When her first baby was born, a mom started investing $200 each month into a college fund earning 6% compounded monthly, how much will be available when the child turns 18 years?

Answer:

12/20 = 0.6

Step-by-step explanation:

The total number of cards in Kayla's hand is:

6 (spades) + 7 (hearts) + 5 (diamonds) + 2 (clubs) = 20

The number of red cards (hearts or diamonds) in Kayla's hand is:

7 (hearts) + 5 (diamonds) = 12

Therefore, the probability of randomly selecting a red card from Kayla's hand is:

12/20 = 0.6

Answer: 0.6

Step-by-step explanation: you add the total amount of cards she has which is 20(6+7+5+2) then the amount of hearts or diamonds is 7+5 for hearts and diamonds, which is =12 so the amount of hearts and diamonds divided by the total amount of cards, 12/20 which is 6/10 when divided by 2, 6/10 is 0.6, if you want to go further 6/10 can be broken down to 3/5 which is also 0.6

The hypotenuse of the right angled triangle is [tex]$14\sqrt{2}$[/tex].

What is hypotenuse?

The hypotenuse is the longest side of a right-angled triangle and is opposite to the right angle. It is the side that is opposite to the 90-degree angle and is located opposite the right angle.

To solve this problem, we can use the concept of special right triangles, specifically the 45-45-90 right triangle. In a 45-45-90 right triangle, the sides are in the ratio of 1:1:sqrt(2).

Let's label the length of the triangle as [tex]$L$[/tex], the hypotenuse as [tex]$H$[/tex], and the angle between the hypotenuse and base length as [tex]45[/tex]°.

We are given that the angle formed between the hypotenuse and the base length is 45 degrees. In a 45-45-90 right triangle, the two legs are congruent, so the ratio of the sides is 1:1:sqrt(2).

Since we know that the ratio of the sides is 1:1:sqrt(2), we can set up the following equation:

[tex]$L:L:H = 1:1:\sqrt{2}$[/tex]

We are given that [tex]$L = 14$[/tex], so we can substitute this value into the equation:

[tex]$14:14:H = 1:1:\sqrt{2}$[/tex]

Solve for H.

Since the ratio of the sides is 1:1:sqrt(2), we know that [tex]$H$[/tex] is equal to [tex]$L$[/tex] multiplied by [tex]$\sqrt{2}$[/tex]. Therefore, we can solve for [tex]$H$[/tex] by multiplying [tex]$14$[/tex] by [tex]$\sqrt{2}$[/tex]:

[tex]$H = 14\sqrt{2}$[/tex]

Therefore, the hypotenuse of the right angled triangle is [tex]$14\sqrt{2}$[/tex].

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Answer:

Sure, I can help you with that!

To start, let's look at the ingredient list and see what information we have:

- 8 cups water

- ½ cup garlic

- ½ cup onion

- 1 ½ cups chopped carrots

- ½ cup tomato paste

- 2 cups sliced potatoes

- 1 cup olive oil

To make the calculations, we can set up ratios that relate the amount of each ingredient to the number of servings of soup. For example, if we want to know how much garlic we need for 40 servings of soup, we can set up the following ratio:

½ cup garlic / 10 servings = x cups garlic / 40 servings

To solve for x, we can cross-multiply and simplify:

(½ cup garlic) * 40 servings = (10 servings) * x cups garlic

20 cups = 10x

x = 2 cups

So we would need 2 cups of garlic to make 40 servings of soup.

Similarly, we can set up ratios for the other questions:

Question 2:

½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings

(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste

30 cups = 10x

x = 3 cups

So we would need 3 cups of tomato paste to make 60 servings of soup.

Question 3:

1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings

(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots

45 cups = 10x

x = 4.5 cups

So we would need 4.5 cups of chopped carrots to make 30 servings of soup.

here I simplified and checked the cross products of the ratios.

Question 1:

½ cup garlic / 10 servings = x cups garlic / 40 servings

Cross-multiplying, we get:

(½ cup garlic) * 40 servings = (10 servings) * x cups garlic

20 cups = 10x

Dividing both sides by 10, we get:

x = 2 cups garlic

Therefore, we need 2 cups of garlic to make 40 servings of soup.

