HELP PLEASEEE, I REALLY DO NOT UNDERSTAND THESE QUESTIONS. THANK YOU HELP IS VERY MUCH APPRECIATED!!! ASAP
5) The mean salary of 5 employees is $40300. The median is $38500. The lowest paid employee's salary is $32000. If the lowest paid employee gets a $3100 raise, then ...


a) What is the new mean?

New Mean = $



b) What is the new median?

New Median = $

Answer:

[tex]\large\boxed{\lim\limits_{x\to7}f(x)=0}[/tex]

Step-by-step explanation:

[tex]f(x)=\left\{\begin{array}{ccc}x^2-8x+7&if&x<7\\-x^2+8x-7&if&x\geq7\end{array}\right\\\\\lim\limits_{x\to7}f(x)=?\\\\\lim\limits_{x\to7^-}(x^2-8x+7)=7^2-(8)(7)+7=49-56+7=0\\\\\lim\limits_{x\to7^+}(-x^2+8x-7)=-7^2+(8)(7)-7=-49+56-7=0\\\\\lim\limits_{x\to7^-}=\lim\limits_{x\to7^+}=0\Rightarrow\lim\limits_{x\to7}f(x)=0[/tex]

In this question, we need to find the limit of the piecewise function f(x) as x approaches 7. After substitution of x=7 in both conditions of the function, we find that the limit of function f(x) exists and equals 0.

To find the limit of the function f(x) as x approaches 7, we need to look at both cases as defined by the function, because f(x) is a piecewise function.

1. For x < 7, we substitute x as 7 in the function x^2 - 8x + 7:

((7)^2 - 8*(7) + 7 = 0)

2. For x >= 7, we substitute x as 7 in the function -x^2 + 8x - 7:

(-(7)^2 + 8*(7) - 7 = 0)

In this case, for both conditional statements the results are the same, so the limit of the function exists and equals:

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Answer:

x =  3 ±sqrt(5)

Step-by-step explanation:

(x - 3)^2 = 5

Take the square root of each side

Sqrt( (x - 3)^)2 =±sqrt( 5)

x-3 = ±sqrt(5)

Add 3 to each side

x-3+3 = 3 ±sqrt(5)

x =  3 ±sqrt(5)

Answer:

[tex]A'(t)=3\sqrt{t}+\frac{3}{2\sqrt{t}}[/tex]          

Step-by-step explanation:

Given : Length of rectangle = 2t+3

           Height of rectangle = [tex]\sqrt{t}[/tex]

To Find: Find the rate of the change of the area with respect to time.

Solution:

Area of rectangle = [tex]Length \times Width[/tex]

                              = [tex](2t+3) \times \sqrt{t}[/tex]

                              = [tex]2t^{\frac{3}{2}}+3t^{\frac{1}{2}}[/tex]

                              = [tex]2t^{\frac{3}{2}}+3t^{\frac{1}{2}}[/tex]

So, [tex]A(t)=2t^{\frac{3}{2}}+3t^{\frac{1}{2}}[/tex]

[tex]\frac{d}{dx} (x^n)=nx^{n-1}[/tex]

[tex]A'(t)=\frac{3}{2} \times 2t^{\frac{3}{2}-1}+\frac{1}{2} \times 3t^{\frac{1}{2}-1}[/tex]

[tex]A'(t)=3t^{\frac{1}{2}}+\frac{3}{2}t^{\frac{-1}{2}}[/tex]

[tex]A'(t)=3t^{\frac{1}{2}}+\frac{3}{2}t^{\frac{-1}{2}}[/tex]          

[tex]A'(t)=3\sqrt{t}+\frac{3}{2\sqrt{t}}[/tex]              

Hence the rate of the change of the area with respect to time is    [tex]A'(t)=3\sqrt{t}+\frac{3}{2\sqrt{t}}[/tex]                                                                                  

To find the rate of change of the area with respect to time, differentiate the area function and substitute the given expressions for the dimensions. The rate of change of the area with respect to time is 2√t + 3/√t.

To find the rate of change of the area of a rectangle with respect to time, we need to differentiate the area function and then substitute the given expressions for the dimensions. The formula for the area of a rectangle is A = length × height. So, A(t) = (2t + 3)(√t). To find the derivative of A(t), which represents the rate of change of the area, we can use the product rule of differentiation.

A'(t) = (2t + 3) × d/dt(√t) + (√t) × d/dt(2t + 3)

Let's differentiate each term of the product separately. Differentiating √t, we get 1/(2√t).

Substituting the values back into the equation and simplifying, we have:

A'(t) = 2√t + 6/(2√t)

Our final answer for the rate of change of the area with respect to time is A'(t) = 2√t + 3/√t.

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Answer:

I don't know if it's low enough,but i can give you another answer.

Step-by-step explanation:

So the probability of finding bacteria in a public swimming are is 0.005.

But if you combine the samples then the probability of finding bacteria is 0.01 because you add the probabilities of finding bacteria of the two swimming pools.

Final answer:

The probability that a computer contains neither a virus nor a worm is found by subtracting the probability of having a virus or worm from 1. Based on the provided probabilities, this calculation results in a probability of 0.82 or 82% for a computer to be free of both.

Explanation:

To calculate the probability that a computer contains neither a virus (V) nor a worm (W), we use the principle of complementation. Given that P(V) = 0.17, P(W) = 0.05, and P(V AND W) = 0.04, we want to find P(neither V nor W). This is the same as finding 1 - P(V OR W). The probability of V OR W is given by P(V) + P(W) - P(V AND W), which simplifies to 0.17 + 0.05 - 0.04 = 0.18. Therefore, the probability of neither V nor W is 1 - 0.18 = 0.82.

So, the probability that the computer is free of both a virus and a worm is 0.82 or 82%.

The probability that you win exactly one game is:

                               0.37

The probability that you win exactly one game is:

Probability you win first but not second+Probability you win second but not first.

=  0.60×0.25+0.40×0.55

=  0.37

( since probability of losing second game when you win first  is: 1-0.75=0.25

and probability that you lose first game is: 1-0.60=0.40 )

Final answer:

The probability of winning exactly one game, rounded to two decimal places, is 0.37.

Explanation:

Probability of winning the first game = 0.60

Probability of winning the second game if the first game is won = 0.75
Probability of winning the second game if the first game is lost = 0.55

To find the probability of winning exactly one game, we calculate the probability of winning the first game and losing the second game, plus the probability of losing the first game and winning the second game:

Answer: 0.345

Step-by-step explanation:

Given: The the setup for this hypothesis test:

[tex]H_0:p=0.65\n\nH_a:p < 0.65[/tex]

Since , the alternative hypothesis is left tail , so the test is left tail test.

[tex]P_0=0.65\n\nQ_0=1-0.65=0.35\n\np=(126)/(200)=0.63[/tex]

The test static for population proportion is given by :-

[tex]z=\frac{p-P_0}{\sqrt{(P_0Q_0)/(n)}}\n\n\Rightarrow\ z=\frac{0.63-0.65}{\sqrt{(0.65-0.35)/(126)}}=−0.409878030638\approx-0.4[/tex]

The p-value of [tex]z = P(z < -0.4)= 0.3445783\approx0.345[/tex]

The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

Utilizing the TI-83, 83+, 84, 84+ Calculator to estimate these probabilities

Go to 2nd DISTR, and select item 2: normalcdf

The syntax is: normalcdf (lower bound, upper bound, mean, standard deviation)

a) P(1100 <= X <= 1500)

= normalcdf(1100, 1500, 1252, 129)

= 0.8534

b) P(X < 1125)

= normalcdf(-1E99, 1125, 1252, 129)

= 0.1624

c) P(X > 1200)

= normalcdf(1200, 1E99, 1252, 129)

= 0.6566 = 65.66%

d) P(X < 1000)

= normalcdf(-1E99, 1000, 1252, 129)

= 0.0254 = approx. 3rd percentile

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In this Physics problem, we calculate the horizontal distance a stone travels when thrown horizontally from a cliff to determine the ratio of heights between two buildings.

The horizontal distance the stone will travel can be calculated using the formula:

d = v*t

Where d is the distance, v is the initial velocity, and t is the time of flight. Using the information given, we can calculate the distance the stone from block A will travel, and then find the ratio of building A's height to building B's height.

Answer:

27, 29, 31

Step-by-step explanation:

We want to find a, b, c so that

a + c = b + 29

and

a = b - 2, c = b + 2

and

b is odd.

This results in

b - 2 + b + 2 = b + 29

with one solution:

b = 29.

