The usual dose of ibuprofen for an 18-month-old child weighing 29 pounds would be approximately 65.772 milligrams.
To calculate the usual dose of ibuprofen for a 18-month-old child weighing 29 pounds, we need to convert the weight from pounds to kilograms. Since 1 pound is approximately 0.4536 kilograms, we can use this conversion factor.
Weight of the child: 29 pounds
Weight in kilograms: 29 pounds × 0.4536 kilograms/pound = 13.1544 kilograms (rounded to four decimal places)
Now that we have the weight of the child in kilograms, we can calculate the usual dose of ibuprofen.
Usual dose of ibuprofen: 5 milligrams/kilogram
Dose for the 18-month-old child: 5 milligrams/kilogram × 13.1544 kilograms = 65.772 milligrams (rounded to three decimal places)
Therefore, the usual dose of ibuprofen for an 18-month-old child weighing 29 pounds would be approximately 65.772 milligrams. It's important to note that this is a general calculation, and it's always best to consult a healthcare professional for accurate dosing instructions based on the specific circumstances of the child.
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Show how you can use the basic fact 5x8=40 to determine the product of 5x800.
We can use the property of Multiplication 5x8=40 to determine the product of 5x800, which is 4000.
To find the product of 5x800 using the basic fact 5x8=40, we can use the property of multiplication that states that multiplying a number by 10 increases its value by one place value. Therefore, we can rewrite 800 as 80x10 and multiply it by 5 as shown below:
5x800 = 5x(80x10) (replacing 800 with 80x10)
= (5x80)x10 (associative property of multiplication)
= 400x10 (using the basic fact 5x8=40)
= 4000
Thus, we can use the basic fact 5x8=40 to determine the product of 5x800, which is 4000.
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solve for x: 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=9
Answer:
Step-by-step explanation:
Sure! Here’s how you can solve the equation 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=9 for x:
First, let’s rewrite the equation in terms of a common base. Since 9 can be written as 3², we can rewrite the equation as 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=3².
Now, let’s isolate the exponential terms on one side of the equation by adding 8.3ˣ⁺¹ to both sides: 3²⁽ˣ⁺¹⁾=3²+8.3ˣ⁺¹.
Next, let’s take the logarithm of both sides with base 3: log₃(3²⁽ˣ⁺¹⁾)=log₃(3²+8.3ˣ⁺¹).
Using the properties of logarithms, we can simplify the left side of the equation: 2(x+1)=log₃(3²+8.3ˣ⁺¹).
Now, let’s solve for x by isolating it on one side of the equation: x=log₃(3²+8.3ˣ⁺¹)/2-1.
This is an approximate solution for x. To find a more precise value for x, you can use a numerical method such as Newton’s method or a calculator.
I hope this helps!
Consider the geometric below:
1 8 27
3.1.1. Determine the number of cubes in the 5th term 3.1.2. Draw the 6th term.
The number of cubes in the 5th term is 125
How to determine the number of cubes in the 5th termFrom the question, we have the following parameters that can be used in our computation:
The sequence of cubes
In the above sequence, we can see that the term is raised to the power of 3 to get the new term
This means that
The nth term is then represented as
f(n) = n³
For the 5th cube, we have
n = 5
Substitute the known values in the above equation, so, we have the following representation
f(5) = 5³ = 125
Hence, the number of cubes in the 5th term is 125
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Can anyone help with this Trig question? Thank you.
a) The area of the shaded region is equal to S'' = 0.25 · sin 2θ + 0.5 · θ.
b) The angle associated with the shaded region is equal to θ ≈ 20.189°.