Checking the cross products:

(½ cup garlic) * 40 servings = (10 servings) * 2 cups garlic

20 cups = 20 cups

The cross products are equal, so my answer is correct.

Question 2:

½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings

Cross-multiplying, we get:

(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste

30 cups = 10x

Dividing both sides by 10, we get:

x = 3 cups tomato paste

Therefore, we need 3 cups of tomato paste to make 60 servings of soup.

Checking the cross products:

(½ cup tomato paste) * 60 servings = (10 servings) * 3 cups tomato paste

30 cups = 30 cups

The cross products are equal, so my answer is correct.

Question 3:

1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings

Cross-multiplying, we get:

(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots

45 cups = 10x

Dividing both sides by 10, we get:

x = 4.5 cups chopped carrots

Therefore, we need 4.5 cups of chopped carrots to make 30 servings of soup.

Checking the cross products:

(1 ½ cups chopped carrots) * 30 servings = (10 servings) * 4.5 cups chopped carrots

45 cups = 45 cups

The cross products are equal, so my answer is correct.

as already suggested, we can simply get the whole volume of the larger cone and then get the volume of the upper-smaller cone and if we subtract the volume of the upper-smaller cone, in essence making a hole in the larger cone, what's leftover is the shaded part.

[tex]\stackrel{ \textit{\LARGE Larger} }{\textit{volume of a cone}}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4\\ h=10 \end{cases}\implies V=\cfrac{\pi (4)^2 (10)}{3} \\\\\\ \stackrel{ \textit{\LARGE Upper-Smaller} }{\textit{volume of a cone}}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=2\\ h=4 \end{cases}\implies V=\cfrac{\pi (2)^2 (4)}{3} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{\pi (4)^2 (10)}{3}~~ - ~~\cfrac{\pi (2)^2 (4)}{3}\implies \cfrac{160\pi }{3}-\cfrac{16\pi }{3}\implies \cfrac{160\pi -16\pi }{3} \\\\\\ \cfrac{144\pi }{3} ~~ \approx ~~ \text{\LARGE 150.80}~cm^2[/tex]

The correct answer is that if someone simply gets a high school certificate, their salary is most likely to make less than $40,000.

In general, the phrase "income" refers to the sum of money, assets, and other transfers that are worth something obtained over a predetermined period period of time as an exchange for goods or services.

Only having completed high school:

51>24>3

Therefore, it is highly likely that they make less than $40,000.

Has a salary of at least 60,000.

6<17<48

Therefore, a Master's degree is most likely their greatest level of education.

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Answer:

[tex]384 \: {cm}^{3} [/tex]

Step-by-step explanation:

Given:

h = 8 cm

a (base) = 48 cm^2

Find: V - ?

[tex]v = a(base) \times h[/tex]

[tex]v = 48 \times 8 = 384 \: {cm}^{3} [/tex]

The answer of the given question based on the matching  the equation with the graph is , Y=3x -5 , Y= -5x + 3  , Y= x - 1  , Y= (x + 3)² -2  , Y= 1/2x + 2 , Y= x .

An equation is  mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by equal sign (=). The LHS and RHS may contain numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. The purpose of an equation is to solve for the value of an unknown variable.

Equations are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are essential for modeling and solving real-world problems and are a fundamental tool for understanding the natural world.

Here are the equations that match the graphs in the given image:

Y=3x -5 (Line passing through points (0,-5), (1,-2), and (2,1))

Y= -5x + 3 (Line passing through points (0,3) and (1,-2))

Y= x - 1 (Line passing through points (0,-1) and (1,0))

Y= (x + 3)² -2 (Parabola opening upwards with vertex at (-3,-2))

Y= 1/2x + 2 (Line passing through points (0,2) and (2,3))

Y= x (Line passing through points (-2,-2), (0,0), and (2,2))

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Answer:

Multiply the given numbers by a factor of 2.5, then find the perimeter by adding up all 4 of the sides.

Step-by-step explanation:

While there isn't a picture given, it can be assumed that the shape given is a rectangle.

Then, simply multiply all 4 sides by a factor of 2.5, since that's the number it is being enlarged by.

Then to find the "framing" of said rectangle, add up all 4 of the sides that you just calculated to find the perimeter.

The length of the hypotenuse is approximately 10.63 inches.

What is hypotenuse?

The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. In other words, the hypotenuse is the side that connects the two acute angles of the triangle. The hypotenuse is always opposite the right angle in a right triangle and is also the side that has the largest length compared to the other two sides of the right triangle.

The length of the hypotenuse can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the right triangle.

According to the question:
We can use the Pythagorean theorem to find the hypotenuse of a right triangle given the lengths of its other two sides. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the length of the opposite side is 7 inches and the length of the adjacent side is 8 inches. Let's label the hypotenuse as c. Then, we can set up the equation:

[tex]c^2 = 7^2 + 8^2[/tex]

[tex]c^2 = 49 + 64[/tex]

[tex]c^2 = 113[/tex]

To solve for c, we take the square root of both sides of the equation:

[tex]c = \sqrt(113)[/tex]

[tex]c \approx 10.63[/tex]

Therefore, the length of the hypotenuse is approximately 10.63 inches.

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Julia can expect to roll a 3 approximately 61 times if she rolls the die 200 times.

Probability is a means to gauge the likelihood that an event will take place. It is symbolized by the numbers 0 and 1, respectively, with 0 denoting an improbable event and 1 denoting an inescapable event. With two equally likely outcomes, switching a valid coin and coin flips have a chance of 0.5, or 50%. head or tail. A subfield of mathematics called probability theory examines random events rather than their attributes. It is employed in many different fields, including finance, science, building, and facts and statistics.

we found the best estimate for the probability of rolling a 3 to be:

p = (30 + 0.5) / 100 = 0.305

This means that the probability of rolling a 3 on any one roll of the die is 0.305.

If Julia rolls the die 200 times, we can use the formula for the expected value of a binomial distribution to find the expected number of 3's she will roll:

E(X) = np

where:

n = number of trials = 200

p = probability of success (rolling a 3) = 0.305

So, plugging in the values:

E(X) = 200 × 0.305

E(X) = 61

Therefore, Julia can expect to roll a 3 approximately 61 times if she rolls the die 200 times.

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Answer:

The quotient is Q(x) = -2x² + x + 6 and the remainder is R(x) = 52.

Step-by-step explanation:

           -2x² + x + 6

    ------------------------

x - 7 | -2x³ + 15x² - x + 10

     -(-2x³ + 14x²)

     ---------------

              x² - x

              -(x² - 7x)

              ---------

                  6x + 10

                  -(6x - 42)

                  ----------

                          52

The tourist has to pay the government $3,825,000.

make 45% into a decimal (0.45) and then multiply it by 8,500,000.

Answer:

  x = 7

Step-by-step explanation:

You want the value of x in the diagram of similar triangles.

Corresponding side segments in the figure are proportional:

  (2x +10)/(3) = (40)/(5)

  2x +10 = 3·8 . . . . . . . . . . multiply by 3

  2x = 14 . . . . . . . . . . . subtract 10

  x = 7 . . . . . . . . . . divide by 2

The value of x is 7.

The length of major arc PQ is 35π units.

What is major arc?

In geometry, an arc is a portion of the circumference of a circle. A major arc is an arc that spans more than 180 degrees of the circle. In other words, a major arc is an arc that is greater than a semicircle (which spans exactly 180 degrees).

we know that,

length of arc = s = 2 π r (θ/360°)

where, r is the radius and θ is the angle of arc.

we have, r = 30

               θ = 210

so, length of major arc PQ :

   =  2 π r (θ/360°)

   = 2 π × 30 × (210/360)

   = 60  π  × 7/12

   = 35π units.

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The table and graph is mentioned below.

In mathematics, a graph is a visual representation of a set of objects, often referred to as vertices or nodes, and the connections or edges that exist between them. Graphs are used to represent a wide range of mathematical concepts, such as functions, equations, and data sets.

A graph can be thought of as a collection of points or vertices that are connected by lines or edges. The way these vertices and edges are arranged can convey important information about the relationships between the objects being represented.

Graphs can be classified into different types, such as directed or undirected graphs, weighted or unweighted graphs, and cyclic or acyclic graphs. They can also be used to model real-world systems, such as social networks, transportation systems, and computer networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

               0                 $75.00

               10                 $95.00

               20                 $115.00

               30                 $135.00

               40                 $155.00

               50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

                0                 $5.75

                10                 $60.75

                20                 $115.75

                30                 $170.75

                40                 $225.75

                50                 $280.75

b) On the same set of axes, the graph is attached below.

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Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished.

In mathematics, a graph is a picture of a collection of things, also known as vertices or nodes, and the links or edges that join them. Numerous mathematical ideas, including functions, formulae, and data sets, are represented by graphs.

A collection of vertices or points linked by lines or edges is referred to as a graph. The arrangement of these vertices and edges can reveal crucial details about the connections between the things being represented.

Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished. Additionally, they can be used to simulate real-world systems like computer networks, transit systems, and social networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

0                 $75.00

10                 $95.00

20                 $115.00

30                 $135.00

40                 $155.00

50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

0                 $5.75

10                 $60.75

20                 $115.75

30                 $170.75

40                 $225.75

50                 $280.75

b) On the same set of axes, the graph is attached below.

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By responding to the prompt, we may deduce that in order to circle and finish the copied triangle, a polygon should be drawn through the points D, E, and F.

A circle, which appears to be a 2D component, is made up of all the points in a jet that are uniformly spaced out from the hub. The capital "O" for the centre and the bottom component "r" for the radius stand for the distance from the origin to any point on a circle, respectively.

The formula πr², where (pi) is a proportionality constant roughly equal to 3.14159, determines the girth (the distance from the centre of the circle). The formula 2πr is used to determine a circle's circumference.

To recreate the original triangle using just two of its sides and the included angle, follow these steps:

Locate the location where the circle and the ray cross. Draw an arc that twice intersects the circle starting at point E on the compass. The point that is adjacent to point B on side AC should be designated as point F.

Create a polygon that passes across points D, E, and F to finish the copied triangle.

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Triangle DEF should be congruent with triangle AED because they share two sides and the included angle.

A circle looks to be a two-dimensional component described as the collection of all equidistant points in a jet from the hub. A circle is usually represented by a capital "O" for the centre and a lower section "r" for the Radius, which refers to the distance between the origin and any point on the circle.

Based on your directions, it appears that you are constructing a triangle using the SAS (side-angle-side) method. The stages are as follows:

Draw a line segment DE of the length determined in component B.

Draw a circle with a radius equivalent to the length of DE using point E as the centre.

Draw an angle equivalent to the measure of angle AED using line segment ED as one of its sides and point E as the vertex. To expand this angle, draw ray EF from vertex E.

Find the spot of intersection of ray EF and the circle and label it F.

Draw a line section connecting points E and F.

Finally, connect the locations D, E, and F with line segments to form the triangle DEF.

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Image is attached below,

Answer:

Step-by-step explanation:

To find out how much shorter the pencil was after the student completed the project, we need to subtract the final length from the initial length:

7 1/2 - 5 7/8

To subtract these two mixed numbers, we need to convert them to a common denominator. The smallest common multiple of 2 and 8 (the denominators of the fractions) is 8, so we can rewrite the numbers as:

15/2 - 47/8

Now we can find a common denominator of 8:

(15/2) * (4/4) - (47/8) = 30/8 - 47/8

Subtracting the numerators, we get:

-17/8

Therefore, the pencil was 17/8 inches shorter after the student completed the project than when the student started the project. We can simplify this fraction to a mixed number:

-2 1/8

So the answer is C) 2 3/8 inches.

Step-by-step explanation:

pi * d  = total 360° circumference....you want 210/360 ths of this total

                pi * 10   *   210 / 360 =   calculate this.....

The determinant of the matrix A is 70.

The determinant of a 3x3 matrix can be found using the following formula:

|A| = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)

where aij represents the element in the ith row and jth column of the matrix.

Using this formula, we can find the determinant of the given matrix:

|A| = 2(82 - 4(-2)) - 3(-12 - 4(-6)) + 0(-1*(-2) - 8*(-6))

= 16 + 54 + 0

= 70

Therefore, the determinant of the matrix A is 70.

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Answer:

[tex]a=3\sqrt{5}[/tex] or 6.7 approximately (Yes you did it correctly)

Step-by-step explanation:

Find leg [tex]a[/tex] of a right triangle if leg [tex]b[/tex] =6 and hypotenuse = 9.

To find side [tex]a[/tex] use Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

After substituting b = 6 and c = 9 we have:

[tex]a^2+6^2=9^2[/tex]

[tex]a^2=9^2-6^2[/tex]

[tex]a^2=81-36[/tex]

[tex]a^2=45[/tex]

[tex]a=\sqrt{45}[/tex]

[tex]a=3\sqrt{5}[/tex]

[tex]a=6.7[/tex]

A) To find the annual rate of change, we can use the formula:

r = (V2/V1)^(1/n) - 1

where:

V1 = initial value ($42,000)

V2 = final value ($11,000)

n = number of years (2006 - 1994 = 12)

Plugging in the values, we get:

r = (11000/42000)^(1/12) - 1 ≈ -0.1135

Therefore, the annual rate of change between 1994 and 2006 is approximately -0.1135.

B) To convert the rate of change to a percentage, we can multiply by 100 and add a percent sign:

r = -0.1135 × 100% ≈ -11.35%

Therefore, the correct answer to part A written in percentage form is approximately -11.35%.

C) Assuming the car value continues to drop by the same percentage, we can use the formula for exponential decay:

V = V0 * (1 - r)^t

where:

V0 = initial value ($11,000 in 2006)

r = annual rate of change (-0.1135)

t = number of years (2010 - 2006 = 4)

Plugging in the values, we get:

V = 11000 * (1 - (-0.1135))^4 ≈ $6,250

Therefore, the value of the car in the year 2010 would be approximately $6,250, rounded to the nearest 50 dollars.

Answer: 4/5

Step-by-step explanation:

Total marbles = 5 + 7 + 3

P(Red) = 5/15

P(Purple) = 7/15

P(Not Blue) = P(Red) + P(Purple)

= 5/15 + 7/15

= 12/15 or 4/5

Answer:

[tex] \frac{ {6}^{5} }{ {6}^{ - 2} } = {6}^{5 - ( - 2))} = {6}^{5 + 2} = {6}^{7} [/tex]

The derivative exists at x=0 and its value is 0. So, f'(0) = 0.

The derivative of a function can be thought of as the slope of a tangent line to the function's graph at a specific point. This tangent line represents the instantaneous rate of change of the function at that point. The derivative of a function can be used to find critical points, which are points where the function reaches a maximum or minimum value, and to find the concavity of the function, which indicates the direction in which the function is changing.

The derivative can be calculated using different methods, including the limit definition of the derivative, the power rule, the product rule, the quotient rule, and the chain rule. The derivative can also be used to calculate the slope of a curve, the velocity of a moving object, and the acceleration of an object.

To find f'(0) using the definition of a derivative, we need to use the following formula:

f'(a) = lim(h->0) [f(a+h) - f(a)]/h

where "a" is the point at which we want to find the derivative, and "h" is a small value that approaches zero.

In this case, we want to find f'(0). Let's use the formula and simplify the expression:

f'(0) = lim(h->0) [f(0+h) - f(0)]/h

= lim(h->0) [h²sin(1/h)]/h (since f(0)=0)

= lim(h->0) [hsin(1/h)]

Now, we need to evaluate this limit. We can rewrite the limit using the squeeze theorem, which says that if we have two functions, g(x) and h(x), such that g(x) ≤ f(x) ≤ h(x) for all x in some interval, and if lim(x->a) g(x) = lim(x->a) h(x) = L, then lim(x->a) f(x) = L.

In our case, we have:

-1 ≤ sin(1/h) ≤ 1 for all h≠0 (using the fact that -1 ≤ sin(x) ≤ 1 for all x)

-h ≤ hsin(1/h) ≤ h for all h≠0 (multiplying by h, which is always non-negative)

Therefore, by the squeeze theorem, we have:

lim(h->0) -h = 0 = lim(h->0) h

Since both limits are equal, we can conclude that the limit of hsin(1/h) as h approaches 0 exists and is equal to 0.

Thus, f'(0) = 0.

Therefore, the derivative exists at x=0 and its value is 0. So, f'(0) = 0.

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Using the formula σr = 3Fx/yz², we can easily compute the Modulus of Rupture.

The term "bending strength" is occasionally used to refer to the measure of a specimen's strength prior to rupture, also known as the "modulus of rupture," or MOR.

Contrary to the modulus of elasticity, which measures the wood's deflection but not its total strength, it can be used to evaluate a species' strength.

The formula σr = 3Fx/yz² for the load force F and the material's size dimensions in the three directions of x, y, and z can be used to compute the modulus of rupture, or "sigma."

The external force applied to the substance of interest in this instance is the load.

Therefore, using the formula σr = 3Fx/yz², we can easily compute the Modulus of Rupture.

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Correct question:

How do you compute MOR?

Answer: 54.43 miligrams

Step-by-step explanation:

To calculate the dose of ibuprofen for an 18-month-old child weighing 24 pounds, we need to convert the weight from pounds to kilograms.

1 pound is equal to 0.453592 kilograms.

So, the weight of the child in kilograms is:

24 pounds × 0.453592 kg/pound = 10.886kg (rounded to three decimal places)

Now we can use the given dosage information to calculate the usual dose of ibuprofen for the child.

The usual dose of ibuprofen is 5 mg/kg of body weight when the fever is under 102.5 degrees Fahrenheit.

So, for the 18-month-old child weighing 10.886 kg, the usual dose of ibuprofen would be:

5 mg/kg × 10.886 kg = 54.43 mg

Therefore, the usual dose of ibuprofen for an 18-month-old child weighing 24 pounds is 54.43 mg.

Answer:

First, we need to convert the weight of the child from pounds to kilograms since the dosage is given in milligrams per kilogram.

We can use the conversion factor: 1 pound = 0.453592 kilograms.

So, 24 pounds = 24 x 0.453592 = 10.8862 kg (rounded to 4 decimal places).

Next, we can calculate the usual dose of Ibuprofen by multiplying the weight of the child (in kg) by the dose per kg:

Usual dose = 5 mg/kg x 10.8862 kg = 54.431 mg

Therefore, the usual dose of Ibuprofen for an 18 month old weighing 24 pounds would be 54.431 mg when the fever is under 102.5 degrees Fahrenheit. However, it is important to note that dosages may vary depending on the specific circumstances, and it is always best to consult a healthcare provider for proper dosing instructions.

Step-by-step explanation:

The randοm variable in this case is the range οf the 12 data values, which is equal tο 27.

The range οf a data set is the difference between the highest and lοwest value in a given set.

The range οf a data set is the difference between the largest and smallest values in the set.

In this case, the smallest value is 38 and the largest value is 65. Therefοre, the range οf the data set is:

Range = Largest value - Smallest value

Range = 65 - 38

Range = 27

Sο, the randοm variable in this case is the range οf the 12 data values, which is equal tο 27.

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Answer:

Let's start by assigning variables to represent the number of nickels, dimes, and quarters in the jar.

Let x be the number of nickels.

Then the number of dimes is 3 times as many as nickels, so the number of dimes is 3x.

And the number of quarters is twice as many as dimes, so the number of quarters is 2(3x) = 6x.

We know that the total amount of money in the jar is $5.55, which is equal to:

0.05x (for the value of the nickels) + 0.10(3x) (for the value of the dimes) + 0.25(6x) (for the value of the quarters)

Simplifying this expression, we get:

0.05x + 0.30x + 1.50x = 5.55

Combining like terms, we have:

1.85x = 5.55

Dividing both sides by 1.85, we get:

x = 3

So there are 3 nickels in the jar.

Using this value, we can find the number of dimes and quarters:

Number of dimes = 3x = 3(3) = 9

Number of quarters = 6x = 6(3) = 18

Therefore, there are 3 nickels, 9 dimes, and 18 quarters in the jar.

Step-by-step explanation: