466 students took the test, which was administered in English. 28 people received a score of 70 or above. The likelihood that the first student will receive a score of 70 or higher is 28/466. The likelihood that the second student will receive a score of 70 or higher is 27/465. The odds of both students receiving a score of 70 or higher are 28/466 × 27/465.
A percentage can be utilized to solve for the unknown distance because the ratio of inches to actual distance is constant. Create a scale to depict the scenario. The question asks for the distance represented by 25 inches using a ratio of 10 inches to 100 feet. Write a proportion that equates the supplied and unknown data, making sure that the units of each ratio are consistent (all inches on top or all inches on bottom):
10 in/100 ft=25 in/x ft
To solve for the unknown, x feet, use cross multiplication as follows:
10x=25∗100
x=25∗100/10
x=250 ft
Remember that the percentage change is equal to the difference between the new and original values, divided by the original value, and multiplied by 100%. The change is an increase if the new value is greater than the previous value. The change is a decline if the new value is less than the previous value. In algebraic form:
Percentage Increase =
Final Value − Original Value/Original Value ∗100%
Substitute the given values and evaluate to find the percentage increase:
=$600−$450/$450 ∗ 100%
=$150/$450 ∗ 100%
=33.3%
The highest number displayed in a mark interval is 128. This number falls between the range of 50-59. 32 + 45 = 77 students make up the grade range of 10-29. Greater than 77 is 128. The mark range between 50 and 59 had the highest proportion of students who took the test, according to the mark intervals displayed.
Using x to represent the unknown integer, convert the question into an equation:
44 = 0.8x
Divide both sides by the decimal:
44/0.8 = x
x = 55
Use the following formula to calculate the average for the entire journey:
Average Speed = Total Distance/Total Time
Calculate the entire distance traveled first:
Total Distance = 2(70) + 5(63)
= 140+315
= 455 km
Next, find the total time:
Total Time=2 hours+5 hours
= 7 hours
To solve, enter these values into the average speed formula:
Average Speed = 455/7
= 65 km/h
The median will be determined by averaging the 233rd and 234th marks once the marks have been arranged in order, as there are 466 students. The 233rd and 234th places will both fall between the ages of 40 and 49. Between 40 and 49 will be the average of these two marks.
10x2 – 11x + 3 = 10x2 – 5x – 6x + 3 10x2 – 5x – 6x + 3 = 5x(2x – 1) – 3(2x – 1) 5x(2x – 1) – 3(2x – 1) = (5x – 3)(2x -1)
The score ranges that denote failure are 0–9, 10–19, 20–29, and 30-39. There were 23, 32, 45, and 67 marks in those categories. 23 + 32 + 45 + 67 = 167. There were 167 pupils that didn't pass the test.
The profit of a corporation is equal to the difference between its total revenue and total costs. The total revenue is calculated by multiplying the number of smartphones sold by the average cost per smartphone:
Total Revenue = 500 phones∗sales price,Y
Total Revenue = 500Y
The total cost is calculated by multiplying the number of smartphones sold by the cost of manufacturing each smartphone:
Total Cost = number of phones∗cost
Total Cost = 500∗$200
Total Cost = $100,000
The total profit is then:
Total Profit = Revenue−Cost
Total Profit = 500Y−$100,000
2x^2−2x−4=2(x2−x−2)=2(x+1)(x−2)=0 x+1=0 or x−2=0 x+1−1=0−1 or x−2+2=0+2 So, the solutions to the equation 2x^2 - 2x - 4 = 0 are x = 2 or x = -1.
(x2 + x + 3) / (x + 2) = ( (-1)2 + (-1) + 3) / ((-1) + 2) when x=-1 ((-1)2 + (-1) + 3) / ((-1) + 2) = (1 – 1 + 3)/ (-1 + 2) (1 – 1 + 3)/ (-1 + 2) = 3 / 1 = 3
(√3 + √2)2 = (√3 + √2)( √3 + √2) =(√3 + √2)( (√3 + √2) =√3×√3 + √3×√2 + √2×√3 + √3×√3 =√3×√3 + √3×√2 + √2×√3 + √3×√3 =3 + √6 + √6 + 2 =5 + 2√6
Given that the sequence in which committees are constituted has no bearing on the overall number of possible committees (committee A, B, C is the same as committee B, A, C), the total number of possible committees can be computed using a combination. The formula gives the number of possibilities to choose r elements from a group of n elements:
nCr = n!/r!(n−r)!
nCr = 5!3/!(5–3)!
nCr = 5∗4∗3∗2∗1/(3∗2∗1)(2∗1) = 5∗4/2∗1
nCr = 10
23 + 32 + 45 = 100 students received a grade of less than 30. 23 + 32 = 55 students received a grade of less than 20. 55/100 = 55% of pupils had a grade of less than 20, less than 30, or less than 30.
A linear equation is an equation that connects an input variable to an output variable by raising both variables to the first power. The slope is the constant ratio of the change in y coordinates to the change in x coordinates in a linear equation. The algebraic expression for the slope is:
m=y2−y1x2−x1
The slope-intercept form of the equation for a line is y=mx+b, where m is the slope, b is the y-intercept, and (x,y) is a line point. The slope is 3 in this question, and the slope-intercept form of the line is provided.
To solve for x, perform the relevant operations to simplify the issue, then combine like terms. To get rid of the parentheses, start by dispersing the terms.
Through the parentheses, multiply the 5 and the 4:
14.5x−5x−10≤4+16−1/2x
Combine like terms on both sides of the inequality:
9.5x−10≤20−1/2x
Add 1/2x to both sides:
10x−10≤20
Add 10 to both sides:
10x≤30
Divide both sides by 10:
x≤3
It was not essential in this situation, but keep in mind that when both sides of an inequality are multiplied or divided by a negative number, the inequality's direction changes.
(2^4 x 3^2) / (2 x 3)= 2^4-1 × 3^2-1. 2^4-1 × 3^2-1 = 2^3 × 3^1 2^3 × 3^1 = 2^3 × 3
Treat the three people who want to sit next to each other as a single group. The group consists of 4 units, each with three individuals. 4 arrangements of the 4 units are possible! on the bench, positions. The trio in the group can be arranged into threes. ways. There are four arrangements in total. × 3! = 144.
To compare the fractions to the decimal values already provided, first convert them to decimals:
1/6=0.1667
1/3=0.333
3/22=0.13636
The correct order of the numbers will be:
0.13636
0.16
0.1667
0.333
0.4
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