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3 years ago

Find n so that the number sentence below is true:

Mathematics

1 answer:

adell [148]3 years ago

6 0

Answer: n=6

Step-by-step explanation:

2^3 x 4^3 = 2^3 x 2^n = 2^9

(2×2×2) ×(4×4×4) = (2x2x2) ×2^n=(2x2x2x2x2x2x2x2x2)

8 x 64 = 8x 2^n = 512

512= 8x 2^n = 512

divide all through by 8 so that 2^n can stand alone

512/8 = (8x 2^n)/8 = 512/8

64 = 2^n = 64

express 64 as a base of 2

2^6 = 2^n = 2^6

since they all have same base, cancel out the base.

therefore,

6=n=6

n = 6

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3 years ago

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Logan multiplied 54,216 by a number less than 1. He thinks the product will be greater than 54,216. Explain why he is incorrect.

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3 years ago

Help with quadratic graphs asap!

zlopas [31]

x= -0.25 and 1.25

x = -0.5 and 1.5

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Step-by-step explanation:

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(ii)

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So, x = -0.5 and 1.5

Given equation of the curve is

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$3x^2-3x +2 =2$

$\Leftrightarrow 3x^2-3x -1 = -1$

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3 years ago

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4 years ago

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A random sample of 25 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.54 mm and sample stan

lisabon 2012 [21]

Answer: (3.46, 3.62)

Step-by-step explanation:

The formula to find the confidence interval for population mean is given :-

$\overline{x}\ \pm\ t_{\alpha/2}\dfrac{s}{\sqrt{n}}$

, where n = sample size.

$t_{\alpha/2}$ = Two-tailed t-value for significance level of $(\alpha)$ and degree of freedom df= n-1.

$s$ = sample standard deviation.

As per given , we have

$\overline{x}= 3.54$ mm

s= 0.20 mm

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Significance level $=\alpha=1-0.95=0.05$

Since population standard deviation is not given , it means the given problem has t- distribution.

Two-tailed t-value for significance level of $(0.05)$ and degree of freedom df= 24:

$t_{\alpha/2\ ,df}=t_{0.025,\ 24}=2.0639$

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$3.54\ \pm\ (2.0639)\dfrac{0.20}{\sqrt{25}}$

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$=3.54\ \pm\ (2.0639)(0.04)$

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Hence, the 95% two-sided confidence interval for the mean glass thickness = (3.46, 3.62)

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4 years ago