There are 90 penguins in a zoo. there are two types- humboldt and emperor. 52 are female, of the 6 are emperor penguins. there are 5 male emperor penguins. use this information to complete the frequency tree.

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. the original photo was 800 pixels wide by 600 pixels high. the new photo will be 1,260 pixels wide. what will the new height be?

The input to the function is x and the output is y. write the function such that x can be a vector (use element-by-element operations). a) use the function to calculate y(-1.5) and y(5). b) use the function to make a plot of the function y(x) for -2 ≤ x ≤ 6.