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saul85 [17]
2 years ago
15

At a regional soccer​ tournament, tickets for two adults and seven students cost ​$60. Tickets for three adults and eleven stude

nts cost ​$93. Determine the price of an adult ticket and the price of a student ticket.
The price of an adult ticket is ​$, and the price of a student ticket is ​$
Mathematics
1 answer:
den301095 [7]2 years ago
8 0

Answer:

The price of an adult ticket is $9 and the price of a student ticket is $6

Step-by-step explanation:

Create a system of equations where x is the price of an adult ticket and y is the price of a student ticket:

2x + 7y = 60

3x + 11y = 93

Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2, to cancel out the x terms:

6x + 21y = 180

-6x - 22y = -186

Add them together:

-y = -6

y = 6

Then, plug in 6 as y into one of the equations to solve for x:

2x + 7y = 60

2x + 7(6) = 60

2x + 42 = 60

2x = 18

x = 9

So, the price of an adult ticket is $9 and the price of a student ticket is $6

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What value of B will make the product equal of 17 in the following expression: 17xb/7
Katyanochek1 [597]

The value B is 7. If we apply B=7 the answer is 17 for the expression 17×\frac{b}{7}

Step-by-step explanation:

            The given expression is 17×\frac{b}{7}  

Step:1

            Form an equation from given data,

            17×\frac{b}{7}= 17..............................(1)

                                                         (∵ product equal to 17)

Step:2

            Check for alternatives by apply the value of B in eqn (1)

            Assume be value of B for check the equation

            B=1

            Equation becomes,

            17×\frac{1}{7} = 2.4286 ≠ 17

            Take, B=2,

            17×\frac{2}{7} = 4.8571 ≠ 17

            Take, B=3,

            17×\frac{3}{7} = 7.2857 ≠ 17

similarly,

            B=7,

            17×\frac{7}{7} = 17                       (∵ The product equals to 17)

Result:

         So, the answer for B is 7.

7 0
3 years ago
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The temperature of a city changed -24 degrees Celsius over a 6 week period. Write an expression the show the average change in t
Ne4ueva [31]

Answer:

The expression is (-24) / 6 = -4degrees which means that in each week the average change in temperature was -4 degrees Celsius.

Step-by-step explanation:

Change in a quantities can as well be interpreted as rate of change which is used in many everyday problems, such as weather forecast, traveling , in science and so on.When we are talking about rate of change it's is usually in ratio such as Miles per hour or feet per second can be used in calculation involving rates of speed. It is how one quality is changing with respect to time , for instance, rate equals distance divided by time: r = d/t.

In finance rate of change is also applicable we can have Unit price which is a particular rate that compares a price to some unit of measure. Example is $64 per dozen.

Therefore, Given from the question,

The temperature of a city changed -24 degrees Celsius ,

Time =6 weeks period.

Then change is r = d/t.

= (-24) / 6

Change = (-24) / 6 = -4 degrees

This means that each week the average change in temperature was -4 degrees Celsius.

3 0
3 years ago
A center for medical services reported that there were 295,000 appeals for hospitalization and other services. For this group, 4
pshichka [43]

Answer:

a) 0.0025 = 0.25% probability that none of the appeals will be successful.

b) 0.0207 = 2.07% probability that exactly one of the appeals will be successful.

c) 0.9768 = 97.68% probability that at least two of the appeals will be successful

Step-by-step explanation:

For each appeal, there are only two possible outcomes. Either it is succesful, or it is not. The probability of an appeal being succesful is independent of other appeals, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

45% of first-round appeals were successful.

This means that p = 0.45

Suppose 10 first-round appeals have just been received by a Medicare appeals office.

This means that n = 10

(a) Compute the probability that none of the appeals will be successful.

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.45)^{0}.(0.55)^{10} = 0.0025

0.0025 = 0.25% probability that none of the appeals will be successful.

(b) Compute the probability that exactly one of the appeals will be successful.

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{10,1}.(0.45)^{1}.(0.55)^{9} = 0.0207

0.0207 = 2.07% probability that exactly one of the appeals will be successful.

(c) What is the probability that at least two of the appeals will be successful

This is P(X \geq 2)

Either less than two appeals are succesful, or at least two are. The sum of the probabilities of these events is decimal 1. So

P(X < 2) + P(X \geq 2) = 1

P(X < 2) = P(X = 0) + P(X = 1) = 0.0025 + 0.0207 = 0.0232

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0232 = 0.9768

0.9768 = 97.68% probability that at least two of the appeals will be successful

6 0
2 years ago
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