MATHEMATICS COLLEGE

Amir went on a bike ride of 60 miles. He realized that if he had gone 5 mph faster, he would have arrived 6 hours sooner. How fast did he actually ride? Amir rode mph on his trip.

Answers

Answer 1

Answer:

Step-by-step explanation:

distance / rate = time

x = original speed mph

60/x = t

Then at 5 mph faster

60/(5+x) = t - 6 re-arranged for t = 60/(5+x) + 6

equate the two definitions of 't' then solve for 'x'

60/x = 60/(5+x) + 6

60 = 60x/(5+x) + 6x

60(5+x) = 60x +6x(5+x)

300 + 60x = 60x + 30x + 6x^2

6x^2 +30x -300 = 0 Use Quadratic Formula to find x = 5 m/hr

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A bicycle is traveling at 20 miles per hour. How many feet will it cover in 30 seconds? Round your answer to the nearest tenth of a foot.

Answers

Answer:

$Distance = 880ft$

Step-by-step explanation:

Given

$Speed = 20(miles)/(hour)$

$Time = 30\ seconds$

Required

Determine the distance

To answer this question, we make use of speed-distance relationship

$Speed = (Distance)/(Time)$

Make Distance the subject

$Distance = Speed * Time$

$Distance = 20 miles/hour * 30 seconds$

Convert seconds to hour

$Distance = 20 miles/hour * (30)/(3600) hour$

$Distance = 20 miles * (30)/(3600)$

$Distance = (20 miles * 30)/(3600)$

$Distance = (600\ miles)/(3600)$

$Distance = (1)/(6) miles$

Convert to foot

$Distance = (1)/(6) * 5280\ ft$

$Distance = (1* 5280\ ft)/(6)$

$Distance = (5280\ ft)/(6)$

$Distance = 880ft$

Suppose that B1 and B2 are mutually exclusive and complementary events, such that P(B1 ) = .6 and P(B2) = .4. Consider another event A such that P(A | B1) = .2 and P(A | B2) = .5. Find P(A).

Answers

Answer:

So, we get that is P(A)=0.32.

Step-by-step explanation:

We know that:

$P(B_1)=0.6\n\nP(B_2)=0.4\n\nP(A|B_1)=0.2\n\nP(A|B_2)=0.5\n$

We have the formula for probability:

$P(A|B)=(P(A\cap B))/(P(B))\n\n\implies P(A\cap B)=P(A|B)\cdot P(B)$

So, we calculate:

$P(A\cap B_1)=P(A|B_1)\cdot P(B_1)\n\nP(A\cap B_1)=0.2\cdot 0.6=0.12\n\n\nP(A\cap B_2)=P(A|B_2)\cdot P(B_2)\n\nP(A\cap B_2)=0.5\cdot 0.4=0.2\n$

We calculate:

$P(A)=P((A\cap B_1)\cup(A\cap B_2))\n\nP(A)=P(A\cap B_1)+P(A\cap B_2)\n\nP(A)=0.12+0.2\n\nP(A)=0.32$

So, we get that is P(A)=0.32.

Final answer:

To find P(A), use the law of total probability given that B1 and B2 are mutually exclusive and complementary events. Substituting the provided values, P(A) = 0.32.

Explanation:

The question is asking us to calculate P(A), given the values for P(A | B1) and P(A | B2), and the knowledge that B1 and B2 are mutually exclusive and complementary events. In probability, if events B1 and B2 are mutually exclusive and complementary, this means that one and only one of them can occur, and their occurrence covers all possible outcomes. We can use the law of total probability to find the overall P(A). The law of total probability states that P(A) = P(A | B1) * P(B1) + P(A | B2) * P(B2). Plugging the provided values into this formula, we get P(A) = .2 * .6 + .5 * .4 = .12 + .2 = .32. Therefore, P(A) is .32.

Learn more about Probability here:

brainly.com/question/22962752

#SPJ11

Can someone plz help me wit this?

Answers

Answer:

11. True

12. false

13. True

14. False

15. true

16. True

sry if number 15 & 16 are wrong,

17. Line AE, Line FE, Line HE

18. Plane ABCD

19. Plane ABCD , Plane CDHG

20. Plane CDHG, Plane ABCD, Plane ADHE

hope this helps :)

Y=BD-5, for B. solve for B

Answers

Answer:

Step-by-step explanation:

BD - 5 = Y

BD = Y + 5

B = (Y + 5)/D

y=BD-5
5+y=BD
B=D(y+5)

A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that men have a longer mean nose length than women. A statistical test is done and the p-value is 0.225. Which of the following is the most appropriate way to state the conclusion? a. The mean nose lengths of the populations of men and women are identical. b. There is not enough evidence to say that the populations of men and women have different mean nose lengths. c. Men have a greater mean nose length. d. The probability is 0.225 that men and women have the same mean nose length

Answers

Answer:

b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.

See explanation below.

Step-by-step explanation:

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different (men have longer mean nose length than women), the system of hypothesis would be:

Null hypothesis: $\mu_(men) \leq \mu_(women)$

Alternative hypothesis: $\mu_(men) > \mu_(women)$

Assuming that we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_(men)-\bar X_(women)}{\sqrt{(\sigma^2_(men))/(n_(men))+(\sigma^2_(women))/(n_(women))}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Let's assume that the calculated statistic is $z_(calc)$