the point on 0 on the number line represents what?

The first four terms of the binomial series are  1,  x³/5,  (12/25)x⁶ and  respectively.

The binomial provided to us is (1+x^3)^-1/5.

To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.

[tex](1+x)^n = 1 + nx + [n(n - 1)/2!] x^{2} + [n(n - 1)(n - 2)/3!] x^{3} +...[/tex]

As we can see here,

The value of x = x³,

The value of n = -1/5.

We get,

[tex](1+x^{3})^{-\frac{1}{5} } = 1 - \frac{1}{5} (x^{3} ) + [\frac{-1}{5} (\frac{-1}{5} -1)/2!]x^{6} + [\frac{-1}{5} (\frac{-1}{5} -1)(\frac{-1}{5} -2)/3!]x^{27} +[/tex]

From the expansion, we can see,

First term = 1

Second term = x³/5

Third term = (12/25)x⁶

Fourth term = (-13/125)x²⁷

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The difference between the depths in February and July is D. 13 feet.

From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.

Therefore, it should be noted that the depth in July is -18.

Therefore, the difference between the depths in February and July will be:

= -5 - (-18)

= -5 + 18

= 13

Therefore, the depth is 13 feet.

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slope= 1/4

y intercept= -5

Hello! So...

We are given the following:

[tex](5-9i)-(2-6i)+(3-4i)[/tex]

_____________________________________________

1. Simplify the given expression.

[tex](5-9i)-(2-6i)+(3-4i)=5-9i-(2-6i)+3-4i[/tex]

_____________________________________________

2. Group the like terms.

[tex]-9i-4i(-2-6i)+5+3[/tex]

_____________________________________________

3. Add similar elements ( [tex]-9i-4i=-13i[/tex] ).

[tex]=-13i-(2-6i)+5+3[/tex]

_____________________________________________

4. Add the numbers ( [tex]5+3=8[/tex] ).

[tex]-13i-(2-6i)+8[/tex]

_____________________________________________

5. Remove the parentheses ( [tex]-(a+bi)=-a-bi[/tex] ).

[tex]-13i+-2-(-6)i+8[/tex]

_____________________________________________

6. Group the like terms.

[tex]-13i-(-6)i-2+8[/tex]

_____________________________________________

7. Add similar elements ( [tex]-13i-(-6)i=-7i[/tex] ).

[tex]-7i-2+8[/tex]

_____________________________________________

8. Add the numbers ( [tex]-2+8=6[/tex] ).

[tex]-7i+6[/tex]

_____________________________________________

9. Rewrite in standard complex form.

[tex]6-7i[/tex]

^Hence, our solution.

_______________________________________________________

Hope this helps! If so, lmk! If you need anything else, feel free to comment below and I'll see what else I can do to assist you further. But for now, thank you for your time and good luck!

Answer:

  A: y = 10

  B: ∠A = 42; ∠C = ∠D = 138

Step-by-step explanation:

Given vertical angles A and B, with A marked 5y-8 and B marked 42, you want to know the value of y and the measures of supplementary angles C and D.

Vertical angles A and B are congruent, so we have ...

  ∠A = ∠B

  5y -8 = 42

  5y = 50 . . . . . . . add 8

  y = 10 . . . . . . . divide by 5

As we noted above, angle A has the same measure as vertical angle B:

  ∠A = 42

Angle C forms a linear pair with angle B, so is supplementary:

  ∠C = 180 -∠B = 180 -42

  ∠C = 138

Angle D is a vertical angle to angle C (and is also supplementary to angle B).

  ∠D = 138

Using the normal distribution and the central limit theorem, the probabilities are calculated as follows:

a) One meter stick greater than 100.17 cm: 0.1357 = 13.57%.

b) Group of 10 with mean less than 100.3: 0.1711 = 17.11%.

c) Group of 44 with mean greater than 100.08: 0.0918 = 9.18%.

d) Group of 50 with mean between 100.05 and 100.07: 0.5222 = 52.22%.

e) 92nd percentile of sample of 24: 100.09.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

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

Considering the Central Limit Theorem, the z-score formula can be given as follows:

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

The mean and the standard deviation of the lengths are given as follows:

[tex]\mu = 100.06, \sigma = 0.1[/tex]

For item a, we have that n = 1 and the probability is one subtracted by the p-value of z when X = 100.17, hence:

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

[tex]Z = \frac{100.17 - 100.06}{\frac{0.1}{\sqrt{1}}}[/tex]

Z = 1.1

Z = 1.1 has a p-value of 0.8643.

1 - 0.8643 = 0.1357.

For item b, we have that n = 10 and the probability is the p-value of Z when X = 100.03, hence:

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

[tex]Z = \frac{100.03 - 100.06}{\frac{0.1}{\sqrt{10}}}[/tex]

Z = -0.95

Z = -0.95 has a p-value of 0.1711.

For item c, we have that n = 44 and the probability is one subtracted by the p-value of Z when X = 100.08, hence:

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

[tex]Z = \frac{100.08 - 100.06}{\frac{0.1}{\sqrt{44}}}[/tex]

Z = 1.33.

Z = 1.33 has a p-value of 0.9082.

1 - 0.9082 = 0.0918 = 9.18%.

For item d, we have that n = 50 and the probability is the p-value of Z when X = 100.07 subtracted by the p-value of Z when X = 100.05, hence:

X = 100.07:

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

[tex]Z = \frac{100.07 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]

Z = 0.71.

Z = 0.71 has a p-value of 0.7611.

X = 100.05:

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

[tex]Z = \frac{100.05 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]

Z = -0.71.

Z = -0.71 has a p-value of 0.2389.

0.7611 - 0.2389 = 0.5222 = 52.22%.

For item e, we have that n = 24, and the 92th percentile is X when Z = 1.405, hence;

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

[tex]1.405 = \frac{x - 100.06}{\frac{0.1}{\sqrt{24}}}[/tex]

x - 100.06 = 1.405 x 0.0204

X = 100.09.

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The sales of the number of hammers that give the maximum revenue of 32400 is 1800

The equation of the revenue function is given as

R = 36x − 0.01x2

Rewrite the equation properly as a quadratic function

So, we have the following equation

R = 36x − 0.01x^2

Differentiate the above function

So, we have the following equation

R' = 36 - 0.02x

Set the differentiated function to 0

So, we have the following equation

36 - 0.02x = 0

This gives

0.02x = 36

Divide both sides by 0.02

So, we have

x = 1800

In (a), we have

36 - 0.02x = 0

0.02x = 36

x = 1800

Substitute x = 1800 in R = 36x − 0.01x^2

So, we have

R = 36 x 1800 − 0.01 * 1800^2

Evaluate

R = 32400

Hence, the maximum revenue is 32400

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STEP - BY - STEP EXPLANATION

Increasing amount = $10000

Median = Middle value = $40000

then

New median salary = $40000 + $10000 = $50000

Then answer is

OPTION C) $50-59 thousand

Correct Unit rate is 4 pounds per gallons.

An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate. A unit rate is a ratio between two separate units with one as the denominator. Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc.

Given Data

[tex]\frac{1}{4}[/tex] pounds = [tex]\frac{1}{16}[/tex] gallons

Rate = [tex]\frac{1}{4}[/tex] pounds ÷ [tex]\frac{1}{16}[/tex] gallons

Rate = [tex]\frac{1}{4}[/tex] × 16

Rate = 4

Unit rate is 4 pounds per gallons.

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zymiyas, this is the solution:

Brandon mows 1/4 an acre every 1/2 hour, therefore:

1/2 hour * 2 = one hour

1/4 * 2 = 2/4 or 1/2 an acre

Brandon will mow 1/2 an acre every hour

The volume of this triangular prism 7yd x 7yd x 8yd is calculated as 196 [tex]yd^3\\[/tex] as per answered with the correct unit.

A prism is a kind of a polyhedron in geometry that has n number of parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the present first base, and the n faces.

The bases are all translated into all cross-sections that are parallel to them.

The volume of this prism can be found by applying the formula

1/2 Area x Height

= 1/2 x 7 x 7 x 8

= 196 [tex]yd^3\\[/tex]

V=Bh

V=Bh, where B can be said as the base area and h as the height, is the formula for a prism’s volume. The prism has a rectangular base.

The total area that any kind of prism takes up in three dimensions is known as its volume. It is defined in mathematically as the result of the base’s area and length.

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Answer:

D). Angle B ≈ Angle E

Step-by-step explanation:

ASA means that for the relation to be true, there not only has to be the 3 given proportionate values, but 2 have to be angles and 1 has to be a side.

Since we already have the 1 side, option 1 and 2 are voided.

Then since we already have Angle A and D option 3 is as well, so through this we know the answer is number 4 or Angle B = Angle E

Hope this helps.

We have:

And

After that, we proceed as follows:

The Maximum height of the object is 2888.9 feet which is at 23.06 seconds

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let h represent the height of an object after t seconds. Given that:

h(t) = -4.9t² + 226t + 283

The maximum height is at h'(t) = 0, hence:

h'(t) = -9.8t + 226

-9.8t + 226 = 0

9.8t = 226

t = 23.06 s

h(23.06) = -4.9(23.06)² + 226(23.06) + 283 = 2888.9

Maximum height is 2888.9 ft

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Prism is the mathematical model with different dimensions but same volume.

As given in the question,

Mathematical model represent different dimensions but same volume.

Prism is the mathematical model with different dimensions but same volume.

To prove it consider two different dimensions of prism.

Prism 1

length = 4cm

Width = 4cm

Height = 4cm

Surface area of the prism1 = 2( 4×4 + 4×4 +4×4)

                                            = 2(48)

                                            = 96cm²

Volume of prism1 = 4×4×4

                             = 64cm³

Prism 2

length = 8cm

Width = 2cm

Height = 4cm

Surface area of the prism1 = 2( 8×2 + 2×4 +4×8)

                                            = 2(56)

                                            = 112cm²

Volume of prism1 = 8×2×4

                             = 64cm³

Therefore, prism is the mathematical model with different dimensions but same volume.

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The expression to represent the number of tomato plants he planted this year  1 / 5 x  + 6.

This year Nelson planted 6 more than one fifth of the tomato plants he planted last year.  

The expression that can be used to represent the number of tomato plant he planted this year can calculated as follows:

Therefore,

let

x = number of tomato he planted last year.

Hence, the final expression is as follows:

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Step-by-step explanation:

i2o2k2wkekekekk2k2o2o2o2o2o292

By using the method of addition, the equation is 12x + 1.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.

Given that,

5x - 4 > 12 adding 4 to both sides;

5x - 4+ 4 > 12 + 4

5x > 16 dividing both sides by 5;

x > 16/5

12x + 5-4

12x + 1

Therefore, the equation is 12x + 1.

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Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.

The future value formula is given by:

[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]

In which:

For this problem, the parameters are given as follows:

P = 2000, r = 0.06, n = 10.

Hence the value of the account will be of:

[tex]V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right][/tex]

V(10) = $26,361.59.

The complete problem is:

"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).

What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"

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Answer:

you accidentally put x+6 for the 1st part

Given data:

The series is 1 + 2 + 4 + 8 + 16 + 32 + ....

The given series is G.P because the common ratio for GP is,

Here, the common ratio is 2.

Sum of the first five numbers ,

Here, a is first term that is 1

r is common ratio that is 2

n is the number

Therefore, sum is given as

Thus, the sum of first five terms is 31

The correct option is (2).

The estimates for the average content is 0.9.

The variation in nitrogen content in the colony is 0.0036.

The average of a data set or the mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

The sum of the data set is calculated as follows;

total = 0.98 + 0.83 + 0.99 + 0.86 + 0.9 + 0.81 + 0.94 + 0.92 + 0.87

total = 8.1

The estimated average of the nitrogen content  = 8.1/9 = 0.9

The deviation of each data from the mean;

= (0.98 - 0.9), (0.83 - 0.9), (0.99 - 0.9), (0.86 - 0.9), (0.9 - 0.9), (0.81 - 0.9), (0.94 - 0.9), (0.92 - 0.9), (0.87 - 0.9)

= 0.08, -0.07, 0.09, -0.04, 0, -0.09, 0.04, 0.02, -0.03

The sum of the square of each data from the mean;

= (0.08)² + (-0.07)²  + (0.09)² + (-0.04)² + (0.0)² + (-0.09)² + (0.04)² + (0.02)² + (-0.03)²

= 0.032

The variation of the data sample = (0.032)/9 = 0.0036

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Answer:Hence, the measure of angle whose measure is 32∘ less than its supplement is 74∘.

Step-by-step explanation:

We are given w^2 + 5w and we are asked to identify the terms for each of its parts.

First, let's start with w. The letter w is used to represent an unknown value. Thus, it is called a variable.

ext, 2. Here, 2 is useda as an exponent of w in the first term.

Meanwhile, 5 is used as a multiplier or a numerical coefficient of w in the second term.

Finally, the expression w^2 + 5w is

This just means that the y coordinate will  always be 3 for all coordinates of x that means that the y coordinate of the point ( -7,1) will change to

(-7,3)

The graph of the line y=kx+1 given that the  point M(1,3) belongs to the line is shown below .

In the question ,

it is given that

the line y=kx+1 has point (1,3) on it ,

which means that the point (1,3) will satisfy the equation y=kx+1 .

So, substituting x=1 and y=3 , we get

3=k*1+1

3-1=k

k=2

Hence , the equation of the line becomes y=2x+1 .

On comparing the equation with point slope form of the the line, y=mx+c ,

we get , the slope of the line = 2 and y intercept of the line = 1 .

the graph of the line y=2x+1 is shown below .

Therefore , the graph of the line y=kx+1 given that point M(1,3) belongs to the line is shown below .

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