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(AMC8, 2008) In square ABCE, A F = 2FE and CD = 2DE. What is the ratio of the area △BDF to the area of square ABCE?
A. 1/6 B. 2/9 C. 5/18 D. 1/3 E. 7/20

There are a total of 70 lattice paths that start at (2, 2) and end at (10, 10).

To find the number of lattice paths between two points, you can use the formula:
n! / (k! * (n-k)!)
In this case, the total number of steps needed to get from (2, 2) to (10, 10) is 8 steps to the right and 8 steps up, for a total of 16 steps. So n = 16.

The number of steps in one direction (either right or up) is 8, so k = 8.
Plug in these values to the formula:
16! / (8! * (16-8)!)
= 16! / (8! * 8!)
= 20922789888000 / 40320 * 40320
= 70

So there are 70 lattice paths between (2, 2) and (10, 10).
I hope this helps! Let me know if you have any further questions.

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Step-by-step explanation: it will be c because 45 divided by 15 = 3

Answer:

-3/17

Step-by-step explanation:

4/17 times -3/4 - divide both fours by 4 gets as 1

1/17 times -3/1-----      -3/17

Answer:

-3/17

Step-by-step explanation:

4x3 is 12

17x3 is 68

Divide both by 4 and you get -3/17

i hope this is helps!

To determine if triangle XYZ and triangle X'Y'Z' are the same shape and size, we need to compare their corresponding angles and side lengths.

Angle Comparison: Check if the corresponding angles in both triangles are equal. If all three angles of triangle XYZ are congruent to the corresponding angles of triangle X'Y'Z', then they have the same shape. However, this does not guarantee they have the same size.

Side Length Comparison: Compare the lengths of the corresponding sides. If all three sides of triangle XYZ are equal in length to the corresponding sides of triangle X'Y'Z', then they have the same size.

If both the angles and side lengths are equal for the corresponding parts of the triangles, then triangle XYZ and triangle X'Y'Z' are congruent, meaning they are the same shape and size.

It's important to note that without specific measurements or additional information about the triangles, it is not possible to definitively determine if they are the same shape and size.

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hope it helped

3(y-1)=2x+2

3(y-1)/3=2x+2/3

y-1=2x/3+2/3

y=2x/3+2/3+1

y=2x/3+5/3

m=2/3

1.1.1 Short-term investment: An example of a short-term investment is investing in a 3-month Treasury bill. These are government-issued debt securities with a maturity of less than one year, providing a relatively low-risk investment option with a fixed interest rate.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a maturity of 5 years. Corporate bonds offer a higher yield compared to government bonds, making them suitable for investors with a moderate risk appetite seeking stable income over a longer time horizon.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. Stocks represent ownership in a company and have the potential for higher returns over an extended period, although they also involve higher risk.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. These bonds pay a fixed interest rate over the bond's duration, providing a predictable stream of income for the investor.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. The mortgage payment remains constant throughout the loan term, typically spanning several years, and includes both the principal repayment and the interest charged by the lender.

1.1.1 Short-term investment: A short-term investment option is the 3-month Treasury bill. Treasury bills are considered low-risk investments issued by the government, and they offer a fixed interest rate that is determined through an auction process. Investors can purchase Treasury bills directly from the government or through a broker.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a 5-year maturity. Corporate bonds are issued by companies to raise funds, and they pay a fixed interest rate to bondholders over the bond's duration. The bond's yield and risk profile depend on the creditworthiness of the issuing company.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. A diversified portfolio consists of a mix of stocks from different sectors and regions, spreading the risk across multiple companies. The goal is to achieve long-term capital appreciation and potentially earn dividends from the stocks held in the portfolio.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. Government bonds are issued by national governments to finance their operations. The bond's interest rate is fixed at the time of issuance, and the investor receives periodic interest payments until the bond reaches maturity, at which point the principal amount is returned.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. When purchasing a property with a mortgage loan, the borrower agrees to make fixed monthly payments that include both the principal repayment and the interest charged by the lender. The monthly payment amount remains constant throughout the mortgage term, typically ranging from 15 to 30 years.

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Answer:

Step-by-step explanation:

complex numbers , real numbers , rational numbers , natural numbers , whole numbers

Answer:

Prepare. You dread public speaking because you don't know what to say.

Psych yourself. ...

Know your audience. ...

Be an expert on your topic. ...

Visualize. ...

Conduct an ocular inspection. ...

Read, watch, and listen to good speakers.

Step-by-step explanation:

To scope a speech you need to narrow dow. what you are talking about into the relevant topic. A easy way to effectivly scope your speech is to ask yourself "what information do I want my audience to know at the end of my speech." Once you've answered his for yourself, use it as your focal point for your speech. Keep what you're talking about relevant to the purpose and thesis of your speech. And make sure to use anything superfluous or extraneous because it will broaden your scope and take the speech away from the ultimate goal.

The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

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On a circle with a radius of 4 and center at (0, 0), to find the x and y coordinates at an angle of 180 degrees (or π in radian measure), we can use the trigonometric functions.

At 180 degrees, the x-coordinate will be 0, as it lies on the y-axis. The y-coordinate can be found by using the sine function.  Using the equation y = r * sin(θ), where r is the radius and θ is the angle in radians, we can substitute the values. In this case, r is 4 and θ is π (since 180 degrees equals π radians).

Therefore, the x-coordinate is 0 and the y-coordinate is 4 * sin(π) = 0. So, the x-coordinate is 0 and the y-coordinate is also 0.
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Answer:$p$ =$4 when $q=49$.

Step-by-step explanation:

If $p$ and $q$ are inversely proportional, then mathematically, they are represented as

$p$ ∝ 1/$q$

So that introducing the constant of proportionality,k becomes

$p$ =k 1/$q$

$p$ =k /$q$

When $p=28$ when $q=7$,K becomes

$p$ =k /$q$

$28=K/ $7

k=$28 x $7 =$196

Now when $q=49$.,  $p$ becomes?

$p$ =k /$q$

$p$ =$196/49$

$p$ =$4

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

7.94 is your answer

Step-by-step explanation:

......

Answer:

It was 1,474.65ft last year.

Step-by-step explanation:

1,305ft x 1.13 = 1,474.65

1,474.65 / 1.13 = 1.305

Answer:

1474.65 feet

Step-by-step explanation:

13% of 1305 = 169.65

LAST YEARS DEPTH = 1305 + 169.65 = 1474.65 feet

Answer:

The y intercept for the equation is (0,-7)

The rate of change of the potential at P in the direction of u is 15/√26.

To find the rate of change of the potential at point P(3, 2, 7), we need to calculate the gradient vector of V and then evaluate it at P.

The gradient vector of V is given by:

grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k

where i, j, and k are unit vectors in the x, y, and z directions, respectively.

Taking partial derivatives of V with respect to x, y, and z yields:

dV/dx = 8x + 5y + yz

dV/dy = 5x + xz

dV/dz = xy

Plugging in the coordinates of P(3, 2, 7), we get:

dV/dx|P = 8(3) + 5(2) + (2)(7) = 41

dV/dy|P = 5(3) + (3)(7) = 26

dV/dz|P = (3)(2) = 6

Therefore, the gradient vector of V at P is:

grad(V)|P = (41)i + (26)j + (6)k

The rate of change of the potential at P in the direction of a unit vector u is given by the dot product of the gradient vector of V at P and u. If we let u be the unit vector in the direction of (3, -4, 1), then:

u = (3/√26)i - (4/√26)j + (1/√26)k

Taking the dot product of u and grad(V)|P yields:

grad(V)|P · u = (41)(3/√26) + (26)(-4/√26) + (6)(1/√26)

= 123/√26 - 104/√26 + 6/√26

= 15/√26

Therefore, the rate of change of the potential at P in the direction of u is 15/√26.

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The difference between a negative integer and a positive integer is not always positive.

Option 2 is correct - it's positive only if the negative integer is greater than the positive integer.

If the positive integer is greater, then the difference will be negative. If the two integers have the same absolute value but opposite signs, then the difference will be zero.

For example,

if we subtract 3 from -5, the difference is -8, which is negative.

if we subtract -5 from 3, the difference is 8, which is positive. And

if we subtract 4 from -4, the difference is 0.

Therefore, the sign of the difference between a negative integer and a positive integer depends on the relative magnitude of the two integers.

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The maximum volume of the largest rectangular box that can be inscribed in the ellipsoid can be calculated by finding the x, y, and z coordinates in the first octant that satisfy the equation (x^2/4) + (y^2/64) + (z^2/49) = 1.

Since the box must have edges parallel to the axes, the coordinates will also be the lengths of the box's edges. From the equation, we get the x coordinate to be 2, the y coordinate to be 8, and the z coordinate to be 7.

The volume of the box is the product of its edges, so the maximum volume of the box is V = 8xyz = 8 * 2 * 8 * 7 = 896.

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The probability that the random;y selected point will be in the triangle = 0.33

solve for area covered by the trangke

The area of the triangle is guven as 1/2 x b * h

b = base

h = height

The base = 10

The height = 24

The area = 1 / 2 x 10 x 24

= 240 / 2

= 120

Then we know that the complte angle of a cirle = 360 degrees

The probability that the random;y selected point will be in the triangle = 120 / 360

= 12 / 36

= 0.33

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Answer.

0.23

find area of triangle =120 then find area of circle= 530.66 then divide area of triangle by area of circle

The first molecule will have a ZERO dipole moment since all the F atoms are at 120 degree making the net dipole zero.

A molecule is a group of two or more atoms held together by chemical bonds; depending on the context, the term may or may not include ions that meet this criterion.

A molecule is a particle composed of two or more atoms that are chemically bonded together; the number of atomic nuclei constituting a molecule is fixed. HCl(g), for example, is a molecule composed of one hydrogen atom bonded to one chlorine atom. It is a diatomic molecule because it is composed of two atoms.

The second molecule will have a NON ZERO dipole moment. The net dipole moment will be downwards. The third molecule will have a NON ZERO dipole moment.

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Answer:

W=x/7+ 8z/7 + 4/7

Step-by-step explanation:

When the radius is 9 cm, the area of the circular pool is increasing at a rate of 288π cm square/min.

To find how fast the area of the circular pool is increasing when the radius is 9 cm, we can use the formula for the area of a circle, which is A = πr^2, where A represents the area and r represents the radius.

Given that the radius is increasing at a rate of 4 cm/min, we can differentiate the formula for the area with respect to time (t) using the chain rule:

dA/dt = dA/dr * dr/dt

Here, dA/dt represents the rate of change of the area with respect to time, dr/dt represents the rate of change of the radius with respect to time, and dA/dr represents the derivative of the area with respect to the radius.

To find dA/dr, we can differentiate the formula for the area of a circle:

dA/dr = d/dt (πr^2)

= 2πr * dr/dt

Plugging in the given values, we have:

dr/dt = 4 cm/min

r = 9 cm

Substituting these values into the equation for dA/dr:

dA/dr = 2π(9) * 4

= 72π cm^2/min

Now, we can find dA/dt by multiplying dA/dr by dr/dt:

dA/dt = (72π cm^2/min) * (4 cm/min)

= 288π cm^2/min

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The statement does not make sense. Both sin⁻¹(√3/2) and cos⁻¹(√3/2) represent angles within the same range of [π/6, π/3], which is positive. Therefore, it is incorrect to claim that sin⁻¹(√3/2) is negative while cos⁻¹(√3/2) is positive.

The statement does not make sense.

In mathematics, the inverse sine function (sin⁻¹) and inverse cosine function (cos⁻¹) are defined such that their outputs lie within specific ranges. The inverse sine function has a range of [-π/2, π/2], meaning the output values are between -π/2 and π/2. On the other hand, the inverse cosine function has a range of [0, π], meaning the output values are between 0 and π.

Given that sin⁻¹(√3/2) represents an angle with a sine value of √3/2, it lies in the range of [π/6, π/3], which is a positive angle. Similarly, cos⁻¹(√3/2) represents an angle with a cosine value of √3/2, which also lies in the range of [π/6, π/3], and is therefore positive. Therefore, it does not make sense to claim that sin⁻¹(√3/2) is negative while cos⁻¹(√3/2) is positive, as both angles fall within the same range.

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a) The central 95% of all copper contents would be bounded by the values of 26.02 and 35.58.

b) The distribution of the sample mean copper content follows an approximately normal distribution with a mean of 30.8 and a standard error of \($\frac{2.45}{\sqrt{16}}\) =0.6125.

c) If we were to randomly sample 16 brake pads from this distribution, the bounding values for the central 95% of possible means would be (29.6, 32)

a) Since the copper content in sintered brake pads follows an approximately normal distribution with a mean of 30.8 and a standard deviation of 2.45, we can use the standard normal distribution to find the values that bound the central 95% of all copper contents. The 95% confidence interval corresponds to z=1.96 in the standard normal distribution. Thus, the values that bound the central 95% of all copper contents are given by:

30.8−1.96×2.45=26.02,30.8+1.96×2.45=35.58

b) The sample mean of copper content for a sample of 16 pads is also normally distributed with a mean of 30.8 and a standard deviation of \($\frac{2.45}{\sqrt{16}}=0.6125$\), which is called the standard error. The distribution of the sample mean is given by:

c) The bounding values for the central 95% of possible means can be found by using the formula:

where \($\sigma$\) is the population standard deviation, n is the sample size and \($z^*$\)is the critical value of the standard normal distribution that corresponds to a 95% confidence interval. Substituting the values, we get:

Therefore, the bounding values for the central 95% of possible means are given by:

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In the word problem , the number of students in each group is 16.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here Number of student in first class = 21

Number of students in second class = 25

Number of students in third class = 18

Total number of students = 21+25+18 = 64

Now the group is split into 4. Then number of students in each group is,

=> 64 / 4 = 16

Hence the number of students in each group is 16.

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The chi-square values for a sample size of n=10 at 95% confidence are 2.700 and 19.023, which corresponds to option (a).

1. Identify the degrees of freedom: Since the sample size is n=10, the degrees of freedom (df) will be n-1 = 9.
2. Look for the chi-square values corresponding to 95% confidence level: For a 95% confidence interval, we will look for the values corresponding to 2.5% (0.025) in the lower tail and 97.5% (0.975) in the upper tail of the chi-square distribution table.
3. Locate the values in the table: Using the table, find the chi-square values for df=9 and the specified tail probabilities.

Based on the chi-square distribution table, the values corresponding to df=9 at 95% confidence are:
a. 2.700 (for 0.025 tail probability) and 19.023 (for 0.975 tail probability).

So, the chi-square values for a sample size of n=10 at 95% confidence are 2.700 and 19.023, which corresponds to option (a).

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The store pays $842.00 for the crystal sculpture and marks the price up by 29%,  then the amount of the markup is $243.98.

What is the arithmetic operation?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

we have given,

The store pays $842.00 for the crystal sculpture and marks the price up by 29%,

so, the amount of the mark-up can be calculated as follows:

$842.00 * 29% = $842.00 * 0.29 = $243.98

Therefore, the amount of the markup is $243.98.

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Correct question:

A store pays $842.00 for a crystal sculpture and mark the price by 29%. What is the amount of the mark-up?

The store pays $842.00 for the crystal sculpture and marks the price up by 29%,  then the amount of the markup is $243.98.

A subfield of mathematics known as arithmetic operations deals with the study and manipulation of numbers, which are essential to all other subfields of mathematics. Basic operations like addition, subtraction, multiplication, and division are included in it.

The four mathematical operations are functions that take input values, or numbers, as inputs and turn one number into another. They are: multiplication, division, addition, and subtraction.

According to contemporary mathematicians, the Riemann Hypothesis is possibly the most significant open problem in all of mathematics. One million dollars will be awarded to the person who can solve it, which is one of the seven Millennium Prize Problems.

we have given,

The store pays $842.00 for the crystal sculpture and marks the price up by 29%,

so, the amount of the mark-up can be calculated as follows:

\(842.00 \times 29% \\= $ 842.00 \times 0.29 \\= $243.98\)

Therefore, the amount of the markup is $243.98.

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Correct question:

A store pays $842.00 for a crystal sculpture and mark the price by 29%. What is the amount of the mark-up?

This is the answer. If this helps you please give brainliest.

Work Shown:

\(\frac{2^x \times 3^y}{2^4 \times 3^2} = 6\\\\\frac{2^x \times 3^y}{2^4 \times 3^2} = 2\times3\\\\\frac{2^x \times 3^y}{2^4 \times 3^2} = 2^1\times3^1\\\\2^x \times 3^y = (2^4 \times 3^2)(2^1\times 3^1)\\\\2^x \times 3^y = (2^4\times2^1) (3^2\times 3^1)\\\\2^x \times 3^y = 2^{4+1} \times 3^{2+1}\\\\2^x \times 3^y = 2^{5} \times 3^{3}\\\\\)

The 2^x matches with 2^5, showing that x = 5.

3^y matches with 3^3 to get y = 3

Therefore, x+y = 5+3 = 8