the mean of a normal probability distribution is 480; the standard deviation is 12. a. about 68% of the observations lie between what two values?

Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.

Simple interest (SI) is calculated as a percentage added to the principle amount deposited or borrowed for a given period of time. SI is typically expressed as years.

Given data:

Simple interest formula:

SI = PRT / 100

SI = 3500*7.5*5 / 100

SI = 1312.5

Now,

Amount = principal + simple interest

Amount = 3500 + 1312.5

Amount = $4812.50

Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.

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Answer: Bret spent $52.92 on the lunch, including tax and tip.

Step-by-step explanation:

Given:

The bill before tax = $42

Sales tax = 6%

Tip = 20% before tax

To find:The total amount of money Bret spent

Solution: Calculate the sales tax:

Sales tax = 0.06 * $42 = $2.52

Calculate the total bill, including tax:

Total bill = $42 + $2.52 = $44.52

Calculate the bill before tax, based on which the tip is calculated:

Bill before tax = $44.52 - $2.52 = $42

Calculate the tip amount:

Tip = 0.2 * $42 = $8.40

Calculate the total amount spent by Bret:

Total spent = $44.52 + $8.40 = $52.92

Therefore, Bret spent $52.92 on the lunch, including tax and tip.

The number of outcomes that are in the sample space = 20

The number of outcomes that are in the event = 5

To calculate the probability of an event, the formula that should be used is given as follows;

Probability = possible event/sample space.

possible outcome = 5

sample space = 20

Probability = 5/20 = 1/4

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A function can have zero to many parameters, and it can return only one (option c).

In mathematics, a function is a rule that maps each element from one set, called the domain, to a unique element in another set, called the range.

The number of parameters a function can take determines the number of arguments required to call the function.

For instance, a function f(x) takes one parameter, and it requires one argument to be called.

On the other hand, a function g(x,y,z) takes three parameters, and it requires three arguments to be called. However, a function h() takes no parameters and does not require any argument to be called.

Hence the correct option is (c).

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The type of error that could have occurred in this scenario is a Type II error. A Type II error occurs when the null hypothesis is not rejected, even though it is false.

In this case, the null hypothesis is that the proportion of defective bulbs in the shipment is greater than or equal to 5%. By not rejecting this null hypothesis, the company is accepting the possibility that the shipment has a high proportion of defective bulbs, when in reality it does not. This can lead to significant costs for the company, such as the cost of returning the shipment or the cost of replacing defective bulbs in the future.

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The vectors that join the center of a clock to the hours :

At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)

At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)

At 3:00: (cos(π/2), sin(π/2)) = (0, 1)

What is Vector?

A vector is a object that has both magnitude (size) and direction. In other words, a vector is a quantity that can be represented by an arrow or line segment, where the length of the arrow corresponds to the magnitude of the vector.

To find the vectors that join the center of a clock with radius 1 unit to the hours 1:00, 2:00, and 3:00, we can use basic trigonometry.

First, we can find the angle (in radians) between the 12:00 position and each of the desired hour positions. Since there are 12 hours on a clock and the circle has a circumference of 2πr = 2π(1) = 2π, the angle between each hour mark is:

2π/12 = π/6 radians

Therefore, the angles between the center of the clock and the hour marks are:

At 1:00, the angle is π/6 radians clockwise from the 12:00 position.

At 2:00, the angle is 2π/6 = π/3 radians clockwise from the 12:00 position.

At 3:00, the angle is 3π/6 = π/2 radians clockwise from the 12:00 position.

Next, we can use the cosine and sine functions to find the x and y components of each vector. The x-component of each vector is given by the radius times the cosine of the angle, and the y-component is given by the radius times the sine of the angle.

Therefore, the vectors that join the center of the clock to the hours 1:00, 2:00, and 3:00 are:

At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)

At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)

At 3:00: (cos(π/2), sin(π/2)) = (0, 1)

Note that these vectors are unit vectors, meaning that they have a length of 1 unit.

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Answer:

Step-by-step explanation:

36

Answer:

2x²- 10x + 8

3x² - x - 4

Step-by-step explanation:

Answer:

hope this helps..........

The missing angles are sides are;

We can see that we would have to first apply the cosine rule here;

[tex]a^2 = b^2 + c^2 - 2abCos A\\a^2 = (17)^2 + (19.6)^2 - 2(17 * 19.6)Cos 30\\a^2 = 673.16 - 666.4Cos 30[/tex]

a = 9.8

We can now apply the sine rule to obtain the angle B

[tex]a/Sin A = b/Sin B\\SinB = bSin A/a\\B = Sin-1 ( bSin A/a)\\B = Sin-1(17 * Sin 30/9.8)[/tex]

B = 60

Then;

C = 180 - (30 + 60)

C = 90 degrees

Thus the triangle in the problem have been solved.

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Answer:

f(x) = 2(x + 1)² + 1

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

given

f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms

    = 2(x² + 2x) + 3

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 2x

f(x) = 2(x² + 2(1)x + 1 - 1) + 3

     = 2(x + 1)² - 2(1) + 3

     = 2(x + 1)² - 2 + 3

    = 2(x + 1)² + 1 ← in vertex form

55/63 is already in its simplified form.

To simplify 55/63, we can divide both the numerator and denominator by their greatest common factor (GCF). To find the GCF of 55 and 63, we can use prime factorization:

55 = 5 × 11

63 = 3 × 3 × 7

The common factors of 55 and 63 are 1, so the GCF is 1. We can divide both the numerator and denominator by 1:

55/1/63/1

Therefore, 55/63 in simplest form is 55/63.

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The requried side length of the square is approximately 9.695 units.

To find the side length of a square with an area of 94 square units, we need to take the square root of the area.

a² = 94
a = √94

a ≈ 9.695

Therefore, the side length of the square is approximately 9.695 units.

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For a 10,000 linear feet of fencing and wants to enclose a rectangular field, the maximum area of each pasture is equals to the 2,083,333.33 square feet .

A rancher wants to enclose about 10,000 linear feet of fencing in a rectangular field. There are two equal pastures. Let, W the Width and L the Length with 3 pieces. The total length will be equal to 2W + 3L. As we know, the Area of rectangle, A = L×W ---(1)

Perimeter of rectangle = 10,000 feet, so sum of all sides of rectangle, 2W + 3L = 10000

Solve for determining value of L, 3L

= 10000 - 2W

[tex]L = \frac{ 10000 - 2W }{3}[/tex]

Substitutes for L into the first equation, A = L×W

[tex]A = W(\frac{ 10000 - 2W }{3})[/tex]

For maximum area, set the 1st derivative = 0.

differentiating above Area equation w.r.t W,[tex] A = \frac{(10000 \: W - 2W^2)}{3}[/tex]

[tex] \frac{dA}{dW} = \frac{d(\frac{10000 \: W - 2W^2}{3})}{dW}[/tex]

=> [tex]\frac { 1}{3}(10000 - 4W) = 0 [/tex]

=> W = 2500 meters

Now, using above relation, 2W + 3L= 10000

=> 5000 + 3L = 10000

=> 3L = 5000

=> L = 1667 meters

Area = 2500× 5000/3 = 4,166,666.67 sq feet. Now, maximum area of each pasture

= 4,166,666.67/2 = 2,083,333.33333 sq. feet. Hence, required value is 2,083,333.33 sq. feet.

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Answer:

The radius of the circle is 3, so

Circumference = 2(3)π = 6π = 18.84

Area = π(3^2) = 9π = 28.26

AC and BD are  the diagonals of the MNOP, the diagonals of the rectangle MNOP bisect each other and are congruent.

 A rectangle and a rectangle  are quadrilaterals that share the following properties: Opposite sides are equal. Two diagonals are the same length. It has two  class 2 reflection symmetries and a rotational symmetry (through 180°).  To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following proof:

Proof:

Let MNOP be a rectangle whose diagonal MO and diagonal NP intersect at  Q.

First we  show that the diagonals bisect each other. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, we can draw segment MP and segment NO which are both parallel  and congruent to each other.

Now consider the triangle MON. Since segment MP is parallel to segment NO, we know that angles MNO and MON are alternate interior angles and are congruent. Similarly, the angles NMO and ONM are also congruent. Therefore, triangle MON is an isosceles triangle with legs MO and NO. This means that the height drawn from Q to the side MN (which is the perpendicular bisector of MO and NO) bisects MO and NO. Similarly, the height drawn from Q to the side OP bisects OP. Therefore we have shown that the diagonals of a rectangle bisect each other.

 Next, we  show that the diagonals are congruent. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, MP is compatible with NO and MO is compatible with NP. Using the fact that the diagonals bisect each other, we can write:

MQ = QO (because the height drawn by Q to the side MN divides MO and NO)

and

NQ = QP (because the height drawn from Q to the side OP divides NP and MO)

Combining these two equations, we get:

MQ + NQ = QO + QP

But we also know that MO is NP-consistent, so we can substitute:

MQ+ NQ = MO + MO

Simplification:  

MQ + NQ = 2MO

Therefore, we have shown that the diagonals of a rectangle are congruent.  Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent as necessary.

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Understanding the meaning of addition and subtraction will allows us to make predictions about how changing the value of a variable will affect the value of an expression.

In mathematics, integers are a set of whole numbers that include both positive and negative numbers, as well as zero. The set of integers is denoted by the symbol Z, and it includes all the natural numbers (1, 2, 3,...), their negatives (-1, -2, -3,...), and zero (0). Integers are used in a variety of mathematical contexts, including algebra, number theory, and geometry. Integers can be used to represent many real-world situations, such as temperatures above or below zero, changes in altitude, gains or losses in money, and more. They are also used extensively in computer programming and other fields that rely heavily on mathematics.

Knowing what addition and subtraction mean allows you to understand how changing the value of a variable can affect the value of an expression.

For example, consider the expression x + 2. If x has a value of 3, then the value of the expression is 5. However, if x increases to 4, then the value of the expression increases to 6. This is because we are adding 2 to the value of x.

On the other hand, if we have the expression x - 2 and x has a value of 3, then the value of the expression is 1. If x increases to 4, then the value of the expression decreases to 2. This is because we are subtracting 2 from the value of x, so as x increases, the value of the expression decreases.

Understanding the meaning of addition and subtraction is essential to be able to manipulate expressions and variables, and it allows us to make predictions about how changing the value of a variable will affect the value of an expression.

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The account value after forty years is approximately $489,074,140.57.

To calculate the account value after forty years, we need to use the formula for the future value of an annuity:

[tex]FV = P * [(1 + r)^n - 1] / r[/tex]

where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods.

In this case, we have:

P = $3,000 in year 1, and then $3,300 in year 2, $3,600 in year 3, and so on

r = 8.35% = 0.0835 (assuming the interest rate is compounded annually)

n = 40 years

To compute the future worth of the annuity, we really want to ascertain the aggregate sum of installments over the 40 years. This should be possible involving the equation for the amount of a number-crunching series:

S = n/2 * [2a + (n-1)d]

where S is the sum, a is the first term, d is the common difference, and n is the number of terms.

In this case, we have:

a = $3,000

d = $300

n = 40

Plugging these values into the formula, we get:

S = 40/2 * [2($3,000) + (40-1)($300)] = $2,340,000

Thus, the aggregate sum of installments more than 40 years is $2,340,000.

We can now enter these figures into the formula for annuity future value:

[tex]FV = P * [(1 + r)^n - 1] / r[/tex]

[tex]FV = $2,340,000 * [(1 + 0.0835)^{40} - 1] / 0.0835[/tex]

FV = $2,340,000 * 209.251

FV = $489,074,140.57

Consequently, after forty years, the account's value is approximately $489,074,140.57.

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slope= y2 - y1/ x2 - x1 ( take (-4, -6) as 1 and (8,9) as 2 where 9 and -6 are y2 and y1 respectively and 8 and -4 as x2 and x1 respectively)

- slope = 9 - (-6) / 8 - (-4)= 9 + 6/ 8 + 4

- slope = 15 / 12 (simplify)

- slope = 5/ 4

Step-by-step explanation:

'3'  is greater than 0     so we use the second portion of f(x)

f(3) =   x+1

     =   3 + 1   = 4  

The correct list of functions ordered from 0 ≤ x ≤ 3 is:

h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x

Line connecting the interval's endpoints in order to compute the average rate of change for each function over range 0 x 3.

For f(x) = x^2, the slope between x = 0 and x = 3 is:

[tex](f(3) - f(0)) / (3 - 0) = (9 - 0) / 3 = 3[/tex]

For g(x) = 2x + 1:

[tex](g(3) - g(0)) / (3 - 0) = (7 - 1) / 3 = 2[/tex]

For h(x) = sin(x):

[tex](h(3) - h(0)) / (3 - 0) = (sin(3) - sin(0)) / 3[/tex] ≈ 0.279

For k(x) = e^x, the slope between x = 0 and x = 3 is:

[tex](k(3) - k(0)) / (3 - 0) = (e^3 - 1) / 3[/tex] ≈ 6.076

Therefore, correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3 is:

[tex]h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x[/tex]

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--The complete Question is, Consider the following four functions:

f(x) = x^2

g(x) = 2x + 1

h(x) = sin(x)

k(x) = e^x

What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3? --

To discover the t-value for testing a person parameter at the 1% level, we ought to isolate the coefficient appraise by its standard deviation and compare it to the t-distribution with suitable degrees of flexibility.

For case, to test the parameter gauge for x1, we would calculate the t-value as: t = (-3.682) / 2.630 ≈ -1.4

At that point compare this t-value to the t-distribution with 485 degrees of flexibility (which compares to the leftover degrees of opportunity), and decide on the off chance that it surpasses the basic esteem at the 1% level (which is around 2.977).

In any case, the given yield does not demonstrate which parameter appraise is being tried, so we cannot decide the comparing t-value. Hence, none of the reply choices are rectified.

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Answer:

20 3/5

Step-by-step explanation:

this is the correct result when 30 9/10 is multipled by 2/3

The simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.

To find the ratio of corydoras catfishes to the total number of fish, we need to add up the number of corydoras catfishes to the total number of fish, and express the ratio as a simplified fraction.

The total number of fish is 7 + 12 + 4 + 11 = 34.

The ratio of corydoras catfishes to the total number of fish is 9:34.

To simplify this ratio, we can divide both sides by the greatest common factor, which is 1 in this case.

So the simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.

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the total amount of water lost between 9 and 11 am is 5 liters.

To find out how much water is lost between 9 and 11 am, we need to calculate the total amount of water that leaks out during that time period.

First, we need to find the number of hours between 7 am and 9 am, which is 2 hours. Similarly, the number of hours between 7 am and 11 am is 4 hours.

Next, we can use the given rate of water leakage to calculate the amount of water lost during each of these time periods:

Amount of water lost between 7 am and 9 am:

2.5 liters/hour × 2 hours = 5 liters

Amount of water lost between 7 am and 11 am:

2.5 liters/hour × 4 hours = 10 liters

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Answer:

141 degrees

Step-by-step explanation:

First find the value of the other interior angle that is not shown. To find it u add 108 n 33 which gives you 141

Then subtract 141 from 180 which gives u 39 degrees

After subtract 39 from 180 which gives you 141 degrees

The confidence interval for the difference in average lifespan between the two groups of children (-43, 9) years includes 0, which means that we cannot conclude with confidence that there is a significant difference between the two groups.

Since the confidence interval includes negative values, we cannot even conclude that the garlic pills were beneficial in prolonging the life of the children. It is possible that the garlic pills had no effect or even a harmful effect on the lifespan of the children.

Therefore, based on this information, we cannot conclude that garlic pills are effective in prolonging the life of children with deliops disease. Further research would be needed to determine whether garlic pills have any beneficial effects on the lifespan of these children.

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The graph that correctly displays the data is this: C. bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

A graph plots values to show the relationship between two variables often depicted by the x and y axes. The correct graph to display this data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students."

The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.

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The coordinates of the point which is an outlier would be ( 14, 13).

The correlation between the 13 British towns is Linear.

The number of hours of sunshine for the British town with the maximum of 17.4 degrees Celsius is 13 hours of sunshine.

The coordinates of the outlier would be ( 14, 13). This is because, that point on the graph is far from the other points and does not follow their correlation.

The rest of the towns seem to be increasing in the same direction so they are linear.

The number of hours of sunshine in the British town with the maximum temperature of 17.4 degrees Celsius, based on the line of best fit drawn, would be 13 hours of sunshine.

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Full question is:

The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.

A line of best fit has also been drawn.

One of the points in an outliner.

a) Write down the coordinates of this point. (1)

b) For all the other points write down the type of correlation in just one word. (1)

On the same day, in another British town, the maximum temperature was 17.4C.

c) Estimate the number of hours of sunshine in this town on this day. (2)