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Questions in mathematics

[Done] Create your own examples for: Commutative property (one for addition, one for multiplication) Associative property (one for addition, one for multiplication) Distributive property (one example) Solve each expression. Explain in 2-3 sentences how the property works and why it helps learners understand number operations.

[Done] What is the sum of the series 1 + 3 + 9 + ... up to 6 terms? a) 346 b) 364 c) 64

[Done] For her youngest son's birthday party, Mother bought 6 1/4 kg of hotdogs and 5 1/3 dozens of bread rolls. Hotdogs cost ₱160.00 per kilogram and a dozen of bread rolls costs ₱25.00. How much did she spend in all?

[Done] A kiddie pool holds miniature plastic ducks in different colors. Sophia randomly picks up a duck and then replaces it. She repeats this process 100 times. The table shows the results of her experiment. | Duck Color | Times Picked | | ---------- | ------------ | | red | 30 | | green | 20 | | yellow | 40 | | blue | 10 | What is the relative frequency of choosing a red duck? What color of duck is there likely to be the most of in the pool? A. The relative frequency is 0.3. It is likely that most ducks are blue. B. The relative frequency is 0.2. It is likely that most ducks are yellow. C. The relative frequency is 0.3. It is likely that most ducks are yellow. D. The relative frequency is 0.2. It is likely that most ducks are green.

[Done] Write $y=-4 x^2-16 x-14$ in vertex form.

[Done] Which statement explains why 49 is a perfect square? A. 49 can be multiplied by 49. B. 49 is equal to 7 plus 7. C. 49 is between 36 and 64. D. 49 is equal to 7 times 7.

[Done] 2. Solve: [tex]$\left(0^{\circ} \leq \theta \leq 180^{\circ}\right)$[/tex] a. [tex]$4 \sin \theta=3 \operatorname{cosec} \theta$[/tex]

[Done] The table below shows the amount of carbohydrates in similar servings of different fruits. Amount of Carbohydrates in Fruit | 237 mL of Fruit | Carbohydrates (Grams) | |---|---| | Apples | 17 | | Bananas | 34 | | Cherries | 19 | | Grapefruit | 24 | | Oranges | 21 | | Peaches | 16 | | Watermelons | 12 | If this data was placed in a bar graph, which statement would describe the graph? A. The graph would have only four bars shorter than the bar for grapefruits. B. The graph would have five bars taller than the bar for apples. C. The graph would have grapefruits and oranges as the tallest bars.

[Done] A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table. | Color | Number | | :----- | :----- | | blue | 1 | | green | 2 | | red | 0 | | orange | 4 | | yellow | 3 | Which statements are true about Yuri's experiment? Select three options. A. The theoretical probability of spinning any one of the five colors is 20%. B. The experimental probability of spinning blue is [tex]$\frac{1}{5}$[/tex]. C. The theoretical probability of spinning green is equal to the experimental probability of spinning green. D. The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow. E. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

[Done] Change the following to radical form: [tex]x^{\frac{3}{5}}[/tex] A) [tex]\sqrt{x^{\frac{3}{5}}}[/tex] B) [tex]x \sqrt{\frac{2}{5}}[/tex] C) [tex]\sqrt[3]{x^6}[/tex] D) [tex]\sqrt[5]{x^3}[/tex]