Answer:
The answer is "728 routes"
Step-by-step explanation:
The number of ways to proceed from (0, 0) to (5, 7) is as follows:
[tex]\Rightarrow \frac{(7+5)!} {(7! \times 5!)} \\\\ \Rightarrow \frac{12!}{(7! \times 5! )}\\\\\Rightarrow \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{7! \times 5!}\\\\\Rightarrow \frac{12 \times 11 \times 10 \times 9 \times 8}{5!}\\\\\Rightarrow \frac{12 \times 11 \times 10 \times 9 \times 8}{5\times 4 \times 3 \times 2 \times 1}\\\\\Rightarrow \frac{ 11 \times 9 \times 8}{1}\\\\\Rightarrow 11 \times 9 \times 8\\\\\Rightarrow 11 \times 72\\\\\Rightarrow 792[/tex]
We would like to delete the ways of (0, 0) to (2, 3) That's the resolution:
[tex]\Rightarrow \frac{(3+2)!}{(3!\times2!)} \\\\ \Rightarrow \frac{5!}{(3!\times2!)} \\\\\Rightarrow \frac{5\times 4\times 3! }{(3!\times2 \times 1)} \\\\\Rightarrow \frac{5\times 4}{(2 \times 1)} \\\\\Rightarrow \frac{5\times 2}{1} \\\\\Rightarrow 10 \ ways[/tex]
[tex]So, \\\\ \Rightarrow 792 -10 \\\\ \Rightarrow 782 \ routes[/tex]
Container X contained 1200g of sand.Container Y contained 7.2kg of sand.After an equal amount if sand was removed from each container,Container Y had 7 times as much sand as container X.how much sand was removed from each container?
Billy’s Boat Rentals charges a yearly fee of $105 and $9.50 each time a member wants to rent a boat. Lisa’s Boat Rentals does not charge a yearly fee but charges $14.75 every time a member rents a boat. How many times does a person have to rent a boat for Billy’s and Lisa’s to cost the same amount?
Answer:
It will take 20 times for both cost to be same
Step-by-step explanation:
What we want to do here is to calculate the number of times it will take someone who’s wants to rent a boat by Billyboat will be able to rent Lisa boat.
The first thing to do here is calculate how much that is charged to rent Billyboats
That would be;
Let the number of times be n
so the amount will be
105 + 9.50n
Now, renting at 14.75 at n times would be 14.75n
Mathematically, we equate both
14.75n = 105 + 9.5n
14.75n - 9.5n = 105
5.25n = 105
n = 105/5.25
n = 20 times
a card is drawn at random from a pack of 52 playing cards. find the probability tht the card drawn is neither an ace nor a king
Answer:
[tex]\frac{11}{13}[/tex]
Step-by-step explanation:
There are 4 aces and 4 kings.
[tex]\frac{8}{52} =\frac{2}{13}[/tex]
Now just subtract that from 1.
[tex]\frac{11}{13}[/tex]
An arithmetic sequence has this recursive formula. a1=9 and 1-3 .
The required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
Given, an arithmetic sequance is given in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex] .
Explicit formula for the sequence is to be determined.
Arithmetic progression is the sequence of numbers that have common differences between adjacent values.
Example, 1, 2, 3, 4, 5, 6. this sequence as n = 6 number with a = 1 (1st term) and common differene d = 2- 1 = 1.
Given arithmetic sequance is in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex]
From above expression
[tex]a_n-a_{n-1}= -3[/tex]
common difference (d) = -3
with d = -3 and [tex]a_1 = 9[/tex]
The equation for the nth term in an arithmetic sequence is given by
[tex]a_n =a +(n-1)d[/tex]
[tex]a_n = 9 +(n-1)(-3)[/tex]
The above expression is the explicit form of the arithmetic equation.
Thus, the required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
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Exactly 1 1/3 yard of ribbon is needed to make a bow. Which of the following lengths of ribbon could be used to make a bow with the least amount remaining?
The answer choice which could be used to make a bow with the least amount remaining is; 1 2/5 yards.
Which Length of ribbon renders the least remainder?It follows from the task content that the amount of ribbon remaining in each case can be evaluated as follows;
For 1 2/5 yards: 1 2/5 - 1 1/3 = 1/15. renders only 1/15 a yard to waste.
For 1 and 1/6 yards would render a waste of 1 1/6 yards since it is not possible to make a ribbon out of it.
1 2/10 yards would render a waste of 1 and 1/5 yards since it is not possible to make a ribbon out of it.
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I need help ASAP!!!!
Answer:
look on symbolab got my answer from there'
Step-by-step explanation:
PLEASE HELP - PLEASE SHOW WORK Given the following functions, find each of the values: f(x)=x^2−7x+6 g(x)=x−1 (f+g)(−5)= ______ (f−g)(4)= ______
Answer:
(f+g)(-5) = 60(f-g)(4) = -9Step-by-step explanation:
These are the values we will need:
f(-5) = (-5)^2 -7(-5) +6 = 25 +35 +6 = 66
f(4) = 4^2 -7(4) +6 = 16 -28 +6 = -6
g(-5) = -5 -1 = -6
g(4) = 4 -1 = 3
__
(f+g)(-5) = f(-5) +g(-5) = 66 +(-6)
(f+g)(-5) = 60
__
(f-g)(4) = f(4) -g(4) = -6 -3
(f-g)(4) = -9
Simplify: (2x2 − 9x + 3) + (−7x2 + 4x − 2)
Answer:
-5x^2-5x=+1
Step-by-step explanation:
A student does an experiment and wants to make a graph comparing various amounts of materials. Which type of graph should the student choose?
Answer:
The plotting the points 1 and then you will be able to compare the materials and how they work in comparison to the other material
Answer:
Bar graph
Step-by-step explanation:
Cuz he will make bars in order to show the materi
which of these statements us true for f(x)=3•(9)^x
Answer:
C
Step-by-step explanation:
The y-intercept is at x=0, y=3.
A rectangular field measures 616m by 456m. Fencing posts are placed along it's sides at equal distances. What will be the distance between the posts if they are place as far apart as possible?
Answer: 766.41m
Step-by-step explanation:
Hi, since the situation forms 2 right triangles (see attachment) we have to apply the Pythagorean Theorem for one triangle.
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the diagonal distance between corners of the field, which is the distance between the posts if they are placed as far apart as possible ) and a and b are the other sides.
Replacing with the values given:
c^2 = 616^2 + 456^2
c^2 = 379,456+207,936
c^2 =587,392
c = √587,392
c = 766.41m
So, she is within the area serviced by the tower (20 miles)
Feel free to ask for more if needed or if you did not understand something.
Approximate the value of positive square root 5 to the nearest hundredth
Answer:
2.2
Step-by-step explanation:
Joey and Nolan are each solving the equation 13x - 42 = 18 - 7x. Joey's first step was to rewrite the equation as 20x - 42 = 18 while Nolan's first step was to rewrite the equation as 13x = 60 - 7x. Who is correctly applying the addition property of equality in the first step of his work? A. Only Joey B. Only Nolan C. Both Joey and Nolan D. Neither Joey nor Nolan
Answer:
Correct option: C.
(Both Joey and Nolan)
Step-by-step explanation:
The step Joey did is:
Add 7x to both sides of the equation
Then, he got:
13x - 42 + 7x = 18 - 7x + 7x
20x - 42 = 18
The step Nolan did is:
Add 42 to both sides of the equation
Then, he got:
13x - 42 + 42 = 18 - 7x + 42
13x = 60 - 7x
So both of them used correctly the addition property of equality in the first step of their work.
Correct option: C.
The science club is experiencing a growth in membership. On average, they are
seeing 2 new members sign up each week. If they started with 10 members which
function, S(x), represents the number of members in the science club after x weeks?
Answer:
S(x)= 10+2^x
Step-by-step explanation:
The correct function which represents the number of members in the science club after x weeks is,
S (x) = 10 + 2ˣ
We have,
The science club is experiencing a growth in membership.
On average, they are seeing 2 new members sign up each week.
Here, they started with 10 members.
Hence, The function S (x) which represents the number of members in the science club after x weeks is,
S (x) = 10 + 2ˣ
Where, x is number of weeks.
Therefore, The function is,
S (x) = 10 + 2ˣ
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tell me weather 16641 is a perfect square by division method an please show me the solution too
Answer:
yes
Step-by-step explanation:
you see we need to make pairs and then we divide each one by square numbers and I have given picture
Answer:
Yes, the number 16,641 is a perfect square.
Step-by-step explanation:
16641 is the 129th perfect square number
__________________________________________
1 2 9
1 1 66 41
1
22 66
44
249 22 41
22 41
258 0
Number = 16641
Square Root = 129
________________________________
Step-1 :
Make pair of digits of given number starting with digit at one's place. Put bar on each pair.
1 66 41
Step-2 :
Now we have to multiply a number by itself such that the product ≤ 1
Here 1×1=1≤1, So divisor is 1 and quotient is 1. Now do the division and get the remainder.
1
1 1 66 41
1
0
Step-3 :
Now , we have to bring down 66 and quotient 1 is multiplied by 2 becomes 2, which is starting digit of new divisor
1
1 1 66 41
1
2 66
Step-4 :
2 should be the digit at one's place of new divisor because when 22 is multiplied by 2 we get 44.
