Find the arclength of the curve r(t) = ⟨ 10sqrt(2)t , e^(10t) , e^(−10t)⟩, 0≤t≤1

Answer:

1/4 ÷ 3/8 = 2/3

Step-by-step explanation:

When dividing fractions, you have to take the reciprocal of the second fraction, then multiply from there. The reciprocal of a fraction is basically flipped. So then, 1/4 ÷ 3/8 becomes 1/4 x 3/8. Multiplying fractions should be pretty straight forward as you just need to multiply numerator (top number of a fraction) with numerator and vice versa for the denominators (bottom number of a fraction).

So then you get: (1 x 8)/(3 x 4) = 8/12. Then you just simplify it by dividing the numerator and denominator by their greatest possible factor, which in this case is 4. So then, (8 ÷ 4)/(12 ÷ 4) = 2/3.

Answer:

540 miles per hour and 50 miles per hour respectively.

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50

Answer:

B

Step-by-step explanation:

they have the same intercepts

Line geometry are caused from the intersection of two line. The measure of angle x from the diagram is 110degrees

Line geometry are caused from the intersection of two lines. From the given figures, you can see that <KOH and <IOK forms a linear pair, hence;

<KOH + <IOK = 180

110 + <IOK = 180
<IOK = 180 - 110
<IOK = 70 degrees

Similarly <x and MIOK are linear pair pair such that <x + 1<IOK = 180
<x + 70 =180
<x = 180 - 70
<x = 110degrees

Hence the measure of angle x from the diagram is 110degrees

Learn more on line geometry here: https://brainly.com/question/7098341

#SPJ1

Answer:

<IOK = 70 degrees

<x and <IOK form a linear pair, so m<x is = 110

Step-by-step explanation:

i did it on khan and got it right, i hope your day goes well and you get all your other questions right :)

Answer:

19 bags of peanuts and 31 bags of pistachios

9514 1404 393

Answer:

  C  ∛((x+2)/5) -3

Step-by-step explanation:

To find the inverse function, solve for y:

  x = f(y)

  x = 5(y +3)³ -2 . . . . . . substitute f(y)

  x +2 = 5(y +3)³ . . . . . add 2 -- already you know C is the answer

  (x +2)/5 = (y +3)³ . . . . divide by 5

  ∛((x +2)/5) = y +3 . . . . take the cube root

  ∛((x +2)/5) -3 = y . . . . subtract 3

  f^-1(x) = ∛((x +2)/5) -3 . . . . matches expression C

Answer:

-x - 13

Step-by-step explanation:

5(x-4) + 3x - 9x + 7

First we use the distributive property to remove the parenthesis

5x -20 + 3x - 9x + 7

then we combine the like terms

-x - 13

Answer:

139 ( D )

Step-by-step explanation:

Interest rate on loan = 4% = 0.04

Number of payments = 15

First 10 payments = 100 each

last 5 payments = 200 each

Calculating the value of K

K = [ ( 100 / 0.04 * ( 1-1 / 1.04^10 ) + 200/0.04 * ( 1-1 / (1 +0.04)^5)*  1 /1.04^10)

*  1.1 - 100 / 0.04 * ( 1-1 / (1+0.04)^5 ) - 200/0.04 * (1-1 /1.04^5) * 1/1.04^10)*0.04 / ( 1-1 / 1.04^5) * (1 + 0.04)^5

= 138.6051 ≈ 139

Answer:

a

Step-by-step explanation:

The correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given equation is ( x-1 )² + ( y + 2 )² = 4

The graph of the equation is attached with the answer below when we plot the graph we will get the circle that is lying in the third and the fourth quadrant.

Therefore the correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.

To know more about graphs follow

https://brainly.com/question/25020119

#SPJ2

Answer:

Reject H0 ; and conclude that call length does not follow a normal distribution.

