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2 years ago

A science teacher is planning a field trip to either the aquarium or science center.

Mathematics

2 answers:

Ilya [14]2 years ago

8 0

$\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}$

Let the no. of students be x

total cost = y

Then the first equation will be

8x + 20 = y

And the second equation will be

3x + 40 = y

katovenus [111]2 years ago

4 0

A system of two equations where each equation models the total cost y to take x students on each field trip is;

8x + 20 = y

3x + 40 = y

The total cost y is 48 to take x = 4 students on each field trip.

<h3>What is the system of equations?</h3>

In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables.

A science teacher is planning a field trip to either the aquarium or the science center.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

The science center charges $3 per student and has a class lab fee of $40.

Let the total cost y to take x students on each field trip.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

8x + 20 = y

The science center charges $3 per student and has a class lab fee of $40.

3x + 40 = y

On solving both the equation

Substitute the value of y in the equation 2

3x + 40 = y

3x + 40 = 8x+20

8x - 3x = 40-20

5x = 20

x = 20/5

x = 4

Substitute the value of x in the equation 1

3x + 40 = y

2(4) + 40 =y

8 + 40 = y

y = 48

Hence, the total cost y is 48 to take x = 4 students on each field trip.

Learn more about the system of the equation here;

brainly.com/question/8119922

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3 years ago

A psychologist obtains a random sample of 2020 mothers in the first trimester of their pregnancy. The mothers are asked to play

leva [86]

Answer:

First of all, we need to determine the system of hypothesis, which must have a null and alternative hypothesis.

In all hypothesis proof procedure, we must work with the null one, rejecting it or accepting it. If we reject the null hypothesis, it will mean that our principal hypothesis is true.

According to the problem, the null hypothesis must be: $H_{o} : u = 100$ ; because it says that 100 is the normal mean that is used.

The alternative hypothesis must be: $H_{a} : u > 100$ ; because the question is asking if there's enough evidence to say that they children have a higher IQ than 100.

Then, we must calculate the P-value, which is the probability value that we are gonna use to accept or reject the null hypothesis. This P-value we can calculate it with the formula: $Z=\frac{x-u}{\frac{o}{\sqrt{n} } }$ ; where x is the sample mean, u is the hypothetical mean parameter, o is the sample deviation and n is the sample.

Extracting all values from the problem: x = 104.3; u = 100; o = 14 and n = 20.

Applying all values to the formula: $Z=\frac{104.3 - 100}{\frac{14}{\sqrt{20} } } = \frac{4.3}{\frac{14}{ 4.5} }=\frac{4.3}{3.1}=1.4$

Then, this Z-value will give us the P-value by using the Z-table with the 0.05 level of significance. In table attached, we can see that the result is 0.9265. However, the P-value is 1 - 0.9265 = 0.735. We need to do this subtraction because, the result 0.9265 belong to the bigger area (as it's shown is the image in blue colour), and we need the smaller area, which belong to the 0.05 level of significance.

<em>In this problems, if the P-value is more than the level of significance, the null hypothesis is accepted. If the P-value is less than the level of significance the null hypothesis is rejected.</em>

Therefore, there is no enough evidence to say that the sample children have higher IQs, because the P-value is higher than the level of significance. (0.735>0.05).