So new divisor is 22 and next digit of quotient is 2. Now do the division and get the remainder.
1 2
1 1 66 41
1
22 66
44
22
Step-5 :
Now , we have to bring down 41 and quotient 12 is multiplied by 2 becomes 24, which is starting digit of new divisor
1 2
1 1 66 41
1
22 66
44
24 22 41
Step-6 :
9 should be the digit at one's place of new divisor because when 249 is multiplied by 9 we get 2241.
So new divisor is 249 and next digit of quotient is 9. Now do the division and get the remainder.
1 2 9
1 1 66 41
1
22 66
44
249 22 41
22 41
0
Answer: 129 (proof 129^2) = 16,641 or 129 x 129 = 16,641
______________________________
Second Solution shortcut:
A perfect square is a number that can be expressed as the product of two equal integers.
The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work.
Try these steps first:
A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.
Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.
All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.
Let's try it...
Step 1:
What is the last number of 16,641? It is this number: 16641. The answer is 1. Is 1 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?
Answer: NO, 1 is not in the list of numbers that are never perfect squares. Let's continue to the next step.
Step 2:
We now need to obtain the digital root of the number. Here's how you do it:
Split the number up and add each digit together:
1 + 6 + 6 + 4 + 1 = 18
If the answer is more than one digit, you would add each digit of the answer together again:
1 + 8 = 9
What is the digital root of number 16,641?
Answer: 9
Step 3:
So now we know the digital root of 16,641 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 16,641 could be a perfect square!
Factoring
OK, so now we know that 16,641 could be a perfect square. We have to find the factors of the number to be sure.
Here are all of the factors of 16,641:
1 x 16,6413 x 5,5479 x 1,84943 x 387129 x 129
Highlighted in orange above is the factor combination that makes 16,641 a perfect square. Do you see why? A number can only be a perfect square if the product of two exactly the same numbers is equal to the original number.
Here's the proof: 129 x 129 = 16,641
a family of 8 has 3 of them being males what proportion of the family is female
Answer: not very sure but i think that may be 5
Step-by-step explanation:
E is in the corner by 10.5 on question 9
Answer:
see below
Step-by-step explanation:
7. The similar rectangles are W and Z.
8. EF = 18 * 1.8 = 32.4
9. BD = 20 / 2.5 = 8.
What is the measure of < B, in degrees?
Answer:
B. 32°
Step-by-step explanation:
Since two of the sides are 10 in length, then we can infer that ∠A and ∠C are congruent. So, both equal 74°. You add 74 + 74 + x = 180, x would equal 32°.
Answer:
B
Step-by-step explanation:
sum of angle in triangle is 180
and since its isosceles triangle, it means <C will be same with <A
so we know that A + C = 148.
so the value of B will be like this
B = 180° - (A+C)° = 180 - 148 = 32°
Which of the following expressions are equivalent to this expression: –1(0) = ? im lazy and dont wanna do it
Answer:
0
Step-by-step explanation:
Okay...um. Any number times 0 is 0 so the expression you choose should equal 0.
Which circle C shows a chord that is not a diameter?
Circle C is shown. A line is drawn from one side of the circle to the other side and goes through point C.
Circle C is shown. A line is drawn on the outside of the circle and intersects the circle at one point.
Circle C is shown. A line is drawn from point C to a point on one side of the circle.
Circle C is shown. A line goes from one point on the circle to another point on the circle.
Answer:
The answer is option D
Step-by-step explanation:
Just got it right on edge :)
Answer:
d
Step-by-step explanation:
HELPPP PLEASEE l
The gasoline mileage for two cars can be compared by finding the distance each car traveled and the amount of gasoline used. The table shows the distance that car M traveled using x gallons of gasoline.
The graph shows the distance, y, that car P traveled using x gallons of gasoline
Answer:
Car M:
50.4/2 = 25.2
car M uses up 1 gallon every 25.2 miles
Car P:
Just from the graph, you can see that it uses up 1 gallon every 30 miles
The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.
A class has 18 students. The teacher asks how many students in the class have pets and finds 5/9 of the students have pets. How many students have pets? * 1 point 9 8 10 11
Answer:
9 students
Step-by-step explanation:
5/9 of 18 is 10
Which data set is least Likely to resemble a normal distribution?
Look at picture
Answer: B) The heights of girls who live on a certain street in the city of Buffalo
Every answer choice starts with "the heights of all 14-year-old girls who", so we can ignore that part. Choice A describes the largest population while choice B describes the smallest population. In other words, choice A is very general and broad, while choice B is very specific and narrow. The more specific you get and the smaller the population is, the less likely its going to be normally distributed.
A number is selected from the set (1, 2, 3, 5, 15, 21, 29, 38, 500). If equal elemental probabilities are assigned, what is
the probability that the number chosen is either less than 29 or odd?
