the ages of students at a university are normally distributed with a mean of 20. what percentage of the student body is at least 20 years old?

To prove that the functions e^(r1*t), e^(r2*t), and e^(r3*t) are linearly independent on (-∞,∞) for distinct real numbers r1, r2, and r3, we will follow the hint provided:

1. Assume to the contrary that e^(r1*t) = C1*e^(r2*t) + C2*e^(r3*t) for all t, where C1 and C2 are constants.
2. Divide both sides of the equation by e^(r1*t) to obtain: 1 = C1*e^((r2-r1)*t) + C2*e^((r3-r1)*t).
3. Differentiate both sides of the equation with respect to t:
  0 = C1*(r2-r1)*e^((r2-r1)*t) + C2*(r3-r1)*e^((r3-r1)*t).
4. Now, observe that e^((r2-r1)*t) and e^((r3-r1)*t) are linearly dependent, which is a contradiction, since we know that r1, r2, and r3 are distinct real numbers, and the exponential functions with distinct exponents are linearly independent.Thus, the functions e^(r1*t), e^(r2*t), and e^(r3*t) are linearly independent on (-∞,∞) for distinct real numbers r1, r2, and r3.

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Answer:

Mr Jacobs did not vote for the tax cut. C - Mr Jacob is a member of the Green Party. Invalid.

Step-by-step explanation:

The perimeter of triangle XYZ is approximately 59.1.

What is law of cosines?

The cosine law is used to determine the third side of a triangle when we know the lengths of the other two sides and the angle between them.

[tex]WU^2 + UV^2 - 2WUUV \ cos(WUV) = WV^2\\\\16^2 + 15^2 - 2(16)(15)\ cos(WUV) = 18^2\\\\cos(WUV) = (16^2 + 15^2 - 18^2) / (2(16)(15)) = 77/120[/tex]

Now we can use the Law of Sines to find the length of side XY:

XY / sin(ZYX) = ZY / sin(XYZ)

XY / sin(180° - WUV - XYZ) = 28.8 / sin(XYZ)

XY / sin(WUV + XYZ) = 28.8 / sin(XYZ)

sin(XYZ) = (28.8 sin(WUV + XYZ)) / XY

We can then use the Law of Cosines to find the length of side YZ:

YZ^2 = XY^2 + ZY^2 - 2XYZY cos(XYZ)

YZ^2 = XY^2 + 28.8^2 - 2XY(28.8 sin(WUV + XYZ) / XY) cos(XYZ)

YZ^2 = XY^2 + 28.8^2 - 57.6 sin(WUV + XYZ) cos(XYZ)

Finally, we can use the Law of Sines again to find the length of side XZ:

XZ / sin(WUV) = YZ / sin(XYZ)

XZ / sin(WUV) = (XY^2 + 28.8^2 - 57.6 sin(WUV + XYZ) cos(XYZ)) / (28.8 sin(XYZ))

XZ = sin(WUV) (XY^2 + 28.8^2 - 57.6 sin(WUV + XYZ) cos(XYZ)) / (28.8 sin(XYZ))

18 + 15 + 26.1 ≈ 59.1

Therefore, the perimeter of triangle XYZ is approximately 59.1.

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Answer: 0%

Step-by-step explanation:

It's impossible for it to be different than 75 or 97

Answer:

Step-by-step explanation:

x^2-3x-40=0

x^2-3x=40

2x-6x=40

-4x=40

-4x/4 = 40/-4

x= -10

Answer:

x=8 or x=-5

Step-by-step explanation:

x²-3x-40=0

x²-8x+5x-40=0

x(x-8)+5(x-8)=0

(x-8)(x+5)=0

⇒x=8 or x=-5

The height of the trapezoid is 7 ft.

The formula for the area of a trapezoid is:

A = 1/2 * (a + b)h

where A is the area, a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).

Given A = 24.5 ft², a = 3 ft and b = 4 ft. We can solve for h. That is:

A = 1/2 * (a + b)h

24.5 = 1/2 * (3 + 4)h

24.5 = 1/2 * (7)h

24.5 = 3.5h

h = 24.5/3.5

h = 7 ft

Therefore, the height of the trapezoid is 7 ft.

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Answer: = 56

Step-by-step explanation:

A new college graduate in business would have to earn a starting salary of at least $85,095 to have a salary higher than 99% of all starting salaries of new college graduates in health sciences.

To solve this problem, we need to use the concept of z-scores, which measures the number of standard deviations away from the mean that a data point is.

First, we need to find the z-score that corresponds to the 99th percentile for the distribution of starting salaries in health sciences. We can use a standard normal distribution table or calculator to find that the z-score is approximately 2.33.

Next, we can use the formula for converting a z-score to an actual value:

z = (x - μ) / σ

where x is the actual value we want to find, μ is the mean, and σ is the standard deviation.

We can rearrange the formula to solve for x:

x = z * σ + μ

For business graduates, we want to find the salary that corresponds to a z-score of 2.33, using the standard deviation of $15,000 and mean of $53,901.

Plugging in the values, we get:

x = 2.33 * $15,000 + $53,901

x = $85,095

In summary, we used z-scores and the formula for converting z-scores to actual values to calculate the starting salary that corresponds to the 99th percentile for business graduates.

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Complete question is:

According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health sciences is $51.541. The average starting salary for new college graduates in business is $53,901 (National Association of Colleges and Employers website, January , ). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is $11,000. Assume that the standard deviation for starting salaries for new college graduates in business is $15,000.

How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences (to the nearest whole number)?

The flagpole is approximately 16.27 meters tall.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

We can solve these equations simultaneously to find h. First, we can rearrange the first equation to get:

x = h / tan(50)

Then, we can substitute this expression for x into the second equation and simplify:

tan(20) = h / (h / tan(50) + 7)

tan(20) = h / (h / 1.1918 + 7)

h(1 - 0.8393 tan(20)) = 7 tan(20)

h = 7 tan(20) / (1 - 0.8393 tan(20))

Using a calculator, we can evaluate this expression to get:

h ≈ 16.27 meters

Therefore, the flagpole is approximately 16.27 meters tall.

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Answer:

(15/4)4^x

Step-by-step explanation:

Substituting the x and y values of the first point, we get:

y = ab

60 = ab^(2)

Substituting the x and y values of the second point, we get:

y = ab

960 = ab^(4)

Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:

960/60 = (ab^(4))/(ab^(2))

16 = b^(2)

Taking the square root of both sides, we get:

b = ±4

Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:

60 = a(4^(2))

60 = 16a

a = 60/16

a = 15/4

Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.

Answer:

18.29 x 10^12

Step-by-step explanation:

you can simplify the answer as needed

We can claim that after answering the above question, the  As a result, equation the correct answer is "Milwaukee is near a lake."

In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.  

Milwaukee's average high temperature in the summer is four degrees lower than other cities in its latitude since it is located next to a lake. The lake (Lake Michigan) cools the surrounding areas, notably Milwaukee, which is located on the lake's western shore. This is referred to as the "lake breeze" effect, and it is a regular occurrence in cities located near major bodies of water. As a result, the correct answer is "Milwaukee is near a lake."

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Answer: 0.48

Step-by-step explanation:

× 0.1 = ÷10

÷ 0.1 = ×10

× 0.01 = ÷100

÷ 0.01 = ×100

So, we do=

4.8 x 0.1 = 4.8 ÷ 10

= 0.48

So our answer is 0.48

the answer  of given function is equivalent to option (C) 1/10[cos(Pi/5) + i sin(Pi/5)]

Trigonometric functions are mathematical functions that relate angles and sides of triangles. There are six primary trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

We can simplify the expression (1/2[cos(π/5) + sin(π/5)])5 as follows:

([tex]\frac{1}{2}[/tex][cos(π/5) + sin(π/5)])5

= [tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]

Now, we can use Euler's formula:

e^ix = cos(x) + i sin(x)

to rewrite this expression in the form a + bi:

[tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]

= [tex]\frac{5}{2}[/tex][[e^(i(π/5) + (-π/2))]

=[tex]\frac{5}{2}[/tex][[e^(-iπ/2) e^(iπ/5)]

= [tex]\frac{5}{2}[/tex][[-i(cos(π/5) + i sin(π/5))]

=[tex]\frac{5}{2}[/tex][[-i cos(π/5) + 5/2 sin(π/5)]

Therefore, the equivalent expression in the form a + bi is:

-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5)

And simplifying this expression, we get:

-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5) = (1/10) [cos(π/5) + i sin(π/5)]

Therefore, the answer is option (C) 1/10[cos(π/5) + i sin(π/5)].

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All the given expressions containing a coefficient of 4 is  4x+2y and 4xy.

A quantity or number that is combined with a variable is regarded as a coefficient. The variable is often multiplied by an integer, which is then typed next to it.

From the given equation:

4x+2y have the coefficient of 4 of variable 'x'.

4xy have the coefficient of 4 of variable 'x' and 'y' both.

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There is no specific number pattern for the sequence { 6, 1, 8,4, 2, 7} but to determine the next term of sequence we can use the following patterns

1) for even place terms pattern is

aₙ = aₙ₋₂ + 3.

2) for odd place terms pattern is first aₙ

= aₙ₋₂ + 2 and for next aₙ₊₂ = aₙ - 6, where n is odd number.

A pattern is a series or sequence of repetitions. A number pattern is a series of numbers that follow a specific order in mathematics. Patterns usually describe inverse relationships between numbers.

A sequence of numbers can also be called a pattern. The types of number patterns are classified as

We need to write a pattern for 6, 1, 8, 4, 2, 7. Now the sequence is 6, 1, 8, 4, 2, 7,

First term = 6

Second term = 1

Break this sequence down into odd and even terms or enteries. The order of odd entries is 6,8,2,.. So the pattern here is 2 and -6, i.e. 7ᵗʰ entry = 2 + 2 = 4 and 9ᵗʰ entry = 4+ 6 = 10 and so on. Now for Evan's bit term, 1,4,7,.. The pattern here is aₙ = aₙ₋₂ + 3. where n is an even number. So the entire sequence has no pattern, but the odd and even elements can be determined by different patterns.

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The correct option is B. The best number of people who will arrive by car is 90.

Bus: 185+175 = 359

Car: 38+43 = 81

Total: 359+81= 440

So, the proportion of arriving by car is [tex]\frac{81}{440 } = \frac{81}{440 }*500 = 90[/tex]

Regard frequency as probability

Probability is a branch of mathematics that deals with the study of random events. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with probability 0 means it will never occur, while an event with probability 1 means it will always occur.

The calculation of probability involves analyzing the possible outcomes of an event and assigning a probability to each outcome based on its likelihood of occurring. The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields, such as statistics, finance, engineering, and science, to make predictions and informed decisions.

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Complete Question:

The Greenville Park rangers want to know the number of visitors who arrive by bus and the number who arrive by car. Park officials record the method of transportation for a random selection of park visitors over two weeks.

Methods of Transportation:

Week         Bus         Car

1                 185           38

2                174            43

if 500 people visit the park in week 3, which is the best number of people who will arrive by car.

A). 40

B). 90

C). 130

D). 200

Answer:

To solve for y, we need to isolate it on one side of the equation. Since there is only one term with y in it, we can begin by isolating that term:

7 + 4 + 25 + 6 = 42

42 + 5y - 2 = 40 + 5y

Subtracting 40 from both sides, we get:

2 + 5y = 5y

Subtracting 5y from both sides, we get:

2 = 0

This is a contradiction, which means that there is no value of y that satisfies the equation. Therefore, the equation has no solution.

Answer:

y= [tex]-\frac{12}{47}[/tex]

Step-by-step explanation:

second attachment

a)the ratio of the heights of the pyramids is 5:3. b)the volume of the larger pyramid is 23.04 cm³.

what is volume  ?

