Last year's average score on a high school exit exam was 500 with a standard deviation of 100. Mathie scored a 410; what % of students scored lower than Mathie?

Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.

The probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.

We shall determine the answer to the question as follows;

People in the sport centre = 125

People who used the 3 facilities = 6

People who accessed only gym = 59 - (6 + 11 + 19) = 26

People who accessed only track event = 55 - (6 + 11 + 24) = 14

People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21

People who accessed only gym and swimming pool events = 29 - 6 = 19

People who accessed only gym and track events = 17 - 6 = 11

People who accessed only swimming pool and track events = 30 - 6 = 24

Total number of people who accessed at least any one of the facilities = 121

The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.

Therefore, the probability that the person selected doesn't use any facility = 1/4

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Answer:

4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles

Step-by-step explanation:

Pattern blocks are a set of geometric shapes commonly used in math education. The set typically includes six different shapes: triangle, rhombus, trapezoid, hexagon, square, and equilateral triangle. Each hexagon in a pattern block set is made up of six equilateral triangles.

To make 4 hexagons using pattern blocks, we would need to calculate the total number of equilateral triangles required. Since each hexagon is made up of 6 equilateral triangles, we can multiply the number of hexagons by 6 to get the total number of equilateral triangles needed.

4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles

So, you would need 24 pattern block triangles to make 4 hexagons using pattern blocks.

Answer:

Let's use pattern blocks to visualize the situation and say that a hexagon is 1 whole. Since 3 rhombuses make a hexagon, 1 rhombus represents and 2 rhombuses represent . We can see that 6 pairs of rhombuses make 4 hexagons, so there are 6 groups of in 4.

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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Answer:

d. 132

Step-by-step explanation:

12 + 8 x 15

do 8 x 15 first because PEMDAS

12 + 120

132

The expression that represents the perimeter of A’B’C’ is 2(a + b + c).

The correct option is b).

Given:

BC = a = 4

CA = b

AB = c

B'C' = 8

To find the perimeter of triangle A'B'C', we need to add up the lengths of all three sides, A'B', B'C', and C'A'.

To find the length of B'C' in terms of a, b, and c, we can use the fact that the triangles are similar. Since the sides of similar triangles are proportional, we can set up the following equation:

BC / AB = B'C' / A'B'

Plugging in the given values, we have:

4 / c = 8 / A'B'

Solving for A'B', we find:

A'B' = (8 x c) / 4

      = 2c

Now, we can calculate the perimeter of A'B'C' by adding up the lengths of A'B', B'C', and C'A':

Perimeter of A'B'C' = A'B' + B'C' + C'A'

= 2c + 8 + b

Comparing this expression to the options provided, we can see that the correct expression is:

b) 2(a + b + c)

Therefore, the perimeter of triangle A'B'C' is given by 2 times the sum of the lengths of its corresponding sides, a, b, and c.

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The complete question:

The diagram shows the lengths of corresponding sides of similar triangles A'B'C' and ABC. Which expression gives the perimeter of A'B'C'?

Options:

a) 4(4 + b + c)

b) 2(a + b + c)

c) 4(a + b + c)

d) 8(a + b + c)

The diagram is given in the attached image below.

There is nothing inherently wrong with any of the statements in question 21. Sampling rate and sound frequency both use hertz (Hz) as their unit of measurement.

The sample rate is a setting that can be adjusted during the digitization process, as is the sound frequency. It is also true that a higher sampling rate does not necessarily result in a higher pitch.

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Answer:

Hey buddy, here is your answer. Hope it helps you.

Step-by-step explanation:

8+8=16.

The surface area of a hexagonal prism willl be 251.13844 cm².

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

A=6ah+3√3a²

A=6×4×7+3√3×4²

A≈251.13844

Hence the surface area of a hexagonal prism willl be 251.13844 cm².

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Answer:

B) The distance between -2.2 and x is greater than 3.

Step-by-step explanation:

The required sign between -12.7a and -12.7b should be greater than sign (>).

If a is less than b, then -12.7a will be greater than -12.7b, because multiplying a smaller number by a negative constant (-12.7 in this case) will result in a larger negative value than multiplying a larger number by the same constant.

To see this, suppose we have two positive numbers x and y such that x < y. Then, multiplying both by a negative constant c will result in two negative numbers with magnitudes that are greater for x:

cx < cy, because c is negative and (x < y)

Therefore, if a is less than b, then:

-12.7a > -12.7b

So the sign between -12.7a and -12.7b should be greater than sign (>).

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The solution is x = 0 and y = 22.

Equation 1: y = -3x + 22

Substitute y in Equation 2:

5x + 2(-3x + 22) = 44

Simplify and solve for x:

5x - 6x + 44 = 44

-x + 44 = 44

-x = 0

x = 0

Substitute x = 0 back into Equation 1 to find Y:

Y = -3(0) + 22

Y = 0 + 22

Y = 22

So the solution is x = 0 and y = 22.

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The volume of the given solid over the indicated region of integration, f(x,y) = 2x + 2y - 5 and R = {(x,y): -4 ≤ x ≤ 1, 3 ≤ y ≤ 6}, is 63 units³.

To find the volume, we will integrate the function f(x,y) over the region R. Follow these steps:

1. Set up the double integral: ∬R (2x + 2y - 5) dA

2. Set up the limits of integration: ∫(from -4 to 1) ∫(from 3 to 6) (2x + 2y - 5) dy dx
3. Integrate with respect to y: ∫(from -4 to 1) [(2xy + 2y²/2 - 5y)] (evaluated from 3 to 6) dx
4. Simplify and evaluate: ∫(from -4 to 1) [6x + 18 - 5(6-3)] dx
5. Integrate with respect to x: [3x² + 18x - 15x] (evaluated from -4 to 1)
6. Simplify and evaluate: (3 + 18 - 15) - (-12 + 72 + 60)
7. Calculate the final result: 6 - (-30) = 36

The volume of the region is 63 units³.

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Using Average formula,

Jack's average for second nine weeks is 77.

Average: Average of observations is fraction of sum of observations values to the total number of observations.

Mathematically, Average = ∑ X/ n

where, X ---> observations values

n --> total number of observations taken

We have given that ,

Average for first nine weeks of Jack's marks in maths (A₁) = 88

i.e sum of marks in maths obtained by jack

= 88×9= 792

Also have , Average of jack's marks in maths for second nine weeks (A₂ ) is decreased by 12.5% from first nine weeks.

In Mathematically, A₂ = A₁ - 12.5% of A₁

=> A₂ = 88 - 12.5%of 88

=> A₂ = 88 - (125/100)88

=> A₂ = 88 - 11 = 77

Hence, Jack's average for second nine weeks is 77.

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Answer:

yes

Step-by-step explanation:

i gussed

Answer: Yes

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Answer:

smile

Step-by-step explanation:

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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First find the center, then graph all the points that are at a distance of R units from that center.

A circle of radius R is the set of all points that are at a distance R from a given point (the center of the circle).

So to graph it, we need to know these two things, radius and center.

Once we do, first we graph the center on the coordinate plane.

Once we find the center, we can find all the poiints that are at a distance of R units from our center, so we need to graph these. Once we do, we will have the graph of our circle on the coordinate plane.

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In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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The main double angle formulas are: sin(2θ) = 2sin(θ)cos(θ), cos(2θ) = cos^2(θ) - sin^2(θ) = 2cos^2(θ) - 1, and tan(2θ) = (2tan(θ)) / (1 - tan^2(θ))

Double angle formulas are mathematical identities that relate to the trigonometric functions of double angles. They are useful in solving problems involving the double angle of a given angle in a right triangle. These formulas are important in trigonometry, calculus, and engineering.

The double angle formulas are derived from the basic angle relationships between the sides and angles of a right triangle. They are expressed in terms of the trigonometric functions sine, cosine, and tangent and allow us to find the values of these functions for angles that are twice a given angle.

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Answer:

Option A, B and E

Step-by-step explanation:

Determinant = ad-bc

Let's look at the picture and solve all

Option A)

If the row ( c and d ) is zero, the determinant will be zero

=> a(0)-b(0)

=> 0-0

=> 0 (So, True)

Option B)

If a = b = c = d (Let's say 1), the determinant will be

=> (1)(1)-(1)(1)

=> 1-1

=> 0  (So, True)

Option C)

An Identity matrix is

=> \(\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\)

So , it's determinant will be

=> (1)(1)-(0)(0)

=> 1-0

=> 1  (So, False)

Option D)

The determinant with matrix will all positive numbers can be negative as well as positive. This is not necessary that it would be positive. (So, False)

Option E)

A zero matrix is

=> \(\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]\)

So, it's determinant is:

=> (0)(0)-(0)(0)

=> 0-0

=> 0 (So,True)

Answer: A B E

A. If any row of a square matrix is zero, its determinant is zero.

B. If all numbers in a matrix are equal, its determinant is zero.

E. The determinant of any zero matrix is zero

Step-by-step explanation:

edge assignment

Answer:

Its A

Step-by-step explanation:

Answer:

A i did this before

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

An isosceles triangle has 2 sides of the same length, those sides being the sides that aren't the base. The perimeter is the total length of all 3 sides of the triangle. We know that the base is 5 inches, and that one side is 8. Because the triangle is isosceles, we know that the others ide is also 8 inches. Therefore, the perimeter is 8+8+5, which is 21.

Answer:

21 in.

Step-by-step explanation:

If the triangle is isosceles, then two of its three sides are of equal length.  We can assume that the side lengths are 5 in., 8 in and 8 in.  Summing these up, we get total length 21 in.  That's the perimeter of the triangle.

Step-by-step explanation:

hold up let me work it out and i will answer with full explanation

Answer:

A. \(y \leq 9\)

Step-by-step explanation:

The range is the set of y-values, which can be read off the graph.

The equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.

To find the equation of the tangent line to the curve at the given point, we will differentiate the equation implicitly with respect to x.

Differentiating both sides of the equation x^(2/3) + y^(2/3) = 4 with respect to x, we get:

(2/3)x^(-1/3) + (2/3)y^(-1/3) * (dy/dx) = 0

Now we need to find the value of dy/dx at the point (-3sqrt3, 1).

Substituting x = -3sqrt3 and y = 1 into the equation, we have:

(2/3)(-3sqrt3)^(-1/3) + (2/3)(1)^(-1/3) * (dy/dx) = 0

Simplifying, we get:

(2/3)(-1/sqrt(3)) + (2/3) * (dy/dx) = 0

Simplifying further, we have:

-2/(3sqrt3) + (2/3) * (dy/dx) = 0

Now we can solve for (dy/dx):

(dy/dx) = 2/(2sqrt3) = 1/sqrt3

So the slope of the tangent line at the point (-3sqrt3, 1) is 1/sqrt3.

Now we have the slope of the tangent line and the point (-3sqrt3, 1), we can use the point-slope form to find the equation of the tangent line. The equation is given by:

y - y1 = m(x - x1)

Substituting the values, we have:

y - 1 = (1/sqrt3)(x - (-3sqrt3))

Simplifying, we get:

y - 1 = (1/sqrt3)(x + 3sqrt3)

y - 1 = (1/sqrt3)x + 3

Finally, rearranging the equation, we have:

y = (1/sqrt3)x + 4

So the equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.

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Answer:

2m = m + m

2m = 2m

Step-by-step explanation:

hope that will help you

Nice time

The coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Also, if we are aware of the ratio that the line segment connecting two places has produced, we may locate the point of division. The two may be accomplished using a section formula from coordinate geometry.

The position of a point that splits a line segment connecting two points into two portions with a length ratio of m:n is found using the section formula.

The coordinates of the point A and B from the given figure is:

A = (1, 3) and B = (10, 3)

The section formula is given as:

(x, y) = (mx2 + nx1 / m+n , my2 + ny1 / m+n)

Substitute the values of m = 1 and n = 2, and the coordinates of the point A and B.

(x, y) = ((1)(10) + (2)(1)/ 3 , (1)(3) + (2)(3) 3)

D(x,y) = (4, 3)

Hence, the coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

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