The difference between the fractions 5 minutes of an hour and 20 seconds of an hour is:
\( \frac{0.7}{9} \)
\( \frac{7}{12} \)
\( \frac{16}{180} \)
\( \frac{28}{270} \)
To find the difference between the given fractions, we first need to convert all time units into a common unit, preferably seconds, to express them as fractions of an hour. Then, we will perform the subtraction and simplify the resulting fraction.
Convert minutes to a fraction of an hour:
There are 60 minutes in an hour. So, 5 minutes as a fraction of an hour is:
\[ \text{Fraction}_1 = \frac{5 \text{ minutes}}{60 \text{ minutes}} = \frac{5}{60} = \frac{1}{12} \]Convert seconds to a fraction of an hour:
There are 60 seconds in 1 minute, and 60 minutes in 1 hour. So, there are \(60 \times 60 = 3600\) seconds in an hour. 20 seconds as a fraction of an hour is:
\[ \text{Fraction}_2 = \frac{20 \text{ seconds}}{3600 \text{ seconds}} = \frac{20}{3600} = \frac{1}{180} \]Find the difference between the two fractions:
The difference is \( \text{Fraction}_1 - \text{Fraction}_2 \):
\[ \text{Difference} = \frac{1}{12} - \frac{1}{180} \]To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 12 and 180 is 180.
\[ \text{Difference} = \frac{1 \times 15}{12 \times 15} - \frac{1}{180} = \frac{15}{180} - \frac{1}{180} \] \[ \text{Difference} = \frac{15 - 1}{180} = \frac{14}{180} \]Simplify the resulting fraction:
Both the numerator and the denominator are divisible by 2:
\[ \text{Difference} = \frac{14 \div 2}{180 \div 2} = \frac{7}{90} \]Check the options:
Let's convert the options to a common format or compare our result with them.
Option A is \( \frac{0.7}{9} \). We can write this as \[\frac{7/10}{9} = \frac{7}{10 \times 9} = \frac{7}{90}\].
This matches our calculated difference.
A) \( \frac{0.7}{9} \) is equivalent to \[\frac{7/10}{9} = \frac{7}{90}\], which is the correct difference calculated.
The question asks to identify the inventor of the World Wide Web (WWW). This requires knowledge of key figures in the history of computing and the internet.
Correct Option: D) Tim Berners-Lee
Sir Tim Berners-Lee, a British computer scientist, is credited with inventing the World Wide Web in 1989 while working at CERN. He developed the first web browser, web server, and the fundamental protocols (HTTP, HTML, URL) that form the basis of the web.
In a school the ratio of the number of boys and girls is 5:6. 20% boys and 25% girls are scholarship holders. What percentage of students did not get a scholarship?
\( \frac{750}{11} \)%
\( \frac{950}{11} \)%
\( \frac{850}{11} \)%
\( \frac{8000}{11} \)%
To find the percentage of students who did not get a scholarship, we will first assume a total number of students based on the given ratio. Then, we will calculate the number of boys and girls, and subsequently, the number of scholarship holders among them. Finally, we will determine the number of students without scholarships and express it as a percentage of the total students.
Assume a common multiple for the ratio:
The ratio of boys to girls is 5:6. Let the number of boys be \(5x\) and the number of girls be \(6x\).
Calculate the total number of students:
Total students \( = 5x + 6x = 11x\).
Calculate the number of boys and girls who are scholarship holders:
Calculate the total number of scholarship holders:
Total scholarship holders \[= x + \frac{3}{2}x = \frac{2x + 3x}{2} = \frac{5x}{2}\].
Calculate the number of students who did not get a scholarship:
Students without scholarship = Total students - Total scholarship holders
\[ = 11x - \frac{5x}{2} = \frac{22x - 5x}{2} = \frac{17x}{2} \]Calculate the percentage of students who did not get a scholarship:
Percentage = \[\left( \frac{\text{Number of students without scholarship}}{\text{Total number of students}} \right) \times 100\]
\[ = \left( \frac{\frac{17x}{2}}{11x} \right) \times 100 \] \[ = \left( \frac{17x}{2 \times 11x} \right) \times 100 \] \[ = \left( \frac{17}{22} \right) \times 100 \] \[ = \frac{1700}{22} = \frac{850}{11} \]So, \(\frac{850}{11}\)% of students did not get a scholarship.
C) \(\frac{850}{11}\)%
The problem involves a coding-decoding pattern where letters are assigned numerical values, and these values are then manipulated (e.g., multiplied or added) to produce the given code. We need to identify the pattern from the given examples (DO = 60, SO = 285) and then apply it to find the code for RED.
A) 360 is the correct code for RED, derived by multiplying the alphabetical positions of its letters (18 x 5 x 4 = 360).
To determine what the product of any two consecutive even numbers is always divisible by, we can represent two consecutive even numbers algebraically and then analyze their product. We will test the divisibility by the given options.
Correct Option: A) 8
The problem states that \(-5\) is a root of two quadratic equations. We will use this information to find the values of \(p\) and \(k\). First, substitute \(-5\) into the first equation to find \(p\). Then, substitute \(-5\) and the value of \(p\) into the second equation to find \(k\).
Use the first quadratic equation to find \(p\):
The first quadratic equation is \( 2x^{2} + px - 15 = 0 \). Since \(-5\) is a root, substituting \(x = -5\) into the equation must satisfy it:
\[ 2(-5)^{2} + p(-5) - 15 = 0 \]\[ 2(25) - 5p - 15 = 0 \]\[ 50 - 5p - 15 = 0 \]\[ 35 - 5p = 0 \]\[ 5p = 35 \]\[ p = \frac{35}{5} \]\[ p = 7 \]Use the second quadratic equation and the value of \(p\) to find \(k\):
The second quadratic equation is \( p(kx^{2} + x) = 0 \). We found \(p = 7\), and \(-5\) is also a root of this equation. Substitute \(p = 7\) and \(x = -5\) into the equation:
Since \(p=7 \neq 0\), we can divide the equation by \(p\):
\[ kx^{2} + x = 0 \]\[ k(-5)^{2} + (-5) = 0 \]\[ k(25) - 5 = 0 \]\[ 25k = 5 \]\[ k = \frac{5}{25} \]\[ k = \frac{1}{5} \]\[ k = 0.2 \]State the values of \(p\) and \(k\):
We found \(p = 7\) and \(k = 0.2\).
A) 7, 0.2 — This matches our calculated values for \(p\) and \(k\).
The question asks to identify the Bollywood celebrity who collaborated with David Letterman for a Netflix show. This requires knowledge of specific celebrity collaborations and Netflix original programming.
Correct Option: C) Shahrukh Khan
Shahrukh Khan appeared on David Letterman's Netflix talk show, "My Next Guest Needs No Introduction with David Letterman," in 2019. This episode featured an in-depth interview with the Bollywood superstar, covering various aspects of his life and career.
This is a blood relation question. We need to decode the relationship described by Ashish step-by-step, working backward from the end of the statement to determine Ashish's relationship with Deveshi.
C) Father — As derived from the step-by-step analysis, Ashish is Deveshi's father.
This problem involves calculating simple interest for two different scenarios and then using the given difference in interest to find the principal amount. We will use the formula for simple interest: \(I = \frac{P \times R \times T}{100}\), where \(I\) is the interest, \(P\) is the principal, \(R\) is the rate of interest, and \(T\) is the time period.
A) ₹3,000.00 is the correct amount invested by them, as calculated from the difference in simple interest.
The area of triangle ABC is 39 cm². D and E are two points on BC such that BD = DE = EC, then what is the area of triangle ADC?
The problem involves finding the area of a sub-triangle within a larger triangle. The key principle here is that if two triangles share the same height, the ratio of their areas is equal to the ratio of their bases. Also, if a triangle is divided into smaller triangles by segments from a common vertex to points on the opposite side, and these points divide the base into equal segments, then the areas of the smaller triangles formed with the common vertex will be equal.
Let the area of triangle ABC be denoted as \(\text{Area}(\triangle \text{ABC})\). We are given that \(\text{Area}(\triangle \text{ABC}) = 39 \text{ cm}^2\).
D and E are two points on BC such that \(\text{BD} = \text{DE} = \text{EC}\). This means that the base BC is divided into three equal segments by points D and E.
Let the length of each segment be \(x\). So, \(\text{BD} = x\), \(\text{DE} = x\), and \(\text{EC} = x\).
The total length of the base BC is \(\text{BC} = \text{BD} + \text{DE} + \text{EC} = x + x + x = 3x\).
Consider the triangles \(\triangle \text{ABD}\), \(\triangle \text{ADE}\), and \(\triangle \text{AEC}\). All these triangles share the same vertex A, and their bases lie on the same line segment BC. Therefore, they all have the same height with respect to their bases on BC. Let this height be \(h\).
The area of a triangle is given by the formula \(\frac{1}{2} \times \text{base} \times \text{height}\).
Since \(\text{BD} = \text{DE} = \text{EC}\), and they share the same height \(h\), their areas must be equal:
\[ \text{Area}(\triangle \text{ABD}) = \text{Area}(\triangle \text{ADE}) = \text{Area}(\triangle \text{AEC}) \]The sum of these areas is the area of \(\triangle \text{ABC}\):
\[ \text{Area}(\triangle \text{ABC}) = \text{Area}(\triangle \text{ABD}) + \text{Area}(\triangle \text{ADE}) + \text{Area}(\triangle \text{AEC}) \]Since the three smaller areas are equal, let \(\text{Area}(\triangle \text{ABD}) = \text{Area}(\triangle \text{ADE}) = \text{Area}(\triangle \text{AEC}) = A'\). Then,
\[ \text{Area}(\triangle \text{ABC}) = A' + A' + A' = 3A' \]We are given \(\text{Area}(\triangle \text{ABC}) = 39 \text{ cm}^2\). So,
\[ 3A' = 39 \text{ cm}^2 \]\[ A' = \frac{39}{3} = 13 \text{ cm}^2 \]Therefore, \(\text{Area}(\triangle \text{ABD}) = 13 \text{ cm}^2\), \(\text{Area}(\triangle \text{ADE}) = 13 \text{ cm}^2\), and \(\text{Area}(\triangle \text{AEC}) = 13 \text{ cm}^2\).
We need to find the area of \(\triangle \text{ADC}\). The base of \(\triangle \text{ADC}\) is DC. From the given information, \(\text{DC} = \text{DE} + \text{EC} = x + x = 2x\).
The area of \(\triangle \text{ADC}\) can also be expressed as the sum of the areas of \(\triangle \text{ADE}\) and \(\triangle \text{AEC}\):
\[ \text{Area}(\triangle \text{ADC}) = \text{Area}(\triangle \text{ADE}) + \text{Area}(\triangle \text{AEC}) \]Substituting the value of \(A'\):
\[ \text{Area}(\triangle \text{ADC}) = 13 \text{ cm}^2 + 13 \text{ cm}^2 = 26 \text{ cm}^2 \]Correct Option: A) 26 cm²