Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students. You may use your calculator to solve.

Answers

Answer 1

Confidence interval for the mean score of all students is (91.679, 98.321)

Given:

Sample mean = 95

Standard deviation = 6.6

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

We have to construct a 99% confidence interval for the mean score of all the students.

Sample Standard Error =

[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]

= 1.205

t-value for the 99% confidence interval = 2.756

(use the t-tables for this)

Margin of error = 2.756 x 1.205 = 3.321

If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.

So, for the 99% confidence interval:

(95 - 3.321, 95 + 3.321) = (91.679, 98.321)

This is the final confidence interval.

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Related Questions

what number is 16 2/3% more than 240

Answers

280 is the number which is 16 2/3% more than 240

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.

(1/6) th of 240 = 240/6 = 40

40 more than 240 = 280

So, 280 is the number which is 16 2/3% more than 240

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A random sample of 75 students at the University of Minnesota spend an average of $614 per month in rent
with a standard deviation of $219. The distribution is moderately skewed to the high end. Which of the
following statements are true?
i. 95% of students at the university spend $564 to $664 on rent.
ii. We are 95% confident that the average rent for students at the university is between $564 and $664.
iii. Because we cannot examine other characteristics of the students in the random sample, it is not
advisable to construct a confidence interval.
Oi only
O ii only
O iii only
Oi and ii
Oi, ii, and iii
Check Answer

Answers

The correct option is b) ii only

From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.

What is meant by distribution?

The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.

What are the 3 types of distribution?

The Three Types of Distribution

Intensive Distribution: As many outlets as possible. The goal of intensive distribution is to penetrate as much of the market as possible.Selective Distribution: Select outlets in specific locations. ...Exclusive Distribution: Limited outlets.

What are the 5 factors of distribution?

Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.

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The function below has at least one rational zero. Use this fact to find all zeros of the function. f(x)=7x^4 +27x^3 -40x^2 +x +5

Answers

The rational zeros of the function can be found using the Rational Zero Theorem. The possible rational zeros of the function are ±1, ±5, ±1/7, ±5/7.

Zeros:

x=-5, -1/7, 0, 1, 5

The Rational Zero Theorem states that if a polynomial function of degree n has integer coefficients, then the possible rational zeros of the function will be of the form ±p/q, where q is a factor of the leading coefficient and p is a factor of the constant term.

In this case, the degree of the polynomial is 4, which means that the leading coefficient is 7 and the constant term is 5. Thus, the possible rational zeros of the function will be of the form ±p/q, where p is a factor of 5 and q is a factor of 7. The factors of 5 are ±1 and ±5, and the factors of 7 are ±1 and ±7. This means that the possible rational zeros of the function are ±1, ±5, ±1/7, and ±5/7.

To find the zeros of the function, we can use the rational zeros we found and plug them into the original equation. We can then solve for the zeros and find that the zeros of the function are x=-5, -1/7, 0, 1, 5.

x=-5: 7(-5)^4 +27(-5)^3 -40(-5)^2 +(-5) +5= 0

x=-1/7: 7(-1/7)^4 +27(-1/7)^3 -40(-1/7)^2 +(-1/7) +5= 0

x=0: 7(0)^4 +27(0)^3 -40(0)^2 +(0) +5= 0

x=1: 7(1)^4 +27(1)^3 -40(1)^2 +(1) +5= 0

x=5: 7(5)^4 +27(5)^3 -40(5)^2 +(5) +5= 0

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Can anyone solve I need help urgent thank you

Answers

Answer:

Step-by-step explanation:

3.14 x 3=9.42

NO LINKS!! Please help me with this problem. Part 8ff​

Answers

Answer:

[tex]\dfrac{1}{36n^2+6n}[/tex]

Step-by-step explanation:

Given factorial expression:

[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]

[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]

Apply the factorial rule to the numerator and denominator of the given rational factorial expression:

[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]

[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]

Answer:

[tex]\cfrac{1}{6n(6n+1)}[/tex]

--------------------------------

We know that:

n! = 1·2·3·4·...·n

Therefore:

(6n + 1)! = (6n - 1)!·6n·(6n + 1)

Therefore:

[tex]\cfrac{(6n-1)!}{(6n+1)!} =\cfrac{(6n-1)!}{(6n-1)!(6n)(6n+1)} =\cfrac{1}{6n(6n+1)}[/tex]

The function f(x)=9.25x + 3 represents the amount radda earns dog walking for X hours

Answers

Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.

How to write a linear function for the total amount of money Radda earns?

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;

T = mx + b

Where:

T represents the total amount of money earned.m represents the rate of change (slope) per hour.x represents the number of hours or time.b represents the y-intercept or initial amount.

Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;

f(x) = T = 9.25x + 3

When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;

f(1) = T = 9.25(1) + 3

f(1) = T = 9.25 + 3

f(1) = T = $12.25.

In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.

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Complete Question:

The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?

Help with this plsssss !!!

Answers

Answer:

58

Step-by-step explanation:

There are 5 lines between 50 and 60

60 - 50 = 10

10 / 5 = 2

This means that each increment is 2.

We see the end of the box plot is above the fourth increment above 50.

4 x 2 = 8

50 + 8 = 58

|x+9|=|-x-9|

How do I solve this equation and graph it?

Answers

The value of x is :

x≤ -9 or x > -9

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

|x+9|=|-x-9|

Both the sides have absolute symbols, consider as below:

x+9 =  -x-9

=> 2x = -9 - 9 = -18

=> 2x = -18

=> x= -9

This means,  x≤ -9 or x > -9

For graph:

consider as below:

y =  |x+9|

y = |-x-9|

graph them without absolute symbols

consider upper v shaped graph. ignore downward v shaped graph

By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).

By plotting and joining those points, we get the graph as shown in the attachment.

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Heights are generally normally distributed. Men have a mean of 69.5 inches and standard deviation 2.4 inches. Women have
a mean of 63.8 inches and standard deviation 2.6 inches. The US Air Force has a height requirement for their pilots to be
between 64 inches and 77 inches.
Make sure you are rounding z-scores properly to two places.
Part A: Find the two z-scores for women who meet this height requirement z =
and z=
I
(larger value)
For Blank 1
Part B: Using the z-scores from part A, find the proportion of women who meet the height requirement. Give this answer as a
decimal.
Z=
(smaller value)
Part C: Find the two z-scores for men who meet this height requirement z =
(larger value)
Part D: Using the z-scores from part C, find the proportion of men who meet the height requirement. Give this answer as a
decimal.
QUESTION 2
(smaller value) and
Part E: If the height requirement were changed to exclude only the shortest 1% of women and tallest 1% of men, what are the
new heights? The short value would be
in inches and the tall value would be
in inches. Please give these two values rounded properly to one decimal place.

Answers

Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.

What is meant by normal distribution curve?

A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.

In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.

According to the normal distribution curve:

"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.

Area from a value (Use to compute p from Z)

Value from an area (Use to compute Z for confidence intervals)

Let the parameters be

Mean 64

Standard deviation 2.75

Above 1.96

Below 1.96

Between 64 and 69.5

Outside -1.96 and 1.96

Area (probability) 0.4772

And that value is 95 % of the whole data

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a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of

Answers

The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]

Given that,

Length of the ladder is, [tex]l=9ft[/tex]

Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.

Now, from triangle ABC,

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

[tex]h^{2} +b^{2} =l^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = 81               (Equation-1)

Differentiating the above equation with respect to time, 't'.

So,

We can write,

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0

[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0

[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0                (Equation-2)

In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.

