The missing values a, b, c, d and e are included in the given two-way table. The correct values from the options are: a =15, b=18,e=31
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]
List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex] (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
For this case, the table given is:
[tex]\begin{array}{cccc}\rm &\rm \text{Likes swimming}&\rm \text{Doesn't like swimming}&\rm Senior\\\rm \text{Likes baseball}&a&b&33\\\rm \text{Doesn't likes baseball}&c&13&d\\\rm Total & 39& e& 70 \end{array}[/tex]
From this table, we can make 5 equations as:
[tex]a+b = 33\\a+c=39\\b+39=e\\33+d = 70\\39+e=70[/tex]
From the last two equations, we get the values of d and e as:
[tex]d = 70-33 = 37\\e = 70-39 = 31[/tex]
Putting this value of 'e' in last third equation, we get:
[tex]b + 13 = 31\\b = 31-13= 18[/tex]
From this, and first equation, we get:
[tex]a +18 = 33\\a=33-18=15[/tex]
And from this value of a, and second equation, we get:15+c = 39
[tex]c = 39-15 = 24[/tex]
Thus, the correct values are: [tex]a =15, b=18,e=31[/tex]
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Answer:
a,b,e
Step-by-step explanation:
please help! What fractional part of one semicircle does the labeled angle represent? Express
your answer as a fraction in simplest terms. Then, express the labeled angle in radian
measure.
280°
Let's consider what the problem wants us to find:
fractional part covered by the labeled angleangle in radiansLet's find the fractional part:
⇒ the fractional part is equal:
[tex]\frac{degree-covered-by-angle}{total-angle} =\frac{280}{180} =\frac{2*2*7*10}{2*2*3*3*5} =\frac{7*10}{3*3*5} =\frac{70}{45}=\frac{14}{9}[/tex]
Answer: The angle 280 degrees covers 14/9 of a semicircle.
Let's find the angle measure in radians:
⇒ we know that [tex]2\pi[/tex] radians are equal to 360 degrees
⇒ to convert any degree to radians, you must multiply [tex]\frac{\pi }{180}[/tex]
so [tex]280*\frac{\pi }{180} =\frac{28}{18}*\pi =\frac{28\pi }{18}=\frac{2*14*\pi }{2*9} =\frac{14\pi }{9}[/tex]
Answer: The angle 280 degrees in radians is [tex]\frac{14\pi} {9}[/tex] which in terms of [tex]\pi[/tex] is
14/9
Hope that helps!
What is the capacity of a cylinder if it’s 2.60m high and has a diameter of 160.0cm
Answer:
Step-by-step explanation:
pi = 3.14
h = 2.60 m
d = 160.0 cm
Radius
r = d/2
r = 160.0 / 2
r = 80.0 cm
height
There are 100 cm in 1 meter. The units have to agree.
2.6 m * 100 cm / m
2.6 * 100 = 260 cm
Formula
V = pi * r^2 * h
V = 3.14 * 80^2 * 260
V = 5224960 cm^3
If you want a more manageable number, you could convert this into m^3
That's done by
V = 5224960 / 1000000 = 5.22 m^3
What is the surface area of this shape?
I tried getting the answer twice and both times I got 228, which the teacher said was wrong.
(each cube is one inch squared)
Step-by-step explanation:
the answer shoukd be 324
because in cube there are 6 sides
and one side contain 54 box
so... 54 × 6 = 324
HELP WILL GIVE 20PTS PLEASE HELP ASAP
Answer:
hi, where's mt 20pts
Step-by-step explanation:
0.3
12+6+9+13=40
12/40 (or 3/10 simplified)
Thus, 0.3 as a decimal
Hope this helps!
Please help and explain.
Answer: Plant A
Step-by-step explanation: In the graph for plant A, the X axis is the months and the Y Axis is the inches. You can compare the data for Plant B in the graph for Plant A and see that Plant A has a larger number of inches for each number of months. For example, if you look at 6 months. The chart for Plant B says Plant B is 3 inches, while if you look at 6 months on the graph for Plant A, Plant A is at 10 inches.
What is the next term of the following sequence? 20, 10, 5, 2, ...
Answer:
40/2 = 20
20/2 = 10
10/2 = 5
5/2 = 2.5
2.5/2 = 1.25
85, 58, 72, 85, 46, 93 Mean:? Median:? Mode:? Range:?
Answer:
Mean is 73.2. Median is 85. Mode is 85. Range is 47.
Step-by-step explanation:
First order the numbers. 46, 58, 72, 85, 85, 93. The mode is all of these numbers added up to get 439. divided by the amount of numbers there are. there are 6. so 439 divided by 6 is 73.166 or 73.2. Median is the middle of the data set which is 85. the mode is the number that appears the most in a data set which is also 85. the range is the highest number minus the lowest number so we get 93 - 46 to get 47.
Answer:
Step-by-step explanation:mode 85
mean 73.2
median 85
range 47
What is the purpose of tax deffered retirement accounts
The two common retirement accounts that allow people to minimize their tax bills are tax-deferred and tax-exempt accounts. Just to be clear, both types of retirement account minimize the amount of lifetime tax expenses someone will incur, which provides incentives to start saving for retirement at an early age.
Hope this helps :)
pls helpT-T
(3rd periodical test in mathematics)
where are u from and why u need thes answer
graph the line y=3x-7
What is the value of x?
Answer:
x = 27 units
Step-by-step explanation:
39 / ( 39+ 26) = x / (x+18)
x = 27
Ponzi saves dimes and quarters. She has 12 coins adding up to $1.80. How many dimes does she have?
Factor 35x + 7
F. 7(1 + 5x)
G. 7(1 + 35x)
J. 7(x + 5x)
Answer:
Did this at school today… the answer is F. 7(1+5x)
Step-by-step explanation:
rewrite 35 as 7x5
Rewrite 7 as 7x1
That will be 7(5x+7x1) factor out the 7 and the answer will be 7(5x+1)
∠ROP forms a right triangle.
Find the measure of ∠ROQ.
31°
hope it helps......!!!!!
Nadia needs one cup of ice cream for every student in her class for their year-end party. The ice cream is only sold in pints. If there are 24 students in her class, how many pints of ice cream will she need? Describe how to solve this problem.
The pints of ice cream for the students is an illustration of metric units
Nadia needs 12 pints of ice cream for the 24 students
How to determine the pints of ice cream?The given parameter is:
Students = 24
She needs one cup for each student in the class.
So, the number of cups needed is:
Cups = 24
1 cup makes 1/2 pint.
So, we have:
Pint = 1/2 * 24
Pint = 12
Hence, Nadia needs 12 pints of ice cream for the 24 students
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answer please it would help
Answer: x=99.54
Step-by-step explanation:
Answer:
94.2
Step-by-step explanation:
We are given a reference angle of 34, we are also given opposite and hypotenuse side of the triangle, following SOHCAHTOA, We know that to solve this question, we have to use sine.
sin(34) = x/178
Get x alone
178sin34 = x
178sin34 is equal to 94.17, since we are looking for one decimal, we can round to the tenths place. The number next to the tenths is seven so we round up.
Our answer is 94.2
Last year, rusty’s tools experienced $67,550 in net sales, creating a gross profit of $50,338. if rusty had a total operating expense of $35,200 last year, what was his net profit margin? a. 22.4% b. 52.1% c. 74.5% d. 79.0%
The Net profit margin is 22.41%
Rusty's Tool experienced $67550 in net sales, creating a gross profit of $50338.
If Rusty had a total operating expense of $35200 then we have to find the net profit margin.
Since profit $50338 includes the operating expense of $35300 then net profit will be
= $50338 - $33500
= $15138
Now the selling price is given as $67550.
What is the formula for profit margin?
Profit margin = (Net profit/selling price) 100
Profit margin =151.38/675.50=22.41 %
Therefore, the answer is profit margin = 22.41%.
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A rectangular driveway is 7 feet wide, and it has an area of a square feet. How long is the driveway?
Please give how to solve every step
☆ Thank you ☆
Answer:
x = a/7
Step-by-step explanation:
Area is length x width, so let's call our unknown, the length, x
So the total area is 7 (the width) times x
If the total area is a, then we can write the equation a = 7(x)
Next, we have to isolate the variable for the length, x
To do this, we divide both sides by 7, leaving a/7 = x, or x = a/7
Need help ASAP khan Academy geometry practice
Answer:
426.16
Step-by-step explanation:
v=r^2h π
π =3.14
v=6^2*4*3.14
v=426.16
The circle above has center O, the length of arc ADC is 57, and x = 100. What is the length of arc ABC ?
The length of arc ABC with center O and radius of 9 units is 13π.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let r represent the radius of the circle. Hence:
arc ADC = (100 / 360) * 2πr
5π = (100 / 360) * 2πr
r = 9 units
arc ABC = (260 / 360) * 2π(9) = 13π
The length of arc ABC with center O and radius of 9 units is 13π.
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The average daily temperature, t, in degrees fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation t = 35 cosine (startfraction pi over 6 endfraction (m 3) 55, where m = 0 represents january 1, m = 1 represents february 1, m = 2 represents march 1, and so on. which equation also models this situation? t = negative 35 sine (startfraction pi over 6 endfraction m) 55 t = negative 35 sine (startfraction pi over 6 endfraction (m 3)) 55 t = 35 sine (startfraction pi over 6 endfraction m) 55 t = 35 sine (startfraction pi over 6 endfraction (m 3)) 55
The answer will be t=-35Sin{[tex]\pi[/tex]/6m)+55 average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.
What is temperature?Temperature is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.
For the equation: 35cos(pi/6(m+3)+55)
Simplify it by multiplying pi/6 in the bracket values:
[tex]=35 Cos (\dfrac{\pi m}{6}+\dfrac{3\pi }{6}+55)[/tex]
[tex]=35 Cos(\dfrac{\pi m}{6}+55+\dfrac{\pi}{2})[/tex]
Now suppose x = m.pi/6+55, while pi/2 = 90⁰
As per law cos(x+90⁰)=-sin(x)
so,cos((m.pi/6)+55+90⁰=-sin((m.pi/6)+55)
Hence answer will be
[tex]=-35Sin(\dfrac{\pi m}{6}+55)[/tex]
The law cos(x+90⁰)=-sin(x) can be proved by putting y=90⁰ in the following formula,
cos(x+y)=cos(x).cos(y)-sin(x).sin(y)
Hence the answer will be t=-35Sin{[tex]\pi[/tex]/6m)+55 average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.
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Answer:
A
Step-by-step explanation:
t = negative 35 sine (StartFraction pi Over 6 EndFraction m) + 55
what is the length of the line segment that has the endpoints A (-3,2) and B (1,0)
Distance measure how far an object have gone. The length of the line segment that has the endpoints A (-3,2) and B (1,0) is 2√5.
How to calculate the distance between two pointsThe formula for calculating the distance between two coordinates is expressed as:
D = √(x2-x1)²+(y2-y1)²
Given the coordinate points A (-3,2) and B (1,0), the length of the line segment that has the endpoint is given as:
D = √(0-2)²+(1+3)²
D = √(2)²+(4)²
D = √16+4
D=√20
D = 2√5
Hence the length of the line segment that has the endpoints A (-3,2) and B (1,0) is 2√5
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6 - v = 260
Solve for V.
Answer:
............
Step-by-step explanation:
help
Use the diagram to complete the statement.
m∠ECF=
Answer:
37°
Step-by-step explanation:
Angle ECF is vertical to angle ACG, so has the same measure. Angle ACG is the second acute angle in right triangle ACG, so is complemetary to angle CAG. It has measure ...
∠ECF = ∠ACG = 90° -∠CAG = 90° -53°
∠ECF = 37°
Liz flips a coin 60 times. The coin lands heads up 36 times and tails up 24 times. Complete each statement.
