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3 years ago

Help on question 11. A) please

Mathematics

1 answer:

lana [24]3 years ago

7 0

They didn't follow PEMDAS. according to pemdas, exponents come first (since there are no parentheses here), so they were right to simplify 4^2 to 16. However, multiplication and division come before addition and subtraction, which means they should have multiplied 5 by 3 and then subtracted the product from 16.

So, the work really should have shown 16-15=1.

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Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

2 years ago

In 12 games last season the school baseball team scored 5, 11, 2, 0, 4, 8, 9, 6, 7, 4, 1, and 2 runs. What is the average number

Mashcka [7]

Hello there!

First, we need to put our data set into proper numerical order (least to greatest).

Set: , 1,2,2,4,4,5,6,7,8,9,11

Now, to find the mean, we need to add them all up.

1 + 2 + 2 + 4 + 4 + 5 + 6 + 7 + 8 + 9 + 11 = 59

Then, divide it by how many numbers there are : 12

59 divided by 12 = 4.9166667

Round it to the nearest tenth.

4.9166667 = 4.9

This means the average number of runs scored per game is 4.9 runs.

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3 years ago

In class, Matthew stated, "I think that a negative is like an opposite. That is why multiplying a negative times a negative equa

Black_prince [1.1K]

Two negatives being multiplied DOES equal a positive
In my response to is that is a correct term to answer. <span />

3 0

2 years ago

Solve for x<br>8x - 20 4x + 32

Alenkinab [10]

Answer:

Step-by-step explanation:

8x - 20 = 4x + 32 ( F rule angles)

8x-4x=32+20

4x=52

x=52/4

x=13

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2 years ago

All 10,000 California students in the beginning of 8th grade are given an entrance exam that will allow them to attend a top aca

lys-0071 [83]

Answer:

1.32% of students have the chance to attend the charter school.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

This year the mean on the entrance exam was an 82 with a standard deviation of 4.5.

This means that $\mu = 82, \sigma = 4.5$

a.What is the percentage of students who have the chance to attend the charter school?

Students who achieve a score of 92 or greater are admitted, which means that the proportion is 1 subtracted by the pvalue of Z when X = 92. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{92 - 82}{4.5}$

$Z = 2.22$

$Z = 2.22$ has a pvalue of 0.9868

1 - 0.9868 = 0.0132

0.0132*100% = 1.32%

1.32% of students have the chance to attend the charter school.

7 0

3 years ago