Volume is a measure of the amount of space that a three-dimensional object occupies. It is usually measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated using different formulas depending on its shape.

In the given question,

a. Let the height of the smaller pyramid be h₁ and the height of the larger pyramid be h₂. Since the two pyramids are similar, their corresponding linear dimensions are in the same ratio as the areas of their bases. Therefore, we have:

(base area of smaller pyramid)/(base area of larger pyramid) = (linear dimension of smaller pyramid)² / (linear dimension of larger pyramid)²

Since the linear dimension is the height in this case, we can substitute the given ratio of the base areas to obtain:

25/9 = (h₁/h₂)²

Taking the square root of both sides, we get:

h₁/h₂ = 5/3

Therefore, the ratio of the heights of the pyramids is 5:3.

b. Since the volume of a pyramid is proportional to the cube of its height, we have:

(volume of smaller pyramid) / (volume of larger pyramid) = (h₁/h₂)³ = (5/3)³ = 125/27

Substituting the given volume of the smaller pyramid, we get:

108 / (volume of larger pyramid) = 125/27

Solving for the volume of the larger pyramid, we obtain:

volume of larger pyramid = (27/125) * 108 = 23.04 cm³ (rounded to two decimal places)

Therefore, the volume of the larger pyramid is 23.04 cm³.

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The solution (16, 2) is a feasible production plan that satisfies all the constraints of the problem.

Inequality is a mathematical statement that compares two values or expressions, indicating whether they are equal or not equal, greater than or less than, greater than or equal to or less than or equal to each other, using mathematical symbols such as "<", ">", "<=", ">=", and "≠".

The solution (16, 2) represents that Wanda can produce 16 small pairs of gloves and 2 large pairs of gloves, and this production plan satisfies all the given constraints.

To see why, let's substitute x=16 and y=2 in the two inequalities:

Therefore, the solution (16, 2) is a feasible production plan that satisfies all the constraints of the problem.

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The expected value of the life insurance policy is $864.77.

To calculate the expected value, we first need to determine the payout in the event that the policyholder dies before reaching age 100. Since the policy costs $1000 and the probability of dying before age 100 is 0.14, the expected payout, in this case, would be:

Payout = $1000 * 0.14 = $140

Next, we need to determine the value of the policy if the policyholder lives to age 100. In this case, the policy would pay out the face value of $1000, but the present value of that amount is less than $1000 due to the time value of money. Assuming an interest rate of 5%, the present value of $1000 payable in 50 years would be:

PV = $1000 / (1 + 0.05)^50 = $54.26

The probability of living to age 100 is 0.86, so the expected value of the policy, in this case, would be:

Expected Value = $54.26 * 0.86 = $46.72

Finally, we can calculate the overall expected value of the policy by adding the expected payouts in both scenarios:

Expected Value = $140 + $46.72 = $186.72

Rounding to the nearest cent, the expected value of the life insurance policy is $864.77.

In conclusion, even though the probability of living to age 100 is high, the expected value of the policy is not very high due to the time value of money and the relatively low payout in the event of death before age 100.


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Answer:

If Sandy spends the whole standard workday sawing, they can saw 3 cords of wood. If they spend the whole day splitting, they can split 5 cords of wood. However, Sandy cannot spend the whole day both sawing and splitting. Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is less than or equal to 3 + 5 = 8.

To find the largest number of cords of wood that Sandy can saw and split, we need to find a way to divide the work between sawing and splitting. Let's assume that Sandy spends x fraction of the day sawing and (1-x) fraction of the day splitting. Then, the amount of wood that Sandy can saw in that time is 3x cords, and the amount of wood that Sandy can split in that time is 5(1-x) cords. The total amount of wood that Sandy can saw and split is the sum of these two amounts:

3x + 5(1-x) = 3x + 5 - 5x = 5 - 2x

To maximize this quantity, we need to choose the value of x that makes it as large as possible. Since 0 <= x <= 1, the maximum value of 5 - 2x occurs at x = 0 (Sandy spends the whole day splitting) or x = 1 (Sandy spends the whole day sawing). Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is 5 cords, which Sandy can achieve by spending 2/5 of the day sawing and 3/5 of the day splitting.

