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2 years ago

15

Lisa is building a structure to be used in the school play. The structure is in the shape of a right triangular prism. A sketch

is shown.

1 answer:

dybincka [34]2 years ago

8 0

Solution:

<u>Note that:</u>

Surface area = Area of all faces

<u>Finding the area of the two triangles</u>

2(1/2 x 8 x 6)
=> 8 x 6
=> 48 ft²

<u>Finding the area of rectangle₁</u>

12.6 x 10
=> 126 ft²

<u>Finding the area of rectangle₂</u>

12.6 x 6
=> 75.6 ft²

<u>Finding the area of rectangle₃</u>

12.6 x 8
=> 100.8 ft²

<u>Finding the surface area of the figure</u>

48 + 126 + 75.6 + 100.8
=> 350.4 ft²

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Answer:

d. x-axis

Step-by-step explanation:

Consider a point on curve P and its (nearest) image on curve P'. The midpoint between those points is on the line of reflection. That line is the x-axis.

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<em>Additional comment</em>

The curve is symmetrical about the y-axis, so each point on P also has an image point that is its reflection across the origin. The reflection of P could be across both the x- and y-axes, or (equivalently) across the origin. We don't know the meaning of "xy-axis", so we suspect that is a red herring. The best choice here is "x-axis."

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Read 2 more answers

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation

aliina [53]

Answer:

a. X~N(2,885, 651)

b. 0.086291

c. 0.00058

d. 3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

$P(X$

#substitute the given values in the formula to solve for P:

$P(X$

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

$P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058$

Hence, the proportion of customers consuming over 5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

$0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09$

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

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3 years ago

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Taya2010 [7]

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