Numbers of ways to distribute 10 identical cards into 3 boxes is 36
Combination is is a way of selecting items from a collection where the order of selection does not matter.
Formula of combination:
Let a x-combination of a set is a subset of x distinct elements of S. If the set has n elements, the number of x-combinations is equal to the binomial coefficient.
ⁿCₓ = n(n-1)(n-2)(n-3). . . (n-x+1) / (x-1)(x-2)(x-3) . . . .(1)
which can be written as ⁿCₓ = n! / (n-x)! x! , when n > x
ⁿCₓ = 0 , when n < x
Where n = distinct object to choose from
C = Combination
x = spaces to fill
According to the question,
Number of identical cards : n =10
Number of box cards are being distributed : x = 3
Number of ways to distribute when no condition is given : ⁿ⁺ˣ⁻¹Cₓ₋₁
If we place one one card in each box then
Number of cards left with us = 10 - 3
= 7
Now, condition of at least one cards in each box is satisfied ,
Then total number of ways to distribute 7 cards into 3 = ⁷⁺³⁻¹C₃₋₁
=> ⁹C₂ = 9! / (9 - 2)! 2!
=> 9×8×7! / 7!2!
=> 9×8/2
=> 9×4
=>36 ways
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it isexpectedthatthehomevaluesinsandiegowillrise,on average,3percent eachyear.how muchisthevalueofahome in sandiegoexpectedtorise after20years?
The value of a home in San Diego will increase by 80.6% in 20 years.
Here, we are given that the value of a home in San Diego increases by 3 percent each year.
This means that suppose the value of a home today is V, then its value in a year from now will be V(1 + 0.03)
Thus, its value in 20 years will be-
V(1 + 0.03)(1 + 0.03).......(1 + 0.03)
This, can be written as-
[tex]V(1 + 0.03)^{20}[/tex]
= V × [tex]1.03^{20}[/tex]
= V(1.806)
= 1.806V
Thus, we see that the value of the home increases from V to 1.0806V in 20 years. The percentage change will be-
100(1.806V - V)/V
= 100 × 0.806V/V
= 80.6%
Thus, the value of a home in San Diego will increase by 80.6% in 20 years.
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at a price of $8 in this diagram, profit per unit is approximately , and total profit is approximately . $2.50; $36 $8.00; $114 $5.00; $60 $5.50; $78
The profit per bag is approximately $2.50 and the total profit is approximately is $36 , the correct option is (c) .
In the question ,
a graph of relation of price and quantity is given .
Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost
that means P = MC .
price is given as = $8 ,
Form the graph ATC = $5.5
per unit profit can be calculated using the formula ,
Per unit profit = Price - ATC
per unit profit = 8 - 5.5
= $2.5
From the graph , the quantity is Q = 14.4 (approximately)
Total profit is calculated using the formula
Total Profit = (profit per unit) × (quantity)
Total Profit = 2.5 × 14.4
= $36
Therefore , The profit per bag is approximately $2.50 and the total profit is approximately is $36 .
The given question is incomplete , the complete question is
This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is and the total profit is .
(a) $5.50 , $78
(b) $5.00 , $60
(c) $2.50 , $36
(d) $8.00 , $114
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A quare room ha a floor area of 25 quare feet the height of the room i 6 feet what i the total area of all 4 wall
The total area of all four walls is 150sq.m
What do you mean by surface area?
A solid object's surface area is a measurement of the total area that the surface of the object takes up. In mathematics, the area of a plane region or plane area refers to the area of a shape or planar lamina, whereas the area of a surface or the boundary of a three-dimensional object is referred to as the surface area.
Solution Explained:
Given in question,
Base floor area = 25sq.ft
Height = 6ft
So, the total area of all four walls is,
= Area of base X Height
= 25 X 6
= 150 sq.m
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Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 484848 paintings to the local museum. Each of the 121212 collectors will donate the same number of paintings.
The expression for the number of paintings Sergio will have in his art collection after his donation is p - 4
How to calculate the expression?Number of Sergio's paintings = p
Total number of paintings to donate = 48
Number of collectors to donate (including Sergio) = 12
Number of paintings donated by each collector = Total number of paintings to donate ÷ Number of collectors to donate
= 48 ÷ 12
= 4 paintings per collector
Therefore,
Number of paintings Sergio will have in his art collection after his donation = Number of Sergio's paintings - Number of paintings donated by each collector
= p - 4
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Complete question
Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings. How many paintings will Sergio have in his art collection after his donation? Write your answer as an expression
Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was 160160160 meters away. After 333 seconds of driving, she was 858585 meters away from the safe zone.
Complete the equation for the relationship between the distance and number of seconds.
Answer:
The required function formula is,
D(t) = 160 - 25 t
Given,
The total distance of her from the safe zone = 160 meters,
And, after 3 seconds she is 85 meters far away from the safe zone,
Thus, the total distance she covered in 3 seconds = 160 - 85 = 75 meters, Since, she drove at a constant speed,
Also,
Thus, the distance she will cover in t seconds = 25 t
( Because, Distance = Speed × Time )
Hence, the total distance of her from the safe zone after t seconds, D(t) = 160 - 25t
Which is the required function formula.
Step-by-step explanation:
a solid aluminum cylinder with density equal to 2700 kg/m3 has a weight equal to 0.66 n in air and an apparent weight of 0.26 n when immersed in an unknown liquid.
The density of unknown liquid is 7.447 kg/m³
According to the question,
Density of a solid aluminum cylinder : d = 2700 kg/m³
Weight of cylinder in the air = 0.66N
Weight of cylinder when immersed in an unknown liquid = 0.26N
The volume of the cylinder : v = m /d
where , m is mass of cylinder and d is density
Mass of cylinder : m = g/W
Where , g is acceleration due to gravity = 9.8m/s²
And w is weight of cylinder in air = 0.66N
Substituting the values of g and w
Therefore , m = 9.8 / 0.66
=> m = 14.8 kg
So, Volume of cylinder = 14.8 / 2700
=> V = 5.481 × 10⁻³m³
To calculate the density of liquid ,
Density of liquid = Upthrust / (volume of object × acceleration due to gravity)
Upthrust of the liquid = 0.66 - 0.26
=> 4 × 10⁻¹N
Volume of cylinder = 5.481 × 10⁻³m³
Acceleration due to gravity = 9.8m/s²
Therefore , The density of unknown liquid = 4 × 10⁻¹N / (5.481 × 10⁻³m³ × 9.8m/s²)
=> 4 × 10⁻¹N / 53.71× 10⁻³
=> 0.4 / 0.05371
Hence , the density of liquid is 7.447 kg/m³
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What is the place value of 432?.
Place value of 432 is 400 +30+02 .
What is place value?
In math, each digit in a very variety features a place value. Place value is outlined because the price pictured by a digit in a very variety on the premise of its position within the variety.
Main body:
The place value of a digit will increase by 10 times as we move left on the place worth chart and reduces by ten times as we tend to move right.
The place of digit 4 will be hundreds.
The place of digit 3 will be tens.
The place of digit 2 will be ones.
Hence place value of 432 is 400 +30+02 .
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when short-run aggregate supply decreases, it means that the short-run aggregate supply curve shifts to the _____ and the quantity of aggregate output that producers are willing to supply _____.
Answer:
Step-by-step explanation
33
Tim sells two types of pizza. He charges
$10 for a cheese pizza
and $15 for a
pepperoni pizza. Yesterday he sold
64 pizzas in all.
For every cheese pizza,
he sells 3 pepperoni
pizzas. How
much
money did he make selling pizzas
yesterday?
I understand the first part but the second I don’t understand
Answer:
The answer to the second question is B
Step-by-step explanation:
Cosine is a trigonometric function that is the ratio between the side next to an acute angle in a right triangle and the hypotenuse.
The base of S is a circular disk with radius 5r. Parallel cross-sections perpendicular to the base are isosceles triangles with height 5h and unequal side in the base. (a) Set up an integral for the volume of S. b) By interpreting the integral as an area, find the volume V of S.
The volume of the given shape is 392.7hr² sq. units.
Given, the base of S is a circular disk with radius 5r.
Parallel cross-sections perpendicular to the base are isosceles triangles with height 5h and unequal side in the base.
we have to find the volume of the shape we are given,
As, Volume = area × height
Now, area = πr²
area = 3.14×(5r)²
area = 78.54r²
as, height = 5h
then, Volume = 78.54r²×5h
Volume = 392.7hr²
Hence, the volume of the given shape is 392.7hr² sq. units.
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consider the matrix . part (a): find the eigenvalues, a basis for each eigenspace, and the algebraic and geometric multiplicity of each eigenvalue for the matrix .
The eigen values of the given matrix [tex]\left[\begin{array}{ccc}0&0&-2\\1&2&1\\1&0&3\end{array}\right][/tex] is 1 , 2 and 2 .
In the question ,
the matrix is given as [tex]\left[\begin{array}{ccc}0&0&-2\\1&2&1\\1&0&3\end{array}\right][/tex] .
The eigen values can be determined by using the characteristic equation ,
|A - λI | = 0
So , [tex]\left|\begin{array}{ccc}0-\lambda&0&-2\\1&2-\lambda&1\\1&0&3-\lambda\end{array}\right| = 0[/tex]
simplifying the above determinant , we get
-λ [(2-λ)(3-λ) - 0| - 0 -2[0 -(2-λ)] = 0
-λ[λ² - 5λ + 6] + 4 - 2λ = 0
-λ³ [tex]+[/tex] 5λ² -8λ [tex]+[/tex] 4 [tex]=[/tex] 0
λ³ - 5λ² + 8λ -4 = 0
Substituting λ = 1 in the above equation ,
we get ,
1 - 5 + 8 - 4 = 0
0 = 0
So , yes λ = 1 is a factor of the equation.
So , the characteristic equation can be written as
(λ - 1)(λ² - 4λ + 4) = 0
(λ -1)(λ² - 2λ -2λ + 4) = 0
(λ - 1)(λ - 2)(λ - 2) = 0
So , λ = 1 , λ = 2 and λ = 2 .
Therefore , the eigen values are λ = 1 , λ = 2 and λ = 2 .
The given question is incomplete , the complete question is
Consider the matrix [tex]\left[\begin{array}{ccc}0&0&-2\\1&2&1\\1&0&3\end{array}\right][/tex] . Find the eigen values of A .
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Please help, I do give brainiest
Answer:
5 units
Step-by-step explanation:
The formula is [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
You have to plug in the information you are given, into the formula, and you will have: [tex]d=\sqrt{(2-(-1))^2 + (0-4)^2}[/tex]
Then simplify.
[tex]d=\sqrt{(3)^2+(-4)^2}[/tex]
[tex]d=\sqrt{9+16}[/tex]
[tex]d=\sqrt{25}[/tex]
And the square root of 25 is 5.
A bond has a $1,000 par value, 12 years to maturity, and an 8% annual coupon and sells for $980. a. what is its yield to maturity (ytm)?
The Yield to Maturity (YTM) of the Bond is 8.27%
Given data,
A bond has a $1,000 par value, 12 years to maturity, and an 8% annual coupon and sells for $980,
Par Value = $1,000
Annual Coupon Amount = $80 [$1,000 * 8%]
Bond Price = $980
Maturity Years = 12 Years
To find its yield to maturity (YTM),
Therefore, Yield to Maturity
[YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [ (Par Value + Bond Price) / 2 ]
= [$80 + {($1,000 – $980) / 12 Years)] / [($1,000 + $980) / 2]
= [($80 + $1.67) / $990]
= [$81.67 / $980]
= 0.0827
= 8.27%
Hence, the Yield to Maturity (YTM) of the Bond is 8.27%
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How do you determine if something is a factor of a function?.
if the function is divided and we get the remainder of zero then it is said to be a factor of a function
According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.
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Suppoe that a population parameter i 0. 4 and many ample are taken from the population. If the ize of each ample i 100, what i the tandard error of the ditribution of ample proportion?
The standard error of the distribution of sample proportion is 0.0490.
What is the standard error of the distribution?
The standard error of a statistic's sampling distribution, denoted as x, describes how much the computed statistics should differ from one another when calculated from a sample of similar size and drawn from similar population models.
We have,
Population parameter (P) = 0.4,
n = 100,
The standard error (S.E.) =?
The formula of standard error (S.E.) = [tex]\sqrt{\frac{P(1 - P)}{n} }[/tex]
By using the formula:
S.E. = √0.4(1 - 0.4)/100
S.E. = √0.0024
S.E. = 0.0489
S.E. = 0.0490
Hence, the standard error of the distribution of sample proportion is 0.0490.
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A comic book store is having a sale. You can buy 20 comic books for $35. What is the cost of 8 comic books during the sale?
You're correct answer would be $14.
[tex]35/20 = 1.75[/tex]
[tex]8x1.75=14[/tex]
Answer:
14
Given:
[tex]20 books= 35[/tex]
Step-by-step explanation:
[tex]35/20=1.75[/tex]
[tex]8*1.75= 14[/tex]
a is the one in which every two pairs of vertices are connected. a. directed graph b. weighted graph c. complete graph d. connected graph
A Connected Graph is the one in which every two pairs of vertices are connected.
The correct option is (d)
Given,
In the question:
A_____ is the one in which every two pairs of vertices are connected.
a. directed graph
b. weighted graph
c. complete graph
d. connected graph
To choose the correct answer.
What is connected graph with example?
A graph is said to be connected if there is a path between every pair of vertex. From every vertex to any other vertex, there should be some path to traverse. That is called the connectivity of a graph. A graph with multiple disconnected vertices and edges is said to be disconnected.
Now According to the question:
The right option is :
Connected Graph.
Hence, A Connected Graph is the one in which every two pairs of vertices are connected.
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Given A(–1, 4), B(2, –5), and C(3, 4), which coordinate will make perpendicular AB to CD?
The coordinate will make perpendicular AB to CD is D(x, x/3 + 3). We have used the slope concept to solve this problem.
The slope of a line segment between two points (x1,y1) and (x2,y2) is given by the ratio of change in the y coordinate to the change in the x coordinate.
Slope = (y2 - y1)/(x2- x1)
Slope of line AB = (-5-4)/(2-(-1)) = -9/3 = -3
Let the slope of another segment CD be m.
As the product of two perpendicular segments is equal to -1.
So,
-3m = -1
m = 1/3.
Let,s assume point D is (x,y)
Slope of segment CD = (y - 4) / (x-3)
(y - 4) / (x-3) = 1/3
3(y-4) = (x-3)
3y = x+9
y = x/3 + 3
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in a golden rectangle the ratio of the length to the width equals the ratio of the length plus width to the length. find the value of this golden ratio.
The value of this golden ratio = 1/2 (1 + √5) = 1.618
Ratio:
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.
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A manufacturing company finds that they can sell 25 items at $3.50 per item and 150 items at $3.00 per item. If
the relationship between the number of items sold z and the price per item p is a linear one:
Find a formula that gives a in terms of p: x= ____
Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell ___ items if the price is $1.50.
your slope is -50 and your equation of x = mp + b becomes
x = -50 * p + b
How to establish linear relationship ?you want a linear relationship between x and p
that would be a straight line equation with the general form of y = mx + b
m is the slope
b is the y-intercept
since you x in terms of p, then:
let y = x
let x = p
the equation of y = mx + b is the same as the equation of x = mp + b after you replace y with x and x with p.
in the equation of x = mp + b, you have coordinate points in the form of (p,x)
since y = x and x = p, this is the same as the form of (x,y), which is the standard form of the linear equation coordinate points.
we'll work with x = mp + b and then later translate to y = mx + b for graphing purposes.
your standard form is x = mp + b with coordinate points of (p,x).
you have two coordinate points they are (3.5,25) and (3,50)
m is equal to slope which is equal to (y2-y1)/(x2-x1) which is then translated to (x2-x1)/p2-p1 when you replace y with x and x with p.
assign (3.3,25) to (p1,x1) and assign (3,50) to (p2,x2) and the slope equation becomes (50-25)/(3-3.5) which becomes 25/-0.5 = -50
your slope is -50 and your equation of x = mp + b becomes
x = -50 * p + b
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what variable are you solving for? are all of the variables in the correct units? if not, which variable needs to be converted to the correct units?
For the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Given that, P equals atmospheric pressure (atm), V equals liters of volume (L), n equals the number of moles, R is the gas constant (0.0821 Latm/(molK)), and T equals Kelvins of temperature (K).
