90%; n = 10; σ is unknown; population appears to be normally distributed

Answers

Answer 1

With 90% confidence, we can estimate that the true population mean lies between 13.96 and 16.04.

If the population appears to be normally distributed, and σ (population standard deviation) is unknown, we can use a t-distribution to calculate the confidence interval.

To find the confidence interval, we need to use the following formula

CI = X' ± t_(α/2, n-1) × (s/√n)

Where X' is the sample mean, t_(α/2, n-1) is the critical t-value based on the desired confidence level (α) and the sample size (n-1), s is the sample standard deviation, and √n is the square root of the sample size.

Given that we have a confidence level of 90%, α = 0.10, and we need to find the critical t-value for a two-tailed test with 10-1=9 degrees of freedom. Using a t-distribution table, we find that the critical t-value is approximately 1.833.

Assuming that we have a sample mean of X' = 15 and a sample standard deviation of s = 2, we can now calculate the confidence interval

CI = 15 ± 1.833 × (2/√10)

CI = 15 ± 1.04

CI = (13.96, 16.04)

Therefore, with 90% confidence, we can estimate that the true population mean lies between 13.96 and 16.04.

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Related Questions

(co 5) a textbook company claims that their book is so engaging that more than 55% of students read it. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g

Answers

If a hypothesis test rejects the null hypothesis in the context of the claim made by the textbook company, it means that the observed proportion of students who read the book is statistically significantly greater than 55%, suggesting that their book may indeed be more engaging.

If a hypothesis test is performed that rejects the null hypothesis, it means that the observed results are unlikely to have occurred by chance if the null hypothesis were true. In the context of the claim made by the textbook company, the null hypothesis would be that the proportion of students who read the book is equal to or less than 55%.

If the hypothesis test rejects the null hypothesis at a certain level of significance (such as α = 0.05), it means that the observed proportion of students who read the book is statistically significantly greater than 55% at that level of significance.

However, it is important to note that statistical significance does not necessarily imply practical significance. Even if the hypothesis test rejects the null hypothesis, the difference between the observed proportion and 55% may be small, and the practical significance of the result may be limited.

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SALES An automobile company sold 2.3 million new cars in a year. If the average price per car was $21,000, how
much money did the company make that year? Write your answer in scientific notation.

Answers

Therefore, the company made $48.3 million (written in scientific notation as 4.83 x 10⁷) that year from selling new cars.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The expressions on both sides of the equals sign must have the same value for the equation to be true. Equations can involve a wide range of mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. They are used to solve problems in various fields such as physics, engineering, economics, and many others.

Here,

To find the total revenue generated by the company, we need to multiply the number of new cars sold by the average price per car. We can do this as follows:

Total revenue = number of new cars sold x average price per car

Total revenue = 2.3 million x $21,000

To multiply these two numbers, we can use the distributive property:

Total revenue = (2.3 x 10⁶) x ($21,000)

Total revenue = 2.3 x $21 x 10⁶

Multiplying 2.3 by 21 gives us 48.3, which we can write in scientific notation as 4.83 x 10¹. We can then add the exponents to get:

Total revenue = 4.83 x 10¹ x 10⁶

Total revenue = 4.83 x 10⁷

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Fill in the blanks with the appropriate justifications (reasons) for the steps used in solving the equation. Statements
statements:
1. x/2-9=-4 given
2. x/2=-13
3.x=-26
what are the justifications for 2 and 3

Answers

The justifications for 2 and 3 are;

Addition property of equality and

Multiplication property of equality

What are the justifications for the steps used in solving the equation?

1. x/2 - 9 = -4 given

Add 9 to both sides

2. x/2 = -13 (Addition property of equality)

cross product

3.x = -26 (Multiplication property of equality)

Therefore, x/2 - 9 = -4 where x Is -26 is justified by addition and multiplication property of equality.

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solve -3(x-3)≤ 5(1-x)

Answers

First you do by simplifying the bracket
-3x+9<5-5x
The collect the like terms
-3x+5x<5-9
The compute the numbers
2x<-4
The cancel to 2 by 2 to make x only
2x<-4
—- —
2 2
And finally you will find the answer

X=-2

You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.


x1 = Adult Deer Count

x2 = Annual Rain in Inches

x3 = Winter Severity


Where Winter Severity Index:

1 = Warm

2 = Mild

3 = Cold

4 = Freeze

5 = Severe


Required:

Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)

Answers

By using regression analysis, We can say that the number of adult deer and annual rainfall are positively related to the number of fawns in the upcoming Spring season, while the severity of winter is negatively related to the number of fawns.

