Answer:
There are 79,800 ways in which this is possible.
Step-by-step explanation:
The order in which the students are chosen is important(due to different roles), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
2 sophomores from a set of 20.
2 freshmen from a set of 15. So
[tex]P_{20,2}*P_{15,2} = \frac{20!}{18!}*\frac{15!}{13!} = 20*19*15*14 = 79800[/tex]
There are 79,800 ways in which this is possible.
It is commonly said that 10 of people are left-handed, but Lilianna suspected that a higher proportion of art students at her university are left-handed. To test this theory, she took a sample of 150 art students and found that p^=14% of the sample was left-handed.
To see how likely a sample like this was to happen by random chance alone, Lilianna performed a simulation. She took a sample of n=150 students from a population where 10% of the students were left-handed, and she recorded what proportion of the sample was left-handed. She repeated this process for a total of 50 samples. Here are the sample proportions from her 50 samples:
She wants to test H0:p=10% vs. Ha:p>10% where p is the proportion of art students at her university who are left-handed.
Based on these simulated results, what is the approximate p-value of the test?
Note: The sample result was p^=14%.
Answer: p-value ≈ 0.08
Step-by-step explanation:
The approximate p-value of the test is 0.0136 as per the data given in question.
What is p-value?The p value is a number calculated from a statistical test that describes the likelihood of finding a specific set of observations if the null hypothesis is true.
To find the approximate p-value of the test, we need to compare the sample proportion p^ to the hypothesized proportion p0 = 10% under the null hypothesis H0:p=10% vs. Ha:p>10%.
Since the sample size n is large (n = 150) and the null hypothesis assumes a normal distribution.
We can use the normal approximation to the binomial distribution. Under the null hypothesis, the test statistic z is given by:
z = (p^ - p0) / sqrt(p0 * (1 - p0) / n)
Plugging in the values, we get:
z = (0.14 - 0.1) / sqrt(0.1 * 0.9 / 150)
z = 2.22
The approximate p-value for this one-tailed test can be found by looking up the area to the right of z = 2.22 under the standard normal distribution.
Using a standard normal distribution table or calculator, we find that the area to the right of z = 2.22 is approximately 0.0136.
Therefore, the approximate p-value of the test is 0.0136. This means that if the true proportion of left-handed art students at the university is 10%, there is approximately a 1.36% chance of getting a sample proportion of 14% or higher by random chance alone.
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Help #1-4 please please just add the symbol addition , subtraction , multiplication or division . I tried 1.subtraction 2&3 division & 4 multiplication but they are wrong so please help
Problem 1
Operation = Subtraction
Estimated answer = 8 dollars
----------------------------
Explanation:
The regular price is estimated at $45, while the sale price is estimated at $37. The two subtract to get 45-37 = 8 dollars, which is about how much you save if you go for the discount price.
The actual amount saved is 45.32-36.50 = 8.82
==========================================================
Problem 2
Operation = Division
Estimated answer = 75 cents
----------------------------
Explanation:
$3.45 rounds to $3
Divide this over 4 to get 3/4 = 0.75, meaning each battery is 75 cents
The actual cost per battery is 3.45/4 = 0.86 dollars = 86 cents.
==========================================================
Problem 3
Operation = Division
Estimated answer = $10
----------------------------
Explanation:
Round $37.45 to the nearest ten to get $40; we could round to 37 but that's an oddball number in my opinion compared to 40. Plus 40 is divisible by 4, leading to 40/4 = 10. Each person chips in about 10 dollars.
The actual amount each person pays is 37.45/4 = 9.36
==========================================================
Problem 4
Operation = Multiplication
Estimated answer = 180 miles
----------------------------
Explanation:
18.75 rounds to 20, which we multiply by 9 to get 180
So the car can travel about 180 miles on 9 gallons. This is an overestimate because 18.75 rounded up to 20
The actual value is 18.75*9 = 168.75
Determine which of the lines, if any, are parallel or perpendicular. Explain.
When Natalie runs the 400 meter dash, her finishing times are normally distributed with a mean of 71 seconds and a standard deviation of 2.5 seconds. What percentage of races will her finishing time be between 71 and 77 seconds, to the nearest tenth?
Answer:
49.2%
Step-by-step explanation:
President Obama wrote a children's book about extraordinary Americans. One of those
Americans was Albert Einstein. One of Einstein's equations is shown below. Rearrange the
equation to solve for c
E = mc² where Eis energy, m is mass, and c is the speed of light
A) c = (E2 - m)1/2
B) c = E - m2
C) c = (E/m) 1/2
D) c = Em2
plz help me 5th grade work
Answer:
8 AND 12
Step-by-step explanation:
MAURICE 8
MIRANDA 12
What is the measure of angle 1?
PLEASE HELP ME 8 NEED THIS FPR A TEST TMRW
Class A has 12 pupils and class B has 25 pupils.
Both classes sit the same maths test.
The mean score for class A is 80.
The mean score for both classes is 74.
What is the mean score (rounded to 2 DP) in the maths test for class B?
Answer:
71.12
Step-by-step explanation:
80*12= 960
37*74=2738
2738-960=1778
1778/25=71.12
Answer:
71.12
Step-by-step explanation:
80*12= 960
37*74=2738
2738-960=1778
1778/25=71.12
Mark it as brainly please
12 ly
Which statement is true regarding the functions on the
graph?
10
8
-6
4
919
Of(6) = g(3)
O f(3) = g(3)
Of(3) = g(6)
Of(6) = g(6)
-6-
2
3 4 5 6 x
4 -3 -2 -12
- fix
-6
-8
-10
-12
Answer: f(3)=g(3)
Step-by-step explanation:
The graphs intersect at x = 3.
The statement "f(6) = g(3)" is true.The correct option is A.
What is a graph?A graph is a structure that amounts to a set of items where some pairs of objects are in some manner "related" in discrete mathematics, more specifically in graph theory.
From the graph, we can see that the value of f(6) is 2, and the value of g(3) is also 2.
The statement "f(3) = g(3)" may or may not be true, as we do not know the values of f(3) and g(3) from the graph.
The statement "f(3) = g(6)" is not true, as the value of f(3) on the graph is -2, and the value of g(6) is 4.
The statement "f(6) = g(6)" is also not true, as the value of f(6) on the graph is 2, and the value of g(6) is 4.
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the perimeter of a square bulletin board is 280 cm how long is one of its side
i follow who answer this;)
Answer:
70cm
Step-by-step explanation:
Perimeter of square= 4×Side
280/4=Side
70=Side
70cm
hope it helps
[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]
Perimeter of square = 4a
280 = 4a
a =
[tex]280 \div 4 = 7 0 [/tex]
Side = 70cmThanks Hope it helpsThe sum of a number and 45 plz need the answe
Answer:
n + 45
Step-by-step explanation:
The question is asking to write an algebraic expression for the sum of a number and 45. We know we are adding a number to 45. So we use addition. But, we don't which number we are adding to 45. So we just use a variable. I used "n", but use whatever letter you want ( x, y, z, etc). I recomend using the same variable that your intrcuctor uses.
Hope this helps.
which parent function have a domain of all real numbers? select all that apply.
Answer:
1 2 4 and 6 i believe these are right i checked
Write a sine function that has an amplitude of 5, a midline of 2 and a period of 8pi/5.
Answer:
f(x) = 5*sin( (5/4)*x) + 2
Step-by-step explanation:
A general sine function can be written as:
f(x) = A*sin(w*x) + M
Where:
A is the amplitude
w is the frequency of the function
M is the midline
Here we know that we want to have:
An amplitude of 5. Then, A = 5
A midline of 2, then M = 2
And a period of (8/5)*pi
For now, we can write our function as:
f(x) = 5*sin(w*x) + 2
Now, we know that for a function of period T, is always true that:
f(x) = f(x + T)
here, the period is T = (8/5)*pi
knowing that sin(0) = sin(2*pi)
Then we must have:
sin(0) = sin(w*0) = sin(w*( 0 + (8/5)*pi)) = sin(2*pi)
Then the arguments of the third and fourt parts must be the same, thus:
w*(8/5)*pi = 2*pi
We can solve this for w now:
w*(8/5) = 2
w = 2*(5/8) = (5/4)
Then the function is:
f(x) = 5*sin( (5/4)*x) + 2
Chelsea bought a computer on Monday for $1,300. Its value is predicted to decrease by $250 per year. Her brother George also bought a computer on Monday. The function g(x) = 1,100 – 175x predicts how the value of his computer is expected to change after x years.
Whose computer is expected to have a greater value when it is 3 years old, and how much greater will it be?
A) Chelsea’s computer is expected to have a value of $25 greater.
B) George’s computer is expected to have a value of $25 greater.
C) Chelsea’s computer is expected to have a value of $125 greater.
D) George’s computer is expected to have a value of $125 greater.
Answer:
The correct answer is B. George’s computer is expected to have a value of $25 greater.
Step-by-step explanation:
Since Chelsea bought a computer on Monday for $ 1,300, and its value is predicted to decrease by $ 250 per year, while her brother George also bought a computer on Monday, and the function g (x) = 1,100 - 175x predicts how the value of his computer is expected to change after x years, to determine whose computer is expected to have a greater value when it is 3 years old, and how much greater will it be, the following calculation must be performed:
Chelsea:
1,300 - (250 x 3) = X
1,300 - 750 = X
550 = X
George:
1,100 - (175 x 3) = X
1,100 - 525 = X
575 = X
Therefore, George’s computer is expected to have a value of $ 25 greater.
please help asap!!! 20 points!! 6th grade math.
Answer:
What? i can't even read it
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
From a 60-ft observation tower on the coast, a Coast Guard officer sights a capsized boat. The angle of depression to the
boat is 5º. How far is the boat from the shoreline?
A. 173 ft
B. 523 ft.
C. 686 ft.
D. 60 ft.
C
How far is the boat from the shoreline? C. 686 ft.
the product of 6 less than a number and 4 more than the
number
Answer:
(x-4)(x+8)
Step-by-step explanation:
Simplify [tex]\frac{4}{\sqrt{6} }[/tex]
you have money for the amusement park you spent $6 on bumper cars and have $12 left and solve an equation that gives the amount of money you started with.
Answer:
The expression ( Unsolved equation ) would be 12 + 6 = X .
The answer would be X = 18 .
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A town is trying to determine if a new recycelin incentive would increase the number of people thatseperate their garbage from recycable iems. to make this determination a simple random sample of 10 streets and the number of people that recycle on these streets is countedonce before and once after the recycling incentive has been intitated. the date shows a mean difference of3.78 and a standard deviation of 1.33.
Required:
Determie if the recycling incentive was effectiive with a 5% significnc level.
Answer:
The recycling incentive was effective at 5% significance level.
Step-by-step explanation:
The null and alternative hypothesis are
H0 u1≤ u2 against the claim Ha: u1> u2
or
H0 ud=0 against the claim Ha: ud > 0
The significance level is ∝=0.05
Data given
d`= 3.78
sd= 1.33
n= 10
The test statistic is
t= d`/ sd/ √n
t= 3.78/1.33/√10
t= 9.3889
The critical region for ∝=0.05 and df.= (n-1)= 9 is t> 1.833
Since the calculated value of t lies in the critical region it is concluded that new recycling incentive would increase the number of people that seperate their garbage from recyclable items.
H0 is rejected and Ha is accepted.
You randomly select a card from a 52-card deck. Find the probability of selecting a 7 or an Ace.
Answer:
15.38%
Step-by-step explanation:
There are 4 7's in a deck of 52 cards.
There are 4 Aces in a deck of 52 cards.
4+4 = 8
8/52, or 15.38%
=================================================
Explanation:
There are four cards labeled "7", and four cards that are aces. We have 4+4 = 8 cards that we want to find. This is out of 52 total.
The probability we're after is 8/52 = (4*2)/(4*13) = 2/13
2/13 = 0.1538 = 15.38% approximately
Which set of angle measures would determine a triangle?
A. 750, 150, 10°
B. 150°, 20°, 50°
O C. 50°, 50°, 100°
D. 75º, 5º, 100°
E. 70°, 60°, 40°
Answer: I think it’s E
Step-by-step explanation:
Answer:
D. 75°, 5•, 100°
Step-by-step explanation:
All angles in a triangle add up to 180°
what is 4 2/5 - 1 1/4 how would you get the answer
Step 1 [tex]4\frac{2}{5}-1\frac{1}{4}[/tex]
Step 2 [tex]4\frac{2*4}{5*4} - 1 \frac{1*5}{4*5}[/tex]
Step 3 [tex]4 \frac{8}{20} - 1 \frac{4}{20}[/tex]
Step 4a [tex]4 - 1 = 3[/tex]
Step 4b [tex]\frac{8}{20} - \frac{4}{20} = \frac{4:4}{20:4} = \frac{1}{5}[/tex]
Step 5 (final answer) [tex]3\frac{1}{5}[/tex]
there were 7 pizzas. 5 people ate all of the pizzas, each person ate an equal amount of pizza. how much pizza did each person eat
Answer:
1 2/5 pizza each
Step-by-step explanation:
I think this is QUITE obvious but
you divide 7 by 5 because its an equal amount per person which gives you 7/5 = 1 2/5
Answer:
1.4 of the pizza or [tex]1\frac{2}{5}[/tex] of the pizza
Step-by-step explanation:
Do 7 ÷ 5 (7 pizzas divided among 5 people)
Each person ate 1.4 or [tex]1\frac{2}{5}[/tex] pizza
The length of the base of an isosceles triangle is 8 yards. The height of the triangle is 11 yards. Find the area of the triangle.
Answer:
A=44yd²
Step-by-step explanation:
Select the correct answer. What is the domain of y=cos(x)? PLEASE HELP
y = cos (x) y = cos (x) The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Cos function defines in all range the domain of the y = cos(x) will be all real number.
What is a trigonometric function?The domain input value for the six basic trigonometric operations is the angle of a right triangle, and the result is a range of numbers.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
It will be possible to comprehend the graphs, domains, differentiation, and integration of the four quadrants' trigonometric functions.
The domain of the function y=cos(x) is all real numbers.
Cosine is defined as any angle measure
The range of the angle y will be -1 to 1 which is −1≤y≤1.
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Allie made the line plot below to show the lengths of strings she cut for her art project.
What is the difference in length between the length of string she used most often and the length of string she used least often?
how can she die Lol free pts man LOL
Answer:
1/4, or 0.25 inches
Step-by-step explanation:
You count the dots. The number of dots tell you how many of each length of string she used.
You first find the column with the most dots, and then you find the column with the least. Then you just subtract them, the number of inches it displays on the bottom, 12 1/2 - 12 1/4, which is 1/4. I did this in my head and you can use a calculator if you want.
Thanks for the points, and have a blessed day. Hope this helps.
Answer:
Im pretty sure you acc was deleted so whatever dude the length was 69 inches and 420 millimeters
Help !!!!!!!!!!!!!!!!!!!!!
Answer:
sorry but I am not able to answer the question