Step-by-step explanation:

Given :

The hypothesis :

H0: Call lengths outside normal customer roaming areas follows normal distribution

H1: Call lengths outside normal customer roaming areas do not follows normal distribution

Mean, μ = 14.3

Standard deviation, σ = 3.7

From the frequencies Given :

Expected values can be calculated :

Observed values :

16, 75, 139, 105, 37, 18 ; Total = 400

P(Z < (x - μ) / σ)) * total frequency

x = frequency

For x = 5 ;

P(Z < (5 - 14.3) / 3.7)) * 400 = 2.391

For x = 10;

P(Z < (10 - 14.3) / 3.7)) * 400 = 46.644

For x = 15;

P(Z < (15 - 14.3) / 3.7)) * 400 = 180.960

For x = 20;

P(Z < (20 - 14.3) / 3.7)) * 400 = 145.32

For x = 25;

P(Z < (25 - 14.3) / 3.7)) * 400 = 23.92

For x = 30;

P(Z < (30 - 14.3) / 3.7)) * 400 = 0.766

χ² = Σ(O - E)²/E

O = observed values

E = Expected values

χ² = (26-2.391)^2 / 2.391 + (75-46.644)^2 / 46.644 + (139-180.96)^2 / 180.96 + (105-145.32)^2 / 145.32 + (37-23.92)^2 / 23.92 + (18-0.766)^2 / 0.766 = 666.17

χ² = 666.17

The critical value "; df = n - 1= 6-1 = 5

α = 0.05

χ²critical(0.05 ; 5) = 11.07

χ²statistic > χ²critical ; Reject the Null, H0 ; and conclude that call length does not follow a normal distribution.

Answer:

Step-by-step explanation:

Answer:

431.2

Step-by-step explanation:

Area of a regular polygon = # of sides * side length of 1 side * apothem

We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters

So # of sides = 7

apothem = 8

side length = 7.7

so the area would equal 7 * 8 * 7.7 = 431.2

It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth

Answer:

That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2

15.6

Step-by-step explanation:

Step-by-step explanation:

you have to type shift an cos button together at one time and then write 0.35 youwill get answer

Answer:

0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3

Step-by-step explanation:

We have the mean, which means that the poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily.

This means that [tex]\mu = 6.3[/tex]

What is the probability that, for any day, the number of special orders sent out will be exactly 3?

This is P(X = 3). So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 3) = \frac{e^{-6.3}*6.3^{3}}{(3)!} = 0.0765[/tex]

0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3

Answer:

2116.8 in^3

Step-by-step explanation:

V = l*w*h

All the units need to be the same

Convert 1.4 ft to inches

1.4 ft * 12 inches/ ft = 16.8 inches

V = 14 * 16.8  * 9

   = 2116.8 in^3

Answer:

38 ft²

Step-by-step explanation:

The shape consists of a rectangle and two triangles.

Area of the shape = area of rectangle + area of the two triangles

✔️Area if the rectangle = L × W

L = 8 + 2 = 10 ft

W = 3 ft

Area of rectangle = 10 × 3 = 30 ft²

✔️Area of the large triangle = ½ × bh

b = 4 ft

h = 3 ft

Area of large triangle = ½ × 4 × 3 = 6 ft²

✔️Area of the small triangle = ½ × bh

b = 2 ft

h = 2 ft

Area of large triangle = ½ × 2 × 2 = 2 ft²

✅Area of the shape = 30 + 6 + 2 = 38 ft²

Answer:

The proportion of products that exhibit edge roughness is 0.029 = 2.9%.

Step-by-step explanation:

Proportion of products that exhibit edge roughness:

2% of 25%(new blades).

3% of 60%(average sharpness).

4% of 15%(worn). So

[tex]p = 0.02*0.25 + 0.03*0.6 + 0.04*0.15 = 0.029[/tex]

The proportion of products that exhibit edge roughness is 0.029 = 2.9%.

The scatterplot is below.

I used GeoGebra to make the scatterplot. Though you could use other tools such as Excel or Desmos, or lots of other choices.

Side note: I'm not sure why, but you repeated the point (0.7,1.11) three times.

Let X be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

P(X ≤ 0.37) = P((X - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(Z ≤ -2)

where Z follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform X to Z using the rule Z = (X - mean(X))/sd(X).)

Given the required precision for this probability, you should consult a calculator or appropriate z-score table. You would find that

P(Z ≤ -2) ≈ 0.0228

You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,

P(-2 ≤ Z ≤ 2) ≈ 0.95

which means

P(Z ≤ -2 or Z ≥ 2) ≈ 1 - 0.95 = 0.05

The normal distribution is symmetric, so this means

P(Z ≤ -2) ≈ 1/2 × 0.05 = 0.025

which is indeed pretty close to what we found earlier.

