The given function is C(x) = 936 + 80x + 0.12x^2, where x represents the number of mountain bikes produced daily. The average cost function is also given by C(x).
To make the mountain bike as affordable as possible, the company should target a production level of 333.33 mountain bikes daily, where the average cost function is at its minimum. Rounded to 2 decimal places, the answer is
c = 333.33.
First, let's correct the given cost function: C(x) = 936x + 80x^2 + 0.12x^3. Now, we'll use the terms "function," "average," and "increases."
To find the average cost function, we need to divide the total cost function, C(x), by the number of mountain bikes produced daily, x. Let A(x) represent the average cost function:
A(x) = C(x) / x
Now, let's substitute C(x) into this equation:
A(x) = (936x + 80x^2 + 0.12x^3) / x
Simplify by canceling out an x term:
A(x) = 936 + 80x + 0.12x^2
To find the production level c where the average cost function decreases and then increases, we need to find the minimum point on the A(x) curve. To do this, we'll differentiate A(x) with respect to x to obtain the first derivative:
A'(x) = 80 + 0.24x
Now, set the first derivative equal to zero and solve for x:
80 + 0.24x = 0
0.24x = -80
x = c = -80 / 0.24
Round to 2 decimal places:
c ≈ 333.33
So, to make the mountain bike as affordable as possible, the company should target a production level of approximately 333.33 mountain bikes daily.
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A sorted list of numbers contains 128 elements, Which of the following is closest to the maximum number of list elements that can be examined when performing a binary search for a value in the list? A. 2
B. 8 C. 64 D. 128
8 is closest to the maximum number of list elements that can be examined when performing a binary search for the value in the list.Therefore option B is correct.
To find the maximum number of list elements:
When performing a binary search on a sorted list of 128 elements, you would repeatedly divide the list in half until you find the target value or the list cannot be divided further.
In this case, you can divide the list a maximum of 7 times (2^7 = 128) before you reach a single element.
However, since the options provided do not include 7, the closest option is 8 (option B).
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On June 1, 2013 the number of hours of daylight in Anchorage, Alaska was18.4 hours what was the number of hours without daylight
The number of hours without daylight will be 5.6 hours.
On June 1, 2013, the number of hours of daylight in Anchorage, Alaska was 18.4 hours.
There are 24 hours a day. Then the number of hours without daylight is calculated as,
⇒ 24 - 18.4
⇒ 5.6 hours
The number of hours without daylight is 5.6 hours.
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(co 6) a university wants to plan how many classes to run next semester. to do this, it needs to estimate on average how many students register each semester. which statistical method would be best to use in this situation? g
The statistical method that would be best to use in this situation is b) Regression analysis.
Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.
Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.
Hence the answer is Regression analysis.
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The germination rate for bush bean seeds from a particular company is 92% (ie, 92% of seeds planted and tended according to the directions will sprout). Seeds are sold in varying smaller-sized size packets as well as in bulk. Assume that the selection of seeds for packets is random and all seeds are independent of one another. Let X be the number of seeds that sprout If I buy a packet of 50 seeds, how many should I expect to sprout?
You can expect approximately 46 seeds to sprout from a packet of 50 seeds.
Based on the given information, we know that the germination rate for the bush bean seeds is 92%, which means that 92 out of 100 seeds planted and tended according to the directions will sprout. We also know that the selection of seeds for packets is random and all seeds are independent of one another. Therefore, we can use the binomial probability formula to determine the expected number of seeds that will sprout:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
n = 50 (number of seeds in the packet)
k = number of seeds that sprout
p = 0.92 (probability of a seed sprouting)
1-p = 0.08 (probability of a seed not sprouting)
Using this formula, we can calculate the expected value of X as follows:
E(X) = n * p
E(X) = 50 * 0.92
E(X) = 46
Therefore, we can expect around 46 seeds to sprout out of the 50 seeds in the packet. However, it's important to note that this is only an expected value and the actual number of seeds that sprout may vary.
