Answer:
p = 8
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 4 + 5p and d = 5, then
a₁ + 8d = 4 + 5p, that is
a₁ + 8(5) = 4 + 5p
a₁ + 40 = 4 + 5p ( subtract 40 from both sides )
a₁ = 5p - 36
a₂ = 5p - 36 + 5 = 5p - 31
a₃ = 5p - 31 + 5 = 5p - 26
a₄ = 5p - 26 + 5 = 5p - 21
Given that the sum of the first 4 terms = 7p - 10, then
5p - 36 + 5p - 31 + 5p - 26 + 5p - 21 = 7p - 10, that is
20p - 114 = 7p - 10 ( subtract 7p from both sides )
13p - 114 = - 10 ( add 114 to both sides )
13p = 104 ( divide both sides by 13 )
p = 8
Answer:
D(-2, 5).
Step-by-step explanation:
We are given that M is the midpoint of CD and that C = (10, -5) and M = (4, 0).
And we want to determine the coordinates of D.
Recall that the midpoint is given by:
Let C(10, -5) be (<em>x</em>₁<em>, y</em>₁) and Point D be (<em>x</em>₂<em>, y</em>₂). The midpoint M is (4, 0). Hence:
This yields two equations:
Solve for each:
And:
In conclusion, Point<em> </em>D = (-2, 5).
Answer:
70
Step-by-step explanation:
First, set up the ratio of c:t, which is 12:8. Then set up your new ratio of c:t, which is 105:?. The way I find the easiest is to divide 105 by 12, which is 8.75, then multiply that by 8, which is 70. To check if it's right, just divide 12 by 8, and 105 by 70, and if they're the same number, you've got it right.
Ps. I'm guessing you meant to ask the minimum number of trucks, not cars.
Answer:
1/2 lb of pecans would cost $1.9
3 lbs of pecans would cost $11.4
Step-by-step explanation:
The rate given is 5 lb of pecans for $19
FIND THE UNIT RATE OF DOLLARS PER POUND OF PECANS BY:
19 ÷ 5 = 3.8
THE UNIT RATE IS $3.8 per pound of pecans.
Use unit rate to determine how much will the following amounts of pecans cost:
1/2 lbs
1/2 x 3.8 = $1.9
3 lbs
3 x 3.8 = $11.4
Count the numbers between 0 and 5: 84
Count total numbers: 150
Percent of elderly in table:
84 / 150 = 0.56 = 56%
Count the number of Boxes that have all three numbers higher than 5: 4
total number of boxes: 50
Probability it will take at least 4 patients: 4/50 = 0.08 = 8%
Count boxes with 2 numbers 5 or under: 17
Probability: 17/50 = 0.34 = 34%
