Kate begins solving the equation StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 3) = StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 4). Her work is correct and is shown below. StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 3) = StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 4) 4x – 2 = 3x – 2 When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x ? The equation has infinite solutions. The equation has one solution: x = 0. The equation has one solution: x = StartFraction 4 Over 3 EndFraction.. The equation has no solution.

Answer:

(a) 5

(b) 10

(c) 10

Step-by-step explanation:

There are 20 people who like A or B.  There are 4+6=10 people who like B, so there are 10 people who like A but not B (the region of the Venn diagram that is outside B and inside A).  This answers part b.

Since there are 3 people who like A only, there are 10−3=7 people who like A and C but not B (the intersection of A and C that is outside B).

Next, there are 22 people who like B or C.  There are 4+6=10 people who like B, and 7 people who like A and C but not B.  Therefore, there are 22−10−7=5 people who like C only.  This answers part a.

Finally, there are 7 people who don't like A or C (the region of the diagram that is outside of the circles but inside the rectangle).  And as previously found, there are 5 people who like C only.  So the number of people who don't like A or B (but may or may not like C) is 7+5=12.

Answer:

1

Step-by-step explanation:

The most precise name for the quadrilateral WXYZ is a parallelogram

From the question, we have the following parameters that can be used in our computation:

Quadrilateral WXYZ with vertices W(-3,4), Y(2,4), W(3,-1), and Z(-2,-1)

Next, we plot the vertices W(-3,4), Y(2,4), W(3,-1), and Z(-2,-1) on a graph

See attachment for the graph

From the attached graph, we can see that:

The quadrilateral has a pair of parallel sides

This means that the best name is a parallelogram

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The function y(t) that satisfies the differential equation dy/dt = e^(4t) and the initial condition y(0) = 5 is given by y(t) = (1/4)e^(4t) + 4.

The time when y(t) increases to 100 is approximately t = 1.6583. However, y(t) never drops to 1 as the equation 1 = (1/4)e^(4t) + 4 has no real solutions.

Step-by-Step Explanation:

Given the differential equation dy/dt = e^(4t) and the initial condition y(0) = 5, we need to find the function y(t) that satisfies the differential equation.

Integrate both sides of the differential equation with respect to t to get ∫(dy/dt) = ∫(e^(4t) dt).

Using the chain rule, we can simplify the left-hand side of the equation to get ∫(dy/dt) dt = ∫dy = y + C, where C is the constant of integration.

Integrating the right-hand side with respect to t results in (1/4)e^(4t) + K, where K is another constant of integration. Substituting this into the equation from step 3, we get y + C = (1/4)e^(4t) + K.

Using the initial condition y(0) = 5, we can solve for the constant of integration C: y(0) + C = (1/4)e^(4*0) + K. Simplifying this equation, we get C + K = 5.

Substituting the values of C and K into the equation from step 4, we get y(t) = (1/4)e^(4t) + 4.

To find when y(t) increases to 100, we set the equation from step 6 equal to 100 and solve for t:

100 = (1/4)e^(4t) + 4

(1/4)e^(4t) = 96

e^(4t) = 384

4t = ln(384)

t = ln(384)/4 ≈ 1.6583 (rounded to four decimal places)

To find when y(t) drops to 1, we set the equation from step 6 equal to 1 and solve for t:

1 = (1/4)e^(4t) + 4

(1/4)e^(4t) = -3

e^(4t) = -12

Since e^(4t) is always positive, there are no real values of t that satisfy this equation. Therefore, y(t) never drops to 1.

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Answer:

D 57

Step-by-step explanation:

The value of X

Answer:

5301

Step-by-step explanation:

There are 9 companies that needed to print 589 coupons each. Multiply the two numbers:

9 * 589 = 5301

Answer:

Step-by-step explanation:

\(a) 15*\frac{2}{5}=6\\\\\frac{30}{5}=6\)

Two division equations:

30 ÷ 5 = 6

30 ÷ 6 = 5

\(b) 6*\frac{4}{3}=8\\\\\frac{24}{3}=8\)

Two division equations:

24 ÷ 3 = 8

24 ÷ 8 = 3

\(c) 16*\frac{7}{8}=14\\\\\frac{112}{8}=14\)

Two division equations:

112 ÷ 8 = 14

112 ÷ 14 = 8

Explanation

First, we will have to get the diameters of the circles

A has a diameter of 8 units or a radius of 4 units

B has a diameter of 6 units or a radius of 3 units

Also, we have that Circle A has the equation

For circle B

Thus, we have

Hence, we can establish that the relationship between circles A and B will be:

Circle A was dilated by a factor of 0.75 about the centre (28,4)

The general solution to the recurrence relation for vectors an = 4an-1 is an = c1 × 4n + c2 × n × 4n, and the specific solutions for the given initial conditions are an = 4n - (3/4) × n × 4n when a0 = 1 and a1 = 2, and an = 4n + 2 × n × 4n when a0 = 1 and a1 = 8.

To find the general solution to the recurrence relation an = 4an-1, let's solve it step by step:

Assume the solution has the form an = rn.

Substitute this into the recurrence relation: rn = 4rn-1.

Divide both sides by rn-1: r = 4.

We have a repeated root r = 4.

The general solution is given by an = c1 × 4n + c2 × n × 4n, where c1 and c2 are constants.

Now, let's find the specific solutions for the given initial conditions:

a) When a0 = 1 and a1 = 2:

Substitute these values into the general solution.

Solve the resulting system of equations to find c1 = 1 and c2 = -3/4.

The solution is an = 4n - (3/4) × n × 4n.

b) When a0 = 1 and a1 = 8:

Substitute these values into the general solution.

Solve the resulting system of equations to find c1 = 1 and c2 = 2.

The solution is an = 4n + 2 × n × 4n.

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4 * (13 + 7) -5

4 * 20 - 5 = 80 - 5 = 75

75 / 5 = 15

Step-by-step explanation:

The phrase "4 times 5 less than the sum of 13 and 7" can be written as:

4 * (13 + 7) - 5

which simplifies to:

4 * 20 - 5 = 80 - 5 = 75

The phrase "divided by the difference of 11 and 6" refers to:

(11 - 6) = 5

Therefore, the entire expression can be written as:

75 / 5 = 15

So, "4 times 5 less than the sum of 13 and 7 divided by the difference of 11 and 6" is equal to 15.

a. Rounded to the nearest mile, the distance from New York City to Los Angeles is 2556 miles.
b. Rounded to one decimal place, we can expect to use 82.4 gallons of gas driving from New York to Los Angeles.

a. To convert the distance from kilometers to miles, we can use the given unit fraction: 1 mile ≈ 1.6 kilometers. First, set up the conversion using the given distance:

4090 kilometers × (1 mile / 1.6 kilometers)

The kilometers units will cancel out, leaving the result in miles:

4090 / 1.6 ≈ 2556.25 miles

Rounded to the nearest mile, the distance is approximately 2556 miles.

b. To calculate the number of gallons of gas needed, we can use the car's average of 31 miles per gallon. Set up the conversion using the distance in miles:

2556 miles × (1 gallon / 31 miles)

The miles units will cancel out, leaving the result in gallons:

2556 / 31 ≈ 82.5 gallons

Rounded to one decimal place, you can expect to use approximately 82.5 gallons of gas driving from New York to Los Angeles.

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D. None of these, as neither option B nor option C can be obtained using the Law of Detachment.

The Law of Detachment states that if a conditional statement "if p, then q" is true and p is true, then q must also be true.

Analyzing the given options:

A. The conclusion "There is no school" can be obtained by applying the Law of Detachment to the given information, as it matches the format of the law: "If today is Saturday (p), then there is no school (q)." Since today is Saturday (p), the conclusion that "There is no school" (q) can be derived using the Law of Detachment.

B. The conclusion "He is able to buy a new set of headphones" is not directly obtained by using the Law of Detachment. It involves an additional conditional statement and is not in the form of the given "if p, then q" structure.

C. The conclusion "George lives in both Brick and Ocean County" cannot be derived using the Law of Detachment. It is not in the form of a conditional statement, and there is no given information that connects George's residence to the conditional statement provided. Therefore, D is the right answer. None of them are possible utilizing the Law of Detachment, as neither option B nor option C can be obtained. Therefore, Option D is correct.

The question was incomplete. find the full content below:

Which of the following conclusions is true AND obtained by using the Law of Detachment

A. If today is Saturday, then there is no school.

Today is Saturday.

There is no school.

B. If you work 8 hours, then you'll earn $100.

If you earn $100, you'll be able to buy a new set of headphones.

