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3 years ago

When paying for a restaurant order, a customer's total for food was $28.50. What is a 16% tip for that total?

Mathematics

1 answer:

vredina [299]3 years ago

6 0

Answer:

33.06

Step-by-step explanation:

you would do 28.5*0.16 and you would get 4.56 ss you would add that to the cost and you would get 33.06

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Jacob solves the system of equations by forming a matrix equation.

Lyrx [107]

Simultaneous equations can be solved using inverse matrix operation.

The complete steps of Jacob's solution are:

$\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]^{-1} \cdot \left[\begin{array}{cc}4&1\\-2&3\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14}\left[\begin{array}{cc}3&-1\\2&4\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

We have:

$4x + y = 2$

$-2x + 4y = -22$

Calculate the determinant of $\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

$|A| = 4 \times 3 -1 \times -2$

$|A| = 12 +2$

$|A| = 14$

So, the inverse matrix becomes

$A = \frac{1}{14}\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

Replace the first column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of x

$x = \frac{1}{14}\left[\begin{array}{cc}2&1\\-22&3\end{array}\right]$

So, we have:

$x = \frac{1}{14}(2 \times 3 - 1 \times -22)$

$x = \frac{1}{14}(6 +22)$

$x = \frac{1}{14}(28)$

$x = 2$

Replace the second column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of y

$y = \frac{1}{14}\left[\begin{array}{cc}4&2\\-2&-22\end{array}\right]$

So, we have:

$y = \frac{1}{14}(4 \times -22 - 2 \times -2)$

$y = \frac{1}{14}(-88 +4)$

$y = \frac{1}{14}(-84)$

$y = -6$

Hence, the complete process is:

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

Read more about matrices at:

brainly.com/question/11367104

6 0

3 years ago

What number is 80% of 66

Anni [7]

52.8 is the answer.

Hope this helps!

4 0

4 years ago

Plot the following radian measures on the given unit circle

son4ous [18]

By our very goofy system the circle constant $\pi$ denotes half a circle, $180^\circ$ . So the conversion factor from radians to degrees is

$\dfrac{ 180^\circ}{\pi}$

$\dfrac{\pi}{3} \times \dfrac{ 180^\circ}{\pi} = 60 ^\circ$

Calling the rightmost dot [1] and counting counterclockwise, that's dot [4].

$\dfrac{2\pi}{3} \times \dfrac{ 180^\circ}{\pi} = \dfrac{2}{3} \times 180^\circ = 120^\circ$

That's dot [6]

$\dfrac{4\pi}{3} \times \dfrac{ 180^\circ}{\pi} = \dfrac{4}{3} \times 180^\circ = 240^\circ$

That's dot [12]

$\dfrac{5\pi}{3} \times \dfrac{ 180^\circ}{\pi} = \dfrac{5}{3} \times 180^\circ = 300^\circ$

That's dot [14]

5 0

3 years ago

Read 2 more answers

The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.

Vadim26 [7]

Answer: a) y=0.50x+15

b) The graph of this equation form on a coordinate plane is a line.

c) Slope =0.50 and y-intercept = 15

Step-by-step explanation:

Let x = Number of miles driven by car

Given: The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.

a) Total cost = 0.50x+15

If y =total cost of renting the car, then y=0.50x+15 (i)

b) Above equation is similar to y= mx+c (ii) [m = slope , xc=y-intercept] which a linear equation .

So the graph of this equation form on a coordinate plane is a line.

c) Comparing (i) and (ii)

m=0.50 , c=15

Slope =0.50 and y-intercept = 15

3 0

3 years ago

4. Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean

Karo-lina-s [1.5K]

Answer:

Yes, Tom must be admitted to this university.

Step-by-step explanation:

We are given that the scores on national test are normally distributed with a mean of 500 and a standard deviation of 100.

Also, we are provided with the condition that Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test.

Let, X = score in national test, so X ~ N( $\mu=500 , \sigma^{2} = 100^{2}$ )

The standard normal z distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, z score of probability that tom scores 585 is;

Z = $\frac{585-500}{100}$ = 0.85

Now, proportion of students scoring below 85% marks is given by;

P(Z < 0.85) = 0.80234

This shows that Tom scored 80.23% of the students who took test while he just have to score more than 70%.

So, it means that Tom must be admitted to this university.

4 0

4 years ago