called a a. probability distribution. b. table of binomial probability. c. bivariate distribution. d. empirical discrete distribution.
A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution. The correct answer is a.
A probability distribution is a mathematical function that describes the possible values of a random variable and the likelihood of each value occurring. It provides a complete description of the probabilities of all possible outcomes of a random experiment or event.
Probability distributions can be classified into two types: discrete probability distributions and continuous probability distributions. Discrete probability distributions are used when the possible outcomes of a random variable are countable or finite, such as the number of heads in a coin toss.
Continuous probability distributions, on the other hand, are used when the possible outcomes of a random variable are infinite, such as the time it takes for a person to complete a task.
Probability distributions are used in various fields, such as statistics, finance, engineering, and science, to model and analyze random phenomena and make predictions about future events. They are an essential tool for understanding uncertainty and making informed decisions based on probabilistic outcomes.
The correct answer is a.
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In a newspaper, it was reported that the number of yearly robberies in Springfield in 2011 was 64, and then went down by 50% in 2012. How many robberies were there in Springfield in 2012?
Answer: 32
Step-by-step explanation:
50% of last year is divided by 2 (50/100 = 1/2). 64/2 = 32
The function f(x) = -4(3)-4+3 represents the value of a savings account in dollars, x months after the individual opened
the account.
In how many months will be account have a balance of $0?
O 0.26 months
O 2.46 months
O 3.74 months
O 4.26 months
NEED HELP ASP
Answer: A
Explanation:
need help! please give example if can
The two statements are;
The area of sector 1 is 20n² + 15n square meters
The total distance around the garden is 20n + 2 meters
Option A and C
How to determine the valueThe formula for the area of a rectangle is expressed as;
A = lw
Such that the parameters are;
A is the area of the rectangle l is the length of the rectanglew is the width of the rectangleFor the first sector, we have that;
Length = 4n + 3
Width = 6n - 2 - 5n = n - 2
Substitute the values
Area of sector 1 = (4n + 3)(5n)
expand the expression
Area of sector 1 = 20n² + 15n square meters
Area for the sector 2
Area = (3n - 3)(n -2)
expand the bracket
Area = 3n² - 6n - 3n + 6 = 3n² - 9n + 6
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Jody bought 20 shares of Amazon at the close price of $121.00. She bought
20 more shares a year later at the price of $127.00. Two years later, she sold
all of her shares at the price $133.00. If her broker charges $40 for each
transaction, how much money will Jody have after selling her shares?
OA. $5320.00
OB. $5160.00
OC. $5280.00
D. $5430.00
The money Jodi will have after selling her shares will be B. $5160.00
What is meant by selling?
Selling typically refers to the exchange of goods or assets for money or other valuable consideration. It is the process of transferring ownership of a product or item from the seller to the buyer in return for an agreed-upon price or value.
What is meant by shares?
Shares refer to units of ownership in a company or corporation. When a company sells shares, it is raising funds from investors who then become shareholders and have a claim on the company's profits and assets.
According to the given information
Jody bought 20 shares of Amazon at $121.00, which costs her 20 x $121.00 = $2420.00.
One year later, she bought 20 more shares at $127.00, which costs her 20 x $127.00 = $2540.00.
The total cost of buying all the shares is $2420.00 + $2540.00 = $4960.00.
Jody sold all her shares two years later at $133.00 per share, which gives her 40 x $133.00 = $5320.00.
Her total profit is $5320.00 - $4960.00 = $360.00.
After deducting the broker's fees, Jody will have $360.00 - $80.00 = $280.00.
Therefore, the correct answer is option B. $5160.00.
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Write an exponential function, f( x), to represent the number of new participants of the challenge as a function of the day number, x
The exponential function that represents the number of new participants as a function of the day number is:
f(x) = 12 * 4ˣ
What is the exponential function?
An exponential function is a mathematical function of the form:
f(x) = aˣ
where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.
Let's assume that each person who receives a selfie and accepts the challenge sends selfies to 4 new friends the next day.
Then, the number of new participants on Day 1 will be the number of friends that Aliyah, Kim, and Reese each sent selfies to, which is 4 friends each, or a total of 12 new participants.
On Day 2, the 12 new participants each send selfies to 4 new friends, resulting in 4*12 = 48 new participants.
On Day 3, the 48 new participants each send selfies to 4 new friends, resulting in 4*48 = 192 new participants.
We can see that the number of new participants is growing exponentially, with each new day resulting in a larger number of new participants than the previous day.
To write an exponential function that represents the number of new participants as a function of the day number, we can use the general form of an exponential function:
f(x) = a * bˣ
where a is the initial value (the number of new participants on Day 1), b is the growth factor (the factor by which the number of new participants increases each day), and x is the day number.
In this case, we know that a = 12 (the initial number of new participants) and b = 4 (the factor by which the number of new participants increases each day, since each participant sends selfies to 4 new friends).
Therefore, the exponential function that represents the number of new participants as a function of the day number is:
f(x) = 12 * 4ˣ
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Select all expressions equivalent to 162x^2 – 72.
2(9x - 6)^2
2 (81x^2 – 36)
2 (9x - 6) (9x + 6)
18(3x^2 – 2)^2
18 (3x - 2) (3x + 2)
Expressions (i) and (v) are equivalent to the original expression [tex]162x^2 - 72.[/tex]
What is expression?In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a quantity. It can consist of constants, variables, arithmetic operators, and other mathematical functions or operations.
According to given information:The expression [tex]162x^2 - 72[/tex] can be factored using the difference of squares formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex].
First, we can factor out 18 from the expression:
[tex]162x^2 - 72 = 18(9x^2 - 4)[/tex]
Now, we can apply the difference of squares formula by setting a = 3x and b = 2:
[tex]9x^2 - 4 = (3x)^2 - 2^2 = (3x + 2)(3x - 2)[/tex]
Substituting this back into the original expression, we get:
[tex]162x^2 - 72 = 18(9x^2 - 4) = 18(3x + 2)(3x - 2)[/tex]
Therefore, expressions (i) and (v) are equivalent to the original expression [tex]162x^2 - 72[/tex].
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Help solve this! ASAP
Answer:
2
Step-by-step explanation:
You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].
Average rate of changeThe average rate of change of f(x) on the interval [a, b] is computed as ...
m = (f(b) -f(a))/(b -a)
For the given function f(x), this is ...
m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2
The average rate of change of f(x) on the interval [-7, 3] is 2.
__
Additional comment
The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:
-2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.
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At a soda fountain 22 quarts of ice cream were used to make 105 milk shakes. How many quarts are needed to make 922 milk shakes?
193.18 quarts of ice cream are needed to make 922 milkshakes.
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
A proportion is an equation that sets two ratios at the same value.
To find the number of quarts needed to make 922 milkshakes, we can set up a proportion:
22 quarts / 105 milkshakes = x quarts / 922 milkshakes
Cross-multiply:
[tex]22\times 922 = 105 \times x[/tex]
Calculate the products:
[tex]22 \times 922 = 105 \times x[/tex]
Divide by 105 to solve for x:
[tex]20284 \times 105 = x[/tex]
Calculate the quotient:
[tex]20284 \times 105 = x[/tex]
Therefore, approximately 193.18 quarts of ice cream are needed to make 922 milkshakes.
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A survey is taken at a mall in Westingbrook. The first 75 people who entered the mall were asked about their favorite restaurant in the food court. What is true about this situation? The population is the first 75 people at the mall, and the sample is the total number of people who go to the mall. O The population is the total number of people who go to the mall, and the sample is the first 75 people at the mall. The population is the number of people who go to the mall, and the sample is the number of people in the town of Westingbrook. O The population is the number of people in the town of Westingbrook, and the sample is the number of people who go to the mall.
The answer to this problem is "The population is the total number of people who go to the mall, and the sample is the first 75 people at the mall".
What is true about this situation?
When conducting a survey, it's important to carefully define the population of interest and the sample being surveyed. The population is the entire group that you want to draw conclusions about, while the sample is the group of individuals that you actually survey. In this situation, the population of interest is the total number of people who go to the mall, as this is the group that we want to make inferences about.
The sample is the first 75 people who entered the mall and were asked about their favorite restaurant in the food court. This sample was likely selected in a way that is meant to be representative of the larger population of mall-goers. However, it's worth noting that the sample is still a subset of the population, and therefore there is some risk of sampling error. For example, if the first 75 people who entered the mall were all from the same demographic group, the survey results might not be representative of the larger population.
Overall, it's important to be clear about the population and sample when conducting a survey, as this helps to ensure that the results are meaningful and accurate.
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What’s the first term for 3, 7, 11, 15, 19, 23
Therefore, the first term of the sequence is 3.
What is sequence?A sequence is an ordered list of numbers, usually generated by a pattern or a rule. Each number in the sequence is called a term, and the position of a term in the sequence is called its index. Sequences can have a finite or infinite number of terms, and they can be defined in various ways, such as recursively (where each term is defined in terms of the previous terms) or explicitly (where the formula for each term is given).
Here,
The given sequence is an arithmetic sequence, where the common difference between consecutive terms is 4. To find the first term, we can use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the position of the term in the sequence, and d is the common difference.
For this sequence, we know that a6 = 23 (since 23 is the last term given in the sequence), n = 6, and d = 4. Substituting these values into the formula, we get:
a6 = a1 + (6 - 1)4
23 = a1 + 20
a1 = 23 - 20
a1 = 3
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Complete question:
What’s the first term for the given sequence: 3, 7, 11, 15, 19, 23?
Find the number of terms in this polynomial
Step-by-step explanation:
where is. the. polynomial.
Divide. Write the missing
numbers.
62) 5,472
1
9
16
R
62 5 4 7 2
"
R
9
1 6
(Type whole numbers.)
we get the quotient as 161 and remainder as 11.So the missing numbers are:R = 11
9, 1, 6
What is long division method ?First divide the greater number by the smallest number and then divide the smaller number by the remainder. We continue the process until we get 0 remainder. The divisor is the HCF of the given numbers.
To divide 5,472 by a two-digit number, we can use long division method as follows:
34) 5 4 7 2( 34
- 4 0
______
1 4 7
- 1 3 6
_______
1 1
Therefore, we get the quotient as 161 and remainder as 11.
So the missing numbers are:
R = 11
9, 1, 6
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Which expression can be used to find the surface area of the following rectangular prism? Choose 1 answer: (Choice A) A 15+15+10+10+6+615+15+10+10+6+615, plus, 15, plus, 10, plus, 10, plus, 6, plus, 6 (Choice B) B 10+10+6+610+10+6+610, plus, 10, plus, 6, plus, 6 (Choice C) C 15+15+10+10+615+15+10+10+615, plus, 15, plus, 10, plus, 10, plus, 6 (Choice D) D 10+610+6
The expression used to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.
Let us consider 'l' be the length of the rectangular prism.
'w' be the width of the rectangular prism .
'h' be the height of the rectangular prism.
From the attached figure we have,
Length of the rectangular prism l = 3 units
Width of the rectangular prism w = 2 units
Height of the rectangular prism h = 5 units
Surface of the rectangular prism = 2(lw + wh + hl )
Substitute the values in the formula we get,
⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )
⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)
⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15
Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.
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The above question is incomplete, the complete question is:
Which expression can be used to find the surface area of the following rectangular prism?
Attached figure.
How can I turn this equation into standard form
Answer:
which equation i cant see a question or a photo of question
Can someone help me asap? It’s due tomorrow.
Answer:
I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.
HELLLPPP Quick
What is the mean of this data set?
12, 17, 16, 10, 20
35
25
15
Answer:
15
Step-by-step explanation:
The numbers in the given data = 12, 17, 16, 10, 20
Total number = 5
12 + 17 + 16 + 10 + 20 = 75
Mean = 75/5
Mean 15
Kelley surveyed people to find their favorite hat color. She is making a circle graph of the data. What is the measure in degrees of the
central angle in the graph for the people that chose red?
Number of Hats
brown: 180
Black: 60
Red: 90
Blue: 120
The measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.
What is the central angle?A central angle is an angle formed by two radii (or rays) that intersect at the center of a circle. It is an angle whose vertex is at the center of the circle, and its sides are the radii that intersect the circle's circumference.
According to the given information:
To find the measure in degrees of the central angle for the people that chose red, we need to calculate the percentage of people that chose red out of the total number of people surveyed, and then convert that percentage into degrees.
Total number of people surveyed = 180 (brown) + 60 (black) + 90 (red) + 120 (blue) = 450
Percentage of people that chose red = (Number of people that chose red / Total number of people surveyed) * 100 = (90 / 450) * 100 = 20%
Now, we can convert the percentage into degrees using the formula for calculating the central angle in a circle graph:
Central angle = (Percentage / 100) * 360
Plugging in the percentage of people that chose red:
Central angle for red = (20 / 100) * 360 = 72 degrees
So, the measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.
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quiz 7the following table shows the individual measurements for five samples taken every 15 minutes starting at 10:00 am to be used in monitoring the quality of a process.10:00 am2.01.82.01.810:15 am2.02.02.02.010:30 am1.81.92.12.210:45 am2.12.11.91.911:00 am1.62.02.21.71. how many measurements are in each sample?2. suppose a mean control chart is being used with an upper limit of 2.2 and a lower limit of 1.8. using the data above, what would be the first point to plot on the control chart?
The first point to plot on the mean control chart would be at 1.9 at control chart with both limits.
1. There are four measurements in each sample, as shown in the table.
2. To plot the first point on the mean control chart, we need to calculate the mean of the first sample. Adding up the four measurements from the 10:00 am sample (2.0 + 1.8 + 2.0 + 1.8) gives a total of 7.6. Dividing by the number of measurements in the sample (4) gives a mean of 1.9. Since the mean is within the control limits of 1.8 and 2.2, the first point on the chart would be plotted at 1.9.
1. To determine how many measurements are in each sample, we simply count the number of measurements provided for each time.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
Each sample contains 4 measurements.
2. To plot the first point on a mean control chart, we need to calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4
Mean = 7.6 / 4
Mean = 1.9
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1. There are 4 measurements in each sample.
2. The first point to plot on the mean control chart would be 1.9, corresponding to the 10:00 am sample.
To determine the number of measurements in each sample, simply count the number of values for each time point.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
There are 4 measurements in each sample.
To plot the first point on the mean control chart, calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4 = 7.6 / 4 = 1.9.
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You are enclosing a circular flower garden with a fence that costs 2.99 per foot. The radius of the garden is 7 feet. How much will it cost to buy the fence?
Answer:
460.46
Step-by-step explanation:
If a fence costs $2.99 per foot, the cost of the feence will be 154(2.99) = $460.46
How to find the area of the circular flour
The formula for finding the area of a circle is expressed as:
A = πr²
r is the radius of the circle
Given that r = 7 feet
A = π(7)²
A = 49 * 22/7
A = 22 * 7
A = 154 square feet
If a fence costs $2.99 per foot, the cost of the fence will be 154(2.99) = $460.46
a box model will be used to keep track of the number of winning plays for a gambling game that has chance 15% of winning and 85% of losing. is it appropriate to use the normal approximation to find the chance of winning at least 10 times out of 75 total plays of the game?
Yes , it is appropriate to choose normal approximation to calculate the chance of winning at least 10 times out of 75 total plays of game.
Use the normal approximation,
Chance of winning at least 10 times out of 75 total plays of the game,
Conditions for using the normal distribution are met.
Binomial distribution can be approximated by the normal distribution,
The number of trials 'n' is large enough usually n > 30.
The probability of success 'p' is not too close to 0 or 1.
The trials are independent.
Here,
n = 75 trials and p = 0.15 probability of winning.
To check if the normal approximation is appropriate,
Calculate the mean and standard deviation of the binomial distribution,
mean = n × p
= 75 × 0.15
= 11.25
Standard deviation
= √(n × p × (1 - p))
= √(75 × 0.15 × 0.85)
= 3.09
Mean is 11.25 and the standard deviation is 2.44.
The condition for independence is satisfied since each play is independent of the others.
If the other two conditions are met,
Check if np and n(1-p) are both greater than or equal to 10,
np = 75 × 0.15
= 11.25
n(1-p) = 75 × 0.85
= 63.75
Both np and n(1-p) are greater than or equal to 10,
So the conditions for using the normal approximation are satisfied.
Therefore, it is appropriate to use the normal approximation to find the chance of winning at least 10 times out of 75 total plays of the game.
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If you spin the spinner 36 times, what is the best prediction possible for the number of times it will not land on yellow?
The best prediction possible for the number of times the spinner will not land on yellow is 18.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.
The probability of the spinner not landing on yellow in one spin is:
P(not yellow) = P(green) + P(blue) + P(red)
= 1/6 + 1/3 + 1/6
= 1/2
Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:
E(not yellow) = 36 x P(not yellow)
= 36 x 1/2
= 18
So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.
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there are four blood types, and not all are equally likely to be in blood banks. in a certain blood bank, 49% of donations are type o blood, 27% of donations are type a blood, 20% of donations are type b blood, and 4% of donations are type ab blood. a person with type b blood can safely receive blood transfusions of type o and type b blood. what is the probability that the 4th donation selected at random can be safely used in a blood transfusion on someone with type b blood? ( to the nearest thousandth)
The probability that the fourth donation selected at random can be safely used in a blood transfusion on someone with type B blood is 0.69.
How to find the probability?Since a person with type B blood can safely receive blood transfusions of type O and type B blood, the fourth donation selected at random must be either type O or type B blood. From the information given, the probability of the fourth donation being type O blood is 49%, and the probability of it being type B blood is 20%. Therefore, the probability that the fourth donation can be safely used in a blood transfusion on someone with type B blood is:
P(type O or type B) = P(type O) + P(type B) = 0.49 + 0.20 = 0.69
So, the probability that the fourth donation selected at random can be safely used in a blood transfusion on someone with type B blood is 0.69 (rounded to the nearest thousandth).
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A rectangular prism has a length of 113yards, a width of 212 yards, and a height of 4 yards. Enter the volume of the prism as a mixed number in simplest form in the box.
____ yd³
EXPLANATION
Given the dimensions of a rectangular prism:
Length = 113 yards
Width: 212 yards
Height: 4 yards
We have to find its volume.
The volume of a prism is the product of its dimensions,
Hence, the volume of this prism is 95,824 cubic yards.
I need help with this it's hard. Thanks!
The measure of angle JKL is 105⁰.
The measure of angle KJM is 75⁰.
What is the property of opposite angles of isosceles trapezoid?
In an isosceles trapezoid, the property of opposite angles is that they are congruent or equal in measure. Specifically, the two angles that are formed by the intersection of the non-parallel sides with the bases of the trapezoid are opposite angles, and they have the same measure.
The measure of angle JKL is calculated as;
m∠JKL = 27⁰ + 78⁰ = 105⁰
m∠JKL = 105⁰
The measure of angle KJM is calculated as;
m∠KJM = ¹/₂ (360 - 2x105)
m∠KJM = 75⁰
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