Answer:
B. 0.21
Step-by-step explanation:
The problem statement tells you 21% of males play the guitar. That means the probability is 0.21 that a randomly chosen male will play the guitar.
Answer:
The probability that a randomly selected subject in the state plays the guitar is:
0.21
Step-by-step explanation:
Let 'x' be the number of male.
Now it is given that 21% of males play the guitar.
That means 21% of x play the guitar.
i.e. 21%×x play the guitar.
Hence, the probability that a randomly selected subject in the state plays the guitar, given that the subject is male is calculated as:
Probability=( number of male members playing the guitar)/(Total number of males)
Probability=0.21
Hence, Probability is 0.21
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Question 35/40
Correctly complete this sequence: 131,517,?,
123
Xe-b+ b² - 4ac.
VO
Mathematics
y=2.x²
Question:
Correctly complete this sequence: 131, 517, ?, 123
Answer:
The completed sequence: 131, 517, 192, 123
Step-by-step explanation:
Given sequence is 131, 517, ?, 123
Step 1: Now, write the given numbers without any commas as below,
131517?123
Step 2: Then, split it into two digit numbers as 13, 15, 17, _ _, 23
Step 3: Fill the sequence with the missing two digit odd numbers. So, we can write as below
13, 15, 17, 19, 21, 23
Step 4: Again, rewrite and form the sequence without any commas.
131517192123
Step 5: Place the class after every three digits.
131, 517, 192, 123
Step 6: At last, found that the missing number is 192.
This is a simple addition sequence. The next number in the sequence would be 903, resulting from the addition of 386 to the previous term 517. So, the completed sequence is 131, 517, 903, 123.
Explanation:The sequence in question appears to be a simple addition sequence between consecutive terms. If you subtract the first number from the second number, you get 386 (517-131 = 386). Assuming this addition pattern continues, you can find the next number in the sequence by adding 386 to 517. So, the next number in the sequence would be 903 (517 + 386).
This means the completed sequence should read: 131, 517, 903, 123. Always remember to check the difference between your terms when working with sequences like this one.
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hey guys
im new here
please solve this for me with steps!
ill mark as the best answer
Answer:
The factors of [tex]2(x+y)^2-9(x+y)-5[/tex] is ((x+y)-5)(2x+2y+1)
Step-by-step explanation:
Given polynomial
=>[tex]2(x+y)^2-9(x+y)-5[/tex]
To Find:
The factors of the polynomial =?
Solution:
Lets assume k = (x+y)
Then [tex]2(x+y)^2-9(x+y)-5[/tex] can be written as [tex]2k^2-9k-5[/tex]
Now by using quadratic formula
k =[tex]\frac{-b\pm\sqrt{(b^2-4ac}}{2a}[/tex]
where
a= 2
b= -9
c= -5
Substituting the values, we get
k =[tex]\frac{-b\pm\sqrt{(b^2-4ac)}}{2a}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{((-9)^2-4(2)(-5)}}{2(2))}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{(81+40)}}{4}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{(121)}}{4}[/tex]
k =[tex]\frac{-(-9) \pm 11}}{4}[/tex]
k= [tex]\frac{ 9 \pm 11}{4}[/tex]
k = [tex]\frac{20}{4}[/tex] k = [tex]\frac{-2}{4}[/tex]
[tex]k_1 =5[/tex] [tex]k_2 = -\frac{1}{2}[/tex]
[tex]2k^2-9k-5= 2(k-5)(k+\frac{1}{2})[/tex]
Solving the RHS we get
[tex]\frac{2}{2}(k-5)(2k+1)[/tex]
[tex](k-5)(2k+1)[/tex]
Substituting k = x+y
[tex]((x+y)-5)(2(x+y+1)[/tex]
[tex]((x+y)-5)(2x+2y+1)[/tex]
a moving walkway at an airport moves at a pace of 1.75 feet per second
if you stand on the walkway as it moves how long will it take to transport you 280 feet
Answer:
The time taken to move distance of 280 feet at the speed of 1.75 feet per second is 160 seconds
Step-by-step explanation:
Given as :
The speed of the moving walkway at an airport = s = 1.75 feet per second
The distance cover on the walkway = d = 280 feet
Let The time taken to move 280 feet = t sec
Now, According to question
Time = [tex]\dfrac{\textrm distance}{\textrm speed}[/tex]
t = [tex]\dfrac{\textrm d}{\textrm s}[/tex]
t = [tex]\dfrac{\textrm 280 feet}{\textrm 1.75 ft per sec}[/tex]
t = 160 seconds
So, The time taken to move distance of 280 feet at the speed of 1.75 feet per second = t = 160 seconds
Hence, The time taken to move distance of 280 feet at the speed of 1.75 feet per second is 160 seconds . Answer
Robert has seven more than five times the number of video games Sam has. All together they have 25 video games. How many video games does Robert have?
