The correct option is B) 0.0634.
1) Standard deviationThe table is shown as below:Number of Times Frequency 1 34 2 73 3 249 4 127 5 72 6 30 7 24 Total 915The given population contains 915 people. Let X be the number of times per week a person dines out for a person sampled at random from this population.The population standard deviation is given by the formula below:$$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$where N is the population size, X is the value of the individual element of the population, μ is the mean value of the population. $$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$$$= \sqrt{\frac{\sum X^2 - 2X\mu + \mu^2}{N}}$$We need to compute the variance first.$$\sigma^2 = \frac{\sum X^2 - 2X\mu + \mu^2}{N}$$$$= \frac{(1^2 \cdot 34 + 2^2 \cdot 73 + 3^2 \cdot 249 + 4^2 \cdot 127 + 5^2 \cdot 72 + 6^2 \cdot 30 + 7^2 \cdot 24) - 2\cdot 3.176 \cdot (34 + 2\cdot 73 + 3\cdot 249 + 4\cdot 127 + 5\cdot 72 + 6\cdot 30 + 7\cdot 24) + 3.176^2 \cdot 915}{915}$$$$= 3.5689$$Therefore, the population standard deviation is given by:$\sigma = \sqrt{3.5689} = 1.8911\approx 1.9$Hence, the correct option is C) 1.92) The probability of a binomial experiment can be calculated by the formula below:$${\rm P}(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$$where n is the number of trials, k is the number of successes, p is the probability of success for each trial, and $1-p$ is the probability of failure for each trial.Here, n = 15 and p = 0.4.We need to find the probability of getting 12 successes out of 15 trials. Hence, k = 12.Using the formula above, we get$${\rm P}(X=12) = \binom{15}{12}0.4^{12}0.6^{3}$$$$= \frac{15 \times 14 \times 13}{3 \times 2 \times 1} \cdot 0.4^{12} \cdot 0.6^{3}$$$$= 0.0633605376$$Hence, the correct option is B) 0.0634.
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Suppose you roll a special 37-sided die. What is the probability that one of the following numbers is rolled? 35 | 25 | 33 | 9 | 19 Probability = (Round to 4 decimal places) License Points possible: 1 This is attempt 1 of 2.
Answer:
5/37
Step-by-step explanation:
There are 37 possible outcomes when rolling a 37-sided die, so the probability of rolling any one specific number is 1/37.
To find the probability of rolling any of the given numbers (35, 25, 33, 9, or 19), we need to add the probabilities of rolling each individual number.
Probability of rolling 35: 1/37
Probability of rolling 25: 1/37
Probability of rolling 33: 1/37
Probability of rolling 9: 1/37
Probability of rolling 19: 1/37
The probability of rolling any one of these numbers is the sum of these probabilities:
1/37 + 1/37 + 1/37 + 1/37 + 1/37 = 5/37
So the probability of rolling any of the given numbers is 5/37, which is approximately 0.1351 when rounded to four decimal places.
Calculate (3.7 x 10¹⁴) + (9 × 10¹²) Give your answer in standard index form.
Answer:3.79*10^14
Step-by-step explanation:
370000000000000+9000000000000=379000000000000
=3.79 x 10^14
Answer:
(3.79×10^14)
Step-by-step explanation:
sjskakakzks
With respect to the average cost curves, the marginal cost curve: Intersects average total cost, average fixed cost, and average variable cost at their minimum point b. Intersects both average total cost and average variable cost at their minimum points Intersects average total cost where it is increasing and average variable cost where it is decreasing d. Intersects only average total cost at its minimum point
With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.
The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.
The marginal cost is the cost added to the overall cost of producing one extra unit of output. MC initially falls until it hits a minimum and then increases. When both AVC and ATC are at their minimal points, MC equals both. Also, when AVC and ATC are dropping, MC is lower; when they are growing, it is higher.Initially, the marginal cost of manufacturing is lower than the average cost of preceding units. When MC falls below AVC, the average falls. The average cost will reduce as long as the marginal cost is smaller than the average cost.When MC surpasses ATC, the marginal cost of manufacturing one more extra unit exceeds the average cost.Learn more about Marginal cost curve:
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Complete question:
With respect to the average cost curves, the marginal cost curve:
A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point
B) Intersects both average total cost and average variable cost at their minimum points
C) Intersects average total cost where it is increasing and average variable cost where it is decreasing
D) Intersects only average total cost at its minimum point
Who ever helps me, Get 100 points
Step-by-step explanation:
a) Area=144m²
side²= 144
side=12m
b) perimeter=32m
4×side=32
side=32/4
side=8m
Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to
0.008.
0.02.
0.03.
0.04.
0.208.
The proportion of students who can roll their tongues will be estimated and the margin of error for a 95 percent confidence interval for the true proportion of tongue rollers among students will be determined. There were 317 tongue rollers out of a sample of 400 students.
As a result, the sample proportion is 317/400 = 0.7925.
We'll compute the margin of error next. The margin of error (E) for a 95 percent confidence interval is:
E = zα/2 * sqrt[p(1 - p) / n]
where zα/2 is the z-score that corresponds to the level of confidence α/2, p is the sample proportion, and n is the sample size.
E = 1.96 * sqrt[0.7925 * (1 - 0.7925) / 400]E
= 1.96 * sqrt[0.7925 * 0.2075 / 400]E
= 1.96 * sqrt(0.00040875)E
= 1.96 * 0.0202E
= 0.0395
The margin of error is approximately 0.04 or 4 percent. Hence, the correct option is 0.04.
The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to 0.04
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(24p- 10) + (-22p - 2)
Answer:
2p - 12
Step-by-step explanation:
(24p - 10) + (-22p - 2)
24p - 10 - 22p - 2
2p - 12
So, the answer is 2p - 12
I need help on this question(PLEASEEEE)
Answer:
Yes, No, No.
Explanation:
For the first system of equations, we substitute x=2 and y=1 into each equation and we see that both are satisfied. So (2, 1) is a solution for this system.For the second system of equations, substituting x=2 and y=1 into each equation, we get 1=-3 and 1=-2, which are not true, so (2, 1) is not a solution for this system.For the third system of equations, substituting x=2 and y=1 into each equation, we get -3=-2 and 1=-3, which are not true, so (2, 1) is not a solution for this system.
Answer:
Place an X for the first box as [Yes], [No], [No]
Step-by-step explanation:
When we enter x=2 and y=1 into the first system of equations, we can see that both conditions are met. Thus the answer to this system is (2, 1).
When x=2 and y=1 are substituted into the second system of equations, we obtain 1=-3 and 1=-2, which are false, and so (2, 1) is not a solution for this system.
When x=2 and y=1 are substituted into the third system of equations, the results are -3=-2 and 1=-3, which are false, hence (2, 1) is not a solution for this system.
Put these numbers in order, from least to greatest. If you get stuck, consider using the number line. 3.5, -1, 4.8, -1.5, -0.5, -4.2, 0.5, -2.1, -3.5
The numbers are as follows, going from lowest to highest:
-4.2, -3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4.8.
How are numbers on a number line determined?We must compare and organize these numbers from least to greatest in order to put them in numerical order. The two smallest figures, which are -4.2 and -3.5, can be used as a starting point. Afterwards, we add the remaining numbers to the list in ascending order of least to largest after comparing them to these two. We arrive at the list above after continuing this approach.
Visualizing these numbers in order can alternatively be done by using a number line. In the number line, we can mark each number and arrange them in ascending order from left to right. We can see from the number line that the least number is -4.2.
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based on historical data, it takes students an average of 48 minutes with a standard deviation of 15 minutes to complete the unit 5 test. what is the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test?
Using central limit theorem, the probability that the class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is 0.00017332
What is the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test?We can use the Central Limit Theorem (CLT) to approximate the distribution of the sample mean completion time for the class. According to CLT, the distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean is given as 48 minutes, the population standard deviation is given as 15 minutes, and the sample size is 20. Therefore, the mean of the sample mean completion time is also 48 minutes, and the standard deviation of the sample mean completion time is 15/√20 ≈ 3.3541 minutes.
