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2 years ago

If an 8" X 8" square cake serves 8 people, how many 24" X 24" square cakes are needed for a

Mathematics

1 answer:

tigry1 [53]2 years ago

4 0

Answer:

2 24" X 24" square cakes are needed.

Step-by-step explanation:

This question is solved by proportions.

Area of a square:

The area of a square of side l is given by:

$A = l^2$

8" X 8" square cake serves 8 people

Thus:

$A = 8*8 = 64$

Area of 64 serves 8 people, so for 1 people, an area of 64/8 = 8 is needed.

144 people

The total area needed is:

$A = 144*8 = 1152$

How many 24" X 24" square cakes?

24*24 = 576

1 cake - 576

x cakes - 1152

Applying cross multiplication:

1152/576 = 2

2 24" X 24" square cakes are needed.

You might be interested in

A bag contains 4 blue marbles and 2 yellow marbles. Two marbles are randomly chosen (the first marble is NOT replaced before dra

VMariaS [17]

Answer:

0.4 = 40% probability that both marbles are blue.

0.0667 = 6.67% probability that both marbles are yellow.

53.33% probability of one blue and then one yellow

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

Step-by-step explanation:

To solve this question, we need to understand conditional probability(for the final question) and the hypergeometric distribution(for the first three, because the balls are chosen without being replaced).

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

What is the probability that both marbles are blue?

4 + 2 = 6 total marbles, which means that $N = 6$

4 blue, which means that $k = 4$

Sample of 2, which means that $n = 2$

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,6,2,4) = \frac{C_{4,2}*C_{2,0}}{C_{6,2}} = 0.4$

0.4 = 40% probability that both marbles are blue

What is the probability that both marbles are yellow?

4 + 2 = 6 total marbles, which means that $N = 6$

2 yellow, which means that $k = 2$

Sample of 2, which means that $n = 2$

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,6,2,2) = \frac{C_{2,2}*C_{4,0}}{C_{6,2}} = 0.0667$

0.0667 = 6.67% probability that both marbles are yellow.

What is the probability of one blue and then one yellow?

Total is 100%.

Can be:

Both blue(40%)

Both yellow(6.67%)

One blue and one yellow(x%). So

40 + 6.67 + x = 100

x = 100 - 46.67

x = 53.33

53.33% probability of one blue and then one yellow.

If you are told that both selected marbles are the same color, what is the probability that both are blue?

Conditional probability.

Event A: Both same color

Event B: Both blue

Probability of both being same color:

Both blue(40%)

Both yellow(6.67%)

This means that $P(A) = 0.4 + 0.0667 = 0.4667$

Probability of both being the same color and blue:

40% probability that both are blue, which means that $P(A \cap B) = 0.4$

Desired probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.4667} = 0.8571$

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

8 0

2 years ago

Calculate the value of the exterior angle

aev [14]

What we know is that the sum of a triangle's internal angles are 180º, and a straight angle makes 180º.

first, we have to find the third internal angle(let's call it n) so that we can use it to find the exterior angle.

(3x + 20) + (4x + 5) + n = 180

simplify:

7x + 25 + n = 180

7x + n = 155

n = 155 - 7x

Now we can add it to the external angle to find x.

(155 - 7x) + (8x + 15) = 180

simplify:

170 + 8x - 7x = 180

170 + x = 180

x = 10

Now we can substitute it to the external angle.

8 x 10 + 15 = 95

the exterior angle is 95º.

8 0

3 years ago

Simplify 108 over 308

erik [133]

Answer:

Step-by-step explanation:

27/ 77 (Decimal: 0.350649)

8 0

3 years ago

Read 2 more answers

Choose the equation that represents the graph.

Sergeu [11.5K]

Answer:

y=-2x-4

Step-by-step explanation:

y=mx+b

count the slope (-2/1)

find the y-intercept(0,-4)

write it out (-2/-1)x-4

simplify (-2x-4)

7 0

3 years ago

Read 2 more answers

g Suppose you are rasterizing a triangle with vertices (1, 1), (5, 1), and (2, 9), and the intensity values (e.g., redness) of t

Ivahew [28]

Answer:

6.333

Step-by-step explanation:

Our triangle vertices are

(1,1)(5,1)(2,9)

We are to perform interpolation at point(3,5)

x and y values are interpolated

On vertices (5,1)(2,9)

x = 3

x1 = 5

X2 = 2

Y1 = 1

Y2 = 9

Formula for interpolation

Y = [y1+(x-x1)(y2-y1)]/x2-x

Y = 1+(3-5)(9-1)/2-5

Y = 1+[-2*8/-3]

Y = 1+16/3

From here we use use LCM to get:

19/3 = 6.333

6 0

2 years ago