There are 331 ways when 66 identical coins can be separated into three nonempty piles
Let the piles have a, b and c coins, with 0<a <b <c. Then, let b=a+k₁, and
c=b+k₂, such that each ki≥1.
The sum is then a+a+k₁+a+k₁+k₂= 66 ⇒ 3a+2k₁+k₂ = 66.
This is simply the number of positive solutions to the equation
3x+2y+z = 66.
If a = 1, then 2k₁ + k₂ = 63⇒ 1≤k₁ ≤31. Each value of k₁ corresponds to a unique value of k₂, so there are 31 solutions in this case.
Similarly, if a = 2, then 2k₁+k₂= 60⇒ 1≤k₁ ≤29, for a total of 29 solutions in this case.
If a = 3, then 2k₁+ k₁= 57 ⇒ 1 ≤ k₁ ≤28, for a total of 28 solutions.
In general, the number of solutions is just all the numbers that aren't a multiple of 3, that are less than or equal to 31.
We then add our cases to get
=1+2+4+....31=1+2+3+...31-3(1+2+3+...10)
=31*(32)/2-3(55)
=31*16-165
=496-165
=331
To know more about identical coins:
https://brainly.com/question/2397962
#SPJ4
I am a number. If you know the sum of 14 and 6 that will help you. I am that sum sqquered. I am
Answer: 4.4
Step-by-step explanation:
Answer:
400
Step-by-step explanation:
let the number be x
x= (14+6)²
x= 20²
x=400
What is the equation of the transformed function, g(x), after the transformations are applied to the graph of
the base function f(x)=√x to obtain the graph of g(x)?
A g(x) +4=√√√x+4
B g(x)=√√x+4 +5
C g(x) +5=√√x+4
D g(x)=√√x+5+4
Check the picture below, that's just a transformations template
so since we know that f(x) = √x, that means when x = 0, y = 0, so it touches the origin, so f(x) is the graph down below.
now, f(x) has moved to the left by 5 units and up by 4 units, based on the template that means C = 5 and D = 4 whilst B = 1
[tex]g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{5}} ~~ +\stackrel{D}{4}\implies g(x)=\sqrt{x+5} ~~ +4[/tex]
Question 8
Find the measure of each angle indicated
47
We know the angles in a triangle add up to 180 degrees. Adding the two angles we know, ( 47 and 86) we get 133. Simply subtract 133 from 180 to get 47 degrees.
Squaroot of p^10 where p>0
Answer:
p^5
Step-by-step explanation:
p^10/2=p^5
consider a grid of points. find the number of squares with all their vertices belonging to the points of this grid.
The number of squares that can be formed on a grid with n points on one side is (n² - (n-1)²).
The number of squares that can be formed with all their vertices belonging to the points of a grid can be calculated using the formula:
n² - (n-1)²
where n is the number of points on one side of the grid.
This is because there are n² total points on the grid, and each point can be used as a vertex for n-1 squares (when n>1) in the horizontal and vertical directions. However, each of these squares is counted twice, once for each corner point. So we subtract (n-1)² to account for the overcounting.
For example, if there are 4 points on one side of the grid, the number of squares that can be formed is 4² - (4-1)² = 16 - 9 = 7 squares.
In general, the number of squares that can be formed on a grid with n points on one side is (n² - (n-1)²).
To learn more about the grid of points at
https://brainly.com/question/11618662?referrer=searchResults
#SPJ4
In a randomly generated list of numbers from 0-6, what is the chance that each number will concur
In a randomly generated list of numbers from 0 to 6, each number has an equal chance of occurring. Since there are 7 numbers total (0, 1, 2, 3, 4, 5, and 6), the chance of each number occurring is 1/7 or about 14.3%.
A probability simple definition is what?
A probability is a measure of the likelihood of a particular event occurring. It is a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. A probability of 0.5, for example, indicates that the event has an equal chance of occurring or not occurring. A probability can be expressed as a fraction, decimal, or percentage.
Learn more about probability
https://brainly.com/question/13604758
#SPJ1
There were 20 dolphins near the shore. 15 more dolphins swam in. How many dolphins are near the shore now?
Answer: 35
Step-by-step explanation: 20 +15= 35
In the town of Tower Hill, the number of cell phones in a household is a random variable W with the following distribution:
W 0 1 2 3 4 5
P(W) 0.1 0.1 0.25 0.3 0.2 0.05
The probability that a randomly-selected household has at least two cell phones is
A. 0.20.
B. 0.25.
C. 0.55.
D. 0.70.
E. 0.80.
Answer:
the answer is alphabet c
For the function v (t) = 4t² - 6t + 2, determine the value(s) of t on the closed interval [0, 3] where the value of the derivative is the same as the average rate of change.
The slope of a secant line or the average rate of change over a relatively brief period of time can be used to approximate the derivative. The closer the interval is to the actual instantaneous rate of change, slope of the tangent line, or slope of the curve, the more accurate the result is.
What is average rate?Average Rate is a single rate that applies to property at many locations and is calculated as the weighted average of the separate rates that are appropriate at each site. Examples of average rates of change include: 80 kilometers per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.Therefore,
[tex]& \int_0^6\left|t^2-8 t+12\right| d t \quad \quad \text { Distance traveled over }[a, b] \\[/tex]
[tex]\int_0^2 t^2-8 t+12 d t+-\int_2^6 t^2-8 t+12 d t & \text { distance }=\int_a^b\left|x^{\prime}(t)\right| d t \\[/tex]
[tex]t^2-8 t+12=0[/tex]
To learn more about average rate, refer to:
https://brainly.com/question/24313700
#SPJ4
Chris baked 45 cookies. His family are n of them. Using n, write an expression for the number of cookies that remained
The expression that shows the number of cookies that remained is:
C = 45 - n
How many cookies remained?We know that Crhis baked a total of 45 cookies, and his family ate n of them.
The number of cookies that remained is equal to the difference between the initial amount, which is 45, and the number of cookies that the family ate, which is n.
(Where a difference refers to a subtraction)
Then the expression for the number of cookies that remained is:
cookies = 45 - n
That is the expression that depends on the value n.
Learn more about expressions by reading:
https://brainly.com/question/723406
#SPJ1
ron ate 2/5 of a pie, carolyn ate 3/10 of the same pie. how much of the pie is left
Answer: 3/10
Hope this helps :)
Step-by-step explanation:
2/5= 4/10
4/10 + 3/10= 7/10
3/10 of the pie is left
HELP!!!!! Brainliest!!!
Pic
The slope of the given linear relationship is 5 (A).
From the question, we have 5 different points that create a linear relationship. To determine the slope of the linear relationship, we can choose 2 random sequence points.
We might choose:
Point 1 = (0,-2)
Point 2 = (1,3)
We can find the slope of the relationship using formula of:
m = y2 - y1
x2 - x1
m = 3- (-2)
1 - 0
m = 5
1
m = 5
To ensure our finding, we can choose another pair of random points, for example:
P1 = (-2, -12)
P2 = (-1, -7)
We can use the slope formula:
m = y2 - y1
x2 - x1
m = -7 - (-12)
-1 - (-2)
m = 5
1
m = 5
Hence, the slop of the linear relationship between all the given points are 5.
Learn more about Slope here: brainly.com/question/29291376
#SPJ1
use the definition of continuity and the properties of limits to show that the function is continuous at the number a
Continuity is the formulation of a function that varies with no breaks or jumps. The concepts of limits and continuity have been used to show that the function is continuous at the number a below.
If a graph has no holes asymptotes or breaks at any point then the function is said to be continuous. Or if we can draw the function without lifting our pen then it is called continuous.
The conditions which it should satisfy are,
1)The limit must exist at that point.
2) The function must be defined at that point, and
3)The limit and the function must have equal values at that point. So,
A function f(x) is said to be continuous at x=a if,
lim f(x) = f(a)
x→a
A function is said to be continuous on the interval [a,b] if it is continuous at each point in the interval.
Learn more about Continuity on
https://brainly.com/question/24898810?referrer=searchResults
#SPJ4
Congress is debating a proposed law to reduce tax rates. If the current tax rate is r%, then the proposed rate after x years is given by this formula: r/1+1/1+1rRewrite this formula as a simple fraction. Use your formula to calculate the new tax rate after 1 year, 2 years, 5 years, and 15 years. 1 year____2 years____5 years___15 years____
Would tax rates increase or decrease over time? O increase O decrease Congress claims that this law would ultimately cut peoples' tax rates by 75%. Do you believe this claim? Explain.
The simple fraction is [tex]= \frac{x + 1}{2x + 1}r[/tex]
In math, what is a fraction?
A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction.
Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
[tex]= \frac{r}{1 + \frac{1}{\frac{1 + 1/x }{} } }[/tex]
[tex]= 1 + 1/x[/tex]
= x + 1/x we have
= [tex]\frac{1}{x + 1/x}[/tex]
[tex]= \frac{x}{x + 1}[/tex]
[tex]= 1 + \frac{x}{x + 1}[/tex]
[tex]= \frac{ 2x + 1}{x + 1}[/tex]
r%*x+1/(2x+1)
[tex]= \frac{x + 1}{2x + 1}r[/tex]
reduce to the appropriate fraction. The denominator was then brought up and the numerator down as I normalized.
Learn more about fraction
brainly.com/question/10354322
#SPJ4
The complete question is -
Congress is debating a proposed law to reduce tax rates. If the current tax rate is r%, then the proposed rate after x years is given by this formula: r 1 1 1 1 x . Rewrite this formula as a simple fraction.
How is a thermometer different than a number line
Answer:
A thermometer is different than a number line because a thermometer goes from the bottom up with a minimum count. As a number line goes both ways with a pointer indicating where the point stands on either side.
Step-by-step explanation:
WHAT IS THIS?: Evaluate 4+ (m - n)^4 when m = 7 and n =5.
Evaluation of 4+ (m - n)^4 when m = 7 and n =5 is -108
What is Foil method?To combine binomials, utilize the FOIL Method.
An abbreviation is F O I L. First, Outside, Inside, and Last are represented by the letters, denoting the sequence of multiplying terms. For your solution, multiply the first word, an outside term, the inside term, the very last term, and then join like terms.
FOIL specifies the specific terms to multiply and their order.
First - multiply the first terms
Outside - multiply the outside/outer terms
Inside - multiply the inside/inner terms
Last - multiply the last terms
Given;
4+ (m - n)^4
m=7, n=5
Now, the binomial formula of (m - n)^4 by foil method
=m^4-4m^3n+6m^2n^2-4mn^3+n^4
=2401-4(343)(5)+6(49)(25)-4(7)(125)+500
=2401-6860+7350-3500+500
=-109
Therefore, the value of expression by foil method will be -109
To know more about foil method:
brainly.com/question/28527940
#SPJ1
For this exercise, use the position function s(t) = −4.9t^2 + 160, which gives the height (in meters) of an object that has fallen for t seconds from a height of 160 meters. The velocity at time t = a seconds is given by lim t→a s(a) − s(t) a − t . When will the object hit the ground? At what velocity, v, will the object impact the ground?
Answer:
5
Step-by-step explanation:
u just know
Find the perimeter of the following trapezoid:
Answer:
17 feet
Step-by-step explanation:
perimeter is the measurement of the border of a shape
2.5 + 6 + 8 + 2.5 = 17
e solid has a triangular base in the x y-plane. the solid has ---select--- in the x z-plane. the solid has ---select--- in the y z-plane. the solid has ---select--- in the plane z
The triangular base in the xy plane can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
In the xz plane, the solid has a plane defined by the equation z = f(x). This equation can be derived from the equation of the base by substituting the y values with the corresponding mx + b values. Similarly, in the yz plane, the solid has a plane defined by the equation z = g(y). This equation can be derived from the equation of the base by substituting the x values with the corresponding (y - b)/m values. To calculate the area of the solid, we can use the formula A = 1/2h(b1 + b2), where h is the height of the solid and b1 and b2 are the lengths of the two bases. The area of the solid can then be found by substituting the appropriate values into this formula.
Learn more about triangular base here:
https://brainly.com/question/16909441
#SPJ4
what is the slope through the line of (9, 10) and (7, 2)
The slope of a line is calculated as the change in the y-coordinates (rise) divided by the change in the x-coordinates (run). Using the coordinates (9, 10) and (7, 2), we can calculate the slope as:
(10 - 2) / (9 - 7) = 8 / 2 = 4
So, the slope through the line of (9, 10) and (7, 2) is 4.
Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132.$
$\textbf{(A) }5\qquad\textbf{(B) }7\qquad\textbf{(C) }9\qquad\textbf{(D) }11\qquad \textbf{(E) }12$
132 is the total of all two-digit numbers and their reversal digits. The solution is (C) 9. Nine two-digit numbers, including 21 + 12 = 33, 32 + 23 = 55, 43 + 34 = 77, 54 + 45 = 99, 65 + 56 = 121, 76 + 67 = 143, 87 + 78 = 165, 98 + 89 = 187, and 109 + 901 = 132, meet this characteristic.
132 is the total of all two-digit numbers and their reversal digits. We must look at all potential two-digit numbers and add the number to its reversed digits in order to count the number of two-digit numbers that satisfy this property. The range of the two-digit numbers is 10 to 99. Starting with the number 11, which does not satisfy the stated criteria because 10 + 01 = 11 is not equal to 132. Then, we will look at 11 + 11, which is not equal to 132, and find that it is 22. This method will be repeated until a two-digit number is found that meets the specified attribute. As an illustration, 21 + 12 Equals 33, which is not the same as 132. This technique will be repeated until a two-digit number, such as 65 + 56 = 121, is found that satisfies the property. This operation will be repeated until nine two-digit values, such as 109 + 901 = 132, satisfy the property. As a result, the response is (C) 9.
Learn more about reversal digits here
https://brainly.com/question/2142858
#SPJ4
Express 2x=5 in the form of ax+ by+c=0 and find the value of a,b and c
Answer:
[tex]2x = 5 \\ 2x + 0y - 5 = 0 \\ a = 2 \\ b = 0 \\ c = - 5[/tex]
Simplify. Rewrite the expression in the form x^nx n x, start superscript, n, end superscript. \dfrac{x^{5}}{x^2}= x 2 x 5
The rewritten expression in the form of xⁿ is x^3
In math, the expression refers the combination of variables, constants and exponents.
Given,
Here we have the expression x^5 / x^2
Now, we have to rewrite this expression into the form of xⁿ.
As per the law of exponents, we have rewrite the given expression as,
=> x^5*x^-2
Now, as per the law of exponent of multiplication, we can write it as,
=> x^5-2
Now, it can be further simplified as,
=> x^3
expression can be with one variable two variable or any number similar concept for constant also that is it can be any number
To know more about Expression here.
brainly.com/question/14083225
#SPJ4
What is 3(4 + x) + 2 x 3 = ?
Suppose it takes 6.4 pounds of seed to completely plant one acre of land. Boris has 18.5 acres of land. Find the amount of seed he needs.
Answer:
1.2 Acres
Step-by-step explanation:
Match the following:
Whole Number:
Fraction:
Answer Choices: If the similar figure is smaller than the original then the scale factor is a ______. If the similar figure is larger than the original then the scale factor is a __________
If the similar figure is smaller than the original then the scale factor is a fraction. If the similar figure is larger than the original then the scale factor is a whole number.
How do scale factors work ?The scale factor is a ratio that compares the corresponding side lengths of two similar figures. If the similar figure is smaller than the original, the scale factor is a fraction less than 1, for example, 2/3 or 3/4. This means that the corresponding side lengths of the similar figure are 2/3 or 3/4 of the corresponding side lengths of the original figure.
On the other hand, if the similar figure is larger than the original, the scale factor is a whole number greater than 1, for example, 2 or 3.
Find out more on scale factors at https://brainly.com/question/29967135
#SPJ1
What equation(s) represent the vertical asymptote(s) of the graph of y = 1/x^2 -4? J) x= -4 and x =4 K) x= -2 and x =2 L) x= 0 only M) x= 2 only N) x= 4 only
The denominator of the function, n(x), is the place where vertical asymptotes can be located. If the numerator, t(x), is not zero for the same value of x, then the vertical asymptotes can be determined by solving the equation n(x) = 0 where n(x) is the denominator.
How to find the calculation?Despite not being a part of the function graph, a vertical asymptote is a vertical line that serves as a guide.
It happens at an x-value that is outside the function's domain, therefore the graph can never cross it.
1/x^2 -4
Domain of 1/x² - 4 :
Solution : x < -2 or -2 < x < 2 or x > 2
Interval Notation ; ( -∝ , -2) ∪ (-2 ,2) ∪ (2 , ∝).
Range of 1 / x² - 4 :
Solution : f(x) ≤ - 1/4 or f(x) > 0
Interval Notation : ( -∝ , - 1/4) ∪ (0,∝)
Axis interception points of 1 / x² - 4 :
y Intercepts : (0 , - 1/4)
Asymptotes of 1 / x² - 4:
Verticals x = -2. x = 2,
Horizontal y = 0
Extreme Points of 1/x² - 4 :
Maximum (0, -1/4).
To Learn more About vertical asymptotes refer To:
https://brainly.com/question/26124207
#SPJ1
Write the expression in simplest form. 5/3-√2=
Answer:
[tex] \sf \: \frac{5 - 3 \sqrt{2} }{3} [/tex]
Step-by-step explanation:
Given expression,
→ (5/3) - √2
Let's simplify the expression,
→ (5/3) - √2
→ (5/3) - ((√2 × 3)/(1 × 3))
→ (5/3) - (3√2/3)
→ (5 - 3√2)/3
Hence, answer is (5 - 3√2)/3.
Answer:
[tex]\dfrac{15+5\sqrt{2}}{7}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{5}{3-\sqrt{2}}[/tex]
To write the given rational expression in its simplest form we need to rationalise the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of an expression is where we change the sign in the middle of the two terms. Therefore, the conjugate of the denominator of the given expression is:
[tex]3+\sqrt{2}[/tex]Multiply the numerator and denominator by the conjugate of the denominator:
[tex]\dfrac{5}{3-\sqrt{2}} \cdot \dfrac{3+\sqrt{2}}{3+\sqrt{2}}[/tex]
Simplify:
[tex]\implies \dfrac{5(3+\sqrt{2})}{(3-\sqrt{2})(3+\sqrt{2})}[/tex]
[tex]\implies \dfrac{15+5\sqrt{2}}{9+3\sqrt{2}-3\sqrt{2}-2}[/tex]
[tex]\implies \dfrac{15+5\sqrt{2}}{9-2}[/tex]
[tex]\implies \dfrac{15+5\sqrt{2}}{7}[/tex]
which expression is equivalent to 5M-3N when M=3x-2 and N=2x-5
A9x+5
B9x-25
C21x+5
D21x-25
Answer:
A. 9x+5
Step-by-step explanation:
[tex]5(3x-2)-3(2x-5)\\15x-10-6x+15\\9x+5[/tex]
which of the following shows a correct side-by-side bar chart with store location on the horizontal axis and side-by-side bars of the percentage of time spent on each task?
The resulting bar chart would show that in Store A, the employees spend 30% of their time on stocking, 40% on cashiering, and 30% on cleaning.
To create a side-by-side bar chart for this data, we would first organize the data into a table with store locations as the rows and tasks as the columns. Each cell in the table would contain the percentage of time spent on that task at that store location.
For example, the table might look like this:
Stocking Cashiering Cleaning
Store A 30% 40% 30%
Store B 25% 35% 40%
Store C 35% 25% 40%
To create the bar chart, we would then place the store locations on the x-axis and use different colors to represent the different tasks. The length of each bar would correspond to the percentage of time spent on that task at that store location.
The resulting bar chart would show that in Store A, the employees spend 30% of their time on stocking, 40% on cashiering, and 30% on cleaning.
Similarly, the chart will provide an easy visual representation of the time spent on each task at each store location.
Learn more about bar charts here:
https://brainly.com/question/30119156
The complete question is -
The management of a retail company wants to analyze the time spent by employees on different tasks at different store locations. The data collected shows the percentage of time spent on tasks such as stocking, cashiering, and cleaning at three store locations: Store A, Store B, and Store C. Create a side-by-side bar chart to represent this data and analyze the results.
#SPJ4
