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Rasek [7]
3 years ago
11

Solve the system of linear equations using the elimination method x=3y;3x-2y=14

Mathematics
1 answer:
vladimir1956 [14]3 years ago
7 0

Answer:

<h2>x = 6 and y = 2 → (6, 2)</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}x=3y&\text{subtract}\ 3y\ \text{from both sides}\\3x-2y=14\end{array}\right\\\\\left\{\begin{array}{ccc}x-3y=0&\text{multiply both sides by (-3)}\\3x-2y=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+9y=0\\3x-2y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad7y=14\qquad\text{divide both sides by 7}\\.\qquad\qquad y=2\\\\\text{put the value of y to the first equation:}\\x=3(2)=6

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We draw a random sample of size 25 from a normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confide
Helen [10]

Answer:

<h2>11.2≤\mu12.8 </h2>

Step-by-step explanation:

Confidence interval for the population mean is expressed by the formula;

CI = xbar ± Z(S/√n) where;

xbar is the sample mean = 12.5

Z is the z score at 99% confidence = 2.576

S is the standard deviation = √variance

S = √2.4 = 1.5492

n is the sample size = 25

Substituting the given values into the formula given above,

CI = 12.5 ± 2.576(1.5492/√25)

CI = 12.5 ± 2.576(0.30984)

CI = 12.5 ± 0.7981

CI = (12.5-0.7981, 12.5+0.7981)

CI = (11.2019, 12.7981)

Hence the 99% confidence interval for the population mean is 11.2≤\mu12.8 (to 1 decimal place)

7 0
3 years ago
Kai calculates that he spends 15% of a school day in science class. If he spends 75 minutes in science class, how many minutes d
bazaltina [42]

Answer:

500 minutes

Step-by-step explanation:

100% = x

15% = 75

We multiply 75 by 100 and divide the answer by 15

7500 / 15 = 500 minutes

4 0
3 years ago
HHHHHEEEEELLLLLPPPPPP
sp2606 [1]
The length of an arc is given by θ/360×2πr, where θ is angle subtended by the arc to the center and r is the radius of the circle.
 The length is 12 units, and θ/360 is 1/3
Therefore, 12 = 1/3 × 3.142 ×r
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5 0
3 years ago
A 4-oz. filet of salmon contains 500 mg of potassium. The daily recommended amount of potassium is 3,500 mg. If you ate a 6-oz.
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The answer is 21% because a 6-oz fillet of salmon contains about 750 mg of potassium. 3500-750 equals 2750, meaning that whichever percent closest to that answer is correct. 3500 - 21% = 2760 which is the closest number to the correct percentage therefore A. Is the answer.
5 0
2 years ago
20 POINTS AND BRAINLIEST
emmainna [20.7K]
To solve this equation we must first plug in 5 for x.

\frac{1}{3}<span> (5 - 4x)
               </span>↓ 
\frac{1}{3} (5 - 4 · 5)

The next step would be to multiply 4 by 5 to get rid of the parenthesis within our main parenthesis.

\frac{1}{3} (5 - 4 · 5)

\frac{1}{3} (5 - 20)

The next step would be to subtract both of the numbers within the parenthesis.

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Now we must multiply.

- \frac{1}{3} · 15 =  - \frac{1×15}{3}

- \frac{15}{3}

Now we simplify our answer to get our final answer.

-5
8 0
3 years ago
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