The plane y=1 intersects the surface z=x5+2xy−y5 in a certain curve. Find the slope of the tangent line of this curve at the point P=(1,1,2).

Answer:

Range of the function → {24, 375}

Step-by-step explanation:

Domain of the function f(x) = 3x³ is {2, 5}

we have to find the range when its domain is {2, 5}

Since x-values of any function define the domain and y-values define the range.

For x = 2,

f(2) = 3(2)³ = 24

For x = 5,

f(5) = 3(5)³ = 375

Therefore, range of the given function for the given domain will be {24, 375}.

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24  

    Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24  

(b) The​ P-value is 0.004.

(c) Reject Upper H 0 because the​ P-value is less than the alpha = 0.01 level of significance.

(d) There is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Step-by-step explanation:

We are given that a simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be x overbar = 18.3 and the sample standard deviation is found to be s = 6.3.

Let [tex]\mu[/tex] = population mean

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24      {means that the population mean is 24}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24     {means that the population mean is different from 24}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 18.3

            s = sample standard deviation = 6.3

            n = sample size = 15

So, the test statistics =  [tex]\frac{18.3-24}{\frac{6.3}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                    =  -3.504

The value of t-test statistics is -3.504.

(b) Now, the P-value of the test statistics is given by;

               P-value = P( [tex]t_1_4[/tex] < -3.504) = 0.002 or 0.2%

For the two-tailed test, the P-value is calculated as = [tex]2 \times 0.002[/tex] = 0.004 or 0.4%.

(c) Since the p-value of the test statistics is less than the level of significance as 0.002 < 0.01, so we will reject our null hypothesis.

(d) This means that we have sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Answer:

Speeds of car 1 and car 4 are same.

Step-by-step explanation:

Speed of an object = [tex]\frac{\text{Distance traveled}}{\text{Time}}[/tex]

For car 1,

Speed of car 1 = [tex]\frac{350}{5}[/tex]

                        = 70 miles per hour

For car 2,

Speed of car 2 = [tex]\frac{240}{4}[/tex]

                         = 60 miles per hour

For car 3,

Speed of car 3 = [tex]\frac{320}{5}[/tex]

                        = 64 miles per hour

For car 4,

Speed of car 4 = [tex]\frac{420}{6}[/tex]

                         = 70 miles per hour

Therefore, speeds of car 1 and car 4 are same.

Answer:

We conclude that the population standard deviation is greater than 50.

Step-by-step explanation:

We are given that a sample of 16 items provides a sample standard deviation of 9.5.

Let [tex]\sigma^{2}[/tex] = population standard deviation

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma^{2} \leq[/tex] 50     {means that the population standard deviation is less than or equal to 50}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma^{2}[/tex] > 50      {means that the population standard deviation is greater than 50}

The test statistics that will be used here is One-sample chi-square test statistics;

                        T.S.  =  [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2}__n_-_1[/tex]

where, s = sample standard deviation = 9.5

           n = sample of items = 16

So, the test statistics =  [tex]\frac{(16-1) \times 9.5^{2} }{50 }[/tex]  ~ [tex]\chi^{2}__1_5[/tex]

                                    =  27.08

The value of chi-square test statistics is 27.08.

Now, at 5% level of significance the chi-square table gives a critical value of 25.00 at 15 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of chi as 27.08 > 25.00, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population standard deviation is greater than 50.

Answer:

Midpoint of segment AB= (-0.5, 0)

Step-by-step explanation:

The midpoint coordinates of the midpoint has the x coordinate on .5 and the y coordinate on 0.

Answer:

[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

Replacing we got:

[tex]\bar X=58.875[/tex] represent the mean

[tex]s=5.083[/tex] represent the sample standard deviation for the sample  

[tex]n=8[/tex] sample size  

[tex]\mu_o =60[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 60[/tex]  

Alternative hypothesis:[tex]\mu < 60[/tex]  

The statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Answer:

Perimeter = 317 m

Step-by-step explanation:

Given track is a composite figure having two semicircles and one rectangle.

Perimeter of the given track = Circumference of two semicircles + 2(length of the rectangle)

Circumference of one semicircle = πr  [where 'r' = radius of the semicircle]

                                                       = 25π

                                                       = 25 × 3.14

                                                       = 78.5 m

Length of the rectangle = 80 m

Perimeter of the track = 2(78.5) + 2(80)

                                     = 157 + 160

                                     = 317 m

Therefore, perimeter of the track = 317 m

Answer:

  [tex]\textbf{J. }\dfrac{1}{x^2-x}[/tex]

Step-by-step explanation:

Factor the denominator and cancel the common factor.

