For a randomly chosen deceased person from this population in a certain population,
the probability that the person (a) (5 points) did not die due to a shark attack is 6/5.the probability that the person (b) (5 points) was a surfer, given that the person did not die due to a shark attack is 3/200.the probability that the person died due to a shark attack, given that the person was a surfer is 3/5.the probability that the person did not die due to a shark attack, given that the person was not a surfer 6/5.Probability can be defined as the rate of the number of favorable issues to the total number of issues of an event. For an trial having 'n' number of issues, the number of favorable issues can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability( Event) = Favorable issues /Total issues = x/ nProbability of car accidents was 1.2% i,e 12/10 → 6/5
Probability of deaths due to sharks are 0.0005% → 1/2000
If a person is a surfer then,
Probability of surfer dying in a car accident is 1% → 1/10Probability of surfer dying by shark attack is 60%→ 3/5 Probability of surfer dying by other causes is 0.5%→ 1/200Learn more about Probability:
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an automobile insurer has found that repair claims are normally distributed with a mean of $530 and a standard deviation of $490.
There is a 68% chance that a repair claim will be between $40 and $1020.
The normal distribution is a continuous probability distribution that is symmetric around the mean, with mean and variance being the same. In this case, the mean is $530 and the standard deviation is $490. This means that the repair claims are normally distributed, with the majority of the claims being between $530-$490 and $530+$490. This gives us a range of $40-$1020.
The normal distribution is often used to describe random variables because it is the most common probability distribution. In this case, it implies that the repair claims are randomly distributed around the mean of $530. The standard deviation of $490 indicates that there is a 68% chance that a repair claim will be within one standard deviation of the mean. In this case, that means that there is a 68% chance that a repair claim will be between $40 and $1020.
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The perimeter of the rectangle below is 108 units. Find the length of side AD.
Write your answer without variables.
D
A
2z + 1 C
3z + 3
B
AD =
Answer: [tex]AD=33[/tex]
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
[tex]2(2z+1+3z+3)=108\\\\2(5z+4)=108\\\\5z+4=54\\\\5z=50\\\\z=10\\\\\implies BC=33 \implies AD=33[/tex]
Mover R U rents moving trucks for an initial fee of $45 and charges $0.25 per mile. Trunks to Use rents trucks for an initial fee of $35 and charges $0.30 per mile. At how many miles is the cost the same?
At 200 miles, the cost will be the same.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Mover R U rents moving trucks for an initial fee of $45 and charges $0.25 per mile.
And, Trunks to Use rents trucks for an initial fee of $35 and charges $0.30 per mile.
Now, Let in x miles the cost will be the same.
Hence, We can formulate;
For Mover R U rents moving trucks for an initial fee of $45 and charges $0.25 per mile.
⇒ $45 + $0.25x
And, For Trunks to Use rents trucks for an initial fee of $35 and charges $0.30 per mile.
⇒ $35 + $0.30x
Equate both equation, we get;
⇒ 45 + 0.25x = 35 + 0.30x
⇒ 45 - 35 = 0.30x - 0.25x
⇒ 10 = 0.05x
⇒ x = 10/0.05
⇒ x = 1000/5
⇒ x = 200
Thus, At 200 miles, the cost will be the same.
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describe fully the transformation
Answer: The transformation is a reflection over the line x=0. The original square OABC is reflected over the line x=0 and the only invariant point is (0,2).
Step-by-step explanation:
This transformation is a reflection over the line with equation y = 2. The original square OABC is reflected over this line, mapping point A to C and C to A, while the only invariant point is (0, 2).
Δ
A
B
C
is a right triangle. Choose the equation that represents the sum of the angles in the triangle. What is the value of x, the missing angle?
Therefore , the solution of the given problem of triangle comes out to be x value of right triangle is 65° .
What exactly does a triangle mean?Due to their four sides or more, triangles are considered polygons. It has a straightforward, geometric form. A triangle is a square angle formed by the letters ABC. A singular rectangle or square is produced by Euclidean geometry when the sides are still not collinear. Triangles are polygons because they have three sides and three corners. Where three sides of a triangle come together are its corners. A triangle's angles sum up to 180 degrees.
