Grace is collecting dimes and quarters in a jar. She has collected \( \$ 7.50 \) so far and has \( d \) dimes and \( q \) quarters. The relationship between the number of dimes and quarters and the amount of money Grace has in dollars in the jar can be represented by the equation \( 0.1 d+0.25 q=7.50 \). Select all th ordered pairs \( (d, q) \) that are solutions to this equation.

How did scientists boost the spacecraft Juno on its way to Jupiter, helping it overcome the gravitational pull of the Sun? A. by using two rockets B. by using a gravitational slingshot C. by decreasing the mass of Juno D. by increasing the fuel on the rocket

For the polynomial function \( f(x)=-x^{2}(x-2)(x+5) \), answer parts a through e. a. Use the Leading Coefficient Test to determine the graph's end behavior. A. The graph of \( f(x) \) rises to the left and falls to the right. B. The graph of \( f(x) \) rises to the left and rises to the right. C. The graph of \( f(x) \) falls to the left and rises to the right. D. The graph of \( f(x) \) falls to the left and falls to the right.

An engineer wants to design an oval racetrack such that \( 3.20 \times 10^{3} \mathrm{lb} \) racecars can round the exactly 1000 ft radius turns at \( 105 \mathrm{mi} / \mathrm{h} \) without the aid of friction. She estimates that the cars will round the turns at a maximum of \( 175 \mathrm{mi} / \mathrm{h} \). Find the banking angle \( \theta \) necessary for the race cars to navigate the turns at \( 105 \mathrm{mi} / \mathrm{h} \) without the aid of friction.

For the polynomial function \( f(x)=-x^{2}(x-2)(x+5) \), answer parts a through e. (Type an integer or a decimal. Use a comma to separate answers as needed.) At which zero(s) does the graph of the function cross the \( x \)-axis? Select the correct choice below ant A. The graph crosses the x-axis at the zero(s) 2 , -5 . There are no zeros at which the graph crosses the \( x \)-axis. (Type an integer or a decimal. Use a comma to separate answers as needed.) A. The graph touches the \( x \)-axis and turns around at the zero(s) does the graph of the function touch the \( x \)-axis and turn around? Select the correct (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no zeros at which the graph touches the \( x \)-axis and turns around. c. Find the y-intercept. The \( y \)-intercept is \( \square \). (Simplify your answer.)

Express \( P\left(C^{\prime} \mid D\right) \) in words. A. The probability of a customer not cashing a check, given that the customer did not make a deposit. B. The probability of a customer not cashing a check, given that the customer made a deposit. C. The probability of a customer cashing a check, given that the customer made a deposit. D. The probability of a customer making a deposit, given that the customer cashed a check. \( P\left(C^{\prime} \mid D^{\prime}\right)=\square \) (Type an integer or decimal rounded to two decimal places as needed.)