The volume of the sphere given to the nearest tenth is 329,167.37 cubic millimeters.
What is the volume the sphere?surface area of the sphere = 23,047 square millimeters
Surface area of a sphere = 4πr²
23,047 = 4 × 3.14 × r²
23,047 = 12.56r²
divide both sides by 12.56
r² = 23,047 / 12.56
r² = 1834.952229299363
Find the square root of both sides
r = √1834.952229299363
r = 42.84 millimeters
Volume of a sphere = 4/3πr³
= 4/3 × 3.14 × 42.84³
= 4/3 × 3.14 × 78,622.778304
= 987,502.09549824 / 3
= 329,167.36516608
Approximately,
Volume = 329,167.37 cubic millimeters
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Given the following ANOVA table for three treatments each with six observations: df Mean square Source Treatment Error Total Sum of squares 1,118 1,074 2,192 What is the computed value of F? Multiple Choice 7.45 7.81 8.81 8 O
Based on the given ANOVA table, we can compute the F-value as follows:
F = (Mean Square Treatment) / (Mean Square Error)
Given:
Mean Square Treatment = 1,118
Mean Square Error = 1,074
F = (1,118) / (1,074) ≈ 1.04
None of the provided multiple-choice options (7.45, 7.81, 8.81, 8) match the computed F-value of 1.04. Please double-check the given information or the available answer choices.
An ANOVA table (analysis of variance table) is a table used in statistical analysis to summarize the results of an analysis of variance test. It typically includes the following components:
Source of Variation: This column lists the different sources of variation in the data, such as treatment groups or error.
Degrees of Freedom (df): This column lists the degrees of freedom associated with each source of variation.
Sum of Squares (SS): This column lists the sum of squared deviations from the mean for each source of variation.
Mean Square (MS): This column lists the sum of squares divided by the degrees of freedom for each source of variation.
F Ratio: This column lists the F statistic, which is the ratio of the mean square for each source of variation divided by the mean square for error.
Significance (p-value): This column lists the p-value associated with the F statistic for each source of variation, which indicates the probability of obtaining such a large F value by chance.
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Charlie has 2 gallons of milk. He uses 2 pints a day. How long can he use the milk?
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
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!
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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A pattern on a wall is formed by rhombus shapes. Each rhombus has diagonals of 6.8 inches and 9.5 inches. What is the area covered by one rhombus shape?
The area covered by one rhombus shape is,
⇒ A = 32.2 in²
We have to given that;
A pattern on a wall is formed by rhombus shapes.
And, Each rhombus has diagonals of 6.8 inches and 9.5 inches.
Now, We know that;
For the area of the rhombus, you can use the formula ;
⇒ A = (d1 × d2) / 2,
where d1 and d2 are the lengths of the two diagonals.
Here, Each rhombus has diagonals of 6.8 inches and 9.5 inches.
Hence, We get;
⇒ A = (d1 × d2) / 2,
⇒ A = (6.8 × 9.5) / 2
⇒ A = 32.2 in²
Thus, The area covered by one rhombus shape is,
⇒ A = 32.2 in²
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what is x divided by 3
you conduct a hypothesis test. assuming you have made no errors in your calculations, what should we conclude if the test statistic ends up being negative? a. the sample size is small. b. the sample statistic is larger than the claimed population parameter. c. it is unlikely the results would have occurred just by chance alone. d. the sample statistic is smaller than the claimed population parameter. e. the null hypothesis is false.
If the test statistic ends up being negative the sample statistic is smaller than the claimed population parameter that is option a.
In hypothesis testing, the test statistic measures how many standard errors the sample statistic is away from the hypothesized population parameter under the null hypothesis. A negative test statistic indicates that the sample statistic is smaller than the claimed population parameter, which means that the observed effect is in the opposite direction of what was expected under the null hypothesis.
Therefore, if the test statistic ends up being negative, we can conclude that the sample statistic is smaller than the claimed population parameter. This suggests that there may be a significant difference between the sample and population, which could be due to factors such as sampling error or a true difference in the population.
Options a, b, and c are not correct because the sample size, sample statistic, and probability value do not determine the sign of the test statistic. Option e is not necessarily true because a negative test statistic does not always lead to rejection of the null hypothesis; it depends on the significance level and the directionality of the test.
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You are offered a job with a start $39000 turning the 1st year with an annual increase of 10% per year in the 2nd year. beginning in year 2 your to your salary will be 1.1 times What is was in the previous year? What can we expect in the following year for the job?
The salary of the previous year is $36,000 and salary of the following year is $43,560.
Given that, You are offered a job with a start $39000 turning the 1st year with an annual increase of 10% per year in the 2nd year.
Beginning in year 2 your to your salary will be 1.1 times
1st year: $36,000
According to the question, we can formulate 36,000(1.1)³
2nd year: $36,000(1.1) = $39,600
3rd year: $39,600(1.1) = $43,560
4th year: $43,560(1.1) = $47,916
Therefore, the salary of the previous year is $36,000 and salary of the following year is $43,560.
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Assume that the carrying capacity for the US population is 800 million. Use it and the fact that the population was 282 million in 2000 to formulate a logistic model for the US population. (Let t = 0 correspond to the year 2000. Use k for your constant.) P (t) = ____ millions
(t) = 326millions. The logistic model for the US population would be:
P(t) = 800 / (1 + e^(-k(t-2000)))
Where P(t) is the population in millions at time t (measured in years after 2000), k is the growth rate constant, and e is the base of the natural logarithm.
Using the fact that the population was 282 million in 2000, we can solve for k:
282 = 800 / (1 + e^(-k(0-2000)))
282(1 + e^(-k(2000))) = 800
1 + e^(-k(2000)) = 2.83687943
e^(-k(2000)) = 1.83687943
-k(2000) = ln(1.83687943)
k = -ln(1.83687943) / 2000
k ≈ 0.0071
Now we can plug in the value of k to get the logistic model for the US population:
P(t) = 800 / (1 + e^(-0.0071(t-2000)))
So, for example, the population in 2020 (t = 20) would be:
P(20) = 800 / (1 + e^(-0.0071(20-2000))) ≈ 326 million
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If the probability that the Islanders will beat the Rangers in a game is 0.69, what is the probability that the Islanders will win at most two out of five games in a series against the Rangers? Round your answer to the nearest thousandth.
0.056 is the probability of the Islanders winning at most two out of five games
Use the binomial probability formula:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of successes in five trials.
The probability of getting zero successes (the Islanders losing all five games) is:
P(X = 0) = (1 - 0.69)⁵ = 0.00028 (rounded to 3 decimal places)
The probability of getting one success (the Islanders winning one game and losing four) is:
P(X = 1) = ⁵C₁ * 0.69¹ * (1 - 0.69)⁴ = 0.0067 (rounded to 3 decimal places), where 5C1 is the binomial coefficient, which represents the number of ways to choose one success out of five trials.
The probability of getting two successes (the Islanders winning two games and losing three) is:
P(X = 2) = ⁵C₂ * 0.69² * (1 - 0.69)³ = 0.0495 (rounded to 3 decimal places).
Therefore, the probability of the Islanders winning at most two out of five games is:
P(X ≤ 2) = 0.00028 + 0.0067 + 0.0495 = 0.056 (rounded to 3 decimal places).
So, the probability of the Islanders winning at most two out of five games is approximately 0.056.
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he image of trapezoid ABCD has coordinates A′(–2, –5), B′(–1, –2), C′(2, –2), and D′(3, –5). It was translated by the rule T–1, –3(x, y). Which diagram shows the pre-image? On a coordinate plane, a trapezoid has points A (negative 1, negative 2), B (0, 1), C (3, 1), D (4, negative 2). On a coordinate plane, a trapezoid has points A (negative 3, negative 2), B (negative 2, 1), C (1, 1), D (2, negative 2). On a coordinate plane, a trapezoid has points A (negative 4, negative 5), B (negative 3, negative 2), C (0, negative 2), D (1, negative 5). On a coordinate plane, a trapezoid has points A (0, negative 2), B (1, 1), C (4, 1), D (5, negative 2).
The diagram that shows the pre-image? On a coordinate plane, a trapezoid has points is A (negative 1, negative 2),
What is a trapezoidA trapezoid is a quadrilateral that has at least one pair of parallel sides.
Here, the image of trapezoid ABCD has coordinates A′(–2, –5), B′(–1, –2), C′(2, –2), and D′(3, –5) and was translated by the rule T–1, –3(x, y).
The diagram that shows the pre-image is that on a coordinate plane, a trapezoid has points A (negative 1, negative 2).
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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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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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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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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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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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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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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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(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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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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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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A lantern is represented by the pentagonal prism shown.
A pentagonal prism is shown. The volume is three hundred eighty-six and one tenth cubic inches. The height is sixteen and five tenths inches.
What is the area of the base of the lantern? Explain your reasoning. Round to the nearest tenth.
The area of the base of the lantern is approximately 59.6 square inches.
We have,
The formula for the volume of a pentagonal prism is:
V = (1/4) x (5tan(π/5) x s)² x h
where s is the length of each side of the base, and h is the height of the prism.
In this case, we are given the volume of the prism as 386.1 cubic inches and the height as 16.5 inches.
We can use this information to solve for the area of the base as follows:
386.1 = (1/4) x (5tan(π/5) x s)² *x16.5
Simplifying, we get:
(5tan(π/5) x s)² = (386.1 x 4) / (16.5 x 5tan(π/5))²
Taking the square root of both sides, we get:
5tan(π/5) x s = √[(386.1 x 4) / (16.5 x 5tan(π/5))²]
Simplifying, we get:
s = √[(386.1 x 4) / (16.5 x 5tan(π/5))]
Using a calculator, we get:
s ≈ 4.88 inches
Now that we have the length of one side of the base, we can use the formula for the area of a regular pentagon to find the area of the base:
A = (5/4) x s² x tan(π/5)
Using a calculator, we get:
A ≈ 59.6 square inches
Therefore,
The area of the base of the lantern is approximately 59.6 square inches.
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The height above the ground in meters of a model rocket on a particular launch can be
modeled by the equation h = -4.9t2 + 102t + 100, where t is the time in seconds after its engine
burns out 100 m above the ground. Will the rocket reach a height of 600 m? Use the
discriminant to explain your answer.
The height above the ground in meters of a model rocket on a particular launch can be modeled by the equation h = -4.9[tex]t^{2}[/tex] + 102t + 100, where t is the time in seconds after its engine burns out 100 m above the ground. The rocket reach a height of 600 m.
To determine whether the rocket will reach a height of 600 m, we need to solve the equation
-4.9[tex]t^{2}[/tex] + 102t + 100 = 600
We can simplify this equation by moving all the terms to one side
-4.9[tex]t^{2}[/tex] + 102t - 500 = 0
Now we can use the quadratic formula to solve for t
t = (-b ± [tex]\sqrt{(b^{2}-4ac) }[/tex]) / 2a
In this case, a = -4.9, b = 102, and c = -500. By putting these values into the formula gives
t = (-102 ±[tex]\sqrt{102^{2}-4(-4.9)(-500) }[/tex])) / 2(-4.9)
Simplifying the expression under the square root
t = (-102 ± [tex]\sqrt{10404}[/tex]) / -9.8
t = (-102 ± 102) / -9.8
t = 0 or 10.408
Since we are interested in the time after the engine burns out (100 m above the ground), we can discard the solution t = 0. Therefore, the rocket will reach a height of 600 m at t = 10.408 seconds.
To use the discriminant to explain our answer, we can look at the expression under the square root in the quadratic formula
[tex]b^{2}[/tex] - 4ac
If this expression is positive, there are two real solutions to the quadratic equation, which means the rocket will reach a height of 600 m at some point in its flight. If the expression is zero, there is one real solution, which means the rocket just reaches a height of 600 m at its highest point and then falls back down. If the expression is negative, there are no real solutions, which means the rocket never reaches a height of 600 m.
In this case, the expression [tex]b^{2}[/tex] - 4ac is equal to 10404, which is positive.
Hence, there are two real solutions to the equation, and the rocket will reach a height of 600 m.
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the population of the city Martin was approximately 12,420 in the year 2005 and has been continuously growing at a rate of 1.6% each year
The function that describes the population of Martin is[tex]P(t) = 12,420 \times (1 + 0.016)^t[/tex]
The predicted population of Martin in 2015 is 14557
The predicted population of Martin in 2002 is 10,658
The function that describes the population of Martin as a function of the number of years t, since 2005, can be written as:
[tex]P(t) = 12,420 \times (1 + 0.016)^t[/tex]
where P(t) is the population of Martin t years since 2005.
To predict the population of Martin in 2015, we need to substitute t = 10 into the equation:
P(10) = 12,420 × (1 + 0.016)¹⁰
= 14556.5
Therefore, the predicted population of Martin in 2015 is approximately 14556.5 people.
To predict the population of Martin in 2002, we need to find the number of years between 2005 and 2002, which is 3 years.
We can substitute t = -3 into the equation:
P(-3) = 12,420 × (1 + 0.016)⁻³)
= 10,658
Therefore, the predicted population of Martin in 2002 is approximately 10,658 people.
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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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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
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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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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HELP PLEASE I WILL GIVE BRAINLIEST AND 50 POINTS EACH ONLY IF U HELP PLS PLS
Answer:
4 cm^2
Step-by-step explanation:
The area of a triangle is Base * Height / 2
Base: 4
Height: 2
2 * 4 = 8
8 / 2 = 4 cm^2
Remember, a triangle is half of a rectangle/square, which is why we half the total area!