A bag of marbles contains three blue, one black, and four
yellow marbles. If two marbles are chosen at random
without replacement, what is the probability that both
marbles will be yellow?
Answer:
3/14Step-by-step explanation:
Blue = 3Black = 1Yellow = 4Total = 3 + 1 + 4 = 8
Probability of two yellows:
4/8*3/7 = 3/14. The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.† Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes. Suppose that the sample standard deviations were 25 minutes for the U.S. sample and 49 minutes for the Mexico sample. The report concludes that on average, adults in the United States get less sleep on work nights than adults in Mexico. Is this a reasonable conclusion? Support your answer with an appropriate hypothesis test. (Use
= 0.05.
Use 1 for Mexico and 2 for the United States.)
Answer:
Yes the conclusion in the question is a reasonable conclusion
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_1 = n_2 = n = 250[/tex]
The sample mean for USA is [tex]\= x_1 = 391 \ minutes[/tex]
The sample mean for Mexico is [tex]\= x_2 = 426 \ minutes[/tex]
The sample standard deviation for USA is [tex]s_1 = 25 \ minutes[/tex]
The sample standard deviation for Mexico is [tex]s_2 = 49 \ minutes[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 < \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x_1 - \= x_2 }{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2 } } }[/tex]
=> [tex]z = \frac{ 391 - 426 }{ \sqrt{ \frac{25^2}{250} + \frac{49^2}{250} } }[/tex]
=> [tex]z = -10[/tex]
From the z table the area under the normal curve to the left corresponding to -10 is
[tex]p-value = P(Z < -10 ) = 0.00[/tex]
Generally from the value obtained we see that
The p-value is < [tex]\alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
The is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico
Hence the conclusion in the question is a reasonable conclusion
The p-value is less than [tex]\alpha[/tex] hence reject the null hypothesis. This is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico and hence it is a reasonable conclusion given in the problem.
Given :
The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night.For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes.Suppose that the sample standard deviations were 25 minutes for the U.S. sample and 49 minutes for the Mexico sample.According to the given data the sample size of the US and Mexico is [tex]\rm n_1=n_2=250[/tex].
The hypothesis are as follows:
Null Hypothesis is [tex]\rm H_0 : \mu_1=\mu_2[/tex]
Alternate Hypothesis is [tex]\rm H_1 : \mu_1<\mu_2[/tex]
Now, the mathematical representation of test statistics is:
[tex]\rm z = \dfrac{\bar{x_1}-\bar{x_2}}{\sqrt{\dfrac{\sigma^2_1}{n_1}+\dfrac{\sigma^2_2}{n_2}} }[/tex]
[tex]\rm z = \dfrac{391-496}{\sqrt{\dfrac{25^2}{250}+\dfrac{49^2}{250}} }[/tex]
z = -10
According to the z-table:
p - value = p (Z < -10) = 0
The p-value is less than [tex]\alpha[/tex] hence reject the null hypothesis.
This is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico and hence it is a reasonable conclusion given in the problem.
For more information, refer to the link given below:
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HELP ME PLEASEEEEEEEEEE
PLEASE HELP WILL GIVE BRAINLIEST
Does the following table represent a linear function? If so, find the linear equation that models the data.
A classroom is painting the classrooms. Each classroom takes 1/3 of a gallon of
paint. If the school buys 6 gallons of paint, how many classrooms can they paint?
Plz help
Answer: try 18
Step-by-step explanation:
easy question if your having big problem
Answer:
whats the problem
Step-by-step explanation:
Answer:
yup
Step-by-step explanation:
Solve this equation 5x -7 = -12
Answer:
The answer is x = -1
Step-by-step explanation:
Answer:
x=-1
Step-by-step explanation:
5x-7=-12
5x=-5
x=-1
A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. Answer parts a and b.
a. To what percent of its capacity is the large container filed?
The container is filled to % of the maximum capacity.
Answer:
The container is filled to 87.5% of the maximum capacity.
Step-by-step explanation:
Given
Maximum capacity of container = m = 64 ounces
Filled capacity=> as it is 8 less than maximum capacity = 64-8 = 56 ounces
The container is 56 ounces full.
To find the percentage:
[tex]percentage = \frac{56}{64}*100\\= 0.875*100\\=87.5\%[/tex]
Hence,
The container is filled to 87.5% of the maximum capacity.
Which container holds more, a half-gallon milk jug or a 2-liter juice bottle
Answer:
1 gallon=3.79 liters 2 liter juice bottle would hold more
Step-by-step explanation:
Simplify:
3^x-1 × 27^x+1
___________
81^x
Answer:
3^x-1×27^x+1
___________
81^x
81^x+x-1+1
_________
81^x
81^2x
_____
81^x
81^2x-1x
81^1x
4(2x-15)+7(3x+2)=70?
Answer:
the answer is [tex]x=4[/tex]
Step-by-step explanation:
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.
hope this helps :)
What is the difference between ploting (2, 3) and (3, 2)
on a coordinate plane? Explain.
For every 24 cookies, there are 12 students. Which ratio does not represent cookies to students?
Answer: 12:24
Step-by-step explanation:
You can’t have 12 students to each cookie
Answer:
D: 2 students for every cookie
Step-by-step explanation:
D does not represent the ratio of cookies to students because it claims there are 2 students to every cookie, where there are 2 cookies for every student.
Please answer, will give brainliest.
Answer:
third one
Step-by-step explanation:
Answer:
I think one solution
Step-by-step explanation:
*Sorry if this did not help. I'm only in 5th grade*
(b) 25% of what number is 17?
Answer:
68
Step-by-step explanation:
derive that 25 percent of 68 equals 17.
Answer:
25 percent of 68 equals 17.
Step-by-step explanation:
Which number line correctly shows -3-(1.5)
Write a cubic function whose graph is shown
Answer:
f(x) = x³ - 2x² - x + 2
Step-by-step explanation:
Since, the graph attached has three zeros (x-intercepts) at x = -1, 1 and 2,
Equation of the given function will be,
f(x) = (x + 1)(x - 1)(x - 2)
By solving this equation,
f(x) = (x² - 1)(x - 2)
= x²(x - 2) - 1(x - 2)
= x³ - 2x² - x + 2
Therefore, answer will be f(x) = x³ - 2x² - x + 2.
According to the given graph,
Three zeros,
x = -1, 1, and 2The function will be:
→ [tex]f(x) = (x+1)(x-1)(x-2)[/tex]
By solving this, we get
[tex]= (x^2-1)(x-2)[/tex]
[tex]= x^2(x-2)-1(x-2)[/tex]
[tex]= x^3-2x^2-x+2[/tex]
Thus the function above is right.
Learn more about cubic function here:
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Mrs. Dimitri purchased a case of yogurt cups. Out of every 10 yogurt cups, 6 are strawberry. There are 30 yogurt cups in the case. How many yogurt cups are strawberry?
Answer:
18
Step-by-step explanation:
The ratio of strawberry yogurt cups to all of the yogurt is 6:10. We know that there are 30 total yogurt cups, which is the same as 3 times 10. to find the number of strawberry cups, 6 should be multiplied by 3 as well to equal 18. 18:30 is still the same ratio as 6:10
Please helpp I’ll give brainleist
Answer:
87 for lo and om is 56
Step-by-step explanation:
Answer:
<LON= 98 Degrees
Step-by-step explanation:
180-55(2)=70
70+28=98
Rob is setting up a model train track that is 3 and 3 over 8 feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole every 3 over 8 foot apart. How many telephone poles does he need? (Input number values only.
Answer:
9?
Step-by-step explanation:
Answer:
sorry dont understaand
Step-by-step explanation:
If a wagon is accelerating at a rate of 2 m/s and the
force acting on it is 20 N, what is the mass of the
wagon?
Answer:
40kg
Explanation:
a=2m/s^
f=20N
M=?
we know
f=m*a
or, 20=m*2
or, 2m=20
or, m= 20/2
:. m=10 kg
Element X is a radioactive isotope such that every 40 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 110 grams, how much of the element would remain after 29 years, to the nearest whole number?
Answer:67 or 66.549674907
Step-by-step explanation:
Man women baby
In an arithmetic sequence, the seventh term is −9 and the nineteenth term is 39.
Find the common difference. Give only the exact value as your answer.
Answer:
37.5% that is the answer
Step-by-step explanation:
The required common difference is 4.
What is an arithmatic progression?An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.
Now it is given that,
the seventh term, T₇ = −9 and
the nineteenth term, T₉ = 39.
Let a be the first term, d is the common difference and n is the number of term.
Since Tn of the series is given as,
Tn = a + (n-1)d
Therefore,
T₇ = a + (7-1)d
⇒ -9 = a + 6d ...(i)
and,
T₉ = a + (19-1)d
⇒ 39 = a + 18d ...(ii)
Subtracting equation (ii) by (i) we get,
48 = 12d
or, d = 48/12
⇒ d = 4
Thus, the required common difference is 4.
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which point of the number line represents negative 4/5?
A
B
C
D
Answer:
the answer is A
Step-by-step explanation:
find the slope intercept form of the equation of the line that passes through (-1,5) and is parallel to the line y=2x+4
Answer:
y = 2x + 7
Step-by-step explanation:
Simplify 18 - 6x + 5x - 11
Answer:
7-x
Step-by-step explanation:
18-11=7
-6x+5x=-x
therefore, the answer is 7-x
The solution of the expression is,
⇒ - x + 7
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,
⇒ 18 - 6x + 5x - 11
Now, We can solve the expression as;
⇒ 18 - 6x + 5x - 11
Rearrange as;
⇒ - 6x + 5x + 18 - 11
Combine like term as;
⇒ - x + 7
Thus, The solution of the expression is,
⇒ - x + 7
Learn more about the mathematical expression visit:
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find the lowest common multiple (LCM) of 15 and 30.
A) 5
B) 15
C)30
D)60
Answer:
L.C.M of 15 and 30 is 30.
please help UwU
if correct you get Brainiest
Answer: C
Step-by-step explanation:
Could someone answer this I am a bit confused I will give a brainlist for the right answer I promise :)
Answer:
NP=14
BC=44
Step-by-step explanation:
[tex]60-24-22=14\\NP=14\\MN=BP=PC\\BC=2(MN)\\BC=44[/tex]
Mrs. Savino runs 3 miles in 28 minutes. At this rate, how many minutes would it take her to run 15 miles? * Need it ASAP
Answer:
she would take 140 minutes to run 15 miles
Step-by-step explanation:
28 X 5 os equal to 140
Answer:
139.95
Step-by-step explanation:
28 divided by 3 is 9.33 so 9.33x 15=139.95