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Elena-2011 [213]

4 years ago

15

What is the solution to the linear system x=-6y+15 and -2y+5x =11

1 answer:

Cerrena [4.2K]4 years ago

7 0

After solving the linear system, value of x=3 and value of y=2

Step-by-step explanation:

We need to find the solution to the linear system $x=-6y+15\,\,and\,\, -2y+5x =11$

$x=-6y+15\,\,\,\,(1)\\-2y+5x =11\,\,\,\,(1)$

Putting value of equation (1) x=-6y+15 in equation(2)

$-2y+5x =11\\-2y+5(-6y+15)=11\\-2y-30y+75=11\\-32y=11-75\\-32y=-64\\y=\frac{-64}{-32}\\y=2$

value of y=2

Now putting the value of y in equation (1)

$x=-6y+15\\x=-6(2)+15\\x=-12+15\\x=3$

value of x = 3

After solving the linear system, value of x=3 and value of y=2

Keywords: Linear system

Learn more about Linear system at:

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If g(t) = 2/ (t + 3), then g (?) = 2/ (4a + 3)

marishachu [46]

Answer:

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Step-by-step explanation:

g(4a) = 2/(4a +3)

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3 years ago

. A discount brokerage selected a random sample of 64 customers and reviewed the value of their accounts. The mean was $32,000 w

koban [17]

Answer:

The 90% confidence interval is $\$ \ 30313.9< \mu < \$ \ 33686.13$

Step-by-step explanation:

From the question we are told that

The sample size is n = 64

The sample mean is $\= x = \$ 32, 000$

The standard deviation is $\sigma= \$ 8, 200$

Given that the confidence interval is 90% then the level of significance is mathematically evaluated as

$\alpha = 100 - 90$

$\alpha = 10 \%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table , the value is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }$

=> $E = 1.645 * \frac{ 8200 }{ \sqrt{64} }$

=> $E = 1686.13$

The 90% confidence interval is mathematically represented as

$\= x - E < \mu < \= x + E$

=> $32000 - 1689.13 < \mu < 32000 + 1689.13$

=> $\$ \ 30313.9< \mu < \$ \ 33686.13$

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4 years ago

A 3% salt solution weighing 100g represents 100g of water in which 3g of salt is dissolved (=3/10). What amount of salt would be

Nadya [2.5K]

Answer:

There would be 12 g of salt (12.3 g actually but rounded) and 88g of water (88.7 g actually but rounded)

Step-by-step explanation:

From the question, a 14% salt solution means 14g of salt in 100g of water.

What this means is that, the fraction of salt to water in the solution would be 14/100 which is same as 7/50

Now, we want to know the amount of salt and the amount of water in a 100g of 14% salt solution.

Looking at the ratio salt to water, we have 7 to 50

For every 50 parts of water, there are 7 parts of salt.

So the ratio of both is 7:50

For salt, the amount in grammes present will be ;

7/(50 + 7) * 100g = 7/57 * 100 = 12.3 g or 12g to the nearest whole number

The amount in grammes of water present will be ;

50/(50 + 7) * 100g = 50/57 * 100 = 87.7g or 88g to the nearest whole number

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