Kelly runs a distance of 100 metres in a time of 10.52 seconds.
The distance of 100 metres was measured to the nearest metre.

The time of 10.52 seconds was measured to the nearest hundredth of a second.

(a) Write down the upper bound for the distance of 100 metres.

Answer:

n lesser than or equal to - 6

The probability that the airline will have no mishandled bags is 0.0022.

Given that airline A had 6.06 mishandled bags per 1,000 passengers.Let us find the probability that in the next 1,000 passengers, the airline will have no mishandled bags. Here, the mean number of mishandled bags = 6.06.

We need to find the probability that the airline will have no mishandled bags.

Probability of having no mishandled bags = P(X = 0)

The Poisson distribution formula is

P(X = x) = (e^(-λ) * λ^x) / x!

Where λ is the mean number of occurrences of an event in a given interval of time/space.

Here, λ = 6.06 and x = 0.

Thus, the Poisson distribution formula will be:

P(X = 0) = (e^(-6.06) * 6.06^0) / 0!

P(X = 0) = (e^(-6.06) * 1) / 1

P(X = 0) = e^(-6.06)

P(X = 0) = 0.0022011124290586392 (approximately)

Therefore, the probability that in the next 1,000 passengers, the airline will have no mishandled bags is 0.0022 (rounded to four decimal places).

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The required answer is m = n, provided that b ≠ 0

To consider the following statement:
Select the answer that best completes the given statement: If b^m = b^n, then

The completeness of the real numbers,

Complete uniform space, a uniform space where every Cauchy net in converges .Complete measure, a measure space where every subset of every null set is measurable. Completeness, a statistic that does not allow an unbiased estimator of zero. Completeness a notion that generally refers to the existence of certain suprema or infima of some partially ordered set.

Exponentiation to real powers can be defined in two equivalent ways, extending the rational powers to reals by continuity , or in terms of the logarithm of the base and the exponential function. The result is always a positive real number, and the identities and properties shown above for integer exponents remain true with these definitions for real exponents. The second definition is more commonly used, Then it is generalizes straightforwardly to complex exponents.

The exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation the base and n is the power; this is pronounced as "b to n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base.

The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices.

Then: m = n, provided that b ≠ 0

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Answer:

Step-by-step explanation:

For a function g(x) = aˣ the domain is (-∞, ∞) and tha range is (0,∞)

For \(f(x)=a^{(x+h)} +k\) the h means moving function g(x)=aˣ along X-axis {the domain doesn't change as it is R} and the k means moving function g(x)=aˣ along Y-axis {the begining of the range moves from 0 to k}

The annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

To determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (6.63%)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (8)
Plugging in the values, we have:
A = 1200(1 + 0.0663/365)^(365*8)
Calculating this, we get A ≈ $1,968.49.
To find the annual percentage yield, we need to find the interest earned:
Interest = A - P = $1,968.49 - $1200 = $768.49
Now, we can find the annual percentage yield using the formula:
Annual percentage yield = (Interest / P) * 100
Plugging in the values, we have:
Annual percentage yield ≈ ($768.49 / $1200) * 100 ≈ 64.04%
Therefore, the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

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Answer:

50 hours a week

Step-by-step explanation:

10 times 5

Answer:

50

Step-by-step explanation:

The fabric needed for both pieces is 94/12 yards

Fractions are ratio of two integers. Fractions are written in the form of a/b.

Given the following parameters

Measure of dress fabric = 4 1/4 yards

If the matching jacket requires 2/3 yards less fabric, the amount of the other fabric is (17/4 - 2/3) = 17(3)-2(4)/12= 43/12 yards

Determine the total fabric.

Total fabric = 17/4 + 43/12

Total fabric = 51+43/12

Total fabric = 94/12

Hence the fabric needed for both pieces is 94/12 yards

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Answer:

The answer would be 80.

Step-by-step explanation:

First you want to add 16 and 24.

Next you want to multiply that answer by 2.

Then you have your answer and I hope this helps

Answer:

49

Step-by-step explanation:

7^2=49

We can rewrite the above expression as:(1+x)⁽ᵏ⁺¹⁾ ≥ 1 + (k+1)x

this shows that the statement holds true for k+1.

(a) to prove the statement (1+x)ⁿ ≥ 1 + nx for all natural numbers n, we will use the principle of mathematical induction.

step 1: base casefor n = 1, we have (1+x)¹ = 1 + x, which satisfies the inequality. so, the statement holds true for the base case.

step 2: inductive hypothesis

assume that the statement holds for some arbitrary positive integer k, i.e., (1+x)ᵏ ≥ 1 + kx.

step 3: inductive stepwe need to prove that the statement holds for the next natural number, k+1.

consider (1+x)⁽ᵏ⁺¹⁾:

(1+x)⁽ᵏ⁺¹⁾ = (1+x)ᵏ * (1+x)

using the inductive hypothesis, we know that (1+x)ᵏ ≥ 1 + kx.so, we can rewrite the above expression as:

(1+x)⁽ᵏ⁺¹⁾ ≥ (1 + kx) * (1+x)

expanding the right side, we get:(1+x)⁽ᵏ⁺¹⁾ ≥ 1 + kx + x + kx²

rearranging terms, we have:

(1+x)⁽ᵏ⁺¹⁾ ≥ 1 + (k+1)x + kx²

since k is a positive integer, kx² is also positive. step 4: conclusion

by the principle of mathematical induction, we can conclude that the statement (1+x)ⁿ ≥ 1 + nx holds for all natural numbers n.

(b) i'm sorry, but it seems that part (b) of your question is incomplete. could you please provide the missing information or clarify your question?

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okay well for a) the line is perpendicular meaning that it need to go the opposite way of 2/3x+6 so in the new equation would have a negative value times x. also when you are trying to find a perpendicular line i believe you use the inverse of the slope meaning that you would have -3/2 time x. Then you  know that the line goes through (-6,4) so you just replace x with -6, add a varible (for example n) and then set the equation equal to 4 since 4 should be the y value that you get when you plug in 4. so it should look like

(-3/2)-6+n=4   you're doing this so that you can figure out the x intercept. Move the n to the right and subtract 4 from both sides, and then solve the numbers on the left. (-3/2)-6 =9 and then 9-4=5 so the y intercept you get is five. then the new eqaution you shoud have is (-3/2)x-5=y

b.) well the x values are both positive meaning that you subtract so there is a distance of 2 units between then and the y values have a negative number and a positive number meaning you add so there is a distance of 5. The slope should be rise over run so the slope is 5/2 and then you can plug in a value of x to find the y intercept. lets use (6,-3) so

(5/2)6+n=-3. isolate the variable and tadaa you get a y intercept of -18. so the equation for the second one is (5/2)x-18=y

Answer: 254.34

Step-by-step explanation:

The equation for area is: \(r^{2} * \pi\)

So you find  9 squared which is 81. Then, you multiply it by pi(using 3.14). This equals 254.34

Using the given information, the volume of the rectangular prism is 6,048 cubic units.

A rectangular prism is a three-dimensional geometric shape that has six rectangular faces, each with an identical size and form.

To compute the volume of a rectangular prism, multiply the length (L), width (W), and height (H).  

In this case, we are given:

L = 18

W = 21

H = 16

Volume = L × W × H

= 18 × 21 × 16

= 6,048 cubic units

Therefore, the volume of the rectangular prism is 6,048 cubic units.

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Step-by-step explanation:

Image 1:

Blank 1: (0,5)

Blank 2: (5,0)

Blank 3: (0,-5)

Blank 4: (-5,0)

Image 2:

C, Both B and D only have one line of symmetry. Choice A has more than 2 because you can evenly split the kite by its vertices and its lengths.

Image 3:

B, a regular quadrilateral is named this way because it contains both the point and linear symmetry. By definition, a regular quadrilateral must have 4 equal sides and angles and must have its diagonals bisect each other.

Image 4:

B, Point symmetry only. This is because when flipped upside down, the shape would still look the same. This would not be rotational symmetry because it does not look 100% like the original after rotating it to a certain degree.

Answer:

Slope: 1

Y-intercept: -1

Step-by-step explanation:

The line touches the y-axis at -1, and using rise over run for the slope, it would be 1, since you go up 1 unit and move to the right 1 unit. 1/1 which is our rise/run would be 1 and that would make the slope 1.

I hope it helps! Have a great day!

bren~

Answer:

4 pieces

Step-by-step explanation:

To perform the calculation, it's easier for both values to have the same denominator.

2/3 yards is the same as 4/6 yards.

Now we have two values with the same denominator: 4/6 and 1/6.

(4/6) / (1/6) = 4.

Answer: 7m⁵ -3m³ - 3

Working:

= (6m⁵ + 3 - m³ - 4m) -(-m⁵ + 2m³- 4m +6)

= 6m⁵ + 3 - m³ - 4m +m⁵-2m³+4m - 6

= 6m⁵ + m⁵-m³ -2m³ -4m + 4m - 6 +3

= 7m⁵ -3m³ - 3

Answered by Gauthmath must click thanks and mark brainliest

Answer:

b

Step-by-step explanation:

Answer:0.78

Step-by-step explanation:

Answer:

6l², where l is the length of one side.

If the side is increased 10 times,

6(10l)²

=100 x6l²

The surface area increases 100 times. Thus, the new surface area is

272 * 100

= 27,200 sq in

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

cuz me smart no i did the question and its right

Answer:

12

Step-by-step explanation:

In an equation left side = right side.

Answer:

5.830952

Step-by-step explanation:

Distance Equation Solution:

d=(−3−(−8))2+(4−7)2

√d=(−3−(−8))2+(4−7)2

d=(5)2+(−3)2

√d=(5)2+(−3)2

d=25+9

√d=25+9

d=3–√4d=34

d=5.830952

The score needed on the final exam to achieve a C grade is 79.33, rounded to 2 decimal places.

Homework is worth 30% of the grade, which is also a significant portion. The average homework score is 90, which means the average of all homework scores is 90.

Test reviews are only worth 5% of the grade, so they have the smallest impact on the overall average. The average test review score is 72, which means the average of all test review scores is 72.

Finally, the final exam is worth 15% of the grade, and we need to find out what score is needed on the final exam to achieve a C grade, which is 72%.

To calculate the overall average, we can use the weighted average formula.

Overall Average = (Tests Average x 0.5) + (Homework Average x 0.3) + (Test Reviews Average x 0.05) + (Final Exam Score x 0.15)

Substituting the values we know, we get:

Overall Average = (59 x 0.5) + (90 x 0.3) + (72 x 0.05) + (Final Exam Score x 0.15)

Simplifying this equation, we get:

Overall Average = 29.5 + 27 + 3.6 + (Final Exam Score x 0.15)

Overall Average = 60.1 + (Final Exam Score x 0.15)

To get a C grade, the overall average needs to be 72%. So we can set up an equation and solve for the Final Exam Score:

72 = 60.1 + (Final Exam Score x 0.15)

Solving for Final Exam Score, we get:

Final Exam Score = (72 - 60.1) / 0.15

Final Exam Score = 79.33

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Answer:

$45

Step-by-step explanation:

Answer:

the battery rate is 6.5

Step-by-step explanation:

Answer:

2 percent per minute

Step-by-step explanation:

The rate at which the battery was charged is equivalent to the rate of change of this relationship. In linear relationships, the rate of change is represented by the slope of the line. We can calculate this slope from any two points on the line. Two points whose coordinates are clearly visible from the graph are (0,40) and (5,50). Now, to find the slope, let's take the ratio of the corresponding differences in the y-values and the x-values: 50-40/5-0=10/5=2. The slope of the line is 2, which means the battery was charged at a rate of 2 percent per minute.

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Random variable and its functions provides a solid foundation for analyzing data, making predictions, performing statistical analyses, and making informed decisions across a wide range of fields and applications.

Knowing the distribution of a random variable and its functions can provide several benefits and insights in various fields, including statistics, probability theory, and data analysis. Here are some of the gains you can achieve by understanding the distribution of a random variable and its functions:

Probability calculations: The distribution of a random variable provides information about the probabilities associated with different outcomes or events. By knowing the distribution, you can calculate probabilities of specific events occurring, determine the likelihood of certain values, and make predictions about the variable's behavior.

Statistical inference: Understanding the distribution of a random variable is crucial for statistical inference. It allows you to perform hypothesis testing, estimate parameters, and construct confidence intervals. With this knowledge, you can make informed decisions and draw conclusions about the population based on the sample data.

Model selection and fitting: In many cases, random variables are assumed to follow specific distributions (e.g., normal, exponential, Poisson). By knowing the distribution, you can select an appropriate model that accurately represents the data. This is particularly important in regression analysis and other modeling techniques.

Data analysis and interpretation: The distribution of a random variable and its functions provide insights into the characteristics and properties of the data. You can examine measures such as the mean, variance, skewness, and kurtosis to understand the central tendency, spread, and shape of the data. This knowledge helps in interpreting the data and drawing meaningful conclusions.

Risk assessment and decision-making: In finance, insurance, and other risk-related fields, understanding the distribution of random variables is crucial. It enables the assessment of potential risks, calculation of expected values and variances, and the determination of optimal strategies. This information aids decision-making and risk management processes.

Simulation and modeling: The distribution of a random variable is often utilized in simulations and modeling exercises. By incorporating the appropriate distribution, you can generate random samples that mimic the behavior of the variable. This allows you to explore various scenarios, assess system performance, and evaluate the impact of different factors.

Overall, understanding the distribution of a random variable and its functions provides a solid foundation for analyzing data, making predictions, performing statistical analyses, and making informed decisions across a wide range of fields and applications.

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Answer:

A

Step-by-step explanation:

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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