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2 years ago

The March family go out for dinner, and their bill comes to $118.40. If they leave a 20% tip, how much is the tip they leave?

Mathematics

1 answer:

erica [24]2 years ago

6 0

Answer:

tip amount = $23.68

Step-by-step explanation:

t = tip percentage (as decimal, so 5% would be 0.05)

c = cost

tip amount = c * t

tip amount = (118.40) * (0.20) = $23.68

hope this helps :)

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A denotes an mn matrix. Determine whether the statement is true or false. Justify your answer. The row space of AT is the same a

ziro4ka [17]

Answer: true

Step-by-step explanation:

For an m*n matrix, the column space of A will be a space formed by the lineal combination of all the columns of A.

column space = a1*c1 + a2*c2 + ...

where a1, a2, ... are scalars, and c1 is the vector of column 1.

Then we should write:

Column space = a1*(A₁₁, A₂₁, A₃₁, ...) + a2*(A₁₂, A₂₂, A₃₂, ...) + ...

Now, the transpose is defined as:

[At]₁₃ = A₃₁

Here i used the element with subindex 3 and 1, but is the same for every subindex.

Notice that if A is m*n, then [At] is n*m

Now, the row space of [At] will be, same as before.

Row space = b1*r1 + b2*r2 + ...

Where b1, b2, ... are scalars and the r's are the vector of each row.

= b1*( [At]₁₁ , [At]₁₂, [At]₁₃, ...) + b2*([At]₂₁, [At]₂₂, [At]₂₃, ...) + ...

Now we replace each term of the transpose by the associated element in the original matrix.

= b1*( A₁₁, A₂₁, A₃₁, ...) + b2*(A₂₁, A₂₂, ...) + ....

If we take:

b1 = a1, b2 = a2, b3 = a3, ...

We will have that the row space of [At] is the same as the column space of A.

4 0

2 years ago

Clinton had his sister sell some of their toys at a garage sale. Clinton makes $12.94 at the sale, and his sister makes $20.18.H

erastovalidia [21]

Answer:

$7.24

Step-by-step explanation:

it just is

4 0

2 years ago

PLEASE HEKLPP<br> IF ITS RIGHT ILL GIVE BRSAINLIEST

tino4ka555 [31]

Answer:

We conclude that:

h(f(-1)) = -2

∴ option D i.e. -2 is correct.

Step-by-step explanation:

Given

f(x) = 4x² - 1

g(x) = 1/2x + 5

h(x) = 2(x - 4)³

To determine

h(f(-1)) = ?

In order to determine h(f(-1)) first we need to determine f(-1).

substitute x = -1 in the function f(x) = 4x² - 1

f(-1) = 4(-1)² - 1

f(-1) = 4(1) - 1

f(-1) = 4-1

f(-1) = 3

h(f(-1)) = h(3)

now substitute h = 3 in the function h(x) = 2(x - 4)³

h(x) = 2(x - 4)³

h(3) = 2(3 - 4)³

h(3) = 2(-1)³

h(3) = 2(-1)

h(3) = -2

Thus,

h(f(-1)) = h(3) = -2

Hence, we conclude that:

h(f(-1)) = -2

∴ option D i.e. -2 is correct.

4 0

3 years ago

Factor completely 5ab + 3ay + 5b + 3y. (5b + 3y)(a + 1) (5b − 3y)(a + 1) (5b + 3y)(a − 1) Prime

Katen [24]

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3 years ago

Read 2 more answers

Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence i

mash [69]

Complete Question

A biologist reports a confidence interval of (3.5,4.9) when estimating the mean height (in centimeters) of a sample of seedlings. What is the estimated margin of error and the sample mean?

Answer:

The margin of error is $E = 0.7$

The sample mean is $\= x = 4.2$

Step-by-step explanation:

from the question we are told that

The upper limit is $k = 4.9$

The lower limit is $r = 3.5$

Generally the margin of error is mathematically represented as

$E = \frac{k - r}{ 2}$

$E = \frac{ 4.9 - 3.5 }{2}$

$E = 0.7$

Generally the sample mean is mathematically evaluated as

$\= x = k - E$

=> $\= x = 4.9 - 0.7$

=> $\= x = 4.2$

4 0

3 years ago