Jonathan works 8 hours.

He is able to buy a new set of headphones.

C. If a person lives in Long Beach Island, then they live in Ocean County.

Brick is in Ocean County.

George lives in both Brick and Ocean County

D. None of these.

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The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.

What is probability?

To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.

We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.

The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.

So, there are equal chances of both.

Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.

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The estimated relationship may not hold for all levels of TV advertising, and there may be non-linearities or interactions with other variables that should be taken into account in a more sophisticated model.

What is the interpretation of this relationship?

To develop an estimated regression equation to estimate weekly gross revenue with the amount of television advertising as the independent variable, we would need a dataset that includes information on both variables. Assuming we have such a dataset, we could use linear regression to estimate the relationship between the two variables.

The estimated regression equation would take the form:

Weekly Gross Revenue = \(b_0 + b_1\)×Amount of TV Advertising + error

where \(b_0\) is the intercept (the value of weekly gross revenue when the amount of TV advertising is zero), \(b_1\) is the slope (the estimated increase in weekly gross revenue associated with a one unit increase in TV advertising), and error represents the random variation in the relationship between the two variables that is not explained by the model.

The interpretation of the relationship between weekly gross revenue and amount of TV advertising would depend on the sign and magnitude of the slope coefficient

\((b_1)\). If \(b_1\) is positive, it would suggest that an increase in TV advertising is associated with an increase in weekly gross revenue. The magnitude of \(b_1\) would indicate the strength of this relationship - a larger positive value of\(b_1\) would indicate a stronger relationship between TV advertising and weekly gross revenue.

If \(b_1\) is negative, it would suggest that an increase in TV advertising is associated with a decrease in weekly gross revenue. This could occur if the advertising is perceived as irritating or offensive to viewers, leading them to avoid the advertised product or service.

It is important to note that correlation does not imply causation, and there may be other factors that affect weekly gross revenue that are not captured in the model.

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A plane flying just above the equator around the world 3 1/2 times would cover a distance of 4.375 x 10⁴ miles.

If an airplane travels around the world just above the equator once, it covers a distance of 1.25 x 10⁴ miles. To find how many miles it would cover if it flew around the world 3 1/2 times, we need to multiply this distance by 3.5:

1.25 x 10⁴ miles x 3.5 = 4.375 x 10⁴ miles

To understand this calculation, we need to know that 3 1/2 times means 3.5 times. So, we multiply the distance covered in one round of the world by 3.5 to find the total distance covered in 3 1/2 times around the world.

We use standard form to express the answer in a more compact and convenient way, where 4.375 x 10⁴ represents the number 43,750 in scientific notation.

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Answer:

89

Step-by-step explanation:

Toni had 17 points, Effie had 25 points and Linda had 18 points.

The question is asking to find the number of points each girl had in a girl's basketball game. To find out how many points Effie had, you must multiply Toni's points by 3, subtract 8, and then multiply the difference by 2. To find out how many points Linda had, you must add 9 to Toni's points and divide the sum by 3. The given information is that Effie scored 9 more than Toni and Linda combined.

Formula and Calculation:

Toni's Points = x

Effie's Points = 3x-8

Linda's Points = (x+9)/3

Effie scored 9 more than Toni and Linda combined, so:

3x-8 = x+9/3 + 9

2x-8 = x+9

x = 17

Therefore, Toni had 17 points, Effie had 25 points and Linda had 18 points.

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Answer:

please give me the clear photo of questions

Answer:

y=-4x-2

Step-by-step explanation:

Gradient of the given line is -4

Plug m=-4 into the other parallel line

y-2=-4(x--1)

y-2=-4(x+1)

y-2=-4x-4

y=-4x-4+2

y=-4x-2

The probability of rolling a total of 7 on the two dice is 8/63

Probability:

In Mathematics, Probability is a branch that deals with the occurrence of possible outcomes in a random event or experiment. It is also defined as the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of an event is denoted by P(E). And the probability of all the events in the sample space will equal to 1.  

Probability P(E) = No of favorable outcomes /Total No of outcomes  

Here we have,

The probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die, are in the ratio 1: 2: 3: 4: 5: 6  

Let x, 2x, 3x, 4x, 5x, and 6x are the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die [ since they are in ratio 1: 2: 3: 4: 5: 6 ]  

As we know the total events in a probability = 1

=> x + 2x + 3x + 4x + 5x + 6x = 1  

=> 21 x = 1

=> x = 1/21  

From the above calculations,

The probabilities of rolling 1, 2, 3, 4, 5, and 6 are  \(\frac{1}{21} , \frac{2}{21}, \frac{3}{21}, \frac{4}{21}, \frac{5}{21}, \frac{6}{21}\) respectively.  

The possible combinations of two dies that can give a total of 7 are

(1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)

Therefore, the probability of rolling a total of 7 on the two dice

=  the sum of the probabilities of rolling each combination

=  \(\frac{1}{21} . \frac{6}{21} + \frac{2}{21} .\frac{5}{21} + \frac{3}{21} . \frac{4}{21} + \frac{4}{21} . \frac{3}{21} + \frac{5}{21} .\frac{2}{21} + \frac{6}{21} .\frac{1}{21}\)  

=  \(\frac{6}{441} + \frac{10}{441} + \frac{12}{441} + \frac{12}{441} + \frac{10}{441} + \frac{6}{441}\)  

=  \(\frac{56}{441}\)

=  \(\frac{8}{63}\)

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The complete question is

For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die are in the ratio 1:2:3:4:5:6. What is the probability of rolling a total of 7 on the two dice

Answer:

Explanation:

Given the expression;

simplifying;

we have;

Therefore;

These are the four 4th roots of the complex number 16[cos(π) + i sin(π)]. They are evenly spaced along the circumference of the circle with a radius of 4, and the arguments of two successive roots differ by π/2 radians.

To find the 4th roots of the complex number 16[cos(π) + i sin(π)], we can express it in polar form:

16[cos(π) + i sin(π)] = 16e*(iπ)

Now, we can find the 4th roots by taking the 4th root of the magnitude and dividing the argument by 4:

Magnitude of the 4th root = √16 = 4

Argument of the 4th root = π/4 (π units divided by 4)

Now, we can locate the 4th roots on a circle with a center at the pole (origin) and a radius of 4. The arguments of two successive roots will differ by π/2 radians (π units divided by 4) along the circumference of the circle.

Starting from the positive x-axis (real axis) and moving counterclockwise, we can locate the 4th roots as follows:

Root 1: Argument = π/4, located at (4, π/4)

Root 2: Argument = π/4 + π/2 = 3π/4, located at (-4, 3π/4)

Root 3: Argument = π/4 + 2π/2 = 5π/4, located at (-4, 5π/4)

Root 4: Argument = π/4 + 3π/2 = 7π/4, located at (4, 7π/4)

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The chance that a simple random sample of 12 individuals chosen from a population consisting of 6 individuals in each of 4 categories contains equal numbers of individuals in each category is (20^4) / 2704156.

To find the chance that a simple random sample of 12 individuals chosen from a population containing 6 individuals in each of 4 categories (let's denote them as A, B, C, and D) contains an equal number of individuals from each category, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Let's calculate the probability step by step:

1. Determine the favorable outcomes:

  For the sample to contain equal numbers of individuals in each category, we need to select 3 individuals from each category. Since there are 6 individuals in each category, we can choose 3 individuals from each category in (6 choose 3) ways for a total of [(6 choose 3)]^4 favorable outcomes.

2. Determine the total number of possible outcomes:

  We are selecting 12 individuals from the entire population, so the total number of possible outcomes is (24 choose 12) since we have 24 individuals in total to choose from.

3. Calculate the probability:

  The probability is given by the ratio of favorable outcomes to the total number of possible outcomes:

  P(equal numbers) = [(6 choose 3)]^4 / (24 choose 12)

Calculating the values, we have:

(6 choose 3) = (6! / (3! * (6 - 3)!)) = 20

(24 choose 12) = (24! / (12! * (24 - 12)!)) = 2704156

Substituting these values into the probability formula:

P(equal numbers) = (20^4) / 2704156

Simplifying this expression gives us the chance or probability that the sample contains equal numbers of individuals in the four categories.

In conclusion, the chance that a simple random sample of 12 individuals chosen from a population consisting of 6 individuals in each of 4 categories contains equal numbers of individuals in each category is (20^4) / 2704156.

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Answer:

-36

Step-by-step explanation:

4 x -9 = -36

This is how I interpreted the question, feel free to correct me if I am wrong.