Here,
Given :
triangle has an right angle so its 90 degree.
The triangle sum of angle is 180 degree.
Thus,
=> x + 25° + 90° = 180°
=> x + 115° = 180°
=> x = 180° -115°
=> x = 65°
Thus , x value is 65° .
Therefore , the solution of the given problem of triangle comes out to be
x value of right triangle is 65° .
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Write an exponential function y=abx whose graph passes through the points (1,2) and (3,50) .
Answer:
y = 0.4·5^x
Step-by-step explanation:
You want an exponential function y = a·b^x that passes through the points (1, 2) and (3, 50).
SetupThe given point values give two equations in two unknowns when used in the given exponential form:
y = a·b^x
2 = a·b^1
50 = a·b^3
SolutionDividing the second equation by the first, we find b:
50/2 = (ab^3)/(ab)
25 = b^2 . . . . . simplify
5 = b . . . . . . . . . square root
Then the value of 'a' can be found from the first equation:
2 = a·5
a = 2/5 = 0.4
Exponential functionUsing these values of 'a' and 'b', we have the exponential function ...
y = 0.4·5^x
__
Additional comment
The exponential regression function of your calculator can tell you the same thing.
% of 80 = 4 what dose it =
(1 point) calculate the double integral ∫r(8x 6y 48)da where r is the region: 0≤x≤3,0≤y≤4.
The value of the double integral ∫r(8x 6y 48)da where r is the region: 0≤x≤3,0≤y≤4. is 864
Double integrals are a way to integrate over a two-dimensional area. In some cases, the integral of one variable function, a double integral, is defined as a limit of a Riemann sum.
Double integrals are used to calculate the area of a region, the volume under the surface, and the average value of a function of two variables over a rectangular region. In a double integral, the outer limits must be constant, but the inner limits can depend on the outer variable. This means, we must put y as the inner integration variables, as was done in the second way of computing
∬R(8x+6y+48)dA=∫04∫03(8x+6y+48)dxdy
=∫04(4x2+6xy+48x)∣03dy
=∫04(36+18y+144)dy
=∫04(180+18y)dy
=(180y+9y2)∣04
=720+144=864
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Find the domain for which the functions f(x)=2x^2−1 and g(x)=1−3x are equal.{-2,2}{2,1/2}{-2,1/2}none of these
The domain for which functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal:{-2, 1/2}
When the functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal,
f(x) = g(x)
2x² - 1 = 1 - 3x
2x² + 3x -1 - 1 = 0
2x² + 3x - 2 = 0
We solve above quadratic equation to find the value of x.
2x² + 3x - 2 = 0
2x² + 4x - x - 2 = 0
2x(x + 2) - 1(x + 2) = 0
(x + 2)(2x - 1) = 0
x + 2 = 0 OR 2x - 1 = 0
x = -2 OR x = 1/2
This means, for x = -2 as well as x = 1/2 the functions f(x)=2x^2−1 and g(x)=1−3x are equal.
Thus, the required domain is: {-2, 1/2}
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Alan sold t-shirts and hats at a festival. His total profit was $125. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. How many t-shirts did he sell?
Write an equation that could be used to answer the question above. First chose the appropriate form. Then fill in the blanks with the numbers 125, 5, 40. Let x represent the number of t-shirts.
A. _x + _ = _
B. _x - _ = _
Answer:
17
Step-by-step explanation:
First you have to subtract 125-50 since we are trying to find the amount he made from selling t-shirts. That equals 85. So now we divide 85 by 5 and that gives us 85.
Answer:
Step-by-step explanation:
a._x+_=_
5x+40=125
-40 -40
5x=85
/5
x=17
he sold 17 shirts
what is the probability that x is within 1 standard deviation from its mean value? hint: find the p(x-x ≤ x ≤ x x) (round your answer to four decimal places.)
The probability that x is within 1 standard deviation from its mean value is 0.68.
Probability is the measure of the likelihood of an event occurring. In statistics, it is used to describe the chance of a particular value falling within a certain range.
A standard deviation is a measure of the spread of a set of data from its mean.
Typically, 68% of the data falls within 1 standard deviation from the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.
In order to find the probability that x is within 1 standard deviation from its mean value, we need to use a normal distribution.
In a normal distribution, 68% of the data falls within 1 standard deviation from the mean.
So, in this case, the probability that x is within 1 standard deviation from its mean value is 0.68 or 68%.
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Madeline went to the store to buy some cherries. The price per pound of the cherries is $6.50 per pound and she has a coupon for $1 off the final amount. With the coupon, how much would Madeline have to pay to buy 2 pounds of cherries? Also, write an expression for the cost to buy
p
p pounds of cherries, assuming at least one pound is purchased
The cost of 2 pounds of cherries without the coupon would be $6.50 x 2 = $13.
With the coupon, Madeline would have to pay $13 - $1 = $12 for 2 pounds of cherries.
The expression for the cost of buying x pounds of cherries with the coupon is:
(6.5*x) - 1
Based on the information in the model, which equation represents the Pythagorean theorem?
From the given figure, equation represents the Pythagorean theorem is 13²=12²+5². Therefore, option D is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given figure, area of a largest square is 169 square units, area of a larger square is 144 square units and the area of a smaller square is 25 square units.
We know that, the area of a square is side².
Now, the side(a) of a largest square is side²=169
So, a=13 units
The side(b) of a larger square is side²=144
So, b=12 units
The side(c) of a smaller square is side²=25
Then, c=5 units
Here, a, b and c form a right angle triangle.
By using Pythagoras theorem, we get
a²=b²+c²
13²=12²+5²
Therefore, option D is the correct answer.
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Today, everything at a store is on sale. The store offers a 20% discount.
1. The regular price of a T-shirt is $16. What is the discount price?
2. Write an expression for the discount price of x dollars.
3. The discount price of a hat is $20. What is the regular price?
Answer:
1. $16-20%= 12.8 US$
2. $x-20%=x
3. >>>>>?
Step-by-step explanation:
A 20% discount means that you subtract 20% of the normal price. Suppose the normal price is $100. 20% of this is $20. Subtract this from $100 and you have the new price---$80.
Note that "subtracting 20%" is the same as multiplying by 0.8----the general formula is:
discount price = normal price * (1-d) , where d is the decimal equivalent of the percentage discount.
From the example above:
discount price = normal price * (1-d) = 100(0.8)
to go the other way, simply rearrange the formula:
normal price = discount price / (1-d)
The polling reult how the ratio of vote for Candidate A to Candidate B. Candidate A Candidate B
12 20
18 30
27 45
36 ?
At thi rate, if Candidate A received 36 vote, how many vote did Candidate B receive?
36
50
60
72
If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.
The correct option is (C)
Now, According to the question:
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.
12 : 20 in its simplest form is 3 : 5
18 : 30 in its simplest form is 3 : 5
27 : 45 in its simplest form is 3 : 5
Now, determine the factor second factor of 36 if the first factor is 3.
36 / 3 = 12
Now multiply 12 by 5: 12 x 5 = 60
Hence, If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.
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mary has 8 apples. john has 1/4 the number of apples as mary. how many apples does john have?
The number of apples that John have is 2 if Mary has 8 apples and Jahn has 1/4 the number of apples as Mary.
Therefore the answer is 2.
This is a problem based on use of fractions. A fraction is a mathematical expression that represents a part of a whole.
John has 1/4 the number of apples as Mary, which means that for every 4 apples that Mary has, John has 1 apple.
To find the number of apples John has, you would divide the number of apples Mary has by 4. In this case, Mary has 8 apples, so John would have
1/4 * 8 = 2 apples
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There are 12 Year 13 pupils in a football club, out of a total of 35 pupils.
Write this proportion as a percentage.
Give your answer correct to 1 decimal place when appropriate.
Answer:
Step-by-step explanation:
The proportion of Year 13 pupils in the football club is 12/35. To convert this to a percentage, we need to multiply it by 100.
12/35 * 100 = 34.285714285714285 (approximately 34.3% when rounded to 1 decimal place)
Answer:
[tex] \frac{13}{35} \times \frac{100}{100} = 37.14\%[/tex]
My houe wa at the very tip of the egg, only fifty yard from the Sound, and queezed between two huge place that rented for twelve or fifteen thouand a eaon. The one on my right wa a coloal affair by any tandard – it wa a factual imitation of ome Hotel de Ville in Normandy, with a tower on one ide, panking new under a thin beard of raw ivy, and a marble wimming pool, and more than forty acre of lawn and garden. It wa Gatby’ manion
Fitzgerald used setting in the exposition of this passage by creating atmosphere and establishing geographic context.
In The Great Gatsby, the narrator mentions that the house is located "at the very tip of the egg" and is "squeezed between two huge places" which rent for a high season price. The description of Gatsby's mansion as a "colossal affair" with a tower, marble swimming pool, and vast lawns and gardens further emphasizes Gatsby's wealth and sophistication.
By painting this picture of the setting, Fitzgerald sets the stage for the events of the story and prepares the reader to encounter the characters and conflicts that will emerge.
Hence, the setting described in this passage helps to establish the geographic context of the story and create an atmosphere for the reader.
The question seems incomplete, it must have been...
"My house was at the very tip of the egg, only fifty yards from the Sound, and squeezed between two huge places that rented for twelve or fifteen thousand a season. The one on my right was a colossal affair by any standard—it was a factual imitation of some Hotel de Ville in Normandy, with a tower on one side, spanking new under a thin beard of raw ivy, and a marble swimming pool, and more than forty acres of lawn and garden. It was Gatsby’s mansion.
How does Fitzgerald use setting in the exposition of this passage?
-He underscores the cultural differences between West Egg and East Egg.
-He introduces the reader to the themes of jealousy and undying love.
-He suggests that Gatsby is sophisticated and very wealthy.
-He creates atmosphere and establishes geographic context."
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Edward takes many photos every week. He took 320
photographs last week. The number of photographs he took
his week decreased by 5% due to his busy work. How many
Photographs did he take this week?
According to the problem this week Edward took 304 photographs.
What is week?A week is a unit of time typically spanning seven days, representing the time it takes for one cycle of the days of the week to be completed. Generally, a week is divided into seven days, beginning with Sunday and ending with Saturday. During a week, people usually work five days, with weekends off for leisure or relaxation.The term “week” is believed to be derived from the Germanic word “wih”, which means “turning” or “change”.
This week Edward took 304 photographs. This is calculated by taking the 320 photographs he took last week and subtracting 5% (or 16 photographs). 320 - 16 = 304.
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help!! i can’t get my mind on it
Answer:c=25 d=9 final answer c2+3d= 225
Step-by-step explanation:
c=25 because 5^2 is 5×5=25. D is 9 because 3×3=9. And the final answer is 25×9=225
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{c^2 + 3d}\\\mathsf{= 5^2 + 3(3)}\\\mathsf{= 5\times 5 + 3(3)}\\\mathsf{= 25 + 9}\\\mathsf{= 34}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{34}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
3/5 divided by 4 = ?
Answer: 3/20
Step-by-step explanation:
3/5 x 1/4
Please Help! I Have Limited Time! A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 9 inches long and is melting at a rate of 0.6 inches per hour. Find and interpret the slope for this relationship.
A. 9; the length of the icicle when the student first measures it.
B. −9; the length of the icicle when the student first measures it.
C. 0.6; for every additional hour, the length of the icicle increases by 0.6 inches.
D. −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches.
Answer:
D
Step-by-step explanation:
The correct answer is D. −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches.
The slope of a line represents the rate of change of one variable with respect to the other variable. In this case, the length of the icicle (y) is changing with respect to time (x). The slope of the line represents the change in the length of the icicle (y) for every additional hour (x).
Since the icicle is melting at a rate of 0.6 inches per hour, the length of the icicle decreases by 0.6 inches for every additional hour. The slope of the line representing this relationship is -0.6. This means that for every additional hour, the length of the icicle decreases by 0.6 inches.
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ftware LLC. All right
Thursday January 5, 2023
Evaluate each function for the given value.
1) f(x) = 4x - 3; Find f(0)
A) 6
B) -2
C) -4
D) -3
Dima weighs 129 pounds. How many kilograms does she weigh? Use the conversion table to find the answer. Round to the nearest hundredth.
Units of Weight
Customary System Units
Metric System Units
1 ounce
28.35 grams
1 pound
0.45 kilograms
1 ton
907.2 kilograms
The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.
Define pounds?A weight measuring unit: One pound equals 454 grams. One kilogram is roughly equivalent to 2.2 pounds.
One pound contains 16 ounces.
The word "poundus" means "weight" in Latin.
The £ symbol is derived from an ornate L in Libra.
We are given the weight of Dima as 129 pounds.
we know by conversion that:
1 pound= 0.453592 kilograms
Hence 129 pounds= 129×0.453592 kilograms
129 pounds=58.513368 kilograms.
Therefore, The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.
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Explain how to find the center pc, the radius r, and the unit normal vector n of the circle that goes through three points p1, p2, and p3 in 3D space. Find pc, r, and n for p1=(5,0,7), p2=(1,3,6), and p3=(7,5,4)
Find the midpoint of each pair of points, and then take the average of those midpoints to find the center pc. The radius r is the distance from pc to any of the given points. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc.
To find the center pc, the radius r, and the unit normal vector n of the circle that goes through the three points p1=(5,0,7), p2=(1,3,6), and p3=(7,5,4) in 3D space, follow these steps:
1. Find the midpoint of each pair of points:
Midpoint of p1 and p2 = (3,1.5,6.5)
Midpoint of p2 and p3 = (4,4,5)
Midpoint of p3 and p1 = (6,2.5,5.5)
2. Take the average of the three midpoints to find the center pc:
pc = (4.33, 2.83, 6.17)
3. Calculate the radius r as the distance from pc to any of the given points:
r = √((5-4.33)2+(0-2.83)2+(7-6.17)2)
r = 2.66
4. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc:
v1 = (5-4.33, 0-2.83, 7-6.17)
v2 = (1-4.33, 3-2.83, 6-6.17)
n = v1 x v2
n = (-11.67, 5.67, -7.33)
n = (-0.79, 0.37, -0.48)
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what is Y=4x^2-4x+3 in parabola
Answer:
The y-intercept is (0, 3).
The equation is not factorable.
Step-by-step explanation:
We are given the equation:
Y=4x^2-4x+3
and we are asked to graph it.
To do this, let's first find the vertex of the parabola that a quadratic equation creates.
[tex]V(-\frac{b}{2a}),f(x))[/tex]
Here, a = 4 and b = -4. So the vertex must be:
[tex]V(-\frac{-4}{2(4)},f(x))[/tex]
[tex]V(\frac{1}{2},f(\frac{1}{2}))[/tex]
[tex]V(\frac{1}{2},2)[/tex]
Next, let's find the intercepts.
[tex]x=0[/tex]
[tex]y=4(0^{2})-4(0)+3=3[/tex]
The y-intercept is (0, 3).
The equation is not factorable.
A parallelogram with ide and t ha perimeter 22t. Kelly i decorating the edge of her parallelogram-haped craft table. The tabletop ha ide that are 30 inche and 14. 5 inche. What i the perimeter of the tabletop?
Write your anwer a a whole number or decimal
The perimeter of the tabletop is 79 inches. To calculate the perimeter of a parallelogram, you would use the following formula:
Perimeter = 2(length + width).In this case, the length is 30 inches and the width is 14.5 inches, so the perimeter would be 2(30 + 14.5) = 79 inches.
To calculate the perimeter of a parallelogram, use the following steps:
Identify the length and width of the parallelogram. In this case, the length is 30 inches and the width is 14.5 inches.Use the formula Perimeter = 2(length + width) to calculate the perimeter.Plug in the values for length and width and calculate the perimeter. In this case, the perimeter would be 2(30 + 14.5) = 79 inches.Learn more about parallelogram
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Find the greatet common factor of the term of the polynomial. 5x3–5x
Write your anwer a a contant time a product of ingle variable raied to exponent
The value of the GCF will be = 5*x = 5x
The greatest common divisor of two or more integers that are not all zero in mathematics is the biggest positive integer that divides each of the integers.
The biggest common factor is the factor that splits both numbers in half. To get the greatest common factor, first list each number's prime factors.
A set's greatest common factor (GCF) is the biggest factor that all of the numbers share. For example, the numbers 12, 20, and 24 all have two common factors: 2 and 4. The greatest is 4, hence the GCF of 12, 20, and 24 is 4. GCF is frequently used to locate common denominators.
As we have, two different terms as: 5x^3, –5x
Prime factorisation of 5x^3 = 5*x*x*x
While the prime factorisation of -5x = -1*5*x
So, the value of the GCF will be = 5*x = 5x (As only 5 and x are common in the prime factorisation of both the numbers)
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C=/5(F−32)
The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 95 degree Celsius.
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III. A temperature increase of 95 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius
a. I only
b. II only
c. III only
d. Iand II only
At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.
What is meant by Fahrenheit ?Fahrenheit is named for German scientist Daniel Gabriel Fahrenheit, who was born there in 1686 as part of the Polish-Lithuanian Commonwealth. He was the first to develop a constant, accurate method of measuring temperature. At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.
To assist us remember that we go from colder to hotter as we walk up the scale on our thermometer, let's label it. In other terms, a higher number of degrees Fahrenheit is hotter than a lower number.
[tex]$$\begin{aligned}& \text { Given:- } \mathrm{C}=\frac{5}{9}(\mathrm{~F}-32) \\& \Rightarrow \mathrm{F}=\frac{9}{5} \mathrm{C}+32\end{aligned}$$[/tex]
(I) If [tex]$F^{\prime}=F+1$[/tex]
[tex]$$\begin{aligned}\mathrm{C}^{\prime} & =\frac{5}{9}\left(\mathrm{~F}^{\prime}-32\right) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}+1-32) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}-32)+\frac{5}{9} \times 1 \\\mathrm{C}^{\prime} & =\mathrm{C}+\frac{5}{9}\end{aligned}$$[/tex]
Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Celsius.
Therefore, statement I exists true.
(II) If [tex]$\mathrm{C}^{\prime}=\mathrm{C}+1$[/tex]
[tex]$$\begin{aligned}& \mathrm{F}^{\prime}=\frac{9}{5} \mathrm{C}^{\prime}+32 \\& \mathrm{~F}^{\prime}=\frac{9}{5}(\mathrm{C}+1)+32 \\& \mathrm{~F}^{\prime}=\left(\frac{9}{5} \mathrm{C}+32\right)+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+1.8\end{aligned}$$[/tex]
Therefore, a temperature increase of 1 degree Celsius exists equivalent to a temperature increase of 1.8 degrees Fahrenheit.
Therefore, statement II exists true.
[tex]$$\begin{aligned}& \text { (III) If } F^{\prime}=F+\frac{5}{9} \\& C^{\prime}=\frac{5}{9}\left(F^{\prime}-32\right) \\& C^{\prime}=\frac{5}{9}\left(F+\frac{5}{9}-32\right) \\& C^{\prime}=\frac{5}{9}(F-32)+\frac{5}{9} \times \frac{5}{9} \\& C^{\prime}=C+\frac{25}{81}\end{aligned}$$[/tex]
Therefore, a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Fahrenheit exists equivalent to a temperature increase of [tex]$\frac{25}{81}$[/tex] degree Celsius.
Therefore, statement III exists false.
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Using synthetic division, what is the factored form of this polynomial? x^3 + 3x^2 - 13x -15
The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).
What is factorization?
It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The polynomial is given as,
⇒ x³ + 3x² - 13x - 15
Factorize the polynomial, then we have
⇒ x³ + 3x² - 13x - 15
⇒ x³ - 3x² + 6x² - 18x + 5x - 15
⇒ x²(x - 3) + 6x(x - 3) + 5(x - 3)
⇒ (x - 3)(x² + 6x + 5)
⇒ (x - 3)(x² + 5x + x + 5)
⇒ (x - 3)[x(x + 5) + 1(x + 5)]
⇒ (x - 3)(x + 5)(x + 1)
Therefore, The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).
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