Geometry
A.)10 units
B.)17 units
C.)14 units
D.)7 units

Answer:

Step-by-step explanation:

Since 18,24,36 all three are divided by 6

So option B is the correct option

Answer:

D. x = 18 cm , y = 9

Step-by-step explanation:

With reference angle 60

perpendicular (p) = 9\(\sqrt{3}\)

base(b)= y

hypotenuse (h) = x

Then

sin 60 = p/h

\(\frac{\sqrt{3} }{2} = \frac{9\sqrt{3} }{x}\)

x = 18

Now

cos 60 = b/h

1/2 = y/18

y = 9

Hope it will help :)

Answer:

it's answer is

D. = 18 and y = 9

Answer: w= -18

Step-by-step explanation:

1.) 3(6t2+5t+-4)

2.) 12(-2)power of 2+15(-2)-12

3.) 24-30-12

4.) -6-12

5.) -18

\(8 (\sqrt{4} \times 2 + 6) \\ \sqrt{4} = 2 \\ 2 × 2 = 4 \\ 4 + 6 = 10 \\ 8(10) = 80\)

The volume of the solid is \(\frac{32}{3}\) cubic units.

To find the volume of the solid, we need to integrate the area of each cross section taken perpendicular to the y-axis over the range of y-values that the ellipse covers.

the height of each cross section will be equal to the y-coordinate of the ellipse at that point, since the triangles are isosceles and right-angled. The base of each cross section will be twice the height, since the triangles are isosceles, and the hypotenuse will lie in the ellipse.

So, for a given y-value, the area of the cross section will be:

\(A(y) = \frac{1}{2} \cdot 2y \cdot y = y^2\)

To find the limits of integration for y, we need to find the y-coordinates of the points where the ellipse intersects the y-axis. We can do this by setting x = 0 in the equation of the ellipse:

\(4x^2 + 9y^2 = 36\\9y^2 = 36\\y^2 = 4\\y = \pm 2\)

So, the limits of integration for y are -2 and 2.

The volume of the solid can now be found by integrating the area of the cross sections over the range of y-values:

\(V = \int_{-2}^{2} A(y) dy\\V = \int_{-2}^{2} y^2 dy\\\\V = \frac{1}{3}y^3 \Bigg|_{-2}^{2}\\V = \frac{1}{3}(2^3 - (-2)^3)\\V = \frac{32}{3}\)

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Answer:

r = 7 ft

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

Here C = 43.96 , then

2πr = 43.96 ( divide both sides by 2 × 3.14 ← for π )

r = \(\frac{43.96}{2(3.14)} \) = \(\frac{43.96}{6.28} \) = 7 ft

The area of the parallelogram is approximately 193.73 square meters.

How to find the area?

To find the area of a parallelogram, we need to multiply the length of one side of the parallelogram by the perpendicular distance between that side and the opposite side.

In this case, we know that one side of the parallelogram is 11.8 m and the other side is 18.5 m. Let's call these sides "a" and "b" respectively.

To find the perpendicular distance between these two sides, we need to draw a perpendicular line from one of the endpoints of side "a" to side "b". Let's call this perpendicular distance "h".

We can use the formula for the area of a parallelogram:

Area = base x height

where the base is side "a" and the height is "h".

To find "h", we can use the Pythagorean theorem:

h² = b² - (a/2)²

where "a/2" is half of side "a".

Plugging in the values we know, we get:

h² = 18.5² - (11.8/2)²

h² = 302.25 - 34.81

h² = 267.44

h ≈ 16.36

Now that we know the height of the parallelogram, we can calculate its area:

Area = 11.8 x 16.36

Area ≈ 193.73 m²

Therefore, the area of the parallelogram is approximately 193.73 square meters.

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Awenser 101 Simplified 86 +15 X 3

Step-by-step explanation:

i did 4-9 got -5 times 3 = -15 then 86- (-15) = 101

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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Step-by-step explanation:

First term (a)=10

Common ratio r=20/10 =2

14th term =ar^n-1

Where n is the number of terms

14th term = 10(2)^14-1

=20^13

=8.192^16

The stiffness of the members, km is 7.81 kip/in.

Given data:

Bolt is 1/4 in.

20 UNE 8 Mpsis

Hexagonal nut

Problem 2.5 clamped together with a bolt and a regular hexagonal nut.

1. Determine a suitable length for the bolt, rounded up to the nearest Volny

The bolt is selected from the tables of standard bolt lengths, and its length should be rounded up to the nearest Volny.

Volny is defined as 0.05 in.

Example: A bolt of 2.4 in should be rounded to 2.45 in.2.

2. Determine the carbon steel (E - 30.0 Mpsi) bolt's stiffness, kus

To find the carbon steel (E - 30.0 Mpsi) bolt's stiffness, kus,

we need to use the formula given below:

kus = Ae × E / Le

Where,

Ae = Effective cross-sectional area,

E = Modulus of elasticity,

Le = Bolt length

Substitute the given values,

Le = 2.45 in

E = 30.0 Mpsi

Ae = π/4 (d² - (0.9743)²)

where, d is the major diameter of the threads of the bolt.

d = 1/4 in = 0.25 in

So, by substituting all the given values, we have:

\($kus = \frac{\pi}{4}(0.25^2 - (0.9743)^2) \times \frac{30.0}{2.45} \approx 70.4\;kip/in\)

Therefore, the carbon steel (E - 30.0 Mpsi) bolt's stiffness,

kus is 70.4 kip/in.2.

3. Determine the stiffness of the members, km.

The stiffness of the members, km can be found using the formula given below:

km = Ae × E / Le

Where,

Ae = Effective cross-sectional area

E = Modulus of elasticity

Le = Length of the member

Given data:

Area of the section = 0.010 in²

Modulus of elasticity of member = 29 Mpsi

Length of the member = 3.2 ft = 38.4 in

By substituting all the given values, we have:

km = \(0.010 \times 29.0 \times 10^3 / 38.4 \approx 7.81\;kip/in\)

Therefore, the stiffness of the members, km is 7.81 kip/in.

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The maximum number of elements that can be chosen from the set

\({1,2,…,2005}\) {1,2,…,2005} such that the sum of any two chosen elements is not divisible by 3 is 3.

To find the maximum number of elements that can be chosen from the set

{1,2,…,2005}

{1,2,…,2005} such that the sum of any two chosen elements is not divisible by 3, we can analyze the possible remainders when dividing the numbers by 3.

Let's consider the three possible remainders after dividing a number by 3: 0, 1, and 2. We need to ensure that no pair of chosen elements has a remainder of 0 when their sum is divided by 3.

If we choose an element with a remainder of 0 (divisible by 3), we cannot select any other element with a remainder of 0 because the sum would also have a remainder of 0 and violate the condition. Therefore, we can choose at most one element with a remainder of 0.

Now, let's consider the elements with a remainder of 1. If we choose one element with a remainder of 1, we cannot select any other element with a remainder of 2. Otherwise, their sum would have a remainder of 0, which is not allowed. Similarly, if we choose one element with a remainder of 2, we cannot select any other element with a remainder of 1. Hence, we can choose at most one element with a remainder of 1 and at most one element with a remainder of 2.

To maximize the number of elements chosen, we select one element with a remainder of 0, one with a remainder of 1, and one with a remainder of 2. This ensures that no pair of chosen elements sums to a multiple of 3. Therefore, the maximum number of elements that can be chosen is

1

+

1

+

1

=

3

1+1+1=3.

In summary, the maximum number of elements that can be chosen from the set

{

1

,

2

,

…

,

2005

}

{1,2,…,2005} such that the sum of any two chosen elements is not divisible by 3 is 3.

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Answer:

-n^3 – 5n + 4

Step-by-step explanation:

f(n) = -n^3 – 4

g(n) =  -n +4

f(n)+ g(n) = (-n^3 – 4n)+(-n +4)

               = (-n^3 – 4n -n +4)

               = -n^3 – 5n +4

As a result, the angle CBF has a 61 degree value.

When two consecutive lines or beams intersect at a single terminus, an angle is created. The apex of an arc is the location where two points come together.

Since Ray BF splits angle BCD into two equal portions because it is an angle bisector, the measures of angle CBF and angle DBF are the same. Consequently, we can write:

3z + 7 = 5z - 29

Simplifying and solving for z:

2z = 36

z = 18

Now we can substitute z = 18 into the expression for the measure of angle CBF:

3z + 7 = 3(18) + 7 = 61

Therefore, the measure of angle CBF is 61 degrees.

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Represent the situation by using a function. If Sue swims 1.5 laps per minute, the equation that represents this situation is

Where y is the number of laps and x is the time in minutes

With this equation you can make a table

Finally, make the graph

The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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The expected frequency of east campus and passed is C. 42 students

The table for expected frequency is ,

East Campus West Campus Total

Passed (84*100)/22=42 (84*100)/200 =42 84

Failed (116*100)/200=58 (116*100)/22=58 116

Total 100 100 200

Passed = 84×100/200

= 42

Therefore, the expected frequency of East Campus and Passed is 42 students.

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Answer:

your going to do super good and get %100

Step-by-step explanation:

Answer:

Did you ace it? %100?

Step-by-step explanation:

Step-by-step explanation:

\( \huge \: 9,140,000 = 9.14 \times {10}^{6} \)

Answer:

False.

Step-by-step explanation:

Using the property of distribution, (a + b)² will be a² + b², never a² + b.

No, for any two integers a and b, (a + b)² ≠ a² + b is a false statement.

