An African elephant has a mass of
8139
kg
8139 kg8139, start text, space, k, g, end text.
Choose the best approximation of the mass of an African elephant.
Choose 1 answer:
Choose 1 answer:
(Choice A)
8
⋅
1
0
3
kg
8⋅10
3
kg8, dot, 10, cubed, start text, space, k, g, end text
A
8
⋅
1
0
3
kg
8⋅10
3
kg8, dot, 10, cubed, start text, space, k, g, end text
(Choice B)
8
⋅
1
0
4
kg
8⋅10
4
kg8, dot, 10, start superscript, 4, end superscript, start text, space, k, g, end text
B
8
⋅
1
0
4
kg
8⋅10
4
kg

Hence by using Pythagoras the height of tree before it break is 47.02m

Describe Pythagoras.

The Ionian Greek philosopher and mathematician Pythagoras is credited with creating Pythagoreanism. He was born in 570 BCE in Samos, Ionia (Greece), and passed away at Metapontum, Lucania, between 500 and 490 BCE. (Italy). The three sides of a right-angled triangle are the subject of Pythagoras' most famous theorem, which is now referred as as Pythagoras' theorem.

Let A'CB represent the tree before it broke at point C, and let A' be the point at which the tree's top contacts the earth after it broke. Then, at B, ABC is a right triangle.

AB=20 m and BC=15 m

Using Pythagoras theorem,   H²  = P²+ B²

In ΔABC

(AC) ²

=(AB)² +(BC) ²

(AC) ²

=(20) ²+15)²

(AC) ² =400+625

(AC) ²=1025

AC=  32.02

​Hence total height is 32.02+15 =47.02m

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Answer:

$18.28

Step-by-step explanation:

To complete this problem is a straightforward answer:

First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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The length and width of the rectanhle are Length = 7y and Width = 2y^2 - 9

To find the expressions for the greatest common factor (GCF) of the length and width of a rectangle with an area of 14y^3 - 63y, we can factor the area expression and look for common factors.

14y^3 - 63y = 7y(2y^2 - 9)

The GCF of the length and width will be factors of both 7y and 2y^2 - 9.

The only common factor is y, so the length and width expressions are:

Length = 7y

Width = 2y^2 - 9

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The first monthly payment is for interest in dollars for the mortgage loan of $750,000 at an interest rate of 7% is equal to $437,475.00 with first principal payment is $612.75.

Amount balance of mortgage loan = $750,000

Interest rate = 7%

To calculate first monthly payment is for interest

= calculate the portion of the payment that goes towards interest and the portion that goes towards the principal.

First, find the monthly interest rate by dividing the annual interest rate by 12.

Monthly interest rate

= 7% / 12

= 0.5833%

Next, calculate the interest portion of the first payment by multiplying the loan balance by the monthly interest rate,

Interest portion of first payment

= Loan balance x Monthly interest rate

= $750,000 x 0.5833%

= $437,475.00 /100

= $4374.75

Principal portion of first payment

= Total payment - Interest portion

=$4,987.50 - $4374.75

= $612.75

Therefore, $437,475.00 of the first monthly payment of $4,987.50 is for interest.

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Answer:

107.7

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be horizontal dimension of 16 inches, and an approximate hypotenuse of 28.84 inches.

A polygon is a hexagon if it has at least one additional segment. Its shape is a straightforward rectangle. Only edges between A and B can separate anything similar from a regular triangle form. The cube is only partially formed by Euclidean geometry, even though the edges are entirely collinear. A circle with four sides and three angles make compose a triangle.

Here,

The backrest is described as having a 24 inch vertical dimension and a 16 inch horizontal dimension. Although the hypotenuse is not named, we may nevertheless determine its length using the Pythagorean theorem:

=> h² = 24² + 16²

=> h² = 576 + 256

=> h² = 832

=> h= 28.84 inches high

As a result, the backrest has the following measurements: a vertical dimension of 24 inches, a horizontal dimension of 16 inches, and an approximate hypotenuse of 28.84 inches.

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[tex]8x^3y^9\\[/tex] is equivalent to [tex]8x^4y^12[/tex] when expressed in terms of factors.

An expression is a combination of numbers, variables, and mathematical symbols that represent a mathematical relationship or formula. Expressions can be simple or complex and can include operations such as addition, subtraction, multiplication, and division, as well as exponents, radicals, and functions.

In the given question,

One possible expression that is equivalent to [tex]8x^3y^9[/tex] is:

[tex](2x^2y^3)^2 * (2y^6)\\[/tex]

When we expand this expression, we get:

[tex](2x^2y^3)^2 = (2^2)(x^2)^2(y^3)^2 = 4x^4y^6(2y^6) = 2y^6[/tex]

Multiplying these two expressions together, we get:

[tex](4x^4y^6) * (2y^6) = 8x^4y^12[/tex]

So [tex]8x^3y^9[/tex] is equivalent to [tex]8x^4y^12[/tex] when expressed in terms of factors.

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Each game should cost us roughly 8 cents.This game's expected value is negative, thus playing it is not a good idea because you will most likely lose money in the long run.

Given problem describes that there can be 4 unique ball colour combinations as :

Provided that each colour contains two balls in the respective boxes, each combination has a probability of happening of 2/4 * 1/3 = 1/6. The likelihood that the payoff will be zero is thus 4 * 1/6 = 2/3.

Red balls make two different combinations as: (red, red) in left box and (red, red) in  right box. Due to the fact that each box contains just one red ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. The likelihood that the dividend will be $0.50 is thus 2 * 1/12, or 1/6

Blue balls makes two different combinations as: blue and blue in the left box and (blue, blue) in the right box. Due to the fact that each box contains just one blue ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. Hence, the likelihood that the payoff will be $1 is 2 * 1/12, or 1/6.

In the left box, there is only one conceivable pair of balls that are both green: (green, green). Given that there is only one green ball in the left box, this combination has a probability of happening of 1/4 * 1/3, or 1/12. Hence, there is a 1/12 chance that the payment will be $16.

[tex]Payout\; |\;Probability\\ \ $0 \qquad \qquad 2/3\\$0.50 \quad \qquad 1/6\\$1 \qquad \qquad 1/6\\$16 \qquad \qquad 1/12[/tex]

By multiplying each payout by the associated probability and adding them together, the anticipated value is determined. The predicted outcome in this situation is:

[tex]\$ 0 * 2/3 + \$0.50 * 1/6 + \$1 * 1/6 + \$16 * 1/12 - \$1 = -\$0.0833[/tex]

The anticipated value of playing this game, according to the revised figures above, is [tex]-\$0.0833[/tex], which indicates that you should anticipate losing on average roughly $0.08 every game. Thus, it is unprofitable game to play if played on regular basis.

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The average rate of change for this function for the interval from x=2 to x=4 is B. 27.5.

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

For this special case from the info in the table, we have:

a = 2, f(2) = 9

b = 4, f(4) = 64

And replacing the data into the average rate formula we got:

m = 64-9/4-2 = 27.5

Thus, the correct option is B. 27.5.

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Answer: Use the steps that are easiest to draw a parabola!

Step-by-step explanation:

I used Desmos, here are the key points.

Vertex: (-5,-2)

Extra points to graph:

Hope this helps!

The volume of the right rectangular prism is 1/18 cubic feet.

What is a rectangular prism?

A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a rectangular parallelepiped or a rectangular cuboid.

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.

In this case, the length l is 2/3 ft, the width b is 1/3 ft, and the height h is 1/4 ft. Therefore, the volume of the prism is:

V = lbh = (2/3 ft)(1/3 ft)(1/4 ft) = 1/18 cubic feet

So the volume of the right rectangular prism is 1/18 cubic feet.

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Answer:

The answer to your problem is, A. 4(2a • 5) = (4 • 2a) • 5

Step-by-step explanation:

The APM ( Association Property of Multipaction ) states that multiplication of group of numbers in any combination of any type of number.

Like: a × ( b×c ) = ( a × b ) × c

Option A. Has that;

4(2a • 5) = (4 • 2a) • 5

Thus the answer to your problem is, A. 4(2a • 5) = (4 • 2a) • 5

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

[tex]3x^2 + 2x - 1[/tex]

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial[tex]l x^3 + kx^2 + 2kx[/tex] + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

[tex]x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30[/tex]

where q(x) is the quotient when. [tex]x^3 + kx^2 + 2kx + 6[/tex] is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

[tex]2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30[/tex]

Simplifying the left-hand side, we get:

[tex]8 + 4k + 4k + 6 = 30[/tex]

[tex]16k = 16[/tex]

[tex]k = 1[/tex]

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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Answer:

The perimeter is 5 + 12 + 13 = 26 units.

After answering the presented questiοn, we can cοnclude that equatiοn Therefοre, there are 144 wοrds οn the vοcabulary list.

A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.

A mathematical fοrmula describes the cοnnectiοn between the twο sentences that οccur οn οppοsite sides οf a letter. The symbοl and the single variable are frequently the same. As in 2x - 4 Equals 2, fοr instance.

1/4 x = tοtal number οf wοrds Miguel has nοt memοrized

1/4 x = x - 36

x/4 = 36

x = 144

Therefοre, there are 144 wοrds οn the vοcabulary list.

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Answer: Approximately 21.093 grams of silicon-32 will be present after 200 years.

Step-by-step explanation: The formula for the amount of substance remaining after a certain amount of time can be given by:

A = A0 (1/2)^(t/T)

where:

A0 = initial amount of substance

A = amount of substance remaining after time t

T = half-life

Plugging in the given values:

A0 = 30 grams

t = 200 years

T = 710 years

A = 30 * (1/2)^(200/710)

A ≈ 21.093 grams

Therefore, approximately 21.093 grams of silicon-32 will be present after 200 years.

The reasonable prediction through which a green or black marble will be drawn is 35 times.

What about prediction?

In mathematics, prediction refers to the process of using existing data or patterns to make an educated guess about a future event or outcome. It is the process of estimating an unknown value or quantity based on a set of known data or observations.

Prediction is often used in statistics, where data analysis techniques are used to identify patterns and trends in data. Once these patterns are identified, they can be used to make predictions about future events or outcomes. For example, in finance, prediction models are often used to forecast stock prices or market trends.

The accuracy of predictions in mathematics can be improved by using more data, improving the quality of the data, or refining the models and algorithms used to make the predictions. However, even with the best models and data, there is always some degree of uncertainty or error associated with predictions, and this should be taken into account when using predictions to make decisions.

According to the given information:

Given, there are  5 red marbles, 6 blue marbles, 3 green marbles

4 black marbles, 2 yellow marbles .

Here, it is given that marble will be drawn and replace 100 times.

To find reasonable prediction for no of times green or black marble will be drawn

⇒ Total no of times = 100 times

⇒ [tex]\frac{4}{20}[/tex] x 100 +   [tex]\frac{3}{20}[/tex]  x 100

⇒ [tex]\frac{7}{20}[/tex]  x 100

⇒ 35 times

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[tex]3.9ft^{2}[/tex]

The empirical probability of getting exactly 3 heads in 6 coin flips is 20/64 = 0.3125 or 31.25% and the theoretical probability of getting exactly 3 heads in 6 coin flips is also 0.3125 or 31.25%.

What is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event is certain to occur.

Empirical Probability:

If you flip a coin 6 times and record the outcomes, there are a total of [tex]2^6 = 64[/tex] possible outcomes, where each flip can result in either heads or tails.

