what is the aroc of  $f\left(X\right)=x^2-4x+7$ƒ (X)=x²−4x+7 on the interval 1 $\le$≤  $x$x  $\le$≤ 3

In the game backgammon, when you roll doubles with two dice you can double the total on the dice. what is the probability of rolling doubles

a bag has 3 red tiles, 1 yellow tile and 2 green tiles 

b) how does the value change if the first tile is not replaced? 

A child has some LEGO bricks to play with . They have 19 identically shaped bricks in these colours.  4red 6 yellow 5 white 3 blue 1green , how many different combinations of bricks can they choose to build something with if they have to use at least 1 brick

The teacher in your classroom surveys her 30 students in an attempt to help them understand Venn Diagrams in the most complex form, when there are 3 counting options. She asks all the people wearing red shirts to stand up, 8 people stand. She asks them to sit down. Then she asks all those wearing blue pants to stand, 24 stand up. She asks them to sit. Then she asks all the people wearing black shoes to stand, and 10 stand up. She asks them to sit. While asking these questions, she notices 3 people have stood up for all questions, 4 are wearing both red shirts and blue pants, 7 are wearing both blue pants and black shoes and finally, 5 are wearing both red shirts and black shoes. Draw a 3 circle VENN diagram, label what each area represents and CALCULATE numbers for each area (show all your calculations using proper mathematical and statistical form for full marks).

A home computer costs $9/year in electricity costs. If a new computer costs $2000 to purchase and lasts for 5 years find the total annual cost for this computer

Factor x^{3 +} 2x² - 5x - 6 fully.

The point (2,3) is on the graph of y=f(x). Determine the corresponding coordinates of this point on the graph of y=-2(f(2(x+5)) -4

Angles x and y are located in the first quadrant such that sinx= 3/5 and cosy= 4/5. Determine the exact value of sin(x+y).

You have chosen an five-character password for an online account.  The characters can be a combination of UPPER CASE letters and lower case letters.

a)  How many possible passwords can be created?