Can anyone explain how to check perfect square or not using repeated subtraction?
Answers
Let's say we wanted to check if 16 was a perfect square or not.
What we do is subtract off the list of odd numbers {1,3,5,7,9,...}. If we reach 0 at any point, then the step number is what the square root will be.
So we'll start with 16 and subtract off 1 to get 15. Then from 15, we subtract off 3 to get 12. From 12, we subtract off 5 to get 7. This process is laid out below
16-1 = 1515-3 = 1212-5 = 77-7 = 0By step 4, we reach 0. This indicates that \(\sqrt{16} = 4\)
Note: The numbers to the left of the decimal point indicate the step number. All values mentioned are whole numbers.
-------------------
Here's another example. I'll start with 49
49 - 1 = 4848 - 3 = 4545 - 5 = 4040 - 7 = 3333 - 9 = 2424 - 11 = 1313 - 13 = 0We reach 0 at step 7, therefore \(\sqrt{49} = 7\)
-------------------
If we started with some non-perfect square, say 50, then we'd get this:
50 - 1 = 4949 - 3 = 4646 - 5 = 4141 - 7 = 3434 - 9 = 2525 - 11 = 1414 - 13 = 11 - 15 = -14As you can see, we don't reach 0, which means 50 is not a perfect square. The closest we get is 1 and that happens on the 7th step. This suggests \(\sqrt{50}\) is closest to 7. It turns out that \(\sqrt{50} \approx 7.071\) which helps confirm that previous statement.
Related Questions
Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3+y2/3=4;(−3√3,1)�2/3+�2/3=4;(−33,1)
Answers
To find the equation of the tangent line to the curve at the given point, we need to use implicit differentiation. This involves differentiating both sides of the equation with respect to x, treating y as a function of x.
Taking the derivative of both sides of the equation, we get:
(2/3)x^(-1/3) + (2/3)y^(-1/3)*dy/dx = 0
Now we can solve for dy/dx:
dy/dx = -(y^(1/3)/x^(1/3))
To find the equation of the tangent line, we need to find the slope of the tangent line at the given point. Plugging in the coordinates (-3√3,1) into our expression for dy/dx, we get:
dy/dx = -(1^(1/3)/(-3√3)^(1/3)) = -(1/3)
So the slope of the tangent line is -1/3.
Next, we need to find the y-intercept of the tangent line. To do this, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Plugging in the values we have so far, we get:
y - 1 = -(1/3)(x + 3√3)
Simplifying this equation, we get:
y = -(1/3)x - √3 + 1
So the equation of the tangent line to the curve x^(2/3) + y^(2/3) = 4 at the point (-3√3,1) is y = -(1/3)x - √3 + 1.
To start, we'll use implicit differentiation to find dy/dx (the derivative of y with respect to x). Differentiating both sides of the equation with respect to x, we get:
(2/3)x^(-1/3) + (2/3)y^(-1/3)(dy/dx) = 0.
Now, we can solve for dy/dx:
(2/3)y^(-1/3)(dy/dx) = -(2/3)x^(-1/3).
dy/dx = -[x^(-1/3)/y^(-1/3)].
Next, plug in the given point (-3√3, 1) into the expression for dy/dx:
dy/dx = -[(-3√3)^(-1/3) / 1^(-1/3)] = -(-1/3).
Therefore, dy/dx = 1/3 at the given point.
Now, we have the slope of the tangent line (1/3) and the point (-3√3, 1). Using the point-slope form of a linear equation, we can find the equation of the tangent line:
y - 1 = (1/3)(x + 3√3).
Thus, the equation of the tangent line to the curve x^(2/3) + y^(2/3) = 4 at the point (-3√3, 1) is y - 1 = (1/3)(x + 3√3).
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Which parameter is often associated with enzyme affinity for substrates? \( k_{1} \) \( k_{-1} \) \( k_{2} \) \( K_{m} \)
Answers
The parameter often associated with enzyme affinity for substrates is Km.
