Numbers & Operations

Problem 3101

How many unique 4-letter passwords can be formed from the 26-letter English alphabet without repeating letters? [?] ways

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Problem 3102

Determine the center and radius of the circle given by (x2)2+(y+3)2=36(x-2)^{2}+(y+3)^{2}=36.

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Problem 3103

How many ways can you choose 3 books from 11? Use the formula for combinations: (113)\binom{11}{3}.

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Problem 3104

Find xx such that f(x)=0f(x)=0 for f(x)=x33x+1f(x)=x^{3}-3x+1 using the Intermediate Value Theorem.

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Problem 3105

Megan has 55 prizes and fills 12 bags equally. After filling 6 bags, what fraction of the prizes remains?

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Problem 3106

Find the limit: limx0f(x)\lim_{x \rightarrow 0} f(x) where f(x)=2xcos(1x2)f(x)=2 x \cos \left(\frac{1}{x^{2}}\right).

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Problem 3107

Calculate: 9+(15)-9 + (-15)

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Problem 3108

Calculate 3×93 \times 9.

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Problem 3109

Find mABCm \angle A B C if mABD=76m \angle A B D=76^{\circ} and mDBC=68m \angle D B C=68^{\circ}.

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Problem 3110

Convert 15lb15 \mathrm{lb} to ounces.

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Problem 3111

Calculate the distance dd between points A(11,5)A(11,-5) and B(1,7)B(1,7).

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Problem 3112

What is the converse of "If I studied for it, then I did well on the exam"?

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Problem 3113

How many computers were delivered to the third store if 28,500 were assembled and 9,300 and 6,860 went to the first two stores?

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Problem 3114

Calculate the expected value of winnings with payouts 2,3,4,5,62, 3, 4, 5, 6 and probabilities 0.40,0.20,0.17,0.13,0.100.40, 0.20, 0.17, 0.13, 0.10. Round to the nearest hundredth.

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Problem 3115

Simplify the expression: 4x2x2y34xy234xy23\frac{4 x}{\sqrt[3]{2 x^{2} y}} \cdot \frac{\sqrt[3]{4 x y^{2}}}{\sqrt[3]{4 x y^{2}}}.

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Problem 3116

Is the Garamycin dose of 35mg35 \mathrm{mg} every 6h6 \mathrm{h} safe for a 42lb42 \mathrm{lb} child? Justify your answer.

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Problem 3117

A child weighing 32 lb needs acetaminophen. Calculate mg in 1/2 tsp and check if it's safe based on 25-35 mg/kg/day.

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Problem 3118

Is a daily dose of 175mcg175 \mathrm{mcg} of Levothyroxin safe for an 8-year-old weighing 29.5 kg29.5 \mathrm{~kg}? Explain.

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Problem 3119

Calculate the mg per dose of Augmentin for a 66 lbs child, given the dosage is 50mg/kg/50 \mathrm{mg} / \mathrm{kg} / day, divided q 6 h6 \mathrm{~h}.

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Problem 3120

Find the ratio of men to total persons in a company with 112 men out of 288 total. Options: 0.3042, 0.2625, 0.3875, 7:8.

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Problem 3121

A child weighing 80 lbs needs Phenytoin 60mg60 \mathrm{mg} every 8 hours. Find the safe dose range in mg\mathrm{mg} per day.

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Problem 3122

A child weighing 80 lbs needs Phenytoin elixir 60mg60 \mathrm{mg} every 8 hours. How many mls per dose? (Round to 1 decimal place)

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Problem 3123

Is a 600mg600 \mathrm{mg} dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the 150350mg150-350 \mathrm{mg} daily range?

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Problem 3124

A child weighs 72 pounds. Gentamicin is prescribed at 8mg/kg/8 \mathrm{mg} / \mathrm{kg} / day every 6 hours. How many mls\mathrm{mls} per dose?

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Problem 3125

Calculate the dose of Ceclor in mg for a 12 lb infant, and find the mL needed per dose. Ceclor is 20mg/kg/day20 \mathrm{mg} / \mathrm{kg} / \mathrm{day} and 100mg/2mL100 \mathrm{mg} / 2 \mathrm{mL}.

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Problem 3126

Is a dose of Eryped drops 120mg120 \mathrm{mg} every 6 hours safe for a 27-pound child given the safe range of 3050mg/kg/day30-50 \mathrm{mg} / \mathrm{kg} / \mathrm{day}?

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Problem 3127

A child weighing 35 pounds needs Amoxicillin. How many 200mg200 \mathrm{mg} tablets for a 600mg600 \mathrm{mg} dose every 6 hours?

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Problem 3128

A child weighing 58 pounds needs Tetracycline elixir at 40mg/kg/40 \mathrm{mg} / \mathrm{kg} / day every 6 hours. How many mls per dose?

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Problem 3129

A child weighing 58 pounds needs Tetracycline elixir at 40mg/kg/40 \mathrm{mg} / \mathrm{kg} / day every 6 hours. How many mgs\mathrm{mgs} per dose?

