You should purchase 1/2 pound of cashews and 1/2 pound of peanuts
Answer: The other two observations are 97 and 107.
Explanation:
We know that
Mean = 100
Mode = 98
Range = 10
And from the formula,
Range = Highest - Lowest.
Let’s set the highest observation as x and the lowest as y.
Thus, we have the equation x - y = 10 (equation 1).
The observations can be represented as:
x, 98, 98, y.
Using the mean formula yields:
Mean = 
.
This means our second equation is:
x + y = 204.
By applying the elimination method to solve these linear equations, we find:
x = 97.
and
.
Therefore, the other two observations are 97 and 107.
Given: The angle < CEB is divided by EF.
< CEF = 7x +31.
< FEB = 10x -3.
We will find the values of x and the measures of < FEB, < CEF, and < CEB.
Solution: The angle < CEB is divided into two angles < FEB and < CEF.
Therefore, < FEB is equal to < CEF.
By substituting the values of < FEB and < CEF, we obtain:
10x -3 = 7x +31
By adding 3 to both sides, we have:
10x -3 +3 = 7x +31 +3.
Thus, 10x = 7x + 34
After subtracting 7x from both sides, we conclude:
10x -7x = 0 + 34.
This simplifies to 3x = 34.
Dividing both sides by 3 yields:
x = 11.33.
Substituting x=11.33 into < CEF = 7x +31 gives us:
< CEF = 7(11.33) +31 = 79.33 +31 = 110.33.
< FEB = < CEF = 110.33 (approximately)
< CEB = < FEB + < CEF = 110.33 +110.33 = 220.66 (approximately)
When creating a garden with potted plants, you would determine the soil requirements for each pot and multiply that figure by the total number of pots desired. After this, you’d head to the store for potting soil, which I’ll assume comes in smaller packages, thus necessitating a bulk purchase. Utilize multiplication estimation to gauge how many bags you’d need. I realize this might seem trivial, but it's a memory from my fourth-grade math teacher, haha.
We have seven pathways (let’s call them A, B, C, D, E, F, and G) leading to the summit of a hill. We must choose one road to ascend and then select a different road for the descent.
Initially, we can choose from any of the seven roads. Hence, there are 7 options to reach the top.
Upon reaching the peak, the first road is disqualified from further selection, leaving us with six remaining roads to descend. Therefore, there are 6 choices for going back down.
Consequently, the total number of routes = 7 × 6 = 42 distinct ways.
In summary, there are 42 unique routes available to ascend to the peak and to return, assuming different roads for ascent and descent.