To find the probability that the class mean completion time is greater than 60 minutes, we can standardize the distribution of the sample mean completion time using the z-score formula:
z = (x - μ) / (σ / √n)
where x is the value we want to find the probability for (in this case, x = 60), μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (60 - 48) / (15 / √20) = 3.5777
Using a standard normal distribution table (or calculator), we can find the probability that a z-score is greater than 3.5777.
P = 0.00017332
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Use the equation, 8^2x = 32^x+3, to complete the following problems.
(a) Rewrite the equation using the same base.
(b) Solve for x. Write your answer in simplest form.
Given: ,8^2x= 32^x+3
a: (2³)^2x = (2⁵)^x+3
b: Solving, we get
2^6x = 2^5x+15
Since bases are same, we have
=>6x=5x+15
=> x = 15
what types of inferences will we make about population parameters? (select all that apply) causation estimation implied testing regression
The types of inferences that will be made about population parameters are causation, estimation, and regression on the basis of relationship.
What are the types of inferences?Causation is the process of showing the cause-and-effect relationship between two variables. In this case, one variable influences the other variable. This type of inference is significant when making decisions because it helps us understand how a change in one variable leads to a change in another variable.
Estimation: In statistical analysis, estimation refers to determining the possible value of an unknown population parameter. It is impossible to calculate the population parameters directly, and hence we use sample statistics to estimate them.
Regression analysis is the statistical technique used to identify the relationship between two variables. It involves estimating the coefficients of the model that best fit the data.
This type of inference helps us predict the value of a dependent variable based on an independent variable.
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Can someone help me with this
The number of bicycles they need to sell to make equal money is 5. The amount they would make is $500.
What is fixed and variable cost?In contrast to variable costs, which change depending on the volume of production or sales, fixed costs are expenses that remain constant. Rent, insurance, and salary are examples of fixed costs that are constant regardless of the volume of output or sales. Materials, labour, and shipping expenses are examples of variable costs that change according to the volume of output or sales.
Let us suppose the number of bicycle sold = x.
Then the equation for Jimmy is:
$250 + 50x
The equation for Tom is:
$400 + 20x
To make the same amount we equate the two equations as follows:
250 + 50x = 400 + 20x
30x = 150
x = 5
Substituting the value of x in equation 1 we have:
J = 250 + 50(5)
J = 250 + 250
J = 500
Hence, the number of bicycles they need to sell to make equal money is 5. The amount they would make is $500.
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Write down the smallest possible answer.
The answer of the given factor and multiplication term for the positive integers are 3.
What about integers?Positive, negative, and zero digit whole numbers are all included in the category of integers. They can be stated without any fractional or decimal components and are a subset of the real numbers. On a number line, integers can be visualized as positive numbers to the right of zero and negative numbers to the left.
Define Multiplication term:In mathematics, a multiplication term is a mathematical expression that involves the multiplication of two or more factors. The factors can be numbers, variables, or a combination of both. Multiplication terms are commonly represented using the multiplication symbol "×" or the dot "." symbol.
For example, in the expression 2x × 3y, the multiplication term is 2x × 3y, which involves the multiplication of the factors 2x and 3y.
According to the given information:If you want to find the smallest possible value of the given term we have that,The smallest factor of 15 is 1.
The smallest multiple of 3 is 3so, the smallest answer is 1x3 = 3.
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what is -0.33333333333 as a fraction
Answer:
-1/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
help, please!
how do i complete the cumulative frequency table?
This procedure is repeated for each interval until the overall frequency of 35 is reached.
what is frequency distribution?A data summary called a frequency distribution displays the frequency, or amount of occurrences, of each value or range of values in a data set. It is frequently displayed as a table or graph, with the values enumerated along one axis and the frequencies of those values listed along the other. The pattern or shape of a data collection can be described using frequency distributions, which can also be used to spot outliers or other unusual values. They can also shed light on the data's central trend and variability.
given
To complete a cumulative frequency table:
Class interval Frequency Cumulative frequency
0-10 5 5
10-20 8 13
20-30 12 25
30-40 7 32
40-50 3 35
Total 35 35
The number of the first class interval is 5.
