The radioactive substance uranium-240 has a half-life of 14 hours. The amount At) of a sample of uranium-240 remaining (in grams) after thours is given by


the following exponential.


A (t) = 5600


100(3)*


Find the amount of the sample remaining after 11 hours and after 50 hours.


Round your answers to the nearest gram as necessary.


Amount after 11 hours: grams


Amount after 50 hours: grams

If regular hexagon, regular octagon are inscribed in circle, perimeter of hexagon is greater than perimeter of octagon, each perimeter is greater than circumference of circle. Therefore, statement B is true.

The perimeter of a polygon is the sum of the lengths of all its sides. In a regular polygon, all sides have equal length, so the perimeter is simply the number of sides multiplied by the length of one side. The circumference of a circle is the distance around its outer edge.

Since both polygons are inscribed in the same circle, they have the same circumcircle, which means that their perimeters are both less than the circumference of the circle.

To compare the perimeters of the two polygons, we need to know the number of sides of each polygon and the length of one side. A regular hexagon has six sides, and a regular octagon has eight sides. Since the circle is inscribed in both polygons, the sides of each polygon are tangents to the circle, forming right angles with the radii of the circle.

Thus, we can draw a right triangle with the radius of the circle as the hypotenuse, and the side of the hexagon (or octagon) as one leg. Using trigonometry, we can find the length of one side of the hexagon (or octagon) in terms of the radius of the circle.

After calculating the lengths of one side of each polygon, we can compare their perimeters. It turns out that the perimeter of the octagon is greater than the perimeter of the hexagon, since the octagon has more sides.

Therefore, statement B is true.

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Complete question is:

A regular hexagon and a regular octagon are both inscribed in the same circle. which of these statements is true?

A) the perimeter of the hexagon is less than the perimeter of the octagon, and each perimeter is less than the circumference of the circle.

B) the perimeter of the hexagon is greater than the perimeter of the octagon, and each perimeter is greater than the circumference of the circle.

the inflection points are x = 0 and x = 2, and the intervals of concavity are (-∞, 0) and (2, ∞) for concave down, and (0, 2) for concave up.

To find the inflection points and intervals of concavity of the function f(x) = x^4 - 4x^3, we need to find its second derivative.

f'(x) = 4x^3 - 12x^2
f''(x) = 12x^2 - 24x

The inflection points occur where f''(x) = 0 or is undefined. Therefore, we set 12x^2 - 24x = 0 and solve for x.

12x(x - 2) = 0
x = 0 or x = 2

These are the two possible inflection points.

To determine the intervals of concavity, we need to look at the sign of the second derivative in each interval. We can use test points to determine the sign.

Test point x = 1:
f''(1) = 12 - 24 = -12, so the function is concave down on the interval (-∞, 0) and concave up on the interval (0, ∞).

Test point x = 3:
f''(3) = 108 - 72 = 36, so the function is concave up on the interval (2, ∞) and concave down on the interval (-∞, 2).

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The discrepancy in the results: The theoretical probability may not be calculated correctly and enough trials have not been performed to give the desired result

In the given scenario, 81% of money spent at full-service restaurants in America is through debit, credit, or pre-paid cards. However, one restaurant found that 421 out of 973 customers used these payment methods. Possible reasons for the discrepancy in the results are:

1. The theoretical probability may not be calculated correctly: The 81% figure might not accurately represent the actual proportion of customers using cards in full-service restaurants. It could be due to incorrect data collection or interpretation.

3. Enough trials have not been performed to give the desired result: The data from one restaurant for one week might not be enough to accurately reflect the overall trend. A larger sample size and longer time frame would give a more accurate representation.

It's important to note that there might not necessarily be a discrepancy in the result; it could be a difference due to variations in individual restaurant data compared to the overall average.

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We have found the altitude of the aircraft, we can determine its distance from station P, which is simply the value of d1

We can use the concept of triangulation to find the distance of the aircraft from station P. Let's assume that the aircraft is at point A, and let d1 and d2 be the distances of the aircraft from stations P and Q, respectively. Then we have:

[tex]d1^2 + h^2 = r1^2 ------ (1)\\d2^2 + h^2 = r2^2 ------ (2)[/tex]

where h is the altitude of the aircraft, r1 and r2 are the distances from the aircraft to stations P and Q, respectively. We want to find d1, which is the distance of the aircraft from station P.

We know that the distance between the two radar stations is 120 miles, so we have:

[tex]r2 = r1 + 120 (3)[/tex]

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

[tex]d2^2 - d1^2 = r2^2 - r1^2\\d2^2 - d1^2 = (r1+120)^2 - r1^2\\d2^2 - d1^2 = 120*240 + 120^2\\d2^2 - d1^2 = 40800[/tex]

Adding equations (1) and (3), we get:

[tex]2h^2 + 2*r1*120 = r1^2 + (r1+120)^2\\2h^2 + 2*r1*120 = 2*r1^2 + 120^2\\2h^2 = 4*r1^2 - 2*r1*120 + 120^2\\h^2 = 2*r1^2 - r1*120 + 120^2 / 2\\h^2 = r1^2 - r1*60 + 120^2 / 4[/tex]

Substituting h^2 into equation (1), we get:

[tex]d1^2 + (r1^2 - r1*60 + 120^2 / 4) = r1^2\\d1^2 = r1*60 - 120^2 / 4\\d1^2 = 15*r1^2 - 18000[/tex]

Substituting d2^2 - d1^2 from the previous calculation, we get:

[tex]d2^2 - (15*r1^2 - 18000) = 40800\\d2^2 = 15*r1^2 + 58800[/tex]

Now we have two equations with two unknowns (d1 and r1). Solving for r1 in equation (4) and substituting into equation (5), we get:

[tex]d2^2 = 15*(d1^2 + 120*d1) + 58800\\d2^2 = 15*d1^2 + 1800*d1 + 58800\\15*d1^2 + 1800*d1 + 58800 - d2^2 = 0[/tex]

This is a quadratic equation in d1, which can be solved using the quadratic formula:

[tex]d1 = (-b \± sqrt(b^2 - 4ac)) / 2[/tex]

where a = 15, b = 1800, and c = 58800 - d2^2. Note that we should take the positive root, since d1 is a distance and therefore cannot be negative.

Once we have found d1, we can use equation (1) to find h, the altitude of the aircraft, as:

[tex]h = sqrt(r1^2 - d1^2)[/tex]

Finally, the distance of the aircraft from station P is simply d1.

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When the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

To calculate the taxable income (loss) for each year, we need to apply the corresponding tax rate to the pretax financial income (or loss) figures. Here's the breakdown:

2017:

Taxable income = Pretax financial income * Tax rate

Taxable income = $77,000 * 0.25

Taxable income = $19,250

2018:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($38,000) * 0.20

Taxable income = ($7,600)

2019:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($33,000) * 0.20

Taxable income = ($6,600)

2020:

Taxable income = Pretax financial income * Tax rate

Taxable income = $122,000 * 0.20

Taxable income = $24,400

2021:

Taxable income = Pretax financial income * Tax rate

Taxable income = $90,000 * 0.20

Taxable income = $18,000

Please note that when the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

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The approximate area of the figure is 40 square meters. So, the correct answer is B).

Recall the formula for the area of a kite, which is

Area = (1/2) x Base x Height

where "Base" is the length of one of the diagonals and "Height" is the length of the other diagonal.

Identify the base and height of the given kite from the problem statement. Here, it is given that the height is 10 meters and the base is 8 meters.

Substitute the values of the base and height into the formula for the area of a kite

Area = (1/2) x 8 meters x 10 meters

Simplify the expression by multiplying the base and height together and dividing by 2

Area = 40 square meters

Round the answer to the nearest whole number or keep the answer as a decimal, depending on the instructions of the problem.

Therefore, the approximate area of the given kite is 40 square meters. So, the correct answer is B).

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The amplitude of the current I is 16.9 Amperes

To find the amplitude of the current I in the given circuit with an alternating current E(t) = 120sin(12t), inductance L = 0.31 H, resistance R = 7 ohms, and capacitance C = 0.029 F, we need to determine the impedance (Z) of the circuit first.

