Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 to that considered integer. The number of ways Mrs Evans can display the 5 baskets is 120.
What is factorial?Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 to that considered integer.
Thus, if we want to take the factorial of 'n',(n being a positive integer), then:
[tex]n! = 1 \times 2 \times \cdots \times (n-1) \times n[/tex]
We usually write it in reverse order because, in calculations, its cancellation comes useful. Thus, we have:
[tex]n! = n \times (n-1) \times \cdots \times 2 \times 1[/tex]
Mrs. evans has 5 spaces in which to display 5 baskets. Therefore, the number of ways Mrs Evans can display the 5 baskets are,
Number of ways = 5! = 5×4×3×2×1 = 120
Hence, the number of ways Mrs Evans can display the 5 baskets is 120.
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A carpenter purchased 60 ft of redwood and 80 ft of pine for a total cost of $308. A second purchase, at the same prices, included 90 ft of redwood and 70 ft of pine for a total cost of $397. Find the cost per foot of redwood and of pine?
Answer:
Price of redwood= $3.4
Pine =$1.3
In 1898, L. J. Bortkiewicz published a book called The Law of Small Numbers, where using data he collected for twenty years, he showed that the number of soldiers killed by horse kicks each year in the Prussian army followed a Poisson distribution with a mean of 0.61. What is the probability that there will be exactly three deaths in two years?
hurry please will pick brainly and step by step appreacite it
Answer:
given : 0.61 per year
formula poisson probability : p(x=k)=xke-x/k!
(a) The parameter λ is the product of the rate per year and the number of years. The number of years is 1 year in this case.
λ=0.61×1=0.61
Evaluate the formula of the Poisson probability at k=0,1:
P(X=0)= 0!
(0.61)
0
e
−0.61
≈0.5434
P(X=1)=
1!
(0.61)
1
e
−0.61
≈0.3314
Add the corresponding probabilities:
P(X≤1)=P(X=0)+P(X=1)=0.5434+0.3114=0.8748
Use the complement rule:
P(X>1)=1−P(X≤1)=1−0.8748=0.1252
Note: The solution in the back of the book is the probability of at least one death instead of more than 1 death, thus the solution in the back of the book is not correct.
Step-by-step explanation:
this is prob wrong so im sorry in advance!
The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.
City Police Number of Crimes City Police Number of Crimes
Oxford 12 17 Holgate 15 6
Starksville 15 13 Carey 8 18
Danville 20 6 Whistler 6 21
Athens 22 7 Woodville 17 7
Click here for the Excel Data File
a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)
The regression equation is calculated as: ŷ = -0.99299X + 26.39918
How to solve for the regression equationWe have these data for the x axis
12 15 20 22 15 8 6 17
These are the values for the y axis
17 15 6 7 6 18 21 7
Sum of X = 115
Sum of Y = 97
Mean X = 14.375
Mean Y = 12.125
Sum of squares (SSX) = 213.875
Sum of products (SP) = -212.375
Regression Equation = ŷ = bX + a
b = SP/SSX = -212.38/213.88 = -0.99299
a = MY - bMX = 12.13 - (-0.99*14.38) = 26.39918
ŷ = -0.99299X + 26.39918
These values where inputted into a regression analysis calculator and the output is ŷ = -0.99299X + 26.39918
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The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not? Explain your reasoning.
The $1 belongs in the box.
What are the equations that represent the question assuming the $1 does not belong in the box?s + c = 47 equation 1
5s + 4c = 200 equation 2
How many singles and couples bought the ticket assuming that the $1 does not belong in the box?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 35
Subtract 35 from 47
c = 47 - 35 = 12
35 couples tickets and 12 individual tickets were sold. This is not possible since the couples tickets were sold in 2.
What are the linear equations that represent the question if the 1 dollar belonged in the box?s + c = 47 equation 1
5s + 4c = 201 equation 2
How many couples tickets were sold?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 34
34 is divisible by 2 so the $1 belongs in the box.
Here is the complete question:
Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said,
I wonder whether the dollar belongs inside the cash box or not.
The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?
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There are chocolates in a box, all identically shaped. There are 8 filled with nuts, 16 with caramel, and 14 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
Answer:
P = [tex]\frac{91}{703}[/tex] ≅ 12.95%.
Step-by-step explanation:
The total amount of chocolates in the box is 8 + 16 + 14 = 38, 14 of which are solid.
