1. Find the square root of each of the following numbers: (i) 152.7696
Answers
1. Start by making pairs of digits from the right: 15, 27, 69, 6.
2. Find the largest integer whose square is less than or equal to the first pair, which is 15. Since 3^2 = 9 < 15 and 4^2 = 16 > 15, the integer we are looking for is 3.
3. Write the digit 3 as the first digit of the square root.
4. Subtract the square of 3 from 15 to get 6.
5. Bring down the next pair of digits, 27, and append them to 6 to get 627.
6. Double the first digit of the current root estimate (which is 3) to get 6.
7. Find the largest digit to fill in the blank in "3_ × _ = 6" such that the resulting product is less than or equal to 627. This digit is 7, since 3×7 = 21 < 627 and 3×8 = 24 > 627.
8. Write down the digit 7 as the second digit of the root estimate.
9. Subtract the square of 37 from 627 to get 60.
10. Bring down the next pair of digits, 69, and append them to 60 to get 6069.
11. Double the first digit of the current root estimate (which is 37) to get 74.
12. Find the largest digit to fill in the blank in "37_ × _ = 606" such that the resulting product is less than or equal to 6069. This digit is 1, since 37×1 = 37 < 6069 and 37×2 = 74 > 6069.
13. Write down the digit 1 as the third digit of the root estimate.
14. Subtract the square of 371 from 6069 to get 152.769.
Therefore, the square root of 152.7696 is approximately 12.36 (rounded to two decimal places).
Related Questions
A recipe calls for 1 1/2 cups of flour for 1 dozen of cookies. How much flour is needed for 32 cookies?
Answers
Explanation: 1 1/2 is = to 12 so 1/2 is equal to 4. 1 then is equal to 8 and you multiply by 4 to get 32.
What is the discriminant of the quadratic equation 0 = -x² + 4x − 2?
Answers
Answer: 8
Step-by-step explanation:
The discriminant is \(b^2-4ac\)
in the equation:
\(-x^2+4x-2\)
A = -1, B = 4, C = -2
plug into equation
\(4^2-4(-1)(-2)\)
\(16-8\)
⇒ \(8\)
PLEASE HELP I AM DYINGG RYT NOW
Answers
Answer:
4x^2+14x−44
Step-by-step explanation:
4x^2-8x+22x-44
4x^2+(-8x+22x)-44
Answer:
4x+7Step-by-step explanation:
2x+11+2x-4=
2x+2x-4+11= 4x+ (11-4)
4x+7I really hope this is what you're looking for because I am only in 4th grade I don't know for sure.:)
what is the range of the function y=-8x+5 when the domain is {-2,2,4}
Answers
Answer:
{-27, -11, 21}
Step-by-step explanation:
\(x=-2 \implies y=-8(-2)+5=21 \\ \\ x=2 \implies y=-8(2)+5=-11 \\ \\ x=4 \implies y=-8(4)+5=-27\)
Plz help solve them thank you in advance!
Answers
#1
\(\\ \sf{:}\dashrightarrow 20m+(-16)m=20m-16m=4m\)
#2
\(\\ \sf{:}\dashrightarrow 5m+(-16m)=5m-16m=-11m\)
#3
\(\\ \sf{:}\dashrightarrow -9m+11m=2m\)
#4
\(\\ \sf{:}\dashrightarrow -9m+(-11m)=-9m-11m=-20m\)
a restaurant bill is $53.15. what is the estimated total cost of the bill with a
15% tip?
not a multi choice you enter a answer !
Answers
Answer: the answer is 7.95 because 15% tip on 53.15 is 7.95
if w≠0, what is the additive inverse of the expression -3/w
Answers
The additive inverse of the expression -3/w is 3/w.
A number is known as the additive inverse of another, if the sum of the two numbers comes out to be zero. For example- given a number 3, its additive inverse will be -3, as 3 + (-3) = 0. The additive inverse of 0 is 0 itself.
