a car is traveling at 57 mi/h before it enters into a skid. the drag factor of the road surface is 1.1, and the braking efficiency is 100%. how long might the average skid mark be to the nearest tenth of a foot?

Answer:

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

Step-by-step explanation:

sin(-5x)=0.1

-sin(5x)=0.1

sin(5x)=-0.1

sin(5x)=1/10

5x=arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)+2kπ

5x=π-arcsin(- 1/10)+2kπ

x=arcsin (1/10)/5 + 2kπ/5

x=arcsin (1/10)/5 + 2kπ/5

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

They should produce 1091 units each day to yield a minimum cost.

What is the vertex formula?

When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).

We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.

We have,

C = 70,000 - 120x + 0.055x²

C = 0.055x² - 120x + 70,000

Hence, for this equation, the graph will be parabola opening upward.

For that, the vertex will be the minimum cost

x = (-b) / 2a

Here, a = 0.055 , b = -120

Now, find and put the values of x.

minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )

                           = 120 ÷ 0.11

                           = 120 ÷ 0.11

                           = 1090.90  ≈ 1091 units

The minimum cost will be yield for 1091 units.

Therefore, They should produce 1091 units each day to yield a minimum cost.

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The derivative of the given polynomial equation is 16x³ - 6x + 6.

We are given an equation. The equation represents a polynomial in one variable. The degree of the polynomial is four; hence, it is called biquadratic. We need to find the derivative of the given polynomial. The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.

The equation is given below.

y = 4x^4 - 3x² + 6x + 14

dy/dx = (d/dx)(4x^4 - 3x² + 6x + 14)

dy/dx = (d/dx)(4x^4) - (d/dx)(3x²) + (d/dx)(6x) + (d/dx)(14)

dy/dx = [4*4x^(4 - 1)] - [3*2x^(2 - 1)] + [6*1x^(1 - 0)] + [14*0x^(0 - 1)]

dy/dx = 16x³ - 6x + 6

Hence, the derivative of the given polynomial equation is 16x³ - 6x + 6.

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[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]

Answer:

A = 13 B = 3 C = -7 D = -12

Step-by-step explanation:

Just insert the x values for a, b, c, and d. for example if we were to find a.

The x value for a is -3 so we would put -3 in place of x in the equation.

-5(-3) - 2

Remember: Two negative numbers multiplied with each other equal a positive.

15 - 2 = 13

Answer: I would say non linear. I have done problems like these before and anytime there is an exponent in the equation it always ends up being non linear. Also remember for it to be linear it most form a straight line that passes through the origin.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

function because for every x there is only one y

the domain are the value of x

the range are the value of y

Answer:

Step-by-step explanation:

If one spins a six-space spinner and then flips a coin, then the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]

As per the question statement, a person spins a six-space spinner and then flips a coin,

And we are required to determine the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes.

Now, on spinning a six-space spinner, any one of the 6 faces will come as outcomes, and if these outcomes are denoted by (1, 2, 3, 4, 5, 6).

And after spinning the six-space spinner, if one flips a coin, either of "heads" face or "tails" face will come as outcome, which can be denoted by {H, T}.

Therefore, If one spins a six-space spinner and then flips a coin successively as mentioned above, every possible outcome of the spinner will be accompanied by one of two the possible outcomes the coin. Hence, the sample space (S) of possible outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]

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With the help of probability we can conclude our answer.

acc to our question-,

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The required value of a₄ is 10,202 to the given recursive formula.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The given recursive formula in the question as:

aₙ = (aₙ ₋₁ )² + 1 ....(i)

And, a₁ = 3

Substitute the value of a₁ = 3 in equation (i), and solve for n = 2

a₂ = (a₁)² + 1

a₂ = (3)² + 1

a₂ = 9 + 1 = 10

Substitute the value of a₂ = 10 in equation (i), and solve for n = 3

a₃ = (10)² + 1

a₃ = 100 + 1 = 101

Substitute the value of a₃ = 101 in equation (i), and solve for n = 4

a₄ = (101)² + 1

a₄ = 10,201 + 1

a₄ = 10,202

Therefore, the required value of a₄ is 10,202.

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Step-by-step explanation:

3.

we need to find the map size based on actual miles.

so, we find how many map ft are 1 actual mile :

5 ft / 20.5 corresponds to 1 actual mile.

5 / 20.5 = 10/41 ft

now, we have 15.5 actual miles, that is 15.5 times the 1 standard actual mile.

and so, this is

10/41 × 15.5 = 155/41 = 3.7804878048780... map ft

4.

30.5 model cm = 70.6 actual m

1 model cm = 70.6/30.5 = 2.314754098... actual m.

8 model cm = 8×2.314754098... =

= 18.51803279... actual m

5.

7 map m = 14 actual miles

1 map m = 14/7 = 2 actual miles.

14 map m = 14×2 = 28 actual miles.

6.

8 map km = 6 actual miles

we need to calculate the map km, so we need the standard actual mile

1 actual mile = 8/6 = 4/3 = 1.3333333... map km.

50.2 actual miles = 50.2×1.333333... =

= 66.93333333... map km.

7.

80.2 model cm = 40.2 actual m

1 model cm = 40.2/80.2 = 0.501246883... actual m

10 model cm = 10×0.501246883... =

= 5.01246883... actual m

8.

6 map m = 15 actual miles

1 map m = 15/6 = 5/2 = 2.5 actual miles

8.8 map m = 8.8×2.5 = 22 actual miles

9.

5 map ft = 16.5 actual miles

1 actual mile = 5/16.5 = 0.303030303... map ft

45.6 actual miles = 45.6×0.303030303... =

= 13.81818181... map ft

10.

65.8 model cm = 95.6 actual m

1 model cm = 95.6/65.8 = 1.452887538... actual m

12 model cm = 12×1.452887538... =

= 17.43465046... actual m

Answer:

= (2x + 5y) * (2x - 5y)

Step-by-step explanation:

4x²-25y²
= (2x)² - (5y)²
= (2x + 5y) * (2x - 5y)

Answer:

[tex]\huge\boxed{\sf (2x + 5y)(2x - 5y)}[/tex]

Step-by-step explanation:

[tex]4x^2-25y^2[/tex]

Both of the terms are perfect squares.

[tex](2x)^2-(5y)^2[/tex]

= (2x + 5y)(2x - 5y)

[tex]\rule[225]{225}{2}[/tex]

The theatre sold 178 adult tickets and 261 children tickets for the play.

It is given that the total number of seats is 439 seats.

There are two types of tickets available- children and adults.

The price for adult tickets is $48 and that for children is $28.

Let the number of adult tickets sold be x

Let the number of children's tickets sold be y.

The show was a sold-out

Hence,

x + y = 439                                 [1]

48x + 28y = 15852                    [2]

From equation [1] we get

x = 439 - y

putting this result in equation [2] gives us

48(439 - y) + 28y = 15852

or, 21072 - 48y + 28y = 15852

or, -20y = - 5220

or, y = -5220/ -20

or, y = 261

Therefore,

x + 261 = 439

or, x = 439 - 261

or, x = 178

Hence, 178 adult tickets were sold and 261 children's tickets were sold.

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Answer:

x=-3

Step-by-step explanation:

we can fill the y into the first equation since we already know what it is equal to

5x+4(1-x)=1

5x+4-4x=1

x+4=1

  -4. -4

x=-3

Hopes this helps please mark brainliest

Answer:

5x + 4y = 1

Answer: x = 1/5 - 4y/5

y = 1 - x

Answer: x = −y + 1

Step-by-step explanation:

Please give the brainliest, really appreciated.

Using a 98% confidence interval, the total number of customers that should be sampled is 87.

The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.

Given,

Standard deviation σ=300

Confidence level: 0.98

Maximum allowable error: ε=75

The critical value is calculated using the standard normal table at the level of significance (0.02)

The critical value in this case is 2.326.

Sample size is calculated by,

n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²

n=((2.326)²×(300)²)/(75)²

n=86.564≈87

Therefore, the required sample size is 87.

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y= -4/3=-1.333

y= 5/2=2.500

Answer:

4.5 ounces of rice per container

Step-by-step explanation:

27 / 6 = 4.5

Hope this helps :)

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

Given, that

The 19-unit percent change is 45 %

Now, 1-unit percent change is 45/19

17-unit percent change is (45/19)×17%

= 40.26%

The 16-unit percent change is 43 %

Now, 1-unit percent change is 43/16

12-unit percent change is (43/16)×12%

= 32.25%

The 20-unit percent change is -25%

Now, 1-unit percent change is -25/20

18-unit percent change is (-25/20)×18%

= -22.5%

The 5-unit percent change is -50 %

Now, 1-unit percent change is -50/5

8-unit percent change is (-50/5)×8%

= -80%

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

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The mean sleep time is 16.54 hours per day for newborn babies

acc to our question-

The mean sleep time is 16.54 hours per day for newborn babies.

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Josiah read  at the rate of 17.5 pages per  hour.

Speed of reading is the number of pages read per hour.

Given here, Josiah read 28 pages in  1 ³/₅ hours which is in mixed fraction

now   1 ³/₅ = ⁸/₅ = 1.6 hours

therefore the speed of reading is = 28 / 1.6 = 17.5 pages hour.

Hence, Josiah's the speed of reading is  17.5 pages hour.

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Answer:

surface area=2(lb+lh+bh)

surface area=2(9)(4)+(9)(12)+(4)(12)

surface area=384cm2

The fraction of all the circles in the shapes  is 23/90

Given that the:

Ratio of the number of white shapes to the number of black shapes is 7:3

Ratio of the number of white circles to the number of white squares is 2:7

Ratio of the number of black circles to the number of black squares is 1:2

Total share for both white and black shape = 7+3 = 10

share for white shape = 7/10 and share for black shape = 3/10

Total share for white circles and white squares = 2+7 = 9

share for white circles = 2/9 and share for white squares = 7/9

Total share for black circles and black squares = 1+2 =3

share for black circles = 1/3 and share for black squares = 2/3

White circles will take 2/9 of white colors i.e. 2/9 x 7/10 =   14/90 = 7/45

Black circles will take 1/3 of  black colors i.e. 1/3 x 3/10 = 3/30 = 1/10

Fraction of circles = 7/45 + 1/10

                              =  14+9/ 90

                             = 23/90

Therefore, the fraction of all the shapes that are circles is 23/90

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Answer:

(0, 6)

Step-by-step explanation:

Given function:

[tex]y=\log_4(2x+64)+3[/tex]

The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.

Therefore, to find the y-intercept, substitute x = 0 into the function:

[tex]\implies y=\log_4(2(0)+64)+3[/tex]

[tex]\implies y=\log_4(64)+3[/tex]

Rewrite 64 as 4³:

[tex]\implies y=\log_4(4)^3+3[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies y=3\log_4(4)+3[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies y=3(1)+3[/tex]

[tex]\implies y=3+3[/tex]

[tex]\implies y=6[/tex]

Therefore, the y-intercept of the given function is (0, 6).

After evaluating those terms,

we get the answer as

1.  -7/6 - (-1/9) =[tex]\frac{-19}{18}[/tex]

2.  -1/3 + 5/7   = = [tex]\frac{8}{21}[/tex]

A fraction is a number that has a numerator as well as a denominator.

1 / 2  is an example of a fraction. The top part of the fraction is the numerator and the bottom part of the fraction is the denominator.

Fractions represent one value. Dividing the numerator by the denominator shows what decimal value fractions have. For example,  1/2  is equal to 1  ÷  2 which equals 0.5.

in this we have to evaluate

1.    -7/6 - (-1/9)

= [tex]\frac{-7}{6}[/tex]  - ([tex]\frac{-1}{9}[/tex])

= [tex]\frac{-21+2}{18}[/tex]

=[tex]\frac{-19}{18}[/tex]

Hence , after solving we get the desired result as -19/18 .

2. -1/3 + 5/7

= [tex]\frac{-1}{3}[/tex] + [tex]\frac{5}{7}[/tex]

= [tex]\frac{-7 + 15}{21}[/tex]

= [tex]\frac{8}{21}[/tex]

Hence, after solving we get the desired result as 8/21 .

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The distance driven in city is 386.4 miles and same in highway is 213.6 miles.

Let the distance driven in city be x and driven in highway be y.

Now given that the mileage in city is 46 miles per gallon and in highway same is 51 miles per gallon.

The car is driven 621 miles in 13 gallon.

So suitable system of linear equations in two variables to solve this is,

x+y = 621 ……(1)

x/46+y/51 = 13 …….(2)

From (2) we get,

51x+46y = 30498

5x+46(x+y) = 30498

5x+46*621 = 30498

5x = 30498-28566

5x = 1932

x = 386.4

So from (1) we get,

y = 621-x = 621-386.4 = 213.6

Hence the car drove 386.4 miles in city and 213.6 miles in highway.

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Answer:

y+6 =-2(x-5)

Step-by-step explanation:

The question is asking for the equation of the line

The equation for point-slope form is always written as y-y₁=m(x-x₁)

y₁ and x₁ are the points given to you in this order (x₁, y₁)

so x₁=5 and y₁=-6

Now you plug in all the numbers you have into the point slope form

y- (-6)= -2(x-5)

When you subtract a negative (a double negative you get a positive)

y+6=-2(x-5)

Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).

Notes:

For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be

y-2=-2(x-1)

Answer:

(15-3x³) is the answer.

Step-by-step explanation:

2*15-2*3x³

which is 30-6x³.

Answer:

A

Step-by-step explanation:

It is perpendicular because it forms a right angle with the second line