Answer the following questions regarding convergence of series. It is possible that the correct answer would be "cannot be determined". (a) Suppse that sum Ak is a convergent series with known sum L Bk a convergent series with known
k=1
sum M. If L < M, does this guarantee that ax < bx for all k > 1? If not, provide a counter example.

If the sum of the roots of a quadratic equation is 1 and the product of the roots is -35/4 and the equation is [tex]4x^2-4x-35=0[/tex] and the roots are 3.5 and -2.5

If the quadratic equation is [tex]ax^2+bx+c=0[/tex]

The sum of the roots = [tex]-\frac{b}{a}[/tex]

The product of the roots = [tex]\frac{c}{a}[/tex]

Sum of the roots = 1 = [tex]-\frac{b}{a}[/tex]

Product of the roots = [tex]-\frac{35}{4}[/tex] = [tex]\frac{c}{a}[/tex]

If we assume a as 1, then the equation comes out to be:

[tex]x^2-x-\frac{35}{4} =0[/tex]

Multiply the equation by 4 to get a simplified equation:

[tex]4x^2-4x-35=0[/tex]

[tex]4x^2[/tex] - 14x + 10x - 35 = 0

2x (2x - 7) + 5 (2x - 7) = 0

(2x - 7)(2x + 5) = 0

x = 3.5 and -2.5

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The mean of the fifth-grade jump distance data set.

To determine the mean of the data set for fifth-grade jump distances, we need the actual data values. Without the specific data set, it is not possible to calculate the mean.

The mean is the sum of all the values in a data set divided by the number of values. Therefore, we would need the individual jump distances for each fifth-grade student to calculate the mean accurately.

Once we have the complete data set, we can add up all the distances and divide by the total number of students to find the mean. Without the specific data, we cannot provide a numerical answer for the mean of the fifth-grade jump distance.

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An expression for the sequence of operations described "Subtract three from the product of seven and eight." is (7 × 8) - 3.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

Expression: (7 × 8) - 3

56 - 3

53

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The main threat to concluding that the tutor was effective in helping students understand confounding and obscuring variables is the issue of 'practice effects'.

Practice effects occur when exposure to specific materials or questions during a study can artificially inflate performance on subsequent measures, such as an exam.

In this case, if the practice questions from the tutor were exactly the same as those on the exam.

Then the students who interacted with the tutor may have had an advantage on the exam .

Due to familiarity with the questions rather than a true understanding of the material.

The use of the same practice questions in the tutor and on the exam .

It represents a potential confounding variable that could affect the interpretation of the results.

It is possible that the tutor may have been effective.

But it is also possible that the practice effect of the repeated questions contributed to the observed improvement in performance.

Future research could use different practice questions in the tutor and on the exam.

Use a different exam altogether to assess performance.

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The expression that shows how many beads are on the necklace in all is:

b + 12.

An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.

In the given question,

To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:

Start with the initial number of beads on the necklace, which is 12.

To this, add the number of beads Josie added, which is b.

Combine the two terms to form the final expression: 12 + b.

Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.

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The average time patients waited in 2014 was approximately 76 minutes, calculated by dividing the 2015 waiting time by 0.89 as patients waited 11% less time in 2015.

Let's call the average time patients waited in 2014 as per Wenford Hospital records "x" (in minutes). According to the problem statement, patients waited 11% less time in 2015 compared to 2014, so,

0.89x = 68

Solving for x,

x = 68 / 0.89

x ≈ 76.4

Therefore, the average time patients waited in 2014 was approximately 76 minutes (rounded to the nearest minute).

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The number of adult tickets purchased that day was 36 if the charge is $3.25 for each adult and $1.50 for each student and 400 people paid $1237

Let the number of adults be x

the number of students be y

Total people = 400

x + y = 400

Total receipts = $1,237

Cost of an adult ticket = $3.25

Cost of a student ticket = $1.50

Cost of x adults tickets = 3.25x

Cost of y student tickets = 1.50y

3.25x + 1.50y = 1237

Multiply the first equation by 1.50

1.50x + 1.50y = 600

Subtract the second and above equation

1.75x = 637

x = 364

364 + y = 400

y = 36

Thus, the number of adult tickets purchased is 36.

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The graph of the exponential function [tex]y = 2^{3x}[/tex] is given as follows:

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The function in this problem is given as follows:

[tex]y = 2^{3x}[/tex]

Hence the parameter values are:

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A figure with slope of consecutive sides -2/3 and 3/2 is a rectangle and it is not a parallelogram.

To prove that it is a parallelogram or a rectangle, we need to show that the opposite sides are parallel and the adjacent sides are perpendicular.

Let's first check if the opposite sides are parallel. The slope of one side is -2/3, and the slope of the adjacent side is 3/2. For opposite sides to be parallel, the slopes must be equal. However, -2/3 and 3/2 are not equal, so we can conclude that the given figure is not a parallelogram.

Now, let's check if the adjacent sides are perpendicular. The product of the slopes of the adjacent sides is

(-2/3) x (3/2) = -1, which is the slope of a line perpendicular to both sides. Since the product of the slopes is -1, we can conclude that the adjacent sides are perpendicular.

Therefore, figure is not a parallelogram, but it is a rectangle.

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Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3 then:

a) Pr(E|F) = 0.6

b) Pr(F|E) = 0.75

c) NO, E and F are not independent.

a) To find Pr(E|F), we use the formula: Pr(E|F) = Pr(EnF)/Pr(F). Substituting the given values, we get Pr(E|F) = 0.3/0.5 = 0.6.

b) Similarly, to find Pr(F|E), we use the formula: Pr(F|E) = Pr(EnF)/Pr(E). Substituting the given values, we get Pr(F|E) = 0.3/0.4 = 0.75.

c) We can check for independence by seeing if Pr(E) = Pr(E|F) or Pr(F) = Pr(F|E). However, since Pr(E) ≠ Pr(E|F) and Pr(F) ≠ Pr(F|E), we can conclude that E and F are not independent.

In other words, the occurrence of one event affects the probability of the other event occurring. Specifically, the fact that Pr(EnF) ≠ Pr(E)Pr(F) indicates that the events are dependent.

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Answer:

Step-by-step explanation:

tried my best as the first two got me stuck

wouldn't recommend trying my answer and Id wait for another answer

Answer: 344cm²

Step-by-step explanation:

7x7=49

49x5=245

3x2=6

49-6=43

245+43=288

5x2=10 10x2=20

5x3=15 15x2=30

288+30+20+6=344

Answer:

It will cost $288 to carpet the living room at $36 per square yard.

Step-by-step explanation:

First, we need to convert the room dimensions to square yards, since the carpet price is given in square yards.

The area of the living room is:

[tex]\sf:\implies 6\: ft \times 12\: ft = 72\: ft^2[/tex]

To convert this to square yards, we divide by 9 (since there are 9 square feet in a square yard):

[tex]\sf:\implies \dfrac{72\: ft^2}{9} = 8\: yards^2[/tex]

So the living room is 8 square yards in area.

To find the cost of carpeting the room, we multiply the area by the cost per square yard:

[tex]\sf:\implies 8\: yards^2 \times \$36/square\: yard = \boxed{\bold{\:\:\$288\:\:}}\:\:\:\green{\checkmark}[/tex]

Therefore, it will cost $288 to carpet the living room at $36 per square yard.

Answer:

275 miles

Step-by-step explanation:

Therefore, the missing value of G is 7.608 cm, which is option A.

If G is two and one-half times smaller than 19.02 cm, we can find the value of G by multiplying 19.02 cm by 2/5, since two and one-half is equal to five halves, or 2/5 when expressed as a fraction.

G = (2/5) x 19.02 cm

Simplifying this expression:

G = 7.608 cm

Therefore, the missing value of G is 7.608 cm, which is option A.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]

A 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.

Let's start by defining some variables. Let "r" represent the radius of the tire and "n" represent the number of revolutions it makes over a fixed distance. We are given that the number of revolutions is inversely proportional to the radius of the tire. This means that as the radius increases, the number of revolutions decreases, and vice versa. We can express this relationship mathematically as follows:

n = k/r

Here, "k" is the constant of variation, which remains the same for any given tire traveling over the same distance. To solve the problem, we need to find the value of "k" first. We know that a 12-inch radius tire makes 100 revolutions to travel a certain distance. Substituting these values into the equation, we get:

100 = k/12

Solving for "k," we get k = 1200. Now we can use this value to find the number of revolutions required by a 16-inch radius tire to travel the same distance:

n = 1200/16 = 75

Therefore, a 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.

In summary, we defined the variables, identified the constant of variation, wrote the equation (n=k/r), found the value of the constant by using the given information, and used it to solve the problem by finding the number of revolutions required by a tire with a different radius.

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There are 252 different combinations of shirts, the correct option is B.

Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:

[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]

There are 252 different combinations, so the correct option is B.

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Answer: C Distribution is symmetric

Step-by-step explanation:

To model the volume of a rectangular prism with length 26cm and width w and height h such that the sum of the width and height is 32cm, we can use the following function:

V(w, h) = 26wh

subject to the constraint:

w + h = 32

We can solve for one of the variables in the constraint equation and substitute it into the volume equation, giving us:

w + h = 32  =>  h = 32 - w

V(w) = 26w(32 - w) = 832w - 26w^2

To find the maximum possible volume, we can take the derivative of this function with respect to w and set it equal to zero

dv/dw= 832 - 52w = 0

Solving for w, we get:

w = 16

Substituting this value back into the constraint equation, we get:

h = 32 - w = 16

Therefore, the maximum possible volume of the prism is:

V(16, 16) = 26(16)(16) = 6656 cubic cm

So the function to model the volume of the rectangular prism is V(w) = 832w - 26w^2, and the maximum possible volume is 6656 cubic cm when the width and height are both 16cm.

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The explicit equation for the nth term of the arithmetic sequence is an = 9 - 2.7n.

What is the implicit equation?

An implicit equation is an equation in which the variables are not explicitly expressed in terms of each other. In other words, the equation does not give a direct formula for one of the variables in terms of the other(s), but rather relates the variables through some function or equation.

What is the explicit equation?

An explicit equation is an equation in which one variable is expressed directly in terms of the other(s). In other words, the equation gives a formula for one of the variables in terms of the other(s).

According to the given information:

the first term of the sequence is a1 = 6.3, and the common difference between consecutive terms is d = -2.7 (since we subtract 2.7 from each term to get to the next term). Therefore, the explicit equation for the nth term of the sequence is:

an = 6.3 + (n - 1)(-2.7)

Simplifying this expression, we get:

an = 6.3 - 2.7n + 2.7

an = 9 - 2.7n

So the correct equation for the nth term of the arithmetic sequence 6.3, 3.6, 0.9, -1.8, -4.5, ... is:

an = 9 - 2.7n

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Since the population standard deviation is unknown, we use a t-distribution to find the critical value. The degrees of freedom for the t-distribution is n-1, where n is the sample size. In this case, n = 7, so the degrees of freedom is 7-1 = 6. The critical value for a t-distribution with 6 degrees of freedom and a significance level of α = 0.200 (two-tailed) can be found using a t-table or calculator. The critical value is approximately ±1.94.

Yermin's point is the best approximation of the square root of 0.50.

To know whose point is the best approximation of the square root of 0.50 on a number line. We have the points plotted by Pedro, Lena, Harriet, and Yermin.

Step 1: Calculate the square root of 0.50.
[tex]\sqrt{0.50} = 0.707[/tex]

Step 2: Compare the plotted points to the calculated square root value.
Pedro: Between 0.2 and 0.3
Lena: Between 0.4 and 0.5
Harriet: At 0.5
Yermin: Just to the right of 0.7

Step 3: Determine the closest approximation.
Yermin's point (just to the right of 0.7) is the closest to the calculated value of 0.707.

Your answer: Yermin's point is the best approximation of the square root of 0.50.

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The Equation of the line which is parallel to the line "y = 3x + 6", and also passes through (4,7) is "y = 3x - 5".

In order to find an equation of a line which passes through point (4,7) and is parallel to line "y = 3x + 6", we use the fact that parallel lines have the same slope.

The given line ""y = 3x + 6" has a slope of 3,

So, the "parallel-line" we want to find must also have a slope of 3.

Now, by using the "point-slope" form of the equation of a line, which is : y - y₁ = m(x - x₁),

where m is slope and (x₁, y₁) is a point on the line,

So, we substitute "m = 3" and (x₁, y₁) = (4,7) to get:

⇒ y - 7 = 3(x - 4),

⇒ y - 7 = 3x - 12,

⇒ y = 3x - 5

Therefore, the equation of the required line is y = 3x - 5.

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If the cake is in the shape of a rectangular prism, the total surface area of the cake that will be covered in frosting is 314 sq. inches.

To find the total surface area of the cake that will be covered in frosting, we need to calculate the area of all sides except the bottom. A rectangular prism has 6 sides, and we will be considering 5 of them.

Surface area of top: length × width = 13 × 8 = 104 sq. inches
Surface area of front: length × height = 13 × 5 = 65 sq. inches
Surface area of back: length × height = 13 × 5 = 65 sq. inches
Surface area of left side: width × height = 8 × 5 = 40 sq. inches
Surface area of right side: width × height = 8 × 5 = 40 sq. inches

Now, we will sum the areas of all these sides:
104 + 65 + 65 + 40 + 40 = 314 sq. inches

So, the total surface area of the cake that will be covered in frosting is 314 sq. inches. None of the provided options match this answer, so it is important to double-check the question for any discrepancies.

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Using the given function, we can plug in x=3 and t=5 to find the concentration of the drug in the blood:

C = f(x,t) = 26te^-(5-x)
C = f(3,5) = 26(5)e^-(5-3)
C = f(3,5) = 130e^-2

Using a calculator, we can simplify this to:

C = f(3,5) ≈ 32.22 mg/liter

Therefore, the concentration of the drug in the blood 3 hours after injection with a dosage of 5 mg is approximately 32.22 mg/liter.
Hi! To find the concentration C at f(3,5), you'll need to plug in the values for x and t into the given function f(x,t) = 26te^-(5-x).

So, f(3,5) = 26(5)e^-(5-3) = 130e^(-2).

Now, calculate the exponential value: e^(-2) ≈ 0.1353.

Finally, multiply this value by 130: 130 * 0.1353 ≈ 17.589.

Thus, f(3,5) = 17.589 mg/liter (rounded to 3 decimal places).

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The sum of terms 8 to 30 in the arithmetic series is -826.

In an arithmetic series, the nth term is given by the formula an = a1 + (n-1)d, where a1 is the first term and d is the common difference between terms.

We are given that a8 = 1 and a30 = -43. Using the formula above, we can write:

a8 = a1 + 7d = 1 (1)

a30 = a1 + 29d = -43 (2)

Subtracting equation (1) from equation (2), we get:

22d = -44

d = -2

Substituting d = -2 into equation (1) and solving for a1, we get:

a1 = 15

Now we can use the formula for the sum of an arithmetic series to find the sum of terms 8 to 30:

S = (n/2)(a1 + an)

S = (23/2)(15 + (-43))

S = -826

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The system of equations is.

x + y = 80

12x + 10y = 900

And the solutions are y = 30 and x = 50

Let's define the two variables:

x = number of calculators.

y = number of calendars.

With the given information we can write two equations, then the system will be:

x + y = 80

12x + 10y = 900

Now let's solve it.

We can isolate x on the first equation to get:

x = 80 - y

Replace that in the other equation to get:

12*(80 - y) + 10y = 900

-2y = 900 - 960

-2y = -60

y = -60/-2 = 30

Then x = 50

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Answer:

If Mohal waits on 16 tables, he can expect to earn $25 wages + ($15 tips x 16 tables) = $265 in a day.

If Mohal waits on 1 table, he can expect to earn $25 wages + ($15 tips x 1 table) = $40 in a day.

The correct arrangement of problem is explained below and their solution are as follows:

(1) Zaira will arrive at her grandmother's house at 9:00 am.

(2) The total distance covered by bus is 207.5 km.

(3) The average-speed of the train was 28 km/h.

Part (1) : The Problem is : Zaira goes to her grandmother's house. If she leaves home at 6:00 in the morning, she cycles 30 km at a steady speed of 10 km. What time will she arrive?

Solution:

Zaira cycles at a steady speed of 10 km, she will cover the distance of 30 km in 30/10 = 3 hours.

So, she will arrive at her grandmother's house at 6:00 + 3:00 = 9:00 am.

Part (2) : Problem : A bus had an average speed of 65 kph for 1.5 hours in the morning. It had average speed of 55 kph for 2 hours in afternoon. What was total distance covered by bus?

Solution:

The distance covered by the bus in the morning can be calculated as:

Distance = Speed × Time = 65 kph × 1.5 hours = 97.5 km,

The distance covered in the afternoon can be calculated as:

Distance = Speed × Time = 55 kph × 2 hours = 110 km

So, total-distance covered by bus is = 97.5 km + 110 km = 207.5 km.

Part (3) : Problem : A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. The distance between the two stations is 14 km. What was  average speed of train?

Solution:

The time taken by the train to cover the distance of 14 km can be calculated as:

Time = Arrival Time - Departure Time = 9:30 am - 9:00 am = 0.5 hours

The average speed of the train = Distance/Time = 14 km/0.5 hours = 28 km/h;

Therefore, the average speed of the train was 28 km/h.

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The given question is incomplete, the complete question is

Directions: Arrange the sentences in the box to form a problem. Then solve each problem.

(1) If she leaves home at 6:00 in the morning

What time will she arrive?

Zaira goes to her grandmother's house

She cycles 30 km at a steady speed of 10 km

(2) I had an average speed of 55 kph for 2 hours in the afternoon

What was the total distance covered by the bus

A bus had an average speed of 65 kph for 1. 5 hours in the morning.

(3) What was the average speed of the train?

The distance between the two stations is 14 km

A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. ​