MATHEMATICS HIGH SCHOOL

The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to –z standard deviations from the mean?

Answers

Answer 1

Answer:

Answer:

B: The probability is equal to p%.

Step-by-step explanation:

Answer 2

Answer: P(Z≥z)=p% may help out... (:

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A total of 60 children signed up for hockey. There were 3 boys for every 1 girl who signed up. How many of the children who signed up for hockey were girls?

Answers

Answer: The answer is 15.

Step-by-step explanation: Given that there are a total of 60 students who signed up for hockey, where there were 3 boys for every 1 girl who signed up. We are to find the number of girls who signed up.

The ratio of the number of boys to the number of girls will be 3 : 1.

Let '3x' and 'x' be the number of boys and number of girls respectively who signed up.

Therefore, we have

$3x+x=60\n\n\Rightarrow 4x=60\n\n\Rightarrow x=15.$

Thus, the number of girls is 15.

60÷(3+1)=15 1*15 = 15 girls 3*15 = 45 boys

*** Solve 2x + y = 7 for y.

Answers

Answer:

y = 7 - 2x

Step-by-step explanation:

Start with the equation: 2x + y = 7.

To isolate y, you can subtract 2x from both sides of the equation:

2x + y - 2x = 7 - 2x.

The 2x on the left side cancels out, leaving you with:

y = 7 - 2x.

Ex 2.8
3. find the maximum value of the curve y=x²-4x+4 for -3≤x≤3

Answers

$y=x^2-4x+4\ny'=2x-4\n\n2x-4=0\n2x=4\nx=2\n2\in[-3,3]\n\ny''=2>0 \Rightarrow \text{ There's a minimum at } x=2$

In this case you have find the values of $y(-3)$ and $y(3)$ .

$y(-3)=(-3)^2-4\cdot(-3)+4=9+12+4=25\ny(3)=3^2-4\cdot3+4=9-12+4=1\n\ny(-3)>y(3) \Rightarrow y_(max)=25$

Solve the equation for y. 8x – 9y = 11a. .y=-9/8x-9/11
b. .y=9/8x 11/8
c. .y=-8x-11
d. .y=8/9x-11/9

Answers

8x - 9y = 11 (subtract 8x from each side)

- 9y = -8x + 11 (divide -9 from each side)

$(-9y)/(-9) = (-8x+11)/(-9)$

y = $(-8)/(-9) x - (11)/(9)$

D. $y=(8)/(9) x - (11)/(9)$

Help solving statistic children participating at a one week summer camp made five new friends on average during the first six days of camp. If each child made two more friends on the last day of camp, then how many friends on average did the children make during the one week summer camp

Answers

Answer:

On average the children on the camp made 7 new friends in the week.

Step-by-step explanation:

Given:

Average number of new friends camp made in 6 days = 5

Number of new friends made on the last day = 2

We need to find the number of new friends on average did the children make during the one week summer camp.

Solution:

Now we can say that;

to find the number of new friends on average did the children make during the one week summer camp is equal to sum of Average number of new friends camp made in 6 days and Number of new friends made on the last day.

framing in equation form we get;

the number of new friends on average made in 1 week = $5+2 =7$

Hence On average the children on the camp made 7 new friends in the week.

Final answer:

On average, each child made 30 friends in the first six days of camp and another 2 on the last day, totaling an average of 32 friends made during the one week summer camp.

Explanation:

The children participating at the summer camp made an average of five new friends each for the first six days. This means they made a total of 5 friends/day * 6 days = 30 friends on average in the first six days. On the last day of camp, each child made two more friends. So, for the week as a whole, each child made an average of 30 friends from the first six days + 2 friends from the last day = 32 friends on average during the week-long summer camp.

Learn more about average here:

brainly.com/question/34817150

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If the shadow of a pole 12m high is 2/3 of its length, what is the angle of elevation of the sun?

Answers

To find the angle of elevation of the sun, you can use the tangent function. Given that the shadow of the pole is 2/3 of its length (12 meters), you can set up the following trigonometric relationship:

tan(angle of elevation) = (height of the pole) / (length of the shadow)

tan(angle of elevation) = 12 / (2/3 * 12)

Now, calculate the length of the shadow:

2/3 * 12 = 8 meters

So, tan(angle of elevation) = 12 / 8

tan(angle of elevation) = 3/2

To find the angle of elevation, take the arctan (inverse tangent) of 3/2:

angle of elevation = arctan(3/2)

Using a calculator or trigonometric tables:

angle of elevation ≈ 56.31 degrees

So, the angle of elevation of the sun is approximately 56.31 degrees.

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