Correct question is ;
The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of nine students and eleven faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of six students and two faculty?
Answer:
A) 7.144 × 10^(-5)
B) 0.00131
C) 0.0367
Step-by-step explanation:
We are given;
Number of students = 9
Number of faculty members = 11
A) Now, the number of ways we can select eight students from 9 =
C(9, 8) = 9!/(8! × 1!) = 9
Also, number of ways of selecting 8 individuals out of the total of 20 = C(20,8) = 20!/(8! × 12!) = 125970
Thus, probability of selecting a jury of all students = 9/125970 = 7.144 × 10^(-5)
B) P(selecting a jury of all faculty) = (number of ways to choose 8 faculty out of 11 faculty)/(Total number of ways to choose 8 individuals out of 20 individuals) = [C(11,8)]/[C(20,8)] = (11!/(8! × 3!))/125970 = 0.00131
C) P(selecting a jury of six students and two faculty) = ((number of ways to choose 6 students out of 9 students) × (number of ways to choose 2 faculty out of 11 faculty))/(Total number of ways to choose 8 individuals out of 20 individuals) = [(C(9,6) × C(11,2)]/125970
This gives;
(84 × 55)/125970 = 0.0367
sasha has some pennies nickels and dimes in her pocket. the number of coins is 18 the expression is 0.01p+0.05n+0.10d represents the value of the coins which is 1.08 she has twice as many dimes as pennies. How many of each coin does Sasha have
Answer:
3 pennies, 9 nickels, and 6 dimes
Step-by-step explanation:
We have three conditions:
(1) p + n + d = 18
(2) 0.01p + 0.05n + 0.10d = 1.08
(3) d = 2p
Multiply (2) by 100 and rearrange (3) to get a standard array.
(4) p + n + d = 18
(5) p + 5n + 10d = 108
(6) -2p + d = 0
Subtract (4) from (5). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(6) -2p + d = 0
Multiply (4) by 2 and add to (6). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(8) 2n + 3d = 36
Double (8) and subtract from (7). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(9) 3d = 18
Divide (9) by 3. This gives
(10) d = 6
Substitute (10) into (7). This gives
4n + 9(6) = 90
4n + 54 = 90
4n = 36
(11) n = 9
Substitute (10) and (11) into (4). This gives
p + 9 + 6 = 18
p + 15 = 18
p = 3
Sasha has 3 pennies, 9 nickels, and 6 dimes.
find the value of each variable and the measure of each angle
Answer:
Left angle = 60°
Top angle = 120°
Right angle = 60°
Step-by-step explanation:
Use what you know about angle relationships to set up equations you can solve for each variable.
The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.
You have two variables, so you need at least two equations (I made three but only used two).
The work is in my attachment, comment of you have questions.
2.
The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site
are approximated by
77
S=56.9–40.7cos
6
where t is the time in months), with t=1 corresponding to January. Determine the months when
sales exceed 7700 units at any time during the month.
O May through September
O March through August
O March through September
O April through August
O August through April
Answer:
March through August
Step-by-step explanation:
Ok, in order to solve this problem, we must start by building an equation to solve. The original equation was:
[tex]S=56.9-40.7cos (\frac{\pi}{6}t)[/tex]
and we need to figure out the months when the sales exceed 7700 units. Since the equation is given in hundreds of units, we need to divide those 7700 units into one hundred to get 77 hundred units. So we can go ahead and substitute that value in the equation:
[tex]77=56.9-40.7cos (\frac{\pi}{6}t)[/tex]
if you wish you can rewrite the equation so the variable is on the left side of it but it's up to you. So you get:
[tex]56.9-40.7cos (\frac{\pi}{6}t)=77[/tex]
and now we solve for t
[tex]-40.7cos (\frac{\pi}{6}t)=77-56.9[/tex]
[tex]-40.7cos (\frac{\pi}{6}t)=20.1[/tex]
[tex]cos (\frac{\pi}{6}t)=\frac{20.1}{-40.7}[/tex]
[tex]cos (\frac{\pi}{6}t)=-0.4938[/tex]
[tex]\frac{\pi}{6}t=cos^{-1}(-0.4938)[/tex]
[tex]\frac{\pi}{6}t=2.087[/tex]
[tex]t=\frac{2.087(6)}{\pi}[/tex]
[tex]t=3.98 months[/tex]
but there is a second answer to this problem. Notice that the function cos can be 2.87 at [tex]2\pi-2.087=4.1962 rad[/tex] as well, so we repeat the process:
[tex]\frac{\pi}{6}t=4.1962[/tex]
[tex]t=\frac{4.1962(6)}{\pi}[/tex]
[tex]t=8.014 months[/tex]
So now we need to determine on which period of times the number of items sold exceed 77 hundred units so we build different intervals for us to test:
(1,3.98) (3.98,8.014) and (8,014, 13)
and find a test value for each of the intervals and test it.
