answer:**Analysis** This question examines the negation form of propositions containing quantifiers, the truth and falsehood of proposition p and its negation neg p, and the necessary and sufficient conditions for a quadratic inequality to always hold, considering the direction of the opening and the axis of symmetry. Convert exists to forall and negate the conclusion to write out the negation of proposition p; use the truth and falsehood of p and neg p to determine that neg p is a true proposition; setting the discriminant less than 0 to find a. **Solution** The negation of proposition p: exists x in mathbb{R}, x^2 + 2ax + a leqslant 0 is proposition neg p: forall x in mathbb{R}, x^2 + 2ax + a > 0, Since proposition p is a false proposition, Therefore, proposition neg p is a true proposition, That is, x^2 + 2ax + a > 0 always holds, Therefore, Delta = 4a^2 - 4a < 0, Solving this yields 0 < a < 1. Hence, the answer is boxed{(0,1)}.

answer:To solve the given inequality x^{3}+x > x^{2}y+y, we will manipulate and simplify the inequality step by step, following closely the solution provided. 1. Start by rearranging the inequality: [x^{3}+x > x^{2}y+y] 2. Factor common terms on the right side: [x^{3}+x > y(x^{2}+1)] 3. Move all terms to one side to compare them directly: [x^{3}+x - y(x^{2}+1) > 0] 4. Notice that x^{3}+x can be factored as (x^{2}+1)x, so rewrite the inequality using this factorization: [(x^{2}+1)x - y(x^{2}+1) > 0] 5. Factor out the common term (x^{2}+1): [(x^{2}+1)(x-y) > 0] 6. From the factored form, it's clear that for the inequality to hold, (x-y) > 0 since (x^{2}+1) is always positive for all real numbers x: [x-y > 0] Therefore, the statement "x-y > -1" is a necessary but not sufficient condition for "x^{3}+x > x^{2}y+y". This is because "x-y > 0" is a stricter condition than "x-y > -1", meaning that while the former is required for the original inequality to hold, it does not encompass all scenarios where "x-y > -1". In conclusion, the correct choice is: [boxed{B}]

answer:The function is given by f(x) = x ln(x) + a. Differentiating with respect to x, we get f'(x) = ln(x) + 1. At the point (1, f(1)), we have f'(1) = 1 and f(1) = a. Therefore, the equation of the tangent line is y = x - 1 + a. Since the tangent line passes through the point (2, 2), we can substitute these values into the tangent line equation: 2 = 2 - 1 + a Solving for a, we get a = 1. So, the answer is: boxed{a = 1}.

answer:Let's denote the total number of female cows as F. According to the information given, 50% of the female cows are pregnant, and there are 11 pregnant female cows. Therefore, we can write the following equation: 0.50 * F = 11 To find the number of female cows (F), we solve for F: F = 11 / 0.50 F = 22 So there are 22 female cows on Terez's farm. To find the percentage of the cows that are female, we use the total number of cows, which is 44. The formula to calculate the percentage is: (Female cows / Total cows) * 100 = Percentage of female cows Plugging in the numbers we have: (22 / 44) * 100 = Percentage of female cows This simplifies to: 0.5 * 100 = Percentage of female cows So: 50% = Percentage of female cows Therefore, boxed{50%} of the cows on Terez's farm are female.