b. A lap pool has a length of 27 yards, a width of 23 yards, and a depth of 5 yards. Find the pool's surface area (the water surface) and the total volume of water that the pool holds.

Using the normal distribution, it is found that:

a) 167 students in the class can be expected to receive a score over 60.

b) 11.07% of the class is expected to receive a score between 82 and 90.

The z-score of a measure X of a normally distributed variable with mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the scores are given, respectively, by:

\(\mu = 72, \sigma = 9\)

The proportion of students who scored over 60 is given by one subtracted by the p-value of Z when X = 60, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (60 - 72)/9

Z = -1.33.

Z = -1.33 has a p-value of 0.0918.

1 - 0.0918 = 0.9082.

Out of 184 students:

0.9082 x 184 = 167.

167 students in the class can be expected to receive a score over 60.

For item b, the proportion is the p-value of Z when X = 90 subtracted by the p-value of Z when X = 82, hence:

X = 90:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (90 - 72)/9

Z = 2.

Z = 2 has a p-value of 0.9772.

X = 82:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (82 - 72)/9

Z = 1.11

Z = 1.11 has a p-value of 0.8665.

0.9772 - 0.8665 = 0.1107.

Hence:

11.07% of the class is expected to receive a score between 82 and 90.

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Answer:

1073333/5000000

Step-by-step explanation:

Convert to a simplified fraction by placing the numbers to the right of the decimal over 10000000. Reduce the fraction.

Answer:

Yes it is

Explanation:

If you check the number line youll see

Answer:

Step-by-step explanation:

You have to get more than 460 Dollars

to get the surfboard with the money you have

so you can get it in only 26 Weeks / About 6 Months / 182 Days / Half a Year

Hope this helps! <3

Answer:

I can't answer the first par I'm sorry but i can answer the second part

Step-by-step explanation:

my favorite song has to be swim or right here by chase atlantic or at least my 2 favorite songs i'm listening to by them

\(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\) is the possible root

What is a root ?

Mathematicians refer to a number as having a root if it can be multiplied by itself to give the original number. The square root of 49, for instance, is 7, as 77=49. 7 is referred to as the square root of 49 in this instance because it takes 49 to multiply 7 by itself twice. Considering that 333=27, the cube root of 27 is 3.

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfill the equation. In other words, if f() = 0, then x = is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

3x^4 -10x^3 -9x^2 + 40x - 12

=\(\left(3x-1\right)\frac{3x^4-10x^3-9x^2+40x-12}{3x-1}\)

=\(\left(3x-1\right)\left(x^3-3x^2-4x+12\right)\)

= \(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\)

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9514 1404 393

Answer:

  B, D

Step-by-step explanation:

The quadratic expands to ...

  (2n -1)² = (2n)² +2(2n)(-1) +(-1)² = 4n² -4n +1

The coefficients can be factored out of the sum, so ...

  ∑(4n²) = 4∑n² for example

The sum of 60 ones is 60:

  \(\displaystyle\sum_{n=1}^{60}{1}=1+1+1+\dots+1=60\)

So, the sum can be written as ...

  \(\displaystyle\sum_{n=1}^{60}{(2n-1)^2}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+\sum_{n=1}^{60}{1}}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+60}\)

_____

It appears that the key to choosing the correct answers is paying attention to signs.

Answer: Step number 2 is 287,980

Step-by-step explanation:

Just did the assignment.

Answer: the correct answer is B 1+\/~3,1-\/~3

edge 2021-2022

Step-by-step explanation:

Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

When budgeting for housing, it is generally recommended to allocate a certain percentage of your income towards housing expenses. The recommended percentage varies depending on factors such as location, personal financial goals, and individual circumstances.

A common guideline is to spend no more than 30% of your monthly income on housing expenses. To determine the maximum amount Freya should budget for housing, we can calculate 30% of her monthly income:

Maximum housing budget = 30% of $1575

Maximum housing budget = 0.30 × $1575

Maximum housing budget = $472.50

Therefore, Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

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Answer:

20

Step-by-step explanation:

Initial figure times scale factor = result

10 times 2 = 20

I hope this helps!

Answer:

K

Step-by-step explanation:

im guessing its K if not then its none!

Answer:yes

Step-by-step explanation:

As the Amount is unknown Hence X = Any amount Unless the water amount is given the instructions is yes as she added 120ML Of juice into water which is currently X

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(3x+y=5\implies y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line that has a slope oif -3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{2}) \implies y +4 = - 3 ( x -2) \\\\\\ y+4=-3x+6\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}\)

now, keeping in mind that perpendicular lines have negative reciprocal slopes

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -3 \implies \cfrac{-3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-3} \implies \cfrac{1}{ 3 }}}\)

so for this one, we're looking for the equation of a line whose slope is 1/3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +4 = \cfrac{1}{3} ( x -2) \\\\\\ y+4=\cfrac{1}{3}x-\cfrac{2}{3}\implies y=\cfrac{1}{3}x-\cfrac{2}{3}-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{14}{3} \end{array}}\)

Figure P can be mapped onto figure Q using reflection or rotation.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Reflection is flipping of a figure across a line. Rotation is the turning of a shape about a point.

Figure P can be mapped onto figure Q using reflection or rotation.

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Answer:

» Reflection or rotation

Step-by-step explanation:

i got it right on the quiz :)

The square root of 7 is approximately 2.65 when rounded to the nearest hundredth.

Answer:

centroid = (3, 2)

Step-by-step explanation:

The centroid of a triangle is the point of intersection of the medians.  

Given that S (3, 1) is the middle point of QR, this indicates that triangle PQR is an isoceles triangle with sides QP = PR and base QR.  Therefore, the x-coordinate of the centroir will be x = 3.

Vertical distance between S and P = 3 units

Therefore, centroid will be 1/3 of SP.  1/3 of 3 = 1.

Therefore, y-coordinate of centroid = 1 + 1 = 2.

Answer:

40

Step-by-step explanation:

\(8=2^3 \\ \\ 20=2^2 \times 5 \\ \\ \lcm(8,20)=2^3 \times 5=40\)

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

  -89

Step-by-step explanation:

The first term of the sequence is a1 = -12.

The common difference between terms is ...

  d = -13 -(-12) = -1

The generic term is given by ...

  an = a1 +d(n -1)

Then the 78th term is ...

  a78 = -12 +(-1)(78 -1) = -12 -77

  a78 = -89

Answer:

164=82+82 or 164=82 x 2

Step-by-step explanation:

Hope that works

The scale factor of figure B to figure A is 1/2.

To find the scale factor of figure B to figure A, we need to determine how much the corresponding sides of the two figures have been multiplied or divided by.

Looking at the figures, we can see that the corresponding sides of figure B are half the length of the corresponding sides of figure A. For example, the length of side AB in figure A is twice the length of side AB' in figure B, and the length of side BC in figure A is twice the length of side B'C' in figure B.

Since the corresponding sides of figure B are half the length of the corresponding sides of figure A, the scale factor of figure B to figure A is 1:2 or 1/2.

Therefore, the scale factor of figure B to figure A is 1/2.

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Answer:

A. Punch in "1 divided by 11"

Step-by-step explanation:

Answer:

The answer is 1.4 because you have to simplify it. Hope this helps :)

Step-by-step explanation:

Answer: 45 words per minute.

Step-by-step explanation: I'm not exactly sure what you're asking, but Connie types 45 words per minute (675/15 = 45).

Answer:

Step-by-step explanation:

Multiply both sides by 14 to find the missing value: