Select the correct answer.
-Plato- The Tangent line problem: Mastery test

Answer:

[tex]\sum\limits_{i=1}^{n} c \cdot a_i \ is \ equal \ to \ c = \ c \cdot \sum\limits_{i=1}^{n} a_i[/tex]

[tex]\sum\limits_{i=1}^{n} i \ is \ equal \ to \ b = \dfrac{n \cdot (n + 1)}{2}[/tex]

[tex]\sum\limits_{i=1}^{n} c \ is \ equal \ to \ d = c \cdot n[/tex]

[tex]\sum\limits_{i=1}^{n} i^3 \ is \ equal \ to \ e = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2[/tex]

[tex]\sum\limits_{i=1}^{n} i^2 \ is \ equal \ to \ a = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6}[/tex]

Step-by-step explanation:

1) The sum of a series of the cubes of numbers 'i' is given as follows;

Sₙ = n/2 × (1st term + Last term)

∴ Sₙ = n/2 × (1 + n) = n·(n + 1)/2

It can be shown that the sum of a series of the cubes of numbers 'i²' is given as follows;

Sₙ = (n·(n + 1)·(2·n + 1))/6

It can be also be shown that the sum of a series of the cubes of numbers 'i³' is given as follows;

Sₙ = (n·(n + 1)/2)²

Therefore, we have;

[tex]\sum\limits_{i=1}^{n} c \cdot a_i= c \cdot \sum\limits_{i=1}^{n} a_i = c[/tex]

[tex]\sum\limits_{i=1}^{n} i = \dfrac{n \cdot (n + 1)}{2} = b[/tex]

[tex]\sum\limits_{i=1}^{n} c = c \cdot n = d[/tex]

[tex]\sum\limits_{i=1}^{n} i^3 = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2 = e[/tex]

[tex]\sum\limits_{i=1}^{n} i^2 = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6} = a[/tex].

Answer:

c, b, d, e, a

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

360 minus 120 degree give 240 degree

Answer: 60

Step-by-step explanation:

120/2= 60

Answer:

24

Step-by-step explanation:

Here is the complete question

Priscilla has some grapes that she wants to give to her friends. She wants to give 1/4 of a kilogram of grapes to each friend. If Priscilla has 6 kilograms of grapes, to how many friends can she give grapes?

Number of friends she can give grapes to = total kilograms / kilogram she wants to give to each friend

6 ÷[tex]\frac{1}{4}[/tex]

6 x 4 = 24 friends

Answer:

8

Step-by-step explanation:

2*1*4=8

Answer:

Step-by-step explanation:

they want you to recognize that it's a linear relationship

Answer:

A, C, and D

Step-by-step explanation:

Answer:

i got 616 for the answer good luck!!

Step-by-step explanation:

Answer:

B.) 205.3³

Step-by-step explanation:

                          Volume = (length·width·height) divided by 3

                                                            ⬇

                                                    V = (lwh)/3

                                                            ⬇

                                        V = (11·7·8)/3 ≈ 205.33333

                                                            ⬇

                                                        205.3³

Answer:

6-   D

4-   A

3-   A

Step-by-step explanation:

Answer:

6. = D

4. = A

Step-by-step explanation:

6. 2(2.5)= 5

4(2.5)= 10

6(2.5) =15

9(2.5) is not 21 its 22.5

4. 125÷5 = 25

Answer:

so first you would find out the whole equation after you plug in x and it would be

y=8-6

y=2

so the answer is A. 2

The value of y is 2.

The correct option is (A).

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given equation is: y = 8 – 2x.

So, when x=3

y= 8-2*3

 =8-6

 = 2.

Hence, the answer is A. 2

Learn more about equation here:

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Answer:

Step-by-step explanation:

Equation is below

Step 1

(3x^2 y^5)^4  

Step 2

(3x^2 y^5)^4  Simplify

81x^8y^20

Step 3

81x^8y^20  check

Answer

81x^8y^20

Hope this helped

Answer:

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3)  = 0.9922

Step-by-step explanation:

Step(i):-

Given that the mean of the Normal distribution = 4.1mm

Given that the standard deviation of the Normal distribution = 0.0075mm

Let 'X' be the random variable in a normal distribution

Given that X₁ = 3.9mm

[tex]Z_{1} = \frac{X_{1} -mean}{S.D}[/tex]

[tex]Z_{1} = \frac{3.9 -4.1}{0.075} = -2.666[/tex]

Given that X₂ = 4.3mm

[tex]Z_{2} = \frac{X_{2} -mean}{S.D}[/tex]

[tex]Z_{1} = \frac{4.3 -4.1}{0.075} = 2.666[/tex]

Step(ii):-

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3) = P(-2.666≤Z≤2.666)

                     = P(Z≤2.666)-P(Z≤-2.666)

                    = 0.5 +A(2.666) - (0.5-A(2.666)

                   = 2 × A(2.666)

                 = 2×0.4961

                 = 0.9922

Final answer:-

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3)  = 0.9922

Answer:

4.6

Step-by-step explanation:

2^2+x^2=5^2

4+x^2=25

x^2=25-4

x^2=21

x=square root 21

x=4.58=4.6

Answer:

This is how your function looks on a graph table. Hope this helps.

Answer:if it's 25% red, it's 50/50 that it will not be orange

Step-by-step explanation:

Answer:

1.False

2. True

3.) True

4. False

5.) False

6.) True

Step-by-step explanation:

1.)

Range = maximum - minimum

New year's eve :

Maximum = 22 ; minimum = 3

Range = 22 - 3 = 19

2.)

Median for Thanksgiving = 17

50% up to 17 ;hence the remaining 50% is also 17 and above

4.)

IQR for Thanksgiving

Q3 - Q1

23 - 12 = 11

5.)

The median number of people at new year's eve for dinner was 7 (line in between the box)

6.)

3/4th of new year eve's dinner = Q3 = 15

1/4 = Q1 ; have up to 5 people

Therefore ; the remaining (1 - 1/4) = 3/4 have 5 and above

Answer:

1.False

2. True

3.) True

4. False

5.) False

6.) True

Step-by-step explanation:

Answer:

I.  most probably

Hope it helps!!!

Step-by-step explanation:

Answer:

nickel and a quarter

Step-by-step explanation:

One is a nickel, the other is NOT a nickel... it is a quarter.

Answer:

The correct angle is 45.3°

Step-by-step explanation:

Since the opposite side of the angle is 32 feet, and the hypotenuse of the right triangle is 45 feet, you would know that the sine of x° is equivalent to [tex]\frac{32}{45}[/tex]. To find the value of x, take the arcsin of both sides and you'll get that [tex]x = arcsin(\frac{32}{45})[/tex] ⇒ [tex]x[/tex] ≈ 45.3°.

Answer:

Negative consumption externalities. When certain goods are consumed, such as demerit goods, negative effects can arise on third parties. Common example include cigarette smoking, which can create passive smoking, drinking excessive alcohol, which can spoil a night out for others, and noise pollution.

they made $1125 and the new balance is $8625

Answer:

earned in intrest would be 450.

Step-by-step explanation:

i did the assingment

Answer: 6

Step-by-step explanation:

The area of the triangle EDF is 6 in².

Two triangles are said to be similar if their corresponding angles are congruent, and their corresponding sides are in equal ratios.

Given that, two triangles are similar, ABC and EDF,

We know that, the area of two similar triangles implies that if two triangles are similar to each other, the ratio of their areas will be proportional to the square of their corresponding side ratios.

Therefore,

ar(ΔABC)/ar(ΔEDF) = (2/4)²

24/ar(ΔEDF) = 1/4

ar(ΔEDF) = 6

Hence, the area of the triangle EDF is 6 in².

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Answer: in statistics deviation is the difference between the value of one number in a series of numbers and the average value of all numbers in the series (  i hope this helped)

Step-by-step explanation:

Answer:

Step-by-step explanation:

it's like this Loving ,    62.90 / 330 = 0.1906...

so she paying about 19 cents per mile  :)

Answer:

hope this helps you out ask me if you need more help

Answer:

Step-by-step explanation:

The answer would be (G)

The value of w is greater than -4 which will best represent the inequality 3.3w - 9 > -22.27 on number line.

Number lines are simple, visual pictures of how the values of numbers increase and decrease.

Given an inequality 3.3w - 9 > -22.27

On solving, we get,

3.3w - 9 > -22.27

3.3w > -22.27 + 9

3.3w > -13.27

w > -4

Hence, the value of w is greater than -4 which will best represent the inequality 3.3w - 9 > -22.27 on number line.

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Answer:

1/10

Step-by-step explanation:

Answer: 0.1

Step-by-step explanation:

Answer:

AED 18.85

Step-by-step explanation:

Given that:

Radius, r = 1cm

Length = height, h = 12

Cost per cm³ = AED0.50

VOLUME OF CYLINDER = pi * r² * h

Volume = 3.14 * 1² * 12

Volume = 37.699 cm³

Cost per cm³ = AED 0.5

TOTAL COST :

AED 0.5 * 37.699

= AED 18.849

= AED 18.85