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den301095 [7]
4 years ago
11

Simplify the expression below: 5 (3z – 7z + 4)

Mathematics
2 answers:
Alla [95]4 years ago
7 0
15z -35z +20 is the answer
sweet-ann [11.9K]4 years ago
4 0
<span>5 (3z – 7z + 4)=</span>-20z+20
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Find the area of the shaded region .
Greeley [361]

Calculate area of the white region inside circle.

Area of the two white triangles in top left and bottom right:

2 \cdot \frac{1}{2}(6)(6) = 36 ft^2

Area of the two white quarter circles in the bottom left and top right:

2 \cdot \frac{1}{4}\pi (6)^2 = 18\pi ft^2

Total area of unshaded white region inside circle:

(36 + 18\pi)ft^2

Area of entire circle including the white and shaded regions

\pi(6)^2 = 36\pi ft^2

Area of shaded region is area of entire circle - area of unshaded white region

36\pi - (36 + 18\pi) = (18\pi - 36) ft^2

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Step-by-step explanation:

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In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3
Serggg [28]

Answer:

The correct option is (C) (2.769, 3.231).

Step-by-step explanation:

The confidence interval for mean when the standard deviation is not known is:

CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}

Given:

\bar x = 3\\s=0.3\\n=9\\\alpha =1-0.95=0.05

Compute the critical value as follows:

t_{\alpha/2, (n-1)}=t_{0.05/2, (9-1)}=t_{0.025, 8}=2.31

**Use a <em>t</em>-table.

The 95% confidence interval for true mean length of the bolt is:

CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}\\=3\pm 2.31\times \frac{0.30}{\sqrt{9}}\\ =3\pm 0.231\\=(2.769, 3.231)

Thus, the 95% confidence interval for true mean length of the bolt is (2.769, 3.231).

The correct option is (C).

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