Skip to content
🤔prompts chat🧠
🔍
question:Find the product of the following matrices: left( begin{array}{ccc} 2 & -2 & -2 2 & 2 & -3 2 & -3 & 1 -1 & -2 & 2 end{array} right) and left( begin{array}{cc} 1 & -2 0 & -2 2 & -1 end{array} right).

answer:To multiply two matrices, we multiply the elements of each row of the first matrix with the elements of each column of the second matrix and add the products. left( begin{array}{ccc} 2 & -2 & -2 2 & 2 & -3 2 & -3 & 1 -1 & -2 & 2 end{array} right) x left( begin{array}{cc} 1 & -2 0 & -2 2 & -1 end{array} right) = left( begin{array}{cc} 2(1) + (-2)(0) + (-2)(2) & 2(-2) + (-2)(-2) + (-2)(-1) 2(1) + 2(0) + (-3)(2) & 2(-2) + 2(-2) + (-3)(-1) 2(1) + (-3)(0) + 1(2) & 2(-2) + (-3)(-2) + 1(-1) (-1)(1) + (-2)(0) + 2(2) & (-1)(-2) + (-2)(-2) + 2(-1) end{array} right) = left( begin{array}{cc} -2 & 2 -4 & -5 4 & 1 3 & 4 end{array} right) The answer is left( begin{array}{cc} -2 & 2 -4 & -5 4 & 1 3 & 4 end{array} right)

question:From a population of 200 elements, a sample of 49 elements is selected. The sample mean is 56 and the sample standard deviation is 14. What is the standard error of the mean?

answer:The standard error of the mean (SE) is a measure of how much the sample mean is likely to vary from the true population mean. It is calculated as the sample standard deviation divided by the square root of the sample size. In this case, we have: SE = σ / √n = 14 / √49 = 14 / 7 = 2 Therefore, the standard error of the mean is 2. The standard error of the mean is 2.

question:If the maximum magnetic field in the region of space where the electromagnetic waves are radiating is 0.00254 T, and the frequency of charge oscillation is 2 cycles/s, what is the wavelength of the emitted waves?

answer:Given Data: Amplitude of magnetic field {eq}(B_{0})= 0.00254, rm T {/eq} Frequency {eq}(f) = 2 , rm cycles/s = 2, rm Hz {/eq} Speed of light {eq}(c)=3, times 10^{8}, rm m/s {/eq} The magnitude of amplitude of the Electric field is given by: {eq}E_{0} = c cdot B_{0} {/eq} {eq}, , ,, , ,, = (3, times 10^{8}, rm m/s) cdot (0.00254, rm T) {/eq} {eq}, , ,, , ,, = 762000, rm V/m {/eq} The wavelength of the electromagnetic wave is given by: {eq}lambda = dfrac{c}{f} {/eq} {eq}, , ,, , ,,= dfrac{3, times 10^{8}, rm m/s}{2, rm Hz} {/eq} {eq}, , ,, , ,,= 1.5, times 10^{8}, rm m {/eq}

question:If the sum of four consecutive even numbers is 100, what is the largest number?

answer:Let's analyze the question: * Sum: Addition. * Four consecutive even numbers: Numbers that follow each other and are all even. * 100: The total sum. Let's represent the first even number as 2n, where n is an integer. Then the next three consecutive even numbers would be 2(n+1), 2(n+2), and 2(n+3). Their sum would be: 2n + 2(n+1) + 2(n+2) + 2(n+3) = 100 Simplifying the equation: 8n + 10 = 100 8n = 90 n = 11.25 Since n is not an integer, we round up to 12. Therefore, the first even number is 2(12) = 24. The largest number is the fourth consecutive even number, which is 2(12+3) = 30.

Released under the MIT License.

has loaded