A rectangular pool is 20 feet by 30 feet. The depth of the pool is 60 inches, but the depth of the water is 3/4 of the depth of the pool. Find each measure to the nearest tenth. (Lesson 1-7)
b. the volume of water in the pool

Statistical analyses are least likely to be found in a (D) qualitative research.

Therefore, statistical analyses are least likely to be found in a (D) qualitative research.

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Answer: 21.2

Step-by-step explanation:

The number 16.8 in the equation means the points with which his score will increase in every game.

The stated equation has the constant 16.8 associated with the number of years. The number indicates that the person earns 16.8 additional points after each game. This number adds on to the total score. In other words, it indicates the points by which his score increase per game. Considering the equation, it p = 16.8t + 80.5. Here, p refers to y-axis, 16.8 is the slope and t is the x-axis. The 80.5 is the y-intercept and indicates the starting average per game.

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Answer:

Option C

Step-by-step explanation:

First, knowing that two angles on a horizontal line split by a vertical line at any angle is equal to 180 degrees, I try to find which of the combinations of angle x and z equal 180.

A. x = 63, and z = 104 and together they equal 170, so not A

B. x = 76 and z = 63 and together they equal 139 so not B

C. x = 76 and z = 104 and together they equal 180 so it could be C, but we must check D to make sure.

D. x = 63 and z = 76 and together they equal 139 so not D.

From all of this it must be option C

Answer:

Step-by-step explanation:

perp. -4/3

y + 2 = -4/3(x - 3)

y + 2 = -4/3x + 4

y = -4/3x + 2

It will take 6 month to reach the same height for both maple tree and oak tree.

the country, region, or geographic area's yearly average rate of change in population size over a certain time period.

The given data is -

Let the number of months when both will have the same height be 'x'.

Thus,

For maple tree,the final height be-

125 + 3x

For oak tree,the final height be-

83 + 10x

Equating both

125 + 3x = 83 + 10x

7x = 125 - 83

7x = 42

x = 6 months

Thus, it will take 6 month to reach the same height for both maple tree and oak tree.

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Using sine ratio in trigonometric ratio, the length of the ladder is 29.6 feet

Trigonometric ratios are ratios of the sides of a right triangle that are used to describe the angles of the triangle. They are used in many different branches of mathematics, including geometry, calculus, and trigonometry. The most common trigonometric ratios are sine, cosine, and tangent.

To solve this problem, we have to determine which of the ratio we need.

Data;

Since we have the opposite side and angle, we can find the hypothenuse using sine ratio

sinθ = opposite / hypothenuse

sin 71 = 28 / x

x = 28 / sin 71

x = 29.6 feet

The length of the ladder is 29.6 feet

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Answer:

29.61

Step-by-step explanation:

Answer:

I think letter D is the closest answer

Answer:

y = 3 /2 x + 5

Step-by-step explanation:

Answer:

h=60

h is on the same line as 120°, and every line is 180°, so 180 - 120 gives you the answer

Answer:

b=3.464 a=2.121

Step-by-step explanation:

The solutions for 0 ≤ x ≤ π where 4sin(x)cos(x) = 2sin(x) are x = π/3 and x = 5π/3.

To solve the equation 4sin(x)cos(x) = 2sin(x), we can simplify it by dividing both sides of the equation by sin(x):

4cos(x) = 2

Next, we can divide both sides of the equation by 4 to isolate cos(x):

cos(x) = 2/4

cos(x) = 1/2

Now, we need to find the values of x that satisfy the equation cos(x) = 1/2 in the given interval 0 ≤ x ≤ π.

In the interval 0 ≤ x ≤ π, the cosine function is positive (cos(x) > 0) in the first and fourth quadrants.

In the first quadrant (0 < x < π/2), there is a solution for cos(x) = 1/2, which is x = π/3.

In the fourth quadrant (3π/2 < x < 2π), there is also a solution for cos(x) = 1/2, which is x = 5π/3

Therefore, the solutions for 0 ≤ x ≤ π where 4sin(x)cos(x) = 2sin(x) are x = π/3 and x = 5π/3.

Expressing the answers in the requested format, we have:

π/3 π/π 5π/3

Therefore, the solutions, in ascending order, are π/3, π/π, and 5π/3.

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Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

Equations are mathematical statements with the equals (=) sign on each side and two algebraic expressions in the center.

Coefficients, variables, operators, constants, terms, and the equal to sign are just a few of the components that make up an equation. The "=" symbol and terms on both sides are always needed when writing an equation.

calculation

Let s = brittany 's age now

Let t = steve's age now

s = 3t

s + 9 = 2 (t+9)

s + 9 = 2t + 27

s = 2t + 27 - 9

s = 2t + 18

Substitute 3t for s and find t

3t = 2t + 18

3t - 2t = 18

t = 18 yrs is steve's age

then

s = 3(18)

s = 54 yrs is brittany's age

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

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Answer:

You need a bigger picture of the circle but to get the answer just take the radius (the number given in the circle) and multiply it by 2

Step-by-step explanation:

Hope this helps!

Answer:

yes

Step-by-step explanation:

the function does not cross the same point of x twice.

Answer:

B.) Yes; The graph passes the vertical line test!

Step-by-step explanation:

This graph does indeed show a function! A parabola, it looks like!

A function on a graph is determined when the function passes the vertical line test, meaning no matter where you go on the function, a specific vertical line will only pass through one point!

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False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Answer:

5

Step-by-step explanation:

Sketch the diagram

AE is equal to the other half of the diagonal EC

3x + 12 = 27

Subtact 12 from both sides

3x = 15

Divide both sides by 3

X = 5

When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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Answer:

92% of Income is  Rs 18400

Step-by-step explanation:

I = 18400/.92 = Rs 20000

It is true that statistics summarize and organize groups of numbers to make them easier to comprehend.

Statistics involves the collection, analysis, interpretation, presentation, and organization of numerical data. One of the key purposes of statistics is to summarize and organize groups of numbers to make them more meaningful and easier to comprehend. This can be done through various statistical techniques, such as measures of central tendency (e.g., mean, median, mode), measures of variability (e.g., range, standard deviation), graphical representations (e.g., histograms, bar charts), and summary statistics (e.g., percentiles, correlations). By summarizing and organizing data, statistics provide valuable insights and facilitate better understanding, interpretation, and communication of numerical information.

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We are given the slope and the y-intercept so using the slope-intercept form:

Substitute values to get:

To graph a line we need two points, one is given, (0, - 7) - the y-intercept.

Find one more point,  take even value of x to cancel the fraction, let it be x = 4, find its y-coordinate:

So our points are:

Plot the points and connect to graph the line.

See below.

The graph of the linear equation:y = (3/2)*x - 7 can be seen in the image at the end.

A general linear equation is written as:y = a*x + b

Where a is the slope and b is the y-intercept. Then our linear equation is:y = (3/2)*x - 7

To graph it, we need to know two points in our line, to do so, we evaluate it in two different values of x. if x = 0y = (3/2)*0 - 7y = -7So we have the point (0, -7)

And if x = 2 then:y = (3/2)*2 - 7y = 3 - 7y = -4So we have the point (2, -4)

Now we just need to graph these two points and connect them with a line. You can see the graph below.

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The minimum possible value for the density of the material is 7.22 g/cm³.

Given data: Mass of the cube, m = 100 g

Side of the cube, l = 2 cm = 20 mm

Formula used: Density = Mass/Volume

Volume of the cube = l³

Here, the side of the cube is accurate to the nearest millimeter which means the side of the cube could vary in the range 1.5 cm to 2.4 cm. We need to consider the minimum possible value of the density of the material in this case.As we know, the volume of the cube is given by:

Volume of cube = (Side of cube)³

Volume of cube = (2 cm)³

Volume of cube = 8 cm³Converting cm³ to mm³, we get:

1 cm³ = (10 mm)³1 cm³ = 1000 mm³

Volume of cube = 8 cm³ = 8000 mm³

Therefore, Density of material = (Mass of cube) / (Volume of cube)

Density = 100 g / 8000 mm³

Minimum possible value of density will be when the side of the cube is maximum.

Therefore,Side of the cube, l = 2.4 cm = 24 mm

Density = (100 g) / (24 mm)³

Density = (100 g) / (13824 mm³)

Density = 0.00722 g/mm³

Density = 7.22 g/cm³

Therefore, the minimum possible value for the density of the material is 7.22 g/cm³.

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Answer:

Step-by-step explanation:

Given:

Angles A and C are equal. This makes triangles similar:

Ratio of corresponding sides is same:

Side measures are:

Using the product rule of exponents, the expression can be simplified to 3²⁰/25.

What is expression?
Expression in math is a combination of numbers, symbols, and other mathematical terms used to represent a quantity or an operation. It can be defined as a statement that uses mathematical symbols to form a mathematical equation or to express a mathematical relationship. Expressions are used to calculate the value of a mathematical equation and to determine the solution to a problem. They can also be used to represent relationships between different variables.


The given expression can be simplified using the product rule of exponents which states that when two terms with the same base are multiplied together, the exponents can be added together.

Therefore, 3¹¹/5 ÷ 3⁻⁹/⁵ can be rewritten as 3¹¹/5 x 3⁻⁹/⁵

Using the product rule of exponents, the expression can be simplified to 3²⁰/25.

Therefore, the simplified expression is 3²⁰/25.

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Complete questions as follows-
Simplify the following expression. 3^11/5 divided by 3^-9/5

Answer:

(a+1)(a+1) or (a+1)^2

Step-by-step explanation:

a^2+2a+1=(a+1)(a+1)

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The product of (−21)(19)(−5) is 1995.

What is product?

In mathematics, the product is the result of multiplying two or more numbers or expressions together. The product is an important concept in mathematics and is used in many areas, including arithmetic, algebra, calculus, and geometry.

The problem asks us to find the product of (−21)(19)(−5). To solve this problem, we can multiply the three numbers together in any order because multiplication is associative.

So, let's multiply the numbers from left to right:

(−21)(19)(−5) = (−399)(−5)

We then simplify this expression by multiplying -399 and -5 together:

(−399)(−5) = 1995

Therefore, the product of (−21)(19)(−5) is -1995.

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If all the data points fall on the least-squares regression line in simple linear regression this is indication of overfitting. The correct answer is E. None of the above statements are true.

In simple linear regression, if all the data points fall exactly on the least-squares regression line, it means that the regression model perfectly explains the relationship between the independent variable and the dependent variable. However, this scenario is highly unlikely in practice and is often an indication of overfitting.

Here's a breakdown of each statement:

A. F-statistic = 0: The F-statistic is used to test the overall significance of the regression model. If all data points fall on the regression line, it suggests a perfect fit, and the F-statistic would be large rather than zero.

B. MS(Regression Model) = 100%: MS stands for mean square, and this statement implies that all the variation in the dependent variable can be attributed to the regression model. However, in reality, there is typically some degree of error or residual variation that cannot be explained by the model.

C. SS(Total) = 0: SS stands for sum of squares, and SS(Total) represents the total sum of squares of the dependent variable. If all data points fall on the regression line, it would imply that there is no variation in the dependent variable, which is highly unlikely.

D. SS(Regression Model) = SS(Total): SS(Regression Model) represents the sum of squares explained by the regression model. If all data points fall on the regression line, it implies that the regression model perfectly explains all the variation in the dependent variable. However, in practice, there is typically some residual variation that cannot be explained by the model.

Therefore, none of the statements mentioned are true when all the data points fall on the least-squares regression line.

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The largest discrepancy between experimental and expected probability can be determined by comparing observed frequencies of the outcomes with expected probabilities for each face of the cube.

To calculate the expected probabilities, we divide the number of favorable outcomes (1 for each face) by the total number of possible outcomes (6 for a standard cube). Thus, the expected probability for each face is 1/6 or approximately 16.67%.  For example, let's say the observed frequencies are as follows: Face 2 (3 occurrences), Face 4 (5 occurrences), Face 6 (4 occurrences), Face 8 (6 occurrences), Face 10 (2 occurrences), and Face 12 (4 occurrences). The observed probabilities can be calculated by dividing the observed frequencies by the total number of trials (in this case, the sum of all observed frequencies, which is 24).

Next, we calculate the difference between the observed probabilities and the expected probabilities for each face. We find the absolute value of each difference to consider both overestimations and underestimations.In this case, let's assume the largest absolute difference is 0.07. To convert the discrepancy to a percentage form, we multiply the largest absolute difference by 100.

In conclusion, the largest discrepancy between the experimental and expected probability in this experiment is 7% when rounded to the nearest whole number.

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The bus 2 will pass bus 1 at 12.30 pm, when both are at 360 miles.

The bus 1 starts half hour earlier than bus 2. But since bus 2 is faster, it will overtake at some point. At 8 am, bus 1 will start. By the time 8.30, it will cover a distance of 40 miles.

Bus 2 starts at 8.30, So it will be at 0 miles.

By 10, the bus 1 will be at 160 miles, bus 2 at 135 miles

By 10.30, the bus 1 will be at 200 miles, bus 2 at 180 miles.

By 11.30, bus 1 will be at 280 miles, bus 2 will be at 270 miles

By 12.30, bus 1 will be at 360 miles, bus 2 will be at 360 miles.

So at the 360 the, the both the buses passes each other.

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