Standardized tests for certain subjects, given to high
Which of the following is the correct interpretation of P(X
school students, are scored on a scale of 1 to 5. Let X
> 4)?
represent the score on a randomly selected exam. The
distribution of scores for one subject's standardized test
• The probability of a of a randomly selected test having
is given in the table.
score of at most 4 is 0.36.
• The probability of a randomly selected test having a
Score
score of at least 4 is 0.36.
Probability
0.18
0.20
0.26
0.21
0.15
• The probability of a randomly selected test having &
score lower than 4 is 0.85.
• The probability of a randomly selected test having a
score higher than 4 is 0.15.
Answer: • The probability of a randomly selected test having a score higher than 4 is 0.15.
This is the correct interpretation of P(X > 4). P(X > 4) represents the probability of a randomly selected test having a score that is greater than 4. This is calculated by summing up the probability of all the scores that are greater than 4 in the distribution table.
Step-by-step explanation:
A population of bacteria grows according to function p (t) = p. 1. 42', where t is measured in hours. If the initial population size was 1,000 cells, approximately
how long will it take the population to exceed 10,000 cells? Round your answer to the nearest tenth
The time duration for the population to exceed 10,000 is approximately 6.6 hours
What is time ?
In mathematics, time is described as a continuing and continuous series of events that take place in chronological order from the past through the present and into the future. The duration of events, the gaps between them, or even the sequencing of occurrences can all be quantified, measured, or compared using time.
the time frame that an activity, process, or state lasts or continues to exist: duration is a non-spatial continuum that is measured in terms of subsequent occurrences from the past, present, and future.
The mathematical symbol used to represent the multiplication process and its subsequent product is the multiplication sign, sometimes referred to as the times sign or the dimension sign.
t = The time duration in hours
The initial population of the cells = 1,000
Therefore, at t = 0, P(0) = 1,000 = P₀ × 1.42^0
∴ P(0) = 1,000 = P₀ × 1 = P₀
P₀ = 1,000
When the population is 10,000, we have;
P(t) = 10,000 = 1,000 × 1.42^t
∴ 1.42^t = 10,000/1,000 = 10
㏒(1.42^t) = ㏒(10) = 1
∴ t × ㏒(1.42) = 1
t = 1/㏒(1.42) = 6.56649071898
∴ The time duration for the population to exceed 10,000, t ≈ 6.6 hours.
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Annie bought a brand new car for $32,000. The car is now worth $21,000.
(This is percent over change!!)
Using percentages we know that the value of a car decreases by 34% on average.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, we know that:
Annie brought a car at: $32000
Current price of the car: $21000
The decline in car percentage:
21000/32000 * 100
65.625%
⇒ 100 - 65.625 = 34.375%
Rounding off: 34%
Therefore, using percentages we know that the value of a car decreases by 34% on average.
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Complete question:
Annie bought a brand-new car for $32,000. The car is now worth $21,000.
By what percentage does the car's worth decrease?
Write an equation of the line that passes through the given point and is perpendicular to the given line.
(2, 5); x = -6
well, since the given line is a horizontal line, a perpendicular line to that will just be, yeap, you guessed it, a vertical line, Check the picture below.
Find the product of the factors 8.075*0.08
To find the distance from the edge of a lake to the tree on the island in the lake, Lisa sets up a
triangular configuration as show in the diagram. The distance from Location A to Location B is 97
meters. The measures of the angles at A and B are 46 and 103 °. What is the distance from the
edge of the lake at B to the tree on the island at C? Round the distance to the nearest tenth of a
meter.
A
B
C
Answer:
135.5 m
Step-by-step explanation:
Given a triangle with angles A=46°, B=103°, and side c=97 m, you want to find the length of side 'a'.
Law of SinesGiven one side and two angles we can solve the triangle using the Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
In order to do that, we need to have a (side, angle) pair, so we need to find the measure of angle C.
A + B + C = 180°
46° +103° +C = 180° . . . use the given measures
C = 31° . . . . . . . . . . . . . subtract 149°
Now, we can find 'a' from ...
a/sin(A) = c/sin(C)
a = c·sin(A)/sin(C) = (97 m)·sin(46°)/sin(31°) ≈ 135.477286 m
The distance from B to the tree at C is about 135.5 meters.
How do you solve equivalent questions?
One of the way by which we can solve equivalent questions is by multiplying both the numerator and the denominator by a same number .
The number chosen for the purpose should be same and should be a non zero number. Example, if we want to find the equivalent of 2/8 then we can simply multiply 2 and 8 which are the numerator and the denominator by a same number say 3 .
Then we will get the result as 2 x 3 /8 x 3 = 6 / 24 .
The result will be a number equivalent to the given fraction. This can be checked by reducing the result to its lowest terms.
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150 people went to see "Ode to Algebra" performed in the school auditorium. If the number of children that attended the performance was c, how many adults attended?
Answer:
150-c
Step-by-step explanation:
150= total
c= children
adults=x
x=150-c
What is the answer of 7 to the power of 2?
The answer to 7 to the power of 2 is 49.
This is because when a number is raised to a power, it means that it is multiplied by itself that number of times. 7 to the power of 2 is 7 multiplied by itself 2 times, which is 7 x 7, which equals 49.
An expression known as "power" denotes the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.
As an illustration, the power 63 demonstrates how three times the number 6 is multiplied.
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A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at 14 miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of 3 miles per hour. How long will it be before the rescued sailors are 57 miles from their lifeboat?
The time it will take for the rescued sailors to be 57 miles from their life boat is given as follows:
3.35 hours.
What is relative velocity?Relative velocity is obtained considering the direction in which the objects are traveling, as follows:
Opposite direction: the relative velocity is given by the sum of the velocities of each object.Same direction: the relative velocity is given by the subtraction of the velocities of each object.For this problem, the sailors and the lifeboat are traveling in opposite directions, hence the relative velocity, considering each of their velocities is given as follows:
v = 14 + 3 = 17 miles.
(meaning that they get 17 miles farther each hour).
Velocity is distance divided by time, hence the time it will take for them to be 57 miles apart is given as follows:
17 = 57/t
17t = 57
t = 57/17
t = 3.35 hours.
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Write the equation of the line, that passes through the points (- 6, 1) and (10, 0)
Equation:
Now, write an equation of a line that is parallel to the above line and passes through point (-7, 2) in all three forms below.
Point-Slope Form
Slope-Intercept Form
Standard Form
The equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that the line passes through the points (- 6, 1) and (10, 0).
The slope of the line will be -
{m} = (0 - 1)/(10 + 6) = -1/16
{m} = -1/16
We can write the equation as -
y = - (1/16)x + c
For the point (10, 0), we can write -
0 = - (1/16) x 10 + c
0 = - (10/16) + c
c = 10/16
c = 5/8
So, we can write the equation as -
y = - (1/16)x + (5/8)
The equation of a line that is parallel to the above line and passes through point (-7, 2) is as follows -
y = - (1/16)x + c
2 = - (1/16) x - 7 + c
c = 2 - 7/16
c = 25/16
y = - (1/16)x + (25/16)
Therefore, the equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
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What are the 7 different triangles?
The seven different types of triangles are Equiangular Triangle , Acute Angled Triangle , Right Angled Triangle , Obtuse Angled Triangle , Equilateral Triangle , Isosceles Triangle and Scalene Triangle .
The Triangle is defined as a polygon with three sides having three vertices .
The Seven different types of Triangles are :
(i) Equiangular Triangle :
It is a type of triangle in which the measure of all the three sides of triangle are equal .
(ii) Acute Angled Triangle :
It is a type of triangle in which all the angles of triangle are acute , that means angle is less than 90 degree .
(iii) Right Angled Triangle :
It is the type of triangle in which the measure of one angle is 90 degree .
(iv) Obtuse Angled Triangle :
It is defined as a triangle in which one angle of the triangle is obtuse , that means the angle is greater than 90 and less than 180 degree .
(v) Equilateral Triangle :
It is a triangle in which the measure of all the sides of the triangle are equal .
(vi) Isosceles Triangle :
It is a type of triangle in which the measure of the two sides of the triangle are equal .
(vii) Scalene Triangle :
It is defined as a triangle in which the measure of all the sides of triangle are different ,
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A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events. The probabilities assigned were , , and a. If an individual recalls seeing the advertisement, what is the probability that the individual purchased the product (to 1 decimals)
0.30 is the probability that the individual purchased the product
What is probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.
Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.
Let, B = individual purchased the product
S = individuals recalls seeing the advertisement.
Here, P(B) = 0.20
P(S) = 0.40
P(B ∩ S) = 0.12
Thus, P(B | S) = P(B ∩ S) / P(S)
= 0.12/0.40
= 0.30
P(B) = 0.20 < P(B | S) =0.30
Yes, thus the probability that an individual will purchase the product will increase if the individual sees the advertisement first.
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The complete question is as follows:
OPEN ENDED NOT MULTIPLE CHOICE
Some recent studies suggest that a teenager sends an average of 60 texts per day. For each of
the following scenarios, find the linear function that describes the relationship between the input
value and the output value. Then, determine whether the graph of the function is increasing,
decreasing, or constant.
a. The total number of texts a teen sends is considered a function of time in days. The input is
the number of days, and output is the total number of texts sent.
b. A teen has a limit of 500 texts per month in his or her data plan. The input is the number of
days, and output is the total number of texts remaining for the month.
c. A teen has an unlimited number of texts in his or her data plan for a cost of $50 per month.
The input is the number of days, and output is the total cost of texting each month
What is a power of 3 equation called?
A power of 3 equation is called as cubic equation.
The term equation in math is known as a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Here we need to find the term that has been used for power of 3 equation.
Here we have to know that the power of 3 equation is known as cubic equation.
in other terms the polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.
As we all know that the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.
The general form of the power of 3 equation is written as
=> ax³ + bx² + cx + d = 0
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A forest covers 78,000 acres. A survey finds that 0. 4% of the forest is old-growth trees. How many
acres of old-growth trees are there?
There are
acres of old-growth trees.
Answer:
There would be 312 acres of old tree growth for 0.4% of the forest. There would be 31.2 acres of old tree growth for 0.04%. I wasn't sure if you meant 0.4 or 0.04.
Flow chart to find the biggest of 3 numbers
The flowchart to find the biggest of 3 numbers is mentioned below:
Define Flowchart.A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.
Define Algorithm.An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.
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Dylan opened a credit card account with $575.00 of available credit. Now that he has made some purchases, Dylan's account only has $465.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
Answer:
19%
Step-by-step explanation:
First, we have to find how much did he spend by taking
$575.00 - $465.75 = $109.25
Then we find the percentage decrease by taking
109.25 divided by 575, then times 100% = 19%
So, the percentage decrease of the amount of available credit in Dylan's account is 19%
The probability that a student studied is 0.85. The probability that a student will not pass, given that the student studied is 0.10.
a) Find the probability that a student will study and will pass.
b) Suppose that the probability that a student will either study or pass is 0.8. Find the probability that a student will pass.
a) The probability that a student will study and will pass is 0.765.
b) The probability that a student will pass is 0.715.
What is probability?
Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.
Define some events -
A: A student studies.
B: A student will pass.
Given that P(A)=0.85 and
P(B|A)=1-P([tex]\bar{B}[/tex]|A)
=1-0.10
=0.90
a) P(a student will study and will Pass)= P(A∩B)
= P(A)·P(B|A)
= 0.85×0.90
= 0.765
b) Given that P( student will either study or pass), the probability is -
=P(A∪B)= 0.8 then P(a student will pass)
=P(B)
It is known that P(A∪B)= P(A)+P(B)-P(A∩B)
Then P(B)=P(A∪B) -P(A) +P(A∩B)
=0.8-0.85 + 0.765
=0.715
Therefore, the probabilities are 0.765 and 0.715.
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How do you write 10000000 in words?
F18) if y varies jointly as x and the inverse of z, and y = -5 and z = 6, find y when x = 5 and z = -8
Answer:
gfifhdrtjttt9668ztjt*
A manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth.
Probability that computer chosen at random has defect is 0.0075.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.
What is probability?It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12.
Total number of computers=1200
Total number of damage computers=9
Probability that question chosen at random has defect = 9/1200=0.0075
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Baldwin took a total of 35 quizzes over the course of 7 weeks. After attending 9 weeks of school this quarter how many quizzes will Baldwin have taken in total
The total number of quizzes in 9 weeks will be 45.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Baldwin took a total of 35 quizzes over the course of 7 weeks. After attending 9 weeks of school this quarter.
The number of quizzes in 9 weeks will be,
7 weeks = 35 quizz
1 week = 35 / 9 quizz
9 week = ( 35 x 7 ) / 9
9 weeks = 45 quizzes.
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Is 6 A positive number?
Yes, 6 is an positive number.
Now, According to the question:
What Is A Positive Number?
A positive number is any number that represents more than zero of anything. If you are talking about dollars in your bank account, a positive number will definitely make you feel positive too.
1, 2, 3, 4, 5, 6, 7, ........ are positive integers and -1, -2, -3, -4, -5, -6, -7, ........ are negative integers. 0 is an integer which is neither positive nor negative. On an integer number line, all numbers to the right of 0 are positive integers and all numbers to the left of 0 are negative integers.
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expand this expression using the distributive property. 4(-2g+4-3t)
Answer:
-8g+16-12t is the answer
Step-by-step explanation:
multiply everything by 4
3x + 2y = 5
x = 2y + 7
Answer:
I hope this helps you...
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Refer to the equation a-6 equals b if a equals 45 what is the value of b?
Answer:
Step-by-step explanation: a=4, b=2.
Answer:
b = 39
Step-by-step explanation:
[tex]a-6=b[/tex]
if a = 45:
[tex]45-6=b\\39=b[/tex]
Hope this helps
( r - 8 ) - ( r + 15 )
Find the Sum or Difference! :)
Answer:
-23
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
Answer:-23 ITS SUPER EASY:0
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
Julian went shopping for a new pair of sneakers. Sales tax where he lives is 5.75%. If the price of the pair of sneakers is pp dollars and cents, which expression represents the total price plus tax?
The expression that represents the total price plus tax that Julian paid during shopping is 1.0575pp
How to write the expression of the total price Julian paid
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
5.75%
= 5.75 percent
= 5.75 / 100
= 0.0575
The factor 0.0575 of the price (pp dollars and cents) gives the total price paid
when the price paid is pp dollars and cents
= 0.0575 * pp + pp
= 1.0575pp
The total price paid is 1.0575pp
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a club treasurer is solving a problem using the expression shown. -23.50 + 5 which problem is the treasurer MOST LIKELY solving? A. There is a club member who pays 23.50$ in dues each month for 5 months. What is the total amount, in dollars, that the member pays in dues? B. There are 5 club memebers who each owe the club 23.50$ in dues. What is the total balance, in dollars, of the members accounts? C. a total of 23.50$ in dues is owed to the club. There are 5 club memebrs who each owe the same account in dues. What is the amount, in dollars, that each member owes in dues? D. A total of 23.50$ in dues is owed to the club. There are 5 club members who each owe the same amount in dues. What is the balance,in dollars, of each members account?
When the treasurer is solving a problem using the expression shown. -23.50 ÷ 5, the problem that the treasurer is lost likely solving is D. A total of -$23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues. What is the balance,in dollars, of each members account?
How to illustrate the expression?From the information, the club treasurer is solving a problem using the expression shown. -23.50 ÷ 5. An expression show the relationship between the variables.
In this case, a total of $23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues.
The correct option is D.
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