A rucksack can hold a maximum of 5.5 kg. A particular textbook has a mass of 590 g. What is the maximum number of these textbooks that the rucksack can hold?

The x-component of fluid acceleration in terms of x and y is 2.

To find the x-component of fluid acceleration (ax), we need to differentiate the x-component of velocity (u) with respect to time.

However, the given equations provide the expressions for u in terms of x and y, not time. Therefore, we need to differentiate u with respect to x and y instead.

Given: u = 2x + y^2

To find the x-component of fluid acceleration (ax), we differentiate u with respect to x while treating y as a constant:

ax = ∂u/∂x = ∂(2x + y^2)/∂x = 2

The x-component of fluid acceleration, ax, is simply 2.

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Answer:

The cost of an adult ticket is 7.

Step-by-step explanation:

4t + 21 = 49

    - 21 = 28

4t = 28

/4 = 7

t = 7

Option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

The given rectangle is ABCD.

The length of segment AB is 9x-16 units

The length of segment AD is 1.5x+42 units

We have to find the inequality which represents the  length of segment AB is greater than  length of segment AD

> is the symbol used to represent greater than

AB>AD

9x-16>1.5x+42

Hence, option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

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The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( \(e^{(-λ)\) * \(λ^k\)) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = (\(e^{(-72.8)\)* \(72.8^(70)\)) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

\(Z = (X - mean) / \sqrt{(variance)\)

Fοr X = 70, we have:

Z = (70 - 1.4) / \(\sqrt{(1.4)\) ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

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Answer:

58.50

Step-by-step explanation:

Multiply 50 and .17 which equals 8.5 then add that to 50.

The amount of money in the account in December with a rate of 17% of the initial amount of $50 is $58.5.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

A teenager puts $50 into an investment account in January.

Let, he deposited on first January.

If by December the balance in the account increases by 17%,

Let the amount by the 31 first of December will be

Then the amount will be given as

\(A = P (1 + \dfrac{r}{100})^t\)

P = $50

r = 17%

t = 1

Then we have

\(\rm A = 50(1 + \dfrac{17}{100})^1\\\\A = 50(1 + 0.17)\\\\A = 50 * 1.17 \\\\A = 58.5\)

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The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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The probability that the mean daily precipitation will be 0.098 inches or less for a random sample of 40 November days is 0.355.

Step 1: Calculate the standard error of the mean (SEM):

SEM = σ / √n

where σ is the standard deviation and n is the sample size.

In this case, σ = 0.06 inches and n = 40.

SEM = 0.06 / √40

Step 2: Standardize the desired value using the z-score formula:

z = (x - μ) / SEM

where x is the desired value, μ is the mean, and SEM is the standard error of the mean.

In this case, x = 0.098 inches, μ = 0.10 inches, and SEM is calculated in Step 1.

Step 3: Find the cumulative probability associated with the standardized value using a standard normal distribution table or calculator.

P(X ≤ 0.098) = P(Z ≤ z)

where Z is a standard normal random variable.

Step 4: Round the final probability to at least three decimal places.

By following these steps and using the Central Limit Theorem, we can calculate the probability that the mean daily precipitation will be 0.098 inches or less for a random sample of 40 November days. The probability is obtained by standardizing the value using the z-score and finding the cumulative probability associated with it in the standard normal distribution.

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Answer:

7.8

Step-by-step explanation:

The best estimate of the quotient of 523 divided by 67 is 7 and the remainder is 54.

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

The number 523 divided by 67,

When you first divide the 523 by 67 then the quotient will be 7 and the remainder will be 54.

The above phrase can be written as,

523 ÷ 67 = 67 × 7 + 54

Thus, the quotient is 7 and the reminder is 54.

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Answer:

They aren't

Step-by-step explanation:

9/25 / 3= 3/8.3

3/10 x 3 = 9/30

none of those equal to each other

Answer:

6

Step-by-step explanation:

1 /4 x^2 = 9     (Given)         Multiply both sides of the equation by 4

x^2 = 36               sq rt both sides

x = 6

Check the picture below.

Answer:

1.

1) The area of the sector is 168.8π mi²

2) The area of the sector is 529.9 mi²

2.

1) The area of the sector is 42.3π in²

2) The area of the sector is 132.7 in²

Step-by-step explanation:

The formula of the area of a sector in a circle is A = \(\frac{x}{360}\) × π r², where

1.

∵ The central angle subtended by the arc of the circle is 270°

∴ x = 270°

∵ The radius of the circle is 15 mi.

∴ r = 15

→ Substitute them in the formula of the area above

∵ A = \(\frac{270}{360}\) × π (15)²

∴ A = 168.75π mi²

→ Round it to the nearest tenth

∴ A = 168.8π mi²

1) The area of the sector is 168.8π mi²

∵ π = 3.14

∴ A = 168.75 × 3.14

∴ A = 529.875 mi²

→ Round it to the nearest tenth

∴ A = 529.9 mi²

2) The area of the sector is 529.9 mi²

2.

∵ The central angle subtended by the arc of the circle is 90°

∴ x = 90°

∵ The radius of the circle is 13 in

∴ r = 13

→ Substitute them in the formula of the area above

∵ A = \(\frac{90}{360}\) × π (13)²

∴ A = 42.25π in²

→ Round it to the nearest tenth

∴ A = 42.3π in²

1) The area of the sector is 42.3π in²

∵ π = 3.14

∴ A = 42.25 × 3.14

∴ A = 132.665 in²

→ Round it to the nearest tenth

∴ A = 132.7 in²

2) The area of the sector is 132.7 in²

Answer:

68%

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

calculate the two deposits add them and take them away from the total. find the percentage of the remaining.

Answer:

90% Confidence Interval for difference in Proportion = (-0.106, -0.034)

Step-by-step explanation:

The formula for difference in proportions is given as:

p1 - p2 ± z × √p1(1 - p1)/n1 + p2(1 - p2)/n2

p = x/n

In a 2017 pre-Hurricane Irma

survey, 486 out of 1,080 adults answered in the affirmative.

x1 = 486

n1 = 1080

p1 = 486/1080 = 0.45

In a 2017 post- Hurricane Irma survey, 546 out of 1,050 answered affirmatively.

x2 = 546

n2 = 1050

p2 = 546/1050 = 0.52

Z score for 90% confidence interval = 1.645

Confidence Interval

=0.45 - 0.52 ± 1.645 × √0.45 (1 - 0.45)/1080 + 0.52(1 - 0.52)/1050

= -0.07 ± 1.645 × √0.0002291667 + 0.0002377143

=-0.07 ± 1.645 × √(0.000466881)

= -0.07 ± 1.645 × 0.0216074293

= -0.07 ± 0.0355442212

Confidence Interval

-0.07 - 0.0355442212

= 0.1055442212

Approximately = -0.106

-0.07 + 0.0355442212

= -0.0344557788

Approximately = -0.034

Therefore, 90% Confidence Interval for difference in Proportion = (-0.106, -0.034)

Answer:

Step-by-step explanation:

0.70x + 50 = 0.20x + 120

0.50x + 50 = 120

0.50x = 70

x = 140 miles

Upon answering the query  As a result, the following is the system of equations' solution: x = -150, y = 120.

An equation in math is an expression that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between each of the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The sign and only one variable are frequently the same. as in, 2x - 4 equals 2, for instance.

To solve

\(Y/4 - x/5 = 6 ........ (1)\\x/15 + y/12 = 0 ....... (2)\\\)

After using the substitution approach to find the value for one of the variables, we can use that value to find the value for the other variable.

We can solve for x in terms of y using equation (2):

\(x = - (5/4) y ........ (3)\)

Equation (1) may now be changed to an equation in terms of y by substituting equation (3) for equation (1):

\(y/4 - (-5/4)y/5 = 6\\5y - 4y = 120\\y = 120\\x = - (5/4) (120) = -150\\\)

As a result, the following is the system of equations' solution:

x = -150, y = 120.

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Answer:

36

Step-by-step explanation:

Just add the students with doing this: number of studentsxsiblings

Answer:

For number one count all dots and for two start counting from 4 siblings

Step-by-step explanation:

Answer I think

:randomly survey six grade students in the school cafeteria

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Randomly surveying 6th graders in the school cafeteria would give jacob valid results because A wouldn't be reliable, because he just wants 6th graders, and B and D would be selective as it would be inside a football store, implying that most 6th graders in there would be tending towards football, and D would be inside a tennis shop, which would imply that most 6th graders there would prefer football. Therefore, the cafeteria would yield the most reliable results.

Answer:

since it is isosceles right triangle, both legs = 5 inches.

using pythagoras theorem,

hypotenuse^2 = 5^2 +5^2 = 25+25 = 50 taking square root on both sides, hypotenuse = sqrt 50 = 5 sqrt 2 or 7.071

rounded to nearest tenth, length of hypotenuse is 7.1 inches.

Step-by-step explanation:

yan lang alam ko ʘ‿ʘ

Answer: 15.5 inches

Step-by-step explanation:

We’re accepting that legs = 11 inches.

hypotenuse^2 = 11^2+ 11^2 = 121+121 = 242 taking square root on both sides, hypotenuse = √242 => 11√2 or 15.5 inches.

Answer:

14.65

9.2

Step-by-step explanation:

For this question I will be using SOH CAH TOA and I will assume that you know that that means

For the first use I have the adjacent side and need to solve for the hypotonouse which means I will be using CAH

which means that cos35=12/x

solve for x and get 14.65

For the second one I have the opposite side and need the adjacent so I will use TOA

Tan41=8/x

I will do the same thing for the last one and get x=9.2

 \( L_{1} \) does not belong to the regular language class.

The language \( L_{1}=\left\{01^{a} 0^{a} 1 \mid a \geq 0\right\} \) consists of strings with a single '01', followed by a sequence of '0's, and ending with a '1'.

The language \( L_{1} \) cannot be described by a regular expression and is not a regular language. In order for a language to be regular, it must be possible to construct a finite automaton (or regular expression) that recognizes all its strings. In \( L_{1} \), the number of '0's after '01' is determined by the value of \( a \), which can be any non-negative integer. Regular expressions can only count repetitions of a single character, so they cannot express the requirement of having the same number of '0's as '1's after '01'. This makes \( L_{1} \) not regular.

