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Mathematics

1 answer:

ikadub [295]3 years ago

6 0

Answer:

The number of tickets purchased costing $21 each = 18

The number of tickets purchased costing $ 27 each = 11

Step-by-step explanation:

The total number of tickets purchased = 29

Here, let us assume that:

The number of tickets purchased costing $21 = m

The number of tickets purchased costing $ 27 = 29 - m

So, now the cost of m tickets costing $21 each = m x ( $21) = 21 m

Also, the cost of purchasing ( 29-m) tickets costing $27 each

= (29-m)x $27 = 783 - 27 m

Also, the total cost of purchasing 29 tickets = $ 675

⇒ The total cost of m tickets + (29- m ) tickets = $ 675

or, 21 m + 783 - 27 m = 675

⇒ - 6 m = 675 - 783 = -108

or, m 108/6 = 18

⇒ m = 18

Hence the number of tickets purchased costing $21 each = m = 18

The number of tickets purchased costing $ 27 each = 29 - m

= 29 - 18 = 11

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The number of minutes that Samantha waits to catch the bus is uniformly distributed between 0 and 15 minutes. What is the probab

Drupady [299]

Using the uniform distribution, it is found that there is a 0.3 = 30% probability that Samantha has to wait less than 4.5 minutes to catch the bus.

<h3>What is the uniform probability distribution?</h3>

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{x - a}{b - a}$

In this problem, the time is uniformly distributed between 0 and 15 minutes, hence the bounds are a = 0 and b = 15.

The probability that Samantha has to wait less than 4.5 minutes to catch the bus is given by:

$P(X < 4.5) = \frac{4.5 - 0}{15 - 0} = 0.3$

More can be learned about the uniform distribution at brainly.com/question/13889040

7 0

2 years ago

What is the solution to 2logg(x) = logg8+log,(x-2)?<br> x=-4<br> x=-2<br> X=4<br> X= 8

astra-53 [7]

Answer:

x = 4

which agrees with the third listed answer among the given options

Step-by-step explanation:

We can re-write the logarithmic equation using the properties of logarithms:

$2\,log(x)=log(8)+log(x-2)\\log(x^2)=log(8*(x-2))\\log(x^2)=log(8x-16)$

Therefore, the arguments of the log functions must also be equal (and we can solve for "x" by noticing that this expression is the perfect square of a binomial:

$x^2=8x-16\\x^2-8x+16=0\\(x-4)^2=0$