Answer:
a. There are 1365 choices of eleven questions.
b. 1764 groups of eleven questions contain five that require proof and six that do not.
Step-by-step explanation:
The order in which the questions 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]
a. How many different choices of eleven questions are there?
Eleven questions from a set of 15. So
[tex]C_{15,11} = \frac{15!}{11!4!} = 1365[/tex]
There are 1365 choices of eleven questions.
b. Suppose seven questions require proof and nine do not. How many groups of eleven questions contain five that require proof and six that do not?
5 from a set of 7 and 6 from a set of 9. So
[tex]C_{7,5}C_{9,6} = \frac{7!}{5!2!} \times \frac{9!}{6!3!} = 1764[/tex]
1764 groups of eleven questions contain five that require proof and six that do not.
Which coordinate K on the line segment with endpoints J (4,2) and L (4,6) divides JL such that the ratio of JK:KL is 3:1? helpp for finals!!
A. (4,5)
B. (5,4)
C. (4,3)
D. (3,4)
The coordinate of K on the line segment JL is (4,5).
What is section formula?When a point divides a line segment externally or internally in some ratio, we use section formula to find the coordinates of that point.
Internal section formula[tex]P(x, y) = (\frac{mx_{2} +nx_{1} }{m+n} ,\frac{my_{2}+ny_{1} }{m+n})[/tex]
Where,
(x, y) are the coordinates of point P.
[tex](x_{1},y_{1} )[/tex] are the coordinates of point A.
[tex](x_{2},y_{2})[/tex] are the coordinates of point B.
m and n are the ratio values in which P divides the line segment AB internally.
According to the given question.
Coordinates of points J and L are (4, 2) and (4, 6) respectively.
K divides the line segment JL in the ration 3:1.
Therefore, the coordinates of K by section formula is given by
[tex]K(x, y) = (\frac{3(4)+1(4)}{3+1} , \frac{3(6)+1(2)}{3+1} )[/tex]
⇒ [tex]K(x, y) = (\frac{12+4}{4} , \frac{18 + 2}{4} )[/tex]
⇒ [tex]K(x, y) = (\frac{16}{4} ,\frac{20}{4})[/tex]
⇒[tex]K(x, y) = ( 4, 5)[/tex]
Hence, the coordinate of K on the line segment JL is (4,5).
Find out more information about section formula here:
https://brainly.com/question/20320420
#SPJ2
v
=
√
20
L
v
=
20
L
to estimate the speed of a car,
v
v
, in miles per hour, based on the length,
L
L
, in feet, of its skid marks when suddenly braking on a dry, asphalt road. At the scene of an accident, a police officer measures a car's skid marks to be 168 feet long. Approximately how fast was the car traveling? Round your answer to the nearest tenth (one decimal place) of a unit.
Answer:
sorry no idea hhcchuucghhf
50 points!
What is the area of triangle xyz? Use special right triangles to help find the height. Leave your answer in terms of radical. Show work.
What is the difference of the polynomials?
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
Answers:
A.) -x^3 + 6x^2 + 9
B.) -x^3 + 2x^2 - 9
C.) 5x^3 - 2x^2 - 2x - 9
D.) 5x^3 - 2x^2 + 2x + 9
Answer:
D
Step-by-step explanation:
We want to find the difference between the two polynomials:
[tex](5x^3+4x^2)-(6x^2-2x-9)[/tex]
Distribute the negative:
[tex]=(5x^3+4x^2)+(-6x^2+2x+9)[/tex]
Rearrange the terms:
[tex]=(5x^3)+(4x^2-6x^2)+(2x)+(9)[/tex]
Combine like terms. Hence:
[tex]=5x^3-2x^2+2x+9[/tex]
Our answer is D.
Which statement best describes the area of Triangle ABC shown below? A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 4, vertex B is on ordered pair 7 and 2, and the vertex C is on ordered pair 1 and 2. (5 points) It is one-half the area of a square of side length 6 units. It is twice the area of a square of side length 6 units. It is one-half the area of a rectangle with sides 6 units × 2 units. It is twice the area of a rectangle with sides 6 units × width 2 units.
Answer:
It is one-half the area of a rectangle with sides 6 units × 2 units
Step-by-step explanation:
area of the triangle is 6
base = 6
height = 2
so are is 6 x 2 / 2
Answer:did this a few months ago this answer is
It is one-half the area of a rectangle with sides 6 units × 2 units.
Step-by-step explanation:
like the person up there
PLEASE HELP WILL MARK BRAINLIEST‼️‼️‼️
Question: Write the equation of the piece wise function that is represented by its graph.
(Graph and Answers Pictured)
9514 1404 393
Answer:
D
Step-by-step explanation:
The left portion of the curve is defined for x < 1, except x=0. The right portion of the curve is defined for x ≥ 1. The only answer choice with these domain segments is the last one.
HELP ME OMG HSLPEKSSMW
I don’t really understand how to do this
Answer:
<A = 63degrees
Step-by-step explanation:
From triangle DEF;
<D + <E + <F = 180
87 + 30 + <F = 180
117 + <F = 180
<F = 180 - 117
<F = 63degrees
Since <A = <F based on similarities, then <A = 63degrees
Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Select zero, 1, or more than 1. There is/are ? line(s) of symmetry.
Answer:
This Symbol has 4 lines of Symmetry
Assume that the tunnel in Exercise 3.132 is observed during ten two-minute intervals, thus giving ten independent observations Y1, Y2,..., Y10, on the Poisson random variable. Find the probability that Y > 3 during at least one of the ten two-minute intervals
Answer: hello the exercise is missing from your question below is the missing exercise for reference
answer:
0.1745
Step-by-step explanation:
Determine P ( Y > 3 )
Given that y follows Poisson distribution with mean
P( Y = y ) = [tex]\frac{e^{-1} }{y!}[/tex]
assuming that yi represents number of autos that will enter the tunnel and
also let A represent Y > 3 at one of the ten two-minute interval
step 1 : hence finding P(A )
= P(Y > 3 ) = 1 - P( Y≤ 3 )
= 1 - [ [tex][\frac{e^{-1} }{0!} +\frac{e^{-1} }{1!} +\frac{e^{-1} }{2!} +\frac{e^{-1} }{3!} ][/tex]
= 0.018988
since the ten observations are independent
P(X≥ 1 ) = 1 - P( X = 0 )
= 1 - [tex]\left[\begin{array}{ccc}10\\0\\\end{array}\right][/tex] * (0.018988)^0 ( 1 - 0.018988)^10-0
= 1 - 0.8255 = 0.1745
Peter Piper picked a pickled pepper out of a pepper jar. If the probability of drawing a pickled pepper was 2/5,
how many total peppers could be in the jar (psst. you can't have a half of a pepper)?
Answer:
5
Step-by-step explanation:
2/5 pickled peppers means that there are 2 pickled peppers out of 5 total peppers.
constant
r is the counting number from 7 to 9
The price for digital downloads of music is represented by the linear function f(x) shown on the graph. The price for digital downloads of movies is represented by g(x) = x, where x is the number of movies downloaded and g(x) is the total cost in dollars.
You want to make 2 downloads, and you have $5. Determine the least expensive option.
1. You download 2 songs.
2. You download 2 movies.
3. You download 1 song and 1 movie.
4. You don't have enough money for 2 downloads.
Answer:
The second answer is the correct one
Step-by-step explanation:
Two circles with the same center are called
Select one:
a. externally tangent
b. circumscribed
c. inscribed
d. concentric
Answer:
d
Step-by-step explanation:
Circles with the same centre are concentric circles
Answer:
concentric
Step-by-step explanation:
as well all know that two circles with the same center are called Concentric and there is no doubt about that
A college has 7 science batches and each batch has 48 students, It is compulsory for each student to do 24 hours of community service in a year. How many hours of community service does the college contribute in a year ?
Answer:
Hello There!!
Step-by-step explanation:
Firstly, find out how many students there are in 7 batches. You can do this by timesing 48 by 7 to get 336. So there are 336 students in 7 batches. Each student does 24 hours of community service in a year so do 336 times by 24 which is 8,064. Therefore,the college contributes 8,064 hours of community service in a year.
hope this helps,have a great day!!
~Pinky~
Urgent!!!!! please help
Answer:
A
Step-by-step explanation:
I will edit and add my explanation
The 3 and 2 are both positive if the information that was given in the screenshot is standalone.
So if the numerals are both positive, they must be traveling to the right because the number line is increasing towards the right.
We can narrow the choices down to A and C because they both move right.
Since neither of the numbers are negative, it must start from the center 0 and increase, so it must be A.
3 * 2 is also 6, so it must end on 6.
Next number of 5,11,23,42,69,105,151
Three brothers wunmi, niyi and dare shared a quantity of walnuts in the ratio 3:4:5 if wunmi got 21 walnuts how many did niyi get?
.
Answer:
28 walnuts
Step-by-step explanation:
3 times 7 is 21 so 4 times 7 is how many walnuts niyi gets
A rectangular. Garden bed measures 8 x 6 feet a water faucet is at one corner of the bed hose must be long enough to reach opposite corner when stretched straight. Find required length of hose
Answer:
10 ft
Step-by-step explanation:
The word problem is basically asking the length of one corner of the rectangle to the other. We can split the rectangle up into two right triangles and we will use the Pythagorean theorem to find the hypotenuse or the length from one corner to another. A^2 + B^2 = C^2 A and B are the lengths of the rectangle, 8 and 6. 8^2 + 6^2 = C^2
8^2 = 64 and 6^2 = 36
64 + 36 = 100.
the square root of 100 is 10 so the length of the hose is `10.
Which of the following theorems verifies that DEF = XYZ?
Answer:
AA
Step-by-step explanation:
HL = requires actual measurements of sides
LL = There are no measurements for the legs
HL = There are no measurements for the legs or hypotenuse
HA = Doesn't exist
can anyone solve 3?
9514 1404 393
Answer:
a) $7715.10
b) $6022.02
c) 15263.10
Step-by-step explanation:
A calculator or spreadsheet can evaluate the formulas for you using the given parameters.
The compound interest formula is ...
A = P(1 +r/n)^(nt)
where P is the principal amount, r is the annual rate, n is the number of times interest is compounded per year, and t is the number of years.
The continuously compounded interest formula is ...
A = Pe^(rt) . . . . where P, r, t are defined as above
Often the function e^x is defined as the exp(x) function.
__
A calculator or spreadsheet can perform rounding for you, but we elected not to confuse the issue with that step. The calculator results below are rounded in the answer list above.
For part (a), we have ignored the fact that 7 years will have an additional week, since there are 1 or 2 extra days (beyond 52 weeks) in each year. Taking that into account adds a penny to the account balance.
The extra day in a leap year affects the account balance in the 8th significant figure. Our balance has only 6 significant figures, so we do not need to be concerned with the effect of a possible leap year in the 3-year period of part (b).
Find the quotient of 4x^3-12x² + 8x/ - 4x
O x2 + 3x - 2
O x²-12x + 4
O -x2 – 3x + 2
O x² + 12x - 4
Answer:
-x^2+3x-2
Step-by-step explanation:
I think one of the signs are wrong in the equation.
The mean score in an exam given to 40 students is 70. What is the sum of the 40 exam scores? A. 1500 B. 2000 C. 2800 D. 3000
Answer:
C
Step-by-step explanation:
Mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] , then
[tex]\frac{sum}{40}[/tex] = 70 ( multiply both sides by 40 )
sum = 40 × 70 = 2800 → C
Use interval notation to express the following:
The set of all numbers less than 2.
Answer:
( - infinity, -3 ] [ -2, infinity )
square bracket means it includes the end point.
Step-by-step explanation:
(-∞, -3]U [-2,∞)
Find the slope of a line that is PRRPENDICULAR to the line that goes between (3,-8) and (5,2).
5
1/5
-5
-1/5
3
-3
1/3
-1/3
Answer:
-1/5
Step-by-step explanation:
Slope of the line = (y2-y1)/(x2-x1)
(2-(-8)/(5-3)
10/2 = 5
Perpendicular line = the slope is opposite of the reciprocal
-1/5
I have 8 carrots my Brother Ate 2
How Much I have left?
Answer:
6?Step-by-step explanation:
..........................
PLEASE HELP ME !!!!
At a real estate agency, an agent sold a house for $358,000. The commission rate is
4.5% for the real estate agency and the commission rate for the agent is20 % of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The agency made $___ on the house.
Answer:
The agency makes 16110
The agent makes 3222
Step-by-step explanation:
First find the real estate commission
358000 * 4.5%
358000*.045
16110
The agent gets 20 percent of that amount
16110*20%
16110*.2
3222
Suppose one network executive is selected at random. find the indicated probabilities
Answer:
na answer ran nyo na po
Step-by-step explanation:
What is the graph of 4x + 2 < 10
Assume that Z has a standard normal distribution. Determine the value for z that solves each of the following.
a. P(-z < Z < z) = 0.95 (Round your answer to two decimal places (e.g. 98.76))
b. P(-z < Z < z) = 0.99 (Round your answer to two decimal places (e.g. 98.76))
c. P(-z < Z < z) = 0.68 (Round your answer to three decimal places (e.g. 98.765))
d. P(-z < Z < z) = 0.9973 (Round your answer to two decimal places (e.g. 98.76))
Answer:
a) P ( - 1.96 < Z < 1.96 )
b) P ( - 2.58 < Z < 2.58)
c) P ( -0.995 < Z < 0.995 )
d) P ( - z < Z < z ) = P ( ( Z ± 3σ ) then that is close to 1
Step-by-step explanation:
a) P ( - z < Z < z ) = P ( - 1.96 < Z < 1.96 )
CI = 95 % significance level α = 5 % α = 0.05 α/2 = 0.025
z = 1.96
b) P ( - z < Z < z ) = P ( - 2.58 < Z < 2.58)
CI = 99 % significance level α = 1 % α = 0.01 α/2 = 0.005
z = 2.58
c) P ( - z < Z < z ) = P ( -0.995 < Z < 0.995 )
CI = 68 % significance level α = 32 % α = 0.32 α/2 = 0.16
z ≈ 0.9954
We interpolate in this case
1 ⇒ 0.1587
0.99 ⇒ 0.1611
0.01 ⇒ 0.0024
x ⇒ 0.0013 x = 0.01 *0.0013 / 0.0024
x = 0.005416
and z = 0.99 + 0.005416
z = 0.9954
d) P ( - z < Z < z ) = P ( - 0.00 < Z < 0. 00)
CI = 0.9973 % significance level α = 0.0027 % α = 0.000027 α/2 = 0.0000135
z = 0.00003375 ⇒ z = 0.00
NOTE: The value of α is too small. The Empirical Rule establishes that 99.7 % of all values in a normal distribution fall in the interval ( Z ± 3σ)
that means all the values. Then the probability of finding the random variable between that range is close to 1 and we can not find in tables a number to approximate just with only two decimal places