Which is the right one?

Given a term in the geometric sequence and the common ratio find the first five terms the explicit form and the recursive formul

Pani-rosa [81]

A1 = 4
a2 = 5a1 = 5 x 4 = 20
a3 = 5a2 = 5 x 20 = 100
a4 = 5a3 = 5 x 100 = 500
a5 = 5a4 = 5 x 500 = 2,500

Tn = ar^(n-1); where a = 4, r = 5
Tn = 4(5)^(n-1) = 4/5 (5)^n
Explicit formular is Tn = 4/5 (5)^n

Recursive formular is $a_{n+1} = 5a_{n-1}$

5 0

2 years ago

Alandra's rectangular cake pan is 33cm by 23 cm. She has enough cake batter to fill it to a depth of 3 cm. Instead, Alandra want

Alisiya [41]

Answer:

Alandra can fill 60 whole cones

Step-by-step explanation:

The volume of a rectangular prism is V = L × W × H, where

L is its length

W is its width

H is its height

The volume of the cone is V = $\frac{1}{3}$ π r² h, where

r is the radius of its base

h is its height

∵ Alandra's rectangular cake pan is 33 cm by 23 cm

∴ L = 33 cm and W = 23 cm

∵ She has enough cake batter to fill it to a depth of 3 cm.

∴ H = 3 cm

→ Find the volume of the batter using the 1st rule above

∵ V = 33 × 23 × 3

∴ V = 2277 cm³

∵ Alandra wants to pour the batter into ice cream cones

∵ She plans to fill each cone to a depth of 9 cm with a diameter of 4 cm

∴ h = 9 cm

∵ r = $\frac{1}{2}$ diameter = $\frac{1}{2}$ (4)

∴ r = 2 cm

→ Substitute them in the 2nd rule above to find the volume of each cone

∵ V = $\frac{1}{3}$ (π) (2)² (9)

∴ V = 12π cm³

→ To find the number of cones divide the volume of the batter by

the volume of each cone

∵ Number of cones = 2277 ÷ 12π

∴ Number of cones = 60.3993

→ We will take the whole number only because we need the whole cones

∴ Alandra can fill 60 whole cones

6 0

3 years ago

How wide is rectangular table with a length of 2/3 yard and an area of 1/2 square yards?

Ket [755]

A = Lw
---
1/2 = (2/3)w
w = (1/2)(3/2)
---
w = 3/4 yard
---

5 0

3 years ago

Please help. 2/3 (x - 6) = 6

vagabundo [1.1K]

Answer:

6=6

Step-by-step explanation

if 2/3x=10

therefore

x=3/2x10

x=15

substitute x with 15

2/3 (15 - 6)=6

2/3(9)=6

6=6

6 0

2 years ago

In Canada, households spent an average of $80.63 CDN monthly for high-speed broadband access.24 Assume that the standard deviati

ELEN [110]

Answer:

Step-by-step explanation:

Assuming a normal distribution for the amount spent by Canadian households for high-speed broadband access, the formula for normal distribution is expressed as

z = (x - u)/s

Where

x = amount spent by the Canadian households.

u = mean amount spent monthly.

s = standard deviation

From the information given,

u = $80.63 CDN

s = $27.32 CDN

We want to find the probability that the average amount will exceed $85. It is expressed as

P(x greater than 85) = 1 - P(x lesser than or equal to 85)

For x = 85

z = (85 - 80)/27.32 = 0.18

Looking at the normal distribution table, the corresponding z score is 0.57142

P(x greater than 85) = 1 - 0.57142 = 0.43

3 0

3 years ago