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Problem 3130

Find the safe dose range for a 35-pound child taking Amoxicillin, with a daily dose of 150mg350mg150 \mathrm{mg}-350 \mathrm{mg}.

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Problem 3131

A child weighing 80 pounds needs Phenytoin 60mg60 \mathrm{mg} every 8 hours. How many mls per dose? (Round to 1 decimal place)

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Problem 3132

A child weighs 29 pounds. Find the safe Digoxin dose range in mg/day for a weight under 15 kg: 11.318.8mg/kg11.3-18.8 \mathrm{mg} / \mathrm{kg}.

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Problem 3134

A child weighing 19.5kgs19.5 \mathrm{kgs} needs Prednisolone 200mcg/kg200 \mathrm{mcg} / \mathrm{kg}. How many mls will the nurse prepare?

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Problem 3135

Calculate the safe dose range for a 27-pound child given Eryped drops of 3050mg/kg/day30-50 \mathrm{mg} / \mathrm{kg} / \mathrm{day}.

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Problem 3136

A child weighing 72 pounds needs Gentamicin 8mg/kg/8 \mathrm{mg} / \mathrm{kg} / day every 6 hours. How many mls per dose?

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Problem 3137

Solve the system of equations: x+y=5x + y = 5 and xy=1x - y = -1.

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Problem 3138

A child weighs 29 pounds. Is a dose of 0.125mg0.125 \mathrm{mg} every 12 hours safe, given the range 11.318.8mg/kg/day11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}?

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Problem 3139

Calculate: 12(10)-12 - (-10)

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Problem 3140

Calculate 30÷(6)-30 \div (-6).

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Problem 3141

Calculate 82-8 \cdot 2.

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Problem 3142

Solve for xx in the equation 74×7x711=1\frac{7^{4} \times 7^{x}}{7^{11}}=1. Find x=x=

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Problem 3143

Calculate the product of 1-1 and 7-7.

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Problem 3144

Tasha's drawing shows piers 12 cm12 \mathrm{~cm} apart. If 2 cm2 \mathrm{~cm} = 0.5mi0.5 \mathrm{mi}, find the actual distance between the piers.

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Problem 3145

Find the perimeter of a rectangle with length 6 feet and width 3 feet. Use the formula P=2(l+w)P = 2(l + w).

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Problem 3146

Circle the digit in the hundredths place of 8,656.175.

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Problem 3147

Emily's barn drawing is 15 in. wide and 18 in. long. If the actual width is 10 ft, find the actual length.

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Problem 3148

Convert 24 kg to grams. Recall that 1 kg = 1,000 g.

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Problem 3149

Write 814,496 in words.

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Problem 3150

If a wire creates a 10 T10 \mathrm{~T} field at distance rr, what is the net field at rr with another wire at 2r2r?

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Problem 3151

Rosa took 15.6 min to the store and 18.5 min to return. How much longer was her return trip?

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Problem 3152

Hannah baked nn brownies, gave away 12, and ate 6. Write an expression for the remaining brownies.

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Problem 3153

Mrs. Miller uses 4/84/8 cup for cake and 3/83/8 cup for frosting. Total honey used?

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Problem 3154

Find the dimensions of a rectangle scaled by 23\frac{2}{3} if the original is 12 inches long and 8 inches wide.

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Problem 3155

Is 729 divisible by 7? Circle: 729729 is divisible by 77 or 729729 is NOT divisible by 77.

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Problem 3156

Circle the digit in the hundredths place of 3,656.1753,656.175.

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Problem 3157

Prove that sin3θ+sinθ=4sinθ4sin3θ\sin 3\theta + \sin \theta = 4 \sin \theta - 4 \sin^3 \theta.

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Problem 3158

What time is it 14 hours after 5:00 p.m.?

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Problem 3159

Circle the smallest number: 5,211,528,706, 6,078,934, 340,987,126, 349,726,390,418.

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Problem 3160

Giá trị của aa, bb sau khi chạy code: a=1a=1, a+=aa+=a, b=a+12+16/a+3b=a+1*2+16/a+3, b=4+5b^*=4+5. Tính aa, bb.

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Problem 3161

Find ddxf1(0)\frac{d}{d x} f^{-1}(0) for f(x)=x+sinxf(x)=x+\sin x. At x=0x=0, ff has slope 2, so f1f^{-1} slope is 12\frac{1}{2}.

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Problem 3162

Find the derivative of f(x)=x2f(x) = x^2 using the limit definition: f(x)=limh0f(x+h)f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}.

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Problem 3163

Find the value of 69\sqrt{69}.

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Problem 3164

Find the annual interest rate for an investment of \$3500 that doubles in 5 years. Options: 40\%, 50\%, 30\%, 20\%.

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Problem 3165

Solve for xx in the equation: 2x+5=102 x + 5 = 10.

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Problem 3166

What is the concentration in g/fl.oz\mathrm{g}/\mathrm{fl.oz} for 90oz7gr/gal90 \mathrm{oz} 7 \mathrm{gr}/\mathrm{gal}?

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Problem 3167

Find the debt-equity ratio given a cost of equity of 14.9%, cost of debt of 7.3%, and return on assets of 12.6%.

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Problem 3168

Malkin Corp. has no debt, WACC 9.6%, borrowing at 5.9%. Find cost of equity with 0%, 30%, and 60% debt. What are WACCs?

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Problem 3169

Nyatakan sama ada semua segi empat tepat adalah segi empat sama: benar atau palsu?

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Problem 3170

Tentukan tinggi tiang silinder dengan isi padu 404 cm3404 \mathrm{~cm}^{3} dan jejari 2 cm2 \mathrm{~cm}.

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Problem 3171

Buat kesimpulan umum secara induksi untuk urutan nombor 12,32,256,-\frac{1}{2}, \frac{3}{2}, \frac{25}{6}, \ldots mengikut pola yang diberikan.

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Problem 3172

Dalam Rajah 5, cari (a) titik tengah garis PQP Q, (b) panjang QRQ R untuk trapezium PQRS dengan P(-2,4), Q(4,6), R(9,1).

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Problem 3173

Demuestra la ley de Boyle: pV=p V= const, la ley de Charles: V/T=V / T= const, y la ley de Gay-Lussac: p/T=p / T= const.

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Problem 3174

A particle with mass m1m_{1} and momentum p1p_{1} collides elastically with mass m2m_{2} at rest. Show E3E_{3} and p3p_{3} formulas.

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Problem 3175

Find the parametrization of the circle centered at 1i1-i with radius 3: z(t)=z(t)=.

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Problem 3176

Expand the expression (4+3x)5(4+3 x)^{5}.

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Problem 3177

Simplify the expression: 1x+21x+12\frac{\frac{1}{x+2}}{\frac{1}{x}+\frac{1}{2}}.

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Problem 3178

Find the limit: If f(z)=z+zˉzf(z)=\frac{z+\bar{z}}{z}, then limx0f(x+0i)=\lim _{x \rightarrow 0} f(x+0 i)=.

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Problem 3179

Solve the equation by factoring: x3+5x24x20=0x^{3}+5 x^{2}-4 x-20=0.

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Problem 3180

Solve the equation: 3x5x2+1=x73x - 5x^{2} + 1 = x - 7.

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Problem 3181

How many trucks does a factory produce in 8 days at 18 trucks per day? Calculate 8×188 \times 18.

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Problem 3183

How many liters of alcohol are needed to make 500,000 patches if each contains 0.3 mL0.3 \mathrm{~mL} of alcohol?

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Problem 3184

Find the real and imaginary parts of f(z)=z2+izˉf(z)=z^{2}+i \bar{z}: u(x,y)=u(x, y)= and v(x,y)=v(x, y)=.

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Problem 3185

How many kg of aluminium hydroxide gel are needed for 250,000 bottles with 100 tablets each, if each tablet has 80mg80 \mathrm{mg}?

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Problem 3186

Find side BCBC of triangle ABCABC with AB=8AB=8, AC=82AC=8\sqrt{2}, ABC=45\angle ABC=45^{\circ}, ACB=30\angle ACB=30^{\circ}.

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Problem 3187

A 15-ml nasal spray has 20 sprays/ml, each with 1.5mg1.5 \mathrm{mg}. (a) Total sprays? (b) Total mg of drug in the package?

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Problem 3188

Determine if a perfect hedge exists using the matrix AA and vector bb. Solve for x^\hat{x} using x^=(AA)1Ab\hat{x}=(A^{*} A)^{-1} A^{*} b.

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Problem 3189

Find limx0f(x+0i)\lim _{x \rightarrow 0} f(x+0 i) and limy0f(0+iy)\lim _{y \rightarrow 0} f(0+i y) for f(z)=z+zˉzf(z)=\frac{z+\bar{z}}{z}.

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Problem 3190

Evaluate the limit as xx approaches 0: limx0x225x24x5\lim _{x \rightarrow 0} \frac{x^{2}-25}{x^{2}-4 x-5}.

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Problem 3191

Calculate 12/2012 / 20 and find the missing number in the sequence: 100, 93, 84, 73.

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Problem 3192

Find the next number in the sequence: 7, 11, 16, 22, 29, ?

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Problem 3193

Find the next number in the sequence: 6,3,12,9,36,336, 3, 12, 9, 36, 33.

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Problem 3194

Find the algebraic expression for "a number plus 17 equals 30".

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Problem 3195

True or false: For a population proportion confidence interval, we use z\mathrm{z}-distribution, not t\mathrm{t}-distribution.

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Problem 3196

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known σ\sigma and Z, 4) unknown σ\sigma and S, 5) t vs z for population proportion.

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Problem 3197

Find the test statistic zz for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at α=0.05\alpha = 0.05.

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Problem 3198

Identify which statements are true or false regarding confidence intervals and distributions.

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Problem 3199

Identify the number that doesn't fit the pattern: 2,20,4,8,3002, 20, 4, 8, 300.

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Problem 3200

How much will you pay in total if you borrow \$400 for 2 years at an annual interest rate of 15%?

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