(a) The number of pathways in the plane from point (0, 0) to point (110, 111) when each step consists of walking one unit up or one unit to the right is known as the number of ways to go to a point in a grid using just right and up moves.
This is a classic combinatorial problem known as a binomial coefficient. The binomial coefficient C(110+111, 110) = C(221, 110) = 221!/(110!111!) is the number of ways to travel from (0, 0) to (110, 111).
(b) The number of paths from (0, 0) to (210, 111) where each step consists of walking one unit up or one unit to the right and the path must pass through (110, 111) is the product of two binomial coefficients.
First, as calculated in section 1, the number of pathways from (0, 0) to (110, 111) is C(110+111, 110) = C(221, 110). Second, there are C(210+211, 210) ways to get from (110, 111) to (210, 111). (210, 211). (421, 210). C(221, 110) * C is the total number of paths found by multiplying these two binomial coefficients (421, 210).
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question is on the picture
Answer:
C. √5 =2.236.
Step-by-step explanation:
it's the sq root of 2²+1² = 5.
An object is dropped from 28 feet below the tip of the pinnacle atop a 928-ft tall building. The height h the object after t seconds is given by the equation h=-16t^(2)+900. Find how many seconds pass before the object reaches the ground.
Answer: it takes 7.5 seconds for the object to reach the ground.
Step-by-step explanation:
The equation for the height of the object is h=-16t^2+900. To find the time when the object reaches the ground, we need to find the value of t when h=0.
Therefore, we can set h=-16t^2+900 = 0 and solve for t:
-16t^2+900 = 0
-16t^2 = -900
t^2 = 56.25
t = sqrt(56.25)
t = 7.5
So, it takes 7.5 seconds for the object to reach the ground.
There are 28 students in a class. Fourteen of those students are men.
What percent of the class are men ?
Answer: 50%
Step-by-step explanation:
If fourteen are men, and there are twenty-eight in the class, then the fraction that are men are -
14/28.
14/28 is 1/2 which is equal to 0.5
0.5 converted to percent is 50%
Find the inequality represented by the graph!
The inequality is y ≥ 1/2x.
How to find the calculation?We must first identify the linear equation that describes the line in the graph in order to determine the inequality it reflects.
So, using the two points (0, 0) and (2, 1), we first get the slope of the line:
m = y2 - y1 /x2 - x1 = 1-0 / 2-0 = 1/2
Now, we can determine the linear expression using one point, the slope, and the slope-point formula.
y - y1 = m( x - x1)
y - 0 = 1/2(x - 0 )
y = 1/2 x
Then, to evaluate the linear equation, we only need to select a test point from the shaded region, which will be (0,1):
y = 1/2 x
1 = 1 / 2 (0)
1 = 0
Because 1 is greater than 0 and the line is solid, we can infer that the inequality sign is in the proper position.
Therefore, the inequality is y ≥ 1/2x.
The Complete Question is inequality.
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The length of a rectangle is 6 less than twice its width. The perimeter is 90. Find the dimensions of the rectangle
The length of the rectangle is 20 and the width is 13.
What are the dimensions?The perimeter of a rectangle = 2(length + width)
Width = w
Length = 2w - 6
90 = 2(w + 2w - 6)
In order to determine the value of w, take the following steps:
Divide both sides of the equation by 2
90/2 = w + 2w - 6
45 = w + 2w - 6
Combine and add similar terms:
45- 6 = w + 2w
39 = 3w
Divide both sides of the equation by 3
w = 39/3
w = 13
In order to determine the length, substitute for w in the equation that represents the length.
Length = 2(13) - 6
= 26 - 6
= 20
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The inequality d < 4. 75 represents the prices d in dollars that Paige is willing to pay for popcorn. The inequality d < 8. 00 represents the prices d in dollars that Paige is willing to pay for a movie ticket. At how many theaters would Paige be willing to buy a ticket and popcorn?
At two theaters Paige would be willing to buy a ticket and popcorn.
Consider the following table that shows ticket and popcorn prices at five movie theater chains.
Here, the inequality d < 4. 75 represents the prices d in dollars that Paige is willing to pay for popcorn.
And the inequality d < 8. 00 represents the prices d in dollars that Paige is willing to pay for a movie ticket.
To find: the number of theaters that would Paige be willing to buy a ticket and popcorn
We can observe that the number of theaters that has the movie ticket price less than 8 dollars are two.
The number of theaters that has the popcorn price less than 4.75 dollars are three.
And the number of theaters that has the popcorn price less than 4.75 dollars as well as the movie ticket price less than 8 dollars are two.
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suppose the probability is 0.25 that a certain athlete wins in each race. find the expected number of races until she needs to run to win a race.
Answer:
4 races
Step-by-step explanation:
Four races is expected to win
P = 0.25 = 25% = 1/4
Hope this helps
if k+7=16 then find the value of 8k-72
Answer:
0
Step-by-step explanation:
[tex]k + 7 = 16\\k = 9\\8k - 72\\8(9) - 72 = 0[/tex]
What is the domain of the function
f(x) =
X+2
x≤-B
*>B
x2-6
Answer:
x ≥ -6
Step-by-step explanation:
Answer: x ≥-6
explanation: im pretty good at math
Scholars measured how two different class plants grew over a week. They wrote the equations below to represent the height of each plant.
● Bean plant: h = 0.25d, where h is the height in inches and d is the number of days
● Sunflower: h = 10 + 0.02d, where h is the height in inches and d is the number of days
Brie says that both plants have a proportional relationship between the height and number of days because each plant grows by the same amount each day.
Do you agree or disagree with Brie? Explain why
I disagree with Brie.
Only the bean plant has a proportional relationship. The sunflower does not have a proportional relationship.
How to determine whether to agree or disagree with Brie?In a proportional relationship, the ratio of the dependent variable (height) to the independent variable (number of days) is constant. In this case, the ratio of height to number of days is not constant for both plants.
For the bean plant, the ratio of height to number of days is 0.25, which is constant. This means that the bean plant grows by 0.25 inches per day.
For the sunflower, the ratio of height to number of days changes as the number of days increases, it starts with 10 and increases by 0.02 each day. This means that the growth rate of the sunflower is not constant, it starts with 10 and increases by 0.02 inches per day.
Thus, I disagree with Brie.
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If $\angle A=20^\circ$ and $\angle AFG=\angle AGF,$ then how many degrees is $\angle B+\angle D?$
The angles b and d have 80° degrees.
Trigonometry is the branch of mathematics that studies and defines the relations between the side lengths and angles of a triangle.
One key fact to know in all trigonometry problems is that all angles within a normal triangle = 180 degrees.
By creating algebraic equations based on the information given in the question, we can find missing values using this key fact.
Given:
Angle a = 20 deg
Angle b = Angle d = x
x = ?
We know that since two angles are equal, it is an isosceles triangle.
Using algebra and the given information, we create an equation:
20+2x=180
2x=180-20
2x=160
x=80
Therefore, we know that angles b and d are 80° degrees.
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2x - 3 y = -1 y = x - 1 Solve each system of equations. Show all your work.
x = 4, y = 3 for the given equation 2x - 3 y = -1 , y = x - 1 .
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in various languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfil the equality are known as the equation's solutions.Given data :
2x - 3 y = -1
y = x - 1
In a system of equations, there are multiple equations present. We actually look for the point at which these equations are identical when we attempt to solve a system of equations problem. In order to solve such an issue, we typically employ the substitution method, which involves inserting the values of one variable into the initial expression in order to determine the value of the second variable.
3y=2x+1
y= (2/3)x + 1/3 = x-1
x/3 =4/3
x = 4, y=3
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I took a random sample of size 49 students score from their sampling distribution test. The
score was selected from the Regular Statistics class. The mean of the score of the population of
Regular statistics is 63 and standard deviation is 14. What is the probability in the sample selected will have mean score more than 65.
The probability of a sample mean more than 65 is given as follows:
0.1587 = 15.87%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 63, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2[/tex]
The probability of a sample mean above 65 is one subtracted by the p-value of Z when X = 65, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (65 - 63)/2
Z = 1
Z = 1 has a p-value of 0.8413
1 - 0.8413 = 0.1587 = 15.87%.
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Find the area of a circle with radius, r = 7.27m. Give your answer rounded to 2 DP.
The area of a circle is given by the formula:
A = πr^2
Where A is the area of the circle, π is approximately 3.14 and r is the radius of the circle.
Given the radius, r = 7.27m, we can substitute this into the formula and calculate the area of the circle.
A = π * 7.27^2 = π * 52.5129
A = 165.9 m^2
The area of the circle is 165.9 m^2. Rounded to 2 decimal places, the area of the circle is 165.90 m^2
how to graph
y=-1/2x + 3
y=5
Answer:
The graph would look like this
Step-by-step explanation:
Determine if the given point is a solution of the system of inequalities.
Help please.
The inequality equations is
a) The point ( -9 , 4 ) lies on the inequality relation
b) The point ( 6 , -2 ) lies on the inequality relation
c) The point ( 0 , -4 ) does not lie on the relation
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
a)
Now , let the first point be represented as P ( -9 , 4 )
The shaded region is below 4 in the y axis and less than -4 in the x axis
So , the point ( -9 , 4 ) does lies on the inequality equation graph
b)
Now , let the first point be represented as Q ( 6 , -2 )
The shaded region is below -8 in the y axis and less than 8 and more than 4 in the x axis
So , the point ( 6 , -2 ) does lies on the inequality equation graph
c)
Now , let the first point be represented as R ( 0 , -4 )
The shaded region is above -8 in the y axis and more than -4 in the x axis and less than -1
So , the point ( 0 , -4 ) does not lie on the inequality equation graph
Hence , the inequality equations is solved
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John was able to assemble 10 bicycles in 8 hours. Considering that he is consistent assembling each bicycle, how many bicycles can John assemble in 1 hour?