Answer:

B could be used to show the formula to describe the sentence

Answer:

Yes

Step-by-step explanation:

Using the commutative property (a + b = b + a), we can easily calculate that 12 + 2x is equal to 2x + 12.

Answer:

Given that the equation of a circle is :

[tex] \green{ \boxed{\boxed{\begin{array}{cc} {x}^{2} + {y}^{2} = 6x - 8y \\ = > {x}^{2} + {y}^{2} - 6x + 8y = 0 \\ = > {x}^{2} + {y}^{2} + 2 \times ( - 3) \times x + 2 \times 4 \times y = 0 \\ \\ \sf \: standard \: equation \: o f \: circle \: is : \\ {x}^{2} + {x}^{2} + 2gx + 2fy + c = 0 \\ \\ \sf \: by \: comparing \\ \\ g = - 3 \\ f = 4 \\ c = 0 \\ \\ \sf \: radius \: \: r = \sqrt{ {g}^{2} + {f}^{2} - c } \\ = \sqrt{ {( - 3)}^{2} + {4}^{2} - 0 } \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = 5 \: unit \\ \\ \bf \: area \: = \pi {r}^{2} \\ = \pi \times {5}^{2} \\ =\pink{ 25\pi \: { unit }^{2} }\end{array}}}}[/tex]

Answer:

it's easy you need to do 6%×4 it's 24%

Answer:

A

Step-by-step explanation:

i think so..sorry if im wrong

Answer:

A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32

Step-by-step explanation:

f(x)= 1∕2(2)^x,

Let x = 1

f(1)= 1∕2(2)^1 = 1/2 ( 2) = 1

Let x = 3

f(3)= 1∕2(2)^3 = 1/2 ( 8) = 4

Let x = 1

f(6)= 1∕2(2)^6 = 1/2 ( 64) = 32

Answer:

A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32

Step-by-step explanation: I took the test

Answer:

0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

n instances of a normal variable:

For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

Sum of normal variables:

When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.

Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.

This means that:

[tex]\mu_A = 10000*50 = 500000[/tex]

[tex]s_A = 1000\sqrt{50} = 7071[/tex]

Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.

This means that:

[tex]\mu_B = 20000*50 = 1000000[/tex]

[tex]s_B = 2000\sqrt{50} = 14142[/tex]

Distribution of the total of the 100 claims:

[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]

[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]

Find the probability the total of the 100 claims exceeds 1,530,000.

This is 1 subtracted by the p-value of Z when X = 1530000. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]

[tex]Z = 1.9[/tex]

[tex]Z = 1.9[/tex] has a p-value of 0.9713

1 - 0.9713 = 0.0287

0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.

Answer:

3 pages per hour

Step-by-step explanation:

Take the number of pages and divide by the time

1 1/2 ÷ 1/2

Write the mixed number as an improper fraction

3/2÷1/2

Copy dot flip

3/2 * 2/1

3

9514 1404 393

Answer:

  3 pages per hour

Step-by-step explanation:

To find the number of pages per hour, divide pages by hours.

  (1.5 pages)/(0.5 hours) = 3 pages/hour

Hi there!  

»»————-　★　————-««

I believe your answer is:  

"Isolate the variable  using inverse operations."

»»————-　★　————-««  

Here’s why:

To solve for a variable, we would have to isolate it on one side.

To isolate it, we would use inverse operations on both sides on the equation until the variable is isolated.

There are no like terms in the given equation.

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'z'...}}\\\\\frac{z}{6} = 36\\-------------\\\rightarrow (\frac{z}{6})6 = (36)6\\\\\rightarrow \boxed{z = 216}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

First option: Isolate the variable using inverse operations

Step-by-step explanation:

z/6 = 36

Since we already have the equation set up and cannot simplify any further, we must try to isolate the variable, z, by using inverse operations.

The inverse operation of division is multiplication, so to isolate z, we multiply 6 on each side:

z/6 · 6 = 36 · 6

z = 216