how many cubic feet of water fell on you lot?

Answer:

\(A=20 units^2\)

Step-by-step explanation:

I would separate out the shape into two equal right triangles over a square.  The total area can then be found by adding these areas together:

\(A_t=2A_\Delta +A_s\\A_t=2(\frac{1}{2}bh)+(s)^2\\b=2 units\\h=2units\\s=4units\\A_t=2[\frac{1}{2}(2units)(2units)]+(4units)^2\\A_t=4units^2+16units^2\\A_t=20units^2\)

Given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ).

Given the expression:
sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ))
Let's simplify this expression step by step:
1. First, recognize that cos(θ) * cos(θ) can be written as cos²(θ). So, the expression becomes:
sin(θ) + cos²(θ) * (1 - cos(θ))
2. Next, we'll distribute cos²(θ) to both terms inside the parentheses:
sin(θ) + cos²(θ) - cos³(θ)
At this point, we have simplified the expression as much as possible. The final expression is:
sin(θ) + cos²(θ) - cos³(θ)
In summary, given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ). Remember that this is a general expression and its specific value depends on the angle θ.

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The area of the parallelogram formed by the given vertices A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), and D(0, 3, 2) is 2√21 square units.

To calculate the area of a parallelogram, we can use the cross product of two vectors formed by the sides of the parallelogram. The vectors AB and AD can be calculated by subtracting the coordinates of the initial and final points.

The cross product of these vectors gives us a vector representing the area of the parallelogram. Taking the magnitude of this vector gives us the area of the parallelogram. The magnitude of the cross product of AB and AD is 24, so the area of the parallelogram is 24 square units.

In this case, the vector AB is (-3, 7, 3), and the vector AD is (-1, 3, 3). Taking the cross product of these vectors gives us the vector (-12, 6, 24). The magnitude of this vector is √(12² + 6² + 24²) = √756 = 2√21. Therefore, the area of the parallelogram is 2√21 square units.

Complete Question:

Find the area of the parallelogram whose vertices are A(1, 0, −1), B(1, 7, 2), C(2, 4, −1), D(0, 3, 2).

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Answer:

The angles are supplementary.

x = 31

Step-by-step explanation:

The way the two angles lay together and make a straight line shows that they are supplementary. Supplementary means that they add up to 180°

Use this idea to write an equation.

2x + 3x + 25 = 180

combine like terms

5x + 25 = 180

subtract 25

5x = 155

divide by 5

x = 31

Answer:

x = 31

Step-by-step explanation:

(3x + 25) and 2x are a linear pair and are supplementary, that is

3x + 25 + 2x = 180

5x + 25 = 180 ( subtract 25 from both sides )

5x = 155 ( divide both sides by 5 )

x = 31

Answer:

make y the subject first

Step-by-step explanation:

y=5/7(x) -27/7

parallel lines have equal gradient m1=m2

y-y1=m(x-x1)

y-(-3)=5/7(x-4))

y=5/7(x) -20/7 -3

final answer

y=5/7(x) -41/7

Answer:

-1 Not in domain

0 In domain

1 In domain

Step-by-step explanation:

The domain for the square root function is all positive numbers including (0). The domain is the set of real numbers which when substituted into the function will produce a real result. While one can substitute a negative number into the square root function and get a result, however, the result will be imaginary. Therefore, the domain for the square root function is all positive numbers. It can simply be expressed with the following inequality:

\(x\geq0\)

Therefore, one can state the following about the given numbers. Evaluate if the number is greater than or equal to zero, if it is, then it is a part of the domain;

-1 => less than zero; Not in domain

0 => equal to zero; In domain

1  => greater than zero: In domain

Answer:

the  percentage of the students in the band that play a percussion instrument is 14.6%

Step-by-step explanation:

The computation of the percentage of the students in the band that play a percussion instrument is as followS;

= number of students played percussion instrument ÷ total number of students

= 6 students ÷ 41 students

= 14.6%

Hence, the  percentage of the students in the band that play a percussion instrument is 14.6%

The same is relevant

The equation of the line is perpendicular to the line y = -4x  - 3 and passes through the point (10, 6) is y = 1 / 4 x + 7 / 2.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line is perpendicular to the line y = -4x  - 3 and passes through the point (10, 6).

Perpendicular lines follows the rule:

m₁ m₂ = -1

-4m₂ = -1

m₂ = 1 / 4

Let's find the y-intercept of the equation using (10, 6)

y = 1 / 4 x + b

6 = 1 / 4 (10) + b

6 = 5 / 2 + b

b = 6 - 5 / 2

b =  12 - 5/ 2

b = 7 / 2

Therefore, the equation of the line is y = 1 / 4 x + 7 / 2

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The tree has at least 3n-2 nodes and 2n-2 edges. It has n leaves, each with a parent node, and then one internal node for each additional edge. This means that the total number of nodes is 3n-2 and the total number of edges is 2n-2.

A tree with n leaves is composed of a number of nodes and edges. Each leaf node has one parent node and one edge connecting it to the parent node. Each internal node has at least 3 children, meaning it has 3 edges connecting it to 3 different child nodes. This means that the total number of nodes in the tree is at least 3n-2, where n is the number of leaves. Similarly, there are at least 2n-2 edges in the tree, where n is the number of leaves. This is because each leaf has 1 edge and each internal node has 3 edges. Therefore, the total number of nodes in the tree is 3n-2 and the total number of edges is 2n-2.

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The statement is false given in the question pointing to the ratio of a pair of corresponding sides is 9/16, under the condition that two similar hexagons have areas 36 sq. inches and 64 sq.inches

Now the ratio of the areas of two given similar polygons is equal to the square of the ratio of their corresponding sides .

Then, if two similar hexagons have areas of 36 square inches and 64 square inches,

Therefore, the ratio of their corresponding sides is

√(64/36) = 4/3

But, the problem gives the ratio of a pair of corresponding sides is 9/16 .

Then,

9/16 ≠ 4/3,

The statement is false given in the question pointing to the ratio of a pair of corresponding sides is 9/16.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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Answer:

5xn+5

Step-by-step explanation:

if you times 5 by n amount of days you will get how much he would have on that day but you need to add 5 as he added 10 on the first day

hope that helps

(if that doesn't work try 5xn+10)

Answer:

(i) mean: 5.4 median: 5.5 mode: 8

(ii) mean: 4.6 median: 5 mode: 5

(iii) mean: 17.5 median: 4 mode: 4

Step-by-step explanation:

Hope this helps :) please mark me Brainliest

Answer: 140

Step-by-step explanation:

Answer: 50

Step-by-step explanation:

Khan academy answer

Answer:

This can be done in two ways -

- horizontal

- vertical

so I chose Vertical :

The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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Answer:

  no real solutions

Step-by-step explanation:

If it is a quadratic equation, there are always two solutions, regardless of the value of the discriminant.

When the discriminant is negative there are no real solutions, but there are two complex solutions.

Answer:

the 1st one is: 2

the 2nd one is: 3

To create opposite like terms of x variables, the first equation can be multiplied by 2 and the second equation by 3

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

Given that, the system of equation given in the problem is,

-3x+2y = 20......(i)

2x+11y = -1.....(ii)

As the coefficient of x is 2 in eq(ii) equation by 3 to make the opposite term as,

6x+33y = -3.......(iii)

As the coefficient of y is -3, thus multiply the above eq(i) by 2 to make opposite wise term as,

-6x+4y = 40....(iv)

Compare the equation 3 and 4, we get that both the equation has the equivalent system of equations with opposite like terms of x variables.

Hence, to create opposite like terms of x variables, the first equation can be multiplied by 2 and the second equation by 3

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By graphing both equations on the same axis and findin where do they intercept, we willsee that the solution is (-2, 6).

Here we have the following system of equations:

y = x + 8

y = -(1/2)x+5

And we want to solve it graphically.

To solve it in that way, we just need to graph both equations on the same coordinate axis and find the ponit where the graphs intercept, that point will be the solution for the system.

The graph of the system of equations can be seen in the image below:

There, we can see that the lines intercept at the point (-2, 6), so that is the solution of our system.

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the area of the surface of this design is 31 in long

Answer:

392 inches²

Step-by-step explanation:

10 inches × 6 inches = 60 inches²

60 inches² × 2 = 120 inches²

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

(6 inches + 4 inches) × 6 inches = 10 inches × 6 inches = 60 inches²

60 inches² × 2 = 120 inches²

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

(10 inches × 6 inches) + (4 inches × 4 inches) = 60 inches² + 16 inches² = 76 inches²

76 inches² × 2 = 152 inches²

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

Add them all together ~

120 inches² + 120 inches² + 152 inches² = 392 inches²

Answer:

\(\frac{1}{a}\)

Step-by-step explanation:

the product of a number and its multiplicative inverse = 1 , then

a × \(\frac{1}{a}\) = 1

multiplicative inverse of a is then \(\frac{1}{a}\)

Answer:

Step-by-step explanation:

k/9=10/3 multiply both sides by 9

k=90/3

k=30

Answer:

Hello

\( \frac{10}{3} = \frac{k}{9} \\ 10 \times 9 = 3k \\3 k = 90 \\ k = 90 \div 3 \\ k = 30\)

hope it helps

Have a nice day

Answer:

0.50x=0.40x+3

0.50x-0.40x=3

0.1x=3

————-

0.1

x=30

Answer:

(0,0) is a saddle point

(-4,4) is a local maximum

Step-by-step explanation:

\(\displaystyle z=3x^3-36xy-3y^3\\\\\frac{\partial z}{\partial x}=9x^2-36y\\\\\frac{\partial z}{\partial y}=-36x-9y^2\)

Determine critical points

\(9x^2-36y=0\\9x^2=36y\\\frac{x^2}{4}=y\)

\(-36x-9y^2=0\\-36x-9(\frac{x^2}{4})^2=0\\-36x-\frac{9}{16}x^4=0\\x(-36-\frac{9}{16}x^3)=0\\\\x=0\\\\-36-\frac{9}{16}x^3=0\\-36=\frac{9}{16}x^3\\-64=x^3\\-4=x\)

When x=0

\(9x^2-36y=0\\9(0)^2-36y=0\\-36y=0\\y=0\)

When x=-4

\(9x^2-36y=0\\9(-4)^2-36y=0\\9(16)-36y=0\\144-36y=0\\144=36y\\4=y\)

So, we need to check what kinds of points (0,0) and (-4,4) are.

For (0,0)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(0))(-18(0))-(-36)^2\\\\H=-1296 < 0\)

Therefore, (0,0) is a saddle point since \(H < 0\).

For (-4,4)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(-4))(-18(4))-(-36)^2\\\\H=(-72)(-72)-1296\\\\H=5184-1296\\\\H=3888 > 0\)

Because \(H > 0\) and since \(\frac{\partial^2z}{\partial x^2}=-72 < 0\), then (-4,4) is a local maximum

The lower limit for the 95% confidence interval for the true graduation rate is 0.704.

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level.

We can use the formula for the confidence interval for a proportion:

lower limit = sample proportion - z * √((sample proportion * (1 - sample proportion)) / sample size)

where z is the z-score corresponding to the desired level of confidence (95% in this case), and sample size is 500.

The sample proportion is 371/500 = 0.742.

The z-score for a 95% confidence level can be found using a standard normal distribution table or calculator, and is approximately 1.96.

Plugging in the values, we get:

lower limit = 0.742 - 1.96 * √((0.742 * 0.258) / 500)

lower limit = 0.704

Rounding to three decimal places, the lower limit for the 95% confidence interval for the true graduation rate is 0.704.

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Answer:

60

Step-by-step explanation:

To find the range you subtract the highest and lowest value

The highest value on this graph is 105 from the month of May and the lowest value is 45 from the month of March.

When you do 105-45 you get 60 which is the range

Answer:

d is the answer of the question

Answer:

No solutions

Step-by-step explanation:

The lines are parallel, meaning that they will never meet each other even if they extend indefinitely. Thus, there are no solutions.

The probability of a horse winning a race can be calculated based on the odds given is 33.33%. In this case, the odds are 2 to 1.

To determine the probability, we first need to convert the odds into a fraction. In this case, the odds of 2 to 1 can be expressed as 2/1.

Next, we calculate the probability by dividing the denominator of the fraction (1) by the sum of the numerator and denominator (2 + 1 = 3).

1 / 3 = 0.3333...

Therefore, the probability of this horse winning the race is approximately 0.3333, or 33.33% when expressed as a percentage.

If the odds of a horse winning a race are 2 to 1, the probability of this horse winning the race is approximately 33.33%.

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