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CM
24 tháng 1 2018
Số phần tử của không gian mẫu là n Ω = C 30 5 = 142506
Gọi A là biến cố: “đề thi lấy ra là một đề thi tốt”.
Vì trong một đề thi “tốt” có cả ba câu dễ, trung bình và khó đồng thời số câu dễ không ít hơn 2 nên ta xét các trường hợp sau:
Trường hợp 1: Đề thi gồm 3 câu dễ, 1 câu trung bình và 1 câu khó có C 15 1 C 10 1 C 5 1 cách.
Trường hợp 2: Đề thi gồm 2 câu dễ, 2 câu trung bình và 1 câu khó có C 15 2 C 10 2 C 5 1 cách.
Trường hợp 3: Đề thi gồm 2 câu dễ, 1 câu trung bình và 2 câu khó có C 15 2 C 10 1 C 5 2 cách.
Suy ra n A = C 15 3 C 10 1 C 5 1 + C 15 2 C 10 2 C 5 1 + C 15 2 C 10 1 C 5 2 = 56875
Vậy xác suất cần tìm là P A = n A n Ω = 56875 142506 = 625 1566
Đáp án D
K
15 tháng 4 2021
1: Only with careful environmental planning can we protect the world in which we live.
D. We can protect the world we live in only with careful environmental planning.
2: You should take regular exercises instead of sitting in front of the television all day.
A. Taking regular exercises is better than sitting in front of the television all day.
3: It was not until after I got home that I realized I had not set the burglar alarm in the office.
C. I didn’t turn the burglar alarm on before I left the office, but I only became aware of this after I'd arrived home.
4: He did not remember the meeting. He went out for a coffee with his friends then.
D. Not remembering the meeting, he went out for a coffee with his friends.
5: They left their home early. They didn’t want to miss the first train.
C. They left their home early so as not to miss the first train.
6: I’m sure Luisa was very disappointed when she failed the exam
B. Luisa must have been very disappointed when she failed the exam.
7. “You had better see a doctor if the sore throat does not clear up.” she said to me.
D. She suggested that I see a doctor if the sore throat did not clear up.
8: Without her teacher’s advice, she would never have written such a good essay
C. She wrote a good essay as her teacher gave her some advice.
9. She tried very hard to pass the driving test. She could hardly pass it.
C. No matter how hard she tried, she could hardly pass the driving test.
10. Mary loved her stuffed animal when she was young. She couldn’t sleep without it.
A. When Mary was young, she loved her stuffed animal so much that she couldn't sleep without it.
DT
Đỗ Thanh Hải
CTVVIP
15 tháng 4 2021
1: Only with careful environmental planning can we protect the world in which we live.
A. Careful environmental planning protects the world we live in.
B. Planning the environment carefully, we can protect the world in which we live.
C. Protecting the world we live in, we plan the environment carefully.
D. We can protect the world we live in only with careful environmental planning.
2: You should take regular exercises instead of sitting in front of the television all day.
A. Taking regular exercises is better than sitting in front of the television all day.
B. Sitting in front of the television all day helps you take regular exercises.
C. Sitting in front of the television all day and taking exercises are advisable.
D. Don’t take regular exercises, just sit in front of the television all day.
3: It was not until after I got home that I realized I had not set the burglar alarm in the office.
A. On the way home, I suddenly realized that I had forgotten to turn on the burglar alarm in the office.
B. Fortunately, I realized that I hadn't set the burglar alarm just before I left for home; otherwise, I would have had to travel all the way back to the office.
C. I didn’t turn the burglar alarm on before I left the office, but I only became aware of this after I'd arrived home.
D. I wish I had realized before I arrived home that I hadn't turned on the burglar alarm in the office, then it would have been easier to go and set it.
4: He did not remember the meeting. He went out for a coffee with his friends then.
A. Not remember the meeting, he went out for a coffee with his friends.
B. Not to remember the meeting, he went out for a coffee with his friends.
C. Not remembered the meeting, he went out for a coffee with his friends.
D. Not remembering the meeting, he went out for a coffee with his friends.
5: They left their home early. They didn’t want to miss the first train.
A. They left their home early so as to not miss the first train.
B. They left their home early for fear that they wouldn’t miss the first train.
C. They left their home early so as not to miss the first train.
D. They left their home early in order that not to miss the first train.
6: I’m sure Luisa was very disappointed when she failed the exam
A. Luisa must be very disappointed when she failed the exam.
B. Luisa must have been very disappointed when she failed the exam.
C. Luisa may be very disappointed when she failed the exam.
D. Luisa could have been very disappointed when she failed the exam.
DM
5 tháng 6 2021
câu rất có ý nghĩa, giúp mình có tinh thần thi vô lớp sáu. Nhưng bạn có thể đăng cái này lên Facebook dùm mình vì mình ko rảnh đọc những cái này mà chỉ lướt lướt xem câu nào biết thì giải thôi.
dù sao cũng rất cảm ơn bạn nhé!
17 tháng 1 2021
Câu 4b:
Ta có \(a-\sqrt{a}=\sqrt{b}-b\Leftrightarrow a+b=\sqrt{a}+\sqrt{b}\). (1)
Áp dụng bất đẳng thức Cauchy - Schwarz ta có:
\(a^2+b^2\ge\dfrac{\left(a+b\right)^2}{2};\sqrt{a}+\sqrt{b}\le\sqrt{2\left(a+b\right)}\).
Kết hợp với (1) ta có:
\(a+b\le\sqrt{2\left(a+b\right)}\Leftrightarrow0\le a+b\le2\).
Ta có: \(P\ge\dfrac{\left(a+b\right)^2}{2}+\dfrac{2020}{\left(\sqrt{a}+\sqrt{b}\right)^2}\) (Do \(a^2+b^2\ge\dfrac{\left(a+b\right)^2}{2}\))
\(=\dfrac{\left(a+b\right)^2}{2}+\dfrac{2020}{\left(a+b\right)^2}\) (Theo (1))
\(\Rightarrow P\ge\dfrac{\left(a+b\right)^2}{2}+\dfrac{2020}{\left(a+b\right)^2}\).
Áp dụng bất đẳng thức AM - GM cho hai số thực dương và kết hợp với \(a+b\le2\) ta có:
\(\dfrac{\left(a+b\right)^2}{2}+\dfrac{2020}{\left(a+b\right)^2}=\left[\dfrac{\left(a+b\right)^2}{2}+\dfrac{8}{\left(a+b\right)^2}\right]+\dfrac{2012}{\left(a+b\right)^2}\ge2\sqrt{\dfrac{\left(a+b\right)^2}{2}.\dfrac{8}{\left(a+b\right)^2}}+\dfrac{2012}{2^2}=4+503=507\)
\(\Rightarrow P\ge507\).
Đẳng thức xảy ra khi a = b = 1.
Vậy Min P = 507 khi a = b = 1.
17 tháng 1 2021
Giải nốt câu 4a:
ĐKXĐ: \(x\geq\frac{-1}{2}\).
Phương trình đã cho tương đương:
\(x^2+2x+1=2x+1+2\sqrt{2x+1}+1\)
\(\Leftrightarrow\left(x+1\right)^2=\left(\sqrt{2x+1}+1\right)^2\)
\(\Leftrightarrow\left(x+1\right)^2-\left(\sqrt{2x+1}+1\right)^2=0\)
\(\Leftrightarrow\left(x+1-\sqrt{2x+1}-1\right)\left(x+1+\sqrt{2x+1}+1\right)=0\)
\(\Leftrightarrow\left(x-\sqrt{2x+1}\right)\left(x+\sqrt{2x+1}+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\sqrt{2x+1}=0\left(1\right)\\x+\sqrt{2x+1}+2=0\left(2\right)\end{matrix}\right.\).
Ta thấy \(x+\sqrt{2x+1}+2>0\forall x\ge-\dfrac{1}{2}\).
Do đó phương trình (2) vô nghiệm.
Xét phương trình (1) \(\Leftrightarrow x=\sqrt{2x+1}\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x^2=2x+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\left(x-1\right)^2=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\left[{}\begin{matrix}x-1=\sqrt{2}\\x-1=-\sqrt{2}\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\left[{}\begin{matrix}x=\sqrt{2}+1>0>-\dfrac{1}{2}\left(TM\right)\\x=-\sqrt{2}+1< 0\left(\text{loại}\right)\end{matrix}\right.\end{matrix}\right.\).
Vậy nghiệm của phương trình là \(x=\sqrt{2}+1\).
CM
22 tháng 5 2018
Đáp án A
Số cách sắp xếp 50 câu cho một đề thi là 50!
Số cách chọn 20 câu nhận biết để xếp chúng vào đầu tiên là: 20!
Số cách chọn 10 câu thông hiểu để xếp chúng vào vị trí thứ hai là 10!
Số cách chọn 15 câu vận dụng để xếp chúng vào vị trí thứ ba là 15!
Số cách chọn 5 câu vận dụng cao xếp chúng vào vị trí cuối cùng là 5!
Xác suất cần tìm được tính bằng: P = 20 ! 10 ! 15 ! 5 ! 50 ! = 4 , 56 . 10 - 26
Chọn phương án A
Chắc là đơn giản với ng học giỏi:))