The number of ways 3 courses can be selected is 3654.
How to calculate combination?
The sequence of the results is irrelevant when calculating the overall outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n denotes the total number of items and r denotes the number of things being chosen at a time.The sum of all positive integers that are greater than zero and less than your number is known as a factorial. An exclamation point is written after the number to represent a factorial.Total no. of courses available = 29
Courses needed to graduate = 3
No of ways these courses can be selected:
= ²⁹C₃
= 29!/ [(29-3)! - 3!]
= 29! / 26! 3!
= 29 * 28 * 27 * 26!/ 26! 3*2
= 29* 14* 9
=3654
So, the number of ways 3 courses can be selected is 3654.
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Brandon went to the store to buy some walnuts. The price per pound of the walnuts is $6.50 per pound and he has a coupon for $3.75 off the final amount. With the coupon, how much would Brandon have to pay to buy 5 pounds of walnuts? Also, write an expression for the cost to buy
p
p pounds of walnuts, assuming at least one pound is purchased.
Answer:
Step-by-step explanation:
$28.75
what is the difference between the critical value of z and the observed value of z (test statistic)?
The critical value of z separates the rejection region from the nonrejection region while observed value of z is the value calculated for a sample statistic such as x.
A critical value of z is used when the sampling distribution is normal, or close to normal. The critical value of z refers to the point that cuts off area under graph for the standard normal distribution separating the rejection and nonrejection region of the data. The Critical value of z can indicate what probability any particular variable will have. These values are typically obtained from a table such as the standard normal distribution table. The observed value of z is a value determined for a sample statistic x. It is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation.
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the manufacturer of a new compact car claims that the car will average at least 35 miles per gallon in general highway driving. for 100 test runs, the car averaged 35.5 miles per gallon with a standard deviation of 2.5 miles per gallon. suppose that the manufacturer tests the following hypotheses: h subscript 0 : mu equals 35 h subscript 1 : mu greater than 35 consider the 1% significance level. what is the power of the test if the actual average fuel efficiency is 36 miles per gallon?
The power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.
What is the standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
We want to test [tex]\mu_0 > 35[/tex] at the level [tex]\alpha=0.01[/tex], where the true mean is [tex]\mu_1=36,\sigma\approx4, n=100[/tex]
The power of a right-tailed test is given by
[tex]1-\beta=P(Z > [z_\alpha-\frac{\sqrt{n}}{\sigma}(\mu_1-\mu_0)])\\\\1-\beta=P(Z > [2.33- \frac{\sqrt{100}}{4}(36-35)])\\\\1-\beta=P(z > -0.17)\\\\power=0.5675[/tex]
Hence, the power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.
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In a urvey of 300 houe wire. It wa dicovered that 150 had read magazine A, 200 had read Magazine B and 156 had read magazine C It wa further dicovered that 48 had read A and B 60 had read B and a while 52 hand read A and a. Find The number of houewive that had read. All three magazine
Answer:b
Step-by-step explanation:
a coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 19.0 cm. reflection from the surface of the shell forms an image of the 1.5-cm-tall coin that is 6.50 cm behind the glass shell. part a where is the coin located? express your answer in centimeters. s
The location of the coin next to the convex side of a thin spherical glass shell is 3.68 cm.
According to the question,
Radius of curvature : 19 cm
Size of image formed : 1.5cm
Distance of coin from glass shell : 6.5cm
The position of the coin placed next to the convex side of a thin spherical glass shell is calculated as follows;
1/d = 1/f - 1/d'
where;
d' is the position of the coin's image
d position of the coin
f is focal length
Focal length = r/2 =19/ 2 = 9.5 cm
=> 1/d = 1/9.5 - (-1/6.5)
=> 1/d = 1/9.5 + 1/6.5
=> 1/d = 0.1052 + 0.1538
=> 1/d = 0.259
=>d = 1/0.259
d = 3.86 cm
Thus, the position of the coin placed next to the convex side of a thin spherical glass shell is 3.86 cm.
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how many different passwords are there that contain only digits and lower-case letters and satisfy the given restrictions? 1) length is 1010.
There are 36^10 ways that contain only digits and lower-case letters and having the length is 10.
What is password?
A password, also known as a passcode, is private information that typically consists of a string of characters and is used to verify a user's identity.
We have to find the number of ways that contain only digits and lower-case letters and having the length is 10.
Since, there are total 10 digits from '0 to 9' and 26 lower case letters from
'a to z'.
The 10 slots in the password can be anything - digits as lower case letters.
that is,
10 + 26 = 36 options for each slot.
So, the total number of ways are, 36^10.
Hence, there are 36^10 ways that contain only digits and lower-case letters and having the length is 10.
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Divide. Write your answer in scientific notation.
7 x 10 -5
7 x 10 -6
Answer:
(65) (64)
Step-by-step explanation:
One historic earthquake had a magnitude of 9.0 on the Richter scale. How many times more intense was this than another historic earthquake that had a magnitude of 8.3? (Round your answer to the nearest whole number.)
Answer:
1
Step-by-step explanation:
9/8.3 = 1.0843, rounded to the nearest whole number is 1
three less than the product of negative 12 1/2 and 4.8
Answer:
- 63
Step-by-step explanation:
Let's translate the sentences into expressions:
1. "product of negative 12 1/2 and 4.8" means:
(-12 1/2)*(4.8)
I'll simplify this by stating (-12.5)*(4.8)
2. "three less than" means subtract 3, or
-3
Now combine the two expressions:
(-12.5)*(4.8) - 3
(-60) - 3
= - 63
stocks a and b each have an expected return of 12%, a beta of 1.2, and a standard deviation of 25%. the returns on the two stocks have a correlation of 0.6. portfolio p has 50% in stock a and 50% in stock b. which of the following statements is correct?
The correct answer is The standard deviation for Portfolio P is less than 25
This response is accurate because a portfolio made up of two stocks with a correlation of less than one will always have a standard deviation that is lower than the standard deviation of the stocks added in accordance with their weight in the portfolio. For example, in this scenario, both stocks have a weight of 50% and a standard deviation of 25%, so their sum will be.
The portfolio standard deviation will be smaller than 25% since (0.5*25%) + (0.5*25%) = 25%.
Therefore, the standard deviation for Portfolio P is less than 25
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Maya spent 40% of her savings to pay for a bicycle that cost her $85. How much money was in her savings, to begin with? How much does she have left after buying the bicycle?
Answer: 212.50
Step-by-step explanation: she has 60% or 127.5
given a point p(x,y), if you change the sign of its x coordinate and y- coordinate, what will happen to the location of the point?
If the given point is p(x, y) and change the sign of its x coordinates and y coordinates, then the new location will be on third quadrant
The coordinates of the point p = (x, y)
In the graph, there are four quadrants.
In first quadrant the x axis value and y axis value will be positive. In second quadrant the value of x will be negative and y will be positive. In the third quadrant the value of and y will be negative. In fourth quadrant the value of x will be positive and y will be negative
Here at first both x and y are positive and it will be on first quadrant. The the sign of the x coordinates and y coordinates will change sign. So both of them will be negative.
Therefore, the location of will be on third quadrant
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I WILL OPEN MY ALT AND COMENT AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE
Answer:
b = -3
Step-by-step explanation:
1. Rearrange Terms
-3(3 + 6b) = 36 - 3b
-3(6b + 3) = 36 - 3b
2. Distribute
-3(6b + 3) = 36 - 3b
-18b - 9 = 36 - 3b
3. Rearrange Terms
-18b - 9 = 36 - 3b
-18b - 9 = -3b + 36
4. Add 9 to both sides
-18b - 9 = -3b + 36
-18b - 9 + 9 = -3b + 36 + 9
5. Simplify
-18b - 9 + 9 = -3b + 36 + 9
-18b = -3b + 45
6. Add 3b to both sides
-18b = -3b + 45
-18b +3b = -3b + 45 + 3b
7. Simplify
-15b = 45
8. Divide both sides by the same factor
-15b = 45
[tex]\frac{-15b}{-15}[/tex] = [tex]\frac{45}{-15}[/tex]
9. Simplify
b = -3
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
WWWWWW
Step-by-step explanation:
Find the value of x that will make A||B
A-
2x + 50
5x - 80
B-
x = [?]
Answer:
WE need to factorise (2x+4y)(2x−4y)
Given identity is (x+a)(x+b)=x
2
+(a+b)x+ab
Here x=2x,a=b=4y
Thus we have (2x+4y)(2x−4y)=(2x) 2
+(4y−4y)+(4y)(−4y)=4x2
−16y 2
the average age of 33 fifth-graders is 11. the average age of 55 of their parents is 33. what is the average age of all of these parents and fifth-graders?
Since, the average age of 33 fifth-graders is 11. the average age of 55 of their parents is 33. The average age of all of these parents and fifth graders is 24.75.
Average age of the population calculated as the arithmetic mean. Another parameter determining the average age of the population is the median age. High-level terms.
Given In the question:
Average age of 33 fifth graders is 11 years.
Average age of parents is 33 Years.
Therefore,
The sum of the ages of the fifth graders is 33 × 11,
and, the sum of the ages of the parents is 55 × 33.
Therefore, the total sum of all their ages must be 2178,
and given 33 + 55 = 88 people in total, their average age is
= 2178/88
= 99/4
= 24.75
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help fast plsssssssss
Answer:
2 2/3
Step-by-step explanation:
a small combination lock on a suitcase has wheels, each labeled with the 10 digits from 0 to 9. if an opening combination is a particular sequence of digits with no repeats, what is the probability of a person guessing the right combination?
The probability of a person guessing the right combination be
1/720.
Given, a small combination lock on a suitcase has wheels, each labeled with the 10 digits from 0 to 9.
we have to find the probability of a person guessing the right combination if there is no repeating of any digit.
as, we need three digit number to unlock the suitcase.
total combinations of the lock be,
10×9×8
= 720
only one combination can open the suitcase,
So, the probability of a person guessing the right combination be
1/720.
Hence, the probability of a person guessing the right combination be
1/720.
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If the area of the pentagon is 36, what is the area of the larger pentagon?
Answer:48?
Step-by-step explanation:
I as of now am not completely sure of this is the correct answer.
Help me pls 1,2,and 3 plssssssssssssssss
it's from statistical reasoning
In ΔNOP, p = 490 inches, ∠N=57° and ∠O=55°. Find the length of n, to the nearest inch.
Using law of sine and triangle rule, the value of n will be; 443 inches
What is Sine Rule?The law of sines establishes the relationship between the sides and angles of an oblique triangle(non-right triangle). Law of sines and law of cosines in trigonometry are important rules used for "solving a triangle".
We can apply the sine rule to find the missing angle or side of any triangle using the requisite known data.
The formula is given as;
a / sin A = b / sin B = c / sin C
In this triangle NOP, we can find the value of angle P then;
∠N + ∠O + ∠P = 180
57 + 55 + ∠P = 180 :
since Sum of angles in a triangle is equal 180 degrees
∠P= 180 - 112
∠P = 68
Using law of sine;
p / sin P = n / sin N
490 / sin68 = n / sin57
n = [(490 x sin 57) / sin 68]
n = 443 inches
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which assessment finding(s) are likely to cause noncompliance with antiretroviral treatment? select all that apply.
A. Poor understanding of HIV
B. Cognitive impairment
C. Substance abuse
D. Unstable housing
Avery is a songwriter who collects royalties on her songs whenever
they are played in a commercial or a movie. Avery will earn $40 every
time one of her songs is played in a commercial and she will earn $140
every time one of her songs is played in a movie. Avery earned a total
of $480 in royalties on 7 commercials and movies. Determine the
number of commercials and the number of movies on which Avery's
songs were played.
Avery's songs were played on
commercials and
movies.
The number of movies on which Avery's songs were played is 2 times
How to determine the number of movies on which Avery's songs were played.From the question, we have the following parameters that can be used in our computation:
Songs played in commercial = $40
Songs played in movie = $140
Total earnings = $480
Number of times played on commercial = 7
The above parameters when represented as an equation is
Total earnings = Songs played in commercial * Number of times played on commercial + Songs played in movie * Number of times played in a movie
Substitute the known values in the above equation, so, we have the following representation
40 * 7 + 140 * Number of times played in a movie = 480
Evaluate the products
280 + 140 * Number of times played in a movie = 480
So, we have
Number of times played in a movie = 200/140
Evaluate
Number of times played in a movie = 2
Hence, the number of times is 2 times
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Please hurry!!!! 50 points!
The diameter of a regulation soccer ball is about 8 3/5 inches. This number was graphed on a number line. (Ill show the number line below) With point could be the point representing the graph of the diameter of the ball?
Answer:
D
Step-by-step explanation:
8 3/5 is a number greater than 8 but minor than 9
Answer:-9.9 -7 7.9 9.7
Step-by-step explanation:
the function f(x) = –0.3x2 + 2.5x + 5 can be used to approximate the distance a thrown ball is from the ground, where x is the distance between the ball and the person throwing the ball. the mathematical domain of the function is all real numbers.
The mathematical domain of the function is 0<or = 5<or = -0.3
What is a simple definition of function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
What is the main meaning of function?the type of behavior that is appropriate for a given person, object, or institution; the reason why something exists; a role. any formal event or gathering that is public or social. a variable connected to or reliant upon another variable: A price depends on both supply and demand.
According to the above statements:-
The mathematical domain of the functions are:-
0<or = 5<or = -0.3
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I need help right now!! The assignment I’m doing is about solving problems using division assignment!
Answer:
A
Step-by-step explanation:
The others involve more multiplication and addition/subtraction rather than division.
A plot of land for sale has a width of x ft. , and a length that is 8ft less than its width. A farmer will only purchase the land if it measures 240 square feet. What value of x will cause the farmer to purchase the land?.
If width i.e. x is 20 ft then the farmer will purchase the land.
Given,
width of land = x ft
length of land = ( x - 8 ) ft
Area of land =240 square feet
To determine x use formula,
Area of land =length * width
[tex]240=(x-8)*x\\\\240=x^2-8x\\\\x^2-8x-240=0\\\\x^2+12x-20x-240=0\\\\x(x+12)-20(x+12)=0\\\\(x+12)(x-20)=0\\\\x=-12\ or\ 20[/tex]
x cannot be negative.
x=20 ft
Thus, if width i.e. x is 20 ft then the farmer will purchase the land.
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What is the value of x?
Enter your answer In the box
X =
A+B+C=180
55+80+x=180
135+x=180
x=180-135
x=45
The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (t/s)|이 6.2 | 10.8 | 14.9 | 18.1 19.4 20.2 Step 1 We will use either Ls or Rs for the upper and lower estimates. Since the runner's speed is an increasing function, then will give the lower estimate, andR will give the upper estimate. ˇ Step 2 The sub-interval widths At for this situation are At- L--JX
The speed of the runner calculated by the properties of average speed is given by 33.45 feet and the upper limit is 43.45 feet in the last 3 seconds.
The first three seconds of a race saw a runner's speed rapidly grow.
The time is therefore 3 seconds.
The table provides her speed at half-second intervals.
We are aware,
Distance x Time = Speed
Similarly
Distance equals speed x time.
Δt equals 0.5 seconds
Then, the minimum distance travelled overall is equal to
0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).
Terms are multiplied and added.
= 0.5 × 66.9
= 33.45 feet
The maximum distance travelled is equal to
0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)
= 0.5 × 86.9
= 43.45 feet
As a result, her maximum distance in three seconds is 43.45 feet, and her maximum distance in three seconds is 33.45 feet.
Velocity is the rate at which an item's position changes as perceived from a certain point of view and as measured by a given unit of time (for example, 60 km/h northbound).
Velocity is also the direction at which an object is travelling. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.
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If Amy is tardy, then she will get a detention
Write the CONTRAPOSITIVE of this statement
Answer:If Amy is not tardy, then she will not get a detention
Step-by-step explanation:
Of people who died in the United States in recent years, 86% were white, 12% were black, and 2% were Asian. (This ignores a small number of deaths among other races.) Diabetes caused 2.8% of deaths among white people, 4.4% among black people, and 3.5% among Asians. What is the probability that a randomly chosen death is a white person who died of diabetes? (Round your answer to three decimal places.)
The probability that a randomly chosen death is a white person who died of diabetes is 0.024 determined using the law of total probability.
The law of total probability is a fundamental rule that connects marginal probabilities to conditional probabilities and expresses the total probability of an outcome via several distinct events. The rule states that if the probability of an event is unknown, it can be calculated using the known probabilities of several distinct events. It is given by P(A ∩ B) = P(A|B)P(B)
In order to determine the probability of an event (D) with not enough information to calculate it directly, a related event, say W can be taken and use that to calculate the probability for D.
Let the events that a person from a certain race die be denoted as:
P(W) = 0.86; P(B) = 0.12; P(A) = 0.02
Let the events that a person from a certain race dies of diabetes be denoted as:
P(D/W) = 0.0.028; P(D/B) = 0.044; P(D/A) = 0.035
Probability that a randomly chosen death is a white person who died of diabetes
P(W) x P (D/W) = 0.86 x 0.028 = 0.02408 ≈ 0.024
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