Answer:
The committee of 8 members can be selected in 990,675 different ways.
Step-by-step explanation:
The order in which the teachers and the students are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
4 teachers from a set of 6.
4 students from a set of 37.
Then
[tex]T = C_{6,4}C_{37,4} = \frac{6!}{4!2!} \times \frac{37!}{4!33!} = 990675[/tex]
The committee of 8 members can be selected in 990,675 different ways.
PLEASE HELP ME WITH THIS ONE QUESTION
How many combinations without repetition are possible if n = 4 and r = 3?
A) 16
B) 12
C) 3
D) 4
Given:
[tex]n=4[/tex] and [tex]r=3[/tex].
To find:
The combinations without repetition are possible if [tex]n=4[/tex] and [tex]r=3[/tex].
Solution:
Combination of selecting r item from total n items is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
We have [tex]n=4[/tex] and [tex]r=3[/tex]. By using the above formula, we get
[tex]^4C_3=\dfrac{4!}{3!(4-3)!}[/tex]
[tex]^4C_3=\dfrac{4\times 3!}{3!1!}[/tex]
[tex]^4C_3=4[/tex]
Therefore, the correct option is D.
Answer:
Step-by-step explanation:
the average score on mid term examination of 25 students was 78.8 out 100
after the mid term exam, however, a student whose score was 41 out of 100 dropped the course. what is the average (mean) score amount of the 24 students?
please help meeeeeeeee
pt 3
Answer:
1st option
Step-by-step explanation:
Given the zero product
(x - 3)(x + 5) = 0 , then
x - 3 = 0 ; x + 5 = 0
I need to know how to solve this completely not just the answers plz :)
You and your family are planning a roadtrip. You determine that the distance you need to drive is 660 miles and that you can average 60 miles per hour for the entire trip. How many hours will your trip take?
Answer:
11 hours
Step-by-step explanation:
Find how many hours the trip will take by dividing the number of miles by the rate in miles per hour:
660/60
= 11
So, the trip will take 11 hours
Which statement is true.?
Answer:
B
Step-by-step explanation:
In the number 1326308 is between which two numbers in a million?
Answer:
1326308 is in between 1326307 and 1326309
In a sale, Ali buys a television for $195.80.
The original price was $220.
Calculate the percentage reduction on the original price.
11%
Hope this helps! :)
______________
Answer:
[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]
A particular fruit's weights are normally distributed, with a mean of 275 grams and a standard deviation of 19 grams. If you pick one fruit at random, what is the probability that it will weigh between 244 grams and 305 grams?
Answer:
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 275 grams and a standard deviation of 19 grams
This means that [tex]\mu = 275, \sigma = 19[/tex]
What is the probability that it will weigh between 244 grams and 305 grams?
This is the p-value of Z when X = 305 subtracted by the p-value of Z when X = 244.
X = 305
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{305 - 275}{19}[/tex]
[tex]Z = 1.58[/tex]
[tex]Z = 1.58[/tex] has a p-value of 0.9429.
X = 244
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{244 - 275}{19}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a p-value of 0.0516
0.9429 - 0.0516 = 0.8913
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.
Researchers believe that 24.5% of the adults in the United States are obese. A Gallup poll examined the rate of obesity in America with a survey 86,664 randomly sampled U.S. adults. Of the adults surveyed, 23,053 said that they were obese. Is this enough evidence to state that more than 24.5% of all adults in the U.S. are obese
Answer:
The p-value of the test is 0 < 0.05(standard significance level), which means that this is enough evidence to state that more than 24.5% of all adults in the U.S. are obese
Step-by-step explanation:
Researchers believe that 24.5% of the adults in the United States are obese. Test if there is enough evidence to state that more than 24.5% of all adults in the U.S. are obese.
At the null hypothesis, we test if the proportion is of 24.5% or less, that is:
[tex]H_0: p \leq 0.245[/tex]
At the alternative hypothesis, we test if this proportion is greater than 24.5%, that is:
[tex]H_1: p > 0.245[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.245 is tested at the null hypothesis:
This means that [tex]\mu = 0.245, \sigma = \sqrt{0.245*0.755}[/tex]
Survey 86,664 randomly sampled U.S. adults. Of the adults surveyed, 23,053 said that they were obese.
This means that [tex]n = 86664, X = \frac{23053}{86664} = 0.266[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.266 - 0.245}{\frac{\sqrt{0.245*0.755}}{\sqrt{86664}}}[/tex]
[tex]z = 14.37[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion of 0.266 or higher, which is 1 subtracted by the p-value of z = 14.37.
The p-value of z = 14.37 is 1.
1 - 1 = 0
The p-value of the test is 0 < 0.05(standard significance level), which means that this is enough evidence to state that more than 24.5% of all adults in the U.S. are obese
Expand and simplify (n-2)(3n+7) + 2n(2n+3)
It is a beautiful day at the beach and ten beach volleyball players have shown up at the volleyball courts. Each two-person volleyball team should consist of a setter and a spiker. Five of the players prefer to be a spiker, four of the players prefer to be a setter, and one player is fine either way.
In how many ways can a two-person team be assembled such that no player feels out of position?
Answer:
4 i think
Step-by-step explanation:
Can you help me on this?
Answer:
ez 1 + 1 = 1 is the correct answer
PLS HELP ! THANK YOU
Will mark Brainliest
Answer:
I think. . . sphere? SO SORRY IF IM WRONG!!
Step-by-step explanation:
(a)A train completed a journey of 850 kilometres with an average speed of 80 km/hr.
