Independent is x. Dependent is y
Answer:
Independent : x
Dependent: y
Step-by-step explanation:
y= 5x
The independent variable is the variable we change
Independent : x
The dependent variable depends on the value of the other variable
Dependent: y
What is the area of a right triangle with side lengths of 12 cm 16 cm and 20 cm
Answer:
A = (1/2)(16 cm)(12 cm) = 96 cm^2
Step-by-step explanation:
Because this is a right triangle, we know that the leg lengths are 12 cm and 16 cm respectively, and that these legs are at right angles to one another.
We can assume that the base of this triangle is 16 cm and that the height is 12 cm. Then, according to the area-of-a-triangle formula, A = (1/2)(base)(height), the area of this particular triangle is
A = (1/2)(16 cm)(12 cm) = 96 cm^2.
Answer:
A
Step-by-step explanation:
The hypotenuse is the longest side of a triangle, meaning the hypotenuse is 20 cm. The equation for the area of a triangle is base multiplied by height multiplied by one half. (1/2bh) 12 × 16 = 192. 192 × 1/2 = 96. The area of this triangle is 96 cm^2.
Find an n-degree polynomial function with real coefficients satisfying the given condition.
1. n=3; 4 and 2i are zeros; f(-1)=50
2. n=3; 4 and -5+2i are zeros; f(2)= -636
3. n=4; -2, -1/2, and i are zeros; f(1)=18
4. n=4; -4, 1/3, and 2+3i are zeros; f(1)=100
5. n=4; 1+i and i are zeros; f(1)=2
In all cases, if [tex]f[/tex] has real coefficients, then any complex roots occur in conjugate pairs, so if [tex]a+bi[/tex] is a root, then so is [tex]a-bi[/tex]. Also, by the fundamental theorem of algebra, if [tex]r_1,\ldots,r_n[/tex] are roots to [tex]f[/tex], then for some constant [tex]a\in\mathbb R[/tex],
[tex]f(x)=a(x-r_1)\cdots(x-r_n)[/tex]
1. If [tex]n=3[/tex] and [tex]f(3)=f(2i)=0[/tex], then
[tex]f(x)=a(x-3)(x-2i)(x+2i)=ax^3-3ax^2+4ax-12a[/tex]
Given that [tex]f(-1)=50[/tex], we have
[tex]f(-1)=a(-1-3)(-1-2i)(-1+2i)=-20a=50\implies a=-\dfrac52[/tex]
[tex]\implies\boxed{f(x)=-\dfrac52x^3+\dfrac{15}2x^2-10x+30}[/tex]
2.
[tex]f(x)=a(x-4)(x-(-5+2i))(x-(-5-2i))=a x^3 + 6 a x^2 - 11 a x - 116 a[/tex]
With [tex]f(2)=-636[/tex], we have
[tex]f(2)=a(2-4)(2+5-2i)(2+5+2i)=-106a=-636\implies a=6[/tex]
[tex]\implies\boxed{f(x)=6x^3+36x^2-66x-696}[/tex]
The rest are done in the same exact way.
What is the simplified form of the expression? (m^3/4c^5)-4
Final answer:
To find the simplified form of the quadratic equation at² + bt + c = 0 with constants a = 4.90, b = -14.3, and c = -20.0, we use the quadratic formula to calculate the discriminant and then the two possible solutions for t.
Explanation:
The original expression provided: [tex](m^3/4c^5)-4[/tex] does not match the information given about quadratic equations. Instead, here's how we would solve a quadratic equation using the provided constants:
A quadratic equation is of the form at² + bt + c = 0. Given constants a = 4.90, b = -14.3, and c = -20.0, the solutions to the quadratic equation can be found using the quadratic formula, which is t = (-b ± √(b²-4ac)) / (2a).
To find the solutions for the given quadratic equation, plug in the values for a, b, and c into the quadratic formula:
Calculate the discriminant (b² - 4ac).Determine the square root of the discriminant.Apply the values to the quadratic formula to find the two possible values of t.The simplified form of the quadratic equation will be two solution values of t.
0.5 kilograms (kg) is equal to how many ounces? Round your answer to the nearest tenth.
Answer:
17.6 ounces per 500 g
Step-by-step explanation:
Knowing one ounce equals 28.34 g, all we have to do is divide half a kilo (500 g) by the equivalent of an ounce to get the number of ounces in a kg. So,
O = 500 g / 28.34g/ounce = 17.64 ounces
We round that to the nearest tenth... to get 17.6 ounces per 500 g
Converting between metric and imperial/US system is always complicated.
Answer:
0.5 kilograms (kg) is equal to 17.6 ounces
Step-by-step explanation:
We have
1 kg = 35.274 ounces
0.5 kg = 0.5 x 35.274 = 17.637 ounces
Rounding to nearest tenth
0.5 kg = 17.637 ounces = 17.64 ounces = 17.6 ounces
So we have 0.5 kilograms (kg) is equal to 17.6 ounces
Having trouble with add or subtracting the given polynomials
7.
(2b^2+7b^2+b)+(2b^2-4b-12)
(9b^2+b)+(2b^2-4b-12)
9b^2+b+2b^2-4b-12
11b^2+b-4b-12
11b^2-3b-12
8.
(7g^3+4g-1)+(2g^2-6g+2)
7g^3+4g-1+2g^2-6g+2
7g^3-2g-1+2g^2+2
7g^3-2g+1+2g^2
7g^3+2g^2-2g+1
Hope this helps!
Problem 7:
(2b² + 7b² + b) + (2b² - 4b - 12)
= 11b²-3b-12
Problem 8:
(7g³ + 4g - 1) + (2g² - 6g + 2)
= 7g³ + 2g² - 2g + 1
graph of f(x) = 3^x + 1?
Answer:
Step-by-step explanation:
PLEASE SOLVE
If 5a+3b=35 and a/b = 2/5 , what is the value of a?
(A) 14/5 (B) 7/2 (C) 5 (D) 7 (E) 9
Answer:
14/5
Step-by-step explanation:
So first i manipulated a/b= 2/5. i multiplied both sides by 5 making it 5a/b=2. Then i multiplied both sides by b making it 5a=2b. Then i substituted 2b into 5a+3b=35. Making it 2b+3b=35. then i simplified it making it 5b=35. Then i solved for b making it b=7. Then i substituted b into 5a+3b=35. So that it looked like this 5a+3*7=35. then it became 5a+21=35. Then you subtract 21 making it 5a=14. You then divide by 5 making it a=14/5
Answer:
[tex]a = \frac{14}{5} [/tex]
Step-by-step explanation:
[tex]5a + 3b = 35 \\ 3b = 35 - 5a \\ b = \frac{35}{3} - \frac{5}{3} a \\ put \: b\: = \frac{35}{3} - \frac{5}{3} a \: into \: \frac{a}{b} = \frac{2}{5} \\ \frac{a}{ \frac{35}{3} - \frac{5}{3} a} = \frac{2}{5} \\ \frac{a}{ \frac{35 - 5a}{3} } = \frac{2}{5} \\ \frac{3a}{35 - 5a} = \frac{2}{5} \\ 5(3a) = 2(35 - 5a) \\ 15a = 70 - 10a \\ 15a + 10a = 70 \\ 25a = 70 \\ a = \frac{70}{25} \\ a = \frac{14}{5} [/tex]
Iola has $75. She buys a pair of shoes on sale for one-half off and a pair of socks for $6. She has $32 left. Which equation can be used to find x, the regular price of the shoes?
The correct equation to find the original price of the shoes that Iola bought is [tex]\frac{x}{2}[/tex] + 6 + 32 = 75, where x represents the regular price of the shoes.
The student is looking for an equation to find the regular price of the shoes that Iola bought. Since Iola has $32 left after buying the shoes and socks, and the socks cost $6, we can state that she spent $75 - $32 - $6 on the shoes on sale. If we represent the regular price of the shoes as x, then the sale price is [tex]\frac{x}{2}[/tex]. The equation that represents this scenario is:
[tex]\frac{x}{2}[/tex] + 6 + 32 = 75
Which equation has the same solution as this equation?
Answer:
3rd Option is correct.
