3pts) Suppose the man is traveling from (0,0) to (50, 51). How many unique paths can the man take to make this trip
Answers
The man has approximately 1.5820708e+30 unique paths to choose from to make the trip from (0,0) to (50,51).
To calculate the number of unique paths the man can take to travel from point (0,0) to point (50,51), we can use the concept of combinatorics.
The man needs to take a total of 50 steps horizontally (to reach the x-coordinate 50) and 51 steps vertically (to reach the y-coordinate 51). He can only move either to the right (horizontally) or upwards (vertically) at each step.
To reach the destination, the man needs to make a total of 50 + 51 = 101 steps.
Now, we need to determine in how many ways the man can arrange these 101 steps.
The number of unique paths can be calculated using the binomial coefficient formula, which is given by:
C(n, k) = n! / (k!(n-k)!),
where n represents the total number of steps and k represents the number of steps in one direction (either horizontally or vertically).
In this case, n = 101 (total steps) and k = 50 (number of steps in one direction).
Using the formula, we can calculate the number of unique paths as:
C(101, 50) = 101! / (50!(101-50)!) = (101! / 50!51!) = 101C50.
Calculating this combination:
C(101, 50) = 101C50 = 101! / (50!51!) ≈ 1.5820708e+30.
Therefore, the man has approximately 1.5820708e+30 unique paths to choose from to make the trip from (0,0) to (50,51).
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Related Questions
slope of 1,-7 and -3-4
Answers
\(\large \mathfrak{Solution : }\)
Slope of the given line is :
\( \dfrac{y_2 - y_1}{x_2 - x_1} \)where ,
\(x_2 = 1\)\(x_1 = - 3\)\(y_2 = - 7\)\(y_1 = - 4\)let's solve :
\( \dfrac{ - 7 - ( - 4)}{1 - ( - 3)} \)\( \dfrac{ - 3}{4} \)Slope = -3 / 4
Please solve this in fully simplified slope-intercept form
Answers
Answer:
y = (1/4)x-1
y=\(\frac{1}{4}\) x - 1
Step-by-step explanation:
y=mx + b where m is the slope and b is the y intercept.
Just a quick look at the graph - - - the line is increasing, as x increases, y increases, so our slope should be positive.
We can see the y intercept is -1.
y=mx -1
m = slope = rise/run = (y2-y1)/(x2-x1)
Pick 2 points (any 2!) so we can find the slope.
(-4,-2) and (8,1)
slope = (-2-1)/(-4-8)
= -3/-12 = 1/4
y = (1/4)x-1
The midpoint M of line segment AB has
coordinates (-3,4). If point A is the origin, (0,0),
what are the coordinates of point B?
Answers
Answer:
(-6,8)
Step-by-step explanation:
Find the coordinates of the unknown endpoint: (-6,8)
Answer: (-6,8)
The value of \(\sqrt{6}\) is not -4 because ______.
Answers
The solution of the value is mathematically given as
√6 =2.449
This is further explained below.
What is square Root?Generally, In mathematics, the term "square root" refers to a component of a number that, when multiplied by itself, results in the same value as the original number.
As an example, both 3 and –3 are square roots of the number 9.
A number y is said to have a square that is equal to a given number x if and only if it satisfies the following condition: y2 = x.
Another way to express this is to say that the number y has the same value as its own square. For example, the square roots of 16 are 4 and -4, since 42 divided by 2 is 16.
In conclusion,
√6 is not -4
because
√6 =2.449
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Given that the econd term of a equence i 8 and the fourth term i 2, Franci wrote the explicit rule an = 4 · ( 1 4 )n − 1 for the equence. Complete the explanation of hi error
Answers
Francis made an error in writing the explicit formula. The correct formula should be an = 4 * (1/4)⁽ⁿ⁻¹⁾, not an = 4 * (1/4)ⁿ⁻¹. The exponent should be (n-1), not just n, to correctly represent the sequence where the second term is 8 and the fourth term is 2.
Explicit Formula Error CorrectionTo determine the error in Francis' formula, we need to apply it to the known terms of the sequence and see if it produces the correct values. For example, for the second term, n = 2, so using Francis' formula:
an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)¹ = 4 * 1/4 = 1
But the second term of the sequence is 8, not 1. So the formula is incorrect.
Similarly, for the fourth term, n = 4, so using Francis' formula:
an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)³ = 4 * 1/64 = 1/16
But the fourth term of the sequence is 2, not 1/16. So the formula is still incorrect.
Therefore, we can conclude that the formula written by Francis is not correct and needs to be corrected to accurately describe the sequence.
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write it as an equation show all work
For a field trip 4 students rode in cars and the rest filled nine busses. How many students were in each bus if there were 472 students on the trip.
ps. i will give brainlest an 100 points
Answers
Answer:52 in each buss
Step-by-step explanation: 472 - 4 (the students in the car)= 468
468 divide by 9(how many busses)
= 52 (students in each buss)
9x + 4=472
9x=468
X= 52
Given the function f(x) = -5|x + 1| + 3, for what values of x is f(x) = -12?
Answers
Answer:
x = 2 or x = -4
Step-by-step explanation:
-5|x + 1| + 3 = -12
Add -3 to both sides.
-5|x + 1| = -15
Divide 5 into both sides.
|x+1| = 3
Possibility 1:
x + 1=3
x = 2
Possibility 2:
x + 1 = - 3
x = -4
Answer:
Step-by-step explanation:
This is our absolute value equation for which we want the values of x that make it true:
-5 | x + 1 | + 3 = -12. Subtracting 3 from both sides gives us
-5 | x + 1 | = = -15. Divide both sides by -5 to get
| x + 1 | = 3
This says, in words, "how many units from 3 is -1 on a number line?"
We have the following 2 equations:
x + 1 = 3 and x + 1 = -3
Solving the first one for x:
x = 2
Solving the second one for x:
x = -4
Both 2 and -4 are 3 units from -1 on a number line.
What scientific value for n will make this equation true? (4. 8 × 10–3)(n) = 9. 6 × 109 2. 0 × 10–6 2. 0 × 10–3 2. 0 × 103 2. 0 × 1012.
Answers
The scientific value/notation for n that makes the equation true is 2.0 × 10^(12). o find the value of n that makes the equation true, we need to solve for n in the equation: (4.8 × 10^(-3))(n) = 9.6 × 10^(9).
Step 1: Divide both sides by (4.8 × 10^(-3)):
We divide both sides of the equation by (4.8 × 10^(-3)) to isolate the variable n. This step is performed to cancel out the coefficient (4.8 × 10^(-3)) on the left side of the equation. The division yields:
n = (9.6 × 10^(9)) / (4.8 × 10^(-3))
Step 2: Simplify the expression on the right side:
To simplify the expression on the right side, we divide the numbers (9.6 / 4.8) and subtract the exponents (9 - (-3)).
9.6 / 4.8 = 2
9 - (-3) = 9 + 3 = 12
n = 2 × 10^(12)
The simplified expression is 2 × 10^(12). This means that the value of n that satisfies the equation is 2.0 × 10^(12).
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1. Which of the
following
most accurately describes the
translation of the graph from
y = x² to y = (x - 2)² +1?
Answers
The translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B. shift of 2 units left and then shift of 1 unit up.
Explain about the translations:In geometry, a translation is a transfer that occurs either horizontally to a left or right as well as vertically up or down. It may also consist of a mix of the two.
In mathematics, a translation moves an object throughout the coordinate plane while preserving its dimensions and shape. After a translation, its area and orientation remain unchanged.A vertical shift, horizontal shift, or indeed a combination of the two can be referred to as a translation in mathematics.Given data:
Parent function- y = x²
New function - y = (x - 2)² +1
First there is a shift of 2 units to the left as 2 is subtracted from x value.Now, there is shift of 1 unit upward, as 1 is added to the function.Thus, the translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B. shift of 2 units left and then shift of 1 unit up.
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Complete question:
1. Which of the following most accurately describes the translation of the graph from y = x² to y = (x - 2)² +1?
A. shift of 2 units right and then shift of 1 unit up.
B. shift of 2 units left and then shift of 1 unit up.
Rizwan writes down three numbers a, b and c
(a) (i) Find a: b: c
a: b = 1:3
b:c= 6:5
Answers
If a: b = 1: 3 and b: c= 6: 5, then a: b: c = 2: 6: 5
It is given that a:b = 1:3, so let
a = x .....(i)
b = 3x .....(ii)
where x => some number
Also, it is given that b:c= 6:5, so let
b = 6y .....(iii)
c = 5y .....(iv)
where y => some number
Now, from equations (ii) and (iii),
b = 3x
b = 6y
This implies that
3x = 6y
=> x = 2y .....(v)
Using equation (v) in equation (i), we get
a = x
=> a = 2y .....(vi)
Using equations (vi), (iii) and (vi), we can say
a = 2y
b = 6y
c = 5y
a : b : c
=> (2y) : (6y) : (5y)
=> 2 : 6 : 5
Therefore, a: b: c = 2 : 6 : 5
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The monthly rent charged for a store at Center Street Mall is $ 2 per square foot of floor area. The floor plan of a store at Center Street Mall is shown in the figure below, with right angles as indicated and all distances given in feet. How much monthly rent is charged for this store?
$1,656
$1,872
$6,624
$7,380
$7,488
Answers
NEED HELP WITH THIS PLEASE. NEED THE ANSWER ASAP
Answers
Answer:
PY = 8
Step-by-step explanation:
Lets run down the other three to show why they're wrong
MY=8
By P.T, that's wrong (PERPENDICULAR)
PM=MY
We can't prove that with the given
XY=42
Again, by P.T., this is false
BTW: You can prove PY=8 by proving XMP congruent to YMP by SAS
Marcos decide abrir una cuenta de ahorro para financiar en el futuro los estudios de su hijo recien nacido. Por suerte, el banco le ofrecio la tasa de interes anual de 4,8%. El monto que deposito Marcos en la cuenta fue de $1000 000.Si no retira el dinero ni los intereses, ¿que capital tendra a los 5 años? ¿que capital tendra cuando su hijo cumpla 18 años?
Answers
Answer:
Resultados debajo
Step-by-step explanation:
Dada la siguiente información:
Tasa de interes anual (i)= 4,8%
Inversión inicial (VP)= $1.000.000
Para calcular el valor final (VF), debemos usar la siguiente formula:
VF= VP*(1 + i)^n
Para 5 años:
VF= 1.000.000*(1,048^5)
VF= $1.264.172,72
Para 18 años:
VF= 1.000.000*(1,048^18)
VF= $2.325.429,02
¿Como se escribe 4 790,40 en letra?
Answers
479040 in the international system of number names is Four Hundred and Seventy-nine Thousand and Forty.
What is the international system of number names?First, it is important to know about natural numbers. Natural numbers are those integers that are greater than or equal to 1.The international system of writing number names involves writing number names according to the system ones, tens, thousands, ten thousand, hundred thousand, million, ten million, hundred million, etc.So, 479040 in words:
In the international system of number names.Four Hundred and Seventy-nine Thousand and Forty.Therefore, 479040 in the international system of number names is Four Hundred and Seventy-nine Thousand and Forty.
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Solve this I’ll give you brainliest
Answers
Answer:
44+18x-3=6+25x
41+18×=6+25x
35=7x
×=5
Ana needs 40 mg of medicine twice a day. Each medicine tablet contains 15 mg, how many tablets will Ana need for 2 days?
Answers
Answer:
She will need 10 full tablets and two thirds of a tablet
Step-by-step explanation:
First we will find how many tablets ana needs for one day:
In each day ana needs 40x2 mg of medicine, they come in tablets of 15 mg. In one day, she needs 80 / 15 = 5 and 1/3 of a tablet.
In two days, she needs double that amount. (5 and 1/3) x 2 = 10 and 2/3
Ana need to take 10 and 2/3 tablets for 2 days.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
It is given that,
Ana need 40 mg tablet twice a day.
So, Total mg taken in a day = 40*2 mg = 80 mg
Since each tablet contains 15 mg
So, Total tablets taken in a day = Total mg taken / 15
⇒ Total tablets taken in a day = 80 / 15
⇒ Total tablets taken in a day = 5 and 1/3 tablets
Therefore Tablets needed in 2 days = 2*Total tablets taken in a day
⇒ Tablets needed in 2 days = 2*16/3
or, Tablets needed in 2 days = 32/3
or, Tablets needed in 2 days = 10 and 2/3 tablets
Thus,Ana need to take 10 and 2/3 tablets for 2 days.
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Which of the following angle pairs would apply to the alternate exterior angles theorem?
Answers
Answer:
First option, angles 1 and 7
Step-by-step explanation:
The alternate exterior angles theorem is talking about angles that are on opposite sides of the "middle line" we'll call it that are on the outside of the parralel lines. In this case, it's 1 and 7 & 2 and 8.
(Edit: Thank you for Brainliest!)
Answer: If I remember the theorem correctly, It would be
8 and 2,
1 and 7,
4 and 6,
5 and 3.
I think that’s it although I’m not 100% sure.
Which ordered pair is a solution to the equation? 3x-4y=13
A, (3, 1)
B. (3, -1)
C. (-1, 3)
D. (1, 3)
Need asap (will give brainliest to the best answer*
Answers
When you put the values of x and y in the equation
3(3) - 4(-1) = 13
9 + 4 =13
13=13 (correct answer)
When you try putting the rest of the values in the equation the answer doesn’t match ,hence ,the correct answer is B.I hope I get the brainliest answer!
If There was a game and the game cost 130$ and you only have 53$ what would you do to find the amswer
Answers
Answer:
130-53= $77
Step-by-step explanation:
Step-by-step explanation: games dont cost 130 dollars
I need help with this it’s geometry this is my 2nd time asking for help
Answers
Answer:
The measure of angle WVX is 140°.
Step-by-step explanation:
Let x be the measure of angle WVX.
\( \frac{14}{9} \pi = 2x\)
\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)
Answer:
angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.
so, the answer is 140 degrees.
PLSSS HELP IF YOU TURLY KNOW THISSS
Answers
Answer: divide both sides by 5
Answer: C. divide both sides by 5
Step-by-step explanation:
Just a fun game....
1. Pick a number 1-10
2. Now add 5
3. And then add 2
4. Subtract with the number you started with
5. Your answer is 7.
If it isn’t 7, put what number you picked to start with and the number you ended with.... copy and paste this on your page for others to have fun and do it too! Don’t leave out anything... Good luck
Answers
Step-by-step explanation:
omg it actually got seven lol
Can you solve for X inside the correct code for question four?
Answers
Answer
CIAD
Step-by-step explanation
The Pythagorean theorem states:
\(c^2=a^2+b^2\)where a and b are the legs and c is the hypotenuse of a right triangle.
Applying this theorem to triangle 1:
\(\begin{gathered} x^2=77^2+36^2 \\ x^2=5929+1296 \\ x^2=7225 \\ x=\sqrt{7225} \\ x=85 \end{gathered}\)Then, the first letter is C.
Applying the theorem to triangle 2:
\(\begin{gathered} x^2=39^2+80^2 \\ x^2=1521+6400 \\ x^2=7921 \\ x=\sqrt{7921} \\ x=89 \end{gathered}\)Then, the second letter is I.
Applying the theorem to triangle 3:
\(\begin{gathered} x^2=25^2+100^2 \\ x^2=625+10000 \\ x^2=10625 \\ x=\sqrt{10625} \\ x=103.08 \end{gathered}\)Then, the third letter is A.
Applying the theorem to triangle 4:
\(\begin{gathered} x^2=17^2+52^2 \\ x^2=289+2704 \\ x^2=2993 \\ x=\sqrt{2993} \\ x=54.71 \end{gathered}\)Then, the fourth letter is D.
I’m not sure I need help
Answers
Answer:
D) \(1 < x\leq 4\)
Step-by-step explanation:
1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)
Which of the following allows for someone to draw conclusions about a population from the information collected in a population sample? a. magnitude statistics b. central tendency c. inferential statistics d. effect size
Answers
The correct answer is c. Inferential Statistics.
Inferential statistics is the branch of statistics that allows for drawing conclusions about a population based on the information collected from a sample. When conducting research or surveys, it is often impractical or impossible to collect data from an entire population.
Instead, a representative sample is chosen, and inferential statistics are used to make inferences or predictions about the larger population. By analyzing the characteristics and patterns observed within the sample, inferential statistics enable researchers to make generalizations or draw conclusions about the population as a whole.
This process involves applying various statistical techniques, such as hypothesis testing and confidence intervals, to estimate population parameters and assess the reliability of the conclusions. Magnitude statistics, central tendency, and effect size are important concepts in statistics, but they do not specifically address the ability to draw population-level conclusions from sample data.
Magnitude statistics focuses on the size of the effect or relationship between variables, central tendency measures summarize the central values of a dataset, and effect size quantifies the strength of an effect or relationship.
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Find the value of Y. Please help. Will give Brainlyest if your correct.
Answers
Answer:
Step-by-step explanation:
by intersecting chord theorem, 27*y = 13*17
y=13*17/27=8.185=8.19
please solve thanks lovee
Answers
Answer:
m∠1 = 93.5°
Step-by-step explanation:
By theorem of intersecting chords inside a circle,
If two chords intersect inside a circle, angle formed between the chords measure half the sum of the measures of the intercepted arcs.
m∠1 = \(\frac{1}{2}(92+95)\)
= \(\frac{187}{2}\)
= 93.5°
Therefore, measure of angle 1 is 93.5°.
Prove that: √(sec x + 1)/(sec x - 1) = 1/(cosec x - cot x)
Answers
Answer:
Sorry Bro
Step-by-step explanation:
I don't know the ans plzz donnot mind
\(\large\underline{\sf{Solution-}}\)
Consider LHS
\(\rm :\longmapsto\: \sqrt{\dfrac{secx + 1}{secx - 1} } \)
can be rewritten as
\(\rm \: = \: \sqrt{\dfrac{\dfrac{1}{cosx} + 1 }{\dfrac{1}{cosx} - 1} } \)
\(\rm \: = \: \sqrt{\dfrac{\dfrac{1 + cosx}{cosx}}{\dfrac{1 - cosx}{cosx}} } \)
\(\rm \: = \: \sqrt{\dfrac{1 + cosx}{1 - cosx} } \)
On rationalizing the numerator, we get
\(\rm \: = \: \sqrt{\dfrac{1 + cosx}{1 - cosx} \times \dfrac{1 - cosx}{1 - cosx} } \)
\(\rm \: = \: \sqrt{\dfrac{1 - {cos}^{2} x}{ {(1 - cosx)}^{2} } } \)
We know,
\(\red{\rm :\longmapsto\:\boxed{\tt{ {sin}^{2}x + {cos}^{2}x = 1}}}\)
So, using this, we get
\(\rm \: = \: \dfrac{ \sqrt{ {sin}^{2} x} }{1 - cosx} \)
\(\rm \: = \: \dfrac{ sinx }{1 - cosx} \)
\(\rm \: = \: \dfrac{1}{ \: \: \: \: \dfrac{1 - cosx}{sinx} \: \: \: \: } \)
\(\rm \: = \: \dfrac{1}{ \: \: \: \: \dfrac{1}{sinx} - \dfrac{cosx}{sinx} \: \: \: \: } \)
\(\rm \: = \: \dfrac{1}{ \: \: \: \: cosecx - cotx \: \: \: \: } \)
Hence, Proved
\(\rm \implies\:\: \boxed{\tt{ \sqrt{\dfrac{secx + 1}{secx - 1} } = \frac{1}{cosecx - cotx}}}\)
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MORE TO KNOWAdditional Information:-
Relationship between sides and T ratios
sin θ = Opposite Side/Hypotenuse
cos θ = Adjacent Side/Hypotenuse
tan θ = Opposite Side/Adjacent Side
sec θ = Hypotenuse/Adjacent Side
cosec θ = Hypotenuse/Opposite Side
cot θ = Adjacent Side/Opposite Side
Reciprocal Identities
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
sin θ = 1/cosec θ
cos θ = 1/sec θ
tan θ = 1/cot θ
Co-function Identities
sin (90°−x) = cos x
cos (90°−x) = sin x
tan (90°−x) = cot x
cot (90°−x) = tan x
sec (90°−x) = cosec x
cosec (90°−x) = sec x
Fundamental Trigonometric Identities
sin²θ + cos²θ = 1
sec²θ - tan²θ = 1
cosec²θ - cot²θ = 1
And 7/8 hours Greg reads 2/3 chapters what’s the unit rate in chapters per hour?
Answers
The unit rate in chapters per hour is 21/16 hours
How to calculate the unit rate?Greg read 7/8 hours in 2/3 chapter
The unit rate can be calculated as follows
7/8= 2/3
1= x
cross multiply both sides
2/3x= 7/8
x= 7/8 ÷ 2/3
x= 7/8 × 3/2
x= 21/16
Hence 21/16 chapters is read in one hour
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when there are two coefficients, the resulting confidence sets are: part 2 a. rectangles. b. trapezoids. c. squares. d. ellipses.
Answers
Depending on the two coefficients, the confidence sets are either rectangles, trapezoids, squares, or ellipses.
When a confidence set contains two coefficients, the coefficients determine the shape of the confidence set. Depending on the two coefficients, the confidence sets are either rectangles, trapezoids, squares, or ellipses. When the coefficients are the same, as in a linear regression, rectangles are created. When the coefficients are different, as they are in a quadratic regression, trapezoids are created. When the coefficients are inversely connected, squares are created. Finally, ellipses are created when the coefficients, as in a cubic regression, are both distinct. The resulting confidence set can therefore take any of the four previously described shapes depending on the coefficients.
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