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ANEK [815]
3 years ago
11

Linear equations. write the standard form of an equation of the

Mathematics
1 answer:
erastova [34]3 years ago
7 0

Answer:

The standard form of an equation of the line that passes through the given point having slope is y-y_{1} =m(x-x_{1}

Step-by-step explanation:

The standard form of an equation of the line that passes through the given point ((x_{1} ,y_{1} ) and having slope m is

y-y_{1} =m(x-x_{1}

another form of an equation of the line that passes through the given point ((x_{0} ,y_{0} ) and having slope m is

y-0 =m(x-0)

   y=m x

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How many solutions does the equation x_1 +x_2+x_3+x_4+x_5=21 have where x_1, x_2, x_3, x_4, and x_5 are nonnegative integers and
omeli [17]

Step-by-step explanation:

x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 21\\     (given)

Let us consider :

x_{1} = t_{1} + 1

x_{2} = t_{2}

x_{3} = t_{3}

x_{4}  = t_{4}

x_{5} = t_{5}

Now, by substituting the above considerations in the above equation, we get:

t_{1} + 1 + t_{2} + t_{3} + t_{4} + t_{5} = 21\\

t_{1}  + t_{2} + t_{3} + t_{4} + t_{5} = 20\\

where,

t_{i} \geq 1

then it follows

n = 20

r = 4

then no. of solutions for the eqn = _{r}^{n + r}\textrm{C}

                                                      = _{4}^{24}\textrm{C}

                                                      = 10626

Answer :

no. of solutions for the eqn 10626

4 0
3 years ago
Brent bought shirts for $50. Each shirt cost $10. How many shirts did he buy?
AVprozaik [17]
ANSWER: the man bought 5 shirts
6 0
2 years ago
Read 2 more answers
The CDC national estimates that 1 in 68 = 0.0147 children are diagnosed with have been diagnosed with Autism Spectrum Disorder (
kakasveta [241]

Answer:

Null hypothesis: p= 0.0147

Alternative hypothesis: p\neq 0.0147

A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.  

Solution to the problem

On this case we want to test if the proportion of children diagnosed with Autism Spectrum Disorder (ASD) is different from 0.0147, so the system of hypothesis would be:

Null hypothesis: p= 0.0147

Alternative hypothesis: p\neq 0.0147

A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).

7 0
3 years ago
Read 2 more answers
What is the volume of this prism?
Alex73 [517]

Answer:

47.7

Step-by-step explanation:

length x width x height

6 x 3 x 2.65

5 0
2 years ago
Find sin(a) in the triangle.<br> Choose 1 answer:
Studentka2010 [4]

Answer:

5/13

Step-by-step explanation:

Find the diagram to the question attached

Given the following considering angle A

Hypotenuse = 13 = AB

Opposite = 5 (side facing the angle A) = BC

Adjacent = 12

According to SOH CAH TOA;

Sin theta = opposite/hypotenuse

Sin(a) = BC/AB

Sin(a) = 5/13

Hence the value of sin(a) is 5/13

3 0
3 years ago
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