For the given two integers a and b,

The given expression

(a + b)² = a² + b (false statement)

The correct statement is-

(a + b)² = (a + b)(a + b)

(a + b)² = a² + b² +  2ab

Thus, no, for any two integers a and b, (a + b)² ≠ a² + b.

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The equation that relates the y-displacement to the acceleration in the y-direction, the initial velocity in the y-direction, and the time is:\(y = (1/2)at^2 + v_{i}t\)

where y is the vertical displacement, a is the acceleration in the y-direction, t is time, and \(v_{i}\) is the initial velocity in the y-direction.

This equation is derived from the kinematic equations of motion, specifically the one that relates the displacement, velocity, acceleration, and time for motion in one dimension. The first term of the equation represents the displacement due to the acceleration, while the second term represents the displacement due to the initial velocity. The equation can be used to calculate the vertical displacement of an object with a known initial velocity and acceleration in the y-direction after a certain amount of time has passed.

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Answer:

500=D 100=M

Step-by-step explanation:

I hope that helps :D

Answer:

It will take him 7 hours to drive 441 miles

Step-by-step explanation:

Answer:

I wanna say 7 hours

Answer:

it's the second option

Step-by-step explanation:

Answer:

Translate 2 units up and reflect over the line x = 1

Step-by-step explanation:

If the semi-annual rate is 0.5%, then the Annual Percentage Rate is 0.0001%.

To find the Annual Percentage Rate (APR), we need to double the semiannual rate since there are two semiannual periods in a year.

So, the APR would be 1% (0.5% * 2).

2. To find the Effective Annual Rate (EAR), we can use the formula:

\(EAR = (1 + r/n)^n - 1\)

where r is the nominal interest rate and n is the number of compounding periods per year.

In this case, the nominal interest rate (r) is 0.5% and the compounding periods per year (n) is 2 (since it's a semiannual rate).

Plugging in these values into the formula:

EAR = (1 + 0.005/2)^2 - 1

EAR = (1.0025)^2 - 1

EAR = 1.005025 - 1

EAR = 0.005025

Therefore, the EAR (rounded to 6 decimal points) is 0.005025.

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Answer:

x= -11

Step-by-step explanation:

1/2(x-8)=3/2x+7

distribute

1/2x-4 = 3/2x+7

subtract 1/2x from both sides

1/2x cancels out

-4 = 1x+7

subtract 7 from both sides

-11 = 1x (1x is the same as "x")

Answer:

x=-11

Step-by-step explanation:

The solution to the equation is -11.

First I set up the equation.

1/2(x-8)=3/2x+7

Next, I simplified the equation. 1/2x-4=3/2x+7.

Then, I added 4 to both sides. 1/2x=3/2x+11.

Next, I subtracted 3/2x on both sides. -1x=11.

Then, I divided -1 on both sides, so I would have x by itself.

x=-11.

In conclusion, the solution to the equation is x= -11.

To check to make sure this is the correct answer, I put -11 into the x values of the equation.

1/2(-11-8)=3/2(-11)+7

Both sides of the equation equal -19/2.

the area of triangle is 7 sq.units

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

1- A = 23.55

2- In the 7th payment, the interest is $50 and the principal is $193.55.

To find the value of A, we can use the formula for calculating the monthly payment on a loan. Given that you took a loan of $5000 for 24 months at an interest rate of 1% per month, we can substitute these values into the formula. By doing so, we find that A is equal to $23.55.

To determine the interest and principal in the 7th payment, we need to understand how loan payments are typically structured. Each monthly payment consists of both interest and principal components. Initially, the interest portion is higher, while the principal portion gradually increases over time.

In this case, we know the loan amount is $5000, and the loan term is 24 months. To find the interest and principal in the 7th payment, we need to calculate the remaining balance after the 6th payment.

To calculate the remaining balance after the 6th payment, we subtract the total amount paid from the initial loan amount. The total amount paid after 6 payments can be calculated by multiplying the monthly payment (A) by the number of payments (6). In this case, 6 * $23.55 equals $141.30.

Next, we subtract the total amount paid ($141.30) from the initial loan amount ($5000) to get the remaining balance, which is $4858.70.

Now, we can calculate the interest in the 7th payment. Since the interest rate is 1% per month, the interest for the 7th payment can be found by multiplying the remaining balance ($4858.70) by 1% (0.01), resulting in $48.59. Therefore, the interest in the 7th payment is $48.59.

To find the principal in the 7th payment, we subtract the interest ($48.59) from the monthly payment ($23.55). This gives us $174.96. However, we need to adjust the principal amount to match the remaining balance after the 6th payment. Therefore, we subtract the remaining balance after the 6th payment ($4858.70) from $174.96 to find the adjusted principal, which is $193.55.

In summary, in the 7th payment, the interest is $48.59 and the principal is $193.55.

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Answer:

8.1061

8.209

8.26

8.6

Step-by-step explanation: