What is an open line of credit?
a. A line of credit which has no current balance
b. A line of credit with a variable interest rate.
c. A line of credit against which additional debt may be drawn.
d. A line of credit which has no credit history requirements.
Please select the best answer from the choices provided

Answer: The answer is p = 343

Given that 'p' is inversely proportional to the square of 'q', we first found the constant of proportionality (k) by substituting the given 'p' and 'q' values. With 'k' known, we substituted the new value of 'q' to find the corresponding value of 'p', which turned out to be 343 when q=2.

The given question describes an inverse proportionality. Specifically, it states that p is inversely proportional to the square of q. To express this mathematically, we write it as p = k/(q^2), where k is the constant of proportionality. For finding this constant, we use the given values of p and q, so 28 = k/(7^2), which means k = 28*49 = 1372.

Now, we substitute the value of k and the new value of q into the equation to find the corresponding value of p. Hence, when q = 2, p = 1372/(2^2) = 1372/4 = 343. Therefore, when q = 2, p equals 343.

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Answer: y = 0.25*f(x - A) + 3

Step-by-step explanation:

Initially we have the graph of y = f(x)

If we do a vertical compression, this means that we multiply the function by the scale factor, in this case the scale factor is 0.25

So now our graph is y = 0.25*f(x)

A translation to the right by A units means that now we valuate the function in x - A, in this case A = 4, so our graph now is:

y = 0.25*f(x - 4)

A vertical translation means that we add a constant to the function, if the constant is positive the tranlsation is upwards, if the constant is negative the translation is downwards.

Here the translation is of 3 units upwards, so our new graph is:

y = 0.25*f(x - A) + 3

Answer:

12

Step-by-step explanation:

Answer:

y = 1/2x -1

Step-by-step explanation:

to find the y-intercept you find where the line crosses the y axis

for the slope you need to use the equation

change of y2 - change of y1

change of x2 - change of x1

y=ax+b

(-2; -2); (0;-1); (2; 0)

-1=a*0+b => b=-1

0=a*2+b

0=a*2-1

a*2=1 => a=1/2

y=x/2 -1

Answer: a) 21 cans

b) 10.83 square inches.

Step-by-step explanation:

The cans are cylinders of 4 and 1/4 inches tall (or 4.25 in)

and the diameter is 3 inches.

The surface of a cylinder is equal to:

S = pi*r^2 + h*2*pi*r

where r is the radius, half of the diameter, so we have that r = 3in/2 = 1.5 in.

h is the height, h = 4.25 in

pi = 3.14

Then the surface needed for a can is:

S = 3.14*1.5^2 + 4.25*2*3.14*1.5 = 47.1 square inches.

if the sheet is 1000 in^2, we can make an amount of:

N = 1000/47.1 = 21.23  

but we can not do a 0.23 of a can, so we need to round down.

A) we can make 21 cans out of a sheet of metal.

B) the 0.23 of a can that we removed earlier is the amount of metal leftover. The total is 0.23*47.1 in^2 = 10.83 in^2

Answer:

Step-by-step explanation:

To determine the amount of metal needed to make each can, we would determine the total surface area of each can. Since the cans are cylindrical, the formula for determining the total surface area of a cylinder is used. It is expressed as

Total surface area = πr² + 2πr

r = radius of the can

h = height of the can

π = 3.14

From information given,

Diameter = 4.25 inches

Radius = diameter/2 = 4.25/2 = 2.125 inches

Total surface area = 3.14 × 2.125² + 2 × 3.14 × 2.125 = 27.5 in²

1) since 1000 in² sheet material is available, the number of cans that can be made is

1000/27.5240625 = 36 cans

2) The amount of metal sheet left is

1000 - (36 × 27.5) = 10 in²

Answer:

The solution to the differential equation y'(y + 7)y'' = (y')²

y = Ae^(Kx) - 7

Step-by-step explanation:

Given the differential equation

y'(y + 7)y'' = (y')² ..................(1)

We want to solve using the substitution u = y'.

Let u = y'

The u' = y''

Using these, (1) becomes

u(y + 7)u' = u²

u' = u²/u(y + 7)

u' = u/(y + 7)

But u' = du/dy

So

du/dy = u/(y + 7)

Separating the variables, we have

du/u = dy/(y + 7)

Integrating both sides, we have

ln|u| = ln|y + 7| + ln|C|

u = e^(ln|y + 7| + ln|C|)

= K(y + 7)

But u = y' = dy/dx

dy/dx = K(y + 7)

Separating the variables, we have

dy/(y + 7) = Kdx

Integrating both sides

ln|y + 7| = Kx + C1

y + 7 = e^(Kx + C1) = Ae^(Kx)

y = Ae^(Kx) - 7

Final answer:

To solve the given differential equations by using the substitution u = y', substitute u for y' and find the values of u. Then, solve the resulting first order ordinary differential equation by separating variables and integrating to determine the solution.

Explanation:

To solve the given differential equations by using the substitution u = y', we need to substitute u for y' and find the values of u. Let's take the first equation as an example:

Start by substituting u for y' in the equation: (y + 7)y'' = (y')^2

Replace y' with u in the equation: (y + 7)u' = u^2

Then, we can solve this first order ordinary differential equation by separating variables and integrating:

Divide both sides by (y + 7): u' = (u^2) / (y + 7)

Separate the variables: (y + 7)dy = (u^2)du

Integrate both sides: (1/2)(y^2 + 14y) = (1/3)u^3 + C (where C is the constant of integration)

Solve for y by rearranging the equation: y^2 + 14y = (2/3)u^3 + 2C

This is the solution to the given differential equation.

Answer: The answer is y = 18(1.15)^x

Step-by-step explanation:

Answer:

y = (18) * (1.15)^x

Step-by-step explanation:

A limited edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20. 70. Which equation can be used to find the y value after x years.

To find this equation, this is an exponential equation, meaning that the number increases at a rapid rate. In this case the post increases each year by 15% and started at $18. The equation you would use to find this is: y = a * b^x. We can fill in the a and b values based off the given information. Since the value is increasing by 15% we will add 1 to 15% to get 1.15. This will be the b value. The a value is our initial value which in this case is $18. Now we can plug everything in to get: y = (18) * (1.15)^x.

Answer:

x+9

Step-by-step explanation:

1/3x[8-5]+9=1/3x(3)+9

1/3x(3)+9=x+9

x+9

The final result of the expression 1/3x[8-5]+9 is 10.

To evaluate the expression 1/3x[8-5]+9, we need to perform the operations in the correct order, following the PEMDAS/BODMAS rule. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS is similar but is used in some regions with the 'O' representing "Orders" or "Indices" instead of Exponents.

Step 1: Inside the brackets, we solve the expression 8 - 5, which gives us 3.

Step 2: Now, we have 1/3x3 + 9. According to PEMDAS/BODMAS, we must perform multiplication before addition. So, we proceed with 1/3 times 3, which equals 1.

Step 3: The expression now simplifies to 1 + 9.

Step 4: Finally, we perform the addition, which yields 10.

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Answer:

Step-by-step explanation:

2: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

3: 3 6 9 12 15 18 21 24 27 30 33 36 39 42

7: 7 14 21 28 35 42

Answer:

Step-by-step explanation

First five multiples of 2030 are: 2, 5, 7, 10 an 14

Answer:

T(n) = cn +(a-c)

Step-by-step explanation:

Note that T(1) = a, then T(2) = a+c, T(3) = (a+c)+c = a+2c, T(4) = (a+2c)+c = a+3c. Thus, our hypotheis is that T(n) = a+(n-1)c. We will prove this by strong induction.

Note that T(1) = a = a+(1-1)c. So the base case is proved. Assume that the result is true for all k<n. Then

T(n) = T(n-1)+c = (a+(n-2)c)+c = a+(n-1)c= cn+ (a-c).

So, by induction, the result holds.