Answer:
Step-by-step explanation:
r = 5s + 7
r + s = 25
5s + 7 + s = 25
6s + 7 = 25
6s = 25 - 7
6s = 18
s = 18/6
s = 3 <=== sam has 3 video games
r = 5s + 7
r = 5(3) + 7
r = 15 + 7
r = 22 <=== robert has 22 video games
How long did the sound take(in seconds) from the rocket motors at Time=0 to reach the people 500 meters away.
The speed of sound in early mornomg temperatures is 339.5 meters per second.
Sound will generally obey the basic equation of distance=rate×time
Answer:
It takes approximately 1.5 seconds to reach the people 500 metres away
Step-by-step explanation:
Since ; distance=rate×time
time= distance/ rate
Distance= 500 metres ,rate= 339.5 m/s
Time= 500/339.5
Time= 1.5 seconds
Each member of the school chess team receives a chess set and clock. The total cost of these items for 5 members is $125. Jenna knows that a chess set costs $10, but she does not know how much a clock costs. She sets up the equation below to solve for the cost of a clock, represented in her equation by x.
The question deals with setting up and solving an equation to find the cost of a clock, when the total cost for a chess set and clock is given. The cost of a clock is found to be $15.
Explanation:The subject of this question is Mathematics, specifically dealing with setting up and solving an equation. The total cost of the chess set and clock for each member is $125/5 = $25. Jenna knows that the chess set costs $10. So, the cost of a clock would be $25 - $10 = $15. Therefore, the cost of a clock is $15.
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The area of a trapezium is 34 cm and the length one of its parallel side is
10.4cm and its height is 4cm.Find the length of the other parallel side.
Answer:
6.6 cm.
Step-by-step explanation:
The area of a trapezium A = (h/2)(a + b) where h = the height, a and b are the length of the parallel sides.
So substituting the given values in this formula:
34 = (4/2)(10.4 + b)
34 = 2(10.4 + b
34 = 20.8 + 2b
2b = 34 - 20.8 = 13.2
b = 6.6 cm.
KE= 1/2 mvsquared
for v
Answer:
v=sqrt(2KE/m), -sqrt(2KE/m)
Step-by-step explanation:
KE=1/2mv^2
v^2=KE/(1/2m)
v^2=KE/(m/2)
v^2=KE(2/m)
v^2=2KE/m
v=sqrt(2KE/m), -sqrt(2KE/m)
Solve both equations.
Equation 1:
Answer:
x = 1.22
Step-by-step explanation:
[tex]\frac{5x-1}{8} -\frac{5-7x}{2} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{2(5x-1) - 8(5-7x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(10x-2) - (40-56x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(10x-2-40+56x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(66x-42)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(66x-42)}{16} = \frac{(18-3x)}{6}[/tex]
[tex](66x-42) \times 6 = (18-3x) \times 16[/tex]
[tex](396x-252) = (288-48x)[/tex]
[tex](396x +48x) = (288+252)[/tex]
[tex]444x = (540)[/tex]
[tex]x = \frac{540}{444}[/tex]
x = 1.22
Equation 2:
Answer:
x = -13.97
Step-by-step explanation:
[tex]\frac{x}{3} - \frac{7(x-2)}{9} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-3(7(x-2))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-3(7x-14))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-(21x-42))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-(21x-42)}{27} = \frac{24 - (2x-5)}{6}[/tex]
[tex]\frac{-12x+42}{27} = \frac{-2x+29}{6}[/tex]
[tex](-12x+42) \times 6 = (-2x+29) \times 27[/tex]
[tex](-72x+252) = (-34x+783) [/tex]
[tex](252-783) = (-34x +72x) [/tex]
[tex](-531) = (38x) [/tex]
[tex]x =\frac {-531}{38}[/tex]
x = -13.97
Select the correct answer.
Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
y = 3:2 – 93 + 20
A.
neither a relation nor a function
B. both a relation and a function
C.
function only
D.
relation only
Answer:
A
Step-by-step explanation:
neither a relation nor a function
Answer:
NOTE: This is the answer for the equation (y=3x^2-9x+20) Both a Relation and a Function
Step-by-step explanation:
Because a Relation can be represented as a verbal descriptions, graphs, mapping diagrams, equations, list ordered pairs, and tables. Which in this case is an equation so its a RELATION.
A function is a type of relation in which every x-value in the domain is paired with exactly one y-value. Which in this case every x-value is paired with one Y-value.
