Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨2,−3,4⟩, b=⟨−4,5,−1⟩, and c=⟨−2,−1,5⟩.

Answer:

[tex]\Large \boxed{\mathrm{5.71 \ g/cm^3 }}[/tex]

Step-by-step explanation:

[tex]\sf \displaystyle density = \frac{mass}{volume}[/tex]

[tex]\displaystyle \rho = \frac{m}{V}[/tex]

[tex]\sf Mass \rightarrow 20 \ g \\ Volume \rightarrow 3.5 \ cm^3[/tex]

[tex]\displaystyle \rho = \frac{20}{3.5}[/tex]

[tex]\rho \approx 5.71[/tex]

Density is defined as the mass per unit volume of an object and It is calculated using the equation: density (d) = mass (m) / volume (v).

In this scenario, the mass of the object is given as 20 grams and the volume is given as 3.5 cm^3. To find the density, we can substitute these values into the equation: density =[tex]20 g / 3.5[/tex] cm^3 To simplify the unit of the measurement, we can convert cm^3 to mL (since 1 cm^3 is equal to 1 mL).

Thus, the equation becomes: density = [tex]20 g / 3.5[/tex]  mL Calculating the division: density ≈ 5.71 g/mL Therefore, the density of the object is approximately 5.71 g/mL.

To know more about unit of the measurement visit:

https://brainly.com/question/33652292

#SPJ2

Answer:

The dimensions of the box are:

x =  8,93 cm       and     h  =   5,95 cm

C(min) =  850,69 cents

Step-by-step explanation:

The volume of the box is:

V = x²*h          where    x is the side of the square base  and h the height

then    h  =  V/ x²  ⇒    h = 475 / x²

The total cost of box C is:

C  = C₁  +  4*C₂      Where C₁  and C₂  are the costs of the base and one lateral side respectevily

Then cost C =  8*x²   + 4* 6*h*x

The cost C as a function of x is

C(x)  =  8*x²  + (24* 475 /x² )*x

C(x)  =  8*x²  +  11400/x

Tacking derivatives on both sides of the equation

C´(x)  =  16*x -  11400/x²

C´(x)  =  0     ⇒    16*x  -  11400/x²  = 0

16*x³  =  11400     ⇒   x³  =  11400/16

x³ =  712,5

x  =  8,93  cm

and    h   =  475 / (8,93)²      ⇒      h  =  5,95  cm

C(min)  =  8*79,77  +  4* ( 8,93)*5,95

C(min)  =  638,16  +  212,53

C(min)  =  850,69 cents

To check if value x = 8,93 would make C(x) minimum we go to the second derivatives

C´´(x) =  16  +  22800/x³ > 0

Then we have a minimum of C at  x = 8,93

Answer:

562.29

Step-by-step explanation:

you would just multiply 525.50 by 7 which is 3678.5 and divide that by 100 which is 36.785 and add that to 525.50 which is 562.285 which can be rounded to 562.29

Answer:

3L

Step-by-step explanation:

Perimeter is the sum of side lengths

Since the triangle is equilateral, it has all sides equal and each has length of L

So perimeter is:

Answer:

1067

Explanation:

The formula that will be used to calculate the sample size if population proportion isn't given is expressed as;

Sample size n = |Z|² × 0.25/E² where;

Z is the z-score at 95% confidence

E is the margin of error

Given parameters

Z score at 95% confidence interval = 1.96

E = 0.03

Substituting the given values into the formula to get the sample size n we will have;

n = 1.96²×0.25/0.03²

n = 3.8416×0.25/0.0009

n = 0.9604/0.0009

n = 1067.11

n ≈ 1067

Hence, the minimum sample size required to estimate a population proportion is approximately 1067

Answer:

61 rows

Step-by-step explanation:

Set up a proportion:

[tex]\frac{15}{22}[/tex] = [tex]\frac{x}{90}[/tex]

Cross multiply:

22x = 1350

x = 61.36

= approx. 61 rows

Step-by-step explanation:

(i) Sum the forces at point M in the x direction.

∑F = ma

-T sin 30° − T sin 30° + 5 N = 0

2T sin 30° = 5 N

T = 5 N

(ii) Sum the forces on the ring in the x direction.

∑F = ma

T sin 30° − N = 0

N = 2.5 N

Sum the forces on the ring in the y direction.

∑F = ma

T cos 30° − mg − Nμ = 0

Nμ = T cos 30° − mg

2.5 μ = 5 cos 30° − 2

μ = 0.932

(iii) Sum the forces on the ring in the y direction.