Answer: 58.33%
Step-by-step explanation:
So, Liz flipped the coin a total of 60 times
Let this be the denominator.
Probability of coin landing up: 35/60
Probability of coin landing down: 24/60
We need the probability of the coin landing up.
So, convert 35/60 into a percentage
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1003560 × 100100= (35 × 10060) × 1100 = 58.33/100
So, the probability is 58.33%
Bruce collects the data on four electric circuits listed in the table. a 3 column table with 4 rows. the first column is labeled circuit with entries w, x, y, z. the second column is labeled voltage in volts with entries 18, 24, 34, 12. the last column is labeled resistance in ohms with entries 38, 34, 70, 18. bruce must report any circuits that deliver more than 4.0 c of charge in 8.0 s. which lists every circuit that bruce must include in his report? x and z x and y w and y w and z
The Bruce must include X and Z in his report.
We have given the data on four electric circuits listed in the table
For w :
Voltage, V=18\ V
resistance, [tex]R=38\ \Omega[/tex]
What is the formula for ohm's low?The formula of Ohm's low is V=IR
[tex]I=\dfrac{V}{R}[/tex]
[tex]I=\dfrac{18\ V}{38\ \Omega}[/tex]
I=0.47
[tex]q=0.47\times8[/tex]
So charge,q=It
q=3.76\ C
For x :
Voltage, V=24\ V
[tex]resistance, R=34\ \Omega[/tex]
so, V=IR...(Ohm's low)
[tex]I=\dfrac{V}{R}[/tex]
[tex]I=\dfrac{24\ V}{34\ \Omega}[/tex]
I=0.705
[tex]q=0.705\times8[/tex]
So charge,q=It
q=5.64\ C
For y :
Voltage, V=34\ V
resistance, [tex]R=70\ \Omega[/tex]
so, V=IR.......(Ohm's low)
[tex]I=\dfrac{V}{R}[/tex]
[tex]I=\dfrac{34\ V}{70\ \Omega}[/tex]
I=0.485
[tex]q=0.485\times8[/tex]
So charge,q=It
q=3.88\ C
For z :
Voltage, V=12\ V
resistance, [tex]R=18\ \Omega[/tex]
so, V=IR......(Ohm's low)
[tex]I=\dfrac{V}{R}[/tex]
[tex]I=\dfrac{12\ V}{18\ \Omega}[/tex]
I=0.66
[tex]q=0.66\times8[/tex]
So charge,q=It
q=5.28\ C
Therefore, the circuits X and Z deliver 5.64 C and 5.28 C of charge.
Hence, Bruce must include X and Z in his report.
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Answer: A) X and Z
Step-by-step explanation:
Got it right on edge.
What's the answer? I need it asap!
Volume of rectangle is
10 times 5 times 3
150 cm
3.14 times radius times 2 times height
So, 50.24 Cm
So its 200.24 Cm
Delta Math: Angle Terminology with Equations
Answer:
x = 13
Step-by-step explanation:
The relevant fact about vertical angles is that they are congruent, their measures are equal. This lets you write an equation relating the expressions for the measures of angles A and B.
__
∠A = ∠B
(8x -12)° = (6x +14)° . . . . . substitute given expressions
2x = 26 . . . . . . . . . . . divide by °, add 12-6x
x = 13 . . . . . . . . . . divide by 2
3x2-9=0 GCF. It’s Precalculus btw
Answer:
x = ± [tex]\sqrt{3}[/tex]
Step-by-step explanation:
3x² - 9 = 0 ( add 9 to both sides )
3x² = 9 ( divide both sides by 3 )
x² = 3 ( take square root of both sides )
x = ± [tex]\sqrt{3}[/tex]
or
3x² - 9 = 0 ← factor out 3 from each term
3(x² - 3) = 0
equate x² - 3 to zero and solve for x
x² - 3 = 0 ( add 3 to both sides )
x² = 3 ( take square root of both sides )
x = ± [tex]\sqrt{3}[/tex]
what is 5x90-100 and divided by 2