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monitta
2 years ago
6

Byron has 1 7/10 kilograms of black pepper. He uses 7/8 of the black pepper and splits between 7 pepper shakers. How much pepper

will be in each shaker?
Mathematics
1 answer:
IrinaVladis [17]2 years ago
4 0
Amount of black pepper = 1 7/10 kg = 17/10 kg.
Amount used is
(7/8)*(17/10) = 119/80 kg

This amount is split between 7 shakers. Each shaker has
(119/80)/7 = 17/80 kg = 0.2125 kg

Answer: 17/80 kg (or  0.2125 kg)
You might be interested in
​Cameron, Arthur, and Jamie are playing soccer. Their locations are recorded by a motion tracking system. The grid shows distanc
Luden [163]

Answer:

1. Arthur is about 54 meters away from Cameron.

2. Jamie is about 56 meters away from Cameron.

3. Arthur is closer to Cameron.

Step-by-step explanation:

We have been given the locations of Cameron (70,10), Arthur (20,30) and Jamie (45,60) on the the grid in meters.

1. To find the distances of Arthur and Jamie from Cameron we will use distance formula.

\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}

\text{Distance between Cameron and Arthur}=\sqrt{(70-20)^{2}+(10-30)^{2}}

\text{Distance between Cameron and Arthur}=\sqrt{(50)^{2}+(-20)^{2}}

\text{Distance between Cameron and Arthur}=\sqrt{2500+400}

\text{Distance between Cameron and Arthur}=\sqrt{2900}

\text{Distance between Cameron and Arthur}=53.8516480713450403\approx 54

Therefore, the distance Arthur is about 54 meters away from​ Cameron.

2. Let us find the distance between Cameron and Jamie.

\text{Distance between Cameron and Jamie}=\sqrt{(70-45)^{2}+(10-60)^{2}}

\text{Distance between Cameron and Jamie}=\sqrt{(25)^{2}+(-50)^{2}}

\text{Distance between Cameron and Jamie}=\sqrt{625+2500}

\text{Distance between Cameron and Jamie}=\sqrt{3125}

\text{Distance between Cameron and Jamie}=55.9016994374947424\approx 56

Therefore, Jamie is about 56 meters away from​ Cameron.

3. We can see that 56 is greater than 54, therefore, Arthur is closer to Cameron.


4 0
2 years ago
Read 2 more answers
Data berikut ialah suhu yang dicatat untuk 5 hari.
murzikaleks [220]

\frac{25 + 2 7 + 34 + 28 + 29}{5}

119.8

5 0
2 years ago
For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t
Alexeev081 [22]

Answer: check explanation

Step-by-step explanation:

Let K(n) be the sum of the interior angles in any n-sided convex polygon which is exactly 180(n −2)

degrees.

CASE: n = 3. A 3-sided polygon is a triangle, whose interior angles were shown always to sum to be 180 degree

INDUCTION HYPOTHESIS: Suppose that K(b) holds for some b ≥ 3. Which means that the interior angles in any b-sided convex

polygon is exactly 180(n −2) degrees.

INDUCTION STEP: We need to show that K(n is greater than or equals to 3) . That is, the interior angles of any b+1-sided convex polygon

is exactly 180(b−2) = 180(b −1) degrees,

Let X be any (b+1)-vertex convex polygon, say with successive vertices x1, x2,..., xb+

Now Y is also a convex polygon , so by the induction hypothesis K(b), the sum of the interior

angles of Y is 180(k −2).

Now let T be the triangle with vertices xk , xb+1, x1. The sum of the interior angles in X is the sum of those

in Y plus the sum of those in T .

So the sum of the interior angles in X is

180(b −2)+180 = 180((b +1)−2) = 180(b −1).

Since X was arbitrary, we conclude that the sum of the interior angles of any (b +1)-sided convex polygon

is 180((b−2)+1) = 180(b−1). That is, P(b +1) holds.

And which means that n is greater or equals to 3

8 0
2 years ago
Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is cons
kap26 [50]

Answer:

If in each row of the supposed coefficient matrix, there is a pivot position. Therefore, it is true that the bottom row of the coefficient matrix also has a pivot position. As a result, there will not be space for the augmented column to have a. Thus, we say the system is consistent.

Step-by-step explanation:

In the problem, we have a coefficient matrix comprising linear equations. If in each row of the supposed coefficient matrix, there is a pivot position. Therefore, it is true that the bottom row of the coefficient matrix also has a pivot position. As a result, there will not be space for the augmented column to have a. Thus, we say the system is consistent based on the theorem.

7 0
2 years ago
A guy wire is used to support flagpoles in windy areas. These wires are anchored in the ground to provide constant stability. Yo
r-ruslan [8.4K]

Answer: a) Length of wire to replace old one=9ft

b) Length of wire=3.09ft

Leftover wire=0.91ft

Step-by-step explanation: from the right angle triangle, Tan&=20/15

&=53.13°

Length of wire,x=cos 31.13=x/15

15cos31.13

X=9

b) Tan&=10/6

Tan^-110/6

&=59.05

Length= 6cos59.04

X=3.09

4-3.09=.91= leftover wire

8 0
2 years ago
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