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2 years ago

15

12 gallons of water are used to completely fill 5 fish tanks. If each tank holds the same amount of water, how many gallons will

each tank hold?
Express your answer as a mixed number.

2 answers:

vlabodo [156]2 years ago

6 0

Answer:

2.4 gallons/tank

Step-by-step explanation:

12/5=2.4 gallons

raketka [301]2 years ago

5 0

I think is 2 4/10 or 2 2/5 hope this helps

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From the airport hanger H, an areoplane A is 18km away on the bearing of 115° while another aeroplane B is 29km away on a bearin

maks197457 [2]

The difference in distance between Aero plane A and B is; 34.67 km

<h3>How to calculate bearing?</h3>

To get the bearing;

∠H = (115 - 90) + (270 - 203)

∠H = 92°

Then, we will use cosine rule to get the distance between both Planes A and B.

d_ab = √(18² + 29² - 2(18 * 29) * cos 92)

d_ab = √(324 + 841 + 36.435)

d_ab = 34.67 km

Read more about bearing at; brainly.com/question/22518031

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6 0

1 year ago

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

Help asap my last question GIVING BRAINLIST!!!!

Alex

Answer:

1) $x < 0$

2) $x > 0$

3) $x < 10$

4) $x < -\frac{31}{55}$

5) $x \geq 0$

6) $x \geq -1$

Step-by-step explanation:

1) $-3 > 2x -3$

$2x- 3 < -3$

$2x - 3 + 3 < -3 +3$

$2x < 0$

$\frac{2x}{2} < \frac{0}{2}$

$x < 0$

2) $5 > -x + 5$

$-x + 5 < 5$

$- x + 5 -5 < 5 - 5$

$-x < 0$

$\frac{-x}{-1} < \frac{0}{-1}$

$x > 0$

3) $\frac{x}{5} -2 < 0$

$5 \times (\frac{x}{5} - 2 ) \times 5 < 0$

$x - 10 < 0$

$x -10 + 10 < 0 +10$

$x < 10$

4) $-5x + 11 > 31$

$-5x \cdot 11 < 31$

$-55x < 31$

$\frac{-55x}{-55} > \frac{31}{-55}$

$x < -\frac{31}{55}$

5) $\frac{1}{2}x - 4 \geq -4$

$\frac{1}{2}x -4 +4 \geq -4 +4$

$\frac{1}{2}x \geq 0$

$\frac{\frac{1}{2}x }{\frac{1}{2} } \geq \frac{0}{\frac{1}{2} }$

$x \geq 0$

6) $-4x + 2 \leq 6$

$-4x +2 - 2 \leq 6 -2$

$-4x < 4$

$\frac{-4x}{-4} \leq \frac{4}{-4}$

$x \geq -1$

6 0

3 years ago

Which solid figure has the following net? Pentagonal prism hexagonal prism hexagonal pyramid pentagonal pyramid

mars1129 [50]

ANSWER:

Pentagonal prism.

EXPLANATION:

We see that all the sections in the net are rectangles. Also there are 5 of them and a prism has 5 faces.

5 0

3 years ago

Read 2 more answers

An arc has a length of 123.53 millimeters and a radius of 28 millimeters. What is the measure of the angle of the sector in degr

nadezda [96]

Answer:

Step-by-step explanation:

The formula for arc length in terms of degrees is

$A.L.=\frac{\theta}{360}*2\pi r$ and we have everything we need to fill in to find the angle measure.

$123.53=\frac{\theta}{360}*56\pi$ which is the same as

$123.53=\frac{56\pi \theta}{360}$ and

$360(123.53)=56\pi \theta$ and

$\frac{360(123.53)}{56\pi}=\theta$ so

θ = 253°

4 0

3 years ago