Here, we are given an expression -3/w, such that w ≠ 0
Let us assume that the additive inverse of -3/w is x
Then, the sum of -3/w and x must be equal to zero
⇒ -3/w + x = 0
adding 3/w to both sides
⇒ x = 3/w
Thus, the additive inverse of -3/w is 3/w.
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identify the solution to system graphed y=-3x +4 y = 3x - 2
Answers
To find the solution for this system in a graph manner we need to graph both equations and look for the point at which they intercept.
For the first equation we know that the y-intercept is 4. So we will calculate the x-intercept by making y=0.
\(\begin{gathered} 0=-3x+4 \\ 3x=4 \\ x=\frac{4}{3} \end{gathered}\)The first line goes through the points (0,4) and (4/3, 0).
For the second equation we know that the y-intercept is -2. So we will calculate the x-intercept by making y-.
\(\begin{gathered} 0=3x-2 \\ 3x=2 \\ x=\frac{2}{3} \end{gathered}\)The second line goes through the points (0,-2) and (2/3,0).
To graph each line we can draw a line between the points that belong to it. We have:
Since the solution for the system is the point at which they cross, the ordered pair is (1,1).
1. Answer only (ii)
2.
These are real analysis problems. Please
help me answer all these questions. It would be your biggest gift
for me if you can answer all these questions since joining c
2. (20 points) When do we say that a subset E C R is Lebesgue measurable and explain the construction of the Lebesgue measure? (6) Show that if E1, E2 € M, then m(EU E2) + m(En Es) = m(E1) + m(E2).
Answers
If E1 and E2 are Lebesgue measurable sets, the equality m(E1 ∪ E2) + m(E1 ∩ E2) = m(E1) + m(E2) holds.
(ii) A subset E ⊆ ℝ is Lebesgue measurable if it can be approximated from the outside by open sets with arbitrary precision. More formally, for any ε > 0, there exists an open set O ⊆ ℝ such that E ⊆ O and the Lebesgue outer measure of the set O \ E is less than ε.
The construction of the Lebesgue measure involves defining the Lebesgue outer measure as the infimum of sums of lengths of intervals covering a set. This outer measure is used to define Lebesgue measurable sets as those that can be approximated from the outside by open sets.
To show that if E1, E2 ∈ M (the class of Lebesgue measurable sets), then m(E1 ∪ E2) + m(E1 ∩ E2) = m(E1) + m(E2):
By the definition of the Lebesgue measure, we have:
m(E1 ∪ E2) = m*(E1 ∪ E2) - m*(ℝ \ (E1 ∪ E2))
m(E1) = m*(E1) - m*(ℝ \ E1)
m(E2) = m*(E2) - m*(ℝ \ E2)
Note that ℝ \ (E1 ∪ E2) = (ℝ \ E1) ∩ (ℝ \ E2) and ℝ \ E1 ⊆ ℝ \ (E1 ∪ E2) and ℝ \ E2 ⊆ ℝ \ (E1 ∪ E2).
Using the subadditivity property of the Lebesgue outer measure, we have:
m*(ℝ \ (E1 ∪ E2)) ≤ m*(ℝ \ E1) + m*(ℝ \ E2)
Subtracting m*(ℝ \ E1) and m*(ℝ \ E2) from both sides, we get:
m*(ℝ \ (E1 ∪ E2)) - m*(ℝ \ E1) - m*(ℝ \ E2) ≤ 0
Now, by the definition of the Lebesgue measure, we have:
m(E1 ∪ E2) - m(E1) - m(E2) ≤ 0
Rearranging the terms, we obtain:
m(E1 ∪ E2) + m(E1 ∩ E2) = m(E1) + m(E2)
Therefore, if E1 and E2 are Lebesgue measurable sets, the equality m(E1 ∪ E2) + m(E1 ∩ E2) = m(E1) + m(E2) holds.
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find the T.A for the prism
Answers
Answer:
I dont know
Step-by-step explanation:
I have no clue I know nothing about math
Can anyone help me with this proportion ,please?? I'm having a really hard time trying to solve it
'The ratio of the weight of an object on Jupiter to its weight on Earth is 8 to 3. How much would a 120 pound person weight on Jupiter?'
Answers
Answer:
320 pound
Step-by-step explanation:
Ratio is decently easy after u understand the concept
So... This is what the question gave
Jupitar : earth
8 : 3
In other words, if u weigh 8 pound on Jupitar, u would weigh 3 pounds on earth
Therefore now they say on earth, the person weighs 120 pound, so let's just put in this value
Jupitar : earth
8 : 3
? : 120
Now its called ratio bcuz the increase at the same pace
So now look at the earth part, u got to find out how did 3 become 120, so just divide them
120/3 = 40 , so 3 x 40 = 120
So if they multiplied the right ( earth) by 40, u do the exact same on the left ( Jupitar)
8 x 40 = 320
Thats your answer my friend
What time is it on the clock?
Answers
Answer:
About 2:18
The minute hand points toward the \(\frac{1}{4}\) marker, meaning that is 15 minutes.Count the other ticks, and that's 18.Since the hand is not exactly on the 3, that means it is 2:00With this information, we can make a hypothesis or come to a conclusion that the clock says 2:18
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answers
The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data
How to explain the informationThe answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.
In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.
Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.
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Evaluate x2 - 7xy for x = 7 and y = 3.
Answers
Answer:
-98
Step-by-step explanation:
I hope this help
On the contrary, the first relation we looked at, of Brianna's earnings, is ______. Continuous relations include an _______ number of points and graph as a _____ or a curve.
Answers
"On the contrary, the first relation we looked at, of Brianna's earnings, is discrete. Continuous relations include an infinite number of points and graph as a line or a curve."
What are Continuous relations?Generally, The first relation that was discussed about Brianna's earnings could be discrete, meaning that it consists of a finite number of individual points or values.
On the contrary, continuous relations include an infinite number of points and graphs as smooth curves.
Continuous relations are characterized by being able to take on any value within a certain range or interval, rather than just a finite set of specific values.
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A container full of oranges were shared among 12 market women in such a way that the first woman received 50 oranges, the sec ond woman received 70 oranges, the third woman received 90 oranges, and so on.
(a)How many oranges received by the
(i)8th woman (ii)last woman?
(b)How many oranges altogether were in the container?.
Answers
Using an arithmetic sequence, it is found that:
a) The number of oranges received are given as follows:
8th woman: 190.Last woman: 270.b) The total number of oranges in the container is of 1920.
What is an arithmetic sequence?It is a sequence in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
\(a_n = a_1 + (n - 1)d\)
In which \(a_1\) is the first term of the sequence.
The sum of the n terms of an arithmetic sequence is:
\(S_n = \frac{n(a_1 + a_n)}{2}\)
The first term and the common difference of this sequence are given as follows:
\(a_1 = 50, d = 20\)
Hence the equation is:
\(a_n = a_1 + (n - 1)d\)
\(a_n = 50 + 20(n - 1)\)
a(n) = 30 + 20n.
Hence the numbers received are given as follows:
8th women: a(8) = 30 + 20(8) = 190.12th women and last: a(12) = 30 + 20(12) = 270.The sum of the 12 terms of the sequence is:
S = 6 x (50 + 270) = 1920.
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What are Nilpotent groups?
Answers
Answer:
that is your answer hope this helps u
please help asp!! write an equation for each line
Answers
Answer:
line p - x=0-4
line l - y=0+4
line n - y=x-1
line m - y=-2x+4
Graph The Curve. x = cos(t) + ln(tan(t/2)), y = sin(t), π/4 ≤ t ≤ 3π/4
Answers
To graph the curve x = cos(t) + ln(tan(t/2)) and y = sin(t) with the domain π/4 ≤ t ≤ 3π/4, follow these steps: 1. Create a table of values for t within the given domain, such as t = π/4, π/2, and 3π/4. 2. Calculate the corresponding x and y values for each t value using the given equations. 3. Plot the (x, y) coordinates on a Cartesian plane.
To graph the curve, we first need to understand what each term means.
