Find the future value P of the amount Po=$100,000 invested for time period t= 5 years at interest rate k= 7%, compounded continuously. *** If $100,000 is invested, what is the amount accumulated after 5 years? (Round to the nearest cent as needed.)

The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.

If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.

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Answer:5/28

Step-by-step explanation:

multiply 2/8 by 5/7

(a) To find the elasticity of demand E(p), we need to compute the derivative of the demand function D(p) with respect to price p and then multiply by the ratio of price to demand:
E(p) = (dD(p)/dp) * (p / D(p))
First, let's find the derivative of D(p) with respect to p:
D(p) = 6000e^(-0.02p)
dD(p)/dp = -0.02 * 6000e^(-0.02p) = -120e^(-0.02p)

Now, we can compute E(p):
E(p) = (-120e^(-0.02p)) * (p / (6000e^(-0.02p)))
E(p) = -120p / 6000
E(p) = -p / 50

(b) Now, we can determine whether the demand is elastic, inelastic, or unit-elastic at the price p = 30:
E(30) = -30 / 50 = -0.6

Since the absolute value of E(p) is less than 1 (0.6 < 1), the demand is inelastic at the price p = 30. So the correct answer is:
b. -inelastic

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Answer:

t=5

Step-by-step explanation:

y represents height above the ground.

so when it touches the ground height above the ground =0

y=-16t²+80 t

it will hit the ground when y=0

-16t²+80t=0

-16t(t-5)=0

either t=0 or t-5=0

or t=5

t=0 gives initial value.(rejected)

t=5

Answer:

98 units.

Step-by-step explanation:

Circumference = 2 * pi * radius

615.44 = 2 * 3.14 * r

r = 615.44 / (2 * 3.14)

 =2 * 3.14

 = 98 units.

Answer:

p=-13

-13+16=3

As a result of this, 20,160 different words can be made from the letters inside the word multiply.

There are three distinct sorts, classes, groups, and categories. The two plants are very different from one another (from one another). Every herb has a unique flavor. The phrase can signify one of three things.

The word MULTIPLY has 8 letters. To find the number of distinct words that can be formed, we can use the formula for permutations with repeated elements:

n!/(n1!n2!...nk!)

where n is the total number of items, and n1, n2, ..., nk are the numbers of times each item is repeated.

In this case, there are 8 letters, but the letter L appears twice. So we have:

n = 8

n1 = 2 (for the L's)

n2 = n3 = ... = nk = 1 (for the other letters)

Substituting into the formula, we get:

8!/(2!1!1!1!1!1!1!) = 8×7×6×5×4×3 = 20160

As a result of this, 20,160 different words can be made from the letters inside the word multiply.

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To answer this problem we have to remember that the break even point occur where the revenue function and the cost function have the same value.

Then, this happens when

Pluggin the expressions of our functions and solving for x we have:

Therefore the break even point occurs when x=74000. In this points both functions have value

To solve this problem, we can use the binomial distribution formula, which calculates the probability of a certain number of successes (in this case, business travelers who say their reason for the trip was an internal company visit) out of a given number of trials (950 business travelers). The formula is:
P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where:
- P(x) is the probability of getting x successes
- n is the number of trials (950 business travelers)
- x is the number of successes we're interested in (between 133 and 171)
- p is the probability of success (19% or 0.19)

To find the probability that between 133 and 171 business travelers say their reason for the trip was an internal company visit, we need to calculate the sum of the probabilities of getting 133, 134, 135,..., 170, 171 successes. This can be quite tedious to do by hand, but fortunately, we can use a calculator or a statistical software program to do it for us.

Assuming that we use a calculator or software, we can find that the probability of getting between 133 and 171 business travelers who say their reason for the trip was an internal company visit is approximately 0.919. This means that out of three random paragraphs of this length, it's likely that one would show the probability of the business travelers who say their reason for the trip was an internal company visit to be between 133 and 171.

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Answer:

About 55.9 degrees

Step-by-step explanation:

The cosine of an angle is equivalent to the length of the adjacent side divided by the length of the hypotenuse. Therefore:

\(\cos x= \dfrac{14}{25} \\\\x=\cos^{-1}\left( \dfrac{14}{25}\right) \approx 55.9\)

Hope this helps!

Answer:

a) 39 meters

b) t = 1.8 seconds

Step-by-step explanation:

a)

To find the starting height of the riders, we just need to use the value of t = 0 in the equation of h(t):

h(0) = -9.8*0^2 - 5*0 + 39

h(0) = 39 meters

b)

To find when the height will be equal 0, we just need to use the value of h(t) = 0 and then find the value of t:

0 = -9.8*t^2 - 5*t + 39

Delta = b^2 - 4ac = 25 + 4*39*9.8 = 1553.8

sqrt(Delta) = 39.418

t1 = (5 + 39.418)/(-2*9.8) = -2.2662 s (A negative value for the time is not suitable for the problem)

t2 = (5 - 39.418)/(-2*9.8) = 1.756 s

Rounding to nearest tenth, we have t = 1.8 s

The relationship between chocolate sales and student happiness can be tested using the mean difference.

Specifically, a statistical test such as a correlation analysis or regression analysis can be used to examine the relationship between the amount of chocolate sales and the level of student happiness.

The mean difference refers to the difference in the average level of student happiness between two groups, such as those who consume more chocolate and those who consume less chocolate. This can help determine if there is a significant association between chocolate consumption and student happiness.

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The corresponding angles and sides of the two triangles need to be given in order to prove congruence by side-angle-side.

In order to prove congruence by side-angle-side, the corresponding angles and sides of the two triangles must be given. The sides must be proportional, which means that two sides of one triangle must be equal to two sides of the other triangle, and the angles between these two sides must also be equal. In other words, if two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal, then the two triangles are congruent. This can be expressed as “If two sides and the included angle of one triangle are equal to the corresponding sides and angle of a second triangle, then the two triangles are congruent.” In order to prove congruence by side-angle-side, all of the corresponding sides and angles must be given in order to show that they are equal.

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The additional information that is needed to prove the triangles are congruent by Side-Angle -Side us that the corresponding angles and sides of the two triangles need to be given .

What is Side-Angle-Side Congruence ?

The Two Triangles can be called as  Congruent by Side-Angle-Side rule  if any 2 sides and angle included between sides of one triangle is equivalent to corresponding 2 sides and angle between sides of second triangle .

In order to prove the Congruence by Side-Angle-Side, the corresponding angles and the sides of the 2 triangles must be given.

The sides must also be in proportional, that means that the two sides of one triangle must be equal to two sides of other triangle, and

the angles between these two sides of the triangle must  be equal.

So , In order to prove a triangle congruent by Side-Angle-Side, all of the corresponding sides and angles must be given in order to prove  that they are equal.

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(a) (i) 0.3174 = 31.74% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 317.

(b) (i) 0.0026 = 0.26% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 3.

(C) Reduces the process standard deviation and causes no change in the number of defects.

When the distribution is normal, we use the z-score formula.

In a set with mean  and standard deviation, the score of a measure X is given by:

         Z = X-μ /σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

We have that: μ = 10 and σ = 0.12

(i). Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

  Z = X-μ /σ

⇒ Z = 9.88 - 10/0.12

⇒ Z = -1, has a p-value of 0.1587

⇒ 2× 0.1587 = 0.3174

This means 0.3174 = 31.74% probability of a defect

(ii)  Calculate the expected number of defects for a 1,000-unit production run.

The expected number of defects is 31.74% of 1000. So

0.3174*1000 = 317.4

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 317.

Question (b):

The mean remains the same, but the standard deviation is now

(i) Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

   Z = X-μ /σ

⇒ Z = 9.88 -10/0.04

⇒ Z = -3

⇒ Z = -3, has a p-value of 0.0013

which means 2× 0.0013 = 0.0026

from which 0.0026 = 0.26% probability of a defect

(ii) Calculate the expected number of defects for a 1,000-unit production run. The expected number of defects is 31.74% of 1000. Thus,

⇒ 0.0026*1000 = 2.6

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 3.

(C) The advantage of reducing process variation, thereby causing problem limits to be at a greater number of standard deviations from the mean Reduces the process standard deviation and causes no change in the number of defects.

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Answer:  c

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = w h l

V = 7.5 * 7.5 * 6

V = 337.5cubic feet * 0.05

V = 16.875Lbs

V = 17Lbs (Rounded to nearest pound)

Answer:

RH = 8.2 units

Step-by-step explanation:

total circumference = 2rπ = 2(10)(3.14) = 62.8 units

RH = (47°/360°)(62.8) = 8.2 units

Answer:

Step-by-step explanation:

5- -4=1 +3=4

For two different values of r, the function y(t) = tr satisfies the differential equation t²y'' - 8ty' + 14y = 0. The two values of r are:2, 7

We can solve the given differential equation by using the method of characteristic equations. The characteristic equation is: r² - 8r + 14 = 0. Solving this quadratic equation gives: r = (8 ± √(8² - 4*1*14))/2r = (8 ± √4)/2r₁ = 2r₂ = 7.

Now, let's find the solution of the differential equation for each value of r:For r = 2:Let y = t². Putting it into y = tr, we have y = 2t². Therefore, the solution for r = 2 is: y(t) = 2t².

For r = 7: Let y = t⁷. Putting it into y = tr, we have y = 7t⁷. Therefore, the solution for r = 7 is: y(t) = 7t⁷. Thus, the two values of r are 2 and 7.

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The boats are approximately 9.4 units apart.

To find the distance between two points in a coordinate plane, we can use the distance formula:

distance =\(\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

Using this formula, we can find the distance between Boat A at (4.2, -2) and Boat B at (-5.2, -2):

distance = \(\sqrt{((-5.2 - 4.2)^2 + (-2 - (-2))^2)}\)

distance = \(\sqrt{((-9.4)^2 + (0)^2)}\)

distance =\(\sqrt{(88.36)}\)

distance ≈ 9.4

Therefore, the boats are approximately 9.4 units apart.

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Answer:

4.5 seconds

Step-by-step explanation:

subtraction 38.4 - 33.9 is the difference in the race times

note some teachers mark off if you don't put the units (seconds in this case) in your answer

Answer:

there are 40% black ball a

white ball we don't know

so, we let = x

40\100 × x

now we cutting

ans is 10x

Lengths of time it takes for new light bulbs to burn out are an example of continuous numerical data type.

Quantitative information that can be measured precisely and that can take on any value within a range is known as continuous numerical data. Measurements of length, time, weight, temperature, and many other quantifiable physical qualities are examples of continuous numerical data.

Continuous numerical data can have any value as long as it falls within a specified range, and using mathematical operations like addition, subtraction, multiplication, and division, it is possible to compare and analyze the numbers.

Since it alludes to a continuous range of precise numerical values. The duration of time in this scenario is expressed in hours, minutes, or seconds and can have any value within a specific range, for example, 0.5 hours, 1.25 hours, 2.75 hours, and so on.

Numerical data types like float and decimal can be used to represent continuous numerical data.

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Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.

We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:

( 3, 4 ) and ( − 2, 1 )

We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.

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The data set is 2, 7, 7, 8, 9, and 9, with a mean of 7. The outlier is 2, and the mean without the outlier is 6.6. The outlier pulls the mean lower than the center, but once removed, the mean becomes more representative of the data set.

To find the mean of a set of values, we add up all the values and divide by the total number of values.

In this case, we know that the mean of six values is 7, so we can set up the following equation

(2 + 7 + 7 + 8 + 9 + 9) / 6 = 7

Simplifying the equation, we get

42 / 6 = 7

So, the sum of the six values is 42.

Now, we know that there is one outlier that pulls the mean higher than the center. In other words, one of the values is much larger than the others. Let's assume that the outlier is 20.

So, the new sum of the six values would be

2 + 7 + 7 + 8 + 9 + 20 = 53

To find the mean without the outlier, we need to subtract the outlier from the sum and divide by the remaining number of values. In this case, there are five values remaining. So, we get

(2 + 7 + 7 + 8 + 9) / 5 = 33 / 5 = 6.6

Therefore, the possible data set is 2, 7, 7, 8, 9, and 9, and the mean without the outlier is 6.6.

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--The given question is incomplete, the complete question is given

" The mean of six values is 7. There is one outlier that

pulls the mean higher than the center. What could the

data set be? What is the mean without the outlier?  

The possible data set is 2, 7, 7, 8, 9, and 9. "--

Answer:

Step-by-step explanation:

What is the question?

g(x) = -0.5x² + 4x - 2 is a down-opening parabola. Do you need to know how to put it in vertex form?

vertex (4,6)

focus (4,5.5)

Answer:

The answer is 65.1844660194175...

The value of the function (f - g)(x) would be \((f-g)(x)=x^2-11x+4\).

Option (A) is correct.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.'

Given:

                \(f(x)=4x^2-5x\\\\g(x)=3x^2+6x-4\)

Now by using the definition of composite functions we can write,

      \((f-g)(x)=f(x)-g(x)\\\\(f-g)(x)=4x^2-5x-(3x^2+6x-4)\\\\(f-g)(x)=4x^2-5x-3x^2-6x+4\\\\(f-g)(x)=x^2-11x+4\)

Hence, the value of the function (f - g)(x) would be \((f-g)(x)=x^2-11x+4\).

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