To determine how many bush bean seeds you can expect to sprout from a packet of 50 seeds, you can use the germination rate provided and the assumption that all seeds are independent of one another.
Given:
- Germination rate = 92%
- Total seeds in the packet = 50
Since the seeds are independent, you can simply multiply the germination rate by the total number of seeds to calculate the expected number of seeds that will sprout.
Expected sprouts (X) = Germination rate × Total seeds
X = 0.92 × 50
X ≈ 46
So, you can expect approximately 46 seeds to sprout from a packet of 50 seeds.
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suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. use this information to answer questions 6 - 9.
The probability that a cell phone user makes or receives less than 12 calls per day is 0.3971.
What is probability that user makes or receives less than 12 calls?To find P(x < 12), we need to standardize the value of 12 using the formula: z = (x - μ) / σ where z = z-score, x = value of interest, μ = mean, and σ = standard deviation.
Substituting the values, we get:
z = (12 - 13.1) / 4.3
z = -0.25581
Using a calculator, we can find the probability that z is less than -0.25581, which is:
P(z < -0.25581) = 0.3971
P(z < -0.25581) = 39.71%.
Full question "Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Find P (x <12)".
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1 1/2 + ___ = 4
please help really confused.
Answer:
Step-by-step explanation:
2 and 1/2
Answer:
2 1/2 or 2.5
Step-by-step explanation:
1. Rewrite:
1 1/2 + x = 4
2. Subtract 1 1/2 from both sides:
4 - 1 1/2 = 2 1/2
x = 2 1/2 or 2.5
Write an iterated integral of a continuous function f over the following region. The region bounded by y = 8 - x, y = 1, and x = 2 Choose the correct answer below. Select all that apply. A. integral^6_2 integral^1_8 - x f(x, y) dy dx B. integral^6_1 integral^8 - y_2 f(x, y) dx dy C. integral^6_1 integral^8 - x_1 f(x, y) dy dx D. integral^7_2 integral^8 - x_1 f(x, y) dy dx E. integral^7_2 integral^8 - y_2 f(x, y) dx dy F. integral^7_1 integral^2_8 - y f(x, y) dx dy
A. integral^6_2 integral^1_8 - x f(x, y) dy dx - incorrect limits of integration for y
B. integral^6_1 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
C. integral^6_1 integral^8 - x_1 f(x, y) dy dx - correct
D. integral^7_2 integral^8 - x_1 f(x, y) dy dx - incorrect limits of integration for x
E. integral^7_2 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
F. integral^7_1 integral^2_8 - y f(x, y) dx dy - incorrect limits of integration for x
The region is bounded by the lines y = 8 - x, y = 1, and x = 2. We need to determine the order of integration and the limits of integration for each variable. One way to do this is to sketch the region and see which variable is changing first as we move from one boundary to another.
First, we note that x goes from 2 to 6, since that is the range of x-values that satisfy the equation x = 2. Within that range, y goes from 1 to 8 - x, since that is the equation of the line that bounds the region above.
So the iterated integral should be of the form:
integral_(lower x limit)^(upper x limit) integral_(lower y limit)^(upper y limit) f(x, y) dy dx
Using the limits we just determined, we can eliminate some of the answer choices:
A. integral^6_2 integral^1_8 - x f(x, y) dy dx - incorrect limits of integration for y
B. integral^6_1 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
C. integral^6_1 integral^8 - x_1 f(x, y) dy dx - correct
D. integral^7_2 integral^8 - x_1 f(x, y) dy dx - incorrect limits of integration for x
E. integral^7_2 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
F. integral^7_1 integral^2_8 - y f(x, y) dx dy - incorrect limits of integration for x
Therefore, the answer is C. integral^6_1 integral^8 - x_1 f(x, y) dy dx, Your answer: B. integral^6_1 integral^8 - y_2 f(x, y) dx dy
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Three less than two times a number is equal to 21 more than five times the number. What is the equation and the answer?
The equation is 2x - 3 = 5x + 21. Solving for "x" gives the solution of x = -8.The equation for this issue is as follows:
2x - 3 = 5x + 21
where "x" stands for the unidentified number.
We can separate the variable term on one side of the equation and the constant terms on the other side in order to solve for "x".
To begin, we can take away 2x from both sides to obtain:
-3 = 3x + 21
Then, we can take 21 away from both sides to get at:
-24 = 3x
Finally, multiplying both sides by 3 gives us:
x = -8
Consequently, x = -8 is the answer to the equation.
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If the chi-square statistic is less than 3.84, the p-value is greater than 0.05, so there isn't enough evidence to conclude that the relationship in the population is real. Equivalent ways to state this result are
Equivalent ways for chi-square statistic are: variables relationship is not statistically significant, insufficient evidence to suggest association, and observed relationship might be due to chance.
If the chi-square statistic is less than 3.84 and the p-value is greater than 0.05, then there is insufficient evidence to support the existence of a significant relationship in the population. This means that we cannot confidently conclude that the variables are related.
If the chi-square statistic is less than 3.84 and the p-value is greater than 0.05, there isn't enough evidence to conclude that the relationship in the population is real. Equivalent ways to state this result are:
1. The relationship between the variables is not statistically significant.
2. There is insufficient evidence to suggest a significant association between the variables.
3. The observed relationship may be due to chance and cannot be considered a true relationship in the population.
Remember, this conclusion is based on the chi-square statistic and p-value, which help determine if there's a significant relationship between variables in a population.
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Ella makes a model of a log cabin that is 8 inches long at a scale of 1/2.5 feet. She makes a second model of the same building at a scale of 1/2.5 feet. How much longer is the second model than the first?
The second model is 3.2 inches shorter than the first model.
The first model of the log cabin is 8 inches long at a scale of 1/2.5 feet.
To determine the actual length, we need to convert the scale to feet.
1/2.5 feet can be simplified to 2/5 feet. So, the length of the first model in feet is
(8 inches) × (2/5 feet per inch)
= 16/5 feet
= 3.2 feet.
Now, let's calculate the length of the second model. Since it is also at a scale of 1/2.5 feet, the length would be
(1/2.5 feet) × 12 inches
= 4.8 inches.
To find the difference in length between the two models, we subtract the length of the first model from the length of the second model:
(4.8 inches) - (8 inches)
= -3.2 inches.
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Y=^2+6x+8 and y=(x+2)(x+4)
The two equations y=x²+6x+8 and y=(x+2)(x+4) are equal.
The given two equations are y=x²+6x+8 and y=(x+2)(x+4)
We have to check whether the two equations are equal or not
y=x²+6x+8 ----(1)
y=(x+2)(x+4) ---(2)
y=x² + 4x+2x+8
y=x² + 6x+8 ....(2)
From equation (1) and (2), y=x²+6x+8 and y=(x+2)(x+4) are equal.
Hence, the two equations y=x²+6x+8 and y=(x+2)(x+4) are equal.
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T/F : In a 5 by 5. If A has three pivots, then ColA is a (two-dimensional) plane
True.
If A is a 5 by 5 matrix and has three pivots, then its row reduced echelon form will have three leading 1's, and the other two rows will be zero rows.
If A is a 5 by 5 matrix and has three pivots, then its row reduced echelon form will have three leading 1's, and the other two rows will be zero rows. This means that the three pivot columns of A are linearly independent, and they span a three-dimensional subspace of R^5.
Since the pivot columns of A are the columns of ColA, we can say that ColA is a subspace of R^5 that is spanned by three linearly independent vectors. Since the dimension of this subspace is three, it is a three-dimensional subspace of R^5. Geometrically, a three-dimensional subspace of R^5 is a (two-dimensional) plane, sincsincesincsinceee it is the intersection of two three-dimensional spaces. Therefore, we can conclude that ColA is a (two-dimensional) plane in R^5.
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Please help:
Select the equation that correctly describes the following real-world situation.
15 pieces of candy are given to s students from a bag of candy containing 310 pieces. There are 10 pieces left over.
A.) (s x 15) ÷ 10 = 310
B.) (s + 15) = 310 ÷ 10
C.) (310 − 10) ÷ 15 = s
D.) 310 ÷ (s + 15) = 10
The equation that correctly describes the situation is( 310-10)÷15 = S
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
15 pieces of candy are given tons students, therefore the total number of candy given out is
15 × s = 15s
there are 310 pieces of candy in the bag and 10!is left
Therefore the equation that represents the situation is;
310-15s = 10
15s = 310-10
s = (310-10) ÷15
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Which of the following are assumptions for the confidence interval for the different between two population means?
Data is Quantitative.
Data is from a Convenience Sample
Random Sample
Both sample sizes are greater than 30 or the data from a Normal Distribution
Data is Categorical.
There are at least 15 successes and 15 failures.
The valid assumptions for constructing a confidence interval for the difference between two population means are: Data is Quantitative, Random Sample and Both sample sizes are greater than 30 or the data is from a Normal Distribution.
To answer your question, when constructing a confidence interval for the difference between two population means, certain assumptions must be met. These assumptions include:
1. Data is Quantitative: Since we are dealing with population means, the data should be quantitative, meaning it consists of numerical values. This is a correct assumption.
2. Data is from a Convenience Sample: This is not a valid assumption. To ensure the reliability of the confidence interval, data should be collected through random sampling, which ensures that each individual in the population has an equal chance of being included in the sample.
3. Random Sample: This is a correct assumption. A random sample is necessary to ensure the sample's representativeness and accuracy in estimating the population means.
4. Both sample sizes are greater than 30 or the data is from a Normal Distribution: This is a valid assumption. If both sample sizes are greater than 30, the Central Limit Theorem can be applied, which states that the sampling distribution of the sample means will be approximately normal. If the data is already from a normal distribution, the normality assumption is met.
5. Data is Categorical: This assumption is incorrect. As previously mentioned, the data should be quantitative for this analysis.
6. There are at least 15 successes and 15 failures: This assumption is not relevant for confidence intervals for the difference between two population means. This criterion is related to proportions rather than means.
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Which are the appropriate measures to describe the center and spread of the distribution?
Responses
A median and modemedian and mode
B mean and medianmean and median
C mode and interquartile rangemode and interquartile range
D median and interquartile rangemedian and interquartile range
Symmetrical data has an approximate line of symmetry. In this case, however, the data is skewed by an unusually high value w/out a corresponding low value to balance it out. The data set is NOT symmetrical. The MEAN & standard deviation are the most often-used measures of center & spread. Unfortunately, the mean's value can be greatly affected by the presence of even a single outlier. When outliers are present, the MEDIAN & iqr provide more appropriate measures of center & spread
D) Median and interquartile rangemedian and interquartile range
Symmetrical data has an approximate line of symmetry.
When describing a distribution, it's important to use applicable measures of center and spread that reflect the shape and nature of the data. For symmetrical data, the mean and standard divagation are generally used as measures of center and spread, independently. still, when the data is disposed or contains outliers, these measures may not be applicable.
In similar cases, the standard and interquartile range( IQR) are more robust measures of center and spread. The standard is the value that separates the lower 50 of the data from the upper 50, and is thus innocent by outliers. The IQR is the difference between the 75th percentile and the 25th percentile, and represents the range of the middle 50 of the data. It's also less sensitive to outliers than the range or standard divagation.
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Tysm if you help due tomorrow
Answer:
C. 54cm²
Step-by-step explanation:
Split the figure into 2. A=LW. the top shape is easy, 8x5 = 40
As for the bottom one, we need to figure out the height. The whole left side is 12cm, and the part in the top shape is 5cm since it is across from the labeled side, and is a rectangle. 12-5= 7, the height of the smaller shape.
From there, we use LW to figure that out. 7x2 = 14
Now we know the area of both shapes, so we must add them together. Think of it as finding the area of each shape seperately, which is what we did. 40 + 14 = 54 and don't forget the label!
