Factor completely

72w^2-50w^4

The populations of Anville and Brinker will become equal in around 15.23 years.

Let's represent the current population of Anville by A and the current population of Brinker by B. Then we have:

A = 21000

B = 9000

Let t be the number of years we want to find. Then the population of Anville after t years will be:

A_t = A * (1 + 0.07)ᵗ

And the population of Brinker after t years will be:

B_t = B * (1 + 0.08)ᵗ

We want to find the value of t such that A_t = B_t. Substituting the above equations, we get:

A * (1 + 0.07)ᵗ = B * (1 + 0.08)ᵗ

Dividing both sides by A and B, respectively, we get:

(1 + 0.07)ᵗ = (1 + 0.08)ᵗ * (B/A)

Taking the natural logarithm of both sides, we get:

t * ln(1 + 0.07) = t * ln(1 + 0.08) + ln(B/A)

Simplifying and solving for t, we get:

t = ln(B/A) / (ln(1 + 0.07) - ln(1 + 0.08))

Substituting the given values of A and B, we get:

t = ln(9000/21000) / (ln(1 + 0.07) - ln(1 + 0.08)) ≈ 15.23

Therefore, it will take approximately 15.23 years for the populations of the two towns to be equal.

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In a reaction that is first order reaction with respect to x and first order with respect to y, the change will have no effect overall on the rate is doubling [x]. The answer is option (b).

If the reaction is first order with respect to x and first order with respect to y, then the rate equation is given by Rate = k [x]^1 [y]^1 = k [x][y].Option (a) Doubling [x] and doubling [y] will increase the rate by a factor of Option (c) Quadrupling [y] will increase the rate by a factor of 4 x 4 = 16.

Option (d) Halving [x] and doubling [y] will have no overall effect on the rate since rate will increase by a factor of 2/1 = 2 and then decrease by a factor of 1/2 = 0.5, for an overall effect of 1. Option (e) Halving [x] and halving [y] will decrease the rate by a factor of 2 x 2 = 4.

Thus, option (b) Doubling [x] is the correct answer. If the concentration of a reactant is tripled and the rate increases by a factor of nine, then we can write k [x][y] = 9 k [x (3)][y]k = 9 k / 3 = 3 k. Since the concentration of x is raised to the power of 1, the order with respect to that reactant is 1.

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Answer:

Median = 42
LQ = 33
UQ = 52

Step-by-step explanation:

median is given by the term that divides the groups in two equally quantities. In this case is (n+1)/2 = (13+1)/2 = 14/2 = 7

the 7th term is: 42
(notice this means 6 values are below 42 and 6 values are above 42, the definition of a median)

the first (lower) quartile is given then by the (n+1)/4 value

(13+1)/4=3.5, this is the half between 3th and 4th terms.

since the term is the same (3th value is 33 and 4th value is 33)

LQ=33
(25% of the values are below 33)

for the upper quartile the value represents the top 75%, this is given by

3(13+1)/4 = 10.5

this is the half between 10th and 11th terms

(51+53)/2=52

(25% of the values are above 52)

Answer:

D is the only possible answer

Answer: D. Population: all the first-year students at the university

Sample: a group of 185 incoming first-year students

Conclusion: The reason for the majority of the students to choose the university was affordability.

Answer:

D. Population: all the first-year students at the university

Sample: a group of 185 incoming first-year students

Conclusion: The reason for the majority of the students to choose the university was affordability..

Therefore, any of these two points lies on the circle represented by the equation. [tex](x - 3)^2 + (y+4)^2=6^2.[/tex]

A circle is a geometric shape that consists of all the points that are a fixed distance, called the radius, from a given point, called the center. The distance from the center to any point on the circle is always the same. A circle can also be defined as the set of points in a plane that are equidistant from a given point, which is the center of the circle. Circles are often studied in geometry and have a number of important properties, such as their circumference, area, and diameter. They are also widely used in mathematics, physics, and engineering, and have many practical applications in fields such as architecture, art, and design.

by the question.

The equation of the circle in standard form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is the radius.

Comparing this with the given equation:

[tex](x - 3)^2 + (y + 4)^2 = 6^2[/tex]

we can see that the center of the circle is at point (3, -4) and the radius is 6.

To find a point on the circle, we can substitute any value for x or y and solve for the other variable. For example, let's choose x = 0:

[tex](0 - 3)^2 + (y + 4)^2 = 6^2[/tex]

[tex]9 + (y + 4)^2 = 36[/tex]

[tex](y + 4)^2 = 27[/tex]

[tex]y + 4=±\sqrt{27}[/tex]

[tex]y = -4±\sqrt{27}[/tex]

So, the two points on the circle are:

(0, -4 + √27) and (0, -4 - √27)

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Option (c) is true i.e. y is not a function of x, since the x-values do not correspond to exactly (precisely) one y-value.

A function in mathematics from a set X to a set Y allocates exactly (precisely) one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The items that make up a set are referred to as its elements (or members), and the set is said to contain the elements when they are claimed to belong to it.

The mapping shows a relationship between x and y in this mapping is y is not a function of x, since the x-values do not correspond to exactly one y-value.

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The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.

To determine whether the medication affects performance, we can perform a one-sample t-test with the following hypotheses:

Null hypothesis: The mean score for the population (μ) is 64.

Alternative hypothesis: The mean score for the population (μ) is less than 64.

We will use a significance level of α = 0.1.

First, we need to compute the t-statistic:

t = (M - μ) / (s / sqrt(n))

t = (58 - 64) / (7 / sqrt(16))

t = -2.29

Next, we need to find the corresponding p-value for this t-value with 15 degrees of freedom (n-1=16-1=15). We can use a t-distribution table or calculator to find that the p-value is 0.017.

Since the p-value (0.017) is less than the significance level (0.1), we reject the null hypothesis and conclude that the medication affects performance.

To measure the size of the treatment effect, we can calculate Cohen's d, which is a standardized measure of effect size. Cohen's d is computed as the difference between the sample mean and population mean, divided by the sample standard deviation:

d = (M - μ) / s

d = (58 - 64) / 7

d = -0.86

The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.

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The expression 27/(27x + 18) can be rewritten as 3/(3x + 2).

What are common factors?

Common factors are factors that two or more numbers share. In other words, they are factors that divide into two or more numbers without leaving a remainder. For example, the common factors of 12 and 18 are 1, 2, 3, and 6. These are the numbers that divide evenly into both 12 and 18.

Finding common factors is useful in simplifying fractions and factoring expressions. When simplifying a fraction, you can divide both the numerator and denominator by a common factor to reduce the fraction to its simplest form. When factoring an expression, you can factor out a common factor to simplify the expression and make it easier to work with.

It's worth noting that the greatest common factor (GCF) is the largest common factor that two or more numbers share. For example, the GCF of 12 and 18 is 6, which is the largest number that divides evenly into both 12 and 18.

To rewrite the expression 27/(27x + 18), we can factor out the greatest common factor in the denominator, which is 9. This gives:

27 / (9 * (3x + 2))

We can simplify this expression further by dividing both the numerator and denominator by 9, which results in:

3 / (3x + 2)

Therefore, the expression 27/(27x + 18) can be rewritten as 3/(3x + 2).

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The probability that you test more than 9 people before getting a positive test is 0.42 (rounded to three decimals).

What is probability ?

Probability is a measure of the likelihood or chance that a particular event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

Given that 42% of the population has a virus, the probability that any given person has the virus is 0.42. We can use this information to answer the following questions:

a. The probability that the first positive test is person number 9 can be calculated using the binomial distribution:

[tex]P(X = 1) = (9-1)C(1) * 0.42^{1} * (1 - 0.42)^{(9-1)} = 0.251[/tex]

Therefore, the probability that the first positive test is person number 9 is 0.251 (rounded to three decimals).

b. The probability that the first positive test happens on or before person number 9 can be calculated using the cumulative binomial distribution:

P(X <= 1) = P(X = 0) + P(X = 1) = 0.58

Therefore, the probability that the first positive test happens on or before person number 9 is 0.58 (rounded to three decimals).

c. The probability that you test more than 9 people before getting a positive test can be calculated using the complementary probability:

P(X > 1) = 1 - P(X <= 1) = 1 - 0.58 = 0.42

Therefore, the probability that you test more than 9 people before getting a positive test is 0.42 (rounded to three decimals).

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If Ling plans to collect data and plot them in a scatterplot to look for a relationship, the relationship is positive.

