What is the greatest common factor of 38 and 30?

After the expansion of the series represented by -

∑ r(r + 1)   [r = 0 to r = 5] , we can say that the -

1st term of series = 0

2nd term of series = 2

3rd term of series = 6

Last term = 30

A series is the sum of a few or all elements of the sequence in which the elements are arranged according to some specific pattern.

Given in the question is a series represented by -

∑ r(r + 1)    [r = 0 to r = 5]

We can determine any term of this series by replacing it with r. The series given to us however only contains six terms. So, we will write the complete series in numeral form and then determine the terms.

We have -

∑ r(r + 1)    [r = 0 to r = 5]

Expanding the series, we get -

∑ r(r + 1)    [r = 0 to r = 5] = (0 x 1) + (1 x 2) + (2 x 3) + (3 x 4) + (4 x 5) + (5 x 6).

∑ r(r + 1)    [r = 0 to r = 5] = 0 + 2 + 6 + 12 + 20 + 30.

Hence, the numeral form of the series with elements position is -

0 + 2 + 6 + 12 + 20 + 30.

[1]   [2]  [3]   [4]   [5]     [6]

Therefore, after the expansion of the series represented by -

∑ r(r + 1)   [r = 0 to r = 5] , we can say that the -

1st term of series = 0

2nd term of series = 2

3rd term of series = 6

Last term = 30

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Answer:

The 100 emoji is used in digital communication to express or emphasize achievement, support, approval, and motivation. It also generally means “absolutely” or “keep it 100” (keep it real). Related words: keep it 100. keep it hot.

Answer:

The function is exponential

Its equation is [tex]y = \frac{7}{3} \cdot(\frac{1}{3} )^x[/tex]

Step-by-step explanation:

We can see that, as x increases by a constant y increases by a factor of [tex]\frac{1}{3}[/tex]

So the table represents an exponential equation

The form of the equation is [tex]a\cdot(\frac{1}{3})^{x}[/tex]

All we have to do is determine a

Take the entry for x = 0

At x = 0, the equation becomes y = [tex]a\cdot(\frac{1}{3}) ^ 0[/tex]

Any number raised to the power 0 is 1

So at [tex]x = 0, y = a\cdot1 = a[/tex]

But we know the y value at x = 0 is [tex]\frac{7}{3}[/tex]

So [tex]a = \frac{7}{3}[/tex]

The equation of the function is

[tex]y = \frac{7}{3} \cdot(\frac{1}{3} )^x[/tex]  

We can verify by plugging in a few values for x into the above equation and seeing if the corresponding calculated values concur with the one in the table

For [tex]x = - 1, y = \frac{7}{3}\cdot (\frac{1}{3})^{-1} = \frac{7}{3}\cdot 3 = 7[/tex]

You can try the other x values and see that computed and given y values concur

Answer:

12/6 but if you simplify it's 2

Step-by-step explanation:

4+8 = 12

6-3 = 3

2 x 3 = 6

12/6 = 2

Answer:

(3, 4)

Step-by-step explanation:

Answer:

sorry , i don't

know

Step-by-step explanation:

Answer: Step-by-step explanation:X= number of driver that drive to work alone  the probability that at most 7 drove to work alone is equal to 1 - probability that exactly 8 drive to work alone  P(x<=7)= 1 - P(x>7) = 1- P(x=8)  Probability of driving to work alone = 0.77  Probability of not driving to work alone = 0.23Total number of workers = 8  

Step-by-step explanation:

The required probability that exactly 3 out of 8 workers drive to work alone is 0.0165.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

We have to find the probability that exactly 3 of the workers drive to work alone.

Using the binomial probability formula:

[tex]P(X = k) = (^nC_k) \times p^k \times (1-p)^{(n-k)}[/tex]

where X is the number of workers who drive to work alone, k is the number of successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient.

As per the question, k = 3, n = 8, p = 0.77

Substitute the given values, and we get:

[tex]P(X = 3) = (^8 C_3) \times 0.77^3 \times (1-0.77)^{(8-3)}[/tex]

= 0.0165

Therefore, the probability that exactly 3 out of 8 workers drive to work alone is 0.0165.

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Part A

x = number of years

275x = number of people that left the city after x years go by

37000 - 275x = number of remaining people after x years

37000 - 275x = 35350  is the final answer to part A

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

Part B

37000 - 275x = 35350

-275x = 35350 - 37000

-275x = -1650

x = -1650/(-275)

x = 6

It takes exactly 6 years to have the population reach 35350.

The coordinates of point P on the number line are 16 or 21.

In this question we find a line segment set on a number line and whose endpoints and segment ratio are known. Then, we can determine the location of the point P by using the line segment formula:

P(x) = A(x) + k · [B(x) - A(x)]

Where k is the partition ratio.

If we know that A(x) = 6, B(x) = 31 and k = 3 / 5, then the location of the point P is:

P(x) = 6 + (3 / 5) · (31 - 6)

P(x) = 6 + (3 / 5) · 25

P(x) = 6 + 15

P(x) = 21

P(x) = 6 + (2 / 5) · (31 - 6)

P(x) = 6 + (2 / 5) · 25

P(x) = 6 + 10

P(x) = 16

The coordinates of point P on the number line are 16 or 21.

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Answer:

5 over 11

Step-by-step explanation:

add 5+4=9 then 9+2=11 so it would be 5/11

In Addison's novel collection on her bookshelf, the ratio of fiction novels to all novels is, 5/11. So Option C is correct

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Type of Novel Number of Books

Nonfiction 2

Mystery 4

Fiction 5

the ratio of fiction novels to all novels = number of fiction novels/all novels

                                                               = 5/11

Hence, the ratio is 5 over 11

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Answer:

40,300,520 is greater because if you line the numbers up you’ll see that the one with more numbers is always greater

Step-by-step explanation:

Answer:

40,300,520 is greater how u can tell is that there is more digits at the end of the numbers

Step-by-step explanation:

The capacity utilisation of the team is 57.14%

The efficiency is 76.22%

Design capacity= ((number of workers* total hours per day)/time per customer call out)* number of working days in a week

Design capacity = (50*7)/2)*5

Design capacity= 875 jobs per week

The effective capacity = ((number of workers* actual hours per day)/time per customer call out)* number of working days in a week

Effective capacity=(50*5.25)/2)*5

Effective capacity=656 jobs per week

Efficiency rate= Actual capacity/ effective capacity

Efficiency rate=500/656

Efficiency rate=0.7622 or 76.22%

Utilization rate=Actual capacity/Design capacity

Utilization rate = 500/875

Utilization rate = 0.5714 or 57.14%

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Answer:

118

Step-by-step explanation:

We need to calculate the surface square of the cylinder. The formula for that is S=2*pi*r*(r+h). r is radius of the cylinder which is diameter/2=3/2=1.5. The formula becomes: S=2*pi*1.5(1.5+11)=37.5pi=~117.5 which is approximated to 118 since if the decimal you're approximating is 5 or higher it just increments the previous one, so here we just add 1 to 117

Using the combination formula, it is found that you can draw 10 different combinations of three letters.

The order in which the letters are drawn is not important, as stated in the problem, ACE and CAE are counted as the same combination, hence the combination formula is used instead of the permutation formula.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For this problem, three balls are taken from a urn with five balls(labeled A, B, C, D and E), hence n = 5, x = 3 and:

[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]

You can draw 10 different combinations of three letters.

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2.45

add the 2 numbers and divide by 2

The possible solution for x can be 22.5.

We are given that the side of the regular pentagon = 2 x + 9

So, the perimeter will be:

P ( Regular pentagon) = 5 × ( 2 x + 9 )

P ( Regular pentagon) = 10 x + 45

Also, we are given that the side of a square is 3 x

Perimeter will be:

P ( square) = 4 × 3 x

P ( square) = 12 x

Now, we are given that P ( Regular pentagon) = P ( square)

So, we get that:

10 x + 45 = 12 x

12 x - 10 x = 45

2 x = 45

x = 45 / 2

x = 22.5

Therefore, the possible solution for x can be 22.5.

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Your question was incomplete. Please refer the content below:

A regular pentagon has a side length of 2x-9. A square has a side length of 3x. If both polygons have the same perimeter, what is a possible solution of x?

The width of the table is 63 because 21 x 3 = 63

Answer:The answer would be a.

Step-by-step explanation:I hope this helps.

Answer: -$150

Step-by-step explanation:

withdrawal is removing funds from bank account.

withdrawals of $25 ==> -$25 change

-25*6=-$150

Recall the beta function definition and gamma identity,

[tex]\displaystyle \mathrm{B}(x,y) = \int_0^1 t^{x-1} (1-t)^{y-1} \, dt = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)}[/tex]

Consider the sum

[tex]\displaystyle S(x) = \sum_{m=1}^\infty \frac{\Gamma(m) \Gamma(x)}{\Gamma(m+x)}[/tex]

Compute it by converting the gammas to the beta integral, interchanging summation with integration, and using the sum of a geometric series.

[tex]\displaystyle S(x) = \sum_{m=1}^\infty \mathrm{B}(m,x) \\\\ ~~~~ = \sum_{m=1}^\infty \int_0^1 t^{m-1} (1-t)^{x-1} \, dt \\\\ \int_0^1 (1-t)^{x-1} \sum_{m=1}^\infty t^{m-1} \, dt \\\\ ~~~~ = \int_0^1 (1-t)^{x-2} \, dt \\\\ ~~~~ = \int_0^1 t^{x-2} \, dt \\\\ ~~~~ = \frac1{x-1} = \frac{(x-2)!}{(x-1)!} = \frac{\Gamma(x-1)}{\Gamma(x)}[/tex]

It follows that

[tex]\displaystyle S(n+x) = \sum_{m=1}^\infty \frac{\Gamma(m) \Gamma(n+x)}{\Gamma(m+n+x)} = \frac{\Gamma(n+x-1)}{\Gamma(n+x)}[/tex]

Now we compute the sum of interest. It's just a matter of introducing appropriate gamma factors to condense the double series into a single hypergeometric one.

Recall the definition of the generalized hypergeometric function,

[tex]\displaystyle {}_pF_q \left(\left.\begin{array}{c} a_1,a_2,\ldots,a_p\\b_1,b_2,\ldots,b_q\end{array}\right\vert z\right) = \sum_{n=0}^\infty \frac{(a_1)_n (a_2)_n \cdots (a_p)_n}{(b_1)_n (b_2)_2 \cdots (b_q)_n} \frac{z^n}{n!}[/tex]

where [tex](a)_n[/tex] denotes the Pochhammer symbol, defined by

[tex]\begin{cases}(0)_n = 1 \\ (a)_n = a(a+1)(a+2)\cdots(a+n-1) = \frac{\Gamma(a+n)}{\Gamma(a)}\end{cases}[/tex]

We'll be needing the following identities later.

[tex](1)_n = n! = \dfrac{\Gamma(n+1)}{\Gamma(1)}[/tex]

[tex](x)_n = \dfrac{\Gamma(n+x)}{\Gamma(x)}[/tex]

[tex](x+1)_n = \dfrac{\Gamma(n+x+1)}{\Gamma(x+1)}[/tex]

The [tex]m[/tex]-sum is

[tex]\displaystyle \sum_{m=1}^\infty \frac{\Gamma(m)}{\Gamma(n+m+x)} = \frac1{\Gamma(n+x)} \sum_{m=1}^\infty \frac{\Gamma(m)\Gamma(n+x)}{\Gamma(n+m+x)} \\\\ ~~~~~~~~ = \frac{S(n+x)}{\Gamma(n+x)} \\\\ ~~~~~~~~ = \frac{\Gamma(n+x-1)}{\Gamma(n+x)^2}[/tex]

Then the double sum reduces to

[tex]\displaystyle \sum_{n=1}^\infty \sum_{m=1}^\infty \frac{\Gamma(n)\Gamma(m)\Gamma(x)}{\Gamma(n+m+x)} = \sum_{n=1}^\infty \frac{\Gamma(n)\Gamma(x)\Gamma(n+x-1)}{\Gamma(n+x)^2}[/tex]

Rewrite the summand. We use the property [tex]\Gamma(x+1)=x\Gamma(x)[/tex] to convert to Pochhammer symbols.

[tex]\displaystyle \frac{\Gamma(n)\Gamma(x)\Gamma(n+x-1)}{\Gamma(n+x)^2} = \frac{\Gamma(n)\Gamma(x)^2\Gamma(n+x-1)}{\Gamma(n+x)^2 \Gamma(x)}[/tex]

[tex]\displaystyle . ~~~~~~~~ = \frac1{x^2} \frac{\Gamma(n)\Gamma(x+1)^2\Gamma(n+x-1)}{\Gamma(n+x)^2\Gamma(x)}[/tex]

[tex]\displaystyle . ~~~~~~~~ = \frac1{x^2} \frac{\Gamma(n) \frac{\Gamma(n+x)}{\Gamma(x)}}{\frac{\Gamma(n+x-1)^2}{\Gamma(x+1)^2}}[/tex]

[tex]\displaystyle . ~~~~~~~~ = \frac1{x^2} \frac{(n-1)! (x)_{n-1}}{\left[(1+x)_{n-1}\right]^2}[/tex]

Now in the sum, shift the index to start at 0, and introduce an additional factor of [tex]n![/tex] to get the hypergeometric form.

[tex]\displaystyle \sum_{n=1}^\infty \frac1{x^2} \frac{(n-1)! (x)_{n-1}}{\left[(1+x)_{n-1}\right]^2} = \frac1{x^2} \sum_{n=0}^\infty \frac{(n!)^2 (x)_n}{\left[(1+x)_n\right]^2} \frac1{n!} \\\\ ~~~~~~~~ = \frac1{x^2} \sum_{n=0}^\infty \frac{[(1)_n]^2 (x)_n}{\left[(1+x)_n\right]^2} \frac1{n!} \\\\ ~~~~~~~~ = \boxed{\frac1{x^2} \, {}_3F_2\left(\left.\begin{array}{c}1,1,x\\1+x,1+x\end{array}\right\vert1\right)}[/tex]

Answer:

(5,6)

Step-by-step explanation:

subtract 7-2 and add 3+3.

The velocity of the particle, in meters per second is 0.78 m/s

The position function is given as:

x(t) = e-(t - 3)2

Rewrite properly as

x(t) = e^-(t - 3)^2

Next, we differentiate the above function to determine the velocity function.

Using a graphing calculator, we have:

x'(t) = -2(t - 3) * e^-(t - 3)^2

At t = 2.5 s, we have:

x'(2.5) = -2(2.5 - 3) * e^-(2.5 - 3)^2

Evaluate

x'(2.5) = 0.78

Hence, the velocity of the particle, in meters per second is 0.78 m/s

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x = 1, y = -1 and z = -2.

Here, we are given 3 equations-

4x+12y+4z = -16 ...(1)

12x-12y+8z = 8   ...(2)

4x+12y-4z = 0    ...(3)

Firstly, we add equations 1 and 2, we get,

4x + 12y + 4z + 12x - 12y + 8z = -16 + 8

16x + 12z = -8

4x + 3z = -2 ...(4)

Adding 2 and 3, we get,

12x - 12y + 8z + 4x + 12y - 4z = 8

16x + 4z = 8

4x + z = 2 ...(5)

Now, subtracting equation 4 from 5, we get-

4x + z - 4x - 3z = 2 + 2

-2z = 4

z = 4/-2

z = -2

Thus, 4x - 2 = 2

4x = 4

x = 4/4

x = 1

and 4(1) + 12y + 4(-2) = -16

4 + 12y -8 = -16

12y = -16 + 4

12y = -12

y = -12/12

y = -1

Thus, x = 1, y = -1 and z = -2.

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Answer:

a)   Number of laundries he can do with this box  = 78 laundries.

b)   Price he paying for each load =  0.26 $

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x + 5 = 6x  Subtract 6x from both sides

7x - 6x +5 = 6x -6x

x + 5 = 0 Subtract  5 to both sides

x + 5 - 5 = 0 - 5

x = -5

Answer:

16 1/2 miles

Step-by-step explanation:

If 1 inch = 11 miles and the distance between cities is 1 1/2 inches, then we can solve by multiplying [tex]1 \frac{1}{2} *11=16 \frac{1}{2}[/tex].

Hope this helps!

Answer:

See below.

Step-by-step explanation:

Part A: The Vertical Angles Theorem states that the opposite (vertical) angles of two intersecting lines are congruent.

Part B: b & 40, a &c

Part C: a=140, b=40, c=140

Hope this helps.

Step-by-step explanation:

-3a + 10 < -11

-3a < -21

-a < -7

a > 7

remember, when multiplying with a negative number the inequality sign flips the direction.

Answer:

See below

Step-by-step explanation:

When you see PER think fractions. Miles PER hour is

[tex] \frac{miles}{hour} [/tex]

We are given miles and told to solve for time. Use your knowledge of fractions to get what you need

The reciprocal of mi/hr would get what we need

[tex]miles \times \frac{hours}{miles} [/tex]

Miles cancels out here. So that means you can do this

[tex] \frac{1hour}{50miles} \times 999.9 \: miles[/tex]

In your calculator. Same with the other rate.

The cost of purchase of the employee for a shirt worth $46.99 is $42.30 .

In the question , It is given that

amount of discount  employee receives = 10%

Price of the shirt = $46.99        ...(i)

amount of discount the employee got for the shirt = 10% of 46.99

= 0.10*46.99             ...(as 10%=0.10 )

= 4.699           ...(ii)

So the amount of discount the employee got for the shirt = $4.699

The cost of purchase = Price of shirt - discount

Substituting the values from equation (i) and equation (ii) we get,

cost of purchase = 46.99 - 4.699

= 42.291

≅ 42.30

Therefore , the cost of purchase of the employee for a shirt worth $46.99 is $42.30 .

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