(1,3.98) t=2
[tex]S=56.9-40.7cos (\frac{\pi}{6}(2))[/tex]
S=36.55
this is less than 77 so this is not our answer.
(3.98,8.014) t=5
[tex]S=56.9-40.7cos (\frac{\pi}{6}(5))[/tex]
S=92.15
this is more than 77 so this is our answer.
(8.014,13) t=10
[tex]S=56.9-40.7cos (\frac{\pi}{6}(10))[/tex]
S=36.55
this is less than 77 so this is not our answer.
so, since our answer is the interval (3.98,8.014)
this means that between the months of march and august we will be sellin more than 7700 units.
Jerry was given some birthday money He puts the money in an account Every month after that he deposits the same amount of money The equation that models this situation y=50x+75 where y is the amount of money int he account and x is the number of deposits What does the y- intercept means in this situation
Answer: He was given $75 for his birthday
Step-by-step explanation:
The y - intercept represents the rate of which the money is being deposited in the account.
What is linear equation in two variable ?"An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero."
"The solution of linear equations in two variables, ax+by = c, is a particular point in the graph, such that when x-coordinate is multiplied by a and y-coordinate is multiplied by b, then the sum of these two values will be equal to c.
Basically, for linear equation in two variables, there are infinitely many solutions."
The given equation is y = 50x + 75
The y intercept represents the amount of money to be deposited in account. The rate of change of money in the account with represent to the months.
Hence, y represents money deposited in the account.
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Find the area of the shaded triangle below.
Answer:
A = 12 square units
Step-by-step explanation:
Area of a Triangle = base * height / 2
The triangle might look weird and doesn't look like it has a base, but if you look at the left side you see there is a straight line which means there is a base, so we flip the picture until we see that the flat line on the bottom or the base.
The base is 4 units.
To find the height, we don't need a straight line, we just need to see how the tall the triangle is, to do that you must start from the lowest point and count up to the highest point.
You now get 6 units.
A = bh/2
A = 4*6/2
A = 24/2
A = 12 square units
Which solution value satisfies the inequality equation x – 5 ≤ 14?
Answer:
Any value that has x less than or equal to 19 is a solution
Step-by-step explanation:
x – 5 ≤ 14
Add 5 to each side
x – 5+5 ≤ 14+5
x ≤ 19
Any value that has x less than or equal to 19 is a solution
Answer:
[tex]\boxed{x\leq 19}[/tex]
Step-by-step explanation:
[tex]x-5\leq 14[/tex]
[tex]\sf Add \ 5 \ on \ both \ sides.[/tex]
[tex]x-5+5 \leq 14+5[/tex]
[tex]x\leq 19[/tex]
What is the product of 8.0425 x 2.6?
Answer:
20.9105
Step-by-step explanation:
8.0425
2.6
80425*26=2091050
there is 5 decimals so you move the decimal over to the left 5 times
20.9105 :)
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³ – 1, what is p(t)?
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]
Cheers.
Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
What is composite functionThe composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.
In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.
Solving a composite function means finding the composition of two functions.
Function p(t)The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:
s(t)= q[p(t)]
4t -21= 4[p(t)]³ – 1
Solving:
4t -21 +1= 4[p(t)]³
4t -20 = 4[p(t)]³
(4t -20)÷ 4 = [p(t)]³
4t÷4 -20÷ 4 = [p(t)]³
t -5 = [p(t)]³
[tex]\sqrt[3]{t-5}=p(t)[/tex]
Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
Learn more about composite function:
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Anna is paid $14.75 per hour. She works a
12 hour shift, the last 4 hours being at a double
time pay rate. What is Anna's wage before
tax?