Answer:
[tex]\frac{7}{9}[/tex] OR 77.78%
Step-by-step explanation:
So, we first need to find out how many numbers fit the "less than 29 or odd" group.
This would be: 1, 2, 3, 5, 15, 21, and 29, which is a total of 7 numbers.
Next, we figure out the total amount of numbers in the population.
This would be: 1, 2, 3, 5, 15, 21, 29, 38, and 500, which is a total of 9 numbers.
Finally, we put the first number (7) over the total (9) = [tex]\frac{7}{9}[/tex]
[tex]\frac{7}{9}[/tex] is now able to be written in a percentage, if you need.
The probability is [tex]\frac{7}{9}[/tex] OR 77.78%
Please help, I need this answer
Answer:
6.4
Step-by-step explanation:
By the Pythagorean Theorem:
[tex]c=\sqrt{5^2+4^2}= \\\\\sqrt{25+16}= \\\\\sqrt{41}\approx 6.4[/tex]
Hope this helps!
Answer:
To solve we need to use pythogorean theorm. So first we take the square of both giving us 25, 16. Then we add them and get 41. So the answer is squareroot of 41 and if you round you get 6.4
Answer: is approx. 6.4Point B has coordinates (3,2). The x-coordinate of point A is negative 9. The distance between point A and point B is 15 units. What are the possible coordinates of point A?
Answer:
(-9,9) or (-9,-7) are the possible coordinates
Step-by-step explanation:
We can use the formula for the distance between two points to get this
Mathematically, this can be;
d = √(x2-x1)^2 + (y2-y1)^2
Now let our point A be (x1,y1) = (-9,n)
let’s say y1 is n for now
For point B, we have (x2,y2) = (3,2)
and our d is 15 units
Inputing the values, we have
15^2 = (3+9)^2 + (2-n)^2
225 = 144 + (2-n)^2
225-144 = (2-n)^2
(2-n)^2 = 81
(2-n) = √(81)
2-n = -9
or 2-n = 9
n = 11 or n = -7
Now the possible coordinate values of point A are;
(-9,9) or (-9,-7)
Answer:
Step-by-step explanation:The distance between points is given by the following equation:
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
Substituting we have:
15 = root ((- 9 -3) ^ 2 + (a-2) ^ 2)
We clear the value of a:
(15) ^ 2 = (root ((- 12) ^ 2 + (a-2) ^ 2)) ^ 2
225 = (- 12) ^ 2 + (a-2) ^ 2)
Rewriting:
225 = 144 + (a-2) ^ 2
225-144 = (a-2) ^ 2
81 = (a-2) ^ 2
a-2 = +/- root (81)
a = +/- 9 + 2
The possible values are:
a1 = 9 + 2 = 11
a2 = -9 + 2 = -7
Then, the possible coordinates of point a are:
(-11, 11)
(-11, -7)
Answer:
the possible coordinates of point a are:
(-11, 11)
(-11, -7)
What is the equation for ⨀C?
Answer:
A
Step-by-step explanation:
r^2 = (x - k)^2 + (y - h)^2
Work Shown:
(h,k) = (2,-2) is the center. So h = 2 and k = -2
r = 4 is the radius. We go 4 units from the center C to point P
Therefore,
(x-h)^2 + (y-k)^2 = r^2
(x-2)^2 + (y-(-2))^2 = 4^2
(x-2)^2 + (y+2)^2 = 16
Find the surface area of this triangular prism shown below
Answer:
Step-by-step explanation:
area of side triangles=2(1/2×6×4)=24 units²
area of 3 rectangles=6×7+2(5×7)==42+70=112 units²
or=(6+5+5)×7=16×7=112 units²
Total surface area=24+112=136 units²
Find the missing factor
Answer:
The missing factor is (9s+1)
Step-by-step explanation:
The missing factor is (9s+1) because of the following
(9s^2 + s) + (18s+2)
If we factor out s from 9s^2+s, we get s(9s+1).
If we factor out 2 from 18s+2, we get 2(9s+1)
putting these together, we get s(9s+1) + 2(9s+1). Factoring out the common term of 9s+1, we get (9s+1)(s+2). therefore, the missing factor is 9s+1
Arnold always sits in the second row of seats in his classroom. If there are 5 rows of seats behind Arnold and each row has 6 seats, how many seats are in the classroom?
Answer:
42 Seats.
Step-by-step explanation:
If Arnold is in the second row and there are 5 rows behind him, there are 7 rows because 2 + 5 equals 7.
So then, you multiply 6 times 7 since there are 7 rows and 6 seats in each row. And that equals 42.
Answer:
b:42
Step-by-step explanation: