Evaluate the exponent expression for a = 1 and b = -2
A) -2
B)-1/16
C)-2/5
D)1/16

Answer:  -4 ,-2, 0 ,2  ,4

Step-by-step explanation:

The slope of graph is 4.17 (a+1). It represents the annual rise in dose a.

Excellent understanding of medications, their mechanisms of action, side effects, interactions, mobility, and toxicity are prerequisites for practicing pharmacy. Thus, pharmacists are the key healthcare professionals who maximize the use of medicine for the benefit of patients. They are also the world's foremost authorities on drug therapy.

The pharmacist use equation C= 0.0417 d (a+1)

Applying in (mg)

So d = 100 mg

Therefore c = 0.0417×100 (a+1)

C= 4.17 (a+1)

4.17 (a+1) is the slope for the graph of c, which reflects the annual rise in dose a.

kid requires. Given that a newborn is age 0, the appropriate dosage is

c(0) = 4.17 (a+1)

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417D(a + 1). Suppose the dosage for an adult is 200 mg.

(a) Find the slope of the graph of c. What does it represent?

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say we're going to add "x" gallons of water, now how many gallons of alcohol is in pure water? well 0%, and 0% of "x" is (0/100) * x = 0.

the 3 gallons we know are 100% alcohol, how many gallons of alcohol is in it?  well (100/100) * 3 = 3.

the resulting mix will have x + 3 gallons total and it's going to be 15% alcohol, how many gallons of alcohol is that? (15/100) * (x+3).

now, the amount of alcohol never increased, so the original 3 gallons of only alcohol will remain even after the water has been added, so.

\(\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{pure water}&x&0.00&0\\ \textit{pure alcohol}&3&1.00&3\\ \cline{2-4}&\\ mixture&x+3&0.15&0.15(x+3) \end{array} \begin{array}{llll} \\[3em] \leftarrow \textit{this amount}\\\\ \leftarrow \textit{must be equal to this one} \end{array} \\\\\\ 3 = 0.15(x+3)\implies 3=0.15x+0.45\implies 2.55=0.15x \\\\\\ \cfrac{2.55}{0.15}=x\implies 17=x\)

The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).

In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.

Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).

Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).

Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).

To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:

Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)

Simplifying this expression, we get:

Total number of strings = (n-1) x (n-2)

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Answer: a

Step-by-step explanation:

Answer:

$8.29

Step-by-step explanation:

Answer:

The answer is $8.29

Step-by-step explanation:

The answer is $8.29 because if the gloves cost $41.45 for 5 pairs of gloves, you would divide $41.45 by 5 to get the answer $8.29.

hope this helps :))))

Answer:

  tan(θ) = 2/3

Step-by-step explanation:

You want the tangent of the angle θ between the x-axis and the line connecting the origin to point (3, 2).

The tangent ratio is given by ...

  Tan = Opposite/Adjacent

In the attachment, you can see that the side opposite the angle of interest is the y-coordinate of the point. The side adjacent is the x-coordinate. That means ...

  tan(θ) = y/x

  tan(θ) = 2/3

__

Additional comment

In general, the tangent of the angle a line makes with the x-axis is the slope of the line. Your line has slope 2/3, and that is the tangent of the angle it makes with the x-axis.

The experimental probability of landing on a number greater than 4 is 18/60

The experimental probability will be given by the number of times that the outcome was greater than 4 (so a 5 or a 6) over the total number of trials.

We can see that the total number of trials is 60, and we have:

The outcome 5 a total of 10 times.

The outomce 6 a total of 8 times.

Adding these values we will get 10 + 8 = 18

Then the experimental probability of a number greater than 4 is:

E = 18/60

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If the support threshold for given integers is 5 , then (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25, 30, and 60) items are frequent.

The following pairs of items will be frequent: (1,2), (1,3), (1,4), (1,5), (1,6), (1,10), (1,12), (1,15), (1,20), (1,30), (2,4), (2,6), (2,10), (2,12), (2,20), (3,6), (3,12), (4,12), (5,10), and (5,20).

The confidence of the following association rules are 100% and 50%.

(a) The items that are frequent, if the support threshold is 5, can be found by counting the number of baskets that contain each item. The following items will be frequent: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25, 30, and 60. These are the items that appear in at least five baskets.

(b) The pairs of items that are frequent if the support threshold is 5 can be found by counting the number of baskets that contain each pair of items. The following pairs of items will be frequent: (1,2), (1,3), (1,4), (1,5), (1,6), (1,10), (1,12), (1,15), (1,20), (1,30), (2,4), (2,6), (2,10), (2,12), (2,20), (3,6), (3,12), (4,12), (5,10), and (5,20).

(c) The confidence of the following association rules is as follows:

1. {5,7}→2 has a confidence of 100%, since 2 appears in all baskets that contain both 5 and 7.

2. {2,3,4}→5 has a confidence of 50%, since 5 appears in only half of the baskets that contain 2, 3, and 4.

(d) The basket that is the largest is basket 60, which consists of the following items: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. This is because 60 is divisible by all of these items.

