Answers
After answering the provided question, we can conclude that As a result, probability the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.
What is probability?Probability of how likely an event is to occur. It is represented by a number is for both 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Shifting a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a mathematical discipline that investigates random events instead than their properties. It is applied in many fields, including facts and figures, finance, scientific knowledge, and engineering.
After eliminating one of the six possible answers, the remaining five options are equally likely to be correct, so the probability of correctly guessing is now 1/5 and the probability of incorrectly guessing is 4/5.
Point value expected = (probability of gaining points x point value) - (probability of losing points x point value)
(1/5 x 1) is the expected point value. - (4/5 x 1/6)
1/5 - 1/30 = expected point value
5/30 - 1/30 = expected point value
4/30 is the expected point value.
The expected point value is 0.13. (rounded to two decimal places)
It is advantageous to guess because the expected point value is positive.
As a result, the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.
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Related Questions
On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digits in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digits successfully, she will hear five random digits on the next trial. The participant's score is the longest string of digits she can successfully repeat. A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. She measures the number of digits successfully repeated for 36 randomly selected students. The professor knows that the distribution of scores is normal, but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with a standard deviation of 1.610 digits. The expected value of the mean of the 36 randomly selected students, M, is______. (Hint: Use the population mean and/or standard deviation just given to calculate the expected value of M.) The standard error of M is_____. (Hint: Use the population mean and/or standard deviation just given to calculate the standard error.)
Answers
The expected value of the mean of the 36 randomly selected students, M, is 7.06 digits and the standard error of the mean is 0.268 digits.
The expected value of the mean of the 36 randomly selected students can be calculated using the formula:
E(M) = μ
where μ is the population mean, which is given as 7.06 digits.
Therefore, expected value of mean of 36 randomly selected students is:
E(M) = 7.06 digits
The standard error of the mean (SE) can be calculated using the formula:
SE = σ / √(n)
where σ is the population standard deviation, which is given as 1.610 digits, and n is the sample size, which is 36 in this case.
Therefore, the standard error of the mean is:
SE = 1.610 / √(36) = 0.268 digits
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You tell your parents that you will pay the 15% tip for dinner. The bill was $130.56. You have $20.
a. Do you have enough to pay the tip?
b. How much should the tip be?
Responses
Answers: Yes; $15.75 No; $22.30 Yes; $19.60 No; $20.15
Answers
Yes.$19.60. you have enough money to pay the 15% tip for the bill of $130.56, and the amount of the tip should be $19.60.
a. Do you have enough to pay the tip?
To determine if you have enough to pay the tip, you need to calculate 15% of the bill and compare it to the amount of money you have.
15% of $130.56 = 0.15 x $130.56 = $19.58
Since you have $20, you do have enough to pay the tip.
Therefore, the answer is "Yes".
b. How much should the tip be?
The tip should be 15% of the bill, which is $19.60.
Therefore, the answer is "$19.58".
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an angle that measures 125 is composed of 23 smaller angles two of the smaller angles measure of 25 and 40 Tom things you can use an equation 125+40-25 = s to find the measure of the unknown smaller angle s explain why Tom is incorrect, and tell how to find the measure of the third smaller angle s
Answers
Answer:
60
Step-by-step explanation:
The measure of the other angle is 60°.
What is an Angle ?
An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
As given in the question
An angle that measures 125° is composed of three smaller angles.
Two of the smaller angles measure 25° and 40 degrees
Tom thinks he can use the equation 25 degrees + (40 degrees - 25 degrees) = s to find the measure of the unknown smaller angle, s
Tom is incorrect because the sum of the smaller angles will be equal to the bigger angle and the equation he has written is wrong.
The right equation and method will be
25 +40+x = 125
x = 125-40-25
x = 60°
Therefore the measure of the other angle is 60°.
If one meter is approximately 3.28 feet, how many meters are in 20 feet?
Answers
Answer:
65.6
Step-by-step explanation:
1 meter = 3.28 feet
20 feet = 3.28 x 20
= 65.616798
= 65.6 (1 dp)
:)
Write an exponential function that passes through the points (1, 12) and (5, 972)
Answers
Answer:
Step-by-step explanation:
An exponential function can be written in the form y = ab^x, where a is the initial value and b is the base. To find the specific exponential function that passes through the points (1, 12) and (5, 972), we need to solve for a and b.
Using the point (1, 12), we get:
12 = ab^1
12 = ab
Using the point (5, 972), we get:
972 = ab^5
We can use the equation ab from the first point to solve for a in terms of b:
a = 12/b
Substituting this expression for a into the second equation, we get:
972 = (12/b)b^5
Simplifying this equation, we get:
972 = 12b^4
Dividing both sides by 12, we get:
81 = b^4
Taking the fourth root of both sides, we get:
b = 3
Substituting this value of b into the equation a = 12/b, we get:
a = 4
Therefore, the exponential function that passes through the points (1, 12) and (5, 972) is:
y = 4(3^x)
Which expression can be used to find the sum of the polynomials?
(9 − 3x²) + (−8x² + 4x + 5)
A [(-3x²)+(-8x²)] +4x+ [9+(-5)]
B [3x²+8x²]+4x+ [9+(-5)]
C [3x²+(-8x²)]+4x+ [9+5]
D [(-3x²)+(-8x²)] +4x+ [9+5]
Answers
The expression that can be used to find the sum of polynomials is:
D [(-3x²)+(-8x²)] +4x+ [9+5].
Explain about the sum of polynomials?Polynomials are sums containing terms that have the shape k⋅xⁿ, in which k is any number and n is a positive integer.
For particular, 3x+21x-51 is a polynomial. a description of polynomials. Polynomial addition is the process of adding like terms from two maybe more algebraic equations while maintaining the sign of each term. It closely resembles a typical addition procedure.The given polynomials:
(9 − 3x²) + (−8x² + 4x + 5)
Addition will be done in such a way that signs of each term will remain same.
Opening the brackets.
= 9 − 3x² −8x² + 4x + 5
Rewriting the expression as:
= − 3x² −8x² + 4x + 5 + 9
Arranging them in brackets again.
= [(-3x²)+(-8x²)] +4x+ [9+5]
Thus, the expression that can be used to find the sum of polynomials is:
D [(-3x²)+(-8x²)] +4x+ [9+5].
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simplify the expression 6c+ – 4–8c+ – 2c
Answers
Answer:
-4c-4
Step-by-step explanation:
The simplified expression for 6c + (-4) - 8c + (-2c) is -4 - 4c.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression is (Number/variable, Math Operator, Number/variable)
We have the expression, 6c + (-4) - 8c + (-2c)
Now, simplifying the expression as
6c - 4 - 8c - 2c
= -4 + c(6 - 8 - 2)
= -4 + c(-4)
= -4 - 4c
Thus, the simplified expression is -4 -4c.
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54. Sally has an average score of exactly k points on 6 equally
weighted tests. How many points higher than k must Sally
score on the 7th equally weighted test to raise her average
score after the 7th test to k + 2.5 points?
PLEASE SHOW WORK
Answers
Answer:
Sally's score on the 7th test needs to be 17.5 points points more than the average of her first 6 tests.
Step-by-step explanation:
Let T be the sum of the scores of Sally's first 6 tests. Her average score would be:
Avg. Score (S) =T/6
Let S stand for Sally's average score.
We are told her average is k, so we can write: S = k
Let N stand for the score of her New (7th) test. Her total score would be:
T + N [This is the sum of all 7 of her tests]
Her average would become (T+N)/7
The goal is to raise her average score by 2.5 points to (k+2.5) points.
That means (T+N)/7 = k+2.5 [Her new average is 2.5 points higher]
(T + N)/7 = k + 2.5
T+N = 7k+17.5
Note that T = 6k [her total score for the first 6 tests is her average, k, times 6]
We'll use this definition of T in the equation:
T+N = 7k+17.5
(6k)+N = 7k+17.5 [Substitute 6k for T, since T=6k]
N = 7k+17.5-6k [Rearrange]
N = 1k+17.5
This is telling Sally, and us, that her new test, N, must score 17.5 points higher than her average score, k.
