Based on the two way frequency table above, what is the percentage of individuals that selected sports cars as their preferred vehicle?

65%

35%

55%

45%

Answer:

[tex]r=1.57[/tex], [tex]P(t)=71e^{3t\ln2}[/tex], [tex]P(8)=1191182336[/tex],[tex]P'(8)=2476994033[/tex]  [tex]t=2.713\; hr[/tex]

Step-by-step explanation:

[tex](a)[/tex] Find the relative growth rate.

[tex]P=Ae^{rt}[/tex] where given [tex]A=71, P(t)=120\;\;and \;\; t=\frac{1}{3}[/tex]

Find the value of [tex]r[/tex]

[tex]\Rightarrow 120=71 e^{\frac{r}{3} }[/tex]

[tex]\Rightarrow \frac{120}{71} =e^{\frac{r}{3} }[/tex]

[tex]\Rightarrow 1.69=e^{\frac{r}{3} }[/tex]

[tex]\Rightarrow \ln1.69=\frac{r}{3}[/tex]

[tex]\Rightarrow 3\ln1.69=r \;\;\; or \;\;\; r=1.57[/tex]

[tex](b)[/tex]   Find an expression for the number of cells after t hours.

[tex]P(t)=71e^{3t\ln2}[/tex]

[tex](c)[/tex]  Find the number of cells after 8 hours.

[tex]P(8)=71e^{3\times 8\times \ln2}[/tex]

[tex]\Rightarrow P(8)=1191182336[/tex]

[tex](d)[/tex]  Find the rate of growth after 8 hours.

  [tex]P(t)=71e^{3\times t\times \ln2}[/tex]

Now differentiate w.r.t. [tex]t[/tex]

[tex]\Rightarrow P'(t)=71\times 3\ln2\times e^{3t\ln2}[/tex]

[tex]\Rightarrow P'(8)=3573547008\ln2[/tex]

             [tex]=2476994033[/tex]

[tex](e)[/tex]  When will the population reach 20,000 cells?

     [tex]20,000=71e^{3t\ln2}[/tex]

[tex]\Rightarrow \ln\frac{20000}{71} =3t\ln2[/tex]

[tex]\Rightarrow \frac{ \ln\frac{20000}{71}}{3\ln2} =t[/tex]

S0, [tex]t=2.713 hr[/tex]

Step-by-step explanation:

done....................I hope its right

Answer:

1. 3x + 36

2. 14 + 12x

3. 40x-18

Step-by-step explanation:

1. 3(x+12)

3x + 36

2. 2(7+6x)

14 + 12x

3. 9(5x-2)

40x-18

Ace Carlos

Answer:

For number 2 it is = x(f + h)

For number 3 it is = x(g + h)

For number 4 it is = x(h + f)

For number 5 it is = x(f - g)

Hope this helps:)

Answer:

[-5, 5] the Y value has a minimum of -5 and max of 5 so that is what your range is!

Step-by-step explanation:

[tex]\boxed{\boxed{\pink{\bf \leadsto The \ range \ of \ y \ is \ y \ \in \ [-5,5] .}}}[/tex]

A function is given to us and we need to find its range. So the given function is ,

[tex]\bf\implies y = -5\:sin(x) [/tex]

The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.

[tex]\bf \implies y = (-5) [/tex]

The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.

[tex]\bf \implies y = (5) [/tex]

Hence the range is ,

[tex]\boxed{\red{\bf -5 \leq y \leq 5 }}[/tex]

Interval Notation :-

[tex]\boxed{\red{\bf y \in [-5,5] }}[/tex]

Set builder Notation :-

[tex]\boxed{\red{\bf \{ y | -5 \leq y \leq 5 }}[/tex]

Graph of the function is attached .

Answer:

21

Step-by-step explanation:

Ratios are used.

10/30 = 12/36 = 7/x

1/3 = 7/x

x = 3*7 = 21

Answer: 14 lbs

Step-by-step explanation:

shoot i hope this right

Answer:

B) -6 is the answer :) :) *-*

Answer: 3x+y=5

Step-by-step explanation:

Equation of a line that has slope(m) and passes through point (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Given: Point = (3,-4)

Slope =-3

Then, the equation of the required line:

[tex](y-(-4))=-3(x-3)\\\\\Rightarrow\ (y+4)=-3(x-3)\\\\\Rightarrow\ y+4=-3x+9\\\\\Rightarrow\ 3x+y=9-4\\\\\Rightarrow\ 3x+y=5\ \ \ \ [\text{Standard form: Ax+By=C}][/tex]

Hence, required equation: 3x+y=5

Multiply both sides by 2pi:

F(2pi) = sqrt(g/l)

Square both sides:

F^2 (2pi)^2 = g/l

Solve for l by dividing both sides by F^2 (2pi)^2

L = g/ F^2 (2pi)^2

Simplify:

L = g / 4pi^2(f^2)

Answer:

1/4

aus74ebsi2neissnejws

Answer:

1/4 or . 25

Step-by-step explanation:

pls mark brainliest to help my rank :)

Answer:

Step-by-step explanation:

Answer:

$27.14

Step-by-step explanation:

Price of 1 DVD: $9.10

Price of 4 DVDs: 4 * $9.10 = $36.40

Discount: 25%

Now we find 25% of $36.40.

25% of $36.40 =

= 0.25 * $36.40

= $9.10

The 25% discount amounts to $9.10. We now subtract $9.10 from $36.40 to find the discounted price.

$36.40 - $9.10 = $27.30

Now we need to apply the 6.75% tax to $27.30.

6.75% of $27.30 =

= 0.0675 * $27.30

= $1.84

The sales tax is $1.84.

Now we add the sales tax amount to the total discounted price.

$27.30 + $1.84 = $29.14

Answer: $27.14

Answer:

84.1%

Step-by-step explanation:

Add up 0.1, 2.2, 13.6, 34.1, and 34.1 and you get that number. this is because that is the numbers in each column and you add those because they are below 79 mark.

Answer:

k47n4

Step-by-step explanation:

Answer: would it be the 12th year and a half

Step-by-step explanation: because since it increases then half of the year it would be $30,400

Answer:

A 7/25

Step-by-step explanation:

1. Take inverse of theta

2. Substitute the inverse theta in the equation given in question

Answer:

No

Step-by-step explanation:

SD=8+2+5+4+11+9÷6

13=10+9+20÷6

13=19+20÷6

13=39÷6

13=6.5-False=No

13 is not a usual number. A further solution of the given query is provided below.

Given:

Number of observations = 6

Series 8, 2, 5, 4, 11, 9

The Mean will be:

= [tex]\frac{Sum \ of \ observation}{Total \ number \ of \ observations}[/tex]

By substituting the values, we get

= [tex]\frac{8+2+5+4+11+9}{6}[/tex]

= [tex]\frac{32}{6}[/tex]

= [tex]6.5[/tex]

Now,

The Standard deviation will be:

= [tex]\sqrt{\frac{|x-\bar x|^2}{n} }[/tex]

= [tex]\sqrt{\frac{(1.5)^2+(4.5)^2+(1.5)^2+(2.5)^2+(4.5)^2+(2.5)^2}{6} }[/tex]

= [tex]3.0956[/tex]

13 is not within the range of standard deviation. Thus it is not a usual number.

Learn more about standard deviation here:

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Answer:

6x

Step-by-step explanation:

add the terms to make one term

Answer:

6/7

Step-by-step explanation:

First you just have to plug the numbers in so you get 3*-4/-2+(-12) which simplifies to -12/-14 which can be simplified to 6/7

The value of expression bd/a+c will be 6/7.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The expression is ,

bd / a+c

And, The values are a=−2 , b=3 , c=−12 , and d=−4.

Now, Find the value of the expression we can substitute all the given values in the expression;

⇒ bd / a+c

⇒ 3 × (-4) / -2+(-12)

⇒ -12/-2-12

⇒ -12/-14

⇒ 12/14

⇒ 6/7

Thus, The value of expression bd/a+c will be 6/7.

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Answer:

The answer is 1,122

Step-by-step explanation:

33 x 34

Answer:

d. The common ratio is 1.1

Step-by-step explanation:

To see if the data has a common ratio or common difference, we have to see if the division between them is equal(common ratio), or if the difference between them is equal(common difference).

In this case, since [tex]60.5 - 55 \neq 55 - 50[/tex], it has a common ratio.

To find it, we divide consecutive terms. For example:

[tex]\frac{55}{50} = 1.1[/tex]

So the correct answer is:

d. The common ratio is 1.1

Answer:

( -2, 3 )

Step-by-step explanation:

3x + y = -3

y = x + 5

Since "y" has been given to us, all we need to do is substitute.

3x + x + 5 = -3

Combine like terms

4x + 5 = -3

Subtract 5 onto both sides

4x + 5 - 5 = -3 - 5

4x = -8

Divide by 4 into both sides to isolate the variable

4x/4 = -8/4

x = -2

Now that we have x ( -2 ), we can substitute that to get what y is.

y = x + 5

y = -2 + 5

y = 3

( x, y ) ---> ( -2, 3 )

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:

$33.60

Step-by-step explanation:

%20 of 28 is 5.6

add $5.60 to 28= 33.60

Answer:

$33.6

Step-by-step explanation:

28 x 0.20 = 5.6 ...tip

total cost = 28 + 5.6 = 33.6

Why should anyone help you when you just post absurd answers for other people?

Answer:

The answer is option 1.

Step-by-step explanation:

You have to substitute the expressions of s into the formula of volume :

s = 4x² + 3

V = s³

V = (4x² + 3)³

Then, you have to expand it :

V = (4x² + 3)³

V = (16x⁴ + 24x² + 9)(4x² + 3)

V = 16x⁴(4x²) + 16x⁴(3) + 24x²(4x²) +

24x²(3) + 9(4x²) + 9(3)

V = 64x⁶ + 48x⁴ + 96x⁴ + 72x² + 36x² + 27

V = 64x⁶ + 144x⁴ + 108x² + 27

The required volume of the cube is 64x⁶ + 144x⁴ + 108x² + 27. Answer: A.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property

The volume of the cube is given by V = s^3. Substituting s = 4x^2 + 3, we get:

V = (4x² + 3)³

= (4x²)³ + 3(4x²)²(3) + 3(4x²)(3²) + 3³

= 64x⁶ + 144x⁴ + 108x² + 27

Therefore, the volume of the cube is 64x⁶ + 144x⁴ + 108x² + 27. Answer: A.

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Answer:

Step-by-step explanation:

Lets pick to columns in the table

Lets so (6,228) and (7,266)

To find the slope you need to do y1-y2/x1-x2

7-6/266-228=1/38.

1/38 is the slope.

y=1/38x+b

to find B you have to plug any of the y with the corresponding x values back in and solve for b.

Lets choose 228.

228=1/38(6)+b

228=6/28+b

(28/6)(228)=b

b=1064

the equation will be y=1/38x+1064

Answer:

A

Step-by-step explanation:

This is because the shaded regions are not required

Answer:

A

Step-by-step explanation:

its not shaded

Answer:

24

Step-by-step explanation:

4! = 4*3*2*1 = 24

24 numbers can be formed

Answer:

The cost function is simply the initial cost plus the manufacturing cost.

C(x)=500+20x-5x^3/4+0.01x^2

The demand function was given to us.

p(x)=320-7,7x

The revenue function is simply x multiplied by the demand function.

R(x)=xp(x)=320x-7.7x^2

We find that when 20 planes are produced, that profit is currently maximized

We know that to maximize profit, marginal revenue must equal marginal cost.

C'(x)=20-15/4x^-1/4+0.02x

R'(x)=320-15.4x

x=19,57

We find that when 20 planes are produced, that profit is currently maximized.

Step-by-step explanation:

An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function: , where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell  planes.

(a) Find the cost, demand, and revenue functions.

(b) Find th eproduction level and the associated selling price of the aircraft that maximizes profit.

9514 1404 393

Answer:

  no solution

Step-by-step explanation:

The equations are inconsistent. The set of equations reduces to ...

  x + 2y + 3z = 12

  x + 2y + 3z = 30

  x + 2y + 3z = 60

No values of x, y, and z can satisfy all three equations. There is no solution.