use a power series to approximate the definite integral, i, to six decimal places. 0.3 x4 1 x7 dx 0

Answer:

Dimensions: 15 cm × 7 cm

Step-by-step explanation:

For the given binomial expression the coefficients of (a+b)³ are 1, 3, 3, 1

The constant coefficient is the coefficient that is not connected to any variables in an expression. For example, the constant coefficients in the formulas above are 3 and c, respectively. The leading coefficient is the coefficient associated to the variable with the highest degree in a polynomial. For example, in the formulas above, the leading coefficients are 2 and a, respectively.

We have,

The binomial expansion (a + b)³,

We know that,

The formula for binomial expansion,

(u + v)ⁿ = ⁿC₀uⁿv⁰ + ⁿC₁uⁿ⁻¹v¹ + ⁿC₂uⁿ⁻²v² + ⁿC₃uⁿ⁻³v³

Now,

u = a,

v = b,

And, n =3

Now,

By putting values,

(a + b)³ = ³C₀a³b⁰ + ³C₁a³⁻¹b¹ + ³C₂a³⁻²b² + ³C₃a³⁻³b³

(a + b)³ = ³C₀a³b⁰ + ³C₁a²b¹ + ³C₂a¹b² + ³C₃a⁰b³

Now,

By using combination formula,

On solving we get,

(a + b)³ = a³+3a²b+3ab²+b³

So,

Now,

The coefficients of :

a³ = 1,

3a²b = 3,

3ab² = 3,

b³ = 1,

So,

For the given binomial expression the coefficients of (a+b)³ are 1, 3, 3, 1

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Answer: the answer is d

Step-by-step explanation:

I took the tes

The odds of randomly generating an even number with the first two odd numbers and unique numbers =  [tex]\frac{10}{16}= \frac{5}{8}[/tex].

Sum will be even if either both numbers are odd or both numbers are even .

So, Total no. of way to select numbers for making sum even

= 5C2 ​+ 4C2 ​= 10 + 6 = 16

And, Total numbers of ways to select two odd numbers such that sum is even = 5C2 ​= 10

Probability that both numbers are odd = [tex]\frac{10}{16}= \frac{5}{8}[/tex]

Hence the answer is the odds of randomly generating an even number with the first two odd numbers and unique numbers =  [tex]\frac{10}{16}= \frac{5}{8}[/tex].

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After using the mean, the expected number of cups of coffee is 1.28. So the option a is correct.

In the given question, a sample of 2,500 people was asked how many cups of coffee they drink in the morning.

We have to find the expected number of cups of coffee.

x            Frequencyf(x)       x^2            x∙f(x)            x^2∙f(x)

0                600                    0                 0                  0

1                 800                    1                 800               800

2                900                    4                1800             3600

3                200                    9                600               1800

Total        2500                                     3200             6200

Mean = Sum of f.x/Sum of f

Mean = 3200/2500

Mean = 1.28

Mean = 1.28

The expected number of cups of coffee is 1.28.

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Answer:

K=F/q

Step-by-step explanation:

The function's one sided limit is [tex]+\infty[/tex].

Given function,

[tex]\lim_{x \to 2^-} \frac{x-3}{x-2}\\\\= \frac{2-3}{2-2}\\\\=\frac{-1}{0}\\\\=\infty[/tex]

Thus, it reaches infinity then the limit does not exist.

From the given function, it is observed  x belongs to [tex]2^-[/tex] it means it's graph will start from left.

To determine it's one sided limit, substitute a smaller number which is very close to 2 i.e.1.9999

It's one sided limit will be

[tex]\lim_{x \to 2^-} \frac{x-3}{x-2}\\\\=lim_{x \to 2^-}(x-3)*lim_{x \to 2^-}(\frac{1}{x-2})\\\\=(1.9999-3)*(\frac{1}{1.99999-2})\\\\=-1.0001*(\frac{1}{-0.0001})\\\\[/tex]

When denominator is a very small number in a fraction then the fraction equals to infinity.