The impedance Z can be calculated using the formula:

Z = √((R²) + (XL - XC)²)

Where XL is the inductive reactance, and XC is the capacitive reactance. XL can be calculated as:

XL = 2πfL

And XC can be calculated as:

XC = 1/(2πfC)

Here, f is the frequency of the alternating current, which can be determined from the given function E(t) = 120sin(12t) as:

f = 12/(2π) = 1.91 Hz

Now, we can calculate XL and XC:

XL = 2π(1.91)(0.31) = 3.74 ohms

XC = 1/(2π(1.91)(0.029)) = 2.89 ohms

Next, we can find the impedance Z:

Z = √((7²) + (3.74 - 2.89)²) = √(49 + 0.72) = 7.1 ohms

Finally, we can find the amplitude of the current I using Ohm's law:

I = E(t)/Z

Since we're looking for the amplitude, we only need the maximum value of E(t), which is 120 V:

I = 120/7.1 = 16.9 A

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The first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]

To find the first derivative of g(a), we need to use the power rule and the constant multiple rule.

First, we use the power rule to take the derivative of each term:

[tex]- The derivative of 6x^3 is 18x^2

- The derivative of -9x^2 is -18x

- The derivative of -36x is -36[/tex]

Next, we use the constant multiple rule to combine these derivatives:

g'(a) = 18x^2 - 18x - 36

Therefore, the first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]

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The ordered pair that is a reflection over the x-axis for the point shown include the following: A. (6, 4)

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

Next, we would apply a reflection over or across the x-axis to the point;

(x, y)                →      (x, -y)

(6, -4)                →      (6, -(-4)) = (6, 4)

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The total length of the race is approximately 28.24 miles.

To determine the total length of the race, we can use the given information: Piotr has completed 24 miles, which represents 85% of the race. We can set up a proportion to find the total length. Let 'x' represent the full length of the race:

(24 miles) / x = 85% / 100%

To solve for 'x', we can first convert the percentage to a decimal by dividing 85 by 100, resulting in 0.85:

24 / x = 0.85

Next, we can cross-multiply:

0.85 * x = 24

Now, we can solve for 'x' by dividing both sides by 0.85:

x = 24 / 0.85

x ≈ 28.24 miles

Therefore, the total length of the race is approximately 28.24 miles. Piotr has completed 85% of this distance, which means he has run 24 miles and has around 4.24 miles remaining to finish the race.

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The estimated population proportion is 0.622, with a margin of error of +/- 0.096.

The value of the population proportion of people from Hawaii who exercised for at least 30 minutes a day 3 days a week can be estimated using the sample proportion of 62.2%. However, we need to calculate the margin of error to determine a range in which the true population proportion is likely to fall.

Using the formula for the margin of error:

Margin of error = z*sqrt(p*(1-p)/n)

where z is the z-score for the desired level of confidence (let's use 95% confidence, which corresponds to a z-score of 1.96), p is the sample proportion (0.622), and n is the sample size (100).

Plugging in the values, we get:

Margin of error = 1.96*sqrt(0.622*(1-0.622)/100) = 0.096

So the margin of error is 0.096, meaning that we can be 95% confident that the true population proportion of people from Hawaii who exercise for at least 30 minutes a day 3 days a week falls within a range of 0.622 +/- 0.096.

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The area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

When two side length of a triangle and the angle between them is given, the area is half the multiplication of the two sides and the sine of the angle.

Area of the triangle = 1/2 × 4.7 × sin162

Area of the triangle = 11.4738/2

Area of the triangle = 5.7369.

Therefore, the area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

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Note that where the above function is given, the equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold. See the graph attached.

To change the given equation to slope-intercept form, we need to solve for y.

2x + 3y = 1470

3y = -2x + 1470

y = (-2/3)x + 490

Therefore, the slope of the line is -2/3 and the y-intercept is 490.

To graph this line using the slope-intercept method, we can plot the y-intercept first, which is (0, 490). Then, using the slope of -2/3, we can find another point by moving 2 units to the right and 3 units down from the first point. We can continue this pattern to plot additional points and then draw a straight line through them.

The equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold.

To graph the function, we can plot the intercepts (0, 490) and (735, 0), where 735 is the x-intercept. Then, using the slope of -2/3, we can find other points and draw a straight line through them.

