Use FOIL to explain how to find the product of
(a + b)(a − b). Then describe a shortcut that you could use to get this product without using FOIL.

The propositions that are true for the given domain of all integers are, A. \((\forall m\forall n(mn = 2n))\), D. \((\forall m\forall n(mn = 2n))\) and E. \((\forall m\forall n(m^2 \ge -n^2))\) . These propositions hold true because they satisfy the given conditions for all possible integer values of m and n.

Proposition A. \((\forall m\forall n(mn = 2n))\), states that there exists an integer n such that for all integers m, the equation mn = 2n holds. This proposition is true because we can choose n = 0, and for any integer m, \(0 * m = 2^0 = 1\), which satisfies the equation.

For proposition D. \((\forall m\forall n(mn = 2n))\), it states that for all integers m, there exists an integer n such that the equation mn = 2n holds. This proposition is true because, for any integer m, we can choose n = 0, and \(0 * m = 2^0 = 1\), which satisfies the equation.

For proposition E. \((\forall m\forall n(m^2 \ge -n^2))\), it states that for all integers m and n, the inequality \(m^2 \ge -n^2\) holds. This proposition is true because the square of any integer is always non-negative, and the negative square of any integer is also non-positive, thus satisfying the inequality.

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Answer:

b hope this helps

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

1. 36 \(m^{2}\)

2. 333.125 \(ft^{3}\)

3. 210 \(ft^{3}\)

4. Yes, Martina's estimate is reasonable.

Step-by-step explanation:

Numbering the rectangular surfaces, we have:

Area of a rectangle = length x width

For surface 1: Area = 2 x 2.4

                                = 4.8 \(m^{2}\)

For surface 2: Area = 3 x 2.4

                                = 7.2 \(m^{2}\)

For surface 3: Area = 3 x 2

                                = 6.0 \(m^{2}\)

For surface 4: Area = 3 x 2.4

                                = 7.2 \(m^{2}\)

For surface 5: Area = 2 x 2.4

                                = 4.8 \(m^{2}\)

For surface 6: Area = 3 x 2

                                = 6.0 \(m^{2}\)

Total surface area of the rectangular prism = (2 x 4.8) + (2 x 7.2) + (2 x 6.0)

                                        = 36 \(m^{2}\)

2. length = 10.25 ft

width = 5 ft

height = 6.5 ft

Thus,

volume = l x w x h

            = 10.25 x 5 x 6.5

            = 333.125 \(ft^{3}\)

3. length = 15 ft

width = 7 ft

height = 2 ft

So that,

volume = l x w x h

            = 15 x 7 x 2

            = 210 \(ft^{3}\)

4. For a rectangular prism, area of the opposite surfaces are equal. So that;

Area of rectangle = length x width

For surface 1: Area = 13.0 x 6

                               = 78.0 \(ft^{2}\)

For surface 2: Area = 13.0 x 8

                                = 104.0 \(ft^{2}\)

For surface 3: Area = 6 x 8

                                = 48 \(ft^{2}\)

Surface area of the prism = (2 x 78.0) + (2 x 104.0) + (2 x 48)

                                          = 460.0 \(ft^{2}\)

Therefore, Martina's estimate is reasonable.

Based on the time it took the patient to recover and the mean and standard deviation, the z-score is 1.5.

The z-score for this patient who takes 7 days to recover can be found as:

= (Time taken to recover - Mean) / Standard deviation

Solving for the z-score gives:

= (7 - 5.2) / 1.2

= 1.8 / 1.2

= 1.5

The first part of the question is:

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 1.2 days.

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Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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(a) To find the profit or loss, we need to use the formula: profit = total revenue - total cost. The total revenue can be found by integrating the marginal revenue function: TR = ∫MR dQ = 900Q, where Q is the quantity of the product. The total cost can be found by integrating the marginal cost function: TC = ∫MC dQ + FC = 15Vx^2 + 4Q + 1000. Therefore, the profit function is: π = TR - TC = 900Q - 15Vx^2 - 4Q - 1000 = 896Q - 15Vx^2 - 1000.

(b) To find the maximum profit, we need to take the derivative of the profit function with respect to Q and set it equal to zero: dπ/dQ = 896 - 4 = 892 = 0. Solving for Q, we get Q* = 892/896 = 0.994. Therefore, the maximum profit is achieved when producing 0.994 units of the product.

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the value of the given integral using spherical coordinates is 1/96 π.

To evaluate the given integral using spherical coordinates, we first need to express the limits of integration in terms of spherical coordinates. Since the solid E is defined between the cone z=sqrt(x^2+y^2) and the sphere x^2+y^2+z^2=1, we can write the limits of integration as follows:
0 <= r <= 1
0 <= θ <= 2π
arctan(r) <= φ <= π/2
Here, r is the radial distance, θ is the azimuthal angle (measured from the x-axis), and φ is the polar angle (measured from the z-axis).
Next, we need to express y^2z^2 in terms of spherical coordinates. Since y=r*sin(φ)*sin(θ) and z=r*cos(φ), we have y^2z^2 = r^5*sin^2(φ)*cos^2(φ)*sin^2(θ).
Finally, we can express the integral in terms of spherical coordinates and evaluate it as follows:
∫∫∫ E y^2z^2 dV = ∫0^1 ∫0^2π ∫arctan(r)^π/2 r^5*sin^2(φ)*cos^2(φ)*sin^2(θ) r^2*sin(φ) dr dθ dφ
= 1/6 ∫0^2π ∫arctan(r)^π/2 sin^2(θ)cos^2(θ) dφ dθ ∫0^1 r^7 dr
= 1/12 π/2 ∫0^1 r^7 dr
= 1/96 π
Therefore, the value of the given integral using spherical coordinates is 1/96 π.

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m∠AVC+m∠CVB=m∠AVB. Option b is correct.

Given a figure in which point C is inside ∠AVB and ∠AVB=62°.

A geometric figure formed by two lines starting from a common point or two planes starting from a common line is called an angle. The space between these lines or planes is measured in degrees.

Knowing that a point C is between ∠AVB and ∠AVC=39° and ∠CVB=23°, then

From the figure, we can see that C is inside ∠AVB, so ∠AVB is divided into two parts, namely ∠AVC and ∠CVB

m∠AVC+m∠CVB=m∠AVB

Now substitute the values ​​we get

39°+23°=62°

62°=62°

So both sides are equal and it's proven.

Hence, a point C is between ∠AVB and ∠AVB=62° then m∠AVC+m∠CVB=m∠AVB.

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Answer:

The total weight of one die, one ball, and one marble is 75 grams.

Step-by-step explanation:

Consider the provided information.

Let d represents the number of dice, b represents the number of balls and m represents the number of marbles.

So according to the question.

The combined weight of 2 identical dice, 5 identical balls and 4 identical marbles was 260 grams.

\(2d+5b+4m=260\)  ....(1)

The combined weight of one die and one marble was 55 grams.

\(d+m=55\)

\(m=55-d\)  ....(2)

3 balls weighed the same as two dice.

\(3b=2d\)

Multiply both sides by 5 and divide by 3.

\(5b=\frac{10}{3}d\)  .....(3)

Now put the value of equation 2 and 3 in equation 1.

\(2d+\frac{10}{3}d+4(55-d)=260\)

\(2d+\frac{10}{3}d+220-4d=260\)

\(\frac{6d+10d-12d}{3}=40\)

\(4d=120\)

\(d=30\)

Put d=30 in equation 2.

\(m=55-30\)

\(m=25\)

Put d=30 in equation 3.

\(5b=\frac{10}{3}\times 30\)

\(5b=100\)

\(b=20\)

The total weight (in grams) of one die, one ball, and one marble is:

\(d+m+b=25+20+30\)

\(d+m+b=75\)

The total weight of one die, one ball, and one marble is 75 grams.

Answer:

The quantity of water in the tank after 15 days is 1610.0 gallons OR 1.61 × 10³ gallons.

Step-by-step explanation:

The amount of water in the tank after 15 days is given by the series

910+(−710)+810+(−610)+⋯+310+(−110)+210

From the series, we can observe that, if water is added for a particular day then water will be drained the following day.

Also, for a day when water is to be added, the quantity to be added will be 100 gallon lesser than the quantity that was last added. Likewise, for a day when water is to be drained, the quantity to be drained will be 100 gallons lesser than the quantity that was last drained.

Hence, we can complete the series thus:

910+(−710)+810+(−610)+710(-510)+610(-410)+510(-310)+410(-210)+310+(−110)+210

To evaluate this, we  get

910-710+810-610+710-510+610-410+510-310+410-210+310-110+210

= 1610.0 gallons

Hence, the quantity of water in the tank after 15 days is 1610 gallons OR 1.61 × 10³ gallons.

Answer:

That would be wrong becuase its starting on march 2nd not March 1st, if march 1st, then it would be resoanble if she used both machines during the same day. It would be on the 17th before she uses both machines on the same day.

Answer:

2/7 + 7/14 = 11/14

Step-by-step explanation:

7 x -2 = -14 Each seventh is going to be worth 2 fourteenths!

This means 2/7 = 4/14

4/14 + 7/14 = 11/14

Answer:

eleven fourteenths

Step-by-step explanation:

The coordinates of the image is (4,-1) that is option D) is correct.

According to the question we have been given that

        the point to be rotated = (-4,1)

           center = (-3,0)

        Rotation = 180° counterclockwise.

Note that when the point is rotated 180° counterclockwise then the coordinate of the image point will be

   (x , y ) = (-x , - y)

For the coordinates of the image first we translate the center to the origin that is

    (-3,0) = (-3+3,0) = (0,0)

Now we will do same for the point that is,

   (-4 , 1) = (-4+3 , 1) = (-1,1)

Now the points are (-1,1). Thus the image will be  

   (-1,1) = (-(-1), -1) = (1,-1)

Now undoing the original translation :

  (1,-1) = (1+3,-1) = (4,-1)

Hence the coordinates of the image is (4,-1) that is option D) is correct.

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The smallest p-value is always associated with the z-score that is furthest away from the mean. This is because the tails of the normal distribution curve have less area and thus represent smaller p-values. The correct answer is option (d) z = -3.24.

In a hypothesis test, there are two hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1).

The null hypothesis is the one we're testing, while the alternative hypothesis is the one we're trying to support or prove.

A two-tailed alternative hypothesis is one in which we are interested in whether a parameter is not equal to a certain value, as opposed to one-tailed alternative hypotheses, in which we are interested in whether the parameter is greater than or less than a certain value.

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Answer:

Midpoint={5.5,1}

Step-by-step explanation:

M={x1+x2/2,y1+y2/2}

M={6+5/2,-2+4/2}

M={11/2,2/2}

M={5.5,1}

The percentage of 322 out of 450 using the percentage formula was found out to be approximately 71.56%.

To find the percentage of 322 out of 450, we can use the following formula:

percentage = (part/whole) x 100

where, "part" is the value we want to express as a percentage (in this case, 322), "whole" is the total value (in this case, 450), and "x" means "multiply".

Using the formula mentioned above, we get:

percentage = (322/450) x 100

percentage = 0.7156 x 100

percentage = 71.56%

Therefore, percentage of 322 out of 450 is approximately 71.56%.

A percentage is a way to express a number as a fraction of 100. It is often denoted using the "%" symbol.

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Answer: C

Step-by-step explanation:

           just took the test

then people are willing to buy approximately 0.0778 pounds of chocolate candy per day.

The price-demand equation for a gourmet food store, which states that people are willing to buy x pounds of chocolate candy per day at p dollars per quarter pound, is given by the formula 180 x = 10 + 2 < p < 10.

We need to determine the number of pounds of chocolate candy that people are willing to buy at various prices using this formula.

In this given gourmet food store, people are willing to buy x pounds of chocolate candy per day at p dollars per quarter pound, as given by the price-demand equation 180 x = 10 + 2 < p < 10.

To find the number of pounds of chocolate candy that people are willing to buy at different prices, we can use the price-demand equation.

Let's take a look at the price-demand equation and see what it means. The price-demand equation is given by 180 x = 10 + 2 < p < 10,

which means that the demand for chocolate candy at the store is directly proportional to the price of the candy. In other words, as the price of the candy goes up, the demand for the candy goes down, and vice versa.

Using the formula, we can find the number of pounds of chocolate candy that people are willing to buy at various prices. For example, if the price per quarter pound is 2 dollars, then we can plug in the value of p into the formula to find the corresponding value of x. We get:

180 x = 10 + 2(2)
180 x = 14
x = 14/180
x = 0.0778

So, if the price per quarter pound is 2 dollars, then people are willing to buy approximately 0.0778 pounds of chocolate candy per day.

Thus, the price-demand equation can be used to determine the number of pounds of chocolate candy that people are willing to buy at various prices. As the price of the candy goes up, the demand for the candy goes down, and vice versa.

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The fact that the ratio of 0.75 to 0.375 is a small whole number is an illustration of "Law of Multiple Proportions."

When two elements combine to form and over one compound, the weights with one element which combine with such a fixed weight of the second are in a ratio of small whole numbers, according to the law of multiple proportions.

Some key features regarding the Law of Multiple Proportions are-

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The complete question is-

Carbon monoxide can be broken down into carbon and oxygen in a mass ratio of 3:4 or 0.75. Carbon dioxide can be broken down into carbon and oxygen in a mass ratio of 3:8 or 0.375. The fact that the ratio of 0.75 to 0.375 is a small whole number is an illustration of

Answer:

Step-by-step explanation:

You want to know how to determine the y-intercepts of a rational function, and their possible number.

A rational function f(x) is the ratio of two polynomial functions p(x) and q(x):

  f(x) = p(x)/q(x)

As such, both numerator and denominator have single function values for any value of the independent variable. The y-intercept of f(x) is ...

  f(0) = p(0)/q(0)

The values of p(0) and q(0) are simply the constant terms in those respective functions.

The simple way to find the y-intercept is to look at the ratio of the constant terms in the polynomial functions making up the rational function. If that is defined, there is one y-intercept. If it is undefined (q(0)=0), then there are no y-intercepts.

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In this the maximum level of inventory is 1250 units, and the total minimal yearly cost is $25,000.

To determine the optimal production quantity, we need to find a balance between the holding cost and the production cost. The holding cost is given as a function of the number of units, and the production cost is constant at $150 per cycle. The machines have a capacity of 7500 units per year, and the annual demand is 5000 units. Since the demand is less than the machine capacity, we need to produce the full demand each cycle to minimize the holding cost. Thus, the optimal production quantity is 5000 units.

The time between two production cycles can be calculated by dividing the number of working days in a year (250 days) by the number of cycles per year. Since we produce 5000 units per cycle and the annual demand is 5000 units, there is only one production cycle per year. Therefore, the time between two production cycles is 250/1 = 250 days.

The maximum level of inventory occurs just after production and is equal to the production quantity. Hence, the maximum level of inventory is 5000 units.

The total minimal yearly cost can be calculated by multiplying the holding cost per unit by the average inventory level throughout the year. Since the average inventory level is half of the maximum level (5000/2 = 2500 units), the total minimal yearly cost is (2500 * lof) + ($150 * 1) = $25,000.

To illustrate the model graphically, you can create a plot with the number of days on the x-axis and the inventory level on the y-axis. The plot will show a horizontal line at the maximum inventory level of 5000 units, indicating the production time. After production, the inventory level drops to zero until the next production cycle. This cycle repeats throughout the year, resulting in a sawtooth pattern on the graph.

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Answer:

E 3/2

Step-by-step explanation:

The slope of the line that passes through the points (1,-4) and (3,-1) is 3/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁)

The given coordinate points are (1,-4) and (3,-1).

Substitute, (x₁, y₁)=(1,-4) and (x₂, y₂)=(3,-1), we get

m= (-1+4)/(3-1)

= 3/2

Therefore, the slope of the line that passes through the points (1,-4) and (3,-1) is 3/2.

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Answer:

1530 is the tax she needs to pay

A manufacturer of compact fluorescent light bulbs advertises have a standard deviation of 1,000 hours so the values are:

A normal distribution with,

μ = 9000

σ = 1000

a) The standardized score is the value x decreased by the mean and then divided by the standard deviation.

x = 105000 - 9000 / 1000 ≈ 1.50

Determine the corresponding probability using the normal probability table in appendix,

P(X>10500) = P(Z>1.50) = 1 - P(Z<1.50)

= 1 - 0.9332 = 0.0668.

b) n = 15

The sampling distribution of the mean weight is approximately normal, because the population distribution is approximately normal.

The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

μ = 1000/√15 = 258.19

c) The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

The z-value is the sample mean decreased by the population mean, divided by the standard deviation:

z = x-u/σ/√n = 10500-9000/1000√15 = 5.81

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\(\int\limits^a_b {3tan^{5}(x) } \, dx\), with the appropriate use of absolute values and the constant of integration represented as 'C', is equal to (-3/4) ln|sec²(x)| - (3/2) tan³(x) + C.

To evaluate the integral ∫3 tan⁵(x) dx, we can use integration techniques and trigonometric identities. First, we can rewrite tan⁵(x) as \((tan^{2}(x)) ^{2}\) * tan(x). The integral of tan²(x) can be found by using the identity sec²(x) - 1 = tan²(x). Rearranging this identity, we get tan²(x) = sec²(x) - 1. Substituting this back into the original expression, we have ∫3 [\((sec^{2}(x)-1) ^{2}\)* tan(x)] dx.

Next, we can expand the expression \((sec^{2}(x)-1) ^{2}\)using the binomial theorem, which gives us sec⁴(x) - 2sec²(x) + 1. The integral becomes ∫3 [sec⁴(x) - 2sec²(x) + 1] tan(x) dx. Using the power rule for integration, we can find the integral of each term individually.

The integral of sec⁴(x) tan(x) dx can be evaluated by substituting u = sec(x) and using the fact that du = sec(x) tan(x) dx. This simplifies the integral to ∫3 u⁴ du, which can be easily integrated as (u⁵/5) + C.

Similarly, the integral of sec²(x) tan(x) dx can be evaluated by substituting v = sec(x) and using du = sec(x) tan(x) dx. This simplifies the integral to ∫3 v² dv, which can be integrated as (v³/3) + C.

Lastly, the integral of tan(x) dx is simply ln|sec(x)| + C.

Combining the results, we have (-3/4) ln|sec²(x)| - (3/2) tan³(x) + C as the final answer, where C represents the constant of integration.

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The points in a scatter plot cluster closely around the regression line, the correlation can be said to be the proportion of variance in Y that is determined or explained by X.

It is critical to understand that a correlation coefficient of zero indicates that there is no linear courting, but there can also nonetheless be a strong relationship among the 2 variables.

If one point of a scatter diagram is farther from the regression line than a few other factor, then the scatter diagram has as a minimum one outlier. If two or extra points are the identical farthest distance from the regression line not a commonplace prevalence), then every of those points is an outlier.

When the y variable has a tendency to increase because the x variable increases, we say there may be a high-quality correlation between the variables. when the y variable has a tendency to lower as the x variable increases, we are saying there's a bad correlation between the variables.

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