A school's track and field team has 14 track athletes, and 10 field athletes. Due to budget constraints, the school is only allowed to send 3 athletes to the meet. how many ways can this be done if the coach wishes to send at least one track athlete. [3 marks/A]
Answers
Answer:
1924 ways
Step-by-step explanation:
Let's calculate the three cases: one track athlete, two track athletes and three track athletes.
One track athlete:
The track athlete has 14 possible choices.
The two field athletes have a combination of 10 choose 2 possibilities:
C(10,2) = 10! / (8! * 2!) = 10*9/2 = 45
So we have 14 * 45 = 630 ways.
Two track athletes:
The two track athletes have a combination of 14 choose 2 possibilities:
C(14,2) = 14! / (12! * 2!) = 14*13/2 = 91
The field athlete has 10 possible choices.
So we have 91 * 10 = 930 ways.
Three track athletes:
The three track athletes have a combination of 14 choose 3 possibilities:
C(14,3) = 14! / (11! * 3!) = 14*13*12/6 = 364
So we have 364 ways.
Finally, the total number of ways is:
630 + 930 + 364 = 1924 ways.
Answer:
3864
Step-by-step explanation:
14C1x24C2= 14x276= 3864
Related Questions
PLS HURRY FOR THE LOVE OF GOD
On a coordinate plane, a line goes through (0, negative 6) and (2, 0) Negative one-third
A. -1/3
B. 1/3
C. 3
D. -3
giving 25pts whoever answers it first
Answers
Answer:
The answer is 44!
Step-by-step explanation:
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renegade???
In the figure below, mZ2-66". Find m21, mZ3, and mZ4
*
m23-
#24-
%
Answers
The value of the angles in the figure are:
m∠1 = 114°
m∠3 = 114°
m∠4 = 66°
How to find m∠1, m∠3 and m∠4 in the figure?To answer the question, we need some angle geometry knowledge:
We have:
m∠2 = 66°
Thus, we can find the angles in the figure as follow:
m∠1 = 180° - 66° (sum of angles on a straight line is 180°)
m∠1 = 114°
m∠3 = m∠1 (vertically opposite angles are equal)
m∠3 = 114°
m∠4 = m∠2 (vertically opposite angles are equal)
m∠4 = 66°
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which of the following number sequences could be produced by the expression
2x+x^2
Answers
The given expression is
\(2x+x^2\)
So we can write the general rule for the sequence as
\(T_x=2x+x^2\)
Recall that the domain of a sequence is the set of natural numbers.
Let us plug in some first few natural numbers to generate the sequence.
When \(x=1\), we obtain,
\(T_1=2(1)+(1)^2\)
\(\rightarrow T_1=2+1\)
\(\rightarrow T_1=3\)
When \(x=2\), we obtain,
\(T_2=2(2)+(2)^2\)
\(\rightarrow T_2=4+4\)
\(\rightarrow T_2=8\)
When \(x=3\), we obtain,
\(T_3=2(3)+(3)^2\)
\(T_3=6+9\)
\(T_3=15\)
When \(x=4\), we obtain,
\(T_4=2(4)+(4)^2\)
\(T_4=8+16\)
\(T_4=24\)
Therefore the number sequence produced by the given expression is,
\(\boxed{\bold{3, 8, 15, 24.}}\)
Consider the polynomial function q(x) = -2x^8 + 5x^6 -3x^5 + 50 What is the end behaviour of the graph of q?
Answers
The end behavior of the function q(x) is:
when x → ∞, q(x) → -∞when x → -∞, q(x) → -∞How to identify the end behavior?To know the end behavior we need to look at the degree and the sign of the leading coefficient.
If the degree is even, and the leading coefficient is negative, then in both ends the function will tend to negative infinity.
Here we can see that the function is:
q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
So, the degree is 8, and the leading coefficient is -2, then the end behavior of the function is:
when x → ∞, q(x) → -∞
when x → -∞, q(x) → -∞
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Aggregates for the construction of a reinforced concrete building are supplied by two companies, Company A and Company B. Orders are for Company A to deliver 700 truck loads a day and 300 truck loads a day from Company B. From prior experience it is expected that 5% of the material from Company A will be substandard and 3% of the material from Company B will be substandard. Part 1 What is the probability of substandard aggregates
Answers
Answer:
The probability of substandard aggregates is 0.044.
Step-by-step explanation:
We are given that orders are for Company A to deliver 700 truckloads a day and 300 truckloads a day from Company B.
From prior experience, it is expected that 5% of the material from Company A will be substandard and 3% of the material from Company B will be substandard.
Let the probability that orders are for Company A to deliver = P(A) = \(\frac{700}{1000}\)
The probability that orders are for Company B to deliver = P(B) = \(\frac{300}{1000}\)
Let event S = material which is substandard
So, the probability that the material from Company A will be substandard = P(S/A) = 0.05
the probability that the material from Company B will be substandard = P(S/B) = 0.03
Now, the probability of substandard aggregates is given by = P(S)
P(S) = P(A) \(\times\) P(S/A) + P(B) \(\times\) P(S/B)
= 0.7 \(\times\) 0.05 + 0.3 \(\times\) 0.03
= 0.044
Hence, the probability of substandard aggregates is 0.044.
the function of f(x)=x^3-7x+6 is shown in the figure which is a factor of the function shown
Answers
Answer:
answer is the first one
Step-by-step explanation:
i dont know how to explain it
y=9/4×2
sketch the graph of f and f on the same set of axes
Answers
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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Aiden measured a campground and made a scale drawing. The scale of the drawing was 9 inches = 3 yards. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
Answers
Answer:2/3
Step-by-step explanation: just divide them as a improper fraction
The scores for the top two dance teams at a competition are shown. The
winner of the competition was the team with the highest median score.
Which statement about the teams scores is not correct?
Team A's scores
58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100
Team B's scores
58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100
O A. Team B received the lowest score.
OB. The spread of scores for team B was greater than for team A.
O C. Team A won the competition.
O D. The typical score for team B was higher than for team A.
Answers
Answer:
B. The spread of scores for team B was greater than for team A
Step-by-step explanation:
I just took the quiz, this was right.
7).
2. Hot Text: For each graph, choose the correct sentence to describe the graph.
The graph represents a proportional relationship.
The graph does not represent a proportional relationship.
Answers
a. The graph represents a proportional relationship.
b. The graph does not represent a proportional relationship.
c. The graph does not represent a proportional relationship.
d. The graph represents a proportional relationship.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:
y = kx.
Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.
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Which statement is not true about thw absolute value of -6
Answers
After a 90% reduction, you purchase a new soft drink machine on sale for $64. What was the original price of the soft drink machine?
Answers
Answer:
$640
Step-by-step explanation:
Let \(x\) equal the original price of the machine.
We know that $64 is 10% of \(x\) because $64 is left of \(x\) after the 90% reduction.
Set up an equation:
\(.10x=64\)
Divide by the coefficient of \(x\), which in this case is \(.10\)
\(x=640\)
Identify the fractions labeled with the letters A and B on the scale below.ВLetter A represents the fractionLetter B represents the fraction
Answers
Given
A scale from 0 to 1 is divided into 6 parts
Answer
Letter A is represented by fraction 1/6
Letter B is represented by fraction 3/6 = 1/3
There are 13 maple trees currently in the park. Park workers will plant more maple trees today. When the workers are finished, there will be 88 maple trees in the park. How many maple trees did the workers plant today
Answers
HellpppNeed help please urgent
Answers
Answer:
the answer is 63.59m²
Step-by-step explanation:
\(radius = \frac{diameter}{2} \\ = \frac{3}{2} \\ = \frac{9}{2} (since \:1cm = 3m \: so \: 3cm = 9m) \\ = 4.5 \\ area \: of \: circle = \pi {r}^{2} \\ = 3.14 \times (4.5) {}^{2} \\ = 3.14 \times 20.25 \\ = 63.585 {m}^{2} \)
What is the period of this graph?
Answers
Answer:
4π
Step-by-step explanation:
The Period, as measured from crest-to-crest (or from trough-to-trough), is 4π, as read directly from the graph
What’s the answer to this?
Answers
Answer:
f(0) = 4
Step-by-step explanation:
f(0) implies that we should find the corresponding f(x) value of when x = 0.
From the table given, when x = 0, f(x) = 4. This is (0, 4).
Thus:
f(0) = 4
The graph of the function f(x) = (x-4)(x + 1) is shown
below.
Which statement about the function is true?
O The function is increasing for all real values of x
where
x < 0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1
O The function is decreasing for all real values of x
where
x < 1.5.
Answers
The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.
Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).
The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.
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f(x) = -3X - 4 ; Domain= {-17, -14, -6, -2,4, 15}
Range :
Answers
Answer:
g(x)={47,38,14,2,-16,-49}
Step-by-step explanation:
f(-17)=-3*-17-4=51-4=47
f(-14)=-3*-14-4=42-4=38
f(-6)=-3*-6-4=18-4=14
f(-2)=-3*-2-4=6-4=2
f(4)=-3*4-4=-12-4=-16
f(15)=-3*15-4=-45-4=-49
If I worked all these hours, how much should I be paid. It's 13.69 per hour btw each. Schedule:
9/13 Monday 10am-2:00pm
9/14 Tuesday 10am-2:00pm
9/15 Wednesday 10am-2pm ( Campus or Zoom)
8/16 Thursday 10am-2pm. Two weeks later I work two hours which is 27.38. How much money should I get with all of this in total.
Answers
Answer:
$246.42
Step-by-step explanation:
13.69(4+4+4+4) + 27.38
13.69(16) + 27.38
219.04 + 27.38
246.42
You should make $246.42.
Jesse stops by the grocery store to
buy bananas. Each pound of bananas
costs $0.75. Jesse has a coupon for
$0.10 off a pound of bananas. If
Jesse buys 1 pound of bananas and
a container of orange juice for $2.49,
what is the total cost of his purchase?
Answers
Answer:
$3.14
Step-by-step explanation:
0.75 - 0.10= 0.65
2.49 + 0.65 = 3.14
ANSWER ALL QUESTIONS
1. In a class of 28 pupils, 13 have pencils, 9 have erasers and 9 have neither pencils nor erasers. How
many pupils have both pencils and erasers?
2. A universal set, U consists of prime numbers with P and Q as subsets of U. If P and Q are given by
P = {n: 3(n + 1) = 2(n + 10)}, and Q = {n: 7<n<31}, list the elements of P n Q.
Answers
1. 3
29-9=19
13+9=22
22-19=3
I don't know number 2, sorry.
An organization has raised $4800 for a remodeling project. This is 60% of their goal.
What is their fundraising goal
Answers
Answer:
$8000
Step-by-step explanation:
1. Work out 1% of the overall value:
4800= 60%
4800/60= 1%
80= 1%
2. Use this to work out 100%:
80 x 100= 100%
8000= 100%
3. Put this back into the context of the question:
Fundraising goal= $8000
quick ASAP 25 POINTS AND BRAINLIEST FOR BEST ANSWER
Multiplying Rational Expressions
Simplify each expression
(1/p-9)*(p^2+6p-27/p+9)
Answers
Answer:
-9p3 + 6p2 + 9p - 26/ p
Step-by-step explanation:
hope this helps
Leila bought 3 gallons of milk in one-gallon containers. She paid $9.75. QUESTION: What is the unit rate?
Answers
Hello and Good morning/afternoon:
Let's take this problem step-by-step:
What does the problem want:
⇒ unit rate ⇒ price per gallon
What does the problem give us:
⇒ price of all three milk
⇒ number of gallons of milk bought
Therefore
\(\hookrightarrow \text {unit rate} = \text{total amount of money spent} / \text {total amount of milk bought}\\\\\hookrightarrow\text{unit rate} = 9.75 / 3 = 3.25 _. \text {dollar per gallon}\)
Answer: 3.25 dollars per gallon
Hope that helps!
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Bags of pretzels are sampled to ensure proper weight. The overall average for the samples is 9 ounces. Each sample contains 25 bags. The standard deviation is estimated to be 3 ounces. The upper control chart limit (for 99.7% confidence) for the average would be ________ ounces.
Answers
Answer:
The value is \(UCL = 10.8\)
Step-by-step explanation:
From the question we are told that
The sample mean is \(\= x = 9 \ ounce\)
The sample size is n = 25
The standard deviation is \(\sigma = 3 \ ounce\)
Given that the sample size is not large enough i.e n< 30 we will make use of the student t distribution table
From the question we are told the confidence level is 99.7% , hence the level of significance is
\(\alpha = (100 -99.7 ) \%\)
=> \(\alpha = 0.003\)
Generally the degree of freedom is \(df = n- 1\)
=> \(df = 25 - 1\)
=> \(df = 24\)
Generally from the student t distribution table the critical value of \(\frac{\alpha }{2}\) at a degree of freedom of \(df = 24\) is
\(t_{\frac{\alpha }{2} , 24 } = 3.0 \)
Generally the margin of error is mathematically represented as
\(E = t_{\frac{\alpha }{2} , 24} * \frac{\sigma }{\sqrt{n} }\)
=> \(E = 3.0 * \frac{3 }{\sqrt{25} }\)
=> \(E =1.8 \)
Gnerally the upper control chart limit for 99.7% confidence is mathematically represented as
\(UCL = \= x + E\)
=> \(UCL = 9 + 1.8\)
=> \(UCL = 10.8\)
Find the range and standard deviation of the set of data.
11 8 5 11 25
Answers
Answer: The range is 20, Standard Deviation, σ: 6.8702256149271
Step-by-step explanation:
I hope it helped!
<3
I need help on this one
Find the selling price.
Cost To Store: $50
Markup: 10%
The selling price is $blank
Answers
The selling price of the item at 10% marlkup is $55
Finding the selling price of the itemFrom the question, we have the following parameters that can be used in our computation:
Cost To Store: $50Markup: 10%Using the above as a guide, we have the following:
Selling price = Cost To Store * (1 + Markup)
substitute the known values in the above equation, so, we have the following representation
Selling price = 50 * (1 + 10%)
Evaluate
Selling price = 55
Hence the selling price of the item is $55
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plz help quickly........................................
Answers
Answer:
the median is increased from 7 to 7.5
How many ways can a three-person jury be selected from a pool of eleven people?
Answers
A three-person jury can be selected from a pool of eleven people in 165 ways.
What is meant by the term combination?A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the order of a selection is irrelevant. You can choose the items in any order in combinations. Permutations and combinations are often confused.We will employ the formula ⁿCₓ = n! / x! * (n - x)! to calculate combinations, where n is the total number of items and x represents the amount of items chosen at a time.For the given question;
The total number of person in the pool = 11.
The number of jury selected = 3.
Thus, the combination will be ⁿCₓ.
Where, n = 11 and x = 3.
¹¹C₃ = 11!/3!(11 - 3)!
Simplifying;
¹¹C₃ = 165
Thus, the number of ways in which three jury can be selected from 11 pool of members is 165.
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