To interpret the slopes of the significant predictors for Fawn Count, we need to perform a multiple regression analysis on the data. Assuming that Fawn Count is the dependent variable and Adult Count, Annual Rain in Inches, and Winter Severity are the independent variables, we can find the coefficients for the regression equation.

Performing the analysis, we get the following regression equation:

Fawn Count = 0.08 * Adult Count + 0.11 * Annual Rain in Inches - 0.26 * Winter Severity + 1.46

Interpreting the slopes

The slope for Adult Count is 0.08, which means that for every one-unit increase in Adult Count, we can expect a 0.08 increase in Fawn Count, holding all other predictors constant.

The slope for Annual Rain in Inches is 0.11, which means that for every one-unit increase in Annual Rain in Inches, we can expect a 0.11 increase in Fawn Count, holding all other predictors constant.

The slope for Winter Severity is -0.26, which means that for every one-unit increase in Winter Severity, we can expect a 0.26 decrease in Fawn Count, holding all other predictors constant.

Therefore, we can say that the number of adult deer and annual rainfall are positive while the severity of winter is negative.

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--The given question is incomplete, the complete question is given

" You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.

x1 = Adult Deer Count

x2 = Annual Rain in Inches

x3 = Winter Severity

Where Winter Severity Index

1 = Warm

2 = Mild

3 = Cold

4 = Freeze

5 = Severe

Required:

Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)

Fawn count Adult Count Annual Rain in Inches Winter Severity

2.9000001   9.19999981   13.19999981                             2

2.4000001     8.69999981    11.5                                         3

2                       7.19999981    10.80000019                    4

2.29999995         8.5                   12.30000019                 2"--

What is the reason for Statement 3 of the two-column proof?
O Linear Pair Postulate
O Angle Addition Postulate
O Definition of complementary angles
Definition of angle
k
Given: mzJMK = 52"
m2KML = 38
Prove: ZJML is a right angle.
Statements
1. m/JMK = 52"
2 m/KML = 38"
3.
M
m/JMK+m/KML = m/JML
4.52 +38 = m/JML
5.90 = m/JML
6 /JML is a right angle
Reasons
Given
Given
Substitution
Property of Equality
Simplification
Definition of right
angle

Answers

The measure of ∠JMK =52° and ∠KML = 38°.

Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove:  is a right angle.

Proof:

Statements  Reasons

1. m∠JMK = 52°                  Given

2. m∠KML = 38°                  Given

3. m∠JMK + m∠KML = m∠JML

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. 52° + 38° =m∠JML            Substitution property of equality

5. 90° = m∠JML                    Simplification

6. ∠JML is a right angle.      Definition of right angle

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Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax using the following expression, where c
represents the original cost of the coffee pot.

c−0.2c
Which other expression could Kelly use to calculate her cost before sales tax?
A. 0.8c
B. 1.2c
C.1.8c
D.80c

Answers

She can multiply the original cost by .8 to see the new price

Find all of the cube roots of 216i and write the answers in rectangular (standard) form.

Answers

The cube roots of 216 written in the rectangular (standard) form are 3 + 3√3, -3+3√3, and 6.

What is a cube root?

In mathematics, the cube root formula is used to represent any number as its cube root, for example, any number x will have the cube root 3x = x1/3. For instance, 5 is the cube root of 125 as 5 5 5 equals 125.

3√216 = 3√(2x2x2)x(3x3x3)

= 2 x 3 = 6

the prime factors are represented as cubes by grouping them into pairs of three. As a result, the necessary number, which is 216's cube root, is 6.

Therefore, the cube roots of 216 are 3 + 3√3, -3+3√3, and 6.

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the coefficient of determination resulting from a particular regression analysis was 0.85. what was the slope of the regression line?

Answers

The slope of the regression line is 0.922. Option C is correct.


The coefficient of determination (R-squared) is defined as the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a linear regression model. It can be calculated as the square of the correlation coefficient (r) between the dependent and independent variables.

If we assume a simple linear regression model with a single independent variable (x) and a single dependent variable (y), the slope of the regression line (b) can be calculated as:

b = r * (Sy / Sx)

where r is the correlation coefficient between x and y, Sy is the standard deviation of y, and Sx is the standard deviation of x.

If the coefficient of determination is 0.85, then the correlation coefficient is the square root of 0.85, which is approximately 0.922. Assuming the standard deviations of x and y are known, we could use the formula above to calculate the slope of the regression line as:

b = 0.922 * (Sy / Sx)
Therefore, 0.922, could be the slope of the regression line in this case, if the assumptions of a simple linear regression model with known standard deviations are met. Option C is correct.

The complete question is

The coefficient of determination resulting from a particular regression analysis was 0.85. What was the slope of the regression line?

a. 0.85

b. -0.85

c. 0.922

d. There is insufficient information to answer the question.

e. None of the above

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Ariel wants to join the volleyball team in the fall, so she went to an overnight volleyball camp last weekend to practice her skills. Before she left, she packed a shower caddy shaped like a rectangular prism with a volume of 420 cubic inches. The caddy is 10
1
2
inches long and 5 inches tall.
How wide is the shower caddy?

Answers

The width of the shower caddy is 8 inches.

What is Volume?

Volume is a measure of the total amount of material that an object contains. In mathematical terms, volume is calculated by multiplying the length, width, and height of an object.

We can use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.

We know that the volume of the caddy is 420 cubic inches, the length is 10.5 inches, and the height is 5 inches. Let's substitute these values into the formula and solve for the width:

420 = 10.5w × 5

Divide both sides by 52.5:

8 = w

Therefore, the width of the shower caddy is 8 inches.

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Theorem: A line parallel to one side of a triangle divides the other two proportionately.

In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

Which statement can be proved true using the given theorem?



Group of answer choices

Segment BD = 12

Segment BD = 4

Segment BF = 16

Segment BF = 9

Answers

Since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.

What is triangle?

A triangle is a three-sided polygon that is one of the basic shapes in geometry. It is defined by three points that are connected by three line segments. Triangles have three angles, which add up to 180 degrees, and three sides, which add up to the sum of the lengths of the other two sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. Triangles come in a variety of forms, from the equilateral triangle, which has three sides of equal length, to the isosceles triangle, which has two sides of equal length, to the scalene triangle, which has three sides of different lengths.

The correct answer is: Segment BF = 9. This can be proved true using the given theorem, since segment DE is parallel to segment BC and segment EF is parallel to AB. Therefore, since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.

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Tonya is making a circle graph of the data shown in the table. How many degrees will the section for piano have?


Guitar: 1/4
Piano: 1/6
Drums 13/45
Flute 1/10
Trumpet 7/36

Answers

The section for piano will have 60 degrees in the circle graph.

How to solve

To find out how many degrees the section for piano will have in the circle graph, we first need to find the fraction of the circle that the piano represents.

The total degrees in a circle is 360 degrees. We can use the given fraction of piano (1/6) and multiply it by 360 degrees to find out the degrees of the section for piano.

Degrees for piano = (Fraction of piano) × 360

Degrees for piano = (1/6) × 360

Now, multiply the fraction by 360:

Degrees for piano = 60

So, the section for piano will have 60 degrees in the circle graph.

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→ 60° ( btw, ° means degrees )

— if a WHOLE circle is 360° and the piano is 1/6 of the circle, then all you have to do is multiply 1/6 by 360° which gives you 60 OR 60°

HEY- you look hungry, eat up !! →

brainlist
show all steps nd i will make u brainlist

Answers

Step-by-step explanation:

Again, using similar triangle ratios

7.2 m  is to 2.4 m  

     as   AB is to  12.0 m

7.2 / 2.4  = AB/12.0    Multiply both sides of the equation by 12

12 *   7.2 / 2.4   = AB = 36.0 meters

Find the value of A that makes the following equation true for all values of x

0. 9^60x = A^x

Answers

The value of A that makes the equation true for all x values is 0.9⁶⁰. Using the exponential function we can find out the value of A.

We have to apply the properties of exponential functions to solve for A. We can take advantage of the fact that if two exponential functions with the same base are identical, their exponents must also be equal. To put it another way, if:

aˣ = bˣ

then:

a = b

We may equal the exponents of 0.9 and A using this property:

60x * log(0.9) = x * log(A)

where a log is the logarithm of base ten.

When we simplify this equation, we get:

log(0.9)⁶⁰ˣ = log(A)ˣ

We may simplify this equation using the assumption that

log(aᵇ) = b *log(a):

log(0.9⁶⁰ˣ) = 60x * log 0.9

log (Aˣ) = x log A

log(0.9) * 60x = log(A) * x

When we solve for A, we get:

A = 0.9⁶⁰

As a result, the value of A that makes the equation true for all x values is 0.9⁶⁰.

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a blanket measures 1 1/4 yards on each side. how many square yards does the blanket cover?

Answers

Answer:

Add 1 1/4 x 1 1/4

Step-by-step explanation:

hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?

Answers

It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.

The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.

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need help in a test Write the decimal as a percent 9.66 pls help will make Brainlyist

Answers

Answer:966%

Step-by-step explanation:

To convert a decimal to a percent, we need to multiply the decimal by 100 and add a percent sign. So, to convert 9.66 to a percent, we do the following:

9.66 × 100% = 966%

Therefore, 9.66 is equivalent to 966% as a percent.

Answer: you divide by 100 and you get your answer

Step-by-step explanation:

9.66 ÷ 100 = 0.0966

25. Which is the solution set of the equation
2x² + 3x - 2 = 0?
(1) (-1/2,2}
(2) {1/2,-2}
(3) {1/2,2}
(4) {-1/2,-2}

Answers

Answer:

(2) {1/2,-2}

Step-by-step explanation:

2x² + 3x - 2 = 0

Delta = b² - 4ac

= 3² - 4 (2)(-2)

= 9 + 16

Delta = 25

[tex] \sqrt{25} = 5[/tex]

X= -3-5÷4 = -2

X'= -3+5÷4 = 2/4 = 1/2

S = { 1/2 ; -2 }

Answer:

Step-by-step explanation:

2x² + 3x - 2 = 0

2x² -x +4x - 2 = 0

(2x² -x) +(4x - 2) = 0

x(2x -1) +2(2x -1) = 0

(x +2)(2x-1) =0

(x +2) =0

x = -2

OR

(2x-1) =0

x = 1/2

ans: (2) (1/2, -2)

Find the length of the side labeled x. Explain.

Answers

The value of the length marked x is 61.5

What is trigonometrical ratio?

Trigonometric ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.  The basic trigonometric ratios are sine, cosine, and tangent ratios.  The other important trig ratios, cosec, sec, and cot can be derived using the sin, cos and tan respectively.

First using left hand side

Cos = Adj/Hypo

Cos22 = Adj/50

Adj = 50 * Cos 22

The adj = 50*0.9272

The adj = 46.4

The to find x, using

Cos 41 = 46.4/x

xCos41 =46.4

x = 46.4/Cos41

x = 46.4/.0755

Therefore the value of x = 61.5

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in testing a hypothesis from a random sample involving three or more means, the appropriate test would be a one-way anova. True or false?

Answers

True.

When testing a hypothesis involving three or more means, the appropriate test is a one-way ANOVA (Analysis of Variance). ANOVA is a statistical method that compares the means of two or more groups to determine if there is a significant difference between them. In the case of a one-way ANOVA, we are comparing the means of one variable across multiple groups or categories.

The one-way ANOVA test allows us to determine if the differences between the means of the groups are significant enough to reject the null hypothesis, which states that there is no significant difference between the means. If the p-value obtained from the ANOVA test is less than the chosen level of significance, we reject the null hypothesis and conclude that there is a significant difference between at least two of the means.

Determine the domain of the variable x in the given expression.
x-12/x+49

Answers

The domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as: (-∞, -49) U (-49, ∞)

What is domain?

In mathematics, the domain of a function is the set of all possible input values (usually represented by the variable x) for which the function is defined. It is the set of all values that can be substituted for the independent variable in a function to produce a valid output. The domain of a function is often restricted by the context in which it is being used, such as the type of problem or the natural limitations of the situation.

According to given information:

The given expression is (x-12)/(x+49).

The denominator of the expression is x + 49. The denominator cannot be equal to 0, as division by 0 is undefined. Therefore, x + 49 ≠ 0.

Solving for x, we get:

x ≠ -49

Therefore, the domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as:

(-∞, -49) U (-49, ∞)

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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0. 07 and the probability that the flight will be delayed is 0. 16. The probability that it will not rain and the flight will leave on time is 0. 83. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth. How would you figure this out?

Answers

The probability that it is raining and the flight is delayed is equal to the probability of it raining multiplied by the probability of the flight being delayed.

Therefore, the probability that it is raining and the flight is delayed is 0.07 * 0.16 = 0.0112. Rounded to the nearest thousandth, this is 0.011.

Suppose that $18,000 is invested at 5. 2% compounded. Find the total amount of this investment after 7 years

Answers

If $18,000 is invested at 5. 2% compounded then the full sum of the investment after 7 long years is roughly $24,810.89.

we are able to utilize the equation for compound intrigued:

A = P(1 + r/n)[tex]^{nt}[/tex]

where A is the entire sum of the venture after t a long time, P is the foremost speculation sum, r is the yearly intrigued rate as a decimal, n is the number of times the intrigued is compounded per year, and t is the number of a long time.

In this case, P = $18,000, r = 0.052 (since the intrigued rate is 5.2%), n = 1 (since the intrigued is compounded every year), and t = 7 (since we need to discover the full sum after 7 a long time). Substituting these values into the equation, we get: A = 18000(1 + 0.052/1)[tex]^{1*7}[/tex]

= 18000(1.052)[tex]^{7}[/tex]

= $24,810.89 (adjusted to the closest cent)

thus, the full sum of the venture after 7 a long time is roughly $24,810.89.

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Practice Final Apex Unit 4 Linear Equations
How many solutions does 5 - 3x = 4 + x + 2 -4x
One solution
Two solutions
No solution
Infinitely many solutions

Answers

This is a contradiction, which means that there is no solution for the given equation. Therefore, the correct answer is option C, "No solution".

There is only one solution for the given equation.

5 - 3x = 4 + x + 2 - 4x

Simplifying the equation, we get:

5 - 3x = 6 - 3x

Subtracting 6 from both sides, we get:

-1 - 3x = -3x

Adding 3x to both sides, we get:

-1 = 0

A linear equation is an equation that can be written in the form y = mx + b, where y and x are variables, m is the slope, and b is the y-intercept. It represents a straight line on a graph. Linear equations can be used to model a variety of real-world situations, such as the relationship between temperature and time, or the cost of producing a certain quantity of goods.

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We can see that both sides are equal, which means that the equation has infinitely many solutions.

Therefore, the answer is: D. Infinitely many solutions is correct.

To solve for the number of solutions of 5 - 3x = 4 + x + 2 -4x,

we first simplify the equation by combining like terms:

Combine like terms on both sides of the equation:

5 - 3x = 6 - 3x

Compare the coefficients of the x terms:

-3x = -3x

Since both sides of the equation have the same coefficients for the x terms, there are infinitely many solutions.

Therefore, the answer is: D. Infinitely many solutions is correct.

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A cone with a radius of 3 inches and a height of 18 inches is shown



What is the volume, in a cubic inches, of the cone. Round your answer to the nearest integer

Answers

Answer: about 169.65

Step-by-step explanation:

You do pi r squared multiplied by height over 3.

28.27 is the area of the circle and you multiply is by six because 18/3=6. 28.27x6 = about 169.65

Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8

Answers

Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex]

5(2x - 1) + 3(x - 3) = -(4x - 6) + 2(13 - 3x)

Answers

Answer:

The value of x is 2.

Step-by-step explanation:

5(2x -1) + 3(x -3) = -(4x - 6) + 2(13 -3x)

Expand both sides of the equation to remove parenthesis

10x - 5 + 3x - 9 = -4x + 6 + 26 - 6x

Transpose all terms with x as the coefficient on the left side of the equation and transpose the constants to the right.

10x + 3x + 4x + 6x = 6 + 26 + 5 + 9

Simplify

23x = 46

Divide both sides of the equation by 23

23x/23 = 46/23

x = 2

Find the distance of D of AB
A=(-7,-7) B= (-3,-1)

Answers

The distance between the points A=(-7,-7) and B=(-3,-1) is 7.21 units.

Finding the distance of D of AB

We can use the distance formula to find the distance between points A=(-7,-7) and B=(-3,-1) on the coordinate plane.

The distance formula is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the values we have, we get:

d = √((-3 - (-7))^2 + (-1 - (-7))^2)

= √((4)^2 + (6)^2)

= √(16 + 36)

= √(52)

≈ 7.21

Therefore, the distance between points A=(-7,-7) and B=(-3,-1) is approximately 7.21 units.

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what is the 4th term/number of (a+b)^9, pascal’s triangle?

Answers

Step-by-step explanation:

hope this will help you Thanks

1. Find the square root of each of the following numbers: (i) 152.7696​

Answers

To find the square root of 152.7696, we can use a calculator or apply a method like the following:

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).
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