∑F = ma

T cos 30° − m₁g − m₂g + Nμ = 0

m₂g = T cos 30° − m₁g + Nμ

m (10) = 5 cos 30° − 2 + (2.5)(0.932)

m = 0.466 kg

Answer:

The probability that at least one of the three smoke detectors functions properly = 0.996625

Step-by-step explanation:

Given that:

a certain brand of smoke detector functions properly 85 percent of the time

Let X represent the certain brand of smoke detector

X = 85%

X = 0.85

Let the probability that at least one of the three smoke detectors functions properly be P(Y)

P(Y) = 1-  (1 - X)³

P(Y) =1 -  (1 - 0.85)³

P(Y) = 1 -  0.003375

P(Y) = 0.996625

∴

The probability that at least one of the three smoke detectors functions properly = 0.996625

Answer:

Step-by-step explanation:

$39 for 24 months comes to ...

$39 × 24 = $936

The "carrying charges" are the difference between the cash price and the installment price:

$936 -750 = $186

 Saving at the rate of $39 per month, it would take ...

  $750/$39 = 19.23 months   about 20 months to save up the cash price.

Often, such savings would come from a once-a-month paycheck, so it would take more than 19 such paychecks to save the required amount.

hope it will help :)

Answer:

the right answer is d

Step-by-step explanation:

please give 5 star i need it

Complete Question

An urn contains eight red, six white, and four green balls. Four balls are drawn at random.

(a) The probability that all four balls are red is

(Type an integer or a decimal. Round to two decimal places as needed.)

(b) The probability that there are exactly two red balls and exactly two green balls is

(Type an integer or a decimal. Round to two decimal places as needed.)

(c) The probability that there are exactly two red balls or exactly two green balls is

Answer:

(a) The probability that all four balls are red is

0.023

(b) The probability that there are exactly two red balls and exactly two green balls is

0.055

(c) The probability that there are exactly two red balls or exactly two green balls is

1.398

Step-by-step explanation:

An urn contains

Red balls = 8

White balls = 6

Green balls = 4

Total number of balls = 18 balls

(a) The probability that all four balls are red is?

The probability that a ball drawn is red = 8/18

The probability of drawing a ball that is not red = 1 - 8/18 = 10/18

The probability that all the 4 balls drawn are red = 8/18 × 7/17 × 6/16 x 5/15

= 1680/73440

= 0.022875817

Approximately = 0.023

(b) The probability that there are exactly two red balls and exactly two green balls is

There are 6 ways by which this can be achieved. Where R = Red balls and G = Green Balls

RRGG

GGRR

RGRG

GRGR

RGGR

GRRG

P(Exactly two red balls and two green balls) = P(Exactly two red balls × Exactly two green balls)

=[ (8/18 × 7/17) ×( 4/16 × 3/15)] × 6 ways

= 672/73440 × 6 ways

= 0.0091503268 × 6 ways

= 0.0549019608

Probability of drawing out exactly two two red balls and two green balls is

= 0.055

(c) The probability that there are exactly two red balls or exactly two green balls is

P(Exactly two red balls or two green balls) = P(Exactly two red balls + Exactly two green balls)

P(Exactly two red balls or two green balls) = P(Exactly two red balls or Exactly two green balls)

=[ (8/18 × 7/17) + ( 4/16 × 3/15)] × 6 ways

=0.1830065359 + 0.05

= 0.2330065359 × 6 ways

= 1.3980392154

≈1.398

Answer:

Answer: $428.00

Step-by-step explanation: First, we need to calculate the person’s total hours, (30 x 2 = 60 hours) then the money per hour (60 x 9) then take away the taxes and account deductions.

Answer:

yes

Step-by-step explanation:

Because the point lie on the plane they are coplanar

Answer:

subtract 5

Step-by-step explanation:

subtract 5 from each side of the equal sign..

Answer:

the answer is subtract 5

Step-by-step explanation:

Answer:

the rectangle's width is approximately 3.39 inches

and the length is approximately 13.56 inches.

Step-by-step explanation:

Recall that the area of a rectangle is Length times Width

If we name the length "L" and the width "W", we have:

L * W = 46

Also: "the length is 4 times the width" can be written in math form as:

L = 4 * W

and now we can replace the length L by 4 * W in the formula for the area:

[tex]L\,*\,W = 46\\(4\,W) \,W = 46\\4\,W^2=46\\W^2=\frac{46}{4} =11.5\\W=\sqrt{11.5} \\W\approx 3.39[/tex]

and now we find the value of L:

[tex]L=4\.(3.39) = 13.56[/tex]

Therefore, the rectangle's width is approximately 3.39 inches

and the length is approximately 13.56 inches.

Answer:

People like oranges

Step-by-step explanation:

Given:

Mo likes oranges. Jai likes oranges. Ben likes oranges.

We have a few different options;

Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given people who like oranges.

Option B: People on like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.

Option C: People like oranges. This can be possible because Mo, Jai, and Ben likes oranges

Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not

People like oranges.

the action or process of inducting someone to a position or organization.

We have a few different options;

Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given to people who like oranges.

Option B: People like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.

Option C: People like oranges. This can be possible because Mo, Jai, and Ben like oranges

Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not

Learn more about Induction:

https://brainly.com/question/26366866

#SPJ2

La mentalidad de crecimiento, ya que a diferencia de la mentalidad fija, nos permite ver en otras personas la mentalidad de mejorar y perseverar.