To find out how many bicycles John can assemble in 1 hour, you can use the formula:
rate = work/time
where rate is the number of bicycles John can assemble in 1 hour, work is the total number of bicycles he assembled, and time is the total time it took him to assemble the bicycles.
In this case, the work is 10 bicycles and the time is 8 hours. So, we can substitute these values into the formula:
rate = 10 bicycles / 8 hours
rate = 1.25 bicycles/hour
So John can assemble 1.25 bicycles in 1 hour, assuming he works at a consistent pace.
The teacher gave a true and false quiz where P(true) = 0.5 for each question. Interpret the likelihood that the first question will be true.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
Answer: Don't trust me on this.
Step-by-step explanation:
I want to say it will be equally unlikely and equally likley, because it's 0.5, which is half. (Tell me if im right.)
2x²+4x+5=ax²+(2b-6)x+c what does a,b,c represent
Answer: A=2 B=4 C=5
Step-by-step explanation:
Simplify 4(7 - 3) + 11.
Answer:
27
Step-by-step explanation:
First do the () part which is (7-3) equal 4×4 equal 16 so then u will add 16+11 getting 27
Draw number line to show the following
0>x≥5
The graph of the inequality 0 > x ≥ 5 can be seen on the image at the end.
How to graph the inequality?Here we want to graph the following inequality:
0 > x ≥ 5
So, x is strictly larger than 0 and smaller than or equal to 5.
Because x = 0 is not a solution, we will draw an open circle at x = 0.
Then a line that goes to the right until x = 5, where we will draw a closed circle, because that value belongs to the solution set, then the inequality is the one you can see below.
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A y=x
The graph shown above is the graph of which parent function after a vertical shift up 1 unit?
y=x²
y=x³
Dy=x²
B
1
C
X
The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.
What happens when a function is shifted vertically?
Because this transformation involves adding a positive or negative constant to the function, a vertical shift, which moves the graph up or down, is the simplest shift. In other words, regardless of the input, the output result of the function receives the same constant.
The y-value adjusts when a function shifts vertically. While the y-value modifies the shift's magnitude, the x-value remains constant.
We add the value to the y-term if it changes upward. We shall deduct that amount from the y-term if it shifts downward.
The simplest transformation is a vertical shift, which entails moving the graph up or down. This is because this transformation only requires changing the function's sign from positive to negative.
The only variable that alters in vertical shifts of the fundamental linear equation y = mx + b is the b value, or the y-intercept.
The graph shown above is the graph of the parent function y=x after a vertical shift up 1 unit.
Hence, The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.
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Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.
What will be the location of T' in the image trapezoid S'T'U'V'?
answers
12,6
12,7
16,7
16,6
Point T becomes (18, 2), which equals T', when we transform STUV using the technique above.
What is meant by transformation?Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.
The movement of two-dimensional figures about a plane or coordinate system is described by mathematical transformations. A preimage, also known as an inverse image, is a two-dimensional shape that exists without any change. After transformation, the figure is shown in the image.
If we pay attention to the transformation, it is obvious that every point in the rectangle JKLM is changed to a point that is 13 units to the right and 3 units to the bottom.
The T in STUV is currently at (5, 5).
When we transform STUV using the formula above, point T becomes (5 + 13, 5 - 3) (18, 2), which equals T'.
Therefore, the correct answer is option b. (18, 2).
The complete question is:
Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied to trapezoid STUV.
What will be the location of T' in the image trapezoid S'T'U'V'?
a. (18, −2)
b. (18, 2)
c. (15, −2)
d. (15, 2)
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Factor the expression completely. x^3 y^4 −x^4 y^4
The algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF
What is HCFThe H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.
The two terms x³y⁴ and x⁴y⁴ of the algebraic expression x³y⁴ - x⁴y⁴ have their highest common factor to be x³y⁴ such that:
x³y⁴ × 1 = x³y⁴
x³y⁴ × x = x⁴y⁴
and
x³y⁴ - x⁴y⁴ = x³y⁴ × 1 - x³y⁴ × x
x³y⁴ - x⁴y⁴ = x³y⁴(1 - x)
Therefore, the algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF
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In the diagram below, Ray AB bisects Angle CAD. Solve for x and the measure of Angle CAD. Show all of your work.
La base de un cuadrado sin marco mide el doble de su altura si el marco tiene 2 pulgadas de ancho y su área es de 208 pulgada cuadradas encuentre las dimensiones del cuadrado sin marco
If the frame has 2 inches of width and its area is 208 inches of square. The dimensions of square without frame is 6.75 and 13.50.
Let the width of rectangle without frame is b.
Let the height of rectangle without frame is h.
Since the base of a square without frame is the double of its height. So
b = 2h...............(1)
The frame has 2 inches of width, so;
The width of rectangle with frame = b + 4
The height of rectangle with frame = h + 4
The area of the rectangle with frame = 208 inches of square
The formula of area of rectangle
A = Height × Width
(h + 4) × (b + 4) = 208
Putting the value of b from the equation 1
(h + 4) × (2h + 4) = 208
Simplify
h(2h + 4) + 4(2h + 4) = 208
2h^2 + 4h + 8h + 16 = 208
2h^2 + 12h + 16 = 208
Subtract 208 on both side, we get
2h^2 + 12h - 192 = 0
Taking common 2 from the equation, we get
h^2 + 6h - 86 = 0
After factoring the equation we get
h = (−3+√95, −3−√95)
h = 6.75, -12.75
The height can't be negative so we use the positive value of h.
Now putting the value of h in the equation 1.
b = 2×6.75
b = 13.50
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The complete question is:
The base of a square without frame is the double of its height, if the frame has 2 inches of width and its area is 208 inches of square. Find the dimensions of the square without frame.
To weave a bracelet, Charlene needs 7 pieces of brown thread. Each piece of thread must be 1/3 yard long. How many thread should she buy to weave the bracket?
Charlie must buy 7/3 yards long brown thread to weave a bracelet.
Based on number of pieces of brown thread and length of each piece, the formula that will be formed is -
Length of thread required = number of threads × length of each piece
Keep the values in formula to the length of piece required to weave a bracelet
Length of thread required = 7 × 1/3
Performing multiplication on Right Hand Side of the equation
Length of thread required = 7/3 yards
Thus, 7/3 yards of length is required to weave the bracelet.
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Determine the solution to the inequality.
one third times the absolute value of the quantity x plus 1 end quantity is greater than or equal to 3
x ≤ −8 or x ≥ 8
x ≤ −10 or x ≤ 9
x ≤ −2 or x ≥ 2
x ≤ −10 or x ≥ 8
The solution of the inequality |x + 1| ≥ 3 is:
x ≥ 2 or x ≤ -4
How to solvethe inequality?Here we want to solve the absolute value inequality:
|x + 1| ≥ 3
The absolute value can be decomposed into two inequalities, these are:
(x + 1) ≥ 3
(x + 1) ≤ -3
Now we can solve these two inequalities to get:
x ≥ 3 - 1 = 2
x ≤ -3 - 1 = -4
Then the solution is:
x ≥ 2 or x ≤ -4
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Answer: Its D
Step-by-step explanation:
I looked up the answer
Let us assume that you started a job on 08/21/2019. You graduated on 05/20/2022. How many days have you been working at the job as a student?Group of answer choices121512879051003
I began my job as a student on 08/21/2019 and worked for a total of 905 days until my graduation on 05/20/2022. This is calculated by taking the total number of days between the start and end date - 3 years - which is 1095, and then subtracting the weekends and holidays - 190 days - during that period. This demonstrates my commitment to my job as a student.
08/21/2019 - 05/20/2022
= 3 years
= 1095 days
- 190 days (weekends and holidays)
= 905 days
Starting on 08/21/2019, I have been working at my job as a student for 905 days as of 05/20/2022. This is determined by taking the total number of days - 3 years - between the start date and end date, which is 1095 days, and then subtracting 190 days for the weekends and holidays during that period. This leaves me with 905 days of work as a student.
I began my job as a student on 08/21/2019, and my graduation was on 05/20/2022. After calculating the total number of days between the two dates - 3 years - which is 1095, and then subtracting the weekends and holidays during that period - 190 days - I have worked as a student for 905 days up until my graduation date. This demonstrates the commitment and dedication I had to my job as a student.
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Which inequality describes the relationship between points A and B on the number line?
A. A > B
B. B ≤ A
C. B > A
D. B = A
From the Number in the graph , the inequality that describes the relationship between points A and B on number line is (c) B > A .
In the Number Line we can see that , Both the points A and B are between 0 and 1 on the number line ,
We know that , On a number line , the further right we move the higher numerical values we get ;
On the number line the point B is further to the right , as well as closer to 1 than A , So , we can conclude that B is greater than A .
Therefore , The point B is greater than point A .
The given question is incomplete , the complete question is
Which inequality describes the relationship between points A and B on the number line ?
(a) A > B
(b) B ≤ A
(c) B > A
(d) B = A
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