To calculate the empirical probability of getting exactly 3 heads, you would need to count the number of outcomes in which exactly 3 of the 6 flips result in heads.

For example, one possible outcome is HTHTHH, which has exactly 3 heads.

By enumerating all possible outcomes, we can count that there are 20 outcomes with exactly 3 heads.

Therefore, the empirical probability of getting exactly 3 heads in 6 coin flips is 20/64 = 0.3125 or 31.25%.

Theoretical Probability:

The theoretical probability of getting exactly 3 heads in 6 coin flips can be calculated using the binomial distribution formula, which is:

[tex]P(X=k) = (n\ choose\ k) * p^k * (1-p)^{(n-k)[/tex]

where P(X=k) is the probability of getting exactly k successes, n is the number of trials, p is the probability of success in a single trial, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n.

In this case, we have n=6 trials, k=3 successes, and p=0.5 (assuming a fair coin).

Plugging in these values, we get:

[tex]P(X=3) = (6\ choose\ 3) * 0.5^3 * (1-0.5)^{(6-3)} = 20 * 0.125 * 0.125 = 0.3125 or 31.25%[/tex]

Therefore, the theoretical probability of getting exactly 3 heads in 6 coin flips is also 0.3125 or 31.25%.

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Answer:

x^2 - 4x + 1 = 0

x^2 - 4x + 4 = 3

(x - 2)^2 = 3

x - 2 = +√3

x = 2 + √3

Answer:

x = 2 ± √3

Step-by-step explanation:

     x² - 4x + 1 = 0

          x² - 4x = -1

Divide the co-efficient of x by 2. Co-efficient of x is 4, 4÷ 2 = 2.

Add the square of 2 to both sides. Square of 2 is 4.

    x² - 4x + 4 = -1 + 4

x² - 2*2x + 2² = 3

{LHS is in the from a² - 2ab + b² = (a -b)²}

          (x - 2)² = 3

Take square root,

          x - 2 = ±√3

Add 2 to both sides,

               x = 2 ± √3

Answer:

4.8 litres

Step-by-step explanation:

Based on the given information, Elizabeth needs 5 boxes of blueberries for each litre of smoothie. She has 24 boxes of blueberries available.

So, the total amount of smoothie that Elizabeth can make in litres would be:

24 boxes of blueberries / 5 boxes of blueberries per litre

This can be calculated as:

24 boxes ÷ 5 boxes per litre = 4.8 litres

So, Elizabeth can make 4.8 litres of smoothie using the available 24 boxes of blueberries.

angle ACD=20°

Therefore option A is correct

ABCD is a cyclic quadrilateral..

so angle b+ angle D = 180°

angle d = 180°-110°

angle d=70°

AB is the diameter

so angle ACB is 90°

angle CAB+ Angle ABC+ Angle BCA =180° ( corrresponding to angle sum property)

=70°+90°+BAC=180°

angle BAC=20°

We have seen that angle BAC= angle ACD (interior alternate) (because in trapezium it's parallel)

Therefore angle ACD=20°

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To find out how many pounds of cheese there are, you can divide the total cost by the cost per pound:

$58.88 ÷ $3.68/lb ≈ 16 lbs

So there are approximately 16 pounds of cheese.

Answer:

0,95

Step-by-step explanation:

[tex] \frac{19}{20} [/tex]

Multiply the fraction by 5, so that the denominator would be equal to 100:

[tex] \frac{19 \times 5}{20 \times 5} = \frac{95}{100} = 0.95[/tex]

The predictions for the number of times that the following sums would occur are as follows:

To make accurate predictions, we need to follow the binomial distribution rule that assumes the darts to be independent each of other. By this rule, the number of possibilities of the darts being thrown is 2 * 80 which equals 160.

