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vichka [17]
3 years ago
8

Using Ratios to Solve Problems - Item 1457 Question 4 of 7 Evan's family drove to a theme park for vacation. They drove the same

speed throughout the trip. The first day, they drove 300 300 miles in 6 6 hours. The second day, they drove 250 250 miles in 5 5 hours. The third day, they arrived at the park after driving for 3 3 hours. How many miles did they drive on the third day?
Mathematics
1 answer:
azamat3 years ago
5 0

Answer:

150 miles

distance travelled on the third day = 150 miles

Step-by-step explanation:

Note: it was given that they drove the same speed throughout the trip. That means their speed is constant for all days;

For the first day

distance = 300 miles

time = 6 hours

Speed = distance/time

Speed = 300/6 = 50 mph

on the third day;

time = 3 hours

Speed = speed on first day = 50 mph

distance = speed × time

distance = 50 mph × 3 hours

distance = 150 miles

distance travelled on the third day = 150 miles

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A claw arcade machine contains stuffed animals and mystery boxes. There are 51 items in the machine. Winning a stuffed animal ha
Oliga [24]
Answer: 34 stuffed animals & 17 mystery boxes.

First off, split 51 into three parts, trying to find how much 1/3 is of 51. It equals 17.

The stuffed animals in the machine are “twice as much” of the mystery boxes, so you need to multiply 17 x 2 to find the amount of stuffed animals.

17 x 2 = 34

As for the mystery boxes, you need to multiply it by one.

17 x 1 = 17.

In summary, the answer is 34 stuffed animals and 17 mystery boxes.
4 0
3 years ago
A lawn mower is pushed a distance of 100 ft. Along a horizontal path by a constant force of 60 lbs. Yhe handle of the lawn mower
stira [4]
For this case we have the following equation:
 w = F • PQ
 Where,
 w: work done
 F: is the force vector
 PQ: is the vector of the direction of movement.
 Rewriting the equation we have:
 w = || F || • || PQ || costheta
 Substituting values:
 w = (60) * (100) * (cos (45))
 w = (60) * (100) * (root (2) / 2)
 w = 4242.640687 lb.ft
 Answer:
 
The work done pushing the lawn mower is:
 
w = 4242.6 lb.ft
7 0
3 years 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
Question 28 (1 point)
aniked [119]

Answer:

+ 16

Step-by-step explanation:

x² - 8x = - 10

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + (- 4) = - 10 + (- 4)²

x² - 8x + 16 = - 10 + 16

thus 16 is added to both sides to complete the square

4 0
2 years ago
!!50 POINTS!! Please answer all, don't just answer to get the points or you'll be reported. And please, do not copy from the int
diamong [38]
G. The shape would be similar since dilation at the origin is just a translation and a translation doesn't affect the shape's size or shape.

h. They will still be similar because adding length to each side will just make the shape larger, and if the shape hasn't changed (which it hasn't) it will remain similar.

I. This is simple, just write an equation of the changes you could do the shape and it would be similar. You would have to explain how many you should move and from which sides (should be all sides). It is better for you to do this because there are millions of possible equations, and if you use the same one then it might be striked.
8 0
3 years ago
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