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3 years ago

You drink a cup of coffee with 120 mg of caffeine. Each

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

8 0

Answer:

91.2 mg of coffee left in your system 2 hours from consumption

Step-by-step explanation:

120 x .12 = 14.4

14.4 x 2 = 28.8

120 - 28.8 = ...

91.2 mg

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Two lines or equations are described in each part. Decide whether each system has one solution, no solution, or infinitely many

olga55 [171]

To get the solution of a set of equations means to get a point that satisfies both equations.

Part (1):
The first line has a rate of change of 7, this means that slope of first line is 7
The second line has a rate of change of -7, this means that slope of second line is -7
Since the slope of the first line = - slope of the second line, then these two lines are definitely perpendicular to each other.
Two perpendicular lines will meet only in one point. This means that one point only will satisfy both equations (check the image showing perpendicular lines attached below)
Therefore, only one solution exists in this case

Part (2):
The first given equation is:
2x + 3y = 5.5
The second given equation is:
4x + 6y = 11
If we simplified the second equation we will get: 2x + 3y = 5.5 which is exactly similar to the first equation.
This means that the two given equations represent the same line.
Therefore, we have infinite number of solutions

Part (3):
We are given that the two lines are parallel. This means that the two lines are moving the same path side by side. Two parallel lines can never intersect. This means that no point can satisfy both equations (check the image showing parallel lines attached below).
Therefore, we have no solutions for this case.

7 0

3 years ago

Read 2 more answers

Line AB contains points A (4,5) and B(9,7). What is the slope of AB

ki77a [65]

This line crosses the point (4,5)so we can make an equation to find the slope:
$4 = a \times 5 \\ 4 = 5a \\ a = \frac{4}{5}$
hope this helps

8 0

3 years ago

Read 2 more answers

labwork [276]

Domain is the numbers you can use
range is the result of inputing the domain

an interesting fact is that the inverse of a function switches the domain and range

basically
the domain of f(x) becomes the range of f^-1(x)
the range of f(x) becomes the domain of f^-1(x)
so just find the domain and range of f(x)

$f(x)=3x- \frac{1}{2}$
there are no restrictions
all real numbers can be used
all real numbers can result

so the answer is domain and range for both is all real numbers

D is answer

7 0

2 years ago

1) A school has 1600 students and they are going to vote as to whether they will completely convert the school completely off fo

fredd [130]

Answer:

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote

= 0.408 X 1600

= 652.8

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given sample size 'n' = 1600

95% confidence interval of the margin error is determined by

$M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }$

Level of significance = 0.05

Z₀.₀₅ = 1.96

Given Margin of error = 2% = 0.02

$M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }$

$0.02 = \frac{1.96 X S.D}{\sqrt{1600} }$

0.02 X √1600 = 1.96 X S.D

$S.D = \frac{0.02X\sqrt{1600} }{1.96} = 0.408$

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote

= 0.408 X 1600

= 652.8

5 0

2 years ago

Using the side lengths

In-s [12.5K]

Given

The three sides are given 24, 30 and 18.

Explanation

To find the triangle is acute, obtuse or right triangle.

To determine whether the triangle is acute, right, or obtuse.add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute.

If the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.

Now c.

$\begin{gathered} 30^2=24^2+18^2 \\ 900=576+324 \\ 900=900 \end{gathered}$

Answer

Hence the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.

The correct option is A.

3 0

8 months ago