raphs of Quadratic Function ivity: What will be the vertex and new equation of the parabol if the graph of the function \( y=5(x-2)^{2} \) is shifted 12 uni to the right. What will be the vertex and new equation of the parabol if the graph of the function \( y=x^{2}+3 \) is shifted 6 units downward. What will be the vertex and new equation of the parabola if graph of the function \( y=(x-5)^{2}-1 \) is shifted 4 units to the ht and 8 units upward

Un trapezio rettangolo ha il perimetro di 130 cm , l'altezza di 21 cm e il lato obliquo di 29 cm . Calcola le misure delle basi sapendo che una è \( 5 / 3 \) dell'altra. \[ [50 \mathrm{~cm} ; 30 \mathrm{~cm} \text { ] } \]

Evaluate the following Integrals 1. \( \int \sin ^{2} x \cos ^{5} x d x \quad(6 \) Marks) 2. \( \int \frac{d x}{\sqrt{-5-6 x-x^{2}}} \quad \) (7 Marks) 3. \( \int \frac{x^{2}+2}{(x+3)\left(x^{4}+2 x^{2}+1\right)} d x \quad \) (8Marks) 4. \( \int \frac{2 x^{3}+x^{2}-6 x+7}{x^{2}+x-6} d x \quad \) (7Marks)

18. В основі піраміди лежить прямокутний трикутник з катетом \( b \) і протилежним йому кутом \( \beta \). Бічні ребра піраміди утворюють із площиною основи кут \( \gamma \). Знайдіть висоту піраміди.

Quostlon 6 A box contains 6 balls of the same size of which 2 are red, 3 are yellow and 1 is white. If 2 balls are selected at random from the box without replacement, what is the probability that the first ball will be red and second one yellow?

Certain private water utilities in South Carolina charge a variable rate for the drinking water they provide to residence One customer's bills over a 23 -month period were used to fit a linear regression in an attempt to predict charges on future bills according to gallons consumed. The resulting regression equation is \( \hat{y}=23.2+7.67 x \), where \( x \) is the amount of water used, in thousands of gallons and \( \hat{y} \) is the predicted bill amount in dollars. Which of these choices an a correct statement resulting from this regression line? On average, the amount consumed increased by 23.2 thousand gallons for each additional dollar added to the bill amount. On average, the bill amount increased by 23.2 dollars for each additional thousand gallons consumed. On average, the amount consumed increased by 7.67 thousand gallons for each additional dollar added to the bill amount.