Answer all questions: 1) The electric field of an electromagnetic wave propagating in air is given by E(z,t) = 4cos(6 x 10^8 t - 2z) +3 sin(6 x 10 t -2z) (V/m). Find the associated magnetic field H(z,t)

Answer:

40514.837 kg

Step-by-step explanation:

The weight of the main axle of the 1893 ferris wheel built by George Washington Gale Ferris Jr. in Chicago, USA was 89,320 pounds (lb).

1 kg=2.20462 pounds (lb)

[tex]\Rightarrow 1 lb=\frac{1}{2.20426}[/tex]

[tex]\Rightarrow 1 lb=0.453592 kg[/tex]

[tex]\Rightarrow 89320 lb=89320\times 0.453592[/tex]

[tex]\therefore 89320 lb=40514.837 kg[/tex]

Answer:

25/29

Step-by-step explanation:

see the attached picture.

The probability that marble is small or white is 25/29.

Probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

How to find If a marble is randomly selected from the box, what is the probability that it is small or white?

Given A box contains 19 large marbles and 10 small marbles.

Each marble is either green or white.

8 of the large marbles are green, and 4 of the small marbles are white.

Then P(s or w) = P(s) +P(w)

and P(s)=10/29

P(w)=11+4/29 = 15/29.

So,  P(s or w) = P(s) +P(w)

=> P(s or w) = 10+15/29

=> 25/29.

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Answer:

2/21

Step-by-step explanation:

We start out with a full tank.  Once the trucks take from it, it is down to 1/3 of a tank.  Therefore,

[tex]\frac{3}{3} -\frac{1}{3} =\frac{2}{3}[/tex]

So the trucks took 2/3 of the gas.  

If there were 7 trucks and we need to know how much of that 2/3 was taken by each truck, we divide 2/3 by 7:

[tex]\frac{\frac{2}{3} }{7}[/tex]

When dividing fractions, we bring up the lower fraction and flip it and multiply:

[tex]\frac{2}{3}*\frac{1}{7}=\frac{2}{21}[/tex]

The capacity of each truck is 2/21 of the total gasoline tank, which is calculated by dividing the used part of the gasoline tank (2/3) by the number of trucks (7).

Let's denote the total gasoline tank volume as one unit, or 1. Seven trucks share 2/3 of the gasoline tank capacity (since 1/3 is still left); each truck capacity could be gotten by dividing this 2/3 equally among the seven trucks. By dividing 2/3 by 7, we get each truck's capacity as 2/21 of the total gasoline tank capacity. Therefore, the correct answer is d) 2/21.

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Answer:

A transitive property

Step-by-step explanation:

There isn't much to this.

This is the the transitive property.

I guess I can go through each choice and tell you what the property looks like or postulate.

A)  If x=y and y=z, then x=z.

This is the exact form of your conditional.

x is AB here

y is BC here

z is DE here

B) Segment Addition Postulate

If A,B, and C are collinear with A and B as endpoints, then AB=AC+CB.

Your conditional said nothing about segment addition (no plus sign).

C) Distributive property is a(b+c)=ab+ac.

This can't be applied to any part of this.  There is not even any parenthesis.

D) The symmetric property says if a=b then b=a.

There is two parts to our hypothesis where this is only part to the symmetric property for the hypothesis .  

The statement 'If AB = BC  and BC = DE, then AB = DE' is justified by the Transitive Property of Equality, stating that, if two quantities both equal a third, they are equal to each other.

The justification for the statement 'If AB = BC  and BC = DE, then AB = DE' is the Transitive Property of Equality. This property states that if two quantities are both equal to a third quantity, then they are equal to each other. In this case, AB and DE are both equal to BC, therefore, according to the transitive property, AB must be equal to DE.

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Answer: 0.3758

Step-by-step explanation:

Given : The  probability that a milk container is underweight throughout of packaging line: [tex]p = 0.20[/tex]

The number of containers : n= 10

The formula binomial distribution formula :-

[tex]^nC_rp^{n-r}(1-p)^r[/tex]

The probability that at least nine milk containers in a box are properly filled is given by :-

[tex]P(X\geq9)=P(9)+P(10)\\\\=^{10}C_9(0.2)^{10-9}(1-0.20)^9+^{10}C_{10}(0.2)^{10-10}(1-0.2)^{10}\\=10(0.2)(0.8)^9+(1)(0.8)^{10}\\=0.3758096384\approx0.3758[/tex]

Answer:

The critical numbers/values are x = 0, 4/7, 2

Step-by-step explanation:

This is a doozy; no wonder you have it up here for help!

The critical numbers of a function are found where the derivative of the function is equal to 0.  To find these numbers, you have to factor the deriative or simply solve it for 0.  This one is especially difficult since it involves rational exponents that have to be factored.  But this is fun, so let's get to it.

First off, I am assuming that the function is

[tex]f(x)=x^{\frac{4}{5}}*(x-2)^2[/tex] which involves using the product rule to find the derivative.

That derivative is

[tex]f'(x)=x^{\frac{4}{5}}*2(x-2)+\frac{4}{5}x^{-\frac{1}{5}}(x-2)^2[/tex] which simplifies down to

[tex]f'(x)=x^{\frac{4}{5}}(2x^{\frac{5}{5}}-4)+\frac{4}{5}x^{-\frac{1}{5}}(x^{\frac{10}{5}}-4x^{\frac{5}{5}}+4)[/tex] and

[tex]f'(x)=2x^{\frac{9}{5}}-4x^{\frac{4}{5}}+\frac{4}{5}x^{\frac{9}{5}}-\frac{16}{5}x^{\frac{4}{5}}+\frac{16}{5}x^{-\frac{1}{5}}[/tex]

Let's get everything over the common denominator of 5 so we can easily add and subtract like terms:

[tex]f'(x)=\frac{10}{5}x^{\frac{9}{5}}-\frac{20}{5}x^{\frac{4}{5}}+\frac{4}{5}x^{\frac{9}{5}}-\frac{16}{5}x^{\frac{4}{5}}+\frac{16}{5}x^{-\frac{1}{5}}[/tex]

Combining like terms gives us

[tex]f'(x)=\frac{14}{5}x^{\frac{9}{5}}-\frac{36}{5}x^{\frac{4}{5}}+\frac{16}{5}x^{-\frac{1}{5}}[/tex]

This, however, factors so it is easier to solve for x.  First we will set this equal to 0, then we will factor out

[tex]\frac{2}{5}x^{-\frac{1}{5}}[/tex]:

[tex]0=\frac{2}{5}x^{-\frac{1}{5}}(7x^2-18x+8)[/tex]

By the Zero Product Property, one of those terms has to equal 0 for the whole product to equal 0.  So

[tex]\frac{2}{5}x^{-\frac{1}{5}}=0[/tex] when x = 0

And

[tex]7x^2-18x+8=0[/tex] when x = 2 and x = 4/7

Those are the critical numbers/values for that function.  This indicates where there is a max value or a min value.

To find the critical numbers of the function F(x) = x^(4/5)(x - 2)^2, take the derivative, set it equal to zero, and check for undefined values.

To find the critical numbers of the function F(x) = x4/5(x - 2)2, we need to find the values of x where the derivative of the function is equal to zero or undefined.

Step 1: Find the derivative of F(x) using the product rule and simplify.

Step 2: Set the derivative equal to zero and solve for x.

Step 3: Check if the derivative is undefined at any values of x.

The critical numbers of the function are the values of x where the derivative is equal to zero or undefined.

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Final answer:

P(D ∪ F') is the probability of drawing a black card that is not a 10 from a standard 52-card deck, which is 24 black non-10 cards out of 52 total cards, resulting in a probability of 12/13.

Explanation:

The student is asking about probability in relation to drawing cards from a standard 52-card deck. Specifically, they want to find the probability of the event D (drawing a black card) or the complement of event F (not drawing a 10 card), denoted as P(D ∪ F'). In a standard deck, there are 26 black cards and four 10 cards (two of which are black), so the complement of F (F') is drawing any card that is not a 10, which is 52 - 4 = 48 cards. To find P(D ∪ F'), we consider the number of black cards that are not 10s, which is 24, since there are 26 black cards and 2 are 10s. Therefore, P(D ∪ F') is the probability of drawing one of these 24 cards out of the 52-card deck.

Calculating this probability:

P(D ∪ F') = number of black cards that are not 10s / total number of cards = 24/52 = 12/13.

The key concept here is that we're looking for the union of a black card and a non-10 card, which includes black cards that are also not the number 10.

Answer:

Step-by-step explanation:

We have to graph a line y = 3 - x which has the slope = -1 and y intercept 3.

We will select two points where line intersects at x = 0 and y = 0

The given line will intersect x-axis at (3, 0) and at y- axis (0, 3).

Joining these two points we can draw a straight line showing y = -x + 3

Now we will draw the parabola given by equation y = x² + x - 12

We will convert this equation in vertex form first to get the vertex and line of symmetry.

Standard equation of a parabola in vertex form is

y = (x - h)² + k

Where (h, k) is the vertex and x = h is the line of symmetry.

y = x² + x - 12

y = x² + 2(0.5)x + (0.5)²- (0.5)²-12

y = (x + 0.5)² - 12.25

Therefore, vertex will be (-0.5, -12.25) and line of symmetry will be x = 0.5

For x intercept,

0 = (x + 0.5)² - 12.25

x + 0.5 = ±√12.25

x = -0.5 ± 3.5

x = -4, 3

For y- intercept,

y = (0+0.5)² - 12.25

 = 0.25 - 12.25

y = -12

So the parabola has vertex (-0.5, - 12.25), line of symmetry x = 0.5, x intercept (4, 0), (and y-intercept (0, -12).

Now we have to find the points of intersection of the given line and parabola.

For this we will replace the values of y

3 - x = x² + x - 12

x² + 2x - 15 = 0

x² + 5x - 3x - 15 = 0

x(x + 5) - 3(x + 5) = 0

(x - 3)(x + 5) = 0

x = 3, -5

For x = 3

y = 3- 3 = 0

For x = -5

y = 3 + 5 = 8

Therefore, points of intersection will be (3, 0) and (-5, 8)

Answer:

D. 40 < t < 60

Step-by-step explanation:

Given function,

[tex]N(t) = -3t^3 + 450t^2 - 21,600t + 1,100[/tex]

Differentiating with respect to x,

[tex]N(t) = -9t^2+ 900t - 21,600[/tex]

For increasing or decreasing,

f'(x) = 0,

[tex]-9t^2+ 900t - 21,600=0[/tex]

By the quadratic formula,

[tex]t=\frac{-900\pm \sqrt{900^2-4\times -9\times -21600}}{-18}[/tex]

[tex]t=\frac{-900\pm \sqrt{32400}}{-18}[/tex]

[tex]t=\frac{-900\pm 180}{-18}[/tex]

[tex]\implies t=\frac{-900+180}{-18}\text{ or }t=\frac{-900-180}{-18}[/tex]

[tex]\implies t=40\text{ or }t=60[/tex]

Since, in the interval -∞ < t < 40, f'(x) = negative,

In the interval 40 < t < 60, f'(t) = Positive,

While in the interval 60 < t < ∞, f'(t) = negative,

Hence, the values of t for which N'(t) increasing are,

40 < t < 60,

Option 'D' is correct.

Answer:

For maximum volume of the box, squares with 4.79 inches should be cut off.

Step-by-step explanation:

A candy box is made from a piece of a cardboard that measures 43 × 23 inches.

Let squares of equal size will be cut out of each corner with the measure of x inches.  

Therefore, measures of each side of the candy box will become

Length = (43 - 2x)

Width = (23 - 2x)

Height = x

Now we have to calculate the value of x for which volume of the box should be maximum.

Volume (V) = Length×Width×Height

V = (43 -2x)(23 - 2x)(x)

  = [(43)×(23) - 46x - 86x + 4x²]x

  = [989 - 132x + 4x²]x

  = 4x³- 132x² + 989x

Now we find the derivative of V and equate it to 0

[tex]\frac{dV}{dx}=12x^{2}-264x+989[/tex] = 0

Now we get values of x by quadratic formula

[tex]x=\frac{264\pm \sqrt{264^{2}-4\times 12\times 989}}{2\times 12}[/tex]

x = 17.212, 4.79

Now we test it by second derivative test for the maximum volume.

[tex]\frac{d"V}{dx}= 24x - 264[/tex]

For x = 17.212

[tex]\frac{d"V}{dx}= 24(17.212)-264=413.088-264=149.088[/tex]

This value is > 0 so volume will be minimum.

For x = 4.79

[tex]\frac{d"V}{dx}=24(4.79)-264=-149.04[/tex]

-149.04 < 0, so volume of the box will be maximum.

Therefore, for x = 4.79 inches volume of the box will be maximum.

To find the size of the square to cut from each corner to attain maximum volume, one needs to create a function for the volume based on the size of the cut, derive it, and solve for x when the derivative equals zero. However, this solution might require advanced calculus.

In this case, we're dealing with a problem in maximum volume. Let's say the size of the square cut is x. The length, width, and height of the box would then be 43-2x, 23-2x, and x, respectively. The volume of the box will then be (43-2x)(23-2x)*x.

To find the maximum volume, we take the derivative of this function (V'(x)) and find for which value of x it equals zero. But as this is a somewhat complex calculus problem, an alternative approach might be to solve it graphically or computationally, seeking for what value of x the volume becomes maximum.

For more detailed calculus solution, consult a mathematics teacher or resources that delve deeper into maximum and minimum problems within calculus.

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Answer with explanation:

The expansion  of

  [tex](1+x)^n=1 + nx +\frac{n(n-1)}{2!}x^2+\frac{n(n-1)(n-2)}{3!}x^3+......[/tex]

where,n is a positive or negative , rational number.

Where, -1< x < 1

Expansion of

 [tex](1-x^2)^{-5}=1-5 x^2+\frac{(5)\times (6)}{2!}x^4-\frac{5\times 6\times 7}{3!}x^6+\frac{5\times 6\times 7\times 8}{4!}x^8-\frac{5\times 6\times 7\times 8\times 9}{5!}x^{10}+\frac{5\times 6\times 7\times 8\times 9\times 10}{6!}x^{12}+....[/tex]

Coefficient of [tex]x^{12}[/tex] in the expansion of [tex](1-x^2)^{-5}[/tex] is

        [tex]=\frac{5\times 6\times 7\times 8\times 9\times 10}{6!}\\\\=\frac{15120}{6\times 5 \times 4\times 3 \times 2 \times 1}\\\\=\frac{151200}{720}\\\\=210[/tex]

⇒As the expansion [tex](1-x^2)^{-5}[/tex] contains even power of x , so there will be no term containing [tex]x^{17}[/tex].

Answer:

-1/4 meter per minute

Step-by-step explanation:

Since, the volume of a cube,

[tex]V=r^3[/tex]

Where, r is the edge of the cube,

Differentiating with respect to t ( time )

[tex]\frac{dV}{dt}=3r^2\frac{dr}{dt}[/tex]

Given, [tex]\frac{dV}{dt}=-3\text{ cubic meters per minute}[/tex]

Also, V = 8 ⇒ r = ∛8 = 2,

By substituting the values,

[tex]-3=3(2)^2 \frac{dr}{dt}[/tex]

[tex]-3=12\frac{dr}{dt}[/tex]

[tex]\implies \frac{dr}{dt}=-\frac{3}{12}=-\frac{1}{4}[/tex]

Hence, the rate of change of an edge is -1/4 meter per minute.

The rate of change of an edge of the cube when the volume is exactly 8 cubic meters is -0.25 meters per minute, calculated using the formula for the volume of a cube and the chain rule for differentiation.

The student seeks to find the rate of change of an edge of a cube when the volume is decreasing at a specific rate. Given that the volume decreases at a rate of 3 cubic meters per minute, we can find the rate at which the edge length changes using the formula for the volume of a cube, which is V = s^3, where V is volume and s is the edge length.

To determine the rate of change of the edge length, we can use the chain rule in calculus to differentiate the volume with respect to time: dV/dt = 3( s^2 )(ds/dt). We know that dV/dt = -3 m^3/min and that when the volume V = 8 m^3, the edge length s can be found by taking the cube root of the volume, which is 2 meters. By substituting these values, we solve for ds/dt, which is the rate of change of the edge length. The resulting calculation is ds/dt = (dV/dt) / (3s^2) = (-3 m^3/min) / (3(2m)^2) = -0.25 m/min.

Answer:

The cost difference between lowest and highest bid $ 251.20

Step-by-step explanation:

Given,

The average quote for the traffic control subcontractor = $ 1570,

Also, the lowest bid is 4 % under average,

That is, lowest bid = average quote - 4% average quote

= 1570 - 4% of 1570

[tex]=1570-\frac{4\times 1570}{100}[/tex]

[tex]=1570-\frac{6280}{100}[/tex]

[tex]=1570-62.80[/tex]

[tex]=\$1507.2[/tex]

While, the highest bid is 12% above average,

That is, the highest bid = average quote + 12% average quote

= 1570 + 12% of 1570

[tex]=1570+\frac{12\times 1570}{100}[/tex]

[tex]=1570+\frac{18840}{100}[/tex]

[tex]=1570+188.4[/tex]

[tex]=\$1758.4[/tex]

Hence,  the cost difference between lowest and highest bid = $ 1758.4 - $ 1507.2 = $ 251.20

Answer:

So the vectors are linearly independent.

Step-by-step explanation:

So if they are linearly independent then the following scalars in will have the condition a=b=c=0:

a(2,3,1)+b(2,-5,-3)+c(-3,8,-5)=(0,0,0).

We have three equations:

2a+2b-3c=0

3a-5b+8c=0

1a-3b-5c=0

Multiply last equation by -2:

2a+2b-3c=0

3a-5b+8c=0

-2a+6b+10c=0

Add equation 1 and 3:

0a+8b+7c=0

3a-5b+8c=0

-2a+6b+10c=0

Divide equation 3 by 2:

0a+8b+7c=0

3a-5b+8c=0

-a+3b+2c=0

Multiply equation 3 by 3:

0a+8b+7c=0

3a-5b+8c=0

-3a+9b+6c=0

Add equation 2 and 3:

0a+8b+7c=0

3a-5b+8c=0

0a+4b+13c=0

Multiply equation 3 by -2:

0a+8b+7c=0

3a-5b+8c=0

0a-8b-26c=0

Add equation 1 and 3:

0a+0b-19c=0

3a-5b+8c=0

0a-8b-26c=0

The first equation tells us -19c=0 which implies c=0.

If c=0 we have from the second and third equation:

3a-5b=0

0a-8b=0

0a-8b=0

0-8b=0

-8b=0 implies b=0

We have b=0 and c=0.

So what is a?

3a-5b=0 where b=0

3a-5(0)=0

3a-0=0

3a=0 implies a=0

So we have a=b=c=0.

So the vectors are linearly independent.

Final answer:

To find out if the vectors (2, 3, l), (2, -5, -3), and (-3, 8, -5) are linearly dependent or independent, set up a linear system with the vectors and look for non-trivial solutions.

Explanation:

To determine whether the vectors (2, 3, l), (2, -5, -3), and (-3, 8, -5) are linearly dependent or linearly independent, we set up the equation a(2, 3, l) + b(2, -5, -3) + c(-3, 8, -5) = (0, 0, 0), where a, b, and c are scalars.

If only the trivial solution exists, where a = b = c = 0, then the vectors are linearly independent. If a non-trivial solution exists, then the vectors are linearly dependent.

Let's solve the system of linear equations generated from the above equation:

Using the methods for solving systems of linear equations, such as Gaussian elimination, we can determine whether a unique solution exists.

If the determinant of the coefficients matrix is non-zero, the system has a unique solution, indicating linear independence. Otherwise, a non-unique solution indicates linear dependence, and we can express

Frequency--

It is the number of times an outcome occurs while performing an experiment some " n " number of times.

Relative frequency--

It is the ratio of the frequency of an outcomes to the total number of times an experiment is been performed.

Here there are TOTAL : 120 responses and three outcomes A , B and C.

The frequency table is given as follows:

Outcome         A           B            C

Frequency       64         23           33

and the Relative frequency table is given as follows:

Outcome                          A              B               C

Relative frequency         64/120     23/120      33/120

i.e. the Relative frequency table is given by:

Outcome                         A              B               C

Relative frequency         0.53         0.19          0.28    

The frequency distribution for the given sample is: A: 64, B: 23, C: 33. The relative frequency distribution is: A: 0.53, B: 0.19, C: 0.28.

To find the frequency distribution, we simply count the number of occurrences of each response. For the given sample of 120 responses, we have:

A: 64 responses

B: 23 responses

C: 33 responses

To find the relative frequency distribution, we divide the frequency of each response by the total number of responses (120). The relative frequencies, rounded to two decimal places, are:

A: 0.53

B: 0.19

C: 0.28

Answer: -0.9 ; inelastic

Explanation:  

Given:

The average price of wheat per metric ton in 2012 = $305.75

Demand (in millions of metric tons) in 2012 = 672

The average price of wheat per metric ton in 2013 =  $291.56

Demand (in millions of metric tons) in 2013 = 700

We will compute the elasticity using the following formula:

ε = [tex]\frac{\frac{(Q_{2} - Q_{1})}{\frac{(Q_{2} +Q_{1})}{2}}}{\frac{(P_{2} - P_{1})}{\frac{(P_{2} +P_{1})}{2}}}[/tex]

ε = [tex]\frac{\Delta Q}{\Delta P}[/tex]

Now , we'll first compute  [tex]\Delta Q[/tex]

i.e.  [tex]\frac{\Delta Q}{\Delta P}[/tex] = [tex]\frac{(700 - 672)}{\frac{(700 +672)}{2}}[/tex]

[tex]\Delta Q[/tex] = 0.04081

Similarly for  [tex]\Delta P[/tex]

i.e. [tex]\Delta P[/tex] = [tex]\frac{(291.56 - 305.75)}{\frac{(261.56 +305.75)}{2}}[/tex]

[tex]\Delta P[/tex] = -0.0475

ε = [tex]\frac{0.04081}{-0.0475}[/tex]

ε = -0.859 [tex]\simeq[/tex] -0.9

[tex]\because[/tex] we know that ;

If, ε > 1 ⇒ Elastic

ε < 1 ⇒ Inelastic

ε = 1 ⇒ unit elastic

[tex]\because[/tex] Here , ε = -0.859 [tex]\simeq[/tex] -0.9

Therefore ε is inelastic.

