an aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. the aquarium is filled with water to a depth of 37 cm. a rock with volume $1000 \text{cm}^3$ is then placed in the aquarium and completely submerged. by how many centimeters does the water level rise? express your answer as a decimal to the nearest 100th.

a. The probability of guessing a wrong answer is 4/5

Since there are three guesses, the probability of the first 2 guesses being wrong and the 3rd being correct can be calculated using the multiplication rule as follows: P(2 wrong and 1 correct) = (4/5)^2 * 1/5 = 0.128.

b. The complete list of possibilities for 2 wrong and 1 correct is: WWC, WCW, CWW.

The probability of each can be calculated using the multiplication rule as follows: P(WWC) = (4/5)^2 * 1/5 = 0.128, P(WCW) = (4/5) * (1/5) * (4/5) = 0.128, and P(CWW) = 1/5 * (4/5)^2 = 0.128.

c. The probability of getting exactly one correct answer when 3 guesses are made is the sum of the probabilities of the three possible outcomes of 2 wrong and 1 correct, which is 0.128 + 0.128 + 0.128 = 0.384.

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The width of the automobile parking space is 52.8 meters.

First, we want to convert the duration of the second one base from centimeters to meters

3760 cm = 37.6 m

Subsequent, we're suitable to use the system for the vicinity of a trapezoid

A = ( b1 b2) h/ 2

In which b1 and b2 are the lengths of the two bases, h is the height( or range) of the trapezoid, and A is the area.

Substituting the given values, we have

= (73.437.6) h/ 2

= 111h/ 2

Multiplying both angles through 2 and dividing by 111, we get

h = 52.8

Hence, the width of the automobile parking space is 52.8 meters.

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New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

The area of the tennis court is given by:

A = lw

where l is the length of the court and w is the width of the court.

Substituting the given values, we have:

[tex]$$260.7569 = l \cdot 10.97$$[/tex]

Solving for l, we get:

[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]

To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:

w' = w - 0.25w = 0.75w

Substituting the given values, we have:

[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]

where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:

[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]

Therefore, the new area of the court is reduced by 25%.

To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:

[tex]$w' = 0.75w$$[/tex]

Dividing both sides by w, we get:

[tex]$\frac{w'}{w} = 0.75$$[/tex]

This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

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Answer:

148.5 π

Step-by-step explanation:

Cone = 1/3 * base * height

1/3 * 22 * (9/2)^2 π = 148.5 π

the correct answer is option C: The company rejects H0, making a Type II error. In this hypothesis test, the null hypothesis H0 is that the machine produces no more than 98% high-quality candy, and the alternative hypothesis Ha is that the machine produces more than 98% high-quality candy. The significance level is α = 0.05.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true. A p-value of 0.15 is greater than the significance level of 0.05, which means that the result is not statistically significant.

However, the company is unaware that the machine is actually producing 99% high-quality candy. This means that the null hypothesis is actually false, and the alternative hypothesis is true. In other words, the machine is producing more than 98% high-quality candy.

Based on these observations, the company failing to reject the null hypothesis (option B) would be a Type II error, as it would mean that the company is not detecting a significant difference in the candy quality when, in fact, the machine is producing candy of higher quality than the null hypothesis assumes.

Therefore, the correct answer is option C: The company rejects H0, making a Type II error.

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The characteristic of a reliable scientific poll is small sampling error. The small sampling error is a characteristic of a reliable scientific poll.

What is a scientific poll?Scientific polls are surveys that gather and evaluate people's opinions or responses to questions. These surveys are done in a scientific way, implying that pollsters use scientifically proven techniques to gather responses and analyze data.A reliable scientific poll must have a small sampling error. A sampling error is the deviation of the sample mean from the population mean due to random error. The smaller the sample size, the more likely it is that the results will be imprecise. As a result, it's essential to conduct a reliable scientific poll with a sample size that is representative of the population as a whole.The option for the correct answer to this question is; (choice a) small sampling error.

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The number of claims filed by the policyholders has a poisson distribution. Therefore, the variance of the number of claims filed will be about 2.5.

We need to use the Poisson Distribution for solving the question, which is as follows:

P(x) = (λˣ/x!) × [tex]e^(-lambda)[/tex]

where is the mean value of distribution and x is the number of events we want to calculate.

If a random variable follows a Poisson distribution, its variance is equal to its mean.

So, the mean will be λ.

Let the probability of filing four claims be p1.

Then, probability of filing two claims will be ⁵p₁

We know the sum of probabilities of different events of Poisson distribution will always be equal to 1.

