Answers
The analysis of the logical statement from among the options indicates that the inference that is not true is the option;
If not p, not q. q therefore not not qWhat is a logical statement?A logical statement is one which draws a conclusion based on an hypothesis.
The logical statement which is incorrect can be found by examining the specified statements as follows;
If p then q,
The converse statement , found by switching the positions of the hypothesis and the conclusion is therefore;
q therefore p
The inference is correct
The statement, if not p, not q . q therefore not not p
According to the law of contraposition, a conditional statement is true when the contrapositive statement is also true.
The statement if not p, not q. which is the contrapositive of the statement if q then p
The inference, q, therefore not not q is incorrect
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Related Questions
PLS HELP ASAP DUE IN 6 MINS PLEASE!!!!!!!! 30 points, giving brainliest!!! ( DO ONLY 5-8) (USE RISE OVER RUN) (FIND SLOPE)
picture is attached :) ty!!
Answers
Answer:
5/ Slope is 0
6/ Slope is 4/1
7/ Slope is -4/2 = -2
8/ Slope is undefined
Step-by-step explanation:
5/ Slope is 0 when it goes straight to the right
6/ We see that the y goes up 4, x over 1, so the slope is 4/1
7/ We see that the y goes down by 4, and x over by 2, so the slope is -2
8/ Slope is undefined when it goes straight up!
If you can please give me a Brainliest, thank you!
Solve the problem by entering and solving an equation.
The Wilsons have triplets and another child who is eleven years old. The sum of the ages of their children is 38. How old are the triplets?
The equation is __n + __ = __
. The triplets are _______ years old.
Answers
Answer:
9
Step-by-step explanation:
Equation
[tex]3n + 11 = 38[/tex]
3n=38-11
n=27/3
n=9
therefore triplets are 9 years old
Check
[tex]3n + 11 = 38[/tex]
[tex]3 \times 9 + 11 = 38 \\ 27 + 11 = 38 \\ 38 = 38[/tex]
Answer:
equation: 3n+11=38
The triplets are 9 years old.
Step-by-step explanation:
3n : triplets x their age
11 : the sum
38 : the sum of the ages
We must isolate n to know their age so,
<=> 3n+11=38
<=> 3n=38-11
<=> n=(38-11)/3
<=> n=9
Devora tested two engines. As each engine's rotation got faster, its temperature increased at a constant rate.
The first engine's temperature (in degrees Celsius) as a function of its rotation speed (in cycles per second) is given by the following table of values:
\text{Rotation}Rotationstart text, R, o, t, a, t, i, o, n, end text (cycles per second) \text{Temperature}Temperaturestart text, T, e, m, p, e, r, a, t, u, r, e, end text (degrees Celsius)
888 26.426.426, point, 4
111111 28.828.828, point, 8
141414 31.231.231, point, 2
The graph of the second engine's temperature (in degrees Celsius) as a function of its rotation speed (in cycles per second) is shown below.
The temperature of which engine increased more for each increase of 111 cycle per second?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The first engine
(Choice B)
B
The second engine
(Choice C)
C
The temperatures of both engines increased the same
Which engine was hotter when it rotated at 202020 cycles per second?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The first engine
(Choice B)
B
The second engine
(Choice C)
C
Both engines were equally hot
Answers
The correct option is B in the given Temperature problem by Calculation T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius,
T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius
According to the given information:
For the first question, we need to compare the rate of change of temperature with respect to rotation speed for both engines. We can do this by calculating the difference in temperature for a change in rotation speed of 111 cycles per second for both engines.
For the first engine, the temperature increased by:
31.2 - 28.8 = 2.4 degrees Celsius
For the second engine, the temperature increased by:
60 - 50 = 10 degrees Celsius
Since the temperature increase for the second engine is greater, we can conclude that the second engine's temperature increased more for each increase of 111 cycles per second. Therefore, the answer is (B) The second engine.
For the second question, we can use linear interpolation to estimate the temperature of each engine at 20 cycles per second.
For the first engine, we can use the two closest data points (8.8 and 11.1 cycles per second) to estimate the temperature at 20 cycles per second:
T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius
For the second engine, we can use the same method with the two closest data points (10 and 20 cycles per second):
T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius
Therefore, we can conclude that the second engine was hotter when it rotated at 20 cycles per second. The answer is (B) The second engine.
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Line q passes through the points (3,5) and (-2,4)
Answers
10) The second pair of coordinate on the line parallel to q and passes through the point (1, 0) is (-5, 0).
11) The second pair of coordinate on the line perpendicular to q and passes through the point (3, 5) is (2, 0).
What is a slope?When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.
Given,
Line q passes through (3, 5), (-2, 4)
(y-y₁)=m(x-x₁)
(y-5)=((4-5)/(-2-3))(x-3)
(y-5)=(-1/-5)(x-3)
-5y+25=-x+3
x-5y+22=0
10) Given point is (0,1)
Slopes are equal for parallel lines.
So, (y-1)/(x-0)=(-1/-5)
-5y+5= -x
x-5y+5=0Let y=0 then,
x= -5
Therefore, the second pair of coordinate on the line parallel to q and passes through the point (1, 0) is (-5, 0).
11) The equation of a line perpendicular to q is,
(y-y₁)=(-1/m)(x-x₁)
(y-5)=5(x-3)
y-5=5x-15
5x-y-10=0
Let y=0 then,
5x-10=0
x=2
Therefore, the second pair of coordinate on the line perpendicular to q and passes through the point (3, 5) is (2, 0).
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Why does 0.5x0.11 is equal to 0.055
Answers
0.5 x 0.11 is equal to 0.055 because of the zeros and the decimal placements.
Step-by-step explanation:How does it work?Even though it would seem like the answer would be 0.55, the decimal placement of 0.5 makes it so that the number would change to an extra zero in the final result.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Give proper explanation
Answers
Answer:
a = 84°
b = 21°
c = 48°
Step-by-step explanation:
Step 1.)
The first step is recognizing the angle of 75° is sticking out from a straight-line, PQ. That straight-line represents an angle of 180°
180°-75° = 105 = a° + b°
Step 2.)
We also know that the line RS is 180°. Therefore, it must be true that
75° + 4b° + b° = 180°
or simply
5b + 75 = 180°
Now solve for b. Subtract both sides by 75 and divide the right side by 5
5b = 105°
b = 21°
4b° = 4 x b = 4 x 21° = 84° = 4b°
Step 3)
Since we know that a + b = 105°, we use substitution to get:
a + 21° = 105
Now subtract both sides by 21
a = 84°
Now let's double check if a + b + 75 = 180
84 + 21 + 75 = 180 [check]
Step 4.)
Since we know that PQ is a straight-line that is 180°, we can say:
180° = 4b° + 2c°
Now substitute 4b with 84°
180° = 84° + 2c
Now solve by subtracting 84 from 180 and divide by 2, if needed.
96° = 2c°
48° = c°
Now double check
96° + 84° = 180° [check]
Therefore:
a = 84°
b = 21°
c = 48°
Hope that helps.
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PLEASE HELP ASAP!!!!!! I DO NOT KNOW HOW TO DO THIS!!!!! AND IT IS DUE TOMORROW ON FRIDAY!!!!!!! (Part 1) I will post part 2
Answers
1) We can explain why the area is πr² by assuming the figure as a rectangle, 2) Diameter = 24.20 cm, Area = 452.91 cm² and 3) the area of the table is 1074.66 in²
What is a circle?The circle is a 2D geometrical figure, with no side or angle, and is made a collection of points.
Given that, 1) a circle with circumferences = 2πr and radius = r, 2) a circle having circumferences = 76 cm and 3) Jada is painting a table having diameter 37 in.
1) Assume the figure as a rectangle, (refer to attached figure)
We get, the length of it is πr and width is r.
And the area of a rectangle is = the Product of length and width.
So, we can conclude that the area of this rectangle is = πr×r = πr²
Therefore, by assuming the figure as a rectangle, we can explain why the area of a circle is πr²
2) circumferences = 2πr
2πr = 76
πr = 38
r = 38/3.14 (π ≈ 3.14)
r = 12.01 cm
Diameter = 2r
D = 2x12.01 = 24.20 cm
Area = πr²
= 3.14x12.01²
= 452.91 cm²
3) Diameter = 37 in
r = 37/2 = 18.5 in
Area = πr²
= 3.14x18.5²
= 1074.66 in²
Therefore, the area of the table is 1074.66 in²
Hence, the answers are 1) We can explain why the area is πr² by assuming the figure as a rectangle, 2) Diameter = 24.20 cm, Area = 452.91 cm² and 3) the area of the table is 1074.66 in²
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how many ways can you write two different letters, so that they are in alphabetical order? for example, am and iq count, but om does not.
