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Eva8 [605]
3 years ago
14

Cramer's rule:

Mathematics
1 answer:
Irina18 [472]3 years ago
5 0

Answer:

a. \quad\dfrac{\left|\begin{array}{cc}148&14\\246&5\end{array}\right|}{\left|\begin{array}{cc}-2&14\\3&5\end{array}\right|}=52

Step-by-step explanation:

To find the value of x, Cramer's rule says you replace the x-coefficients with the equation constants to form the matrix whose determinant is the numerator of the fraction. The denominator is the determinant of the matrix of coefficients. The equation constants are 148 and 246, so you expect to find those in the first column of the numerator (answer choices A and C).

\dfrac{\left|\begin{array}{cc}148&14\\246&5\end{array}\right|}{\left|\begin{array}{cc}-2&14\\3&5\end{array}\right|}=\dfrac{-2704}{-52}=52

The calculation is carried out correctly only in answer choice A.

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The perimeter of the picture frame is 38 inches. The width of the frame is 7 inches, what is the length?
o-na [289]

Answer:

12 inches

Step-by-step explanation:

So you know that the perimeter of a picture frame (a rectangle) is 2 widths plus 2 lengths.

Let x= lengths and w= widths

From the question we already know that w=7, so we can set up an equation that says:

2x + 2w = 38

2x + 2(7) = 38

2x+14 = 38

2x +14 -14 = 38-14

2x = 24

2x/2 = 24/2

x= 12

Since x= lengths =12

the length of the frame is 12 inches.

7 0
3 years ago
A line passes through the point (-4,1) and has a slope of 3/2
anzhelika [568]

Answer:

y=3/2x+7

Step-by-step explanation:

y=mx+b

m=3/2

b=7

4 0
3 years ago
4 (3x + 2)-6<br> I neeeed help
yuradex [85]

Answer:

12x - 2

Step-by-step explanation:

Step 1: Write expression

4(3x + 2) - 6

Step 2: Distribute 4

12x + 8 - 6

Step 3: Combine like terms

12x - 2

5 0
3 years ago
Can someone put an example of how to do bearings for precal?
Reika [66]

Answer:

A bearing is used to represent the direction of one point relative to another point. For                                                                                                                          example, the bearing of A from B is 065º. The bearing of B from A is 245º.

4 0
2 years ago
The most recent public health statistics available indicate that 23.6​% of American adults smoke cigarettes. Using the​ 68-95-99
artcher [175]

Answer:

There is a​ 68% chance that between 17​% and 30​% are​ smokers.

There is a​ 95% chance that between 10​% and 37​% are​ smokers.

There is a​ 99.7% chance that between 4​% and 44​% are​ smokers.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of the sampling distribution of sample proportion is:

 \mu_{\hat p}=p\\

The standard deviation of the sampling distribution of sample proportion is:

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

Given:

<em>n</em> = 40

<em>p</em> = 0.236

Compute the mean and standard deviation of this sampling distribution of sample proportion as follows:

\mu_{\hat p}=p=0.236

\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.236(1-0.236)}{40}}=0.067

The Empirical Rule states that in a normal distribution with mean <em>µ</em> and standard deviation <em>σ</em>, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be divided into three parts:

  • 68% data falls within 1 standard-deviation of the mean.  

        That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.

  • 95% data falls within 2 standard-deviations of the mean.

        That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.

  • 99.7% data falls within 3 standard-deviations of the mean.

        That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.

Compute the range of values that has a probability of 68% as follows:

P (\mu_{\hat p} - \sigma_{\hat p} \leq  \hat p \leq  \mu_{\hat p} + \sigma_{\hat p}) = 0.68\\P(0.236-0.067\leq  \hat p \leq 0.236+0.067)=0.68\\P(0.169\leq  \hat p \leq0.303)=0.68\\P(0.17\leq  \hat p \leq0.30)=0.68

Thus, there is a​ 68% chance that between 17​% and 30​% are​ smokers.

Compute the range of values that has a probability of 95% as follows:

P (\mu_{\hat p} - 2\sigma_{\hat p} \leq  \hat p \leq  \mu_{\hat p} + 2\sigma_{\hat p}) = 0.95\\P(0.236-2\times 0.067\leq  \hat p \leq 0.236+2\times0.067)=0.95\\P(0.102\leq  \hat p \leq 0.370)=0.95\\P(0.10\leq  \hat p \leq0.37)=0.95

Thus, there is a​ 95% chance that between 10​% and 37​% are​ smokers.

Compute the range of values that has a probability of 99.7% as follows:

P (\mu_{\hat p} - 3\sigma_{\hat p} \leq  \hat p \leq  \mu_{\hat p} + 3\sigma_{\hat p}) = 0.997\\P(0.236-3\times 0.067\leq  \hat p \leq 0.236+3\times0.067)=0.997\\P(0.035\leq  \hat p \leq 0.437)=0.997\\P(0.04\leq  \hat p \leq0.44)=0.997

Thus, there is a​ 99.7% chance that between 4​% and 44​% are​ smokers.

7 0
3 years ago
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