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# Math answers to 41 questions

“S” best completes the sequence A E F H Z V U. this is so because in analyzing the letters involved in the sequence, it is noticed that between letter A and letter E, there are five existing letters between…

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Answer: C. You'll make a profit of $150. One share of stock is quoted at 25 ¼ in the Lofty Cheese Company. If you hold around 30 shares of that exact stock, which was bought at 20 ¼. If that…

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Answer: B. p(-0.5≤z≤0.5) Using the picture of normal distribution, it is noticed that all internals listed in the option are 1 unit long option B is the interval which covers the most area of 34%. With this, it is seen…

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Answer: A. Point and line Two lines are said to be parallel to each other when they do not intersect themselves at any point. In other words, parallel lines will continue to move in a single straight direction without meeting…

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Answer: C. circumference The distance around a circle is called the circumference. This is the perimeter of the circle as well as its arc length. The diameter of a circle is any line that divides the circle into two equal…

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15 cents = two lemons 60 cents = x lemons Cross multiply: 15x = 60 x 2 15x = 120 x = 8 Therefore, 60 cents will buy 8 lemons

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2/3 x 2/3 = 4/9 This is because when multiplying two fractions, the numerator of one fraction is multiplied by that of the other while the denominator of the first fraction is multiplied by that of the other. With this,…

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Answer: B. A line has one dimension because it is made up of all points that extend infinitely in either direction. A line has a single dimension because it consists of points that extend in either direction without limit. Shapes…

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Parallel lines are lines that can never intersect each other no matter how long you make them. Triangles therefore have no parallel lines as they are polygons having three sides which sums up to 1800. All sides of a triangle…

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The prime factor of a number is simply the prime numbers capable of multiplying together to make the original number. Factors are just numbers that can be multiplied together to get another number but prime factors are made up only…

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Answer: D. In a right triangle, the square of the hypotenuse equals the sum of the square of the legs. The Pythagorean Theorem is a mathematical law that states that the sum of the square of the lengths of the…

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Answer: A. 2 acute and 1 right The total angle in a triangle must equal 180. Two acute and one right angle is very capable of forming a triangle as the sum of the three angles can be assumed to…

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Solution: The density of Styrofoam is 32kg/m3 Since it’s on a lake, then the density of water is 1000kg/m3 Buoyant Force = the boy’s weight + mass of ice V (ρwater – ρice) = m V= m/(ρwater-ρice) Thus, V=42/1000-32= 0.0434m3…

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Answer: 2. negative square root 21 over 5 Cos Θ = -2/5 = -0.4 Tan Θ > -1 Sin Θ = ? Sin²Θ + Cos²Θ = 1 Sin²Θ = 1 – Cos²Θ Sin²Θ = 1 – (–0.4)² Sin²Θ = 1…

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One slug would equal 14.59 kilogram and 1ft would equal 0.3048m. 15N would be equal to 15 kilogram meter per second square. 1 slug = 14.59kg 1ft=0.3048m 15 N = 15 kg m / s^2 = 15 * (1/14.59) slug…

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A hexagonal pyramid is a geometric shape that has just one base (a hexagonal base), and its sides are made entirely of six isosceles triangles. The isosceles triangles are arranged along the edges of the hexagonal base, and they stretch…

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Answer: D. P(z≤-a)+P(-a≤z≤a)+P(Z≥a) Explanation: or a standard normal distribution, the expression must always equal 1. This is because P(z≤-a)+P(-a≤z≤a)+P(Z≥a) represents all the possible values in the total area of any given curve. In agreement with the formula for expressing standard…

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Answer: E =172.932 μm Step-by-step solution: When E is located at point (-40, -20) According to Pythagoras' theory, the displacement of E from its point of origin = √(40² + 20²) = 44.721 μm. Total distance travelled = AB +…

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No. Not all integers are whole numbers, but all whole numbers are integers. Integers, typically, are all positive numbers, zero digits, and negative numbers. Whole numbers only comprise positive and zero digits. All natural numbers (counting numbers that are known:…

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Answer: Take Θ=30 Cos 150° If Cos (180° - Θ)= -Cos Θ, Then Cos (180 - 30)= -Cos Θ. Cos 150 = -Cos 30 (√3 /2),= 0.8660 Sin 150° If Sin (180° - Θ)= Sin Θ, Then Sin (180 -…

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It takes one thousand thousand to make up a million. In the arrangement of numbers according to the place value system from right to left according to the numbering system of the Indians, it is thus: Units, Tens, Hundreds, Thousands,…

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No, 0 is not a rational number because it cannot be expressed as a simple fraction with a non-zero denominator. Rational numbers are numbers that can be expressed in the form of simple fractions, where the denominator is a non-zero…

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The difference between normal and binomial distribution is that normal distribution in statistics refers to a data set in which the probability of the outcomes of the events are closer to the average value. Examples include blood samples, IQ scores,…

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The exclamation mark in math is used in permutation to indicate factorials. When the exclamation mark is used in front of a positive integer, it means that one should find the product of the integers from the positive integer to…

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We can solve this using the trig unit circle. sin x = 1/2 = sin (π/6) → x = π/6

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To find the answer, we have to divide the area of a circle for bull's eye by the area of the circle for dart board. The area of a circle formula is: A = π * r2 Dart board radius…

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Here are the calculations: 16. 91% of 84% = 0.91 X 0.84 = 0.7644, (which equals 76.44%) 84 - 76.44 = 0.0756 This means that the probability of an incorrect conclusion equals 7.6% (nearest tenth)

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5’ 10’ in inches is 70 inches! Normally, doctors and scientists do not measure height in inches and feet. Height is measured by these professionals in centimetres. If you know your height in feet and inches but need to provide…

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All months have 28 days (and more) but only February is 28 days long in normal years and 29 days long in leap years. However, all twelve months in a year have up to 28 days. Others apart from February…

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One dollar is equal to 100 pennies. Therefore, 1 million pennies converts to 10,000 dollars. However, why would you want to save pennies instead of dollars for ease of calculation? According to the San Diego Union-Tribune, the Pride of Lions…

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