Step-by-step explanation:
Given Equation:
x² - 16x + 12 = 0
First We need to find solution of the given equation.
x² - 16x + 12 = 0
here, a = 1 , b = -16 & c = 12
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-16)\pm\sqrt{(-16)^2-4(12)}}{2}[/tex]
[tex]x=\frac{16\pm\sqrt{256-48}}{2}[/tex]
[tex]x=\frac{16\pm\sqrt{208}}{2}[/tex]
[tex]x=\frac{16\pm4\sqrt{13}}{2}[/tex]
[tex]x=8+2\sqrt{13}\:\:andx=8-2\sqrt{13}[/tex]
Now,
Option 1).
( x - 8 )² = 144
x - 8 = ±√144
x - 8 = ±12
x = 8 + 12 = 20 and x = 8 - 12 = -4
Thus, This is not correct Option.
Option 2).
( x - 4 )² = 4
x - 4 = ±√4
x - 4 = ±2
x = 4 + 2 = 6 and x = 4 - 2 = 2
Thus, This is not correct Option.
Option 3).
( x - 8 )² = 52
x - 8 = ±√52
x - 8 = ±2√13
x = 8 + 2√13 and x = 8 - 2√13
Thus, This is correct Option.
Option 4).
( x - 4 )² = 16
x - 4 = ±√116
x - 4 = ±4
x = 4 + 4 = 8 and x = 4 - 4 = 0
Thus, This is not correct Option.
Therefore, 3rd Option is correct.
How do i solve this
Check the picture below.
using the 30-60-90 rule.
NEED HELP FAST PLEASE !!!!Which of the following is an equation of the translation y = cos x, shifted π units to the right?
y = cos (x + π)
y = cos x + π
y = cos (x − π)
y = cos x − π
Answer:
The correct answer is y = cos (x - π)
Step-by-step explanation:
2. The answer after that is y = sin x + π
3. Zero, minimum, zero, maximum, zero
4. Graph C
5. The answer is 4
Hope this saved some time for some people
The equation of the translation y = cos x, shifted π units to the right is y = cos (x − π).
Whar is the translation?A translation is a slide from one location to another, without any change in size or orientation.
The given equation is;
y = cosx
We want to translate the graph in the x-direction, so our final equation should look like:
y = cos(x-b)
Where b is the number of units translated.
We are translating the graph π units to the right, so b should be equal to π. Therefore, our final equation should look like:
[tex]\rm y = cos(x-b)\\\\y = cos(x-\pi )[/tex]
Hence, the equation of the translation y = cos x, shifted π units to the right is y = cos (x − π).
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Find the solution to the system of the equations shown below:
y = -4x + 11
y = 1/2x + 2
a.
(4, 1)
c.
(2, 3)
b.
(11, 2)
d.
(3, 2)
Answer:
(2,3)
Step-by-step explanation:
The given equations are:
[tex]y=-4x+11[/tex]
and
[tex]y=\frac{1}{2}x+2[/tex]
Equate both equations:
[tex]\frac{1}{2}x+2=-4x+11[/tex]
Multiply through by 2:
[tex]x+4=-8x+22[/tex]
[tex]x+8x=22-4[/tex]
[tex]9x=18[/tex]
x=2
Put x=2 into the first equation:
[tex]y=-4(2)+11[/tex]
[tex]y=-8+11[/tex]
y=3
The solution is (2,3)
Answer:
C. (2, 3)
Step-by-step explanation:
A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.
Solve a system of equations is to find the value of each unknown so that all the equations of the system are met.
Ordering both equations
First equation
[tex]y=-4y+11[/tex]
[tex]4x+y=11[/tex]
Second equation
[tex]y=\frac{1}{2} x+2[/tex]
[tex]-\frac{1}{2}x+y=2[/tex]
Ordering in a system of equations
[tex]\left \{ {{4x+y=11} \atop {-\frac{1}{2}x+y=2}} \right.[/tex]
Using the reduction method which consists of operating between the equations, such as adding or subtracting both equations, so that one of the unknowns disappears. Thus, we obtain an equation with a single unknown.
We're going to subtract the second equation from the first to eliminate the unknown y.
4x + y = 11
- ((-1/2)x + y = 2)
(9/2)x = 9 ------> x= [(2)(9)]/9 -----> x = 2
Substituing the value x = 2 in [tex]y=\frac{1}{2} x+2[/tex]
y = (1/2)x + 2 ---------> y = (1/2)(2) + 2 -------> y = (2/2) + 2
y = 1 + 2 --------> y = 3
The solution of the system of equations is (2, 3).
Agatha Christie's company held a local 2-day training program for her and 3 co-workers.
They were all paid their regular wages for the time they were released from their regular
work. These wages totaled $850 for the group. Refreshments and lunch were served for a
cost of $45 per person. The instructor who conducted the training charged $300 per day.
Supplies for the program were $17 per person. Travel expenses for the group totaled $105.
What was the total cost for the seminar?
Answer:
$1803
Step-by-step explanation:
850 + 45(4) + 300(2) + 17(4) + 105 = 1803
Amber's punch recipe called for 3 quarts of soda and 2 1/2 quarts of fruit juice how many quarts of soda will she need to make 100 quarts of the same punch is
Answer:
The answer is C.
Step-by-step explanation:
The integer form is 60 as the answer
Brainliest Answer. If the speed is represented by x and the distance covered is represented by y, the equation of the best line of fit is y = _________________
She covered about ___________________miles at the speed of 50 miles per hour.
Answer:
x=.5x
25 miles
Step-by-step explanation:
What type of angle is this?
A. Linear pair
B. Vertical
C. Adjacent
The answer will be B
Each year a town holds a winter carnival this year 40% of the attendees were children under the age of 10 if 304 children under the age of 10 attended the carnival how many attendees were there
Answer:
760 attendees
Step-by-step explanation:
40% of the attendees is 304. That means you can add 304 to 304 (304 x 2) to get 608. To get the last 20%, divide 304 by 2, because 40(%) divided by 2 is 20(%). The answer to that is 152. Now, add it all up. 608 + 152 = 760.
In conclusion, there were 760 attendees at the carnival.
richard is filling his fish tank with water from a hose at the rate of 600 cubic inches per minute. how long will it take, to the nearest minute to fill the tank to a depth of 15 inches? Base =16 inches; width = 24 inches; height = 18 inches.
Answer:
10 minutes
Step-by-step explanation:
The question is on volume/capacity
Volume of the tank is given by = l×w× d where l is length, w is width and d is the depth
l=16 in w= 24 in and d=15in
v=16×24×15 =5760 in³
Time to fill tank
Given that 600 in³= 1 min
5760 in³=?
=(5760×1) /600 = 9.6 min
Final answer:
To fill the tank to a depth of 15 inches with a flow rate of 600 cubic inches per minute, it will take approximately 10 minutes, rounded to the nearest minute.
Explanation:
The student asks how long it will take to fill a fish tank to a depth of 15 inches using a hose with a flow rate of 600 cubic inches per minute. The dimensions of the tank's base are 16 inches by 24 inches, and the desired fill height is 15 inches. First, we calculate the volume of water needed to fill the tank to the desired depth by multiplying the base and the height (Volume = length × width × depth).
Volume needed = 16 inches × 24 inches × 15 inches = 5760 cubic inches.
Now, we divide the total volume by the flow rate to find out how long it will take to fill the tank.
Time = Volume needed / Flow rate = 5760 cubic inches / 600 cubic inches per minute = 9.6 minutes.
To provide an answer to the nearest minute, we round 9.6 to 10 minutes.
Which transformation is a rigid transformation?
Answer:
A rigid transformation includes only rotation and translation.
Answer:
Step-by-step explanation:
Which term can be defined as the steepness of a line
Answer:
Slope
Step-by-step explanation:
Slope is the gradient or steepness of a line.
The term slope defines steepness of a line
What is steepness of a line?Steepness of a line is the the inclination of the line.
How to know which term can be defined as the steepness of a line ?Steepness of the line can be defined by the term slope.
Slope is the inclination of the line towards x-axis.
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Use the data set below to answer the following question.
2, 4, 7, 2, 3, 7, 9, 3, 1,7
What is the median of this data set?
Arranging the given data in ascending order:
1, 2, 2, 3, 3, 4, 7, 7, 7, 9
Meadian is the middle-most observation.
i.e. The Median here is average of 3 and 4.
= (3+4)/2
= 7/2
=3.5
Hope it helps...
Regards;
Leukonov/Olegion
Please Help!!
Write in exponential form.
ANSWER
c.
[tex]5{e}^{i \frac{5\pi}{3} }[/tex]
EXPLANATION
The exponential form of complex numbers is given by;
[tex]z =r {e}^{i \theta} [/tex]
The given complex number in polar form is:
[tex]5( \cos( \frac{5\pi}{3} + i \sin( \frac{5\pi}{3}) ) [/tex]
We have r=5 from the question and
[tex] \theta = \frac{5\pi}{3} [/tex]
We substitute these values to obtain the exponential form:
[tex]z =5{e}^{i \frac{5\pi}{3} }[/tex]
The correct answer is C
Solve for x when x² = 0.0025
[tex]\bf x^2=0.0025\qquad \textit{let's convert the decimal to a fraction} \\\\[-0.35em] ~\dotfill\\\\ 0.\underline{0025}\implies \cfrac{00025}{1\underline{0000}}\implies \cfrac{25}{10000} \\\\[-0.35em] ~\dotfill\\\\ x^2=0.0025\implies x^2=\cfrac{25}{10000}\implies x=\sqrt{\cfrac{25}{10000}}\implies x=\cfrac{\sqrt{25}}{\sqrt{10000}} \\\\\\ x=\cfrac{5}{100}\implies x=\cfrac{1}{20}[/tex]
PLEASE HELP ME!!!
P and Q are two geometrically similar solid shapes
The total surface area of shape P is 720cm^2.
The total surface area of shape Q is 2880cm^2
The volume of shape P is 3200cm^3
Calculate the volume of shape Q.
Answer:
The volume of shape Q is [tex]25,600\ cm^{3}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z----> the scale factor
x----> surface area of shape Q
y----> surface area of shape P
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=2,880\ cm^{2}[/tex]
[tex]y=720\ cm^{2}[/tex]
substitute
[tex]z^{2}=\frac{2,880}{720}[/tex]
[tex]z=2[/tex]
step 2
Find the volume of shape Q
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z----> the scale factor
x----> volume of shape Q
y----> volume of shape P
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=2[/tex]
[tex]y=3,200\ cm^{3}[/tex]
substitute
[tex]2^{3}=\frac{x}{3,200}[/tex]
[tex]x=(8)(3,200)=25,600\ cm^{3}[/tex]
What is the solution to this set of equations? Show your work.
y=5x−9
y=x^2−3x+7
Answer:
(4, 11)
Step-by-step explanation:
Given the 2 equations
y = 5x - 9 → (1)
y = x² - 3x + 7 → (2)
Substitute y = x² - 3x + 7 = 5x - 9 ( subtract 5x - 9 from both sides )
x² - 8x + 16 = 0 ← quadratic equation in standard form
(x - 4)² = 0 ← in factored form as a perfect square, so
x - 4 = 0 ⇒ x = 4
Substitute x = 4 into (1) for corresponding value of y
y = 20 - 9 = 11
Solution (x, y) → (4, 11)
need help with stats!
Answer:
A. a) 24
A. b) 4
B. a) 40320
B. b) 576
Step-by-step explanation:
General formula for Permutations:
[tex]P(n,r) = \frac{n!}{(n - r)!}[/tex]
A. Concert seats: 2 couple --- total of 4 persons.
a) without restrictions
Since there are no restrictions, but that the order is important (John, Mary, Paul, Michelle isn't the same as Michelle, Mary, Paul, John), it's a permutation calculation.
Then we calculate the permutations of 4, out of 4, so...
[tex]P(4,4) = \frac{4!}{(4 - 4)!} = 4! = 24[/tex]
24 different ways for them to sit.
b) couples together
Now, we can see the problem as having 2 levels of permutations, first the couples, then inside the couples.
There are 2 ways for the first level or order... couples AB or BA, so 2 possibilities.
Inside each couple, man then woman (MW) or woman then man (WM), so 2 possibilities there too on 2nd level.
