MATHEMATICS HIGH SCHOOL

A school has ordered 16 buses that each have 40 seats for a school trip. There are 32teachers and 576 students. Each bus must have 2 teachers and the rest students. If the
students are distributed evenly amongst the buses, how many students would be on each
bus? How many empty seats will there be in total?

Answers

Answer 1

Answer:

36 students will be in each buses for the trip.

The total number of empty seat in the buses is 32

How to find the total number of seats?

The school ordered 16 buses that each have 40 seats for a school trip.

There are 32 teachers and 576 students.

Each bus must have 2 teachers and the rest students.

The students were distributed evenly amongst the buses.

Therefore,

number of student in each buses = total number of student / number of buses

number of student in each buses = 576 / 16

number of student in each buses = 36

Therefore, 36 students will be in each buses for the trip.

Each buses has 40 seats.

Recall, 2 teachers are even distributed in each buses.

Therefore

number of empty seat in total = 16 × (40 - 36 - 2)

number of empty seat in total = 16 × 2

number of empty seat in total = 32

Therefore, the total number of empty seats in the buses is 32.

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A statement that is proved by deductive logic is called a ______.

Answers

A theorem is the statement that is provided by deductive logic.......

16= -5+z/4
a. 69
b. -1
c. 9
d. 59

Answers

If you would like to solve the equation 16 = (- 5 + z) / 4, you can do this using the following steps:

16 = (- 5 + z) / 4 /*4
16 * 4 = - 5 + z
16 * 4 + 5 = z
z = 69

The correct result would be a. 69.

$16 = (-5+z)/(4)$

Multiply both sides by 4

$16* 4 = (-5+z)/(4) * 4$

$64 = -5+z$

Rearrange the terms

$64 = z - 5$

Add 5 on both sides.

$64 + 5 = z - 5 + 5$

$\boxed{\bf{z = 69}}$

Your final answer is a. 69.

Consider the following pair of equations: y = 3x + 3
y = x − 1

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answers

The coordinate (x,y)=(-2,-3).

We have given the following pair of equations

y = 3x + 3.....(1)

y = x − 1.....(2)

Here we use the substitution method

What substitution method?

The value of one variable from one equation is substituted in the other equation

So the given system of linear equation

We have substitute the value of y from equation 2 into the value of y in equation one

So we get

x − 1= 3x + 3

add like terms

x-3x=3+1

-2x=4

x=4/-2

x=-2

Plug x=-2 in equation 2 we get,

y = -2 − 1

y=-3

Therefore we get the coordinate(x,y)=(-2,-3).

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$3x + 3 = x - 1 \n 3x - x = - 1 - 3 \n 2x = - 4 \n x = ( - 4)/(2 ) = - 2$
Take X=-2 into y
$y = x - 1 \n y = - 2 - 1 \n y = - 3$
(x, y) =(-2,-3)

Probability theory predicts that there is a 22.4% chance of a particular soccer player making four penalty shots in a row. If the soccer player taking four penalty shots is simulated 2500 times, in about how many of the simulations would you expect at least one missed shot?

Answers

If there is a 22.4% chance that a soccer player will make 4 shots in a row, then the probability that he/she WON'T make 4 shots in a row is...

100 -22.4 = 77.6%

So the number of simulations that he/she will miss at least one shot in 2500 simulations would be...

2500 x 77.6% =
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Write an expression that is equivalent to 3/4(5z+16).

Answers

An expression equivalent to 3/4(5z+16) is 15/4z + 12.

Given is an expression 3/4(5z+16), we need to find the equivalentexpression,

An equivalent expression to 3/4(5z+16) can be obtained by distributing the fraction 3/4 to both terms inside the parentheses.

Here's the expression:

(3/4) x (5z + 16)

To simplify further, you can multiply the fraction 3/4 by each term inside the parentheses:

(3/4) x 5z + (3/4) x 16

This simplifies to:

15/4z + 12

Therefore, an expression equivalent to 3/4(5z+16) is 15/4z + 12.

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Distributive property must be applied to simplify this equation:-

3/4*5z + 3/4*16

3.75z+12

An equation that is equivalent to that equation is :- 3.75z+12

A blimp can be seen flying at an altitude of 5500 feet above a motor speedway during a race. The slanted distance directly to the pagoda at the startdashfinish line is d feet. Express the horizontal distance h as a function of d.