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n200080 [17]
3 years ago
9

I don’t know how to solve this problem

Mathematics
1 answer:
miss Akunina [59]3 years ago
7 0

The draws are independent, so

P(\text{red then blue})=P(\text{red})\cdot P(\text{blue})

There is a total of 11 marbles in the bag, so

P(\text{red})=\dfrac3{11}

and

P(\text{blue})=\dfrac5{11}

So

P(\text{red then blue})=\dfrac{15}{121}

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A shipping box is shaped like a rectangular prism. The box is 1 1/5 feet wide, 3 feet long, and 4 1/2 feet tall. What is the vol
Goshia [24]

Answer:

4.95

Step-by-step explanation:

8 0
2 years ago
A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

7 0
3 years ago
Student performance across discussion sections: A professor who teaches a large introductory statistics class (197 students) wit
adell [148]

Answer:

The test is not significant at 5% level of significance, hence we conclude that there's no variation among the discussion sections.

Step-by-step explanation:

Assumptions:

1. The sampling from the different discussion sections was independent and random.

2. The populations are normal with means and constant variance

H_0: There's no variation among the discussion sections

H_1: There's variation among the discussion sections

\alpha =0.05

                Df     Sum Sq       Mean sq    F value     Pr(>F)

Section     7       525.01         75             1.87            0.99986

Residuals  189    7584.11        40.13

Test Statistic = F= \frac{75}{40.13} =1.87

Pr(>F) = 0.99986

Since our p-value is greater than our level of significance (0.05), we do not reject the null hypothesis and conclude that there's no significant variation among the eight discussion sections.

3 0
3 years ago
What are the coordinates of the x-intercept of the graph?
alex41 [277]

Answer:

d. (9, 0)

Step-by-step explanation:

(x, y) so...

Where the line crosses the x-plane, x = 9

Since this is the x-intercept y will always equal zero

Therfore x-int = (9, 0)

6 0
2 years ago
The Lcm of 24 and 56
sp2606 [1]
The least common multiple is 8
4 0
3 years ago
Read 2 more answers
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