A store receives 2,000 decks of popular trading cards. The number of decks of cards is a function, c, of the number of days, t, since the shipment arrived.




Calculate the average rate of change for day 0 to day 5

The expressions that yield a product greater than 45 are options B and E.

To find which expressions yield a product greater than 45, we can simply calculate the value of each expression and check if it is greater than 45.

A) 1/4 x 45 = 11.25, which is less than 45. So, option A does not yield a product greater than 45.

B) 3/2 x 45 = 67.5, which is greater than 45. So, option B yields a product greater than 45.

C) 2/2 x 45 = 45, which is equal to 45. So, option C does not yield a product greater than 45.

D) 3/5 x 45 = 27, which is less than 45. So, option D does not yield a product greater than 45.

E) 5/4 x 45 = 56.25, which is greater than 45. So, option E yields a product greater than 45.

Therefore, the expressions that yield a product greater than 45 are options B and E.

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Always remember to set your calculator to **degrees** when working with Law of Sines & Cosines.

When working with Law of Sines & Cosines, it's important to remember to set your calculator to "degree" mode if you're working with angles measured in degrees.

This is because the equations for Law of Sines & Cosines use trigonometric functions that are dependent on the units used for the angles.

If you use the wrong mode on your calculator, your answers will be incorrect.

The Law of Sines and the Law of Cosines are two important formulas in trigonometry that help us solve triangles.

The Law of Sines, also known as the Sine Rule, is used to find the length of a side or measure of an angle in a triangle when we know the length of two sides and the angle between them or the length of one side and the measures of the angles opposite to it.

The formula for the Law of Sines is:

sin A / a = sin B / b = sin C / c

where A, B, and C are the angles of the triangle, and a, b, and c are the sides opposite to those angles, respectively.

The Law of Cosines, also known as the Cosine Rule, is used to find the length of a side or measure of an angle in a triangle when we know the lengths of the other two sides and the angle between them.

The formula for the Law of Cosines is:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where c is the side opposite to the angle C, and a and b are the other two sides of the triangle.

This formula can be rearranged to solve for any of the three sides or any of the three angles of the triangle.

Both the Law of Sines and the Law of Cosines are useful tools for solving triangles in a variety of real-world and mathematical contexts.

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There are 7 months in the year that have thirty-one days.

These months are January, March, May, July, August, October, and December.

There are seven months in the Gregorian calendar that have thirty-one days: January, March, May, July, August, October, and December.

This pattern of months with 31 days followed by months with fewer days repeats throughout the year.

This pattern was established by the Roman calendar, which had ten months totaling 304 days in a year.

The months of January and February were later added by King Numa Pompilius to align the calendar with the lunar year.

The months of January and February initially had 29 and 28 days respectively, but in 45 BC, Julius Caesar added one day to January and one day to August, which was originally a 30-day month, to make them both 31-day months.

In the Gregorian calendar, which is the most widely used calendar in the world, January, March, May, July, August, October, and December all have 31 days.

The remaining five months have fewer days, with February having 28 days most of the time, and 29 days in a leap year.

Knowing the number of days in each month is important for various reasons, such as planning events, scheduling appointments, and calculating pay periods.

There are several mnemonics used to remember the number of days in each month, such as "30 days hath September, April, June, and November, all the rest have 31, except February, with 28 days clear, and 29 in each leap year."

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The area of metal needed to make the tool is r² times the sum of 1/2π and the square root of 3.

To determine the area of metal needed to make the tool, we need to find the areas of the semicircle and the isosceles triangle and then add them together.

The area of a semicircle with radius r is:

A(semi-circle) = 1/2πr²

Since the tool consists of a semicircle, we can use the diameter of the semicircle to represent the width of the isosceles triangle.

Let the height of the isosceles triangle be h and the base be b.

Since the triangle is isosceles, we can divide it in half and treat it as a right triangle.

