The total cost of the rental if Dana drives the car for 15 miles is $90.2
How to determine the total cost?From the question, we have the following parameters that can be used in our computation:
C = 73.25 + 1.13m
Where
m = number of miles
This means that
m = 15
SO, we have the following equation
C = 73.25 + 1.13 * 15
Evaluate
C = 90.2
Hence, the total cost is $90.2
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"Dana and her family are going to Six Flags Great America the sum- mer after her Sophomore year. She is excited, because she will be doing all driving: After doing some complicated analysis, she calcu; lates that it will cost a certain amount per mile to pick up everyone and drive to the park, plus flat amount for everyone's admission tickets. The equation below models the total cost, €,and the variable m represents the number of miles driven: C = 73.25 + 1.13m
if the average height of a male in the u.s. is 70 inches and the standard deviation of male heights is 3 inches, what is the probability that a randomly selected male will be between 70 and 73 inches? (assume a normal distribution.)
The probability of men whose height falls between 70 and 73 inches is 0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.
The standard deviation is a quantity that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
We are informed that the heights of men in the U.S are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. We need to determine the percent of men whose height falls between 70 and 73 inches. We would first evaluate the probability that the height of a randomly selected individual would fall between 70 and 73 inches;
This can be done in stat-crunch;
Click Stat, highlight on Calculators then click Normal
In the pop-up window that appears click Between
Enter the given values of mean and standard deviation; 70 and 3 respectively
Enter the values 70 and 73 in the next set of boxes in that order
Finally, click on compute;
Stat-Crunch returns a probability of 0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.
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Find the table that follows this rule: multiply by 8 and add 5.
A.
Input 5 6 7 8 9 10
Output 40 48 56 64 72 80
B.
Input 5 6 7 8 9 10
Output 45 53 61 69 82 90
C.
Input 5 6 7 8 9 10
Output 45 53 61 59 67 75
D.
Input 5 6 7 8 9 10
Output 45 53 61 69 77 85
Answer:
D
Step-by-step explanation:
multiply by 8 and add 5.
so,
we need to do this for every unit value and see, if the result is the same as the listed output value.
5 -> 5×8 + 5 = 45
6 -> 6×8 + 5 = 53
7 -> 7×8 + 5 = 61
8 - > 8×8 + 5 = 69
9 -> 9×8 + 5 = 77
10 -> 10×8 + 5 = 85
so, D is the correct answer.
Mr.eder’s dog is on a special diet from the vet. The dog is to eat 1/4 kg of food per day. Me.Eder buys a 6 pound bag of dog food. If mr.Eder follows the vet’s diet, how many days will this bag of food last
For 10 days that bag will last when Mr. Eder's buys 6 pound bag of dog food, using kg to pound conversion and simple basic arithmetic operation.
How to convert kg to pound ?
We know that 1 Kg = 2.20 pound.
The dog is to eat 1/4 * 2.20 = 0.55 pound food
Weight of bag brought by him = 6 pound
The basic operations are :
Addition : (+) To get sum of two or more values
e.g. a = 3, b = 5
Addition = 3+5
= 8
Subtraction : (-) The result of subtraction is the “difference”
e.g. Subtraction of a and b = a-b
= 3-5
= -2.
Multiplication : (*) The result of multiplication is the “product”
e.g. Multiplication of a and b = 3*4
= 12
Division : (/) The result of division is the “quotient”
e.g. Division of 4 and 2 is = 4/2
= 2.
so, the number of days bag can be used = 6/0.55
= 10.90
So, the bag can be used for complete 10 days.
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you are skiing down a mountain with a vertical height of 2900 feet. the distance from the top of the mountain to the base is 5800 feet. to the nearest degree, what is the angle elevation from the base to the top of the mountain?
Answer:
30°
Step-by-step explanation:
You want the angle of elevation to a point 2900 feet up that is 5800 feet distant on a straight line.
SineThe sine of the angle is the ratio of the height to the straight-line distance.
sin(θ) = h/d = 2900/5800 = 1/2
θ = arcsin(1/2) = 30°
The angle of elevation is 30° from the base to the top.