Let me know if this helps. :)
a 168 cm tall barrel has a circumference of 69.08 cm. what is the volume of the barrel using the formula for the volume of a cylinder as an estimate. round to the nearest hundredth of a cubic centimeter
Answer:
[tex]V=63,829.92\ cm^3[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=69.08\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]69.08=2(3.14)r[/tex]
solve for r
[tex]69.08=6.28r[/tex]
[tex]r=69.08/6.28[/tex]
[tex]r=11\ cm[/tex]
step 2
Find the volume of the cylinder
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]h=168\ cm[/tex]
[tex]r=11\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]V=(3.14)(11)^{2}(168)[/tex]
[tex]V=63,829.92\ cm^3[/tex]
Help me to prove the given below. Thank you in advance
Answer:
Construct MO, where O is the midpoint of CG. (As shown in the attached figure)
(1) LM = MG //given, CM is the median to the hypotenuse
(2) CO = OG // construction
(3) MO is a mid-segment //(1), (2) , Definition of a mid-segment
(4) MO // LC //triangle mid-segment theorem
(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)
(6) m∠LCO=90° //given, ΔLCG is a right triangle
(7) m∠MOG=90° //(5), (6), definition of congruent angles
(8) m∠MOC=180° – 90° = 90° // linear pair
(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles
(10) MO=MO //common side, reflexive property of equality
(11) ΔMCO ≅ ΔMGO //(2), (9), (10) Side-Angle-Side postulate
(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)
(13) MG= ½LG // Given, CM is the median to the hypotenuse
(15) MC = ½LG //(12) , (13), substitution
An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20\text{ cm}d=20 cmd, equals, 20, start text, space, c, m, end text.
What is the area AAA of the circular cross section of this pipe?
Give your answer in terms of pi.
Area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter
Solution:
Given that an engineer is going to install a new water pipe. The diameter of this circular pipe is, d = 20 cm
We have to find the area 'A' of the circular cross-section of the pipe.
Given, diameter of the circular section is:
diameter = 20 cm
Let us find the radius
[tex]radius = \frac{diameter}{2}\\\\r = \frac{20}{2} = 10[/tex]
Thus radius = r = 10 cm
The area 'A' of the circular cross-section of the pipe measn we can use the area of circle formula
The area of circle is given as:
[tex]area = \pi r^2[/tex]
Where "r' is the radius of circle
We have to find area in terms of pi
[tex]area = \pi (10)^2\\\\area = \pi \times 10 \times 10\\\\area = 100 \pi[/tex]
Thus area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter
Find the constant of proportionality if y is directly related to x when y = 12 and x = 6
Answer:
2
Step-by-step explanation:
Please see attached picture for full solution.
88511, 16351, ?, 10251
Complete the sequence
Answer:
73155
Step-by-step explanation:
To find sequence, we need to find the pattern of number.
88511= [tex]8 + 8, 8-5, 5\times 1, \frac{1}{1} = 16351[/tex]
16351= [tex]1+6,6-3,3\times 5,\frac{5}{1} = 73155[/tex]
73155= [tex]7+3, 3-1, 1\times 5, \frac{5}{5} = 10251[/tex]
10251
The missing number in the sequence '88511, 16351, ?, 10251' is 60809, as the pattern in this sequence is to subtract 77160 from the previous number and take its absolute value.
Explanation:This is an example of a number sequence problem. Let me explain how we can find the missing number in the sequence '88511, 16351, ?, 10251'. To solve this, we need to identify the pattern used to generate this sequence. In this case, it appears the number 77160 (88511 - 16351) is subtracted to get the next number.
So if we subtract 77160 from 16351, we get -60809. But given the pattern of the sequence, all numbers are positive. Therefore, we need to take the absolute value of the result to fit the sequence. So our missing number would then be 60809.
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May someone please help me???
Answer
14x+8y=6
Step-by-step explanation:
9x+5x=14, 7y+y=8y , 15-9=6
Answer:
?
Step-by-step explanation:
?
Find the slope of the line passing through the points (2,3) and (2,-4)
Answer:
Undefined
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-3)/(2-2)
m=-7/0
undefined
Answer:
UndefinedStep-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\text{The first coordinates of the points (abscissa) are the same.}\\\text{Conclusion: This is a vertical line.}\\\text{The vertical line has the equation x = a (here x = 2). It has no slope.}\\\\\boxed{\text{Answer: unde}\text{fined}}[/tex]
[tex]\bold{METHOD\ 2:}\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the coordinates of the given points}\ (2,\ 3)\ \text{and}\ (2,\ -4).\\\\m=\dfrac{-4-3}{2-2}=\dfrac{-7}{0}\\\\\text{The denominator must be different from 0.}\\\text{The expression}\ \dfrac{-7}{0}\ \text{ has no numerical sense.}\\\\\boxed{\text{Conclusion and naswer: unde}\text{fined}}[/tex]
another 10second challenge is wich expresion has a lesser value?
Answer:
Therefore
Greater Value Expression is Expression ( 2 ) i.e [tex]3\times (492 - 166)\\[/tex]
Lesser Value Expression is Expression ( 1 ) i.e [tex]\frac{1}{3}\times (492 - 166)\\[/tex]
Step-by-step explanation:
Given:
[tex]\frac{1}{3}\times (492 - 166)\\[/tex] ............Expression ( 1 )
[tex]3\times (492 - 166)\\[/tex] ............Expression ( 2 )
To Find:
Which Expression has a lesser value ?
Solution:
First we will solve Expression ( 1 ) we get
[tex]\frac{1}{3}\times (492 - 166)=\frac{1}{3}\times 326=108.66[/tex]
Now we will solve Expression ( 2 ) we get
[tex]3\times (492 - 166)=3\times 326=978[/tex]
Therefore
Greater Value Expression is Expression ( 2 ) i.e [tex]3\times (492 - 166)\\[/tex]
Lesser Value Expression is Expression ( 1 ) i.e [tex]\frac{1}{3}\times (492 - 166)\\[/tex]
If you awnser please iclude work
Answer:
B and D
Step-by-step explanation:
The graph of a proportional relationship is a straight line graph which must pass through the origin.
The only straight line graphs which pass through the origin are B and D
What is the measure of angle A?
What is the final price with discount off 25% off $30
Answer:
$22.50
Step-by-step explanation:
25% of $30 is 22.5
Answer:
$22.50
Step-by-step explanation:
25% of 30 is 22.5
find the exact values of sin θ/2 and cos θ/2 for sin θ = 3/4 on the interval 0° ≤ θ ≤ 90°
Answer:
Step-by-step explanation:
If our interval is between 0 and 90 degrees, that means that our angles are first quadrant angles. Since the formulas for the half angles of sin and cos consider both the positive and negative roots, knowing that we are in QI leaves us using only the principle, or positive, root.
Also, if we know that the sin of angle is 3/4, we can set up a right triangle in QI and find the missing side of that triangle using Pythagorean's Theorem. Sin of an angle is the ratio opposite side/hypotenuse. That means that, according to Pythagorean's Theorem,
[tex]4^2=3^2+b^2[/tex] and
[tex]16-9=b^2[/tex] and
[tex]b=\sqrt{7}[/tex]
Now for the forula for the sin of a half-angle:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{1-cos\theta}{2} }[/tex]
Referring to the right triangle we created and found the missing side for, we see that the cosine of that same triangle is [tex]\frac{\sqrt{7} }{4}[/tex]
Filling in the formula then:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{1-\frac{\sqrt{7} }{4} }{2} }[/tex]
Get a common denominator on the upper fraction:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{\frac{4-\sqrt{7} }{4} }{2} }[/tex]
Bring up the 2 as 1/2 to multiply and get:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{4-\sqrt{7} }{8} }[/tex]
When you do the exact same thing to find the cos of the half angle, you are using a + sign instead of a - sign under the radical. That gives you as your exact value:
[tex]cos(\frac{\theta}{2})=\sqrt{\frac{4+\sqrt{7} }{8} }[/tex]
10. What is the distance between (8,7) and (3,-5)?
Answer:
distance between points=13 units
Step-by-step explanation:
distance between points=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
put [tex](x_1,x_2)[/tex]=(8,7) and [tex](y_1,y_2)[/tex]=(3,-5)
distance between points=[tex]\sqrt{(3-8)^2+(-5-7)^2}[/tex]
distance between points=[tex]\sqrt{(-5)^2+(-12)^2}[/tex]
distance between points=[tex]\sqrt{25+144}[/tex]
distance between points=[tex]\sqrt{169}[/tex]
distance between points=13 units answer
if an object has an acceleration of 7 m/s, and a mass of 3 kg, what is its force?
Answer:
force = 21 kg m/s^2 = 21 N
Step-by-step explanation:
If an object has mass (m) 3 kg, and its acceleration (a) is 7 m/s^2, its force is given by Newton's second law of motion: Force = M * a
Force = 3 kg * 7 m/s^2= 21 kg * m/s^2
This combinations of units (kg * m/s^2) is defined as Newtons in physics and abbreviated "N".