HELP
Answer:
$336
Step-by-step explanation:
$14.75(8) + $14.75(2)(4) - (8 hours of normal shift) + (double pay rate)(for 4 hours)
= $118 + $118 - Add
= $336
Which expression is equivalent to x12 + 5x6 – 14?
Given g(x) = -x - 2, find g(3).
Answer:
g(3) = -5
Step-by-step explanation:
g(3) is basically the value of g(x) when x = 3. Therefore, g(3) = -3 - 2 = -5.
Answer:
[tex] \boxed{\sf g(3) = -5} [/tex]
Given:
g(x) = -x - 2
To Find:
g(3) i.e. g(x) where x = 3
Step-by-step explanation:
[tex]\sf Evaluate \ -x - 2 \ where \ x = 3:[/tex]
[tex] \sf \implies - x - 2 = - 3 - 2[/tex]
[tex] \sf - 3 - 2 = - (3 + 2) : [/tex]
[tex] \sf \implies - (3 + 2)[/tex]
[tex] \sf 3 + 2 = 5 : [/tex]
[tex] \sf \implies - 5[/tex]
A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of seven marbles include at least one yellow one but no green ones
Answer: 8
Step-by-step explanation:
Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.
Total marbles other than green = 8
Total marbles other than green and yellow = 6
Then the number of sets of seven marbles include at least one yellow one but no green ones:-
[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]
Number of sets of seven marbles include at least one yellow one but no green ones = 8
Find the sum of the first 30 terms in the sequence in #2. (Sequence is 16, 7, -2, …) Just need sum of first 30 solved :)
The sequence is arithmetic, since the forward difference between consecutive terms is -9.
7 - 16 = -9
-2 - 7 = -9
etc.
This means the sequence has the formula
[tex]a_n=16-9(n-1)=25-9n[/tex]
The sum of the first 30 terms is
[tex]\displaystyle\sum_{n=1}^{30}a_n=25\sum_{n=1}^{30}1-9\sum_{n=1}^{30}n[/tex]
Recall the formulas,
[tex]\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n[/tex]
[tex]\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2[/tex]
Then the sum we want is
[tex]\displaystyle\sum_{n=1}^{30}a_n=25\cdot30-\frac{9\cdot30\cdot31}2=\boxed{-3435}[/tex]
A line passes through (-5, -3) and is parallel to -3x - 7y = 10. The equation of the line in slope-intercept form is _____
Answer:
-3x - 7y = 36
Step-by-step explanation:
The given line -3x - 7y = 10 has an infinite number of parallel lines, all of the form -3x - 7y = C.
If we want the equation of a line parallel to -3x - 7y = 10 that passes through (-5, -3), we substitute -5 for x in -3x - 7y = 10 and substitute -3 for y in -3x - 7y = 10:
-3(-5) - 7(-3) = C, or
15 + 21 = C, or C = 36
Then the desired equation is -3x - 7y = 36.
find the unknown angles
Answer:
y=135
x=45
Step-by-step explanation:
x= 45
It is an isosceles so
180-90=90
90/2= 45
y=135
angles on a straight line add up to 180 so
180-45=135
Hope this helps!
A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are as follows: 22 17 27 20 23 19 24 18 19 24 We want to determine at the 5% significance level that the population mean is not equal to 20. What is the rejection region?
Answer:
0.09
Step-by-step explanation:
Let x = ages of mother
x : 22 17 27 20 23 19 24 18 19 24
N = 10
Mean = ∑x/N = 218/10 = 21.8
Difference in mean = 21.8 - 20 = 1.8
If significance level = 5% or 0.05
∴ Rejection region = 1.8 X 0.05 = 0.09
helpppppppppppppppppppppppppppp give bralienst
Answer:
Brainliest! Hope I helped!
Step-by-step explanation:
you know its greater than 1cm and less than 2cm,
1 and 7hundreths cm is = 1.07 cm
thats not right because you know it is greater than that for sure!
so the only answer left is 1.7 cm
You answer is 1.7 cm
another way...
read the ruler and see the answer
Answer:
1.7 cm.
Step-by-step explanation:
The midpoint of 1 - 2 is 5 so count the lines after 5 and you get .7 to add to one cm.
Hope this helps, have a good day :)
how much would it cost to buy 100 shares in ODX group Inc and 300 shares
Complete Question
The complete question is shown on the first uploaded image
Answer:
The cost to buy 100 shares in ODX group Inc and 300 shares peer Comms Lts is
[tex]C = \$ 775[/tex]
Step-by-step explanation:
From the chat we that the cost of 100 ODX shares is [tex]\$175[/tex]
The cost of 100 peer Comms Lts is [tex]\$ 200[/tex]
Hence the cost 300 peer Comms Lts is [tex]k = 3 * 200 = \$ 600[/tex]
Now the cost of 100 shares in ODX group Inc and 300 shares of peer Comms Lts is mathematically evaluated as
[tex]C = 175 + 600[/tex]
[tex]C = \$ 775[/tex]
The cost to buy 100 shares in ODX group Inc and 300 shares in peer comm LTD is $775.
Given in question the graph here is missing.
We have to calculate the total cost of 100 shares in ODX group Inc and 300 shares in peer comms limited in year 5.
From the graph it is clear that, the x axis shows the no. of year and y axis shows the cost of 100 shares for each type.
From graph, the cost of 100 shares of ODX group in year 5 is $175.
And the cost of 100 shares of peer comm Ltd in year 5 is $ 200.
So the total cost of 300 shares of peer comm Ltd in 5 year is $([tex]200\times3[/tex]) or $600.
Now final cost of 100 shares in ODX group Inc and 300 share in peer comm Ltd is [tex]($600+$175)[/tex] dollars.
Hence the cost to buy 100 shares in ODX group Inc and 300 shares in peer comm LTD is $775.
For more details on graph follow the link:
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Which option is correct and how would one solve for it?
Answer:
28
Step-by-step explanation:
We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]
We know that,
[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]
Here, n = 3
So,
[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]
So,
[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]
So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).
How many solutions does the following equation have?
-5(z+1)=-2z+10
Choose 1 answer:
A: No solutions
B: Exactly one solution
C: Infinitely many solutions
Answer:
B
Step-by-step explanation:
-5z +1 = -2z +10
-3z = 9
z=9/-3
Z= -3
Answer:
the answer is exactly one solution
Step-by-step explanation:
this is the answer because i just took this question on khan academy and the one solution is z = -5 for the equation
I need help will rate you brainliest 10
Answer:
It is option A
Step-by-step explanation:
A is correct option
A simple random sample of 60 households in city 1 is taken. In the sample, there are 45 households that decorate their houses with lights for the holidays. A simple random sample of 50 households is also taken from the neighboring city 2. In the sample, there are 40 households that decorate their houses. What is a 95% confidence interval for the difference in population proportions of households that decorate their houses with lights for the holidays
Answer:
The calculated value of z = - 0.197 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays
Step-by-step explanation:
We formulate the null and alternative hypotheses as
H0: p1= p2 there is no difference in population proportions of households that decorate their houses with lights for the holidays
against Ha : p1≠ p2 (claim) ( two sided)
The significance level is set at ∝= 0.05
The critical value for two tailed test at alpha=0.05 is ± 1.96
or Z∝= 0.05/2= ± 1.96
The test statistic is
Z = p1-p2/√pq(1/n1 +1/n2)
p1= proportions of households decorating in city 1 = 45/60=0.75
p2= proportions of households decorating in city 2 = 40/50= 0.8
p = the common proportion on the assumption that the two proportion are same.
p = [tex]\frac{n_1p_1 +n_2p_2}{n_1+n_2}[/tex]
Calculating
p =60 (0.75) + 50 (0.8) / 110
p= 45+ 40/110= 85/110 = 0.772
so q = 1-p= 1- 0.772= 0.227
Putting the values in the test statistic and calculating
z= 0.75- 0.8/ √0.772*0.227( 1/60 + 1/50)
z= -0.05/√ 0.175244 ( 110/300)
z= -0.05/0.25348
z= -0.197
The calculated value of z = - 0.197 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays
After setting up the width of the compass using the original line segment, why is it important to keep the compass the same
width before drawing an arc? (1 point)
If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn
smaller or larger, so it would not match the original.
of the width of the compass changed, it would make the arc smaller or larger. This would change the angle the new line segment is
drawn at, so it would not match the original.
O if the width of the compass changed, it would be possible for the arc to intersect the original line segment, which is not allowed.
The width of the compass does not matter. All that matters is that a straightedge is used to draw the line segment
Answer:
If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn smaller or larger, so it would not match the original.
Step-by-step explanation:
We assume your construction is trying to copy the length of a line segment. That length is "measured" by the width of the compass. If it is changed, it no longer matches the length of the segment you're trying to copy, so you will not get the copy you want.
What number is the opposite of -3?
Explain your reasoning
Find the measure of ∠BEF
Please HELP ASAP
Answer:
100°
Step-by-step explanation:
We know that angles EFD and AEF are the same as they are alternate interior angles.
We also can note that BEF and AEF are supplementary, meaning their angle lengths will add up to 180°.
So we can create an equation:
(2x + 60) + (3x + 20) = 180
Combine like terms:
5x + 80 = 180
Subtract 80 from both sides
5x = 100
Divide both sides by 5
x = 20.
Now we can use this to find the measure of BEF.
[tex]2\cdot20 + 60[/tex]
[tex]40 + 60 = 100[/tex]
Hope this helped!
Answer:
BEF = 100
Step-by-step explanation:
The angles are same side interior angles and same side interior angles add to 180 degrees
2x+60 + 3x+20 = 180
Combine like terms
5x+80 = 180
Subtract 80
5x = 100
Divide by 5
5x/5 = 100/5
x = 20
We want BEF
BEF = 2x+60
= 2x+60
= 2*20 +60
= 40+60
= 100
If the sin of angle x is 4 over 5 and the triangle was dilated to be two times as big as the original, what would be the value of the sin of x for the dilated triangle? Hint—Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces. (4 points)
Answer:
Sin of x does not change
Step-by-step explanation:
Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.
From trigonometry,
Sin(x)=opposite/hypotenose
Where x=4/5
Sin(4/5)= opposite/hypotenose
But we were given the scale factor of 2 which means the dilation is to two times big.
Then we have
Sin(x)=(2×opposite)/(2×hypotenose)
Then,if we divide by 2 the numerator and denominator we still have
Sin(x)=opposite/hypotenose
Which means the two in numerator and denominator is cancelled out.
Then we still have the same sin of x. as sin(4/5)
Hence,Sin of x does not change
Answer:
Step-by-step explanation:
sin of angle x = [tex]\frac{4}{5}[/tex]
If the triangle is dilated 2 times - it becomes two time larger.
4 times 2 = 8 and 5 times 2 = 10
So the ratio would be [tex]\frac{8}{10}[/tex], which when reduced (divide numerator and denominator by 2) becomes [tex]\frac{4}{5}[/tex].
This is correct as dilation changes the size of an image - but not its angles or proportions, meaning ratios remain the same.
So the answer is 4/5.
football team, won 35 out of 39 games over a period of 4 years. if they keep winning pace, predict how many games you would expect them to win over the next 78 football games
Answer:
70
Step-by-step explanation:
If the team continues with same pace, they expected wins as per previous ratio:
35/39*78 = 70Expected wins 70 out of 78 games
2 less than five times a number.
Answer:
X will be the number.
5 times that number X is 5X
2 less than 5 times the number is 5X - 2
Hope this helps! Plz mark brainliest! （づ￣3￣）づ╭❤～
Answer
5x + 2
Step-by-step explanation:
5x + 2 or 5x - 2
If 4 pounds of cherries cost $10, what is the unit price
Answer:
2.5$ per pound
Step-by-step explanation:
The cost of 4 pounds of cherries cost 10$
So to khow the price of 1 pound we must divide 10 by 4.
● 10/4 = 2.5
So 1 pound costs 2.5$
Given the following computer printout for a set of sample data, which one of the following represents the value of the Interquartile Range?
Descriptive Statistics: Cycle Time
Variable N Mean StDev Variance Minimum Q1 Median Q3 Maximum
Cycle Time 52 31.808 5.333 28.436 21.700 27.825 31.000 36.075 44.000
A. 22.3
B. 3.175
C. 5.075
D. 8.25
Answer: D. 8.25
Step-by-step explanation: A data set can be divided into 4 equal parts, called Quartile. A quartile divides the data into three points:
Lower quartile: Q1;Median: Q2;Upper quartile: Q3;Interquartile Range (IQR) is a measure of variability based on data divided into quartiles or the measure of where the bulk of the values are.
To calculate interquartile range:
IQR = Q3 - Q1
The table shows Q1 = 27.825 and Q3 = 36.075, then
IQR = 36.075 - 27.825
IQR = 8.25
The value of interquartile range is 8.25.
