The sum of all possible values of N is 336.
What is an integer?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
Here, we have
Let the three integers be a, b, and c.
N = abc = 6(a + b + c) and c = a + b.
Then N = ab(a + b) = 6(a + b + a + b) = 12(a + b).
Since a and b are positive, ab = 12
so {a, b} is one of {1, 12}, {2, 6}, {3, 4}
a + b is one of 13, 8, 7
N is one of 12× 13 = 156, 12× 8 = 96, 12×7 = 84
156 + 96 + 84 = 336.
Hence, the sum of all possible values of N is 336.
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suppose a is a set with m elements and b is a set with n elements. a. how many relations are there from a to b? explain. b. how many functions are there from a to b? explain. c. what fraction of the relations from a to b are functions?
a)There are [tex]2^m^n[/tex] possible relation
b)Similarly [tex]n^m[/tex]
c)[tex]\frac{n^m}{2^m^n}[/tex]
a)Set A has m elements and set B has n elements
Firstly determine the number of elements A*B by using the multiplication rule
Number of elements[tex]=A*B=m*n=mn[/tex]
For each element, [tex]A*B[/tex] we have two option
First element 2 ways
Second element 2 ways
mn element 2 ways
By using the multiplication rule
[tex]2*2*2......=2^m^n }[/tex]
Then there are [tex]2^m^n[/tex] possible relation
b)Similarly [tex]n^m[/tex]
c)[tex]\frac{n^m}{2^m^n}[/tex]
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find the average rate of change for the following equation over the interval -4≤x≤1
y=x^2 + 4x -1
To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:
m = (y2 - y1) / (x2 - x1)
For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:
m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))
Simplifying this expression, we get:
m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)
This simplifies to:
m = -20 / -3
Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.
Question 3
Answer choices:
A) copy an angle
B) copy a segment
C) construct a perpendicular line to a point not on the line
D) bisect an angle
"Copy an angle" construction has been performed.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
Observe that angles BAC and TSR are same.
This means, construction is done to copy the angle BAC.
So, "copy an angle" construction has been performed.
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How many km do you travel in 1 hour?
Answer:
100 km
Step-by-step explanation:
On a certain hot summer's day, 354 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $548.25. How many children and how many adults swam at the public pool that day?
The number of children and adults that swam at the public pool is
331 and 23.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
Example:
2x + 5 = 9 is an equation.
We have,
The total number of people = 354.
Cost for children = $1.50
Cost of adults = $2.25
Total amount = $548.25
Now,
Number of children = x
Number of adults = y
Now,
x + y = 354 _____(1)
x = 354 - y ____(2)
1.50x + 2.25y = 548.25 _____(3)
Putting (2) in (3).
1.50 (354 - y) + 2.25y = 548.25
531 - 1.50y + 2.25y = 548.25
0.75y = 548.25 - 531
0.75y = 17.25
y = 17.25/0.75
y = 23
Now,
x = 354 - y
x = 354 - 23
x = 331
Thus,
The number of children is 331.
The number of adults is 23.
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please anyone help me with this question i need it ASAP!! all it’s asking is to Write the equation of a line perpendicular to y=2x-4 and
goes through the point (4,-1). please anyone help meee!!
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 4 ← is in slope- intercept form
with slope m = 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 2 + c ⇒ c = - 1 + 2 = 1
y = - [tex]\frac{1}{2}[/tex] x + 1 ← equation of perpendicular line
You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 28 inches long. The first bend is made 10 inches from one end. Describe two ways you could complete the triangle.
Answer:
2 ways below
Step-by-step explanation:
To complete the triangle, you would need to bend the other end of the strip of metal so that it is also 10 inches from the first bend. One way to do this would be to measure 10 inches from the first bend and mark the spot, then use a bending tool to carefully bend the metal at the mark.
Another way would be to hold the metal strip against a ruler or measuring tape, aligning the first bend with the 10-inch mark, then use the bending tool to make the second bend at the 20-inch mark. In either case, the resulting triangle would have two equal sides that are 10 inches long, and a base that is 8 inches long.
a t test can be used to compare results from two different methods. of the difference in the results is significant, it means that
By using testing of hypothesis, it can be concluded that
There is a systematic error in atleast one of the methods
First option is correct
What is testing of hypothesis?
Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.
A t test can be used to compare results from two different methods.
Here, the difference in the results is significant, it means that
So the null hypothesis has to be rejected
There is a systematic error in atleast one of the methods
First option is correct
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Complete Question
The complete question has been attached
What are the 3 types of infinitives in Spanish?
Three types of infinitives in Spanish are the word that ends with the letters -er , -ar, and -ir.
Explanation:
Infinitive : In general sense infinitive represent the action or the purpose.
They do not represent the person or the time.Infinitive in Spanish are generally non -conjugated verbs and they are ending with -er , -ar , -ir.
Basically infinitive in Spanish classified into three groups.
-er : Aprender meaning camping.
-ar : Acampar meaning Camping and so on.
Spanish infinitives are equivalent to English verbs ending with ing.Therefore, the three types of Spanish infinitives are word ends with -er , -ar, and -ir.
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The table below shows how long it took Tamara to swim different distances.
Time
(in minutes) (x)
0.5
1.25
2.0
2.0
2.5
Distance
(in meters) (y)
50
100
200
225
300
A. List the domain and range values.
B. Is the relation a function? Explain. Use the table to support your argument.
The domain and the range are {0.5, 1.25, 2.0, 2.5} and {50, 100, 200, 225, 300}
The relation is not a function
How to determine the domain and the range?From the question, we have the following parameters that can be used in our computation:
Time (in minutes) (x) 0.5 1.25 2.0 2.0 2.5
Distance (in meters) (y) 50 100 200 225 300
The domain is the list of the x values (without repetition)
So, we have
Domain = {0.5, 1.25, 2.0, 2.5}
The range is the list of the y values (without repetition)
So, we have
Range = {50, 100, 200, 225, 300}
Is the relation a function?For a relation to be a function, the x values must not be repeated for different y values
From the table, we have: (2.0, 200) and (2.0, 225)
The x value 2.0 is repeated for y values 200 and 225
Hence, the relation is not a function
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In 2005, the total waste generated in a certain country was 8.618 x 10^8 pounds. Also in 2005, the country's population was 2.76 x 10 ^5 people. Determine the garbage per capita (per person) in that
country in the year 2005.
(use scientific notation to answer this question)
Answer:
To determine the garbage per capita, we need to divide the total waste generated by the population. In 2005, the total waste generated was 8.618 x 10^8 pounds and the population was 2.76 x 10^5 people, so the garbage per capita in that country in 2005 was 3.12 pounds per person. This can be calculated as follows:
8.618 x 10^8 pounds / 2.76 x 10^5 people = 3.12 pounds/person
Alternatively, we can rewrite the population in scientific notation to make the calculation easier:
8.618 x 10^8 pounds / (2.76 x 10^5) people = 8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people
Now we can cancel out the common factors of 10^2 from the numerator and denominator to get the final result:
8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people = 8.618 x 10^8 pounds / (2.76 x 10^3) people
= 8.618 x 10^5 pounds / (2.76) people
= 3.12 pounds/person
This shows that in 2005, the garbage per capita in that country was 3.12 pounds per person.
In an experiment, equal amounts of water and sand were heated under a lamp. The initial and final temperatures of each were recorded. A partial record of the temperature is shown.
Experimental Record
Substance Initial Temperature Final Temperature
Sand 20 °C 26 °C
Water 20 °C ?
Which statement about the final temperature of water is correct?
It will be less than 26 °C as sand has a relatively higher specific heat than water.
It will be less than 26 °C as water has a relatively higher specific heat than sand.
It will be more than 26 °C as sand needs relatively higher energy than water to raise its temperature.
It will be more than 26 °C as water needs relatively higher energy than sand to raise its temperature.
It will be less than 26 °C as water has a relatively higher specific heat than sand is true statement about the final temperature of water.
Define temperature.Temperature is a unit used to represent hotness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).
Given,
In an experiment, equal amounts of water and sand were heated under a lamp. The initial and final temperatures of each were recorded. A partial record of the temperature is shown.
Experimental Record
Substance Initial Temperature Final Temperature
Sand 20 °C 26 °C
Water 20 °C
The quantity of heat energy absorbed by one unit of a substance when its temperature rises by one unit is measured as the substance's specific heat.
This allows you to calculate the equation for a substance's specific heat:
Specific heat equals heat / (mass Δ T)
Given that both samples have the same amount (mass) and that all of the heat from the lamp is applied to them, you can assume that the specific heat of the samples will be as follows:
particular heat is equal to constant / ΔT.
Therefore, the two quantities are inversely connected.
Since sand has a lower specific heat than water, the sand on the shore of a beach is warmer during the day. When walking on a sandy beach on a bright day, your feet get scorched since it's hotter than the ocean.
When equal amounts of water and sand are heated as per the experiment's instructions, water will increase in temperature more slowly and, as a result, reach a lower end temperature than sand. This is because water has a higher specific heat than sand. This is the second option; because water has a substantially higher specific heat than water, the end temperature of water is less than 26°C.
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a rectangular swimming pool has the same depth everywhere. the combined surface area of the floor of the pool and the four sides is $4800$ square feet. what is the maximum volume of the swimming pool in cubic feet?
the maximum volume of the swimming pool in cubic feet = 29744[tex]ft^{3}[/tex]
volume:A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere.
Different shapes have different volumes. In 3D geometry, we have studied the various shapes and solids such as cubes, cuboids, cylinders, cones, etc., that are defined in three dimensions. For all these shapes, we are going to learn to find the volume.
Unit of Volume:
Volume of a solid is measured in cubic units. For example, if dimensions are given in meters, then the volume will be in cubic meters. This is the standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimeters, cubic feet, cubic inches, etc.
given that
the combined surface area of the floor of the pool and the four sides is $4800$ square feet.
each side (there are 4) = 4 x w x w
and the bottom w x w
total surface area 5 w^2 = 4800
w = depth = 30.984 ft
volume= 30.984^3 = 29744.89[tex]ft^{3}[/tex]
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The diameter of a circle is 4 feet. What is the circle's circumference?
Answer: Your answer will be 12.57.
Step-by-step explanation:
Using the formulas
C=2 x π x r
d=2 x r
Solving for C.
C = πd = π·4 ≈ 12.56637
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
22 feet
26 feet
33 feet
44 feet
136 degrees
Answer:
Step-by-step explanation:
So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:
x + 2x = 66
3x = 66
x = 22
That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.
Hope I helped!
if the set alpha is at 0.05 for a two tailed hypothesis test, what is the p value required to reject a null hypothesis
The required answer is fail to reject a null hypothesis.
What is Null hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
Given that:
α = 0.05
then
z0.05 = 1.645
Hence, the rejection region is {z < −1.645}.
Hence, The required answer is fail to reject a null hypothesis.
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Harry's mother makes cakes for a local restaurant. She buys flour and sugar in large amounts. She has 157.86 pounds of flour and 82.69 pounds of sugar. If she uses 15 pounds of flour and 8 pounds of sugar each day, for about how many days will the flour last?
The flour will last for about 11 days.
What is equation ?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.
Suppose, the flour will last for x days.
She uses 15 pounds of flour each day.
So, the total amount of flour used in x days 15x pounds.
Given that, she has 157.86 pound of flour.
So, the equation will be
15 x = 157.86
x = 157.86 / 15
= 10.524
≈ 11
Thus, the flour will last for about 11 days.
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PLS HELP ME WITH THE QUESTION
Answer: 175
Step-by-step explanation: So the formula for finding the area of a rhombus is A= 1/2 d1+d2. So, we multiply 14 x 25 to get 350, then we divide by 2, and get 175! I hoped this helped you solve your problem :)
What is the slope of ½?
The slope of ½ is 0. A line with a zero slope is neither rising nor falling when seen from left to right or the other way around. Simply put, the slope of a horizontal line is zero.
y=m x + b, where m is the slope and b is the y-intercept, is the slope-intercept form.
where y= 0 and
y = m x + b
The slope is 0 when expressed in the slope-intercept form, or m = 0.
A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
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Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis for 40 minutes longer than he swims. Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. Part B: How much time does Melvin spend swimming every day? Show your work. Part C: Is it possible for Melvin to have spent 70 minutes playing tennis if he plays and swims for a total of exactly 110 minutes and plays tennis for 40 minutes longer than he swims? Explain your reasoning.
The answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, (A):
Y indicates the volume of swimming
X denotes the quantity of tennis.
Making two equations now:
y + 40 = x
x + y = 110
(B)
X in the other equation is changed to match the first equation.
Please plug this in:
y + 40 + y = 110
2y = 70
35 minutes of swimming equals Y.
Including: 35
35 + 40 = 75 minutes every day of swimming.
(C)
No, given that equation: 70 + (70 - 40) = 100
This statement is false as a result.
Therefore, the answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
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What is the equation of the line with slope of 7 and y-intercept equals to 4?
The equation of a line with slope m and y-intercept is Y = mx + b. (0,b). y = 7x + 4 is the equation of the line with slope of 7 and y-intercept equals to 4?
Since the slope of the line is 7 and the y-intercept is 4, the equation of the line can be written as y = 7x + 4.
The equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In mathematics, the slope or gradient of a line is a numerical representation of the line's steepness and direction.
In the equation y = 7x + 4, 7 is the slope of the line and 4 is the y-intercept. This means that the line has a slope of 7 and the y-intercept is 4.
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A 20-cm wrench is used to loosen a bolt. The force is applied 0. 20m from the bolt. It takes 100n to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30o angle from perpendicular? round-off your answer to the nearest whole number.
The force that it will take if applied perpendicular at 30° = 58 N
According to the formula of torque = τ and force = F,
τ = r x F x sinθ --- equation 1
Given, F = 100 N , r = 0.2 m (r = radius)
We have to find the force when θ (angle) = 30°
Putting value in equation 1,
τ = 0.2 x 100 x sin (30°)
τ = 10 Nm
Value of torque from here = 10 Nm
Now to calculate the force perpendicular at 30° the equation will change as,
τ = r x F x cosθ --- equation 2
10 = 0.2 x F x cos 30°
Taking τ on the right side and F on left,
F = 10/ (0.2 x cos 30°)
F = 57.73 N
F = 58 N
Therefore, The force that it will take if applied perpendicular at 30° = 58 N
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pls answer this questions for 15 points
Answer:
B
Step-by-step explanation:
by plugging in f, you can see that B, is the only correct answer
A fails at values greater than or equal to f = 2
C fails for all values
and D fails for all values
B works for all given values
2(1) + 3 = 5
2(2) + 3 = 7
2(3) + 3 = 3
2(4) + 3 = 11
2(5) + 3 = 13
Given: BD and AC bisect each other.
Prove: AB
CD.
Note: quadrilateral properties are not permitted in this proof.
Step
1
try
Statement
BD and AC bisect each other
Type of Statement
A
Reason
Given
B
The proof of AB ≅ CD is given below.
What is triangle?
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
Given: BD and AC bisect each other.
So, AE = AC and BE = ED
Consider the triangles ΔAEB and , ΔECD
Given,
AE = EC ...S
BE = ED ....S
Here, lines BC and AD intersects at point E, so
m ∠AEB = m ∠DEC ....A
Therefore, from SAS congruency,
ΔAEB ≅ ΔECD
Hence, AB ≅ CD
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Someone help Please ASAP
A full pond containing 625 gallons of water begins losing its water at a rate of 20% per week. If the pond now contains 320 gallons of water, how many weeks has it been since the pond was at full capacity?
(Use the digits 0 – 9 to enter a number. Use a decimal point only if necessary.)
Answer:3
Step-by-step explanation:
Based on the model what would be Jamall salary and dollars for a month where he made no sales y=3400 + 0.05x
Jamall's salary when he made no sales is $3400
How to determine the salary?From the question, we have the following parameters that can be used in our computation:
y = 3400 + 0.05x
When he made no sales, the value of x is 0
So, we have the following representation
y = 3400 + 0.05 x 0
Evaluate
y = 3400
Hence, the salary is $3400
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Required
Question 1- Which parallelogram has an area of 60 square units? *
A
12
15
10
C
15
15
12
B
10
10.2
6
D
6
6
10
Show your reasoning
Answer:
To find the area of a parallelogram, we can use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given that the area is 60 square units, so we can use this information to find the value of b and h for each of the options given.
Option A: 12 15 10
In this option, we can see that the base is 12 units and the height is 15 units, so we can plug these values into the formula to find the area: A = 12 * 15 = 180 square units. This is much larger than the given area of 60 square units, so option A cannot be correct.
Option B: 10 10.2 6
In this option, we can see that the base is 10 units and the height is 6 units, so we can plug these values into the formula to find the area: A = 10 * 6 = 60 square units. This matches the given area of 60 square units, so option B could be correct.
Option C: 15 15 12
In this option, we can see that the base is 15 units and the height is 12 units, so we can plug these values into the formula to find the area: A = 15 * 12 = 180 square units. This is much larger than the given area of 60 square units, so option C cannot be correct.
Option D: 6 6 10
In this option, we can see that the base is 6 units and the height is 10 units, so we can plug these values into the formula to find the area: A = 6 * 10 = 60 square units. This matches the given area of 60 square units, so option D could be correct.
Therefore, the correct answer is either option B or option D.
PLEASE HELP QUICKLY
MEJEJEJDNE
What’s 3(4x + 6) + 7x
in october, marshal drove 217 miles ,which was 62% of the distance he drove in september. How far in miles did marshal drive in september?
Answer:
350 miles
Step-by-step explanation:
62 : 100 = 217 : x
x = 217 · 100 / 62
x = 21 700 / 62
x = 350