Answer:
We know that every number can be written as a product of prime numbers.
The method to find the factorized form of a number depends on the number, we just try to find the different factors by dividing by them, for example for the number 1000 we have:
1000 is an even number, then we can divide it by 2 (2 is a prime number)
1000 = 2*500 (so we already found a prime factor)
500 is also an even number, so we can divide it by 2
1000 = 2*500 = 2*2*250 (we found another prime factor)
dividing by 2 again we get:
1000 = 2*2*250 = 2*2*2*125
1000 = (2*2*2)*125
now we just need to factorize 125
we know that 125 is a multiple of 5, such that:
125 = 5*25 = 5*5*5
(5 is a prime number, so it is completely factorized).
Then the factorization of 1000 is:
1000 = (2*2*2)*(5*5*5) = 2^3*5^3
Now with another example, 1422
1422 is an even number, so we again start using the factor 2:
1422 = 2 = 711
then:
1422 = 2*711
we already found a factor.
711 is a multiple of 3 (the sum of its digits is a multiple of 3), then:
711/3 = 237
We can write our number as:
1422 = 2*3*237
237 is also a multiple of 3
237/3 = 79
then:
1422 = 2*3*3*79
and 79 is a prime number, so we already have 1422 completely factorized.
How many composite number between 1 and 50
Step-by-step explanation:
There are 34 composite numbers between 1 to 50 which are as follows: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50.
−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
Find the mean 9,1,8,3,2,1 graphically.
0.6 reoccurring decimal as a fraction in the simplest term
Answer:
3/5
Step-by-step explanation:
here,
0.6
in fraction = 6/10
in simplest form 6/ 10 both term can be divided by 2 so,
6/10 ÷2
= 3/5
what is the HCF of 216
Answer:
The answer for this question is 1
A cylinder Container must
hold al or 2,000 cm3 of
liquid, which of the following
is the optimazation equation
in terms of the radius r.
if the anaunt of material
used to make the container
is to be minimized?
In this problem, assume that the probability that a person is born on a given day is 1/365. (For simplicity, ignore Feb 29.) In a group of 100, what is the expected number of pairs of people who have the same birthday
Answer:
the expected number of pairs of people who have the same birthday is 14
Step-by-step explanation:
The computation of the expected number of pairs of people who have the same birthday is as follows:
= 100 (100 - 1) ÷ 2 × 365
= 100 × 99 ÷ 730
= 9900 ÷ 730
= 13.5616
= 14
Therefore, the expected number of pairs of people who have the same birthday is 14
Biểu diễn 1 ràng buộc trên mặt phẳng tọa độ Oxy là
Step-by-step explanation:
yah kaun se language mein likha hai aapane
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
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
If you want to learn more, you can read:
https://brainly.com/question/12561612
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
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ7
if a point is chosen inside the large circle what is the probability that it will also be inside the small circle?
Answer:
1/4
Step-by-step explanation:
The probability will be equal to 1 - (probability that it will not be inside the small circle) = 1 - (pi*4-pi)/(pi*4)=1/4
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
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....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 equation of a circle with a center at (4, -9) and a radius of 5?
Answer:
(x - 4)² + (y + 9)² = 25
Step-by-step explanation:
The equation of a circle is written as seen below.
(x – h)² + (y – k)² = r²
Where (h,k) represents the center of the circle and r represents the radius
We want to find the equation of a circle that has a center at (4,-9) and a radius of 5.
We know that (h,k) represents the center so h = 4 and k = -9
We also know that r represents the radius so r = 5
Now to find the equation of this specific circle we simply plug in these values into the equation of a circle formula
Equation: (x – h)² + (y – k)² = r²
h = 4, k = -9 and r = 5
Plug in values
(x - 4)² + (y - (-9))² = 5²
5² = 25
The two negative signs in front of the 9 cancel out and it changes to + 9
The equation of a circle with a center at (4,-9) and a radius of 5 is
(x - 4)² + (y + 9)² = 25
What is the perimeter of the octagon below!!
Answer:
C) sixty five units
Step-by-step explanation:
have a great day
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)
Graph the function f(x) = 1/2(2)^x
Answer; Down
Step-by-step explanation:The graph of the squaring function has the shape of a parabola that opens up. Its vertex is at (0,0). The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).
I need help! I will give brainliest, if correct!
For a certain value of $k$, the system
x + y + 3z = 10,
-4x + 3y + 5z = 7,
kx + z = 3
has no solutions. What is this value of k?
kx + z = 3 means z = 3 - kx. Substitute this into the first two equations:
x + y + 3 (3 - kx) = 10 ==> (1 - 3k) x + y = 1
-4x + 3y + 5 (3 - kx) = 7 ==> (-4 - 5k) x + 3y = -8
Multiply through the first equation by -3 :
-3 ((1 - 3k) x + y) = -3 (1) ==> (-3 + 9k) x - 3y = -3
Add this to the second equation to eliminate y :
((-3 + 9k) x - 3y) + ((-4 - 5k) x + 3y) = -3 + (-8)
(-7 + 4k) x = -11
Normally, you would solve for x by dividing both sides by -7 + 4k. But you can't do that if this turns out to be equal to 0, which happens for
-7 + 4k = 0 ==> k = 7/4
Answer:
k = 7/4
Step-by-step explanation:
Solve for x in the diagram
Answer:
x = 20°
Step-by-step explanation:
x + 2x + (x+10) =90° {being a right angle triangle}
3x + x + 10 = 90°
or, 4x = 90° - 10°
or, 4x = 80°
or, x = 80°/4
so, x = 20°
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
The number of lines that can be drawn perpendicular to a given line at a given point on that line in space is:
A. 3
B. 0
C. not enough information
D. infinitely many
Answer:
D. infinitely many
Step-by-step explanation:
Perpendicular lines can be drawn everywhere on the lone in infinitely different places, making the answer infinite.
The number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.
The correct answer is an option (D)
What is perpendicular to line?"It is a straight line that makes an angle of 90° with another line. "For given question,
Lines are perpendicular to each other if their intersection with one another forms a right angle. Through any given line, there are an infinite number of perpendicular lines.Through a specific point on a line, there exists only one perpendicular line. Similarly, for a line and a point not on that line, there is only one perpendicular line through the point.We can draw infinite perpendicular lines to a
Therefore, the number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.
The correct answer is an option (D)
Learn more about the perpendicular lines here:
https://brainly.com/question/18271653
#SPJ2
Transposition
make (m) the subject.
E = mc²
Answer:
m = [tex]\frac{E}{c^2}[/tex]
Step-by-step explanation:
Given
E = mc² ( isolate m by dividing both sides by c² )
[tex]\frac{E}{c^2}[/tex] = m
Answer:
m=E over c2
Step-by-step explanation:
u divide both sides by c2.then on the right side the c2 cancel each other .
then u will m=E over c2
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.
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.
Learn more about interval of function here:
https://brainly.com/question/29197921
#SPJ1
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.
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.
one-sixteenths are there in 3 wholeshow many 1/16 are in 3 wholes
Answer:
48
Step-by-step explanation:
3 divided by 1/16 = 48/16 divided by 1/16
= 48 1/16 in 3 wholes
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.
