Which is the decimal expansion of 7/22? – 0.318 (all repeated)
The correct answer is: $0.3181818\ldots$ (i.e. $0.3\overline{18}$). Explanation Let $x=0.3181818\ldots$. Then$$100x=31.8181818\ldots$$Subtract:$$100x-x=31.8181818\ldots-0.3181818\ldots$$$$99x=31.5$$$$x=\frac{31.5}{99}=\frac{315}{990}=\frac{7}{22}.$$ Note: the repeating block is “18” (after the initial 3). The form $0.\overline{318}$ is different (it equals $106/333$), so it is not equal to $7/22$.
Pedro is going to use SAS to prove that ΔPQR ≅ ΔSQR. Which of these is a necessary step in Pedro’s proof? A. Prove that ∠QPR ≅ ∠QSR by the Isosceles Triangle Theorem. B. Prove that QR ≅ QR by the reflexive property. C. Prove that PQ ≅ SQ by CPCTC. D. Prove that ∠PQR ≅ ∠SQR by vertical angles.
The correct answer is B. Explanation To use SAS you need two pairs of corresponding sides and the included angle between them. A common and necessary step is to note the shared side: QR ≅ QR (reflexive property). Why the others are wrong: A: The Isosceles Triangle Theorem applies only if you already know a […]
Enter the following expression in the answer box below: 2gλ.3m—–√, where λ is the lowercase Greek letter lambda.
The correct answer is: $\sqrt{6gm\lambda}$ Explanation You have a square root over the product $2g\lambda\cdot3m$. Multiply the numeric factors $2$ and $3$ to get $6$, then combine the remaining symbols under the radical. Steps: $$2\times3=6$$ $$\sqrt{2g\lambda\cdot3m}=\sqrt{6gm\lambda}$$ Therefore the expression simplifies to $\sqrt{6gm\lambda}$.
Which option best completes the table?Title: The United Nations: 1, Made up of nations worldwide. 2, Purpose is to promote cooperation on world issues ?A. Is funded only by voluntary dues B. Has the authority to enforce international laws C. Has the most powerful military in the world D. Is intended to promote international trade
The option that best completes the table about the United Nations is A: Is funded only by voluntary dues. This reflects the UN’s reliance on member contributions based on their economic size. The United Nations focuses on global cooperation, peace, and security rather than military enforcement or direct trade promotion. Explanation To complete the table […]
20.- The circle graph gives the distribution of salad dressing chosen by customers at a restaurant. If approximately 200 customers order salad each day at the restaurant, which of the following is closest to the difference per day between the number who choose Italian dressing, and the number who chose vinaigrette dressing?
a) 10 Salad Dressing. Explanation
A computer randomly puts a point inside the rectangle. What is the probability that the point does not land in triangle T?
Concepts Probability, Area of rectangle, Area of triangle, Geometric probability Explanation To find the probability that a point lands in triangle T when randomly placed in the rectangle, we find the ratio of the area of triangle T to the area of the rectangle. The presence of square S does not affect this, since the […]
Identify the elements correctly shown by decreasing radii size. N3to N S->S2- N>N3- Cu2+>Cu+ K+>K
The correct answers are: Cu2+ > Cu+ K+ > K Explanation Notice This question focuses on understanding the periodic trends related to atomic and ionic radii. The core concept here is how the size of an atom or ion changes across a period and down a group in the periodic table, and how ionization affects […]
Apex Learning Apex χ Algebra I Sem 1 7.5.3 Test (CST): Sequences and Functions Question 22 of 25 Which of the sequences is an arithmetic sequence? A. 1, -2, 3, -4, 5, … B. -3, -10, -17, -24, -31, … C. 1, 8, 16, 24, 32, … D. 3, 6, 9, 15, 24, …
The answer is B. -3, -10, -17, -24, -31, … Explanation Notice This question focuses on identifying arithmetic sequences. An arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. This constant difference is called the common difference. To solve this, you need to examine each option and calculate the […]
Which division expression could this model represent?
The division expression that the model may represent is 3÷0.5, which indicates how many halves fit into three whole units. This expression can be seen as a division that corresponds to multiplication by its reciprocal. Therefore, understanding this model requires seeing division as partitioning a whole into smaller parts. Explanation To determine which division expression the […]
What is 125% as a fraction?
The correct answer is: $\frac{5}{4}$ Explanation Percent means “per hundred”, so convert 125% to a fraction by writing it over 100 and simplifying. Steps: First step: $$\frac{125}{100}$$ Second step (simplify by dividing numerator and denominator by 25): $$\frac{125\div25}{100\div25}=\frac{5}{4}$$ Final step (mixed number form): $$1\frac{1}{4}$$ Therefore, 125% = $\frac{5}{4}$ (which is also $1\frac{1}{4}$).