Caroline has a mass of 41,390,000 and her baby sister has a mass of 3,415 grams.what is their total mass 8n kilograms

Answer:

No, q=15 is not a solution to the inequality.

Step-by-step explanation:

As given, q=15. So, substituting is the best way to solve this problem.

Step 1: Substitute

[tex]\frac{15}{5}=3[/tex]

[tex]15-20=-5[/tex]

Step 2: Substitute values into inequality

[tex]3 < -5[/tex]

Equation is false since 3 is a bigger value than -5.

Hope this helps ya!

The number c that satisfies the conclusion of the Mean Value Theorem for the function f(x) = x + 3/x on the interval [1, 14] is approximately c = 3.75.

To find the number c that satisfies the conclusion of the Mean Value Theorem for the function f(x) = x + 3/x on the interval [1, 14], follow these steps:

1. Verify the conditions of the Mean Value Theorem:
  The function f(x) = x + 3/x is continuous on the closed interval [1, 14] and differentiable on the open interval (1, 14).

2. Calculate the average rate of change of the function on the interval:
  f(14) = 14 + 3/14 ≈ 14.214
  f(1) = 1 + 3/1 = 4
  Average rate of change = (f(14) - f(1)) / (14 - 1) ≈ (14.214 - 4) / 13 ≈ 0.786

3. Differentiate the function to find the instantaneous rate of change:
  f'(x) = 1 - 3/x²

4. Set f'(x) equal to the average rate of change and solve for x:
  1 - 3/x² = 0.786
  x² = 3 / (1 - 0.786)
  x² ≈ 14.056
  x ≈ √14.056 ≈ 3.75

The number c that satisfies the conclusion of the Mean Value Theorem for the function f(x) = x + 3/x on the interval [1, 14] is approximately c = 3.75.

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The equation for calculating the number of pairwise comparisons in a pairwise ranking matrix is: (n*(n-1))/2 where n is the number of items being compared in the matrix.

A pairwise ranking matrix is a tool that is used to rank items on the basis of pair-wise comparisons of the items. In order to find out the number of pairwise comparisons in such a matrix, one needs to use the following formula:(n*(n-1))/2where n is the number of items being compared in the matrix.

The formula works on the principle that every item in the matrix needs to be compared with every other item, but each comparison needs to be done only once. This is why the formula divides the total number of comparisons by two.

Therefore, the equation is: (n*(n-1))/2


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Answer:

diameter = 34 radius = 17

Step-by-step explanation:

Look at the line in the middle of the circle that is the diameter, diameter is a straight line passing from side to side through the center of a circle.

radius is the distance from the center of the circle to any point on its circumference.

The value for a is 1 and the remainder when P(x) is divided by x - 1 is 2.

What is polynomial remainder theorem?

It states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r).

The divisor in this case is x - a, where "a" is the value we need to determine.

We can see that the given polynomial 2x³ + 5x² - 12x + 9 + x - 3 has a term of x in addition to the other terms. This means that the divisor must also have a term of x in it.

So, we can write the divisor as x - a and set x - a = 0 to solve for "a":

x - a = 0

=> x = a

Therefore, "a" must be equal to 1 since there is a term of x in the polynomial.

To find the remainder, we need to evaluate P(a) where P(x) = 2x³ + 5x² - 12x + 9 + x - 3 and a = 1.

P(a) = 2(1)³ + 5(1)² - 12(1) + 9 + (1) - 3 = 2 + 5 - 12 + 9 + 1 - 3 = 2

So, the remainder when P(x) is divided by x - 1 is 2.

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Answer:

Step-by-step explanation:

First, I believe you would go in and mulitiply that 3 and the 1/6 and from there we will get 0.5. Next you are going to add the 2/5 to that 0.5 and you will get 0.9.

Answer: 0.9

250 is the total surface area of the solid.

How do you determine surface area?

The whole surface of a three-dimensional form is referred to as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face.

                         Instead, you may write out the cuboid's length, width, and height and apply the formula surface area (SA)=2lw+2lh+2hw.

Each side of a cube with side length = 5  has an area of 25; the overall area is 6 x 25 = 150

A cube with sides of length 5 has an area of 25 on each side, making its overall area 6 x 25 or 150.

Both have a combined area of 150 + 150 = 300

300 - 25 - 25 = 250 is the result from each of the two cubes.

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Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 7 !

__________________

hope it helps ⸙

Answer:

1500 g

Step-by-step explanation:

part a) is correct

part b)
The ratio of syrup to oats for one flapjack is 1:4

That means for each g of syrup you will require 4 g of oats

For 12 flapjacks you require 250 g

Therefore quantity of oats needed for 12 flapjacks = 250 x 4 = 1000 g

If you were to make 18 flapjacks then you would need 18/12 x quantity needed for 12 flapjacks

18/12 = 3/2  (dividing numerator and denominator by 6)

Quantity of oats needed for 18 flapjacks
= 18/12 x 1000

= 3/ 2 x 1000
= 3 x 500
= 1500 g

The test static for sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago is 0.2377.

A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.

In order to determine whether to accept or reject your null hypothesis, the test statistic is utilised to calculate the p value of your findings.

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago.

In a sample of 50 women, 48 women said that they had less leisure time than they

had 10 years ago.

p-hat men:: 44/50 = 0.22

p-hat women:: 48/50 = 0.24

Test Stat:

z(0.24-0.22) =[tex]\frac{0.02}{\sqrt{[(0.22*0.78/50)+(0.24*0.76/50)]} }[/tex] = 0.2377

At [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women

[tex]p-value = 2*P(z > 0.2377) = 0.8121[/tex]

Since the p-value is greater than 5%, fail to reject H.

H: p(men)-p(women) = 0

Ha: p(men)-p(women) # 0 = .05, is there a difference in the proportions between the men and women

p-value = 2*P(z > 0.2377) = 0.8121

Since the p-value is greater than 5%, fail to reject H.

H: p(men)-p(women) = 0

Ha: p(men)-p(women) # 0

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Complete question:

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. What is the test statistic? At  [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women?

Answer:

Let's call the length of the hypotenuse SD as x.

Since the altitude from T to SD divides SD into two parts, let the length of the shorter part be y. Then the length of the longer part is x-y.

Using similar triangles, we have:

TU/TS = ST/TD

Substituting the values we have:

TU/(3√5) = √5/UD

TU = (3/5)UD

Using the Pythagorean theorem in triangle TUS, we have:

TU² + (3√5)² = TS²

(3/5 UD)² + 45 = ST²

9/25 UD² + 45 = ST²

Using the Pythagorean theorem in triangle TUD, we have:

TU² + UD² = TD²

(3/5 UD)² + UD² = x²

9/25 UD² + UD² = x²

34/25 UD² = x²

UD² = (25/34)x²

Substituting the value of UD² in the equation ST² = 9/25 UD² + 45, we get:

ST² = 9/25 (25/34)x² + 45

ST² = 45/34 x² + 45

Since y = x-y-1, we have y = (x-1)/2.

Using the Pythagorean theorem in triangle TUD, we have:

(1/4) (x-1)² + UD² = x²

(1/4) (x² - 2x + 1) + (25/34)x² = x²

(1/4)(x²) + (25/34)x² - (1/2)x + (1/4) = 0

(59/68)x² - (1/2)x + (1/4) = 0

Using the quadratic formula, we get:

x = [1/2 ± √(1/4 - 4(59/68)(1/4))]/(2(59/68))

x = [1/2 ± (3√34)/17]/(59/34)

x = 17/59 ± 6√34/59

Since x is the hypotenuse SD, we have:

UD² = (25/34) x²

UD² = (25/34) [(17/59 ± 6√34/59)²]

UD² = 136/59 ± 204√34/295

Therefore, the exact lengths of the two parts of the hypotenuse are:

SD = x = 17/59 ± 6√34/59

SU = x-y = (x-1)/2 = 8/59 ± 3√34/59

UD = y = (x-1)/2 = 8/59 ± 3√34/59

TU = (3/5) UD = (3/5) [8/59 ± 3√34/59] = 24/295 ± 9√34/295

ST² = 45/34 x² + 45 = 45/34 [(17/59 ± 6√34/59)²] + 45

ST = √[45/34 [(17/59 ± 6√34/59)²] + 45]

Answer: (-3,-2)

Step-by-step explanation:

y²+2y+11 = 5-3y

y^2+2y+11-5+3y =0

y^2+5y+6=0

y^2+3y+2y+6=0

y(y+3)+2(y+3)=0

(y+3)(y+2)=0

y= -3, -2

All you do is plug in the x value to the equation

Hope it helps:)

The numbers that will round to 19 when rounded to the nearest whole number are 19.46 and 19.91.

