How much fruit juice (100%) is equivalent to 1 cup of fresh fruit?

Destiny's class packs school lunches for the local homeless shelter. They pack the same number of lunches each minute. In 6 minu

Leno4ka [110]

Make is a proportion
6/18=28/x
Cross multiply
18•28=6•x
504=6x
x=84

8 0

2 years ago

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 teacher decides to purchase a new car and considers two options. Option one is the new Zoomba for $60,000 with an expected dep

kupik [55]

Answer:

She chose Option 2 which is a linear option, because it offers a smaller lose

in value compared to option 1 which is an exponential option.

The final value for option 2=$32,800

Step-by-step explanation:

Option 1

New Zoomba for 60000 with a depreciation rat of 2%per month for 3 years

Exponential equation;

y=a(1-r)^t

where;

y=future value

a=initial value=60000

r=depreciation rate=2% per month

t=time interval=12×3=36 months

Replacing;

y=60000(1-2/100)^36

y=60000(0.98)^36=28,992.79

The value after 3 years=$28,992.79

Initial value-Final value=(60000-28992.79)=$31007.21

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(31007.21/60000)×100=51.68%

Option 2

New starfish for $40,000 with a depreciation of $200 per month for 3 years

Linear equation;

y=a-bt

where;

y=Future value

a=Initial value=$40,000

b=the depreciation amount per time interval=$200 per month for 3 years

t=time interval=(3×12)=36 months

Replacing;

y=40000-(200×36)

y=32,800

Final value=y=$32,800

Initial value-Final value=(40000-32800)=$7200

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(7200/40000)×100=18%

Option 1(51.68%)>Option 2(18%) therefor Option 1 loses value at a faster rate than Option 2

She chose Option 2 which is a linear option, because it offers a smaller lose

in value compared to option 1 which is an exponential option

4 0

2 years ago

Find the integer a such that<br> a.a ≡ 43 (mod 23) and −22 ≤ a ≤ 0.

Margaret [11]

Given that a is an integer from -22 to 0 such that a is equivalent to 43 (mod 23).

Such a can be obtained as follows:

a = 43 (mod 23) - 23 = 20 - 23 = -3.

Therefore, a = -3.

8 0

2 years ago

The solutions to the linear differential equation d2u/dt2 = u form a vector space (since combinations of solutions are still sol

maw [93]

Serious high school. This is one of the few differential equations I can solve.

The usual particular solution is $u=e^t$ because $e^t$ is its own derivative.

An independent solution is $u=e^{-t}$ which has a negative sign in the first derivative which turns back to positive in the second.

The arbitrary linear combination spans the solution space:

$u= c_1 e^t + c_2 e^{-t}$

But we only are asked for the basis.

Answer: $\textrm{. } \quad e^t, \quad e^{-t}$

5 0

2 years ago

How much fruit juice (100%) is equivalent to 1 cup of fresh fruit?​

How much fruit juice (100%) is equivalent to 1 cup of fresh fruit?