13 over 15 divided by 7 over 10 in simplest form

Answer: Zeno consumed 51 hot dogs.

The total number of hot dogs consumed was 676.

Step-by-step explanation:

Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.

The formula for finding the nth term in an arithmetic series is given by

Tn = a + (n - 1)d

Where

a denotes the first term in the sequence.

d signifies the common difference.

n stands for the total terms in the sequence.

<pBased on the details provided,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs

The formula to calculate the sum of n terms in an arithmetic sequence is

Sn = n/2[2a + (n - 1)d]

Hence, to find the total number of hot dogs consumed by 26 contestants, S26 is calculated as

S26 = 26/2[2 × 1 + (26 - 1)2]

S26 = 13[2 + 50]

S26 = 13 × 52 = 676 hot dogs

Response:

Her brother catches up to her at 11 am + 4 hours = 15 p.m

Detailed explanation:

Provided information;

Ariel's speed = 45 mph

She departed at 9 a.m

Her brother's speed = 60 mph

He began at 11 a.m

Inferred from the question: Since Ariel's speed is 45 mph, after two hours she is ahead by 90 miles.

Meanwhile, her brother travels at 60 mph, hence he is traveling (60 - 45) = 15 mph faster

Therefore, with this speed, he will catch up to her in = 4 hours.

So her brother catches up with her at 11 am + 4 hours = 15 p.m

The initial time was 15.7 minutes.

Explanation of steps:

Let x represent the initial time (in minutes).

The relay team is working on minimizing their relay race duration.

First, they cut down their time by 2.1 minutes.

Afterwards, they manage to reduce that time by 10 percent.

If the concluding time ends up being 3.96 minutes, then

x-t1-t2= 3.6
x= 3.6+ t1+ t2
x= 3.6+ 2.1+ 10
x= 15.7

Thus, their starting time was 15.7 minutes.

<span>As the restaurant owner, The likelihood of hiring Jun is 0.7 => p(J) The likelihood of hiring Deron stands at 0.4 => p(D) The chance of hiring at least one of them is 0.9 => p(J or D) We can formulate the probability equation: p(J or D) = p(J) + p(D) - p(J and D) => 0.9 = 0.7 + 0.4 - p(J and D) p(J and D) = 1.1 - 0.9 = 0.2 Thus, the probability that both Jun and Deron are hired is 0.2.</span>

The problem's sample space consists of a selection of roses and hibiscus in various colors, totaling 315 flowers. Among these, 20 are pink roses, making the probability of selecting a pink rose 20/315, or approximately 0.063.