At snack time, Ms. Rivera passes out 24 cookies to her class. She also passes out 1 glass of lemonade to each student. This equation correctly represents the total number of items distributed, where a is the number of students in the class.

a(2+1)=36
What is the value of a?

-291x+10

:)))))) Have fun

Base case (n = 1):

• left side = 1×2² = 4

• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4

Induction hypothesis: Assume equality holds for n = k, so that

1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12

Induction step (n = k + 1):

1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²

= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²

= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)

= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

On the right side, we want to end up with

(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12

which suggests that k + 2 should be factor of the cubic. Indeed, we have

3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)

and we can rewrite the remaining quadratic as

3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10

so we would arrive at the desired conclusion.

To see how the above rewriting is possible, we want to find coefficients a, b, and c such that

3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c

Expand the right side and collect like powers of k :

3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c

==>   a = 3   and   2a + b = 17   and   a + b + c = 24

==>   a = 3, b = 11, c = 10

Answer:

0.1151 = 11.51% probability of completing the project over 20 days.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Expected completion time of the project = 22 days.

Variance of project completion time = 2.77

This means that [tex]\mu = 22, \sigma = \sqrt{2.77}[/tex]

What is the probability of completing the project over 20 days?

This is the p-value of Z when X = 20, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20 - 22}{\sqrt{2.77}}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a p-value of 0.1151.

0.1151 = 11.51% probability of completing the project over 20 days.

Answer:

Confidence Interval

Lower Limit = $4,233.3

Upper Limit = $4,766.7

With 95% confidence, the mean profit per customer that SoftBus can expect to obtain is between $4,233.30 and $4,766.7 based on the given sample data.

Step-by-step explanation:

The z-score of 95% = 1.96

             Profit         Mean      Square Root

                          Difference    of MD

P1        $5,000       $500        $250,000

P2         4,500          0              0

P3         4,000       -500         $250,000

Total $13,500                        $500,000

Mean $4,500 ($13,500/3)    $166,667 ($500,000/3)

Standard Deviation = Square root of $166,667 = 408.2

Margin of error = (z-score * standard deviation)/n

= (1.96 * 408.2)/3

= 266.7

= $266.7

Confidence Interval = Sample mean +/- Margin of error

= $4,500 +/- 266.7

Lower Limit = $4,233.3 ($4,500 - $266.7)

Upper Limit = $4,766.7 ($4,500 + $266.7)

Answer:

The right solution is:

(a) 0.8849

(b) 12.28%

(c) 4.9935

(d) 28004

Step-by-step explanation:

Given:

Mean,

= 4.5

Standard deviation,

= 0.3

(a)

P(x > 4.14)

As we know,

⇒ [tex]z = \frac{4.14-4.5}{0.3}[/tex]

      [tex]=-1.20[/tex]

then,

⇒ [tex]P(z>-1.20) = P(z<1.20)[/tex]

                          [tex]=0.8849[/tex]

(b)

P(4.8 < x < 5.04)

= [tex]P(\frac{4.8-4.5}{0.3} < \frac{x-\mu}{\sigma} < \frac{5.04-4.5}{0.3} )[/tex]

= [tex]P(1<z<1.80)[/tex]

= [tex]P(z<1.80)-P(z<1)[/tex]

= [tex]0.9641 -0.8413[/tex]

= [tex]0.1228[/tex]

or,

= [tex]12.28[/tex] (%)

(c)

P(x > x) = 0.05

z value will be,

= 1.645

⇒ [tex]1.645 = \frac{x - 4.5}{0.3}[/tex]

         [tex]x = 4.9935[/tex]

(d)

P(x < 5.01)

⇒ [tex]z = \frac{x- \mu}{\sigma}[/tex]

      [tex]=\frac{5.01-4.5}{0.3}[/tex]

      [tex]=1.7[/tex]

P(z < 1.70) = 0.9554

⇒ [tex]n = \frac{27875}{0.9954}[/tex]

       [tex]=28004[/tex]

Answer:

5/6

Step-by-step explanation:

12/3 × 1/2 = 5/6

hope it helps

please mark Brainliest

Answer:

Hello,

Answer B

Step-by-step explanation:

Since A=15*20+B and B<15

The max for B is 14

==> 300+14=314

Answer:

I didn't find the answer in the options

the height of the bigger triangle is 11√6/√3 = 11√2

x = 11√2 × √2 = 11×2 = 22

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

If 7 people can pave the drive in 9 hours, we can use that information in equation form to find out how long it would take 1 person to pave the drive alone.

[tex]\frac{7}{x}=\frac{1}{9}[/tex] and cross multiply

x = 63. That means that it would take 1 person, working alone, 63 hours to get the job done. If that be the case, and assuming that the 2 added people work at the same rate as do the first 9, we simply divide that time alone into 11 parts.

It would take 11 people [tex]5.\bar{27}[/tex] hours to pave that driveway.

Answer:

20/x

Step-by-step explanation:

speed = distance /time

x km/h is speed

20 km is distance

x= 20/t

t= 20/x

Answer:

Step-by-step explanation:

The position function for this is:

[tex]s(t)=-16t^2+88t+9[/tex]. We can use this equation to find the position (or height) of the rocket at ANY TIME during its flight. I could find out the height of the rocket at 3 seconds by plugging in a 3 for t and solving for s(t); I could find the height of the rocket at 12 seconds by plugging in a 12 for t and solving for s(t), etc.

The first derivative of position is velocity:

v(t) = -32t + 88.

If we are looking for the time the rocket reaches it max height, we need to remember from physics class that this happens when the velocity of the object is at 0. We set the velocity equation equal to 0 then and solve for t:

0 = -32t + 88 and

-88 = -32t so

t = 2.75 seconds. This means that 2.75 seconds after the rocket is launched, it reaches its max height. In order to find what that max height is we plug 2.75 into the position equation for t and solve:

[tex]s(2.75)=-16(2.75)^2+88(2.75)+9[/tex] to get that

s(2.75) = 130

The max height is 130 feet and it reaches this point at 2.75 seconds into its motion.

Answer:

9+4y ≥ -15

y ≥ -6

Step-by-step explanation:

Nine Increased by the product of a number

9+4y

is greater than or equal to -15

9+4y ≥ -15

Subtract 9 from each side

9-9+4y ≥ -15-9

4y ≥ -24

Divide by 4

4y/4 ≥ -24/4

y ≥ -6

Answer:

hiuu ui9i io9

Step-by-step explanation:

iu9uj k

9514 1404 393

Answer:

  -1/512

Step-by-step explanation:

The first term is -4, and the common ratio is -2/-4 = 1/2. Then the n-th term is ...

  an = -4·(1/2)^(n-1)

and the 12th term is ...

  a12 = -4(1/2)^(12 -1) = -4/2048

  a12 = -1/512

Answer:

picture not clear what is the length

5+5x>8(x-1)

5+5x>8x-8

5x-8x>-8+5

-3x>-3

5 + 5x > 8(x-1) is equivalent to -3x > -13.

Let, the expression be 5 + 5x > 8(x-1)

By applying Multiplicative Distribution Law, we get

5 + 5x > 8x - 8

Rearrange unknown terms to the left side of the equation, then

5x - 8x > -8 - 5

Combine like terms, we get

-3x > -8 - 5

Calculate the sum or difference

-3x > -13

Divide both sides of the inequality by the coefficient of the variable, then we get

[tex]$x < \frac{-13}{-3}$[/tex]

Determine the sign for multiplication or division:

[tex]$x < \frac{13}{3}$[/tex]

Therefore, the correct answer is -3x > -13.

Complete question:

Which of the following is equivalent to 5 + 5x > 8(x - 1)?

-3x > -12

3x < 13

3x < 6

-4x > -12

To learn more about algebraic expression

https://brainly.com/question/4344214

#SPJ2

Answer:

352

Step-by-step explanation:

I = PRT  where P is the principle, I is the interest rate, T is the time

I = 275 ( .08) ( 16)

I = 352

Answer:

D

Step-by-step explanation:

inverse just means opposite so if its shown dividing it first then adding, then the inverse is multiplying then subtracting

Answer:

2.5

Step-by-step explanation:

i had it

Answer:

Dependent event

[tex]P(Red = 2) = \frac{5}{588}[/tex]

Step-by-step explanation:

Given

[tex]Total = 49[/tex]

[tex]Red = 5[/tex]

Solving (a): Are the events dependent?

Yes, they are.

When the first red candy is selected and eaten, the total number of candies reduced to 48 and the number of red candies also reduced to 4.

So, the probability of selecting a 2nd candy is dependent on the first candy selected.

Solving (b): P(Red = 2)

This is calculated as:

[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]

The first selection has the following probability:

[tex]P(Red) = \frac{Red}{Total}[/tex]

[tex]P(Red) = \frac{5}{49}[/tex]

The second selection has the following probability:

[tex]P(Red|Red) = \frac{Red - 1}{Total - 1}[/tex]

[tex]P(Red|Red) = \frac{5 - 1}{49 - 1}[/tex]

[tex]P(Red|Red) = \frac{4}{48}[/tex]

So, we have:

[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]

[tex]P(Red = 2) = \frac{5}{49} * \frac{4}{48}[/tex]

Reduce fraction

[tex]P(Red = 2) = \frac{5}{49} * \frac{1}{12}[/tex]

Multiply

[tex]P(Red = 2) = \frac{5}{588}[/tex]

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The numerical coefficient is sqrt(8/3), so all you have eliminated is D.

Now you have to consider the literal all by itself.

sqrt(x^2)/sqrt(x) can be written as (sqrt(x^2/x)) = sqrt(x)

x^2 when divided by x leaves x

another way of looking at it is sqrt(x)*sqrt(x) / sqrt(x) = sqrt(x)

So the answer is sqrt(8/3 * x)

Answer:

Step-by-step explanation:

3

Answer:

c

Step-by-step explanation:

hope it helps!!!!!!!!!!!!!!

Answer:

Step-by-step explanation:

I am assuming i is the imaginary number:

Factor:

(3 + i)x - (4-2i) = 0.

In order for this to equal 0, x must be equal to 1-i.

I don't want to be reported to so take my word for it.

Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.

Using BTS he properties, find the unit's digit of the cube of each of the following numbers

Answer:

search up the formula

Step-by-step explanation:

We have a function,

[tex]f(x)=x^2-1[/tex]

and we are asked to find its inverse function.

An inverse function essentially gets you the original value that was dropped into a function.

For example,

If I put 5 into [tex]f(x)[/tex] I will get 24. Now If I take 24 and put it into the inverse function I have to get number 5 back.

The way to determine the inverse function swap the x and the [tex]f(x)[/tex], then solve for [tex]f(x)[/tex],

[tex]x=f(x)^2-1[/tex]

[tex]f(x)^2=x+1[/tex]

[tex]f(x)=\pm\sqrt{x+1}[/tex]

Of course the notation demands that the obtained function be called,

[tex]f^{-1}(x)=\pm\sqrt{x+1}[/tex]

Hope this helps :)

Answer:

7/18

Step-by-step explanation:

1/6 x 3 = 3/18

3/18 + 4/18 = 7/18

Answer:

7/18

Step-by-step explanation:

Make the denominators the same!

You can turn 1/6 into 3/18 by multiplying the numerator and denominator by 3. Then you add the numerators of 3/18 and 4/18 together to get 7/18.

It can't be simplified any further :)

Answer:

Should be (B).

8.5

ED2021

Answer: B

Step-by-step explanation:

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

Hy mate!!

The answer of your question is in the attachment..!!

.

.

Hope this answer helps you..!!

.

.

Select it as the BRAINLIEST..!!