What was the total distance covered by the racers in kilometers

Answer:

20 feet

Step-by-step explanation:

Plug in 4 as t in the equation:

h = 3.5 + 68t - 16t^2

h = 3.5 + 68(4) - 16(4²)

h = 3.5 + 272 - 256

h = 19.5

So, the height of the basketball is 20 feet

Answer:

[tex]f'(3)=100[/tex]

Step-by-step explanation:

Given:

[tex]f(t)=u(t)\cdot v(t)\\u(3)=\left ( 1,2,-2 \right )\\u'\left ( 3 \right )=\left ( 8,1,4 \right )\\v(t)=\left ( t,t^{2},t^{3} \right )[/tex]

To find: [tex]f'(3)[/tex]

Solution:

[tex]v(t)=\left ( t,t^{2},t^{3} \right )[/tex]

At [tex]t=3;[/tex]

[tex]v(3)=(3,3^{2},3^{3} )=(3,9,27)[/tex]

Differentiate with respect to t

[tex]v'(t)=\left ( 1,2t,3t^{2} \right )[/tex]

At [tex]t=3;[/tex]

[tex]v'(3)=\left ( 1,2(3),3(3)^{2} \right )=\left ( 1,6,27 \right )[/tex]

Using product rule, differentiate [tex]f(t)=u(t)\cdot v(t)[/tex] with respect to [tex]t[/tex]

[tex]f'(t)=u'(t)\cdot v(t)+u(t)\cdot v'(t)[/tex]

At [tex]t=3;[/tex]

[tex]f'(3)=u'(3)\cdot v(3)+u(3)\cdot v'(3)\\=\left ( 8,1,4 \right )\cdot \left ( 3,9,27 \right )+\left ( 1,2,-2 \right )\cdot \left ( 1,6,27 \right )\\=24+9+108+1+12-54\\=100[/tex]

yes. It would be an irrational number if it didn't repeat in a pattern.

hope it helps comment if u have any questions

Answer:

Yes.

Step-by-step explanation:

Yes 1 [tex]\frac{1}{2}[/tex] is a rational number because because it can be converted to a decimal, which is 1.5

Answer:

x = y⁴ does not represent y as a function of x

Step-by-step explanation:

Let's first isolate this equation for the 'y' value :

[tex]\mathrm{Switch\:sides} : y^4=x,\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)} : y=\sqrt[4]{x},\:y=-\sqrt[4]{x}[/tex]

So as you can tell, we have two functions. However, they can be rewritten as one function, y = ± ⁴√x. As we have two values of x that correspond to one value of y, this relation is not a function.

Solution: x = y⁴ does not represent y as a function of x

Answer:

0.4

Step-by-step explanation:

Answer: it's 0.4 as a decimal

Step-by-step explanation:

Answer:

-44

Step-by-step explanation:

108 ÷ 9 x (-12) ÷ 6 - (100 ÷ 5)

= 108 ÷ 9 x (-12) ÷ 6 - (20)

= 12 x (-12) ÷ 6 - (20)

= -144÷ 6 - (20)

= -24 - (20)

= -44

Answer:

The solution and the calculation is shown on the first uploaded image

Step-by-step explanation:

Answer:

-60.

Step-by-step explanation:

Let the unknown number be x.

Number is increased by 26 = x+26

Then result is tripled = 3(x+26)

Then the result is increased by 72 = 3(x+26)+72

Final result is [tex]\dfrac{1}{2}[/tex] of the number = [tex]\dfrac{1}{2}x[/tex]

[tex]3(x+26)+72=\dfrac{x}{2}[/tex]

[tex]3x+78+72=\dfrac{x}{2}[/tex]

[tex]3x+150=\dfrac{x}{2}[/tex]

Isolate variable terms.

[tex]3x-\dfrac{x}{2}=-150[/tex]

[tex]\dfrac{6x-x}{2}=-150[/tex]

Multiply both sides by 2.

[tex]5x=-300[/tex]

Divide both sides by 5.

[tex]x=-\dfrac{300}{5}[/tex]

[tex]x=-60[/tex]

Therefore, the required number is -60.

Answer:

Step-by-step explanation:

Composite numbers are positive numbers that have factors, This means that they are divisible by numbers other than 1 and itself provided that number is a factor of the composite number. They possess at the bearest minimum level, a divisor other than  1 and itself. They are a natural number that is expressible as the product of two(or more) numbers other than 1 and itself.

For example:

4 is a composite number because its factors are 1, 2 and 4 which have another divisor apart from 1 and itself (4). That divisor is 2.

We all know that prime numbers are numbers that can be only be divided by 1 and itself.

Therefore, the sum of two composite number, for example:

4 + 6 = 10, We can now see that 10 is never a prime number.

Answer:

Step-by-step explanation:

C(a + b) = f + d

a + b = (f + d)/C

a = (f + d)/C - b

Answer: 371

Step-by-step explanation:

Answer:59

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

1. Listing Information

The number is 10.999244792948.

Simply put, numbers below 5 are rounded down and numbers that are greater than or equal to five are rounded up.

The tenths place value in 10.999244792948 is 9.

2. Solving the Problem

With the previous information in mind, 9 is greater than 5. Because of this, 10.999244792948 should be rounded to 11.

Answer:

The  95% confidence interval is  [tex]244.26 < \mu < 246.95[/tex]  

The pivot function used is  

           [tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]

Step-by-step explanation:

From the question we are told that

  The  data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242

  The  sample  size is  [tex]n= 20[/tex]

Given that the confidence level is 95% then the level of significance is

      [tex]\alpha = (100 - 95)\%[/tex]

      [tex]\alpha = 0.05[/tex]

The  degree of freedom is mathematically represented as

    [tex]df = 20 -1[/tex]

    [tex]df = 19[/tex]

From the student t-distribution table  the critical value of  [tex]\frac{\alpha }{2}[/tex]  is  

          [tex]t_{\frac{\alpha }{2} , 19 } = 2.093[/tex]

The mean is mathematically represented as

          [tex]\= x = \frac{\sum x_i}{ n}[/tex]

         [tex]\= x = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}[/tex][tex]\= x = 246.6[/tex]

The standard deviation is mathematically represented as

            [tex]\sigma = \sqrt{\frac{\sum (x_i - \= x )^2)}{n} }[/tex]

           [tex]\sigma = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..[/tex]

             [tex]\ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...[/tex]

              [tex]\ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+ (242-246.6)^2+ (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...[/tex]       [tex]\sqrt{\frac{ (245-246.6)^2+ (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }[/tex][tex]\sigma = 2.87411[/tex]

The margin of error is mathematically represented as

       [tex]E = t_{\frac{\alpha }{2} , 19} * \frac{\sigma }{\sqrt{n} }[/tex]

      [tex]E = 2.093 * \frac{2.87411 }{\sqrt{20} }[/tex]

      [tex]E = 1.345[/tex]

The 95% confidence interval is mathematically represented as

       [tex]\= x - E < \mu < \= x + E[/tex]

=>   [tex]245.6 - 1.345 < \mu <245.6 + 1.345[/tex]

=>    [tex]244.26 < \mu < 246.95[/tex]  

The pivot function used is  

           [tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]

Answer:

Step-by-step explanation:

$0.30

Step-by-step explanation:

1 bar of candy = $0.20

3 bars of candy = $0.50

To solve, multiply for both:

If you pay for each candy bar individually, they each cost $0.20. Multiply 9 with 0.20:

9 x 0.20 = $1.80

If you pay for the candy bars by 3's, they cost $0.50 each pack. Divide 9 with 3, then multiply by 0.50:

9/3 = 3

3 x 0.50 = $1.50

Subtract the total cost of the individual from the pack:

$1.80 - $1.50 = $0.30

. $0.30 is your answer.

Answer:

5

Step-by-step explanation:

(X1,Y1) = (-1,4)

(X2,Y2) = (2,8)

Answer:

1/26

Step-by-step explanation:

Total no. of tiles = 26

In each tile , a different alphabet is written.

And we need 3 tiles (in which A , B & C are written in it) in one try.

So the probability of choosing tiles with letters A , B & C ( in one try ) = 1/26

Second option, just do Pemdas backwards.

Answer:

Recursive:

[tex] a_1 = 2; a_n = a_{n-1} [/tex]

Explicit:

[tex] a_n = 2 [/tex]

Step-by-step explanation:

She helps the same number of people every day, 2.

Recursive:

[tex] a_1 = 2; a_n = a_{n-1} [/tex]

Explicit:

[tex] a_n = 2 [/tex]

Answer:

f(x) = 3x-4

f(-1)= 3(-1) -4

f(-1) = -3-4

= -7

hope this helps uh!

Answer:

f(-1)= -7

Step-by-step explanation:

We are given the function:

f(x)=3x-4

We want to find f(-1). We must plug -1 in for x and solve.

f(-1)= 3(-1)-4

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

Multiply 3 and -1.

f(-1)= -3 -4

Subtract 4 from -3.

f(-1)= -7

f(-1) is equal to -7.

Answer:

I think it is mean

Step-by-step explanation:

because mean would be the average of the scores

Answer: The mean

Step-by-step explanation:

The mean will show the average of the teams scores.

Answer:

(-6,5]

Step-by-step explanation:

Domain includes all of the x-values a function contains. In this case, it goes from -6 to 5. The open dot on the left indicates that this number is not included in the answer, and in interval notation you would use a parentheses. The filled in dot on the right coordinate indicates that this number is included, so you would use a bracket.

Answer:

9feet

Step-by-step explanation:

B= -34 M=-25

-34-(-25)=-34+25=9

Answer:

9 feet

Step-by-step explanation:

Brett is -34 feet and Max is -25 feet from sea level.

In order to find how many feet Max is above Brett, we can change the numbers to be positive and subtract Brett's distance - Max's distance

34-25=9

Max is 9 feet above Brett

Answer:

zero point 9

0 and nine tenths

Step-by-step explanation:

Answer:

1021

Step-by-step explanation:

i added 34 +987 and got 1021

Answer:

4.7157157

Step-by-step explanation:

because it is a repeating decimal, it will repeat the terms that come first such as 715.

Answer:squares area is. 24

Step-by-step explanation:

6×4 = 24

Answer:

(7) The value of -j is 9.

(8) The value of -(-j) is -9.

(9) The value of (-j)(-j) is 81.

Step-by-step explanation :

Part 7:

Given algebraic expression is:

j = -9

Now we have to determine the value of (-j).

-j = - (-9) = 9

The value of -j is 9.

Part 8:

Given algebraic expression is:

j = -9

Now we have to determine the value of -(-j).

- (-j) = - [-(-9)] = -9

The value of -(-j) is -9.

Part 9:

Given algebraic expression is:

j = -9

Now we have to determine the value of (-j)(-j).

(-j)(-j) = [- (-9)] ×  [- (-9)] = 9 × 9 = 81

The value of (-j)(-j) is 81.