[tex]2n-1,2n+1,2n+3[/tex] - 3 consecutive odd integers

[tex]2n-1+2n+3=2n+1+29\\2n=28\\n=14\\\\2n-1=27\\2n+1=29\\2n+3=31[/tex]

27,29,31

Yes.

1467-776=691

Which means 776 believed the country was protected and 691 believed the country wasn't.

To determine if a majority of surveyed citizens in 1945 believed the US could develop protection against atomic bombs, a one-sample proportion test must be conducted. If the test results in a p-value less than the 0.01 level of significance, we can conclude that a majority did hold this belief. This involves concepts in hypothesis testing and statistics.

The question you're asking requires a basic understanding of hypothesis testing in statistics. Let's denote the proportion of those who answered 'yes' as p and the total number of citizens surveyed as n.

In this case, p = 776 / 1467 = 0.529, meaning 52.9% of the sampled citizens responded yes leading to the claim that a majority believe the US could develop protection against atomic bombs.

However, to determine if this is truly a majority at a 0.01 level of significance, we need to conduct a one-sample proportion test. Our null hypothesis (H0) would state that the population proportion is 0.5 (no majority), while our alternative hypothesis (H1) would be that the population proportion is greater than 0.5 (there is a majority).

If we find a p-value less than the 0.01 level of significance from the test, we reject H0 and conclude that a majority of Americans did believe in the capacity for atomic bomb protection. If the p-value is greater than 0.01, we would fail to reject H0, concluding that a majority belief can't be inferred.

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Answer:

Sheridan Service reduce its debt $1,392, now its due is $1,200.

Step-by-step explanation:

Sheridan Service received a shipment on January 15, with an invoice dated January 14, terms 4/10 E.O.M.

Term written on the invoice means 4% discount if paid within 10 days or full amount is due for the payment at the End of the Month.

Invoice shipment having amount = $2,592

Partial payment of the invoice by check = $1,392

So amount due = 2,592 - 1,392 = $1,200

Sheridan Service reduce its debt $1,392, now its due is $1,200.

Answer:

The difference in volume of the two models is [tex]\frac{128}{3}\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a square pyramid is equal to

[tex]V=\frac{1}{3}b^{2}h[/tex]

where

b is the length of the side of the square base

h is the height of the pyramid

step 1

Find the volume of Amy's model

we have

[tex]b=8\ in[/tex]

[tex]h=5\ in[/tex]

substitute

[tex]V=\frac{1}{3}(8)^{2}(5)[/tex]

[tex]V=\frac{320}{3}\ in^{3}[/tex]

step 2

Find the volume of Alex's model

we have

[tex]b=8\ in[/tex]

[tex]h=3\ in[/tex]

substitute

[tex]V=\frac{1}{3}(8)^{2}(3)[/tex]

[tex]V=\frac{192}{3}\ in^{3}[/tex]

step 3

Find the difference in volume of the two models

[tex]\frac{320}{3}\ in^{3}-\frac{192}{3}\ in^{3}=\frac{128}{3}\ in^{3}[/tex]

Answer: 0.7881446

Step-by-step explanation:

Given : Mean : [tex]\mu = 267\text{ dollars} [/tex]

Standard deviation : [tex]\sigma =20 \text{ dollars}[/tex]

Sample size : [tex]n=64[/tex]

The formula to calculate the z-score :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x=  267 dollars

[tex]z=\dfrac{267-267}{\dfrac{20}{\sqrt{64}}}=0[/tex]

For x= 269 dollars.

[tex]z=\dfrac{269-267}{\dfrac{20}{\sqrt{64}}}=0.80[/tex]

The P-value : [tex]P(0<z<0.8)=P(z<0.8)-P(z<0)[/tex]

[tex]= 0.7881446-0.5= 0.2881446\approx 0.7881446[/tex]

Hence, the probability that they have a mean cost between 267 dollars and 269 dollars.= 0.7881446

Answer:

There is a 28.81% probability that they have a mean cost between 267 dollars and 269 dollars.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex]

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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

In this problem, we have that:

[tex]\mu = 267, \sigma = 20, n = 64, s = \frac{20}{\sqrt{64}} = 2.5[/tex].

Find the probability that they have a mean cost between 267 dollars and 269 dollars.

This probability is the pvalue of Z when X = 269 subtracted by the pvalue of Z when X = 267. So:

X = 269

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{269 - 267}{2.5}[/tex]

[tex]Z = 0.8[/tex]

[tex]Z = 0.8[/tex] has a pvalue of 0.7881.

X = 267

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{267 - 267}{2.5}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.50.

So there is a 0.7881 - 0.50 = 0.2881 = 28.81% probability that they have a mean cost between 267 dollars and 269 dollars.

Answer:

  (a) 120 square units, underestimate

  (b) 248 square units, overestimate

Step-by-step explanation:

(a) left sum

The left sum is the sum of the areas of the rectangles whose width is the total interval width (8-0) divided by the number of divisions (n=4). The height of each rectangle is the function value at its left edge.

We can compute the sum by adding the function values and multiplying that total by the width of the rectangles:

  left sum = (1 + 5 + 17 + 37)×2 = 60×2 = 120 . . . square units

The curve is increasing throughout the interval of interest, so the left sum underestimates the area under the curve.

__

(b) right sum

The rectangles whose area is the right sum are shown in the attachment, along with the table of function values. The right sum is computed the same way as the left sum, but using the function value on the right side of each subinterval.

  right sum = (5 + 17 + 37 + 65)×2 = 124×2 = 248 . . . square units

The curve is increasing throughout the interval of interest, so the right sum overestimates the area under the curve.

_____

The actual area under the curve on the interval [0, 8] is 178 2/3, just slightly less than the average of the left- and right- sums.

The left-hand and right-hand sums are common methods to estimate the area under a curve. Using n=4, the left-hand sum tends to be an underestimate, while the right-hand sum is usually an overestimate of the actual area.

The integral 8(x²+1)dx from 0 to a is the area under the curve defined by the function 8(x²+1). A common way to approximate this area is by using left-hand and right-hand sums.

(a) Left-Hand Sum: Using n=4, we divide the interval [0, a] into 4 equal subintervals. For each subinterval, we find the left endpoint and plug it into our function, then multiply by the length of the subinterval. Sum these values to get the left-hand sum. This sum is usually an underestimate of the true area as it leaves out the area under the curve that lies to the right of the left-hand rectangle in each subinterval.

(b) Right-Hand Sum: The process is similar to the left-hand sum, but we use the right endpoint of each subinterval. The right-hand sum tends to be an overestimate of the true area as it includes the area above the curve that lies to the right of the rectangle in each subinterval.

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Answer:

a. 47

b. 87

c. 127

Step-by-step explanation:

Assume a total of 4 exams ( first 3 plus a final)

Let final score be X,

Hence,  average score = (85 + 71 + 77 + x) / 4 = (233 + x) / 4

a) to get a C, the average score must be 70

70 = (233 + x) / 4

(233 + x) = 70 (4) = 280

x = 280 - 233 = 47 (Ans)

b) to get a B, the average score must be 80

80 = (233 + x) / 4

(233 + x) = 80 (4) = 320

x = 320 - 233 = 87 (Ans)

c) to get a A, the average score must be 90

90 = (233 + x) / 4

(233 + x) = 90 (4) = 360

x = 360 - 233 =  127 (Ans)

Answer:

B

Step-by-step explanation:

(f-g)(x) just means f(x)-g(x)

so let's do that

make sure you distribute the minus in front of g to it's terms

-12x^3+19x^2-5-7x^2-15

-12x^3+12x^2-20

B.

Answer: 0.9660

Step-by-step explanation:

Given: Mean : [tex]\mu =0[/tex]

Variance : [tex]\sigma^2=2.00[/tex]

⇒ Standard deviation : [tex]\sigma = \sqrt{2}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= -3

[tex]z=\dfrac{-3-0}{\sqrt{2}}=-2.12132034356\approx-2.12[/tex]

The P Value =[tex]P(z<-2.12)=0.017003[/tex]

For x= 3

The P Value =[tex]P(z<2.12)=0.9829969[/tex]

[tex]\text{Now, }P(-3<X<3)=P(X<3)-P(X<-3)\\\\=P(z<2.12)-P(z<-2.12)\\\\=0.9829969-0.017003=0.9659939\approx 0.9660[/tex]

Hence, the probability that a given error will be between -3 and 3=0.9660

The table contains the values from (A)

A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.

Given equation:

limx→2 (x^2+8x−2)

Table A  does a nice job getting closer and closer to x=2, equals, 2 from both sides.

Table D does not make it clear which x-value we are approaching,

Table B only approaches x=1, equals, 1 from both side.

Table C is approaching only the positive side.

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Answer:

19) The domain is (12 , ∞) ⇒ answer C

17) The radical notation is [tex]\sqrt[7]{18y^{2} }[/tex]

10) The definition of number i is √(-1) ⇒ answer C

Step-by-step explanation:

19)

* Lets explain the meaning of the domain of the function

- The domain of any function is the values of x which makes the

  function defined

- Examples:

# In the fraction the denominator con not be zero, then if the function

  is a rational fraction then the domain is all the values of x except

  the values whose make the denominator = 0

# In the even roots we can not put negative numbers under the radical

  because there is no even roots for the negative number belonges to

  the real numbers, then the domain is all the values of x except the

  values whose make the quantity under the radical negative

* Now lets solve the question

∵ f(x) = 3 √(x - 12)

- To find the domain let (x - 12) greater than zero because there is

 no square root for negative value

∵ x - 12 > 0 ⇒ add 12 to both sides

∴ x ≥ 12

∴ The domain is all values of x greater than 12

* The domain is (12 , ∞)

17)

* Lets talk about the radical notation

- The radical notation for the fraction power is:

  the denominator of the power will be the radical and the numerator

  of the power will be the power of the base

- Ex: [tex]x^{\frac{a}{b}}=\sqrt[b]{x^{a}}[/tex]

* Lets solve the problem

∵ (18 y²)^(1/7)

- The power 1/7 will be the radical over (18 y²)

∴ [tex](18y^{2})^{\frac{1}{7}}=\sqrt[7]{18y^{2}}[/tex]

* The radical notation is [tex]\sqrt[7]{18y^{2} }[/tex]

10)

* Lets talk about the imaginary number

- Because there is no even root for negative number, the imaginary

 numbers founded to solve this problem

- It is a complex number that can be written as a real number multiplied

  by the imaginary unit i, which is defined by i = √(-1) or i² = -1

- Ex: √(-5) = √[-1 × 5] = i√5

* The definition of number i is √(-1)

a. We're looking for a scalar function [tex]f(x,y)[/tex] such that [tex]\vec F(x,y)=\nabla f(x,y)[/tex]. This means

[tex]\dfrac{\partial f}{\partial x}=y[/tex]

[tex]\dfrac{\partial f}{\partial y}=x[/tex]

Integrate both sides of the first PDE with respect to [tex]x[/tex]:

[tex]\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx=\int y\,\mathrm dx\implies f(x,y)=xy+g(y)[/tex]

Differentating both sides with respect to [tex]y[/tex] gives

[tex]\dfrac{\partial f}{\partial y}=x=x+\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=C[/tex]

so that [tex]\boxed{f(x,y)=xy+C}[/tex]. A potential function exists, so the fundamental theorem does apply.

Green's theorem also applies because [tex]C[/tex] is a simple and smooth curve.

b. Now with (and I'm guessing as to what [tex]\vec G[/tex] is supposed to be)

[tex]\vec G(x,y)=\dfrac y{x^2+y^2}\,\vec\imath-\dfrac x{x^2+y^2}\,\vec\jmath[/tex]

we want to find [tex]g[/tex] such that

[tex]\dfrac{\partial g}{\partial x}=\dfrac y{x^2+y^2}[/tex]

[tex]\dfrac{\partial g}{\partial y}=-\dfrac x{x^2+y^2}[/tex]

Same procedure as in (a): integrating the first PDE wrt [tex]x[/tex] gives

[tex]g(x,y)=\tan^{-1}\dfrac xy+h(y)[/tex]

Differentiating wrt [tex]y[/tex] gives

[tex]-\dfrac x{x^2+y^2}=-\dfrac x{x^2+y^2}+\dfrac{\mathrm dh}{\mathrm dy}\implies h(y)=C[/tex]

so that [tex]\boxed{g(x,y)=\tan^{-1}\dfrac xy+C}[/tex], which is undefined whenever [tex]y=0[/tex], and the fundamental theorem applies, and Green's theorem also applies for the same reason as in (a).

c. Same as (b) with slight changes. Again, I'm assuming the same format for [tex]\vec H[/tex] as I did for [tex]\vec G[/tex], i.e.

[tex]\vec H(x,y)=\dfrac x{x^2+y^2}\,\vec\imath+\dfrac y{x^2+y^2}\,\vec\jmath[/tex]

Now

[tex]\dfrac{\partial h}{\partial x}=\dfrac x{x^2+y^2}\implies h(x,y)=\dfrac12\ln(x^2+y^2)+i(y)[/tex]

[tex]\dfrac{\partial h}{\partial x}=\dfrac y{x^2+y^2}=\dfrac y{x^2+y^2}+\dfrac{\mathrm di}{\mathrm dy}\implies i(y)=C[/tex]

[tex]\implies\boxed{h(x,y)=\dfrac12\ln(x^2+y^2)+C}[/tex]

which is undefined at the point (0, 0). Again, both the fundamental theorem and Green's theorem apply.

The potential functions for the given vector fields F, G and H are f(x,y) = xy, g(x,y) = (1/2)xy² - arctan(x/y), and h(x,y) = (1/2)(x² + y²). Also, Green's theorem and the Fundamental Theorem of Line Integrals apply under certain conditions and constraints on the fields.

The potential function for F is indeed f(x,y) = xy as the partial derivatives of this function are equal to the components of F. The Fundamental Theorem of Line Integrals applies to F • dr C because F is the gradient of the scalar potential f and C is a closed curve. Green's Theorem applies as well since both F = y i + x j and C satisfy the appropriate conditions of continuity and differentiability.

The potential function for G is g(x,y)= (1/2)xy² - arctan(x/y) when y !=0. It is not defined where y=0. The Fundamental Theorem of Line Integrals does not apply because G is not conservative, meaning it doesn't have a potential function with continuous derivatives everywhere. Green's Theorem does apply to G • dr C because both the vector field G and C satisfy the conditions it requires.

The potential function for H is h(x,y)= (1/2)(x² + y²) and it is defined everywhere except at the origin (0,0) where it becomes undefined because of division by zero in its components. The Fundamental Theorem of Line Integrals does apply to H · dr C but only for curves which avoid the origin, because H is not conservative everywhere. Green's Theorem does not apply to H · dr C because H's components are not differentiable at the origin.

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Check the picture below.

The given vertices define a polygon consisting of a rectangle and a triangle. The areas of the shapes are calculated separately and added together to find the total area of the polygon, which is 20 square units.

The given coordinates define two distinct shapes, a rectangle, and a triangle. Considering point A(0,1), B(0,5), C(4,5), and D(6,1), we can see that the rectangle is A, B, C and a point E(4,1) and the triangle is E, C, D. The area of any rectangle is calculated as

width multiplied by height

. In the case of our rectangle, the width is the distance between A and E - 4 units - and the height is from A to B, or 5-1 = 4 units. Thus, the

area of the rectangle

is 4 * 4 = 16 units

2

. The area of a triangle is calculated as 1/2 * base * height. For triangle ECD, the base is the distance from C to D, or 6-4=2 units, and the height (equal to EC) is 4 units. Thus the

area of the triangle

is 1/2 * 2 * 4 = 4 units

2

. The total

area of the polygon

is the area of the rectangle + the area of the triangle = 16 units

2

+ 4 units

2

= 20 units

2

.

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Answer:

(a) 19.

Step-by-step explanation:

The even numbers in the given range are -14, -12, -10, -8, - 6 , -4 and -2. and  7 more of their positive values. Total 14.

The numbers divisible by 3  and not 2 are -9, -3,  3 and 9.

Also 0 is a multiple of any number

Thus,  number of thrift numbers are  14 + 4 + 1 = 19 (answer).

Answer:

owen

Step-by-step explanation:

Answer:

Shaquille

Step-by-step explanation:

To determine the unit rate for each, divide the number of words by the number of minutes typed.

Ella: 640÷16=40

Harper: 450÷15=30

Owen: 560÷14=40

Shaquille=540÷12=45

Since Shaquille's is the most, we can tell he typed fastest.

Hope this helps!

The particle has position function

[tex]\vec r(t)=\cos t\,\vec\imath+\sin t\,\vec\jmath+3t\,\vec k[/tex]

Taking the derivative gives its velocity at time [tex]t[/tex]:

[tex]\vec v(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=-\sin t\,\vec\imath+\cos t\,\vec\jmath+3\,\vec k[/tex]

a. The particle never moves downward because its velocity in the [tex]z[/tex] direction is always positive, meaning it is always moving away from the origin in the upward direction. DNE

b. The particle is situated 15 units above the ground when the [tex]z[/tex] component of its posiiton is equal to 15:

[tex]3t=15\implies\boxed{t=5}[/tex]

c. At this time, its velocity is

[tex]\vec v(5)=-\sin 5\,\vec\imath+\cos5\,\vec\jmath+3\,\vec k\approx\boxed{0.959\,\vec\imath+0.284\,\vec\jmath+3\,\vec k}[/tex]

d. The tangent to [tex]\vec r(t)[/tex] at [tex]t=5[/tex] points in the same direction as [tex]\vec v(5)[/tex], so that the parametric equation for this new path is

[tex]\vec r(5)+\vec v(5)t\approx\boxed{(0.284+0.959t)\,\vec\imath+(-0.959+0.284t)\,\vec\jmath+(15+3t)\,\vec k}[/tex]

where [tex]0\le t<\infty[/tex].

Answer:

[tex]\large\boxed{y=\dfrac{-9x-2}{5}}[/tex]

Step-by-step explanation:

[tex]9x+5y=-2\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\5y=-9x-2\qquad\text{divide both sides by 5}\\\\y=\dfrac{-9x-2}{5}[/tex]

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{125^2}{125^{\frac{4}{3}}}\implies \cfrac{(5^3)^2}{(5^3)^{\frac{4}{3}}}\implies \cfrac{5^{3\cdot 2}}{5^{3\cdot \frac{4}{3}}}\implies \cfrac{5^6}{5^4}\\\\\\ 5^6\cdot 5^{-4}\implies 5^{6-4}\implies 5^2\implies 25[/tex]

Answer:

The probability is 0.20

Step-by-step explanation:

a) Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- Bob's golf score at his local course follows the normal distribution

- The mean is 92.1

- The standard deviation is 3.8

- The score on his next round of golf will be between 82 and​ 89

- Lets find the z-score for each case

# First case

∵ z = (x - μ)/σ

∵ x = 82

∵ μ = 92.1

∵ σ = 3.8

∴ [tex]z=\frac{82-92.1}{3.8}=\frac{-10.1}{3.8}=-2.66[/tex]

# Second case

∵ z = (x - μ)/σ

∵ x = 89

∵ μ = 92.1

∵ σ = 3.8

∴ [tex]z=\frac{89-92.1}{3.8}=\frac{-3.1}{3.8}=-0.82[/tex]

- To find the probability that the score on his next round of golf will

  be between 82 and​ 89 use the table of the normal distribution

∵ P(82 < X < 89) = P(-2.66 < z < -0.82)

∵ A z-score of -2.66 the value is 0.00391

∵ A z-score of -0.82 the value is 0.20611

∴ P(-2.66 < z < -0.82) = 0.20611 - 0.00391 = 0.2022

* The probability is 0.20

Normal distribution and z-scores are applied in this context. The z-scores for the given range are calculated, followed by finding the correlating probabilities from the z-table, resulting in the probability of Bob's next score falling within the range of 82-89.

To answer this question, we will utilize the concept of z-scores in a normal distribution. A z-score basically explains how many standard deviations a data point (in this case, a golf score) is from the mean.

Firstly, we calculate the z-scores for the limits given. Here, 82 and 89. The formula we use is Z = (X - μ) / σ, where X is the golf score, μ is the mean, and σ is the standard deviation.

The calculated z-scores are then used as references, and we refer a z-table (also known as a standard normal table) to find the probabilities which correspond to these z-scores, and the result is a probability of Bob's next golf score being between 82 and 89.

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Positive product:

[tex](\frac{-2}{5})(\frac{-2}{5})\\(\frac{2}{5})(\frac{2}{5})[/tex]

With multiplication if two negative numbers are being multiplied together the answer is positive. If two positive numbers are being multiplied the answer is also positive. Another way to think of it is, that if two numbers with the SAME sign are being multiplied then the product will always be positive

Negative product:

[tex](\frac{-2}{5})(\frac{2}{5})[/tex]

[tex](\frac{2}{5})(\frac{-2}{5})[/tex]

If a negative and positive number are being multiplied then the product is ALWAYS negative

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

  x = 5

Step-by-step explanation:

The table and a graph of f(x) and g(x) are shown in the attachment. The solution is x=5. The table shows you f(5) = g(5) = 2, as does the graph.

It is generally convenient to make use of a graphing calculator or spreadsheet when repeated evaluation of a function is required.