Mathematics focuses on geometry, numbers, and form. For such, axioms and definitions are needed to describe the study's subjects. On the basis of those definitions and axioms, properties are proved using logic.
Mathematical logic help you in using a phone, sending a fax, or operating a vehicle and many other things.
Logic models are composed of mathematical constructs. When it comes to supporting its conclusions, mathematics employs logic. The "science" of reasoning is logic. It deals with arguments, hence learning what constitutes a strong argument is a need for becoming a logician.
Logic can also be applied in everyday conversation about non-mathematical subjects. The amount of reasoning required is typically much more for mathematical inquiries than for non-mathematical ones.
Therefore, logic is a technique that mathematicians (as well as other individuals) employ when it comes to supporting their claims. Proof involves logic.
Mathematical logic has a direct impact on our daily life now more than ever. I'm not only referring to the marks pupils receive or the number of required mathematical subjects. I'm referring to using a phone, sending a fax, or operating a vehicle. I'm referring to making a home, purchasing medication for your family, and enjoying music.
To learn more about mathematical logic in daily life link is here
brainly.com/question/28052598
#SPJ4
There were 640 gallons of water in a 1600-gallon pool. Water is being pumped into the pool at a rate of 320 gallons per hour. Write and solve an equation to find how many hours it will take to fill the pool.
Word problems aren't my strong suit, they always get me confused.
Answer:
Let's call the number of hours it takes to fill the pool "h".
We know that the initial amount of water in the pool is 640 gallons, and water is being added at a rate of 320 gallons per hour. To find out how many hours it will take to fill the pool to 1600 gallons, we can set up the following equation:
640 + (320h) = 1600
To solve for h, we'll subtract 640 from both sides of the equation:
320h = 960
Then divide both sides by 320:
h = 3
So it will take 3 hours to fill the pool with water.
It will take 3 hours to fill the pool.
Amount of water that can fit in the pool= 1600 gallons.
The amount of water already present= 640 gallons.
Therefore, the amount of water required to fill the pool= 1600-640 = 960 gallons
The rate at which the water is being pumped= 320 gallons/ hour
Therefore, the time needed to fill the pool= the quantity to be supplied/ the rate at which the water is being pumped
=> 960/ 320
=> 3 hours.
Therefore, the time required to fill the pool completely is 3 hours.
Learn more about equations at:
https://brainly.com/question/15707224
Giselle works as a carpenter and as a blacksmith. She earns 20$ per hour as a carpenter and 25$ per hour as a blacksmith. last week, Giselle worked both jobs for a total of 30 hours and earned 690$. How long did Giselle work as a carpenter last week and how long did she work as a blacksmith
Giselle worked 12 hours as a carpenter
She also worked 18 hours as a blacksmith
How to calculate the number of hours that Giselle worked as a carpenter and a blacksmith?Giselle worked as both a carpenter and a blacksmith
She earned $20 per hour working as a carpenter
She also earned $25 per hour working as a blacksmith
She worked for 30 hours to earn $690
Let x represent the number of hours that she worked as a carpenter
Let y represent the number of hours that she worked as a blacksmith
x + y= 30........equation1
20x + 25y= 690......equation 2
From equation 1
x + y= 30
x= 30-y
Substitute 30-y for x in equation 2
20(30-y) + 25y= 690
600-20y+25y= 690
collect the like terms
600+5y=690
5y= 690-600
5y= 90
y= 90/5
y= 18
Substitute 18 for y in equation 1
x+y= 30
x+18= 30
x= 30-18
x= 12
Hence Giselle worked 12 hours as a carpenter and 18 hours as a blacksmith
Read more on hours here
https://brainly.com/question/2202719
#SPJ1
drag the labels to the correct locations on the image. each label can be used more than once, but not all labels will be used. consider function m. a line graph depicts x on the horizontal axis versus m of x on the vertical axis. a curve declines from (negative 4, 8) through (negative 2, 0), passes through (0, 0) and (4, negative 8), and rises through (6, 8). what is the domain of function m?
The function's approximate range will be specified by -∞<y≤12.
What is a function?The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y.
The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
Functions were first used to describe the idealized relationship between two varying quantities.
Now, drag as follows:
The collection of output values determines a function's range.
The function's indicated range will be -∞ < y ≤ 12.
From the linked graph,
The function's output values (values on the y-axis) range from zero to f(x)=12.
Therefore, the function's approximate range will be specified by -∞<y≤12.
Know more about function here:
https://brainly.com/question/10439235
#SPJ4
The path of a ball is given by the rectangular equation . Use the result of Exercise 31 to find the position vector. Then find the speed and direction of the ball at the point at which it has traveled feet horizontally.
The direction of the ball at this point is <1/8, -4, 96/8>
The Position Of The VectorThe position vector of the ball can be found by taking the derivative of the rectangular equation with respect to time:
r(t) = <8t, -16t², 32t³>
To find the speed of the ball at the point where it has traveled 64 feet horizontally, we can use the magnitude of the velocity vector, which is the derivative of the position vector with respect to time:
v(t) = <8, -32t, 96t²>
|v(t)| =√(8² + (-32t)² + 96t⁴) = 8*√(1 + t² + 3t⁴)
We need to find the time t at which the ball has traveled 64 feet horizontally. We know that x = 8t, so we can set x = 64 and solve for t:
8t = 64
t = 8
At t = 8, the speed of the ball is:
|v(8)| = 8√(1 + 8² + 3(8⁴)) = 8√(65) = 8*8 = 64
To find the direction of the ball at this point, we can use the unit vector of the velocity vector:
v(t) = <8, -32t, 96t²> / |v(t)|
v(8) = <8, -256, 6144> / 64 = <1/8, -4, 96/8>
So the direction of the ball at this point is <1/8, -4, 96/8>
Learn more about position of vector here:
https://brainly.com/question/14552074
#SPJ4
please help my sisters out!!
Pablo is considering two housekeeping services. Premier housekeeping charges $25 for travel to Pablo's house and $65 per hour for cleaning his house. Best house care does not have a travel fee, but charges $75 per hour for cleaning. PART A: write a system of equations that represents the housekeeping services. PART B: without solving the system of equations, explain what the solution represents.
The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.
What is algebraic equation ?
An algebraic equation is a mathematical expression containing one or more variables and an equal sign, where the goal is to find the value(s) of the variable(s) that make the equation true. The equation is formed by combining numbers, variables.
PART A:
Let x be the number of hours of cleaning that Premier Housekeeping provides, and let y be the number of hours of cleaning that Best House Care provides. The system of equations representing the housekeeping services is:
Premier Housekeeping: 25 + 65x = cost in dollars
Best House Care: 75y = cost in dollars
PART B:
The solution of this system of equations represents the point (x,y) in the coordinate plane, where x represents the number of hours of cleaning that Premier Housekeeping provides and y represents the number of hours of cleaning that Best House Care provides. The cost in dollars of each service will be given by the corresponding equation: the cost of Premier Housekeeping will be 25 + 65x, while the cost of Best House Care will be 75y.
The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.
To learn more about algebraic equation visit : brainly.com/question/953809
#SPJ4
military radar and missile detection systems are designed to warn a country of enemy attacks. a reliability question deals with the ability of the detection system to identify an attack and issue the warning. assume that a particular detection system has a 0.91 probability of detecting a missile attack. answer the following questions using the binomial probability distribution: what is the probability that one detection system will detect an attack? if required, round your answer to two decimal places. fill in the blank 1 if two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack? if required, round your answer to two decimal places. fill in the blank 2 if 3 systems are installed, what is the probability that at least one of the systems will detect the attack? if required, round your answer to four decimal places. fill in the blank 3 would you recommend that multiple detection systems be operated? explain. the input in the box below will not be graded, but may be reviewed and considered by your instructor.
A detection system has a probability of 0.91 to detect a missile attack. It is recommended to have multiple detection systems as it increases the overall probability of detecting an attack and allows for redundancy in case one system fails.
The probability that one detection system will detect an attack is: 0.91If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack is: 1 - (0.09)² = 0.9801If 3 systems are installed, the probability that at least one of the systems will detect the attack is: 1 - (0.09)³ = 0.99291Yes, it is recommended to have multiple detection systems as it increases the overall probability of detecting an attack. It allows for redundancy in case one system fails and increases the chances of detecting an attack even if one system is not functioning properly.To learn more about the probability, visit:
brainly.com/question/30034780
#SPJ4
a 6-foot man is running away from the base of a streetlight that is feet high. if he moves at the rate of feet per second, how fast is the length of his shadow changing?
As per the unitary method, the length of his shadow changing is 30 feet.
The term unitary method is known as a process of finding the value of a single unit, and based on this value.
Here we have given that a 6-foot man is running away from the base of a streetlight that is feet high.
Then let us consider that the man be x feet away from the street light and his shadow length be y,
Here we have also consider that let the tip of the shadow be l feet away from the light is written as
=> l = x + y
Here we are given that,
=> dx/dt=2
Then as per the concept of similar triangles, we can write it as,
=> x/5 = 6x+6/31
=> 31x = 30x + 30
=> x = 30
To know more about unitary method here.
https://brainly.com/question/28276953
#SPJ4
the positive difference between two consecutive even perfect squares is $268$. compute the larger of the two squares.
The larger of the two consecutive even perfect squares is $15,536$.
What is square?Square is a four-sided shape that has four equal sides and four right angles. It is the most basic of all quadrilaterals and is a two-dimensional shape. A square has a line of symmetry that passes through the center and divides it into two equal halves. All four sides of a square are equal in length and all four angles are equal to 90 degrees.
To find this, we need to use the difference between the two squares and solve for the larger number. We know that the difference between the two squares is $268$, so we can write the following equation:
$15,536 - 268 = 15,268$
This equation tells us that the larger of the two squares is $15,536$.
To know more about square click-
https://brainly.com/question/25092270
#SPJ4
The larger of the two consecutive even perfect squares is 15,536.
What is square?Square is a four-sided shape that has four equal sides and four right angles. It is the most basic of all quadrilaterals and is a two-dimensional shape. A square has a line of symmetry that passes through the center and divides it into two equal halves. All four sides of a square are equal in length and all four angles are equal to 90 degrees.
To find this, we need to use the difference between the two squares and solve for the larger number. We know that the difference between the two squares is 268, so we can write the following equation:
So, 15,536 - 268 = 15,268
This equation tells us that the larger of the two squares is 15,536.
To know more about square refer to-
brainly.com/question/25092270
#SPJ4
In asking all 349 second graders in a school district, it is found that on average, these second graders have 2.5 pets. Is this number a parameter or a statistic and why?
O Parameter as it represents the population
O Parameter as it represents the sample
O Statistic as it represents the sample
O Statistic as it represents the population
Answer:
Step-by-step explanation:
O Statistic as it represents the sample
The number 2.5 is considered a statistic because it is calculated from a sample of second graders in a school district. This number is an estimate of the average number of pets that all second graders in the school district have, but it is not the exact number, as the sample may not be fully representative of the population. A parameter, in contrast, is a fixed value that represents a characteristic of a population, such as the population mean or population proportion. Since the number 2.5 is an estimate calculated from a sample and not the exact value of the population, it is considered a statistic.
X-N(5.7, 0.61). Find the z - score corresponding to an observation of 4.7. a. 1.64 b. -1.64 c. 1.02 d. -1.02
The Z-score is (b) -1.64.
Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.
To find the z-score corresponding to an observation of 4.7, we can use the formula:
z = (x - mu) / sigma
where x is the observation, mu is the mean, and sigma is the standard deviation.
Given that X-N(5.7, 0.61) we can substitute
z = (4.7 - 5.7) / 0.61 = -1.64
So the answer is (b) -1.64.
To learn more about statistics visit: brainly.com/question/29093686
#SPJ4
How do you find the absolute value of positive and negative numbers?
The absolute value of a negative number will always be a positive number.
As discussed above, regarding the absolute number, therefore, the absolute value of a negative number will always be a positive number.
for example, |-24| = 24
The absolute value of any number will always be a positive number.
As discussed above, regarding the absolute number, therefore, the absolute value of any number will always be a positive number.
for example, |-24| = 24
Positive numbers will always have a higher absolute value than negative numbers.
As discussed above, regarding the absolute number. therefore, the absolute value of any number will always be a positive number, which will be equal in value.
for example, |-24| = 24
To know more about absolute value:
https://brainly.com/question/24368848
#SPJ4
A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-quarter of
the second number and 5. The situation can be represented by using the graph below, where x represents the second
number.
46-
14-
42-
10+
8-
6
2-
2-
246
8 10 12 14 16 x
Which equations represent the situation?
Mark this and return
Save and Exit
Next
Submit
Answer:
First number 7
Step-by-step explanation:
First, let's make the first number y and the second number x
Next, we write our equations which are y=1/2x+3 and y=1/4x+5
Then, we set those two equations equal to each other and then solve for x
The first step of the equation is to add/subtract like terms, I subtracted 5 on each side of the equation, our new equation is 1/4x=1/2x-2, I then subtracted 1/2x on each side so now our equation is -1/4x=-2. We then multiply 1/4 by its reciprocal on each side. Its reciprocal is -4.
Now that we know x is equal to 8 now we can fill x into the original equations which were y=1/2x+3 and y=1/4x+5 you don't have to solve both, just one of your choosing.
Therefore your answer! .
The photograph club is selling hot chocolate at games to raise money for the new cameras the table shows a profit per game for the first five games based on the average profit per game how much money can the club expect to earn by the end of the 10 game season
The amount of money that the club expects to warn by the end of the 10 game season would be = $27.06
How to calculate profit made by the photograph club?
The profit made at the end of the first game = -12.50
The profit made at the end of the second game= -10.15
The profit made at the end of the third game= 18.65
The profit made at the end of the fourth game= 25.90
The profit made at the end of the fifth game = 45.75
First we find the average profit made in the first five games such as;
= -12.50 + -10.15 + 18.65 + 25.90 + 45.75
= 90.3 −22.65 = 67.65/5 = 13.53
Therefore for the next five games which will make it up to 10 game he is expected to have a profit of 13.53×2 = $27.06.
Learn more about profit cost here:
https://brainly.com/question/29785281
#SPJ1
I need this answer asap
Answer:
According to phythagorian theorem
Hypotenus (square) = Base(square) + perpendicular (square)
H^2 = B^2 + P^2
now by substitution
H^2 = 9 +16
H^2 = 25
taking roots
Hypotenus= 5
f(-5) = 2,ƒ(7) = - 4
Please help
Answer:
f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
f(x) = mx + c ( m is the slope and c the y- intercept )
given f(- 5) = 2, that is when x = - 5 , y = 2
f(7) = - 4, that is x = 7, y = - 4
the 2points (- 5, 2 ) and (7, - 4 ) lie on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 2 ) and (x₂, y₂ ) = (7, - 4 )
m = [tex]\frac{-4-2}{7-(-5)}[/tex] = [tex]\frac{-6}{7+5}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then
f(x) = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the line
to find c substitute either of the 2 points into the partial equation
using (- 5, 2 ) , then
2 = - [tex]\frac{1}{2}[/tex] (- 5) + c = [tex]\frac{5}{2}[/tex] + c ( subtract [tex]\frac{5}{2}[/tex] from both sides )
- [tex]\frac{1}{2}[/tex] = c
f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of line
On a cold day in November, the recorded low temperature was -10 degrees Celsius (ºC) in Pennsylvania. On the same day, the recorded low temperature was in 0ºC Michigan, -20ºC in Minnesota, and 16ºC in Florida. Which list shows the states in order from coldest to warmest?
Florida, Michigan, Pennsylvania, Minnesota
Michigan, Pennsylvania, Florida, Minnesota
Pennsylvania, Minnesota, Michigan, Florida
Minnesota, Pennsylvania, Michigan, Florida
Answer:
The last option:
Minnesota, Pennsylvania, Michigan, Florida
Step-by-step explanation:
Coldest to warmest:
-20°C, -10°C, 0°C, 16°C
Then the order is:
Minnesota, Pennsylvania, Michigan; Florida
the length of a rectangle is 1 yd more than twice the width, and the area of the rectangle is 45 yd2. find the dimensions of the rectangle. length : yd width : yd
On solving the provided question, we can say that in rectangle W = 4.5 yd since we are unable to have a negative length. L = 2W + 1 = 10 yd
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
length rectangle is 1 yd more than twice the width: L = 2*W + 1
e area of the rectangle
[tex]45 = L*W\\45 = (2W + 1)*W\\45 = 2W2 + W\\0 = 2W2 + W - 45\\[/tex]
Factors
x[tex](2W-9)(W+5)\\W = 4.5 and -5[/tex]
W = 4.5 yd since we are unable to have a negative length. L = 2W + 1 = 10 yd
To know more about rectangle visit:
https://brainly.com/question/29123947
#SPJ4
The aquarium has 10 more red fish than blue fish. 60% of the fish are red. How many blue fish are in the aquarium? Show your work.
Answer:
20 blue fish
Step-by-step explanation:
r=red fish, b=blue fish. r = 10+b. 60%r=r+b. (10+b)= 0.6(r+b); 10+b = 0.6(2b+10); 10+b=1.2b+6; 4=0.2b; b=20.
Answer the screenshot
The domain of the given function f(x) = √(x⁴ - 1) include the following: C. {x|x ≤ -1 or x ≥ 1}.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. Additionally, the horizontal extent of a graph represents all domain values (input values) and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Next, we would use an online graphing calculator to plot the graph of the given function f(x) = √(x⁴ - 1). By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain:
Domain = (-∞, 1) U (1, ∞)
By using set builder notation, the domain of this function f(x) = √(x⁴ - 1) can be re-written as follows;
Domain = {x|x ≤ -1 or x ≥ 1}.
Read more on domain here: brainly.com/question/17003159
#SPJ1
whats the axis of symmetry y=|x-5|+1
Answer:
[tex]y \: = | \: x - 5| + 1[/tex]
What is a ratio Class 6?
A ratio is a comparison of two or more numbers expressed as a fraction, such as 3/4 or 4:5. It is used to compare the size or amount of two or more objects or quantities. Ratios can also be expressed as a percent or as a decimal.
A ratio is a comparison of two or more numbers expressed as a fraction. The ratio is written as two numbers separated by a colon (:), or as a fraction. The numbers in the ratio are compared to each other to indicate the size or amount of the objects or quantities being compared. For example, 3:4 means that for every 3 objects, there are 4 of the other object. This can also be written as a fraction, 3/4, to indicate that for every 3 objects, there are 4 of the other object. Ratios can also be expressed as a percent or as a decimal. For example, 3:4 can be expressed as 75% or 0.75.
Learn more about ratio here
https://brainly.com/question/13419413
#SPJ4
Is half and 0.5 same?
Answer: Yes.
Step-by-step explanation:
0.5 is also the same as 1/2
7y+10x=−11 4y−3x=−15
X=
Y=
Answer:
x= 108/61; y=-163/61
Step-by-step explanation:
The difference of 2 times a number and -19 is -5. Find the number.
If we let $f(n)$ denote the sum of all the positive divisors of the integer $n$, how many integers $i$ exist such that $1 \le i \le 2010$ and $f(i)
As per the given positive divisors the second column is the prime number p, then the third is n=p2, and the right column is σ1(n)
Here we have know that Firstly we have to the function that the OP is describing is a well-known divisor function, then here let us use the common notation that can be written as
=> f(n)=σ1(n)
Then the next step is to note that σ1(n) is always an integer and then the square root in the OP's equation means that n must be a square number.
Here we have know that if n=p2 is a square of a prime number (p) then it has exactly 3 divisors then we have the those divisors are 1,p,n
And it can be written as,
=> σ1(n)=1+p+n
Here we have also know that all other square numbers will have additional divisors is written as
=> σ1(n)>1+n−√n
Therefore the answer to the OP’s question is that the number of solutions within the range [1,2010] is equal to the number of primes squared in this range.
Here the term in which is equal to the number of primes in the range [1,√2010] and it has also do in which is number of primes in the range [2,44]
To know more about divisors here
https://brainly.com/question/26086130
#SPJ4
Use the table of values to evaluate the expressions below.
We can use the table to evaluate the compositions of the functions, we will get:
f(g(6)) = 3g(f(0)) = 8f(f(4)) = 4g(g(1)) = 1How to evaluate the expressions below?Here we have a table for functions f(x) and g(x), and we want to use that table to evaluate the compositions of the functions.
First, we want to get f(g(6))
Using the table, we can see that g(6) = 0, then:
f(g(6)) = f(0)
And using the table we can see that f(0) = 3, then:
f(g(6)) = 3
The second composition is:
g(f(0))
We know that f(0) = 3
g(f(0)) = g(3)
And using the table g(3)= 8, then:
g(f(0)) = 8
The third one is:
f(f(4))
We can see that f(4) = 7
So: f(f(4)) = f(7)
And again, you can find f(7) on the table to see that f(7) = 4
Then:
f(f(4)) = 4
The last composition is:
g(g(1))
You can see that g(1) = 1
Then:
g(g(1)) = g(1) = 1
Learn more about composition of functions:
https://brainly.com/question/10687170
#SPJ1
A total of $6,000 is invested in 2 funds. One of the funds is paying 4% interest and the other is paying 6% interest. The total interest earned in one year was $280. What is the amount of money that was invested in each fund?
Answer:
Answer for the investment problem: Fund 1 was $4,000 Fund 2 was $2,000
Answer for the tickets problem: 123 student tickets were sold and 235 non-student tickets were sold.
Step-by-step explanation:
Sorry I have to go so I don't have time to type up the explanation nicely, but here is my work. Have a great night!
(PLS HELP!!!!)
What are the degree and leading coefficient of the polynomial?
-6u+u²-23u-3
Degree:
Leading coefficient:
Degree: 2
Leading coefficient: -1 (The leading coefficient is the coefficient of the term with the highest degree in the polynomial, in this case, the coefficient of u², which is -1)
Isabella filled her pool with water at a constant rate.
The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes)Time Water2 1847 9412 4How fast did Isabella fill her pool?
Isabella fills her pool at a rate of 18 liters per minute as per the given condition.
The slope of the volume can be used to determine how quickly it changes when given Time t in minutes and Volume V in liters. That represents a change in volume relative to a change in time.
m = (v2-v1)/(t2-t1).
selecting the first two points (2, 184) and from the provided data (7, 94).
Volume remains in the pool at what rate =
(94-184)/(7-2) = -90/5 = -18.
Therefore the rate at which Isabella fills her pool is 18 liters/minute as per the given question.
To learn more about Kinematic Formulas, visit: https://brainly.com/question/29062368
#SPJ4
