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Dimas [21]
2 years ago
8

If there is one-third of a pizza left, and Becky only wants to eat one-half of it, how much of the pizza does she want?

Mathematics
2 answers:
netineya [11]2 years ago
6 0

Answer:

1/6

Step-by-step explanation:

natali 33 [55]2 years ago
5 0
She wants to eat 1/6 of the pizza.
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Discuss four ways to keep the nervous system healthy
geniusboy [140]

Exercise regularly.

Do not smoke or use tobacco products.

Get plenty of rest.

Eat a balanced diet.  

7 0
3 years ago
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A train is spotted 10 miles south and 8 miles west of an observer at 2:00 pm. At 3:00 pm the train is spotted 5 miles north and
kodGreya [7K]

Answer:

a. The distance the train travelled in the first hour is approximately 28.3 miles

b. The location of the train at 5:00 p.m. is 53 miles east, and 46 miles west

c. The location of the train at any given time by the function, f(t) = (-8 + 24·t, -10 + 15·t)

d. The train does not collide with the cyclist when the bike goes over the train tracks

Step-by-step explanation:

a. The given information on the train's motion are;

The location south the train is spotted = 10 miles south and 8 miles west

The time the observer spotted the train = 2:00 pm

The location the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east

Therefore, the difference between the two times the train was spotted, t = 3:00 p.m. - 2:00 p.m. = 1 hour

Making use of the coordinate plane for the two locations the train was spotted, we have;

The initial location of the train = (-10, -8)

The final location of the train = (5, 16)

Therefore the distance the train travelled in the first hour is given by the formula for finding the distance, 'd', between two points, (x₁, y₁) and (x₂, y₂) as follows;

d = \sqrt{\left (x_{2}-x_{1}  \right )^{2}+\left (y_{2}-y_{1}  \right )^{2}}

Therefore;

d = \sqrt{\left (5-(-10)  \right )^{2}+\left (16-(-8)  \right )^{2}} = 3 \cdot\sqrt{89}

The distance the train travelled in the first hour, d = 3·√89 ≈ 28.3 miles

b. The speed of the train, v = (Distance travelled by the train)/Time

∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour

The speed of the train in the first hour, v ≈ 28.3 mph

The direction of the train, θ, is given by the arctangent of the slope, 'm', of the path of the train;

\therefore The  \  slope  \  of \ the \  path  \ of \  the \  train, \, m =tan(\theta) = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

∴ m = tan(θ) = (5 - (-10))/(16 - (-8)) = 0.625

c. Distance = Velocity × Time

At 5:00 p.m., we have;

The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours

The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles

Using trigonometry, we have the horizonal distance travelled, 'Δx', in the 2 hours is given as follows;

Δx = d₁ × cos(θ)

∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48

The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles

The vertical distance increase in the two hours, Δy is given as follows;

Δy = 56.6 × sin(arctan(0.625)) ≈ 30

The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles

Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)

The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west

c. The function, 'f', that would give the train's position at time-t is given as follows;

The P = f(28.3·t, θ)

Where;

28.3·t = √(x² + y²)

θ = arctan(y/x)

Parametric equations

y - 5 = 0.625·(x - 16)

∴ y = 0.625·x - 10 + 5

The equation of the train's track is therefore, presented as follows;

y = 0.625·x - 5

d = 28.3·t

The y-component of the velocity, v_y = 3*√89 mph × sin(arctan(0.625)) = 15 mph

Therefore, we have;

y = -10 + 15·t

The x-component of the velocity, vₓ = 3*√89 mph × cos(arctan(0.625)) = 24 mph

Therefore, we have;

x = -8 + 24·t

The location of the train at any given time, 't', f(t) = (-8 + 24·t, -10 + 15·t)

d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph

The distance of the cyclist from the track = The x-intercept = 5/0.625 = 8

The distance of the cyclist from the track = 8 miles

The time it would take the cyclist to react the track, t = 8 miles/10 mph = 0.8 hours

The location of the train in 0.8 hours, is f(0.8) = (-8 + 24×0.8, -10 + 15×0.8)

∴ f(0.8) = (11.2, 2)

At the time the cyclist is at the track along the east-west axis, at the point (8, 0), the train is at the point (11.2, 2) therefore, the train does not collide with the cyclist when the bike goes over the train tracks.

8 0
3 years ago
The underground ride is 861 mater long, what isthis number rounded to the nearest 100?
KATRIN_1 [288]

the underground ride is 861 mater long, what isthis number rounded to the nearest 100?

Answer:

861 ≈ 900

8 0
3 years ago
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What is the solution to the system of equations? y = x +2 y = 3x -2
Mrrafil [7]

Answer:

x=2 and y= 4

Step-by-step explanation:

y = x +2 ----------(i)

y = 3x -2--------(ii)

Now, comparing (i) and (ii)

x+2= 3x-2

=>x-3x = -2-2

=>-2x= -4

=>2x= 4

=>x= 2

From eq (i)

y= x+2 = 2+2= 4

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3 years ago
Kelly is having a party. She wants to make punch. The recipe for punch uses 3 pints of pineapple juice, 5 cups of orange juice,
lorasvet [3.4K]

Answer:

Kelly is wrong and the recipe will make 19 cups of punch.

Step-by-step explanation:

It says:

The amount of ingredients in the recipe of punch after converting the units to 'cups' are given by,

Pineapple juice = 3 pints = 6 cups (1 pint ≈ 2 cups)

Orange juice = 5 cups

Lemonade = 1/4 gallon = 4 cups (1 gallon = 16 cups)

Apricot nectar = 1 quart = 4 cups(1 quart = 4 cups)

Then, the total cups of punch = 6 + 5 + 4 + 4 = 19 cups.

Thus, Kelly is wrong and the recipe will make 19 cups of punch.

4 0
2 years ago
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