In basketball, players who spend more time on the court are likely to have more opportunities to score points. Therefore, as the playing time increases, the number of points scored by a player may also increase. This would result in a positive relationship between playing time and points scored in a basketball game.

A positive relationship in a scatterplot is characterized by a general upward trend in the data points. As one variable increases, the other variable also tends to increase.

In this case, Ling's scatterplot would likely show data points that are positively correlated, meaning that as the playing time increases, the number of points scored by a player would also tend to increase.

It is also possible for there to be no relationship or a negative relationship between playing time and points scored, but given the nature of basketball, a positive relationship is the most likely outcome.

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The quadratic function represented by the given table is:

y = -1*(x - 2)^2 + 3

Here we have a table that defines a quadratic equation, remember a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)^2 + k

Here we can see that the vertex is (2, 3), then we can write:

y = a*(x - 2)^2 + 3

And we can see that it also passes through the point (0, -1), then:

-1 = a*(0 - 2)^2 + 3

-1 = a*4 + 3

-1 - 3 = a*4

-4 = a*4

-4/4 = a = -1

The quadratic function is:

y = -1*(x - 2)^2 + 3

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Answer: To calculate the p-value for a two-proportion z-test, we need to determine the test statistic, which is calculated as:

z = (p1 - p2) / SE

where p1 and p2 are the sample proportions for each group, and SE is the standard error of the difference between the two proportions.

The sample proportion for the group given the milk chocolate option first is:

p1 = (52 + 48) / 100 = 0.50

The sample proportion for the group given the dark chocolate option first is:

p2 = (41 + 59) / 100 = 0.60

The standard error of the difference between two proportions is:

SE = sqrt((p1*(1-p1))/n1 + (p2*(1-p2))/n2)

where n1 and n2 are the sample sizes for each group.

SE = sqrt((0.50*(1-0.50))/100 + (0.60*(1-0.60))/100) = 0.0748

Substituting the values into the test statistic formula, we get:

z = (0.50 - 0.60) / 0.0748 = -1.338

Using a standard normal distribution table or calculator, we find the p-value for a two-tailed test to be approximately 0.1814.

However, since we are testing whether the order of the options affects the response, this is a one-tailed test. To find the one-tailed p-value, we divide the two-tailed p-value by 2, since the area of the distribution in one tail is half of the area in both tails.

p-value = 0.1814 / 2 = 0.0907

Therefore, the correct answer is A. 0.0594 (rounded to four decimal places).

Step-by-step explanation:

we have shown that [tex](3x)^2x = (9x^2)^2,[/tex] which is the equation you provided. This is true for any value of x, so the equation is valid. The statement you have provided is a mathematical equation that involves exponentiation. To understand this equation, we need to know the rules of exponents.

The rule for exponentiation with the same base states that when we have a base raised to multiple exponents, we can simply multiply the exponents. In other words, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can simplify the right-hand side of the equation to [tex](9x^2)^2 = 81x^4.[/tex]

Now, let's look at the left-hand side of the equation:[tex](3x)^2x[/tex]. To simplify this expression, we can use the distributive property of exponents. That is, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can write[tex](3x)^2x as (3x^2)^x.[/tex]Then, using the rule for exponentiation with the same base, we can write this as [tex]3^(2x) * x^(2x).[/tex]

So now we have the equation [tex]3^(2x) * x^(2x) = 81x^4.[/tex]We can simplify this equation further by dividing both sides by[tex]x^(2x) to get 3^(2x) = 81x^(4-2x).[/tex] Simplifying the right-hand side, we get [tex]3^(2x) = 81x^(2(2-x)) = 81x^(4-2x).[/tex]

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The length of the segment QR, obtained using the angle bisector theorem is; SR ≈ 11.4 units

The angle bisector theorem states an angle bisector in a triangle, intersects opposite side, such that the ratio of the two segments formed by the point of intersection is the same as the ratio of the other two sides of the triangle.

The angle congruence marks at angle ∠Q, indicates that the angle ∠PQS and the angle ∠SRQ are congruent.

Therefore, the segment QS is an angle bisector of the angle ∠PQR.

