The number of ways to place 40 identical balls in 4 distinct boxes, with each box getting at least 2 balls and no box getting 18 or more balls, is 6,125.
1. Start by placing 2 balls in each of the 4 boxes, leaving 32 balls to distribute.
2. Since no box can have 18 or more balls, the maximum number of balls in a box is 17. Adjust the problem to consider distributing 32 balls without restrictions.
3. Use the stars and bars method to find the number of ways to distribute the 32 balls. There are 32 stars (balls) and 3 bars (dividing the boxes), resulting in 34! / (32! * 3!) combinations.
4. Now, subtract the number of ways where any box has 18 or more balls. For this, we need to consider cases where at least one box gets an additional 18 balls.
5. Calculate the combinations for each case (3 cases) and subtract them from the total combinations.
6. The result is 6,125 different ways to place the balls according to the given conditions.
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Ruthie is trying to choose what reading material she wants to take on a vacation. She wants to read 1 fiction book, 1 nonfiction book, and 3 magazines. If Ruthie has 8 fiction books, 7 nonfiction books, and 3 magazines to choose from, how many possible combinations of books and magazines could she take with her.
E. 3 F.8 G.56 H.112
The number of possible combinations would be 56.
What is permutation?Permutation is the changing of the order in which things have been arranged or the arranging of things in a certain order.
Analysis:
Total number of fiction books available = 8
number of fiction books Ruthie wants = 1
Number of combination for Ruthie = 8C1 = 8 ways
Total number of non fiction books available = 7
number of non fiction books needed by Ruthie = 1
possible combination = 7C1 = 7 ways
Total number of magazines available = 3 ways.
Total possible combinations for all the Reading materials = 8 x 7 x 1 = 56 ways.
number of magazines Ruthie wants = 3C3 = 1 way
In conclusion, the number of possible combinations of The reading materials is 56.
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A soccer game lasts 90 minutes without running into overtime. The coach
plans to switch players out every 12 1/2 minutes. Approximately how many
switches will the coach make in one game?
Answer: 7 Switches will be made.
Step-by-step explanation:
[tex]\frac{90}{12.5}=[/tex] number of switches
[tex]7.2=[/tex] number of switches
however you cannot have a fraction of a switch so you must round it to a whole number, which in this case is 7.Find the perimeter of each of these rectangles
Answer:
a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm
b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)
= 4√10 cm
c) Simplifying √72: √36 x √2 = 6√2
Simplifying √18: √9 x √2 = 3√2
Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm
Identify the domain of the function shown in the graph
Using it's concept, the domain of the function shown in the graph is:
B. [tex]-6 \leq x \leq 6[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains all values of x.
From this graph, the function is defined for values of x between -6 and 6, hence the domain is given by:
B. [tex]-6 \leq x \leq 6[/tex].
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What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
A) f(x) = −2x
Domain:
Range:
g(x) = ½x2 + 5
Domain:
Range:
For f(x) we have:
domain: set of all real numbers.range: set of all real numbers.And for g(x):
domain: set of all real numbersrange: set of all real numbers such that y ≥ 5.How to get the domain and range of each function?
The domain of a function is the set of inputs that we can use on the function, and the range is the set of outputs.
a) f(x) = -2x
This is just a linear equation, as you can see, for no value of x we have a problem, then the domain is the set of all real numbers.
Similar for the range, it covers the set of all real numbers, then:
domain: set of all real numbers.range: set of all real numbers.b) g(x) = 0.5*x² + 5
This is a quadratic function, so the domain is the set of all real numbers again.
Now the range will have a minimum, which is at the vertex of the parabola.
For the parabola the vertex is at x = 0:
g(0) = 0.5*0² + 5 = 5
Then the range is the set of all real numbers equal to or larger than 5.
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Find the distance between the pair of points: (3,1) and (4,-5).
Answer:
9.2195445 (9.22 rounded)
Step-by-step explanation:
#1: Use the distance formula to determine the distance between the two points:
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
#2: Substitute the actual values of the points into the distance formula:
[tex]\sqrt{((-4)-3)^{2}+(5-(-1))^{2}}[/tex]
#3: Simplify:
- Subtract 3 from -4: [tex]\sqrt{(-7)^{2}+(5-(-1))^{2}}[/tex]
- Raise -7 to the power of 2: [tex]\sqrt{49+(5-(-1))^{2}}[/tex]
- Multiply -1 by -1: [tex]\sqrt{49+(5+1)^{2}}[/tex]
- Add 5 and 1: [tex]\sqrt{49+6^{2}}[/tex]
- Raise 6 to the power of 2: [tex]\sqrt{49+36}[/tex]
- Add 49 and 36: [tex]\sqrt{85}[/tex] (Decimal form: 9.2195445 (9.22 rounded))
The distance between the two points (3,1) and (4,-5) is 9.22.
Check all the true statements.
We can conclude that the true statement from the given expressions are DE || AC and 2DE = AC
Similar trianglesTriangles are similar if the measure of the similar sides are all equal to a constant.
From the given diagram, you can see that the measure of BA is congruent to BC. This shows that the line DE is parallel to AC that is DE || AC.
Also twice the measure of the sides DE will be equivalent to AC that is 2DE = AC.
Hence we can conclude that the true statement from the given expressions are DE || AC and 2DE = AC
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Volume=
Help me please thanks so much
Answer:
30.7
Step-by-step explanation:
It's 30.7 because 707/23
Answer:
16261 u3
Step-by-step explanation:
V = (base area)(height)=(707)(23)= 16261 u3
Hope this helps
Consider the sequence Three-fourths, four-fifths, StartFraction 5 Over 6 EndFraction, StartFraction 6 Over 7 EndFraction, ellipsis
Which statement describes the sequence? 3/4, 4/5, 5/6, 6/7,...
The sequence diverges.
The sequence converges to 1.
The sequence converges to ∞.
The sequence converges to –∞.
Using limits, it is found that the correct statement defining the sequence is:
The sequence converges to 1.
What is the rule that defines this sequence?The numerator starts at 3 and increases by 1, while the denominator starts at 4 and increases by 1, hence the rule is:
[tex]\sum_{n = 0}^{\infty} \frac{3 + n}{4 + n}[/tex]
To verify if it converges, we find the limit as n goes to infinity, hence:
[tex]\lim_{n \rightarrow \infty} \frac{3 + n}{4 + n} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]
Hence the sequence converges to 1.
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Answer:
B i took quiz
Step-by-step explanation:
Please help me
Given the quadratic function, describe in words the transformations and then
provide a sketch of the graph.
y = − 1/²(x+4)² - 7
Choose the function that shows the correct transformation of the quadratic function shifted eight units to the left and one unit down.
ƒ( x) = ( x + 8) 2 + 1
ƒ( x) = ( x - 8) 2 + 1
ƒ( x) = ( x + 8) 2 - 1
ƒ( x) = ( x - 8) 2 - 1
we conclude that the correct option or the translated function is the last one.
f(x) = (x - 8)² - 1
Which is the correct equation for the transformed function?The parent quadratic function is:
y = g(x) = x²
If we translate this function 8 units to the left, then we will have the new function:
f(x) = g(x - 8)
And if now we translate this function one unit downwards, we will get:
f(x) = g(x - 8) - 1
Now we can replace g(x) by the parent quadratic function we willl get:
f(x) = (x - 8)² - 1
From this, we conclude that the correct option is the last one.
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a grandfather age is the same as his granddaughters age in months. Together they are 91. What is the age of the grandfather
The age of the grandfather in years according to the task content is; 84.
What is the age of the grandfather?It follows that the age of the grandfather and granddaughter are; x and y respectively.
Hence, the two equations which follow are;
x = 12y
x + y= 91
Hence, the age of the grandfather, x can be evaluated as follows;
x = 12(91-x)
13x = 1092
x = 1092/13
x = 84 years.
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Harmony earns a $42,000 salary in the first year of her career. Each year, she gets a 4%, percent raise.
Which expression gives the total amount Harmony has earned in her first n years of her career?
Answer:
42000*1.04^(n-1)
Step-by-step explanation:
4% is equal to 0.04, a raise is 1+0.04=1.04
1.04 is now the number we are multiplying by to get a new yearly salary for Harmony.
42000*1.04^(n-1) since n is how many years after she has the job you have to raise it to the power and subtract one.
Need help please someone answer quick
Answer:
2x/19
Quotient = division
Product = multiplication
Difference = subtraction
Sum = addition
Expand.
Your answer should be a polynomial in standard form.
(p²+p-6) (p²-6)
To which place would you estimate the given numbers so as to get answers quickly to the following sums?
(a) 3529 × 3689 (b) 33 × 99 (c) 777 × 523 (d) 495420 × 123512
For easy estimation, option A = nearest hundred,B = nearest ten, C = nearest hundred and D= nearest thousand.
Calculation of numbers using east estimations3529 and 3689
3529 to the nearest hundred = 3500 and,
3689 to the nearest hundred = 3700
∴ Required sum = (3500+3700) = 7200
33 and 99
33 to the nearest ten = 30 and,
99 to the nearest ten = 90
∴ Required sum = (30+90) = 120
120777 × 523
777 to the nearest hundred = 800 and,
523 to the nearest hundred = 500
∴ Required sum = (800+500) = 1300
1300495420 and 123512
495420 to the nearest thousand = 495000 and,
123512 to the nearest thousand = 124000
∴ Required sum = (495000 + 124000 ) = 619000
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In fig. 6.39, side QP and RQ of ΔPQR are produced to points S and T respectively, if ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
Answer:
PRQ = 65 degrees
Step-by-step explanation:
Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).
SPR + QPR = 180
135 + QPR = 180
QPR = 45
TQP + RQP = 180
110 + RQP = 180
RQP = 70
Since interior angles of a triangle add up to 180 ...
QPR + RQP + PRQ = 180
45 + 70 + PRQ = 180
PRQ = 65
Don't get this question
Answer:
17 and 18
Step-by-step explanation:
Writing every 2 digit number gives us :
10-99 including 10 and 99
For the first one we are looking for numbers where the number 3 appears only once so 33 would be invalid.
13,23,30,31,32,34,35,36,37,38,39,43,53,63,73,83,93
There are 17 2-digit numbers that have 3 exactly once
For the second one we are looking for number where the number 3 appears a minimum of once so 33 would be valid :
13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93
There are 18 2-digit numbers that have 3 at least once
Hope this helped and have a good day
Brad has $12 more than John. Together they have $84
Hello,
John : n
Brad : n + 12
n + n + 12 = 84
2n + 12 = 84
2n = 84 - 12
2n = 72
n = 72/2
n = 36
John $36 and Brad $36 + $12 = $48
Answer:
jhon =36 brad=48
Step-by-step explanation:
B=J+12
J+B=84
12+J+J=84
2J=72
J=36
B=J+12=36+12=48
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Using proportions, the lengths of the unknown sides are given as follows:
2x = 10.x - 3 = 2.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the triangles are similar, hence the lengths of it's sides follow the proportion given next:
[tex]\frac{2x}{4} = \frac{5}{x - 3}[/tex]
Applying cross multiplication:
2x(x - 3) = 20
2x² - 6x - 20 = 0
x² - 3x - 10 = 0
(x - 5)(x + 2) = 0.
Then the positive solution is:
x - 5 = 0 -> x = 5.
And the lenghts are:
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Brittany and four of her friends want to join a softball league. The league requires teams to have at least nine players, but teams cannot have more than eighteen players. In interval notation, how many more people can join Brittany's team?
The additional number of people is [4, 13]
How to determine the number of people?Brittany and four of her friends are five people.
So, we have:
n = 5
The conditions are given as
At least = 9At most = 18Let the additional number of people be x
So, we have the following inequalities
x + 5 ≥ 9 and x + 5 ≤ 18
Subtract 5 from both sides
x ≥ 4 and x ≤ 13
Express as interval notation
[4, 13]
Hence, the additional number of people is [4, 13]
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In a zoo, the ratio of female to male tiger is 2:3.
There are 30 male tigers.
How many tigers are female?
Jace ordered a banner in the shape of a parallelogram from a print shop.
A parallelogram is shown. The length of the sides are 9 feet, and the length of the top and bottom sides are 12 feet. A diagonal is drawn from one point to the opposite side. The length of the diagonal is 19 feet.
Heron’s formula: Area = StartRoot s (s minus a) (s minus b) (s minus c) EndRoot
The print shop charges $1.10 per square foot for banners of any shape and size. What is the approximate cost of the banner before tax?
$41.95
$46.14
$83.90
$92.30
Answer: $92.30
Step-by-step explanation:
Finding the area of one of the triangles formed by the diagonal,[tex]s=\frac{9+12+19}{2}=20\\\\A=\sqrt{(20)(20-9)(20-12)(20-19)}=4\sqrt{110}[/tex]
Therefore, the area of the entire parallelogram is [tex]8\sqrt{110}[/tex].
Therefore, the cost is [tex](8\sqrt{110})(1.1) \approx 92.30[/tex]
Answer:
$92.30 i got it right.
Step-by-step explanation:
edg 2023 its right.
Work out the area of the triangle.
