Beth's number, which indicates 60 parts out of 100, can be expressed as 60%, 0.60, 60/100, or in simplest form, 3/5. These representations are commonly used in mathematics to show percentages and their equivalent values.
Beth writes a number that shows 60 parts out of 100. In mathematics, expressing a part out of 100 is essentially describing a percentage. So, Beth's number could be expressed in several ways that all represent 60 out of 100. The simplest form would be 60%, which directly translates to 60 per 100. Another possible representation could be 0.60, which is the decimal form equivalent to 60%. If we were to convert this percentage into a fraction, it would be
60/100, which can also be simplified to
3/5. It cannot be a number such as N(60, 5.477) which suggests a normal distribution with a mean of 60 and a standard deviation of 5.477, nor can it be .9990 which is not equivalent to 60 parts out of 100 in any common mathematical representation.
On the Red Trail, the distance between point A and point B is 7.3 kilometers. You walked this distance back and forth. What is the distance you walked in meters?
Answer:
[tex]d = 14,600\,km[/tex]
Step-by-step explanation:
The distanced travelled is equal to twice the distance between points A and B. The distance that was walked in meters is:
[tex]d = 2\cdot (7.3\,km)\cdot \left(\frac{1000\,m}{1\,km} \right)[/tex]
[tex]d = 14,600\,km[/tex]
Final answer:
The total distance walked on the Red Trail, back and forth, when converted from kilometers to meters, is 14,600 meters.
Explanation:
The question asks for the total distance walked in meters if a person walks from point A to point B and back on the Red Trail, where the distance between point A and point B is 7.3 kilometers.
Firstly, we know that 1 kilometer equals 1,000 meters. Therefore, to find the distance in meters for a single trip from point A to point B, we multiply 7.3 kilometers by 1,000:
7.3 km × 1,000 = 7,300 metersSince the trip was made back and forth, the total distance covered is twice the distance of a single trip:
Total distance = 2 × 7,300 meters = 14,600 metersTherefore, the total distance walked back and forth on the Red Trail, in meters, is 14,600 meters.
If the area of a circle is 121 pi square units, what is its diameter
Answer:22
Step-by-step explanation:
diameter=d
Area=121π
area of circle=π x (d/2)^2
121π=π x d^2/4
121π=πd^2/4
Cross multiplying we get
121π x4=πd^2
484π=πd^2
Divide both sides by π
484π/π=πd^2/π
d^2=484
Taking the square roots of both sides we get
d=√(484)
d=22 diameter=22
A graph shows the horizontal axis numbered 2 to 8 and the vertical axis numbered 10 to 50. A line increases from 0 to 4 then decreases from 4 to 9.
Which type of function best models the data shown on the scatterplot?
Answer:
Quadratic
Step-by-step explanation:
Took a test and got it right
Answer:
quadratic
Step-by-step explanation:
In a random sample of 125 highway bridges around the country, 75 were in need of repair.
What is the sample proportion (point estimate) of highway bridges that need repaired? (Only type ONE decimal place)
Answer:
The sample proportion of highway bridges that need repaired is 0.6.
Step-by-step explanation:
The sample proportion of highway bridges that need repaired is the number of bridges in need of repair divided by the number of bridges around the country.
In this question:
75 bridges in need of repair, out of 125. So
75/125 = 0.6
The sample proportion of highway bridges that need repaired is 0.6.
If f(x) = 2x – 1 and g(x) = 3x + 5, then (f o g)(x) is equal to
Answer:
(f◦g)(x) = 6x +9
Step-by-step explanation:
Use g(x) as the argument to f(x) and simplify.
(f◦g)(x) = f(g(x)) = f(3x +5) = 2(3x +5) -1
(f◦g)(x) = 6x +9
Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 735 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion?
Answer:
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1255, \pi = \frac{735}{1255} = 0.5857[/tex]
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 - 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.5584[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 + 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.6130[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Answer:
The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
Step-by-step explanation:
The interest is the real proportion of Americans who feel that the environment is a major issue with them. The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
Confidence interval
The confidence interval for the true proportion of interest is given by this:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
We want an interval at 95% of confidence, so then the significance level is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value for this case are:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
Replacing into the confidence interval formula we got:
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
14/10 divided by blank equals seven
Answer:
14/10=1.4
7/1.4=5
1.4x5=7
Step-by-step explanation:
In the given equation 14/10 divided by a certain number equals seven, the missing number is 0.2
Explanation:The subject of this question is Mathematics and it appears to be suitable for a Middle School grade level. You're asking for a number that, when 14/10 or 1.4 is divided by it, the result is seven.
To solve it, one can set it up as an equation in the form of 1.4 / x = 7. To find 'x', multiply both sides by 'x' to get rid of 'x' on the denominator of the left side, so the equation becomes 1.4 = 7x. The next step is to isolate 'x' by dividing both sides of the equation by 7. Solving this equation gives x = 1.4/7 = 0.2.So, 14/10 divided by 0.2 equals seven.
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"If a method produces a random error for each measurement of 4%, but a percent error of equal to or less than 1% is required for this value for later analysis, what is the minimum number of measurements that must be collected and averaged? You will need to solve equation 1 for the value of n that meets the criterion of a 1% error in the average."
Answer:
N = 16 measurements
Step-by-step explanation:
A method produces a random error for each measurement of 4%
A percent error of equal to or less than 1% is required.
We want to find out the minimum number of measurements that must be collected.
The standard error is given by
[tex]SE = \frac{S}{\sqrt{N} } \\[/tex]
Where s is the standard deviation and N is the number of measurements.
We are given standard deviation equal to 4% and SE equal to 1%
So re-arranging the above equation for N
[tex]\sqrt{N} = \frac{S}{SE} \\N = (\frac{S}{SE})^{2}\\N = (\frac{0.04}{0.01})^{2}\\N = 16[/tex]
Therefore, a minimum 16 number of measurements are needed.
Translate the triangle left 1 units and up 5 units. What are the coordinates of point C after the translation?
Answer:
b++nfr
Step-by-step explanation:
jjkiki
HELP!! pls pls pls
The average price of a movie ticket in 1990 was $4.22. Since then, the price has increased by approximately 3.1% each year. Write an exponential function to model this situation, then find the price of a ticket in 2016. Is this growth or decay?
Answer:
$9.33
Exponential growth.
Step-by-step explanation:
The formula for an exponential function is:
abˣ = y OR
a(1 + r)ˣ = y
a is the initial value (4.22)
r is the rate of increase (3.1% or 0.031 in dec. form) where 1 + r is b
x is the time (26 years)
y is the ending value.
If we plug those values in, the equation will turn out to be 4.22(1 + 0.031)²⁶ = y
Plug it into a calculator and you will get 9.333354216
This is exponential growth because x, the initial value, increases to get to y, the ending value.
Which of the following is equivalent to tan(x) * csc(x) when simplified?
O
O
O
sec(x)
cos(x)
sin(x)
csc(x)
O
cot(x) + 1
Answer:
Sec(x)
Step-by-step explanation:
Tan(x) = Sin(x)/Cos(x)
Csc(x) = 1/Sin(x)
Sin(x) 1
--------- . ---------
Cos(x) Sin(x)
Sin(x) cancel
1
--------- =
Cos(x)
Sec(x)
The simplified expression is,
⇒ sec x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ tan x × csc x
Now,
We can simplify as;
⇒ tan x × csc x
⇒ ( sin x/ cos x ) × (1 / sin x)
⇒ 1 / cos x
⇒ sec x
Thus, The simplified expression is,
⇒ sec x
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Plot the point (3 comma StartFraction 7 pi Over 4 EndFraction ), given in polar coordinates, and find other polar coordinates (r comma theta )of the point for which the following are true. (a) r greater than 0 comma negative 2 pi less than or equals theta less than 0 (b) r less than 0 comma 0 less than or equals theta less than 2 pi (c) r greater than 0 comma 2 pi less than or equals theta less than 4 pi
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for the step by step solution of the given problem.
The attached file have the solved problem.
Answer: B
Step-by-step explanation:
just did it
What function do you use to find the angle of a vector, when you know its components?
Answer:
[tex]\theta = tan^{-1}(\frac{y}{x})[/tex]
Step-by-step explanation:
If we are given components of a vector then we can find the angle between them.
Suppose we are given a vector v
[tex]v = (x, y)[/tex]
Where x is the horizontal component and y is the vertical component.
The angle can be found by using
[tex]tan(\theta)=\frac{y}{x}\\\\\theta = tan^{-1}(\frac{y}{x})[/tex]
The magnitude of the vector v can be found using
[tex]v = \sqrt{x^{2}+y^{2}}[/tex]
Example:
Lets do a quick example:
[tex]v = (2, 4)[/tex]
The angle of the vector is
[tex]tan(\theta)=\frac{4}{2}\\\\\theta = tan^{-1}(\frac{4}{2})\\\\\theta = 63.43^{\circ}[/tex]
The magnitude of the vector is
[tex]v = \sqrt{x^{2}+y^{2}}\\\\v = \sqrt{2^{2}+4^{2}}\\\\v = \sqrt{4+16}\\\\v = \sqrt{20}\\\\v = 4.47[/tex]
Jean-Patrick found an old unopened bag of lawn fertilizer in his shed. The bag weighs 36 pounds, and the instructions claim it can cover 10,000 ft^2. If his lawn is 7,000 ft^2, how many pounds will he need? Round to the nearest tenth if needed.
Answer:
25.2
Step-by-step explanation:
Weight of one bag of lawn fertilizer = 36
area one bag of lawn fertilizer can cover = 10,000 ft^2
Total area of lawn in the given problem = 7,000 ft^2
no. of bags of lawn fertilizer needed to cover the lawn = total area of lawn in the given problem / area, one bag of lawn fertilizer can cover
= 7,000/10,000 = 7/10 = 0.7 bags
Weight of full bags has 36 pounds of lawn fertilizer.
therefore,
Pounds of lawn fertilizer in 0.7 part of bag = 36 * 0.7 = 25.2 pounds (Answer)
After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you roll it 48 times, recording the number of times each face appears. Do these results cast doubt on the die is fairness
Answer:
The results are
Face Count Face Count
1 6 4 9
2 12 5 5
3 8 6 20
These results are not fair, because they clearly shows that the dice was tricked. We deduct this by observing that he obtained the face 6, 20 times out of 48, which represents 42% of chances to get that result.
Now, a fair dice must have equal probabilities per side, or an approximation to that at least. In this case, we don't have such equality.
So, next time your little brother roll the dice, we probably will get 6.
To check the fairness of a die, use statistical testing. Expect each face to appear equally in a fair die. Discrepancies suggest possible bias, but randomness can make results vary. Conduct a hypothesis test, like Chi-square, for a more statistically sound conclusion.
Explanation:To verify the fairness of the die, we need to conduct a hypothesis test. With a fair six-sided die, each face (numbered 1 to 6) should have an equal probability of appearing on any given roll. That means, if you roll the die 48 times, each face should theoretically appear about 8 times (48 rolls divided by 6 faces).
If the observed frequency of each face being rolled significantly varied from 8, it would suggest that the die might be biased. However, keep in mind that random chance can also result in each face not appearing exactly 8 times. Therefore, a hypothesis test would have more statistical power if more repetitions were performed.
Conduct the hypothesis testing by comparing your observed frequencies to the expected frequencies using a Chi-square test. This would provide a more quantitative and concrete conclusion about whether the die is biased or fair.
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One of the more famous anecdotes in the field of statistics is known as the "Lady Tasting Tea" and involves the renowned statistician Sir Ronald Aylmer Fisher. A woman claimed to be able to tell the difference in a cup of tea depending on whether or not the milk or tea was poured first. You have chosen to recreate this experience with a classmate and have fixed 40 cups of tea, of which your classmate correctly identifies 12. How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.30 as the value for p. n = 42 n = 81 n = 4116 n = 8068
Answer:
[tex]n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36[/tex]
And rounded up we have that n=8068
Step-by-step explanation:
The margin of error for the proportion interval is given by this:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
We want for this case a 95% of confidence desired, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for this case is [tex]ME =\pm 0.01[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
The estimated proportion for this case is [tex]\hat p=0.3[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36[/tex]
And rounded up we have that n=8068
Maria and her friends went on a bike ride. The start and end times are shown below how long did they Ride
Start time: 1:09
End time: 2:05
Maria and her friends rides for 56 minutes
Duration of timeDuration is defined as the length of time that something lasts. Eg. When a film lasts for two hours, this is an example of a time when the film has a two hour durationHow to solve the problem?GivenStart time = 01:09
End time = 02:05
From start and end time we can see that there is 4 minutes to complete 1 hoursSo to find total time we need to subtract 4 minutes from 1 hours i.e 60 minutes∴ Ride Time = 60-4
∴ Ride Time = 56 minutes
Therefore the total ride time that Maria and her friend rode is 56 minutes
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Spanky, Alfalfa, and Buckwheat sit down to take a geography test that has 12 multiple-choice questions. Each question has three possible answers, of which only one is correct. Alfalfa, as usual, has been spending too much time daydreaming about Darla and has not properly studied for the exam. After looking it over, he discovers that he knows the answers to just five of the questions. So, he answers those questions correctly and randomly guesses on the remaining seven. Afterward, as Miss Crabtree is grading Alfalfa’s exam, she selects one question at random and finds that he answered it correctly. What is the exact probability that Alfalfa actually knew the answer to this question? Answer this question by completing the following parts:a. Carefully construct a correct tree diagram using the letters K for the event that he knows the answer to a question, N for the event that he doesn’t know the answer to a question, and C for the event that he answers a question correctly. Also, label each edge with its exact probability (as either a fraction or a whole number).b. Use the definition of conditional probability to compute the exact value of P(K|C), writing your answer as a fraction in simplified form.
The snack bar at the soccer field is charging $12 for 9 hamburgers. At that rate, how many hamburgers could you get for $20?
Answer:
6
Step-by-step explanation:
12 = 9 so u do 12 divided by 9
$20 to get 15 hamburgers. By dividing the price to produce one unit of your product by the number of items you have created, you can use the total variable cost.
locate total variables cost?By dividing the price to produce one unit of your product by the number of items you have created, you can determine the total variable cost.
Multiply the cost of producing one unit of your product by the total number of items you have produced to determine variable costs. Total Variable Costs = Cost Per Unit x Total Number of Units is the calculation for this cost.
For instance, if producing one unit of your product costs $12 and you produced 9 pieces, your total variable cost would be $12 x 9, or $108.
$12/9 = 1.34 then $20 to get 15 hamburgers.
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It was claimed that when tossing a fair coin 4 times it is quite likely to not obtain 2 heads and 2 tails. However, when tossing a fair coin 4,000 times one should expect to obtain number of tails in the range between 1940 and 2060. Let us compare the situation for 2 versus 2,000 coins. Let X be the number of heads when tossing a fair coin 2 times and let Y be the number of heads when tossing a fair coin 2,000 times.
1. P(940 ≤ Y ≤ 1,060) is equal to:______.2. E(X) is equal to:______.3. The standard deviation of X is equal to:______.4. E(Y) is equal to:_______.
Final answer:
The expected value of flipping a coin twice (X) is 1 head, with a standard deviation of 0.7071. The expected value of flipping a coin 2,000 times (Y) is 1,000 heads, but we cannot calculate P(940 ≤ Y ≤ 1,060) from the given information.
Explanation:
The question involves the concept of probability, expected value (E), and standard deviation (SD) in the context of flipping coins. We'll address each part of the query using basic probability and statistics principles.
P(940 ≤ Y ≤ 1,060) would require the use of the Central Limit Theorem for large sample sizes; however, with the information given, we cannot calculate this probability without additional statistical tables or tools, so we must refuse to answer this part.
The expected value of X, E(X), when flipping a coin twice would be the sum of products of each outcome's value and its probability. E(X) = (0 * 0.25) + (1 * 0.5) + (2 * 0.25) = 1.
The standard deviation of X requires calculating the variance first, then the square root of the variance. σ(X) = √[((0-1)^2 * 0.25) + ((1-1)^2 * 0.5) + ((2-1)^2 * 0.25)] = √(0.5) = 0.7071.
The expected value of Y, E(Y), when flipping a coin 2,000 times is simply 0.5 * 2,000 = 1,000 because the probability of a head for each flip is 0.5.
The probability P(940 ≤ Y ≤ 1,060) is approximately 99.63%, E(X) equals to 1, and the standard deviation of X is approximately 0.707. E(Y) is 1000.
To understand the probability and expectations for tossing fair coins, we will address your questions step by step.
P(940 ≤ Y ≤ 1,060) involves using the normal approximation to the binomial distribution.
For large numbers of coin tosses, the binomial distribution can be approximated by a normal distribution.
Since we are tossing the coin 2,000 times, our mean (μ) and variance (σ²) need to be calculated.
μ = n * p = 2000 * 0.5 = 1000 σ² = n * p * (1 - p) = 2000 * 0.5 * 0.5 = 500Hence σ ≈ 22.36.
Now, we standardize the range [940, 1060].
Z-score = (940 - 1000) / 22.36 ≈ -2.68 and (1060 - 1000) / 22.36 ≈ 2.68.From the Z-table, P(-2.68 ≤ Z ≤ 2.68) is approximately 0.9963, or 99.63%.
E(X) represents the expected number of heads when tossing 2 coins. Since each coin is fair and has a probability of 0.5 for heads,
E(X) = n * p = 2 * 0.5 = 1.Standard Deviation = √(n * p * (1 - p)). Here, n = 2, p = 0.5.
= √(2 * 0.5 * 0.5) = √0.5 = 0.707.E(Y) is the expected number of heads when tossing 2,000 coins. Similarly,
E(Y) = n * p = 2000 * 0.5 = 1000.Therefore, probability P(940 ≤ Y ≤ 1,060) is 99.63%, E(X) is 1, and the standard deviation is 0.707. E(Y) is 1000.
The Cartesian coordinates of a point are given.(a) (6, −6)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) = (b) (−1, 3)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) =
To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the equations (r, θ) = (√(x² + y²), atan2(y, x)).
Explanation:To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the following equations:
(r, θ) = (√(x² + y²), atan2(y, x))
(a)(i) For the Cartesian coordinates (6, -6),
(r, θ) = (√(6² + (-6)²), atan2(-6, 6))
(r, θ) = (√(36 + 36), atan2(-6, 6))
(r, θ) = (6√2, -45°)
(a)(ii) For the Cartesian coordinates (6, -6),
(r, θ) = (-√(6² + (-6)²), atan2(-6, 6) + π)
(r, θ) = (-6√2, -45° + π)
(b)(i) For the Cartesian coordinates (-1, 3),
(r, θ) = (√((-1)² + 3²), atan2(3, -1))
(r, θ) = (√(1 + 9), atan2(3, -1))
(r, θ) = (√10, 116.57°)
(b)(ii) For the Cartesian coordinates (-1, 3),
(r, θ) = (-√((-1)² + 3²), atan2(3, -1) + π)
(r, θ) = (-√10, 116.57° + π)
Do political science classes require less writing than history classes? The 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages. The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages. What can be concluded at the α = 0.01 level of significance?
Answer:
We conclude that political science classes require less writing time than history classes at 0.01 level of significance.
Step-by-step explanation:
We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.
The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.
Let [tex]\mu_1[/tex] = average writing time required by political science classes.
[tex]\mu_2[/tex] = average writing time required by history classes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1\geq\mu_2[/tex] {means that political science classes require more or equal writing time than history classes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex] {means that political science classes require less writing time than history classes}
The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_-_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample average pages of essay writing for political science classes = 16.3 pages
[tex]\bar X_2[/tex] = sample average pages of essay writing for history classes = 18.9 pages
[tex]s_1[/tex] = sample standard deviation for political science classes = 4.8 pages
[tex]s_2[/tex] = sample standard deviation for history classes = 5 pages
[tex]n_1[/tex] = sample of political science classes = 55
[tex]n_2[/tex] = sample of history classes = 54
Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }[/tex] = 4.90
So, test statistics = [tex]\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }[/tex] ~ [tex]t_1_0_7[/tex]
= -2.77
The value of t test statistics is -2.77.
Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.
Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that political science classes require less writing time than history classes.
What is the value of this expression when a=3 and b=-1?
Answer:
1/4
Step-by-step explanation:
[tex](\dfrac{3(3)^{-2}(-1)^6}{2(3)^{-1}(-1)^5})^2=[/tex]
[tex](\dfrac{\frac{1}{3}}{-\frac{2}{3}})^2=[/tex]
[tex](-\dfrac{1}{2})^2=[/tex]
[tex]\frac{1}{4}[/tex]
Hope this helps!
HELP ASAP timed question. A table is 4 ft high. A model of the table is 6 in high. What is the ratio of the height of the actual table to the helght of the model table? 3/2 8/1 2.3 1/8
Answer:
The ratio of the height of the actual table to the height of the model table is .
Step-by-step explanation:
As given
A table is 4 ft high. A model of the table is 6 in. high.
As
1 foot = 12 inch
Now convert 4 ft into inches .
4 ft = 4 × 12
= 48 inches
Height of the actual table = 48 inches
Now the ratio of the height of the actual table to the height of the model
table .
Therefore the ratio of the height of the actual table to the height of the model table is .
Simon walks a total of 45.55 miles in March and 35.7 miles in April.
How many miles does Simon walk in all in March and April?
Enter your answer
Answer:
81.25
Step-by-step explanation:
45.55 + 35.7
Answer:I hope that helps
Step-by-step explanation:
Please help 15 points
Answer:
D) Alternate exterior angles
Step-by-step explanation:
Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
87 1/3% into a fraction
Final answer:
87 1/3% is approximately 17433/10000 as a fraction after converting 87.33% to a fraction with a denominator of 100 and simplifying.
Explanation:
To convert 87 1/3% into a fraction, we first recognize that 1/3% is equal to 0.33% (approximately), so 87 1/3% is approximately 87.33%. Next, we write this percent as a fraction with a denominator of 100 to represent the percent: 87.33/100.
To simplify further, we can convert the decimal to a fraction, where 0.33 is approximately 33/100, and add this to 87 to get:
8733/10000 + 8700/10000 = 17433/10000Thus, 87 1/3% is approximately 17433/10000 when expressed as a fraction.
The radial spokes of a bicycle tire are 13 inches long. What is the diameter of the tire?
Answer:
the answer is 5
Step-by-step explanation:
the
HURRY PLEASE
morgan poured 3/4 gallon of punch into each of 6 bottles. how many gallons of punch did she pour in all
Answer:
gallons of punch in all = 4.5 gallons
Step-by-step explanation:
Morgan poured 3/4 gallons of punch into each of 6 bottles . This means Morgan poured 3/4 gallons of punch in each of the available 6 bottle .
He pours 3/4 gallons of punch in 1 bottle . For 6 bottles the gallons of punch poured is calculated below
1 bottle = 3/4 gallons of punch
6 bottles = ? gallons of punch
cross multiply
gallons of punch in all = 3/4 × 6
gallons of punch in all = 18/4
gallons of punch in all = 9/2 gallons
gallons of punch in all = 4.5 gallons
A manager at a shipping company will purchase boxes in the shape of right rectangular prisms. He wants the volume of each box to be exactly 98 cubic feet. Which figure shows a box with the dimensions, in feet, that the manager will purchase?
The manager needs to select dimensions for a right rectangular prism that when multiplied together equal 98 to achieve a volume of 98 cubic feet. Possible dimensions could be 7 feet by 7 feet by 2 feet, or 14 feet by 7 feet by 1 foot.
The question pertains to calculating the volume of right rectangular prisms (boxes) and understanding the relationship between their dimensions and volume. To find a box with a volume of 98 cubic feet, one can use the formula for the volume of a right rectangular prism, which is Volume = length * width * height. The manager needs to identify the dimensions that, when multiplied together, equal 98. For instance, if a box has dimensions of 7 feet, 7 feet, and 2 feet, the volume would be 7 * 7 * 2 = 98 cubic feet, as required. Other possible dimensions could be 14 feet by 7 feet by 1 foot, as 14 * 7 * 1 also gives 98 cubic feet.