Find all sets of three consecutive positive even integers with a sum no greater than 36

Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual

ale4655 [162]

For this problem, we can assume the total money is X, than we can get the equation of: 0.08*X*12=7680, than we can know X=8000, therefore, Mike's grandmother deposit 8000 in the account.

4 0

3 years ago

Algebraic expression for 6 notebooks at S dollars

swat32

6=S
therefore, to find one you must divide both sides by 6
the answer should be = 1=S/6

6 0

4 years ago

Solve the trigonometric equation such that 0 ≤ x ≤ 2????. Round to three decimal places.

raketka [301]

Answer: x= 0.463

Step-by-step explanation:

Given the equation √5 cos(x) − 2 = 0

To make 'x' the subject of the formula

√5cosx = 2

Cosx = 2/√5

Cosx = 0.89

x = arccos 0.89

x = 0.463

5 0

3 years ago

Jon is in a raft 100m from the base of a 54m cliff. What is the angle of depression from the he top of the cliff to the raft? Le

kvv77 [185]

Answer:

28.4 degrees

Step-by-step explanation:

In the diagram attached

Height of the cliff, AB=54 m

Distance of the raft to the base of the cliff, AC=100m

We want to determine the angle of depression from the top of the cliff to the raft. This is angle OBA.

$\angle OBA = \angle BAC $ (Alternate Angles)\\Therefore, in the right triangle ABC\\\tan A =\dfrac{BC}{AC}\\ \tan A =\dfrac{54}{100}\\\tan A =0.54\\A=\arctan 0.54\\A=28.4^\circ$ (to the nearest tenth)$

The angle of depression from the top of the cliff to the raft is 28.4 degrees correct to the nearest tenth.

5 0

3 years ago

One sample has a mean of M= 6, and a second sample has a mean of M = 12. The two samples are combined into a single set of score

lakkis [162]

Answer:

a) 9

b) 10

c) 8

Step-by-step explanation:

We are given the following in he question:

Mean of sample A = 6

Mean of sample B = 12

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$\dfrac{\displaystyle\sum x_a}{n_a} = 6\\\\\dfrac{\displaystyle\sum x_b}{n_b} = 12$

a) original samples have n = 4 scores

$\dfrac{\displaystyle\sum x_a}{4} = 6,\sum x_a = 24\\\\\dfrac{\displaystyle\sum x_b}{4} = 12,\sum x_b = 48\\\\\text{Combined mean} = \displaystyle\frac{\sum x_a + \sum x_b}{4+4}=\frac{24 + 48}{4 + 4} = 9$

b) first sample has n = 3 and the second sample has n = 6

$\dfrac{\displaystyle\sum x_a}{3} = 6,\sum x_a = 18\\\\\dfrac{\displaystyle\sum x_b}{6} = 12,\sum x_b = 72\\\\\text{Combined mean} = \displaystyle\frac{\sum x_a + \sum x_b}{3+6}=\frac{18+72}{3+6} = 10$

c) first sample has n = 6 and the second sample has n = 3

$\dfrac{\displaystyle\sum x_a}{6} = 6,\sum x_a = 36\\\\\dfrac{\displaystyle\sum x_b}{3} = 12,\sum x_b = 36\\\\\text{Combined mean} = \displaystyle\frac{\sum x_a + \sum x_b}{6+3}=\frac{36+36}{6+3} = 8$

7 0

3 years ago