At the annual dog show, Chantel noticed that there were three more Scotties than Schnauzers. She also
realized that the number of Wirehaired Terriers was five less than twice the number of Schnauzers. If there
were 78 dogs in all (counting Schnauzers, Scotties, and Wirehaired Terriers), how many Schnauzers were
there? Write and solve an equation.

The given series is divergent.

We can use the limit comparison test to determine the convergence or divergence of the given series:

First, note that for all n ≥ 1, we have: \(\frac{(n^9 + 1) }{ (n^10 + 1)}\) ≤ \(\frac{n^9 }{n^10} = \frac{1}{n}\)

Therefore, we can compare the given series to the harmonic series ∑ 1/n, which is a well-known divergent series. Specifically, we can apply the limit comparison test with the general term \(a_n = \frac{(n^9 + 1)}{(n^{10} + 1)}\) and the corresponding term \(b_n = \frac{1}{n}\):

lim (n → ∞) \(\frac{a_n }{ b_n}\) = lim (n → ∞) \(\frac{\frac{(n^9 + 1)}{(n^10 + 1)} }{\frac{1}{n} }\)

= lim (n → ∞) \(\frac{ n^{10} }{ (n^9 + 1)}\)

= lim (n → ∞) \(\frac{n}{1+\frac{1}{n^{9} } }\)

= ∞

Since the limit is positive and finite, the series ∑ \(\frac{(n^9 + 1) }{ (n^10 + 1) }\) behaves in the same way as the harmonic series, which is divergent. Therefore, the given series is also divergent.

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Answer:A(n) = 7.2+(n - 1)4.8

Step-by-step explanation:We can recognize this as an arithmetic sequence with first term 7.2 and common difference 4.8

Answer:

Yes

Step-by-step explanation:

Money to put into Savings Account

20% of $250.00 = 0.2 × $250.00

                            = $50.00

Cost of Jeans with sales tax

$75.00 + 5% = 105% of $75.00

                      = 1.05 × $75.00

                      = $78.75

Cost of Coat with sale tax

$110.00 + 5% = 105% of $110.00

                      = 1.05 × $110.00

                      = $115.50

Total money spent

= $78.75 + $115.50

= $194.25

Money left

= $250.00 - $194.25

= $55.75

$55.75 > $50.00

As the money left is more than 20% of $250.00 she does still have the money she planned to put into her savings account.

To describe a linear program for finding the largest axis-aligned square that lies entirely inside a polygon (p), we can define the decision variables, objective function, and constraints as follows:

Decision Variables:

Let x be the side length of the square.

Objective Function:

Maximize x. The objective is to find the largest possible side length for the square.

Constraints:

Square Within Polygon Constraint:

For each vertex (xᵢ, yᵢ) of the polygon p, we can define the following set of inequalities:

xᵢ ≤ x, for all vertices of the polygon.

These inequalities ensure that the square lies entirely within the polygon.

Square Symmetry Constraint:

To ensure that the square is axis-aligned, we can impose symmetry constraints. For example, if the coordinates of the center of the square are (c_x, c_y), then we can add the following constraints:

c_x ± (x/2) = constant, for fixed values of c_x.

c_y ± (x/2) = constant, for fixed values of c_y.

These constraints ensure that the sides of the square are parallel to the x and y axes.

Non-Negative Constraint:

x ≥ 0, to ensure a non-negative side length for the square.

By formulating and solving this linear program, we can find the optimal value for x, which represents the largest axis-aligned square that lies entirely within the given polygon p.

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Answer:

The value of the car will be

4450.15

Step-by-step explanation:

we know that

11.75%=11.75/100=0.1175

so Let

x-----> the value of the car after 11 years

X=17600(1-0.1175)11=4450.15

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

since 1 was 152 you have to add more to get number 8

Answer: 16

Step-by-step explanation: 21.60 / 1.35 = 16

The result of the division 21.60÷1.35 is: 16.

To find the answer for 21.60 ÷ 1.35, you can perform the division operation:

21.60 ÷ 1.35

Divide 21.60 by 1.35:

21.60 ÷ 1.35 ≈ 16

The result of 21.60 ÷ 1.35 is approximately 16.

When dividing decimals, it's essential to align the decimal points and then perform the division as you would with whole numbers.

In this case, dividing 21.60 by 1.35 gives us an approximate quotient of 16.

Hence, The result of the division 21.60÷1.35 is: 16.

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Answer:

y is -1

x is 5

Step-by-step explanation:

x+2y=3.........equation 1

2x+y=9........equation 2

substitution method

x=3-2y

substitute into equation 2

2(3-2y)+y=9

6-4y+y=9

6-3y=9

-3y=9-6

-3y=3

y=3÷-3

y= -1

substitute into any equation

lets use equation 1 to find x now that we know our y is -1

to find x would be

x+2(-1)=3

x-2=3

x=3+2

x=5

Answer:

5.364

Step-by-step explanation:

5.3635 is the given number, and because the number next to the thousandths is a five, the number in the thousandths place can be rounded to 4.

Answer:

45 minutes?

Step-by-step explanation:

Answer:

1) B, 2) C

===========

As per definition, functions have only one y-value per x-value.

Let's test it with given sets and tables.

A)

x y

0 1

0 2

1 3

2 3

B)

x y

1 0

2 0

3 1

3 2

C)

x y

​​−1 −1

0 −1

2 0

3 2

D)

x y

−1 −1

−1 0

0 2

2 3

1) The set of ordered pairs that represents y as a function of x is;

B; {(−1, 1), (−2, 0), (−3, 4), (−3, 3)}

2) The table that represents y as a function of x is; Table 3

An ordered pair is defined as a composition of the x coordinate called the abscissa and the y coordinate called the ordinate having two values written in a fixed order within parentheses.

1) The first function given as  {(−1, 0), (−1, 1), (−2, 2), (0, 3)} ; This cannot be regarded as a function because the input x = - 1 is repeated with different output values.

The second function {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} ; This cannot be regraded as a function because the input x = -3 is repeated with different output values.

The third function {(0, 0), (1, 1), (2, 2), (3, 3)};  This is a function because each input has unique output values.

The fourth function {(0, 0), (1, 0), (2, 4), (2, 3)} ;  This cannot be regraded as a function because the input x = 2 is repeated with different output values.

2) Table 1 cannot be regarded as a function because the input x = 0 is repeated with different output values.

Table 2 cannot be regarded as a function because the input x = 3 is repeated with different output values.

Table 3 is a Function because each input has unique output values.

Table 4 cannot be regarded as a function because the input x = -1 is repeated with different output values.

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The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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The confidence interval for the proportion of registered voters who believe illegal immigrants who have lived in the United States since they were children should be eligible for legal citizenship is 0.5998 to 0.6602.

To analyze the results of the poll, we can use the given information to calculate the confidence interval.

Given:

- Sample size (n): 904 registered voters

- Proportion who answered "should be" eligible for legal citizenship (p): 63%

- Margin of error (E): 3%

- Confidence level: 95%

To calculate the confidence interval, we can use the formula:

Confidence Interval = p ± (Z * √((p * (1 - p)) / n))

First, let's find the critical value (Z) corresponding to a 95% confidence level. Since the confidence level is 95%, the alpha level (α) is 1 - 0.95 = 0.05. Dividing this by 2 (for a two-tailed test), we have α/2 = 0.025. Looking up this value in the Z-table, we find that the critical value Z is approximately 1.96.

Next, we can substitute the values into the formula and calculate the confidence interval:

Confidence Interval = 0.63 ± (1.96 * √((0.63 * (1 - 0.63)) / 904))

Confidence Interval = 0.63 ± (1.96 * √((0.63 * 0.37) / 904))

Confidence Interval = 0.63 ± (1.96 * √(0.23211 / 904))

Confidence Interval = 0.63 ± (1.96 * 0.0154)

Confidence Interval = 0.63 ± 0.0302

Therefore, the confidence interval for the proportion of registered voters who believe illegal immigrants who have lived in the United States since they were children should be eligible for legal citizenship is approximately 0.5998 to 0.6602.

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Answer:

17.5

Step-by-step explanation:

2.8 times 6.25 equals 17.5

Answer:

x = 10, y = 7.5

Step-by-step explanation:

Given the triangles are similar then the ratios of corresponding sides are equal, that is

\(\frac{AE}{AC}\) = \(\frac{DE}{BC}\), substitute values

\(\frac{x}{4}\) = \(\frac{12.5}{5}\) ( cross- multiply )

5x = 50 ( divide both sides by 5 )

x = 10

and

\(\frac{AD}{AB}\) = \(\frac{DE}{BC}\) , that is

\(\frac{y}{3}\) = \(\frac{12.5}{5}\) ( cross- multiply )

5y = 37.5 ( divide both sides by 5 )

y = 7.5

The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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Answer:

75 minutes

Step-by-step explanation: 750 divided by 10 is 75

7500 minutes or 125 hours..

Answer:

Step-by-step explanation:

x=12wb+rb

probability of rb=5/11

12+11=23

5/23

rb=5/23

Answer:

Y= 3b

Step-by-step explanation:

The most helpful substitution for evaluating the integral is x = 4tanθ.

To determine the most suitable substitution, we examine the integral and consider the trigonometric identities that can simplify it. In this case, the presence of the square root suggests a trigonometric substitution. By comparing the given choices, we can identify that x = 4tanθ is the most beneficial substitution.

Using the substitution x = 4tanθ, we find dx = 4sec^2θdθ. Substituting these expressions into the integral, we obtain ∫(4√√3)dx/(x^2 + 16) = ∫(4√√3)(4sec^2θdθ)/(16tan^2θ + 16). Simplifying further, we have ∫(16√√3sec^2θdθ)/(16(tan^2θ + 1)). Canceling out the common factor of 16, we get ∫(√√3sec^2θdθ)/(tan^2θ + 1).

To simplify the denominator, we recall the trigonometric identity sec^2θ = tan^2θ + 1. Substituting this identity, the integral becomes ∫(√√3sec^2θdθ)/(sec^2θ) = ∫√√3dθ. Integrating this expression yields √√3θ + C, where C is the constant of integration.

Finally, substituting back the original variable, we have √√3θ + C = √√3arctan(x/4) + C as the final result of the integral.

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According to the distance, it will take the jet 1 hour to overtake the small plane.

Let's first calculate the distance traveled by the small plane in the time it takes for the jet to overtake it. Since the small plane is flying for an extra 30 minutes, its travel time is "t + 0.5" hours. Therefore, the distance traveled by the small plane is:

Distance of small plane = Speed of small plane x Time of small plane

Distance of small plane = 240 x (t + 0.5)

Now, let's calculate the distance traveled by the jet in "t" hours:

Distance of jet = Speed of jet x Time of jet

Distance of jet = 360 x t

Since both planes are at the same point at the time of overtaking, we can set the distances traveled by both planes equal to each other:

240 x (t + 0.5) = 360 x t

We can solve for "t" using algebra:

240t + 120 = 360t

120 = 120t

t = 1

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Multiplying 3/8 by the whole part and the fractional part is 21/32.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the whole and fractional part can be 1 3/4.

Therefore, the multiplication by 3/8 will be:

= 3/8 × 1 3/4.

= 3/8 × 7/4

= 21 / 32.

The fraction is 21/32.

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Complete question

Multiply 3/8 by 1 3/4 which depicts the whole part and the fractional part.

The question is incomplete. The complete question is :

George, Matthew and Isabelle invest money in a savings account, which pays compound interest of 3% p.a.

a). George invested £ 4800. Work out the total value of his investment after 5 years.

Solution :

It is given that :

George invested amount of, P = £ 4800

Time of investment, t = 5 years

Rate of interest, r = 3 % p. a.

The total value will be :

\($A=P(1+\frac{r}{100})^t$\)

\($A=4800(1+\frac{3}{100})^5$\)

\($A=4800\times (1.03)^5$\)

\(A = 4800 \times 1.1592\)

   = 5564.16

Therefore the total value after 5 years = £ 5564.16

The graph of the equation is added as an attachment below

The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation.

If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.

We have to write the equation in slope-intercept form

y = mx + c

Recall that the function is given as

y + 6 = 4/5(x + 3)

Open the brackets

y + 6 = 4/5x + 4/5(3)

Evaluate the products

y = 4/5x + 12/5 - 6

Evaluate the like terms

y = 4/5x -18/5

Next, we represent the graph on the coordinate plane using a graphing tool

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The correct answer is c. 7.

In the given code snippet, the variable userText is assigned the value "mississippi". The find() function is then called on userText with the arguments "i" (the character to search for) and 3 (the starting index to begin the search from).

The find() function returns the index of the first occurrence of the specified character after the given starting index. In this case, the search starts from index 3.

The letter "i" first appears at index 1 in the string "mississippi". However, since the search starts from index 3, it skips the initial occurrences of "i" and finds the next occurrence at index 7.

Therefore, the value assigned to x is 7.

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Answer:

(3x+1)(x+3) is the factorised form for the expression.

Step-by-step explanation:

:3

x

2

+

10

x

+

3

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like  

a

x

2

+

b

x

+

c

, we need to think of 2 numbers such that:

N

1

⋅

N

2

=

a

⋅

c

=

3

⋅

3

=

9

and,

N

1

+

N

2

=

b

=

10

After trying out a few numbers we get:

N

1

=

9

and  

N

2

=

1

9

⋅

1

=

9

, and  

9

+

(

1

)

=

10

3

x

2

+

10

x

+

3

=

3

x

2

+

9

x

+

1

x

+

3

=

3

x

(

x

+

3

)

+

1

(

x

+

3

)

(

3

x

+

1

)

(

x

+

3

)

is the factorised form for the expression.

is the factorised form for the expression.