Final answer:
To find the remainder of 314162 divided by 7, we use modular arithmetic and find that the powers of 314 mod 7 repeat every 3 powers. Since 162 is a multiple of 3, 314162 mod 7 equals 1.
Explanation:
The question asks for the remainder when 314162 is divided by 7. To solve this problem, we can use a concept known as modular arithmetic, which deals with the remainder upon division. The key here is to find a pattern in the powers of 314 modulo 7, because large numbers can be cumbersome to work with directly. A helpful property is that (a×b) mod n = [(a mod n)×(b mod n)] mod n.
Let's consider the powers of 314 mod 7:
3141 mod 7 = 2
3142 mod 7 = (314 × 314) mod 7 = (2 × 2) mod 7 = 4
3143 mod 7 = (3142 × 314) mod 7 = (4 × 2) mod 7 = 1
Since we reached 1 again, the sequence will repeat every 3 powers. Now, 162 is divisible by 3 (162 = 3 × 54). Therefore, we can conclude that 314162 mod 7 will have the same remainder as 3143 mod 7, which is 1.
A trust is one form of holding property
One leg of a right triangle is 3 millimeters longer than the shorter leg and the hypotenuse is 6 millimeters longer than the shorter leg. find the lengths of the sides of the triangle.
Using the Pythagorean theorem and defining the shorter leg as 'x', we solve the equation x² + (x + 3)mm² = (x + 6)mm² to find that the shorter leg is 9 mm, the longer leg is 12 mm, and the hypotenuse is 15 mm.
Explanation:To solve for the lengths of the sides of a right triangle when given the difference in length between the legs and the hypotenuse, we can use the Pythagorean theorem, which states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the relationship is a² + b² = c².
Let's define the length of the shorter leg as 'x'. According to the problem, the other leg is 'x + 3 mm' (3 millimeters longer than the shorter leg), and the hypotenuse is 'x + 6 mm' (6 millimeters longer than the shorter leg).
Applying the Pythagorean theorem, we get the equation:
x² + (x + 3)mm² = (x + 6)mm²
Expanding the squares and solving for 'x', we get:
x² + x² + 6x + 9 = x² + 12x + 36Combining like terms and simplifying gives us:x² - 6x - 27 = 0Factoring the quadratic equation, we find that (x - 9)(x + 3) = 0Since the length cannot be negative, we discard the negative solution and left with 'x = 9 mm'This means the shorter leg is 9 mm, the longer leg is 9 mm + 3 mm = 12 mm, and the hypotenuse is 9 mm + 6 mm = 15 mm.
Each afternoon she goes to the track and divides her time between running and jogging. she spends a total of 2 hours exercising and does a total of 10 miles. if she runs at 5 miles per hour and jogs at 2.5 miles per hour, how long did she spend on each type exercise?
Find the sales price of the following item.
A toaster originally costing $39.99, marked down $8.50.
4.70
31.49
48.49
339.92
Answer:
The sales price is $31.49
Step-by-step explanation:
If the toaster has a marked down of $8.50 means that is a discount and you need to subtract this value from the originally costing, as follows:
Sales price = Original cost - Discount value
Sales price = [tex]39.99-8.50[/tex]
Finally, the sales price is $31.49
If the expression below models the number of applicants for a credit card, what is the correct interpretation of the second factor?
There were 6.75 times as many people who applied in the 4th month as in the first month.
There were 1.2 times as many people who applied in the 4th month as in the first month.
There were 2.07 times as many people who applied in the 4th month as in the first month.
There were 4.8 times as many people who applied in the 4th month as in the first month.
Why is it that the limit as x approaches zero of sin3x all over x is 3?
The limit as x approaches zero of sin3x all over x is indeed 3.
Below is a step by step display of how to derive this answer.
A bug is traveling at a rate of 18 inches per minute. Write the rate in feet per minute. (12 in. = 1 ft.)
What is the rate of change for y=9x + 4?
Final answer:
The rate of change for the equation y=9x+4 is 9, representing a constant slope where for every unit increase in x, y increases by 9 units.
Explanation:
The rate of change in the linear equation y=9x + 4 is the coefficient of the x term, which represents the slope of the line. In this case, the rate of change is 9. This means that for every one unit increase in x, the value of y increases by 9 units. Since this is a linear equation, the rate of change is constant, meaning it does not change regardless of the value of x.
Can you help me solve this proof please?
A bank sends its customers an e-mail when their accounts fall below -$10. Which inequality models this situation? A) a<-10 B) a>-10 C) a≥-10 D) a≤-10
Answer:
<−10
Step-by-step explanation:
Two linear equations are shown in the graph.
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What are the coordinates of the point where the two lines intersect?
A. (–2, 3)
B. (3, 3)
C. (3, 0)
D. (–3, 3)
count the lines horizontally and vertically to see where the lines connect
x = left to right
y = up and down.
the black lines are the origins ( 0,0)
so 3 to the right of a black line and 3 up from the black line equals (3,3)
Answer is B
Tim earned $16 babysitting and $17.50 mowing a lawn. He paid $8.50 for a movie and bought a small popcorn for $1.95. Write an expression to show how much money he has left.
The expression to show how much money he has left is $(33.5 - 10.45).
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given that, Tim earned $16 babysitting and $17.50 mowing a lawn.
What Tim has earned we'll add which is $(16 + 17.50) = $33.5.
He paid $8.50 for a movie and bought a small popcorn for $1.95.
His spendings we'll also add which is $(8.5 + 1.95) = $10.45.
Now, to write an expression for how much money he has left we'll subtract
his total spending from his total earnings which is,
= $(33.5 - 10.45).
= $23.05.
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the total cost to rent a row boat is $16 times the number of hours the boat is used. how long can you rent the boat for $224
Ifyou are asked to solve a system ofequations in which there is no linear equation to start with, you can sometimes begin by isolating and substituting a variable that is squared in both equations.
Find the Least Common Multiple of these two monomials:
14x^4y^6z^3 and 24x^6y^2z^8
64x^6y^6z^8
2x^4y^2z^3
168x^6y^6z^8
168x^10y^8z^11
LCM 14 & 24 = 168
then use the highest exponents for the variables
answer = 168x^6y^6z^8
If i am driving 63 miles an hour how long will it take to drive 441 miles
Mrs. Gerhard wants to plant grass in her backyard. She wants the grass to cover all of her backyard except the play area.
How many square feet of grass will Mrs. Gerhard need to plant?
A.
12 ft2
B.
34 ft2
C.
60 ft2
D.
84 ft2
A.
12 ft2
B.
34 ft2
C.
60 ft2
D.
84 ft2
What is the value of x?
Seven times a number minus the number is -48. Find the number.
A.)the number is -8
B.)the number is 8
C.)the number is 6
The vertex of the graph is f(x) = |x-3|+6 is located at
4= square root of (-6-2x) plus square root of (31-3x)
Original equation
4 = √-6-2x+√31-3x
Isolate
-√-6-2x = -4+√31-3x
Tidy up
√-6-2x = 4-√31-3x
Raise both sides to the second power
(√-6-2x)2 = (4-√31-3x)2
After squaring
-6-2x = 31-3x+16-8√31-3x
Current equation
-6-2x = 31-3x+16-8√31-3x
Isolate radical on the left hand side
8√31-3x = 6+2x+31-3x+16
Tidy up
8√31-3x = 53-x
Raise both sides to the second power
(8√31-3x)2 = (53-x)2
After squaring
1984-192x = x2-106x+2809
Rearranged equation
x2 + 86x + 825 = 0
This equation has two rational roots:
{x1, x2}={-11, -75}
Original equation, root isolated, after tidy up
√-6-2x = 4-√31-3x
Plug in -11 for x
√-6-2•(-11) = 4-√31-3•(-11)
Simplify
√16 = -4
Solution does not check
4 ≠ -4
Original equation, root isolated, after tidy up
√-6-2x = 4-√31-3x
Plug in -75 for x
√-6-2•(-75) = 4-√31-3•(-75)
Simplify
√144 = -12
Solution does not check
12 ≠ -12
Hopefully this helped You
does 4+3n2 has four term
A car rental company at a major airport on an average rents 70 percent of its fleet of 200 cars per day. The cars are rented for an average of 4 days. What is the average number of rentals processed per day?
