Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=−xi−2yj−zk and C is given by the vector function r(t)=⟨sint,cost,t⟩, 0≤t≤3π/2.

Answer: a. 0.6759    b. 0.3752    c. 0.1480

Step-by-step explanation:

Given : The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes

i.e. [tex]\mu = 6.3[/tex] minutes

[tex]\sigma=2.2[/tex] minutes

Let x be the long-distance call length.

a. The probability that a call lasts between 5 and 10 minutes will be :-

[tex]P(5<X<10)=P(\dfrac{5-6.3}{2.2}<\dfrac{X-\mu}{\sigma}>\dfrac{10-6.3}{2.2})\\\\=P(-0.59<Z<1.68)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(z<1.68)-(1-P(z<0.59))\\\\=0.9535-(1-0.7224)\ \ \ \ [\text{by z-table}]\\\\=0.6759[/tex]

b. The probability that a call lasts more than 7 minutes. :

[tex]P(X>7)=P(\dfrac{X-\mu}{\sigma}>\dfrac{7-6.3}{2.2})\\\\=P(Z>0.318)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.318)\\\\=1-0.6248\ \ \ \ [\text{by z-table}]\\\\=0.3752[/tex]

c. The probability that a call lasts more than 4 minutes. :

[tex]P(X<4)=P(\dfrac{X-\mu}{\sigma}<\dfrac{4-6.3}{2.2})\\\\=P(Z<-1.045)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<1.045)\\\\=1-0.8520 \ \ \ [\text{by z-table}]\\\\=0.1480[/tex]

Answer:

A:{(-9/7,-17/7)}

Step-by-step explanation:

3x - 2y - 1 = 0    ⇒  3x - 2y = 1

y = 5x + 4

then:

3x - 2(5x+4) = 1

3x - 2*5x - 2*4 = 1

3x - 10x - 8 = 1

-7x = 1 + 8

7x = 9

x = -9/7

y = 5x + 4

y = 5(-9/7) + 4

y = -45/7 + 4

y = -45/7 + 28/7

y = -17/7

Answer:

A:{(-9/7, -17/7)}

Greetings from Brasil...

Making the division

(X⁵ + 2X⁴ - 7X² - 19X + 15) ÷ (X² + 2X + 5)

we get

Answer:

x³ − 5x + 3

Step-by-step explanation:

To solve with long division:

Start by dividing the highest terms:

x⁵ / x² = x³

This becomes the first term of the quotient.  Multiply by the divisor:

x³ (x² + 2x + 5) = x⁵ + 2x⁴ + 5x³

Subtract from the first three terms of dividend:

(x⁵ + 2x⁴ + 0x³) − (x⁵ + 2x⁴ + 5x³) = -5x³

Drop down the next two terms and repeat the process.

To use the "box" method:

Each square in the box is the product of the term at the top of the column and the term at the end of the row.  Also, squares diagonal of each other must add up to the term outside the box.

Look at the first diagonal.  There is only one square, so that must be x⁵.  Knowing this, we can say that x³ must be at the top of the column.  We can fill in the rest of the column (2x⁴ and 5x³).

Repeat this process until all squares are filled in.

Answer:

The question is not complete, but I found a possible match:

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us?

86 4 85 83 9 51 24 34 28 43

Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. The​ mode(s) is(are) nothing. ​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.)

B. There is no mode.

Answer:

The correct answer is:

There is no mode (B.)

Step-by-step explanation:

b. The mode of data is the number that repeats the most number of times. The number that occurs most frequently. on the list of the distribution, 86 4 8 5 83 9 51 24 34 28 43, every number occurs just once, hence, there is no mode for the distribution.

a. To calculate the Mean

[tex]Mean: \frac{Sum\ of\ terms}{number\ of\ players}\\ Mean = \frac{86\ +\ 4\ +\ 8\ +\ 5\ +\ 83\ +\ 9\ +\ 51\ +\ 24\ +\ 34\ +\ 28\ +\ 43}{11}\\Mean= 34.09[/tex]

c. To calculate the median:

Median is  the mid-way term of the distribution, but first, we have to arrange the terms in ascending order (descending order can also be used)

4, 5, 8, 9, 24, 28, 34, 43, 51, 63, 86

To find the median, count the numbers equally from the left- and right-hand sides to the middle, the remaining number becomes the median. In this case, the median = 28

d. Midrange:

The midrange is the number mid-way between the greatest and smallest number in a data set. To find the midrange, we will add the smallest (4) and largest number (86), and divide by 2:

Midrange = (4 + 86) ÷ 2

Midrange = 90 ÷ 2 = 45

e. what do the results tell us:

Since only 11 of the jersey numbers were in the sample, the statistics cannot give any meaningful results

Answer:

Eddie spent $26 total

Step-by-step explanation:

15% of 20 is 3

He paid 15% tax which is $3

He also tipped 15% of the $20 which he paid for lunch so another $3

3+3+20= $26

Answer:

d

Step-by-step explanation:

trust

Answer:

x = -733

Step-by-step explanation:

[tex]\sqrt[3]{x+4}[/tex] + 12 = 3

[tex]\sqrt[3]{x+4}[/tex]  = -9 (cube both sides)

x + 4 = -729

x = -733

Answer:52-12=$40

1/8*40 = 5 hours.

Step-by-step explanation:

Complete Question

A newsletter publisher believes that above 41% of their readers own a personal computer. Is there sufficient evidence at the 0.10 level to substantiate the publisher's claim?

State the null and alternative hypotheses for the above scenario.

Answer:

The null hypothesis is  [tex]H_o : p \le 0.41[/tex]

The  alternative hypothesis  [tex]H_1 : p> 0.41[/tex]

Step-by-step explanation:

From the question we are told that

      The population proportion is [tex]p = 0.41[/tex]

        The level of significance is  [tex]\alpha = 0.10[/tex]

The null hypothesis is  [tex]H_o : p \le 0.41[/tex]

The  alternative hypothesis  [tex]H_1 : p> 0.41[/tex]

Answer:

48.96 cm³/min

Step-by-step explanation:

We are given;

Relationship between pressure P and volume V; PV^(1.4) = C

Volume;V = 610 m³

Pressure; P = 89 KPa

Rate of decreasing pressure; dP/dt = -10 kPa/minute.

We want to find the rate at which the volume is increasing at that instance, thus, its means we need to find dV/dt

So, we will differentiate the relationship equation of P and V given.

Thus, we have;

[V^(1.4)(dP/dt)] + d(V^(1.4))/dt = dC/dt

Differentiating this gives us;

[(dP/dt) × (V^(1.4))] + [1.4 × P × V^(0.4) × (dV/dt)] = 0

Plugging in the relevant values, we have;

(-10 × 610^(1.4)) + (1.4 × 89 × 610^(0.4) × (dV/dt)) = 0

This gives;

-79334.44155 + 1620.5035(dV/dt) = 0

Rearranging, we have;

1620.5035(dV/dt) = 79334.44155

Divide both sides by 1620.5035 to give;

dV/dt = 79334.44155/1620.5035

dV/dt = 48.96 cm³/min

Answer:

equal and equivalent sets

Step-by-step explanation:

Answer

[0,-3] should be the right answer

The line should intersect at y axis i.e x=0

Then put the value of x as zero in the equation to find the value of y.

3*0-4y=12

-4y=12

y=12/-4=-3

y=-3 ..

HOPE THIS HELPS YOU

Answer:

The answer is 47200000000

Complete question is;

Use technology and a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.

Claim: μ > 71; α = 0.05

Sample statistics:

¯x = 73.9, s = 3.7, n = 25

A) What are the null and alternative hypotheses?

Choose the correct answer below.

A. H0:μ = 71 ; HA:μ ≠ 71

B. H0:μ ≤ 71; HA:μ > 71

C. H0: μ ≥ 71; HA: μ < 71

D. H0: μ ≠ 71; HA: μ = 71

B) What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.)

C) What is the P-value of the test statistic? P-value = Round to three decimal places as needed.)

D) Decide whether to reject or fail to reject the null hypothesis.

Answer:

A) Option B - Alternative hypothesis: HA: μ > 71

Null hypothesis: H0: μ ≤ 71

B) t = -7.54

C) p-value = 0.000

D) we reject the null hypothesis

Step-by-step explanation:

A) We are told that the claim is: μ > 71. Thus, due to the sign, the alternative hypothesis would be the claim. So;

Alternative hypothesis: HA: μ > 71

Null hypothesis: H0: μ ≤ 71

B)Formula for standardized test statistic with a t-test is;

t = (¯x - μ)/√(s/n)

Plugging in the relevant values, we have;

t = (71 - 73.9)/√(3.7/25)

t = -7.54

C) From online p-value from t-score calculator attached using t = -7.54, n = 25, significance level = 0.05, DF = 25 - 1 = 24 and a one - tailed test, we have;

p-value = 0.00001 ≈ 0.000

D) The p-value of 0.000 is less than the significance value of 0.05,thus we will reject the null hypothesis

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.

(i)    3 to 4

(ii)    3 to 3.5

(iii)    3 to 3.1

(b) Find the instantaneous rate of change when r = 3.  A'(3)

Area of a circle A(r)= πr²

The average rate of change of the area of a circle with respect to its radius

ΔA(r)/Δr = πr₂²-πr₁²/r₂-r₁

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

i) If the radius changes from 3 to 4

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(4²-3²)/4-3

ΔA(r)/Δr = π(16-9)/1

ΔA(r)/Δr = 7π

Hence, average rate of the area of a circle when the radius changes from 3 to 4 is 7π

ii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.5²-3²)/3.5-3

ΔA(r)/Δr = π(12.25-9)/0.5

ΔA(r)/Δr = 3.25π/0.5

ΔA(r)/Δr = 6.5π

Hence, average rate of the area of a circle when the radius changes from 3 to 3.5 is 6.5π

iii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.1²-3²)/3.1-3

ΔA(r)/Δr = π(9.61-9)/0.1

ΔA(r)/Δr = 0.61π/0.1

ΔA(r)/Δr = 6.1π

Hence, average rate of the area of a circle when the radius changes from 3 to 3.1 is 6.1π

iv) Instantaneous rate of change A'(r) = 2πr

When r = 3;

A'(3) = 2π(3)

A'(3) = 6π

Hence, the instantaneous rate of change when r = 3 is 6π

Answer:A number decreased by 4 is the same as 12.5

Step-by-step explanation:

[tex]y=\dfrac{sin(x^2)}{x^3}[/tex]

Apply the quotient rule:

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3\frac{\mathrm d\sin(x^2)}{\mathrm dx}-\sin(x^2)\frac{\mathrm dx^3}{\mathrm dx}}{(x^3)^2}[/tex]

Chain and power rules:

[tex]\dfrac{\mathrm d\sin(x^2)}{\mathrm dx}=\cos(x^2)\dfrac{\mathrm dx^2}{\mathrm dx}=2x\cos(x^2)[/tex]

Power rule:

[tex]\dfrac{\mathrm dx^3}{\mathrm dx}=3x^2[/tex]

Putting everything together, we have

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3(2x\cos(x^2))-\sin(x^2)(2x\cos(x^2))}{(x^3)^2}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^3\cos(x^2)-2x\sin(x^2)\cos(x^2)}{x^6}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^2\cos(x^2)-\sin(2x^2)}{x^5}[/tex]

When [tex]x=\sqrt{\frac\pi2}[/tex], we have

[tex]\cos\left(\left(\sqrt{\dfrac\pi2}\right)^2\right)=\cos\left(\dfrac\pi2\right)=0[/tex]

[tex]\sin\left(2\left(\sqrt{\dfrac\pi2}\right)^2\right)=\sin(\pi)=0[/tex]

so the derivative is 0.

Answer:

0.87

Step-by-step explanation:

Answer:

Estimated cost per capsule = 4.288 (penny)

Step-by-step explanation:

Given:

Cost of 1000 capsule = $42.88

Number of capsules = 1000

Find:

Estimated cost per capsule

Computation:

1 dollar = 100 penny

So,

$42.88 = 4288 penny

Estimated cost per capsule = 4288 / 1000

Estimated cost per capsule = 4.288 (penny)

Answer:

x +13.

where

x is number of people

Step-by-step explanation:

Let the number of people be x

given that number of people increased by 13

increased by 13 means that we whatever is the initial number of people, new number of people is 13 more than that.

thus, new number of people = x +13

to  translate the number of people increased by 13 into an algebraic expression

we add 13 to number of people which can be represented by  x +13.

Answer:

Step-by-step explanation:

42/14 = 57/x

42x = 57*14

42x = 798

x = 19 months

Answer: Actually its 18 months they calculated wrong

Answer:

851- 473 = 373

(751)-378 = 373

Step-by-step explanation:

3x-12 + 6 = 14

3x-12 = 14 - 6

3x = 8 + 12

x= 20 ÷ 3

x = 6.7

Internal Angle Bisector Theoram:

Interior Angle Bisector Theorem : The angle bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

[tex] \Large{ \boxed{ \bf{ \color{limegreen}{Solution:}}}}[/tex]

Here, We can see that angle bisector of an angle is dividing the opposite side.

And,

From here, we can say that the ratio of side being divided is same as the ratio of sides containing this angle.

So, we can write it as,

➝ 14 : 21 = 6 : 3x - 12

Prdouct of means = Product of extremes

➝ 21 × 6 = 14(3x -12)

➝ 126 = 14(3x - 12)

➝ 9 = 3x - 12

Flipping it,

➝ 3x - 12 = 9

➝ 3x = 21

➝ x = 7

☘️ So, Value of x is [tex]\boxed{\sf{x = 7}}[/tex]

━━━━━━━━━━━━━━━━━━━━

Answer: A = 58

Step-by-step explanation: The sketched region enclosed by the curves and the approximating rectangle are shown in the attachment.

From the sketches, the area will be integrated with respect to y.

To calculate the integral, first determine the limits, which will be the points where both curves meet.

In respect to y:

[tex]2x+y^{2} = 48[/tex]

[tex]2x= 48- y^{2}[/tex]

[tex]x= 24 - \frac{y^{2}}{2}[/tex]

Finding limits:

[tex]y= 24 - \frac{y^{2}}{2}[/tex]

[tex]24 - \frac{y^{2}}{2}-y=0[/tex]

Multiply by 2 to facilitate calculations:

[tex]48 - y^{2}-2y=0[/tex]

Resolving quadratic equation:

[tex]y=\frac{-2+\sqrt{2^{2}+192} }{2}[/tex]

y = 6 and y = -8

Then, integral to calculate area will be with limits -8<y<6:

[tex]A = \int {24-\frac{y^{2}}{2}-y } \, dy[/tex]

[tex]A = 24y - \frac{y^{3}}{6}-\frac{y^{2}}{2}[/tex]

[tex]A = 24.6 - \frac{6^{3}}{6}-\frac{6^{2}}{2}-[24.(-8) - \frac{(-8)^{3}}{6}-\frac{(-8)^{2}}{2}][/tex]

A = 58

The area of the enclosed region is 58 square units.

Answer:

a)$15.95

b) 8kg

Step-by-step explanation:

a)Approach this question by finding how much does it cost for 1g

So,

$2.1/50=$0.042per gram

then, multiple 380 to get the cost of sweets for 380 g

$0.042/gram*380gram=$15.96(Note: the gram cancel out each other)

Which is $15.95 as the question requested

b)This question stated that 3/4 of the metal has 15 kg

So, in order to find the total mass of metal we invert the 3/4 fraction

e.g 4/3*15=20kg

now we have the total mass we can find the mass for 2/5 of the metal

2/5*20kg=8kg

Answer:

9 miles

Step-by-step explanation:

Hour = 6 miles

Half an hour = 3

6 + 3 = 9

Answer:

The Stem plot is displayed below.

Step-by-step explanation:

A Stem Plot is a chart for demonstrating the distribution of numeric variables .

It is used to analyze the shape of the distribution.

The data provided is as follows:

S = {46, 65, 55, 43, 51, 48, 57, 30, 43, 49, 32, 56}

The Stem plot is displayed as follows:

3 | 0  2

4 | 3  3  6  8  9

5 | 1  5  6  7

6 | 5

Answer:

Step-by-step explanation:

s = πrl + πr²

First move πr² to the left side of the equation

We have

πrl = s - πr²

Divide both sides by πr to make l stand alone

That's

We have the final answer as

Hope this helps you

Hello, please consider the following.

f is differentiable so g is differentiable and we we can compute the derivative of g.

[tex]\text{derivative of } u^2\text{ is } 2uu'\\\\\text{derivative of } f(f(x^3)+x)\text{ is } (3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{So, }\\\\g'(x)=2f(f(x^3)+x)(3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{ We replace x par 1}\\\\g'(1)=2f(f(1)+1)(3f'(1)+1)f'(f(1)+1)\\\\g'(1)=2f(2)(3f'(1)+1)f'(2)\\\\\text{ We can put f'(2) in one part of the equation}\\\\f'(2)=\dfrac{2f(2)(3f'(1)+1)}{g'(1)}=\dfrac{2*5*(3*(-3)+1)}{2}\\\\=5*(-9+1)\\\\=5*(-8)\\\\=\boxed{-40}[/tex]

Thank you.

Answer:

1, 2, 3 and 6.

Step-by-step explanation:

Factors of 6 are 1, 2, 3 and 6.

Answer:

A. There are four terms.

C. The term [tex]\frac{30}{y}[/tex] is a ratio.

Step-by-step explanation:

The expression given is the sum of four components: a third order monomial ([tex]4\cdot x^{3}[/tex]), a second order monomial ([tex]-7\cdot x^{2}[/tex]), a zero order monomial ([tex]15[/tex]) and a ratio ([tex]\frac{30}{y}[/tex]). There are a sum and two differences. Hence, the correct answers are:

A. There are four terms.

C. The term [tex]\frac{30}{y}[/tex] is a ratio.

Answer:

there are 4 terms

the term 30/y is a ratio

Step-by-step explanation:

got it right on my quiz

Answer: The answer is 209.40625

The fractional equivalent of 33505 divided by 160 is 6701/32 .

Given,

33505/160

Now,

To get the fractional equivalent of 33505/160,

Divide numerator and denominator by the common factor .

So divide numerator and denominator by 5.

33505/5 = 6701

160/5 = 32

Now the simplified fraction is 6701/32.

Know more about fractions,

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