Calculate, giving exact answers, the time taken for this journey in
(1)
hours,
hours, minutes and seconds.
(b)Another train took 10 hours 48 minutes to complete the same 850 km journey.
0 It departed at 19 20.
At what time, on the next day, did thsi train complete the journey?
Calculate the average speed, in kilometres per hour, for the journey.
drintinn
Answer:
a. 850/85 = 10.625 hr or 10 hr 37 min 30 sec
b. 6:08 AM
C. Average time is (10.625 + 10.8)/2 = 10.7125
or 10 hour 42 min 45 sec
For each of the studies described, explain whether the study was an observational study or a randomized experiment.
a. A group of 100 students was randomly divided, with 50 assigned to receive vitamin C and the remaining 50 to receive a placebo, to determine whether or not vitamin C helps to prevent colds.
b. A random sample of patients who received a hip transplant operation at Stanford University Hospital during 2000 to 2010 will be followed for 10 years after their operation to determine the success (or failure) of the transplant.
c. Volunteers with high blood pressure were randomly divided into two groups. One group was taught to practice meditation and the other group was given a low-fat diet. After 8 weeks, reduction in blood pressure was compared for the two groups.
Answer:
B
Step-by-step explanation:
B
Please help me solve this. I keep getting the answer weong
Answer:
21 is the answer I think sike I lied ik its not im just trying get this over with
You can use this formula to work out the area of a triangle when you know two sides and the angle inbwtween them :
1/2 x a x b x sin(C)
where a and b are the two sides you know and C is the angle in between them.
So here a = 7, b = 14, C = 125.
Area = 1/2 x 7 x 14 x sin(125) = 40.138...
= 40.1 (nearest 10th)
Please solve this equation
Answer:
fggggg hasdnkuw
Step-by-step explanation:
Let x be a real number such that x + (1/x) is an integer. Prove that (x^n) + 1/(x^n) is an integer for every positive integer n.
Answer:
sim eu também preciso desta respota
please help thx steps too
Step-by-step explanation:
IN first triangle multiplier factor is 4
and IN second triangle multiplier factor is
[tex] \frac{3}{2} [/tex]
What is the area of a sector when 0=90° and r= 8/3?
Answer:
16π/9
Step-by-step explanation:
the area of sector= ¼×π.r²
= ¼× π× (8/3)²
= ¼×64/9×π
= 16π/9
Answer:
Answer:
16π/9
Step-by-step explanation:
the area of sector= ¼×π.r²
= ¼× π× (8/3)²
= ¼×64/9×π
= 16π/9
Step-by-step explanation:
Which of the following best represents the relationship between functions f and g?
g(x) = -f(x) - 1
g(x) = f(x - 1)
g(x) = -f(x) + 1
g(x) = -f(x)
9514 1404 393
Answer:
(c) g(x) = -f(x) +1
Step-by-step explanation:
We really only need to consider one point on f(x) and/or g(x). We can look at the y-intercepts.
f(0) = 4 and g(0) = -3
Looking at the answer choices, we see ...
A. -f(0) -1 = -4 -1 = -5 ≠ g(0)
B. f(0 -1) = f(-1) = 1 ≠ g(0)
C. -f(0) +1 = -4 +1 = -3 = g(0) . . . . . matches requirements
D. -f(0) = -4 ≠ g(0)
The relation between f(x) and g(x) is g(x) = -f(x) +1.
ANSWER ASAP IM TIMED 30 POINTS
Which shape below will form a tessellation?
A. regular heptagons
B. regular pentagons
C. regular octagons
D. regular hexagons
Answer:
Step-by-step explanation:
D ANSWER D
Answer:
d
Step-by-step explanation:
Can someone help me with this question please.
Answer:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
Step-by-step explanation:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
I don't understand plz help
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
Triangles QST and QSR are congruent, so angle QST is congruent to angle QSR.
(3x +24)° = 30°
3x = 6 . . . . . . . . . divide by °, subtract 24
x = 2 . . . . . . . . . . divide by 3
__
Additional comment
What matters here is the relationship between the two marked acute angles. The fact that point Q is equidistant from the sides of angle TSR tells you that QS is an angle bisector and the two angles have equal measures. (The definition of an angle bisector is that it is equidistant from the sides of the angle.)
Recognition that the two triangles are congruent is another way to see that the marked acute angles have the same measure. The triangle congruence can be claimed on the basis of the HL theorem, since both are right triangles, have the same hypotenuse (QS), and have legs (QT, QR) with the same measure.
if a line intersect x axis at a point (6,0) and y axis at a point (0,-8). then what is equation of a line?
Answer: y = 4/3x -8
Step-by-step explanation:
(6,0) (0,-8)
0-(-8)/6-0 = 8/6 = 4/3
y intercept is given already
If 5^3b-1 = 5^b-3, what is the value of b?
-2
-1
1
2
Answer:
3b-1 = b-3
2b = 4
b = 2
Step-by-step explanation:
NEED HELP ASAP!!!!!!
Answer:
It's a rhombus (if you can check more than one answer, it's also a parallelogram).
Step-by-step explanation:
A rhombus is a flat shape with 4 straight sides that are all equal length.
Also opposite sides are parallel and opposite angles are equal.
It is a type of parallelogram.
Answer:
It's a rhombus
Step-by-step explanation:
because all the 4 sides are equal
And it's like a square that it's top has been pushed
can someone help me with this?
Answer: 22
Step-by-step explanation: 44:2=22
Reflect (-3, 4) across the y-axis. Then reflect the result across the x-axis.