- x = cos(t) + ln(tan(t/2)): This is the equation for the x-coordinate of the curve. It's a combination of the cosine function (cos(t)) and the natural logarithm of the tangent function (ln(tan(t/2))).
- y = sin(t): This is the equation for the y-coordinate of the curve. It's simply the sine function (sin(t)).
Now, let's look at the range of values for t: π/4 ≤ t ≤ 3π/4. This means that t starts at π/4 (45 degrees) and ends at 3π/4 (135 degrees), and it increases in increments of pi/4 (90 degrees).
To graph the curve, we can start by plugging in some values of t to find corresponding (x,y) pairs. Here are a few:
- When t = π/4: x = cos(π/4) + ln(tan(π/8)) ≈ 0.532, y = sin(π/4) ≈ 0.707. So one point on the curve is (0.532, 0.707).
- When t = π/2: x = cos(π/2) + ln(tan(π/4)) = 0 + ln(1) = 0, y = sin(π/2) = 1. Another point on the curve is (0, 1).
- When t = 3π/4: x = cos(3π/4) + ln(tan(3π/8)) ≈ -0.532, y = sin(3π/4) ≈ -0.707. A third point on the curve is (-0.532, -0.707).
We can continue to plug in values of t and plot the corresponding points to create the graph. However, because the equation for x involves the natural logarithm of the tangent function, the curve may not be easy to visualize or sketch by hand.
In general, the curve will have a "wavy" shape due to the combination of the sine and cosine functions. The natural logarithm of the tangent function will also introduce some asymmetry to the curve. To get a more precise sense of the curve's shape, we can use a graphing calculator or software to plot the points and connect them with a smooth curve.
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whαt ís thє vαluє σf х ?
\(x {}^{2} - \: 25 = 144\)
Answers
Answer:
hey mate!!
Step-by-step explanation:
x
2
−25=144
X^2=144+25
x^2=169
x=√169
x=13
Sorry mate check out the answer !
144-25=119
x=119
Max loves fishing. He and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an
average speed of 10 km/hour. Some time later a cruise ship left traveling in the same direction but at an average speed of 14
km/hour. After traveling for ten hours the cruise ship caught up with the fishing boat. How long did the fishing boat travel before
the cruise ship caught up?
Note: Remember to find the time the fishing boat was traveling not just what x is.
Select the correct response:
28 hours
24 hours
14 hours
12 hours
Answers
The fishing boat traveled for 14 hours before the cruise ship caught up.
We have,
Let's assume that the fishing boat traveled for x hours before the cruise ship caught up.
In that time, the fishing boat covered a distance of 10x km.
During the same 10 hours, the cruise ship traveled 14 x 10 = 140 km.
Since both the fishing boat and the cruise ship covered the same distance, we can write:
10x = 140
Solving for x, we get:
x = 14
Therefore,
The fishing boat traveled for 14 hours before the cruise ship caught up.
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4. You're looking at 2 apartments to move into. Mar
Vista has a $500 security deposit and costs $850
each month. Sandy Shores has a $650 deposit and
costs $820 each month. How many months, m, will it
take for the costs to be the same? If you plan to stay
for 6 months, which apartment will be the best cost?
Answers
what is the standard deviation of a sample mean xbar ap stats
Answers
the standard deviation of a sample mean, can be calculated by dividing the population standard deviation, σ, by the square root of the sample size, n.
In statistics, the standard deviation measures the dispersion or variability of a set of data. When calculating the sample mean, from a sample of data, the standard deviation of the sample mean, is a measure of how much the sample means vary from the true population mean.The standard deviation of the sample mean is determined by dividing the population standard deviation, σ, by the square root of the sample size, n. Mathematically, it can be expressed as:
sample mean = σ / √n,Where σ is the population standard deviation and n is the sample size.
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a group consists of 10 kids and 2 adults. on a hike, they must form a line with an adult at the front and an adult at the back. how many ways are there to form the line?
a. 12/2!
b. 2 . 11!
c. 2 . 10!
d. 12!\
Answers
If a group consists of 10 kids and 2 adults, the number of ways are there to form the line are 2 * 10!. So, correct option is C.
To form a line with an adult at the front and an adult at the back, we need to consider the positions of the 10 kids within the line. The two adults are fixed at the front and back, so we have 10 positions available for the kids.
To calculate the number of ways to arrange the kids in these positions, we can use the concept of permutations. Since each position can be occupied by a different kid, we have 10 options for the first position, 9 options for the second position, 8 options for the third position, and so on, until the last position, where only 1 kid remains.
Therefore, the number of ways to form the line is:
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!
However, the problem also mentions that there are 2 adults, so we need to consider the arrangements of the adults as well. Since there are only two adults, there are 2 ways to arrange them in the line (adult at the front and adult at the back or vice versa).
Therefore, the total number of ways to form the line is:
2 x 10! = 2 * 10!
Hence, the correct option is b. 2 * 10!, which accounts for both the arrangements of the kids and the adults.
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Which equation represents the following graph?
Answers
it a or d make your decision
What is the rate of change in this graph?
Answers
The rate of change in the given graph is 21/4.
The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:
Rate of change = Δy / Δx
To calculate the rate of change of the given graph, we need to identify 2 points first. We take:
(0, 0)
(4, 21)
Rate of change = Δy / Δx
Rate of change = y₂ - y₁
x₂ - x₁
Rate of change = 21 - 0
4 - 0
Rate of change = 21/4
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AABC has vertices (-6,2), B (5,-1), and C (4,4). Classify AABC by its sides. Then determine whether it is a right triangle. (Hint: Draw the picture).
Answers
The Pythagorean theorem is not satisfied since dAB² + dBC² ≠ dAC². Therefore, AABC is not a right triangle.
AABC is a scalene triangle with no sides of equal lengths. A triangle is said to be scalene when it has all its sides with different lengths. The side lengths of the AABC triangle can be calculated using the distance formula, which is given by'd = √((x2 - x1)² + (y2 - y1)²)Where d is the distance between two points (x1, y1) and (x2, y2).
Using the distance formula, we can calculate the length of each side of the AABC triangle. For side AB: dAB = √[(5 - (-6))² + (-1 - 2)²]= √(11² + (-3)²)= √130For side AC:dAC = √[(4 - (-6))² + (4 - 2)²]= √(10² + 2²)= √104For side BC:dBC = √[(4 - 5)² + (4 - (-1))²]= √((-1)² + 5²)= √26Since all the three sides have different lengths, the triangle AABC is a scalene triangle.
As for the second part of the question, we will check if it is a right triangle by determining if it has a right angle. We know that a right triangle is one that has one angle measuring exactly 90 degrees, and in such a triangle, the side opposite to the 90-degree angle is called the hypotenuse.
To determine if AABC is a right triangle, we can calculate the length of all the sides. Then we can check if the Pythagorean theorem holds, that is, the sum of the squares of the two smaller sides equals the square of the hypotenuse.If the Pythagorean theorem holds, then the triangle is a right triangle. If it doesn't, then the triangle is not a right triangle.
Using the distance formula above, we can determine the length of the three sides of the AABC triangle. Then we will compare the sides to determine if they satisfy the Pythagorean theorem. We have:dAB² + dBC² = √130² + √26²= 13,000 + 676= 13,676dAC² = √104²= 10,816
The Pythagorean theorem is not satisfied since dAB² + dBC² ≠ dAC².
Therefore, AABC is not a right triangle.
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Select all acute angles:
Answers
Answer:
A, D and F
Step-by-step explanation:
cus they are an acute triangle because they are smaller than 90 degrees
The equation x^2=1 has two solutions of the equation is changed to 4x^2=1 which operation
Answers
Answer:
for the x^2 =1 the first solution is 1x1 the other solution is -1x-1
4x^2=1 the "x" equals to 1/2
Step-by-step explanation:
Because the answer is "1" it is positive. Negative and negative equals to positive. Positive and positive equals to positive.
Hi! I need help on this one. Hope there's someone willing to help!!
Answers
2 of 5 is a 40% chance
40% * 40 = 16
He should expect to be stopped 16 times.