The polynomial -2 x^2 + 500x represents the budget surplus of the town of Alphaville for the year 2010. Alphaville’s surplus in 2011 can be modeled by -1. 5 x^2 + 400x. If x represents the yearly tax revenue in thousands, by how much did Alphaville’s budget surplus increase from 2010 to 2011? If Alphaville took in $750,000 in tax revenue in 2011, what was the budget surplus that year?

Answer:

A(1,2)

Step-by-step explanation:

tracing the point of intersection of the two lines on the y and the x axis,on the y we have 2 and on the x we 1.

The values which could be the slope of the line are numbers > 0.

According to the task content, it follows that the given line originates from the lower left quadrant and continues through the upper right quadrant.

It therefore follows that the line is ascending from left to right in which case, the slope of the line is positive.

Hence, the possible values of the slope include the set of numbers greater than 0.

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Answer: C and D

Step-by-step explanation: Trust me bro

Answer: Anita's

Step-by-step explanation:

Anita's shape would have the longest sides because she only has 4 total sides, while the others have 5, 6, and 10

This means that if the total perimeter for each of the shapes was 10 units,

Anita's shape would have side lengths of about 2.5 units while the others would have side lengths of 2, 1.6, and 1 units.

This means Anita's shape has the longest sides

We find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

Exponential functions are trascedent functions whose form is described below:

[tex]y = a\cdot r^{x}[/tex]     (1)

Where:

There are two conditions for a stretch factor and exponential decay: (i) a > 1, (ii) 0 < r < 1. Thus, we find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

The picture is missing and it cannot be found, but statement is still solvable as there is only one choice that responds the question.

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0.385 is the probability under given conditions.

Lets simplify the above problem,

Given n=20, p=0.05, q=0.95

Probability that in a sample of 20 window frames:

None will need adjustments.

P(x=0)= 0.95^20 = 0.3585

At least one will need adjustment?

P(x>=1) = 1 - P(x=0)

= 1 - 0.3585

= 0.6415

More than two will need adjustment?

P(x>2) = 1 - P(x=0) -P(x=1) -P(x=2)

= 1 - 0.3585 - 20C1(0.05)^1*(0.95)^19 - 20C2(0.05)^2*(0.95)^18

= 0.6415 - 20*0.05*0.3774 - 190*0.0025*0.3972

= 0.2641-0.18868

= 0.0755

Hence 0.385 is the solution of the given problem.

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The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

If A and B are dependent events, then the probability of both events occurring simultaneously is given by:

[tex]P(A \cap B)=P(B) \cdot P(A \mid B)[/tex]

The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:

[tex]P(A \cap B)=P(A) \cdot P(B)[/tex]

Multiplication Theorem of Probability:

The multiplication guidelines that we use in probability have already been taught to us, including;

[tex]\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}[/tex]

Therefore, the relationship between two events is explained by the probability multiplication rule.

Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.

Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.

Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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The lengths of the other two sides of the right triangle are 12 and 13

From the question, we are to determine the lengths of the other sides of the triangle

From the given information,

The other sides have lengths that are consecutive integers

Thus,

If the length of the other side is x

Then,

The hypotenuse will be x + 1

By the Pythagorean theorem, we can write that

(x+1)² = x² + 5²

(x+1)(x+1) = x² + 25

x² + x + x + 1 = x² + 25

x² - x² + x + x = 25 - 1

2x = 24

x = 24/2

x = 12

∴ The other leg of the right triangle is 12

Hypotenuse = x + 1 = 12 + 1 = 13

Hence, the lengths of the other two sides are 12 and 13

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The inequality represented by the graph is; B: y > 3x + 2

We are told that the line goes through the coordinates;

(-3, -7) and (0, 2)

Now, formula to find the slope is;

m = (y2 - y1)/(x2 - x1)

m = (2 - (-7))/(0 - (-3))

m = 9/3

m = 3

Since it's a dashed straight line and everything to the left is shaded, then it means that the inequality represented by the graph is;

y > 3x + 2

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Answer:

B

Step-by-step explanation:

edge 23

The missing indicated angle of the given right angle triangle is; 39°

We can see in the attached image showing the missing figure that it is a right angle triangle and as such we can find the missing angle via trigonometric ratios. In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles

The trigonometric ratios we can use are as follows;

sin x = opposite/adjacent = opp/hyp

cos x = adjacent/hypotenuse = adj/hyp

tan x = opposite/adjacent = opp/adj

Now, we see that the missing angle lies on the side with a length of 28. Thus, adjacent side = 28 and opposite side of it = 23. Thus;

tan x = opposite/adjacent = 23/28

x = tan⁻¹(23/28)

x =  tan⁻¹(0.8214)

x = 39.4° ≈ 39°

Thus, we can conclude that the measure of the indicated angle to the nearest degree 35 and 28 is calculated as 39°.

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The CPT code that is used here is CPT code 11755.

This is the code that is used as the biopsy of the nail bed. The CPT code is used to report this procedure.

Then it would be determined if it is a case of melanoma or lesion that is causing the issues with the individuals nails.

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he correct code for biopsy of the nail bed or nail plate.

The factored expression of the polynomial is (4 - x)(5 + x)

The polynomial expression is given as;

20 - x - x^2

Expand the expression

20 - 5x + 4x - x^2

Factorize the expression

5(4 - x) + x(4 - x)

Factor out 4 - x

(4 - x)(5 + x)

Hence, the factored expression of the polynomial is (4 - x)(5 + x)

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It is likely is it to snow tomorrow in the mountains is 1/4

A chance is the occurrence of events without apparent purpose or cause. It is simply the possibility that something will happen. When chance is defined in mathematics, it is called probability. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the total number of possible cases. Mathematically, the probability that an event occurs is equal to the ratio of the number of cases favorable to a particular event to the number of all possible cases. The theoretical probability of an event is referred to as P(E). P(E) = number of outcomes more favorable to E/Nnumber of all possible outcomes of the experiment

We need to find that what is the chance that it will snow tomorrow in the mountains

According to the weather report, there is a 25% chance of snow in the mountains tomorrow.

Therefore the possible chance that it will snow tomorrow is 25/100 = 1/4

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The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

According to the question,

Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.

First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.

Mean: 10*3 = 30

Standard deviation: 5*3 = 15

Secondly "change of origin" when every score in a data set by a constant, its mean get  added or subtracted by the same constant and standard deviation remains constant.

Applying change of origin in the above mean and standard deviation  

Mean: 30 - 4 = 26

Standard deviation: Remains same = 15

Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

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Answer:

-2

Step-by-step explanation:

The slope of a line is rise/run

So, just see how much the line rises/how much the line runs

In this case, the line rises 2 units for every -1 unit it runs

So, the slope is -2

Answer:

Se below

Step-by-step explanation:

The two angles form a straight line which is 180° angle

4z + z = 180

5z = 180

z = 36  °            4z = 144°

Answer:

2

Step-by-step explanation:

The graphs intersect at 2 points.

The 2 solutions are x = -2 and x = 6.

Answer:

18 posters

Step-by-step explanation:

Posters posted last week: 81/3 = 27 posters

Remaining posters: 81-27 = 54 posters

Posters posted this week: 54/3 = 18*2 = 36 posters

Posters remaining: 54-36 = 18 posters

The isosceles triangle is proved below.

The complete information wasn't found. The proofing of the triangle will be illustrated. It should be noted that the angles opposite to the equal sides of an isosceles triangle are also equal.

Proof: Consider an isosceles triangle ABC where AC = BC.

We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.

We first draw a bisector of ∠ACB and name it as CD.

Now in ∆ACD and ∆BCD we have,

AC = BC                                                                (Given)

∠ACD = ∠BCD                                                    (By construction)

CD = CD                                                               (Common to both)

Thus,  ∆ACD ≅∆BCD                                        (By SAS congruence criterion)

So, ∠CAB = ∠CBA                                              (By CPCT)

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The correct option is c. 7

The summation of the expression  [tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex]  is 7.

The sum of terms that follow a pattern is denoted by the symbol '∑' "summation," which also serves as a shorthand notation.

A sum of several terms is typically represented by the symbol "∑" This symbol is typically accompanied with a variable index that includes all terms that must be taken into account when calculating the total.

The given expression is;

[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex]

The the property of summation, expand the values.

[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{2}\right)^{1-1}+4\left(\frac{1}{2}\right)^{2-1}+4\left(\frac{1}{2}\right)^{3-1}[/tex]

[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{2}\right)^{0}+4\left(\frac{1}{2}\right)^{1}+4\left(\frac{1}{2}\right)^{2}[/tex]

[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{1}\right)+4\left(\frac{1}{2}\right)+4\left(\frac{1}{4}\right)[/tex]

[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4+2+1\\[/tex]

[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=7\\[/tex]

Therefore the solution of the given equation is 7.

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The correct question is;

What is the value of [tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex] ?

a.7/8

b.8

c.7/2

d.7

The equation for the graphed function is (x+20)(x+5)(x-15).

It should be noted that a graph shows the relationship between variables.

From the graph, the equation is x³+10x²-275x-1500.

In this case, this can be  as - (x + 20)(x + 5)(x - 15)

The graph crosses the x axis. The coefficient is negative because the graph rises to the left.

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The missing value from the table is 4.

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained in another value.

In order to determine the missing number, we first have to determine the rate of change of the number of drummers.

Rate of change:

4 - 3 = 1

2 -1 = 1

3 - 2 = 1

So, the rate of change is 1. Thus, the missing number : 3 + 1 = 4

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Answer: missing value is 5

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

to find the zeros equate f(x) to zero , that is

2x² + 8x - 3 = 0 ( add 3 to both sides )

2x² + 8x = 3 ← factor out 2 from each term on the left side

2(x² + 4x) = 3

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 4x

2(x² + 2(2)x + 4 - 4) = 3

2(x + 2)² - 8 = 3 ( add 8 to both sides )

2(x + 2)² = 11 ( divide both sides by 2 )

(x + 2)² = [tex]\frac{11}{2}[/tex] ( take square root of both sides )

x + 2 = ± [tex]\sqrt{\frac{11}{2} }[/tex] ( subtract 2 from both sides )

x = - 2 ± [tex]\sqrt{\frac{11}{2} }[/tex]

that is

x = - 2 - [tex]\sqrt{\frac{11}{2} }[/tex] , x = - 2 + [tex]\sqrt{\frac{11}{2} }[/tex]

Answer:

x  = -2 - √11/2 and - 2 + √11/2.

Step-by-step explanation:

2x^2 + 8x - 3 = 0

Divide first 2 terms  by 2:

2(x^2 + 4x) - 3 = 0

2(x^2 + 4x)  = 3

Complete the square:

2 [ (x + 2)^2 - 2^2)  = 3

2(x + 2)^2  - 8 = 3

2(x + 2)^2 = 11

(x + 2)*2 = 11/2

x + 2 = ± 11/2

x = -2  ± √11/2

By critically observing the graph above, the amount of water in this pond at 0 hour is equal to 2,660 liters.

Similarly, the amount of water in this pond at 1 hour is equal to 3,225 liters.

Next, we would determine the rate of increase:

Rate = Δy/Δx

Rate = (3225 - 2660)/(1 - 0)

Rate = 665.

The amounts given in parts (b) and (c) are not equal because because the line doesn't pass through the origin (0, 0) of the graph.

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Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

Herein we must make use of trigonometric expressions and properties of trigonometric functions to find the right value. According to trigonometry, both cosine and sine are negative in the third quadrant. Thus, by using the fundamental trigonometric expression (sin² α + cos² α = 1) and substituting all known terms we find that:

[tex]\sin \theta = -\sqrt{1 - \cos^{2}\theta}[/tex]

[tex]\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}[/tex]

sin θ ≈ - √731 / 30

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

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The sample variance for distribution of the means is 9

The average of the squared differences from the Mean is called Variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.

The Standard Deviation is a measure of how spread out numbers are.

Its symbol is σ (the Greek letter sigma)

Its formula is the square root of the Variance

Given: Standard Deviation = 3

           Sample size = 36

∴ By formula we get

3 = √(Variance)

∴ 9 = Variance

Thus the sample variance for distribution of the means is 9

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Answer:

Step-by-step explanation:

Area Formula

A = (a + b) × h/2

A = (28 + 14) * 16/2

A = 42 * 8

A = 336 cm²

The expression that represent the total amount Ilean earned last week is 27(18) + 75  

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the total amount Ilean earned last week for working x hours.

Since she worked for 27 hours and earned $75 to design a web page. Hence:

y = 27(18) + 75

The expression that represent the total amount Ilean earned last week is 27(18) + 75  

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Minimum: 202

Quartile (Q1): 208

Median: 218

Quartile Q3: 229

Maximum: 237

The max and min value, the lower and upper quartiles, and the median of a data comprise the five-number summary.

Given the data: 236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208, we would have the following:

Minimum: 202 (least value)

Quartile (Q1): 208 (center of the first half of the data)

Median: 218 (center of the data when ordered)

Quartile Q3: 229 (center of the second half of the data)

Maximum: 237 (highest value).

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Hello,

[tex] \frac{p(x)}{q(x)} = \frac{ {x}^{2} - x - 12}{x + 3} = \frac{(x - 4)(x + 3)}{x + 3} = x - 4[/tex]

Answer:

Step-by-step explanation: