A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.
In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.
what Is the si unit of temperature
Answer:
the Si unit of temprature in Kelvin (K)
Step-by-step explanation:
Answer:
The answer is Kelvin (k).
Step-by-step explanation:
The kelvin (K) is defined by taking the fixed numerical value of the Boltzmann constant k to be [tex]1.380649*10^{-23}[/tex] when expressed in the unit of joule per kelvin. The temperature 0 K is commonly referred to as "absolute zero." On the widely used Celsius temperature scale, water freezes at 0 °C and boils at about 100 °C. One Celsius degree is an interval of 1 K, and zero degrees Celsius is 273.15 K. An interval of one Celsius degree corresponds to an interval of 1.8 Fahrenheit degrees on the Fahrenheit temperature scale.
The kelvin is also the fundamental unit of the Kelvin scale, an absolute temperature scale named for the British physicist William Thomson (known as Lord Kelvin). An absolute temperature scale has as its zero point absolute zero (−273.15° on the Celsius temperature scale and −459.67° on the Fahrenheit temperature scale), the theoretical temperature at which the molecules of a substance have the lowest energy; hence, all values on such a scale are nonnegative.
Find the difference between the result of one sixth of product of 10 and 3 multiplied by 4 and 30
Pleas helppppp ;_-((((((
Answer:
10 or -10,
Read the explanation
Step-by-step explanation:
Rewrite this problem as a numerical expression. As per the wording of this problem, there can be two expressions derived.
1. [tex]((\frac{1}{6}(10*3)*4)-30[/tex]
2. [tex]30-((\frac{1}{6}(10*3)*4)[/tex]
Simplify, remember the order of operations. The order of operations is the sequence by which one is supposed to perform operations in a numerical expression. This order is the following:
1. Parenthesis
2. Exponents
3. Multiplication or division
4. Addition or Subtraction
Use this sequence when simplifying and solving the expression:
Expression 1
[tex]((\frac{1}{6}(10*3)*4)-30\\\\=((\frac{1}{6}(30)*4)-30\\\\=(5*4)-30\\\\=20 - 30\\\\= -10[/tex]
Expression 2
[tex]30-((\frac{1}{6}(10*3)*4)\\\\=30-((\frac{1}{6}(30)*4)\\\\=30-(5*4)\\\\= 30-20\\\\= 10[/tex]
If side A is 10 inches long, and side B is 24 inches, find the length of the unknown side.
Step-by-step explanation:
Right Triangles and the Pythagorean Theorem. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.
14. In a garden 746496 apple trees are arranged in such a way that, there are as inany rows as there are in a row. How many rows are there in the garden
Answer:
864
Step-by-step explanation:
do the square root of the total number
e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hours. What percentage of the bulbs have lifetimes that lie within 1 standarddeviation to either side of the mean
Answer:
Step-by-step explanation:
[tex]p(\overline{X}-\sigma \leq X \leq \overline{X}+\sigma)\\\\=p(\dfrac{\overline{X}-\sigma -\overline{X} }{\sigma} \leq Z \leq \dfrac{\overline{X}+\sigma -\overline{X} }{\sigma} )\\\\=p ( -1 \leq Z \leq 1)\\\\=2*(\ p (Z \leq 1)-0.5)\\\\=2*(0.8413-0.5)\\\\=0.6826\\\\\approx{68\%}[/tex]
i need help with this question asapppppp
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Answer:
$11,680.58
Step-by-step explanation:
Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.
__
The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.
The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...
0.205×21,465 = 4400.325 ≈ 4400.33
The the total tax due on $70,000 is ...
$7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000
_____
Additional comments
The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.
__
Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.
≤ 48535 -- income × 0.15
≤ 97069 -- income × 0.205 -2669.425
≤ 150,473 -- income × 0.26 -8008.22
≤ 214,368 -- income × 0.29 -12,522.41
> 214,368 -- income × 0.33 -21,097.13
In this case, the second row of this simpler table would give the tax on $70,000 as ...
tax = 70,000 × 0.205 -2669.425
tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above
Each time Kristine gets paid, she spends $20 and saves the rest. If the amount Kristine earns is represented by x and the amount she saves is represented by y, which graph models her savings?
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (5, 100) and (10, 200).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 1) and (40, 2).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (0, 20) and (10, 30).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).
Answer:
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).
Step-by-step explanation:
If Kristine spends $20 and saves the rest when she gets paid, the amount she saves should always be 20 less than the amount she earned.
The points (20, 0) and (25, 5) accurately represent this, where x is how much she earns and y is how much she saves.
(20, 0) represents her earning $20 and saving $0, because she spends $20 every time she gets paid.
(25, 5) represents her earning $25 and saving $5, because she spent $20.
So, the correct graph is A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).
Answer:
d
Step-by-step explanation:
Instructions: Find the missing side. Round your answer to the nearest tenth.
22
58°
Answer:
x = 19.2
Step-by-step explanation:
tan(58)=x/12
x=12×tan(58)
x=19.2
Answered by GAUTHMATH
if 2/-5 x=-10/x what is the value of x
Answer:
± 5
Step-by-step explanation:
2x/-5 = -10/x
2x^2 = 50
x^2 = 25
x = ± 5
Answer:
x=5
Step-by-step explanation:
Start with writing it like 2x/-5= -10/x
Then cross multiply: 2[tex]x^{2}[/tex]= 50
Divide by 2: [tex]x^{2}[/tex]=25
Square root of 25: 5
x=5
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Chapter 11 part 2:
What are three different properties of logarithmic functions when encountering the operations of addition, subtraction, and multiplication? Provide an example of each.
The three main log rules you'll encounter are
log(A*B) = log(A) + log(B)log(A/B) = log(A) - log(B)log(A^B) = B*log(A)The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.
Here are examples of each rule being used (in the exact order they were given earlier).
log(2*3) = log(2) + log(3)log(5/8) = log(5) - log(8)log(7^4) = 4*log(7)----------------
Here's a slightly more complicated example where the log rules are used.
log(x^2y/z)
log(x^2y) - log(z)
log(x^2) + log(y) - log(z)
2*log(x) + log(y) - log(z)
Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.
The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities
a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?
Solution :
a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= [tex]$(1-0.75)^3 \times 0.75$[/tex]
= 0.01171875
b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
[tex]$E(X)=\frac{k}{p}$[/tex]
[tex]$=\frac{6}{0.75}$[/tex]
= 8
So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]
[tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]
= 1.6330
The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.
Answer:
0.9332
Step-by-step explanation:
We are given that
Mean diameter, [tex]\mu=73[/tex]
Variance, [tex]\sigma^2=4[/tex]
We have to find the probability that the diameter of a selected bearing is less than 76.
Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]
[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]
[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]
Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]P(x<76)=P(Z<1.5)[/tex]
[tex]P(x<76)=0.9332[/tex]
Hence, the probability that the diameter of a selected bearing is less than 76=0.9332
If 6x + 5y = 10, what is y in terms of x?
Please include an explanation!
what you're trying to do is form an equation for y
6x + 5y = 10
5y = -6x + 10 we need y to be singular so divide by numeral before y
y = - 6x/5 + 10/5
y = - 6x/5 + 2
What is the perimeter of the octagon below!!
Answer:
C) sixty five units
Step-by-step explanation:
have a great day
Help me please and thank you
Answer:
Option C is correct
Step-by-step explanation:
[tex]log( {10}^{3} )[/tex]
Use logarithm rules to move 3 out of the exponent.[tex]3 \: log \: (10)[/tex]
Logarithm base 10 of 10 is 1.[tex]3×1[/tex]
Multiply 3 by 1.[tex]3[/tex]
Hope it is helpful....A grocery store buys cereal using the cost function
c(n) = { 2n when n < 100 1.9n when 100
Sn = 500 1.8n when n > 500 where n is
the number of boxes of cereal the grocery store
buys and c(n) is the cost of the cereal. The grocery
store then sells the cereal using the sales function
s(c) = 1.3c. What is the cost of the cereal if the
grocery store buys 250 boxes?
The cost of the cereal if the grocery store buys 250 boxes is $475
We know that:
The cost function is:
c(n) = 2*n if n < 100
c(n) = 1.9*n if 100 ≤ n ≤ 500
c(n) = 1.8*n if n > 500.
(we can assume that the cost function is in dollars)
This is a piecewise function, this means that we need to see in which interval we have the number n, and then select the correct function to use.
Now, we want to find the cost of the cereal if the store buys 250 boxes.
Then we have n = 250.
We can see that n = 250 is in the second interval, 100 ≤ n ≤ 500, then we will use the second function to find the cost.
We will get:
c(250) = 1.9*(250) = $475
We can conclude that the cost if the store buys 250 boxes is 475
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Please due in 1 hour
I hope that helped you
9514 1404 393
Answer:
d + q = 440.10d +0.25q = 8.30Step-by-step explanation:
The first equation describes the total number of coins. It says the sum of the numbers of dimes and quarters is 44, the total number of coins.
__
The second equation describes the total value of the coins. It will say that 0.10 times the number of dimes plus 0.25 times the number of quarters is 8.30, the total dollar value of the coins.
The two equations are ...
d + q = 44
0.10d +0.25q = 8.30
__
Additional comment
The solution can be found by substituting for d:
0.10(44 -q) +0.25q = 8.30
0.15q = 3.90
q = 26
d = 44 -26 = 18
Vinnie has 18 dimes and 26 quarters in his bag.
f(x) = (2x – 1)(3x + 5)(x + 1) has zeros at I = -
1
cole
2= -1, and x =
What is the sign of f on the interval
5
<<
3
เล
?
Choose 1 answer:
А
f is always positive on the interval.
B
f is always negative on the interval.
f is sometimes positive and sometimes negative on the interval.
Interval of function f(x) is sometimes negative and sometimes positive.
What is interval of function?The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.
Given function,
f(x) = (2x – 1)(3x + 5)(x + 1),
Zeros of function,
x = 1/2 = 0.5
x = -5/3 = - 1.6667
x = -1
From the graph
Interval of function is negative between -∞ < x < -1.6667
Interval of graph is positive between -5/3 < x < -1
Interval of function is negative between -1 < x < 0.5
Interval of graph is positive 0.5 < x < ∞
Hence, f(x) has sometimes positive interval and sometimes negative interval.
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I need help with ged
Answer:
General Educational Development (GED) tests
What do subject do you need help?
Step-by-step explanation:
The GED® exam is made up of 4 subjects, broken into separate exams: Mathematical Reasoning, Reasoning Through Language Arts, Social Studies, and Science.
Can someone help me with this plz
Answer:
170.7
Step-by-step explanation:
We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7
What is the mean of 86, 80, and 95
87 is the mean.
To find the mean, you must
- add all of the numbers
- divide by the amount of numbers given
In this case, you would want to do (86 + 80 + 95)/3. This would give you an answer of 87.
−12x+y=10 in slope-intercept form
Answer:
y=12x+10
Step-by-step explanation:
Slope-intercept form is y=mx+b
1. Add -12x to both sides of the equation
I’m new to this app and I need help with those two questions please help!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
If a state issued license plates using the scheme of 3 letters followed by 3 digits, how many plates could it issue?
Answer:
17,576,000
Step-by-step explanation:
there are 26 english letters (A-Z) and 10 digits(0-9).
there are 3 spaces for letters. therefore Any of the 26 letters can be combined with any 26 other letters and any of those can be combined with any of another 26 letters.
26*26*26= 17576
similarly 10 digits can combined in 1000 ways
10*10*10=1000
17576 letter combination can combine with 1000 digits combination.
so 17,576 x 1000 = 17,576,000 different plates could issue.
Your car can go 2/7 of the way on 3/8 of a tank of gas how far can you go on the remaining gas?
A proportion that can be used is a/b=c/d
Answer:
10/21 of the distance
Step-by-step explanation:
2/7 distance
------------------
3/8 tank
The rest of the tank is 8/8 - 3/8 = 5/8
2/7 distance x
------------------ = ----------------------
3/8 tank 5/8 tank
Using cross products
2/7 * 5/8 = 3/8x
10/56 = 3/8x
Multiply each side by 8/3
10/56 * 8/3 = 3/8x * 8/3
10/3 * 8/56=x
10/3 * 1/7 =x
10/21 =x
10/21 of the distance
Which equation represents an exponential function that passes through the point (2, 36)?
O f(x) = 4(3)
O fx) = 4(x)
O f(x) = 6(3)
O f(x) = 6(x)
Answer: It would be the first equation because:
Step-by-step explanation:
In order to be an exponential function, the X
variable has to be in the exponent, that eliminates
the second and fourth answers
f(X) = 4(3)X
using the point (2,36)
f(2) = 4 (3)2
= 4 (9 )
= 36
The equation which represents an exponential function is f ( x ) = 4 ( 3 )ˣ
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Let the point on the graph be P ( 2 , 36 )
So , when x = 2 , the value of y = 36
f ( x ) = 4 ( 3 )ˣ be equation (1)
when x = 2
f ( 2 ) = 4 ( 3 )²
f ( 2 ) = 4 x 9
f ( 2 ) = 36
Hence , the exponential equation is f ( x ) = 4 ( 3 )ˣ
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Find the coordinates of the vertices of the figure after the given transformation: T<0,7>
A. X′(1,−1),L′(0,2),W′(2,1)
B. X′(−4,2),L′(−5,5),W′(−3,4)
C. X′(3,2),L′(2,5),W′(4,4)
D. X′(0,−3),L′(−1,0),W′(1,−1)
Answer: B
Step-by-step explanation:
Why did historians choose to study this topic?
the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)
9514 1404 393
Answer:
all real numbers
Step-by-step explanation:
The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.
The domain of g(x) = f(-x) is all real numbers.
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)
9514 1404 393
Answer:
b. y = f(x -3)
Step-by-step explanation:
The translation right h and up k units is ...
y -k = f(x -h)
Here, the red graph is translated right 3 and up 0, so the translated function is ...
y = f(x -3)
_____
Additional comment
You can check this if you like by listing a couple of corresponding points:
y = f(x)
1 = f(-3) . . . . left-most point on black graph.
The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...
1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)
Someone help please
9514 1404 393
Answer:
B.
Step-by-step explanation:
The relation between a function f(x) and its inverse g(x) is ...
f(g(x)) = g(f(x)) = x
On can compute these functions of functions, or take an easier route and do the computation with a couple of numbers. It is often easiest to use x=0 or x=1. If we find g(f(x)) ≠ x, then we know the functions are not inverses. If we find g(f(x)) = x for one particular value of x, then we need to try at least one more to verify the relation.
__
If we call the two given functions f and g, then we have ...
A. f(0) = -2/3, g(-2/3) ≠ 0 . . . . not inverses
__
B. f(0) = -3/2, g(-3/2) = 0 . . . . possible inverses
f(1) = 4/2 = 2, g(2) = 7/7 = 1 . . . . probable inverses
__
C. f(0) = -2, g(-2) = 0 . . . . possible inverses
f(1) = 1/2, g(1/2) = -5/3 . . . . not inverses
__
D. f(0) = 5, g(5) = 27 . . . . not inverses
_____
Additional comment
Our assessment above is sufficiently convincing to let us choose an answer. If we want to verify the functions are inverses, we need to graph them or compute f(g(x)). The graph in the second attachment shows each appears to be the reflection of the other in the line y=x, as required of function inverses.
