Question The manager of a night club in Boston stated that 90% of the customers are between the ages of 22 and 26 years. If the age of customers is normally distributed with a mean of 24 years, calculate its standard deviation. (You may find it useful to reference the z table. Round "z" value to 3 decimal places and final answer to 2 decimal places.) Standard deviation 1.00

Supermarket shoppers were observed and questioned immediately after putting an item in their cart. Of a random sample of 220 choosing a product at the regular​ price, 113 claimed to check the price before putting the item in their cart. Of an independent random sample of 280 choosing a product at a special​ price, 250 made this claim. Find a 95​% confidence interval for the difference between the two population proportions. Let Px be the population proportion of shoppers choosing a product at the regular price who claim to check the price before putting it into their cart and let Py be the population proportion of shoppers choosing a product at a special price who claim to check the price before putting it into their cart. The 95​% confidence interval is ? < Px−Py < ?

4. Consider the determinant as a sum of signed products. Recall that there are \( n \) ! elementary products in the determinant expansion of an arbitrary \( n \times n \) matrix \( A \). (a) If \( A \) is a \( 5 \times 5 \) matrix, how many of the elementary products in \( \operatorname{det}(A) \) are guaranteed to be zero if the entry \( a_{12} \) is zero? (b) If \( A \) is an \( n \times n \) matrix, \( n \geq 2 \), how many of the elementary products in \( \operatorname{det}(A) \) are guaranteed to be zero if \( a_{12}=0 \) ? Give your answer in terms of \( n \). (c) If \( A \) is an \( n \times n \) matrix with \( \operatorname{det}(A) \neq 0 \), what is the maximum possible number of zero entries in A? Give your answer in terms of \( n \).

CIRCLE ALL ANSWERS AND PROVIDE UNITS 1. (20 points) Mohr's Circle and Stress Elements Oy An element in plane stress (shown above) is subjected to stresses Ox - 70 MPa, Oy, and Txy - 50 MPa. Using the Mohr's Circle equations, determine the following: a principal stresses, b. the maximum shear stress, C. the principal angle, d. If one of the principal stresses is negative, what does a negative stress mean? **Using just proper equations is acceptable, but Extra Credit will be given if Mohr's Circle is drawn out.

You make a swimming pool 3.92 M in magnesium acetate, Mg(CH3COO)2 hoping to keep it from freezing during the winter. Its density is 1.23 g/ml. What will its normal freezing point be? Give your final answer (remember, you're looking for the new normal freezing point) to 1 decimal place (just to keep CuLearn happy) Put C for your unit (I don't know how to find the degree sign for answers...) Kf(H2O) = 1.86 °C/m

Consider the beam shown in (Figure 1). Suppose that d = 3 m Figure < 1 of 1 w - (***) kN/m d Part A Determine the equivalent resultant force. Express your answer to three significant figures and include the appropriate units. Enter positive value if the force is upward and negative value if the force is downward. HÅ ? FR = Value Units Submit Request Answer Part B Determine the equivalent couple moment at point O. Express your answer to three significant figures and include the appropriate units. Enter positive value if the moment is counterclockwise and negative value if the moment is clockwise. HÅ ? (MR) - Value Units Submit Request Answer

1)A uniform magnetic field is given byB⃗ =btk^, where b= 0.40 T/s. Find the current in a conducting loop with area 280 cm2and resistance 0.20 Ωthat lies in the x-y plane.Express your answer in amperes.2) When a nonideal 1.4-H inductor is short-circuited, itsmagnetic energy drops to one-fourth of its original value in 3.8s.What is its resistance?Express your answer in milliohms.