A high school track​ team's long jump record is 24 ft 2 1/4 in This​ year, Hal​'s best long jump is 23 ft 9 1/2 in If long jumps are measured to the nearest quarter​ inch, how much farther must hal jump to break the​ record?

There are 303600 ways to choose 4 members of the club to serve on an executive committee.

A permutation is the act of putting things or numbers in a certain order. Combinations are a method of picking things or numbers from a set of objects or collections without regard for their order.

No. of members = 25

We are supposed to find the no. of ways to choose a president, vice-president, secretary, and treasurer of the club

No. of posts = 4

The order matters here since each member will get different posts .

So, we will use permutation over here

formula - n P r = n! / (n-r)!

n = 25

r = 4

using calculator

25 P 4 = 303600
Hence there are 303600 ways to choose 4 members of the club to serve on an executive committee.

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11.1% of porcelain tile has strength up to 185 per square inch, while 6% has strength of 206.4 per square inch.

a. To find the percent of its popular porcelain tile that will have breaking strengths at most 185 pounds per square inch, we can use the Z-score formula. The Z-score formula is Z = (x - μ) / σ. In this problem, x is 185, μ is 200, and σ is 6.2. Plugging these values into the formula, we get Z = -2.42. To find the percent of tiles that have a breaking strength of at most 185 pounds per square inch, we can use a Z-score table. Looking up -2.42 on the Z-score table, we get a probability of 0.011, or 11.1%.

Z = (x - μ) / σ.

x=185

μ =200

σ = 6.2

Z = -2.42

Hence, probability = 0.011, or 11.1%.

b. The strongest 6% of its popular porcelain tile will have a breaking strength of 206.4 pounds per square inch. To find this value, we can use the Z-score formula again. This time, we will use a positive Z-score of 1.645, which corresponds to a probability of 0.06. Plugging this value into the formula, we get,

x = μ + (Z * σ).

Thus, x = 200 + (1.645 * 6.2) = 206.4.

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The percent error between the actual water quantity and the estimated water quantity for aquarium is 16.13%.

What is percent error?

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.

Let x be percent error in the quantity of water for aquarium. The estimated quantity of water was 520 cubic feet and the actual quantity of water was needed 620 cubic feet. Then x can be determined  as:

\(x=\frac{Difference\;of\; water\; quantity}{Actual \;quantity\; of\; water} \times 100\)

   \(=\frac{ 620-520}{620} \times100\\\\=\frac{100}{620} \times 100\\\\=16.13 \%\)

Therefore, the percent error between the actual water quantity and the estimated water quantity for aquarium is 16.13%.

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The error interval for x when rounded to one decimal place as 8.7 is (8.65, 8.74).

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,

The rounded value of 8.7 is the midpoint of the error interval and any number between 8.65 and 8.74 would round to 8.7 when rounded to one decimal place.

Thus, the error interval for x when rounded to one decimal place is (8.65, 8.74).

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The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.

To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:

z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906

z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849

Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.

To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:

P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.

As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.

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Answer:

24,282,000 visitors (total)

Step-by-step explanation:

Add these two counts together:

8 306 000

15 976 000

------------------

24 282 000 total number of visitors

Answer:

Add the number of France visitors and Australia visitors and you will get...

Step-by-step explanation:

24,282,000 visitors

Answer:

a)   x² + 6x + 9

Step-by-step explanation:

When we square something, we multiply it by itself:

⇒ (x + 3)² = (x + 3)(x + 3)

Using the FOIL method:  (a + b)(c + d) = ac + ad + bc + bd

⇒ (x + 3)(x + 3) = x² + 3x + 3x + 9

                        = x² + 6x + 9

a.

\(\huge{{x}^{2} + 6x + 9}\)

Step-by-step explanation:

Using Binomial Theorem:

\(\boxed{{(a+b)} ^n= \sum_{k=0}^{n}\binom{n}{k} a^{n-k}b^{k}}\)

.

.

.

\((a+b) ^2 =a^{2} + 2ab +b^{2} \)

The answer seems to be \(x^{2} + 6x + 9\)...

Answer:

If they are seperate, then it is

-149

-3,861

106

If that is a whole equation, then the answer is

-297,506

Answer:

-13x6-(68+3)= -149
54-(-87x45)=  -3969
75+31=106

Step-by-step explanation:

In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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Answer:

500

Step-by-step explanation:

50*10=500

Answer: 1

To find the number with the value x10, multiply 50 by 10.

50 x 10 = 500

500 is in the hundreds place. In the number shown above, 1 is in the hundreds place.

Answer to question = 1

Best of Regards!

Answer:

8/81

Step-by-step explanation:

8/18 x 4/18 = 32/324 = 8/81

The probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

It is given that in a bag of M&MS there are 4 green, 6 yellow, and 8 blue candies.

The probability for blue = 8/18

The probability for green = 4/18

The probabilities of drawing a blue then green if you replace the candy after the draw will be calculated as below:-

Probability = 8/18 x 4/18

Probability = 32/324

Divide the number 32 by 324 to get the probability.

Probability = 8/81

Therefore, the probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.

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Answer: 7.59

Step-by-step explanation: I added all of the miles he traveled up together. ( don't overthink questions like this)

True. In an inductive argument, the conclusion of the inductive step, p(n+1), is demonstrated by substituting n+1 for n in the statement p(n). Inductive reasoning involves making generalizations based on specific instances or patterns observed. In mathematical induction, we aim to prove a statement is true for all natural numbers or a particular subset of numbers.

The process of mathematical induction consists of two steps: the base case and the inductive step. In the base case, we show that the statement p(1) or p(n0) is true for the lowest value in the considered range, typically n=1 or a specific starting value n0. The inductive step involves assuming the statement p(n) is true for some arbitrary value n=k, and then proving that p(k+1) is also true under this assumption. This is achieved by substituting n+1 for n in the statement p(n).

By confirming both the base case and inductive step, we can conclude that the statement p(n) is true for all natural numbers or the specified subset of numbers. Thus, it is correct to say that the conclusion of the inductive step, p(n+1), is shown by substituting n+1 for n in the statement p(n).

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a) The formula for the temperature of the object at any time t is T(t) = 70 + 230e^(-0.0866t)

b) After 3 hours, the temperature of the object will be approximately 136.7°F.

(a) The temperature of the object as it cools can be modeled by Newton's law of cooling, which states that the rate of cooling of an object is proportional to the difference between its temperature and the ambient temperature. Let T(t) be the temperature of the object at time t, and let T' be the ambient temperature (70°F in this case). Then we have:

dT/dt = k(T - T')

where k is a constant of proportionality. To solve this differential equation, we can separate variables and integrate:

1/(T - T') dT = k dt

ln|T - T'| = kt + C

T - T' = e^(kt+C) = Ce^kt

where C = e^C is an arbitrary constant. Using the initial conditions T(0) = 300°F and T(1/11) = 200°F, we can find C and k:

C = (T(0) - T') = 230

k = ln((T(1/11) - T') / C) / (1/11) = -0.0866

Therefore, the formula for the temperature of the object at any time t is:

T(t) = 70 + 230e^(-0.0866t)

(b) To find the temperature of the object after 3 hours, we can simply plug in t = 3 into the formula:

T(3) = 70 + 230e^(-0.0866(3)) ≈ 136.7°F

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Answer:

\(n=\{0,\: 4\}\)

Step-by-step explanation:

\(|3n-6| = 6\\\therefore 3n - 6 = \pm 6\\\therefore 3n = 6 \pm 6\\\therefore 3n =6+6\:\: or\:\: 3n = 6-6\\\therefore 3n =12\:\: or \:\:3n = 0\\\\\therefore n =\frac{12}{3}\:\: or\:\: n =\frac{0}{3}\\\\\therefore n = 4 \:\: or\:\: n = 0\\\\\therefore n=\{0,\: 4\}\\\)

The statement (3) The probability of occurrence in a given unit of time has a fixed number of trials is not true about the Poisson distribution.

