Landon had one string that was 10 meters long. He used 6.275 meters of this string for a progect.

The sample mean and sample standard deviation provide valuable information about a set of data, but they should be used with caution when making inferences about the population. It is important to use statistical methods to determine the reliability of these estimates and to account for sources of variability in the data.

Firstly, the sample mean is a measure of central tendency that represents the average value of a set of data. In this case, the sample mean of 290 rooms occupied per day is the sum of the number of rooms occupied each day over the 25-day period divided by the total number of days. It is important to note that the sample mean is only representative of the specific sample of 25 days and may not accurately reflect the population mean.

Secondly, the sample standard deviation is a measure of dispersion that indicates how spread out the data is from the mean. A smaller standard deviation means that the data points are closer to the mean, while a larger standard deviation means that the data points are more spread out. In this case, the sample standard deviation of 20 rooms indicates that there is some variability in the number of rooms occupied each day.

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The distance from the top of the tree to the tip of the shadow is 15.5 feet.

A tree that is 15 feet tall casts a shadow that is 4 feet long. The distance of the top of the tree to the tip of the shadow can be calculated as follows:

The situation forms a right angle triangle. Therefore, the sides can be found using Pythagoras's theorem.

The height of the tree and the length of the shadow are the legs of the right triangle while the distance of the tree to the tip of the shadow is the hypotenuse side.

Therefore,

c² = a² + b²

where

Hence,

c² = 15² + 4²

c² = 225 + 16

c² = 241

c = √241

c = 15.5241746963

c = 15.5 feet.

Hence the distance is 15.5 feet.

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Answer: A: 15.5 feet

Answer:

They are not congruent because the lines aren't parallel.

Step-by-step explanation:

For all of those angle relation theorems to be valid, PARALLEL lines need to be split by a transversal.

Answer: 64

Step-by-step explanation:

(2 x 2) x (2 x 2) x (2 x 2)= 64

  (4      x     4)    x      4   = 64

           16           x     4   =  64

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Answer:

Step-by-step explanation:

boody boody

Answer:

DG

Step-by-step explanation:

This is a rectangular prism.  BE & AH are also parallel to CF. but they r not in the answers.

Yes the triangle with dimension 3 cm , 4cm , 5 cm is  a right angled triangle.

Given,

Dimensions : 3 cm , 4cm , 5 cm .

Here,

In any right angled triangle the Pythogoras theorem holds trure .

Pythogoras theorem ,

P² + B² = H²

P = perpendicular

B = base

H = hypotenuse .

So,

In triangle ,

3cm , 4cm , 5cm

Apply pythogoras theorem .

Let ,

P =3cm

B = 4cm

H = 5cm

3² + 4² = 5²

25 = 25 .

Thus the triangle is right angled triangle .

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Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

Answer: 3.51

Step-by-step explanation:

Answer: The tip was 3.50$

Step-by-step explanation: Since the tip is 20% you would times the given amount by 20 then divide it by 100.

20 x 17.53 / 100 = 3.506

We're rounding to the nearest cent, so that would be 3.50.

The equivalent value of m is given by the expression m = 1

Given data ,

We can use the properties of exponents to solve this problem. Specifically, when we multiply two powers with the same base, we add their exponents.

So, we have:

(-3)^(m+1) × (-3)⁵ = (-3)⁷

Using the property of exponents, we can add the exponents on the left-hand side:

(-3)^(m+1+5) = (-3)⁷

Simplifying the exponents on the left-hand side:

(-3)^(m+6) = (-3)⁷

We know that two powers with the same base are equal if and only if their exponents are equal. So, we can set the exponents equal to each other:

m + 6 = 7

Subtracting 6 from both sides:

m = 1

Hence , m = 1 is the value that satisfies the equation

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By simple algebra, Jane is 57 9/20 inches taller.

If one object or person's height exceeds that of another, the taller object or person is said to exist. There is a two-object or two-person limit. Taller is a relative term. For instance: Hoppy stands at 7 feet.

You can begin this issue by first figuring out Dwight's height. At 54 3/4 inches, he would be 1 1/2 inches taller than Chloe:

54 3/4 plus 1 1/2 equals 55 + (3/4 + 1/2) equals 55 + (3/4 + 2/4) equals 55 + 5/4 equals 56 1/4 inches.

Dwight stands at 56 1/4 inches.

Dwight is 1 1/5 inches shorter than Jane, so

56 1/4 plus 1 1/5 is 57 plus (1/4 plus 1/5) is 57 plus (5/20 plus 4/20) is 57 plus 9/20 is 57 9/20 inches.

Jane stands at 57 9/20 inches.

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Answer:

54

Step-by-step explanation:

each shelf has 9 books so the equation would be 9x6=54 because there are 6 shelves in total<3

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

The probability that the rate of return of this investment is greater than 10 percent is approximately 0.9214, or 92.14%.

1. Calculate the expected value and variance of the total return:
Since X1 and X2 are independent, we can simply add their means and variances.
Expected Value (E) = Mean of X1 + Mean of X2 = 60 + 60 = 120
Variance (V) = Variance of X1 + Variance of X2 = 25 + 25 = 50

2. Determine the 10 percent rate of return:
A 10 percent return on an initial investment of 100 would yield a total of 110 (100 + 10% * 100).

3. Calculate the Z-score:
The Z-score represents how many standard deviations away the desired value (110) is from the mean (120). To calculate the Z-score, we use the following formula:
Z = (X - E) / sqrt(V)
Z = (110 - 120) / sqrt(50)
Z = -10 / sqrt(50)
Z = -10 / 7.07
Z = -1.414

4. Find the probability:
Now, we need to find the probability that corresponds to the Z-score of -1.414. Using a standard normal distribution table or an online calculator, we find that the probability of a Z-score less than -1.414 is approximately 0.0786.

5. Calculate the probability of a rate of return greater than 10 percent:
Since we want the probability of a rate of return greater than 10 percent, we need to find the complement of the probability we just calculated.
Probability (rate of return > 10%) = 1 - P(Z < -1.414)
Probability (rate of return > 10%) = 1 - 0.0786
Probability (rate of return > 10%) = 0.9214

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Answer:

x = 5

Step-by-step explanation:

using the sine or cosine ratio in the right triangle and the exact value

sin30° = \(\frac{1}{2}\) , then

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{10}\) = \(\frac{1}{2}\) ( cross- multiply )

2x = 10 ( divide both sides by 2 )

x = 5

Answer:

Amount of frozen soup = 2500 mL

Step-by-step explanation:

We are told that tom made 5,000 mL of soup.

We are also told he packed 2.5 Litres into his kids' lunches.

Now, from conversions,

1 liter = 1000 mL

Thus,

2.5 litres = 2.5 × 1000 = 2500 mL

Now, we are told he froze the rest of the soup.

Thus;

Amount of frozen soup = total amount of soup made - amount given to kids' lunch pack.

Amount of frozen soup =

5000 - 2500 = 2500 ml

Answer:

9

Step-by-step explanation:

cuz yes

Answer:

35% I had the same question on a test yesterday...YEAH hehe hope this helps!

Answer:

35%

Step-by-step explanation:

Answer:

10 - 5i

Step-by-step explanation:

Answer:

g(x)=x

4

+3x

3

−x

2

−3x

Step-by-step explanation:

The area of the triangle is 1500ft²

A triangle is a polygon with three sides having three vertices.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

Though the triangle consist of two right angle triangle, we have to calculate area of each and add them together.

The base of the small triangle

= √55²-25²

= √ 3025 - 625

= √ 2400

= 49.0( 1 dp)

The area of small triangle = 1/2bh

= 1/2 × 49 × 25

= 612.5 ft²

The area of the big triangle

= 1/2 × 71 × 25

= 887.5 ft²

Therefore the area of the triangle

= 612.5 + 887.5

= 1500ft²

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A triangle is a polygon with three sides having three vertices.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

Though the triangle consist of two right angle triangle, we have to calculate area of each and add them together.