If Sal's total profit on lunch specials for the next month is $1,593, then the equation would be 2x + 3y = 1593. The graphs of the functions for both months would have the same slope of -2/3, indicating that the profit per lunch special sold remains constant.

However, the y-intercept would be different, indicating a different starting profit for the month. The graphs would have different intercepts and intersect the y-axis at different points, reflecting the difference in starting profits.

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Answer:

62.29

Step-by-step explanation:

100 - 3(4.25) - 13 - 4(2.99)

= 100 - 12.75 - 13 - 11.96

= 62.29

explanation in the picture

the answer is

62,29

The best point estimate for the population mean score on the nationwide examination in psychology is the sample mean of 492.

When we take a sample from a population, the sample mean is a point estimate of the population mean. A point estimate is an estimate of a population parameter based on a single value or point in the sample. In this case, the sample mean of 492 is the best point estimate for the population mean, because it is an unbiased estimator.

An estimator is unbiased if it is expected to be equal to the true population parameter. In this case, the expected value of the sample mean is equal to the population mean. This means that if we were to take many different samples from the population and calculate the sample mean for each sample, the average of all these sample means would be equal to the population mean.

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The given question is incomplete, the complete question is:

You would like to construct a 95% confidence interval to estimate the population mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 492 and a standard deviation of 78. What is the best point estimate, based on the sample, to use for the population mean?

the backup goalie saved 42 shots. Answer: 42 shots. We can start by setting up an equation using the information given

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written with an equal sign (=) between the two expressions. For example, the equation 2x + 3 = 7 is a statement that asserts that the expression 2x + 3 is equal to 7.

In the given question,

We can start by setting up an equation using the information given:

save percentage = (number of shots saved / total number of shots attempted)

For the backup goalie, we know that their save percentage is 0.560, and we also know the total number of shots attempted on the goal is 75. Let's let the number of shots saved by the backup goalie be represented by the variable "t". Then we can write:

0.560 = t / 75

To solve for t, we can cross-multiply:

0.560 * 75 = t

t = 42

Therefore, the backup goalie saved 42 shots. Answer: 42 shots.

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To find the height of the rocket after 2.5 seconds,

you'll need to plug in t = 2.5 into the given equation h(t) = 160t - 16t².

h(2.5) = 160(2.5) - 16(2.5)²
h(2.5) = 400 - 100
h(2.5) = 300 meters

The height of the rocket after 2.5 seconds is 300 meters.

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If the fifth and tenth terms of an arithmetic sequence, respectively, are -2 and 53, the seventh term of the arithmetic sequence is 20.

To find the seventh term of the arithmetic sequence, we need to first find the common difference (d) of the sequence. We know that the fifth term is -2 and the tenth term is 53.

The formula for the nth term of an arithmetic sequence is: an = a1 + (n-1)d

Using this formula, we can set up two equations:

-2 = a1 + 4d  (since the fifth term is a1 + 4d)
53 = a1 + 9d  (since the tenth term is a1 + 9d)

We now have two equations with two variables (a1 and d). We can solve for either variable using substitution or elimination. I'll use elimination:

-2 = a1 + 4d
53 = a1 + 9d

Subtracting the first equation from the second equation, we get: 55 = 5d

Therefore, d = 11

Now that we know the common difference is 11, we can use the formula for the nth term again to find the seventh term:

a7 = a1 + (7-1)d
a7 = a1 + 6d

We still don't know a1, but we can solve for it using one of the previous equations:

-2 = a1 + 4d
-2 = a1 + 4(11)
-2 = a1 + 44
a1 = -46

Now we can substitute a1 and d into the formula for the seventh term:

a7 = -46 + 6(11)
a7 = -46 + 66
a7 = 20

Therefore, the seventh term of the arithmetic sequence is 20.

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Final Answer:  a. The number of units that should be sold in order to maximize the profit is 7 thousand units.

b. The  maximum profit is approximately $5.51

Conceptual part:   a. In order to find maximum profit we need to differentiate the profit function

[tex]dp/dx = (-3x^2+18x+21)/-x^3+9x^2+21x+1[/tex] = 0

[tex]-3x^2+18x+21=0[/tex]

[tex](x-7) (x+1) = 0[/tex]

as profit can't be negative.

hence x=7.

b. We can determine the maximum profit by substituting x=7 in profit function.

