I NEED HELP PLEASE !!!!

helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. she also needs 0.75 cup of sugar pe

tatuchka [14]

The <em><u>correct answer</u></em> is:

She can make 2 loaves of bread and 4 batches of muffins.

Explanation:

Let b represent bread and m represent muffins.

The equation for the amount of flour she needs is 3.5b+2.5m=17.

The equation for the amount of sugar she needs is 0.75b+0.75m=4.5.

To solve this, we will want to eliminate one of the variables. To do this, we will make the coefficients of one of the variables the same. If we multiply 2.5 by 0.3, we get 0.75; this is what we will do to the first equation:

$\left \{ {{0.3(3.5b+2.5m=17)} \atop {0.75b+0.75m=4.5}} \right. \\ \\\left \{ {{1.05b+0.75m=17} \atop {-(0.75b+0.75m=4.5)}} \right. \\ \\0.3b=0.6 \\ \\\frac{0.3b}{0.3}=\frac{0.6}{0.3} \\ \\b=2$

She can bake two loaves of bread.

Substituting 2 for b in the first equation, we have

3.5(2)+2.5m=17

7+2.5m=17

Subtract 7 from each side:

7+2.5m-7=17-7

2.5m=10

Divide both sides by 2.5:

2.5m/2.5 = 10/2.5

m = 4

She can bake 4 batches of muffins.

6 0

4 years ago

Read 2 more answers

A water tank is in the shape of a right circular cone as shown above. The diameter of the cone is 10 feet, and the height is 15

Vsevolod [243]

Answer:

The rate at which the height of the water tank is changing is approximately 0.4244 ft/hour

Step-by-step explanation:

The given parameters are;

The diameter of the cone = 10 feet

The height of the cone = 15 feet

The rate at which water is leaking from the tank, (dV/dt) = 12 ft³/h

The volume of water in the tank = 27·π cubic feet

The volume V of a right circular cone with radius r and height h = 1/3×π×r²×h

The rate of change of the volume, dV, with time dt is given as follows;

The radius of the cone when the volume of the water in the tank is 27·π cubic feet is given as follows;

1/3×π×r²×h = 27·π ft³

The ratio of the height to the radius of the cone is h/r = 15/5 = 3

h/r = 3

∴ r =h/3

The volume of the cone, V = 1/3×π×r²×h = 1/3×π×(h/3)²×h = 1/27×π×h³ = h³/27×π

dV/dt = dV/dh × dh/dt

Which gives;

12 = d(h³/27×π)/dh × dh/dt = π×h²/9 × dh/dt

dh/dt = 12/(π×h²/9)

At 27·π ft³ = 1/27×π×h³ ft³, we have;

27 = 1/27×h³

27² = h³

h = ∛27² = 9

∴ dh/dt = 12/(π×h²/9) = 12/(π×9²/9) = 12/(π×9) = 4/(3·π) ≈ 0.4244 ft/hour

The rate at which the height of the water tank is changing ≈ 0.4244 ft/hour.

6 0

3 years ago

In a week Mike ran 8 km farther than Bill, while Pete ran

LUCKY_DIMON [66]

Answer:

12 km

Step-by-step explanation:

m = b + 8

p = 3b - 1

p = m + 15

p = m + 15....and m = b + 8....so we are gonna sub

p = b + 8 + 15

p = b + 23

b + 23 = 3b - 1

23 + 1 = 3b - b

24 = 2b

24/2 = b

b = 12 <==== Bill ran 12 km

m = b + 8

m = 12 + 8

m = 20 km....this is what mike ran

p = m + 15

p = 20 + 15

p = 35 km....this is what pete ran

7 0

4 years ago

Eighteenpassengers get on an airport shuttle at the airport. The shuttle has a route that includessixhotels, and passengersgetof

xz_007 [3.2K]

Answer:

So, exist 18564 different possibilities.

Step-by-step explanation:

We know that the eighteen passengers get on an airport shuttle at the airport. The shuttle has a route that includes six hotels, and passengers get off the shuttle at their hotel.

We calcuate how many different possibilities exist that eighteen passengers can choose six hotels. We get:

$C_6^{18}=\frac{18!}{6!(18-6)!}=18564$