-6(3 + x) + 2(3x + 5) = 0

By Gauss's Law the approach of solving sum of a sequence of n terms in arithmetic progression is :

[tex]S_n=\dfrac{n}{2}(a_1+a_n)[/tex]        ......1 )

Here, [tex]a_n = 302[/tex] , [tex]a_1=2[/tex] .

We know :

[tex]a_n=a_1+(n-1)d\\\\302=2+3(n-1)\\\\n = 101[/tex]

Putting, all values in equation 1) we get :

[tex]S_n=\dfrac{101}{2}\times (2+302)\\\\S_n=101\times 152\\\\S_n=15352[/tex]

Therefore, the sum of sequence using Gauss's Law is 15352.

Hence, this is the required solution.

Answer:

65 cents

Step-by-step explanation:

divide 10 by 2.25 to get the factor. Next divide 2.9 by that to get your answer. 10/2.25 = 4 4/9. 2.9/ 4 4/9 = 0.6525 --> 0.65

Answer:

Step-by-step explanation:

3 (-4 x - 1) - 2 x + 4 = 43

Expand the terms in the bracket

That's

- 12x - 3 - 2x + 4 = 43

- 14x + 1 = 43

Using the subtraction property subtract 1 from each side of the equation

- 14x + 1 - 1 = 43 - 1

- 14x = 42

Divide both sides by - 14

[tex] \frac{ - 14x}{ - 14} = - \frac{42}{14} [/tex]

We have the final answer as

Hope this helps you

Answer:

7,425 gallons of water

Step-by-step explanation:

Given:

A tank of,

Length = 16.5 ft

Width = 7.5 ft

Height = 8 ft

1 ft³ = 7.5 gallons of water

Required:

Gallons of water that will fill the tank

SOLUTION:

Find the volume of the tank:

Volume of the tank = length*width*height

Volume = 16.5*7.5*8 = 990 ft³

Convert 990 ft³ to gallons of water:

1 ft³ = 7.5 gallons

990 ft³ = [tex] 990*7.5 [/tex]

= 7,425 gallons of water

7,425 gallons of water will fill the tank of the given measurement.

Amount of water in tank is 7,425 gallon

Given that;

Sides of tank = 16.5 ft, 7.5 ft, 8 ft

1 ft³ = 7.5 gallon

Find:

Amount of water in tank

Computation:

Volume of tank = [(16.5)(7.5)(8)]

Volume of tank = 990 ft³

Amount of water in tank = [Volume of tank][7.5]

Amount of water in tank = [990][7.5]

Amount of water in tank = 7,425 gallon

Find out more information about 'Volume'.

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Answer:

15km

hope this helps!

Answer:

14.99 ounces

Step-by-step explanation:

First, find the weight of the 2 cereal bags combined:

16.03 + 18.98

= 35.01

Subtract this from 50 to find the weight of the box, since 50 ounces is the combined weight of the box and the 2 cereal bags

50 - 35.01

= 14.99

So, the box weights 14.99 ounces

Answer:

  80 units

Step-by-step explanation:

The sides of a regular octagon are all the same length.

  x +6 = 14 -x

  2x = 8 . . . . . . add x-6

  x = 4

  x+6 = 10 . . . . the length of each of the 8 sides

P = 8s = 8(10) = 80

The perimeter of the octagon is 80 units.

Answer:

B

0.388 centigrams :)

Answer:

153.2 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent side/ hypotenuse

cos 40 = x/200

Multiply each side by 200

200 cos 40 = x/200 * 200

200 cos 40 =x

153.20888886=x

To the nearest tenth

153.2 =x

Answer:

AC = 153.2 m.

Step-by-step explanation:

cos(Ф) = adj / hyp

cos(40) = AC / 200

AC = cos(40) x 200

AC = 153.2 m

Answer:

3 to 1

Step-by-step explanation:

Because the 6 is the bigger number but is also on the left which means the number on the right has to divide into the six therefore 3 to 1

Answer:

72in

Step-by-step explanation:

area=length x width

a=8x9

Answer:

i believe the answer is 114g of protein. i hope this helps

Step-by-step explanation:

Answer:

22*3=66

Flase

Step-by-step explanation:

The equation ((22)3) = 25 is false.

Two or more expressions with an Equal sign is called as Equation.

The given equation is  ((22)3) = 25.

We have to check whether the left hand side is equal to right hand side.

If the LHS and RHS are equal then the equation is true.

If not then it is false.

The value in LHS is 22×3 = 66

The value in RHS is 25

66 is not equal to 25

Hence, the equation ((22)3) = 25 is a false statement.

To learn more on Equation:

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Answer:

1.449275362

Step-by-step explanation:

Answer:

$0.69

Step-by-step explanation:

Step 1:

$6.21 ÷ 9

Answer:

$0.69

Hope This Helps :)

Given :

A population of protozoa develops with a constant relative growth rate of 0.4142 per member per day.

On day zero the population consists of five members.

Differential equation : [tex]\dfrac{dP}{dt}=0.4142P[/tex]

To Find :

The population size after eight days.

Solution :

Rate of growth , R = 0.4142 .

Now ,

Differential equation is :

[tex]\dfrac{dP}{dt}=0.4142P\\\\P_n=Ce^{0.4142n}[/tex]

For n = 0 .

[tex]5=C(1)\\C=5[/tex]

So ,the relation is [tex]P_n=5e^{0.4142n}[/tex] .

Putting n = 8 .

[tex]P_8=5e^{0.4142\times 8}\\\\P_8=137.42[/tex]

Hence , this is the required solution .

Answer:

The first element of a set which is linked with the element of second set is called domain.

The element of second set is known as range.

Answer:

When functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. These won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. Small sets of points are generally the simplest sorts of relations, so your book starts with those.

for example

State the domain and range of the following relation. Is the relation a function? {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

The above list of points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values. To give the domain and the range, I just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(It is customary to list these values in numerical order, but it is not required. Sets are called "unordered lists", so you can list the numbers in any order you feel like. Just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

While the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). Since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

Answer:

Step-by-step explanation:

[tex]|4w+3|\\w =-2\\[/tex]

Substitute ; w= -2 into the given equation

[tex]|4(-2)+3|\\\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\=\left|-4\cdot \:2+3\right|\\\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2=8\\=\left|-8+3\right|\\\\\mathrm{Add/Subtract\:the\:numbers:}\:-8+3=-5\\=\left|-5\right|\\\\\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a\\[/tex]

Answer:

x = − 5

Step-by-step explanation:

Divide each term by  − 14  and simplify.

Answer: x =5

Step-by-step explanation:

14x/14= 70/14

X = 5

Answer:

Step-by-step explanation:

Sample data

Mean = sum of sample data/sample frequency

Answer choices:

The variation in the sample means makes it possible to make predictions about the population mean.

The actual population mean is greater than 236.

The actual population mean is less than 245.

The actual population mean is greater than 245

The population mean is the average of the sample means.

Answer:

It is numbers 1, 2, and 3!

Step-by-step explanation:

Answer:

12 & 13

Step-by-step explanation:

trust me

Answer:

10

Step-by-step explanation:

Because it is 90% and he shots 12 how much fat away is 90 for 100 it is 10

Answer:

[tex]\frac{11}{12}[/tex],[tex]1\frac{1}{4}[/tex],[tex]1\frac{2}{3}[/tex]

Step-by-step explanation:

It wants you to take these 3 fractions and arrange them from least to greatest.

The first thing I did was look for the fraction with no number in front of it.

[tex]\frac{11}{12}[/tex] is the only fraction that has no numbers in front of it. So

The second thing I did was look for the fraction that had the biggest number in front of it. I see that the remaining fractions have the same number in front.

So, I drew 2 circles. 1 of the circles I shaded in and the other I split into 4 equal halves. I shaded in one of the halves. These 2 circles represent [tex]1\frac{1}{4}[/tex].

The next thing I did was draw 2 more circles. I shaded in one of them and slit the other one into 3 equal halves. I shaded in 2 of the halves. These 2 circles represent [tex]1\frac{2}{3}[/tex].

Last, look at the 4 circles and ask yourself which one is the most shaded in. If you said [tex]1\frac{2}{3}[/tex] you are correct. This fraction is the biggest. Meaning that [tex]1\frac{1}{4}[/tex] is in the middle.