In the Poisson distribution, the number of trials is not fixed, and each event in the Poisson distribution is considered a trial. The Poisson distribution is a type of discrete probability distribution that is used to calculate the probability of a certain number of events occurring in a specified interval of time or space. It is often used to model situations where the number of occurrences is rare but the average occurrence rate is known. The Poisson distribution is described by a single parameter, λ (lambda), which is equal to the expected number of occurrences in the specified interval. The Poisson distribution can also be used to calculate the probability of a certain number of events occurring over a given area, volume, or any other unit of measurement. This makes it a versatile tool in many different fields, including physics, biology, and finance. It is worth noting that the Poisson distribution assumes that the events are independent of each other, meaning that the occurrence of one event does not affect the probability of the occurrence of another event.

In conclusion, the statement (3) The probability of occurrence in a given unit of time has a fixed number of trials is not true about the Poisson distribution. The number of trials is not fixed, and each event in the Poisson distribution is considered a trial.

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Answer:

125

Step-by-step explanation:

They want you to work out  \(\\\frac{5 *10^{6} }{4*10^{4} }\)

5 x 1000000/ 4 x 10000

\(\frac{5000000}{40000}\) = 125

Please let me know if it's not correct.

Hope this helps :)

Answer:

60

Step-by-step explanation:

100%/5%=20

20*3=60

Answer:

1766 using 3.14 for pi

1767 using the pi button

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

we need to know the radius

r =d/2 = 15/2 = 7.5

V = 4/3 (pi)( 7.5)^3

V =562.5 pi

Approximating pi by 3.14

V = 562.5 (3.14)

V =1766.25

To the nearest whole number

V = 1766

If you use the pi button

1767.14586

To the nearest whole number

1767

Answer:

\(V=1767\)

Step-by-step explanation:

Step 1:  Find the volume of the sphere

Volume of a Sphere:  \(V=\frac{4}{3}\pi r^{3}\)

Find the radius

\(Radius = Diameter / 2\)

\(Radius = 15 / 2\)

Plug in the values and solve

\(V=\frac{4}{3}\pi * \frac{15}{2}^{3}\)

\(V=\frac{4}{3}\pi * \frac{3375}{8}\)

\(V=\frac{1125}{2}\pi\)

\(V=1767\)

Answer:  \(V=1767\)

Answer:

-395

Step-by-step explanation:

n - 55 = 25 * (-18)

n - 55 = -450

so

n = -450 + 55 = -395

Answer:

n - 55 = 25 x (-18)

n - 55 = -450

+55        +55

n = -395

Answer:

Domain:[-4,∞)

Range:[0, ∞)

Thus, choice C is the exact answer

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

\((p)(m+m+m)\\(5)(1+1+1)\\(5)(3)\\15\)

Answer:

A reflection over y=-x

Step-by-step explanation:

Im almost positive

The statement that is true about the proportional relationship of the graph is;

C: Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

We are told that the equation c equals one fourth times s. This is expressed as;

c = ¹/₄s

Where;

c is the number bags of cements

s is the number of bags of sands required to make concrete.

We can see that the number of bags of cements is directly proportional to the number of bags of sands required to make concrete.

In this question, the number of bags of sand is the independent variable while the number of bags of cement is the dependent variable.

From the graph attached, we see that the number of bags of sand is on the y-axis, while the number of bags of cement is on the x-axis.

Hence, the correct statement is option (C) Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

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Answer:

Hey there!

A line perpendicular to y=3x+5 would have a slope of -1/3.

Thus, the problem now becomes to write a line in point slope form with a slope of -1/3, and that passes through (4, -1)

y+1=-1/3(x-4), would be your answer.

Hope this helps :)

Answer:

both

Step-by-step explanation:

given sss, you will need to use Law of Cosines.

However, one you get one of the angles, the easiest way to solve for the second angle is to just use law of sines.

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

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