(e) The association rules that have 100% confidence are those where the antecedent and consequent are the same. For example, the following rules have 100% confidence: {1}→1, {2}→2, {3}→3, and so on.The steps for the Apriori Algorithm with support threshold 5 is as follows:

Step 1: Create a list of frequent 1-itemsets. This list includes all items that appear in at least five baskets.  {1,2,3,4,5,6,8,10,12,15,20,25,30,60}

Step 2: Generate candidate 2-itemsets by joining frequent 1-itemsets.  {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {1,10}, {1,12}, {1,15}, {1,20}, {1,30}, {2,4}, {2,6}, {2,10}, {2,12}, {2,20}, {3,6}, {3,12}, {4,12}, {5,10}, {5,20}

Step 3: Count the support of each candidate 2-itemset. Discard those with support less than 5.  {1,2}: 100, {1,3}: 44, {1,4}: 44, {1,5}: 36, {1,6}: 28, {1,10}: 12, {1,12}: 20, {1,15}: 12, {1,20}: 12, {1,30}: 8, {2,4}: 36, {2,6}: 20, {2,10}: 12, {2,12}: 20, {2,20}: 12, {3,6}: 12, {3,12}: 20, {4,12}: 20, {5,10}: 12, {5,20}: 12

Step 4: Generate candidate 3-itemsets by joining frequent 2-itemsets.  {1,2,4}, {1,2,6}, {1,2,10}, {1,2,12}, {1,2,20}, {1,3,12}, {1,4,12}, {2,4,6}, {2,4,10}, {2,4,12}, {2,6,12}

Step 5: Count the support of each candidate 3-itemset. Discard those with support less than 5.  {1,2,4}: 20, {1,2,6}: 12, {1,2,10}: 12, {1,2,12}: 20, {1,2,20}: 12, {1,3,12}: 20, {1,4,12}: 20, {2,4,6}: 12, {2,4,10}: 12, {2,4,12}: 20, {2,6,12}: 12

Step 6: Continue generating candidate k-item sets and counting their support until no frequent item sets of length k can be found.

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The relationship between the volume of a cone and a pyramid:

the volume of cone = volume of pyramid

if and only if the pyramid has circular base and both have equal radii and vertical heights

In this question we need to find the relationship between the volume of a cone and a pyramid.

We know that a pyramid is three dimensional shape with polygon base and trigular lateral faces which meet at vertex.

The formula for the volume of pyramid is,

V = 1/3 * base area * height

As we know a cone is nothing but a pyramid with circular base.

Consider a cone with radius r and vertical height h.

The formula for the volume of cone,

V = 1/3 × π × r² × h

V = 1/3 * area of circle * height

Therefore, the volume of a cone and a pyramid with circular base are equal.

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Answer:

The answer is 2423.35 (Not rounded)

Step-by-step explanation:

This is the formula that I used.

V=πr2h

Volume = π·5.52·25.5 ≈ 2423.34603

Answer:

C, E

Step-by-step explanation:

Answer:

v=pie r² ×h

v=3.14×2²×8

v= 100.48

Step-by-step explanation:

you are using diameter as the radius that is why exactly you are not getting it right! divide the diameter by 2 to get radius and use it with the formula

The number of stores located in California at the end of 2016 was 16, so the answer is (d) 16.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to represent part of a whole or a proportion of a quantity.

At the end of 2010, the business had 140 stores in the United States.

By the end of 2016, the number of stores in the United States had increased by 60%. To find out how many stores there were at the end of 2016, we need to add 60% of the original number of stores to 140:

Number of stores at end of 2016 = 140 + 0.6*140 = 140 + 84 = 224

So there were 224 stores in the United States at the end of 2016.

If 1/14 of these stores were located in California, we can calculate the number of stores located in California as follows:

Number of stores in California = (1/14) * 224 = 16

Therefore, the number of stores located in California at the end of 2016 was 16, so the answer is (d) 16.

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Lorraine can fill 8 jars with the tomatoes from the 2.5-gallon pot.

First, we need to convert the volume of the pot from gallons to quarts, since the jars are measured in quarts:

2.5 gallons = 2.5 * 4 quarts = 10 quarts

Next, we can divide the total volume of the pot in quarts by the volume of each jar in quarts to find the number of jars Lorraine can fill:

10 quarts / 1.25 quarts per jar = 8 jars

So Lorraine can fill 8 jars with the tomatoes from the 2.5-gallon pot.

Mensuration is a branch of mathematics that deals with the measurement of various geometric figures and objects, such as lengths, areas, and volumes. It is concerned with finding the size, shape, and measurement of geometric objects, such as points, lines, circles, polyggon, and solids.

Mensuration is used in various areas of mathematics, science, and engineering to solve problems involving measurements, such as finding the area of a rectangle, the volume of a cylinder, the circumference of a circle, or the surface area of a sphere.

Mensuration provides a set of mathematical formulas and methods for measuring geometric objects, and it requires knowledge of basic concepts such as perimeter, area, volume, and surface area. These concepts are used to find the size of objects and to compare different objects to one another based on their measurements.

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Answer: 8 1/3

Step-by-step explanation: Convert 3/4 to 9/12 then subtract, and simplify.

Answer:

8 and 1/3

Step-by-step explanation:

First, let's subtract the whole numbers:

16 - 8 = 8

Then, find the lowest common multiple of the two denominators, 4 and 12. In this case, 12 is the lowest common multiple. To turn 4ths into 12ths:

4 x 3 is 12, and 3 x 3 is 9

Now, subtract the two fractions:

9/12 - 5/12 = 4/12 = 1/3

That gives us a final answer of 8 and 1/3. Hope this helped!

∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Given:

Three lines AD, CF, and BE are intersecting each other at the midpoint O.

To prove:

∠CFA ≅ ∠EDA

Proof:

Given that AD, CF, and BE intersect at the midpoint O.

By definition of a midpoint, OA ≅ OD, OB ≅ OE.

OA = OD and OB = OE.

Triangle OAD ≅ Triangle OBE (By Side-Side-Side congruence).

∠OAD ≅ ∠OBE (By Corresponding Parts of Congruent Triangles are Congruent).

∠CFA and ∠EDA are vertical angles.

∠OAD ≅ ∠CFA and ∠OBE ≅ ∠EDA (By Vertical Angles are Congruent).

Therefore, ∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Hence, it is proven that ∠CFA ≅ ∠EDA.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The proof that shows that ΔPQR ~ ΔTSR  by the AA similarity theorem is shown below.

According to the AA similarity theorem, two triangles that have two pairs of corresponding congruent angles are said to be similar to each other.

Using this theorem, we can prove that triangles PQR and TSR are similar as shown in the proof below.

Statement                              Reason                                      

1. QR | PT                               1. Given

2. <QPR = <STR                    2. Given

3. <QRP and <SRT are right 3. Definition of perpendicular

angles

4. <QRP ≅ <SRT                     4. All right angles are ≅

5. ΔPQR ~ ΔTSR                     5. AA similarity theorem

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Answer:

62.8

Step-by-step explanation:

165/28.8 = 360/x

360 x 28.8 =10,368/165 = 62.8

hope this helps <3

Answer:

Explanation: The rate of change between two points on a curve can be approximated by calculating the change between two points. Let be the coordinates of the first point and be the coordinates of the second point. Then the formula giving approximate rate of change is

Step-by-step explanation:

calculating the change between two points.

Answer:

x = - 3, x = 0.5

Step-by-step explanation:

Given

10x² + 5x - 15 = - 12 + 8x² ( subtract 8x² from both sides )

2x² + 5x - 15 = - 12 ( add 12 to both sides )

2x² + 5x - 3 = 0 ← in standard form

(x + 3)(2x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5

The given function graph is increasing on the interval [1, 5] and decreasing on the interval [-1, 1] and [5, 7].

The graph of the function is shown below:

In the interval [-1, 1], the slope of the graph is negative because it is decreasing,

hence the function is decreasing.

In the interval [1, 5], the slope of the graph is positive because it is increasing,

hence the function is increasing.

In the interval [5, 7], the slope of the graph is negative because it is decreasing,

hence the function is decreasing.

Therefore, the answer is: Increasing on the interval [1, 5]

Decreasing on the interval [-1, 1] and [5, 7]

And the value of x is not given, hence we cannot find it.

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Answer: Yes, it is a function.

Step-by-step explanation:

This question is:

"A relation between time and distance traveled by a biker is a function?"

Well, as you may know, a function is a relation where each value in the domain or input, has only linked one value in the range or output.

In this relation the domain is time and the range is the distance.

Now, as you know, at each given time, the distance of the biker can be only one (he can not be at different locations at the same time) so this relation is actually a function.

EXPLANATION:

Given;

We are told that a bag contains the following;

Lila selects a ribbon at random and then Jessica selects a ribbon at random from the remaining ones.

Required;

Calculate the probability that Lila selects a black ribbon and Jessica selects a green ribbon.

Step-by-step solution;

The probability of an event is calculated by the formula given below;

For Lila to select a black ribbon, we have;

Now we have 19 ribbons left, note that Jessica had to select from the remaining ribbons.

For Jessica to select a green ribbon, we have;

Next to calculate the probability that Lila selects a black ribbon and Jessica selects a green ribbon we have a product of probabilities;

Therefore,

ANSWER:

The probability that Lila selects a black ribbon and Jessica selects a green ribbon is,

Answer:

41 ft 2 in

Step-by-step explanation:

Since the two triangles in question, that means that the triangles have the same proportions. We know that GH = 16 ft 7 in = 199 in (16x12+7) and HN = 6 ft 3 in = 75 in (6x12+3). GH/HN is 199/75. This is the same ratio that GO/AN will have as well. GO is unknown so we will denote it as x and AN = 15 ft 6 in = 186 in (15x12+6). We know that these two fractions are equal. 199/75 = x/186 solving for x, we get x = 493.52 in and converting that into feet we get 41 ft 1.52 in which rounds to 41 ft 2 in.