The answer is 17.5 points.
A number from 0-9 is randomly selected and then a letter from a-d is randomly selected. What is the probability that the number 3 and a constant are selected?
Answers
If a number from 0-9 is randomly selected and then a letter from a-d is randomly selected, the probability that the number 3 and a constant are selected is 0.1 or 10%.
There are 10 possible numbers that could be selected, ranging from 0 to 9, and 4 possible letters that could be selected, ranging from a to d.
To calculate the probability that the number 3 and a constant are selected, we need to determine how many outcomes satisfy this condition, and then divide that number by the total number of possible outcomes.
There is only one outcome where the number 3 and a constant are selected, which is if the number 3 is selected and any of the four letters (a, b, c, or d) are chosen. Therefore, the number of outcomes that satisfy this condition is 4.
The total number of possible outcomes is found by multiplying the number of possible numbers (10) by the number of possible letters (4).
Total number of possible outcomes = 10 x 4 = 40
Thus, the probability that the number 3 and a constant are selected is,
Probability = number of favorable outcomes / total number of possible outcomes
Probability = 4 / 40
Probability = 0.1
This means that out of all possible outcomes, 10% will result in the selection of the number 3 and any of the four letters.
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I dont know how to do this
pls answer if u know with simple working
Answers
Answer:
21 sticks
Step-by-step explanation:
In order to solve an equation like this its best to count all the sticks each step and figure out the pattern
1st: 6 sticks
2nd: 11 sticks
3rd: 16 sticks
Now we notice that it adds 5 sticks each step so the 4th picture must have 21 sticks.
Hope this helps!
Brainliest and a like is much appreciated!
What type of dilation occurs with a scale factor of 1/4?
Answers
In response to the query, we can state that Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.
what is dilation in transformation geometry ?Dilation is a transform that modifies an object's size. Dilation is a technique used to increase or decrease objects. An picture that is an exact duplicate of the original shape is produced as a result of this change. There is, however, a significant fluctuation in the shape. Dilation should result in a distortion of the initial form.
Dilations are transformations that alter an object's size without altering its shape. When an object dilates by a scale factor of 1/4, its size is decreased by a factor of 1/4, or 0.25.
This implies that each dimension of the object—its length, breadth, and height—will be multiplied by 1/4, or 0.25. For instance, if the original item was 8 units long, the dilated version would be 2 units long (8 x 1/4 = 2). The dilated item would have a width of 1.5 units if the initial object had a width of 6 units (6 x 1/4 = 1.5).
Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.
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Algebraic expression
Constant
Variable
Algebraic operations
Term
Commutative property
Compare each of these.
Answers
Overall , an algebraic expression is a combination of constants, variables, and algebraic operations.
What is algebraic operations?Algebraic operations are mathematical operations (addition, subtraction, multiplication, and division) used to manipulate algebraic expressions.
Algebraic expression: An algebraic expression is a combination of variables, constants, and algebraic operations, such as addition, subtraction, multiplication, and division.
Constant: A constant is a fixed value that does not change throughout an algebraic expression. For example, in the expression 2x + 5, the constant is 5.
Variable: A variable is a symbol or letter that represents a value that can vary or change within an algebraic expression. For example, in the expression 2x + 5, the variable is x.
Algebraic operations: Algebraic operations are mathematical operations used to manipulate algebraic expressions.
Term: A term is a part of an algebraic expression that includes a constant or a variable, or a product of a constant and a variable. For example, in the expression 2x + 5, the terms are 2x and 5.
Commutative property: The commutative property of addition and multiplication states that the order of the terms in an expression can be changed without affecting the value of the expression. For example, a + b = b + a and ab = ba.
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Area of a triangle is 110 cm and its base is 20 CM. find its attitude
Answers
Answer:
11 cm.
Step-by-step explanation:
The formula for the area of a triangle is given by:
A = (1/2)bh
where A is the area, b is the base, and h is the height (or altitude) of the triangle.
We are given that the area of the triangle is 110 cm and the base is 20 cm. Substituting these values in the formula, we get:
110 = (1/2) × 20 × h
Simplifying the equation, we get:
110 = 10h
h = 11 cm
Therefore, the height (or altitude) of the triangle is 11 cm.
Mary makes two blueberry pies
in two pie pans that are 6" in
diameter. What is the total area of
Mary's two pies?
Answers
Answer:
56.54862 in^2
Step-by-step explanation:
area = pi*radius^2
radius = 1/2 diameter
pi=3.14159.....
a=pi*3^2
a=3.14159*9
a=28.27431
two pies=56.54862
The cost of a fish dinner to the owner of the Golden Wharf restaurant is $6 55. The fish dinner is sold for $11. 55. Determine the percent markup
Answers
The markup percentage for the fish dinner at the Golden Wharf restaurant is approximately 76.34%.
How to calculate the markup percent?The markup percent is calculated by dividing the markup amount by the cost and then multiplying it by 100%. The markup is the difference between the selling price and the cost, so in this case:
markup = selling price - cost
markup = $11.55 - $6.55
markup = $5.00
So the markup is $5.00.
Now we can calculate the markup percent:
markup percent = (markup / cost) × 100%
markup percent = ($5.00 / $6.55) × 100%
markup percent = 76.34%
Therefore, the markup percentage for the fish dinner at the Golden Wharf restaurant is approximately 76.34%.
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Spice Parisienne is two-fifths ounce ground clovesone and one-fifth ounces ground nutmeg and one and one-fifth ounces ground gingerone and one-tenth ounces cinnamon. Latisha buys spices to make one batch of Spice Parisienne. Use estimation to decide whether she buys more or less than 4 ounces of spices. Explain your reasoning.
Answers
To estimate whether Latisha buys more or less than 4 ounces of spices, we can round the given amounts to the nearest whole number.
Two-fifths ounce is about 0.4 ounce.
One and one-fifth ounces is about 1.2 ounces.
One and one-tenth ounces is about 1.1 ounces.
Adding these rounded amounts gives:
0.4 + 1.2 + 1.1 = 2.7 ounces
Since 2.7 ounces is less than 4 ounces, we can conclude that Latisha buys less than 4 ounces of spices to make one batch of Spice Parisienne.
53 increased by 68% please help
Answers
Answer:
89.04
Step-by-step explanation:
To find 68% of 53, we can multiply 53 by 0.68:
68% of 53 = 0.68 x 53 = 36.04
So 53 increased by 68% is:
53 + 36.04 = 89.04
Therefore, 53 increased by 68% is 89.04.
the factors of 18.
Answers
Answer:
2*3*3=2*3^2
Step-by-step explanation:
18÷2=9
9÷3=3
3÷3=1
Answer:
See below.
Step-by-step explanation:
[tex]\textsf{We are asked to identify the factors of 18.}[/tex]
[tex]\large \fbox{\textsf{The factors of 18 are: 1, 2, 3, 6, 9, 18.}}[/tex]
[tex]\huge\fbox{What are Factors?}[/tex]
[tex]\textsf{Factors are 2 whole numbers that \bf{multiply} to become a \bf{given number.}}[/tex]
[tex]\textsf{One simple way to identify factors is to divide the given number by positive integers.}[/tex]
[tex]\large\boxed{\textsf{For example;}}[/tex]
[tex]\textsf{Find the factors of 12.}[/tex]
[tex]\mathtt{12 \div 1 = 12 \ (Factor)}\\\mathtt{12 \div 2 = 6 \ (Factor)}\\\mathtt{12 \div 3 = 4 \ (Factor)}\\\mathtt{12 \div 4 = 3 \ (Factor)}\\\mathtt{12 \div 5 = 2.4 \ (Not \ A \ Factor)}\\\mathtt{12 \div 6 = 2 \ (Factor)}[/tex]
[tex]\mathtt{12 \div 7 = 1.714... \ (Not \ A \ Factor)}\\\mathtt{12 \div 8 = 1.5 \ (Not \ A \ Factor)}\\\mathtt{12 \div 9 = 1.\bar{3} \ (Not \ A \ Factor)}\\\mathtt{12 \div 10 = 1.2 \ (Not \ A \ Factor)}\\\mathtt{12 \div 11 = 1.\bar{09} \ (Not \ a \ Factor)}\\\mathtt{12 \div 12 = 1 \ (Factor)}[/tex]
[tex]\large \fbox{\textsf{The factors of 12 are: 1, 2, 3, 4, 6, 12.}}[/tex]
[tex]\textsf{Let's do the same thing, but with 18.}[/tex]
[tex]\textsf{Find the factors of 18.}[/tex]
[tex]\mathtt{18 \div 1 = 18 \ (Factor)}\\\mathtt{18 \div 2 = 9 \ (Factor)}\\\mathtt{18 \div 3 = 6\ (Factor)}\\\mathtt{18 \div 4 = 4.5 \ (Not \ A \ Factor)}\\\mathtt{18 \div 5 = 3.6 \ (Not \ A \ Factor)}\\\mathtt{18 \div 6 = 3 \ (Factor)}[/tex]
[tex]\mathtt{18 \div 7 = 2.574... \ (Not \ A \ Factor)}\\\mathtt{18 \div 8 = 2.25 \ (Not \ A \ Factor)}\\\mathtt{18 \div 9 = 2 \ (Factor)}\\\mathtt{18 \div 10 = 1.8 \ (Not \ A \ Factor)}\\\mathtt{18 \div 11 = 1.\bar{63} \ (Not \ A \ Factor)}\\\mathtt{18 \div 12 = 1.5 \ (Not \ A \ Factor)}[/tex]
[tex]\mathtt{18 \div 13 = 1.384.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 14 = 1.285.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 15 = 1.2 \ (Not \ A \ Factor)}\\\mathtt{18 \div 16 = 1.125 \ (Not \ A \ Factor)}\\\mathtt{18 \div 17 = 1.0588.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 18 = 1 \ (Factor)}[/tex]
[tex]\large \fbox{\textsf{The factors of 18 are: 1, 2, 3, 6, 9, 18.}}[/tex]
10 POINTS.CAN SOMEONE PLEASE HELP ME
Answers
Answer:
x = 60°
y = 60°
Step-by-step explanation:
The three angles of a triangle add up to 180°
In ΔWXY, 60 + 60 + x = 180°
=> 120 + x = 180
=> x = 180 - 120 = 60°
Since lines WZ and XY are parallel, x and y which are alternate interior angles must be equal
So y = x = 60°
helpp subtracting polynomials
Answers
Answer: viedo yt
Step-by-step explanation:
if i was you go look at a yt viedo and it is easier becuase thats what helped me when i was in 6th grade we stared early so hope that helps
Answer:
choice C
Step-by-step explanation:
0 + 3x⁴ + 5x³ - 4x⁸ - 0
- (2x⁵ - 2x⁴ + 4x³ - 0 - 5)
= 2x⁵ +5x⁴ + x³ - 4x² + 5
Subtract column by column of like terms, put 0's where there is no like term, change signs inside the parentheses of the second expression because you are subtracting.
Ts is tangent to the circle at u, find the value of x
Answers
The value of x for the given tangent on the circle is found to be :
x = 74.75.
Explain about the tangent chord theorem?According to the Tangent-Chord Theorem, the angle created by a chord and just a tangent line to a circle equals the inscribed angle on the chord's opposite side.
"The angle generated by a tangent to a circle or a chord is half of the angle measuring of the intercepted arc," is another way to state the Tangent-Chord theorem.
From the given data:
Line SUT is tangent on circle:
So,
Let the chord be UM.
∠TUM + 41° = 180° (linear pair)
∠TUM = 180° - 41°
∠TUM = 139°
Now, as per tangent chord theorem:
∠TUM = 1/2 * arc length (4x -21)
139° * 2 = 4x - 21
278 + 21 = 4x
299 = 4x
x = 299/4
x = 74.75
Thus, the value of x for the given tangent on the circle is found to be :
x = 74.75.
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In an office, each worker eats 2 biscuits per day. There are 20 workers in the office
every day of the week. Biscuits come in packets of 14 and cost £1.30 per packet.
a) How many biscuits are eaten in the office per week?
b) How much does the office spend on biscuits per week?
******
£...
Answers
Answer:
(a) 280
(b) £26
Step-by-step explanation:
(a) 20 workers eat 2 biscuits a day.
20 × 2 = 40
Since there are 7 days a week, multiply the 40 x 7 to find how many biscuits are eaten each week.
40 × 7 = 280
280 biscuits are eaten every week.
(b) Now, divide 280 (the number of biscuits eaten each week) by 14 (the number of biscuits in a packet) to find how many packets are eaten weekly.
280 ÷ 14 = 20
Now you have the number of packets eaten each week, so you can determine the price spent on biscuits. Multiply 20 packets by the price per packet, which is £1.30.
20 × 1.30 = 26
The office spends £26 on biscuits each week.
Roger starts with -$30 in his bank account. He withdraws $30. What is his account balance after he withdraws $30? Roger's account balance after he withdraws $30 is $???
.
Answers
Answer:-60
Step-by-step explanation:
ACDF is a rectangle with an area of (2x² + 2x - 12)cm². B is a point on AC and E is a point on FD such that ABEF is a square with side lengths
of (x-2) cm each.
Calculate the length of ED.
Answers
The length of side ED is x + 8.
What is the length of side ED?
The length of side ED is calculated by applying the formula for area of a rectangle as shown below.
Let the length of ED = L
Then the total length of the rectangle ACDF = L + (x - 2)
The formula for area of a rectangle = Length x Base
where;
the length of the rectangle = L + x - 2the base of the rectangle = x - 2Area = L + (x - 2) · (x - 2)
(2x² + 2x - 12 ) = (x - 2 ) · (L + x - 2 )
2x² + 2x - 12 = xL + x² - 2x - 2L - 2x + 4
2x² + 2x - 12 = xL + x² - 4x - 2L + 4
x² + 6x - 16 = xL - 2L
x² + 6x - 16 = L (x - 2 )
L = (x² + 6x - 16) / ( x - 2)
divide using long division;
x + 8
------------
x - 2 √ x² + 6x - 16
- (x² - 2x)
----------
8x - 16
- (8x - 16)
---------
0
L = x + 8
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ED = 2x - 2 = 2[(13 + √65) / 7] - 2 = (26 + 2√65) / 7
Therefore, the length of ED is (26 + 2√65) / 7 cm.
How do I do this like I really need help with this been on it for two hours not knowing what to do
Answers
The equation of the line in slope-intercept form is given as follows:
y = -5x - 8.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.The graph of the line crosses the y-axis at y = -8, hence the intercept b is given as follows:
b = -8.
When x increases by 1, y decays by 5, hence the slope m is given as follows:
m = -5/1
m = -5.
Hence the function is defined as follows:
y = -5x - 8.
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The line I passes through the points (-4, 0) and (1, –1).
Find the gradient of line L.
Answers
Answer:
gradient = - [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
calculate the gradient ( slope ) m of the line using the slope formula.
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 0 ) and (x₂, y₂ ) = (1, - 1 )
m = [tex]\frac{-1-0}{1-(-4)}[/tex] = [tex]\frac{-1}{1+4}[/tex] = - [tex]\frac{1}{5}[/tex]
PLEASE HELPPP 50 POINTS !!! 4b) Use the Fact that exponents are repeated multiplication to expand the expression 2x^3 • 5x^2 and prove why the Product Rule works. Does 4a match 4b?
Answers
We have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.
What is the prοduct rule οf expοnent?The prοduct rule οf expοnents states that when multiplying twο terms with the same base, yοu can add the expοnents. Specifically, [tex]a^m * a^n = a^{(m+n)[/tex].
Tο expand the expressiοn [tex]2x^3[/tex] •[tex]5x^2[/tex] using the fact that expοnents are repeated multiplicatiοn, we can write:
[tex]2x^3[/tex] • [tex]5x^2[/tex]= (2 • x • x • x) • (5 • x • x)
Using the cοmmutative prοperty οf multiplicatiοn, we can rearrange the factοrs tο grοup the x's and the numbers:
[tex]2x^3[/tex] • [tex]5x^2[/tex] = 2 • 5 • x • x • x • x
[tex]= 10x^5[/tex]
Nοw, let's prοve why the Prοduct Rule fοr expοnents wοrks. The Prοduct Rule states that when multiplying twο expοnential expressiοns with the same base, we can add their expοnents:
[tex]a^m[/tex] • [tex]a^n = a^{(m+n)[/tex]
Tο see why this is true, let's cοnsider the repeated multiplicatiοn οf a base a with expοnent m and a base a with expοnent n:
[tex]a^m[/tex]• [tex]a^n[/tex] = (a • a • ... • a) • (a • a • ... • a)
We can cοmbine the twο grοups οf factοrs by using the assοciative prοperty οf multiplicatiοn:
[tex]a^m[/tex] •[tex]a^n[/tex] = [tex]a^{(1+1+...+1)[/tex]• (a • a • ... • a) (m times)
[tex]= a^{(m+n)[/tex] • (a • a • ... • a) (m times)
Using the fact that a tο the pοwer οf 1 is just a, we can simplify the expressiοn tο:
[tex]a^m[/tex] • [tex]a^n[/tex] [tex]= a^{(m+n)[/tex]•[tex]a^m[/tex]• [tex]a^n[/tex]
Dividing bοth sides by [tex]a^m[/tex] • [tex]a^n[/tex], we get:
[tex]1 = a^{(m+n)[/tex] / ([tex]a^m[/tex] • [tex]a^n[/tex])
Using the rule fοr dividing expοnential expressiοns with the same base, we get:
[tex]1 = a^{(m+n)[/tex] • [tex]a^{(-m)[/tex] • [tex]a^{(-n)[/tex]
Using the rule fοr adding expοnents with the same base, we can simplify the expressiοn tο:
[tex]1 = a^{(m+n-m-n)[/tex]
Simplifying further, we get:
[tex]1 = a^0[/tex]
Therefοre, we have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.
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Which of the following is a rational number?
Answers
Answer:
< because 1\2 is the same as .5 and .5 is less than 3
You read that a statistical test at the a 0. 01 level has probability 0. 14 of making a type ii error when a specific alternative is true. What is the power of the test against this alternative?
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The power of the test against the specific alternative is given by 1 minus the probability of making a Type II error. Therefore, the power is 0.86= 86%
In statistical hypothesis testing, the power of a test is the probability that it correctly rejects a null hypothesis when a specific alternative hypothesis is true. In this case, we are given that the test has a significance level of α = 0.01, which means that the test rejects the null hypothesis if the probability of obtaining the observed result, or one more extreme, under the null hypothesis is less than 0.01.
However, we also know that when a specific alternative hypothesis is true, the test has a probability of making a Type II error of 0.14. This means that there is a 14% chance that the test fails to reject the null hypothesis, even though the alternative hypothesis is true.
Therefore, the power of the test against this specific alternative hypothesis is given by 1 minus the probability of making a Type II error, which is:
Power = 1 - P(Type II error) = 1 - 0.14 = 0.86
So, the power of the test against the specific alternative hypothesis is 0.86 or 86%. This means that when the alternative hypothesis is true, the test correctly rejects the null hypothesis 86% of the time.
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b The pencils cost 2c dollars and the pens
cost 6k dollars.
Fatima spends $30, so 2c +6k = 30
Exercise 10.1
1 The cost of hiring a ladder is a fixed charge of $10 plus $3 per day.
Work out the cost of hiring the ladder for one week.
Explain why y = 3x + 10 where x is the number of days' hire and
y is the total cost in dollars.
Answers
Step-by-step explanation:
y = 3x + 10 the fixed charge is 10$ so our constant should be 10, there is a 3$ fee every day so x represents the days so we can multiply the amount of days with 3 to find the total amount paid in fees.
For example, if we hired a ladder for 3 days then
y = 3x + 10
= 3 x 3 +10
= 9 + 10
= 19$
So, we spent 19$ dollars in total cost