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aleksandr82 [10.1K]
2 years ago
12

Trevor solved the system of equations below. What mistake did he make in his work?

Mathematics
1 answer:
storchak [24]2 years ago
3 0
The answer is <span>He subtracted 10 from the right side instead of adding 10 to the right side

Let's solve it:
</span><span>2x + y = 5
x − 2y = 10
________
Rearrange first equation to get y:
y = 5 - 2x
________
Substitute y into the second equation:
x - 2(5 - 2x) = 10
________
Multiply the terms:
x - 10 + 4x = 10
________
Combine the terms:
5x - 10 = 10
________
Add 10 on the both sides of the equation:
5x = 10 + 10
5x = 20
x = 4</span>
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Step-by-step explanation:

I am not 100% sure that this is correct cause I'm not that good at math if I am hope it helps!

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2 years ago
One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples
JulijaS [17]

Answer:

Step-by-step explanation:

Hello!

To test if boys are better in math classes than girls two random samples were taken:

Sample 1

X₁: score of a boy in calculus

n₁= 15

X[bar]₁= 82.3%

S₁= 5.6%

Sample 2

X₂: Score in the calculus of a girl

n₂= 12

X[bar]₂= 81.2%

S₂= 6.7%

To estimate per CI the difference between the mean percentage that boys obtained in calculus and the mean percentage that girls obtained in calculus, you need that both variables of interest come from normal populations.

To be able to use a pooled variance t-test you have to also assume that the population variances, although unknown, are equal.

Then you can calculate the interval as:

[(X[bar]_1-X[bar_2) ± t_{n_1+n_2-2;1-\alpha /2} * Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }]

Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*(5.6^2)+11*(6.7^2)}{15+12-2} }= 6.108= 6.11

t_{n_1+n_2-2;1-\alpha /2}= t_{15+12-2;1-0.05}= t_{25;0.95}= 1.708

[(82.3-81.2) ± 1.708* (6.11*\sqrt{\frac{1}{15}+\frac{1}{12}  }]

[-2.94; 5.14]

Using a 90% confidence level you'd expect the interval [-2.94; 5.14] to contain the true value of the difference between the average percentage obtained in calculus by boys and the average percentage obtained in calculus by girls.

I hope this helps!

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