Answer:

The quotient is (-x³ + 4x² + 4x - 8) and the remainder is 0

Step-by-step explanation:

Look to the attached file

Answer:

4013.45

Step-by-step explanation:

Given,

Purchased amount of the bond, P = 3500,

Annual rate of simple interest, r = 4.89% = 0.0489,

Time ( in years ), t = 3,

Since, the total amount of a bond that earns simple interest is,

[tex]A=P(1+r\times t)[/tex]

By substituting values,

The amount of the bond would be,

[tex]=3500(1+0.0489\times 3)[/tex]

[tex]=3500(1.1467)[/tex]

[tex]=4013.45[/tex]

Answer:13 revolution

Step-by-step explanation:

Given  data

Wheel initial angular velocity[tex]\left ( \omega \right ) [/tex]=18 rad/s

Contant angular deaaceleration[tex]\left ( \alpha \right )[/tex]=2[tex]rad/s^2[/tex]

Time required to stop wheel completely=t sec

[tex]\omega =\omega_0 + \aplha t[/tex]

0 =18 +[tex]\left ( -2\right )t[/tex]

t=9 sec

Therefore angle turn in 9 sec

[tex]\theta [/tex]=[tex]\omega_{0} t[/tex]+[tex]\frac{1}{2}[/tex][tex]\left ( \alpha\right )t^{2}[/tex]

[tex]\theta [/tex]=[tex]18\times 9[/tex]+[tex]\frac{1}{2}[/tex][tex]\left ( -2\right )\left ( 9\right )^2[/tex]

[tex]\theta [/tex]=81rad

therefore no of turns(n) =[tex]\frac{81}{2\times \pi}[/tex]

n=12.889[tex]\approx [/tex]13 revolution

Answer:

Angle made by secant line equals[tex]56.7251^{o}[/tex]

Step-by-step explanation:

Solpe of a line joining points [tex](x_{1},y_{1}),(x_{2},y_{2})[/tex] is given by

[tex]tan(\theta)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where [tex]y_{i}=f(x_{i})[/tex]

Applying values we get

[tex]tan(\theta)=\frac{7.1-3.9}{3.6-1.5}\\\\\theta =tan^{-1}\frac{32}{21}\\\\\theta=56.7251^{o}[/tex]

Answer:

.008000

Step-by-step explanation:

The first digit is either 0,1,2,3,4

P( right guess) = 1/5

The second digit is either 0,1,2,3,4

P( right guess) = 1/5

The third digit is either 0,1,2,3,4

P( right guess) = 1/5

Since they are independent

P( right,right,right) = 1/5*1/5*1/5 = 1/125 =.008

To six decimal places = .008000

To solve the problem, let's consider each piece of information step by step:
1. The password is 3 digits long.
2. Each digit can be any number from 0 to 4.
Since there are 5 choices for each digit (0, 1, 2, 3, or 4), we calculate the total number of distinct combinations possible for a 3-digit password where each digit has 5 possibilities.
For each place of the three digits, we have 5 choices, which gives us a total combination count using the Multiplication Principle:
- First digit: 5 choices (0-4)
- Second digit: 5 choices (0-4)
- Third digit: 5 choices (0-4)
To find the total number of different password combinations, we multiply the number of choices for each digit:
Total combinations = 5 (choices for the first digit) × 5 (choices for the second digit) × 5 (choices for the third digit) = \( 5^3 = 125 \) possible password combinations.
Each of these combinations is equally likely if the hacker guesses at random. Hence, the probability that the hacker guesses the correct password on the first try is 1 out of the total number of combinations.
Therefore, the probability is:
\( P(\text{correct on first try}) = \frac{1}{125} \)
Let's convert this probability to a decimal and then round it to six decimal places:
\( P(\text{correct on first try}) = \frac{1}{125} = 0.008 \)
When rounded to six decimal places, the probability is:
\( P(\text{correct on first try}) \approx 0.008000 \)
So, the probability that the hacker guesses the password correctly on the first try is approximately 0.008000.

Answer:

H(3) = 288 feet

H(4) = 320 feet

H(5) = 320 feet

H(6) = 288 feet

Step-by-step explanation:

A ball is shot out of a cannon at ground level so the ball will follow a parabolic path.

Since height H and time t of the ball have been described by a function H(t) = 144t - 16t²

Then we have to find the values of H(3), H(4), H(5) and H(6).

H(3) = 144×3 - 16(3)²

       = 432 - 144

       = 288 feet

H(4) = 144×4 - 16(4)²

       = 576 - 256

       = 320 feet

H(5) = 144×5 - 16(5)²

       = 720 - 400

       = 320 feet

H(6) = 144×6 - 16(6)²

       = 864 - 576

       = 288 feet

Here we are getting the value like H(3), H(6) and H(4), H(5) are same because in a parabolic path ball first increase in the height above the ground then after the maximum height it decreases.

Therefore, after t = 3 and t = 6 heights of the canon ball are same. Similarly after t = 4 and t = 5 heights of the canon above the ground are same.

