Pencils sell for 1.98 per dozen a teacher bought 288 pencils for his math classes. How much did the pencils cost?

PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

6 0

2 years ago

A company made $4 million in the second quarter. This is 1/3 more than it made in the first quarter and 4/5 of what it made in t

babunello [35]

BIG BLACK lollipop to suck on

8 0

2 years ago

A company manufacturing oil seals wants to establish X and R control charts on the process. There are 25 preliminary samples of

alisha [4.7K]

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

ii) R control chart : upper limit = 1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 * mean range = 50.15 - 0.577(0.5632) = 49.825

Based on R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2 = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

6 0

2 years ago

Rachel, Adam, Michelle, Hannah, and James are going to the movies. They have $65 to spend on tickets and snacks. Each movie tick

Ann [662]

Answer:

1. By substitution property of inequality

5(9.5)+4.5 $\leq$ 65

2. By using multiplication in equality then we get

47.5+4.5x $\leq$ 65

3. The five friends will have 3 snacks to split.

Step-by-step explanation:

Given

Five friends have total money= $65

Cost of each movie ticket= $9.50

Cost of each snack item= $4.50

Let ,five friends have total snacks = x

Total movie tickets=5

Because total number of friends=5

The inequality expressionis given by

I Step: $5(9.5)+4.5x\leq 65$

Reason: By using substitution property of inequality

$47.5+4.5x\leq 65[/tex2. Step :[tex]4.5x[tex]\leq$ 65-47.5[/tex]

$4.5x\leq 17.5$ ( by subtarction 47.5 from both sides)

$x\leq \frac{17.5}{4.5}$ ( by dividing 4.5 on both sides )

<h3> $x\leq 3.889$ (by simplication)</h3><h3> $x=3$ </h3>

Because they can buy maximum 3 snacks .

Beacause the number of snacks is natural number so we can't take in rational numbers.

<h3>Hence, the five friends will have 3 snacks to split.</h3>

6 0

2 years ago

Read 2 more answers

Line jk passes through points j(-4,-5) and k(-6,3 if the equation of the lines is written in slope-intercept form,y=my+b what is

lidiya [134]

Written in 2-point form, the equation of the line is
y = (y2-y1)/(x2-x1)·(x-x1) +y1
y = (3-(-5))/(-6-(-4))·(x-(-4)) + (-5)
y = 8/-2·(x +4) - 5
y = -4x -21

The value of b is -21.

6 0

2 years ago