Morgan babysits every Saturday. The equation d = 9.5h

Angela has the following coins in her pocket:

GaryK [48]

Answer:

There are 10 different combinations

The list of different combinations is:

(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p), (1p, 50p), (1p, 2p),

(1p, 20p), (50p, 2p), (50p, 20p), (2p, 20p)

Explanation:

The possible combinations are:

1. Assuming the first coin is 10p:

(10p, 1p)
(10p, 50p)
(10p, 2p)
(10p, 20p)

2. Asuming the first coin is 1p

Do not count (1p, 10p) as it is the same combination as (10p, 1p)

(1p, 50p)
(1p, 2p)
(1p, 20p)

3. Assuming the first coin is 50p:

Do not count (50p, 10p) nor (50p, 1p) as they are the same combinations (10p, 50p) and (1p, 50p) counted earlier:

(50p, 2p)
(50p, 20p)

4. Assuming the first coin is 2p:

The only new combination is:

(2p, 20p)

5. All the combinations with 20p have already been listed.

Therefore:

There are 4 + 3 + 2 + 1 = 10 different combinations

The list of different combinations is:

(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p), (1p, 50p), (1p, 2p),

(1p, 20p), (50p, 2p), (50p, 20p), (2p, 20p)

7 0

1 year ago

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

masha68 [24]

By the binomial theorem,

$7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1$

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

7 0

1 year ago

How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]

Darina [25.2K]

Answer:

Step-by-step explanation:

Given the equation

Sin(5x) = ½

5x = arcSin(½)

5x = 30°

Then,

The general formula for sin is

5θ = n180 + (-1)ⁿθ

Divide through by 5

θ = n•36 + (-1)ⁿ30/5

θ = 36n + (-1)ⁿ6

The range of the solution is

0<θ<2π I.e 0<θ<360

First solution

When n = 0

θ = 36n + (-1)ⁿθ

θ = 0×36 + (-1)^0×6

θ = 6°

When n = 1

θ = 36n + (-1)ⁿ6

θ = 36-6

θ = 30°

When n = 2

θ = 36n + (-1)ⁿ6

θ = 36×2 + 6

θ = 78°

When n =3

θ = 36n + (-1)ⁿ6

θ = 36×3 - 6

θ = 102°

When n=4

θ = 36n + (-1)ⁿ6

θ = 36×4 + 6

θ = 150

When n =5

θ = 36n + (-1)ⁿ6

θ = 36×5 - 6

θ = 174°

When n = 6

θ = 36n+ (-1)ⁿ6

θ = 36×6 + 6

θ = 222°

When n = 7

θ = 36n + (-1)ⁿ6

θ = 36×7 - 6

θ = 246°

When n =8

θ = 36n + (-1)ⁿ6

θ = 36×8 + 6

θ = 294°

When n =9

θ = 36n + (-1)ⁿ6

θ = 36×9 - 6

θ = 318°

When n =10

θ = 36n + (-1)ⁿ6

θ = 36×10 + 6

θ = 366°

When n = 10 is out of range of θ

Then, the solution is from n =0 to n=9

So the equation have 10 solutions in the range 0<θ<2π

4 0

1 year ago

A part-time landscaper made $8996.32 last year. if she claimed herself as an exemption for $3650 and had a $5700 standard deduct

Andrej [43]

Answer:

$0

Step-by-step explanation:

A part-time landscaper made $8996.32 last year.

She claimed herself as an exemption for $3650 and had a $5700 standard deduction

Exemption means not subject to taxation.

Deduction means taking some amount of your income for the year, and not have to pay taxes on it.

So, $8996.32-(3650+5700)$

$=-353.68$

Since Her income is lower than the exemption and the standard deduction.

So, her taxable income last year was $0.

Thus Option D is correct.

7 0

2 years ago

Read 2 more answers

Naomi recorded the total weight of different numbers of apples. Her results are shown by using the scatterplot and the trend lin

dybincka [34]

Answer:

It's D. The narrative will change depending on the narrator's tone and point of view.

Step-by-step explanation:

8 0

1 year ago

Read 2 more answers