Answer:
The operation:
(a,b) is equal to the rest of the division of a by b.
Now, if we have:
(a + kb,b) = (a,b) + (k*b,b)
But if we have that k and b are integers, then:
(k*b)/b = k
So b divides k*b into a whole number, this means that (k*b,b) = 0
then:
(a + kb,b) = (a,b) + (k*b,b) = (a,b) + 0 = (a,b)
What is the solution of the system of equations?
y = -3x + 7
y = 2x - 8
Answer:
x = 3, y = -2
Step-by-step explanation:
Since y=y
then, -3x +7 = 2x-8
7+8 = 3x+2x
15 = 5x
x=3
substitute
y = 2(3) - 8
y = -2
Hope that helped!!! k
Answer:
y = -2
x = 3
Step-by-step explanation:
Solve using elimination
1. Rearrange the equations to make it easier to solve
y = -3x + 7 → 3x + y = 7
y = 2x - 8 → 2x - y = 8
2. Multiply the equations to have a matching coefficient
2(3x + y = 7) = 6x + 2y = 14
3(2x - y = 8) = 6x - 3y = 24
3. Subtract
6x + 2y = 14
- 6x - 3y = 24
0 + 5y = -10
4. Solve for y
5y = -10
y = -2
5. Substitute y in any equation to solve for x
-2 = -3x + 7
-3x = -9
x = 3
Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25
x y
1 5
2 20
3 45
4 80
5 125
x y
1 5
2 25
3 125
4 625
5 3125
x y
1 2
2 4
3 7
4 16
5 32
Answer:
The first table on the list:
x 1 2 3 4 5
y 5 10 15 20 25
Step-by-step explanation:
A linear equation is when the slope is the exact same between each point. The way we find slope is by finding the change in "y" over the change in "x".
x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5
x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5
x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5
x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5
The slope for each change in points is 5, which means that this table represents a linear function.
The only table that represents a linear function is; Table 1
Linear functionA linear function is one that has the same slope for every coordinate point.
Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;
At x = 1, y = 5 and;Slope = 5/1 = 5
At x = 2; y = 10 and;Slope = 10/2 = 5
At x = 3, y = 15 and;Slope = 15/3 = 5
At x = 4, y = 20 and;Slope = 20/4 = 5
At x = 5, y = 25 and;slope = 25/5 = 5
In conclusion, only table 1 represents a linear function.
Read more about Linear function at; https://brainly.com/question/15602982
simplest form 2 3/4 x 4/5 *
Answer:
2 1/5
Step-by-step explanation:
2 3/4 * 4/5
Change the mixed number to an improper fraction
( 4*2+3)/4 * 4/5
11/4 * 4/5
The 4 in the numerator and denominator cancel
11/5
Changing back to a mixed number
5 goes into 11 2 times with 1 left over
2 1/5
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]2\frac{3}{4}*\frac{4}{5}\\\frac{11}{4}*\frac{4}{5}\\\frac{11}{5}\\ 2\frac{1}{5}[/tex]
5. If W(-10, 4), X(-3,-1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your
answer.
Answer:
an isosceles right triangle
Step-by-step explanation:
The square of the length of a side can be found from the distance formula:
d^2 = (x2-x1)^2 +(y2-y1)^2
The square of the length of WX is ...
WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74
The square of the length of XY is ...
XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148
The square of the length of YW is ...
YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74
The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.
To make a stemplot of these rainfall amounts, round the data to the nearest 10, so that stems are hundreds of millimeters and leaves are tens of millimeters. Make two stemplots, with and without splitting the stems. Which plot do you prefer
The two stem plots (with and without splitting the leaves) are plotted below using the data given in the attached picture :
The stem and leaf plots are given below:
Rounding the data to the nearest 10;
The values obtained are :
630, 670, 740, 650, 710, 740, 720, 700, 650, 600, 780, 780, 790, 810, 830, 860, 860, 900, 810, 790, 790, 960, 870
Ordering the data allows for easier generation of the plot.
Ordered data : 600, 630, 650, 650, 670, 700, 710, 720, 740, 740, 780, 780, 790, 790, 790, 810, 810, 830, 860, 860, 870, 900, 960
The stem plot without splitting :
STEM __ LEAF
6 ___ 00, 30, 50, 50, 70
7 ___ 00, 10, 20, 40, 40, 80, 80, 90, 90, 90
8 ___ 10, 10, 30, 60, 60, 70
9 ___ 00, 60
KEY : 6 | 00 = 600
The stem plot WITH splitting :
STEM __ LEAF
6 ___ 00, 30
6 ___ 50, 50, 70
7 ___ 00, 10, 20, 40, 40
7 ___ 80, 80, 90, 90, 90
8 ___ 10, 10, 30
8 ___ 60, 60, 70
9 ___ 00
9 ___ 60
KEY : 6 | 00 = 600
The stem plot with splitting gives a cleaner and more arranged output of the data as the values aren't congested on a single line.
Learn more on stem and leaf plot : https://brainly.com/question/12857419?
Philomena put some money in a 1-year CD that compounds interest monthly, and she made $14.06 in interest the first month. If the interest rate of the CD stays the same, how much will she make in interest the second month?
Answer:
Philomena would make more than $14.06 interest in the second month
Step-by-step explanation:
We are not told how much Philomena put initially, but what we are told is that she has more now as she has been making interests.
This means that if the percent interest remains the same, the amount will definitely have to be more.
For example, let's say we had $10 and we had 10% interest that means we now add $1 to make $11. Since we now have $11, 10 percent of that is $1.1. so now we have $11 + $1.1 = $12.1 which is more than $11.
Thus,Philomena would make more than $14.06 interest in the second month.
Answer:
More than 14.06
Step-by-step explanation:
apesex
What is the name of a number that can be written in the form a + bi where a and b are nonzero real
numbers? (1 point)
a pure imaginary number
an imaginary unit
a real number
a complex number
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex]a + bi[/tex]
Required
Determine the type of number in that form
Numbers written in [tex]a + bi[/tex] are referred to as complex numbers
Where [tex]a \neq 0[/tex]; [tex]b\neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]
Note that a and b can either integers or non integers and a and be can also be positive or negative
The following are valid examples of complex numbers
[tex]2 + 3i[/tex]
[tex]2.4 - 5i[/tex]
[tex]-3 - i[/tex]
and lots more..
The table below shows the number of pets kept by the students in a class.
-----------------------------------------------------------
No. of pets | No. of students
-----------------------------------------------------------
0 | 9
1 | k
2 | 2
3 | 1
4 | 2
-----------------------------------------------------------
If the median number of pets is 1, what is the smallest value of k ?
Answer:
The answer for this question is 5
Which of the following is a correct interpretation of the expression -4 - (-7)?
Answer:
D
Step-by-step explanation:
So we have the expression:
[tex]-4-(-7)[/tex]
First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:
[tex]-4-(-7)\\=-4+7[/tex]
When adding on the number line, we move to the right.
Therefore, the correct interpretation is the value 7 digits to the right of -4.
D is the correct answer.
Answer:
D. the number that is 7 to the right of -4 on the number line
Step-by-step explanation:
interpret -4 - (-7)
= -4 +7
therefore
the number that is 7 to the right of -4 on the number line
so its D.
Simplify: [tex]\sqrt{36} - \sqrt{6} + \sqrt{126}[/tex]
Prove that for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
Answer:
Below
Step-by-step explanation:
Suppose that m and n are both even numbers.
So we can express them as the product of 2 and another number.
● n = 2×a
● m = 2×b
● m-n = 2b-2a
● m-n = 2(b-a)
m-n is an even number since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that both n and m are odd numbers.
● n = 2a+1
● m = 2b+1
● m-n = 2b+1-(2a+1)
● m-n = 2b+1-2a-1
● m-n = 2b-2a
● m-n = 2(b-a)
So m-n is even since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that m is odd and n is even ir vice versa
● n = 2a or n= 2a+1
● m = 2b+1 or m = 2b
● m-n = 2b+1-2a or m-n = 2b-2a-1
● m-n = 2(b-a) +1 or m-n = 2(b-a)-1
In both cases m-n isn't even.
■■■■■■■■■■■■■■■■■■■■■■■■■■
So m-n is even if and only if m and n are odd or m and are even
Answer:
Case 1
both m and n are even
Therefore m/2 and n/2 are integers
Then,
m-n
=2(m/2 - n/2)
Since m/2 and n/2 are integers
Then m/2 - n/2 will be an integer
Therefore,
m-n = 2(Z)
Where Z is an integer
Since 2 is a factor of m-n
Therefore m -n is even
Case 2
Both m and n are odd
m-n
= 2(½m - ½n)
When an odd number is divided by 2 it gives an integer and a remainder of 1
Therefore
½m = Y + ½
And
½n = Z + ½
Where Y and Z are integers
Then
m-n = 2(Y+½-Z-½)
= 2(Y-Z)
Y-Z will also be an integer
m-n= 2A
Therefore m-n is even
Case 3
One is odd and the other even
m-n = 2(m/2 - n/2)
Assume m is even and n is odd
From the discussions above
m-n = 2(Y - Z - ½)
m-n = 2(A - ½)
Hence m-n is not even because when is divided by two it doesn't give an integer.
Therefore for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
find the product 538 x 100=
Answer:
Answer=53,800
Step-by-step explanation:
just add the two zero behind the number
Can I get help with this -5-(3^2+2)
Answer:
-16
Step-by-step explanation:
-5-(3^2+2)
Parentheses first
-5-(9+2)
-5-(11)
Subtract
-16
which equation represents a circle with the center at two, -8 and a radius of 11
Answer:
( x-2)^2 + ( y +8) ^2 =121
Step-by-step explanation:
The equation of a circle can be written as
( x-h)^2 + ( y-k) ^2 = r^2
where ( h,k) is the center of the circle and r is the radius
( x-2)^2 + ( y- -8) ^2 = 11^2
( x-2)^2 + ( y +8) ^2 =121
Answer:
(x - 2)² + (y + 8)² = 11²
Step-by-step explanation:
General equation for a circle
( x - h )² + ( y - k )² = r², where (h,k) is the center and r ,radius..
with center ( 2,-8 ) and radius 11
(x - 2)² + (y + 8)² = 11²
(PLEASE ITS ACTUALLY MY LAST ONE HELP)
Which two figures represent circles of the same size?
A) D and G
B) C and G
C) none of them.
D) C and D
Answer:
B) C and G
Step-by-step explanation:
The radius is equal to 1/2 the diameter
r = 1/2 d
G has a diameter of 45
1/2 (45) = 22.5
C and G are the same
Answer:
c and g!
Step-by-step explanation:
rational number between 2 and 3 ?
Answer:
2:3
Step-by-step explanation:
It’s easy
Answer:
2.5
Step-by-step explanation:
i think
perform the following division (-2/3) ÷ (4/7)
Answer:
-7/6
Step-by-step explanation:
-2/3 x 7/4 = -14/12 = -7/6
Answer: -7/6
Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).
Remember that dividing by a fraction is the same thing
as multiplying by the reciprocal of the fraction.
Before multiplying however, notice that we
can cross-cancel the 2 and 4 to 1 and 2.
So multiplying across the numerators and denominator and
remembering our negative in the first fraction, we have -7/6.
What happens to the probability of making a Type II error, beta,as the level of significance, alpha,decreases? Why?
Answer:
Lowering the level of significance, α increases the probability of making a Type II error, β.
Step-by-step explanation:
Lowering the level of significance, α increases the probability of making a Type II error, β.
This is because the region of acceptance becomes bigger, and it makes it less likely for one to reject a null hypothesis, when it is false, the type II error.
the sum of the prime divisors of 2001 is a) 55, b) 56, c) 670, d) 671, e) 2001
Answer:
Option A
Step-by-step explanation:
2001 can be divided by 3, 23, and 29 without remainders. This means that the three numbers are prime divisors of 2001.
2001/3 = 667
2001/23 = 87
2001/29 = 69
The sum of the prime divisors is 55.
3 + 23 + 29 = 55
Option A should be the correct answer.
Hope this helps.
A vector has a magnitude of 43
meters at an angle (0). If the
Y-component of the vector is 30
meters, what is the X-component?