The heights of the ball at different times are calculated by substituting the times into the quadratic function H(t) = 144t - 16t². Some heights are equal because the ball reaches the same height on its way up and on its way down due to the parabolic path of the projectile motion.

The height function for the ball being shot out of a cannon is H(t) = 144t - 16t². This is a quadratic function, which models projectile motion. To find the heights at specific times we substitute these times into the function.

Notice that H(4) = H(5) = 320 feet. This is because the path of the ball follows parabolic motion. The ball reaches the same height of 320 feet on its way up (at 4 seconds) and on its way down (at 5 seconds), which is why some output values are equal.

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Answer:

The solution of the given initial value problems in explicit form is [tex]y=x-x^2-2[/tex]  and the solutions are defined for all real numbers.

Step-by-step explanation:

The given differential equation is

[tex]y'=1-2x[/tex]

It can be written as

[tex]\frac{dy}{dx}=1-2x[/tex]

Use variable separable method to solve this differential equation.

[tex]dy=(1-2x)dx[/tex]

Integrate both the sides.

[tex]\int dy=\int (1-2x)dx[/tex]

[tex]y=x-2(\frac{x^2}{2})+C[/tex]                  [tex][\because \int x^n=\frac{x^{n+1}}{n+1}][/tex]

[tex]y=x-x^2+C[/tex]              ... (1)

It is given that y(1) = -2. Substitute x=1 and y=-2 to find the value of C.

[tex]-2=1-(1)^2+C[/tex]

[tex]-2=1-1+C[/tex]

[tex]-2=C[/tex]

The value of C is -2. Substitute C=-2 in equation (1).

[tex]y=x-x^2-2[/tex]

Therefore the solution of the given initial value problems in explicit form is [tex]y=x-x^2-2[/tex] .

The solution is quadratic function, so it is defined for all real values.

Therefore the solutions are defined for all real numbers.

Answer:

A=331.84 m2

Step-by-step explanation:

Hello

The density of a object is defined by

[tex]d=\frac{m}{v}[/tex]

d is the density

m is the mass of the object

v es the volume of the object

We  have

[tex]thickness= t =2.87 * 10^{-7} m\\\ A=unknown=area\\ Volume=Area*thickness\\m=1 kg \\\\\\d=10500kg/m^{3}[/tex]

[tex]d=\frac{m}{v}\\ v=\frac{m}{d}\\ A*t=\frac{m}{d}\\ A=\frac{m}{d*t}\\ \\A=\frac{1 kg}{10500\frac{kg}{m^{3} }*2.87*10^{-7}m}\\A=331.84m^{2}[/tex]

I hope it helps

Pedro owns 5 7/10 acres of farmland and grows beets on 1/8 of it. The calculation to determine the area used for beets is to convert 5 7/10 to an improper fraction (57/10), multiply by 1/8 to get 57/80, which is 0.7125 acres.

The question asks us to calculate the amount of farmland Pedro uses to grow beets. Pedro owns 5 7/10 acres of farmland and grows beets on 1/8 of his land. To find out how many acres he uses for beets, we do the following calculation:

Therefore, Pedro grows beets on 0.7125 acres of land.

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Final answer:

Pedro grows beets on 57/80 acres of his land. First, convert 5 7/10 acres to the improper fraction 57/10, then multiply by 1/8 to find the area for beets.

Explanation:

The question is asking us to calculate the amount of land Pedro uses to grow beets. Since Pedro owns 5 7/10 acres of farmland and grows beets on 1/8 of the land, we need to find what 1/8 of 5 7/10 acres is. To do this, we convert 5 7/10 to an improper fraction, which is 57/10 acres. Then, we multiply 57/10 by 1/8 to find the portion of the land used for beets.

Here is the calculation step by step:

Convert the mixed number 5 7/10 to an improper fraction: 57/10.

Multiply 57/10 by 1/8 to get the fraction of the land used for beets.

57/10 × 1/8 = (57 × 1) / (10 × 8) = 57 / 80

Convert the fraction 57/80 to its decimal form or directly to acres to get the final answer.

Therefore, Pedro grows beets on 57/80 acres of his farmland, which can be converted to a decimal to get an exact measure in acres if needed.

Answer:

f(-4)=60 and g(-6)=17

Step-by-step explanation:

Plug in -4 for x-values

Square -4

Multiply 3 by 16 and -3 by -4 then solve

Simplify

Plug in -6 for x

Multiply -3 by -6

Subtract 1

Simplify

For this case we have the following functions:

[tex]f (x) = 3x ^ 2-3x\\g (x) = 3x-1[/tex]

We must find the value of the function [tex]f (x)[/tex] when [tex]x = -4[/tex], then:

[tex]f (-4) = 3 (-4) ^ 2-3 (-4)\\f (-4) = 3 * 16 12\\f (-4) = 48 12\\f (-4) = 60[/tex]

We must find the value of the function g (x) when [tex]x = -6[/tex], then:

[tex]g (-6) = 3 (-6) -1\\g (-6) = - 18-1\\g (-6) = - 19[/tex]

Answer:

[tex]f (-4) = 60\\g (-6) = - 19[/tex]

Answer:

option d)378

Step-by-step explanation:

Given that a researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure.

