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oksano4ka [1.4K]

3 years ago

14

Tony is 1 2 of a mile ahead of Laura on a jogging path. If Tony is running at 5 miles per hour, and Laura is running at 7 miles

per hour, how long will it take Laura to catch up with Tony?

1 answer:

tamaranim1 [39]3 years ago

5 0

Laura will catch up after 15 minutes, i hope this helps.

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The equation of the graph is given by y = cos(0.4x) and has an amplitude of 1

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

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2 years ago

What is the 0.9 to the power of 2

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Step-by-step explanation:

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3 years ago

Suppose you toss a fair coin 10 times, let X denote the number of heads. (a) What is the probability that X=5? (b) What is the p

zubka84 [21]

Answer: The required answers are

(a) 0.25, (b) 0.62, (c) 6.

Step-by-step explanation: Given that we toss a fair coin 10 times and X denote the number of heads.

We are to find

(a) the probability that X=5

(b) the probability that X greater or equal than 5

(c) the minimum value of a such that P(X ≤ a) > 0.8.

We know that the probability of getting r heads out of n tosses in a toss of coin is given by the formula of binomial distribution as follows :

$P(X=r)=^nC_r\left(\dfrac{1}{2}\right)^r\left(\dfrac{1}{2}\right)^{n-r}.$

(a) The probability of getting 5 heads is given by

$P(X=5)\\\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}\\\\\\=\dfrac{10!}{5!(10-5)!}\dfrac{1}{2^{10}}\\\\\\=0.24609\\\\\sim0.25.$

(b) The probability of getting 5 or more than 5 heads is

$P(X\geq 5)\\\\=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}+^{10}C_6\left(\dfrac{1}{2}\right)^6\left(\dfrac{1}{2}\right)^{10-6}+^{10}C_7\left(\dfrac{1}{2}\right)^7\left(\dfrac{1}{2}\right)^{10-7}+^{10}C_8\left(\dfrac{1}{2}\right)^8\left(\dfrac{1}{2}\right)^{10-8}+^{10}C_9\left(\dfrac{1}{2}\right)^9\left(\dfrac{1}{2}\right)^{10-9}+^{10}C_{10}\left(\dfrac{1}{2}\right)^{10}\left(\dfrac{1}{2}\right)^{10-10}\\\\\\=0.24609+0.20507+0.11718+0.04394+0.0097+0.00097\\\\=0.62295\\\\\sim 0.62.$

(c) Proceeding as in parts (a) and (b), we see that

if a = 10, then

$P(X\leq 0)=0.00097,\\\\P(X\leq 1)=0.01067,\\\\P(X\leq 2)=0.05461,\\\\P(X\leq 3)=0.17179,\\\\P(X\leq 4)=0.37686,\\\\P(X\leq 5)=0.62295,\\\\P(X\leq 6)=0.82802.$

Therefore, the minimum value of a is 6.

Hence, all the questions are answered.

3 0

4 years ago

A line with slope

spayn [35]

Answer:

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Step-by-step explanation:

I chose to find the y-intercept since it is easy to find with the given information.

The equation for a line is y = mx + b

To find the y-intercept, we must plug in the info we have and solve for b:

4 = -1/3 (-4) + b

4 = -4/3 + b

8/3 = b

To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:

(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)

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2 years ago

Rosa can clean a house in 7 hours. When Rosa and Amy work together, they can clean a house in about 4.2 hours. About how long wi

Step2247 [10]

First we will calculate rate of work of rosa and amy.
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Work done by Amy and rosa=t(1/7+1/4.2)

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t=10.5 hr

Always keep remember those formula or logic below

Work rate × Time to finish the job = 1 job done

Work rate = (1 job done) / (Time to finish the job)

Time of doing the job = (1 job done) / (Work rate)

4 0

3 years ago