To find the probability of getting zero heads in five tosses of a fair coin, we start by defining the scenario. For each toss of the coin, there are two possible outcomes: heads (H) or tails (T). Since we want to calculate the probability of getting zero heads, we focus on only getting tails in … Read more
To find the dimensions of the square lawn, let’s denote the length of one side of the lawn as x meters. The area of the square lawn (A_lawn) can then be calculated as: A_lawn = x² Since this lawn is bordered by a 4m wide path on three sides, we need to consider the overall … Read more
To understand the expression 42/3, we can break it down into more manageable parts. Firstly, 4 can be expressed as 22 because 2 squared gives us 4. This means we can rewrite the entire expression: 42/3 = (22)2/3. Next, when raising a power to another power, we multiply the exponents: (22)2/3 = 2(2 * 2/3) … Read more
Understanding a Normal Distribution with Mean 50 and Standard Deviation 4 A normal distribution is a statistical concept that describes how values are spread out around a central mean. In our case, the mean is 50. This means that if you were to take many measurements, the average or most common value would be 50. … Read more
To find the missing angle of a right triangle, you first need to understand that all the angles in a triangle add up to 180 degrees. In a right triangle, one of those angles is always 90 degrees. Therefore, if you know one of the other angles, you can easily find the missing angle by … Read more
To find the value of the expression 2x³ + 3y² + 17 when x = 3 and y = 4, we will substitute the values of x and y into the expression. First, let’s break down the expression into its components: Calculate x³: Since x = 3, we compute 3³ = 27. Calculate y²: Since … Read more
To find the probability of obtaining at most 30 fives in 200 tosses of a fair die, we can use the binomial probability formula. However, since the number of tosses is large and the expected number of fives will determine the distribution closely resembles a normal distribution, we can apply the normal approximation for simplicity. … Read more
The discriminant is a key component when analyzing the nature of the roots of a quadratic equation, which typically has the form ax² + bx + c = 0. In your example, the equation simplifies to 2x = 0 To find the discriminant, we use the formula: D = b² – 4ac In your case: … Read more
To find a cubic function that has real zeros at x = 3 and x = 7, we need to formulate a function that includes these roots. A cubic function can generally be represented in the form: f(x) = a(x – r1)(x – r2)(x – r3) Here, a is a non-zero constant, and r1, r2, … Read more
To estimate the maximum error in the radius of a sphere when given its circumference using differentials, we can follow these steps: The formula for the circumference (C) of a sphere is given by: C = 2πr where r is the radius. To find the differential of the circumference, we differentiate both sides with respect … Read more