Evaluate using the correct order of operations. (17)/(18)+(6)/(35)-:(5)/(7)*(25)/(4)

The equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

equation of a line using point-slope form is-

y - y1 = m(x - x1)

Points: (17,-12) and  slope -3.

Put the values:

y - (-12) = -3(x - 17)

y + 12 = -3x + 51

y = -3x + 51 - 12

y = -3x + 39

Thus, the equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

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The value of p(3) is p(3)=12.

Here, we have,

Synthetic division :

It is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.

The given function is,

p(z)=8z⁴-17z³-20z²-4z+15                  

We have to find  p(3)  

Substitute z= 3 in above function.

p(3)=8×3⁴-17×3³-20×3²-4×3+15                

     =12      

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solve for t to get t = 4

1. To find the derivative of f(x) = (3 – 2x^3)^3 we can apply the power rule, the chain rule, and the product rule. The power rule states that the derivative of f(x) = x^n is f'(x) = nx^n-1. The chain rule states that the derivative of f(x) = g(h(x)) is f'(x) = g'(h(x))*h'(x). The product rule states that the derivative of f(x) = uv is f'(x) = u'v + uv'. In this case, we can rewrite f(x) as f(x) = (h(x))^3 where h(x) = 3 - 2x^3. We then apply the chain rule to get f'(x) = 3(3 - 2x^3)^2(-6x^2). Similarly, we can find the derivative of f(t) = 100(6-t)/t+3. We can rewrite f(t) as f(t) = u(t)v(t) where u(t) = 100 and v(t) = (6-t)/t+3. Applying the product rule, we get f'(t) = 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2).

2. To find other information about a function, we can use the derivative we just found. For example, if we want to find the maximum or minimum values of a function, we can set the derivative equal to 0 and solve for the x or t values. In the case of f(x), we can set 3(3 - 2x^3)^2(-6x^2) = 0 and solve for x to get x = (sqrt(3/2))^(1/3). Similarly, for f(t) we can set 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2) = 0 and solve for t to get t = 4. We can also use derivatives to find the equation of a tangent line to a function at any given point. In this case, we would use the derivative we found in order to calculate the slope of the tangent line at any given point and then use point-slope form to find the equation of the line.

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The result is the 95% confidence interval for µ.

The Metropolis-Hasting (M-H) algorithm is a Markov Chain Monte Carlo (MCMC) method used to sample from a probability distribution. In this case, we want to sample from the posterior distribution of µ, given the recorded data and the prior distribution. The M-H algorithm works by proposing a new value for µ, calculating the acceptance probability, and then deciding whether to accept or reject the proposed value. Here are the steps to construct the M-H algorithm:

Start with an initial value for µ, denoted as µ0.
Propose a new value for µ, denoted as µp, from the proposal distribution q(µ| µo) : N(θ: mean = µp, std = 2).
Calculate the acceptance probability, denoted as α, using the likelihood function L(µ) and the prior distribution p(µ):
α = min{1, [L(µp)/L(µ0)]*[p(µp)/p(µ0)]*[q(µ0| µp)/q(µp| µ0)]}
Generate a random number u from the uniform distribution U(0,1).
If u ≤ α, accept the proposed value and set µ0 = µp. Otherwise, reject the proposed value and keep µ0 unchanged.
Repeat steps 2 to 5 for a specified number of MCMC draws (15000 in this case), and discard the first 1500 draws as the burn-in phase.
Calculate the 95% confidence interval for µ using the remaining 13500 draws.

The 95% confidence interval for µ can be calculated by finding the 2.5th and 97.5th percentiles of the posterior distribution of µ. This can be done by sorting the 13500 draws of µ in ascending order and finding the values that correspond to these percentiles. The result is the 95% confidence interval for µ.

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15 + 2x = Price

The price of a medium-sized pizza at Desminos Pizza's online menu is $15 plus $2 per topping. The equation for this is 15 + 2x = Price, where x represents the number of toppings.

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Answer:If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. the intersection points (-3,3) Since the system is infinite it means there is 1 line on the graph-

Step-by-step explanation:

The proof that ∠B ≅ ∠C is:

D is the midpoint of of BC - Given...................(1)
Thus
BD = DC ................................................................(2)

∠EDC ≅ ∠FDB  - Given......................................(3)

DE ⊥ AB - Given...................................................(4)
DF ⊥ AC - Given ..................................................(5)
∠AED = ∠DEB = 90° - perpendicular bisector theorem  ....(6)

∠AFD = ∠DFC = 90° - perpendicular bisector theorem ....(7)
∠EAF = ∠EDF = 90° - Properties of the angles of a Quadrilateral

Since ∠EDC ≅ ∠FDB, as in   (3) above, and

Both comprise of ∠EDF,

thus,
(∠EDC - ∠EDF) ≅ (∠FDB - ∠EDF)

Since

∠EDB = (∠FDB - ∠EDF); and

∠FDC = (∠EDC - ∠EDF)

Thus,

∠EDB ≅ ∠FDC

thus,
∠EDB = ∠FDC = 45° (Sum of Angles on a Straight line) that is
∠EDB =  ∠FDC = (180° -∠EDF)/2

Since  ∠EDF = 90°
∠EDB =  ∠FDC = (180° -90°)/2

∠EDB =  ∠FDC = 90/2
∠EDB =  ∠FDC = 45°

Since
∠DEB = 90° (5); and

∠DFC = 90° (7)
ΔBED ≅ ΔDFC

Thus, by Sum of Angles in a Triangle,
∠B ≅ ∠C.

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U is a subspace of R3.  A basis for U is  {(1, -2, 3)}  and dim(U) = 1.

a) To show that U is a subspace of R3, we must verify the three conditions:

1. U is non-empty, since the vector (0,0,0) ∈ U, since 0 + 2(0) - 3(0) = 0.
2. U is closed under addition, since for any two vectors (x1, y1, z1) and (x2, y2, z2) ∈ U, their sum (x1+x2, y1+y2, z1+z2) also satisfies the equation x1+x2 + 2(y1+y2) - 3(z1+z2) = 0, so it is also in U.
3. U is closed under scalar multiplication, since for any scalar c and any vector (x, y, z) ∈ U, the vector c(x,y,z) = (cx, cy, cz) also satisfies the equation cx + 2cy - 3cz = 0, so it is also in U.

Therefore, U is a subspace of R3.

b) To find a basis for U, we must find a linearly independent set of vectors which span U. One such set is the vector (1, -2, 3), since it satisfies the equation x + 2y - 3z = 0. Therefore, {(1, -2, 3)} is a basis for U.

c) The dimension of U is the number of vectors in its basis, which is 1. Therefore, dim(U) = 1.

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To solve the equation, we need to get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD), which is (b^(2)-9). This will give us:
(8)(b^(2)-9)/(b^(2)-9)-(1)(b^(2)-9)/(b+3)=(1)(b^(2)-9)/(b^(2)-9)
Simplifying the equation gives us:
8-(b^(2)-9)/(b+3)=1
Next, we will isolate the variable term by subtracting 8 from both sides of the equation:
-(b^(2)-9)/(b+3)=-7
Now, we will multiply both sides of the equation by (b+3) to get rid of the fraction:
-(b^(2)-9)=-7(b+3)
Expanding the equation gives us:
-b^(2)+9=-7b-21
Rearranging the equation gives us:
b^(2)-7b-30=0
Factoring the equation gives us:
(b-10)(b+3)=0
Setting each factor equal to zero gives us the possible solutions:
b-10=0 or b+3=0
Solving for b gives us the possible solutions:
b=10 or b=-3
However, we need to check for extraneous solutions by plugging the possible solutions back into the original equation. Plugging in b=10 gives us a true statement, but plugging in b=-3 gives us an undefined expression. Therefore, the only solution is b=10.
Answer: b=10

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Based on the information provided, it can be concluded that Manuel measured the height.

The height of a triangle ( a shape with three sides, three angles, and three vertices) can be defined as the distance between the vertex and the opposite. The vertex refers to the highest point of the triangle, which is usually at the top. In the case of the triangle presented, the height is five and this was correctly obtained by Manuel when he measured the distance from the vertex to its base.

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This |x - 32| <= 2 means that the tire pressure can be anywhere between 30 psi and 34 psi.

In order for Ms. Sartain's car to have optimal gas mileage, the tire pressure should remain within 2 psi of 32 psi at all times. This can be modeled with an absolute value inequality.

The absolute value inequality that models this situation is |x - 32| <= 2. This inequality states that the difference between the tire pressure, x, and the optimal pressure, 32, should be less than or equal to 2.

In other words, the tire pressure can be 2 psi above or below the optimal pressure of 32 psi and still be within the acceptable range. This means that the tire pressure can be anywhere between 30 psi and 34 psi.

So the correct answer is |x - 32| <= 2.

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Answer:

Using the difference of squares formula, we have:

(r³ - 6t¹) (r³ + 6t¹) = r³ × r³ - r³ × 6t¹ - 6t¹ × r³ - 6t¹ × 6t¹

= r^6 - 36t²

Therefore, the expression in simplest form is r^6 - 36t².

The volume of the composite solid is 5104 cubic ft.

A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.

The area of a triangular prism is given as:

V = 1/2(bhl)

Here, h = 22 - 12 = 10 ft.

Substituting the values we have:

V = 1/2(13)(10)(32)

V = 2080 cubic ft.

The volume of the rectangular prism is given as:

V = lwh

V = (28)(9)(12)

V = 3024 cubic ft.

The volume of the composite solid is:

V = V1 + V2

V = 2080 + 3024

V = 5104 cubic ft.

Hence, the volume of the composite solid is 5104 cubic ft.

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The volume of the cone is  1004.8 cm³.

Let's calculate the volume of the cone with radius 8 cm and the slant height is 17 cm. Therefore, let's find the volume of the cone as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore,

h² = 17² - 8²

h = √289 - 64

h = √225

h = 15 cm

Therefore,

volume of a cone = 1 / 3 × 3.14 × 8² × 15

volume of a cone = 1 / 3 × 3.14 × 64 × 15

volume of a cone = 3014.4 / 3

volume of a cone = 1004.8 cm³

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The real yeild is 0.65%.

The Estimated 10-year Treasury bond yield is 3.65%.

The 10-year Treasury bond yield can be estimated using the 5-year Treasury bond yield and the expected inflation rate of 3%.

This is done by calculating the real yield, which is the difference between the nominal yield and the expected inflation rate.

The 10-year Treasury bond yield can be estimated by adding the real yield of the 5-year Treasury bond to the expected inflation rate of 3%.

Real yield = Nominal yield - Expected inflation rate

Real yield (5-year Treasury bond) = 3.65% - 3% = 0.65%

Estimated 10-year Treasury bond yield = 0.65% + 3% = 3.65%

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a. 39 work sampling observations. b. By selecting a random time and a random employee to observe. c. The 95% confidence interval for the population standard is approximately 83.56 +/- (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

a. To determine the number of work sampling observations necessary to achieve a 95% confidence level with a margin of error of +10%, we need to use the following formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = Z-score for the desired confidence level (1.96 for 95% confidence level)

p = proportion of beak adjustments estimated from preliminary investigation (0.3)

E = margin of error (0.1)

Plugging in the values:

n = (1.96^2 * 0.3 * 0.7) / 0.1^2

n = 38.15

Rounding up, we need at least 39 work sampling observations.

b. The random observations should be made by selecting a random time of day, and then selecting a random employee to observe. This should be repeated until the required number of observations has been made. This method ensures that all employees have an equal chance of being observed and that the observations are not biased towards certain times or individuals.

c. To determine the standard in hours per hundred beak adjustments, we need to use the following formula:

Standard = (Total time worked / Total number of beak adjustments) * 100

For the six employees summarized in the table:

Granny:

Standard = (82 / 164) * 100

Standard = 50 hours per hundred beak adjustments

Tweety:

Standard = (80 / 161) * 100

Standard = 49.69 hours per hundred beak adjustments

Item:

Standard = (200 / 185) * 100

Standard = 108.11 hours per hundred beak adjustments

Total:

Standard = (82 + 80 + 200 + 121 + 161 + 185) / (164 + 161 + 185) * 100

Standard = 83.56 hours per hundred beak adjustments

The calculated error is the difference between the estimated standard and the true population standard. Since we do not have the population data, we cannot calculate the error. However, we can calculate the variability in the sample data using the following formula:

Standard Error = Standard Deviation / √(n)

Where:

Standard Deviation = √((Σ(x - x-bar)^2) / (n - 1))

n = sample size

Using the data provided in the table, we can calculate the standard deviation and standard error as follows:

Standard Deviation = √(((82-73.5)^2 + (80-73.5)^2 + (200-119)^2 + (121-82.5)^2 + (161-119)^2 + (185-82.5)^2) / (6-1))

Standard Deviation = 55.88

Standard Error = 55.88 / √(6)

Standard Error = 22.83

This means that there is a 95% chance that the true population standard falls within + or - 2 standard errors of the estimated sample standard. Therefore, the 95% confidence interval for the population standard is approximately 83.56 + or - (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

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The complete question goes thus:

ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments). a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a +10 percent of the population data? b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days). c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error? Granny 82 164 Tweety 80 Item Total hours worked Total observations (all elements) Observations involving cataloguing Average rating Operators Speedy Taz Glez 78 76 200 121 Foghorn Leghorn 68 Yosemite Sam 81 161 185 144 51 57 29 42 47 55 78 95 120 85 95 99

Using Poisson distribution, the probability of each scenario is attached below.

(a) The probability of receiving 0 complaints in a 3-day period is given by the Poisson distribution:

P(X=0) = (λ^x * e^(-λ)) / x!

where λ is the expected number of complaints per day, and x is the number of complaints in the time period of interest.

In this case, λ = 1.1 complaints per day, and x = 0 complaints in 3 days.

P(X=0) = (1.1^0 * e^(-1.1 * 3)) / 0! = 0.037

So the probability of receiving 0 complaints in a 3-day period is 3.7%.

(b) The probability of receiving 1 complaint in a 3-day period is:

P(X=1) = (1.1^1 * e^(-1.1 * 3)) / 1! = 0.041

So the probability of receiving 1 complaint in a 3-day period is 4.1%.

(c) The probability of receiving 2 complaints in a 3-day period is:

P(X=2) = (1.1^2 * e^(-1.1 * 3)) / 2! = 0.022

So the probability of receiving 2 complaints in a 3-day period is 2.2%.

(d) The probability of receiving 3 complaints in a 3-day period is:

P(X=3) = (1.1^3 * e^(-1.1 * 3)) / 3! = 0.008

So the probability of receiving 3 complaints in a 3-day period is 0.8%.

(e) The probability of receiving 4 complaints in a 3-day period is:

P(X=4) = (1.1^4 * e^(-1.1 * 3)) / 4! = 0.0022

So the probability of receiving 4 complaints in a 3-day period is 0.22%.

(f) The probability of receiving less than or equal to 4 complaints in a 3-day period is:

P(X ≤ 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) = 0.1102

So the probability of receiving less than or equal to 4 complaints in a 3-day period is 11.02%.

(g) The probability of receiving more than 4 complaints in a 3-day period is:

P(X > 4) = 1 - P(X ≤ 4) = 1 - 0.1102 = 0.8898

So the probability of receiving more than 4 complaints in a 3-day period is 88.98%.

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Answer:

30 Stamps

Step-by-step explanation:

Since 40% of Jon's collection has boat stamps, that means that 20% of his total collection would be 6 stamps (40%/2  and  12/2).

All that's left to do now is get that % to 100, and we can do this by multiplying that and the number of stamps by 5.  (20%*5=100,  6*5=30)

This means that Jon has a total of 30 stamps in his collection.

Another way you could do this is simply to multiply 12 by 40%, or 0.4.
This will also give you an answer of 30 stamps.

The roommate is wrong. The scaled desk should be 1 1/3 inches high, as per Olaf's initial scaling of 1 inch representing 30 inches of actual length in the room. The other dimensions of the scaled desk would be 12 inches long and 6 2/3 inches wide.

When Olaf decided to let 1 inch represent 30 inches of actual length in the room, he created a scale factor of 1:30. This means that for every inch in the scale model, there are 30 inches in the actual room. Using this scale factor, the scaled desk height should be 40/30 = 4/3 inches. Therefore, the roommate's suggestion of 10 inches high is incorrect.

To find the other dimensions of the scaled desk, we need to apply the same scale factor of 1:30. The scaled length would be 36/30 = 12 inches, and the scaled width would be 20/30 = 2/3 inches. However, it's easier to work with whole numbers, so we can multiply both dimensions by 10 to get 120 inches long and 6 2/3 inches wide, which is equivalent to 12 inches long and 2/3 inches wide in the scaled model.

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Note that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.

The postulate indicates that if two lines intersect and make the two adjacent angles equal to each other, then each of the equal angle is a right angle. Also, the two lines that intersect this way is said to be perpendicular to each other.

Since the ∠MRS ≅ ∠MRO, we can state that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.

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Answer:

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The exponential function is y = 5*(∛2)^x and the value after 10 days is 50.4

Here we can see an exponential function of the form y = a*b^x

First, notice that it passes through (0, 5), then:

5 = a*b^0 = a

5 = a

So we got the initial value, so we can write the equaton like:

y = 5*b^x

And now we need to find the value of b.

We also can see that it passes through (3, 10), then:

10 = 5*b^3

10/5 = b^3

2 = b^3

∛2 = b

So the function is:

y = 5*(∛2)^x

b) The value after 10 days is what wet when we evaluate the function above in x = 10, then we will get:

y = 5*(∛2)^10  = 50.4

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The 12th term of the geometric sequence 9, - 18, 36, is 18,432.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -18/9

Common ratio, r = -2

For the 12th term, we have:

a₁₂ = 9(2)¹²⁻¹

a₁₂ = 18,432.

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If ∠PRM = 120°, then the measure of angle MRN is 60°.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

In the figure, segment PN is a line.

So, the angles formed in between are linear pair of angles.

∠PRM and ∠MRN are linear pair of angles.

∠PRM + ∠MRN = 180°

120 + ∠MRN = 180°

∠MRN = 180° - 120°

∠MRN = 60°

Hence the required angle measure is 60°.

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The complete factorization of [tex]-3x^2+6x+9[/tex] is -3(x - 3)(x + 1).

A mathematical expression, equation, or polynomial is factorized, sometimes referred to as factored, when it is broken down into factors or simpler expressions.

A technique for factoring a number or a polynomial is called factorisation. The polynomials are divided into the sums of their component parts. As an illustration, x2 + 2x can be factored as x(x + 2), where x and x+2 are the factors that can be multiplied to obtain the original polynomial.

To factor completely [tex]-3x^2+6x+9[/tex], we first need to factor out the greatest common factor, which is -3:

[tex]-3(x^2 - 2x - 3)[/tex]

Now we can factor the quadratic expression inside the parentheses:

-3(x - 3)(x + 1)

Hence, the complete factorization of [tex]-3x^2+6x+9[/tex] is -3(x - 3)(x + 1).

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Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

What is liability ?

Liability refers to an obligation or debt that an individual, company, or organization owes to another party. In accounting and finance, liabilities are generally classified as current or long-term and can include items such as loans, mortgages, accounts payable, taxes owed, and salaries payable.

The following options would be considered a liability:

Student loan

Money you owe your parents

Mortgage payment

Car payment

Investments and retirement funds would not be considered liabilities as they are assets.

Therefore, Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

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The equation can be written as: x + 24° = 90°.

The measure of the unknown angle is 66°.

An algebraic equation is an equation that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Let the measure of the unknown angle be x.

Since the angle in the corner measures 90° and one piece of the tile will have a measure of 24°. We can write the equation as:

x + 24° = 90°

The measure of the unknown angle can be determined as follow:

​x + 24° = 90°

x = 90° - 24°

x = 66°

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The domain of the correspondence is {-3, -2.5, 0, 4} and the range is {3, 9, -10}. This correspondence is not a function because it is not a one-to-one correspondence; for example, both -3 and 4 are mapped to the same value of 3.

The question is asking for the domain, range, and whether the correspondence is a function for the given set of ordered pairs: {(-3,3), (-2.5), (0,9), (4,-10)}.

The domain of a correspondence is the set of all possible input values. In this case, the domain is the set of x-values from the ordered pairs: {-3, -2.5, 0, 4}.

The range of a correspondence is the set of all possible output values. In this case, the range is the set of y-values from the ordered pairs: {3, -5, 9, -10}.

A correspondence is a function if each input (x-value) is associated with only one output (y-value). To determine if the given correspondence is a function, we need to check if any x-value is repeated with a different y-value.

In this case, there are no repeated x-values, so each x-value is associated with only one y-value. Therefore, the correspondence is a function.

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Answer:

Step-by-step explanation:

No, Selena is incorrect.

answer: Even though there are six

more people than pizzas at the large table and only five more people

than pizzas at the small table, each person at the large table will get

a greater share of pizza than each person at the small table.

The product of the polynomials (4x-7)^(2) is 16x^(2)-56x+49. This is the final answer expressed as a single polynomial in standard form.

To multiply the polynomials using a special product formula, we can use the formula (a-b)^(2)=a^(2)-2ab+b^(2). In this case, a=4x and b=7. Plugging these values into the formula gives us:
(4x-7)^(2)=(4x)^(2)-2(4x)(7)+(7)^(2)

Simplifying the terms on the right side of the equation gives us:
(4x-7)^(2)=16x^(2)-56x+49

Simplifying, we have (4x-7)2 = 16x2 - 56x + 49, which is our answer expressed as a single polynomial in standard form.

Multiplying polynomials require only three steps.

First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.

Add the powers of the same variables using the exponent rule.

Then, simplify the resulting polynomial by adding or subtracting the like terms.

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