  [tex]\dfrac{x+1}{x^3-x}=\dfrac{x+1}{x(x^2-1)}=\dfrac{x+1}{x(x-1)(x+1)}=\dfrac{1}{x(x-1)}\\\\=\boxed{\dfrac{1}{x^2-x}}[/tex]

Answer:

Corporate jet = 370 mph

Smaller plane = 185 mph

Step-by-step explanation:

The relationship between the first leg and the second leg of the flight is:

[tex]2t_1=t_2[/tex]

Total travel time is:

[tex]t_1+t_2=6\ hours\\t_1+2t_1=6\\t_1=2\ hours[/tex]

The speed of the corporate jet is:

[tex]v=\frac{740\ miles}{2\ hours}\\v=370\ mph[/tex]

The speed of the smaller plane is half of that of the jet:

[tex]v_2=\frac{370}{2}\\ v_2=185\ mph[/tex]

Therefore, the corporate jet travels at 370 mph and the smaller plane travels at 185 mph.

Answer:

Step-by-step explanation:

Hey there! I'm happy to help!

You haven't provided any answer choices but I can show you a trick to find any number between two numbers. This is will give you an instant answer to one being greater than one number and less than another.

What you do is you add the two numbers and divide by two!

2/5+3/5=1

1÷2=1/2

Therefore, 1/2 is a possible answer here.

I hope that this helps! Have a wonderful day!

Answer:

17) 53.2

18) 17

Step-by-step explanation:

In similar triangles theorem, the ratio of the corresponding sides of two triangles are equal.

17) To determine x, ratio of the sides of 1st triangle/Ratio of the sides of 2nd triangle.

Ratio of base to the missing side:

7.6/x = 13.6/95.2

7.6/x = 13.6/95.2

7.6/x = 0.1428

7.6= 0.1429x

x = 53.2

18) ratio of shortest side/ longest side

3.4/7.9 = x/39.5

x = 3.4/7.9 × 39.5

x = 17

Answer:

The leg measures 2 I believe

Step-by-step explanation:

Since the squares of the legs equal C ([tex]A^{2} +B^{2} = C^{2}[/tex]) the square root of 16 would be 4.

The Pythagorean theorem is a basic relationship between the three sides of a right triangle. The length of one leg of the triangle is 2√2 cm.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

Let the length of the perpendicular be x.

Given the length of the hypotenuse is 4 centimeters, while the length of the other two sides is the same, therefore, the length of the other two sides is x. Therefore, using the Pythagorus theorem we can write,

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

[tex]4^2 = x^2+x^2\\\\16=2x^2\\\\8=x^2\\\\x= 2\sqrt2[/tex]

Hence, the length of one leg of the triangle is 2√2 cm.

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Answer:

72 feet

Step-by-step explanation:

We have that the vertex at the origin in an upward concave is:

y = a * x ^ 2, we solve for a:

a = y / (x ^ 2)

Thus:

The points from the origin (0,0) are (-48, 8) and (48, 8), we replace:

a = 8 / (48 ^ 2) = 1/288

Therefore the equation would be:

y = (1/288) * x ^ 2

288 * y = x ^ 2

Now, be distance above the vertex to put the receiver, which would be the focus, we have:

4 * p = 288

we replace:

4 * p = 288

p = 288/4

p = 72

The receiver should be placed at [tex](x,y) = (0, 72)\,[ft][/tex].

We assume that the paraboloid is centered at the origin of a rectangular system of coordinates, then we have the following standard equation of the parabola is:

[tex]4\cdot p \cdot y = x^{2}[/tex] (1)

Where:

The coordinates of the vertex are expressed by [tex](x,y) = (0, p)[/tex].

If we know that [tex]x = 48[/tex] and [tex]y = 8[/tex], then the coordinates of the vertex are, respectively:

[tex]4\cdot p\cdot 8 = 48^{2}[/tex]

[tex]p = 72\,ft[/tex]

The receiver should be placed at [tex](x,y) = (0, 72)\,[ft][/tex].

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Answer:

240 m^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

The base is 16 and the height is 30

A =1/2 ( 16*30)

240 m^2

Considering the distance between the two points in units, the real distance between the airports is of 1303 miles.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, the airports are at points at p(1,17) and q(12,10), hence the distance in units is given by:

[tex]D = \sqrt{(10 - 17)^2 + (12 - 1)^2} = 13.03[/tex]

Since each unit represents 100 miles, the distance in miles is given by:

D = 13.03 x 100 = 1303 miles.

