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3 years ago

The dimensions of a rectangular prism are 1 mm, 6 mm, and 11 mm. Find the volume and the surface area.

1 answer:

8 0

The volume is the product of the side lengths which is 1*6*11= 66 mm^3. The surface area is twice the sum of all the possible products of the side lengths, or 2lw+2wh+2hl which is 2(6*11+6*1+11*1) = 166 mm^2 if my mental math is decent.

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A manufacturer of interocular lenses will qualify a new grinding machine if there is evidence that the percentage of polished le

solniwko [45]

Answer:

Does not exceed 2% in both cases.

Step-by-step explanation:

Given that a manufacturer of interocular lenses will qualify a new grinding machine if there is evidence that the percentage of polished lenses that contain surface defects does not exceed 2%.

Sample proportion = $\frac{6}{250} \\=0.024$

Create hypothesses as

$H_0: p = 0.02\\H_a : p >0.02$

(Right tailed test at 5% significance level)

P difference = 0.004

Std error = 0.0089

test statistic Z = p diff/std error = 0.4518

p value = 0.326

Since p >alpha, we accept nullhypothesis

b) For confidence interval 97% we have

Margin of error = 2.17* std error = 0.0192

Confidence interval

= $(0.024-0.0191, 0.024+0.0191)\\= (0.0049, 0.0431)\\$

Since 2% = 0.02 lies within this interval we accept null hypothesis.

Does not exceed 2%

Since

7 0

3 years ago

What is the length of the arc if: 11. r=10 n=20 A15(pi)/ 7 B13(pi)/ 5 C16(pi)/ 2 D11(pi)/ 4 E 10(pi)/ 9 F 9(pi)/ 4 12. r=3 n=6 A

Vilka [71]

Step-by-step explanation:

The formula for arc length [for the angle in degrees] is:

$L = 2\pi r \left(\dfrac{n}{360}\right)$

here,

$n$ = degrees

$r$ = radius

using this we'll solve all the parts:

r = 10, n = 20:

$L = 2\pi r \left(\dfrac{n}{360}\right)$

$L = 2\pi (10) \left(\dfrac{20}{360}\right)$

from here, it is just simplification:

2 and 360 can be resolved: 360 divided by 2 = 180

$L = \pi (10) \left(\dfrac{20}{180}\right)$

10 and 180 can be resolved: 180 divided by 10 = 18

$L = \pi \left(\dfrac{20}{18}\right)$

finally, both 20 and 18 are multiples of 2 and can be resolved:

$L = \pi \left(\dfrac{10}{9}\right)$

$L = \dfrac{10\pi}{9}$ Option (E)

r=3, n=6:

$L = 2\pi r \left(\dfrac{n}{360}\right)$

$L = 2\pi (3) \left(\dfrac{6}{360}\right)$

$L = \dfrac{\pi}{10}$ Option (D)

r=4 n=7

$L = 2\pi r \left(\dfrac{n}{360}\right)$

$L = 2\pi (4) \left(\dfrac{7}{360}\right)$

$L = \dfrac{7\pi}{45}$ Option (C)

r=2 n=x

$L = 2\pi r \left(\dfrac{n}{360}\right)$

$L = 2\pi (2) \left(\dfrac{x}{360}\right)$

$L = \dfrac{x\pi}{90}$ Option (D)

r=y n=x

$L = 2\pi r \left(\dfrac{n}{360}\right)$

$L = 2\pi (y) \left(\dfrac{x}{360}\right)$

$L = \dfrac{xy\pi}{180}$ Option (E)

6 0

4 years ago

A road rises 50 feet over a horizontal distance of 600 feet. What is the slope of the road?

Hatshy [7]

Answer:

1/12 (or 0.833)

Step-by-step explanation:

Recall that the definition of "slope" is the change in vertical distance divided by the change in the horizontal distance. (aka. rise ÷ run)

it is given that rise = 50 feet and the horizontal distance (i.,e "run") = 600feet

hence slope = rise / run = 50 / 600 = 1/12 (or 0.833)

6 0

3 years ago

Read 2 more answers

Solve for p.

Vinil7 [7]

Answer:

p = -2

Step-by-step explanation:

5p - 10 = + 4(1 + 3p)

first get rid of the bracquetes:

5p - 10 = + 4*1 + 4*3p

5p - 10 = + 4 + 12p

subtract left and right of = sign by 5p

5p -5p - 10 = + 4 + 12p -5p

0 - 10 = + 4 + (12p -5p)

subtract left and right of = sign by 4

-10 -4 = 4 -4 + ( 7p )

re arrange

7p + 0 = -14

divide left and right of = sign by 7

7/7 p = -14/7

p = -2

5 0

4 years ago

Read 2 more answers

All pictures are below please help Sandi had the following problem on her math test: . She showed her work on the test as follow

Semmy [17]

Answer/Step-by-step explanation:

The basic rule of maths operation used by Sandi, is the PEMDAS Rule.

Maths operations like the one Sandi was given must follow this rule. According to the rule:

P - Parentheses, solve everything you have in the parentheses first.

E - Exponents, do the exponents.

M - Multiplication or

D - Division operation should come next.

A - Addition or

S - Subtraction comes last.

Let's apply this rule to see if Sandi rightly applied the PEMDAS Rule:

Step 1:

6*4 + 2 ÷ 2 - 7 (given)

Step 2: perform operation involving Multiplication first according to PEMDAS Rule.

24 + 2 ÷ 2 - 7 (multiplication first. I.e. 6*4 = 24)

Step 3: perform division operation next.

24 + 1 - 7 (division operation. i.e. 2÷2 = 1)

Step 4: Subtraction

24 - 6 (i.e. +1 - 7 = -6) this is where Sandi made an error.

Step 5: subtraction

24 - 6 = 18.

Sandi made a mistake in step 4 and 5. Her addition and subtraction operation was wrong. 1 - 7 = -6 not +6.

During operation like this, either subtraction or addition can come first.

6 0

4 years ago

Read 2 more answers