Raymonds parents will pay for him to take sailboard lessons during the summer. he can take half hour group lessons, or half hour private lessobns. the relationship between cost and number of lessons is linear. table—— lessons| 1, 2 , 3 , 4 , group$ | 55,85,115,145 private| 75,125,175,225 ~find the rate of change and initial value for the private lessons. ~ find the rate and the initial value for the group sessions. ~ compare and contrast the rates of change and the initial values.

The initial fee for both is $25. The rate of change for group is $30 per lesson while private is $50 per lesson.

Step-by-step explanation:

To find the rate of change, we find the difference between two of the same sessions and divide that by the difference between lesson numbers.

Private

For instance, we can subtract for Private lessons the cost for 1 which is $75 with the cost for 2 which is $125. 125-75=50. We divide 50 by 2-1 =1(lesson 2-lesson 1). $50 per lesson. This means the first lesson must be $25 plus a $50 lesson fee. The $25 is the initial value.

Group

For instance, we can subtract for Group lessons the cost for 1 which is $55 with the cost for 2 which is $85. 85-55=30. We divide 30 by 2-1 =1(lesson 2-lesson 1). $30 per lesson. This means the first lesson must be $25 plus a $30 lesson fee. The $25 is the initial value.

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).