Integers have a greater and more suitable range to be closed for subtraction than whole numbers.
According to the closure property of subtraction, the difference between two integers will always be an integer.
An integer is a number that ranges from minus infinity and infinity and is not a fraction.
Whereas all positive valued integers including 0 are whole numbers.
Now if we subtract a larger whole number from a smaller whole number, then the difference will obviously be negative. Hence, the result will be an integer and not a whole number.
example= 25 - 30
= -5
Here both 25 and 30 are whole numbers but -5 is not. But all three are considered integers.
Hence, subtraction is closed under integers and not whole numbers.
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a trough is 10ft long and its ends have the shape of isoscles triangles that are 3ft across at the top and have a height of 1ft. if the trough is being filled with water at a rate of 12ft/min, how fast is the water level rising when the water is 6 inches deep?
The rate at which the water level is rising when the water is 6 inches deep is 4/5 ft/min .
In the question ,
it is given that ,
the length of the trough is = 10 ft ,
the width is (w) = 3 ft ,
the height of the trough is (h) = 1 ft ,
we get the relation between width and height is w = 3h ;
The formula for Volume is written as = Area of triangle * length
= 1/2 × h × w × l
= (1/2) × 3h × h × 10
So , V = 15h² .
Differentiating the given with respect to time "t" ,
we get ,
dV/dt = 30×h×dh/dt
given that , the trough is being filled with water at a rate of 12ft/min,
that means ,
dV/dt = 12
So , the rate of change of water level when the water is 6 inches deep can be calculated using the formula .
we know that 6 inches = 6/12 ft
12 = 30×(6/12)×dh/dt
dh/dt = 12/15 = 4/5 ft/min
Therefore , the water level is rising at the rate of 4/5 ft/min .
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the segments shown below could form a triangle?
Answer:
arrange them in a triangle shape, and there is a triangle
Step-by-step explanation:
a reservation center gets on average 12 notifications per hour on weekday mornings. round probability answers to 4 decimal places, i.e. .xxxx do not include leading or ending zeros. what is the probability they get 5 notifications in 30 minutes? what is the probability they get 10 or less notifications in one hour?
Probability of getting 5 notifications in 30 minutes: 0.0625 and Probability of getting 10 or less notifications in one hour: 0.9961
Probability of getting 5 notifications in 30 minutes:
The average number of notifications per hour is 12, so the average number of notifications in 30 minutes is 6.
Therefore, the probability of getting 5 notifications in 30 minutes is
P(5 Notifications) = (6 C 5)*(1/2^6)
P(5 Notifications) = 0.0625
Probability of getting 10 or less notifications in one hour:
The probability of getting 10 or less notifications in one hour is the sum of the probabilities of getting 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 notifications in one hour.
We can calculate this probability as
P(≤ 10 Notifications) = (12 C 0)(1/2^12) + (12 C 1)(1/2^12) + (12 C 2)(1/2^12) + (12 C 3)(1/2^12) + (12 C 4)(1/2^12) + (12 C 5)(1/2^12) + (12 C 6)(1/2^12) + (12 C 7)(1/2^12) + (12 C 8)(1/2^12) + (12 C 9)(1/2^12) + (12 C 10)*(1/2^12)
P(≤ 10 Notifications) = 0.9961
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4/9 + 1/4 less or greater than 1/2
Answer:
greater than
Step-by-step explanation:
4/9+1/4
16/36+9/36
25/36
25/36>18/36
a student has test scores of 70%, 74% and 84%. what must the fourth test score be in order to average at least 80%?
Answer: 92%
Step-by-step explanation:
70+74+84+92=320
320/4=80%
evaluate 7 to the power of negative 2
-14
1/19
-49
-1/19
The value of the expression 7 to the power of negative 2 is 1/49.
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]7^{-2}[/tex]
The value of this expression.
= 1/7²
= 1/49
Thus,
The value [tex]7^{-2}[/tex] is 1/49.
Option B is the correct answer.
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i always get it wrong.
The situations represented by 25/9 are "Melanie equally shares 25 meters of paper to create 9 banners" and "Joe makes 9 equal servings from a 25 ounce bag of peanuts".