Let's calculate the probability of getting a solid chocolate in the first selection:
[tex]P(1S) = \frac{14}{38} = \frac{7}{19}.[/tex]
Given that the first piece was solid, there are now 37 pieces of chocolate in the box, 13 of which are solid. Let's now calculate the probability of selecting another solid chocolate:
[tex]P(2S\,|\,1S) = \frac{13}{37}.[/tex]
Thus, the probability of selecting two solid chocolates in a row is the product of the two probabilities calculated above:
[tex]P = \frac{7}{19}\,.\,\frac{13}{37} = \frac{91}{703}.[/tex]
The Smiths have a pool that is 20 feet by 35 feet. A 5 foot wide deck completely surrounds the pool. The average depth of the pool is 6 feet. How much surface area is covered by the proposed pool deck?
Answer:
550 square feet
Step-by-step explanation:
There are 4 areas where the pool deck is situated on:
Top, Left, Right, and Bottom of the pool.
So if the deck is 5 feet wide:
Top = (35 feet * 5 feet) = 175
Bottom = (35 feet * 5 feet) = 175
Left = (20 feet * 5 feet) = 100
Right = (20 feet * 5 feet) = 100
175 + 175 + 100 + 100 = 550 square feet
Complete the identity: sec(t) - cos(t) = ?
1) sec(t)csc(t)
2) -2tan²(t)
3) 1 + cot(t)
4) sin(t)tan(t)
Step-by-step explanation:
[tex] \sec( \alpha ) - \cos( \alpha ) [/tex]
[tex] \frac{1}{ \cos( \alpha ) } - \cos( \alpha ) [/tex]
[tex] \frac{1}{ \cos( \alpha ) } - \frac{ \cos {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]
[tex] \frac{ \sin {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]
[tex] \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \times \frac{ \sin( \alpha ) }{1} [/tex]
[tex] \tan( \alpha ) \sin( \alpha ) [/tex]
4 is the option
PLEASE HELP ME ASAP!!!!
Part A: Identify the diagonals in the parallelogram.
Part B: Determine the value for x and y. Show your work.
Part C: Identify the length of each diagonal. Show your work.
Part A
[tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex]
Part B
Diagonals of a parallelogram bisect each other, so
[tex]BE=ED \implies 2x+3=3y-4 \implies 3y=2x+7 \implies y=\frac{2}{3}x+\frac{7}{3}\\\\AE=EC \implies y+4=4x-6 \implies y=4x-10[/tex]
Solving by substitution,
[tex]\frac{2}{3}x+\frac{7}{3}=4x-10[/tex]
Multiplying both sides by 3,
[tex]2x+7=12x-30\\\\37=10x\\\\x=3.7[/tex]
So, [tex]y=\frac{2}{3}\left(\frac{37}{10} \right)+\frac{7}{3}=\frac{24}{5}[/tex]
Part C
[tex]BE=ED=2(3.7)+3=10.4\\\\AE=EC=4(3.7)-6=8.8[/tex]
[tex]\therefore BD=2(10.4)=20.8, AC=2(8.8)=17.6[/tex]
Pls, I request ya all, exams are near, I am not able to figure out the answer (along with process) of this question. Pls, I will mark as brainliest tose who answer me with the correct process.
Thank You
What this question is asking us is
A) From -40C to 5 0c How much did it rise
The formula for this would be
Risen Temperature - Initial Temperature
The risen temparauture is 5 so we plug the 5 in first then the 4 so it would look like
5-(-4)=9
And remeber when you have 2 negatives it becomes a positie, 5+4=9
The asnwer for A is 9 degress
B) The tempurater then fell by 7 degress from 5 so we just have to do
5 - 7
which is -2 Celcius
Answer:
a was i believe 10 degrees and b dropped 3- degrees
Step-by-step explanation:
Because 4- 3- 2- 1- 0 1 2 3 4 5
1 2 3 4 5 6 7 8 9
4 is the start don't forget that
And for b 5 dropped from 7 degrees just take 5 now ur at 0 and u have 3 more to take boom ur at 3- hope this hellped :)
Write an equation of the line that passes through the point (5, 6) with slope 3.
Answer:
the answer to that would be y=3x-9
andrew has a cell phone plan that provides 300 free minutes each month fo a flat rate of $19 . for any minutes over 300, andrew is charged 0.39 per minute
The precise equation that represents the situation is as follows:
$19, x ≤ 300x > 300, f(x) = 19 + 0.39(x - 300)How to represent an equation?His cell phone plan provides 300 free minutes each month for a flat rate of $19.
let
x = number of minutes used
Therefore,
$19, x ≤ 300
For any minutes over 300, Andrew is charged 0.39 per minute.
Therefore,
if x > 300
f(x) = 19 + 0.39(x - 300)
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Which type of parent function is f(x) = -
1/?
O A. Absolute value
OB. Reciprocal
OC. Square root
OD. Linear
Answer: B. Reciprocal
Step-by-step explanation:
This is a fact.
The parent function represented by f(x) = -1/x is the reciprocal function.
Therefore, the correct answer is option B.
Reciprocal functions, also known as rational functions, are defined by an algebraic expression where the dependent variable is in the denominator. In this case, the dependent variable is x, and it appears in the denominator as 1/x.
The negative sign in front of the fraction simply indicates that the function is reflected over the x-axis.
The general form of a reciprocal function is f(x) = a/x, where "a" is a constant. In the given function f(x) = -1/x, a is equal to -1.
In the case of f(x) = -1/x, the graph of the function is a hyperbola that opens downwards in the first and third quadrants. It approaches the x-axis as x moves towards positive or negative infinity, and it moves away from the x-axis as x approaches 0.
Therefore, the correct answer is option B, the reciprocal function.
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the students in Mrs. Aubrey's class brought in 15 cans during week 1 of the food drive. during week 2 the students brought in 4 times as many cans. how many cans did the students bring in during week 2?
Answer:
30 cans :)
Step-by-step explanation:
We need to divide to solve so lets do that now :)
15 x 4 = 60
60/2 = 30
Have an amazing day!!
Please rate and mark brainliest!!
Garden table and bench is 657 total. Garden table is $43 less than bench. What cost of bench?
Answer:
$350
Step-by-step explanation:
Let the bench cost $x
Then the garden table costs $x - 43
x + (x - 43) = 657
2x = 657 + 43
2x = 700
x = 350
The cost of the bench is $350.
Nice day to you!
Find the sum of the first five terms of the geometric sequence: - 1, - 6, - 36
The sum of the first five terms of the geometric sequence is -1555
Sum of geometric sequenceThe formula for calculating the sum of geometric sequence is expressed as:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
where
r is the common ratio = 6/1 = 6
a is the first term = -1
n = 5 (number of terms)
Substitute
[tex]S_5=\frac{-1(6^5-1)}{6-1}\\S_5=\frac{-7776+1}{5}\\S_5=-1555[/tex]
Hence the sum of the first five terms of the geometric sequence is -1555
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Consider the rectangle enlargement. a smaller rectangle has a length of 4.3 millimeters and width of 4.5 millimeters. a larger rectangle has a length of x millimeters and width of 24.3 millimeters. the perimeter of the original rectangle is . the side length of the enlarged rectangle is . the perimeter of the enlarged rectangle is .
The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l +w)
If the smaller rectangle has a length of 4.3 millimeters and width of 4.5 millimeters while a larger rectangle has a length of x millimeters and width of 24.3 millimeters, then;
4.3/x = 4.5/24.3
Cross multiply
4.5x = 104.49
x = 23.22mm
Perimeter of original rectangle = 2(4.3 + 4.5)
Perimeter of original rectangle = 17.6mm
Perimeter of enlarged rectangle = 2(23.22 + 24.3)
Perimeter of enlarged rectangle = 95.04mm
The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm
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Answer:
17.6mm, 23.22mm, 95.04mm
Step-by-step explanation:
la mitad mas el tercio mas la cuarta parte de los años que tiene manuel, suman los años que tiene mas tres ¿que edad tiene manuel? ·
Resolviendo una ecuación lineal veremos que que Manuel tiene 36 años.
¿Qué edad tiene Manuel?Vamos a definir la edad de Manuel como x.
Sabemos que la mitad mas el tercio mas la cuarta parte de x es igual que x más 3, entonces:
x/2 + x/3 + x/4 = x + 3
Ahora podemos resolver esta ecuación lineal para x:
x/2 + x/3 + x/4 - x = 3
x*( 1/2 + 1/3 + 1/4 - 1) = 3
x = 3/(1/2 + 1/3 + 1/4 - 1) = 36
Así, concluimos que manuel tiene 36 años.
