How many times larger is

Answer: 7/15

Step-by-step explanation:

The given arithmetic series can be expressed in summation notation as [tex]\sum\limits^8_{n=1} {(2n+5)}[/tex] or in simplified notation [tex]40+2 \sum\limits^8_{n=1} {n}[/tex]

The summation notation is used to express long summation in one expression.

The given arithmetic series is:

       7+9+11+ . . . . . . +21

Find the explicit formula for the nth term in the given series.

Recall:

a(n) = a(1) + (n-1) . d

where:

a(1) = the first term

d = common difference = a(2) - a(1) = a(n) - a(n-1)

From the series, we get:

a(1) = 7

d = 9 - 7 = 2

Hence,

a(n) =  a(1) + (n-1) . d

a(n) = 7 + (n-1) . 2

a(n) = 2n + 5

Find number of terms in the given series.

From the given series, we know that the last term is 21.

Let the last term be a(n), then,

a(n) = 2n + 5

21 = 2n + 5

2n = 16

n = 8

Write the summation notation with lower limit n = 1 and upper limit n = 8.

[tex]\sum\limits^8_{n=1} {a(n)}= \sum\limits^8_{n=1} {(2n+5)}[/tex]

If necessary, simplify the summation.

[tex]\sum\limits^8_{n=1} {(2n+5)}= \sum\limits^8_{n=1} {2n}+ \sum\limits^8_{n=1} {5}[/tex]

[tex]= \sum\limits^8_{n=1} {2n}+ 8\times5[/tex]

[tex]=40+2 \sum\limits^8_{n=1} {n}[/tex]

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An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.

Unbiased Statistic/estimator is defined as the accurate statistic that is used in approximation a population parameter.

In the above statement the word "accurate" means that it should be neither greater than nor less than the population parameter.

If the average value is less than  the population parameter  or greater than the population parameter then the statistic will be termed as "biased".

Therefore , An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.

The correct option is (d) equal to.

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Answer:

a^2+2ab+b^2

Step-by-step explanation:

(a+b)^2

(a+b)(a+b)

a(a+b)+b(a+b)

(a^2+ab)+(ab+b^2)

a^2+2ab+b^2

Answer:

this is super easy...

u first rotate it 90° until the BC is downwards.

then rotate it one round until it comes to the way it was..that means once again BC down...hope it is clear...

Answer:

Answer no. 4

Step-by-step explanation:

1.67 x 10^3 = 1670

16.7 x 10^3 = 16700

those number are clearly the biggest in their categories, so answers 1 and 2 are not worth further consideration. Also note that all the numbers are the same in every answer except 1.67 x 10^3 or 16.7 x 10^3, so the 16.7 might be an error. Fortunately it does not change the answer.

Let's choose between answers 3 and 4. We start with easy numbers:

4^2 = 16

50/3 = 16.6666...

So 50/3 must come after 4^2.

We're left with answer 4.

We can also convert everything to decimal:

[tex]15.75\\\sqrt{250} = 15.8113883...\\4^2 = 16\\50/3 = 16.666666....\\16.7 \cdot 10^3 = 16700\\1.67 \cdot 10^3 = 1670[/tex]

from which we can order conventionally

There is a Constant Ratio between consecutive terms in a geometric sequence.

The consecutive terms in a Geometric Progression or Sequence are separated by a Constant Ratio which remains constant for the whole sequence and all of the terms in that sequence are separated by that Ratio. Generally, the Constant Ratio is denoted by 'r'. The next term of the sequence can be determined by using this Ratio.

To determine the next term or [tex]n^{th}[/tex] term, we need to multiply the previous term with the Ratio. There is a specific formula to determine the [tex]n^{th}[/tex] term in a geometric sequence. The formula for determining the next term or [tex]n^{th}[/tex] term is:           =>   [tex]a_{n} = ar^{(n-1)}[/tex]

Here, [tex]n = n^{th}[/tex] term, [tex]a =[/tex] First term, and [tex]r =[/tex] Constant Ratio

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Answer:

[tex]\mathrm {\dfrac{1}{5} \; or\; 0.2 \; in \; decimal}[/tex]

Step-by-step explanation:

We are asked to find [tex]\dfrac{6.4}{34}[/tex]

Multiply numerator and denominator by 10 to convert them to whole numbers

[tex]\dfrac{6.8}{34} = \dfrac{6.8 \times 10}{34 \times 10} = \dfrac{68}{34 \times 10}\\\\= \dfrac{68}{34} \times \dfrac{1}{10}\\\\= 2 \times \dfrac{1}{10}\\\\= \dfrac{2}{10}\\\\= \dfrac{1}{5}\\\\= 0.2[/tex]

Answer:

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

The shaded section is the difference of sector OAB and triangle OAC.

Use Pythagorean

The volume of the composite figure = 860.7 m³

The volume of the composite figure = volume of rectangular prism - Volume of cylinder.

Volume of rectangular prism = (length)(width)(height)

Volume of rectangular prism = (10)(10)(12)

Volume of rectangular prism = 1,200 m³

Volume of the cylinder = πr²h

r = 3 m

h = 12 m

Volume of the cylinder = π(3²)(12)

Volume of the cylinder = 339.3 m³

The volume of the composite figure = 1,200 - 339.3

The volume of the composite figure = 860.7 m³

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After determining whether y is a function of x we have come to conclusion that y is not a function of x.

x² = 3y + y

x² = 4y

y = x²/ 4

Here x has two values of -x and x as -x² = x². Therefore, y is not a function of x.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Step-by-step explanation:

False!

the correct equation should be ( x - 3)² + 2

3 units shifted to the right and 2 units upward.

also you can expand the equation to find the axis of symmetry to be sure. :)

Based on the fact that Jessica wants to attach ribbons around her wardrobe, the amount more of ribbons that she needs is 5/6 meters of ribbons

Find out the distance wound Jessica's wardrobe:

= 1¹/₃ + ²/₃ + 1¹/₃ + ²/₃

= 58 / 12

= 4 ⁵/₆ meters

The amount more that Jessica needs is therefore:

= 4 ⁵/₆ - 4

= 5/6 meters of ribbons

In conclusion, Jessica needs 5/6 meters of ribbons

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Triangle angle sum property states that the sum of a triangle's interior angles is 180°. parallel to the given triangle's side BC. As a result, the sum of a triangle's interior angles is 180°.

Triangle angle sum property states that the sum of a triangle's interior angles is 180°. parallel to the given triangle's side BC. As a result, the sum of a triangle's interior angles is 180°.

The Triangle Angle-Sum Theorem and the Definition of a Linear Pair serve as the foundation for this proof. Create two equations based on the diagram, one for each of these relationships. When two angles form a linear pair, we know they are supplementary and add up to 180 degrees. At this point in the proof, you can set the two equations equal to each other and simplify to obtain the proof's final conclusion.

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Step-by-step explanation:

well, because the 2 lines are intersecting each other at a right angle (90°), the complete angle CBD is 90°.

that means the sum of the sub-angles must be 90° :

DBE + CBE = 90

2x - 1 + 5x - 42 = 90

7x = 133

x = 19

The required values are x = 2 , AB = 4 , DB = 2 and AD = 2 .

Since D bisects AB , therefore AD = DB

hence , ( 2 ^ 2 ) - x = 2 x - 2

Solving linear equation ,

4 - x = 2 x - 2

3 x = 6

x = 2

AD = 4 - 2 = 2 .

DB = AD = 2 .

AB = AD + DB = 2 + 2 = 4 .

Hence , x = 2 , AB = 4 , DB = 2 and AD = 2 .

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Answer: 3 3/4

Step-by-step explanation:

The plant is 4 3/4 below ground, but then it grows 8 1/2.

Use subtraction to find the difference.

8 1/2 - 4 3/4 = 3 3/4

Answer:the answer would be 3 3/4

Step-by-step explanation:

Answer:  Choice C

(2, 4) and (0, -4)

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

Explanation:

Let's solve the first equation for y

4x - y = 4

-y = -4x+4

y = 4x-4

Now plug this into the other equation and solve for x.

2x^2 - y = 4

2x^2 - ( y ) = 4

2x^2 - ( 4x-4 ) = 4

2x^2 - 4x+4  = 4

2x^2 - 4x+4-4 = 0

2x^2 - 4x = 0

2x(x - 2) = 0

2x = 0 or x-2 = 0

x = 0 or x = 2

-----------------

If x = 0, then,

y = 4x-4

y = 4(0)-4

y = -4

This gives one solution as (0, -4)

-----------------

If x = 2, then,

y = 4x-4

y = 4(2)-4

y = 4

The other solution is (2, 4)

-----------------

To check the answers, plug the x and y coordinates into each equation. You should get the same thing on both sides.

Below is verification using a graph. The points of intersection are the solutions.

Answer:

A prime number has exactly two factors, 1 and itself. For example, 13 is a prime number because the only factors of 13 are 1 and 13

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The amount of money spent and the number of jeans purchased have a direct relationship.

So, in the given situation where several friends buy jeans for $20.00 a price.

Therefore, a direct relationship exists between the amount of money spent and the number of jeans purchased.

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The fluid is redirected by the rudders, which then produce an opposing force that helps the boat move in the desired direction.

According to Isaac Newton's law, whenever an object X applies a force on another object Y, object Y must respond by applying a force that is equal in magnitude but directed in the opposite direction.

In the case of the rudder, it causes the fluid to flow in a different direction while still exerting an equivalent force of the same size. Consequently, this causes the boat to move, making it the best option.

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The given sequence 2, 4, 8, 16,... is geometric, with a₁ = 2 and r = 2.

Now,

Given: 2, 4, 8, 16, ...

The sequence can also be written as: 2¹, 2², 2³, 2⁴,...

Thus, it follows the definition of geometric progression, having a₁ = 2 and a constant increment of 2, i.e., r = 2.

Hence, The given sequence 2, 4, 8, 16,... is geometric, with a₁ = 2 and r = 2.

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The total surface area of the box is 138in².

What is surface area of cuboid?

Formula for calculating the surface area of the box S = 2(LW+LH+WH) where

L is the length of the box

W is the width of the box

H is the height of the box

If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;

S = 2(4(4)+4H + 4H)

S = 2(16+8H)

S = 32+16H

Hence, The function that represents the surface area of this box as a

function of its height is S = 32+16H where H is the height of the box

Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;

S = 32+16H

S = 32+16(6.5)

S = 32+106

S = 138in²

Hence the total surface area of the box is 138in².

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The arithmetic mean a n of the given terms  a n₋₁ =100, an ₋₁ =140 is

a (n) = 20.

a n₋₁ =100, an ₋₁ =140

a (n) = (140-100)/2

a (n) = 20

The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.

The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).

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Answer:

  D. The theory is based on the idea that an explosion did not occur; therefore, evidence of radiation would not be predicted in the theory.

Step-by-step explanation:

You want to identify the statement that best describes why the steady state theory cannot explain the radiation detected in space.

The Big Bang theory explains the cosmic background radiation as remanent thermal energy from the explosion creating the known universe. The Steady State theory presumes there was no explosion. It offers no alternative explanation for the observed cosmic background radiation.

The cosmic background radiation was first observed in 1965 by two radio astronomers who set out to map radio signals from the Milky Way. They found microwave signals that could not be attributed to a specific source, and were of the same intensity in every direction at every time of day or season of the year. The spectrum of this radiation is consistent with a source temperature of about 2.725 K, explained as the cooled remains of the hot plasma that once filled the universe.

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In topology, the Pointcare conjecture is the one that states a 3-dimensional mainfold is the same as the 3-dimensional sphere.

Topology is a branch derived from geometry, this branch focuses on studying and analyzing geometrical properties and spatial relationships. One of the focuses of this area is the equivalences of some shapes or spaces.

This conjecture created by Pointcare in the 19th century proposes a three dimensional mainfold is the same or it is equivalent to a three dimensional sphere.

This conjecture was first proven as valid by Pointcare and other mathematicians/experts in the topic. However, some years later the same Pointcare and other experts showes this conjuction is not always true and therefore it is not valid.

Despide this, to this day this conjecture remains very popular and people around the world are still trying to prove it or dispprove it.

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The length of BC is B. 2.20 cm

As per the known fact, the linear angle is 180°. As per this writing the equation -

∠ BC + 168 = 180

∠ BC = 180 - 168

∠ BC = 12°

Now, using formula  for calculation of length of arc -

Length = angle/360×2πr, where r refers to radius

Calculating radius as -

Radius = diameter ÷ 2

Radius = 21 ÷ 2

Radius = 10.5 centimeters

Now keep the values in formula to find the length of arc, which is the value of BC

Length = 12/360×2×3.14×10.5

Length = 252×3.14/360

Length = 2.2 centimeters

Hence, the length of BC is B 2.20cm.

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The complete question is attached in image.

Answer:

base :6 units

height:4units

area of a triangle: 1/2 ×b×h

1/2× 6×4=12

12sqaure units should be the area

Answer: 0.71

Step-by-step explanation:

Older than 50: 50-60 and >=60

50-60 : 90 customers

>=60 : 52 customers

90+52=142 customers

Younger than 30: <20 and 20-30

<20 : 67 customers

20-30: 100 customers

67+100=167 customers

142+167=309 customers are either older than 50 or younger than 30

Total customers:

67+100+55+72+90+52=

167+127+142=

294+142=434 customers

309/434=0.71