How many ways can you split 12 people into 3 groups?

The mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.

To find the mass of the biscuits left after Jason eats 2/5 of the packet, we need to calculate the mass of the biscuits he ate and then subtract it from the initial mass of the packet.

Given:

Mass of the packet of biscuits = 1 1/3 kg

First, let's convert 1 1/3 kg to an improper fraction:

1 1/3 = 3/3 + 1/3 = 4/3 kg

Now, to find the mass of the biscuits Jason ate, we can use the fact that he ate 2/5 of the packet:

Mass of biscuits Jason ate = (2/5) * (4/3) kg

Now, perform the multiplication:

Mass of biscuits Jason ate = (8/15) kg

To find the mass of biscuits left, we subtract the mass Jason ate from the initial mass of the packet:

Mass of biscuits left = 4/3 kg - 8/15 kg

To subtract fractions, we need to find a common denominator, which is 15 in this case:

Mass of biscuits left = (20/15) kg - (8/15) kg

Now, perform the subtraction:

Mass of biscuits left = 12/15 kg

Finally, let's simplify the fraction:

Mass of biscuits left = (12/15) * (1/3) kg

Mass of biscuits left ≈ 0.8 kg

Therefore, the mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.

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The expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

When the function f(x) is divided by (x - 2) the quotient is 3x² + 8x - 4 and the remainder is 9

By using the division algorithm:

f(x) = (x - 2)(3x² + 8x - 4) + 9

After simplification:

f(x) = 3x³ + 8x² - 4x - 6x² - 16x + 8 + 9

f(x) = 3x³ + 2x² - 20x + 17

Thus, the expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

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Final answer:

Manfred has hiked 1260 miles of the trail, which is calculated by multiplying the total length of the trail (2940 miles) by the fraction of the trail he has completed (3/7).

Explanation:

To calculate the distance Manfred has hiked on the trail, we multiply the total length of the trail by the fraction of the trail he has completed. In this case, Manfred has hiked three sevenths (3/7) of the trail. The total distance of the trail is 2940 miles.

Distance Hiked = (Total Distance of Trail) × (Fraction of Trail Completed)

Distance Hiked = 2940 miles × (3/7)

Distance Hiked = 2940 miles × 0.4286

Distance Hiked = 1260 miles

Therefore, Manfred has hiked 1260 miles of the trail.

Answer:

[tex]\frac 23 \pi [/tex]

Step-by-step explanation:

120 degrees is one third of the whole circle, or [tex] \frac 13 2\pi [/tex]

Answer:

the answer is 2pi/3

Answer:

She walked 5 mi

W is correct. the red line starts at 40 which is the initial fee

 then it crosses 60 and 1.0 and 80 at 2.0 which is 20 dollars for 1 hour

When no bags of sand are bought, you can buy 15 bags of mulch with $105.

To find the number of bags of mulch that can be bought with $105 when no bags of sand are bought, we need to substitute x = 0 into the equation 3x+7y = 105. This will allow us to solve for y.

Since x = 0, the equation becomes:

3(0) + 7y = 105

0 + 7y = 105

7y = 105

Dividing both sides by 7, we get:

y = 15

Therefore, when no bags of sand are bought, you can buy 15 bags of mulch with $105.

Answer:

16!

Step-by-step explanation: Hope this helps.... you made this in 2017 its 2020 now-

To determine the fraction of area of triangle XYZ that is occupied by triangle PQR on a square grid, we can compare their linear dimensions and use the fact that area is proportional to the square of these dimensions, or we can approximate the area through summation of small rectangular areas on the grid. Alternatively, vector methods such as the cross product can provide precise area calculations for triangles with known vertices.

Finding the Area of Triangles on a Square Grid

To find what fraction of the area of triangle XYZ is the area of triangle PQR, we follow several steps. First, we can draw both triangles on a square grid and establish their respective areas. If we assume that XYZ is the larger triangle and PQR is the smaller one, we can use the fact that area scales in proportion to the square of the linear dimensions. This means, if the linear dimensions of PQR are half that of XYZ, the area of PQR would be one-fourth that of XYZ. In mathematical terms, if the side length of XYZ is scaled by a factor of 's', the area is scaled by s².

Another method to approximate the area of irregular shapes like these triangles, as mentioned in a reference, is by dividing the shape into smaller, manageable rectangular areas whose sum approximates the total area. Counting the smallest square units within the grid and making rough estimates of the fractional squares can yield the area as well.

To demonstrate the calculation of the area of a triangle through vector methods, one can use the cross product of two vectors defined by the triangle's vertices. Given vertices A(1,2,3), B(2,4,5), and C(1,-8,0), their position vectors can be used to compute the cross product, and the magnitude of this cross product gives twice the area of the triangle ABC. This is a more advanced method and offers a precise way to calculate the area without relying on the grid.