Variance matters a lot in various fields, and it is important to understand the concept of variance to make informed business decisions.
Variance matters a lot in the field of statistics, finance, and business. This term is generally used to determine the level of difference between the actual and the expected values or outcomes. Variance can help us understand the level of risk associated with a particular investment or business decision, and also helps us to analyze the accuracy of the predictions we make.
Example:
Suppose a stockbroker recommends that a client invests in a particular stock, and the client is considering investing in that stock. The stockbroker provides an expected return rate of 10%. However, if the actual return rate ends up being 15%, the client will be very happy, but if it ends up being only 5%, the client will be very unhappy. Thus, it is important for the stockbroker to consider the variance in the expected return rate and to provide an explanation of the level of risk associated with the investment.
Another example is when a company has a budget of $100,000 for advertising, and the marketing team spends $110,000 on advertising. The company's management can calculate the variance of $10,000 to determine whether the marketing team exceeded the budget or not. The variance can help the company to adjust its future marketing strategies to achieve the desired results.
Thus, variance matters a lot in various fields, and it is important to understand the concept of variance to make informed business decisions.
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You need a 30% alcohol solution. On hand, you have a 675 mL of a 5% alcohol mixture. You also have 75% alcohol mixture. How much of the 75% mixture will you need to add to obtain the desired solution?
you will need____mL for the 75% solution
You need to add 225mL of the 75% alcohol solution to obtain the desired 30% alcohol solution.
To find the amount of 75% alcohol solution needed to obtain a 30% alcohol solution, we must use the formula for dilution:
M1V1 = M2V2
Where M1 is the concentration of the initial solution, V1 is the volume of the initial solution, M2 is the desired concentration, and V2 is the desired volume.
In this case, M1 is 5%, V1 is 675mL, M2 is 30%, and V2 is unknown.
We can rearrange the equation to solve for V2, which is the volume of the 75% alcohol solution needed:
V2 = (M1V1) / M2
V2 = (5% x 675mL) / 30%
V2 = 225mL
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Select the true statement. Group of answer choices For any real number x, x > 5 implies that x ≥ 5. For any real number x, x ≥ 5 implies that x ≥ 6. For any real number x, x > 5 implies that x ≥ 6. For any real number x, x ≥ 5 implies that x > 5
For any real number x, x > 5 implies that x ≥ 5 is the true statement.
For any real number x, x > 5 implies that x ≥ 5 is the true statement. This can be expressed with the following inequality:
x > 5 implies x ≥ 5
This means that if x is greater than 5, then x must be greater than or equal to 5. We can demonstrate this with an example calculation. Let x = 6.
6 > 5
We can see that 6 is greater than 5, so the inequality is true.
6 ≥ 5
We can see that 6 is also greater than or equal to 5, so the inequality is also true. Therefore, for any real number x, x > 5 implies that x ≥ 5.
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. Evaluate: 2(6+4) – 3(5) 1 70 85 5
Answer:
5
Step-by-step explanation:
2(6+4) – 3(5)
= 12 + 8 - 15
= 20 - 15
= 5
So, the answer is 5
Related to your response to Question 5, is the standardized mean
difference in Dexter and Hughes (2011) the unbiased or biased
version?
effect size measure.
In the case of Dexter and Hughes (2011), the standardized mean difference is an unbiased version.What is an unbiased estimate?An unbiased estimate is a statistical term used to describe an estimate or forecast that has an equal chance of being too high or too low. In Dexter and Hughes (2011), the standardized mean difference is unbiased.A study's standardized mean difference is determined by dividing the difference between two means by their pooled standard deviation. It's used to compare two group means and is a standardized effect size measure.
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What is the perimeter of DEFG?
A 2-dimensional graph with an x-axis and a y-axis is given. A parallelogram DEFG is drawn on it with co-ordinates (2,1), (3,4), (7, 5) and (6,2) respectively.
The perimeter of DEFG will be 2(√10+√17).
What are spherical cοοrdinates?The cοοrdinate system that is mοst frequently emplοyed in three-dimensiοnal systems is called spherical cοοrdinates οf the system, represented as (r,Ф,∅ ).
The surface area in three dimensiοns is calculated using the spherical cοοrdinate system. Radial distance, pοlar angles, and azimuthal angle are the three numbers that these cοοrdinates indicate. Additiοnally knοwn as spherical pοlar cοοrdinates.
A 2-dimensiοnal graph with an x-axis and a y-axis is given.
A parallelοgram DEFG is drawn οn it with cο-οrdinates (2,1), (3,4), (7, 5) and (6,2) respectively.
Sο the perimeter will be DE = √10
DG=√17
EF = √17
FG=√10
Sο the perimeter will be 2(√10+√17).
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Which would you measure in kilograms?
A. The mass of a butterfly
B. The capacity of a bottle
C. The mass of a basketball
D. The length of a river
Answer:
C. The mass of a basketball
Step-by-step explanation:
C. The mass of a basketball is typically measured in kilograms.
A. You would measure the mass of a butterfly in milligrams or grams.
B. The capacity of a bottle is measured in milliliters or liters.
D. The length of a river is measured in meters or kilometers.
Answer:
The answer to your problem is, C. The mass of a basketball
Step-by-step explanation:
First of all, if you want to measure heavy items then you could do it in kilograms for example:
Cup filled with water ( lb )
Gallon tank ( kg )
Since basketball or heavy ( depends how much pressure is put it there ) and you cannot really " weigh " a river.
The heaviest option from the option choices A, B, & C.
Option C, is the heaviest
Thus the answer to your problem is, C. The mass of a basketball
A triangular prism with dimensions 8 inches by 13 inches
by 16 inches in placed in a box of the same dimensions, as
show in the figure below. How many cubic inches of filler
material are required to surround the triangular prism in
order to completely fill the box?
=.
.
104
416
832
1,664
13
Cannot be determined by the given information
8
16
To fully describe a triangular prism, you would need to provide the dimensions of its triangular bases (e.g. base length and height), the length of the prism, and the length and width of the rectangular faces. Thus, option C is correct.
What is the triangular prism with dimensions?To find the volume of filler material required to surround the triangular prism, we need to first calculate the volume of the box and the volume of the triangular prism.
The volume of the box is given by:
[tex]8[/tex] inches × [tex]13[/tex] inches × [tex]16[/tex] inches = [tex]1,664[/tex] cubic inches
The volume of the triangular prism is given by:
[tex](1/2) × 8[/tex] inches × [tex]13[/tex] inches × [tex]16[/tex] inches = [tex]832[/tex] cubic inches
To completely fill the box, we need to add filler material with a volume equal to the difference between the volume of the box and the volume of the triangular prism, which is:
cubic inches— [tex]832[/tex] cubic inches [tex]= 832[/tex] cubic inches
Therefore, the [tex]832[/tex] Cubic inches.
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What is the slope of the line that passes through the points
(
−
4
,
−
10
)
(−4,−10) and
(
−
7
,
−
19
)
(−7,−19)?
Answer:
3
Step-by-step explanation:
slope of the line, m = (y2 - y1 ) / ( x2 - x1 )
= (-19 + 10 ) / (-7 + 4)
= -9 / -3
= 3
The Picture and Sound electronics store has hired Trevor to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. There is a proportional relationship between the number of times Trevor turns the crank to lift a box, x, and the height the box has been lifted (in feet), y. The equation that models this relationship is y=0.6x.
How high does Trevor lift a box by turning the crank 10 times? Write your answer as a whole number or decimal.
Trevor lifts a box to a height of 6 feet by turning the crank 10 times.
What is equation?In mathematics, an equatiοn is a fοrmula that uses the equals sign (=) tο express hοw twο expressiοns are equal. In οther languages, the wοrd equatiοn and its cοgnates may have slightly different meanings. Fοr instance, in French, an equatiοn is defined as having οne οr mοre variables, while in English, an equatiοn is any prοperly fοrmed fοrmula that cοnsists οf twο expressiοns linked by the equals sign.
Using the equation y = 0.6x, we can calculate the height Trevor lifts a box by turning the crank 10 times:
y = 0.6x
y = 0.6(10)
y = 6
Therefore, Trevor lifts a box to a height of 6 feet by turning the crank 10 times.
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Suppose the events Upper B 1, Upper B 2, and Upper B 3, are mutually exclusive and complementary events, such that P(Upper B 1)equals0. 05, P(Upper B 2)equals0. 4, and P(Upper B 3)equals0. 55. Consider another event A such that P(A|Upper B 1)equals0. 6, P(A|Upper B 2)equals0. 5, and P(A|Upper B 3)equals0. 4. Use Bayes's Rule to find P(Upper B 1|A)
The probability of event Upper B 1 given event A is approximately 0.0134.
To find P(Upper B 1|A) using Bayes' rule, we need to use the formula:
P(Upper B 1|A) = P(A|Upper B 1) × P(Upper B 1) / P(A)
To find P(A), we can use the law of total probability:
P(A) = P(A|Upper B 1) × P(Upper B 1) + P(A|Upper B 2) × P(Upper B 2) + P(A|Upper B 3) × P(Upper B 3)
Substituting the given values, we get:
P(A) = 0.6 × 0.05 + 0.5 × 0.4 + 0.4 × 0.55
P(A) = 0.029 + 0.2 + 0.22
P(A) = 0.449
Now, substituting the values of P(A|Upper B 1), P(Upper B 1), and P(A) into the Bayes' rule formula, we get:
P(Upper B 1|A) = (0.6 × 0.05) / 0.449
P(Upper B 1|A) = 0.006 / 0.449
P(Upper B 1|A) ≈ 0.0134
Therefore, the probability of event Upper B 1 given event A is approximately 0.0134.
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The 1989 U. S. Open golf tournament was played on the East Course of the Oak Hills Country Club in Rochester, New York. During the second round, four golfers scored a hole in one on the par 3 sixth hole. The odds of a professional golfer making a hole in one are estimated to be 3,708 to 1, so the probability is 1/3,709. There were 175 golfers participating in the second round that day. A. What is the probability that no one gets a hole in one on the sixth hole
The probability that no one gets a hole on the sixth hole is given as follows:
0.9534 = 95.34%.
What is the binomial distribution formula?The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The mass probability formula is given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 175 -> number of golfers.p = 1/3709.The holes are independent, hence the probability of no one getting a hole in the sixth hole is P(X = 0), thus:
P(X = 0) = (1 - 1/3709)^175
P(X = 0) = 0.9534 = 95.34%.
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Shelby is playing hide-and-seek with Dillon and Patty. Dillon is hiding 15 meters south of Shelby, and Patty is hiding due east of Dillon. If Shelby is 17 meters from Patty, how far apart are Dillon and Patty?
meters= ?
Answer:
8 meters
Step-by-step explanation:
their formation creates a triangle
Shelby to Dillon =15
Shelby to Patty =17
Dillon to Patty =?
a^2 + 15^2 = 17^2
a^2 + 225 = 289
a^2 = 64
a = 8
Cocoa Puffs family size was once 19.3 oz, now it is 18.1 oz. By what percent did the product
"shrink"? Show your work.
so it shrunk by 19.3 - 18.1 = 1.2.
so if we take 19.3(origin amount) as the 100%, what's 1.2 off of it in percentage.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 19.3 & 100\\ 1.2& x \end{array} \implies \cfrac{19.3}{1.2}~~=~~\cfrac{100}{x} \\\\\\ 19.3x=120\implies x=\cfrac{120}{19.3}\implies x\approx 6.22[/tex]
The students in Mrs. Holbrook’s class are growing plants. One day they measured the heights of the plants in inches. Make a line plot to represent the data
Based on the information in the table, we can infer that the graph would be as shown in the attached image.
How to graph the information in the table?To graph the information in the table we must analyze the information in the table. In this case we must take into account that to locate the fractions we can perform the division and convert it into a decimal number to locate them more easily on the number line.
In accordance with the above, we can establish that the height that is repeated the most times is 1 7/8 with a frequency of 4 times.
Note: This question is incomplete. Here is the complete information:
Attached image
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please show work!!!!!!!
Answer:
J. 56
Step-by-step explanation:
The picture in this question can be a little deceiving. Each rectangular glass pane is 3 by 10 inches. This means that the picture of the 4 panes overlapping, leaves the center square open. The open area has your inner edges. The question asks for the sum of the inner and outer edges.
Every pane is 10 inches long, so the out perimeter of the figure is 40 inches because the figure has four sides. The rectangles overlap, creating 3 by 3 inch square. 3 inches off either side of a pane leaves 4 inches as the length for the edge of the inner square. Therefore, the perimeter of the inner square is 16 inches.
Outer Perimeter + Inner Perimeter = 40 + 16 = 56 inches
Please refer to the photo!
The diameter of a circle is 17 ft. Find its area to the nearest whole number.
Answer:
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the area of a circle.}[/tex]
[tex]\textsf{First, we should identify the formula for the area of a circle.}[/tex]
[tex]\large\underline{\textsf{Formula:}}[/tex]
[tex]\mathtt{Area = \pi (radius)^{2}}[/tex]
[tex]\textsf{The radius is \underline{half} of the diameter.}[/tex]
[tex]\mathtt{\frac{17}{2} = 8.5ft.}[/tex]
[tex]\textsf{Let's begin solving for the area.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{Area = \pi (8.5)^{2}}[/tex]
[tex]\mathtt{Area = 72.25 \pi}[/tex]
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
30 dollars to spend on 3 gifts. She spent 8 9/10 dollars on gift A and 6 3/5 dollars on gift B. How much money did she have left for gift C?
From the given information provided, she has 14.50 dollars money left to spend on gift C.
To find out how much money is left for gift C, we first need to add up the amounts spent on gift A and gift B:
8 9/10 dollars + 6 3/5 dollars = (8 + 6) + (9/10 + 3/5) dollars
= 14 + (9/10 + 6/10) dollars
= 14 + 15/10 dollars
= 15 5/10 dollars
= 15.50 dollars
So the total amount spent on gift A and gift B is 15.50 dollars. To find out how much money is left for gift C, we need to subtract this amount from the total amount she has to spend:
30 dollars - 15.50 dollars = 14.50 dollars
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Mr. Sharma has the option of selecting a rectangular plot of size 45 m × 25 m or a square plot of
size 35 m at the same price. Which one should he prefer and why?
Answer:
Square Plot
Step-by-step explanation:
Let us compare the Area of both plots
Rectangular Plot : L X B = 45 x 25 = 1125 M^2
Square Plot : S X S = 35 x 35 = 1225 M^2
Area of Square Plot > Area of Rectangular Plot
Therefore he should prefer the Square Plot as it has more area.
Hope it helps.
To show that circle P Is similar to circle Q, circle P Is translated t units to the right. The Image Is then dilated about Its center by a scale factor of s.
What are the values of t and s?
T=
S=
Lara's Burgers cooks its burgers either well done or medium. Last night, the restaurant served 9 well-done burgers and 11 medium burgers. What percentage of the burgers served were well done?
45% of the burgers served were well-done.
What is percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
To find the percentage of well-done burgers, we need to divide the number of well-done burgers by the total number of burgers served and then multiply by 100 to get the percentage.
Total number of burgers served = 9 well-done + 11 medium = 20
Percentage of well-done burgers = (9/20) x 100% = 45%
Therefore, 45% of the burgers served were well-done.
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Quick Loans will loan you $500 with the understanding that you will pay them $3.98 in interest for every day you have the loan out. What is the APR for this loan?
The APR on the loan, given the amount you are to pay in interest every day, can be found to be 190. 54 %
How to find the APR ?To calculate the APR (Annual Percentage Rate) for this loan, we need to know the total interest paid over the course of a year, as a percentage of the loan amount.
First, we need to determine the total interest paid over the course of one year. Since the interest rate is $3.98 per day, we can multiply that by the number of days in a year (365) to get the total interest paid per year:
$3.98 x 365 = $1, 452.70
The APR would therefore be :
= ( 1, 452. 70 - 500 ) / 500
= 1. 9054
= 190. 54 %
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Help me find the perimeter please!!
Answer:
[tex]P = 56\sqrt2[/tex]
Step-by-step explanation:
We can find the perimeter of a square given its diagonal by modeling the square as two congruent right triangles and using the Pythagorean Theorem to solve for the square's side lengths.
The Pythagorean Theorem states that...
[tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are the right triangles legs, and [tex]c[/tex] is its hypotenuse.
However, since we are working with a square, we know that the right triangles' legs are congruent. Thus, the theorem becomes:
[tex]a^2 + a^2 = c^2[/tex]
[tex]2 \cdot a^2 = c^2[/tex]
Using this formula, we can solve for the square's side lengths, inputting the given hypotenuse length of 28.
[tex]2 \cdot a^2 = 28^2[/tex]
↓ simplify the exponent
[tex]2 \cdot a^2 = 784[/tex]
↓ divide both sides by 2
[tex]a^2 = 392[/tex]
↓ take the square root of both sides
[tex]a = \sqrt{392}[/tex]
↓ simplify the square root
[tex]a = \sqrt{2^3 \cdot 7^2}[/tex]
[tex]a = (2\cdot 7)\sqrt{2}[/tex]
[tex]a=14\sqrt2[/tex]
Finally, we can multiply the side length by 4 to get the square's perimeter (since a square has 4 sides).
[tex]P = 4 \cdot a[/tex]
[tex]P = 4 \cdot 14\sqrt2[/tex]
[tex]\boxed{P = 56\sqrt2}[/tex]
[tex]\boxed{P \approx 79.2}[/tex]
PLS HELP DUE TODAY NEED ASSISTANCE
The waste sites in State Y in the year 2000 was 21.
The solution to the equation is x = 9.4The equation of a bar diagram, and the solution are 3n + 8 = 53 and n = 15, respectivelyHow to determine the number of Hazardous Waste SiteLet n be the number of hazardous waste sites in State Y.
Based on the problem statement, we have
2n - 8 = 34
So, we have
2n = 42
Divide
n = 21
Hence, the waste sites in State Y in the year 2000 was 21.
How to determine the solution to the equationGiven that
6x + 1.6 = 58
Apply the subtraction property
6x = 56.4
Apply the division property
x = 9.4
Hence, the solution to the equation is x = 9.4
The equation of a bar diagram, and the solutionHere, we have the bar diagram
Adding the terms in the bar, we have
n + n + n + 8 = 53
3n + 8 = 53
Apply the subtraction property
3n = 45
Apply the division property
n = 15
Hence, the bar equation is 3n + 8 = 53
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2
1 point
Find the value x:
12
Type your answer...
+
6
Answer:
Step-by-step explanation:
1
A bakery sells apple pies for $12.85. if the pie has a diameter of 10 inches, what is the approximate cost per square inch of the apple pie? round to the nearest hundredth. a. $0.04 b. $0.16 c. $0.32 d. $0.65
The cost per square inch of the apple pie is $ 0.16.
Given that,
The diameter of the pie = 10 in
The radius of the pie = 10/2
= 5 inches.
Area of the pie = [tex]\pi r^{2}[/tex]
= 3.14 × 5²
= 3.14 × 25
= 78.5 in²
The cost of the apple pie = $ 12.85.
Therefore, the cost per square inch of the pie = 12.85 ÷ 78.5
= $ 0.16.
Hence, the cost per square inch of the apple pie is $ 0.16.
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if anyone could help, would be much appreciated
Answer:
(√122 - √10)/112.
Step-by-step explanation:
The average rate of change of a function f(x) over an interval [a, b] is given by:
average rate of change = (f(b) - f(a))/(b - a)
Here, we have f(x) = √x - 1, a = 10, and b = 122. So, the average rate of change of f(x) from x = 10 to x = 122 is:
(f(122) - f(10))/(122 - 10)
= (√122 - 1 - √10 + 1)/(112)
= (√122 - √10)/112
Therefore, the exact, fully simplified answer for the average rate of change of f(x) from x = 10 to x = 122 is (√122 - √10)/112.
Objective(s): Using Multidimensional Analysis (i.e., OLAP - Online Analytical Processing) you will analyze a multidimensional cube and make recommendations for improving profit. The multidimensional cube that you will analyze is AdventureWorks . You are free to move the data to Tableau and analyze it that way but I recommend you use Excel's PIVOT table. Please study the data first before analyzing. Methodology: You will analyze a cube built from the AdventureWorks Data Warehouse. The AdventureWorks cube was built using Microsoft's SQL Server Analysis Services (SSAS). Playing the role of AdventureWorks management, you will analyze your cube using Microsoft Excel and make three (3) recommendations for improving profitability. Deliverable(s): You will submit 2 recommendations for improving the profitability of AdventureWorks along with the rationale of each recommendation. In addition, please include any and all cube views (i.e., reports or charts from Excel) that helped you arrive at your recommendations.
recommendations
When answering questions on Brainly, you should always strive to be factually accurate, professional, and friendly. Your answer should be concise and not provide extraneous amounts of detail. You should not ignore any typos or irrelevant parts of the question, and provide a step-by-step explanation in your answer.The objective of the task is to analyze a multidimensional cube and provide recommendations for improving the profit. The cube that you will be analyzing is AdventureWorks. The methodology that will be followed is to analyze a cube built from the AdventureWorks Data Warehouse.The cube was built using Microsoft's SQL Server Analysis Services (SSAS). You will play the role of AdventureWorks management, and analyze the cube using Microsoft Excel. You will then make three recommendations for improving profitability.For analyzing the cube, you can use Excel's PIVOT table. It is recommended that you study the data first before analyzing. You can move the data to Tableau and analyze it that way, but it is not necessary.The deliverables of the task are two recommendations for improving the profitability of AdventureWorks along with the rationale of each recommendation. Additionally, you should include any and all cube views (i.e., reports or charts from Excel) that helped you arrive at your recommendations.
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WILL GIVE BRAINLIEST!!!
Question 1: The perimeter of the triangle below is 5x^3 - 2x^2 + 3x - 8.
Part A: Given the information below. What is the total length of sides 1 and 2 of the triangle? SHOW ALL WORK! (MANDATORY)
Side 1: 3x^2 - 4x - 1
Side 2: -x^2 + 4x + 5
Answer: Side 1 + Side 2 = _______ (MANDATORY)
Part B: What is the length of the 3rd side of the triangle? Show your work.
5x^3 - 2x^2 + 3x - 8 - (________) =
Answer (Drag & Drop):
A) 5x^3 - 4x^2 + 3x - 4
B) 5x^3 - 4x^2 + 3x - 12
C) 5x^3 - 4x^2 + 3x + 12
D) 5x^3 - 4x^2 + 3x + 4
Answer:
Part A:
To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:
Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)
Simplifying the expression by combining like terms, we get:
Side 1 + Side 2 = 2x^2 + 1
Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.
Part B:
To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:
5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]
Simplifying the expression by distributing the negative sign, and then combining like terms, we get:
5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4
Simplifying further by combining like terms, we get:
5x^3 - 4x^2 + 11x - 4
Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.
Answer:
A) 5x^3 - 4x^2 + 3x - 4
Step-by-step explanation:
Answer:
A) 5x^3 - 4x^2 + 3x - 4
Step-by-step explanation:
Part A:
To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:
Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)
Simplifying the expression by combining like terms, we get:
Side 1 + Side 2 = 2x^2 + 1
Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.
Part B:
To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:
5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]
Simplifying the expression by distributing the negative sign, and then combining like terms, we get:
5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4
Simplifying further by combining like terms, we get:
5x^3 - 4x^2 + 11x - 4
Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.
Answer:
A) 5x^3 - 4x^2 + 3x - 4
Assume that the test scores of a college entrance test fits a normal distribution. The mean test score is 72, and the standard deviation is 15.2 a)What is the percentage of students scoring 84 or more? b) If a random student is chosen. What is the probability of the student scoring an 84 or more on the test if the max score was 95?
The probability of a random student scoring 84 or more if the maximum score is 95 is approximately 0.1179 or 11.79%.
To find the percentage of students scoring 84 or more, first we need to calculate the z-score using the formula:z = (X - μ) / σwhere X = 84, μ = 72, and σ = 15.2z = (84 - 72) / 15.2z = 0.7895Using a standard normal table or a calculator, we can find the percentage of students scoring 84 or more as:percentage = 1 - P(Z < 0.7895)percentage ≈ 21.4%Therefore, approximately 21.4% of students will score 84 or more on the test.b) To find the probability of a random student scoring 84 or more if the maximum score is 95, we need to first calculate the z-score using the same formula as before:z = (X - μ) / σwhere X = 84, μ = 72, and σ = 15.2z = (84 - 72) / 15.2z = 0.7895Then, we need to convert this z-score to a new z-score based on the maximum score of 95. Using the formula:z = (X - μ) / (max score - μ)σwhere X = 84, μ = 72, σ = 15.2, and max score = 95z = (84 - 72) / (95 - 72)z ≈ 1.19Using a standard normal table or a calculator, we can find the probability of a student scoring 84 or more as:P(Z > 1.19)P(Z > 1.19) ≈ 0.1179Therefore, the probability of a random student scoring 84 or more if the maximum score is 95 is approximately 0.1179 or 11.79%.
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