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tangare [24]
2 years ago
9

Professor Hopkins is grading the final exam. She notices that the

Mathematics
1 answer:
NeX [460]2 years ago
8 0

Answer:

  143

Step-by-step explanation:

The interval of interest extends from the mean score (71) to 2 standard deviations above the mean (71+2(6) = 83). The area under the normal distribution curve in this interval can be found using a suitable table, probability app, spreadsheet, or web site. It can also be found using the "empirical rule", which tells you that the 95% of the area is within 2 standard deviations of the mean.

__

Since the curve is symmetrical, and we're only interested in the area above the mean, the empirical rule tells us that 95%/2 = 47.5% of the sample will be in the range of interest.

  0.475 × 300 = 142.5 ≈ 143

143 students will have a score between 71 and 83.

__

The attachment shows a calculator output for the same calculation. You will notice it is slightly different from the "empirical rule," which is only an approximation. Either way, we find 143 students have scores in the range.

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If x-2 is one of the factors of x^4-kx^2+4, find the value of k.
Andrei [34K]

Step-by-step explanation:

Given expression is x⁴-kx²+4 =0

x−2 is a factor of the given expression.

So, x=2

Substitute in the equation, we get

2⁴-k(2)²+4

⇒16+4k+4=0

⇒4k=−20

⇒k=−5

8 0
2 years ago
Factor completely 2x2 + 2x − 24.
nalin [4]

2x^2 + 2x - 24

= 2x^2 + 8x - 6x -24

= 2x(x + 4) -6(x + 4)

= (x+4)(2x-6)

7 0
2 years ago
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At his last track meet, Eli ran the 400-meter dash in 54 seconds. His friend Kimberly bet him that he couldn't run a whole kilom
Trava [24]

Answer:

Eli has to run for 2.25 minutes at this pace to win the bet.

Step-by-step explanation:

At his last track meet, Eli ran the 400-meter dash in 54 seconds.

So, the speed of Eli's run is \frac{400}{54} \times 60 = 444.44 meters per minute.

Now, if Eli is determined to run a whole kilometer with the same speed, then it will take Eli to run 1 kilometer within \frac{1000}{444.44} = 2.25 minutes.

Hence, Eli has to run for 2.25 minutes at this pace to win the bet. (Answer)

6 0
3 years ago
A student says that the​ x-intercept of a line is ​(0,-10,​). Is the student​ correct? Explain.
nataly862011 [7]

Answer:

Yes, the student is correct

Step-by-step explanation:

Given

(0,-10)

Required

Does it represent the x intercept

At the x intercept, the value of x is 0.

So, the function (x,y) becomes (0,y)

(0,-10) can be compared to (0,y)

Hence, the student is correct

5 0
2 years ago
I need the equation for this ASAP!
Sindrei [870]

Answer:

5.714 liters of the 5% solution and 4.286 of the 40%.

Step-by-step explanation:

Let x be the volume of 40% solution and y = volume of the 5% solution.

x + y = 10

0.40x + 0.05y = 0.20(x + y)

From the first equation x = 10 -y so we have:

0.40(10 - y) + 0.05y = 0.20( 10 - y + y)

4 - 0.40y + 0.05y = 2

-0.35y = -2

y = 5.714 liters of the 5%.

and x =  10 - 5.714 = 4.286  liters of the 40% solution.

Step-by-step explanation:

8 0
3 years ago
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