Answer:

Translation

Step-by-step explanation:

The object is only moved, which is what happens when a translation occurs

Answer:

b = 7.4

Step-by-step explanation:

b - 3 + 4b = 34

combine like terms:

5b - 3 = 34

5b = 37

divide by 5:

b = 7.4

Answer:

b=7.4

Step-by-step explanation:

1. Combine like terms

5b-3=34

5b=37

2. Isolate x value by dividing

b=7.4

Answer:

16 * √3 cm² or approximately 27.71 cm²

Step-by-step explanation:

Given the 8 cm length of the diagonal and the 30° (π/6 radians) angle with one of the sides, we can calculate the width and height of the rectangle using:

8 * cos(π/6) = 8 * ((√3)/2) = 4 * √3

8 * sin(π/6) = 8 * (1/2) = 4

Multiply those two values together to get the area and you get

16 * √3 cm²

Answer:

Negative change

Step-by-step explanation:

Given

[tex]Monday\ Temperature = 5\ deg[/tex]

[tex]Thursday\ Temperature = -8\ deg[/tex]

First, we need to calculate the overall change in temperature

This is calculated by subtracting the initial temperature from the final temperature

[tex]Overall\ Change = Thursday\ Temperature - Monday\ Temperature[/tex]

[tex]Overall\ Change = -8\ deg - 5\ deg[/tex]

[tex]Overall\ Change = -13\ deg[/tex]

The overall change shows a negative change in the temperature.

This is as a result of a drop in temperature from Monday to Thursday

Answer:

I Think its 8% decrease

Answer:

The answer is

Step-by-step explanation:

To find the percentage change we use the formula

[tex]Percentage \: \: change = \frac{change}{original \: quantity} \times 100[/tex]

To find the change subtract the lesser one from the larger one

Original price = $ 52

Current price = $ 47.82

Change = 52 - 47.82 = $ 4.18

Substitute the values into the above formula

Percentage change is

[tex] \frac{4.18}{52} \times 100[/tex]

We have the final answer as

Percentage change = 8%

Since the current price was lesser than the original price there is a percentage decrease in the amount

Answer:

1:6

Step-by-step explanation:

1 yard = 3 feet. 4 yards = 12 feet.

Ratio of 2 feet:12 feet = 1:6 Ans D

The ratio of 2 feet to 4 yards is 1 : 6

The ratio is given as:

Ratio = 2 feet : 4 yards

Convert yard to feet

Ratio = 2 feet : 4 * 3 feet

Evaluate

Ratio = 2 feet : 12 feet

Divide the ratio

Ratio = 1 : 6

Hence, the ratio of 2 feet to 4 yards is 1 : 6

Read more about ratio at:

https://brainly.com/question/2784798

#SPJ2

Answer:

C

Step-by-step explanation:

Since the exponent on the 10 is negative, we need to move the decimal point to the left instead of the right. After moving the decimal point on the 2.5 to the left 4 places, we see that the answer is 0.00025.

Answer:

[tex]34.12 * 11 = 375.32[/tex]

Step-by-step explanation:

Given

11 * 34.12

Required

Multiply

To start with, we have to ignore the decimal points;

So, we have

    3412

  *      11

---------------

   3 4 1 2

3 4 1 2

------------------------

3 7 5 3 2

The next step is as follows;

34.12 is in 2 decimal places

11 is has no decimal (0 decimal place)

Add the decimal places together

[tex]Decimal\ Place = 2 + 0 = 2[/tex]

This implies that the result will be in 2 decimal placed;

Hence:

[tex]34.12 * 11 = 375.32[/tex]

Answer:

the vetrex

Step-by-step explanation:

Answer: y= -2.5

Step-by-step explanation:

Distribute the -2 and 3 into the parentheses. -6 + 6 cancels out so you are left with 3y on the right side. Add 2y to the right side leaving you with -2=5y. Divide both sides by -2

Answer:

Step-by-step explanation:

[tex] \sf{ - 2(y + 1) = 3(y - 2) + 6}[/tex]

Distribute -2 through the parentheses

Similarly, Distribute 3 through the parentheses

⇒[tex] \sf{ - 2y - 2 = 3y - 6 + 6}[/tex]

Since two opposites add up to zero , remove them

⇒[tex] \sf{ - 2y - 2 = 3y}[/tex]

Move 3y to Left hand side and change it's sign

Similarly, move -1 to right hand side and change it's sign

⇒[tex] \sf{ - 2y - 3y = 2}[/tex]

Collect like term

⇒[tex] \sf{ - 5y = 2}[/tex]

Divide both sides of the equation by -5

⇒[tex] \sf{ \frac{ - 5y}{ -5 } = \frac{2}{ - 5} }[/tex]

Calculate

⇒[tex] \sf{ - 0.4}[/tex]

Hope I helped!

Best regards!