To find the average number of car rentals processed per day, we first calculate that 70% of the 200-car fleet equates to 140 cars. Each car is rented for 4 days, so, therefore, the total number of cars rented in four days is 560. Hence, the average daily rentals are 140 cars.
Explanation:To calculate the average number of car rentals processed per day, we need to consider that the company rents 70% of their 200-car fleet daily. That is, 70/100 * 200 = 140 cars.
Since each car is rented for an average of 4 days, each day's rentals represent 1/4 of the number of cars that will be rented over the next four days. Therefore, the total number of cars rented in four days would be divided by 4 to get the daily average. In this case, it's 140 * 4 = 560, and 560 / 4 = 140 car rentals per day.
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Emma is an artist and has created seven paintings. She plans to paint three additional paintings each week. What statements are true of this scenario? Check all that apply.
Answers are 2, 3, and 4 on e d g e n u i t y
What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
A) 1
B) –1
C) i
D) –i
the answer would be B :) hope this helps
Andre and Sally are playing a number game. Andre tells Sally, "I'm thinking of a number between 1 and 20. If I take the number and add 5, and then subtract 3, I get 19." What number is Andre thinking of?
What is the length of a rectangle if the perimeter is 88 inches and the length is 2 inches more than the width?
The length of a rectangle is 33 inches.
What is a rectangle?The rectangle is a 2D shape having four sides and the opposite sides of the rectangle are equal and parallel. The sum of all angles of the rectangle is 360°.
We have,
The perimeter of the rectangle = 88 inches
And,
The length is 2 inches more than the width.
Now, Let,
Width of the rectangle = a
So,
Length of the rectangle = 3a
Now,
Using the formula of the perimeter of the rectangle,
i.e.
The perimeter of the rectangle = 2(Length + Width)
Now,
According to the question,
i.e.
88 = 2( 3a + a)
i.e.
8a = 88
We get,
a = 11,
i.e.
Width of the rectangle = a = 11 inches
So,
Length of the rectangle = 3a = 3 * 11 = 33 inches
Hence, we can say that the length of a rectangle is 33 inches and the width of the rectangle is 11 inches.
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Using the graph below, what are the common ratio and the general term equation, an, of the geometric sequence?
Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.
OPTIONS:
r = 1/2, a sub n = -16 (1/2) to the power of n-1
r = −2, an = −16(−2)n − 1
r = 2, an = −16(2)n − 1
r = -1/2, a sub n = -16 (-1/2) to the power of n-1
To find the common ratio and general term equation of the geometric sequence, we analyze the given graph and use the formula for the general term of a geometric sequence. By solving the equations (-16)(r)^(n-1) = -8 and (-8)(r)^(n-2) = -16, we find that the common ratio is 1/2 and the general term equation is an = -16(1/2)^(n-1).
Explanation:
To determine the common ratio and general term equation of the geometric sequence, we can examine the given graph.
From the graph, we can see that the first term is -16. Let's identify two points on the graph that correspond to consecutive terms. We can choose the points (-1, -8) and (-2, -16) as the graph passes through these points.
Using the formula for the general term of a geometric sequence, an = a1(r)^(n-1), we can substitute the given values (-16, r) and (-8, r^2) to find the common ratio and the general term equation.
By solving the equations (-16)(r)^(n-1) = -8 and (-8)(r)^(n-2) = -16, we find that the common ratio is 1/2 and the general term equation is an = -16(1/2)^(n-1).
Suppose a right cylinder was bent into a U-shape and was compared to another right cylinder. What can be said about their volumes?
Answer:
The volume of the U-shape will be half the volume of the original right cylinder.
Step-by-step explanation:
If we are given a right cylinder and it was bent into a U shaped then this U-shaped figure could also be considered as a half cylinder.
We could see from the figure attached how this shape looks like.
and now the volume of this half cylinder will be half the volume of the actual right cylinder.
Answer:
B) There is not enough information to tell since they are not between parallel planes.
Step-by-step explanation:
In order for Cavalieri's principle to be true, both cylinders must have the same cross section. They may or may not. The requirement of being between parallel planes was broken. Therefore -- There is not enough information to tell since they are not between parallel planes
Find the value of y so that r⎹⎹ s A. 32 B. 56 C. 64 D. 124 please help