Using the Pythagorean :

h² + (b/2)² = r²

Since the diameter of the semicircle is the same as the base of the isosceles triangle, we have:

b = 2r

Substituting this into the equation above, we get:

h² + r² = 4r²

h² = 3r²

h = √(3)r

The area of an isosceles triangle with base b and height h is:

A(triangle) = 1/2bh

Substituting b = 2r and h = √(3)r, we get:

A(triangle) = 1/2(2r)(√(3)r)

A(triangle) = √(3)r²

Adding the area of the semicircle and the isosceles triangle, we get:

A(tool) = A(semi-circle) + A(triangle)

A(tool) = 1/2πr² + √(3)r²

A(tool) = r²(1/2π + √(3))

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Once the protection period for a new invention expires, the invention is said to be in the public domain.

The invention without permission from the original inventor, and the inventor cannot prevent others from doing so.

In other words, the invention becomes freely available for anyone to use or benefit from, without any legal restrictions.

The length of time for which an invention is protected depends on the type of intellectual property protection granted, such as patents or trademarks, and the laws of the country or region where the protection is sought.

The creator cannot restrict others from using, manufacturing, or selling the innovation without the consent of the original inventor.

In other words, there are no longer any constraints on who can utilise or benefit from the idea.

The kind of intellectual property protection granted, such as patents or trademarks, as well as the legal framework of the nation or region where the protection is sought, determine the duration of an invention's protection.

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The requreid equation of the circle is  x² + y² = 16.

Since each right triangle inside the circle has a hypotenuse of 8, then the radius of the circle is also 8.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

In this case, the center of the circle is (0, 0) and the radius is 8, so the equation of the circle is:

x² + y² = 16

Thus, the requreid equation of the circle is  x² + y² = 16.

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The P-value, or observed significance level, is a statistical measure that indicates the likelihood of obtaining a result as extreme or more extreme than the one observed, assuming that the null hypothesis is true.

It represents the probability of observing a result that is as or more extreme than the one found, given that the null hypothesis is correct. A low P-value indicates that the observed results are unlikely to occur by chance alone, and therefore suggests that the null hypothesis should be rejected in favor of the alternative hypothesis. Generally, a P-value less than 0.05 is considered significant, meaning that there is less than a 5% chance of obtaining the observed result by chance if the null hypothesis is true.

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The costs will be the same for both companies if they produce and distribute 1250 brochures.

To find the number of brochures for which the costs are the same for both companies, we need to set the total cost equations for the two companies equal to each other:

$100 + 0.06x = $75 + 0.08x

Subtracting $75 and 0.06x from both sides, we get:

$25 = 0.02x

Dividing both sides by 0.02, we get:

x = 1250

So, the costs will be the same for both companies if they produce and distribute 1250 brochures.

The method used to get the answer is setting the total cost equations of the two companies equal to each other and solving for the number of brochures.

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The probability of obtaining between 9 and 14 heads, exclusive, in 45 tosses of a coin with probability of heads = 0.25 is approximately 0.6516.

The number of heads obtained in 45 tosses of a coin with probability of heads = 0.25 follows a binomial distribution with parameters n = 45 and p = 0.25.

Let X be the number of heads obtained in 45 tosses. We need to find P(9 < X < 14).

Using the cumulative probability function for a binomial distribution, we can write:

P(9 < X < 14) = P(X < 14) - P(X < 9)

= F(13; 45, 0.25) - F(8; 45, 0.25)

where F(x; n, p) is the cumulative probability function for a binomial distribution with parameters n and p, which gives the probability of obtaining up to x successes in n independent trials with probability of success p.

Using a binomial probability table or a calculator, we can find:

F(13; 45, 0.25) = 0.6961

F(8; 45, 0.25) = 0.0445

Therefore,

P(9 < X < 14) = F(13; 45, 0.25) - F(8; 45, 0.25)

= 0.6961 - 0.0445

= 0.6516

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Note that the volume of the solid is 5,132.32unit³

To find the volume of the solid generated by revolving the region about the line y=14, we can use the method of cylindrical shells.

 We integrate the surface area of each shell from 0 to 13, then multiply by the thickness of ech shell (d x), and finally add up all the shells.

The radius of each shell is given by the distance from the axis of rotation (y =14) to the function y = x, which is r  = 14 - x. The height of each shell is given by the function   y = 13 - x.

Therefore, the volume of the solid is stated as

V = ∫[0,13] 2πrh dx

V = ∫[0,13] 2π(14-x)(13-x) dx

V = 2π ∫[0,13] (182 - 27x + x²) dx

V = 2π [182x - (27/2)x² + (1/3)x³] [0,13]

V = 2π [(182(13) - (27/2)(13)² + (1/3)(13)³) - 0]

V ≈ 5132.32

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We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is[tex]\sqrt{84648464/145145} = 41.77[/tex] minutes.

Therefore, we can standardize the sample mean using the formula:

[tex]z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )[/tex]

where [tex]\bar{x}[/tex]  is the sample mean, [tex]\mu[/tex]  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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The probability that at least one student fails STA 2023 in their first try when selecting three students at random is 0.271.

To solve this problem, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

First, let's find the probability that none of the three students fail the course in their first try. This is (0.9)^3 since the probability of a student passing is 1 minus the probability of failing, which is 0.1. Therefore:

Probability of none failing = (0.9)^3 = 0.729

Now, we can use the complement rule to find the probability that at least one student fails:

Probability of at least one failing = 1 - Probability of none failing
Probability of at least one failing = 1 - 0.729
Probability of at least one failing = 0.271

Therefore, the probability that at least one of the three students fails the course in their first try is 0.271.

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There will be 25 almonds in each snack bag that Mrs. Long is making.

Number of almonds in each snack bag:

If Mrs. Long is making 7 snack bags and she wants to share the 175 almonds evenly among them, we need to find out how many almonds will be in each bag.

To do this, we can divide the total number of almonds by the number of snack bags:

175 almonds ÷ 7 snack bags = 25 almonds per snack bag

Therefore, there will be 25 almonds in each snack bag that Mrs. Long is making.

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Answer: 3/2

Step-by-step explanation:

6 2/6

-4 5/6

then: 5 8/6

       -4 5/6

which equals to 1 3/6 or 9/6 or 3/2

Answer:

Okay, not too bad, this one. Let's organize first by identifying each plan:

A = 70*M

B = 500 + 50*M

Costing the same means equal, so we have the equation:

70M = 500 + 50M

-50M           -50M

20M = 500

20M / 20 = 500 / 20

M = 25 months

Step-by-step explanation:

The power of the test is low and not sufficient to detect a significant difference between the two treatments with the given sample size of 35.

To calculate the expected power of the test, we need to consider the survival rates, the significance level, and the sample size. Let's follow these steps:

Determine the proportions
Old treatment survival rate (p1) = 0.75
New treatment survival rate (p2) = 0.85

Determine the significance level
Two-sided significant difference level (α) = 0.05

Calculate the pooled proportion
Pooled proportion (p) = (p1 + p2) / 2 = (0.75 + 0.85) / 2 = 0.80

Calculate the standard error
Standard error (SE) = √(p × (1 - p) × (1/n1 + 1/n2)) = √(0.80 × (1 - 0.80) × (1/35 + 1/35)) ≈ 0.065

Calculate the test statistic (z)
z = (p2 - p1) / SE = (0.85 - 0.75) / 0.065 ≈ 1.54

Find the critical value for the two-sided significant difference at the 5% level
z_critical = 1.96 (from a standard normal distribution table)

Calculate the power of the test
In this case, since the test statistic is smaller than the critical value (1.54 < 1.96), we cannot reject the null hypothesis at the 5% significance level.
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The volume of the pool when it is half filled is 75.36 ft³.

Given is a cylindrical tube pool, with height of 3 ft and the diameter of 8 ft,

We need to find the volume of the pool when half filled,

The volume of a cylinder = π × radius² × height

= 3.14 × 4 × 4 × 3

= 3.14 × 16 × 3

= 150.72

When it is half filled = 150.72/2

= 75.36

Hence the volume of the pool when it is half filled is 75.36 ft³.

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[tex]\cfrac{7}{9}(-3^3)+5\implies \cfrac{7}{9}(-1\cdot 3^3)+5\implies \cfrac{7}{9}(-1\cdot 27)+5\implies \cfrac{7}{9}(-27)+5 \\\\\\ \cfrac{7(-27)}{9}+5\implies \cfrac{-189}{9}+5\implies -21+5\implies -16[/tex]

Answer:

-16

Step-by-step explanation:

7/9(-3^3) + 5

7/9(-27) + 5

7/9 x -27 = -21

-21 + 5 = -16

(Hope this helps :) )

Answer

[tex]168in^{2}[/tex]

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

The representation that yields the same outcome as the recursive arithmetic sequence is given as follows:

[tex]a_n = -1 + 4n[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the explicit formula presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

The first term of the sequence is given as follows:

[tex]a_1 = 3[/tex]

From the recursive formula, each term is obtained subtracting the previous term by 4, hence the common difference is given as follows:

d = 4.

Then the explicit formula is:

[tex]a_n = 3 + 4(n - 1)[/tex]

[tex]a_n = 3 + 4n - 4[/tex]

[tex]a_n = -1 + 4n[/tex]

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Tₐ = 27 and Tₓ = 24 by solving the equation RₐTₐ + RₓTₓ = 150, where Rₐ = 2, Rₓ = 4, and Tₐ = Tₓ + 3.

We are given a condition RₐTₐ + RₓTₓ = 150, where Rₐ = 2, Rₓ = 4, and Tₐ = Tₓ + 3. We really want to track down the upsides of Tₐ and Tₓ.

Subbing the given qualities, we have:

2(Tₓ + 3) + 4Tₓ = 150

Growing the sections and streamlining, we get:

2Tₓ + 6 + 4Tₓ = 150

6Tₓ + 6 = 150

Taking away 6 from the two sides:

6Tₓ = 144

Partitioning the two sides by 6, we get:

Tₓ = 24

Accordingly, Tₓ is 24.

Now that we know Tₓ, we can track down Tₐ:

Tₐ = Tₓ + 3

Subbing the worth of Tₓ we got before, we get:

Tₐ = 24 + 3

Tₐ = 27

Accordingly, Tₐ is 27.

In outline, we were given the condition RₐTₐ + RₓTₓ = 150, where Rₐ = 2, Rₓ = 4, and Tₐ = Tₓ + 3. We tackled for Tₓ by subbing the given qualities and working on the situation. We observed that Tₓ is 24. Utilizing this worth of Tₓ, we tracked down Tₐ by subbing it into the articulation for Tₐ regarding Tₓ. We observed that Tₐ is 27.

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The expression with the greater value is the second one:

log₀.₅(4)

Here we have two logarithms whose base are 0.5.

Remember that a logarithm of base a can be rewritten as follows:

logₐ(x) = ln(x)/ln(a)

In this case, we have the expressions:

log₀.₅(6)

log₀.₅(4)

We can rewrite these as:

ln(6)/ln(0.5)

lon(4)/ln(0.5)

Remember that ln(x) < 0  if 0 < x < 1

Because the denominator is negative in both cases, the greater number will be the one with the smallest numerator, which is the second option.

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A sample containing 2/3 oz. of liquid is approximately 19.72 milliliters (mL).

To convert 2/3 oz. of liquid to milliliters (mL):
1. Identify the conversion factor: There are approximately 29.5735 mL in 1 ounce (oz).
2. Set up a proportion: To convert 2/3 oz. to mL, we need to multiply the given amount by the conversion factor.
  (2/3 oz.) x (29.5735 mL/1 oz.)
3. Cancel out the units: The "oz" units will cancel out, leaving us with mL.
  (2/3) x (29.5735 mL)

4. Multiply the fraction by the conversion factor: Now, multiply 2/3 by 29.5735.
  (2/3) x 29.5735 = 19.7157
5. Round the result: We'll round the result to two decimal places to make it easier to understand.
  19.7157 mL = 19.72 mL
So, a sample containing 2/3 oz. of liquid is approximately 19.72 milliliters.

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A necessary and sufficient condition for the floor of a real number, x, to equal that number is when x is an integer. The floor of a real number is defined as the largest integer that is less than or equal to that number.

Therefore, if x is already an integer, then it is the largest integer less than or equal to itself, and hence its floor is equal to itself. On the other hand, if x is not an integer, then its floor must be some integer less than x. Therefore, for the floor of x to equal x, x must be an integer.

To see why this is both a necessary and sufficient condition, suppose x is not an integer. Then, the floor of x must be some integer less than x. Hence, x cannot equal its floor. Conversely, if x is an integer, then the floor of x is equal to x. Therefore, x being an integer is both necessary and sufficient for the floor of x to equal x.

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Comparing the e-values, we can see that e(Pujols) = 0.43 is higher than e(Jeter) = 0.36. Therefore, based on the given statistics, it would be favorable to back Albert Pujols in the batting battle.

To determine which player to back in the batting battle, we can compare their expected values (e-values). The e-value represents the average number of points a player would earn per at-bat.

For Derek Jeter:

e(Jeter) = (156 + 9*4) / 488 = 0.36

For Albert Pujols:

e(Pujols) = (125 + 26*4) / 448 = 0.43

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Derek jeter challenges albert pujols to a batting battle. each will earn 1 point for a hit other than a home run and 4 points for a home run in each round. which player should you back given the statistics in the table below? note that home runs are included as hits in the table. data for two batters batter at bats hits home runs jeter 488 156 9 pujols 448 125 26 e(jeter) = 0.38 and e(pujols) = 0.45, so back pujols. e(jeter) = 0.39 and e(pujols) = 0.51, so back pujols. e(jeter) = 0.34 and e(pujols) = 0.34, so it doesn’t matter who you back. e(jeter) = 1.22 and e(pujols) = 0.94, so back jeter.

The distance between Gladville and Colombus is 72 miles.

Given that are two maps A and B we need to determine the distance between the area Gladville and Colombus,

So, the scale =

1 cm = 40 in

So according to the map the distance between Gladville and Colombus, is 1.8 cm apart,

Therefore, in mile these both sites are =

1.8 x 40 = 72 miles apart

Hence the distance between Gladville and Colombus is 72 miles.

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yes, for your x to be positive and to make it remain on the left hand side you actually have to add 4x to both side to eliminate x from the right hand side.

If a is expressed in standard factored form as [tex]a = p1^e1 * p2^e2 * ... * pk^ek[/tex], then to find the standard factored form for [tex]a^3[/tex], we need to raise each prime factor of a to the third power of its exponent in a's standard factored form. That is, we simply multiply each exponent by 3.

For example, suppose [tex]a = 2^2 * 3^3 * 5^1[/tex]. To find the standard factored form for[tex]a^3[/tex], we multiply each exponent by 3:

[tex]a^3 = (2^2)^3 * (3^3)^3 * (5^1)^3\\= 2^(23) * 3^(33) * 5^(1*3)\\= 2^6 * 3^9 * 5^3[/tex]

So the standard factored form for [tex]a^3 is 2^6 * 3^9 * 5^3[/tex], which we obtained by raising each prime factor to the third power of its exponent in a's standard factored form.

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Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

Mr. Raymond will pay $3150 for the topsoil.

The volume of topsoil required to fill a rectangular garden with length 35 feet, width 20 feet, and depth 1.5 feet is:

Volume = Length x Width x Depth

Volume = 35 x 20 x 1.5

Volume = 1050 cubic feet

Since the topsoil costs $3 per cubic foot, the cost of the required amount of topsoil is:

Cost = Volume x Price per cubic foot

Cost = 1050 x $3

Cost = $3150

Therefore, Mr. Raymond will pay $3150 for the topsoil.

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