When $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$?
If
N = a (mod 10)
N = b (mod 13)
gcd(10,13) = 1
then
N = 10 bx + 13 ay (mod 130)
Where
10x + 13y = 1
-> (10x + 13) (mod 2) = 1 (mod 2)
-> y (mod 2) = 1
y = -3, x = 4
-> N = 40b – 39a (mod 130)
It is given that ra + sb should be non-negative:
N = 40b – 39a (mod 130)
N = 40b + (130 – 39)a (mod 130)
N = 40b + 91a (mod 130)
Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).
Final answer:
To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.
Explanation:
To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:
n = 10k + a, where k is some integer
n = 13l + b, where l is some integer
Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.
Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).
What property is illustrated by the equation (8 + 2) + 7 = (2 + 8) + 7? A. Commutative property of addition B. Associative property of Addition C. Distributive property D. Identity Property of Addition
What is the initial value of the function represented by this graph?
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
0
1
2
5
The initial value of a function is the value of the function when x = 0
o when x = 0, y = 2 so the initial value is 2
Answer:
2
Step-by-step explanation:
The initial value is what you start off with, so it is 2! :)
A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed?
Answer:
216
Step-by-step explanation:
i think
One number exceeds another by 11. the sum of the numbers is 3535. what are the numbers?
Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.
A. 13
B. 26
C. 77
D. 38.5
Write an equation that can be used to find the area A of a rectangular rug whose sides are 5 feet long and x feet long
There were 490 people at play. The admission price was $3.00 for adults and $1.00 for children. The admission receipts were $990. How many adults and children attended
Plato-Match each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion (if any) that proves the relationship.
Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition
Answer:
[tex](2+x)+3y[/tex]
Step-by-step explanation:
In associative property , when we add the numbers we can group the numbers in any combination.
for example : [tex]a+(b+c)= (a+b)+c[/tex]
[tex]2 + (x + 3y)[/tex] can be written as [tex](2+x)+3y[/tex] using associative property.
The terms can be grouped in any combination
[tex](2+x)+3y[/tex]
Which regular polygon can be drawn by using rotations in geometry software?
Answer:
n- regular polygon
Step-by-step explanation:
In order to draw n- regular polygons, 360 must be divisible by n.
Therefore, there are many regular polygons such as 12- polygon using 30° rotations and 15-polygon using 24° rotations.
Which expression is equivalent to r^9/r^3
Answer:
The correct option is B.
Step-by-step explanation:
The given expression is
[tex]\frac{r^9}{r^3}[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, we get
[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]
[tex]\frac{r^9}{r^3}=r^{6}[/tex]
The expression [tex]r^{6}[/tex] is equivalent to the given expression.
Therefore the correct option is B.
A box contains seven green marbles, six blue marbles and eight orange marbles. Without looking, you choose two marbles out of the bag. What is the probability that the first two picked will both be green if you don’t replace the marble after the first pick?
The probability is 0.1 (or 10%).
It is required to find the probability.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes.
Given that:
The favorable count is determined as follows: considering Green marbles. There are 7 of them in the box, so 7 possible picks at the first draw.
Since you don't replace the pick, at the next drawing there are only 6 Green ones. So for each of the 7 possible first picks, there are 6 possible second picks: number of possibilities is 7 by 6 = 42.
The total number of possible drawings, irrespective of color is determined as follows: there are 21 marbles in total at first drawing, and 20 at second. So, for each first pick there are 20 possibilities, i.e., total number is 21 by 20 = 420
The probability is P = 42 / 420 = 1 / 10 = 0.1 (or 10%)
So, the probability is 0.1 (or 10%).
Learn more about probability here:
https://brainly.com/question/4609631
#SPJ2
What is the domain of the relation: (0, 7), (8, -1), (2, 3), (-4, 6)?
A. (-4, 0, 2, 8)
B. (-1, 3, 6, 7)
C. (1, 7, 8, -1)
D. (2, 3, -4, 6)
What is the measure of RST?
Answer:
∠TSR = 93°
Step-by-step explanation:
In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]
∠S = [tex]\frac{131+43}{2}[/tex]
= [tex]\frac{174}{2}[/tex]
= 87°
Now we have to find the measure of ∠RST
Since ∠QSR + ∠TSR = 180° [ supplementary angles]
87° + ∠TSR = 180°
∠TSR = 180 - 87 = 93°
Therefore, m∠TSR = 93° is the answer.
A candy factory made 54 boxes of chocolates. Each box weighs 2 pounds. They packed the boxes in 6 cases with the same number of boxes in each case. How many pounds of chocolates were there in each case?
The number of pounds of chocolates in each case is 18 pounds
How to find the number of pounds in each case?
The candy factory made 54 boxes of chocolates.
Each box weighs 2 pounds
Therefore,
each box = 2 pounds
They packed the boxes in 6 cases with the same number of boxes in each case. Therefore,
Boxes in each case = 54 / 6 = 9 boxes
Therefore,
pounds of chocolates in each case = 9 × 2 = 18 pounds
learn more on pounds here: https://brainly.com/question/14686792
#SPJ2
no idea. please help:)
The mean incubation time for a type of fertilized egg kept at 100.2100.2â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 11 dayday. â(a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â(b) what is the probability that a randomly selected fertilized egg hatches between 2222 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?
