An ill patient is administered 100mg dose of a fever-reducing drug. The total milligrams of the drug in the patient's bloodstream is given by the equation V(t) = 60te-t, where t is measured in hours after the medicine was ingested. a.) When does the amount of drug in the patient's bloodstream reach a maximum? How much of the pill is in the patient's bloodstream at this time? b.) What is the function that describes the rate of change in the amount of the drug in the bloodstream? If this rate is positive, does it mean (overall) that the drug is being absorbed into the bloodstream, or removed from the bloodstream? What if the rate is negative; is the drug entering or exiting the bloodstream? c.) At what time is the rate at which the drug is being absorbed into the bloodstream the greatest? d.) At what time is the rate at which the drug is being removed from the bloodstream the greatest? e.) How much of the drug will remain in the patients system in the long run? That is, what is lim V(t)? t2 t 1 (You may use the fact that lim lim lim.) ttoo et ttoo et t+oo et t- = =

To conclusively test the hypothesis "among these four people, those above age 30 definitely have feature a", you need to gather age and feature A information for Anne, Bob, Charlie, and Daniel.

You have the ages of Anne (35) and Bob (24) and feature A status of Charlie (has feature A) and Daniel (doesn't have feature A). You need to ask Anne and Bob about their feature A status and Charlie and Daniel about their ages.


1. Ask Anne if she has feature A.
2. Ask Bob if he has feature A.
3. Ask Charlie his age.
4. Ask Daniel his age.

After obtaining the missing information, compare it with the hypothesis to check if it holds true. The hypothesis will be true if both people above 30 years of age have feature A, and the others do not.

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Answer:

Simple random sampling

Step-by-step explanation:

Luke wants to study average minutes students read each night. For that matter, he has selected a 'sample' of 25 students from entire 'population' of students in school.

He has selected the sample students randomly, for collecting data related to minutes of study each night. He also collects data from them directly ie with primary contact with them.

So, primary data collection, simple random sampling - has been used as a type of data collection.

The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

To simplify the given expression, let's evaluate the square roots individually and then perform the addition.

√900 = 30, since the square root of 900 is 30.

√0.09 = 0.3, as the square root of 0.09 is 0.3.

√0.000009 = 0.003, since the square root of 0.000009 is 0.003.

Now, we can add these simplified values together

√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

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Answer:

(-18)

Step-by-step explanation:

3 . (-6) = (-6) + (-6) + (-6) = (-12) + (-6) = (-18)

or

3 . (-6) = (-18)

Example :

= 4 . (-5)

= (-5) + (-5) + (-5) + (-5)

= (-10) + (-10)

= (-20)

The proportional relationships that model each relation are given as follows:

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the equation below:

y = kx.

Both items in this problem are represented by direct proportional relationships, we just have to identify the constants then graph the relations.

The graph of a proportional relationship is linear with slope given by the constant and intercept at 0, hence the graphs for each item are given at the end of the answer.

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Answer:

C. 3.9375

Step-by-step explanation:

3 15/16

15/16

= 0.9375

0.9375+3

=3.9375

Answer:

C is correct

Step-by-step explanation:

Answer:

Average change in temperature is - 2.8 Fahrenheit per hour.

Step-by-step explanation:

Average change in temperature is the change in temperature divided by the time taken for the change.

Change in temperature = (-11.2) F- 0 F

                                      = -11.2 F

Time taken for the change in temperature = 10 pm

                                                                  = 4 hours

Average change in temperature = Change in temperature / time taken for the change

                                                     = - 2.8 Fahrenheit per hour

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The expression when evaluated is 5x^5y^5∛y^2

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

\(x^{2}y^{3}\sqrt[3]{125x^{8}y^{10}}\)​

When represented properly, we have

x^2y^3∛125x^8y^10

Evaluate the radicand expression

x^2y^3 * 5x^3 * y^2 * ∛y^2

Evaluate the products

5x^5y^5∛y^2

Hence, the expression is 5x^5y^5∛y^2

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there are 45,360 distinguishable arrangements of the letters in the word "SASKATOON" and  there are 34,650 distinguishable arrangements of the letters in the word "MISSISSIPPI".

a. SASKATOON:

To determine the number of distinguishable arrangements of the word "SASKATOON", we can use the formula for permutations of indistinguishable objects, which is n!/a!b!c!…, where n is the total number of objects and a, b, c,… are the frequencies of each indistinguishable object. In this case, there are 9 letters in the word "SASKATOON", but some of them are repeated. Specifically, there are 2 S's, 2 A's, and 2 O's. Using the formula, we get:

9!/(2!2!2!) = 9876543/(222) = 45,360

Therefore, there are 45,360 distinguishable arrangements of the letters in the word "SASKATOON".

b. MISSISSIPPI:

To determine the number of distinguishable arrangements of the word "MISSISSIPPI", we can use the same formula for permutations of indistinguishable objects. In this case, there are 11 letters in the word "MISSISSIPPI", but some of them are repeated. Specifically, there are 4 I's, 4 S's, and 2 P's. Using the formula, we get:

11!/(4!4!2!) = 34,650

Therefore, there are 34,650 distinguishable arrangements of the letters in the word "MISSISSIPPI".

In summary, the number of distinguishable arrangements of a word can be found using the formula for permutations of indistinguishable objects, which takes into account the frequency of each repeated letter. By applying this formula to the words "SASKATOON" and "MISSISSIPPI", we find that there are 45,360 and 34,650 distinguishable arrangements, respectively.

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Answer:

1. n=6

2. n=19

3. n=15

4. n=20

5. n=40

6. n=16

7. n=19

8. n=6

9. n=2.4

10. n=30

Step-by-step explanation:

remember the priorities :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

inside every category you go usually from left to right, but you can use the commutative property where applicable.

4 + 5 - 3 = 4 + 5 - 3 = 4 + 5 - 3 = 4 - 3 + 5 = 6

8×3 - 5 = 24 - 5 = 19

15/3 + 10 = 5 + 10 = 15

8 + 3 - 1×2 = 8 + 3 - 2 = 9

14×3 - 2 = 42 - 2 = 40

(3 + 5)×2 = 8×2 = 16

10 + 7 + 2×1 = 10 + 7 + 2 = 19

16/8 + 4 = 2 + 4 = 6

7 + 5/5 = 7 + 1 = 8

20/4×6 = 5×6 = 30

Answer:

4x +8 -x + 10 = x+4

3x+18= x+4

2x= -14

×=-7

Answer:

The order is 4) → 5) → 6) → 7) → 2) → 1) → 3)

Please find diagram with the arrangements

Step-by-step explanation:

The horizontal width of an hyperbola

For

1) \(\dfrac{(y - 11)^2}{7^2} -\dfrac{(x - 2)^2}{6^2} = 1\)

h = 2, k = 11

The widths are;

Horizontal (h - a, k) to (h + a, k) which is (2 - 7, 11) to (2 + 7, 11) = 14 units wide

(h, k - b) to (h, k + b) which is (2, 11 -6) to (2, 11 + 6) = 12 units wide

2)

\(\dfrac{(y - 1)^2}{5^2} -\dfrac{(x - 7)^2}{12^2} = 1\)

h = 7, k = 1

(h - a, k) to (h + a, k) which is (7 - 5, 1) to (7 + 5, 1) = Horizontal width 10 units wide

(h, k - b) to (h, k + b) which is (7, 1 -12) to (7, 1 + 12) = 24 units wide

3) \(\dfrac{(x - 6)^2}{6^2} -\dfrac{(y + 1)^2}{3^2} = 1\)

h = 6, k = -1

a = 8, b = 3

The widths are;

(6 - 8, -1) to (6 + 8, -1) Horizontal width = 16

(6, -1 - 3) to 6, -1 + 3) width = 6

4) \(\dfrac{(x - 4)^2}{2^2} -\dfrac{(y + 2)^2}{5^2} = 1\)

h = 4, k = -2, a = 2, b = 5

(4 - 2, (-2)) to (4 + 2, (-2)) Horizontal width = 4

(4, -2 - 5) to (4, -2 + 5) width = 10

5) \(\dfrac{(y + 5)^2}{2^2} -\dfrac{(x + 4)^2}{3^2} = 1\)

h = -4, k = -5, a = 2, b = 3

(-4 - 2, (-5)) to (-4 + 2, (-5)) Horizontal width = 4

(-4, -5 - 3) to (4, -5 + 3) width = 6

6) \(\dfrac{(y + 1)^2}{2^2} -\dfrac{(x - 1)^2}{9^2} = 1\)

h = 1, k = -1, a = 2, b = 9

(1 - 2, (-1)) to (1 + 2, (-1)) Horizontal width = 4

(1, -1 - 9) to (1, -1 + 9) width = 18

7) \(\dfrac{(x + 7)^2}{4^2} -\dfrac{(y - 9)^2}{9^2} = 1\)

h = -7, k = 9, a = 4, b = 9

(-7 - 4, 9) to (-7 + 4, 9) Horizontal width = 8

(-7,  9 -9) to (-7, 9 + 9) width = 18

Answer:

288

Step-by-step explanation:

To simplify use the mnemonic device PEMDAS (parenthesis, exponent, multiplication, division, addition, subtraction)

First simply -6 and 13 (since they are in the parenthesis)

-11+5+6(7)^2

Now find out what 7^2 is

-11 + 5 + 6(49)

Next multiply 6 and 49 (294)

Lastly add 5 then subtract 11 from it

299-11

288

Answer:

Hello! :) I hope I am correct!

Step-by-step explanation:

(The answer should be 288)

Below is the steps!!

Steps:

⇒-6+6(-6+13)^2

⇒-6+6(7^2)

⇒-6+(6)(49)

The answer would be 288 if you solve this equation.

The last step:

⇒-6+294

Which equals 288

Therefore your answer would be 288.

Hope this helps!

By:BrainlyAnime! ^-^

(Just in case you didn’t understand, I attached a picture!)

Answer:

9 is the greater x and 2 is the lesser x

Step-by-step explanation:

I really don't know how to explain without simply writing it out for you, which I really can't do. But there's the answer lol

Answer:

x = 2, x = 9

Step-by-step explanation:

Given

x² - 11x + 18 = 0

Consider the factors of the constant term (+ 18) which sum to give the coefficient of the x- term (- 11)

The factors are - 9 and - 2 , since

- 9 × - 2 = + 18 and - 9 - 2 = - 11 , thus

(x - 9)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2 ← lesser value

x - 9 = 0 ⇒ x = 9 ← greater value

The area of a triangle whose sides are 4.5 cm and 1 cm and perimeter 10.5 cm is 2.045 square cm

The area for the triangle whose perimeter and side is given is solved by the formula

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c))

where:

a, b, and c are the sides of the triangle

s = perimeter / 2

perimeter = a + b + c

10.5 = 4.5 + 1 + c

c = 10.5 - 5.5

c = 5

s = (a + b + c) /2

s = 10.5/2

s = 5.25

substituting for s a b and c

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c) )

A= √(5.25 (5.25 ﹣ 4.5) (5.25 ﹣ 1) (5.25 ﹣ 5) )

A = √4.18358

A = 2.045 square cm

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Answer:

3/5

Step-by-step explanation:

3+2=5. 3/5 is the blue marble. You may also say 6/10. It is likely you will pull out a blue marble.

probability that the blue marble was chosen both times 6/10.

It is a branch of mathematics that deals with the occurrence of a random event.

Jar contains 3 blue marbles.

Jar contains 2 red marbles.

Total marbles= 5

If she replaced a marble and second time she choose a marble gets blue.

Then, probability of blue marble= 3/5.

But for both the probability for both instance will be 3/5 i.e.,

=  3/5*2/2

= 6/10

Hence, probability that the blue marble was chosen both times 6/10.

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When a vertical plane passes through a pyramid that has a horizontal base, the figures will be a triangle and a trapezoid.

A plane is a flat, two-dimensional surface that can extend indefinitely. A plane is a two-dimensional analogue of a point, a line, or three-dimensional space. Planes can appear as subspaces of a few higher-dimensional spaces, such as the room's walls that have been extended extremely far away.

If the plane passes through the vertex, it will intersect the slant heights of two lateral faces and the pyramid's base. The cross section then has three sides, two of which are congruent. The resulting cross section is an isosceles triangle.

A vertical direction or plane passing through a given point contains the local gravity direction at that point. If a direction or plane is perpendicular to the vertical direction, it is said to be horizontal.

A triangle is formed when the plane passes through the pyramid's vertex. A trapezoid is formed when it passes through three faces of a square or rectangular pyramid.

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Complete question

A vertical plane passes through a pyramid that has a horizontal base. Which figure or figures can be produced? Select all that apply.

Circle

Triangle

Trapezoid

Rhombus

Answer:

5/6

Step-by-step explanation:

5/6=0.84, 8/10= 0.8

Answer:

42.6

Step-by-step explanation:

To do this question we need to use pythagoras theorem!

\(a^{2}+b^{2}=c^{2}\)

In this situation we will consider a to be 45 and c to 62. This means that we need to find b...

To do this we first need to substitute the values we know into the question

Now we can simplify as much as we can...

We are now left with...

Let's try find the value of '?'...

In the question we have still have to root it...

Now round to nearest tenth...

Answer: C=76.7

Step-by-step explanation:

You're going to be using Pythagoras' Theorem to solve this:

a^2+b^2=c^2

45^2+62^2=C^2

√45^2+62^2≈76.6094

Then after you get your answer for your missing side your going to round to your tenths

So 76.6094

*Remember five or more add one more 4 or less let it rest.

So 9 is over 5 which means in our tenths 6 turns into a 7.

So everything behind would turn into zero so it should look like this: 76.7

Please mark brainlest if this helps you!

Answer:

Q9:D

Q10:B

Step-by-step explanation:

Q9:for two graphs to be perpendicular, the product of their gradients has to be -1

multiplying the gradients of the equation in the question and the equation in option "D", we get -1 hence D is correct

Answer:

D

Step-by-step explanation:

This is an irrational number as it does not repeat and has an infinite number of combinations (as like pi)

The height of the tree to the nearest hundredth of a meter is 29.1m.

We can use the concept of similar triangles to find the height of the tree. The ratio of the height of the tree to the length of its shadow is the same as the ratio of Hunter's height to the length of his shadow.

Let h be the height of the tree.

Hunter's height : h = 1.75m : x (where x is the height of the tree)

Hunter's shadow : Tree's shadow = 1.75m : 30.85m

We know that Hunter is 26.8 meters away from the tree, and the tip of his shadow meets the tip of the tree's shadow.

Hunter's shadow = Hunter's height + Tree's shadow

1.75 + x = 30.85

x = 29.1m

Therefore, the height of the tree to the nearest hundredth of a meter is 29.1m.

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Answer:

A' (-6, 4)

B' (2, 2)

C' (-2, -2)

Step-by-step explanation:

Multiply each number by 2.

The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.

To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.

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area=147 cm squared

7 x 7 = 49

49 x 3 = 147

If the columns of matrix B are linearly dependent, then the columns of AB are also linearly dependent.

Suppose the columns of matrix B are linearly dependent, which means there exist constants c₁, c₂, ..., cₙ (not all zero) such that c₁b₁ + c₂b₂ + ... + cₙbₙ = 0, where b₁, b₂, ..., bₙ are the columns of B.

Now, let's consider the product AB. Suppose A is an m × n matrix.

The jth column of AB is given by the product AB(:, j) = A(b₁j) + A(b₂j) + ... + A(bₙj), where b₁j, b₂j, ..., bₙj are the jth columns of B.

Substituting the linear dependence relation for the columns of B into the expression for AB(:, j), we get:

AB(:, j) = A(c₁b₁ + c₂b₂ + ... + cₙbₙ)

         = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

Since matrix multiplication distributes over column vectors, we have:

AB(:, j) = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

This shows that the jth column of AB can be expressed as a linear combination of the columns of A, multiplied by the corresponding coefficients c₁, c₂, ..., cₙ. Therefore, if the columns of B are linearly dependent, the columns of AB are also linearly dependent.

In conclusion, if the columns of matrix B are linearly dependent, then so are the columns of the product AB.

Complete Question:

Show that if the columns of B are linearly dependent, then so are the columns of AB.

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Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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The probability that the artist will choose a picture that is not a multiple of 13 is 14/15.

Probability:

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event or how likely a statement is to be true. The probability of an event is a number between 0 and 1, with 0 representing an impossibility and 1 representing certainty, roughly speaking. The higher the probability of an event, the higher the probability of an event occurring. A simple example is a fair (unbiased) coin toss. Since the coin is fair, both outcomes ("heads" and "tails") are equally likely. The probability of an "eagle" is equal to the probability of a "tail". And since no other outcome is possible, the probability of getting heads or tails is 1/2.

Now,

The sample space is S = {1,23,4,5,...60}

n(S) = 60

The multiples of 13 are:

E = {13,26,39,52}

n(E) = 4

Probability of choosing a picture that is a multiple of 13 is

   P(E) = n(E)/ n(s)

⇒ P(E) = 4/60

Probability of choosing a picture that is NOT a multiple of 13 is

P(E)  = 1 - 4/60

       = 56/60

       = 14/15

Therefore,  the probability that the artist will choose a picture that is not a multiple of 13

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