Answers
There are 325 ways we can write two different letters so that they are in alphabetical order.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).
A k-combination of a set S is officially defined as a subset of S's k unique elements.
We have 25 ways to have the combo A_
Then 24 ways to have the combo B_
The number of combos = 25 * (26/ 2)
= 25 * 13
= 325 ways
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Solve the inequality by using a table or graph.
x2 − 6x + 8 > 35
x < 3 or x > 9
−3 < x < 9
−9 < x < 3
x < −3 or x > 9
Answers
Method 1: Table
We can create a table of values to find the solution to the inequality:
x | x^2 - 6x + 8 | x^2 - 6x + 8 > 35
-10 | 100 - 60 + 8 | 48 > 35 | false
-5 | 25 - 30 + 8 | 3 > 35 | false
0 | 0 - 0 + 8 | 8 > 35 | false
5 | 25 - 30 + 8 | 3 > 35 | false
10 | 100 - 60 + 8 | 48 > 35 | false
From the table, we can see that the inequality is only true for x < -3 and x > 9. Therefore, the solution to the inequality is x < -3 or x > 9.
Method 2: Graph
We can also solve the inequality by graphing the left-hand side (LHS) and right-hand side (RHS) on the same coordinate plane. The LHS of the inequality is x^2 - 6x + 8, and the RHS is 35.
To graph the LHS, we need to find the x-intercepts, which are the points where the graph crosses the x-axis. The x-intercepts are found by setting y = 0 and solving for x:
0 = x^2 - 6x + 8
x = 3 and x = -2
To graph the RHS, we need to find the y-intercept, which is the point where the graph crosses the y-axis. The y-intercept is found by setting x = 0 and solving for y:
y = 0^2 - 0*6 + 8
y = 8
Now that we have the x-intercepts and y-intercept, we can plot the points and draw the graph of the LHS and RHS:
[asy] /* Made by MRENTHUSIASM */ unitsize(1.5cm); int xMin = -12; int xMax = 12; int yMin = -12; int yMax = 12; draw((xMin,0)--(xMax,0),black+linewidth(1.5),EndArrow(5)); draw((0,yMin)--(0,yMax),black+linewidth(1.5),EndArrow(5)); label("$x$",(xMax,0),(2,0)); label("$y$",(0,yMax),(0,2)); label("$y = 35$",(xMax,35),(0,0),red); label("$y = x^2 - 6x + 8$",(-12,-92),(-2,0),blue); [/asy]
From the graph, we can see that the inequality is only true for x < -3 and x > 9. Therefore, the solution to the inequality is x < -3 or x > 9.
Note: The solution x < 3 or x > 9 and the solution x < -9 or x > 3 are also correct, but they are not the most simplified form of the solution
find the equation of a line with slope 2 and 6 unit away from the origin
Answers
Step-by-step explanation:
find the equation of a line with slope 2 and 6 unit away from the origin
slope intercept form: y = mx + b where m = slope and b = y-intercept.
You are given:
slope = 2
b = 6
answer:
y = 2x + 6
Please answer these questions
Answers
Answer:
Picture 1:
Step 1- Given
Step 2- Addition Property of Equality
Step 3- Division Property of Equality
Picture 2:
Step 1- Given
Step 2- Combine Like Terms
Step 3- Subtraction Property of Equality
Picture 3:
Step 1- Given
Step 2- Distributive Property
Step 3- Combine Like Terms
Step 4- Division Property of Equality
Picture 4:
Step 1- Given
Step 2- Distributive Property
Step 3- Combine Like Terms
Step 4- Addition Property of Order
Step 5- Division Property of Order
Picture 5:
Step 1- Given
Step 2- Distributive Property
Step 3- Subtraction Property of Order
Step 4- Addition Property of Order
Step 5- Combine Like Terms
Step 6- Division Property of Order
Hope this helps :)
Step-by-step explanation:
Get the answer by completing the square
t^2-10t+6=7
Answers
Answer:
[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]
Step-by-step explanation:
Given equation:
[tex]t^2-10t+6=7[/tex]
When completing the square for a quadratic equation, the first step is to move the constant to the right side of the equation:
[tex]\implies t^2-10t+6-6=7-6[/tex]
[tex]\implies t^2-10t=1[/tex]
Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:
[tex]\implies t^2-10t+\left(\dfrac{-10}{2}\right)^2=1+\left(\dfrac{-10}{2}\right)^2[/tex]
Simplify:
[tex]\implies t^2-10t+\left(-5\right)^2=1+\left(-5\right)^2[/tex]
[tex]\implies t^2-10t+25=1+25[/tex]
[tex]\implies t^2-10t+25=26[/tex]
Factor the perfect square trinomial on the left side:
[tex]\implies (t-5)^2=26[/tex]
Square root both sides:
[tex]\implies \sqrt{(t-5)^2}=\sqrt{26}[/tex]
[tex]\implies t-5=\pm \sqrt{26}[/tex]
Add 5 to both sides:
[tex]\implies t-5+5=\pm \sqrt{26}+5[/tex]
[tex]\implies t=5 \pm \sqrt{26}[/tex]
Therefore, the solutions of the given quadratic equation are:
[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]
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Which value is not part of the five-number summary needed for a box plot of this data? { 5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19}.
Answers
The five-number summary required to construct a box plot of this data does not include 11.
What is a five-number summary?When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful.
The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.
So, sort the numbers in the row {5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} from least to largest:
{1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27}
The range starts at 1 and ends at -27.
The middle value in this row—9—is the median.
18 is the median of the right part {12, 15, 18, 19, 27} and 5 is the median of the left part {1, 2, 5, 6, 7}.
The only option missing from A through D is number 11. (numbers 1, 5, and 9 are part of the five-number summary).
Therefore, the five-number summary required to construct a box plot of this data does not include 11.
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Complete question:
Which value is not part of the five-number summary needed for a box plot of this data?
{ 5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19}
A. 1
B. 5
C. 9
D. 11
There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 5?
Answers
The likelihood that the number is 3 or 5 is 0.47.
What is probability?A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
There are 15 identical spaces. Once the spinner has been spun,
Probability is determined by dividing the number of potential outcomes by the number of possible positive outcomes.
5 times: 5, 10, and 15
3 times, 6, 9, 12, and 15.
Different results (3, 5, 6, 9, 10, 12, and 15) (stop doing them).
a variety of successful results 7
3) There are 15 possible outcomes.
4) Probability is equal to 7/15, or 0.47
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Find the value of x and y in the below diagram. TL is the perpendicular bisector of BF. TE = 2x - 10, EL = 8x-17, BE = 3x+6, and BF = 7x-5, m
Answers
Hello,
I hope you and your family are doing well!
To find the value of x, we can use the fact that TL is the perpendicular bisector of BE. This means that TL splits BE into two segments of equal length. Therefore, we have:
EL + BF = BE
Substituting the values for EL, BF, and BE gives:
[tex](8x - 17) + (7x - 5) = (3x + 6)[/tex]
Combining like terms gives:
[tex]15x - 22 = 3x + 6[/tex]
Subtracting 3x from both sides gives:
[tex]12x - 22 = 6[/tex]
Adding 22 to both sides gives:
[tex]12x = 28[/tex]
Dividing both sides by 12 gives:
[tex]x = 28/12 = 7[/tex]
Now that we know the value of x, we can use this value to find the value of y. We can use the equation TE = 2x - 10 to find the value of TE:
TE = 2x - 10 = 2 * 7 - 10 = 14 - 10 = 4
Now we can use the equation EL = 8x - 17 to find the value of EL:
EL = 8x - 17 = 8 * 7 - 17 = 56 - 17 = 39
Since TL is the perpendicular bisector of BE, the length of TL is the average of the lengths of EL and TE. The average of EL and TE is:
(EL + TE)/2 = (39 + 4)/2 = 43/2 = 21.5
So the length of TL is 21.5, and the value of y is 21.5 and x is 7
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Happy Holidays!
A beaker contains 235.5 milliliters of water. If the water is equally distributed among 15 test tubes, how many milliliters will be in each tube?
Answers
Answer: 356 mil
Step-by-step explanation:
Answer:
Each tube will contain 15.7 millimeters
Step-by-step explanation:
Since 235.5 milliliters of water is to be shared among 15 test tubes then the amount of water in each test tube is:
[tex]\frac{235.5}{15} \\\\= 15.7[/tex]
Thus each tube will contain 15.7 millimeters
You buy an I-phone for $800 or pay $75 down and the balance in 12 monthly payments of $65. What is the installment price?
Answers
The installment price is $55.
How to find the price?This can be illustrated through an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Here, you buy an I-phone for $800 or pay $75 down and the balance in 12 monthly payments of $65. The total amount will be:
= 75 + (12 × 65)
= $855
The installment will be:
= $855 - $800
= $55
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Please Help with 4 and 6
Answers
The second-period interest and amount after two months, if The principal amount is $400, The rate of interest is 6% per annum, are $4.02 and $406.02 respectively.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The principal amount, P = 400,
The rate of interest, r = 6% per annum,
The time period, t = monthly = 1 / 12 year,
Calculate the simple interest for the first month as shown below,
Simple interest = [tex]p\times r\times t/100[/tex]
Simple interest = 400 × 6 × 1 / (12 × 100)
Simple interest = 2
Thus, the amount of the first month is the principle for the second month,
Amount of the first month = Principal of the second month = 400 + 2 = 402,
Calculate the simple interest for the second month as shown below,
Simple interest = [tex]p\times r\times t/100[/tex]
Simple interest = 402 × 6 × 2 / (12 × 100)
Simple interest = 4.02
Amount after two months = 402 + 4.02 = 406.02.
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Find g(x), where g(x) is the translation 4 units up of f(x)=x.
Write your answer in the form mx+b, where m and b are integers.
g(x)=
Answers
The equation of the transformed function is g(x) = x + 4
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x
g(x) = translation 4 units up of f(x) = x
The above equations implies that, we have the transformation to be:
Translation 4 units up of f(x)
Mathematically, this can be represented as
g(x) = f(x) + 4
Substitute the known values in the above equation, so, we have the following representation
g(x) = x + 4
Hence, the transformed function si g(x) = x + 4
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Explain the reasoning
Answers
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
[tex] \frac{12}{x} = \frac{8}{6} \\ 12 = \frac{8x}{6} \\ 12 \times 6 = 8x \\ \frac{72}{8} = x \\ 9 = x[/tex]
Check
[tex] \frac{12}{x} = \frac{8}{6} \\ \\ \frac{12}{9} = \frac{8}{6} \\ \\ 1.333 = 1.333[/tex]
~Describe each transformation in words.
10.) ___________________________.
Answers
11. What is the solution to
-2.5(4x-4)= -6?
x=
Answers
[tex]-2.5(4x-4)= -6[/tex]
Distribute:
[tex](-2.5)(4x)+(-2.5)(-4)=-6[/tex]
[tex]-10x+10=-6[/tex]
Subtract 10 from both sides:
[tex]-10x+10-10=-6-10[/tex]
[tex]-10x=-16[/tex]
Divide both sides by -10:
[tex]\dfrac{-10x}{-10} =\dfrac{-16}{-10}[/tex]
[tex]\fbox{x = $\dfrac{8}{5} $}[/tex]
Answer:
-2.5. or - 2.5= they are the same
find the area of shaded region
Answers
Answer:
[tex]1 {p}^{2} + 3p - 3.5[/tex]
Step-by-step explanation:
Look at the picture attached. Hope this helps!
A store is having an inventory reduction sale, so an employee marks down some gold rings from $75
to $39. What percentage is the discount?
Answers
Answer:
48% discount
Step-by-step explanation:
39/75 = 0.52
39 is 52% of 75 but to find the percent discount you have to
1 - 0.52 = .48 *100 = 48%
Determine which integers in the set S:{−4, 4, 6, 21} make the inequality 3(j − 5) > 3(7 − 2j) true.
S:{6, 21}
S:{4, 21}
S:{−4, 6}
S:{−4, 4}
PLS HURRY
Answers
Answer:
b
Step-by-step explanation:
The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.
What is inequality?Inequality is the unequal distribution of resources, opportunities, or rewards among individuals or groups in society. It can occur in many forms, such as unequal access to healthcare, education, employment, or other resources, or unequal treatment based on race, gender, ethnicity, and other factors. Inequality can also manifest as unequal income and wealth distribution, as well as unequal access to political power and decision-making. Inequality can be caused by a variety of factors, including structural factors and personal or individual-level factors, such as discrimination. Inequality can have a negative effect on both individuals and societies, leading to social and economic inequities that can be difficult to overcome.
The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.
First, we will simplify the given inequality.
3(j-5)>3(7-2j)
⇒j-5>7-2j
⇒3j>12
⇒j>4
It means that numbers greater than 4 will satisfy the given inequality.
Numbers greater than 4 in the given set are 6,21.
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22. Sven has 11 more than twice as many customers as when he
started selling newspapers. He now has 73 customers. How many
did he have when he started
Answers
suppose you roll a 6-sided die 6 times. a. how many different (equally likely) outcomes are possible?
Answers
Answer:
You can get the answer of 1,2,3,4,5 or 6. Each are 1/6 likely to be rolled.
Step-by-step explanation:
The die has 6 sides. If you were to roll the die 6 times you have the chance to roll the side with 1. The chances of rolling a 1 are 1/6.
6 possible outcomes
solve the system of equations using the substitution method. state the solution as an ordered pair, (x,y). x+y=2 y=5x-4
Answers
Answer:
(1, 1)
Step-by-step explanation:
x+y=2
y=5x-4
x + 5x - 4 = 2
6x - 4 = 2
6x = 6
x = 1
x + y = 2
1 + y = 2
y = 1
(1, 1)
9. In a combined class of 60 Art and science
Students, the result of their mock examing-
tion showed that 39 of them passed physics
36 Passed Geography and 40 passed History,
of these, 22 passed both physics and History
21 passed both physics and Geography an
23 passed Geography and History. Given
that 10 of them passed all the three subjects
Find:
a. The number of Students who passed only
physics
b. The number of Students who passed
only Geography.
C. The number of student who passed
only History
Answers
The number of students who passed only physics is 6, the number of students who passed only geography is 2, and the number of students who passed only history is 5.
First, let's represent the number of students who passed each subject with the variables P, G, and H. Then, we can represent the number of students who passed multiple subjects with the variables PG, PH, and GH.
We are given the following information:
39 students passed physics (P)
36 students passed geography (G)
40 students passed history (H)
22 students passed both physics and history (PH)
21 students passed both physics and geography (PG)
23 students passed both geography and history (GH)
10 students passed all three subjects (PHG)
We can set up the following equations to represent these relationships:
P = 39
G = 36
H = 40
PH = 22
PG = 21
GH = 23
PHG = 10
We can use these equations to solve for the number of students who passed only physics (P - PH - PG + PHG), only geography (G - GH - PG + PHG), and only history (H - PH - GH + PHG).
So, the number of students who passed only physics is:
P - PH - PG + PHG = 39 - 22 - 21 + 10 = 6
The number of students who passed only geography is:
G - GH - PG + PHG = 36 - 23 - 21 + 10 = 2
The number of students who passed only history is:
H - PH - GH + PHG = 40 - 22 - 23 + 10 = 5
Thus, there are 6 students who passed only physics, 2 students who passed only geography, and 5 students who passed only history.
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The ratio of the numbers of bananas to the number of oranges is 2:3 furthermore there are 24 more oranges to bananas. Calculate the number of bananas Ms Rehka bought.
Answers
The ratio of the numbers of bananas to the number of oranges is 2:3, thus Ms Rehka bought 48 bananas.
What is a ratio?A ratio is a fraction which shows the way of dividing two quantities.
How to calculate the number of bananas Ms Rehka bought?Since the ratio of the numbers of bananas to the number of oranges is 2:3 furthermore there are 24 more oranges to bananas.
Let
x = number of bananas and y = number of ornagesSince the ratio of the numbers of bananas to the number of oranges is 2:3, we have that
x:y = 2:3
x/y = 2/3
Also, there are 24 more oranges to bananas. We have that
y = x +24
Substituting y into the ratio, we have
x/y = 2/3
x/(x + 24) = 2/3
Cross-multiplying, we have
3x = 2(x + 24)
Expanding the brackets, we have
3x = 2x + 48
3x - 2x = 48
x = 48
So, Ms Rehka bought 48 bananas.
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