Next, there are three possible ways to achieve the sum of 8 which are (1, 7), (2, 6), or (3, 5). The probabilities are: 1/20) * (1/20) = 1/400. Now we multiply these by the number of possibilities to arrive at:

160 * (3/400) = 12

For the sum of 10, there are also three possible ways, namely: (1, 9), (2, 8), or (3, 7). The probability of getting a sum of 10 on any given throw is 3/400. When we express this, we arrive at:

160 * (3/400) = 12

For the sum of 14, there are two possible ways, namely: (5, 9) or (6, 8). Given the probability of 1/400, the probability of getting a sum of 14 on any given throw is 2/400. When we express this with the binomial distribution, we will arrive at 160 * (2/400) = 8

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13303.492 ×  (0.875)¹⁰ is  an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth.

What in mathematics is an exponential?

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's basis and must be bigger than 0.

                           The transcendental number, or e, which is roughly equivalent to 2.71828, is the most often used exponential function basis. Calculating the exponential growth or decay of a given collection of data is done mathematically using an exponential function.

According to the question,

  x : 0             1            2        3          4           5             6    

 y  :  13100   11124   10572   9365  8067    6507       6892

so the function

 y = 13303.492 ×  (0.875)ˣ

when x = 10 ,

    y = 13303.492 ×  (0.875)¹⁰   ≈  3500

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The statement "X⁻¹ = X" means that for each element X in the set or group, its inverse is itself.

An even number is any integer ( whole number) that is divisible by 2, i.e., it leaves no remainder when divided by 2. In other words, an even number is a multiple of 2.

For example, 2, 4, 6, 8, 10, and so on are even numbers, while 1, 3, 5, 7, 9, and so on are odd numbers. Zero (0) is also considered an even number because it is divisible by 2.

The statement "an even number of elements X such that X⁻¹ = X" means that there are a certain number of elements (which is even) in a set or group, and for each element X in that set or group, its inverse is also equal to X.

In mathematics, the inverse of an element X in a group is an element Y such that their product XY (or YX) equals the identity element of the group. The identity element is the element in the group that, when combined with any other element, produces that element unchanged. For example, the identity element of the group of real numbers under addition is 0, because 0 + a = a + 0 = a for any real number a.

So, the statement  X⁻¹ = X" means that for each element X in the set or group, its inverse is itself. This is only possible if the set or group has elements that are their own inverses. In other words, each element is equal to its negative (or additive inverse) or its reciprocal (or multiplicative inverse).

The requirement that there must be an even number of such elements in the set or group means that if we count the number of elements that satisfy this condition, the count must be an even number.

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The answer of the given question based on the statistics is , Part A X= 370 , S= 36 , n= 50 . Part B =  5 . Part C = 9.8 . Part D=  360 and 380.   Part E: the reason is explained below.

The mean is measure of central tendency that represents average value of set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values. The mean is a useful statistic for describing the typical or average value of a data set, and is often used in data analysis and statistical inference.

Part A:

X= 370 (sample mean)

S= 36 (sample standard deviation)

n= 50 (sample size)

Part B:

s/n = 36/√50 = 5 (rounded to the nearest whole number)

Part C:

The margin of error for a 95% confidence level can be found using the formula: margin of error = z*(standard error), where z is the z-score associated with a 95% confidence level. z-score can found using  standard normal distribution table or calculator. For a 95% confidence level, the z-score is approximately 1.96. Therefore, the margin of error is:

margin of error = 1.96*5 = 9.8 (rounded to one decimal place)

Part D:

The 95% confidence interval can be found by adding and subtracting the margin of error from the sample mean:

95% confidence interval = X ± margin of error = 370 ± 9.8 = (360, 380)

The confidence interval means that we can be 95% confident that the true population mean number of recharges for IQ laptop batteries from Elusive Electronics falls between 360 and 380.

Part E:

Since the 95% confidence interval does not include the claimed average of 400 recharges, we cannot accept the claim that each IQ laptop battery will last for an average of 400 recharges. It is possible that the true population mean is close to 400 recharges, but based on the sample data, we cannot make that conclusion with 95% confidence.

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