So,

p₁ + ⁵p₁ = 1

p₁ = 1/6

The mean number of claims is λ, which is given by:

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

The mean number of claims is λ, which is given by:

λ = ⁴p₁ + 2⁵p₁ = 2.5

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

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There will be a population of 2,097,152 rabbits after 5 years.

A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.

Given that, population of rabbits is doubling every 3 months.

That is,

5 years = 5 x 12 = 60 months

Number of doublings = 60 / 3 = 20

For every doubling, the population will be twice as large.

Thus,

P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits

Therefore, there will be approximately 2,097,152 rabbits after 5 years.

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The experimental probability of the arrow stopping over section 1 is 7/13, or 0.538.

To calculate this, you need to take the number of times the arrow stopped on section 1 (45) and divide it by the total number of times the arrow was spun (80). This can be expressed as a fraction (45/80), which can be simplified to 7/13. To convert this fraction to a decimal, divide the numerator by the denominator (7/13 = 0.538).

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To check whether the given lines are parallel, perpendicular, skew or neither, we will find their direction vectors. If the direction vectors are parallel, then the lines are parallel. If the direction vectors are perpendicular, then the lines are perpendicular. If the direction vectors are neither parallel nor perpendicular, then the lines are skew. If the direction vectors of one line is parallel to the vector joining two points of the other line, then the lines are neither parallel nor perpendicular.

Line 1:x=t−3, y=3t+8, z=5−2tThis line can be written as(r_1): r= a_1+ t u_1where r_1 is the position vector of any point on the line. a_1 = i(-3) + j(8) + k(5) = -3i + 8j + 5k is the point of intersection of the line with the coordinate axis. And u_1 is the direction vector of the line.u_1 = i + 3j - 2k

Line 2: x=2s−1, y=s−1, z=s−4This line can be written as(r_2): r= a_2+ s u_2where r_2 is the position vector of any point on the line. a_2 = i(-1) + j(-1) + k(-4) = -i - j - 4k is the point of intersection of the line with the coordinate axis. And u_2 is the direction vector of the line.u_2 = 2i + j + k Now we will find the direction vectors of the two lines and then check their properties. The direction vectors of the lines areu_1 = i + 3j - 2ku_2 = 2i + j + kSince the direction vectors are not parallel, we need to check whether they are perpendicular or not.u_1.u_2 = (i + 3j - 2k).(2i + j + k) = 2 + 3 - 2 = 3Since u_1.u_2 is not equal to zero, the two lines are neither parallel nor perpendicular to each other. Therefore, the lines are skew lines.

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Making r the subject of formula in this equation A = V²/r gives r = V²/A.

In Mathematics and Science, the centripetal acceleration of a physical object (body) can be calculated by using the following mathematical expression:

A = V²/r

Where:

In this exercise, you are required to make radius (r) the subject of formula. Therefore, by making radius (r) the subject of formula, we have the following:

Radius, r = V²/A

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Answer:

6 29 25

Step-by-step explanation:

those are the prime numbers on the 2023 feb calendar

Answer:

[tex]\frac{xa}{28}[/tex]

Step-by-step explanation:

   [tex]\frac{4x^2}{y7a^3} * \frac{a^4}{16+8x}[/tex]

= [tex]\frac{2x(2+x)}{7a^3} * \frac{a^4}{8(2+x)}[/tex]

= [tex]\frac{xa}{28}[/tex]

[tex]\frac{x^{2}a }{28}[/tex]

Explination:

Factor the numerator and the denominator and cancel the common factors

The sugar concentration would be approximately 62.5%.

To find the concentration of sugar in the solution, we need to use the formula:

In this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.

We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.

Now we can use the formula to find the concentration of sugar:

So the concentration of sugar in the solution is approximately 0.625 grams per milliliter.

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Answer:

75% correct

Step-by-step explanation:

The shopper must spend at least $444.44 to get the 10% discount.

If a shopper gets a 10% discount, it means they pay only 90% of the original price. Let's say the original spending is represented by x. Then the spending after the 10% discount would be:

d = 0.9x

Now, we know that the shopper must spend at least $400 to get the discount, so we can set up an inequality:

d ≥ 400

Substituting the expression we found for d, we get:

0.9x ≥ 400

Dividing both sides by 0.9, we get:

x ≥ 444.44

So the shopper must spend at least $444.44 to get the 10% discount.

The example of 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx is reflection Ab.

Matrices, the plural form of matrix, are the groupings of numbers, variables, symbols, or phrases in a rectangular table with varying rows and columns. These are rectangular arrays with specified operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, whereas the vertical elements are referred to as columns.

