answer:To find the percent of the budget spent on equipment, we first need to determine the percent spent on salaries. Since the circle graph represents 100% of the budget and the circle itself has 360 degrees, each degree represents a fraction of the total budget. If salaries are represented by 216 degrees of the circle, we can set up a proportion to find the percentage of the budget spent on salaries: ( frac{216 text{ degrees}}{360 text{ degrees}} = frac{x}{100%} ) Solving for x gives us the percentage for salaries: ( x = frac{216}{360} times 100% ) ( x = 0.6 times 100% ) ( x = 60% ) Now that we know 60% of the budget was spent on salaries, we can add up all the known percentages and subtract from 100% to find the percent spent on equipment: ( 100% - (20% + 9% + 5% + 2% + 60%) = 100% - 96% = 4% ) Therefore, boxed{4%} of the budget was spent on equipment.

answer:To calculate the molecular weight of a compound with 2 nitrogen atoms and 3 oxygen atoms, we need to know the atomic weights of nitrogen (N) and oxygen (O). The atomic weight of nitrogen is approximately 14.01 g/mol, and the atomic weight of oxygen is approximately 16.00 g/mol. The molecular weight of the compound is calculated by adding together the atomic weights of all the atoms in the molecule: Molecular weight = (Number of N atoms × Atomic weight of N) + (Number of O atoms × Atomic weight of O) Molecular weight = (2 × 14.01 g/mol) + (3 × 16.00 g/mol) Molecular weight = (2 × 14.01) + (3 × 16.00) Molecular weight = 28.02 + 48.00 Molecular weight = 76.02 g/mol Therefore, the molecular weight of the compound with 2 nitrogen atoms and 3 oxygen atoms is boxed{76.02} g/mol.

answer:To find the length of the train, we can use the formula: Length of the train = Speed × Time taken to cross the pole First, we need to convert the speed from km/hr to m/s because the time is given in seconds. We know that 1 km/hr is equal to 5/18 m/s. Speed in m/s = Speed in km/hr × (5/18) Speed in m/s = 144 × (5/18) Speed in m/s = 8 × 5 Speed in m/s = 40 m/s Now, we can calculate the length of the train: Length of the train = Speed × Time Length of the train = 40 m/s × 2.7497800175985923 s Length of the train = 110.9912007039437 meters Therefore, the length of the train is approximately boxed{110.99} meters.

answer:We are given a circle with center ( O ) and radius ( 10 ). We select a point ( M ) on the radius ( AO ) such that ( OM = x ). On one side of ( AO ) on the circle, we choose points ( B ) and ( C ) such that ( angle AMB = angle OMC = alpha ). We need to find the length of ( BC ), given that ( sin alpha = frac{sqrt{21}}{5} ). 1. **Consider the symmetric point ( B_1 ):** Consider the point ( B_1 ) symmetric to ( B ) with respect to the line ( OA ). Since ( B ) and ( B_1 ) lie on the circle and the symmetric property holds, we have ( angle AMB = angle AMB_1 = alpha ). 2. **Observation of Collinearity:** Notice that the points ( B_1, M, C ) lie on a straight line. Also, the triangle ( triangle B B_1 M ) is isosceles with ( angle BMB_1 = 2alpha ). 3. **Calculation of the angle ( angle B B_1 M ):** The angle ( angle B B_1 M ) is an inscribed angle and equals: [ angle B B_1 M = 180^circ - 2alpha ] Since ( Delta B B_1 M ) is isosceles: [ angle B B_1 M = 90^circ - alpha ] 4. **Central angle and ( Delta BOC ):** The central angle ( angle BOC ) is formed by OB and OC. Using the inscribed angle theorem: [ angle BOC = 2 angle BMC = 2 alpha ] Consequently: [ angle BOC = 180^circ - 2alpha ] The triangle ( triangle BOC ) is also isosceles since ( OB = OC = 10 ). 5. **Determining ( cos alpha ):** Given ( sin alpha = frac{sqrt{21}}{5} ), we find ( cos alpha ): [ cos alpha = sqrt{1 - sin^2 alpha} = sqrt{1 - left( frac{sqrt{21}}{5} right)^2} = sqrt{1 - frac{21}{25}} = sqrt{frac{4}{25}} = frac{2}{5} ] 6. **Finding ( BC ):** The base ( BC ) of the isosceles triangle ( triangle BOC ) can be calculated using the cosine rule or directly from the geometric properties of the isosceles triangle: [ BC = 2 times OB times cos alpha = 2 times 10 times frac{2}{5} = 8 ] # Conclusion: [ boxed{8} ]