[?]m
30.8 m
Step-by-step explanation:
Given: [tex]V = 43\:\text{m}[/tex], [tex]V_y = 30\:\text{m}[/tex]
The x-component of vector [tex]\vec{\text{V}}[/tex] is
[tex]V_x = \sqrt{V^2 - V_y^2} = \sqrt{(43)^2 - (30)^2} = 30.8\:\text{m}[/tex]
The x- component of the vector is 30.8meters.
What is the magnitude and direction of vector?If [tex]v = < a. b >[/tex] be a position vector then the magnitude of vector v is found by [tex]|v| =\sqrt{a^{2}+b^{2} } }[/tex] , where a and b are the x and y component respectively.
And the direction is equals to the angle formed x- axis or y axis.
According to the given question
We have
Magnitude of the vector, |v| = 43meters
Y- component of the vector, b = 30meters
Since, we know that
[tex]|v| =\sqrt{a^{2} +b^{2} }[/tex]
Substitute the value of |v| = 43 and b = 30 in the above formula of magnitude.
⇒ [tex]43 = \sqrt{a^{2}+30^{2} }[/tex]
⇒ [tex]43 = \sqrt{a^{2}+900 }[/tex]
⇒ [tex]43^{2} =a^{2} + 900[/tex]
⇒ [tex]1849 = a^{2} + 900[/tex]
⇒ [tex]1849-900=a^{2}[/tex]
⇒ [tex]949=a^{2}[/tex]
⇒ [tex]a =\sqrt{949}[/tex]
⇒ [tex]a = 30.8[/tex]
Hence, the x- component of the vector is 30.8meters.
Learn more about magnitude and direction of a vector here:
https://brainly.com/question/13134973
#SPJ2
The perimeter of a rectangle is 80 cm. Find the lengths of the sides of the rectangle giving the maximum area.Enter the answers for the lengths of the sides in increasing order.
Answer:
The lengths of the sides are 20 cm and 20 cm
Step-by-step explanation:
Given
Perimeter, P = 80cm
Represent the length and width with L and W, respectively;
[tex]P= 2*(L + B)[/tex]
Substitute 80 for P
[tex]80 = 2 * (L + B)[/tex]
Divide through by 2
[tex]40 = L + B[/tex]
[tex]L + B = 40[/tex]
Make L the subject of formula
[tex]L = 40 - B[/tex]
Area of a rectangle is calculated as thus;
[tex]Area = L * B[/tex]
Substitute 40 - B for L
[tex]Area = (40 - B) * B[/tex]
Express this as a function
[tex]A(B) = (40 - B)* B[/tex]
[tex](40 - B)* B = A(B)[/tex]
Set A(B) = 0 to determine the roots
Hence;
[tex](40 - B)* B = 0[/tex]
[tex]40 - B = 0[/tex] or [tex]B = 0[/tex]
[tex]40 = B[/tex] or [tex]B = 0[/tex]
[tex]B = 40[/tex] or [tex]B = 0[/tex]
The maximum area of a rectangle occurs at half the sum of the roots;
So;
[tex]B= \frac{B_1 + B_2}{2}[/tex]
[tex]B= \frac{40+0}{2}[/tex]
[tex]B= \frac{40}{2}[/tex]
[tex]B = 20[/tex]
Recall that [tex]L = 40 - B[/tex]
[tex]L = 40 - 20[/tex]
[tex]L = 20[/tex]
Hence the lengths of the sides are 20 cm and 20 cm
what is 90.125 written in expanded from?
Answer:
The answer is 90+0+0.1+0.02+0.005.
Step-by-step explanation:
The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.
Individual claim sizes may be modeled by a uniform distribution function on the interval [$1000, $5000]. Eighty claims are examined. Assume claims are independent.
What is the approximate probability that total claims will be between $250,000 and $300,000?
a) 17%
b) 34%
c) 50%
d) 84%
e) 97%
A tennis team played a total of 25 games and won 20 of them. What percent of the games did the team win?
━━━━━━━☆☆━━━━━━━
▹ Answer
80%
▹ Step-by-Step Explanation
20/25 = 0.8 → 80%
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
A manager from a certain well known department store found out the money their customers carry into the store is normally distributed with a mean of $258 dollars and a standard deviation of $35. In a sample of 76 Americans who walked into that store find the probability that a random customer will have more than $260 in his or her wallet
Answer:
0.30924
Approximately ≈ 0.3092
Step-by-step explanation:
To solve for this question, we use the formula:
z = (x - μ)/σ
where x is the raw score
μ is the sample mean
σ is the sample standard deviation.
From the question,
x is the raw score = 260
μ is the sample mean = population standard deviation = 258
σ is the sample standard deviation
= σ/√N
N = 76 samples
σ = Population standard deviation
= 35/√76
= 4.0146919966
Hence,
z = (x - μ)/σ
= 260 - 258/ 4.0146919966
= 0.4981702212
Approximately = 0.498
We find the Probability using z score table for normal distribution
P(x = z) = P( x = 260)
= P( z = 0.498)
= 0.69076
The probability that a random customer will have more than $260 in his or her wallet is calculated as:
P(x>Z) = 1 - P( z = 0.498)
P(x>Z) = 1 - 0.69076
P(x>Z) = 0.30924
Approximately ≈ 0.3092
The count in a bacteria culture was 900 after 15 minutes and 1100 after 35 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Answer:
300
Step-by-step explanation:
1100 = 900 [tex]e^{k*20}[/tex]
1.222222 = [tex]e^{k*20}[/tex]
ln(1.222) = 20k ln(e)
k = ln(1.222)/20
k = .2004
900 = x [tex]e^{15* .20004}[/tex]
900/x = [tex]e^{15* .20004}[/tex]
[tex]e^{15*.2004} = 900/x[/tex]
x = 900/ [tex]e^{15*.2004}[/tex]
x = 300
FIND THE AREA OF THE SHAPE BELOW
PLEASE HELP I HAVE BEEN STUCK ON THIS FOREVERRRR!!
THANK YOU
Answer:
Is answer 22 units sqaure ?
HELP PLEASE 50 POINTS
A mechanic charges $125 plus $25 per hour of labor. The equation c=25n+125
describes the total she would charge for a service visit, where n represents the number of
hours of labor and c is the total cost. Graph the equation and using the graph, find how
much he charges when she works 3 hours.
Answer:
See Attachment for graph
Charges = $200 when number of she works for 3 hours
Step-by-step explanation:
Given
Charges = $25 per hour + $125 (c = 25n + 125)
Required
Graph the equation.
From the graph, determine c when n = 3
To plot the graph; first, we have to determine the points to use;
When n = 1
[tex]c = 25 * 1 + 125[/tex]
[tex]c = 25 + 125[/tex]
[tex]c = 150[/tex]
When n = 2
[tex]c = 25 * 2 + 125[/tex]
[tex]c = 50 + 125[/tex]
[tex]c = 175[/tex]
When n = 3
[tex]c = 25 * 3 + 125[/tex]
[tex]c = 75 + 125[/tex]
[tex]c = 200[/tex]
When n = 4
[tex]c = 25 * 4 + 125[/tex]
[tex]c = 100 + 125[/tex]
[tex]c = 225[/tex]
Plotting n on the x axis and c on the y axis; we have
c || n
1 || 150
2 || 175
3 || 200
4 || 225
(See attachment)
From the attachment;
When she works for 3 hour; This implies that n = 3
And c = $200 when n = 3
See Proof
[tex]c = 25n + 125[/tex]
Substitute 3 for n
[tex]c = 25 * 3 + 125[/tex]
[tex]c = 75 + 125[/tex]
[tex]c = 200[/tex]
Divide and check by multiplying the quotation by the divisor 8m^4+12m^3 over 4m
Answer:
2m^3 + 3m^2
Step-by-step explanation:
8m^4+12m^3
---------------------
4m
2m^3 + 3m^2
Check
4m(2m^3+3m^2)
8m^4 + 12 m^3
Two brothers, Tom and Allen, each inherit $39000. Tom invests his inheritance in a savings account with an annual return of 2.9%, while Allen invests his inheritance in a CD paying 5.7% annually. How much more money than Tom does Allen have after 1 year?
Answer:
Tom:
initial money = $ 39000
% increased per annum = 2.9%
money gained per annum = 39000 * 2.9/100 = $1131
Allen:
initial money = $ 39000
% increased per annum = 5.7 %
money gained per annum = 39000 * 5.7/100 = $2223
Allen has $ (2223 - 1131) = $ 1192 more than Tom