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1 day ago

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A psychological study found that men who were distance runners lived, on average, five years longer than those who were not dist

ance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years.
What is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners?

1 answer:

Inessa [12.1K]1 day ago

8 0

Answer: C

Step-by-step explanation:

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The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of

babunello [11329]

The third option is correct. Step-by-step explanation: Various transformations apply to a function f(x). If a transformation is applied downward by 'k' units, the function shifts down; if upward, it rises 'k' units. Additionally, if scaled vertically by a factor of 'b', it will stretch; if reflected over the x-axis, the operation is indicated. Thus, since the parent function has undergone reflection over the x-axis, a vertical stretch by a factor of 2, and a downward shift of three units, we can derive that the transformed function is presented.

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12 days ago

Students have organized

tester [11908]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: a minimum of 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, therefore

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijah will trail behind until

$D_E$

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: $v_M=3\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijah will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

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1 month ago

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop

lawyer [12109]

Answer:

a. $\frac{1}{15}$

b. $\frac{2}{5}$

c. $\frac{14}{15}$

d. $\frac{8}{15}$

Step-by-step explanation:

There are four desktop computers and two laptops.

On a specific day, we will set up 2 of these computers.

To find:

a. What is the probability that both selected computers are laptops?

b. What is the probability that both computers are desktops?

c. What is the probability that at least one computer is a desktop?

d. What is the probability that at least one of each type of computer is included?

Solution:

Using the probability formula for event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

a. The number of successful outcomes for both computers being laptops = $_2C_2$ = 1

Total possible outcomes = 15

The needed probability is $\frac{1}{15}$ .

b. The successful outcomes for both being desktop computers = $_4C_2=6$

Total possible outcomes = 15

The required probability is $\frac{6}{15} = \frac{2}{5}$ .

c. For at least one desktop:

Two scenarios exist:

1. 1 desktop and 1 laptop:

Successful outcomes = $_2C_1\times _4C_1 = 8$

2. Both are desktops:

Successful outcomes = $_4C_2=6$

Total successful outcomes = 8 + 6 = 14

The needed probability is $\frac{14}{15}$ .

d. 1 desktop and 1 laptop:

Successful outcomes = $_2C_1\times _4C_1 = 8$

Total outcomes = 15

The required probability is $\frac{8}{15}$ .

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1 month ago

If AE=6x-55 and EC=3x-16, find DB. (Hint: Find x first and then substitute.)

Zina [11999]

Answer:

46 units

Step-by-step explanation:

The diagonals of a rectangle intersect at their midpoints, indicating AE = EC. Therefore, set the equations equal and solve for x:

6x - 55 = 3x - 16

3x = 39

x = 13

Additionally, another characteristic of rectangle diagonals is their equal lengths, hence AC = DB. Now, let’s assess the length of AC:

AC = AE + EC = (6 * 13 - 55) + (3 * 13 - 16) = 23 + 23 = 46

Since AC = DB, it follows that DB = 46 units.

I hope this clarifies your question!

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1 month ago

The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of Coho salmon. (b) Estimate the

zzz [11851]

Based on the graph, it seems that S′(5) is approximately 2, while S′(25) seems to be around -2. The key observation is that these values are of opposite signs. This indicates that at roughly 5ºC, the Coho salmon experiences an increase of about 2 cm/sec in its maximum sustainable speed, whereas at 25ºC it encounters a decrease of approximately 2 cm/sec.

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1 month ago

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