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4 years ago

need to find the side lengths for a triangle with sides a=2a, b= 3a, c= 17. need to solve for variable a and not sure how.

Mathematics

2 answers:

Darina [25.2K]4 years ago

8 0

When a = 2a
a-2a = 0
<span>-a = 0
how can a = 0 ????

must be A = 2a</span>

andreyandreev [35.5K]4 years ago

6 0

'a' can't be uniquely found without some more information about the triangle. With only the given information, all we can say is that 5a must be at least 17. Is there a picture of the triangle ? Is there maybe possibly an angle given ? ?

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test statistic $t = -2.27$

P-value $p- value = 0.0198$

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 5$

The first sample mean is $\= x_1 = 1.76 \ mm$

The first standard is $s_1 = 0.55$

The second is $sample \ size\ is\ n_2 = 11$

The second sample mean is $\= x_2 = 2.56$

The second standard deviation is $\sigma = 0.84$

The level of significance is $\alpha = 0.01$

The null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

The alternative hypothesis is $H_a: \mu_1 - \mu_2 < 0$

Generally the test statistics is mathematically represented as

$t = \frac{ (\= x _1 - \= x_2) - ( \mu_1 - \mu_2)}{ \sqrt{\frac{s_1 ^2 }{ n_1 } + \frac{s_1 ^2 }{ n_1 } } }$

=> $t = \frac{ (1.76 - 2.56 ) - 0 }{ \sqrt{\frac{0.55^2 }{ 5 } + \frac{0.84^2 }{11 } } }$

=> $t = -2.27$

Generally degree of freedom is mathematically represented as

$df = n_1 + n_2 - 2$

=> $df = 5 + 11 - 2$

=> $df = 14$

From the student t distribution table the probability value to the left that corresponds to $t = -2.27$ at a degree of freedom of $df = 14$ is

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Answer:

18 numbers between 650 and 780 leave remainders of 4 when divided by 7.

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Step-by-step explanation:

1. Number 655 is the smallest number that leaves the remainder of 4 when divided by 7. Number 774 is the greatest number that leaves the remainder of 4 when divided by 7. So,

$a_1=655\\ \\a_n=774\\ \\d=7\\ \\a_n=a_1+(n-1)d\Rightarrow 774=655+7(n-1)\\ \\7(n-1)=774-655\\ \\7(n-1)=119\\ \\n-1=17\\ \\n=17+1=18$

2. Number 655 is the smallest number that leaves the remainder of 6 when divided by 11. Number 776 is the greatest number that leaves the remainder of 6 when divided by 11. So,

$a_1=655\\ \\a_n=776\\ \\d=11\\ \\a_n=a_1+(n-1)d\Rightarrow 776=655+11(n-1)\\ \\11(n-1)=776-655\\ \\11(n-1)=121\\ \\n-1=11\\ \\n=11+1=12$

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