Note that if a=1 and c = 3 then T(n) = 1+(n-1)3 = 3n-3+1 = 3n-2, which invalidates option b)

If a=3 and c=5 then we have that T(n) = 5n+(3-5) = 5n-2, which invalidates c) and d).

Then the formula is correct.

Answer:

(a) is correct

[tex]T(n) = a+(n-1)c[/tex]

Step-by-step explanation:

Notice that according to the information that you are given

[tex]T(1)=a \\T(2)=T(1)+c = a+c\\T(3)=T(2)+c = a+c+c = a+2c[/tex]

If you think about it there is a clear pattern, it would be

[tex]T(n) = a+(n-1)c[/tex]

Now notice that (a) is correct  if we set a=1 and c=3 we get

[tex]T(n) = 1+3(n-1) = 3n-2[/tex]

This problem involves conducting a hypothesis test, stating the null hypothesis as 78% or fewer readers own a personal computer, and the alternative hypothesis as more than 78% own one. A statistical test (like a z-test) is needed to compare the p-value to the 0.01 significance level. The publisher's claim is supported if the p-value is less than 0.01.

In this context, we are conducting a hypothesis test to examine a newsletter publisher's claim about their audience's computer ownership. The null and alternative hypotheses would therefore be set up as follows:

Null Hypothesis (H0): p <= 0.78, meaning 78% or fewer readers own a personal computer.

Alternative Hypothesis (Ha): p > 0.78, meaning more than 78% of readers own a personal computer.

We can conduct a hypothesis test to prove or disprove this using statistical methods such as a z-test and by comparing the p-value to the significance level (0.01 in this case). If the p-value obtained from the test is less than 0.01, we can reject the null hypothesis providing sufficient evidence to support the publisher's claim. If not, we fail to reject the null hypothesis which means the evidence is insufficient.

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Answer:

The answer is d (13.26)

Step-by-step explanation:

set it up like this: (95/360) times (2 times pi times 8)

after plugging this equation into a calculator you get 13.26450232 and round to 13.26

Final answer:

The arc length of a circle with an 8-inch radius and a central angle of 95 degrees is 13.26 inches when we use 3.14 for π and round to the nearest hundredth.

Explanation:

To find the arc length of a circle, we use the formula arc length (Δs) = rΘ, where 'r' is the radius and Θ is the central angle in radians. Since there are 2π radians in a full 360-degree rotation, we can find the radian measure of 95 degrees by using the conversion ratio π radians/180 degrees. The radian measure is (95/180)π.

Using 3.14 for π and the given radius of 8 inches, the calculation becomes: Δs = 8 * (95/180) * 3.14. Simplifying this equation gives the arc length as 13.26 inches when rounded to the nearest hundredth

Answer:

a

Step-by-step explanation:

The order of four steps are Assessing needs and wants, Considering opportunity costs, Assessing risks and returns and Setting short- and long-term goals, Option C is correct.

Finance is the study and discipline of money, currency and capital assets.

The correct order of the four steps in solving one's personal financial challenges is indeed:

Assessing needs and wants

Considering opportunity costs

Assessing risks and returns

Setting short- and long-term goals

Hence, the order of four steps are Assessing needs and wants, Considering opportunity costs, Assessing risks and returns and Setting short- and long-term goals, Option C is correct.

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Answer:

  √37

Step-by-step explanation:

It is helpful to know the squares of small integers. Then you become aware of the approximate magnitudes of square roots.

Point C is between 6 and 7, so the value of C² will be between 6² = 36 and 7² = 49. Since C is closer to 6 than to 7, it represents the root of a number closer to 36 than to 49.

Only one answer choice is in this range: √37, Option 1.

Answer: A. have the same slope

Step-by-step explanation:

b. bisect means right in half but not fully intersecting kinda looks like this _l_ *oh and it asked you to prove that they bisect so clicking on it don't really make sense*

c. perpendicular means there is four equal angels and that is 90 degree angels

d. parallel... well it's obviously not parallel because parallel are two lines that are exactly the same but never intersect

*intersect means touch*

Answer:

a) If Y is distributed N(1, 4), Pr (Y ≤ 3) = 0.84134

b) If Y is distributed N(3, 9), Pr (Y > 0) = 0.84134

c) If Y is distributed N(50, 25), Pr (40 ≤ Y ≤ 52) = 0.63267

d) If Y is distributed N(5, 2), find Pr (6 ≤ Y ≤ 8) = 0.22185

Step-by-step explanation:

With the logical assumption that all of these distributions are normal distribution,

a) Y is distributed N(1, 4), find Pr ( Y ≤ 3 )

Mean = μ = 1

Standard deviation = √(variance) = √4 = 2

To find the required probability, we first standardize 3

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (y - μ)/σ = (3 - 1)/2 = 1

We'll use data from the normal probability table for these probabilities

The required probability

Pr ( Y ≤ 3 ) = P(z ≤ 1) = 0.84134

b) If Y is distributed N(3, 9), find Pr ( Y > 0 )

Mean = μ = 3

Standard deviation = √(variance) = √9 = 3

To find the required probability, we first standardize 0

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (y - μ)/σ = (0 - 3)/3 = -1

We'll use data from the normal probability table for these probabilities

The required probability

Pr ( Y > 0) = P(z > -1) = 1 - P(z ≤ -1) = 1 - 0.15866 = 0.84134

c) If Y is distributed N(50, 25), find Pr (40 ≤ Y ≤ 52).

Mean = μ = 50

Standard deviation = √(variance) = √25 = 5

To find the required probability, we first standardize 40 and 52.

For 40,

z = (y - μ)/σ = (40 - 50)/5 = -2

For 52,

z = (y - μ)/σ = (52 - 50)/5 = 0.4

We'll use data from the normal probability table for these probabilities

The required probability

Pr (40 ≤ Y ≤ 52) = P(-2.00 ≤ z ≤ 0.40)

= P(z ≤ 0.40) - P(z ≤ -2.00)

= 0.65542 - 0.02275

= 0.63267

d) If Y is distributed N(5, 2), find Pr ( 6 ≤ Y ≤ 8 )

Mean = μ = 5

Standard deviation = √(variance) = √2 = 1.414

To find the required probability, we first standardize 6 and 8.

For 6,

z = (y - μ)/σ = (6 - 5)/1.414 = 0.71

For 8,

z = (y - μ)/σ = (8 - 5)/1.414 = 2.12

We'll use data from the normal probability table for these probabilities

The required probability

Pr (6 ≤ Y ≤ 8) = P(0.71 ≤ z ≤ 2.12)

= P(z ≤ 2.12) - P(z ≤ 0.71)

= 0.983 - 0.76115

= 0.22185

Hope this Helps!!

Answer:

a) The value of N(1, 4) = 0.8413

b) The probability of N(3, 9) = 0.8413

ci) The probability (40≤ Y≤ 52) = 0.4

cii) The probability of N (3, 9) = 0.6236

d) The probability of (6≤Y≤8) = 0.2216

Step-by-step explanation:

Detailed step by step explanation is given in the attached document.

A normal distribution is a bell shaped symmetric distribution. This kind of distribution has a normal probability density function. A standard normal distribution is the one that has a mean 0 and variance of 1. It is often denoted as N (0, 1). If a general variance and mean are given and one has to look up probabilities in a normal probability distribution. The variable is standardized first. Standardizing a variable involves subtracting the general mean from the standard and then dividing the result by 1. In order to find the probabilities, the value of z is located in a normal distribution table.

Answer:

The solution is shown in the picture attached

Step-by-step explanation:

To verify X as a solution to the system, substitute X into the system and check for equality. X is a vector and X' a matrix. Careful calculations with matrices and trigonometric identities are necessary for the verification.

To verify that the vector X is indeed a solution to the given system, we can substitute X into the system and check if both sides are equal. If they are, then X is a solution to the system.

X in this case is a vector whose elements are trigonometric functions of time t. Likewise, X' represents a matrix multiplying the vector X. After applying the multiplication, we can compare the resulting vector with the original vector.

As this involves calculation with matrices and trigonometric identities, careful execution of these steps is necessary to ensure the accuracy of the result.

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The microphone, which is at the focal point of a parabolic microphone, should be placed 5 inches from the vertex of the parabola since the parabola is 40 inches wide and 20 inches deep.

The question deals with a parabolic shape and requires using the properties of a parabola to determine the position of the focal point. In the context of a parabolic microphone, the focal point is where the microphone should be placed to best capture sounds. For a parabola given in the form y = 4px, where p is the distance from the vertex to the focus, and the parabola is 40 inches wide (which is the distance from one end of the parabola to the other at the given depth) and 20 inches deep (which is the distance from the vertex to the directrix), we can find p, using the relationship depth = p. Since the depth is 20 inches, the focus (and thus where the microphone should be placed) is 20/4 = 5 inches from the vertex of the parabola.

Answer:

55 cm2

Step-by-step explanation:

The area of the new parallelogram is 55 sq.cm, the correct option is C.

A polygon with four sides such that the opposite sides are parallel and equal is called a Parallelogram.

The height of the parallelogram is 4 cm

The base of the parallelogram is 9cm

The height of the parallelogram is increased by 1 cm

New height = 5cm

The base of the parallelogram is increased by 2 cm

New base = 11 cm

Area of a parallelogram is =  Base * Height

Area of parallelogram is  = 5 * 11 = 55 sq.cm

Therefore, the area of the new parallelogram is 55 sq.cm.

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Answer:

We conclude that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode.

Step-by-step explanation:

We are given that there are 31 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo.

After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.

Let [tex]p_1[/tex] = true percentage of those in the first group who suffer a second episode.

[tex]p_2[/tex] = true percentage of those in the second group who suffer a second episode.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1-p_2\leq[/tex] 0  or  [tex]p_1\leq p_2[/tex]      {means that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1-p_2[/tex] > 0  or  [tex]p_1>p_2[/tex]      {means that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode}

The test statistics that will be used here is Two-sample z proportion test statistics;

                              T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of people in the first group who suffer a second episode = 11%

[tex]\hat p_2[/tex] = sample proportion of people in the second group who suffer a second episode = 9%

[tex]n_1[/tex] = sample of people in first group = 31

[tex]n_2[/tex] = sample of people in second group = 45

So, the test statistics  =  [tex]\frac{(0.11-0.09)-(0)}{\sqrt{\frac{0.11(1-0.11)}{31}+ \frac{0.09(1-0.09)}{45}} }[/tex]

                                     =  0.283

Now, at 0.1 significance level, the z table gives critical value of 1.2816 for right-tailed test. Since our test statistics is less than the critical value of z as 0.283 < 1.2816, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.

Therefore, we conclude that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode.

A hypothesis test can determine whether there is enough evidence to support the claim that the new drug is effective in reducing second episodes of heartburn. It involves defining null and alternative hypotheses, calculating a test statistic, and comparing it to a critical value based on the set significance level.

We start by defining our null and alternative hypotheses. In this case, we are testing against the claim that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode.

So, our null hypothesis (H0) is: The percentage of heart attempts in group 1 is equal to or less than that of group 2.

And, our alternative hypothesis (Ha) is: The percentage of heart attempts in group 1 is greater than that of group 2.

We conduct the hypothesis test using a standard test of proportions. Calculating our test statistic can be done using the formula: Z = (p1 - p2)/sqrt(p(1 - p)[(1/n1) + (1/n2)])

Where, p1 and p2 are the proportions of the two groups, n1 and n2 are the sizes of the two groups, and p is the combined proportion.

Based on the information in the problem, the calculated test statistic value and the critical z-value for a one-tailed test at the significance level 0.1, we can make a decision to reject or fail to reject the null hypothesis. If the calculated absolute z-value is greater than the critical z-value, we reject the null hypothesis and conclude that there is enough evidence at the 0.1 level. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

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Answer:

Step-by-step explanation:

WE are given that [tex]a_n = \frac{(-1)^{n+1}}{5n-4}[/tex]. Then, to now the first for terms, we must replace n by 1,2,3,4 respectively. Then

[tex]a_1 = \frac{(-1)^2}{5(1)-4} = \frac{1}{1}= 1 [/tex]

[tex]a_2 = \frac{(-1)^3}{5(2)-4} = \frac{-1}{6} [/tex]

[tex]a_3 = \frac{(-1)^4}{5(3)-4} = \frac{1}{11}= 1 [/tex]

[tex]a_4 = \frac{(-1)^5}{5(4)-4} = \frac{-1}{16}= 1 [/tex]

Note that as n increase, [tex]a_n[/tex] gets closer to 0. So, the limit of this sequence is 0.

Final answer:

The function in question, f(x) = 3x^2 + 7x + 2, is a quadratic function, and its properties such as graph shape, intercepts, and vertex can be studied. Additionally, the derivative of this function, obtained through power rule differentiation, is f'(x) = 6x + 7.

Explanation:

The question asks about the function f(x) = 3x2 + 7x + 2. This appears to be a quadratic function, which is a fundamental concept in algebra and pre-calculus. Detailing the characteristics of a quadratic function involves finding its graph, which is a parabola, its vertex, axis of symmetry, intercepts, and possibly its extrema (maximum or minimum values).

In mathematics, finding the derivative of a function is a common operation in calculus. Given the information on different functions and their derivatives from the provided reference text, we can deduce that the derivative of f(x) would be found through power rule differentiation: for f(x) = axn, the derivative f'(x) = naxn-1. Applying this to the given function, we find the derivative f'(x) = 6x + 7.

Answer:

a) 1/6

b) 3/8

Step-by-step explanation:

Even i struggle with fractions but im sure you will get it one day (✿◡‿◡)

A circle with radius r has a circumference of 2πr.

2πr = 18.84  ==>  r = 18.84/(2π) ≈ 2.998 units

The same circle has area πr ² sq. units. So the area is

π (2.998)² ≈ 28.246 sq. units

To find the area of a circle with a given circumference, divide the circumference by 2π to find the radius. Then, plug the radius into the formula A = πr^2 to calculate the area.

To find the area of a circle when given the circumference, you can use the formula A = πr^2.

First, determine the radius of the circle by dividing the circumference by 2π.

In this case, the circumference is 18.84, so the radius would be 18.84 / (2π) = 3.0.

Then, plug the radius into the formula A = πr^2 to find the area:

A = π(3.0)^2 = 9.0π = 28.27 (rounded to two decimal places)

Therefore, the area of the circle with a circumference of 18.84 units is approximately 28.27 square units.

Answer:

9

Step-by-step explanation:

In order to figure this out, I made the proportion:

[tex]\frac{300}{x} =\frac{100}{3}[/tex]

Multiply 3 by 300 and x by 100

300*3=?

x*100=?

900=100x

Divide 900 by 100 to find x

900÷100=9

x=9

Answer:

a) The volume of S is 34.13

b) The volume of S is 14.8

c) The volume of S is 5.17

d) The volume of S is 11.33

Step-by-step explanation:

a) The cross section area is equal to:

[tex]A=a^{2} =((5x-x^{2})-x)^{2} =(4x-x^{2} )^{2}[/tex]

The volume of S is equal to:

[tex]Vol_{S} =\int\limits^4_0 {A(x)} \, dx =\int\limits^4_0 {(4x-x^{2})^{2} } \, dx =34.13[/tex]

b) The cross section area is equal to:

[tex]A=\frac{a^{2}\sqrt{3} }{4} =\frac{\sqrt{3} }{4} ((5x-x^{2} )-x)^{2} =\frac{\sqrt{3} }{4} (4x-x^{2} )^{2}[/tex]

The volume of S is equal to:

