All categories

3 years ago

2x - 3y = 16

Mathematics

2 answers:

KIM [24]3 years ago

8 0

Answer:A

Step-by-step explanation:

brilliants [131]3 years ago

6 0

Step 1: Rewrite equations

2x - 3y = 16
5x - 3y = 13

Step 2: To be able to eliminate, multiply the second equation by -1

-1(5x - 3y = 13) —> -5x+3y=-13

Step 3: Use the elimination method to solve, using new equation

2x-3y=16
-5x+3y=-13
_________
-3x=3

x=-1

Step 4: Using x, substitute it into an equation for y

2x - 3y = 16

2(-1) - 3y =16
-2 -3y =16
+2 +2
________
-3y=18

y=-6

Final answer: A) (-1,-6)

You might be interested in

How much less is -200m than 450m?

saveliy_v [14]

Answer:

-200 metre is less 450m because - 200 metre is negative.

4 0

3 years ago

A square garden is 50 inches long on each side.What is the length of the perimeter in feet?

leva [86]

Answer:

50/3 feet

Step-by-step explanation:

A square has 4 equal sides, so the perimeter is 4*50, or 200 inches.

But we want the answer in feet. There are 12 inches in a foot, so the perimeter in feet is 200/12 or 50/3 feet.

5 0

3 years ago

A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we

weqwewe [10]

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean weighing of specimen = $\frac{3.412+3.416+3.414}{3}$ = 3.414 g

$\sigma$ = population standard deviation = 0.001 g

n = sample of specimen = 3

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } }$ , $3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } }$ ]