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Scrat [10]
2 years ago
10

If 2x + 5y = 21 and x + y = 3, then what is the solution

Mathematics
1 answer:
Viefleur [7K]2 years ago
8 0
2x+5y=21, x+y=3
y=3-x
2x+5y=21
2x+5(3-x) =21
2x+15-5x=21
2x-5x+15=21
-3x+15=21
-3x=21-15
-x=6/3
-x=2
x=-2

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Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable
notsponge [240]

Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.  

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)  

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) Z=2.45

b) P Value=0.0073

Step-by-step explanation:

From the question we are told that:

Probability of Wishart and Leach P=21.4=>0.214

Population Size N=498

Sample size n=12

Therefore

P'=\frac{129}{498}

P'=0.2590

Generally the Null and Alternative Hypothesis is mathematically given by

H_0:P=0.214

H_a:=P>0.214

Test Statistics

Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}

Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}

Z=2.45

Therefore P Value is given as

P Value =P(Z\geq 2.45)

P Value =1-P(Z\leq 2.45)

P Value =1-0.99268525

P Value=0.0073

7 0
2 years ago
I need help 6x-2y=10 x-2y=-5 solve by elimination
dem82 [27]
<h3><u>Explanation</u></h3>
  • Given the system of equations.

\begin{cases} 6x - 2y = 10 \\ x - 2y =  - 5 \end{cases}

  • Solve the system of equations by eliminating either x-term or y-term. We will eliminate the y-term as it is faster to solve the equation.

To eliminate the y-term, we have to multiply the negative in either the first or second equation so we can get rid of the y-term. I will multiply negative in the second equation.

\begin{cases} 6x - 2y = 10 \\  - x  +  2y =  5 \end{cases}

There as we can get rid of the y-term by adding both equations.

(6x - x) + ( - 2y + 2y) = 10 + 5 \\ 5x + 0 = 15 \\ 5x = 15 \\ x =  \frac{15}{5}  \longrightarrow  \frac{ \cancel{15}}{ \cancel{5}}  =  \frac{3}{1}  \\ x = 3

Hence, the value of x is 3. But we are not finished yet because we need to find the value of y as well. Therefore, we substitute the value of x in any given equations. I will substitute the value of x in the second equation.

x - 2y =  - 5 \\ 3 - 2y =  - 5 \\ 3 + 5 = 2y \\ 8 = 2y \\  \frac{8}{2}  = y \\ y =  \frac{8}{2} \longrightarrow  \frac{ \cancel{8}}{ \cancel{2}}  =  \frac{4}{1}  \\ y = 4

Hence, the value of y is 4. Therefore, we can say that when x = 3, y = 4.

  • Answer Check by substituting both x and y values in both equations.

<u>First</u><u> </u><u>Equation</u>

6x - 2y = 10 \\ 6(3) - 2(4) = 10 \\ 18 - 8 = 10 \\ 10  = 10 \longrightarrow \sf{true} \:  \green{ \checkmark}

<u>Second</u><u> </u><u>Equation</u>

x - 2y =  - 5 \\ 3 - 2(4) =  - 5 \\ 3 - 8 =  - 5 \\  - 5 =  - 5 \longrightarrow  \sf{true} \:  \green{ \checkmark}

Hence, both equations are true for x = 3 and y = 4. Therefore, the solution is (3,4)

<h3><u>Answer</u></h3>

\begin{cases} x = 3 \\ y = 4 \end{cases} \\  \sf \underline{Coordinate \:  \: Form} \\ (3,4)

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