Km, also known as the Michaelis constant, is a parameter commonly used to quantify the affinity of an enzyme for its substrate. It is an important parameter in enzyme kinetics and plays a crucial role in determining the efficiency of an enzyme-substrate interaction.
Km represents the substrate concentration at which the rate of the enzymatic reaction is half of its maximum velocity (Vmax). In other words, enzymes with lower Km values have higher affinity for their substrates, as they can achieve half of their maximum velocity at lower substrate concentrations. Therefore, Km serves as an indicator of the enzyme's ability to bind and convert substrates into products efficiently.
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graph a line that contains the point (3,-6) and has the slope of 1/2
Answers
Answer:
y = 1/2x - 7.5
Step-by-step explanation:
The image below shows proof that the equation y = 1/2x - 7.5 is the line that contains the point (3,-6) and has the slope of 1/2.
Hope this helps! :)
Evaluate the integral. (Use C for the constant of integration.)
\inttegral ^4 / sqrt. 1-t^10 dt
Answers
We can substitute back in for u to get our final terms of t:(2/3)(1 - t^10)^(3/2) + CThis is our final answer for the integral, with C representing the constant of integration.
To evaluate the integral, we will use substitution method. Let's begin by assigning a variable to the expression inside the square root. Let's assign u = 1 - t^10. Now, we can rewrite the integral in terms of u:\inttegral ^4 / sqrt. u duNow, we can use the power rule for integration to find the integral of this expression:\inttegral ^4 / sqrt. u du = \inttegral u^(-1/2) du = (2/3)u^(3/2) + CNow, we can substitute back in for u to get our final terms of t:(2/3)(1 - t^10)^(3/2) + CThis is our final answer for the integral, with C representing the constant of integration.
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Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60. What percent did she leave?
answer=
Answers
Answer:20.01%
Step-by-step explanation:Divide the tip left by the cost of the meal and multiply by 100 to get 20.01%
Answer: 20%
Step-by-step explanation:
We will find what percent 2.60 is of 12.99. First, we will divide. Then, we will multiply it by 100 to make a percent.
(2.6 / 12.99) * 100 = 20.0153 ≈ 20.02%
She left a 20.02% tip.
Factor x2 - 4x + 5.
O Prime
O (x + 5)(x - 1)
O (x - 5)(x - 1)
O (x + 5)(x + 1)
Answers
Answer:prime
Step-by-step explanation:
I just took the test and got it right
Find the exact value of cos J in simplest form.
√29
14
15
H
Answers
The cosine of angle J is given as follows:
\(\cos{J} = \frac{14\sqrt{2}}{49}\)
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:
Sine = length of opposite side/length of hypotenuse.Cosine = length of adjacent side/length of hypotenuse.Tangent = length of opposite side/length of adjacent side = sine/cosine.For the angle J in this problem, we have that:
4 is the adjacent side.\(\sqrt{98}\) is the hypotenuse.Hence the cosine of angle J is given as follows:
\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)
\(\cos{J} = \frac{4\sqrt{98}}{98}\)
\(\cos{J} = \frac{2\sqrt{98}}{49}\)
As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:
\(\cos{J} = \frac{14\sqrt{2}}{49}\)
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how to do this question plz answer me step by step plzz plz please
Answers
Answer:
See the attached
Step-by-step explanation:
The solution and filled in Venn diagram is attached
Find the measure of angle y.
A) 19
B) 22
C) 41
D) 120
Answers
Answer:
19
Step-by-step explanation:
because it alternate with A
does anyone know the answer to this? i need it asap
Answers
Please hurry I need it ASAP
Answers
Answer:
x = 18
Step-by-step explanation:
We Know
(10x - 4) + (x - 14) must equal 180°
Find the value of x.
Let's solve
10x - 4 + x - 14 = 180
11x - 18 = 180
11x = 198
x = 18
So, x = 18 is the answer.
A survey asked, "How many tattoos do you currently have on your body?" Of the 1211 males surveyed, 182 responded that they had at least one tattoo. Of the 1041 females surveyed, 144 responded that they had at least one tattoo. Construct a 95% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. Let pi represent the proportion of males with tattoos and p2 represent the proportion of females with tattoos. The 95% confidence interval for p1- p2 is (___,___)
Interpret the interval. a. There is 95% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo. b. There is 95% confidence that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo. c. There is a 95% probability that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo. d. There is a 95% probability that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the nronortion of males and females that have at least one tattoo.
Answers
There is 95% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo. The 95% confidence interval for p1- p2 is (-0.029, 0.053). So, the correct answer is A).
First, we need to calculate the sample proportions for each group
p1 = 182/1211 = 0.150
p2 = 144/1041 = 0.138
The point estimate for the difference in proportions is p1 - p2 = 0.150 - 0.138 = 0.012
The standard error for the difference in proportions is
SE = √((p1(1-p1)/n1) + (p2(1-p2)/n2))
SE = √((0.150(1-0.150)/1211) + (0.138(1-0.138)/1041))
SE = 0.021
Using a 95% confidence level and a z-score of 1.96 for a two-tailed test, we can calculate the margin of error
ME = 1.96 * 0.021 = 0.041
Therefore, the 95% confidence interval for p1 - p2 is
0.012 - 0.041 < p1 - p2 < 0.012 + 0.041
-0.029 < p1 - p2 < 0.053
The interpretation of the interval is option (a): There is 95% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.
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if a snowball melts so that its surface area decreases at a rate of 1 cm min, find the rate at which the diameter decreases when the diameter is 10 cm.
Answers
The rate at which the diameter decreases when the diameter is 10 cm is -0.00798 cm/min.
To find the rate at which the diameter decreases, we can use the relationship between the surface area and the diameter of a sphere.
The surface area of a sphere is given by the formula:
A = \(4\pi r^2\), where A is the surface area and r is the radius (which is half the diameter).
Differentiating both sides of the equation with respect to time t, we get:
dA/dt = 8πr(dr/dt).
We are given that the surface area decreases at a rate of \(1 cm^2/min\), so dA/dt = \(-1 cm^2/min\). We want to find dr/dt when the diameter is 10 cm, which means the radius is r = 10/2 = 5 cm.
Substituting these values into the equation, we have:
-1 = 8π(5)(dr/dt).
Simplifying, we get:
-1 = 40π(dr/dt).
Now, solving for dr/dt:
dr/dt = -1 / (40π).
Using a calculator, this evaluates to approximately -0.00798 cm/min.
Therefore, when the diameter is 10 cm, the rate at which the diameter decreases is approximately -0.00798 cm/min. Note that the negative sign indicates the decrease in diameter.
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Using an integrating factor, solve y-y-5 CD- in the method for solving a first-order linear differential equation, the first step is to put the equation in the standard form y alty bit). is the given equation in the standard form? No Yes Identify a(t) and bit)
Answers
The value of a(t) is -1 and b(t) is 55 + \(e^t\)
No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.
In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.
For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:
μ(t) = e^∫a(t)dt
To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.
To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).
Comparing the given equation with the standard form, we can identify:
a(t) = -1
b(t) = 55 + \(e^t\)
Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)
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Given that f(x) = 3x - 4 complete the table below.
Answers
Answer:
where is the table:0
Step-by-step explanation:
A forest covers 74,000 acres. A survey finds that 0.8% of the forest is old-growth trees. How many
acres of old-growth trees are there?
Answers
Answer:
592
Step-by-step explanation:
0.008(74,000)
592
Hope this helps!!
If I am wrong please tell me I enjoy learning from my mistakes:)
Answer:
592
Step by step explanation:
0.8% = \(\frac{8}{1000}\)
8 out of every 1000 trees are old
74 * 8 = 592
Percent error is a way to determine the accuracy(quality) of your data collection and calculations. Percent error is calculated with the following formula: % error =
theoretical value
∣ theoretical value − experimental value ∣
×100 Calculate the percent error for two of the objects using data from the most accurate method of determining volume.
Answers
The percent error for object A is 6%. The percent error for object B is 5.3%.
Percent error is a measure of the accuracy of your data collection and calculations. Percent error is determined using the following equation:% error = theoretical value | theoretical value - experimental value | × 100For two objects, the percent error should be calculated using the most accurate method of determining volume.
Here is an example: Suppose that the theoretical value of object A is 50 mL. The most accurate method for determining the volume of object A results in a measured value of 47 mL. We can then calculate the percent error using the formula:
% error = |50 - 47|/50 × 100%
error = 6%.
Let's suppose the theoretical value of object B is 75 mL. The most accurate method for determining the volume of object B results in a measured value of 71 mL. We can calculate the percent error using the formula:
% error = |75 - 71|/75 × 100%
error = 5.3%
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The sampling distribution of a statistic _________. Group of answer choices gives all the values a statistic can take gives the probability of getting each value of a statistic under the assumption it had resulted due to chance alone is a probability distribution all of the options
Answers
Answer:
all of the options
Step-by-step explanation:
A sampling distribution is a probability distribution, gives the probability of getting each value and all values a statics can take. It is arrived out through a repeated sampling form of a large population. It truly exists as a population.The graph models the heights, in feet, of two objects
dropped from different heights after x seconds.
Which equation represents g(x) as a transformation of
f(x)?
g(x) = f(x) - 5
g(x) = f(x - 5)
g(x) = f(x) + 5
g(x) = f(x + 5)
Answers
Answer:
A
Step-by-step explanation:
Ed2021
Find X.
Plz solve ASAP! I need help ASAP plz! Thank you!
Answers
Answer:
13x25=455
Step-by-step explanation:
6. Which shape has a larger area: a rectangle that is 7 inches by inch, or a square with
side length of 2 inches? Show your reasoning.
ouch the
aps.
Answers
Answer:
Rectangle = L x b = 7 x 7 = 49 inch^2
square = a^2 = 2^2=4 inch^2
Therefore the area of rectangle is more because it's area is greater than square
rectangle 's area > square's area.
what is the answer to z-0.14z
Answers
Greatest comm
Find the greatest common factor of 80 and 20.
Answers
Hello there!
The GCF of 80 and 20 is 20.
Because both numbers are evenly divisible by 20; this is their greatest common factor (GCF)
Therefore, the GCF is 20.Hope this helps you!
~Just a felicitous girlie
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\(SilentNature\)
Fifth grade students from Garden City Elementary School left for a field trip at the time shown on the clock.(6:54am) They returned from the field trip at 10:24 p.M. How long were the students on this field trip?
Answers
Answer:
15 hour(s) and 30 minute(s).
Step-by-step explanation:
Answer:
krkrkrl4k3?8999kekek
Step-by-step explanation:
the UK. I have been a while. I have been a while. I have been a while. I have been a while 6e5 the UK. I have been a while. I have been a while. I have
. How do we have a look at the moment. The comments for the first time in the UK. I
Can someone help me solve question 2 and 3?
Answers
Answer:
Question 2 = 15 drinks
Question 3 = 7/12
Step-by-step explanation:
Question 2:
For every drink, there are three sizes
Ratio = 1:3
There are 5 flavors
Multiply each side by 5
5:15
15 drinks
Question 3:
5 red, 6 yellow, 8 blue, 3 orange, 2 purple
Possible outcomes = 5 + 6 + 8 + 3 + 2 = 24 possible outcomes
Favourable outcomes = 6 + 8 = 14 favourable outcomes
Fraction = 14/24 = 7/12
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Divide (10x^3 + 19x^2 + x - 7) by (5x + 2)
Answers
Answer:
2x² + 3x - 1 - 5/(5x +2)
Step-by-step explanation:
2x² + 3x - 1
__________________
5x + 2 | 10x³ + 19x² + x - 7
| -10x³ - 4x²
| 15x² + x
| - 15x² - 6x
| - 5x - 7
| 5x +2
| - 5
2x² + 3x - 1 - 5/(5x +2)
The mean for the normal hemoglobin control is 14.0 mg/dL. The standard deviation is 0.15 with an acceptable control range of +/-2 standard deviations (SD). What are the acceptable limits of the control? Please select the single best answer 13.8-14.2 13.4 14.6 13.6-14.4 13.7-14.3
Answers
The acceptable limits of the control is 13.7-14.3.Hemoglobin (Hb) is a red, iron-rich protein that allows red blood cells to transport oxygen throughout the body. Hemoglobin is responsible for the characteristic red color of blood and is responsible for the exchange of oxygen and carbon dioxide in the lungs.
The standard deviation (SD) is a statistical measure of the dispersion of a set of data values relative to its mean. A low standard deviation indicates that the data points are near to the mean, whereas a high standard deviation indicates that the data points are far from the mean. The standard deviation is expressed in the same units as the data points themselves. In the given problem, the mean for the normal hemoglobin control is 14.0 mg/dL and the standard deviation is 0.15. Since the acceptable control range is +/-2 standard deviations (SD), we can calculate the acceptable limits of control using the given formula below: Lower limit = Mean - 2(SD)Upper limit = Mean + 2(SD)Substitute the given values in the formula. Lower limit = 14 - 2(0.15)Upper limit = 14 + 2(0.15)Lower limit = 13.7Upper limit = 14.3Therefore, the acceptable limits of control are 13.7-14.3.Answer: 13.7-14.3
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HELP ASAP PLEASE (answer all parts please)
The upcoming championship high school football game is a big deal in your little town. The problem is, it is being played in the next biggest town, which is two hours away! To get as many people as you can to attend the game, you decide to come up with a ride-sharing app, but you want to be sure it will be used before you put all the time in to creating it. You determine that if more than three students share a ride, on average, you will create the app.
You conduct simple random sampling of 20 students in a school with a population of 300 students to determine how many students are in each ride-share (carpool) on the way to school every day to get a good idea of who would use the app. The following data are collected:
6 5 5 5 3 2 3 6 2 2
5 4 3 3 4 2 5 3 4 5
You will construct a 90% confidence interval and 95% confidence interval for the mean number of students who share a ride to school, then you will compare and interpret the results.
Part A: Decide which partner will construct each confidence interval, and then state the parameter and check the conditions.
Part B: Construct the confidence interval. Be sure to show all your work, including the degrees of freedom, critical value, sample statistics, and an explanation of your process.
Part C: Interpret, share, and compare. Interpret the meaning of the confidence interval, compare your results with your partner, and describe the difference in the width of the interval and the margin of error.
Part D: Use your findings to explain whether you should develop the ride-share app for the football game.
Answers
How to calculate the probability?
The confidence interval based on the information will be:
= 3.85 - 2.09(1.348 / ✓20)
= 3.22
Also, 3.85 + 2.09(1.348 / ✓20) = 4.48
The confidence interval simply means that one is 95% confident that the true mean is between 3.22 and 4.48.
Shivani bought egg at $30 per 10 and old at rate of $46. 80 per dozen. Find gain or lo percentage
Answers
Answer:
30% gain
Step-by-step explanation:
$30 for 10 = $3 each
$46.80 for 12 = $3.9 each
percentage change = (final price- initial price)/inital price *100
3.9-3 = 0.9
0.9/3 = 0.3
0.3 x 100 = 30
so gain of 30%
Express the formula d=rt in terms of the time,t. Use your formula to find the time when the distance is 40 and the rate is 8.
Answers
The expression for d=rt in terms of the time is t = d/r; t = 5.
What is time? Time can be defined as a continuous and ongoing sequence of events that occur consecutively from the past to the present to the future. Time is used to measure, measure or compare the duration of events or the intervals between them, and even the sequence of events. Time is a useful concept that we use in our daily life. We have to watch when we cook, play, study, go to school, meet someone, etc. So knowing the right time is very important. Time is usually the answer to when an event happens or happened. The concept of time determines when a certain event occurs, has occurred or will occur. Time is a measurable quantity and is also infinite. The time is calculated in seconds, minutes, hours, days, months and years.Therefore,
In the equation d=rt
t = d/r
when distance is 40 and the rate is 8
t = d/r
Replace d with 40 and rate with 8
t = 40/8
t = 5
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