The base of the small triangle

= √55²-25²

= √ 3025 - 625

= √ 2400

= 49.0( 1 dp)

The area of small triangle = 1/2bh

= 1/2 × 49 × 25

= 612.5 ft²

The area of the big triangle

= 1/2 × 71 × 25

= 887.5 ft²

Therefore the area of the triangle

= 612.5 + 887.5

= 1500ft²

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The two truckers will leave Los Angeles on the same day again after 36 days. This number of days is equal to the least common multiple (LCM) of their individual trip durations.

Let's denote the trip durations of the two truckers as t1 = 9 days and t2 = 12 days. To find the number of days that will pass before they leave Los Angeles on the same day again, we need to determine the LCM of t1 and t2.

The LCM is the smallest positive integer that is divisible by both t1 and t2. In this case, the LCM of 9 and 12 can be found by considering their prime factors:

9 =\(3^2\)

12 = \(2^2\) * 3

To find the LCM, we take the highest power of each prime factor that appears in either number. Therefore, the LCM of 9 and 12 is \(2^2\) * \(2^2\) = 36.

Therefore, it will take 36 days for the two truckers to leave Los Angeles on the same day again. After 36 days, both truckers will have completed multiple round trips to and from their destination, and their schedules will align with both departing on the same day.

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To approximate the integral using the trapezoid quadrature formula (single version), we divide the interval [0.7, 6.4] into smaller subintervals and approximate the integral over each subinterval using trapezoids.

First, we choose the number of subintervals, denoted as n, which determines the width of each subinterval. A common choice is to use equally spaced subintervals, so the width h is given by h = (b - a) / n, where a = 0.7 and b = 6.4.

Next, we evaluate the function e^(-2.9x^2) at the endpoints of each subinterval and compute the sum of the areas of the trapezoids formed by connecting these function values.

The approximation formula is:

Approximation ≈ (h/2) * [f(a) + 2 * (sum of f(x_i)) + f(b)], where x_i represents the intermediate points within each subinterval.

Using the given integral, we have:

a = 0.7, b = 6.4, n = 12 (to achieve the desired accuracy), and h = (6.4 - 0.7) / 12 = 0.525.

We then compute the function values at the endpoints and intermediate points, sum them up, and apply the approximation formula.

Performing the calculations to at least 12 significant figures, the approximation of the integral I is approximately 3.52535.

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False. let a be a real square matrix. if a is diagonalizable then a is symmetric

Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.

While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.

Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.

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The measurement of AB is given as follows:

AB = 16.23.

The three trigonometric ratios are defined as follows:

For the angle of 52º, we have that:

Hence the measurement of AB is obtained as follows:

cos(52º) = 10/AB

AB = 10/cos(52º)

AB = 10/0.616

AB = 16.23.

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Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. The value of r is 16.

What is speed ?

The speed at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it only has a direction and no magnitude, speed is a scalar quantity.

144/r= t

144/(r-4)-144/r = 3

LCM r(r-4)

144r-144(r-4)/r(r-4)=3

Simplify \($\frac{144 r-144(r-4)}{r(r-4)}: \frac{576}{r(r-4)}$\)

\(\frac{576}{r(r-4)}=3\)

Multiply both sides by r(r-4)

\(\frac{576}{r(r-4)} r(r-4)=3 r(r-4)\)

Simplify

576=3 r(r-4)

Solve \($576=3 r(r-4): \quad r=16, r=-12$\)

r=16, r=-12

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Answer:

0$ or 3$

Step-by-step explanation:

If you are saying right now, then the answer would be zero. But, when we start, we can make and equation. Let's use J as John, A as Allen, and F and Frank. They all have n amount of money. Now, we work backwards: If A didn't give F 2$, then F now has n-2 and A has n+2. If J didn't give A 5$, then J would have n+5 and A would have n+2-5=n-3. The difference between those two is 8. Therefore, John has 8$ more.

Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.

As per the data given in the above question are as bellow,

A material has a half-life when it takes a particular length of time for half of it to disappear or change.

11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.

We thus split the 3 mg sample in half three times.

3 ÷ 2 = 1.5

1.5 ÷ 2 = 0.75

0.75 ÷ 2 = 0.375

After 11.46 days, there will only be 0.375mg of radon-222 left.

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