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Alona [7]
3 years ago
6

Use Cramer's Rule to solve each system. 5x – 3y = 8 -2x - y = 10

Mathematics
2 answers:
mezya [45]3 years ago
8 0

Answer: x = - 2

y = - 6

Step-by-step explanation:

A 2 × 2 matrix would be formed. The steps are shown in the attached photo.

zlopas [31]3 years ago
6 0

Answer:

-2, -6

Step-by-step explanation:

using cramer rule

5    -3    

-2   -1    

calculatiing the determinant = (5 x-1) - (-3x-2) = -5 -(6) = -5-6=-11

using cramer rule

to calculate x we change the coefficient of x with the answer (8,10)

8   -3

10   -1

we calculate determinant = (8x-1)-(-3x10) = -8-(-30) = -8+30 =22

to calculate x

22/-11= -2

to calculate y we change the coefficient of y with the answer (8,10)

5   8

-2   10

we calculate determinant = (5x10)-(8x-2) = 50 -(-16) = 50 +16=66

to calculate y

66/-11= -6

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A box contains three plain pencils and 5 pens. A second box contains three colored pencils and three crayons. One item from each
worty [1.4K]

Answer:

Therefore the probability that a pen from the first box and a crayon from the second box are selected is \frac5{16}

Step-by-step explanation:

Probability:

The ratio of the number of favorable outcomes to the number all possible outcomes of the event.

Probability=\frac{\textrm{The number favorable outcomes}}{\textrm{The number all possible}}

Given that,

Three plain pencils and 5 pens are contained by the first box.

Total number of pens and pencils is =(3+5)=8

The probability that a pen is selected from the first box is

=P(A)

=\frac{\textrm{The number pens}}{\textrm{Total number of pens and pencils}}

=\frac{5}{8}

A second box contains three colored pencils and three crayons.

Total number of pencils and crayons is =(3+3)=6

The probability that a crayon is selected from the second box is

=P(B)

=\frac{\textrm{The number of crayon}}{\textrm{Total number of crayons and pencils}}

=\frac{3}{6}

Since both events are mutually independent.

The required probability is multiple of the events

Therefore the required probability is

=\frac58\times \frac36

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4 0
3 years ago
Company A makes a large shipment to Company B. Company B can reject the shipment if they can conclude that the proportion of def
boyakko [2]

Answer:

z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17  

The p value for this case would be given by:

p_v =P(z>3.17)=0.00076  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

\hat p=\frac{59}{400}=0.1475 estimated proportion of defectives from the company B  

p_o=0.1 is the value to verify

\alpha=0.05 represent the significance level

z would represent the statistic

p_v represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:  

Null hypothesis:p \leq 0.1  

Alternative hypothesis:p > 0.1  

The statistic would be given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing the info given we got:

z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17  

The p value for this case would be given by:

p_v =P(z>3.17)=0.00076  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

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6 and a 4 on the top beside it
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Doss [256]

Answer: Decimal- .33333333333

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Step-by-step explanation: 3x-1=0

0+1=1, 1/3 is the answer

4 0
2 years ago
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