Margin of error should be at most 6% = 0.06

Let us assume p =0.5 as when p =0.5 we get maximum std deviation so this method will give the minimum value for n the sample size easily.

We have std error = [tex]\sqrt{\frac{pq}{n} } =\frac{0.5}{\sqrt{n} }[/tex]

For 98%confident interval Z critical score = 2.33

Hence we have margin of error = [tex]2.33(\frac{0.5}{\sqrt{n} } <0.06\\n>377[/tex]

Hence answer is option d)378

The size of the sample needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 6% is; 376

We are told that Margin of error should be at most 6% = 0.06

Formula for margin of error is;

M = z√(p(1 - p)/n)

we are given the confidence level to be 98% and the z-score at this confidence level is 2.326

Since no standard deviation then we assume it is maximum and as such  assume p =0.5 which will give us the minimum sample required.

Thus;

0.06 = 2.326√(0.5(1 - 0.5)/n)

(0.06/2.326)² = (0.5²/n)

solving for n gives approximately n = 376

Thus, the size of the sample required is 376

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The probability that a drum meets the guarantee is approximately 0.3625. The standard deviation needed for a 0.97 probability is -0.691 pounds.

To find the probability that a drum meets the guarantee, we need to calculate the z-score for the value of 100 pounds using the formula z = (x - mean) / standard deviation. Plugging in the values, we get z = (100 - 101.3) / 3.68 = -0.353. Using a z-score table or a calculator, we can find that the probability is approximately 0.3625.

To find the standard deviation that would give a probability of 0.97, we need to find the z-score that corresponds to that probability. Using a z-score table or a calculator, we find that the z-score is approximately 1.88. Plugging this value into the z-score formula and rearranging for the standard deviation, we get standard deviation = (100 - 101.3) / 1.88 = -0.691. Rounded to three decimal places, the standard deviation would need to be -0.691 pounds.

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(a) The probability that a drum meets the guarantee is approximately 0.6381.

(b) To achieve a 97% probability of meeting the guarantee, the standard deviation would need to be approximately 1.383 pounds.

(a) To determine the probability that a drum contains at least 100 lbs of solvent, we need to find the Z-score. The Z-score formula is:

Z = (X - μ) / σ

Where:

First, compute the Z-score:

Z = (100 - 101.3) / 3.68 = -1.3 / 3.68 ≈ -0.3533

Next, we look up the Z-score in the standard normal distribution table or use a calculator to find the probability:

P(Z > -0.3533) ≈ 0.6381

So, the probability that a drum meets the guarantee is approximately 0.6381.

(b) To find the standard deviation such that the probability of the drum meeting the guarantee is 0.97, we need to solve for σ when P(Z > Z₀) = 0.97.

We know P(Z > Z₀) = 0.97 implies P(Z < Z₀) = 0.03 (since it is the complementary probability).

Using the Z-table or a calculator, we find the Z-score for the 3rd percentile, which is approximately:

Z₀ ≈ -1.88

Now, use the Z-score formula in reverse to solve for σ:

Z₀ = (X - μ) / σ

Plugging in the values:

-1.88 = (100 - 101.3) / σ

Solving for σ, we get:

σ = (101.3 - 100) / 1.88 ≈ 1.383

Thus, the standard deviation would need to be approximately 1.383 lbs to achieve a 97% probability that each drum meets the guarantee.

Answer:

B. Meaningful use

Step-by-step explanation:

Meaningful use is the use of EHRs in a meaningful manner.

Answer: C. 2,272 mg

Step-by-step explanation:

Given : The recommended dose of a particular drug is 0.1 g/kg.

We know that 1 kilogram is equals to approximately 2.20 pounds.

Then ,[tex]\text{1 pound}=\dfrac{1}{2.20}\text{ kilogram}[/tex]

[tex]\Rightarrow\text{50 pounds}=\dfrac{1}{2.20}\times50\approx22.72text{ kilogram}[/tex]

Now, the dose of drug should be given to a 22.72 kilogram patient is given by :-

[tex]22.72\times0.1=2.272g[/tex]

Since 1 grams = 1000 milligrams

[tex]2.272\text{ g}=2,272\text{ mg}[/tex]

Hence , 2,272 mg of the drug should be given to a 50 lb. patient.