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
We have the expression 25/9.
That means 25 divided in 9 equal parts.
Now the expression 1,
Melanie equally shares 25 meters of paper to create 9 banners.
We have to divide 25 meters of paper into 9 equal banners.
The above expression can be written as a mathematical term,
and that is 25/9.
Now the expression 2,
Quill gives away 9 baseball cards from a pack of 25.
In mathematical terms; 25 - 9.
Now the expression 3,
George invites 25 kids and 9 adults to his birthday party.
That means, the total 25 + 9 = 34 people
In mathematical terms : 25 + 9
Now the expression 4,
Becca creates 9 rows with 25 buttons each.
That means, each row has 25 buttons.
So the total 9 rows have 9 x 25 buttons.
In mathematical terms : 9 x 25
Now the expression 5,
Joe makes 9 equal servings from a 25 ounce bag of peanuts.
That means 25 ounce bag of peanuts equally divided into 9 parts.
In mathematical terms : 25/9
Therefore, expression 1 : Melanie equally shares 25 meters of paper to create 9 banners and expression 5: Joe makes 9 equal servings from a 25 ounce bag of peanuts, represented by 25/9.
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the elephants at the norfolk zoo are fed 1/2 a barrel of corn each day. the buffalo are fed 7/10 as much corn as the elephants. how many barrels of corn are the buffalo fed each day?
7/20 barrels of corn are the buffalo fed each day.
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.
Aloud to yourself, read the issue.Make a Drawing.Ask yourself, "What am I looking for?"List the items that have been provided.Locate the key phrases.Solve.Verify your work.Here are some actions to take:
Recognize the issue, including all the terminology used to describe it. Recognize what you need to look for, Recognize the issue's context.Convert the issue into an equation. Give the unknown a variable (or variables) to symbolize, Indicate exactly what the variable stands for.Put the strategy into action and find a solution.Given:
Elephants at the Norfolk zoo are fed = 1/2
Buffalo are fed 7/10 as much corn as the elephants = 7/10 * Elephants fed
= 7/10 * 1/2
= 7/20
Hence, 7/20 barrels of corn are the buffalo fed each day.
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each of the six faces of a cube is painted either black or white. two cubes are considered identical if one cube can be rotated to look like another. how many distinct cubes are possible
the distinct cubes are possible from the arrangement is 10
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
each of the six faces of a cube is painted either black or white.
two cubes are considered identical if one cube can be rotated to look like another.
All 6 sides black.
1 side white and 5 side black.
2 adjacent sides white and other 4 sides black.
2 opposite sides white and other 4 sides black.
3 sides with same corner white and other 3 black.
2 opposite sides and 1 center side white and other 3 black.
2 adjacent sides black and other 4 sides white.
2 opposite sides black and other 4 sides white.
1 side black and 5 sides white.
So total is 10
Hence, the distinct cubes are possible from the arrangement is 10.
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Solve for n in s = (n - 2)180
The value of n in the equation is n = s / 180 + 2
How to make a variable the subject of the formula?The subject of a formula is the variable that is being worked out. Subject of the formula is a variable which is expressed in terms of other variables involved in the formula.
Therefore, we have to make n the subject of the formula in the equation.
Hence,
s = (n - 2)180
open the bracket on the right side
s = 180n - 360
add 360 to both sides of the equation
s = 180n - 360
s + 360 = 180n - 360 + 360
s + 360 = 180n
divide both sides by 180
s + 360 = 180n
s / 180 + 360 / 180 = 180n / 180
Hence,
n = s / 180 + 2
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Which relation is a function of x
its the swcond sorry if its wrong but that what it was for me
Simplify (-5x-4)divided by(-3+5)
The given expression is simplified to obtain as (-2.5x - 2).
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is (-5x - 4) ÷ (-3 + 5)
It can be simplified as follows,
(-5x - 4) ÷ (-3 + 5)
= (-5x - 4) ÷ 2
Divide each term of -5x - 4 by 2 as below,
(-5x/2 - 4/2)
= (-2.5x - 2)
Hence, the simplification of the given expression is obtained as (-2.5x - 2).
