by 10 to convert to hundredths: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 \\times 10 = 50 \\text{ hundredths}\u003C/math-field>\u003C/math-field> 3. Therefore, five tenths is equivalent to fifty hundredths: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 \\text{ tenths} = 50 \\text{ hundredths}\u003C/math-field>\u003C/math-field> Answer: 50 hundredths",1408,282,"model-math-claire-drew-a-model-of-five-tenths-explain-how-claire-could-change-her-model-to-show-how-many-hundredths-are-in-five-tenths",{"id":56,"category":48,"text_question":57,"photo_question":50,"text_answer":58,"step_text_answer":8,"step_photo_answer":8,"views":59,"likes":60,"slug":61},538005,"Prime factor of 1245","First, we identify the smallest prime factor of 1245:\u003Cbr />\n\u003Cbr />\n1. Check if 1245 is divisible by 2: Since 1245 is odd, it is not divisible by 2.\u003Cbr />\n2. Check divisibility by 3: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 + 2 + 4 + 5 = 12\u003C/math-field>\u003C/math-field> \u003Cbr />\n which is divisible by 3, so 1245 is divisible by 3. \u003Cbr />\n Dividing gives:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1245 \\div 3 = 415\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Check if 415 is divisible by 5: Since 415 ends in a 5, it is divisible by 5.\u003Cbr />\n Dividing gives:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>415 \\div 5 = 83\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Determine if 83 is a prime number: 83 is not divisible by 2, 3, 5, or 7 $prime numbers up to the square root of 83$, so 83 is a prime number.\u003Cbr />\n\u003Cbr />\nThus, the prime factors of 1245 are:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3, 5, 83\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n**Answer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3, 5, 83\u003C/math-field>\u003C/math-field>**",929,186,"prime-factor-of-1245",{"id":63,"category":48,"text_question":64,"photo_question":50,"text_answer":65,"step_text_answer":8,"step_photo_answer":8,"views":66,"likes":67,"slug":68},537993,"Khaled has a cube in his hand and takes it to a painter who has 6 different colors. He asks the painter to color the cube so that each face has a different color. In how many ways can this be done?","1. Calculate the total number of permutations of the 6 colors: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6! = 720 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Account for the rotational symmetries of the cube $24$:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{720}{24} = 30 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nThe final answer: 30 ways to paint the cube with each face a different color considering the cube's rotational symmetries.",962,192,"khaled-has-a-cube-in-his-hand-and-takes-it-to-a-painter-who-has-6-different-colors-he-asks-the-painter-to-color-the-cube-so-that-each-face-has-a-different-color-in-how-many-ways-can-this-be-done",{"id":70,"category":48,"text_question":71,"photo_question":50,"text_answer":72,"step_text_answer":8,"step_photo_answer":8,"views":73,"likes":74,"slug":75},537966,"$-9p$$-10+3p$+7p$-9+3p$\nsimplify do not factorise","1. Apply the distributive property to expand $(-9p)(-10+3p)$:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>$-9p$$-10$ + $-9p$$3p$ = 90p - 27p^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Apply the distributive property to expand $7p(-9+3p)$:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>7p$-9$ + 7p$3p$ = -63p + 21p^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Combine like terms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>$-27p^2 + 21p^2$ + $90p - 63p$ = -6p^2 + 27p\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n4. Therefore, the answer is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-6p^2 + 27p\u003C/math-field>\u003C/math-field>",905,181,"9p-10-3p-7p-9-3p-simplify-do-not-factorise",{"id":77,"category":48,"text_question":78,"photo_question":50,"text_answer":79,"step_text_answer":8,"step_photo_answer":8,"views":80,"likes":81,"slug":82},537947,"33/10 - 27/20","Least common multiple of \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$10$\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$20$\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$20$\u003C/math-field>. Convert \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$\\frac{33}{10}$\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$\\frac{27}{20}$\u003C/math-field> to fractions with denominator \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$20$\u003C/math-field>.\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>\u003Cmath-field read-only>\\frac{66}{20}-\\frac{27}{20}\u003C/math-field> \u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Since \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$\\frac{66}{20}$\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$\\frac{27}{20}$\u003C/math-field> have the same denominator, subtract them by subtracting their numerators.\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>\u003Cmath-field read-only>\\frac{66-27}{20}\u003C/math-field> \u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Subtract \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$27$\u003C/math-field> from \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$66$\u003C/math-field> to get \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$39$\u003C/math-field>.\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>\u003Cmath-field read-only>\\frac{39}{20}\u003C/math-field> \u003C/math-field>\n \u003Cbr>\n \u003C/div>",1018,204,"33-10-27-20",{"id":84,"category":48,"text_question":85,"photo_question":50,"text_answer":86,"step_text_answer":8,"step_photo_answer":8,"views":87,"likes":88,"slug":89},537927,"in a geometric sequence a1=125 and a3=5 find the common ratio","1. The formula for the \\(n\\)-th term of a geometric sequence is given by:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a_n = a_1 \\cdot r^{n-1} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Given \\( a_1 = 125 \\) and \\( a_3 = 5 \\). We can substitute into the formula for the third term:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a_3 = a_1 \\cdot r^{3-1} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Substitute the known values:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 5 = 125 \\cdot r^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Solve for \\( r^2 \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r^2 = \\frac{5}{125} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Simplify the fraction:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r^2 = \\frac{1}{25} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Take the square root of both sides to solve for \\( r \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r=\\pm\\frac{1}{5}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Therefore, the common ratio is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r=\\pm\\frac{1}{5}\u003C/math-field>\u003C/math-field>",1383,277,"in-a-geometric-sequence-a1-125-and-a3-5-find-the-common-ratio",{"id":91,"category":48,"text_question":92,"photo_question":50,"text_answer":93,"step_text_answer":8,"step_photo_answer":8,"views":94,"likes":95,"slug":96},537921,"A pilot flew 390 nautical miles in 45 minutes. Find his average speed in knots (nautical miles per hour)","1. Convert time from minutes to hours: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{{Time in hours}} = \\frac{45}{60} = 0.75 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Calculate average speed: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{{Average speed}} = \\frac{390}{0.75} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. The average speed of the pilot is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 520 \u003C/math-field>\u003C/math-field> knots.",1037,207,"a-pilot-flew-390-nautical-miles-in-45-minutes-find-his-average-speed-in-knots-nautical-miles-per-hour",{"id":98,"category":48,"text_question":99,"photo_question":50,"text_answer":100,"step_text_answer":8,"step_photo_answer":8,"views":101,"likes":102,"slug":103},537919,"Write and solve an equation:\nFind a number such that the difference of 97 and eighteen times the number is five times one more than the number","1. Let the number be \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. According to the problem, the difference of 97 and eighteen times the number (\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 18x \u003C/math-field>\u003C/math-field>) is equal to five times one more than the number (\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 5(x+1) \u003C/math-field>\u003C/math-field>).\u003Cbr />\n\u003Cbr />\n The equation can be written as: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 97 - 18x = 5(x + 1) \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Expand the term on the right-hand side: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 5(x + 1) = 5x + 5 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Substitute back into the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 97 - 18x = 5x + 5 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Bring all terms involving \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field> to one side and constant terms to the other:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 97 - 5 = 18x + 5x \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Simplify both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 92 = 23x \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{92}{23} = 4 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the number is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 4 \u003C/math-field>\u003C/math-field>.",1373,275,"write-and-solve-an-equation-find-a-number-such-that-the-difference-of-97-and-eighteen-times-the-number-is-five-times-one-more-than-the-number",{"id":105,"category":48,"text_question":106,"photo_question":50,"text_answer":107,"step_text_answer":8,"step_photo_answer":8,"views":108,"likes":109,"slug":110},537907,"Ivan learned 15 out of 20 questions. What is the probability that the student got a question he did not learn?","- Ivan je naučio 15 pitanja od 20, tako da je broj pitanja koja nije naučio \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 20 - 15 = 5 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Ukupan broj pitanja je 20.\u003Cbr />\n- Vjerojatnost da je Ivan dobio pitanje koje nije naučio iznosi \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{5}{20} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Jednostavnim deljenjem dobijamo vjerojatnost: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{5}{20} = \\frac{1}{4} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\nOdgovor je: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{4} \u003C/math-field>\u003C/math-field>.",518,104,"ivan-learned-15-out-of-20-questions-what-is-the-probability-that-the-student-got-a-question-he-did-not-learn",{"id":112,"category":48,"text_question":113,"photo_question":50,"text_answer":114,"step_text_answer":8,"step_photo_answer":8,"views":115,"likes":116,"slug":117},537870,"Express the repeating decimal as a quotient of two integers. 4.09 (9 is repeating)","1. Let \\( x = 4.099999\\ldots \\). \u003Cbr>\u003Cbr>2. Multiply by 10 to shift the decimal point for the non-repeating part: \\( 10x = 40.99999\\ldots \\).\u003Cbr>\u003Cbr>3. Multiply by 100 to shift the decimal point so that the repeating part aligns: \\( 100x = 409.99999\\ldots \\).\u003Cbr>\u003Cbr>4. Subtract the equation of step 2 from step 3: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 100x - 10x = 409.9999\\ldots - 40.9999\\ldots \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 90x = 369 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Solve for \\( x \\) to get the fraction:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{369}{90} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Simplify the fraction:\u003Cbr>\u003Cbr>Divide both numerator and denominator by 9:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x=\\frac{41}{10}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>",1066,213,"express-the-repeating-decimal-as-a-quotient-of-two-integers-4-09-9-is-repeating",{"first":6,"last":119,"prev":8,"next":10},11,{"current_page":6,"from":6,"last_page":119,"links":121,"path":152,"per_page":146,"to":146,"total":35},[122,125,128,130,132,134,136,139,142,145,148,150],{"url":6,"label":123,"active":124},"1",true,{"url":10,"label":126,"active":127},"2",false,{"url":13,"label":129,"active":127},"3",{"url":16,"label":131,"active":127},"4",{"url":19,"label":133,"active":127},"5",{"url":22,"label":135,"active":127},"6",{"url":137,"label":138,"active":127},7,"7",{"url":140,"label":141,"active":127},8,"8",{"url":143,"label":144,"active":127},9,"9",{"url":146,"label":147,"active":127},10,"10",{"url":119,"label":149,"active":127},"11",{"url":10,"label":151,"active":127},"Next 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