Olivia bought 3 pretzels and 2 hot dogs for $16.75. Noah bought 5 pretzels and 3 hot dogs for $26.50. What is the cost of a pretzel and a hot dog?

pretzels cost  $2.75 and hot dogs cost $4.25

Step-by-step explanation:

Given data

let the cost of pretzels be x and the cost of hot dogs be y

Olivia bought 3 pretzels and 2 hot dogs for $16.75

3x+2y= 16.751

Noah bought 5 pretzels and 3 hot dogs for $26.50

5x+3y= 26.52

solve 1 and 2

3x+2y= 16.75 X 3

5x+3y= 26.5   X 2

   9x+6y= 50.25

-10x+ 6y= 53

-x= -2.75

x= 2.75

put x= 2.75 in 1

3( 2.75)+2y= 16.75

8.25+2y= 16.75

2y= 16.75-8.25

2y= 8.5

y= 8.5/2

y= 4.25

Hence pretzels cost  $2.75 and hot dogs cost $4.25

the correct answer is b) histograms can be used to exhibit the shape of distributions. this is because histograms count the frequency of each possible answer, so one is able to see which results are more common and which are less common.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3