[tex]p(7) = ln(-7^3+9*7+21*7+1)[/tex]

[tex]p(7) = ln(246)[/tex]

p(7) = 5.51

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The maximum number of students allowed to attend the field trip is 59.

To determine the maximum number of students allowed to attend the field trip, given the ticket cost and money raised, we'll need to follow these steps:
1. Subtract the adult ticket cost from the total money raised.
2. Divide the remaining amount by the cost of a student ticket.
Subtract the adult ticket cost from the total money raised.
$580 (money raised) - $75 (adult ticket cost) = $505 (remaining amount)
Divide the remaining amount by the cost of a student ticket.
$505 (remaining amount) / $8.50 (student ticket cost) = 59.41
Since we can't have a fraction of a student, we round down to the nearest whole number.
The maximum number of students allowed to attend the field trip is 59.

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1/70 is the probability of having slips numbered 1, 2, 3, and 4 drawn in order from the box.

To calculate the probability of drawing slips numbered 1, 2, 3, and 4 in order from a box containing slips numbered 1 through 8, we need to first find out the total number of possible outcomes when drawing four slips without replacement from the box.

The number of ways to draw 4 slips from a set of 8 slips without replacement is given by the combination formula:

= 8!/4!(8-4)! = 70

This means there are 70 possible outcomes when drawing four slips from the box.

To calculate the probability of drawing slips 1, 2, 3, and 4 in that order, we need to consider that there is only one way to draw the slips in that specific order, out of the 70 possible outcomes.

Therefore, the probability of drawing slips 1, 2, 3, and 4 in order is:

P(1,2,3,4 in order) =  number of favorable outcomes/total number of possible outcomes = 1/70

So the probability of drawing slips numbered 1, 2, 3, and 4 in order from the box is 1/70.

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The solution of the given inequality, x - 3 ≤ -2, is solved as the possible value of x which is determined as: x ≤ 1.

Given the inequality x - 3 ≤ -2, to find the solution, wr would have to solve for x as explained below:

x - 3 ≤ -2 [given]

Add 3 to both sides:

x - 3 + 3 ≤ -2 + 3 [addition property of equality]

x ≤ 1

This means that the values of x are less than or equal to 1, which is from 1 below.

Thus, the solution to the inequality is solved by finding the possible value of x, which is x ≤ 1.

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Note that the probability that he gives the lifejackets to just two of the three non-swimmers​ is 3/250 or 0.012

Let's define the following events...

A: Two of the three non-swimmers get lifejackets

B: Three lifejackets are given to two non-swimmers and one swimmer

We want to calculate P(A), the probability that two of the three non-swimmers get lifejackets. We can do this using the formula/...

P(A) = P(A|B) * P(B) + P(A|not B) * P(   not B)

P (B), the probability that the Captain gives the lifejackets to two non-swimmers and one swimmer....

P(B )  = (3/5 ) x (2/4) x (1/3) = 1/ 10

Note that  he number of ways to choose 2 non-swimmers from 3 is 3, and the number of ways to choose 1 swimmer from 2 is 2.

The total No.  of ways to choose 3 passengers from 5 is 10, hence

P(A | B) = (3 choose 2) x (2 choose 1) / (10 choose 3) = 6 /50

The No. of ways to choose 2 non-swimmers from 2 is 1, and the number of ways to choose 1 swimmer from 3 is 3. The total number of ways to choose 3   passengers from 5 is 10

P(A|not B) = (1 choose 2) x (3 choose 1) / (10 choose 3) = 0

Plugging in the values, we get....the followint

P(A) = (6/50) * (1/10) + (0) * (9/10) = 3/ 250

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The group of natural numbers is a subset of the whole numbers.

What is Whole number ?

Whole numbers are a set of numbers that includes all positive integers (1, 2, 3, ...) and zero (0). They do not include negative numbers or fractions. Whole numbers are often used to count objects or represent quantities that cannot be divided into smaller parts.

Out of the given options, the group of natural numbers is the only one that is a subset of whole numbers. The other options - Rational numbers, Real numbers, Irrational numbers, and Integers - are not subsets of the whole numbers.

Rational numbers include fractions and decimal numbers, which can be expressed as a ratio of two integers, including non-whole numbers.

Real numbers include all rational and irrational numbers, including non-whole numbers. Irrational numbers are non-repeating, non-terminating decimals that cannot be expressed as a fraction. Integers include both positive and negative whole numbers, as well as zero.

The subset of whole numbers is called natural numbers.

Therefore, the group of natural numbers is a subset of the whole numbers.

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Answer:

252 mi

Step-by-step explanation:

volume= L x W x H

9x 7 x 4 = 252 mi

(a) The expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3).

(b) The least possible integer value of x for the rectangular solid to exist is 4.

a. To express the length, width, and height of the right rectangular prism in terms of x, we can factor the volume expression, 6x³ - 3x² - 45x.

Factoring out the greatest common factor, 3x:

3x(2x² - x - 15)

Now, factor the quadratic expression:

3x(2x² - x - 15)

To factor the quadratic expression further, find two numbers whose product equals the constant term (-15) and whose sum equals the coefficient of the linear term (-1). These two numbers are -5 and 3.

3x(2x + 5)(x - 3)

Thus, the expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3)

b. For the rectangular solid to exist, all dimensions (length, width, and height) must be positive. Let's examine the constraints on x for each dimension:

1. 3x > 0
2. 2x + 5 > 0 → x > -5/2
3. x - 3 > 0 → x > 3

Since x must satisfy all three inequalities, the least possible integer value of x for the rectangular solid to exist is x = 4.

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The number of different combo meals possible in a restaurant that is serving a special dinner combo meal is 90.

We are given that the customers can choose from 5 drinks, 6 main dishes, and 3 desserts. We have to find that how many different combos are possible. It means that we have to do an arrangement for such a situation. Arrangement of things means to group them in a systematic order, in all the possible ways.

We know that the number of possible ways to arrange is n! where n is the number of objects. As we know that the dinner includes 5 drinks, 6 main types of dishes, and 3 types of desserts. The number of different combo meals possible can be found by simply multiplying all the meals. Thus,

n = 5 * 6 * 3

n = 90

Therefore, the number of different combo meals possible in a restaurant that is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 90.

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To get it why radians  have fractional answers, one can use the unit of a circle .  the unit circle could be a circle with a radius of 1, centered at the root of a coordinate plane. To measure points in radians on the unit circle, we measure the  arc length of the comparing other part of the circle, as shown within the image attached:

Radian measures angles based on arc length equal to the radius of a circle, resulting in fractions for non-whole arcs. The unit circle has a radius of 1 and is centered at the origin.

This explains why radians can be fractional. To measure angles in radians, we use arc length on the unit circle. Most angles correspond to fractions of a full circle, like π/2 for a quarter circle.

The angle in radians for one-eighth of a circle is approximately 0.79 (π/4), as most circle arcs are not exact multiples of the radius. Most circle arcs cannot be expressed as a whole number of radii.

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The geometric term that can be used to describe the crossing sign shown is intersecting lines.

In geometry, intersecting lines are two lines that cross one another at a location known as the point of intersection. It is possible to use the point of intersection to solve issues concerning angles, segments, and geometric shapes because it is the sole point that both lines share.

Two pairs of opposite angles that are equal to one another are formed when two lines connect, giving rise to four angles.

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For the solutions to the inequality *> 145, you can consider the given terms: 1. Fractions larger than 14 1/2: These are solutions since 14 1/2 is equivalent to 145/2, which is smaller than 145. 2.

Decimals larger than 14 1/2: These are also solutions as any decimal larger than 14.5 (14 1/2 as a decimal) will be greater than 145/2 and thus smaller than 145. 3. Whole numbers larger than 14 1/2: These are solutions as well, since any whole number greater than 14 is greater than 14 1/2 and therefore greater than 145/2. The numbers that are not solutions to the inequality are: 1. Fractions smaller than 14 1/2 2. Decimals smaller than 14 1/2 3. Whole numbers smaller than 14 1/2 These values are all less than 145/2 and therefore do not satisfy the inequality *> 145.

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