Step-by-step explanation:
Arranging in ascending order
2 , 4 , 7 , 9 , 11 , 15
No of data (N) = 6
Now
Position of median
= (N+1)/2 th item
= ( 6 + 1) /2 th item
= 7/2 th item
= 3.5 th item
Exact Median
= 3 + 0.5 ( 4th term - 3rd term)
= 3 + 0.5( 9 - 7)
= 3 + 0.5 * 2
= 3 + 1
= 4
Hope it will help :)
A review of 200 days-away-from-work injuries for a large, multi-facility corporation was conducted, and it was determined that 18 of them were due to lower back injuries. Only 14.3 were expected under normal conditions. The rest of the injuries were due to other causes where 185.7 were expected. What is the chi-square value? Discuss whether there was a significant difference in observed data vs. the expected data. Also, discuss how the process of hypothesis testing might prove helpful to the safety professional.
Answer:
a) Chi square value = 1.031
b) There is no significant difference between the observed and expected values.
c) Check explanations for the part C of the question
Step-by-step explanation:
a) People away from work due to lower back injuries:
Observed value = 18
Expected value = 14.3
People away from work due to other injuries:
Observed value = 200 - 18 = 182
Expected value = 185.7
The chi square value is calculated by the formula:
[tex]x^{2} = \frac{(O-E)^{2} }{E}[/tex]
For people out of work due to lower back injuries:
Chi square value,
[tex]x^{2} = \frac{(18-14.3)^{2} }{14.3} \\x^{2} = 0.957[/tex]
For people out of work due to other injuries:
Chi square value,
[tex]x^{2} = \frac{(182-185.7)^{2} }{185.7} \\x^{2} = 0.074[/tex]
Total chi square value for the distribution:
[tex]x^{2} = 0.074 + 0.957\\x^{2} = 1.031[/tex]
b) The degree of freedom, df = n -1
n = 2 ( two categories of people are considered)
df = 2-1 = 1
For df = 1 and, chi square = 1.031
P - value = 0.3099
p- value = 0.3099, the result is not significant at p < 0.05
There is no significant difference between the observed and expected values.
c) Hypothesis testing helps the safety professionals to statistically analyse any situations and determine whether or not they are safe. It can help them to predict the outcome of a given situation by making necessary observations.
The distance from Parrot Point Airport to the Ivy Cliffs is 172 miles at and angle of 7.0 degrees northeast. There is a wind blowing southeast at 25 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly?
Answer:
Speed = x/t = 146.61/2 = 73.30 mph
direction y = 22.59° northeast
Step-by-step explanation:
Given;
The distance from Parrot Point Airport to the Ivy Cliffs is 172 miles at and angle of 7.0 degrees northeast;
Resultant distance R = 172 (7° northeast)
Time given to make the trip t = 2 hours
Distance moved by wind during the time dw = 25×2 = 50 miles south east.
Let x represent the distance covered by plane without wind during the time and y the direction;
Resolving into horizontal and vertical component;
horizontal;
x cosy + 50cos45 = 172cos7
xcosy = 172cos7 - 50cos45 .....1
Vertical;
xsiny - 50sin45 = 172sin7
xsiny = 172sin7 + 50sin45 .....2
Divide equation 2 by 1
xsiny/xcosy = (172sin7 + 50sin45)/(172cos7 - 50cos45)
tany = 0.4160
y = taninverse (0.4160)
y = 22.59° northeast
Substituting y into equation 2;
xsin22.59 = 172sin7 + 50sin45
x = (172sin7 + 50sin45)/sin22.59
x = 146.61 miles
Speed = x/t = 146.61/2 = 73.30 miles per hour
Speed = 73.30mph
EXAMPLE 4 Find the moments of inertia Ix, Iy, and I0 of a homogeneous disk D with density rho(x, y) = rho, center the origin, and radius a. SOLUTION The boundary of D is the circle x2 + y2 = a2 and in polar coordinates D is described by 0 ≤ θ ≤ 2π, 0 ≤ r ≤ a. Let's compute I0 first: I0 = D (x2 + y2)rho dA = rho 2π 0 a 0 r2 r dr dθ = rho 2π 0 dθ a 0 r3 dr = 2πrho a 0 = . Instead of computing Ix and Iy directly, we use the facts that Ix + Iy = I0 and Ix = Iy (from the symmetry of the problem). Thus Ix = Iy = I0 2 = .
The moments of inertia are [tex]\( I_x = I_y = \frac{\pi \rho a^4}{4} \)[/tex] and [tex]\( I_0 = \frac{\pi \rho a^4}{2} \).[/tex]
Example 4 involves finding the moments of inertia [tex]\( I_x \)[/tex], [tex]\( I_y \)[/tex], and [tex]\( I_0 \)[/tex] of a homogeneous disk [tex]\( D \)[/tex] with density [tex]\( \rho(x, y) = \rho \)[/tex], centered at the origin, and radius [tex]\( a \)[/tex].
To compute [tex]\( I_0 \)[/tex], we integrate [tex]\( (x^2 + y^2) \rho \)[/tex] over the disk [tex]\( D \)[/tex] using polar coordinates. The bounds for [tex]\( \theta \)[/tex] are [tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], and for [tex]\( r \)[/tex] are [tex]\( 0 \)[/tex] to [tex]\( a \).[/tex]
[tex]\[ I_0 = \int \int_D (x^2 + y^2) \rho \, dA = \rho \int_0^{2\pi} \int_0^a r^3 \, dr \, d\theta = \frac{2\pi \rho a^4}{4} = \frac{\pi \rho a^4}{2} \][/tex]
Since the disk is symmetric about both the x-axis and y-axis, [tex]\( I_x = I_y = \frac{I_0}{2} = \frac{\pi \rho a^4}{4} \).[/tex]
The answer is [tex]\( I_0 = \frac{1}{2} \rho a^4 \pi \).[/tex]
To find the moments of inertia[tex]\( I_x \) and \( I_y \) of a homogeneous disk \( D \) with density \( \rho(x, y) = \rho \),[/tex] centered at the origin, and radius \( a \), we use the following formulas:
[tex]\[ I_x = \int \int_D y^2 \rho(x, y) \, dA \]\[ I_y = \int \int_D x^2 \rho(x, y) \, dA \]where \( dA \) represents the differential area element in polar coordinates.[/tex]
For a disk, we use polar coordinates [tex]\( (r, \theta) \), where \( r \) represents the radius and \( \theta \)[/tex] represents the angle.
The density [tex]\( \rho \)[/tex] is constant, so it can be pulled out of the integrals.
We integrate over the disk, which has a radius [tex]\( a \), and \( \theta \) ranging from \( 0 \) to \( 2\pi \).[/tex]
[tex]Let's calculate \( I_x \):\[ I_x = \int_0^{2\pi} \int_0^a (r \sin \theta)^2 \rho \cdot r \, dr \, d\theta \]\[ = \rho \int_0^{2\pi} \int_0^a r^3 \sin^2 \theta \, dr \, d\theta \]\[ = \rho \int_0^{2\pi} \left[ \frac{1}{4} r^4 \sin^2 \theta \right]_0^a \, d\theta \]\[ = \rho \int_0^{2\pi} \frac{1}{4} a^4 \sin^2 \theta \, d\theta \]\[ = \rho \cdot \frac{1}{4} a^4 \int_0^{2\pi} \sin^2 \theta \, d\theta \]\[ = \rho \cdot \frac{1}{4} a^4 \cdot \pi \][/tex]
Using the trigonometric identity [tex]\( \sin^2 \theta = \frac{1 - \cos(2\theta)}{2} \) and integrating from \( 0 \) to \( 2\pi \), the integral of \( \sin^2 \theta \) over one period is \( \pi \), and thus, the integral over \( 2\pi \) periods is \( 2\pi \).[/tex]
[tex]So, \( I_x = \rho \cdot \frac{1}{4} a^4 \cdot \pi \).Similarly, for \( I_y \), the integral will be:\[ I_y = \rho \int_0^{2\pi} \int_0^a (r \cos \theta)^2 \rho \cdot r \, dr \, d\theta \]\[ = \rho \int_0^{2\pi} \int_0^a r^3 \cos^2 \theta \, dr \, d\theta \]\[ = \rho \cdot \frac{1}{4} a^4 \cdot \pi \]Thus, \( I_y = \rho \cdot \frac{1}{4} a^4 \cdot \pi \), which is the same as \( I_x \).[/tex]
Now, for the moment of inertia \( I_0 \) about the origin:
[tex]\[ I_0 = I_x + I_y = 2 \rho \cdot \frac{1}{4} a^4 \cdot \pi \][/tex]
So, [tex]\( I_0 = \frac{1}{2} \rho a^4 \pi \).[/tex]
For complete question refer to image:
What's the answer to 1/2(x+4)^2-5+=3.
Answer:
x = 0
Step-by-step explanation:
To solve this equation you would need to get x by itself on one side
1/2 (x+4)^2 - 5 = 3
1.) add 5 to both sides
1/2 (x+4)^2 = 8
2.) divide each side by 1/2
(x+4)^2 = 16
3.) find the square root of both sides
(x+4) = 4
4.) subtract 4 from both sides
x = 0
The app "Photomath" is a great way to solve problems like these and it gives a step by step explanation that might be easier to understand than mine :)
Simplify the expression 13+(x+8)
Answer:x+21
Step-by-step explanation:
It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 20 college students and calculated a sample mean of 7.5 hours per night. If the researcher wanted to perform a one-sample t-test, which of the following is a correct statement?
A: By taking a random sample, the researcher has guaranteed that the distribution of number of hours of sleep per night for all college students is normal.
B.The number of hours of sleep per night for all college students must be normally distributed because the sample size is small.
C.By taking a random sample, the researcher has guaranteed that the distribution of sample means is normal.
D.The distribution of sample means will be normal even if the distribution of the data in the population is not normal.
In a one-sample t-test, the normal distribution of sample means is more important than the normality of individual data in the population. This follows the Central Limit Theorem which states that, with a decently large sample size, the distribution of sample means will approach normality regardless of the population distribution.
Explanation:Statement C is the correct option. The Central Limit Theorem indicates that regardless of the population distribution, as long as we have a sufficiently large sample size, the sample means will be approximately normally distributed. However, this doesn't guarantee that the distribution of the individual data (the number of sleep hours) in the population is normal.
It’s important to note two things: First, the idea of random sampling is to avoid bias and to have a representative sample of the population under study. Second, the rule of thumb is that the sample size should be approximately 30 or greater for the Central Limit Theorem to take effect, to provide a decent approximation of a normal distribution of sample means. In this instance, a sample size of 20 is close to 30, so we may anticipate that the sample mean distribution is roughly normal.
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I get HOW to make a box and whisker plot. What I don't get is WHY you would want to make one. From a practical point of view, what can it teach you?
Answer:
I'd say go to Wikipedia and look it up. It is something that cannot be summarized into just a few words.
Step-by-step explanation:
Jimmy is a flag person and earned $321.10 last week for 32.5 hours work. What is his hourly wage? *
Your answer
Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) provides a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
1. Formulate null and alternative hypotheses to test the analyst's claim.
H0: p
Ha: p
2. A sample of 50 stocks traded on the NYSE that day showed that 24 went up. What is your point estimate of the population proportion of stocks that went up (to 2 decimals)?
3. Conduct your hypothesis test using = .01 as the level of significance.
Calculate the value of the test statistic (to 2 decimals).
What is the p-value (to 4 decimals)?
Can you conclude that the proportion of stocks going up is not .30?
Answer:
1) H0: p=0.3
Ha: p≠0.3
2) 0.48
3)•2.78
•0.0054. So, we reject H0.
• No, we cannot conclude
•
Step-by-step explanation:
1) To formulate the null and alternative hypothesis:
• Null hypothesis:
[tex] H_0: p=0.3 [/tex]
•Alternative hypothesis:
Ha: p≠0.3
2) Point estimate of the population proportion stocks that went up:
Since sample is 50 stocks and 24 went up, we have phat as:
[tex]phat = \frac{24}{50} = 0.48[/tex]
3) • Hypothesis test using 0.01 as level of significance:
Test statistic =
[tex] Z = \frac{phat-p}{\sqrt{\frac{p*(1-p)}{n}}}[/tex]
[tex] = \frac{0.48-0.3}{\sqrt{\frac{0.3*0.7}{50}}}[/tex]
= 2.78
•Using standard normal table
P value =
2*(P>2.78) = 0.0054
• The p value (0.0054) is less than level of significance (0.01), we reject null hypothesis H0.
• No, we cannot conclude that the proportion of stocks going up is not .30
A student wants to compare textbook prices for two online bookstores. She takes a random sample of five textbook titles from a list provided by her college bookstore, and then she determines the prices of those textbooks at each of the two websites. The prices of the five textbooks selected are listed below in the same order for each online bookstore. A: $115, $43, $99, $80, $119 B: $110, $40, $99, $69, $109 (a) Are these independent or dependent samples
Answer:
Dependent sample: The same textbook are being compared.
Step-by-step explanation:
We are given the following in the question:
A student wants to compare textbook prices for two online bookstores.
Sample 1 from bookstore A:
$115, $43, $99, $80, $119
Sample 2 from bookstore B:
$110, $40, $99, $69, $109
Dependent and independent sample:
Dependent samples are paired observations for same set of items.Independent samples are observations made on two different sets of items.If the values in one sample affect the observations in the other sample, then the samples are dependent.If the values in one sample have no effect about those of the other sample, then the samples are independent.Thus, the given sample is dependent sample as the same textbook is being compared from two different bookstore.
The textbook prices listed for the two different online bookstores are dependent samples, as the prices are paired for the same textbooks across the two bookstores. Analyzing this data would involve using statistical methods suitable for dependent samples, like paired t-tests.
Explanation:The textbook prices listed by the student for the two different online bookstores represent dependent samples. This is because the prices are paired for the same textbooks across the two bookstores. They are not independent samples because the price of a given book in one store could potentially influence the price of the same book in the other store. For example, if one store lowers its prices, the other might follow suit to remain competitive.
Consideration of such data requires the analysis method suitable for dependent samples. Specifically, using methodologies like paired t-tests in statistics might be appropriate in this scenario to compare the prices from the different online bookstores. These methods account for the fact that measurements within each pair could be correlated.
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in 2010 an enormous sinkhole suddenly appeared in the middle of a guatemalan neighborhood and swallowed a three story building above it. the sinkhole has an estimated depth of about 100 feet/ how much material is needed to fill the sinkhole? determine what information is needed to answer the question. do you think your estimate is more likely to be too high or too low
Answer:
Step-by-step explanation:
Given that :
The enormous sinkhole that appeared in the middle of Guatemalan neighborhood in the year 2010 swallowed a three story building above it and the sinkhole has an estimated depth of about 100 feet
How much material is needed to fill the sinkhole?
Then , the material needed to fill the sinkhole will be dependent on the volume of the sinkhole.
Determine what information is needed to answer the question.
The information that is needed to answer this question are:
the base area of the sinkhole will be required; &
the height should also be known
if the base area is determined then we can proceed to determine how much material is needed to be calculated.
Do you think your estimate is more likely to be too high or too low
No, the estimate is not likely to be too high or too low rather the estimate of the material required will be almost equal to the volume of the sinkhole, but that does not implies that it will be exactly the same since the sinkhole is not uniform and regular in shape.
Hi I need help with this, I am very confused
Answer:
1/81
Step-by-step explanation:
P(1st ticket is a winner) = 1/9
These are independent events
P(2nd ticket is a winner) = 1/9
P (winner, winner) = 1/9 * 1/9 = 1/81
Which expression is equivalent to:
16(w+q)
A. (m + 16) (w + 16) B.16w + 169
C. 16w +9
D. W + 169
The equivalent expression to 16(w+q) is 16w + 16q, but none of the given options A, B, C, or D are correct as they do not accurately represent this distribution. The closest option would be C (16w + 9), though it is still incorrect because it has 9 instead of 16q.
Explanation:The question asks which expression is equivalent to 16(w+q). The correct way to distribute a constant over a sum inside parentheses is to multiply each term inside the parentheses by that constant. So, 16 must be multiplied by both w and q.
Therefore, the equivalent expression is 16w + 16q. Looking at the provided options:
A. (m + 16) (w + 16) includes additional terms and multiplication not present in the original expression.B. 16w + 169 includes the term 169, which is not correct since no such number results from multiplying 16 by q.C. 16w + 16q is correct, but as given in the option just as 16w + 9 it is incorrect because it has 9 instead of 16q.D. w + 169 does not multiply w by 16 and includes the incorrect number 169.Since none of the given options are exactly 16w + 16q, no available option is a correct equivalent expression to 16(w+q).
Sam parents agreed to let him buy a new video game systemic he paid for half of it. His parents gave him the $170 for their portion. If Sam has saved $109.85 so far, how much more does he need before heading to the store?
Answer:
60.15
Step-by-step explanation:
if he needs to pay 170 and he has 109.85
170-109.85=60.15
so he needs 60 dollars and 15 cents to reach his goal
David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station.
(a) What is the probability that more than 8 and less than 12 customers pay in cash?
Answer:
0.09312
Step-by-step explanation:
15C9×0.4⁹×0.6⁶ + 15C10×0.4¹⁰×0.6⁵ × 15C11×0.4¹¹×0.6⁴
0.09311963893
Suppose you deposit $500 in a bank account that pays 8% annual simple
interest. Find the interest earned after 3 years.
Answer:
120
Step-by-step explanation:
I=prt . Where: P = Principal Amount; I = Interest Amount; r = Rate of Interest per year in decimal and time t should be in the same time units such as months or years.
I=500(.08)(3)
Answer:
8% of 500 is 40, For the first year is 540. 8% of 540 is 43.20 dollars. 8% of 583.2 is 46.656. So the total is 630 by rounding but the actual amount is 629.956. The interest is 129.956
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Lonnie has a shutter that is 4 yards, 17 inches long. How many inches long is Lonnie's shutter?
Answer:
161 inches
Step-by-step explanation:
This problem is all about conversion. How many feet are in a yard? 3. How many feet are in 4 yards? 12 feet. There are 12 inches in a foot. 12 feet means 12 x 12 inches, which is 144. 144 + the other 17 inches, is 161.
Answer:
The answer is into the unkown
Step-by-step explanation:
elsa and anna are good sisters olaf olaf anna fiftys ahdpnf3oehisklNHW3q3tsqagwgdraw4gw
Calculate social security taxes
Answer:
there is no any number to caculate social security tax.
Step-by-step explanation:
Social Security taxes are calculated using a deduction rate of 6.2% and 1.45% for Medicare from an employee's gross annual income. Employers also contribute matching amounts. However, the economic impact of employers' contributions often invariably impact employees indirectly.
Explanation:To calculate social security taxes, you need to consider a standard deduction rate of 6.2% for the Social Security and 1.45% from Medicare. These deductions are generally taken directly out of the employee's gross annual income. Employers also contribute matching percentages. However, it is important to note that in reality, the burden of the employer's contribution may in effect fall on the employee as it can result in lower wages. For instance, for those considered as independent contractors or members of the 'gig economy' receiving a 1099 tax statement, the individual must pay both the employer and employee portion of the social security and Medicare taxes.
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Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform LetUse Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) WebAssign Plotf be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = cos(t), 0 ≤ t < π 0, t ≥ π
Answer:
[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex]
Step-by-step explanation:
Using the formula for Laplace the transformations if [tex]F(s)[/tex] is the converted function then
[tex]F(s) = \int\limits_{0}^{\infty} e^{-st} \cos(t) dt = \int\limits_{0}^{\pi} e^{-st} \cos(t) dt[/tex]
To solve that integral you need to use integration by parts, when you do integration by parts you get that
[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex].
Answer:
The laplace transform is [tex] F(s) = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]
Step-by-step explanation:
Let us asume that f(t) =0 for t<0. So, by definition, the laplace transform is given by:
[tex]I = \int_{0}^\pi e^{-st}\cos(t) dt[/tex]
To solve this integral, we will use integration by parts. Let u= cos(t) and dv = [tex]e^{-st}[/tex], so v=[tex]\frac{-e^{st}}{s}[/tex] and du = -sin(t), then, in one step of the integration we have that
[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi- \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]
Let [tex] I_2 = \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]. We will integrate I_2 again by parts. Choose u = sin(t) and dv = [tex]\frac{e^{-st}}{s}[/tex]. So
[tex] I_2 = \left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi + \int_{0}^\pi \frac{\cos(t) e^{-st}}{s^2}dt [/tex]
Therefore,
[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi - (\left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi - \frac{1}{s^2} I[/tex]
which is an equation for the variabl I. Solving for I we have that
[tex]I(\frac{s^2+1}{s^2}) =\left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2}\right|_{0}^\pi[/tex]
Then,
[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2+1}\right|_{0}^\pi[/tex].
Note that since the sine function is 0 at 0 and pi, we must only care on the first term. Then
[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi = \frac{s}{s^2+1}(1-(-1)e^{-s\pi}} = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]
finding the size of angle x on a straight line. 2 of the angles are 29 degree and 82 degrees
Answer:
x = 111°
Step-by-step explanation:
We know that angles in a triangle add up to 180°
Step 1: Find angle supplementary to x
82 + 29 + x = 180
111 + x = 180
x = 69°
Step 2: Find angle x
Both the angles are supplementary, meaning they add up to 180°.
x + 69 = 180
x = 111°
Answer:
Easy = 111 degrees
Step-by-step explanation:
a box of cookies contain 12 chocolate chip cookies, 6 peanut butter cookies, and 6 sugar cookies, what is the probability of selecting a sugar cookie?
Answer:
The answer of this question is 1/4
Step-by-step explanation:
Total no of cookies=12+6+6=24
No.sugar cookies=6
Probability= Possible outcomes/total no of outcomes
= 6/24
= 1/4
Which events have a probability of 25 percent? Select three options.
choosing a green jelly bean out of a bag that contains 2 green jelly beans, 1 red jelly bean, and 5 yellow jelly beans
rolling a number less than 3 on a six-sided die
spinning a number less than 2 on a spinner that has four equal sections numbered from 1 to 4
choosing an Oregon state quarter out a bag that contains 4 California state quarters, 3 Oregon state quarters, 6 Texas state quarters, and 3 New York state quarters
choosing a spade out of a standard deck of cards that contains 13 hearts, 13 clubs, 13 diamonds, and 13 spades
Choosing a green jelly bean.
Spinning a number less than 2 on a spinner.
Choosing a spade out of a standard deck of cards.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of choosing a green jelly bean = number of green jelly bean / total number of beans
2/8 x 100 = 25%
Probability of spinning a number less than 2 on a spinner = number that is less than 2 / total number of sections
1/4 x 100 = 25%
Probability of choosing a choosing a spade= number of spade / total cards in the deck
13/54 x 100 = 25%
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The three options that have a probability of 25 percent are:
- Choosing a green jelly bean
- Spinning a number less than 2 on a spinner
- Choosing a spade from a standard deck of cards
The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. A probability of 25 percent corresponds to a ratio of 1 out of 4 (since 25% is one-fourth of 100%). Let's analyze the options:
1. Choosing a green jelly bean: There are 2 green jelly beans out of a total of 2 + 1 + 5 = 8 jelly beans. The probability is 2/8, which simplifies to 1/4 or 25%. This option has a probability of 25%.
2. Rolling a number less than 3 on a six-sided die: There are 2 favorable outcomes (1 and 2) out of 6 possible outcomes (1 through 6). The probability is 2/6, which simplifies to 1/3 or approximately 33.33%. This option does not have a probability of 25%.
3. Spinning a number less than 2 on a spinner: There is 1 favorable outcome (1) out of 4 possible outcomes (1 through 4). The probability is 1/4 or 25%. This option has a probability of 25%.
4. Choosing an Oregon state quarter: There are 3 Oregon state quarters out of a total of 4 + 3 + 6 + 3 = 16 state quarters. The probability is 3/16, which is not equal to 25%.
5. Choosing a spade from a standard deck of cards: There are 13 spades out of a total of 13 + 13 + 13 + 13 = 52 cards. The probability is 13/52, which simplifies to 1/4 or 25%. This option has a probability of 25%.
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Can someone explain this please???
A function is a rule that assigns exactly one output to a given input. The input is taken from a set called the domain, and the corresponding output belongs to a set called the range.
1. In this exercise, we're calling the pool of patients 1-8 the domain, and the pool of nurses A-D the range. The given table describes a function because any patient is assigned to only one nurse.
2. This wouldn't be a function if at least one patient was assigned to more than one nurse. If this were to happen in practice, the patient could be, say, given the same dose of some medicine twice if the nurses aren't careful.
3. Making the nurse pool the domain and the patient pool the range would give a relation that is not a function, since more than one patient is assigned to one nurse.
Segments ~ Clementine is a kind of mandarin introduced into Florida by the United States Department of Agriculture in 1909. Historically, on average, clementine have 10.25 segments. A fruit lover bought 100 clementine and found that there were 10.66 mean number of segments with a standard deviation of 2.0712. The fruit lover wonders if the actual mean number of segments is more than the historic value and wants to carry out a hypothesis test. What are the null and alternative hypothesis? Question 2 options: Null hypothesis Alternative hypothesis 1. μ = 10.25 2. x⎯⎯ = 10.66 3. μ > 10.25 4. x⎯⎯ > 10.66 5. μ > 10.66 6. x⎯⎯> 10.25 7. μ ≠ 10.25 8. x⎯⎯ ≠ 10.66
Answer:
Step-by-step explanation:
The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.
From the given situation,
Historically, on average, clementine have 10.25 segments. This is the null hypothesis.
The fruit lover wonders if the actual mean number of segments is more than the historic value. This is the alternative hypothesis.
Therefore, the correct null and alternative hypotheses are
H0: μ = 10.25 and HA: μ > 10.25
The null hypothesis for the test is that the population mean number of clementines segments is equal to the historic value (μ = 10.25). The alternative hypothesis is that the population mean number of clementines segments is greater than the historic value (μ > 10.25). The test will determine whether to accept or reject the null hypothesis.
Explanation:In conducting a hypothesis test, the null hypothesis is the statement that is assumed to be true, whereas the alternative hypothesis is what the test is attempting to prove. In this instance, if we are questioning whether the actual mean number of segments in a clementine is more than the historic value, we set our null and alternative hypothesis as follows:
Null Hypothesis (H0): μ = 10.25Alternative Hypothesis (Ha): μ > 10.25In this context, μ represents the population mean number of segments, whilst '10.25' is the historical mean number of segments. The test will determine if there is strong enough evidence to reject the null hypothesis in favour of the alternative hypothesis, hence proving that the mean number of segments is indeed greater than 10.25.
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Find the percentage of people in the sample who prefer blue.
There is no sample given, please provide us with an attachment for your answer.
Kings Department Store has 625 rubies, 800 diamonds, and 700 emeralds from which they will make bracelets and necklaces that they have advertised in their Christmas brochure. Each of the rubies is approximately the same size and shape as the diamonds and the emeralds. Kings will sell each bracelet for $400 and it costs them $150 to make it. Each bracelet is made with 2 rubies, 3 diamonds, and 4 emeralds. Kings will sell each necklace for $700 and it costs them $200 to make it. Each neckalce is made with 5 rubies, 7 diamonds, and 3 emeralds. a) Formulate the above problem as a Linear Programming problem with the objective of maximizing profit
Step-by-step explanation:
Let Xb be the no of braclets made
Let Xn be the no of necklaces made
Max Z=250Xb + 500Xn (Objective Function)
Subject to
2Xb + 5Xn <= 625 (rubies)
3Xb + 7 Xn <= 800 ( diamonds)
4Xb + 3 Xn <= 700 (Emeralds)
Xb>=0 (non-negativity)
Xn >= 0 (non negativity
Answer:
Step-by-step explanation:
We are to Formulate the question given as a Linear Programming problem with the objective of maximizing profit.
From the question;
Kings will sell each bracelet for $400 and it costs them $150 to make it.
This implies that; King will net a profit on $250 on each bracelet made with 2 rubies, 3 diamonds, and 4 emeralds :
Also;
Kings will sell each necklace for $700 and it costs them $200 to make it
i.e King will net a profit of $500 on each necklace made with 5 rubies, 7 diamonds, and 3 emeralds.
Now; let's assume that :
[tex]Y_{br}[/tex] be the no of bracelets made ; &
[tex]Y_{nk}[/tex] be the no of necklaces made
[tex]\\ \\Max \ Z=250 \ Y{_b_r}} + 500 \ Y{_n_k}[/tex] (Objective Function)
Subject to :
[tex]2 \ Y_{br} + 5 \ Y_{nk}[/tex] ← 625 (rubies)
[tex]3 \ Y_{br} + 7 \ Y_{nk}[/tex] ← 800 ( diamonds)
[tex]4 \ Y_{br} + 3 \ Y_{nk}[/tex] ← 700 (Emeralds)
[tex]\\ \\Y_{br} \\[/tex] ⇒ 0 (non-negativity)
[tex]\\\\ \ Y_{nk}\\[/tex] ⇒ 0 (non negativity)
On a recent Saturday, a total of 1086 people visited a local library. Of these people, 269 were under age 10, 466 were aged 10–18, 185 were aged 19–30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is more than 30 years old?
Answer:
The probability that the person is more than 30 years old is 0.153
Step-by-step explanation:
We can obtain the probability that the person sampled is more than 30 years old by dividing the amount of peope with more than 30 years old with the total amount of people that visited the library that Saturday, in other owrds, 1086.
The number of people with more than 30 years old can be obtained by substracting from 1086 (the total amount) the total amount of people with 30 years or less.
There are 269 (under 10) + 466 (between 10 and 18) + 185 (between 19 and 30) = 920 people under 30 years old. Therefore, the total amount of people with more than 30 years old is 1086-920 = 166, and the probability that a person selected is from that group is 166/1086 = 0.153
Suppose that f (400 )equals3000 and f prime (400 )equals10. Estimate each of the following. (a) f (401 )(b) f (400.5 )(c) f (399 )(d) f (398 )(e) f (399.75 )
Answer:
a) [tex]f(401) = 3010[/tex], b) [tex]f(400.5) = 3005[/tex], c) [tex]f(399) = 2990[/tex], d) [tex]f(398) = 2980[/tex], e) [tex]f(399.75) = 2997.5[/tex]
Step-by-step explanation:
The estimation of each value can be found by the following value:
[tex]f(x + \Delta x) = f(x) + f'(x)\cdot \Delta x[/tex]
a) [tex]f(401) = 3000 + 10\cdot (401-400)[/tex]
[tex]f(401) = 3010[/tex]
b) [tex]f(400.5) = 3000 + 10\cdot (400.5 - 400)[/tex]
[tex]f(400.5) = 3005[/tex]
c) [tex]f(399) = 3000 + 10\cdot (399 - 400)[/tex]
[tex]f(399) = 2990[/tex]
d) [tex]f(398) = 3000 + 10\cdot (398-400)[/tex]
[tex]f(398) = 2980[/tex]
e) [tex]f(399.75) = 3000 + 10\cdot (399.75-400)[/tex]
[tex]f(399.75) = 2997.5[/tex]
The decreasing function M represents the mass of a sample of a radioactive element at time t. The rate of change of the sample’s mass is proportional to the mass of the sample. Which of the following differential equations could be used to model the relationship between the mass of the sample and the rate of change of the sample’s mass, where k is a constant?A)dM =kt dtb) d - = KM dtc)DMd)dᎷ .
Answer:
[tex](B) \dfrac{dM}{dt} = kM[/tex]
Step-by-step explanation:
Given the mass M(a decreasing function) of a sample of a radioactive element at time t.
The rate of change of the sample’s mass [tex]\dfrac{dM}{dt}[/tex], is proportional to the mass, M of the sample.
This is written as:
[tex]\dfrac{dM}{dt} \propto M[/tex]
Introducing the decay constant k,
[tex]\dfrac{dM}{dt} = kM[/tex]
This is the equation which model the relationship between the mass of the sample and the rate of change of the sample’s mass.
The other options are therefore invalid.
[tex](A)\dfrac{dM}{dt} = kt (C)\dfrac{dM}{dt} = \dfrac{k}{t} (D)\dfrac{dM}{dt} = \dfrac{k}{M}[/tex]
The correct differential equation is [tex]\(\frac{dM}{dt} = kM\)[/tex], option B) indicating the rate of change of mass is proportional to the mass.
1. Understanding the Problem Statement:
- The mass [tex]\(M\)[/tex]of a sample of a radioactive element is a decreasing function of time [tex]\(t\).[/tex]
- The rate of change of the sample's mass is proportional to the mass of the sample itself.
2. Translating the Statement into a Mathematical Form:
- When a quantity is said to change at a rate proportional to its current value, we can express this mathematically as:
[tex]\[ \frac{dM}{dt} \propto M \][/tex]
- This means the rate of change of [tex]\(M\)[/tex] with respect to time [tex]\(t\)[/tex] is proportional to [tex]\(M\).[/tex]
3. Introducing a Proportionality Constant:
- To express this proportionality as an equation, we introduce a constant of proportionality [tex]\(k\):[/tex]
[tex]\[ \frac{dM}{dt} = kM \][/tex]
- Here, [tex]\(k\)[/tex] is a constant that determines the rate at which [tex]\(M\)[/tex] changes with respect to [tex]\(t\).[/tex]
4. Evaluating Given Differential Equations:
- We need to find which of the provided differential equations matches the relationship [tex]\(\frac{dM}{dt} = kM\).[/tex]
The given differential equations are:
[tex]\[ \begin{aligned} & \frac{dM}{d} = kt \\ & \frac{dM}{dt} = kM \\ & \frac{dM}{d} = \frac{A}{2} \\ & \frac{dM}{d} = \frac{k}{M} \end{aligned} \][/tex]
5. Matching with the Correct Equation:
- Comparing each option with [tex]\(\frac{dM}{dt} = kM\):[/tex]
[tex]- \(\frac{dM}{d} = kt\)[/tex] does not match since it suggests the rate of change depends on [tex]\(t\), not \(M\).[/tex]
[tex]- \(\frac{dM}{dt} = kM\)[/tex] matches our derived equation perfectly.
[tex]- \(\frac{dM}{d} = \frac{A}{2}\)[/tex] suggests a constant rate of change, which does not depend on [tex]\(M\).[/tex]
[tex]- \(\frac{dM}{d} = \frac{k}{M}\)[/tex] suggests an inverse relationship, which is incorrect.
6. Conclusion:
- The differential equation that models the relationship between the mass of the sample and the rate of change of the mass is:
[tex]\[ \frac{dM}{dt} = kM \][/tex]option B)
Complete Question:
Amara needs 454545 kilograms of meat to feed her 222 pet dragons each day. Each pet dragon eats the same amount of meat.
Answer:
2047.5 kg
Step-by-step explanation:
There's a total of 454545 kg of meat, and each dragon gets x kg. There are 222 dragons. So, we have the equation: 222x = 454545
Divide by 222 from both sides: x = 2047.5 kg
Thus, each dragon gets 2047.5 kg of meat.
Hope this helps!