To round a number to the nearest whole number, we look at the decimal part of the number. If it is less than 0.5, we round down to the nearest integer. If it is greater than or equal to 0.5, we round up to the nearest integer.

For the given set of numbers, we can round them to the nearest whole number and check which ones round to 19:

19.46 rounds up to 19

18.48 rounds down to 18

19.91 rounds up to 20

18.82 rounds up to 19

19.33 rounds up to 19

Therefore, the numbers that round to 19 when rounded to the nearest whole number are 19.46 and 19.33.

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The answer to subtracting the two polynomials is 2x2 - 10x - 7.  The process of subtracting polynomials is like that of subtracting any other type of numerical expression.

Polynomials are mathematical expressions consisting of variables, coefficients, and exponents. They are used to represent a variety of functions, such as polynomial equations, rational equations, and trigonometric functions.

In this case, our like terms are 2x2 and 4x2, and -6x and -4x, and -4 and +3. We begin by subtracting the coefficients of the like terms. We subtract the coefficient of the term with the highest power first. In this case, that is 2x2 and 4x2, we subtract 2 from 4 to get 2. Next, we subtract the coefficients of the terms with the second highest power. This is -6x and -4x, so we subtract -6 from -4 to get -2. Thus, our answer now reads 2x2 -2x.

Finally, we subtract the coefficients of the terms with the lowest power. This is -4 and +3, so we subtract -4 from 3 to get -7. Thus, our answer now reads 2x2 -2x -7.

This answer can then be placed in the proper position on the grid.

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The sector area of a circle is quadrupled when the radius is doubled. When the radius is doubled, the arc length of a circle is also doubled. This happens because the sector area and arc length are both dependent on the radius of a circle. Therefore, any change in the radius of a circle affects both its sector area and arc length.

Let us understand both these concepts in detail:

Sector area of a circle: A sector is a region of a circle, and the area enclosed by two radii and an arc is known as a sector area. The formula for the sector area of a circle is given by:

Sector Area = (θ/360)πr²

where θ is the central angle in degrees,

r is the radius of the circle,

and is a constant value.

If we double the radius of a circle, the sector area increases by a factor of 4. This is because the sector area is directly proportional to the square of the radius.

Hence, doubling the radius of a circle results in an increase in the sector area by a factor of 22 (four).

Arc length of a circle: The length of an arc is the distance between two points on a circle. The formula for the arc length of a circle is given:

Arc Length = (θ/360)2πr

where θ is the central angle in degrees,

r is the radius of the circle,

and 2pie is a constant value.

If we double the radius of a circle, the arc length also doubles.

This is because the arc length is directly proportional to the radius.

Hence, doubling the radius of a circle results in an increase in the arc length by a factor of 2.

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Answer:10

Step-by-step explanation: 14/4= 3.5, 35/3.5=10

As a result, we should not be concerned that the sample does not accurately reflect the population.

We can learn more about average, population, and sample.

What is the population?

The entire group of people, items, or objects that we want to draw a conclusion about is known as the population. For example, if we want to learn about the average age of people in the United States, then the entire population is every individual in the United States.

What is a sample?

A smaller group of individuals, objects, or items that are selected from the population is known as a sample. A random sample is a sample in which every individual in the population has an equal chance of being selected for the sample.

What is an average?

A statistic that summarizes the central tendency of a group of numbers is known as an average.

The mean is the most commonly used average in statistics. The mean is calculated by adding up all the numbers in a group and then dividing by the number of numbers in the group. If we want to learn about the average salary of all teachers in the United States, we'd have to sample every teacher. That's not a feasible option. Instead, we take a smaller sample, which should be representative of the population, and then use the information gathered from that sample to make predictions about the population as a whole.

If we assume that the five teachers in the example are a random sample of all teachers in the United States, then we can conclude that the average salary of all teachers in the United States is around $49,000. As a result, we should not be concerned that the sample does not accurately reflect the population.

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The 12 of each type of the ring would give max profit for the company.

Let x = number of VIP rings: let y = number of SST rings

:

The total production inequality;

x + y =< 24

y = 24 - x; arranged to plot graph (purple)

:

The labor inequality;

3x + 2y =< 60

2y = 60 - 3x

y = 60/2 - (3/2)x

y = 30 - 1.5x; arranged to plot the graph (red).

From the graph, the 3 corners of the area of feasibility (at or below the lines whichever is lower):

: x/y;.....profit on each type;... total profit

0,24; 40(0) + 35(24) = 0 + 840 = $840

12,12; 40(12) + 35(12) = 480 + 420 = $900

20,0; 40(20) + 35(0) = 800 + 35(0) = $800.

Therefore, the 12 of each type of the ring would give max profit for the company.

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Answer:

Eighty biscuits.

Step-by-step explanation:

We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits

[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]

We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.

[tex]Biscuits=4*20=80[/tex]

Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.

[tex]Flour:\\1000-4(180) = 280g[/tex]

After making 4 servings we still have 280g of flour left.

The weight range within which the middle 95% of all miniature Tootsie Rolls will fall is approximately between 3.04 grams and 3.56 grams.

Since the weight of miniature Tootsie Rolls is normally distributed with a mean of 3.30 grams and a standard deviation of 0.13 grams, we can use the standard normal distribution to find the weight range within which the middle 95% of all miniature Tootsie Rolls will fall.

We need to find the z-scores that correspond to the middle 95% of the normal distribution. The area between the two z-scores will be 0.95. Using a standard normal distribution table or calculator, we can find that the z-scores that correspond to the middle 95% of the distribution are -1.96 and 1.96.

We can use the formula z = (x - μ) / σ to find the corresponding weight values for these z-scores. Substituting -1.96 for z and solving for x, we get:

-1.96 = (x - 3.30) / 0.13

x = 3.04

Similarly, substituting 1.96 for z and solving for x, we get:

1.96 = (x - 3.30) / 0.13

x = 3.56

Therefore, the weight range within which the middle 95% of all miniature Tootsie Rolls will fall is approximately between 3.04 grams and 3.56 grams.

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The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

The solution to the quadratic equation is determined as follows;

2x² + 12x - 3 = 0

2x² + 12x = 3

divide through by 2

x² + 6x = ³/₂

take half of coefficient of x, square it and add it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

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The roots of the given quadratic functions are -

x = (- 6 ± √42)/2.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that Inga is solving the quadratic equation -

2x² + 12x - 3 = 0

The quadratic equation is given as -

2x² + 12x - 3 = 0

We can writ its solution as -

x = {- 12 ± √(144 + 24)}/4

x = (- 12 ± √168)/4

x = (- 12 ± 2√42)/4

x = (- 6 ± √42)/2

Therefore, the roots of the given quadratic functions are -

x = (- 6 ± √42)/2.

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The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.

Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:

P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]

P(X>=10) = 0.719

Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.

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⇒First take out the highest common factor 2 form the quadratic equation and divide each and every term of that equation by that common factor.

⇒Factorise the equation and equate the factors of the equation to 0 and solve for the unknown variable x.

⇒Below are the steps on solving for the unknown variable.

[tex]2(x^{2} -14x+49)=0 \\\frac{2(x^{2} -14x+49)}{2} =\frac{0}{2} \\x^{2} -14x+49=0\\(x-7)(x-7)=0\\x-7=0\\x=7[/tex]

The probability that the waves are turbulent given that the water is cold is approximately 0.4353.

Suppose the water has a 0.51 chance of being cold and the waves have a 0.57 chance of being turbulent. In the same way, suppose that given the waves are turbulent, the water has a 0.39 chance of being cold. What is the chance that the waves are turbulent given that the water is cold?

To answer the question, we must use Bayes' theorem :P (A|B) = P (B|A) × P (A) / P (B)

Where A and B are arbitrary events. P (A) and P (B) are the probabilities of events A and B happening separately.

P (B|A) is the probability of event B happening, given that event A has happened. P (A|B) is the probability of event A happening, given that event B has happened.

