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cestrela7 [59]
3 years ago
15

Solve 3x to the second power -2x-8=0 using an algebraic method

Mathematics
1 answer:
MatroZZZ [7]3 years ago
7 0

Answer:

x=2\textrm{ or } x=-\frac{4}{3}

Step-by-step explanation:

Given:

The equation is given as:

3x^{2}-2x-8=0\\3x^{2}-6x+4x-8=0\\3x(x-2)+4(x-2)=0\\(x-2)(3x+4)=0\\\\x-2=0\textrm{ or }3x+4=0\\x-2+2=0+2 \textrm{ or }3x+4-4=0-4\\x=2\textrm{ or }3x=-4\\x=2\textrm{ or}\\x=-\frac{4}{3}

Therefore, the possible values of x are 2 and -\frac{4}{3}

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The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly sel
garri49 [273]

Complete question:

The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly selects 45 customers and records the amount of time from the moment they stand in the back of a line until the moment the cashier scans their first item. He calculates the mean and standard deviation of this sample to be barx = 4.2 minutes and s = 2.0 minutes. If appropriate, find a 90% confidence interval for the true mean time (in minutes) that customers at this supermarket wait in a check-out line

Answer:

(3.699, 4.701)

Step-by-step explanation:

Given:

Sample size, n = 45

Sample mean, x' = 4.2

Standard deviation \sigma = 2.0

Required:

Find a 90% CI for true mean time

First find standard error using the formula:

S.E = \frac{\sigma}{\sqrt{n}}

= \frac{2}{\sqrt{45}}

= \frac{2}{6.7082}

SE = 0.298

Standard error = 0.298

Degrees of freedom, df = n - 1 = 45 - 1 = 44

To find t at 90% CI,df = 44:

Level of Significance α= 100% - 90% = 10% = 0.10

t_\alpha_/_2_, _d_f = t_0_._0_5_, _d_f_=_4_4 = 1.6802

Find margin of error using the formula:

M.E = S.E * t

M.E = 0.298 * 1.6802

M.E = 0.500938 ≈ 0.5009

Margin of error = 0.5009

Thus, 90% CI = sample mean ± Margin of error

Lower limit = 4.2 - 0.5009 = 3.699

Upper limit = 4.2 + 0.5009 = 4.7009 ≈ 4.701

Confidence Interval = (3.699, 4.701)

5 0
3 years ago
1) 26 = 8 + v 2) 3 + p = 8
aleksklad [387]

Answer:

268+v2)3+p=8     =p=−3v2−796

Step-by-step explanation:

Let's solve for p.

(268+v2)(3)+p=8

Step 1: Add -804 to both sides.

3v2+p+804+−804=8+−804

3v2+p=−796

Step 2: Add -3v^2 to both sides.

3v2+p+−3v2=−796+−3v2

p=−3v2−796

<em><u>Hope this helps.</u></em>

5 0
3 years ago
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