How to find the angle within a geometric system
In this problem we need to determine the measure of an angle associated with a geometric system formed by a circular arc and a right triangle. a) The area of a triangle is defined by this formula:
S = 0.5 · OA · AB
Where:
S - SurfaceOA - BaseAB - HeightThe base and the height of the triangle are equal to:
OA = sin θ, AB = cos θ
Then, the area of the triangle is:
S = 0.5 · sin θ · cos θ
S = 0.25 · sin 2θ
And the rest of the shaded area is:
S' = 0.5 · θ
The shaded area is described by the following formula:
S'' = S + S'
S'' = 0.25 · sin 2θ + 0.5 · θ
b) If we know that S = 0.5, then the measure of the angle is:
0.5 = 0.25 · sin 2θ + 0.5 · θ
1 = 0.5 · sin 2θ + θ (Please notice that θ is in radians, π radians = 180°)
Then, by numerical methods:
θ ≈ 20.189°
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A software development company is voting to elect a president, a secretary, a treasurer, and three directors. If a total of 11 qualified candidates applied for these positions, in how many ways can the positions be filled?
The ways to elect the candidates from the total is 462
How to determine the ways of selection?From the question, we have
Total number of candidate, n = 11Numbers to selection, r = 6 i.e. the president, a secretary, a treasurer, and three directorsThe number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 11 and r = 6
Substitute the known values in the above equation
Total = ¹¹C₆
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 11!/5!6!
Evaluate
Total = 462
Hence, the number of ways is 462
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DETERMINE THE EQUATION OF FG?
DETERMINE THE EQUATION OF THE CIRCLE
IF THE DISTANCE FROM F TO B IS SQUARE ROOT 69UNITS CALCULATE THE LENGTH OF FA
Answer:
FG is y = -0.5x - 5.5. circle is (x - 1)² + (y + 1)² = 20. Length FA = 7
Step-by-step explanation:
please see attached
only 5 attachments/pics allowed
so FA² = (√69)² - (√20)²
= 69 - 20
= 49
FA = √49 = 7
A company makes a mean monthly income of $20,500 with a standard
deviation of $3,400. In one month, the company makes $29,700
1) Find the Z-score of $29,700 .Round the number to the nearest hundredth (4pts)
2) Assuming that the company's monthly income is normal, what percent of time
the company makes less than $29,700 (Use the table of normal standard
probability) (2pts)
3)same as question 2) what is the probability that the company makes more than 29700 (use the table)
4)If the z-score of 15200 is -1.56 and the Z-score of 25200 is +1.39 what is the probability that the company makes between 15200 and 25200
The Z-score of $29,700 is approximately 2.71 (rounded to the nearest hundredth).
The percentage of time the company makes less than $29,700 is approximately 99.66% (rounded to two decimal places).
The probability that the company makes more than $29,700 is approximately 0.34% (rounded to two decimal places).
The probability that the company makes between $15,200 and $25,200 is approximately 85.83% (rounded to four decimal places).
To solve these questions, we will use the standard normal distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. We'll first standardize the values using the formula:
Z = (X - μ) / σ
Where:
Z is the standard score (Z-score)
X is the value
μ is the mean
σ is the standard deviation
Given:
Mean (μ) = $20,500
Standard Deviation (σ) = $3,400
To find the Z-score of $29,700:
Z = (29,700 - 20,500) / 3,400
Z = 9,200 / 3,400
Z ≈ 2.71 (rounded to the nearest hundredth)
To find the percentage of time the company makes less than $29,700:
We need to find the area under the normal distribution curve to the left of the Z-score -2.71. Referring to the standard normal distribution table or using a calculator, we find that the area to the left of -2.71 is approximately 0.0034.
Therefore, the percentage of time the company makes less than $29,700 is approximately 0.34% (rounded to two decimal places).
To find the probability that the company makes more than $29,700:
Since the total area under the normal distribution curve is 1, and we have already found the area to the left of -2.71 as 0.0034 in question 2, we can subtract this value from 1 to find the probability of making more than $29,700.
Probability = 1 - 0.0034
Probability ≈ 0.9966 (rounded to four decimal places)
Therefore, the probability that the company makes more than $29,700 is approximately 0.9966.
To find the probability that the company makes between $15,200 and $25,200:
We'll first find the Z-scores for the given values using the formula:
For $15,200:
Z1 = (15,200 - 20,500) / 3,400
Z1 = -1.56
For $25,200:
Z2 = (25,200 - 20,500) / 3,400
Z2 = 1.39
Next, we'll find the areas under the normal distribution curve to the left of each Z-score.
From the standard normal distribution table or calculator:
The area to the left of Z1 (-1.56) is approximately 0.0594.
The area to the left of Z2 (1.39) is approximately 0.9177.
To find the probability of the company making between $15,200 and $25,200, we subtract the area to the left of Z1 from the area to the left of Z2:
Probability = 0.9177 - 0.0594
Probability ≈ 0.8583 (rounded to four decimal places)
Therefore, the probability that the company makes between $15,200 and $25,200 is approximately 0.8583.
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Graph the exponential functions
The graph of y = 3(3/5)^x is an exponential growth curve that starts at the point (0, 3) and approaches the x-axis and y = 3 asymptotically.
We have,
The graph of the exponential function y = 3(3/5)^x is an upward curve that approaches but never touches the x-axis, as the base of the exponential term (3/5) is between 0 and 1.
As x approaches negative infinity, the function rapidly approaches the y-axis, which is the vertical asymptote.
As x increases, the value of the function increases rapidly, but at a decreasing rate, as the base of the exponential term is less than 1.
As x approaches infinity, the function approaches but never touches the horizontal line y = 3, which is the horizontal asymptote.
Therefore,
The graph of y = 3(3/5)^x is an exponential growth curve that starts at the point (0, 3) and approaches the x-axis and y = 3 asymptotically.
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Directions: Find each angle or arc measure.
1.
M
N
L
88°
K
107 sylo2
mJML =
Based on the calculations, the measure of angle M is -15°.
The given diagram, it appears that we have a triangle MNL with an angle measure of 88° at point L and an angle measure of 107° at point K.
We are asked to find the measure of angle M, denoted by m∠MLK.
The measure of angle M, we can use the fact that the sum of the angles in a triangle is always 180°.
We can subtract the measures of angles L and K from 180° to find the measure of angle M.
m∠M = 180° - m∠L - m∠K
Substituting the given values:
m∠M = 180° - 88° - 107°
m∠M = 180° - 195°
m∠M = -15°
This result is not physically possible since angles cannot have negative measures.
It is likely that there was an error in the given information or in the calculations.
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How is space used in Art? A. B. C. D. Above the object used as a model Area within, around, above and below an object Area within and below a model Area around an object
Space is used in art Area around an object. Therefore, the correct option is option D.
The term "art" refers to a wide range of human endeavours and the resulting works that reflect technical mastery, aesthetic beauty, emotional heft, or mental concepts. No single definition of what makes art exists, and different cultures and historical periods have interpreted it very differently. Space is used in art Area around an object.
Therefore, the correct option is option D.
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What slope pass through (2,1)(-3,-2)
what you mean but heres the points on the map u were talking about
Answer: The slope m = 3/5
Step-by-step explanation:
The slope can be found by using the formula: m = y2 - y1 / x2-x1
Where m is the slope and (x1, y1) and (x2, y2) are the two points on the line.
x1 = 2 , y1 = 1
x2 = -3 , y2 = -2
Substituting the values from the points in the problem gives :
m = -2-1 / -3-2
m = 3/5
Hence, the slope that passes through (2, 1) and (-3, -2) is 3/5.
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Use the drop-down menus to complete the statement about the number line diagram.
-2x≤6 and 2x≥-6 is the inequalities represented by the number line
The visual representation of the real numbers on a straight lineis known as number line
On a number line each point of is assumed to correspond to a real number, and every real number to a point.
As we observe the graph the red line is directed towards left side which means the values are decreasing and line has solid point at 6 so it is included
Hence, the number line shows that -2x≤6 and 2x≥-6
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Hey i need help on these
Determine if the following side lengths will form a triangle using the Triangle Inequality Theorem.
33.7, 62.9, 96.6
A.The three sides do not form a triangle.
B. The three sides do form a triangle.
Answer:
A. no triangle
Step-by-step explanation:
You want to know if the Triangle Inequality Theorem allows a triangle from side lengths 33.7, 62.9, and 96.6.
Triangle inequality theoremThe theorem requires for any side lengths a, b, c, this inequality must hold:
a + b > c
ApplicationUsing the given side lengths, we have ...
33.7 +62.9 > 96.6
96.6 > 96.6 . . . . . . . . False
The three sides do not form a triangle.
__
Additional comment
These side lengths will join ends to ends to form a "triangle" that looks like a line segment of length 96.6 with a point on it at 33.7 from one end. Most authors do not recognize this figure as a triangle. For those authors who write the theorem as a +b ≥ c, these segments will form a triangle.
You should check your curriculum materials to see whether your Triangle Inequality Theorem uses the > or the ≥ relation.
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The mean weight of male nurses working at a local hospital is equal to 162 lbs. Express the null and alternative hypotheses in symbolic form for this claim.
Null hypothesis: µ = 162 lbs (mean weight of male nurses is equal to 162 lbs)
Alternative hypothesis: µ ≠ 162 lbs (mean weight of male nurses is not equal to 162 lbs)
Hypothesis testing is a method of making decisions about a population based on sample data.
The null hypothesis (H₀) represents the default position that there is no significant difference between specified populations, or that there is no effect of a particular treatment.
On the other hand, the alternative hypothesis (H₁) represents the opposite of the null hypothesis, which is that there is a significant difference between the populations or that there is an effect of the treatment being tested.
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The graph represents the 30-minute run Johnny took today. The x-axis shows the time from the start of the run. The y-axis shows the distance Johnny
traveled
Distance (mi)
2.5
2
1.5
1
0.5
0
5
Johnny's Run
-X
10 15 20 25 30
Time (min)
After how many minutes did Johnny stop running for the first time?
Johnny stopped running after
minutes.
Johnny stopped running for the first time after 15 minutes.
From the graph, we can see that Johnny ran for the first 15 minutes without stopping. During this time, he covered a distance of around 1.5 miles. After 15 minutes, he stopped running for a short time, and then continued running. Therefore, Johnny stopped running for the first time after 15 minutes.
Square root of 125 cubed
Answer:
25
Step-by-step explanation:
Given from the question,
125 cubed = [tex]125^3[/tex]
Therefore square root of 125 cubed is:
[tex]\sqrt{125^3} \\ =125^\frac{2}{3} \\ \\=25[/tex]
.....% of students in Class 7 spent less than 15 minutes on homework
0.0007% of students in Class 7 spent less than 15 minutes on homework.
Total students = 100
Number of students spent less than 7 minutes are: 0.7
Now, the percentage of students less than 15 minute
= 0.7/100 x 100
= 7/1000 x 100
= 0.0007 x 100
= 0.0007%
Thus, 0.0007% of students in Class 7 spent less than 15 minutes on homework.
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In 2014 Susan purchased 24.87 shares of a business supply company for 33.12 per share. Four
years later she sold the 24.87 shares for 28 per share. What was her gross capital loss on the sale
of the stock? Do not include a dollar sign in your answer.
Susan's gross capital loss on the sale of the stock was $127.62.
We have,
Susan's initial investment in the stock.
= 24.87 shares x $33.12/share
= $823.98
Four years later, she sold the shares.
= 24.87 shares x $28/share
= $696.36
To calculate the capital loss, we need to subtract the sale price from the purchase price:
= $823.98 - $696.36
= $127.62
Therefore,
Susan's gross capital loss on the sale of the stock was $127.62.
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pls help meeeee (satistics)!! WILL MARK BRAINLEST!
1. What is a non example of mode?
2. What is a non example of a median?
3. What is a non example of a mean?
4. What is a non example of the range in a set is data?
A non-example of mean, mode, median and range are as follows;
1. A non example of a mode in the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is other numbers except 7. 7 is the mode because it is repeated more frequently.
2. Non-example of median is 9 because it is not the middle value of the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 when arranged orderly.
How do know what is the mean and range of a data set?The mean is the average of all the values in a dataset. And therefore a non-example of mean in the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is 70. Which is gotten by adding all the numbers together.
The mean can be found by saying 7 + 8 + 9 + 7 + 5 + 9 + 7 + 4 + 3 + 7 divided by 10. this should be 7.
The non-example of range in the dataset 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is choosing the lowest value of the set 3.
The range is the difference between the highest and lowest values in a dataset. which is 9-3 = 6
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all solutions to equation
write answer in radians in terms of pi[tex]2cos(theta) - \sqrt{2} = 0[/tex]
To solve the equation [tex]2\cos(\theta) - \sqrt{2} = 0\\[/tex] and express the answer in radians in terms of π, we can follow these steps:
Step 1: Add [tex]\sqrt{2}\\[/tex] to both sides of the equation:
[tex]2\cos(\theta) = \sqrt{2}\\[/tex]
Step 2: Divide both sides of the equation by 2:
[tex]\cos(\theta) = \frac{\sqrt{2}}{2}\\[/tex]
Step 3: Recall the special values of cosine in the first quadrant:
[tex]\cos(\theta) = \frac{\sqrt{2}}{2}\\[/tex]¥ corresponds to [tex]\\ \theta = \frac{\pi}{4}\\[/tex] in radians.
Therefore, the solution to the equation in radians in terms of π is [tex]\theta = \frac{\pi}{4}\\[/tex].
object in the shape of a rectangular prism has a length of 7 centimeters, a width of 6 centimeters, and a height of 2 centimeters. The object's density is 6.7 grams per cubic centimeter
What is the mass of the object to the nearest gram?
Answer:
mass= 563 grams
Step-by-step explanation:
Volume = 7cm * 6cm * 2cm
Volume = 84 cm³
Density = mass / volume
6.7 grs/cm³ = mass / 84cm³
84cm³ * (6.7grs/cm³) = mass
mass = 562.8 gr
To the nearest gram:
mass = 563 gr
NO LINKS!!! URGENT HELP PLEASE!!!
Determine if the two triangles are congruent. If they are, state how you know.
#3 and #4
Answer:
3 and 4 both SAS (Side-Angle-Side) axiom.
Step-by-step explanation:
Note:
There are four basic conditions for two triangles to be congruent. These are:
SSS (Side-Side-Side): If all three pairs of corresponding sides of two triangles are equal, then the triangles are congruent.SAS (Side-Angle-Side): If two pairs of corresponding sides of two triangles are equal, and the angles between those sides are also equal, then the triangles are congruent.ASA (Angle-Side-Angle): If two pairs of corresponding angles of two triangles are equal, and the sides between those angles are also equal, then the triangles are congruent.AAS (Angle-Angle-Side): If two pairs of corresponding angles of two triangles are equal, and the side that includes one of those angles is also equal, then the triangles are congruent.One of the conditions should be needed to fulfill to determine whether the two triangles are congruent.
Over here:
3.
In ΔOMT and ΔOGE
MT=GE Given Side
∡MOT=∡GOE Vertically Opposite angle Angle
MO=OE Given Side
It fulfills the condition of the SAS (Side-Angle-Side) axiom.
ΔOMT ≅ ΔOGE by SAS (Side-Angle-Side) axiom.
4.
In ΔKJL and ΔIJH
JL=JH Given Side
∡KJL=∡HJI Vertically Opposite angle Angle
IJ=JK Given Side
It fulfills the condition of the SAS (Side-Angle-Side) axiom.
ΔKJL≅ ΔIJH by the SAS (Side-Angle-Side) axiom.
help with this calc question pls.
The area of the shaded which is obtained using the composite figure formed the shaded region and the area under the curve of the specified function is; (2·π - 3·√3)/2 square units
What is a composite figure?A composite figure is one that is composed of two or more simpler figures.
The area can be considered of comprising of a composite figure of the area under the curve of the function and the area of the shaded region
The function representing the curve under the shaded region can be presented as follows;
y = 3·cos(x) + 1
The interval specified under the curve can be expressed as follows;
0 ≤ x ≤ π/3
Therefore, the area under the curve can be found as follows;
[tex]\int\limits^\frac{\pi}{3} _3 {3\cdot cos(x) + 1} \, dx = [3\cdot sin(x) + x]^{\frac{\pi}{3} }_0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3} - 0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3}[/tex]
sin(π/3) = (√3)/2
Therefore; 3·sin(π/3) + π/3 = 3·(√3)/2 + π/3 = (2·π + 9·√3)/6
The area of the rectangle = (4 - 0) × (π/3 - 0) = 4·π/3
The area of the shaded region = Area of the rectangle - Area under the curve of the specified function
Therefore, area of the shaded region = 4·π/3 - (2·π + 9·√3)/6 = (2·π - 3·√3)/2
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Julie plotted some points on a graph. Point D is 8 units away from the origin. Select the pair of possible coordinates of point D.
The pair of possible coordinates of point D are (0, 8), (0, -8), (8, 0) and (-8, 0)
How to determine the pair of possible coordinates of point D.From the question, we have the following parameters that can be used in our computation:
D = 8 units away from the origin.
using the above as a guide, we have the following:
The possible coordinates of point D are
(0, ±8), (±8, 0)
When expanded, we have
(0, 8), (0, -8), (8, 0) and (-8, 0)
Hence, the pair of possible coordinates of point D are (0, 8), (0, -8), (8, 0) and (-8, 0)
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Find the areas of the sectors formed by angle acb
Area of small sector is,
⇒ A = 3.28π cm²
And,. Area of large sector is,
⇒ A = 5.73π cm²
We have to given that;
Angle ACB = 131°
And, radius = 3 cm
Since, We know that;
⇒ Area of sector = θ/360 × πr²
Hence, For θ = 131°
So, Area of small sector is,
⇒ A = 131/360 × π × 3²
⇒ A = 1179/360π
⇒ A = 3.28π cm²
For large sector,
Angle = 360 - 131
= 229°
Hence, Area of large sector is,
⇒ A = 229/360 × π × 3²
⇒ A = 2061/360π
⇒ A = 5.73π cm²
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4.9 × 10^-1 into standard form?
Hello!
4.9 × 10⁻¹
= 4.9 × 0.1
= 0.49
What is the distance between point C and point D
Answer:
they're pronounced different
Which of these is a measure of volume?
A) the amount of foil I need to line my crock pot
B) the amount of soup that I can make in my crockpot
C) the size of the tablecloth I need to cover the dining table
D) the number of slices I can cut from a loaf of bread
Answer:
the amount of soup that I can make in my crockpot
Step-by-step explanation:
A) is an area. the foil would be cut into a square or circle, making it an area.
B) is the soup in the pot. the amount is given by the cross-sectional area of the pot (if circular Area of circle = π r ²) multiplied by the depth of the pot. since we have r ² (which is r X r) multiplied by a length (depth of pot) , it is a volume.
C) like A) this would be a two-dimensional item. so it is an area.
D) this will just be a number
A puppy and a kitten are 180 feet apart when they see each other. The puppy can run at a speed of 25 feet per second, while the kitten can run at a speed of 20 feet per second.
How long will it take the kitten to catch up to the puppy if the puppy runs away from the kitten, and the kitten simultaneously starts chasing the puppy?
Answer:
an infinitely long time
Step-by-step explanation:
You want to know the time it takes for a kitten running 20 ft/s to catch a puppy running 25 ft/s when they start 180 ft apart and the puppy runs away from the kitten.
NeverThe kitten runs slower than the puppy, so can never catch up to it.
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If x = 2, and y = -3, then xy^2 =
The equivalent value of the expression is xy² = 18
Given data ,
Let the equation be represented as A
Now , the value of A is
A = xy²
where the value of the first variable x = 2
And , the value of the second variable y = -3
Now , the expression is solved as
A = xy²
On simplifying the equation , we get
A = ( 2 ) ( -3 )²
A = 2 ( 9 )
On further simplification , we get
A = 18
Therefore , the value of A is 18
Hence , the expression is A = 18
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