Let,

[tex]B = \left[\begin{array}{cc}0&1\\1&0&0&0\end{array}\right] , A = \left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right][/tex]

Then,

[tex]AB =\left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right] \left[\begin{array}{cc}0&1&1&0&0&0\\\end{array}\right] \\\\AB = \left[\begin{array}{cc}0&1&1&0\\\end{array}\right][/tex]

Therefore, Ab is reflection about y = x .

As U = Bx and T∘U    

A matrix is a rectangular array of integers, variables, symbols, or expressions that are defined for subtraction, addition, and multiplication operations. The number of rows and columns in a matrix determines its size (also known as the order of the matrix).          

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Answer:

a = 3

Step-by-step explanation:

since the parabola passes through (7, 27 ) then te coordinates of the point make the equation true.

substitute x = 7 and y = 27 into the equation and solve for a

27 = a(7 + 2)(7 - 6) = a(9)(1) = 9a ( divide both sides by 9 )

3 = a

Answer:

$12

Step-by-step explanation:

Cans : Dollars

6 cans : 9 dollars

DIVIDE BY 3

2 cans : 3 dollars

MULTIPLY BY 4

8 cans : 12 dollars

Hope this helps :)

Have a great day!

Answer:

fFind the sum of

4

4

​

 and

4

8

4

8

​

 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

Step-by-step explanation:

Angela's score is in the 87th percentile, which means that 87% of the scores were at or below her score.

To calculate the percentage of scores above her score, we subtract 87% from 100%. Therefore, the percentage of scores above Angela's score is 13%.

In summary, Angela's score is at or below 87% of the scores, and 13% of the scores are above her score. The percentile score indicates the percentage of scores that fall below a particular score. Therefore, Angela performed better than 87% of the test takers who took the aptitude test in accounting.

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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The list after sorting in ascending order is C) {3 17 44 69}.

Sorting means arranging the numbers in ascending or descending order based on their value. In this case, the numbers are arranged in ascending order, meaning that the smallest number comes first, followed by the next smallest number and so on.

To sort the list, we can use any sorting algorithm such as selection sort, bubble sort, insertion sort, or quicksort. One simple way to sort the list is to use the built-in sort function provided by most programming languages. The sort function takes the list as input and returns a new list with the elements sorted in ascending order.

In summary, the sorted list in ascending order is {3 17 44 69}, and we can use sorting algorithms or built-in functions to sort a list in ascending or descending order based on our requirement.

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Answer: 500 cm

Step-by-step explanation:

multiply by 0.5 by 10000

The probability of drawing either a queen or a diamond is 15/52

To determine the probability of drawing either a queen or a diamond, we have to find the sum of the probabilities of drawing a queen and drawing a diamond, then subtract the probability of drawing both a queen and a diamond. This is because the probability of drawing both a queen and a diamond has been added twice when we added the individual probabilities.

Thus, we have:P(queen or diamond) = P(queen) + P(diamond) - P(queen and diamond)

The probability of drawing a queen is 4/52, since there are four queens in a deck of 52 cards. The probability of drawing a diamond is 13/52, since there are 13 diamonds in a deck of 52 cards.

There are two ways to draw a card that is both a queen and a diamond, namely the queen of diamonds and the diamond queen. Thus, the probability of drawing both a queen and a diamond is 2/52. Therefore, P(queen or diamond) = 4/52 + 13/52 - 2/52 = 15/52 = 15/4 = 3.75 As a reduced fraction, this is 15/52.

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The probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.

The possibility of an event occurring can be expressed in terms of probability and odds, but they are not the same thing. The ratio of positive events to all conceivable outcomes, represented as a fraction or decimal, is known as probability. On the other hand, odds represent the proportion of good outcomes to those that are unfavourable. Odds can be stated as a ratio, fraction, or by dividing the favourable outcomes by the total number of outcomes to get their equivalent in probability.

The binomial probability is given as:

[tex]P(x) = (nCx) * p^x * (1-p)^{(n-x)}[/tex]

Here, n = 3, p = 0.11, and q = 1 - p = 0.89.

Thus,

[tex]Pr(exactly 2) = P(2) = (3C2) * 0.11^2 * 0.89^{(3-2)} = 0.0283\\Pr(exactly 1) = P(1) = (3C1) * 0.11^1 * 0.89^{(3-1)} = 0.2901\\Pr(exactly 3) = P(3) = (3C3) * 0.11^3 * 0.89^{(3-3)} = 0.001331[/tex]

Hence, the probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.

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