?m2
The area of the triangle is 557. 7cm²
Area of a triangle
In order to determine the area of a triangle, we have to know the size of the base and the size of the height
The formula for finding the area of a triangle is given as = half the base multiplied by the height
In mathematical form, it is written as;
Area = 1/ 2 × base × height
From the figure given, we have their lengths to be'
base = 57. 2 m
height = 19. 5 m
Let's substitute the values
Area = 1/ 2 × 57. 2 × 19. 5
Area = 1/ 2 × 1115. 4
Find the ratio
Area = 557. 7 m²
The area of the triangle is 557. 7cm²
Hence, the area of the triangle is 557. 7cm²
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For questions 4-5, determine which function is graphed.
im being timed so please be quick thank you !!
Answer:
#3
Step-by-step explanation:
The y-intercept (the point where the line intersects with the y-axis) is -2, and the slope is 2/3 (two units up every three units to the right).
Answer:
C.
Step-by-step explanation:
First, look for the graph that shows a line with a y-intercept of -2. There is only one graph that shows a line with a y-intercept of -2. The graph will be the third graph. Please see attachment for the equation in a graphing calculator.
Hope this helps!
Which statement is correct when a scatterplot is constructed?
The correct statement about when a scatterplot is constructed is the independent variable is the input variable and should be represented by the x-axis. Option A
Steps in constructing a scatterplotChoose independent and dependent variableDraw a known x-axis for the independent variableAdd y-axis for the dependent variableMake all the points in the scatterplotLabel graph and axesFrom the given steps, we can see that when a scatter plot is constructed, the independent variable is the input variable and should be represented by the x-axis.
Hence, the correct statement about when a scatterplot is constructed is the independent variable is the input variable and should be represented by the x-axis. Option A
The complete question is;
Which statement is correct when a scatterplot is constructed? The independent variable is the input variable and should be represented by the x-axis.
The independent variable is the input variable and should be represented by the y-axis.
The dependent variable is the input variable and should be represented by the x-axis.
The dependent variable is the input variable and should be represented by the y-axis.
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Answer: A; The independent variable is the input variable and should be represented by the x-axis.
Step-by-step explanation:
I just know
how do u solve this? what’s the answer?
The functions that have the properties are (d) I and II only
How to determine the functions?The function property is given as:
[tex]a(x) = a^{-1}(x)[/tex]
The above implies that the inverse function and the original function are equal.
From the list of options, we have:
(a) y = x
Make x the subject
x = y --- the same as the original function
(b) y = 1/x
Make x the subject
x = 1/y --- the same as the original function
Hence, the functions that have the properties are (d) I and II only
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Can someone help me with these problems please having trouble and show work!
Answer:
solution will be1. 4x²-6x-4
2. 8x³+4x²-8x-4
3. x⁵-x⁴+3x³+x²+12
Step-by-step explanation:
1. (4x+2)(x-2)
apply foil method (a+b)(c+d)=ac+ad+bc+bd
(4x+2)(x-2)=4x.x + 4x(-2) + 2x + 2(-2)
4x²-8x+2x-44x²-6x-42. (4x²-4) (2x+1)
apply the same method as question no.1
(4x²-4) (2x+1)=4x².2x + 4x².1 + -4.2x-4.1
8x³+4x²-8x-43. (x²+3) (x³-x²+4)
Distributive parentheses
(x²+3) (x³-x²+4)= x².x³ + x²(-x²) + x².4+ 3x³+3(-x²) +3.4
x⁵-x⁴+3x³+x²+12When reuben had 3 years left in college, he took out a student loan for $16,902. the loan has an annual interest rate of 4.5%. reuben graduated 3 years after acquiring the loan and began repaying the loan immediately upon graduation.
Answer:
Reuben will have to pay $19,183.77 when he starts to pay the loan off after 3 years.
Step-by-step explanation:
There are 3 important parts to this equation:
1) 16,902
2) 4.5%
3) 3 years
First, let's find the interest rate in decimal form. This is easy enough to do.
take the interest rate (4.5%) and divide by 100. You can do this in your head by moving the decimal point but I will just write it out for the example:
4.5/100 = 0.045
Now that we have that number. we want to get the dollar amount for the interest. this is done by taking the loan amount and multiplying it by the decimal form of the percentage:
16,902 * 0.045 = 760.59
Since the interest rate is NOT compounding the rest is simple.
760.59 * 3 = 2,281.77
2,281.77 + 16902 = 19,183.77
Hope this helps.