Let us assume,

h = 3 ft and db/dt = 3 ft/s

We can substitute values in equation-1,

[tex]3^{2} +b^{2}[/tex] = 81

9 + [tex]b^{2}[/tex] = 81

[tex]b^{2}[/tex] = 81-9

[tex]b^{2}[/tex] = 72

b = [tex]\sqrt{72}[/tex]

b = 8.48 ft

Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]

3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0

3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0

3*[tex]\frac{dh}{dt}[/tex] = - 25.44

[tex]\frac{dh}{dt}[/tex] = -25.44/3

[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s

Therefore,

The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

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Which choice is equivalent to the quotient shown here when x > 0?
98x³+√72x²
O A. TV₂
OB. √26x
7x
O C. 7
6
OD. √98x3 - 72x²

Answers

Answer:

A.[tex] \frac{7}{6} \sqrt{x} [/tex]

Step-by-step explanation:

Solution Given:

[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]

Bye using indices formula

[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]

we get

[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]

[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]

[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]

[tex] \frac{7}{6} \sqrt{x} [/tex]

Cone W has a radius of 6 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.
Paul and Manuel disagree on the reason why the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?

Answers

Manuel's argument is correct on why the volume of cone W and  square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.

Define cone and square pyramid

A thick or empty device with an approximately round or elliptical base that tapers to a notch is known as a cone.

on the other hand ,

A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.

Calculation

Cone W has a radius of 6 cm and a height of 5 cm.

The base area of the cone will be

A = πr²

A = π (6)²

A = 113.04 square cm

Then the volume of the cone will be

V = (1/3) x base area x height

V = (1/3) x 113.04 x 5

V = 188.4 cubic cm

Square pyramid X has the same base area and height as cone W.

Then the volume of the square pyramid will be

V = (1/3) x base area x height

V = (1/3) x 113.04 x 5

V = 188.4 cubic cm.

Manuel's argument is correct on why the volume of cone W and  square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.

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Helpp!! GIVING BRAINIEST

Answers

The value of the c in the function c = 19m - 15 when m=10 is 175.

What is a function?

A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.

Given the function;

c = 19m - 15,

where m represents the number of months and c represents the total number of car sent to New York.

To find the value of c:

when m = 10,

Substitute the value of m to the function;

c = 19 (10) - 15

c = 190 - 15

c = 175.

Therefore, the value of c is 175.

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What is the quotient of
102 and 5?

Answers

The leftover after dividing 102 by 5 is the quotient, which is:

Quotient 20

Remainder 2

102 5: Quotient and Remainder

The quotient and remainder method is one way to determine the quotient and remainder of a division. The dividend (102) and the divisor are already known to us (5). Now, we need to determine the residual and the quotient:

The Quotient and Remainder procedure is as follows:

20 quotient, 5 | 102 dividend, -10 2, and a reminder

As can be seen:

The remainder is 2, while the quotient is 20.

Sometimes, the remaining part is referred to as the "modulo," or simply "mod." This notation is used to say that:

102 mod 5 = 2

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according to wine-searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. random ratings of a pinot noir recently produced by a newly established vineyard in follow: excel file: data07-11.xlsx 87 91 86 82 72 91 60 77 80 79 83 96 a. develop a point estimate of mean wine score for this pinot noir (to decimals). 82.00 b. develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals). 9.6389

Answers

(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.

Below table showing calculation of Point Estimate of Mean and Standard Deviation:

Score                                  X-X’                                  (X-X’)^2

87                                         5                                         25

91                                         9                                         81

86                                         4                                         16

82                                         0                                         0

72                                        -10                                       100

91                                         9                                         81

60                                        -22                                       484

77                                        -5                                         25

80                                        -2                                         4

79                                        -3                                         9

83                                         1                                         1

96                                         14                                       196

984                                                                                   1022

Mean(X’) = Total Score/n

n = Total number = 12

X’ = 984/12 = 82

Standard Deviation (σ) = √∑(X-X’)^2/(n-1)

σ = √1022/(12-1)

σ = √1022/ 11

σ = 9.6389

(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389

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please help meeeeeeee

Answers

Answer: B & A

Step-by-step explanation: I think?

Please help me with this question

Answers

To derive the formula that goes through these two points, we use the general equation for an exponential equation.

Y = a(b)^x

There we will substitute the two points into this equation to get two equations

45 = a(b)^2

5/9= a(b)^-1

By dividing the first equation by the second, we obtain:

27 = b^3

Therefore b= 3

We plug b=3 into the first equation using the second point:

45 = a(3)^2

We get a = 5

Therefore the equation is y = 5(9)^x

We can verify this equation by plugging in the two points given to see if it works.

5/9 = 5(9)^-1

5/9 = 5/9

And:

45 =5(9)^2

45 = 45

It does, so the equation is correct.

The answer is y =5(9)^x

What is exponential equation?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.Exponential equations are equations in which variables occur as exponents.For example, exponential equations are in the form a x = b y .To solve exponential equations with same base, use the property of equality of exponential functions .

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Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long. Each wreath requires 5 yards of uncut ribbon. How many wreaths can Ms. Brooks make?

Answers

The number wreaths that Ms. Brooks make will be 7 wreaths.

How to illustrate the expression?

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

It should be noted that an expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features. People make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects

Here, Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long.

Since each wreath requires 5 yards of uncut ribbon, the number of wreaths that Ms. Brooks make will be:

= (18 + 17) / 5

= 35 / 5

= 7 wreaths.

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Kevin has an annual salary of $41,732, and he earned $33.52 interest from his savings account. He also paid $1050 in student loan interest and contributed $3900 to an IRA retirement account. Calculate Kevin’s adjusted gross income.

Answers

Kevin's adjusted gross income is $36, 815. 52

What is adjusted gross income?

Adjusted gross income is simply described as gross income minus certain adjustments from the income.

These adjustments includes;

Educator expensesStudent loan interestAlimony paymentsContributions to an account, etc

It is calculated as;

Adjusted gross income = sum total of income - expenses

Now, let's substitute the values into the formula, we have;

Adjusted gross income = $(41,732 + 33.52) - $(1050 + 3900)

Add the values

Adjusted gross income = $(41, 765. 52 - 4950)

Subtract the values

Adjusted gross income = $36, 815. 52

Hence, the value is $36, 815. 52

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Polly borrowed $285 for a new floor lamp. She will make 5 monthly payments of $62 to repay the loan. How much will she pay in interest?

Answers

Interest is the price you pay to borrow money or the cost you charge to lend money.

How do you calculate interest on a loan?Divide your interest rate by the number of payments you'll make that year. If you have a 6 percent interest rate and you make monthly payments, you would divide 0.06 by 12 to get 0.005. Multiply that number by your remaining loan balance to find out how much you'll pay in interest that month.If the payment plan is $62 per month for 5 months, then the whole payment will be: $310To calculate simple interest on a loan, take the principal (P) times the interest rate (R) times the loan term in years (T), then divide the total by 100. To use this formula, make sure you're expressing your interest rate as a percentage, not a decimal (i.e., a rate of 4% would go into the formula as 4, not 0.04).So, $10$ percent per annum means that $10$ percent interest will be charged yearly or annually over a principal amount or a loan. Note: If the rate of interest is $10$ percent per annum, then the interest calculated will be $10$ percent of the principal amount.

To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.

310-285 = 25

So, Polly will pay $25 in interest.

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An aircraft is flying at altitude H when it begins its descent to an airport runway that is at a horizontal ground distance L from the airplane. Assume that the landing path is described by the cubic polynomial function y=ax3+bx2+cx+d where y(-L)= H and y(0)= 0.a. What is dy\dx at x= 0?b. What is dy\dx at x= -L?

Answers

a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]

b.  [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]

a. The derivative of a cubic function

[tex]y=ax^3+bx^2+cx+d[/tex]  is  [tex]y'=3ax^2+2bx+c[/tex].

Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.

b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].

Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]

A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.

A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3

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Please Help!!!
Marshall wants to buy a car in five years worth $20,000. He finds a savings account with a simple interest rate of 4%. How much money must he put in the account now so he has $20,000 to buy the car in five years (round to the nearest dollar). SHOW ALL WORK

Answers

The amount of money he must put in the account is $16666.66

What is meant by interest rate?

A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe.

This year, the Bank of Canada quickly increased its policy rate, taking it from 0.25% in March 2022 to 4.25% in December 2022, and in the process, driving up mortgage and prime rates. An interest rate is the portion of a loan, deposit, or borrowing that must be paid in interest each period. The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.

Given,

r=4%

T=5 years

Total amount=SI+P

=20000

SI+P=20000

SI=20000-P

SI=PTR/100

20000-P=(P×5×4)/100

2000000-100P=20P

120P=2000000

P=16666.66

Therefore, The amount of money he must put in the account is $16666.66.

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57. Center: (0, 0); Radius: 3

Answers

The answer for your question is 0

Find the volume of a cone with a radius of 3 feet and a height of 7 feet. Enter
the answer in terms of pie

Answers

Answer: volume of cone = 21 π ft^3

(Score for Question 1: of 3 points)
1. Represent each situation with an inequality.
(a) The sum of a number and 12 is at most -8.
(b) A number increased by -8 is greater than 12.
(c) -8 less than a number is no more than 12.
Answer:

Answers

Inequality for each part be

a) x + 12 ≤ -8

b)  x - 8 > 12

c) x + 8 < 12

What do you mean by inequality?

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size.

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

Let the number be x

According to the question:

a) The sum of a number and 12 is at most -8.

inequality become:

x + 12 ≤ -8

b) A number increased by -8 is greater than 12

inequality become:

x + (-8) > 12

⇒ x - 8 > 12

c)  -8 less than a number is no more than 12

x - (-8) < 12

⇒ x + 8 < 12

Therefore, inequality for each part be

a) x + 12 ≤ -8

b)  x - 8 > 12

c) x + 8 < 12

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-x+y≤-1
x + 2y ≥ 4
Graph the system of inequalities.

Answers

Answer:

Step-by-step explanation:

[tex]-x+y\leq -1\\x-y\geq 1\\x+2y\geq 4[/tex]

dark blue is the required region.

15. Suppose an economy's marginal propensity to consume (MPC) is 0.6. Then, the multiplier must be

a. 1.96.

b. 3.

c. 1.67.

d. 2.5.

Answers

The investment multiplier must be 2.5 i.e.Option (d).

What is an Investment multiplier?

The amount by which the growth in output or income exceeds the increase in investment is referred to as the investment multiplier. It is represented by the letter "k" and is calculated as the ratio of changes in investment and income.

Multiplier(k) = Change in income / change in investment = 1/ {1-MPC}

where MPC is the marginal propensity to consume

Given, MPC = 0.6

Then, the multiplier(k) = 1/( 1 - 0.6) = 1/ 0.4 = 10/4 = 2.5 times

Hence, the investment multiplier is 2.5 i.e.Option (d).

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let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)

Answers

The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.

Given :

Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,

Let g(x) = f(x) − 5.

g(x) = (x−p)(x−q)(x−r)(x−s)h(x)

The condition f(t) > 5 translates to g(t) > 0.

Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :

the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }

The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.

Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have

f(x)=x(x−1)(x−3)(x−4)+5

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Full question ;

Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?

what is the circumference

Answers

The circumference is 12.56

Given h(x)=-5x-4 find h(3)

Answers

The value of the equation h(x) = -5x-4 is - 19 when h = (3).

What are equations?

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, the equation we have is:

h(x) = -5x-4

Now, solve the equation when h = (3)

h(x) = -5x-4

h(3) = -5(3) -4

h(3) = -15 - 4

h(3) = - 19


Therefore, the value of the equation h(x) = -5x-4 is - 19 when h = (3).

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