[tex]=-1.0001*-\infty\\=+\infty[/tex]

Hence, the function's one sided limit reaches to positive infinity.

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The coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

Any equation of the form [tex]axx^{2} + bx + c = 0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

y = 9 + 18x - 3x²

To find the turning point:

Graph the above quadratic equation;

From the graph:

The maximum point from where the graph starts to decrease is (3,36)

Thus, the coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

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Answer:

a. 4 b.8

Step-by-step explanation:

a.

0 ∈ x<5

f(x)=x+4

f(0)=0+4=4

b.

6 ∈ 5≤x<7

f(x)=8

f(6)=8

The number of pairs of consecutive integers in is no carrying required when the two integers are added are 156.

At the point when the last 3 digits of the continuous numbers are _999 and _000. Just conceivable case-1999, 2000

At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. Potential cases-5 (Comparing to (0,1) (1,2) (2,3) (3,4) (4,5) in the 100th spot)

At the point when the last digit of the successive numbers is of the structure _ _ _ 9 and _ _ _ 0. Potential Cases-5*5 = 25

At the point when none is of that structure. Potential cases-5*5*5 = 125

Reply = 125+25+5+1 = 156

Thus,there are 156 ways to make the pairs of the consecutive integers.

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Using T-test, the upper limit for a 95 percent confidence interval estimate for the true population mean is: 5.965.

T-Test:

When population data are limited, small samples should be used to estimate confidence intervals for the population mean. If your sample size is less than 30 and we don't know the population standard deviation, then you have the normal distribution instead, and use the t distribution instead of the normal distribution.

We have given that,

Estimate the mean number of mile that downtown employee commute to work round trip each day,

sample mean (X-bar) = 4.33

sample size (n) = 20

standard deviations of sample (s) = 3.50

we have to calculate the value of true population .

The degree of freedom is going to be equal to (20 - 1 )= 19 for the sample size, 20. The confidence interval is 95 percent. The level of significance of the alpha is 100% - 95% = 5% that's confidence interval is 5 percent, which is basically in decimal.05.

Upper limit of Population mean = x-bar + t∗s√n

t value at 0.05 and degree of freedom 19 is 2.09

Upper Limit : 4.33 + 2.09×3.50√20

=5.965~ 6

the upper limit for a 95 percent confidence interval estimate for the true population mean is: 5.965.

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Complete Question:

In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given: n=20, Xbar-4.33, s-3.5.

Based on this information, the upper limit for a 95 percent confidence interval estimate estimate for the true population mean is:

a)1,638

b) 3,5

c) 4,33

d) 4.33 +- 1.638

An exponential equation for the growth of the balance in her account is [tex]10(1.06)^t[/tex].

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =[tex]P(1+r/n)^rt[/tex]

We have been given that Quincy has $10 in a savings account. The interest rate is 6%, compounded annually.

The compound interest will be;

Compound Interest =[tex]P(1+r/n)^rt[/tex]

[tex]10(1+6/100)^t\\\\10(1+ 0.06)^t\\\\10(1.06)^t[/tex]

Hence, an exponential equation for the growth of the balance in her account is [tex]10(1.06)^t[/tex].

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To find the critical value that should be used in constructing the 80% confidence interval for the average amount spent by 8 to 11 year olds on a trip to the mall.

the proper z-score for an 80% confidence interval must first be established. Both a z-table and a z-score calculator may be used for this.Using a z-table, i may search up the value of z such that 80% of the area under the standard normal curve is to the left of z to get the z-score. This number is around 0.84.We can then use this z-score to calculate the 80% confidence interval by taking the sample mean and adding or removing the product of the z-score and the standard error of the mean. The standard error of the mean is computed by dividing the standard deviation by the square root of the sample size.

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two polynomials are relatively prime if the greatest common divisor of the two polynomial is 1

How do you prove two polynomials are relatively prime?

Two polynomials from Z[x] are called evaluationally relatively prime if the greatest common divisor of the two polynomials in Z[x] is 1 and gcd(f(t),g(t)) = 1 for all t ∈ Z.

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Probabilities are used to determine the chances of an event.

The probability that both selections are boys is 0.1667

The given parameters are:

boys= 35

girls= 50

total= 85

Since two are chosen to sing a duet, then the selection is without replacement.

So, the probability that both selections are boys is

p=boys/ total * boys-1/ total -1

This gives

p= 0.4118*0.4048

Hence, the probability that both selections are boys is 0.1667

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The given variation y = 7x is a direct variation where any increase in the variable x also increases the value of the variable y.

The given variation is represented as -

y = 7x

We have to identify if the given variation is direct or inverse or joint or combined.

Let us first the different mathematical relationships mentioned here.

Now that we know the definitions of different types of variations, let us look into the given variation, which is -

y = 7x

We can see that the variable y is 7 times the multiple of another variable x. Thus, this is a case of direct variation such that any increase in the variable x also increases the value of the variable y.

Therefore, the given variation y = 7x is a direct variation type.

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There were 1575 boys and 945 girls.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3.

A ratio is a number with no units.

According to the information provided to us, there were 3 girls for every 5 boys.

3 to 5 girls to boys are the ratio.

The sum is 8.

We need to find the number of girls and boys

Out of 2,520, 3 to 5 girls were present.

We have 3/8(2520) = 7560/8 girls, which comes to 945.

For boys, 5/8(2520) = 12600/8 boys, which equals 1575.

Therefore, there were 945 girls and 1575 boys respectively.

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Answer:

70

Step-by-step explanation:

Nut mixture 1:  7 peanuts for every 3 almonds.

Therefore, the container has to hold nuts in multiples of 10, since 7+3=10 and 7 is not divisible by 3.

Nut mixture 2:  9 peanuts for every 5 almonds.

Therefore, the container has to hold nuts in multiples of 14, since 9+5=14 and 9 is not divisible by 5.

To find the number of nuts in the smallest possible container, find the least common multiple (LCM) of 10 and 14.

To find the LCM, list the multiples of each number and locate the smallest multiple that is exactly divisible by both the numbers:

Therefore, the LCM of 10 and 14 is 70.

So there are 70 nuts in the smallest possible container.

Answer:

a) 125 ml milk

b) 7.5g

Step-by-step explanation:

since 8 pancakes you need 250 ml of milk then you divide 250 by 2 since 8/2 is 4

250/2

125 ml milk

b)

We do the same as the other problem we find how much you need for 4 pancakes

5/2

2.5

Now you multiply by 3 since 4x3=12

2.5x3

7.5 g

Hopes this helps please mark brainliest

The equation of the line that passes through the points (-2,-5) and (-4,-4): y = -1/2x - 6.

Given the following points that a line passes through below:

(-2, -5) and (-4, -4).

First, find the slope (m):

Slope (m) = change in y / change in x = (-4 -(-5)) / (-4 -(-2))

Slope (m) = 1/-2

Slope (m) = -1/2.

Find the y-intercept (b) by substituting m = -1/2 and (x, y) = (-4, -4) into y = mx + b:

-4 = -1/2(-4) + b

-4 = 2 + b

-4 - 2 = b

-6 = b

b = -6

To write the equation of the line, substitute m = -1/2 and b = -6 into y = mx + b:

y = -1/2x - 6

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The first 4 terms are 6,7,8,9 and the 10th term is 15 for given sequence.

Given:

n + 5

substitute n = 1,2,3,4....

= n+5

= 1+5

= 6

= 2+5

= 7

= 3+5

= 8

= 4+5

= 9

First four terms are 6,7,8,9

[tex]T_10 =[/tex] a + (n-1)d

= 6 + (10-1)1

= 6+9*1

= 15

10th term = 15

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Full question:

For each sequence find the first 4 terms and the 10th term:

n + 5.

The probability that she succeeds at fewer than 7 free-throws is 0.19

The table of values is given as

5: 0 successes

6: 5 successes

7: 8 successes

8: 6 successes

9: 6 successes

10: 1 success

From the above readings, the throws less than 7 are

5: 0 successes

6: 5 successes

So, the number of success is

Success = 0 + 5

Success = 5

The probability is then calculated as

P = Success/Total

So, we have

P = 5/(0 + 5 + 8 + 6 + 6 + 1)

Evaluate

P = 5/26

So, we have

P = 0.19

Hence, the probability is 0.19

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In a study of the u.s. census, informants would be statisticians respondents would be any U.S.citizens

Detailed meaning of survey research: Survey research is a research method involving the use of standardized questionnaires or interviews to collect data about people and their preferences, thoughts, and behaviors in a systematic manner. Although census surveys were conducted as early as Ancient Egypt, survey as a formal research method was pioneered in the 1930-40s by sociologist Paul Lazarsfeld to examine the effects of the radio on political opinion formation in the United States. This method has since become a very popular method for quantitative research in the social sciences.

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You should consider option B - Translated but also locally adapted for the audience, with regard to your online content.

Any content that exists as digital data is considered online content. Otherwise called advanced media, computerized content is put away in computerized or simple capacity in unambiguous configurations.

A company's website should become more international in terms of content and supported languages if it wants to expand globally.

The content of a website must not only be translated into the language of the audience or user in that country but also adapted to fit the cultural and linguistic characteristics of that language, both of which are essential for expanding a website's or company's presence online internationally.

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(complete question)

If you are looking to expand your company's presence online internationally, which of the following should you consider with regards to your online content?

A . Translated by an automated tool only

B Translated but also locally adapted for the audience

C Translated into the native language

D Left the same, and not translated

If one of the pedestrian death is randomly elected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated 0.6290.

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Answer:

6) x=20.64

7) x=12.423

8) x=26.5

Step-by-step explanation:

The probability that this person is a graduate student is 0.3833.

From the recent census

40% of its students mainly used Ma- cintosh computers.

At the time of the census, 67% of the school's students were undergraduates.

In the census, 23% of the respondents were graduate students who said that they used PCs as their primary computers.

We have to find the probability that this person is graduate student.

Let A represent the event that student uses Mac.

So P(A)=40%=0.4, P(A')=60%=0.6

Then let B be the event that randomly chosen student is undergraduate·

So, P(B) = 67%=0.67, P(B')= 33%=0.33

Further, 23% of respondents were graduate. Students who said they used PCs as their Primary Computers

So P(B'∩A')=23%=0.23

If we select a student at random from among those who were part of the Census and learn that student mainly uses PC, then probability that this person is a graduate student is:

P(B'|A') = P(B'∩A')/P(A')

P(B'|A') = 0.23/0.6

P(B'|A') = 0.3833

Hence, the probability that this person is a graduate student is 0.3833.

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The right question is:

Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Ma- cintosh computers (Macs). The rest mainly used PCs. At the time of the census, 67% of the school's students were undergraduates. The rest were gradu- ate students. In the census, 23% of the respondents were graduate students who said that they used PCs as their primary computers. Suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a PC. Find the probability that this person is graduate student. Show your work.

The greatest common multiple of 10 and 40 is 10.

The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.

In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.

Foe calculating the GCD of 10 and 40, we have to find the factors of 10 and 40.

Factors of 10:

1, 2, 5, 10

Factors of 40:

1, 2, 4, 5, 10, 20, 40

From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 40 are 1, 2, 10, and 5.

So, the greatest common multiple of 10 and 40 is 10.

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By solving the equation we know that 15 players can be brought to the tournament.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, we know that:

Softball players raised $1186.50 to attend a tournament.

They allocated $21.50 for meals per player and paid $842.50 for the bus rental.

We must apply the following calculation to determine the total number of players they are permitted to bring:

Formula: Total amount of money= fixed cost + unitary variable cost × number of players

1186.50 = 842.50 + 21.50 × number of players

1186.50 - 842.50 = 21.50 × number of players

344/21.50 = number of players

15 = Number of players

Therefore, by solving the equation we know that 15 players can be brought to the tournament.

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Answer:

Step-by-step explanation:

it 10