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Jocelyn has a candy box with chocolates and jelly beans. The ratio of chocolates to jelly beans is 8:3. Jocelyn has 24 chocolates in the box. How many jelly beans does she have?
Answer:
9 jelly beans
Step-by-step explanation:
if the ratio representing chocolate is 8 and the number of chocolate is 24 we shall take 8-24 what of 3 which represents jelly beans so
8-24
3
that is 3×24÷8=9
(a) suppose the test for covid is 99.6% accurate, and 6% of the population has covid. if someone tests positive, what is the probability that this person has covid?
Answer: the probability that a person has a positive test result given that person is healthy is 0.01the probability that a patient has a positive test result given that person has COVID is 0.98
Step-by-step What is the probability that a patient has COVID if that person tested positive for COVID?The test seem to have high accuracy. After being tested positive, the probability that you have COVID should be high, right?Before settling down with that guess, let’s use Bayes’ theorem to answer this question.
Can the distributive property be used to rewrite
2 x (7- 4)?
If yes, fill in the blanks below.
(? x ?) - ( ? x ?)
Yes the distributive property can be used to rewrite the equation 2 x (7- 4) to appear in the form
(2 * 7) - (2 * 4)What is the distributive property of multiplication?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
In other words, an equation of the type A (B + C) can be solved as
= A (B + C)
= AB + AC
in accordance with the distributive property.
As it relates to the problem, 2 x (7- 4)
A = 2
B = 7
C = 4
2 x (7- 4)
= 2 * 7 - 2 * 4
The distributive property is also applicable to subtraction as used in the problem,
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if one check in 10,000 is forged, 5% of all checks are postdated, and 80% of forged checks are postdated, find the probability that a postdated check is forged. (round your answer to five decimal places.)
The probability that a postdated cheque is forged is 0.8 .
In the question ,
it is given that ,
there is 1 cheque forged in 10000 cheques.
the percent of postdated cheques = 5% ,
So , the number of Post-dated cheque = 0.05*10,000 = 500
the percent of cheques that the postdated cheque is forged is = 80%
the number of Forged cheque that are post-dated = 0.8*500 = 400
So , Probability (post-dated check is forged) = (Forged check that are post-dated)/(post dated checks)
Substituting the values ,
we get ,
= 400/500
= 0.8
Therefore , the required probability is 0.8 .
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When triangle ABC is dilated by a scale factor of 2 Its image is?
A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2) are the coordinates of the image after dilation.
Given,
Triangle ABC is dilated with a scale factor 2 at the origin.
We have to find the coordinates of the image;
Dilation;
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Here,
The vertices of the triangle; A(1, 1), B(1.5, 3), C(2, 1).
After the dilation of a scale factor 2, the new point;
A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2).
That is,
The coordinates of the image after dilation is, A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2).
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Write the following expression without negative exponents and without parentheses. -6x^{-2} −6x −2
Answer:
[tex]-\frac{6}{x^{2} } -6x-2[/tex]
Step-by-step explanation:
[tex]x^{-2}[/tex] is equivalent [tex]\frac{1}{x^{2} }[/tex]
Then, that is multiplied by the coefficient of -6
Thus [tex]-6x^{-2}[/tex] becomes [tex]-\frac{6}{x^{2} }[/tex]
the airplane you are flying burns 10 gallons of fuel per hour. how many gallons of fuel will you consume during a 120 nautical mile flight with a ground speed of 100 nautical miles per hour.
Total 12 gallons of fuel was burned
What is the relation between Time, Spped and Diatnce?
The formula speed distance time is used to describe the connection between speed, distance, and time. That is, speed = distance / time. To put it another way, distance divided by speed equals time. You can figure out the third input if you know the first two.
Solution:
10 gallons fuel is burned per hour
Distance Travelled by the Plane = 120 nautical miles
Speed of the Plane = 100 nautical miles per hours
Time = Distance / Speed
Time = 120 / 100 = 1.2 hours
Since 10 gallons of fuel is burned every hour, so total fuel burned in 1.2 hours is 12 gallons
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x^2-27=4x ,solve for, x
Answer:
Step-by-step explanation:
x^2-27=4x
x*x (1 x 1)
1-27=4x
-26=4x
divide both sides by 4 and you get...
x=-6.5
(if wrong, i'm sorry.)
How do you solve an equation with x and y in one?
There are infinitely many solutions to an equation with two variables.
We know that an equation is a mathematical statement that contains equal symbol between two mathematical expressions.
In this question need to solve an equation with x and y in one equation.
Consider an equation with two variables: 5x + y = 8
If we solve given equation for x then it would be,
5x + y = 8
5x + y - y = 8 - y
5x/5 = (8 - y)/5
x = (8 - y)/5
for any arbitrary real value value of y we can find the value of x.
This means there are infinitely many solutions.
If we solve given equation for y then it would be,
5x + y = 8
5x + y - 5x = 8 - 5x
y = 8 - 5x
for any arbitrary real value value of x we can find the value of y.
Therefore, an equation with two variables has infinitely many solutions.
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PLEASE help meeeee pleasee
Answer: y = -1/3x -1
Step-by-step explanation:
The slope is -1/3, and it crosses the y axis at (0,-1)
WILL GIVE 50 POINTS
For real-world problems, the domain and range of functions can be constrained by situations that make sense. Janet records how far she runs each day in January. The domain of the function is the date in January. The range of the function is how far Janet runs. How are the domain and range of the function constrained?
Answer: The domain is constrained by the number of days in January, [1,31]. The range is constrained by how far she can run each day.
Step-by-step explanation:
Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away. Zhang leaves the store when aaron starts riding his bike, and he rides his bike toward aaron along the same road at 2 mi/h. How many hours will pass before they meet?.
2 hours will pass before they meet.
"Information available from the question"
In the question:
Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.
Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.
Now, According to the question:
Total distance = 20mi
Aaron starts riding a bike at a rate of = 3mi/h
Zhang rides his bike toward Aaron along the same road at = 2mi/h
Let y be the number of hours for them to meet.
The expression is given as
3y + 2y = 20
solving for y, we have
5y = 20
y = 20/5
y = 4hrs
Therefore, 2 hours will pass before they meet.
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The function f(x) is graphed below. What is true about the graph on the interval from x=−∞ to x=a?
Graph is negative and increasing in the interval x = - to x = a
A graph is included in the question in this case.
If the graph of any function is moving downward over a specific time interval, we know that. Function then starts to decline during that period.
If the graph of any function is rising during a specific interval. Function then increases throughout that specific time period.
A graph is positive when it is oriented above the horizontal axis.
It can be seen in the accompanying graph that the function's graph is below the x-axis between the values of x = - to x = a as it is oriented below the horizontal axis and graph is increasing
So
According to the given information
Graph is negative and increasing in the interval x = - to x = a
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find an equation for the circle that goes through the points (0, 0), (0, 8), and (6, 12). find an equation for the line that is tangent to this circle at (6, 12).
The equation for circle is 28g + 16f =260
and the equation of tangent to this circle is y = [tex]\frac{6}{12}[/tex] x +29
a) the main equation of circle is ax + by +2gx+ 2fy +c =0 --------- (1)
Now,
putting the points (0,0) , (0,8) and (6,12) one by one, we get,
For the point (0,0), we get:
c =o ----------------------------- (2)
For the point (6,12), we get:
6x +12y + c = (6)² + (12)²
⇒ 6x +12y +c = 36 +144
⇒ 6x +12y +c = 180 --------------------------- (3)
For the point (0,8), we get,
8y + c = 64 ----------------------------- (4)
putting c=0,
8y +0 = 64
⇒ y =64/8
⇒ y = 8
Putting c=0 and y =8, we get,
6x + 12×8 +0 = 180
⇒ 6x + 96 =180
⇒ 6x = 84
⇒ x = 14
Putting all the values in equation (1), we get:
(14)² + (8)² +28g +16g + 0 = 0
⇒ 196 + 64 + 28g +16f =0
⇒ 28g + 16f = 260
b) As we know the tangent from the circle:
y = mx + c
⇒ 8 = -12/6 × 14 +c
⇒ c = 29
Therefore, the equation of the tangent is y = [tex]\frac{6}{12}[/tex]x + 29
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In the CapGemini IOT Industry 4.0 case, what dimension focuses on the way that Smart Products are
equipped with computing power that enables autonomous decision-making and self-learning processes
based on algorithms? Connected O Intelligent O Responsive O Aware
The dimension that focuses on the way that Smart Products are equipped with computing power that enables autonomous decision-making and self-learning processes based on algorithms is described as follows:
Intelligent.
What are self-learning systems?Self-learning systems are systems that use machine language and data analysis to give the users what they are looking for.
A simple example is a person logging into an app to look for news for their NFL team. The next time the person logs into the app, the data analysis will know that the person is likely looking for news about their NFL teams, and thus these news will already be on the front page or on adds for the user.
The systems that use these strategies are called Intelligent systems.
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What are functions in Excel how many types of functions do you know give 2 examples for each function?
Important functions in Excel;
The SUM function
The TEXT function
The VLOOKUP function
The AVERAGE function
The CONCATENATE Function
Given,
Functions in Excel;
Functions are pre-written formulas that carry out calculations by utilising particular values, referred to as inputs, in a given order, or structure. Calculations of any complexity can be carried out using functions. The Formulas tab on the Ribbon contains the syntax for all of Excel's functions.
The most important five functions in Excel are given below;
The SUM functionEg; =SUM(A2:A10) Adds the values in cells A2:10. =SUM(A2:A10, C2:C10) Adds the values in cells A2:10, as well as cells C2:C10.
The TEXT functionEg; In Excel, the value 12200000 appears as 12,200,000 if the format string is "#,###". A comma after a placeholder for a digit multiplies the number by 1,000. The format string "#,###. 0," for instance, causes Excel to show the number 12200000 as 12,200.0.
The VLOOKUP functionEg; =VLOOKUP(90,A1:B100,2,TRUE). Exact match - 0/FALSE searches for the exact value in the first column.
The AVERAGE functionEg; if the range A1:A20 contains numbers, the formula =AVERAGE(A1:A20) returns the average of those numbers.
The CONCATENATE FunctionEg; Add double quotation marks with a space between them " ". For example: =CONCATENATE("Hello", " ", "World!").
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You have decided both to open a savings account and to purchase a vehicle. You would like a savings account with the highest interest rate and a vehicle loan with a low interest rate. From the banks listed below, determine with which bank you should open a savings account and at which bank should you apply for your vehicle loan.
Bank A for the savings account and Bank A for the car loan
Bank B for the savings account and Bank B for the car loan
Bank C for the savings account and Bank C for the car loan
Bank C for the savings account and Bank A for the car loan
The bank you should open a savings account with is Bank A and the bank, should you apply for your vehicle loan is Bank B. Thus the correct option is C.
What is Bank?
A bank is referred to as a financial institution that allows an individual to deposit and withdraw cash and allow them to borrow funds with a fixed interest rate for the purpose of investment.
In the given case, it is explained that Both opening a savings account and getting a car are decisions you have made. You want to borrow money for a car at a cheap interest rate and have the greatest interest rate savings account.
In order to avoid any burden you should make decisions with Bank B for the car loan and Bank A for the savings account and enjoy the assets for a lifetime with appropriate benefits.
Therefore, option C is appropriate.
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6. In right triangle ABC, angle C is a right angle, AB is 25 units long, and BC is 24 units
Mong. What is the length of AC?
A. 1
B.2
C. 7
D. 49
Answer:
C. 7
Step-by-step explanation:
Draw out the triangle if you want.
You’ll notice you’ll have a hypotenuse and one other side.
Use Pythagoras’ theorem: a^2 + b^2 = c^2
c = the hypotenuse
24^2 + b^2 = 25^2
solve for b:
576 + b^2 = 625
b^2 = 625 - 576
b^2 = 49
b = 7