What is the best probability distribution to use for simulating the outcome of flipping a single coin? uniform binomial exponential normal poisson none of the other answers is correct
The best probability distribution to use for simulating the outcome of flipping a single coin is the binomial distribution. The binomial distribution is used to model the number of successes in a fixed number of independent trials, where each trial has the same probability of success (in this case, 0.5 for heads or tails).
It is a discrete distribution and is often used in situations where there are only two possible outcomes. The other distributions mentioned (uniform, exponential, normal, and Poisson) are not appropriate for this scenario.
The best probability distribution to use for simulating the outcome of flipping a single coin is the binomial distribution. The binomial distribution is appropriate because it models the number of successes (e.g., heads).
In a fixed number of independent Bernoulli trials (e.g., coin flips) with the same probability of success on each trial. In this case, there are two possible outcomes (heads or tails) and each flip is independent with an equal probability of success (0.5).
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Use the graph to solve x^2+8x+16=0. Select all solutions that apply.
We can see from the graph that the parabola intersects the x-axis at -4 (where the vertex touches the x-axis).
Since the equation is in the form of ax^2 + bx + c = 0, we can identify that a = 1, b = 8, and c = 16.
Using the quadratic formula, we get:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-8 ± sqrt(8^2 - 4(1)(16))) / 2(1)
x = (-8 ± sqrt(0)) / 2
x = -4
Therefore, the only solution is x = -4.
whats the volume please
The volume of the piece is 22, 036. 16 dm³
How to determine the volumeFrom the diagram shown, we have it is a composite shape of a cube and a cylinder.
The volume for calculating the volume of a cube is expressed as;
V = a³
Where 'a' is the length of the side
Substitute the value
Volume = 14³
Volume = 2744 dm³
The volume of a cylinder is expressed as;
Volume = πr²h
Given that r is the radius and h is the height
Substitute the values
Volume =3.14 × 16² × 24
Multiply the values, we have;
Volume = 19, 292. 16 dm³
Total volume = 19, 292. 16 + 2744
Add the values
Total volume = 22, 036. 16 dm³
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Any argument whose premises are p ---> q and q ---> r is valid regardless of the conclusion. true or false
False.
An argument with premises "p ---> q" and "q ---> r" is valid only if its conclusion follows logically from the premises.
An argument with premises "p ---> q" and "q ---> r" is valid only if its conclusion follows logically from the premises.
For example, if the conclusion is "p ---> r," then the argument is valid because:
- If p ---> q and q ---> r, then by transitivity of implication, p ---> r.
However, if the conclusion is "r ---> p," then the argument is not valid because:
- If p ---> q and q ---> r, we cannot infer that r ---> p.
Therefore, the validity of an argument with premises "p ---> q" and "q ---> r" depends on the specific conclusion being drawn, and not all conclusions are valid.
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The weight of football players is normally distributed with a mean of 205 pounds and a standard deviation of 10 pounds. What is the minimum weight of the middle 95% of the players? a. 185.4 b. 221 O c. 189 d. 224.6
The minimum weight of the middle 95% of the players is 185.4 pounds.
To find the minimum weight of the middle 95% of the players, we need to find the weight that separates the bottom 2.5% of the distribution from the top 2.5%.
We can use the z-score formula:
z = (x - μ) / σ
Where:
x = the weight we're looking for
μ = the mean weight of 205 pounds
σ = the standard deviation of 10 pounds
To find the z-score that corresponds to the bottom 2.5%, we can use a z-table or calculator and look up the z-score that has an area of 0.025 to its left. This value is -1.96.
Plugging this into the z-score formula:
-1.96 = (x - 205) / 10
Solving for x:
x = (-1.96 * 10) + 205
x = 185.4
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Test for the best ~ A major financial services company uses a set of pre-employment tests to evaluate potential employees before they are hired. All applicants sign a confidentiality agreement not to divulge any content from the tests, which has allowed the company to use the same tests over many years. The test scores are known to be normally distributed with a mean of 75.2.
In an effort to hire more talented employees, the company recently hired a recruiting firm to find better qualified applicants. A random sample of 24 applicants provided by the recruiting firm had a mean test score of 76.85 and a standard deviation of 9.3.
The company wants to determine if the mean test score for all applicants supplied by the recruiting firm is higher than the historical mean of 75.2.Round all calculated values to 4 decimal places as appropriate.
1. Which inference procedure should the company use?
A. Z confidence interval for a population proportion
B. Z test for one population proportion
C. Randomization test for the difference of two population proportions
D. 2 test of independence
E. t test for a population mean
2. Which set of hypotheses should the company use to answer the research question?
A. H0:x¯=76.85 vs. H:x¯>76.85
B. H0:=75.2 vs. H:≠75.2
C. H0:=75.2 vs. H:<75.2
D. H0:=75.2 vs. H:>75.2
1. The company should use a t-test for the population mean, as we are comparing the mean test score for the sample of applicants supplied by the recruiting firm to the historical mean of 75.2.
2. The set of hypotheses the company should use to answer the research question is: D. H0: μ = 75.2 vs. H1: μ > 75.2
1. The appropriate inference procedure for this scenario is the t-test for a population mean. This is because we are comparing a sample mean (76.85) to a known population mean (75.2) with a known sample standard deviation (9.3). So the correct answer is:
E. t-test for a population mean
2. The company wants to determine if the mean test score for applicants provided by the recruiting firm is higher than the historical mean of 75.2. Therefore, the null hypothesis (H0) should be that the mean test score is equal to 75.2, and the alternative hypothesis (H1) should be that the mean test score is greater than 75.2. The correct set of hypotheses is:
H0: μ = 75.2 (the historical mean)
Ha: μ > 75.2 (the mean for the sample of applicants supplied by the recruiting firm is higher).
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What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $925, if
it pays 8% fixed interest for the duration of the
bond?
yield = [?] %
Give your answer as a percent rounded to the nearest
hundredth.
The yield on the corporate bond is 8.65%.
What is the yield on the corporate bond?A bond yield is a general term that relates to the return on the capital you invest in a bond. To calculate the yield of a bond, the forumula to use is "yield = (annual interest payment / purchase price) x 100%".
Data:
Face value of the bond is $1000
Fixed interest rate is 8%.
Annual interest payment = 8% x $1000
Annual interest payment = $80
The purchase price is $925.
We can substitute these values to find the yield:
= ($80 / $925) x 100%
= 0.0864864865 * 100%
= 8.65%
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Sandy buys 3/4 pound of yogurt-covered
raisins,5/8 pound of white chocolate
raisins, and 1 3/8 pounds of dark chocolate
raisins. How many pounds of raisins does
she buy?
She bought a total of 2 3/4 pounds.
We have,
3/4 pound of yogurt-covered raisins,
5/8 pound of white chocolate raisins,
and 1 3/8 pounds of dark chocolate raisins.
She bought a total of
= 3/4 + 5/8 + 1 3/8
= 6/8 + 5/8 + 11/8
= 22/8
= 11/4
= 2 3/4 pounds
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She can buy 11/4 pounds of raisins.
Given that;
Sandy buys 3/4 pound of yogurt-covered raisins,5/8 pound of white chocolate raisins, and 1 3/8 pounds of dark chocolate raisins.
Hence, Total raisin she buy is,
⇒ 3/4 + 5/8 + 1 3/8
⇒ 6/8 + 5/8 + 11/8
⇒ 22/8
⇒ 11/4 pounds
Thus, She can buy 11/4 pounds of raisins.
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f=1/2m how many cups of flower should be used for 1 cup of milk
The solution is : the expression p in terms of m is p = 2/7 m.
Explanation:
If lana uses 14 cups of milk to make 4 bowls of pudding, we can express this as;
14cups = 4 bowls
If Andrew follows the same recipe and make p bowls of pudding and m cups of milk, this can be expressed as;
m cups = p bowls
Divide both expressions
14/m = 4/p
Cross multiply
4m = 14p
2m = 7p
7p = 2m
p = 2/7 m
Hence the expression p in terms of m is p = 2/7 m
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complete question:
Lana has a recipe for a pudding. She uses 14 cups of milk to make 4 bowls of pudding. Andrew will follow the same recipe. He will make p bowls of pudding and m cups of milk. Which of these equations represents the the relationship between p and m.A. p=1/7m B. p=7m C.p=5/2m D.p=2/7m
Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in europe because of their mobility, ease of operation, and low cost. suppose the maximum speed of a moped is normally distributed with mean value 46.8 km/h and standard deviation 1.75 km/h. consider randomly selecting a single such moped. a button hyperlink to the salt program that reads: use salt. (a) what is the probability that maximum speed is at most 50 km/h? (round your answer to four decimal places.) ___
(b) what is the probability that maximum speed is at least 49 km/h? (round your answer to four decimal places.) ___
(c) what is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations? (round your answer to four decimal places.) ___
(a) We need to find P(X ≤ 50), where X is the maximum speed of a moped. We have:
μ = 46.8 km/h
σ = 1.75 km/h
Using standardization, we get:
Z = (X - μ) / σ
Z follows a standard normal distribution. Therefore,
P(X ≤ 50) = P(Z ≤ (50 - μ) / σ)
= P(Z ≤ (50 - 46.8) / 1.75)
= P(Z ≤ 1.8286)
= 0.9641 (rounded to four decimal places)
Therefore, the probability that the maximum speed is at most 50 km/h is 0.9641.
(b) We need to find P(X ≥ 49). Using standardization, we get:
P(X ≥ 49) = P(Z ≥ (49 - μ) / σ)
= P(Z ≥ (49 - 46.8) / 1.75)
= P(Z ≥ 1.2571)
= 0.1038 (rounded to four decimal places)
Therefore, the probability that the maximum speed is at least 49 km/h is 0.1038.
(c) We need to find P(|X - μ| ≤ 1.5σ). Using standardization, we get:
P(|X - μ| ≤ 1.5σ) = P(-1.5 ≤ (X - μ) / σ ≤ 1.5)
= P(-1.5 ≤ Z ≤ 1.5)
= P(Z ≤ 1.5) - P(Z ≤ -1.5)
= 0.8664 - 0.0668
= 0.7996 (rounded to four decimal places)
Therefore, the probability that the maximum speed differs from the mean value by at most 1.5 standard deviations is 0.7996.
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Question 1 (Essay Worth 30 points)
(10.07 HC)
Consider the Maclaurin series: g of x is equal to sin of x is equal to x minus the quantity x cubed over 3 factorial end quantity plus the quantity x to the fifth power over 5 factorial end quantity minus x to the seventh power over 7 factorial end quantity plus x to the ninth power over 9 factorial end quantity minus dot dot dot plus the summation from n equals 0 to infinity of negative 1 to the nth power times the quantity x to the power of 2 times n plus 1 end quantity over the quantity 2 times n plus 1 end quantity factorial
Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x equals pi over 6 period (10 points)
Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x equals 3 times pi over 2 to approximate g(4.8). Explain why your answer is so close to −1. (10 points)
Part C: The series: summation from n equals 0 to infinity of negative 1 to the nth power times the quantity x to the power of 2 times n plus 1 end quantity over the quantity 2 times n plus 1 end quantity factorial has a partial sum S sub 5 is equal to 305353 over 362880 when x = 1. What is an interval, |S − S5| ≤ |R5| for which the actual sum exists? Provide an exact answer and justify your conclusion. (10 points)
Answer:
Maclaurin series is a power series expansion of a function about 0. The Maclaurin series of the function sin(x) is given by g(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + (x^9)/9! - ... + (-1)^n*(x^(2n+1))/(2n+1)!, where n is a non-negative integer.
Part A of the problem asks us to find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = pi/6. We know that the nth derivative of sin(x) is sin(x) if n is odd and cos(x) if n is even. So, the nth derivative of sin(4x) is cos(4x)*(4^n) if n is even and (-1)^(n/2)sin(4x)(4^n) if n is odd. Since we need the 4th degree term, we only need to consider the even derivatives up to the 8th derivative.
The first few even derivatives of sin(4x) are:
f'(x) = 4cos(4x)
f''(x) = -16sin(4x)
f'''(x) = -64cos(4x)
f''''(x) = 256sin(4x)
Evaluating these derivatives at x = pi/6, we get:
f(pi/6) = sin(4pi/6) = sin(2pi/3) = sqrt(3)/2
f'(pi/6) = 4cos(4pi/6) = 4cos(2pi/3) = -2
f''(pi/6) = -16sin(4pi/6) = -16sin(2pi/3) = -8sqrt(3)
f'''(pi/6) = -64cos(4pi/6) = -64cos(2pi/3) = 32
f''''(pi/6) = 256sin(4*pi/6) = 0
Using the Taylor series formula for the 4th degree term, we get:
f(pi/6) ≈ f(0) + f'(0)(pi/6) + f''(0)(pi/6)^2/2 + f'''(0)(pi/6)^3/6 + f''''(0)(pi/6)^4/24 + R4(pi/6)
= 0 + (-2)(pi/6) + (-8sqrt(3))(pi/6)^2/2 + 32*(pi/6)^3/6 + 0*(pi/6)^4/24 + R4(pi/6)
Simplifying and solving for R4(pi/6), we get:
R4(pi/6) = f(pi/6) - (-2)(pi/6) + (-8sqrt(3))(pi/6)^2/2 + 32*(pi/6)^3/6
= sqrt(3)/2 + pi/3 - 2sqrt(3)pi^2/81 + 16pi^3/243
The coefficient of the 4th degree term is 16*pi^3/243.
Part B of the problem asks us to use a 4th degree Taylor polynomial for sin(x) centered at x = 3*pi/2 to approximate g(4.8) and explain why our answer is so close to -1. The 4th degree Taylor polynomial for sin
For every 4 goals Anthony scored, Kyree scored 11 goals. How many goals will Kyree score if Anthony scored 60 goals?
Kyree would score 165 goals if Anthony scored 60 goals, given that for every 4 goals Anthony scores, Kyree scores 11 goals. This means Kyree scores at a faster rate than Anthony.
If Anthony scored 60 goals and for every 4 goals Anthony scored, Kyree scored 11 goals, we can set up a proportion to find out how many goals Kyree scored. We can use the fact that the ratio of goals scored by Anthony and Kyree is the same as the ratio of 4 to 11. We can express this as:
4/11 = 60/x
Solving for x, we can cross-multiply to get:
4x = 11 * 60
Dividing both sides by 4, we get:
x = 165
Therefore, Kyree would have scored 165 goals if Anthony scored 60 goals. This means that Kyree scores at a faster rate than Anthony, since for every 4 goals Anthony scores, Kyree scores 11 goals.
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what is the interquartile range? 65,67,67,84,96,98,98
The interquartile range for the data is 7.
We have
Data: 65,67,67,84,96,98,98
First Quartile,
Q1 = (n+1)/4
= (7+1)/4
= 8/4 th term
= 2nd term
= 27
Third quartile,
Q3 = 3(n+1)/4
= 3 x 2
= 6 th term
= 98
So, Interquartile range
= Q3- Q1
= 98- 67
= 7
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Chloe has enough sand to fill a rectangular sandbox with an area of
36 square units. She wants the outer edges of the sandbox to use as little material as possible.
Answer: If Chloe wants to minimize the amount of material used for the outer edges of the sandbox, she should make the sandbox a square shape.
Here's why:
- The area of a rectangle is given by the formula A = l x w, where A is the area, l is the length, and w is the width.
- For a square, the length and width are equal, so we can write A = s^2, where s is the length of a side.
- We know that the area of Chloe's sandbox is 36 square units, so we can write s^2 = 36.
- Solving for s, we get s = 6.
- Therefore, Chloe should make the sandbox a square with sides of length 6 units.
- This will minimize the amount of material used for the outer edges of the sandbox, since all sides will be the same length.
Step-by-step explanation: