How many cubic meters of water are required to fill a rectangular swimming pool 15m long and 10 m wide which is 2m deep throughout.How many liters is that?

The value of x is 48⁰ if EF is tangent to the circle at E.

In geometry, a tangent to a circle is a straight line or line segment that touches the circle at exactly one point. This point of contact is called the point of tangency.

To find the center angle we need to join OD and OC as shown in Figure.

∠ODC = ∠OCD = 90⁰ - 70⁰ = 20⁰

∠DOC = 180⁰ - 20⁰ - 20⁰ = 140⁰

Hence,

(5x-20)⁰ = 360⁰ - 140⁰

5x - 20 = 220⁰

5x = 240⁰

x = 48⁰

Hence, the value of x is 48⁰

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"The given question is incomplete, the complete question figure is attached below as Question Figure"

"EF is tangent to the circle at E. Find the value of x"

The limit of the expression as x approaches -12 for x→−12 (√ (x^2 + 25) − 13) / (x + 12) exists and equals -4/5.

To evaluate the limit lim x→−12 (√(x^2+25)−13)/(x+12), we can try to directly substitute x=-12 into the expression. However, this results in an indeterminate form of 0/0, indicating that further algebraic manipulation is necessary.

One approach to evaluate this limit is to use algebraic manipulation to simplify the expression into a form that allows for direct substitution. To do this, we can multiply both the numerator and denominator by the conjugate of the numerator, which is √(x^2+25)+13. This results in the expression lim x→−12 (x^2 - 144) / (x+12)(√(x^2+25)+13).

We can then simplify the expression by factoring the numerator as (x-12)(x+12), canceling the (x+12) term in the numerator and denominator, and taking the limit as x approaches -12. This yields lim x→−12 (x-12)/(√(x^2+25)+13).

Substituting x=-12 into the simplified expression yields (-12-12)/(√(144+25)+13) = -24/30 = -4/5.

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The equations that  could represent f(x) and g(x) are f(x) = 6/x + 3 and g(x) = x

From the question, the equation of the function is given as

f of g of x is equal to 6 over the quantity x squared end quantity plus 3

Rewrite properly

So, we have

f(g(x)) = 6/x² + 3

The above equation can be rewitten as

f(g(x)) = 6/g(x)² + 3

This means that

g(x) = x

Remove the occurrence of g(x) from the equation f(g(x)) = 6/g(x)² + 3

So, we have

f(x) = 6/x + 3

Hence, the possible equations are f(x) = 6/x + 3 and g(x) = x

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Step-by-step explanation:

Step 1: Setting Up the Factors

Our roots are 3, 2, and -4 so

our factors are

\((x - 3)(x - 2)(x + 4)\)

Step 2: Initial Test to see if the result equal 30

Let a be a constant, such we have

\(a(x - 3)(x - 2)(x + 4) = 30\)

Plug in. 1 for x.

\(a(1 - 3)(1 - 2)(1 + 4) = 30\)

\(a( - 2)( - 1)(5) = 30\)

\(a(10) = 30\)

\(a = 3\)

So our equation is

\(3(x - 3)(x - 2)(x + 4)\)

Or if you want it simplifed

\(3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72\)

Answer:

\(f(x)=3(x-3)(x-2)(x+4)\)

Step-by-step explanation:

General form of a cubic polynomial function with 3 roots:

\(f(x)=a(x-b)(x-c)(x-d)\)

where:

Given roots:

Substitute the given roots into the general form of the function:

\(\implies f(x)=a(x-3)(x-2)(x-(-4))\)

\(\implies f(x)=a(x-3)(x-2)(x+4)\)

To find the value of a, substitute the given point (1, 30) into the equation:

\(\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}\)

Therefore, the equation of the cubic polynomial function is:

\(f(x)=3(x-3)(x-2)(x+4)\)

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Answer:

21 <3

Step-by-step explanation:

if you look up vine the first thing there would be 21 the answer to all your problems

The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.

The z score formula is given by;`z = (x - μ) / σ`

Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.

The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`

The value of z is 1.

To find the area in the right tail, use the standard normal distribution table.

The table value for z = 1.0 is 0.8413.

Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

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To solve a differential equation with exponential equations, start by isolating the dependent variable and any coefficients that may exist on either side of the equation. Next, take the natural logarithm of both sides of the equation and use the properties of logarithms to simplify the equation. Solve for the dependent variable. Finally, take the exponential of both sides of the equation and simplify it to get the solution.

For example, consider the differential equation dy/dx = 2y.

Isolate the dependent variable to get y = dx/2.

Then, take the natural logarithm of both sides to get ln(y) = ln(dx/2).

Use the property ln(a/b) = ln(a) - ln(b) to get ln(y) = ln(dx) - ln(2).

Solve for ln(y) to get ln(y) = ln(dx) - ln(2).

Then, take the exponential of both sides to get \(y = e^{ln(dx) - ln(2)}\) and simplify to get the solution \(y = (dx/2) e^{ln(dx)}\).

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Answer:

Square

Rectangle

Step-by-step explanation:

not a pro at shapes.

Answer:

So Andrea and Casey each make $52 after working for 3 hours.

Step-by-step explanation:

Let's call the number of hours that Andrea and Casey work "x".

The amount of money that Andrea makes in a given hour can be represented as 25 + 9x.

The amount of money that Casey makes in a given hour can be represented as 10 + 14x.

We want to find the number of hours it takes for Andrea and Casey to make the same amount of money, which we can represent as:

25 + 9x = 10 + 14x

To solve for x, we can isolate x by subtracting 10 from both sides of the equation:

15 + 9x = 14x

Next, we can isolate 9x by subtracting 14x from both sides of the equation:

15 = -5x

Finally, we can divide both sides of the equation by -5 to solve for x:

-3 = x

So it takes 3 hours for Andrea and Casey to make the same amount of money. To find the amount of money, we can plug in x = 3 back into either of the equations:

Andrea's equation: 25 + 9x = 25 + 9 * 3 = 25 + 27 = 52

So Andrea and Casey each make $52 after working for 3 hours.

An equation that shows the relationship between the two angle measure is 3x + 2 = 180 and the value of x is 59.

Let us consider the two supplementary angles with measures (x + 1) and (2x + 1). Since they are supplementary angles, we know that their sum is equal to 180 degrees. We can write this relationship between the two angle measures as an equation:

(x + 1) + (2x + 1) = 180

Simplifying this equation, we get:

3x + 2 = 180

Now, we can solve for x by isolating it on one side of the equation. To do this, we can subtract 2 from both sides of the equation:

3x = 178

Finally, we can solve for x by dividing both sides of the equation by 3:

x = 59.33

Therefore, we should round the value of x to the nearest whole number, which is 59.

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).

To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.

For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).

As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).

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Answer:

a ratio compares two numbers by division

Step-by-step explanation:

i just know

Answer:

Ratio

Step-by-step explanation:

Ratio – A comparison of two quantities by division.

Answer:

4,600,000,000

Step-by-step explanation:

Don't forget the order of operations

3.243 × 10⁸/7.05

= 46,000,000 × 10²

= 4,600,000,000

or 4.6 × 10⁹

Answer:

4.6x10 to the power of 5

Step-by-step explanation:

7.05×10

2

3.243×10

8

​

Divide them.

\frac{3.243}{7.05}\times \frac{10^8}{10^2}

7.05

3.243

​

×

10

2

10

8

​

Divide numbers and 10's separeately.

0.46\times 10^6

0.46×10

6

Subtract exponents.

(4.6\times 10^{-1})\times 10^6

(4.6×10

−1

)×10

6

Rewrite as a number bigger than 1

4.6\times (10^{-1}\times 10^6)

4.6×(10 −1 ×10 6 )

Associate

4.6\times 10^5

4.6×10 5

Add exponents

Answer:

first one is correct ........

Well I can't be for sure but I know for a fact its not set IV it's not possible to make a triangle out of all right angles. Set II, well, that isn't right either. You can't make a triangle out of all obtuse angles. Like the right angle one, its not possible you can only use one obtuse or right angle in a triangle other wise it's not going to be a triangle. I'd say go try Set III since that would most likely make an equilateral triangle.

With employees ranging in age from 40 to 30, 36 to 22, there is a 46-year age difference between them. The average difference between each age and the population's mean age is measured.

We employ the following formula to determine the variance of a population:

σ² = Σ(x - μ)² / N

σ² = Σ(x - μ)² / N

where:

σ² =  the population variance

Σ = the sum of

x = the value of each element in the population

μ = the population mean

N = the population size

First, we need to find the population mean:

μ = (40 + 30 + 36 + 22) / 4 = 32

Next, we calculate the sum of the squared deviations from the mean:

(40 - 32)² + (30 - 32)² + (36 - 32)² + (22 - 32)² = 64 + 4 + 16 + 100 = 184

Then, we divide the sum of squared deviations by the population size:

σ² = Σ(x - μ)² / N = 184 / 4 = 46

Therefore, the population variance is 46.

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The closest correlation coefficient of the scatter plot with points loosely scattered going up to the right would be: 0.8.

Therefore, the closest correlation coefficient of the scatter plot with points loosely scattered going up to the right would be: 0.8.

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Answer:

0.8

Step-by-step explanation:

Answer:

the answer is 175

Step-by-step explanation:

you will do 2500*7/100

The answer is

31381059609

The value of the probability P(Blue) will be; 0.50

We have the following parameters that can be used in our computation:

Coin = Two-sided coin

Colors = Orange and Blue

Using the above as a guide, we have:

P(Blue) = Number of blue/Number of sides

Substitute the known values in the above equation,

P(Blue) = 1/2

Evaluate;

P(Blue) = 0.5

Hence, the probability is 0.50

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The solution x1(t) for the de-coupled RL-RC circuit can be found by solving the differential equation x1'(t) = A11 * x1(t), where A11 is a constant value.

To solve this differential equation, we can use separation of variables.

1. Begin by separating the variables by moving all terms involving x1(t) to one side of the equation and all terms involving t to the other side. This gives us:

x1'(t) / x1(t) = A11

2. Integrate both sides of the equation with respect to t:

∫ (x1'(t) / x1(t)) dt = ∫ A11 dt

3. On the left side, we have the integral of the derivative of x1(t) with respect to t, which is ln|x1(t)|. On the right side, we have A11 * t + C, where C is the constant of integration.

So the equation becomes:

ln|x1(t)| = A11 * t + C

4. To solve for x1(t), we can exponentiate both sides of the equation:

|x1(t)| = exp(A11 * t + C)

5. Taking the absolute value of x1(t) allows for both positive and negative solutions. To remove the absolute value, we consider two cases:

  - If x1(0) > 0, then x1(t) = exp(A11 * t + C)
  - If x1(0) < 0, then x1(t) = -exp(A11 * t + C)

  Here, x1(0) is denoted as x10.

Therefore, the solution x1(t) for the de-coupled RL-RC circuit, starting at t=0, is given by either x1(t) = exp(A11 * t + C) or x1(t) = -exp(A11 * t + C), depending on the initial condition x10.

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Answer:

Distance:

\(d = 13\)

Step-by-step explanation:

-To determine the distance, use the "distance formula":

\(d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

-Apply the points \((5,-8)\) and \((-7,-3)\) for the distance formula:

\(d = \sqrt{(-7 - 5)^2 + (-3 + 8)^2}\)

-Then, solve the equation:

\(d = \sqrt{(-7 - 5)^2 + (-3 + 8)^2}\)

\(d = \sqrt{(-12)^2 + (5)^2}\)

\(d = \sqrt{144 + 25}\)

\(d = \sqrt{169}\)

\(d = 13\)

So, the actual distance is \(13\).

Answer:

18

Step-by-step explanation:

Always remember negative x negative = positive

-51-(-60)-51-(-60)

-51+60-51+60

9+9

18

I don't know what are the expressions but try yourself

Believe in yourself you can do it

The amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)

The volume of a tennis ball:

The circumference of the tennis ball is 8 inches.

The tennis ball is the form of sphere whose circumference is given by formula \(2\pi r\), where r is the radius.

Thus, if r is the radius then according to condition,

\(2\pi r\) = 8 or

r = 8/2\(\pi\) inches.

Now, the volume of the sphere of radius r is \(\frac{4}{3}\pi r^3\) hence, find the volume of the given tennis ball by substituting r  = 8/2\(\pi\) inches in  \(\frac{4}{3}\pi r^3\) and simplify:

Volume = \(\frac{4}{3}\pi\) × \((\frac{8}{2\pi } )^3\)

Volume = 8.65\(inches^3\)

Hence the required volume of the tennis ball is 8.65\(inches^3\)

The volume of three tennis balls is (3 × 8.65) \(inches^3\) = 25.96 \(inches^3\)

Find the volume of the cylinder:

The volume of the cylinder with radius r units and height h units is given by \(\pi r^2h\) Hence the volume of the given cylinder with radius 1.32 inches , 8.2 height inches is:

\(\pi (1.32)^2\) × 8.2

= 3.14 × \((1.32)^2\) × 8.2

= 44.86 \(inches^3\)

Hence the volume of the cylinder is 44.86 \(inches^3\)

Find the amount of space within the cylinder not taken up by the tennis balls.

The required volume can be obtained by subtracting the volume three tennis balls from the volume of the cylinder as follows:

Volume of cylinder - volume of three tennis balls = (44.86 - 25.96) = 18.9 \(inches^3\)

Hence, the amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)

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The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).

To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.

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A solution to the given system of linear equations is (-2, 1).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = -5/2(x) - 4      ......equation 1.

y = 1/2(x) + 2  ......equation 2.

Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II and it is given by the ordered pair (-2, 1).

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Standardize every test score from Mr. Bowman's class, the new mean would be 0, the new standard deviation would be 1, and the shape of the distribution would remain the same as before.

Let's first understand what standardizing means.
Standardizing test scores involves transforming the original scores to a new scale, called z-scores.

This process is done by subtracting the mean (average) score from each test score and dividing the result by the standard deviation of the scores. The formula for finding the z-score is:
z = (X - μ) / σ
X is the original test score, μ is the mean, and σ is the standard deviation.
Now, let's discuss the properties of the standardized scores:
New mean:

Standardize the test scores, the new mean (average) of the z-scores will always be 0.

This occurs because we subtract the mean from each test score, making the sum of the differences equal to 0.
New standard deviation:

After standardization, the standard deviation of the z-scores will always be 1.

This is because we divide each score by the original standard deviation, results in the new standard deviation being equal to 1.
Shape of the distribution:

The shape of the distribution (i.e., the pattern of the scores) will not be affected by standardization.

If the original scores followed a bell-shaped curve, the standardized scores would maintain the same bell shape.

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Required Probabilty = 161.1

n = 1111

Probability of getting correct P(c)= 1/2

Probability of getting wrong P(w)= 1/2

So it follows binomial distribution

P (x*r) = Ncr .(P)r . (q)n-r = P (33<X<55) = P(X-r) = 1111c4 .  (1/2) power of 44 . (1/2) power of 1111-44

Required Probabilty = 161.1

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