The average score on a standardized test is 500 points with a standard deviation of 50 points. If 2,000 students take the test at a local school, how many students do you expect to score between 500 and 600 points?

write the equation out as given:

2x+3=-6

 subtract 3 from each side

2x = -9

x=-9/2

x = -4.5

The balance in the cash account at the beginning of May was -$6,500.

The balance in the cash account at the beginning of May can be calculated by adding up the debits and credits for the month and subtracting them from the normal balance at the end of May.

In this case, the total debits for May were $12,200 and the total credits were $11,500.

To find the beginning balance, subtract the total credits from the normal balance:

Beginning balance = Normal balance - Total credits

Beginning balance = $5,000 - $11,500 = $-6,500

Therefore, the balance in the cash account at the beginning of May was -$6,500.

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Final answer:

Peter invested $3,700 at a 3% loss and $7,800 at a 4% gain. By setting up a system of equations and solving them, we determined the amount invested in each.

Explanation:

To solve the problem of how much was invested by Peter in each investment, we need to set up a system of equations. Let's call the amount invested at 3% loss x, and the amount invested at 4% gain y. The total amount invested is $11,500, so we have x + y = $11,500.

Peter's net annual receipts were $201, which comes from a loss of 3% on investment x and a gain of 4% on investment y. The equation for this would be -0.03x + 0.04y = $201.

Now we have a system of two equations:

-0.03x + 0.04y = $201

Adding (1) and (2) gives us:

0.03y + 0.04y = $546

Combining like terms, we get:

0.07y = $546

Dividing both sides by 0.07, we find that:

y = $7,800

Substituting y back into the first equation, we get:

x = $11,500 - $7,800 = $3,700

So, Peter invested $3,700 in the investment with a 3% loss and $7,800 in the investment with a 4% gain.

A regular subquery is a standalone query that can be executed independently of the outer query and passes its result to the outer query. Conversely, a correlated subquery is linked with the outer query, executes for each row processed by the outer query, and may be slower due to these repeated executions.

The primary difference between a regular subquery and a correlated subquery resides in the way they operate and when they execute the control flow. A regular subquery is a standalone query, which means it can be executed independently of the outer query. Once it executes, it passes its result to the outer query.

On the other hand, a correlated subquery, as its name suggests, is 'correlated' with the outer query. It cannot be executed independently and must be run for each row processed by the outer query.

For example, if you use a correlated subquery to determine whether a record exists in another table, the subquery will run once for each record in the primary query. This can potentially be slower than a regular subquery due to the repeated executions.

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The question probable may be:

What distinguishes a regular subquery from a correlated subquery in terms of execution and operation? How does the control flow differ, and why might a correlated subquery be slower than a regular subquery in certain scenarios?

Final answer:

Raul did better on the history test relative to his classmates, as indicated by a higher z-score of approximately 0.22, compared to 0.14 for the biology test.

Explanation:

To determine on which test Raul did better relative to the rest of the class, we need to calculate the z-scores for Raul's history and biology test results. A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean. The formula for calculating a z-score is:

z = (X - μ) / σ

where X is the score, μ is the mean, and σ is the standard deviation. Let's apply this to Raul's scores:

For the history test:

z = (72 - 70) / 9 = 2 / 9 ≈ 0.22

For the biology test:

z = (71 - 70) / 7 = 1 / 7 ≈ 0.14

Comparing the two z-scores, we can see that Raul's z-score for history is higher than his z-score for biology. Hence, Raul did better on the history test relative to the rest of the class.

The volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be 30 cubic inches.

Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

V = (Base area x H) / 3

The volume of a pyramid varies jointly with the base area of the pyramid and its height.

The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.

Then the volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be

V = (10 x 9) / 3

V = 30 cubic inches

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The volume of a pyramid is obtained from the joint variation relationship with its base area and height. Given a certain pyramid's dimensions, we can determine the volume of another pyramid if we know its base area and height. The volume of the second pyramid is 30 cubic inches.

The student's question pertains to joint variation, a concept in mathematics, specifically applied here to understand how the volume of a pyramid relates to its base area and height. For a pyramid, this relationship can be expressed as V = k * A * H, where V is volume, A is base area, H is height, and k is the constant of variation.

First, we find the value of 'k' using the given pyramid's measurements; so 24 = k * 24 * 3 gives us k = 1/3.

Then, we use this constant to find the volume of the other pyramid whose base area is 10 square inches and height is 9 inches. Therefore, V = 1/3 * 10 * 9, which simplifies to V = 30 cubic inches.

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255-115 = 140 miles

140/70 = 2 hours

The equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Given that line passes through points (4, 7) and (0, 7)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 4, y₁ = 7

x₂ = 0, y₂ = 7

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 7 = (7 - 7)/(0- 4)[x -4]

⇒ y - 7 = (0)/(-10 )[x -4]

⇒ y - 7 = 0(x -4)

⇒ y - 7 = 0

⇒  y = 7

Therefore, the equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).

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Answer:

$396.93

Step-by-step explanation:

It asks to round to the nearest cent not dollar.

5/8 x 1/2 = 5/16 acre is lawn

5/16 x 2/3 = 10/48 reduces to 5/24 of the lawn was mowed

Given

5(x + 27) ≥ 6(x + 26)

Find

The solution set of x

Solution

Eliminate parenthses.

... 5x + 135 ≥ 6x + 156

Subtract 5x+156

... -21 ≥ x

The solution set is all real numbers less than or equal to -21.

Answer:

18/38

Step-by-step explanation:

edmentum/plato

Slope in math is the difference in y-values divided by x-values.

The slope helps determine the steepness of a line. Y-intercept is the y-value when x=0. The formula for slope, denoted as m, is (y2-y1)/(x2-x1).

Example: For the equation y = 2x - 1, if we have the point (-2, 2), we can calculate the slope by substituting the values into the formula: m = (2-(-1))/(-2-0) = 3/-2 = -1.5.

Y-intercept is the y-value when x=0, or where the graph crosses the y-axis.

-3w+2=-10w+30

add 3 w to each side

2=-7w+30

subtract 30 from each side

-28 = -7w

divide both sides by -7

w = 4

double check

-3(4) +2 = -10

-10(4) +30 = -10

 so w = 4