Alphaville's budget surplus increased by $25,000 from 2010 to 2011. In 2011, with a tax revenue of $750,000, the budget surplus was $75,000.
To find the increase in Alphaville's budget surplus from 2010 to 2011, we need to calculate the difference between the two surplus functions: (-1.5x^2 + 400x) - (-2x^2 + 500x). Simplifying the expression, we get -1.5x^2 + 400x + 2x^2 - 500x = 0.5x^2 - 100x.
Next, we substitute the tax revenue of $750,000 into the equation to find the budget surplus for 2011. Plugging in x = 750, we get 0.5(750)^2 - 100(750) = 281,250 - 75,000 = $206,250.
Therefore, Alphaville's budget surplus increased by $25,000 ($206,250 - $181,250) from 2010 to 2011. In 2011, with a tax revenue of $750,000, the budget surplus was $206,250.
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Ilean works as a welder and web designer. As a welder, she earns $18 per hour. Last week she worked 푥 hours as a welder and her friend paid her $75 to design a web page. Write an expression to represent the total amount Ilean earned last week.
The expression that represent the total amount Ilean earned last week is 27(18) + 75
What is an equation?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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One leg of a right triangle has a length of 5m. The other sides have lengths that are consecutive integers. Find these lengths.
The lengths of the other two sides of the right triangle are 12 and 13
Pythagorean theoremFrom 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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Office procedure note this 39-year-old patient returns to the office today because of a defect on the nail of his left big toe. he was seen three times in the last four months for this problem. this defect is very suspicious, and i felt it best to biopsy a portion of the nail plate and bed. the sample was sent to pathology. i told the patient that he will be called with the results, and then i will decide how to proceed. cpt code(s):
The CPT code that is used here is CPT code 11755.
What is the 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.
Drag each description to the correct location to complete the flow chart proof. Given: . D is the midpoint of . . Prove: is an isosceles triangle.
The isosceles triangle is proved below.
How to illustrate the triangle?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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p(x)= x2-x-12 and q(x)=x+3 find p(x) ÷ q(x) The question of O-MATH
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:
PLEASE HELP IM STUCK
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
A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames: a. None will need adjustment
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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What is the solution to the system of equations graphed below?
OA. (1, 2)
B. (0, -1)
O C. (0.4)
D. (2.0)
X₁
5
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.
How do I solve this?
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
The equations y = 1/2x + 1 and y= √2x+4 are graphed on the coordinate grid.
How many real solutions does the equation y= √2x+4 = 1/2x + 1 have.
A. 0
B. 1
C. 2
D. cannot be determined from the graph
Answer:
2
Step-by-step explanation:
The graphs intersect at 2 points.
The 2 solutions are x = -2 and x = 6.
Find the value of x in each figure
Which function could be a stretch of the exponential decay function shown on the graph?
f(x) = 2(6)x
f(x) = One-half(6)x
f(x) = 2(one-sixth) Superscript x
f(x) = One-half (one-sixth) Superscript x
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)
What function represents a stretch of a exponential decay function?
Exponential functions are trascedent functions whose form is described below:
[tex]y = a\cdot r^{x}[/tex] (1)
Where:
a - Stretch factorr - Growth rateThere 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)
RemarkThe 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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please help I can't answer this question
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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Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
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".
What 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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Part E:
Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form.
The equation for the graphed function is (x+20)(x+5)(x-15).
How to illustrate the equation?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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For a sample size of 36 and a population Standard Deviation of 3, the sample variance for distribution of the means is:
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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What is the area of this trapezoid?
Enter your answer in the box.
_cm²
Answer:
A = 336 cm²Step-by-step explanation:
Area Formula
A = (a + b) × h/2
A = (28 + 14) * 16/2
A = 42 * 8
A = 336 cm²
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The inequality represented by the graph is; B: y > 3x + 2
How to Interpret Inequality Graphs?
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
According to the weather report, there is a 25% chance of snow in the mountains tomorrow. how likely is it to snow tomorrow in the mountains?
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 graph of a relation is shown.
A coordinate plane with a straight line. The line starts in the lower left quadrant and continues up through the uppercase right quadrant. The line passes through the y-axis slightly below the origin, and then passes through the x-axis slightly to the right of the origin.
Which of these values could be the slope of the line? Select two options.
–2
0
The values which could be the slope of the line are numbers > 0.
Which values could be the slope of the line?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
This table shows the ratio of drummers to flute players in the school band.
The missing value from the table is 4.
What is the missing value?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:
can someone please help me
Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.
How to find the value of a trigonometric functionHerein 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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[tex]20-x-x^{2}[/tex]
solve this equation by class 9 course
The factored expression of the polynomial is (4 - x)(5 + x)
How to solve the polynomial?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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Mary had 81 fliers to post around town. last week, she posted 1/3 of them. this week, she posted 2/3 of the remaining fliers. how many fliers has she still not posted?
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
Find the five-number summary for the data.
{236, 202, 218, 208, 225, 229, 211, 237, 223, 206, 217, 216, 232, 225, 208}
Minimum: 202
Quartile (Q1): 208
Median: 218
Quartile Q3: 229
Maximum: 237
What is the Five-Number Summary?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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Select the correct answer. what is the value of ? i=1 a. 8 b. 7/8 c. 7 d. 7/2
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.
What is summation (∑)?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
Question is DOWN↓ PLS ANSWER I WILL MARK BRAINLIEST.....
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
Find the measure of the indicated angle to the nearest degree 35 and 28
The missing indicated angle of the given right angle triangle is; 39°
How to use trigonometric ratios?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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Each score in a set of data is multiplied by 3, and then 4 is subtracted from the result. If the original mean is 10 and the original standard deviation is 5, what are the new mean and new standard deviation
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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Find the unknown angles
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°