The angle bisector theorem, indicates that we get;

30/12 = PS/SR

PS = PR - SR, therefore;

30/12 = 5/2 = (PR - SR)/SR

Plugging in the values, we get;

5/2 = (40 - SR)/SR

5 × SR = 2 × (40 - SR) = 80 - 2 × SR

5 × SR + 2 × SR = 80

7 × SR = 80

SR = 80/7 ≈ 11.4

The length of the segment SR is about 11.4 units

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100

The suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to 100.What is a class width?The class width is the width of each interval in a frequency distribution. It is found by subtracting the smallest value from the largest value and then dividing by the number of classes.Class width = (highest value - lowest value) / number of classesWhere,H = highest observed value = 400L = lowest observed value = 50n = number of observations = 100Using the formula:Class width = (H - L) / nClass width = (400 - 50) / 100Class width = 350 / 100Class width = 3.5Thus, the suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to.

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If the resort gets over 75 inches of snow 40% of years, between 40 and 75 inches 45% of years, and less than 40 inches 15% of years the resort's expected yearly profit is $161,500.

To find the resort's expected yearly profit, we need to calculate the weighted average of its profits under different snowfall conditions, using the probabilities of each condition occurring as weights.

Let P1, P2, and P3 be the probabilities of snowfall being over 75 inches, between 40 and 75 inches, and less than 40 inches, respectively. We are given that P1 = 0.4, P2 = 0.45, and P3 = 0.15.

Let R1, R2, and R3 be the profits that the resort makes under each of these snowfall conditions. We are given that R1 = $250,000, R2 = $160,000, and R3 = -$70,000 (since the resort loses money if snowfall is less than 40 inches).

Then the expected yearly profit, E, is:

E = P1R1 + P2R2 + P3R3

= 0.4250,000 + 0.45160,000 + 0.15(-70,000)

= 100,000 + 72,000 - 10,500

= $161,500

This means that, on average, the resort can expect to make a profit of this amount each year, taking into account the varying probabilities of different snowfall conditions.

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Answer:

It all depends on the linear system

Step-by-step explanation:

A system of linear equations usually has a single solution but sometimes it can have no solution (parrel lines) or infinite solutions (same line).

I hope this helped

The answer is Three.

One solution.

Infinitely many solutions.

No Solutions at all.

Answer:

Train A= 249 tons

Train B= 87 tons

Step-by-step explanation:

Total weight of Train A and Train B= 336 tons

Weight of Train A > Weight of Train B

Difference of their weights= 162 tons

Let the weight of Train A be t.

Then weight of Train B= t-162

Total weight= 336 tons

         t+t-162= 336

                 2t= 336+162

                 2t= 498

                   t= [tex]\frac{498}{2}[/tex]

                   t= 249

t-162= 249-162

       = 87

∴ the weights of Train A and Train B are 249 tons and 87 tons respectively.

Answer:

refer to the attachment

The inclination or grade of the trail from the Alpine Hotel to the scenic overlook is 21.9%.

The inclination or grade of a trail is the ratio of the change in elevation to the length of the trail, expressed as a percentage. To find the inclination of the trail from the Alpine Hotel to the scenic overlook, we need to first calculate the change in elevation.

Change in elevation = 11,100 feet - 8,000 feet = 3,100 feet

Now we can calculate the inclination or grade of the trail as follows:

Grade = (change in elevation / length of trail) x 100%

Grade = (3,100 / 14,100) x 100%

Grade = 0.219 x 100%

Grade = 21.9%

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Answer:

The formula for the area of a circle is A = πr^2, where r is the radius of the circle.

We know that the diameter of the circle is 10 ft, so the radius is half of that:

r = 10 ft ÷ 2 = 5 ft

Now we can plug in this value for r into the formula:

A = π(5 ft)^2

A = π(25 ft^2)

A ≈ 78.54 ft^2

Rounding this to the nearest whole number, we get:

A ≈ 79 ft^2

Therefore, the area of the circle to the nearest whole number is 79 square feet.

Answer:

79ft^2

Step-by-step explanation:

diameter=10ft

radius=5ft

5^2=25ft

25×π=25π

25π= 78.539....

to nearest whole number =79ft^2

The answer is 4A+2B+5. This can be achieved by combining the like terms in the expression 4a-1+2B+6. First we add 4 and -1 to get 3 for the A-coefficient, then we add 2 and 6 to get 8 for the B-coefficient, and finally we combine the coefficients to get 4A+2B+5.

To combine the like terms in the expression 4a-1+2B+6, we need to simplify it. We can do this by combining the A-coefficients and the B-coefficients.

