Who finished the mile first?

In this case to calculate the limit, you simply plug the x value of -2 into the function

[tex]y = \lim_{x \to \--2}( -3x^3+2x^2-4x+5) = 24 + 8+8+5 = 45\\[/tex]

So the limit equals 45.

Hope that helps!

Answer:

[tex]\displaystyle y = 45[/tex]

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                                [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle y = \lim_{x \to -2} \big[ -3x^3 + 2x^2 - 4x + 5][/tex]

Step 2: Find Limit

∴ the limit as x approaches -2 of the given function -3x³ + 2x² - 4x + 5 is equal to 45.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

Step-by-step explanation:

[tex]S_{n}=\dfrac{n}{2}(2a + (n-1)*d)[/tex]

Here, n- number of terms ; d - common difference ;  a - first term

[tex]S_{8}=12\\\\\dfrac{8}{2}[2a+(8-1)*d]=12\\\\4[2a+7d]=12\\\\2a + 7d = \dfrac{12}{4}\\\\\\2a + 7d = 3 \ -----------------------(i)[/tex]

[tex]S_{16}=56\\\\\dfrac{16}{2}(2a+15d)=56\\\\\\8(2a+15d)=56\\\\2a + 15d=\dfrac{56}{8}\\\\\\[/tex]

2a + 15d = 7 ----------------(ii)

Subtract (i) from equation (ii)

(ii)         2a + 15d = 7

(i)          2a +   7d = 3  

           -      -          -  

                       8d = 4

                          d = 4/8

d = 1/2

Plugin d = 1/2 in equation (i)

[tex]2a +7*\dfrac{1}{2}=3\\\\\\2a = 3 -\dfrac{7}{2}\\\\\\2a =\dfrac{6}{2}-\dfrac{7}{2}\\\\\\2a=\dfrac{-1}{2}\\\\\\a=\dfrac{-1}{2*2}\\\\\\a=\dfrac{-1}{4}[/tex]

Second term =  first term + d

                      [tex]=\dfrac{-1}{4}+\dfrac{1}{2}=\dfrac{-1}{4}+\dfrac{2}{4}=\dfrac{1}{4}[/tex]

[tex]Third \ term =\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{2}{4}=\dfrac{3}{4}\\\\\\Fourth \ term =\dfrac{3}{4}+\dfrac{1}{2}=\dfrac{3}{4}+\dfrac{2}{4}=\dfrac{5}{4}\\\\[/tex]

AP is :

[tex]\dfrac{-1}{4}; \dfrac{1}{4};\dfrac{3}{4};\dfrac{5}{4}.......[/tex]

The superhero moves at 3600 km/h and his partner at 4415 km/h. The earth is round, so both him and his partner can get to the same location even travelling at opposite directions.

Speed is the ratio of distance travelled to the total time taken, it is given by:

Speed = distance / time

The superhero flies at 60000 m/min = (60000m * 1 km per 1000 m) / (1 min * 1 hr per 60 min) = 3600 km/h

The earth is round, so both him and his partner can get to the same location even travelling at opposite directions.

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Answer:

8 -9788.8

15-273+4+484

Answer:

153.86

Step-by-step explanation:

Area = Pi*R^2

Or

3.14xRadiusx Radius= Area

so 3.14*7*7=153.86

If this helps can I get Brainliest pls.

Answer:

It is D

Step-by-step explanation:

Answer:96+ a factor of 3

Step-by-step explanation:

48+48=96

1.5+1.5=3

Answer:

Step-by-step explanation:

The cup has 33.(66)% more liters than the jar.

The cup has more water than the jar.

The cup has 11/30 more liters of water than the jar.

Since Angle XYZ equals 70 degrees, thus the sum of the Angle XYW and Angle WYZ equal 70 degrees

      Angle XYW + Ange WYZ = 70

         50 + (3x + 14) = 70

            3x + 14 = 20

              3x = 6

                 x = 2

Hope that helps!

Answer:

x = 2

Step-by-step explanation:

m<XYZ  = 70 and

m<XYZ = m<XYW + m<WYZ

So we can conclude 50 + 3x + 14 = 70 add like terms

64 + 3x = 70 subtract 64 from both sides

3x = 6 divide both sides by 3

x = 2

Answer:

8 x 60

Step-by-step explanation:

Hope it helps.

Answer:

10.429% exceed

Step-by-step explanation:

expected:

150x [100+40]/100=210 parents were expected on first night

210x60/100=126 parents expected on the second night

210+126=326 expected

percentage difference=

210+150=360

360/326 x 100=110,429%

110,429%-100%=10,429% exceed

Part A

Given info:

Because n > 30 is not true, and we don't know the population standard deviation (sigma), this means we must use a T distribution.

The degrees of freedom here are n-1 = 23-1 = 22.

At 90% confidence and the degrees of freedom mentioned, the t critical value is roughly t = 1.717

Use a T distribution table or calculator to determine this. If you don't have a calculator for the task, then you can search out "inverse T calculator" and there are tons of free options to pick from.

The margin of error E is

E = t*s/sqrt(n)

E = 1.717*1.12/sqrt(23)

E = 0.400982

This is approximate and accurate to 6 decimal places.

The confidence interval is going to be xbar plus or minus that E value

L = lower bound = xbar - E = 4.90 - 0.400982 = 4.499018 = 4.50

U = upper bound = xbar + E = 4.90 + 0.400982 = 5.300982 = 5.30

The confidence interval in the format of (L, U) is (4.50, 5.30)

You could also express it as the format L < mu < U and it would be 4.50 < mu < 5.30; however, I'll stick to the first method.

=====================================================

Part B

Since we know sigma = 2.6 is the population standard deviation, we can use a Z distribution now.

At 90% confidence, the z critical value is roughly 1.645; use a table or calculator to determine this.

[tex]n = \left(\frac{z*\sigma}{E}\right)^2\\\\n \approx \left(\frac{1.645*2.6}{0.03}\right)^2\\\\n \approx 20325.254444 \\\\[/tex]

Round this up to the nearest integer to get 20326. For min sample size problems, always round up.

Answer:

$361.675 dollars

Step-by-step explanation:

Multiply by .85 then take new number multiply by 1.15

Solution (5):

Simplifying the expression.

Solution (6):

Simplifying the expression.

Solution (7):

Simplifying the expression.

Solution (8):

Simplifying the expression.

[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: (8x + 1) + ( - x + 7)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x + 1 - x + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x - x + 1 + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 7x + 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: (8x - 3) - (3 x + 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x - 3 - 3x - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x - 3x - 3 - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5x - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 7) + (4x - 10)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 7 + 4x - 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 4x + 7 - 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: (- 7x + 2) - (3x - 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 7x + 2 - 3x + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 7x - 3x + 2 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 10x + 5[/tex]

Answer:

number one is the best one

The loan option that will allow the customer to pay the least amount of interest is 4-year loan with a 5.2% annual simple interest rate.

Formula for simple interest = P ×T × R/100

P = Principal amount borrowed ($12,000)

T = Time in various years given

R = Rate of simple interest generated

To determine which loan option that would allow the customer to pay the least amount of interest, the simple interest of each option is calculated below

Simple interest of a 4 years loan = 12000×4×5.2/100

= $2,496

Simple interest of a 5 years loan= 12000×5×4.2/100

= $2,520

Simple interest of a 6 years loan= 12000×6×4.7/100

= $3,384

Simple interest of a 5 years loan= 12000×3×8.4/100

= $ 18,144

Therefore, the loan option that will allow the customer to pay the least amount of interest is 4-year loan with a 5.2% annual simple interest rate.

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Answer:

y=2.75x+3

Step-by-step explanation:

$2.75 per sandwich (coefficient)

Solid $3 fee (y-intercept)

y=mx+b ---> y=2.75x+3

The probability we consider factors that decide what engine is chosen and the odds of choosing an engine size greater than 3.9 L

An engine size greater than 3.9 L

Generally, This can be defined as the possibility of an event occurring with respect to other possible outcomes.

Probability looks at calculating the possibility of a given event's occurrence.

To determine the possibility of selecting an engine size greater than 3.9 L, we consider factors than decide what engine is chosen and the odds of choosing an engine size greater than 3.9 L

Hence, the probability we consider factors that decide what engine is chosen and the odds of choosing an engine size greater than 3.9 L

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The time difference computed from the personal best given shows that Stan was 15 seconds faster.

From the information given, Stan had a personal best one mile run time of 6 minutes and 35 seconds. After his last run, his new personal best is 6 minutes and 20 seconds.

Therefore, the difference in time till be:

= 6.35 - 6.20

= 15 seconds.

Therefore, Stan was 15 seconds faster.

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Answer:

yes

Step-by-step explanation:

:)

Answer:

Yes

Step-by-step explanation:

since you have brainly and you are very smart and keep up the work

Answer:

∞

Step-by-step explanation:

I assume you meant 3×10 + 3456/3629 + 2341×123 + 123 ∞×90 and x is multiplication and not a variable.

Answer:

Honestly I can't figure it out myself, but I really want to help you.

Step-by-step explanation:

So I don't know how to write a step-by-step explanation

Answer:

v=72 in3

sa=104 in2

Step-by-step explanation:

hope this helps!

Answer:

12/13

Step-by-step explanation:

cos Y = adjacent side/ hypotenuse

The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

An equation is used to show the relationship between two or more numbers and variables.

The pool holds 30 gallons of water. After 5 minutes, the pool is about one fourth full. Hence:

Time to full the pool = 5 minutes * 4 = 20 minutes

Rate of water flow = 30 gallons/20 minutes = 1.5 gallons per minute

The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

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Answer: every 3 feet is a yard

Step-by-step explanation: so the empty boxes top row are going to be ( 3  6 9 21 (yes it 21)

the middle row is going to be ( 1 2 )

the bottom is going to be ( 36 108 72 252 )

Answer:

A =33 units^2

Step-by-step explanation:

The area of a rectangle is found by

A = l*w  where l is the length and w is the width

A = 5.5* 6

A =33 units^2

Answer:

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times {3}^{2} \\ = 3.14 \times 9 \\ = 28.26 \: {mi}^{2} [/tex]