a football squad can elect a captain and an assistant captain in 930 possible ways. how many members does the squad have?
Answers
There are 30 members in the football squad.
To determine the number of members in the football squad, we can use combinatorics. Since there are 2 positions (captain and assistant captain) to be filled, and the order in which they are chosen does not matter, we can use the formula for combinations. The number of ways to choose 2 people from a group of n is given by n choose 2, which is equal to n(n-1)/2. Therefore, we can set up the equation:
n(n-1)/2 = 930
Solving for n, we get:
n^2 - n - 1860 = 0
Factoring this quadratic equation, we get:
(n - 30)(n + 62) = 0
Since n must be a positive integer, we have:
n = 30
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Related Questions
Terrence solves the problem and finds 53.04 x 4.6 = 2,439.84. Tara says that his product is incorrect. Fill in the blanks to help Tara explain Terrence's error. The first factor has _____________ decimal place(s) and second factor has ________ decimal place(s)
Answers
Answer:
Answer:tara was right terrence was close but he put the(.) in the wrong spot the correct answer is 243.984 but terrence put 2439.84
Step-by-step explanation:
Answer:
1st blank: Few
2nd blank: two
3rd blank: one
4th blank: three
5th blank: three
Step-by-step explanation
The amount of numbers behind the decimal of numbers behind the decimal in the answer.
Sam saved $35 buying the suit at a 20% off sale what was the regular price of the suit
Answers
Same bought it for $140. 20% of 175 is 140. And 175-35 is also 140. So 175 is the answer
find the expectation value of the position squared when the particle in the box is in its third excited state. answer this question with the correct coefficient of l2 for the expectation value.
Answers
The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.
The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),
where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to
\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).
This can be written as nine-eighths of the length of the box squared.
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Mark has four and one-fifth yards of rope and gives one-third of it to his friend.
How many yards of rope did Mark give his friend?
one and six-fifteenths
two and five-eighths
four and one-fifteenth
four and two-eighths
Answers
The yards of rope that Mark give his friend is A. one and six-fifteenths
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Mark has four and one-fifth yards of rope and gives one-third of it to his friend.
The fraction given out will be:
= Fraction given × Total yards
= 1/3 × 4 1/5
= 1/3 × 21/5
= 7/5
= 1 2/5
The correct option is A.
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PLEASE PLEASE HELP I WILL GIVE BRAINALIST AND EXTRA POINTS
Answers
Answer:
Step-by-step explanation:
1) phone
38.95 = 0.03 * mins + 29.95
9.00 = 0.03 * mins
9.00 /0.03 = mins
300 = mins
so he used 300 minutes :)
2) books
8.70 =14 * bookPrice + 2.40
6.30 = 14 * bookPrice
6.30 / 14 = bookPrice
0.45 = bookPrice
each book cost 45 cents :)
(Prove that):
2 sin 7A. cos 2A = sin 9A + sin 5A
Answers
Answer:
Below.
Step-by-step explanation:
We use the identity:
sin A + sin B = 2 sin(A+B)/ 2 cos(A-B)/2
so sin 9A + cos 5A
= 2 sin (9A + 5A)/2 cos (9A - 5A)/2
= 2 sin 14/2 cos 4/2
= 2 sin7A cos 2A.
The current flow to a transformer's primary circuit measures 16 amps. The transsformer's secondary current measures 80 amps. What the transformer's turns ratio?
Answers
Answer:
1/5
Step-by-step explanation:
The transformer formula is as expressed as
Ns/Np= Ip/Is
Ns and Np are the number of turns in the secondary and primary coil respectively
is and Ip are the currents in the secondary and primary coil respectively
Given the following
Ip = 16A
Is = 80A
Substitute into the formula
Ns/Np = 16/80
Ns/Np = 1/5
Hence the transformer's turn ratio is 1/5
Answer: for pf, 1:5 is WRONG!
Step-by-step explanation:
Trees planted by a landscaping firm have a 95% one-year survival rate, If they plant 16 trees in a park, what is the following probabilities:
1. All the trees survive one year.
2. At least 14
Answers
The probabilities are given as follows:
1. All trees survive one year: 0.4401 = 44.01%.
2. At least 14 trees survive one year: 0.957 = 95.7%.
What is the binomial distribution formula?The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.
The mass probability formula is given by the equation presented as follows:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters, along with their meaning, are listed as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 16, p = 0.95.
Hence the probability that all the trees survive in one year is given as follows:
\(P(X = 16) = 0.95^16 = 0.4401\)
For at least 14 trees surviving, we have that:
\(P(X = 14) = 120 \times 0.95^14 \times 0.05^2 = 0.1463\)\(P(X = 15) = 16 \times 0.95^15 \times 0.05 = 0.3706\)Hence:
P(X >= 14) = 0.1463 + 0.3706 + 0.4401 = 0.957.
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The diameters of Red Delicious apples in a certain orchard have a mean of 2.63 in. and a standard deviation of 0.25 in and come from a bimodal distribution. A sample of size 100 is taken, what is the shape of the sampling distribution of sample means
Answers
The shape of the sampling distribution of sample means from a sample of size 100 taken from a bimodal distribution of Red Delicious apple diameters with a mean of 2.63 in. and a standard deviation of 0.25 in. is approximately normal.
According to the central limit theorem, when the sample size is sufficiently large (typically greater than 30) and the population distribution is not severely skewed, the sampling distribution of sample means tends to approximate a normal distribution, regardless of the shape of the population distribution.
In this case, even though the population distribution of Red Delicious apple diameters is bimodal, the sample size of 100 is considered large enough for the central limit theorem to apply. As a result, the sampling distribution of sample means will be approximately normal.
This means that if we were to take multiple random samples of size 100 from the orchard and calculate the mean diameter for each sample, the distribution of those sample means would be bell-shaped and follow a normal distribution.
Therefore, the shape of the sampling distribution of sample means from the given sample size and population distribution is approximately normal.
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Select the real-world problem that could be solved using a proportion.
Answers
the answer is D
300/6 = x/10
once solved, it will be proportional
determine if the sequence is geometric. if it is, find the common ratio.
-1, 1, 4, 8, ...
Answers
Due to the lack of a common ratio, the above sequence is not geometric.
What is geometeric sequence?
A series of integers with a common ratio is referred to as a geometric sequence. A geometric sequence has a next number that is a multiple of the one before it.
if the sequence is geometric.the common ratio of the number's
-1, 1, 4, 8, are
-1/1 = -1 ratios of the numbers in the sequence
4/1 = 4
8/4 = 2
There isn't a ratio that unites the numbers.
The lack of a common ratio leads us to the conclusion that the presented sequence is not geometric.
Due to the lack of a common ratio, the above sequence is not geometric.
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many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and stardard deviation of the test scores are 80 and 5, respectively. Assume nothing is known about the distribution, what percentage of test-takers scored better than the trainee who scored 90
Answers
Answer:
At most 25%
Step-by-step explanation:
The fraction of the distribution that can exceed n standard deviations from the mean is 1/n². For a standard deviation of 5 and a mean of 80, a score of 90 is (90-80)/5 = 2 standard deviations from the mean. Scores better than that can be at most (1/2)² = 1/4 = 25% of the total number of scores.
Determine a basis for the subspace of M2(R) spanned by the following. (Enter your answer as a list of matrices. Enter each matrix as a comma-separated list of its components in the form [[a11, a12l, [a21, a221.) 5-10 1 1 1 L-51 -1 2
Answers
[ 5 -1 1 | 0 ]
[-10 1 -1 | 0 ]
[ 1 -1 2 | 0 ]
R2 -> R2 + 2R1
R3 -> R3 - (1/5)R1
[ 5 -1 1 | 0 ]
[ 0 1 -1 | 0 ]
[ 0 -4/5 9/5| 0 ]
R3 -> R3 + (4/5)R2
[ 5 -1 1 | 0 ]
[ 0 1 -1 | 0 ]
[ 0 0 5/3| 0 ]
Now we see that the third row corresponds to the equation (5/3)z = 0, which implies that z = 0. Therefore, the subspace is spanned by the two matrices:
[ 5 -1 1 ]
[ 0 1 -1 ]
We can check that these matrices are linearly independent, which means that they form a basis for the subspace. Therefore, the basis is:
[[5, -1, 1], [0, 1, -1]]
Help I will give brainlyestt!!!
Answers
Answer:
I think the answer is the 3rd table and the 4th
Step by step:
This is because if you were to draw them you would realise it forms a happy face or sad one
ASAP!!! Clever code to calculate the area of a triangle???
Answers
Answer:
1/2 bh
half of base × height
Given that ZQRP = (2x + 20) and ZPSQ = 30°, find the value of x.
Answers
The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.
We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.
If angles QRP and PSQ are supplementary, their sum is 180°:
(2x + 20)° + 30° = 180°
Now, we can solve for x:
2x + 50 = 180
Subtract 50 from both sides:
2x = 130
Divide by 2:
x = 65
(4x2 + 7x - 4) + (x2 – 7x + 14)
What is the answer?
Answers
Answer:
\(5x^2 + 10\)
Step-by-step explanation:
\(4x^2 + x^2 = 5x^2\\7x + (-7x = 0\\-4 + 14 = 10\)
Jenny wants to buy the newest music from her local store. she buys 3 CDs that cost $ 36. If she gives the cashier a 50 dollar bill, how much change should she get back?
Answers
Answer:
$14 will be her change
Step-by-step explanation:
1. subtract the $36 from the 50 dollar bill
$50-$36= 14
Answer:
14 dollars
Step-by-step explanation:
you do 50-36
Select the correct answer. Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will not be a polynomial.
Answers
f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.
Given f(x) and g(x) two polynomial functions in the standard form of the polynomial,
According to Closure Property, when something is closed, the output will be the same as the input.
The polynomials f(x) and g(x) can be seen in the image.
On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.
Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.
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Complete question:
De un grupo de 85 personas, 40 estudien y 50 trabajan, 10 estudian y trabajan.
a) ¿Cuántas no estudian y trabajan?
b) ¿Cuántas personas únicamente se dedican a estudiar?
c) ¿Cuántas personas únicamente se dedican a trabajar?
Answers
Answer:
a) 5
b) 30
c) 40
Step-by-step explanation:
(no entiendo mucho espanol pero voy a ayudar...)
a) hay 10 que haces los dos, 30 que solo estudien, y 40 que solo trabajan. Con eso, 80-10-30-40 = 5, y asi tienes 5 personas que no estudian y no trabajan
b) las personas que estudian son 40, y 10 trabajan tambien, asi solo tienes 30 personas que unicamente se dedican a estudiar.
c) las personas que trabajan son 50, y 10 estudian tambien, asi solo tienes 40 personas que unicamente se dedican a estudiar.
C) Find the probability of rolling an odd number given you have spun a red section:
P(odd numberjred). 0.5 or 50%
2) A different game requires players to spin a five-section spinner and roll a six-sided
standard die to make a move. The spinner has sections of equal area, with each
section containing one of these numbers: 1, 2, 3, 4, and 5. The player gets to move
based upon the sum of the two numbers-one from the spinner and one from the
die.
A) Make a table to display the sample space of the compound events representing
the players making moves during the game.
I
1
2
- Make the columns correspond to the possible rolls of the dice and the
rows correspond to the possible spinner numbers.
For each cell entry, write the sum of the row value and the column value.
B) Find the probability of getting a sum of 4, 5, or 6.
Answers
The probability of getting a sum of 4, 5, or 6. is 0.4
Displaying the sample space of the compound eventsFrom the question, we have the following parameters that can be used in our computation:
Spinner = 1 to 5
Die = 6 sided
This means that the number of outcomes is
Outcomes = 6 * 5
Outcomes = 30
So, the sample space is
Die \ Spinner 1 2 3 4 5
1 2 3 4 5 6
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
Calculating the probabilityThe probability of getting a sum of 4, 5, or 6. is
P = Number/Sample size
From the table, we have
Number of sum of 4, 5, or 6 = 12
So, we have
P = 12/30
Evaluate
P = 0.4
Hence, the probability of getting a sum of 4, 5, or 6. is 0.4
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Which entence correctly place the lah mark between the ubject and predicate of the entence?
The guard were unaware of God' plan for Peter. HELPPPPPPP
Answers
The sentence that correctly places the slash between the subject and the predicate of the stated sentence is, Four groups / of four soldiers guarded / Pedro in jail. Correct answer: letter B.
Is important to consider the context in which the sentence is used. Depending on the situation, the answer may vary. For example, if the sentence is part of a larger dialogue about the strength of a prison guard, then more information about the security measures taken and the number of soldiers deployed to guard Peter would be relevant.
Alternatively, if the sentence is part of a discussion about the importance of loyalty and friendship, then information about the relationship between Peter and the soldiers would be important.
Which sentence correctly places the slash mark between the subject and predicate of the sentence? Four groups of four soldiers watched over Peter in jail.
A) Four groups / of four soldiers watched over Peter in jail.
B) Four groups of four soldiers / watched over Peter in jail.
C) Four groups of four soldiers watched / over Peter in jail.
D) Four groups of four soldiers watched over Peter/in jail.
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Find the value of an investment of $10,000 for 13 years at an annual interest rate of 3. 15% compounded continuously
Answers
The value of the investment after 13 years at an annual interest rate of 3.15% compounded continuously would be approximately $15,345.
The value of an investment of $10,000 for 13 years at an annual interest rate of 3.15% compounded continuously can be found using the formula for continuous compound interest:
\(\[ A = P \cdot e^{rt} \]\)
Where:
A = the final value of the investment
P = the principal amount (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (expressed as a decimal)
t = the time in years
Plugging in the given values:
P = $10,000
r = 0.0315 (3.15% expressed as a decimal)
t = 13 years
We can calculate the final value of the investment using the formula:
\(\[ A = \$10,000 \cdot e^{0.0315 \cdot 13} \]\)To find the value of \(\( e^{0.0315 \cdot 13} \)\), you can use a calculator or a scientific calculator function. For example, using a scientific calculator, you would enter \(\( 0.0315 \cdot 13 \)\), and then use the "e^x" or "exp" function to calculate the exponent.
Let's assume the result of \(\( e^{0.0315 \cdot 13} \)\) is approximately 1.5345.
Now, we can calculate the final value of the investment:
\(\[ A = \$10,000 \cdot 1.5345 \] A = \$15,345 \]\)
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Mr. Turner has two Math 2 classes, with one class, he lectured, and the students took notes.
In the other class, the students worked in small groups to solve math problems. After the first
test, Mr. Turner recorded the student grades to determine if his different styles of teaching
might have impacted student learning,
Class 1: 80, 81, 75, 70, 72, 74, 76, 77, 77, 79, 84, 88, 90, 80, 78
Class 2: 70, 90, 88, 89, 86, 86, 82, 77, 79, 84, 84, 86, 87, 88, 88
Answers
Find the domain of y log(1 + 3x). The domain is: x ≤ A
x < A
x > A
x ≥ A
Answers
The domain of y = log(1 + 3x) is x > -1/3. This means that x must be greater than -1/3 for the function to be defined.
The given function is y = log(1 + 3x). In logarithmic functions, the argument inside the logarithm must be greater than zero for the function to be defined. In this case, the argument is (1 + 3x).
To find the domain, we set the argument greater than zero and solve for x:
1 + 3x > 0
Subtracting 1 from both sides:
3x > -1
Dividing both sides by 3 (since the coefficient of x is 3):
x > -1/3
Therefore, the domain of the function y = log(1 + 3x) is x > -1/3. This means that x must be greater than -1/3 for the function to be defined.
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1. Jack wants to buy a pair of name-brand headphones on a popular auction
website. He enters the brand, make, and model number and searches the site
for what is available. He notices that some headphones are being offered as
"buy now" with a fixed price and others are up for bid in auctions. Below is a
list of all prices at the time he did his search.
$75 $95 $180 $136 $89 $75 $110 $180 $100 $136 $180
$95 $180 $136 $75
$100 $110 $180 $180 $136 $75 $90
a. Construct a frequency distribution for the data.
b. Use the frequency distribution to determine the mean. Round your answer
to the nearest cent.
c. Use the frequency distribution to determine the median and the mode.
Answers
Answer:
Mean = 125.136
Median = 110
Mode = 180
Step-by-step explanation:
Given the data:
75 95 180 136 89 75 110 180 100 136 180 95 180 136 75 100 110 180 180 136 75 90
Frequency distribution:
Value(X) ___freq (F) ____cumm frequency
85 _________ 4 _______ 4
89 _________ 1 _______5
90 __________1 _______6
95 __________2 ______ 8
100 _________ 2 ______10
110 __________2______ 12
136 __________4 _____ 16
180 __________6______22
2) Using the frequency distribution :
Mean = Σfx / Σf
[(85*4) + (89*1) + (90*1) + (95*2) + (100*2) + (110*2) + (136*4) + (180*6)]/ 10
= 2753 / 22
= $125.136
Median of grouped data :
Frequency + 1 / 2 = 23/2 = 11.5 th term
The median value = $110
Mode of the data:
Most frequently occurring = 180 (frequency of 6)
The mean of the frequency distribution is $125.136, the median of the frequency distribution is $110, and the mode of the frequency distribution is $180.
Given :
Jack wants to buy a pair of name-brand headphones on a popular auction website.He enters the brand, make, and model number and searches the site for what is available. He notices that some headphones are being offered as "buy now" with a fixed price and others are up for bid in auctions.a) The frequency distribution is given below:
Prices Frequency Cumulative Frequency
85 4 4
89 1 5
90 1 6
95 2 8
100 2 10
110 2 12
136 4 16
180 6 22
b) The mean is calculated as:
\(\rm Mean = \dfrac{85\times4 + 89\times1 +90\times1 +95\times 2+100\times2 +110\times2 +136\times4 +180\times6 }{10}\)
Simplify the above expression.
Mean = $125.136
c) The median of the frequency distribution is calculated as:
\(\rm Term= Frequency + \dfrac{1}{2}=11.5\)
So, the median is $110.
The mode of the frequency distribution is $180.
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The lengths of the sides of a triangle are consecutive integers. If the perimeter of the triangle is 111, find the lengths of the sides.
Answers
Answer:
we know
perimeter of triangle = sum of all sides
here lengths of sides are consecutive integers so
length of three sides = x, (x+1) and (x+2)
now
Perimeter = 111
or, x + (x+1) + (x+2) = 111
or 3x + 3 = 111
or 3x = 108
x = 36
x = 36
(x+1) = 36 + 1 = 37
(x+2)= 36 + 2 = 38
what is a congruent polygon
Answers
A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.
Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.
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Select all of the ratios that are equivalent to 1/2.
2/6
4/8
50/100
9/18
20/40
35/40
Answers
I need help on this question I don’t get it?
Answers
Step-by-step explanation:
the key is to understand that
12 in = 1 ft
1 ft³ (= a cube of 1 ft × 1ft × 1ft or 12in × 12 in × 12 in = 1728 in³) weighs 40 lbs.
her truck can only carry 1,700 lbs without breaking down.
but it would have space for 66×60×24 = 95040 in³ =
95040/1728 = 55 ft³ of soil, which would weigh
55 × 40 = 2200 lbs (too much for the truck).
the same ratio as for the weight her truck can carry applies for the filled volume of the truck bed with that weight :
1700/2200 = 17/22
so, she can only fill 17/22 of her truck bed volume with soil.
i)
percents are calculated by multiplying the ratio by 100 :
17/22 × 100 = 77.27272727... % ≈ 77%
she can fill about 77% of her truck bed with soil without going over the weight limit.
ii)
since she can transport only 1700 lbs in one trip, and 1 ft³ of soil weighs 40 lbs, she can transport
1700/40 = 42.5 ft³ of soil per trip.
she would then earn
42.5 × 1.5 = $63.75 per trip.