Overall 2 * 2 = 4 ways to sit by couple.
B) Single file
a) without restrictions
Again, order is important, so another permutation, not a combination. And since we have no restriction, it can be any sequence.
We then have to calculate the number of permutations of 8 out of 8...
[tex]P(8,8) = \frac{8!}{(8 - 8)!} = 8! = 40320[/tex]
There are 40,320 ways these 8 kids can pass the door.
b) girls first.
So, the four girls have to enter first.... and these four girls can be in any order.. how many permutations? P(4,4)... so 24 as calculated above.
For the four boys, how many permutations? Yes, again P(4,4)... so 24 again.
Overall, we need to multiply the two... 24 x 24 = 576 ways if the girls enter first, followed by the boys.
Line segment ON is perpendicular to line segment ML.
What is the length of segment NP?
A.
1 unit
B.
4 units
3 units
c
D.
2 units
Answer:
The length of NP is 2 units.
Step-by-step explanation:
Given the radius of 5 units and the length of MP is 4 units in the circle
we have to find the length of NP
OL=OM=5 units ( ∵ Radii of same circle)
In ΔOMP, by Pythagoras theorem
[tex]OM^2=MP^2+OP^2[/tex]
[tex]5^2=4^2+OP^2[/tex]
[tex]OP^2=25-16=9[/tex]
[tex]OP=3 units[/tex]
As we see
[tex]ON=OP+NP[/tex]
[tex]5=3+NP[/tex]
[tex]NP=5-3=2\thinspace units[/tex]
Hence, the length of NP is 2 units.
Option D is correct.
Given the statement "If Jack’s pet is a pig, then Jack’s pet cannot fly,” which statement represents the converse?
q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly
~q → ~p, where p = Jack’s pet cannot fly and q = Jack’s pet is a pig
p → q, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly
q → p, where p = Jack’s pet is not a pig and q = Jack’s pet is a pig
answer : (A) q>p , where p= jacks pet is a pig and q= jacks pet cannot fly
The converse of an implication reverses the order of the original statement. Therefore, the converse of 'If Jack’s pet is a pig then Jack’s pet cannot fly' is 'If Jack's pet cannot fly, then Jack's pet is a pig'.
Explanation:In this problem, we're dealing with a form of logical statement known as an implication, which can be symbolized as p → q. In the original statement, 'If Jack’s pet is a pig (p) then Jack’s pet cannot fly (q)', the implication is that being a pig causes or results in the inability to fly. The converse of an implication reverses the order of the original statement, so 'if q then p'. Therefore, the converse of the given statement would be 'If Jack's pet cannot fly, then Jack's pet is a pig', or symbolically represented as q → p.
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How many one-thirds are there in three-fourths?
Answer:
there are 2.25 one-thirds in a three-fourth.
Hope this helps you out!
In the given Fractions there are 2 and 1/4 (or 2.25) one-thirds in three-fourths.
To find out how many one-thirds are in three-fourths, we need to represent both fractions using a common denominator. In this case, we can see that the smallest common denominator is 12.
So, we can convert both fractions to twelfths by multiplying the numerator and denominator of one-third by 4, and the numerator and denominator of three-fourths by 3. This gives us:
1/3 = 4/12
3/4 = 9/12
Now, we can simply divide the numerator of three-fourths by the numerator of one-third to get our answer:
(9/12) ÷ (4/12) = (9/12) × (12/4) = 27/4 = 2.25
Therefore, there are 2 and 1/4 (or 2.25) one-thirds in three-fourths.
In conclusion, determining how many one-thirds are there in three-fourths requires us to represent both fractions using a common denominator and then dividing the numerator of three-fourths by the numerator of one-third. The answer is 2.25
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Kwan has 4 boxes of crayons. Each box has the same number of crayons. Now he has 27 crayons. How many crayons were in each box?
Kwan would have 6.75 crayons in each box
Answer:
the answer is 8 because...
Step-by-step explanation:
You forgot to put in that he LOST 5 crayons. He has 27 AFTER he lost the five. using inverse operations we would add 5 to 27 to get 32, and then we divide that by the number of boxes he had, we get 8.