The half-life of caffeine in your body is approximately 3 hours. Suppose you drink a cup of coffee at 8 am that contains 120 mg of caffeine and consume no other caffeine for the rest of the day.
a) Write an explicit/closed form function for the amount of caffeine in your body in terms of the number of hours since 8 am.
b) Find the percentage of caffeine eliminated from your body each hour. Use this fact to write a different explicit/closed form function for the amount of caffeine in your body using a base of the form.

At 100°C, the nitrogen molecules in the container have an rms speed of 576 m/s. The pressure inside the container,

which is at a pressure of 2.4 atm, is a result of the collisions of these fast-moving molecules with the walls of the container. The area of the wall is 13 cm x 13 cm, which means there is a total surface area of 169 cm^2.

The collisions of the nitrogen molecules with this surface area will result in a force on the wall, which is what creates the pressure.

Overall, the properties of the nitrogen molecules, including their speed and number, contribute to the overall pressure inside the container.

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Answer:

Step-by-step explanation:

she need to make $50 more you did not put how much shes making a week if she makes $10  it will be five more weeks if she makes $5 it will be 10 more weeks

Answer:

y-intercept: 6

Step-by-step explanation:

Y = -2x 6

The equation is y = mx + b

m = the slope

b = y-intercept

So, the y-intercept is 6

Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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There were 80 inhabitants that had 4 extremities, and 93 that had 3 extremities.

Given that, when astronauts Antoine Weber and Rachel Sun landed on the hypothetical planet Trifour they found the inhabitants had either 3 or 4  extremities, and Weber could not look at the inhabitants' faces so he just  counted their extremities, and he counted 173 extremities, while Sun, on the other hand, could not look at their extremities so she just counted faces, and she counted 51 faces, to determine ow many inhabitants had 3 extremities and how many were there that had 4 extremities, the following calculation has to be done:

Therefore, there were 80 inhabitants that had 4 extremities, and 93 that had 3 extremities.

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Answer:

7m and m = 8

7(8) = 56 one solution and that solution is 56

Step-by-step explanation:

Answer:

Hey there!

There is only one solution.

7(8)=56. It cannot be anything else.

Let me know if this helps :)

Answer:

Step-by-step explanation:

Remark

The formula for this is

Heat = m * c * Δt

Givens

Heat = unknown

m = 200 grams

c = 4.184 Joules / grams oC

Δt = the change in temperature = 35.7 - 22.3 = 13.4

Solution

Heat = 200 * 4.184 * 13.4

Heat = 11213 Joules

Heat = 11.2 Kj

It's hard to get the correct number of sig digs because the 200 is not qualified in any way.

Part 2.

This can really puzzle you until you know that heat given up = the heat taken on. The heat taken on was 11.2 Kj. The Butane lighter must have given that heat on.

Heat of Combustion = Heat Given Up / Number grams burned.

Heat of Combustion = 11.2 Kj / 0.23 grams

Heat of Combustion = 48.8 Kj / gram

Answer:

v = 200 m/s

Step-by-step explanation:

The formula for the speed of a tsunami in deep water is given by :

\(v=\sqrt{gh}\)

Here,

g is acceleration due to gravity

h is the depth of the ocean in meters.

We need to find the speed at which the tsunami that started with an earthquake in Sumatra struck Sri Lanka about 1550 km away. The Bay of Bengal is 4 km (4000 m) deep.

It means we need to find v if h = 4000 m

So,

\(v=\sqrt{10\times 4000}\\\\v=200\ m/s\)

So, the speed of the tsunami is 200 m/s.

If a single card is drawn from a standard deck of 52 cards, the probability it will be a card with a number less than 5 is 4/13.

Probability measures how likely an event occurs. The probability of an event A is defined as:

P(A) = number of ways A can occur / total possible outcomes

In the given problem, let an ace card is considered as 1. Then, for each suit of cards, the card numbers which are less than 5 are cards number: 1, 2, 3, 4.

There are 4 suits, hence:

number of ways the event can occur = 4 x 4 = 16

total possible outcomes = 52

Therefore,

P(<5) = 16/52 = 4/13

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Answer:14/52

Step-by-step explanation:

Answer:

30 cents

Step-by-step explanation:

24=1.20

6=x

Algebra here to solve.

1.20=24

x=6

Divide by 4

1.20÷4=$0.3

$0.3=30 cents

Answer:

4/10 combined

Step-by-step explanation:

Hope this helps, let me know!

Answer: 4/10 or 0.4

Step-by-step explanation:

    You turn the .3 into a fraction. Say it aloud and it's 'three tenths." The cat products are 1/10 so you add 3/10+1/10=4/10 or 0.4.

All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.

1.1 Formulation:

The problem can be formulated as follows:

Minimize: 0 (since it is a feasibility problem)

Subject to:

α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1

α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2

α1, α2, α3, α4 are unrestricted

β is unrestricted

y_i ≥ 0 for all points in S1

z_i ≥ 0 for all points in S2

The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.

1.2 Finding a feasible solution:

To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.

Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.

For S1:

(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible

(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible

(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible

(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible

For S2:

(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible

(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible

(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible

(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible

Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

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Answer:

Step-by-step explanation:

AB + BC = AC if midpoint is B

AB-CB=AC if midpoint is C

\(( - 3) + ( - 19) + 6 \\ - 3 + ( - 19) + 6 \\ - 3 - 19 + 6 \\ = - 16\)

\(( - 41) - 15 + 9 \\ - 41 - 15 + 9 \\ = - 47\)

\( - 16 > - 47\)

Answer:

(-3)+(-19)+6 [>] (-41)-15+9

Step-by-step explanation:

(-3)+(-19)+6= -16

and

(-41)-15+9= -47

so, -16 is greater than -47

Answer:

R93,750. (I have changed R to $ in explanation)

Step-by-step explanation:

To determine the cost of the car inclusive of VAT, trade-in, and other fees, we first need to calculate the VAT amount. Assuming the VAT rate is 15%:

VAT = 0.15 x $75,000 = $11,250

Next, we can calculate the total cost of the car, inclusive of VAT:

Total cost of car = Cost of car + VAT

Total cost of car = $75,000 + $11,250

Total cost of car = $86,250

We also need to take into account the trade-in and the other fees. The trade-in value of $9,500 and the other fees of $2,000 are subtracted from the total cost of the car:

Total cost of car inclusive of VAT and other fees = Total cost of car + Trade-in value - Other fees

Total cost of car inclusive of VAT and other fees = $86,250 + $9,500 - $2,000

Total cost of car inclusive of VAT and other fees = $93,750

Therefore, the cost of the car, inclusive of VAT, trade-in, and other fees, is $93,750.

24

\(Convert\ the\ unit\ for\ \frac{12in}{1ft}:\\ \downarrow\\ 24\)

I hope this helps you

:)

Answer:

Provide with more information the calculus is illegal

Step-by-step explanation:

The equation of the function represented by the table of values is y = 2ˣ + 1

From the question, we have the following parameters that can be used in our computation:

The table of values

By definition, the table of values is an exponential function that has been translated vertically

This means that the rule of the function is

y = abˣ + k

In this case, k = 1

So, we have

y = abˣ + 1

Using the points from the table, we have

ab⁰ + 1 = 2

This gives

a + 1 = 2

So, we have

a = 1

The equation becomes

y = bˣ + 1

Using another point, we have

b² + 1 = 5

So, we have

b² = 4

Evaluate

b = 2

So, we have

y = 2ˣ + 1

Hence, the equation is y = 2ˣ + 1

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Answer:

1. 12

2. 0

3. 9

Step-by-step explanation:

The range of the function is (d) [150, 275]

The graph that completes the question is added as an attachment

From the graph, we have the following properties:

The range is simply the amount of values between the y axis

In this case represented by the graph, we have:

Minimum y value = 150

Maximum y values = 275

Sinfe both values are inclusive, the range would be [150, 275]

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Answer:

C

Step-by-step explanation:

The true statement is b. Parallel ILS approaches provide aircraft with a minimum of 1-1/2 miles of radar separation between successive aircraft on the adjacent localizer course.

Instrument Landing System(ILS) is the name for this type of system. These methods are typically employed by aircraft to successfully land in low visibility conditions. When using ILS approaches to reach the same airport on parallel runways, all the air traffic controllers ensure that a minimum separation is maintained between two or more aircraft in order to reduce the considerable risk of accidents.

Parallel ILS approaches must typically provide at least 1-1/2 miles of radar separation between succeeding aircraft on the adjacent localizer track, according to FAA standards. This distance between the aircraft is effectively measured by radar sensors and is kept horizontally.

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Answer:

hope this helps.............

According to the question the median is most probably less than 36.

For a positively skewed distribution, the mode is the value that occurs most frequently, the mean is the average value, and the median is the middle value when the data is arranged in ascending order.

Given that the mode is \(\(x = 31\)\) and the mean is \(\(36\),\) we can infer that the majority of the data is clustered towards the left (lower values) and there are some relatively high values that pull the mean to the right.

Since the distribution is positively skewed, the median is expected to be lower than the mean. This is because the presence of outliers or higher values on the right side of the distribution affects the mean more than the median.

Therefore, the median is most probably less than 36.

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Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

\(\displaystyle \frac{\cos y}{1-\sin y}=\frac{1+\sin y}{\cos y}\)

On the left, we can multiply both layers by (1 + sin(y)):

\(\displaystyle \frac{\cos y}{1-\sin y}\left(\frac{1+\sin y}{1+\sin y}\right)=\frac{1+\sin y}{\cos y}\)

Multiply:

\(\displaystyle \frac{\cos y(1+\sin y)}{1-\sin^2 y}=\frac{1+\sin y}{\cos y}\)

From the Pythagorean Theorem, we know that sin²(y) + cos²(y) = 1. Hence, 1 - sin²(y) = cos²(y). Substitute:

\(\displaystyle \frac{\cos y(1+\sin y))}{\cos^2 y}=\frac{1+\sin y}{\cos y}\)

Cancel:

\(\displaystyle \frac{1+\sin y}{\cos y}=\frac{1+\sin y}{\cos y}\)

Hence proven.

The expected number of mutual friends Alice and Bob have is 2.5.

In the scenario described, Alice and Bob each have 50 friends out of 1000 people in their town. They believe that the probability of having a mutual friend is low since each of them is only friends with 5% of the population. To calculate the expected number of mutual friends, we can consider it as a matching problem.

Alice's 50 friends can be thought of as a set of 50 randomly selected people out of the 1000, and similarly for Bob's friends. The probability of any given person being a mutual friend of Alice and Bob is the probability that the person is in both Alice's and Bob's set of friends.

Since the selection of friends for Alice and Bob is independent, the probability of a person being a mutual friend is the product of the probability that the person is in Alice's set (5%) and the probability that the person is in Bob's set (5%). Therefore, the expected number of mutual friends is \(0.05 * 0.05 * 1000 = 2.5\).

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To express vector p as a linear combination of vectors u, v, and w, we need to find coefficients (multipliers) for each vector such that p can be written as p = au + bv + cw, where a, b, and c are scalars.

Given vector p = [6 4 5], we will try to find coefficients that satisfy this equation.

Setting up the equation:

p = au + bv + cw

[6 4 5] = a[u1 u2 u3] + b[v1 v2 v3] + c[w1 w2 w3]

We can now form a system of equations based on the components of the vectors:

6 = au1 + bv1 + cw1 ...(1)

4 = au2 + bv2 + cw2 ...(2)

5 = au3 + bv3 + cw3 ...(3)

To determine whether there is a linear combination, we need to solve this system of equations. If there exists a solution (a, b, c) that satisfies all three equations, then p can be expressed as a linear combination of u, v, and w. Otherwise, if no solution exists, then there is no such linear combination.

Solving the system of equations will provide the coefficients (a, b, c) if they exist. However, without the values of u, v, and w, we cannot determine whether a solution exists for this specific case. Please provide the values of u, v, and w for further analysis.

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Answer:

5 cm

Step-by-step explanation:

the perimeter of a square with sides of 9 cm is 36 cm so the rectangle must have the same perimeter

if the length of the rectangle is 13cm, its opposite side is also 13cm

add 13 + 13 to get 26

let 'n' = width of rectangle

perimeter = 26 + n + n

36 = 26 + 2n

2n = 10

n = 5

If the length of the rectangle is 13 cm then the width of the rectangle will be equal to 5 cm.

A shape's perimeter is the whole distance encircling it. It is the perimeter or length of the contour of any two-dimensional geometric body. The circumference of several figures could be compared based on the measurements.

As per the information given in the question,

Length of the side of the square = 8 cm

Then, use the formula of the perimeter of the square = 4 × side

= 4 × 9 = 36 cm

The length of the rectangle = 13 cm

Use the formula of the perimeter of the rectangle,

P = 2(l + w)

36 = 2(13 + w)

36 -26 = 2w

w = 10/2

w = 5 cm

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There is a ''negative correlation'' in the data set.

Hence, Option B is correct.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, By the graph;

The graph shows points that are grouped together and are decreasing.

And, The gathered data shows that there is a possibility to get correlation between them.

Thus, The group of data is decreasing.

So, the correlation of the data will be negative in nature.

Therefore, It can be said that the "There is a negative correlation in the data set".

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Answer:

28

Step-by-step explanation:

Correct option is C)

Matches played between 8 teams =7+6+5+4+3+2+1=21

The number of ways that can 1st and 2nd place be awarded at the end of tournament is 56.

A permutation is an arrangement of objects in a definite order. The members of elements of sets are arranged here in a sequence where order matters.

According to the given question

we have  to find,

Number of ways  for 1st and 2nd place can be awarded

Number of ways for 1st place be awarded  = 8

Number of ways for 2nd place be awarded = 7

Therefore,

The total number of ways can 1st and 2nd place be awarded = (8)×(7)

=56.

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\(-3(2x+2) < 10\\\\\implies -6x -6 < 10\\\\\implies -6x < 10 +6\\\\\implies -6x < 16 \\\\\implies x > -\dfrac{16}6\\\\\implies x > -\dfrac{8}3\)