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1 year ago

Complete the statements about these similar pyramids.

Mathematics

1 answer:

baherus [9]1 year ago

7 0

A ratio shows us the number of times a number contains another number. The ratio of the sides, base area, and volume are equal to 3:1, 9:1, and 27:1, respectively.

<h3>What is a Ratio?</h3>

A ratio shows us the number of times a number contains another number.

Given the two lateral sides of the pyramids, therefore, the ratio of the sides of the pyramid can be written as,

Length of pyramid A: Length of pyramid B = 15:5 = 3:1

Let the length of the base of the pyramid is represented by a.

The ratio of the base area can be written as,

Area of Base of A: Area of base of B = (3a)²:a² = 9:1

The ratio of the volume can be written as,

Volume of A: Volume of B = (3l×3b×3h)/3 : (lbh)/3 = 27:1

Hence, the ratio of the sides, base area, and volume are equal to 3:1, 9:1, and 27:1, respectively.

Learn more about Ratios:

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Students at a major university are complaining of a serious housing crunch. Many of the university's students, they complain, ha

Andrews [41]

Answer:

1) Between 12.5 miles and 21.7 miles.

2) b) 75%

3) c) 95%

4) Between 13.7 miles and 20.5 miles.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by $P = 100(1 - \frac{1}{k^{2}})$ .

1) According to Chebyshev's theorem, at least 36% of the commute distances lie between miles and miles.

Within k standard deviations of the mean, and k is found when $P = 36$ . So

$P = 100(1 - \frac{1}{k^{2}})$

$36 = 100 - \frac{100}{k^2}$

$\frac{100}{k^2} = 64$

$64k^2 = 100$

$k^2 = \frac{100}{64}$

$k = \sqrt{\frac{100}{64}}$

$k = \frac{10}{8}$

$k = 1.25$

Within 1.25 standard deviations of the mean.

1.25*3.7 = 4.6 miles

17.1 - 4.6 = 12.5 miles

17.1 + 4.6 = 21.7 miles

Between 12.5 miles and 21.7 miles.

2) According to Chebyshev's theorem, at least of the commute distances lie between 9.7 miles and 24.5 miles.

17.1 - 9.7 = 24.5 - 17.1 = 7.4 miles, so within 2 standard deviations of the mean, which is 75%, option B.

3) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the commute distances lie between 9.7 miles and 24.5 miles.

Within 2 standard deviations of the mean, by the Empirical Rule, which is 95%, option c.

4) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the commute distances lie between miles and miles.

Within 1 standard deviation of the mean.

17.1 - 3.4 = 13.7

17.1 + 3.4 = 20.5

Between 13.7 miles and 20.5 miles.

6 0

3 years ago

Pleaseee ANWSER ASAP!!!!

Tcecarenko [31]

B-d us 6 to 2 and b-c is 65

8 0

3 years ago

Solve the following equation with the initial conditions. x¨ + 4 ˙x + 53x = 15 , x(0) = 8, x˙ = −19

Katen [24]

$x''+4x'+53x=15$

has characteristic equation

$r^2+4r+53=0$

with roots at $r=-2\pm7i$ . Then the characteristic solution is

$x_c=C_1e^{(-2+7i)t}+C_2e^{(-2-7i)t}=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)$

For the particular solution, consider the ansatz $x_p=a_0$ , whose first and second derivatives vanish. Substitute $x_p$ and its derivatives into the equation:

$53a_0=15\implies a_0=\dfrac{15}{53}$

Then the general solution to the equation is

$x=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)+\dfrac{15}{53}$

With $x(0)=8$ , we have

$8=C_1+\dfrac{15}{53}\implies C_1=\dfrac{409}{53}$

and with $x'(0)=-19$ ,

$-19=-2C_1+7C_2\implies C_2=-\dfrac{27}{53}$

Then the particular solution to the equation is

$\boxed{x(t)=\dfrac1{53}e^{-2t}(409cos(7t)-27\sin(7t)+15)}$

8 0

3 years ago

Look at this graph:

Dmitry_Shevchenko [17]

Answer:

3/2

Step-by-step explanation:

slope=rise/run=30/20=3/2

5 0

2 years ago

2. Explain and correct the error made by a student who simplified this expression.

Ira Lisetskai [31]

Answer:

what this student did was distribute the x to all 3 numbers when what they should have done was just combine 7x and -2x, and the answer should be 5x +8

Step-by-step explanation:

By the student placing x on the outside they are making the equation seem as if 8 also had an x. However if we look at the original problem 8 does not have any variable so right away that was their first mistake. Instead they had to find the numbers that had similar values. In this case it is negative 2x and 7x. We combine those two to get 5x+8 we cannot combine these two because as said previously 8 doesnt have a variable. so the answer stays with the expression 5x+8

6 0

3 years ago