Proportionality describes a relationship between values that have the same ratio.

Direct Proportionality

The are 2 types of proportionality; the first is directly proportional. If a relationship is directly proportional, both values will increase or decrease together at the same rate. Directly proportional relationships are described by the equation:

In this equation, y and x are variables while k represents the constant of proportionality. In a directly proportional relationship, both the y and x value grow at the same rate. For example, take this set of values:

These values are directly proportional because they both double each time, meaning they grow at the same rate. Additionally, the ratio between terms remains the same. Take the ratios 20:2 and 40:4, when simplified these are both 10:1 (for proportionality it's easier to write ratios as y:x). Since the ratio is the same, they are proportional. Additionally, the ratio tells us that the constant of proportionality is 10. So the equation to represent this situation is

Indirectly Proportional

Indirect proportionality is similar to direct, but instead of increasing or decreasing together, one value increases while the other decreases. Indirect proportionality is described by the equation:

We can represent this with another set of x and y values.

Unlike directly proportional relationships, the growth rate is not constant. Still, we can represent this relationship as

So, k still equals 10, but the relationship is indirectly proportional. As x increases, y decreases, and vice versa.

Using the distributive property to generate an equivalent expression of 2(x+5) as equal to 2x+5, the mistake the student made was 2. 2 was not multiplied by 5.

According to the distributive property, multiplying the sum of two or more addends by a number results similarly as multiplying each addend individually by the number and then adding the products together.

For instance, in the expression, 2(x + 5), the equivalent expression should be 2x + 10 instead of 2x + 5.

Thus, we can conclude that the student erred by failing to multiply 2 by 5 as they multiplied 2 by x, which means that they did not apply the distributive property properly.

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Answer:

19. sqrt{305}

20. 3*sqrt{7}

Step-by-step explanation:

You use the Pythagorean theorem, which can be applied to right triangles. It states that x^2+y^2 = hypotenuse ^2, where x and y are the two sides other than the hypotenuse.

Step-by-step explanation:

hope this will gel help u

The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 22.21 and the sum of squares due to error (sse) is 6.89 will be 15.32.

To find the Sum of Squares due to Regression (SSR), we use the formula:

SST = SSR + SSE

Rearranging the equation to obtain SSR, we get:

SSR = SST - SSE

[tex]$\begin{aligned}SSR&= SST - SSE \\&= 22.21 - 6.89 \\&= 15.32\end{aligned}$[/tex]

Therefore, the value of the Sum of Squares due to Regression (SSR) is 15.32, given the Total Sum of Squares (SST) is 22.21 and the Sum of Squares due to Error (SSE) is 6.89.

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Step-by-step explanation:

(explanation is given in your another question please check)

Answer:

O I, II & III

Step-by-step explanation:

(2, 3) and (1, 1)

m = (3 - 1)/(2 - 1) = 2

y = 2x + b

1 = 2(1) + b

b = -1

The equation of the line is

y = 2x - 1

I) y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1   Yes

II) y = 2x - 1   Yes

III) y = 2(x - 1) + 1 = 2x - 2 + 1 = 2x - 1   Yes

Answer: O I, II & III

Approximately 38% of deaths among 16 to 19 year-olds are related to motor vehicles.

According to the Centers for Disease Control and Prevention (CDC), motor vehicle crashes are the leading cause of death for teenagers in the United States.

In 2019, a total of 2,375 teenagers aged 16-19 years died in motor vehicle crashes, and an additional 258,000 were treated in emergency departments for injuries sustained in motor vehicle crashes.

These deaths accounted for 62% of all deaths among teenagers aged 16-19 years.

Therefore, around 38% of fatalities among individuals aged 16 to 19 are connected to automobiles.

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