For the second interval, we multiply the total frequency of 5 plus the frequency of 8 to get 13.
This procedure is repeated for each interval until the overall frequency of 35 is reached.
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The missing value in the cumulative table is 36.
The missing value in the cumulative table can be determined by examining the frequencies given in the table. Let's analyze the frequencies step by step:
1. The frequency for scores less than 145 is given as 16.
2. The frequency for scores less than 150 is given as 26.
3. The frequency for scores less than 155 is given as 36.
4. The frequency for scores less than 160 is not explicitly given in the table, but we can determine it by subtracting the frequency for scores less than 155 (36) from the frequency for scores less than 150 (26).
This gives us a value of [tex]26 - 36 = -10.[/tex]
Since a frequency cannot be negative, we can conclude that there is an error in the given table. The cumulative frequency for scores less than 160 should be 36 instead of -10.
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use the ka values for weak acids to identify the best components for preparing buffer solutions with the given ph values. name formula ka phosphoric acid h3po4 7.5 x 10-3 acetic acid ch3cooh 1.8 x 10-5 formic acid hcooh 1.8 x 10-4
To prepare a buffer solution with a given pH, we need to choose a weak acid and its conjugate base, such that the pKa of the weak acid is close to the desired pH.
The pKa is related to the Ka value as follows:
pKa = -log(Ka)
So, for each of the weak acids given, we can calculate the pKa:
Phosphoric acid (H3PO4): Ka = 7.5 x 10^-3, so pKa = -log(7.5 x 10^-3) = 2.12
Acetic acid (CH3COOH): Ka = 1.8 x 10^-5, so pKa = -log(1.8 x 10^-5) = 4.74
Formic acid (HCOOH): Ka = 1.8 x 10^-4, so pKa = -log(1.8 x 10^-4) = 3.74
Now, let's consider the desired pH values and choose the best components for buffer solutions:
For a pH of 2.5, the best choice would be phosphoric acid (pKa = 2.12).
For a pH of 4.5, the best choice would be formic acid (pKa = 3.74) or a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).
For a pH of 6.5, the best choice would be a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).
Note that a buffer solution can be prepared by mixing a weak acid and its conjugate base in roughly equal amounts, so the appropriate salt can be added to the acid to form the buffer solution. For example, to prepare an acetate buffer, one could mix acetic acid with sodium acetate.
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Suppose an angle has a measure of 140 degrees a. If a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is______ times as long as 1/360th of the circumference of the circle. b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long. What is the length of the arc subtended by the angle's rays? _______ cmc. Another circle is centered at the vertex of the angle. The arc subtended by the angle's rays is 70 cm long. - 1/360th of the circumference of the circle is _____ cm long. - Therefore the circumference of the circle is _______ cm
If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle. Also if a circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long then length of the arc subtended by the angle's rays 8.4 cm. Another circle is centered at the vertex of the angle then arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.
a.) To find the fraction of the circle's circumference subtended by the angle's rays, we divide the angle measure by 360 degrees:
fraction of circle's circumference = 140/360
Simplifying this fraction, we get:
fraction of circle's circumference = 7/18
To find the length of the arc subtended by the angle's rays, we multiply the fraction of the circle's circumference by the circumference of the circle. Let's call the circumference of the circle "C":
length of arc = (7/18)*C
We're also told that the length of 1/360th of the circumference is equal to 0.06 cm. So, we can write:
(1/360)*C = 0.06
Multiplying both sides by 360, we get:
C = 360*0.06 = 21.6 cm
Now, we can substitute this value of C into the expression for the length of the arc:
length of arc = (7/18)*C
length of arc = (7/18)*(21.6)
length of arc = 8.4 cm (rounded to one decimal place)
Therefore, the length of the arc subtended by the angle's rays is 8.4 cm.
b.) We're given that 1/360th of the circumference of the circle is 0.06 cm long. To find the length of the arc subtended by the angle's rays, we need to multiply 140/360 by 0.06:
length of arc = (140/360)*0.06
length of arc = 0.0233 cm (rounded to four decimal places)
Therefore, the length of the arc subtended by the angle's rays is approximately 0.0233 cm.
c.) We're told that the length of the arc subtended by the angle's rays is 70 cm. To find the circumference of the circle, we need to find the length of 1/360th of the circumference first. We can do this by dividing 70 by 1/360:
(1/360)*C = 70
Multiplying both sides by 360, we get:
C = 70*360 = 25,200 cm
Therefore, the circumference of the circle is 25,200 cm. We can also verify this by dividing the length of the arc by the fraction of the circumference subtended by the angle's rays:
length of arc = (7/18)*C
C = (18/7)*length of arc
C = (18/7)*70
C = 180 cm (rounded to one decimal place)
This is a different value than we got earlier, so we need to check our calculations. It turns out that the previous calculation was incorrect - we made a mistake when multiplying 7/18 by 21.6. The correct calculation gives us:
length of arc = (7/18)*C
length of arc = (7/18)*(21.6)
length of arc = 8.4 cm (rounded to one decimal place)
Now, we can calculate the circumference of the circle:
length of arc = (7/18)C
C = (18/7) *length of arc
C = (18/7) *70
C = 180 cm (rounded to one decimal place)
Therefore, the circumference of the circle is 180 cm.
Also, If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle.
b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long.The length of the arc subtended by the angle's rays 8.4 cm
c. Another circle is centered at the vertex of the angle.
The arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.
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describe (x-bar) in words, in the context of the problem. state the distribution of (x-bar), including the expected value and standard error
(x-bar) refers to the sample means in statistics. It is the average of all the data values in a sample. It is calculated by dividing the sum of all the data values by the sample size.
The distribution of (x-bar) follows a normal distribution, and its expected value is equal to the population mean. The standard error of (x-bar) is calculated by dividing the population standard deviation by the square root of the sample size. It is used to estimate how much the sample mean varies from the population mean.
Sample mean (x-bar) is a statistical concept used to calculate the average of a sample, and standard error is a measure of the variability of the sample mean. The distribution of the sample mean is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
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Convince Me! How does the unit rate describe Sergio's cycling speed? How is the unit rate helpful in determining how much farther Sergio must cycle in a given amount of time each time he increases his target speed?
The unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.
What is the formula for Speed?The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel. This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.
In the given question,
The unit rate describes Sergio's cycling speed by giving the distance he travels in a given amount of time, which is 6 miles per hour. This means that for every hour he cycles, he travels a distance of 6 miles.
By expressing Sergio's cycling speed as a unit rate, we can easily compare it to other speeds and determine how long it will take him to travel a certain distance.
For example, if Sergio increases his target speed to 8 miles per hour, we can use the unit rate to calculate how much farther he must cycle in a given amount of time.
If he wants to cycle for 2 hours, we know that he will travel 6 x 2 = 12 miles at his original speed of 6 miles per hour.
If he wants to cycle for the same 2 hours at a speed of 8 miles per hour, we can use the unit rate to calculate that he will travel 8 x 2 = 16 miles.
This means that he must cycle an additional 4 miles to reach his target distance.
Overall, the unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.
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A train leaves the station traveling north at 85 km/h. Another train leaves at the same time and travels south at 95 km/h. How long will it take before the trains are 990 km apart
First before two trains were [tex]990[/tex] kilometers apart, it will require [tex]5.5[/tex] hours.
What is the mathematical formula for train?Train speed is calculated as total distance traveled divided by travel time. The time it takes for two trains to pass each other is equal to (a+b) / (x+y) if the lengths of the trains, say a or b, are known and they are going at speeds of y and x, respectively.
What fuels trains use?Typically, a locomotive fueled by electricity or diesel powers trains. If there are several route networks, complicated signaling methods are used. One of the quickest forms of land transportation is rail.
[tex]distance = rate * time[/tex]
distance between trains [tex]= (85 km/h) * t + (95 km/h) * t[/tex]
distance between trains [tex]= (85 + 95) km/h * t[/tex]
distance between trains [tex]= 180 km/h * t[/tex]
Now, we can set up an equation to solve for the time it takes for the trains to be [tex]990[/tex] km apart:
[tex]180 km/h * t = 990 km[/tex]
[tex]t = 990 km / 180 km/h[/tex]
[tex]t = 5.5[/tex] hours
Therefore, it will take [tex]5.5[/tex] hours before the two trains are [tex]990[/tex] km apart.
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What is the gradient of the line segment between the points 2,4 and 4,6
Answer:
1
Step-by-step explanation:
Given values are:
x1 y1=(2,4)
x2 y2=( 4,6)
slop=(6-4)divide (4-2)=1
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500
Answer:
The following statements about Josiah's solution are true:
He found the proportion of rock songs to the total number of songs correctly: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction.
He solved the proportion correctly: StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
Therefore, the statements that are true are:
He found the proportion of rock songs to the total number of songs correctly.
He solved the proportion correctly.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
A random sample of size 64 is to be used to test the null hypothesis that for a certian age group
the mean score on an achievement test (the mean of a normal population with sigma square (variance)variancesigma square= 256) is
less than or equal to 40 against the alternative that it is greater than 40. If the null hypothesis
is to be rejected if and only if the mean of the random sample exceeds 43.5, nd
(a) the probabilities of type I errors when\mu=37, 38, 39, and 40;
(b) the probabilities of type II errors when\mu= 41, 42, 43, 44, 45, 46, 47, and 48.
Also plot the power function of this test criterion.
Answer:
A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42
Step-by-step explanation:
A right triangular prism is shown.
A right triangular prism is shown. The right triangles have sides with lengths 15 and 8. The hypotenuse has a length of 17. The height of the prism is 15.
What is the volume of the prism?
900 cubic units
1,020 cubic units
1,800 cubic units
2,312 cubic units
Therefore , the solution of the given problem of volume comes out to be the response is 900 cubic units.
What precisely is volume?A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, understanding an object's volume is necessary to calculate its measurements. It is standard practice to convert the weight of an object into mass units like grams and kilograms.
Here,
The formula V = Bh, when B is the area of the bottom and h is the height of the prism, determines the volume of a right triangle prism.
The prism has an area of because its foundation is a right triangle with 8 and 15-foot-long legs.
=> B = (1/2)bh = (1/2)(8)(15) = 60
The prism's height is specified as 15 inches.
As a result, the prism's capacity is:
=> 900 cubic units are equal to V = Bh = 60(15).
Therefore, the response is 900 cubic units.
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Answer:
900 cubic units
Step-by-step explanation:
use a direct proof to show that every odd integer is the difference of two squares. [hint: find the difference of the squares of k 1 and k where k is a positive integer.]
Yes, every odd integer can be written as the difference of two squares.
To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.
To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.
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check 5 greater than or equal to (y-2)
Answer: 5 ≥ y-2 is equivalent to y ≤ 7.
Step-by-step explanation: To check if 5 is greater than or equal to y-2, we need to isolate the variable y on one side of the inequality sign.
5 ≥ y - 2
First, we can add 2 to both sides to get rid of the subtraction of 2 on the right side:
5 + 2 ≥ y - 2 + 2
7 ≥ y
Therefore, we can see that y is less than or equal to 7 for this inequality to hold true.
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour. )
The speed (in knots) at which the distance between the ships A and B is changing at 6 PM is given as 36 knots or 36 nautical miles per hour.
Consider that the ship A is in the west direction and the ship B is in the north direction and both the ships are in regular motion of speed which is 16 knots and 15 knots and the distance between them is 50 nautical miles.
Using the Pythagoras theorem, the relation of the distance x which represents the distance between ships at 6PM to the distances that each ship has travelled can be given as follows:
x^2 = (50 + 16t)^2 + (15t)^2
where, t is the number of hours that has passed since noon.
Differentiating both sides of the above equation with respect to time, we get:
2x*(dx/dt) = 2(50 + 16t)*(16) + 2*(15t)*(15)
t = 6, at 6 PM, therefore substituting the value and solving, we get:
2x(dx/dt) = 2[(50 + 16(6)]*(16) + 2*[15(6)]*(15)
2x(dx/dt) = 4194
dx/dt = 2097/x
Now substituting the value of x that corresponds to 6 PM:
x^2 = (50 + 16(6))^2 + (15(6))^2
x^2 = 3385
x = √3385 ≅ 58.19
Putting this value in dx/dt, we get:
dx/dt = 2097/58.19 ≅ 36.00 knots
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Sarah is a healthy baby who was exclusively breast-fed for her first 12 months. Which of the following is most likely a description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population? 85th percentile at 3 months; 85th percentile at 6 months; 9oth percentile at 9 months; 95th percentile at 12 months 75th percentile at 3 months; 40th percentile at 6 months; 25th percentile at 9 months; 25th percentile at 12 months 30th percentile at 3 months; 50th percentile at 6 months; 70th percentile at 9 months; 80th percentile at 12 months 25th percentile at 3 months; 25th percentile at 6 months; 25th percentile at 9 months; 25th percentile at 12 months
The 12 months of age) as percentiles of the CDC growth chart reference population.
The most likely description of Sarah's weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population is: 85th percentile at 3 months; 85th percentile at 6 months; 90th percentile at 9 months; 95th percentile at 12 months.What is percentile in statistics?In statistics, a percentile is a value below which a specific percentage of observations in a group falls. It is used to split up data into segments that represent an equal proportion of the entire group, resulting in a data set split into 100 equal portions, with each portion representing one percentage point. Sarah's weight is in the 85th percentile at 3 months, 85th percentile at 6 months, 90th percentile at 9 months, and 95th percentile at 12 months is a most likely description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population.
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Anyone know the answer?
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
what is volume ?The quantity of space occupied by a three-dimensional object is measured by its volume. Units like cubic meters (m3), cubic centimeters (cm3), or cubic inches (in3) are frequently used to quantify it. Depending on the shape of the item, different formulas can be used to determine its volume. For instance, the volume of a cube can be calculated by multiplying its length, breadth, and height, while the volume of a cylinder can be calculated by dividing the base's area (typically a circle) by the cylinder's height.
given
We must apply the calculation for the volume of a cone's frustum in order to determine the volume of the Styrofoam collar:
[tex]V = (1/3)\pi h(R^2 + Rr + r^2)[/tex]
where h is the height of the frustum, r is the small radius, and R is the large radius.
Given the numbers, we can determine:
R = 5 in.
3 centimeters is r.
24 inches tall
With these numbers entered into the formula, we obtain[tex]V = (1/3)\pi (24)(5^2 + 5*3 + 3^2)\\\\ 179.594 cubic inches[/tex]
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
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4x 2 +6x−13=3x 2 to the nearest tenth.
The solutions to the equation are x = -4 and x = 1.
What is quadratic formula?The quadratic formula, which is often employed in the disciplines of mathematics, physics, engineering, and other sciences, is a potent tool for resolving quadratic problems. We must first get the values of a, b, and c from the quadratic equation in order to apply the quadratic formula. To get the answers for x, we then enter these values as substitutes in the formula and simplify.
The given equation is 4x² + 6x - 13 = 3x².
Rearranging the equation we have:
x² + 6x - 13 = 0
The quadratic formula is given as:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a = 1, b = 6, and c = -13.
x = (-6 ± √(6² - 4(1)(-13))) / 2(1)
x = (-6 ± √(100)) / 2
x = (-6 ± 10) / 2
x = -8/2 or x = 2/2
x = -4 or x = 1
Hence, the solutions to the equation are x = -4 and x = 1
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