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Answer:

Volume is the amount of space an object occupies. To determine the volume of any rectangular object, multiply the measurements of length, width, and height.

Volume = Length × Width × Height

Calculate the volume of this rectangular object.

Length = 3 cm

Width = 3 cm

Height = 12 cm

Volume = l × w × h

Volume = 3 cm × 3 cm × 12 cm

Volume = 108 cm3

Notice that the units for volume are cubic centimeters (cm3).

So 8 ÷ 25 = 0.32 and the units would be g/ cm3 . Other units of density could be g/L or g/ml or mg/ cm3 or kg/ m3 and the list could go on and on. Any unit of mass divided by any unit of volume.

Step-by-step explanation:

hope this helpa

In this scenario, we are considering if-then statements. Looking at the given statement,

p = angle A is an obtuse angle

q = the measure of angle A = 75 degrees

A statement of if q, then p would be

q - p

where - is an arrow pointing to the right

Looking at the picture, the symbol before p represents negation. It tells us that

if q, then not p. By translation, the correct answer would be

If the measure of angle A = 75 degrees, then angle A is not an obtuse angle

The height is 7.04 feet at the rafter's peak that makes an angle of 28° and 15 feet long.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Length of rafter = 15 feet,

Angle made by rafter with the horizontal = 28°

Apply sin formula to determine the length x of the rafter,

sinθ = x / 15

sin28°  = x / 15

0.469 = x / 15

x = 7.04

The height of the rafter is 7.04.

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Answer:

Step-by-step explanation:

To determine if an observation is an outlier, we need to compute its z-score and see how far it deviates from the mean in terms of standard deviations.

The formula for z-score is:

z = (x - μ) / σ

where x is the observation, μ is the mean, and σ is the standard deviation.

For option (a), the observation is 150, so the z-score is:

z = (150 - 100) / 10 = 5

For option (b), the observation is 100, so the z-score is:

z = (100 - 100) / 10 = 0

For option (c), the observation is 90, so the z-score is:

z = (90 - 100) / 10 = -1

An observation is considered an outlier if its z-score is greater than 3 or less than -3.

Therefore, the only observation that might be an outlier is option (a) with a z-score of 5. The other two options have z-scores within the range of -3 to 3 and are not considered outliers.

So the answer is (a) 150.

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Answer:

I will help

Step-by-step explanation:

Only relations a, c and e are functions.

Here, we are given 6 relations and we need to determine which of them are function.

The basic property of a function is that a function from a set X to a set Y assigns to each element of X exactly one element of Y.

a. In this relation all elements in A are assigned only one value in B, thus, this relation is a function.

b. In this relation -1 in A has two values in B, that is, 5 and 2. Thus, this relation is not a function.

c. In this relation all elements of the first set are assigned only one value in set 2, thus, this relation is a function.

d. In this relation, 9 in set 1 has two values in set 2, that is, 9 and 5. Thus, this relation is not a function.

e. In this, relation, from the graph, we can see that all the x values have exactly one y value corresponding to them. Thus, the relation is a function.

f. In this relation we see that when x = 2, y can be 2 or 7. Thus, this relation is not a function.

Hence, we conclude that only relations a, c and e are functions.

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Answer:

Solution given:

m<ABD=102°

m<EBD=29°

Since BE bisects <CBD

:.

<EBC=<EBD=29°

now

we have

<ABD=<EBD+<EBC+m<ABC

substituting value

102°=29°+29°+m<ABC

m<ABC=102°-29°-29°

m<ABC=44°

Answer:

6x^8 + x^6 + 4x^4 + 0x^2 - 3

Step-by-step explanation:

Rewrite this in descending order by powers of x:

6x^8 + x^6 + 4x^4 + 0x^2 - 3x^0

or

6x^8 + x^6 + 4x^4 + 0x^2 - 3

Answer:

Volume left in the cylinder if all the cone is made full:

\(\bold{345.72 \ ml }\)

Step-by-step explanation:

Given

Radius of cylinder = 5 cm

Height of cylinder = 14 cm

Radius of cone = 6 cm

Height of cone = 20 cm

To find:

Liquid remaining in the cylinder if cone is made full from cylinder's liquid.

Solution:

We need to find the volumes of both the containers and find their difference.

Volume of cylinder is given by:

\(V_{cyl} = \pi r^2h\)

We have r = 5 cm and

h = 14 cm

\(V_{cyl} = \dfrac{22}{7} \times 5^2\times 14 = 1100 cm^3\)

Volume of a cone is given by:

\(V_{cone} = \dfrac{1}{3}\pi r^2h = \dfrac{1}{3}\times \dfrac{22}{7} \times 6^2 \times 20 = \dfrac{1}{3}\times \dfrac{22}{7} \times 36 \times 20 = 754.28 cm^3\)

Volume left in the cylinder if all the cone is made full:

\(1100-754.28 =345.72 cm^3\ OR\ \bold{345.72 \ ml }\)