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atroni [7]
2 years ago
11

A glass bead has the shape of a rectangular prism with a smaller rectangular prism removed. What is the volume of the glass that

forms the bead?

Mathematics
2 answers:
Alexxandr [17]2 years ago
5 0

Answer:

54

Step-by-step explanation:

The formula for the volume V of a prism is V=​Bh, where B represents the area of a base and h represents the height of the prism. Subtract the volume of the small prism from the volume of the large prism.

olganol [36]2 years ago
4 0

The volume of the removed portion is 35 cm³.

Step-by-step explanation:

Given,

The length× width× height (L×B×H) of the outer part = 3 cm×3 cm×7 cm

The length× width× height (l×b×h) of the inner part = 2 cm×2 cm×7 cm

To find the volume of the removed portion.

Formula

The volume of the removed portion = volume of outer part - volume of inner part

Volume of rectangular prism = l×b×h

Now,

Volume of outer part = 3×3×7 cm³ = 63 cm³

Volume of inner part = 2×2×7 cm³ = 28 cm³

Hence,

The volume of the removed portion = 63-28 cm³ = 35 cm³

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Answer:

C

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A random sample of 250 students at a university finds that these students take a mean of 15.2 credit hours per quarter with a st
Orlov [11]

Answer:

95% confidence interval for the mean credit hours taken by a student each quarter is [14.915 hours , 15.485 hours].

Step-by-step explanation:

We are given that a random sample of 250 students at a university finds that these students take a mean of 15.2 credit hours per quarter with a standard deviation of 2.3 credit hours.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                          P.Q. = \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample credit hours per quarter = 15.2 credit hours

             s = sample standard deviation = 2.3 credit hours

             n = sample of students = 250

             \mu = population mean credit hours per quarter

<em>Here for constructing 95% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.</em>

So, 95% confidence interval for the population mean, \mu is ;

P(-1.96 < t_2_4_9 < 1.96) = 0.95  {As the critical value of t at 249 degree of

                                        freedom are -1.96 & 1.96 with P = 2.5%}  

P(-1.96 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u><em>95% confidence interval for</em></u> \mu = [ \bar X-1.96 \times {\frac{s}{\sqrt{n} } } , \bar X+1.96 \times {\frac{s}{\sqrt{n} } } ]

                  = [ 15.2-1.96 \times {\frac{2.3}{\sqrt{250} } } , 15.2+1.96 \times {\frac{2.3}{\sqrt{250} } } ]

                  = [14.915 hours , 15.485 hours]

Therefore, 95% confidence interval for the mean credit hours taken by a student each quarter is [14.915 hours , 15.485 hours].

<em>The interpretation of the above confidence interval is that we are 95% confident that the true mean credit hours taken by a student each quarter will be between 14.915 credit hours and 15.485 credit hours.</em>

8 0
1 year ago
Which statement shows how two polynomials 4x + 6 and 2x2 − 8x demonstrate the closure property when multiplied?
steposvetlana [31]

Answer:

8x^{3} -20x^{2} -48x is a polynomial

Step-by-step explanation:

Given : polynomials 4x+6 and2x^{2} -8x

Solution:

(4x+6)*(2x^{2} -8x)

4x(2x^{2} -8x)+6(2x^{2} -8x)

8x^{3} -32x^{2}+12x^{2} -48x

8x^{3} -20x^{2} -48x

Polynomial :An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable.

Thus 8x^{3} -20x^{2} -48x is a polynomial

Hence option A is correct.




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babymother [125]

Answer:

50 years

Step-by-step explanation:

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Twenty people get into an elevator in a hotel with seven floors, and all of them get off at some point. How many different possi
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140

Step-by-step explanation:

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