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Answer:

B. 1,304 miles.

Step-by-step explanation:

Using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.

How to Apply the Distance Formula?

The distance formula is: d = .

Given the following locations:

P(1,17) = (x1, y1)

Q(12,10) = (x2, y2)

Use the distance formula to find the PQ:

PQ = √[(12−1)² + (10−17)²]

PQ = √[(11)² + (−7)²]

PQ = √170

PQ ≈ 13.04 units

1 unit = 100 miles

PQ = 13.04 × 100

PQ = 1,304 mils

Thus, using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.

Answer:

33

Step-by-step explanation:

2/5x40=16

40-16=24

24+9=33

33 marbles

2/5 is .4

Multiply .4 by 40 to get 16

Subtract 16 from 40 to get 24

Add 9 to 24 to get 33

Hope it helps <3

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Answer:

-6

Step-by-step explanation:

From the line graph, you can see that x = -7 also has the y-coordinate of

y = -6. So the output is -6.

Answer:

32

Step-by-step explanation:

Mean = Average = The data values added together/ the number of data values.

The mean of 5 numbers is 22.6=

[tex]\frac{12+16+n+23+30}{5} = 22.6[/tex]

Multiply both sides by 5.  22.6 becomes 113

12+16+23+30+n=113

n+81 = 113

n= 32

The value of n is 32.

The arithmetic mean of m values [tex]x_1,x_2,..., x_m[/tex] is

[tex]\frac{x_1+x_2+...+x_m}{m}[/tex]

The given

mean = [tex]\frac{12+16+n+23+30}{5}=22.6[/tex]

⇒12+16+n+23+30=22.6×5=113

⇒n=113-81=32

Hence, n=32

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Answer:

x = 4 or x = -13/4 = -4.33

Step-by-step explanation:

log (3x - 2) + log (x + 1) = 2 - log 2

Note 2 is also equals to log 100

log (3x - 2) + log (x + 1) = log 100 - log 2

log (3x - 2)(x + 1) = log (100/2)

log 3x² + 3x - 2x - 2 = log 50

log 3x² + x - 2 = log 50

3x² + x - 2 = 50

3x² + x - 2 - 50 = 0

3x² + x - 52 = 0

find the number to multiply that will give you -52 × 3 = -156 and add to give you 1. The numbers are -12 and 13.

3x² - 12x + 13x - 52 = 0

3x(x - 4) + 13( x - 4) = 0

(3x + 13)(x - 4) = 0

x = 4 or x = -13/4 = -4.33

If you insert 4 in the logarithm equation you will see that the left side is equal to the right

log (3x - 2) + log (x + 1) = log 100 - log 2

log 10 + log 5 = log 50

log 50 = log 50

This is not the complete question, the complete question is:

P18-1 (LO2,3) (Allocate Transaction Price, Upfront Fees)

Tablet Tailors sells tablet PCs combined with Internet service, which permits the tablet to connect to the Internet anywhere and set up a Wi-Fi hot spot. It offers two bundles with the following terms.

1. Tablet Bundle A sells a tablet with 3 years of Internet service. The price for the tablet and a 3-year Internet connection service contract is $500. The standalone selling price of the tablet is $250 (the cost to Tablet Tailors is $175). Tablet Tailors sells the Internet access service independently for an upfront payment of $300. On January 2, 2017, Tablet Tailors signed 100 contracts, receiving a total of $50,000 in cash.

2. After 2 years of the 3-year contract, Tablet Tailors offers a modified contract and extension incentive. The extended contract services are similar to those provided in the first 2 years of the contract. Signing the extension and paying $90 (which equals the standalone selling of the revised Internet service package) extends access for 2 more years of Internet connection. Forty Tablet Bundle A customers sign up for this offer.

INSTRUCTION

a) Prepare the journal entries when the contract is signed on January 2, 2019, for the 40 extended contracts. Assume the modification does not result in a separate performance obligation.

b) Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).

Answer:

Step-by-step explanation:

(A)

Date        Particulars                               Debit                     Credit

2-Jan-19        Cash                                        3600  

                      Unearned Service Revenue                               3600

40 * 90 = 3600

services in the extended period are the same as the services that were provided in the original contract period. As they are not distinct hence the modifications will be considered as part of the original contract.

(B)

Date           Particulars                                    Debit           Credit

31-Dec-19 Unearned Service Revenue            2413  

                       Service revenue                                             2413

internet = 300, price = 550, connection service = 500

(300/550) * 500 = 273

so

Original internet service contract = 40 * 273 = 10,920

Revenue recognized in 1st two years = 10,920 * 2/3 = 7280

Remaining service at original rates = 10920 - 7280 = 3640

Extended service = 3600

3640 + 3600 = $7240  

7240 / 3 = $2413

Step-by-step explanation:

f(g(x))=[tex]\sqrt{g(x)}[/tex]

--> g(x) >= 0 --> x-9>=0 --> x>=9

Answer:

  384.6 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the trig relation involving sides adjacent and opposite the angle. Here, the road distance is adjacent to the angle of depression, and the altitude is opposite. So, you have ...

  Tan = Opposite/Adjacent

  tan(7.5°) = (300 ft)/(distance to car 1)

  tan(9°) = (300 ft)/(distance to car 2)

Solving for the distances, we have ...

  distance to car 1 = (300 ft)/tan(7.5°) ≈ 2278.73 ft

  distance to car 2 = (300 ft)/tan(9°) ≈ 1894.13 ft

Then the separation between the cars is ...

  distance apart = 2278.73 ft - 1894.13 ft

  distance apart = 384.6 ft

Answer:

a. 75,000

b. 50,000

c. 75,000

Step-by-step explanation:

The computation of allocating the joint cost using the physical units method is shown below:

[tex]Allocation\ rate = \frac{Joint\ costs}{Total\ number\ of\ products}[/tex]

[tex]= \frac{\$200,000}{300 + 200 + 300}[/tex]

[tex]Allocation\ rate = \frac{200,000}{800}[/tex]

= 250

For face cream

[tex]= Unit\ produced\times Allocation\ rate[/tex]

= [tex]300\times 250[/tex]

= 75,000

For body lotion

[tex]= Unit\ produced\times Allocation\ rate\\\\ = 200\times 250[/tex]

= 50,000

For Liquid soap

[tex]= Unit\ produced\times Allocation\ rate\\\\ = 300\times 250[/tex]

= 75,000

hence, we simply applied the above formula by multiplying the units produced with the allocation rate so that each one allocation cost could come

Step-by-step explanation:

We know that

14^2=196, and

15^2=225

so we know that sqrt(215) is between 14 and 15.

How do we know if it is between 14.5 and 15?

we need to know the value of 14.5^2, which we can calculate in the head as follows:

The square of all numbers ending in 5 such as 15 can be calculated by breaking up the 5 and the preceding digit(s),

The preceding digit is 1.  We multiply 1 by the next integer, 2 to get 2.

Attach 25 to 2 gives us 225 (as we saw above.

Example, 145*145 = 14*15 | 25 = 210 | 25 = 21025

so

14.5^2 = 210.25, which gives the more precise answer that

14.5^2 < 215 < 15^2, or

14.5 < sqrt(215) < 15  (fourth choice)

Since the third choice says sqrt(215) is between 14 and 1.5 (not 15), so the third choice is incorrect.

Note: if we eliminated the third choice, i.e. discard the likelihood of typo in the question, the only one left is the fourth choice.

Answer:

The test statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

[tex]t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=23.6[/tex] represent the sample mean

[tex]s=8.6[/tex] represent the sample standard deviation

[tex]n=28[/tex] sample size  

[tex]\mu_o =25[/tex] represent the value that we want to test

t would represent the statistic

System of hypothesis

We want to test if the true mean is lower than 25, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 25[/tex]  

Alternative hypothesis:[tex]\mu < 25[/tex]  

The test statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

[tex]t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11[/tex]    

Answer:

m = 0

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in the coordinates into the formula:

m = (-3 + 3)/(4 - 6)

m = 0/-2

m = 0

Answer:

f(2) = 5

Step-by-step explanation:

Simply plug in 2 for x:

f(2) = 2(2) + 1

f(2) = 4 + 1

f(2) = 5

Step-by-step explanation:

Log T = 11.8 + 1.5.M (with T is the amount of energy released by the earthquake, Log refers to the logarithm to the base 10)

-->T = [tex]10^{11.8 +1.5*6.5}[/tex] ≈3.458 *[tex]10^{21}[/tex]

Answer:  2.00 x 10¹⁰⁹

Step-by-step explanation:

log T = 11.8 + 1.5M

Given: M = 6.5

log T = 11.8 + 1.5(6.5)

log T = 11.8 + 9.75

log T = 21.55

      T = 10²¹⁻⁵⁵

      T = 1.995 x 10¹⁰⁹

      T = 2.00 x 10¹⁰⁹       rounded to the nearest hundredth