Answer: When doing a problem like this I always draw an example so I can see it. If you do that you see a right triangle with the hypothenuse, 2500 feet, is the distance from the top to the base. The opposite side is 1250 feet. Then remember sine= o/h, (opposite side over hypothenuse). So divide 1250/2500 and you get .5 Now take your calculator and use "inv" or sin-1 button to get the answer of the angle. x = 30
sinθ 1250/2500 = 1/2; θ = sin-1(1/2) = 30°
Step-by-step explanation:
If EF = 71, FD = 80, ED = 74, IG = 40, and HG = 37, find the perimeter
of AGHI. Round your answer to the nearest tenth if necessary.
The perimeter of the object is the sum of the lengths of all the sides
which is 302 units.
What is the perimeter?Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.
In the case of a circle, we call it perimeter circumference it is the distance around the circle.
Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and
HG = 37.
Now the perimeter of this figure is the sum of the lengths of all the sides which is,
= (EF + FD + ED + IG + HG).
= (71 + 80 + 74 + 40 + 37).
= 302 units.
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Question 2
What is the length of the line segment with endpoints P(2, 1,-4) and Q(-1,5,3)?
The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units
How to find the length of a line segment?To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:
length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Substituting the coordinates of P and Q into the formula, we get:
length = √((-1 - 2))² + (5 - 1))² + (3 - (-4)))² )
= √((-3))² + (4))² + (7))² )
= √(9 + 16 + 49)
= √(74)
= 8.60 units
Therefore, the length of the line segment is 8.60 units
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one leg of a right triangle has length 24 inches; the hypotenuse is 26.7 inches. what is the length of the other leg of the triangle?
The length of the other leg of the triangle is 11.7 inches
Now, According to the question:
We have the right triangle
The length of the right triangle is 24 inches
The length of the hypotenuse is 26.7 inches
To find the length of the other leg of the triangle
We know that the Pythagorean theorem.
The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.
Let the length of the other leg of the triangle be 'x'
According to the information:
[tex]24^2 + x^2 = 26.7^2[/tex]
576 + [tex]x^{2}[/tex] = 712.89
[tex]x^{2}[/tex] = 712.89 - 576
[tex]x^{2}[/tex] = 136.89
x = [tex]\sqrt{136.89}[/tex]
x = 11.7
Hence, The length of the other leg of the triangle is 11.7 inches.
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49: 1 of 1 question 2 with 1 blank 97: 1 of 1 question 3 with 1 blank 113: 1 of 1 question 4 with 1 blank 632: 1 of 1 question 5 with 1 blank 1.781: 1 of 1 question 6 with 1 blank 3.558: 1 of 1 question 7 with 1 blank 1.006.015: 1 of 1 question 8 with 1 blank 67.224.370: 1 of 1 3
Spanish is a Romance language of the Indo-European language family that emerged from the Iberian peninsula's colloquial Latin. It is now a worldwide language with around 500 million native speakers, primarily in the Americas and Spain. Twenty nations have Spanish as their official language.
These numbers in Spanish are:
1. 49: cuarenta y nueve
2. 97: noventa y siete
3. 113: ciento trece
4. 632: seiscientos treinta y dos
5. 1.781: mil setecientos ochenta y uno
6. 3.558: tres mil quinientos cincuenta y ocho
7. 1.006.015: un millon seis mil quince
8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta
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Answer:
49: cuarenta y nueve
2. 97: noventa y siete
3. 113: ciento trece
4. 632: seiscientos treinta y dos
5. 1.781: mil setecientos ochenta y uno
6. 3.558: tres mil quinientos cincuenta y ocho
7. 1.006.015: un millon seis mil quince
8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta
Step-by-step explanation:
PLS HELP W/ THESE LAST FEW QUESTIONS IM STRUGGLING THANK UU!!! (47 PNTS)
1) a
Obtuse and scalene
b
Isosceles and scalene
c
Acute and right
d
Right and scalene
e
Right and equilateral
2)Find the measure of the missing angle.
3)Find the measure of the missing angle.
6) t= ; ∠X
8) x=
10) m∠R = ; SR
Answer:
1. Scalene Triangle
2. 135 degrees
3. 80 degrees
I don't have much time for the rest, i'm sryyyyy
I hope i could helppp :3
If using the method of completing the square to solve the quadratic equation x 2 + x + 9 = 0, which number would have to be added to "complete the square"?
Answer:
Below
Step-by-step explanation:
To complete the square, the coefficient of x^2 must be 1 ( it is already)
then take 1/2 of the x coefficient .... 1/2.... square it and add it to both sides of the equation
x^2 + x + 1/4 + 9 = 1/4
then you can reduce this to
( x+ 1/2)^2 + 9 = 1/4 for further 'solving'
Using composition of functions, determine if the two functions are inverses of each other. , x ≥ 0 , x ≥ 2 A. No, because the functions contain different operations. B. No, because the composition does not result in an answer of x. C. Yes, because F(x) is equal to –G(x). D. Yes, because the composition results in an answer of x for x ≥ 2.
The correct option regarding whether the two functions are inverse functions is given as follows:
B. No, because the composition does not result in an answer of x.
How to verify if the two functions are inverses of each other?Two functions are inverses of each other if the composition of these two function has a result of x.
From the image given at the end of the answer, the two functions in this problem are defined as follows:
[tex]F(x) = \sqrt{x} + 4, x \geq 0[/tex]G(x) = x² - 4, x ≥ 2.Their composition is given as follows:
[tex](G \circ F)(x) = G(\sqrt{x} + 4)[/tex]
[tex](G \circ F)(x) = (\sqrt{x} + 4)^2 - 4[/tex]
[tex](G \circ F)(x) = x + 8\sqrt{x} + 16 - 4[/tex]
[tex](G \circ F)(x) = x + 8\sqrt{x} + 12[/tex]
The composition does not result in x, hence the two functions are not inverses and the correct statement is given by statement B.
The problem is given by the image shown at the end of the answer.
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Lindsey's Cafe uses 5 bags of coffee every day. How many days will 1/2 of a bag of coffee last?
When she uses 5 bags of coffee every day at her café, half of a bag of coffee lasts for 10 days.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. Division is a basic operation that divides an integer. It's best to imagine of it as a group of things being distributed among a group of individuals, as in the preceding example.
Here,
number of bags needed in a day=5
number of days 1/2 bag last,
=5÷1/2
=10 days
Half of bag of coffee last for 10 days when she uses 5 bags of coffee every day in her café.
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PLEASE HELP URGENT WITH 4 AND 6
The solution is
a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01
b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125
The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
a)
Let the principal be P = amount after first period = $ 402
Now , the rate of interest r = 6 %
The compound interest is calculated by compounding monthly
Now , the interest for the second period = ( PRT / 100 x 12 )
Substituting the values in the equation , we get
The interest for the second period = ( 402 x 6 x 1 ) / 1200
The interest for the second period = $ 2.01
The amount after the second period = amount after first period + interest for the second period
The amount after the second period = 402 + 2.01
The amount after the second period = $ 404.01
b)
Let the principal be P = $ 18260
The rate of interest r = 2.5 %
The compound interest is calculated by compounding quarterly
Now , the interest for the first period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the first period = ( 18260 x 2.5 ) / 400
The interest for the first period = 45650 / 400
The interest for the first period = $ 114.125
The amount for the first period = 18260 + 114.125
The amount for the first period = $ 18,374.125
Now , the principal for the second period = interest + amount of first period
The principal for the second period = $ 18,374.125
The rate of interest = 2.5 %
The interest for the second period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the second period = ( 18374.125 x 2.5 ) / 400
The interest for the second period = 45935.3125 / 400
The interest for the second period = $ 114.83828125
The amount for the second period = 18,374.125+ 114.84
The amount for the second period = $ 18,488.96
Hence , the amount and interest is calculated
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A manager of a self-service car wash charges a flat fee in addition to a fee per minute, x, for use of the services. The expression 5+0.75x models the scenario.
Which statement is true?
Responses
The coefficient 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The coefficient 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 5+0.75x.
In the given expression, 5 is constant term and 0.75x is another term.
In the term 0.75x, 0.75 is the coefficient of x
In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.
Therefore, option D is the correct answer.
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the interior angles of a regular polygon each measures 165 degrees. how many sides does the polygon have
w write the total area as a product
ing the GCF as one of the factors.
54+42 = (6.9) + (6-7)
6
+7)
The area expression as products is 7 * (8 + 6)
How to rewrite the area expression as productsFrom the question, we have the following parameters that can be used in our computation:
Area = 54 + 42
Express 54 as a product of 7 and 8
So, we have the following representation
Area = 7 * 8 + 42
Express 42 as a product of 7 and 6
So, we have the following representation
Area = 7 * 8 + 7 * 6
Factor out 7
This gives
Area = 7 * (8 + 6)
Hence, the expression using GCF is 7 * (8 + 6)
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Santiago creates a playlist of Latin dance music. The playlist contains bachata, salsa, and mambo tracks, as shown in the table. Santiago puts the playlist on shuffle mode. What is the probability that the first track he hears is a salsa track?
Santiago creates a playlist of Latin dance music. The playlist contains bachata, salsa, and mambo tracks, as shown in the table. Santiago puts the playlist on shuffle mode. What is the probability that the first track he hears is a salsa track?
Answer:8/20
Step-by-step explanation:i did the quiz and it is correct
What number does B stand for
What number does C stand for
Answer:
B=20
C = 40
These are the answers
PLEASE EXPLAIN WHY YOU GOT YOUR ANSWER PLEASEE!!!!
When Skip was a puppy, he weighed 5.6 lbs. When he visited the vet, he weighed 13.3 lbs. How much weight did Skip gain between the time he was a puppy and his vet visit?
Answer:
7.7
Step-by-step explanation:
I got this by subtracting 13.3 - 5.6
Name the property of real numbers illustrated by the equation. -2(x 4)=-2x-8
Distributive property of real numbers illustrated by the equation. -2(x 4)=-2x-8
The equation -2(x 4)=-2x-8 is an example of the distributive property of real numbers. This property states that when a number is multiplied by a group of numbers that are being added together, the number can be distributed to each of the terms in the group. To rewrite this equation as -2x + (-2)(-4) = -2x - 8, the number -2 is allocated to each of the terms in the group (x and -4) in this equation.Simplifying further, we get -2x - 8 = -2x - 8.
-2(x 4) = -2x - 8
Distribute -2 to each term in the group
-2x + (-2)(-4) = -2x - 8
Simplify
-2x - 8 = -2x – 8
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If using the method of completing the square to solve the quadratic equation x 2 + 2 x + 16 = 0
Answer:
Step-by-step explanation:
[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]
The solution does not exist because all numbers squared are greater than zero.
2 ^ (x + 3) * 3 ^ (x + 4) = 18
The value of the variable x is -2
What is an algebraic expression?An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.
These expressions are also made up of arithmetic or mathematical operations, which includes;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 18
Now, let's find the factors of 18 in 2's and 3's, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2
Collect the common factors, we get;
x+ 3 + x + 4 = 1 + 2
collect like terms
2x = 3 - 7
2x = -4
make 'x' the subject of formula
x = - 2
Hence, the value is -2
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Yujin Pon has a principal of $900 in her savings Iccount on October 1. The money earns interest at a rate of 6.5% compounded quarterly until July 1 of the following year. What is the amount in the account on July 1?
а.$914.63
b. $943.75
c.$943.87
d. $944.59
Answer: The correct answer is c. $943.87.
Step-by-step explanation: To solve this problem, we need to first determine the length of time between October 1 and July 1 of the following year. This is a period of 9 months, or 3 quarters. We can then use this information to calculate the amount of interest earned over this time period.
The principal in Yujin Pon's account is $900, and the interest rate is 6.5% compounded quarterly. This means that for each quarter, the account will earn 6.5/4 = 1.625% in interest. Over the 3 quarters between October 1 and July 1 of the following year, the account will earn a total of 1.625% * 3 = 4.875% in interest.
To calculate the amount of interest earned, we can multiply the principal by the interest rate:
Interest = Principal * Interest Rate
= $900 * 0.04875
= $43.87
The total amount in the account on July 1 will be the original principal plus the amount of interest earned over the 3 quarters:
Total = Principal + Interest
= $900 + $43.87
= $943.87
Therefore, the correct answer is c. $943.87.
Which number line shows the solutions to n > -2?
++++
+
-6-5-4-3-2-1 0 1 2 3 4 5 6
←++++
H
-6-5-4-3 -2 -1 0 1 2 3 4 5 6
+++
++++++
-6-5-4-3-2-1 0 1 2 3 4 5 6
+++++
-6-5-4-3-2-1 0 1 2
3 14 5 6
Done -
2
rotation 90 degrees counterclockwise about the origin
As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).
What is the cartesian plane?The cartesian plane is defined in mathematics as a two-dimensional coordinate plane formed by the intersection of the x- and y-axes. The origin is the point where the x- and y-axes intersect perpendicularly.
What are the quadrants?Quadrant one (QI) is the top right fourth of the coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's top left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.
Given:
The direction of rotation = clockwise, (from the first quadrant to forth quadrant then third quadrant, and so on)
Angle of rotation = 90° about the origin
According to the question, let's take our start point as A(x, y)
So, A( x, y) will lie in the first quadrant.
After 90° rotation about the origin A' will lies in fourth quadrant.
As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).
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Find the sum of 5.21 × 1019 and 3.149 × 1017.
A. 8.359 × 1019
b. 5.24149 × 1019
c. 5.24149 × 1036
d. 8.359 × 1036
Answer:
B
Step-by-step explanation:
5.21 x 10^19 + 3.149 x 10^17
10^17(5.21 x 10^2 + 3.149)
10^17(521 + 3.149)
10^17(524.149)
5.24149 x 10^17 x 10^2
5.24149 x 10^(17+2)
5.24149 x 10^19
Answer: b. 5.24149 × 1019
Step-by-step explanation: I took the test
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins, what net payout will you be promised in a fair betting game in case your bet works out?
Net payout will you be promised in a fair betting game in case your bet works out is $0 .
Given :
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .
P ( browns ) = 60 / 100 = 0.60
P ( steelers ) = 40 / 100 = 0.40
Net payout = Number of wins * 10 - Number of loses * 10
= 1 * 10 - 1 * 10
= 10 - 10
= $0.
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Which of the following expressions are equivalent to 16/24? Select all that apply.
After evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expresion 16/24.
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
So, we have the expression:
16/24
We need to find the equivalent expression from the options as follows:
So, let's take option (E) as it seems the answer and evaluation is:
8/2 * 2/12 (Be LHS)
Now, multiply:
8/2 * 2/12 = 16/24
16/24 = 16/24
Therefore, after evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expression 16/24.
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what is the product of each equation?
[tex]\left(3a^{2}b^{4}\right)\left(-8ab^{3}\right)[/tex]
[tex]\left(3a^{2}b^{7}\right)\left(5a^{3}b^{8}\right)[/tex]
[tex]\left(-2d^{2}+s\right)\left(5d^{2}-6s\right)[/tex]
[tex]\left(3x-6\right)\left(2x^{2}-7x+1\right)[/tex])
[tex]\left(7x^{2}y^{3}\right)\left(3x^{5}y^{8}\right)[/tex]
[tex]\left(y^{2}+3y+7\right)\left(8y^{2}+y+1\right)[/tex]
[tex]\left(4s+2\right)\left(5s^{2}+10s+3\right)[/tex]
The solution to the products of exponents is as follows;
1) -24a³b⁷
2) 15a⁵b¹⁵
3) -10d⁴ + 17sd² - 6s²
4) 6x³ - 33x² + 45x - 6
5) 21x⁷y¹¹
6) 8y⁴ + 25y³ + 60y² + 10y + 7
7) 20s³ + 50s² + 32s + 6
How to find product of exponents?The Product of Powers Property of exponents states that when we multiply two powers with the same base, we add the exponents.
1) (3a²b⁴) * (-8ab³)
= -24a³b⁷
2) (3a²b⁷) * (5a³b⁸)
= 15a⁵b¹⁵
3) (-2d² + s)(5d² - 6s)
Expanding the bracket to get;
(-10d⁴ + 5sd² + 12sd² - 6s²)
= -10d⁴ + 17sd² - 6s²
4) (3x - 6) * (2x² - 7x + 1)
= 6x³ - 33x² + 45x - 6
5) (7x²y³) * (3x⁵y⁸)
= 21x⁷y¹¹
6) (y² + 3y + 7) * (8y² + y + 1)
= 8y⁴ + 25y³ + 60y² + 10y + 7
7) (4s + 2) * (5s² + 10s + 3)
= 20s³ + 50s² + 32s + 6
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The probability of winning a certain game is 0. 5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?.
0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.
What is the binomial theorem on probability?The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).
When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."
The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.
Given that,
p = 0.5, So, q = 1 - 0.5 = 0.5.
If 70% of 'n' games are won then 30% of n games must be lost.
Let n = 10.
Therefore, P ( x = 3) = [tex]^{10}C_3p^7q^3[/tex]
or, P ( x = 3) = [tex]^{10}C_3(0.5)^7(0.5)^3[/tex]
or, P (x = 3) = 120×0.0078×0.125.
or, P (x = 3) = 0.117 Or 11.7% chance.
Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.
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