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Find all polar coordinates of point P where P = ordered pair 6 comma negative pi divided by 5.
A) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + 2nπ)
B) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
C)(6, negative pi divided by 5 + (2n + 1)π) or (-6, negative pi divided by 5 + 2nπ)
D) (6, negative pi divided by 5 + 2nπ) or (6, pi divided by 5 + (2n + 1)π)
All polar coordinates of point P where P = ordered are given are mathematically given as
(6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
Option B is correct.
What are all polar coordinates of point P where P = ordered pair 6 commas negative pi divided by 5.?Generally, the equation for all polar coordinates is mathematically given as
[tex]P= 6,\frac{-pi}{5}[/tex]
Finding the whole set of polar coordinates for An arbitrary point's polar coordinates may be written as (r, ), where (r, ) = (r, +2n) for some n and r.
If n is a positive integer and r is negative, then (r,) = (-r, +(2n+1)).
In conclusion, we may solve the problem by setting r = 6 and = -/6.
If n is an integer and r is positive, then P(6,-/6) = (6, -/6) + 2n, and if n is an integer and r is negative, then P(-6,-/6) = (-6, -/6) + (2n+1).
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The lateral surface area of cone A is equal to the lateral surface area of cylinder B.
True or False?
Answer:
True.
Step-by-step explanation:
Lateral Surface area of cone=πrl=πr×2h=2πrh
Lateral surface area of cylinder=2πrh
A vase with a circular base exerts a force of 15 N on a table with a pressure of 750 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
The radius of the base of the vase in cm to 2 dp is 0.08m
Pressure of an objectThe formula for calculating the pressure of a object is expressed as;
Pressure = Force/Area
Area = Force/Pressure
Area = 15/750
Areas = 0.02m²
Since the area of the circular base is πr², then;
πr² = 0.02
r² = 0.02/3.14
r = 0.0798m
Hence the radius of the base of the vase in cm to 2 dp is 0.08m
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Form the table of backward differences for the function f(x) = x³ +5x-7 for x = -1, 0, 1, 2, 3, 4 5 and 6.
The table of values is
x -1 0 1 2 3 4 5 6
f(x) -13 -7 -1 11 35 77 143 139
How to form the table?The function is given as:
f(x) = x³ +5x-7
And the values of x are
x = -1, 0, 1, 2, 3, 4 5 and 6.
Substitute these values in the function
f(-1) = (-1)³ +5(-1) - 7 = -13
f(0) = (0)³ +5(0) - 7 = -7
f(1) = (1)³ +5(1) - 7 = -1
f(2) = (2)³ +5(2) - 7 = 11
f(3) = (3)³ +5(3) - 7 = 35
f(4) = (4)³ +5(4) - 7 = 77
f(5) = (5)³ +5(5) - 7 = 143
f(6) = (6)³ +5(6) - 7 = 239
Hence, the table of values is
x -1 0 1 2 3 4 5 6
f(x) -13 -7 -1 11 35 77 143 139
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What are the vertex and x-intercepts of the graph of y=x² - 2x - 24? Select
one answer for the vertex and one for the x-intercepts.
A. x-intercepts: (4,0), (-6, 0)
B. x-intercepts: (-4,0), (-6, 0)
C. Vertex: (1, -25)
D. Vertex: (1, 23)
E. Vertex: (-1, -21)
OF. x-intercepts: (-4, 0), (6, 0)
Answer:
C. Vertex (1;-25)
F. x-intercepts: (-4;0), (6;0).
Step-by-step explanation:
1) x-coordinate of the vertex: -b/2a=1; y-coordinate of the vertex: -25;
2) for x-intercepts it needed to solve the equation x²-2x-24=0;
x=6;-4;
3) finally, correct answers are: C. Vertex (1;-25) and F. x-intercepts: (-4;0), (6;0).
What is the least 6 digit multiple of 4 that has all different numbers?
Answer:
We can now take 2 as the third digit, 3 as the fourth digit, 4 as the fifth digit and finally 5 as the sixth digit. Therefore, the smallest 6-digit number having all different digits is 102345.
The smallest 6-digit multiple of 4 with all different numbers is 102,564. This number is obtained by incrementing from 100,000 until finding a divisible number with distinct digits.
A number that is the result of a given number plus another natural number is said to be a multiple of that number.
Since the smallest 6-digit number, is 100,000.
Check if this number is divisible by 4.
In this case, it is not.
Increment the number by 1 to get 100,001.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,002.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,003.
Repeat step 2. Not divisible by 4.
Continue this process until you find a number that is divisible by 4 and has all different digits.
After following these steps, we find that the smallest 6-digit multiple of 4 with all different numbers is 102,564.
Hence,
The required number is 102564.
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Graph the image using the given transformation
1) First find the coordinates of the shape:
G(-1, -2), F(-1, -1), E(2,2), D(2, -2)
2)It asked for dilation of 2 about the origin.
*What is dilation?
Dilation is the expanding/enlarging a transformation by a scale factor
Now we multiply all the coordinates with the factor of 2
G(-1*2, -2*2) = G'(-2, -4)
F(-1*2, -1*2) = F'(-2, -2)
E(2*2, 2*2) = E'(4, 4)
D(2*2, -2*2) = D'(4, -4)
3) Now plot these points and graph the transformation:
Graph the line with slope -3 passing through the point(-3,-2) .
The attached graph represents the graph of the line
How to plot the graph?The given parameters are:
Slope, m = -3
(x1, y1) = (-3, -2)
The equation is calculated as:
y = m(x - x1) + y1
So, we have:
y = -3(x + 3) - 2
Expand
y = -3x - 9- 2
Evaluate the difference
y = -3x - 11
See attachment for the graph of y = -3x - 11
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Find the total surface area of the cylinder shown. Leave the answer in terms of pi radius 4 height 6
Answer: [tex]80\pi[/tex]
Step-by-step explanation:
- the equation for the surface area of a cylinder is [tex]A=2\pi rh+2\pi r^{2}[/tex]
- the equation for this cylinder will be [tex]A=2\pi (4)(6)+2\pi (4^{2})\\[/tex]
- so, [tex]2\pi (4)(6) = 150.7964474[/tex] and [tex]2\pi (4^{2})\\ = 150.7964474[/tex]
- then [tex]150.7964474 + 150.7964474= 251.3274123[/tex]
- finally, [tex]251.3274123/\pi = 80[/tex]
- so the answer in terms of [tex]\pi[/tex] is [tex]80\pi[/tex]
hope this helps :)
What type of polynomial is: 3x+x2+4
Answer:
Quadratic polynomial (Biggest power is 2). It's also a trinomial (3 unlike terms)
$15,074 is invested, part at 14% and the rest at 5%. If the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 5% by $1694.07, how much is invested at each rate? (Round to two decimal places if necessary.)
The rate at 14% and 5% are $12, 883 and $2191 respectively.
How to determine the rateGiven that;
Invested amount = $ 15, 074 at 14% and 5%
Let rate at 14% = x
rate at 5% = y
We have rate at 9% exceeds that of 5% by $1694. 07
Hence,
0. 14x = 0. 05y + $1694. 07 ⇒ equation 1
x + y = $15, 074 ⇒ equation 2
Make 'x' the subject
x = [tex]15, 074 - y[/tex]
Substitute in equation 2
[tex]0. 14(15, 074 - y) = 0. 05y + $1694. 07[/tex]
Expand the expression
[tex]2, 110. 36 - 0. 14y = 0.05y + 1694. 07[/tex]
Collect like terms
[tex]416. 29 = 0. 19y[/tex]
Make 'y' the subject
y = [tex]\frac{416. 29}{0. 19}[/tex]
y = [tex]$2, 191[/tex]
Substitute the value in equation 2
x + y = $15, 074
x = $15, 074 - y
x = [tex]$15, 074 - 2191[/tex]
x = $12, 883
Therefore , the rate at 14% and 5% are $12, 883 and $2191 respectively.
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Gathering information from individuals in a sample is known as _______________. A. data dumping B. data collection C. data diving D. data displaying
Gathering information from individuals in a sample is known as : Data collection. ( B )
What is statistics?Statistics is the science of collecting and analyzing data in quantities, especially for the purpose of informing.
Analysis:
sample collection is the first approach to analyzing any information.
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Mandy has $10.65. she wants to share it with herself and her 2 friends. How much will each friend get
Answer:
3.55 per person
Step-by-step explanation:
To find the amount of money per person, take the total amount of money and divide by the number of people
10.65 /3
3.55 per person
Answer:
$3.55 for everyone