[tex]Vol_{S} =\int\limits^4_0 {A(x)} \, dx =\frac{\sqrt{3} }{4} \int\limits^4_0 {(4x-x^{2})^{2} } \, dx =14.8[/tex]

c)

[tex]y=5x-x^{2} \\\frac{dy}{dx} =0\\5x-x^{2} =0\\x=5/2\\y(5/2)=25/4\\y=5x-x^{2} \\x^{2} -5x+y=0\\x=\frac{5+-\sqrt{25-4y} }{2}[/tex]

The cross section area is equal to:

[tex]A_{1} =\frac{1}{2} \pi r_{1}^{2} =\frac{1}{2} \pi (\frac{1}{2} (\frac{5+\sqrt{25-4y} }{2} -\frac{5-\sqrt{25-4y} }{2} ))^{2} =\frac{1}{8} \pi (25-4y)\\A_{2} =\frac{1}{2} \pi r_{2}^{2}=\frac{1}{2}\pi (\frac{1}{2} (y-\frac{5-\sqrt{25-4y} }{2} ))^{2} =\frac{1}{32} \pi (2y-5+\sqrt{25-4y} )^{2}[/tex]

The volume of S is equal to:

[tex]Vol_{S} =\int\limits^a_b {A_{1}(y) } \, dy+\int\limits^4_0 {A_{2}(y) } \, dy ,where-a=25/4,b=4\\Vol_{S} =\int\limits^a_b {\frac{1}{8}\pi (25-4y)} \, dy +\int\limits^a_b {\frac{1}{32}\pi (2y-5+\sqrt{25-4y} )^{2} } \, dy =5.17[/tex]

d) The cross section area is:

[tex]A_{1} =\frac{1}{2}ab=\frac{1}{2} a^{2} =\frac{1}{2} (\frac{5+\sqrt{25-4y} }{2}-\frac{5-\sqrt{25-4y}}{2} )^{2} =\frac{1}{2} (25-4y)\\A_{1}=\frac{1}{2}ab=\frac{1}{2} a^{2} =\frac{1}{2}(y-\frac{5-\sqrt{25-4y}}{2}} )^{2} =\frac{1}{8} (2y-5+\sqrt{25-4y}})^{2}[/tex]

The volume of S is equal to:

[tex]Vol_{S} =\int\limits^a_b {A_{1}(y) } \, dy +\int\limits^4_0 {A_{2}(y) } \, dy ,where-a=25/4,b=4\\Vol_{S}=\int\limits^a_b {\frac{1}{2}(25-4y) } \, dy +\int\limits^4_0 {\frac{1}{8}(2y-5+\sqrt{25-4y})^{2} } \, dy =11.33[/tex]

Answer:

0.069 = 6.9% probability that a customer has to wait more than 4 minutes.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

In this problem, we have that:

[tex]m = 1.5[/tex]

So

[tex]\mu = \frac{1}{1.5} = 0.6667[/tex]

[tex]P(X \leq x) = 1 - e^{-0.667x}[/tex]

Find the probability that a customer has to wait more than 4 minutes.

Either the customer has to wait 4 minutes or less, or he has to wait more than 4 minutes. The sum of the probabilities of these events is decimal 1. So

[tex]P(X \leq 4) + P(X > 4) = 1[/tex]

We want P(X > 4). So

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - (1 - e^{-0.667*4}) = 0.069[/tex]

0.069 = 6.9% probability that a customer has to wait more than 4 minutes.

Answer:

120

Step-by-step explanation:

add 4 and 2 then multipy by 2 and add a zero

Answer:

17

Step-by-step explanation:

Let x, x +1, x + 2, x + 3 be four consecutive integers.

[tex] \therefore \: x + x +1 + x + 2 + x + 3 = 74 \\ \therefore \: 4x + 6 = 74 \\ \therefore \: 4x = 74 - 6 \\ \therefore \: 4x = 68 \\ \therefore \: x = \frac{68}{4} \\ \huge \red{ \boxed{x = 17}}[/tex]

Hence, first integer is 17.

Answer:

17 is your answer

hope this helps :)

Step-by-step explanation: