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Anika [276]
3 years ago
12

Help I’ll give 50 points 12) 4x- y=8 5x+y=1

Mathematics
1 answer:
Luba_88 [7]3 years ago
4 0

12) 4x- y=8

5x+y=1

Correct.

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Who ever help I will give you the brainliest answer
Gala2k [10]

Answer:

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Step-by-step explanation:

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4 0
2 years ago
60 is 30% of what number?
Phantasy [73]
Percent means parts out of 100
30%=30/100=3/10

'of' means multiply

60 is 30% of what translates to
60=3/10 times what
multiply both sides by 10/3
600/3=what
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7 0
3 years ago
Which set of numbers could represent the lengths of the sides of a right triangle?
DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

<h3>Pair: 8, 15, 17</h3>

By the pythagorean theorem, a triangle is a right triangle if and only if

\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2.

In this case,

\text{longest side}^2 = 17^2 = 289.

\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}.

In other words, indeed \text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2. Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

<h3>Pair: 10, 15, 20</h3>

Factor out the common factor 2 to simplify the calculations.

\text{longest side}^2 = 20^2 = 400

\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}.

\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2.

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

<h3>Pair: 12, 18, 22</h3>

\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121.

\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}.

\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2.

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

<h3>Pair: 7, 9, 11</h3>

\text{longest side}^2 = 11^2 = 121.

<h3>\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}.</h3>

\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2.

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0
3 years ago
A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found
joja [24]

Answer:

(a) 80% confidence interval for the population mean is [109.24 , 116.76].

(b) 80% confidence interval for the population mean is [109.86 , 116.14].

(c) 98% confidence interval for the population mean is [105.56 , 120.44].

(d) No, we could not have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

Step-by-step explanation:

We are given that a simple random sample of size n is drawn from a population that is normally distributed.

The sample​ mean is found to be 113​ and the sample standard​ deviation is found to be 10.

(a) The sample size given is n = 13.

Firstly, the pivotal quantity for 80% confidence interval for the population mean is given by;

                               P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean = 113

             s = sample standard​ deviation = 10

             n = sample size = 13

             \mu = population mean

<em>Here for constructing 80% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>

<u>So, 80% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-1.356 < t_1_2 < 1.356) = 0.80  {As the critical value of t at 12 degree

                                          of freedom are -1.356 & 1.356 with P = 10%}  

P(-1.356 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 1.356) = 0.80

P( -1.356 \times }{\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 1.356 \times }{\frac{s}{\sqrt{n} } } ) = 0.80

P( \bar X-1.356 \times }{\frac{s}{\sqrt{n} } } < \mu < \bar X+1.356 \times }{\frac{s}{\sqrt{n} } } ) = 0.80

<u>80% confidence interval for </u>\mu = [ \bar X-1.356 \times }{\frac{s}{\sqrt{n} } } , \bar X+1.356 \times }{\frac{s}{\sqrt{n} } }]

                                           = [ 113-1.356 \times }{\frac{10}{\sqrt{13} } } , 113+1.356 \times }{\frac{10}{\sqrt{13} } } ]

                                           = [109.24 , 116.76]

Therefore, 80% confidence interval for the population mean is [109.24 , 116.76].

(b) Now, the sample size has been changed to 18, i.e; n = 18.

So, the critical values of t at 17 degree of freedom would now be -1.333 & 1.333 with P = 10%.

<u>80% confidence interval for </u>\mu = [ \bar X-1.333 \times }{\frac{s}{\sqrt{n} } } , \bar X+1.333 \times }{\frac{s}{\sqrt{n} } }]

                                              = [ 113-1.333 \times }{\frac{10}{\sqrt{18} } } , 113+1.333 \times }{\frac{10}{\sqrt{18} } } ]

                                               = [109.86 , 116.14]

Therefore, 80% confidence interval for the population mean is [109.86 , 116.14].

(c) Now, we have to construct 98% confidence interval with sample size, n = 13.

So, the critical values of t at 12 degree of freedom would now be -2.681 & 2.681 with P = 1%.

<u>98% confidence interval for </u>\mu = [ \bar X-2.681 \times }{\frac{s}{\sqrt{n} } } , \bar X+2.681 \times }{\frac{s}{\sqrt{n} } }]

                                              = [ 113-2.681 \times }{\frac{10}{\sqrt{13} } } , 113+2.681 \times }{\frac{10}{\sqrt{13} } } ]

                                               = [105.56 , 120.44]

Therefore, 98% confidence interval for the population mean is [105.56 , 120.44].

(d) No, we could not have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed because t test statistics is used only when the data follows normal distribution.

6 0
3 years ago
A health food store has launched a new pack of vitamins for children. The store records the number of packs ordered by a random
Kisachek [45]

Answer:

The Answer is the second one

Step-by-step explanation:

3 0
2 years ago
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