The A-coefficient is 4, so we add 4 and -1 to get 3. This means the expression is now 4A+2B+6.

The B-coefficient is 2, so we add 2 and 6 to get 8. This means the expression is now 4A+2B+8.

Finally, we combine the A-coefficient and the B-coefficient to get 4A+2B+5.

Therefore, the answer is 4A+2B+5.

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Step-by-step explanation:

the midpoint between 2 points A (xa, ya) and B (xb, yb) is

M ((xa + xb)/2, (ya + yb)/2)

(xa + xb)/2 = 10.5

(ya + yb)/2 = 9

let's say R = A

(1 + xb)/2 = 10.5

(10 + yb)/2 = 9

1 + xb = 21

xb = 20

10 + yb = 18

yb = 8

S = (20, 8)

Answer:

B

Step-by-step explanation:

3x + 3 - x + (-7) > 6

2x + 3 - 7 > 6

2x - 4 > 6

2x > 10

x > 5

Answer:

B. x > 5

Step-by-step explanation:

3x + 3 - x + (-7) > 6

3x - x + 3 - 7 > 6

2x + (-4) > 6

2x - 4 > 6

2x > 6 + 4

2x > 10

x > 10 / 2

x > 5

:D

The number of hours she can afford to rent the paddle boat is  x ≤ 6.8. Option D

we have the equation in the inequality as

1.25x + 6.50 ≤ 15

we would have to solve for x

hence we would take the like terms first

1.25x ≤ 15 - 6.50

then we would have

1.25x ≤ 8.5

Next we have to divide through by 1.25

1.25x / 1.25 ≤ 8.5 / 1.25

x ≤ 6.8

Hence the solution to the inequality is x ≤ 6.8. Elise can afford to rent the paddle boat for x ≤ 6.8

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Elise has $15 to spend on a paddle boat ride she uses this inequality to determine x the number of hours she can afford to rent the paddle boat

1.25x + 6.50 ≤ 15

What is the solution to the inequality?

x ≥ 17.2

x ≥ 6.8

x ≤ 17.2

x ≤ 6.8

​

Answer:

x ≤ 6.8

Step-by-step explanation:

The cost of cementing the walls of the cuboidal well is Rs 3640.

A three-dimensional solid form with six rectangular sides is called a cuboid. It also goes by the name rectangular prism. The shapes and sizes of the faces on either side of each other are identical.

A cuboid's surface area is the sum of all of its faces. We can determine the area of each face and put them together to determine the cuboid's surface area.

Given that, the cost of cementing the walls of the well at the rate Rs 52 per square m.

Thus,

Area of one rectangular face = length x height = 2 x 10 = 20m².

Area of the other rectangular face = width x height = 1.5 x 10 = 15m².

Total surface area of the walls = 2(20) + 2(15) = 70m².

Now, the cost of cementing the walls of the well at the rate of Rs 52 per m² is:

Cost = 70m x Rs 52 = Rs 3640

Hence, the cost of cementing the walls of the well is Rs 3640.

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Answer:

s is inversely proportional to t

Step-by-step explanation:

As s increases, t decreases.  They are inversely proportioanl when that happens.

the number of goals Yolanda scores without penalties is x = 8, and the number of goals Neel scores without penalties is y = 0.

Let x be the number of goals Yolanda scores without penalties, and let y be the number of goals Neel scores without penalties.

According to the problem, Yolanda makes 6 goals and 2 penalties, so her total number of goals is:

x + 6

And her total number of points is:

(x + 6) + 2(1) = x + 8

Similarly, Neel scores 4 goals and 2 penalties, so his total number of goals is:

y + 4

And his total number of points is:

(y + 4) + 2(1) = y + 6

We know that Yolanda ends the game with 16 points, so we can write:

x + 8 = 16

Subtracting 8 from both sides, we get:

x = 8

We also know that Neel ends the game with 6 points, so we can write:

Y + 6 = 6

Subtracting 6 from both sides, we get:

y = 0

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The scale that Wyatt used is 1 inch represents 0.36 yards

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. The scale provides information on the proportional relationship between the scale of the drawing and the original image.

Scale of the drawing = original length / length of the drawing

84 / 231 = 0.36 yards

This means that 1 inch is represented by 0.36 yards

Alternatively, it can be written as 1 : 0.36 yards

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