So we can say that the force on this object is of magnitude 21 N
g is the centroid of triangle abc what is the length of gf
Answer:
26
Step-by-step explanation:
The length of GF if, G is the centroid of the triangle ABC is 26.
What is triangle?
Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Given:
G is the centroid of the triangle ABC,
The line segment BD can be written as,
40 is 2x as long as 9x+2
The equation can be written as for the above statement.
40 = 2(9x + 2)
40 = 18x + 4
36 = 8x
x = 2
Put the value of x = 2 in 19X + 14, and divide that answer by 2, because GF is 2x smaller than AG
19x + 14
19 (2) + 14
52
Thus, the length of GF = 52 / 2 = 26.
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find the x- intercept and y- intercept from the following linear equation
-9x+4y+=36
please help ????
Answer:
x intercept- (-4,0) y intercept- (0, 9)
Step-by-step explanation:
Subsitute 0 for x to get y = 9. That is your y intercept. Subsitute 0 for y and get -4 for your x intercept
rearrange the equation so u is the independent variable. 4u+8w=-3u+2w
The equation in terms of u as independent variable is w = (-7/6)u
What is an Independent Variable ?A variable upon which another variable depends is called an Independent variable , On changing the value of the independent variable , the dependent variable changes .
The equation given is
4u +8w = -3u+2w
8w -2w = -3u - 4u
6w = -7u
w = (-7/6) u
Therefore the equation in terms of u as independent variable is w = (-7/6)u.
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Answer:
the equation rearranged with [tex]\( u \)[/tex] as the independent variable is:
[tex]\[ u = -\frac{6}{7}w \][/tex]
Step-by-step explanation:
To rearrange the equation so that [tex]\( u \)[/tex] is the independent variable, we need to isolate [tex]\( u \)[/tex] on one side of the equation.
Starting with the given equation:
[tex]\[ 4u + 8w = -3u + 2w \][/tex]
First, add [tex]\( 3u \)[/tex] to both sides to get all the [tex]\( u \)[/tex] terms on one side:
[tex]\[ 4u + 3u + 8w = -3u + 3u + 2w \][/tex]
[tex]\[ 7u + 8w = 2w \][/tex]
Next, subtract [tex]\( 8w \)[/tex] from both sides to get all the [tex]\( w \)[/tex] terms on the other side:
[tex]\[ 7u + 8w - 8w = 2w - 8w \][/tex]
[tex]\[ 7u = -6w \][/tex]
Finally, divide both sides by [tex]\( 7 \)[/tex] to solve for [tex]\( u \)[/tex]:
[tex]\[ \frac{7u}{7} = \frac{-6w}{7} \] \[ u = -\frac{6}{7}w \][/tex]
So, the equation rearranged with [tex]\( u \)[/tex] as the independent variable is:
[tex]\[ u = -\frac{6}{7}w \][/tex]
This is the final answer, with [tex]\( u \)[/tex] isolated on one side of the equation.
how do you solve for x on this problem?
3x=7.5
Answer:X=2.5
Step-by-step explanation:
Divide both sides by 3
3 over 3 cancels out and 7.5 over 3 equals 2.5
Answer:
x= 2.5
Step-by-step explanation:
divide both sides by 3
What is an equivalent expression for 1.5(3x + 4) + 0.25(6x + 8)?
Answer:
6x+8
Step-by-step explanation:
To answer this question we just simply use the distributive property to get rid of the parenthesis.
1.5*3x=4.5x
1.5*4=6
So the first parenthesis cancelled out would be : 4.5x+6
Now, onto the second:
0.25*6x=1.5x
0.25*8=2
So the second one is : 1.5x+2
Not that we have distributed both things, we add these.
4.5x+6+1.5x+2 we combine like terms
4.5x+1.5x=6x
6+2=8
So, the answer is 6x+8
Answer:
6x+8
Step-by-step explanation:
Took the question
if 42 butterflies were seen in 3 hours at that rate how many butterflies were seen per hour
Answer: 14 butterflies per hour
Step-by-step explanation: "Per hour" means in 1 hour so we can rewrite the given statement using fractions.
42 butterflies over 3 hours = ___ butterflies per hour.
I have attached my work in the image provided.
To find out what goes in the blank, notice that we have a 1 in the denominator of our second fraction. So we want to find a fraction that is equivalent to 42/3 that has a 1 in the denominator.
If we divide the numerator and denominator of 42/3 by 3, we get the equivalent fraction 14/1 or 14 butterflies over 1 hour. So now we have 14 butterflies over 1 hour = ___ butterflies per hour.
Now we can easily see that a 14 must go in the blank which means that the unit rate for 42 butterflies in 3 hours is 14 butterflies per hour.