We must find P (waves are turbulent | water is cold), which is P (B|A). We know that:

P (water is cold) = 0.51

P(waves are turbulent) = 0.57

P(water is cold | waves are turbulent) = 0.39

Using Bayes' theorem, we can calculate P (waves are turbulent | water is cold) as:

P (waves are turbulent | water is cold) = P (water is cold | waves are turbulent) × P (waves are turbulent) / P (water is cold)

P(waves are turbulent | water is cold) = 0.39 × 0.57 / 0.51

P (waves are turbulent | water is cold) = 0.4353 (rounded to the nearest millionth)

Therefore, the probability that the waves are turbulent given that the water is cold is approximately 0.4353.

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Therefore, the formula for T1 is T1(x1,x2) =[tex](24x1/5 - 18x2/5, -36x1/5 + 6x2/5).[/tex]

Given T is a linear transformation from R2 into R2, we need to show that T is invertible and find a formula for T1.T(x1,x2) = (3x1-9x2, -3x1+5x2)Let A be the standard matrix for T, then we have to find the determinant of A as it will help us determine whether T is invertible or not.The standard matrix for T is given as :A = [3 -9-3 5]Now, to calculate the determinant of A, we have to use the formula as:det(A) = ad - bcwhere a = 3, b = -9, c = -3, d = 5Now, substituting the values of a, b, c, d, we get,det(A) = (3 × 5) - (-9 × -3) = 15 - 27= -12Since the determinant of A is not equal to zero, therefore, T is invertible.

For finding the formula for T1, we need to calculate the inverse of T. We can find the inverse of T as:[tex][A|I] → [I|A-1][/tex]Now, appending the identity matrix to A, we get the following matrix.[A|I] = [tex][3 -9|1 0-3 5|0 1]→ [I|A-1] = [1 3/5|-9/5-3/5][/tex]

Therefore, the inverse of T is T-1(x1,x2) = (3x1/5 + 9x2/5, -9x1/5 - 3x2/5)Now, we can find T1 by substituting T-1 in T, we get,T1(x1,x2) = T(T-1(x1,x2)) =[tex]T(3x1/5 + 9x2/5, -9x1/5 - 3x2/5) = (3((3x1/5 + 9x2/5)) - 9(-9x1/5 - 3x2/5), -3((3x1/5 + 9x2/5)) + 5(-9x1/5 - 3x2/5)) = (24x1/5 - 18x2/5, -36x1/5 + 6x2/5)[/tex]

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Answer: 4/9 ≅ 0.4444444 = four ninths. ... Then simplify the result to the lowest terms or a mixed number.

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.

given

The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.

To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.

As a result, we have:

sin 30° = (6/2x)

Adding two times to both sides:

2x * sin 30° = 6

Using sin 30°, which has a value of 0.5:

x = (6/(2 * 0.5)) = 6/1 = 6

Consequently, the side YZ is 6 units long.

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

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a) The sum of the given series is 7 / (1 + 2z)

b) The domain of convergence is (-∞, -1/2) U (1/2, ∞).

The given series can be expressed as

7 – 14z + 28z^2 - 56z^3 + ...

This is a geometric series with first term (a) = 7 and common ratio (r) = -2z. The formula for the sum of an infinite geometric series is

sum = a / (1 - r)

Substituting the values of a and r, we get

sum = 7 / (1 + 2z)

So, the sum of the given series is 7 / (1 + 2z).

For the series to converge, the absolute value of the common ratio must be less than 1. That is,

|r| = |−2z| < 1

Simplifying this inequality, we get

1/2 < |z|

So, the domain of convergence of the given series is (-∞, -1/2) U (1/2, ∞).

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Julie hourly rate of pay from the given different rates of the day with total earning of $612 is equal to $12per hour.

Total number of hours Julie works in a week is equal to,

On Sunday = 10 hours

On Monday = 10 hours

On Tuesday = 7 hours

On Wednesday = 10 hours

On Thursday = 7 hours

On Friday = 7 hours

On Saturday = 0 hours

Total hours worked in whole week is

= 10 + 10 + 7 + 10 + 7 + 7 + 0

= 51 hours

Total money earned by Julie in whole week = $612

Hourly rate of pay = Weekly earnings / Total hours worked

Substitute the value we have,

⇒ Hourly rate of pay = $612 / 51 hours

⇒ Hourly rate of pay = $12 per hour

Therefore, Julie's hourly rate of pay is $12 per hour.

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The above question is incomplete , the complete question is:

Julie works Sunday, Monday, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612. What is Julie's hourly rate of pay, in dollars?