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alexdok [17]
2 years ago
15

There are 8 candidates for student government: Hal, Mary, Ann, Frank, Beth, John, Emily, and Tom. The three candidates that rece

ive the highest number of votes become candidates for a runoff election. How many 3-candidate combinations are possible?
Mathematics
1 answer:
sveticcg [70]2 years ago
3 0

Answer:

56

Step-by-step explanation:

Given that there are 8 candidates for student government: Hal, Mary, Ann, Frank, Beth, John, Emily, and Tom.

The three candidates that receive the highest number of votes become candidates for a runoff election.

i.e. 3 persons out of 8 to be selected for becoming candidates for a runoff election.

Since order does not matter we use combinations here

3 persons out of 8 can be done in 8C3 ways

= 56

no of 3-candidate combinations  possible are 56

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Match the expression with its name. 10x2 – 5x + 10
puteri [66]

Answer:

Step-by-step explanation:

quadratic trinomial :  YES.  Three terms, 2nd order polynomial.

cubic monomial:  NO; this is neither a cubic nor a monomial (1 term).

not a polynomial :  NOT true; this is definitely a polynomial.

fourth-degree binomial:   NO; it's a second-degree trinomial.

5 0
2 years ago
A softball pitcher throws a softball to a catcher behind home plate. The softball is 3 feet above the ground when it leaves the
Xelga [282]

The <em><u>correct answer</u></em> is:

h(t) = –16t² + 50t + 3

Explanation:

The general form of an equation such as this is h(t) = at² + v₀t + h₀, where a is the constant due to gravity, v₀ is the initial velocity and h₀ is the initial height.

We are given that the constant due to gravity is -16.

The initial velocity is 50, and the initial height is 3; this gives us the equation

h(t) = -16t² + 50t + 3

5 0
2 years ago
Read 2 more answers
You are researching the penguin population in the Falkland Islands. There are 1000 penguins in the beginning of the first year:
kolbaska11 [484]

Answer:

The formula to determine the population of penguins at the end of the 7th year is:

P_7=1.3^7\cdot P_0=6.275\cdot 1000=6275

Step-by-step explanation:

With this information, we know that the initial population at end of year 0 is 1000 penguins.

The first year will born 500 chicks (50% of the population) and also 20% of the total population will die.

We can then model the population for the end of year 1 as:

P_1=P_0+0.5P_0-0.2P_0=1.3P_0

As this dynamic will continue with the years, we can generalize as:

P_2=1.3P_1=1.3\cdot (1.3P_0)=1.3^2P_0\\\\P_n=1.3^nP_0

Then, the value of the population at the end of the 7th year should be:

P_7=1.3^7\cdot P_0=6.275\cdot 1000=6275

8 0
2 years ago
Which of the number(s) below are potential roots of the function? p(x) = x4 + 22x2 – 16x – 12
Neporo4naja [7]

Complete question is;

Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² – 16x – 12

A) ±6

B) ±1

C) ±3

D) ±8

Answer:

Options A, B & C: ±6, ±1, ±3

Step-by-step explanation:

We are given the polynomial;

p(x) = x⁴ + 22x² – 16x – 12

Now, the potential roots will be all the rational numbers equivalent of p/q.

Where;

p are the factors of the constant term of the polynomial

q are the factors of the leading coefficient of the polynomial

Now, in the given polynomial, the constant term is seen as -12 while leading coefficient is 1 which is the coefficient of x⁴.

We know that factors of 12 are any of:

±1, ±2, ±3, ±4, ±6 and ±12

While possible factors of 1 is just ±1.

Thus, all the potential roots of the polynomial function are;

±1, ±2, ±3, ±4, ±6 and ±12

From the options given, option A, B & C could be the potential roots.

6 0
2 years ago
How will the metric system be used in your furture career
Solnce55 [7]

Answer:

i feel as if in the United States, both the metric system and the English system of measurement are used, although the English system predominates. This discussion question has three parts:

Look around you to find something in the U.S. that is measured in metrics. Describe it to the class.

Give an example of how you think the metric system will be used in your future career.

Do you think the U.S. should switch to metric system exclusively? Why or why not?

This week we learned about the metric and U.S. customary measurement systems. Please upload and submit your responses to the following questions in at least 150 words:

In reflecting on both measurement systems, what did you find most important?

Explain how both measurement systems could relate to your life, community, or current/future career.

Expert Answer

Step-by-step explanation:

6 0
2 years ago
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