Take into account the following circumstances: a 3,500 mL tank containing 27 moles of argon gas was pressurized to 12 atm.
The ideal gas equation is,
PV=nRT
There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.
Thus, for the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.
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For the following exercises, find the vertical traces of the functions at the indicated values of x and y, and plot the traces. 30. z=4-x-y; x = 2
The vertical traces of the functions at the indicated values of x and y have been represented on the graph attached.
The trace of a graph can be defined as the point where the graph intersects any single plane. Vertical traces are the traces where the lines meet and intersect at the vertical plane.
We have been given the values of the functions as such =
= x = 2
= z = 4 - x- y
If we solve these for the value of x and y, we will get -
= x = 2
= z= 2 - y
Hence, on equating these values, we get the following graph.
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the ad curve is drawn with the price level ________, and the c i g x curve is drawn with the price level ________.
Answer:
Step-by-step explanation:
76
2.9.AP-2
Write an equation for the line in slope-intercept form.
the equation is ?
The equation of the line in slope-intercept form is: y = 1/4x + 5.
How to Write the Equation of a Line in Slope-intercept Form?To write the equation of a line in slope-intercept form, first, find the slope of the line using two points on the graph.
Slope (m) = change in y / change in x = 1/4
m = 1/4.
The y-intercept is the point where the line intercepts the y-axis, which is at 5. Therefore, the y-intercept is b = 5.
To write the equation of the line in slope-intercept form, substitute m = 1/4 and b = 5 into y = mx + b:
y = 1/4x + 5.
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What are the solutions to the equation? 5x3=405x enter your answers in the boxes. X = or x = or x =.
The solutions to the equation 5x³=405x are x=0, x=9, x=-9.
What is meant by an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions related with an equals sign.
An equation is similar to a scale into which weights are placed. When equal weights of material are placed in the two pans, the scale is balanced and the weights are said to be equal.
Solving an equation with variables entails determining which variables values make the equality true.
Given, 5x³=405x
5x³-405x=0
5x(x²-81)=0
5x=0 and x²-81=0
If 5x=0 then,
x=0
If x²-81=0
x²=81
x=±9
Therefore, x=0, x=±9
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A) how far would the cheetah have traveled in the first 8 minutes? show how you arrived at your answer.
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The cheetah traveled 15.334 miles approximately.
SOLUTION:
Given, Suppose the cheetah sprinted at maximum speed for 8 minutes
Then, slowed to 40mph the next 8 minutes
We have to find how far would the cheetah have traveled
Now, we know that, maximum speed of cheetah is 68 – 75 mph, as we want maximum we are taking 75 which greater than 68.
So, cheetah sprinted at 75 mph for 8 minutes and then sprinted at 40 mph for next 8 minutes.
First let us convert 8 minutes into hours,
Total distance traveled = distance traveled with 75 mph speed + distance traveled with 40 mph speed
Hence, the cheetah traveled 15.334 miles approximately
Answer:
Step-by-step explanation:
What type of triangle is triangle RST?.
Is triangle ABC congruent to triangle ADC?.
Triangle ABC is congruent to ADC.
Two triangles are congruent if all of their corresponding parts are congruent. This means that congruent triangles will have three pairs of congruent sides and three pairs of congruent angles.
Given information,
AB = AD
BC = CD
and
AB = AD
CB = CD
also
AC = AC (common sides)
Hence triangles ABC and ADC are congruent to each other.
Congruence in two or more triangles depends on the measurements of their sodes and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
Given question is incomplete.
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she randomly surveys 83 students and collects data on the number of hours they slept last night. she computes the sample mean to be 6.5 hours with a standard deviation of 1.1 hours. what is the sample size? enter just that number as answer for this question.
The sample size of the given question is 83 and the t-test value is -0.6578.
Hypotheses:
H0 : Ha: ц < 7.
Sample mean = 6.5
SD = 1.1
n = 83
ц =7
Null hypothesis: ц >= 7
Alternative hypothesis: ц < 7
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by
t = (mean - ц )/ ц \sqrt{n}
t-test is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value.
t = -0.5 / 0.76
= -0.6578
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