The closed form sum of

$$12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]$$
for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ Find $an + b.$

Answer:

MAD - mean absolute deviation is indication of the distance of data points from the mean.

Data set B shows the greater variability since has greater MAD.

It means the B data set is more spread compared to A data set.

Answer:

128500

Step-by-step explanation:

This is an arithmetic sequence with a common difference of 3500

The formula for an arithmetic sequence is

an = a1+d(n-1)  where a1 is the first term and d is the common difference

an = 48000+ 3500(n-1)

We want n = 24

a24 = 48000+3500(24-1)

       = 48000+3500(23)

       =48000+80500

       =128500

Answer:

solving for x

Step-by-step explanation:

4 or -6

Answer:

x = 4

Step-by-step explanation:

Those absolute value signs are a trick, well at least for this problem. Solve it how you usually would. However, if +2 was -2 or +/-2, then you would need to pay attention. Basically, those signs make the whole equation incased positive no matter what.

Answer:

C) 81 degrees

Step-by-step explanation:

all quadrilateral's sum of interiror angles is 360 degrees

right angles are 90 degrees

call measure of angle C =y

360=90+90+99+y

180=99+y

y= 81

Answer:

Step-by-step explanation:

let the  numbers be x and y.

x+y=16

x-y=6

add

2x=22

x=22/2=11

11+x=16

x=16-11=5

product xy=11×5=55

Answer:

cos(θ) = -0.95

Step-by-step explanation:

Remember the relation:

sin(θ)^2 + cos(θ)^2 = 1

So if we have:

sin(θ) = 0.3

we can replace that in the above equation to get:

0.3^2 + cos(θ)^2 = 1

now we can solve this for cos(θ)

cos(θ)^2 = 1 - 0.3^2 = 0.91

cos(θ) = ±√0.91

cos(θ) = ± 0.95

Now, yo can see that there are two solutions, which one is the correct one?

Well, you can see that the endpoint of the segment that defines θ is on the second quadrant.

cos(x) is negative if the endpoint of the segment that defines the angle is on the second or third quadrant.

Then we can conclude that in this case, the correct solution is the negative one.

cos(θ) = -0.95

Answer:

5ba^2 +ab^2 6a^2 + 2b

Step-by-step explanation:

ab(6a+b)-3a^2 (b-2)+2b(a^2 +1)

6ba^2 +ab^2 -3ba^2 +6a^2 + 2ba^2 +2b

6ba^2 -3ba^2 +2ba^2 +ab^2 +6a^2 +2b

5ba^2 +ab^2 6a^2 + 2b

Answer:

-39/15

Step-by-step explanation:

=-8/5-4/3+1/3

Taking LCM of 5,3 and 3.

=3(-8)-5(4)+5(1)/15

=-24-20+5/15

=-44+5/15

=-39/15

Note:if you need to ask any question please let me know.

Answer:

A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground

Step-by-step explanation:

f(t) = 4t^2 − 8t + 7

Factor out 4 from the first two terms

f(t) = 4(t^2 − 2t) + 7

Complete the square

(-2/2)^2 =1  But there is a 4 out front so we add 4 and then subtract 4 to balance

f(t) = 4( t^2 -2t+1) -4 +7

f(t) = 4( t-1)^2 +3

The vertex is (1,3)

This is the minimum since a>0

The minimun is y =3 and occurs at t =1

Answer:

The above answer is correct.

Step-by-step explanation:

Answer:

1a. 128

1b. 81

1c. 64

1d. 25

1e. 343

1f. 100000

1g. 64

1h. 0

1i. 13

1j. 1

2a. 243

2b. 64

2c. 36

2d. 625

2e. 1331

2f. 10000000

2g. 81

2h. 0

2i. 17

2j. 1

Answer:

1/9

Step-by-step explanation:

The vertex form is

y =a(x-h)^2 +k where (h,k) is the vertex

The vertex is (-2,-3)

y =a(x--2)^2 +-3

y =a(x+2)^2 -3

Substitute the point into the equation

-2 = a(-5+2)^2 -3

-2=a(-3)^2-3

Add 3 to each side

-2+3 = a(9)

1 = 9a

1/9 =a

y =1/9(x+2)^2 -3

The coefficient of the x^2 is 1/9

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 2, - 3) , then

y = a(x + 2)² - 3

To find a substitute (- 5, - 2 ) into the equation

- 2 = a(- 5 + 3)² - 3 ( add 3 to both sides )

1 = a(- 3)² = 9a ( divide both sides by 9 )

[tex]\frac{1}{9}[/tex] = a

y = [tex]\frac{1}{9}[/tex] (x + 2)² - 3

The coefficient of the x² term is therefore [tex]\frac{1}{9}[/tex]

pls snap the picture well so that the pre information can be seen and considered

Answer:

24 days LCM

prime factor :

4- 2, 2

8-2,2,2

12- 2,2,3

largest factors- 2,2,2,3

2*2*2*3 = 24

Step-by-step explanation:

Answer:

D) 20°

Step-by-step explanation:

Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.

57° + 30° + x = 180°

Simplify: 87° + x =180°

x=93°

By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.

67° + 93° + y = 180°

Simplify: 160° + y = 180°

y=20°

Answer:

(C). 26°

Step-by-step explanation:

Answer:

828

Step-by-step explanation:

Multiple the side length by the dilation

36 x 23 = 828

Answer:

The plane is going 325 kilometers per hour :)

Step-by-step explanation:

To find the average speed per hour, divide 1300 by 4.

1300/4 = 325

Answer:

The area of a regular polygon is A = (1/2)ap, where a is the apothem and p is the perimeter of the polygon.

The apothem is 8 inches and the perimeter is 6(7) = 42 since there are 7 sides of 6 inches.

Then the area is

A = (1/2)(8)(42) = 336/2 = 168 in2

I hope this helped!

[tex]71\% = \frac{70}{100} = \frac{7}{10} = 0.7 \\ 172\% = \frac{172}{100} = 1.72 \\ 6\% = \frac{6}{100} = 0.06[/tex]

Whats 5867 times 382?

answer;

5867×382

=2241194

Hope it helps you.........

Answer:

60 + 12 * g, with g representing the number of extra gigabytes

Step-by-step explanation:

First, we know that Maritza has to pay $60 for 10GB of data, no matter what. Therefore, the base cost of the cell phone plan is 60 dollars, and all extra costs must be added to that. Currently, our expression is therefore 60 + something = cost of cell phone plan.

After that, the plan costs $12 for each gigabyte of data past 10 GB. This means that, for example, if Maritza uses 11 gigabytes, the plan will cost 60 (the base amount) + 12 for each gigabyte past 10 GB. There are 11-10=1 extra gigabytes, so the cost is 60 + 12 * 1 = 72 dollars. For each extra gigabyte, 12 dollars are added, so we can represent this as

60 + 12 * g, with g representing the number of extra gigabytes

Answer:

See picture below

Step-by-step explanation:

Let PK be the length and PS be the width of the rectangle.

Then LW =562

Assuming O is the center of the rectangle then ∠KST = ∠STO = 75/2

Hence tan ( 75/2 ) = PS/PK

Now solve the system of the equations

PS*PK=562

tan ( 75/2 ) = PS/ PK

The market price is Rs. 750 which was obtained by creating a mathematical relationship from the given parameters.

PERCENTAGE DISCOUNT = 20%

VAT LEVIED= 12%

PRICE SOLD = 672

Let the MARKET PRICE = m

Hence,

market price * (1 - discount) * (1 + VAT) = price sold

m * (1 - 20%) * (1 + 12%) = 672

m * (1 - 0.2) * (1 + 0.12) = 672

m * 0.8 * 1.12 = 672

0.896m = 672

m = 672 / 0.896

m = Rs. 750

Learn more :

https://brainly.com/question/20418815

The Market Price of the product is RS. 750.

The Market Price is calculated by dividing the components associated to Discount, which is less than 1, and the Value Added Tax, which more than 1, to the Resulting Price.

[tex]c_{M} = \frac{c_{R}}{\left(1-\frac{r_{D}}{100} \right)\cdot \left(1+\frac{r_{T}}{100} \right)}[/tex] (1)

Where:

[tex]c_{M}[/tex] - Market price, in monetary units.

[tex]c_{R}[/tex] - Resulting price, in monetary units.

[tex]r_{D}[/tex] - Discount rate, in percentage.

[tex]r_{T}[/tex] - Tax rate, in percentage.

If we know that [tex]c_{R} = 672[/tex], [tex]r_{D} = 20[/tex] and [tex]r_{T} = 12[/tex], then the market price is:

[tex]c_{M} = \frac{672}{\left(1-\frac{20}{100} \right)\cdot \left(1+\frac{12}{100} \right)}[/tex]

[tex]c_{M} = 750[/tex]

The market price of the product is RS. 750.

Answer:

a = 60°/2 = 30°

b = 84/2 = 42°

c = (100+60)/2 = 80°

d = 360-100-60-84 = 116°

Answered by GAUTHMATH

Answer:

A) (-8, -16)

B) (0, 48)

C) (-4, 0), (-12, 0)

Step-by-step explanation:

A) the vertex is the minimum y value.

extremes of a function we get by using the first derivation and solving it for y' = 0.

y = x² + 16x + 48

y' = 2x + 16 = 0

2x = -16

x = -8

so, the vertex is at x=-8.

the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16

B) is totally simple. it is f(0) or x=0. so, y is 48.

C) is the solution of the equation for y = 0.

the solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case here

a=1

b=16

c=48

x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =

= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)

x1 = -8 + 4 = -4

x2 = -8 - 4 = -12

so the x- intercepts are (-4, 0), (-12, 0)

Answer:

lol Step-by-step explanation:

Answer:

10, 16

Step-by-step explanation:

List the factors of 160.

1 × 160 = 160

2 × 80 = 160

4 × 40 = 160

5 × 32 = 160

8 × 20 = 160

10 × 16 = 160

(there are more, but we don't need them)

Check to see which factors can be added together to make 26, half of 52.

10 and 16 make 26.

That's the answer!

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

A

Step-by-step explanation:

d = 0.5 * t    There are no conversions. You just substitute the value for t.

d = 0.5 * 27.9

d = 13.95 which is A

Answer:

$45.63

Step-by-step explanation:

[tex]50,145 cm^{3} * 2.6 g/cm^3 = 130,377 g\\130,377 g = 130.377 kg\\130.377 kg * $0.35/kg = $45.63\\[/tex]

or all together    

50,145 cm³  *  2.6 g/cm³ * 0.35/kg =  $45.63

Answer:

Not Enough Information

Step-by-step explanation:

Unfortunately, you did not give us the "given information", so there is no way to prove the two parallel.