To solve this problem, what we have to do is to calculate for the z scores of each condition then find the probability using the standard normal probability tables for z.
The formula for z score is:
z = (x – u) / s
where,
x = sample value
u = sample mean = 23 days
s = standard deviation = 1 day
A. P when x < 21 days
z = (21 – 23) / 1
z = -2
Using the table,
P = 0.0228
Therefore there is a 2.28% probability that the hatching period is less than 21 days.
B. P when 23 ≥ x ≥ 22
z (x=22) = (22 – 23) / 1 = -1
P (z=-1) = 0.1587
z (x=23) = (23 – 23) / 1 = 0
P (z=0) = 0.5
P = 0.5 - 0.1587 = 0.3413
Therefore there is a 34.13% probability that the hatching period is between 22 and 23 days.
C. P when x > 25
z = (25 – 23) / 1
z = 2
P = 0.9772
This is not yet the answer since this probability refers to the left of z. Therefore the correct probability is:
P true = 1 – 0.9772
P true = 0.0228
Therefore there is a 2.28% probability that the hatching period is more than 25 days.
How can you rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations?
You can rearrange formulas to highlight a specific quantity of interest by identifying it and isolating it using inverse operations.
Explanation:In mathematics, you can rearrange formulas to highlight a specific quantity of interest using the same reasoning as in solving equations. The goal is to isolate the variable or the quantity you want to highlight on one side of the formula. Here are the steps to do it:
Identify the quantity of interest you want to highlight.
Apply inverse operations to isolate that quantity on one side of the equation/formula.
Simplify or solve for the highlighted quantity if needed.
For example, if you have the formula for the area of a rectangle, A = L * W, and you want to solve for the length of the rectangle, you can rearrange the formula as L = A / W, highlighting the length as the quantity of interest.
Learn more about Rearranging formulashttps://brainly.com/question/35707641
#SPJ3
Solve for z: 3z -5 +2z=25 -5z
To answer this question you will have to combine like terms.
3z-5+2z=25-5z
Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z
Now you have -5+5z=25-5z
Now you will go ahead and distribute since you can't combine anymore on certain sides.
You can add 5 to 25 on the other side: 25+5=30
Then add 5z to 5z on the other side: 5z+5z=10z
So now your equation should look like this: 10z=30
From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3
So your solution should come to: z=3
The table below shows the surface area y, in square feet, of a shrinking lake in x days: Time (x) (days) 5 10 15 20 Surface area (y) (square feet) 90 85 70 61 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points) Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
What is the difference between discrete vs continuous data
And can someone please help me with 1-5
How do you find the vertex of this parabola? I just plotted the points down on a graphing calculator, but I figure there's a better way.
What is the range of this set of heights in centimeters?
{140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}
38
41
46
50
(If you can help me with this maybe you can help me with my last posted question? It hasn't been answered and I need help!)
Final answer:
The range of the given set of heights is 50 cm, which is determined by subtracting the smallest height (132 cm) from the largest height (182 cm) in the set.
Explanation:
The range of a set of numbers is the difference between the largest and the smallest numbers in the set. To find the range of the given heights in centimeters, you first identify the largest and smallest numbers in the set {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}. The smallest height is 132 cm, and the largest is 182 cm.
Now, subtract the smallest value from the largest value to determine the range:
Range = Largest value – Smallest value
Range = 182 cm – 132 cm
Range = 50 cm
Therefore, the range of the given set of heights is 50 cm.
Probability of a lightbulb failing question? If the probability is .001 that a light bulb will fail on any given day, then what is the probability that it will last at least 30 days?
A.) How many ways can you select 1 flavor of ice cream, 1 topping and 1 drink if there are 5 flavors of ice cream, 3 toppings and 4 drinks to choose from?
B.) How many ways can you select a 4-digit passcode without repeating any digit?
C.) How many ways can you select 3 toppings for a pizza with 8 toppings to choose from?
D.) What is the probability of rolling a single die and it landing on a prime number? (Remember, the number 1 is not considered prime.)
E.) How many items are in the sample space for rolling a die and spinning a spinner with 4 different colored sections (red, yellow, green and blue)?
F.) What is the probability of rolling the die and spinning the 4-sectioned spinner described in part E, and getting the number 5 and the color red?
G.) If you wanted to purchase a size T-shirt that "most" people could wear, would you purchase the mean size, the median size or the mode size?
Jessica plans to purchase a car in one year at a cost of $30,000. how much should be invested in an account paying 10% compounded semiannually to have the funds needed?
Find x 58 degrees and adjacent 4.0
Mika wrote the table of points below. x y 0 2 3 5 6 8 Which explains whether or not Mika has described a proportional relationship, and why?
Answer:
B
Step-by-step explanation:
Edg 2020
Answer:
Step-by-step explanation: Answer B
Can you use matrix multiplication with a matrix with three rows and a matrix with two columns