Need help, i have the answer just need the steps

(8^2/7)(8^1/4)

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

Step-by-step explanation:

Which statements about the relationship between the two triangles below are true? Check all that apply.Mark this and return

Answer:

5

Step-by-step explanation:

14+10+6= 30 (6/30 = 0.2) 0.2 x 25=5

Answer: True

Step-by-step explanation: because bias can lead to personal errors

Step 1: Concept

The axis of symmetry always passes through the vertex of the parabola. The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Step 2: Find the axis of symmetry using the formula

The axis of symmetry is a vertical line.

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Therefore, the axis of symmetry is x= 1

Step 3: Find the vertex

To find the vertex, you substitute x = 1 in the equation of a parabola.

The vertex = (1,9)

\(slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=8x+2 \qquad \begin{cases} x_1=x\\ x_2=x+h \end{cases}\implies \cfrac{f(x+h)-f(x)}{(x+h)-x} \\\\\\ \cfrac{[8(x+h)+2]~~ -~~[8x+2]}{h}\implies \cfrac{[8x+8h+2]-8x-2}{h} \implies \cfrac{8h}{h}\implies 8\)

The correct answer is: O c. 0.

The Matlab command shown below will assign what value to the variable abcabc = sin(pi. )The value that will be assigned to the variable abc is 0, this is because the sin function returns the sine of an angle in radians. When an angle is an odd multiple of pi, the sine function will return 0. In this case, the angle is pi which is an odd multiple of pi and therefore the sin function will return 0.

Matrix Laboratory is referred to as MATLAB. It is a technical computing language with great performance. In the year 1984, Cleve Molar of the business MathWorks.Inc. developed it.It is created using Java, C++, and C. It permits the manipulation of matrices, the graphing of functions, the application of algorithms, and the development of user interfaces. MATLAB Library includes a large collection of built-in functions. Most of the mathematical operations carried out by these functions include sine, cosine, and tangent. They also carry out more complicated tasks including finding a matrix's inverse, determinant, cross product, and dot product.

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Answer:

5n = $10.25

Step-by-step explanation:

We know that the tub is 5 pounds, and costs $10.25. We also know that n is in dollars per pound. Dollars per pound can be written as the product of dollars, divided by pounds, so we can plug that in being n = $10.25/5, next we want to make the equation contain an integer on both sides and not contain any fractions, so we multiply both sides by 5, resulting in 5n = $10.25

In conclusion, the chance of having HIV, assuming a positive test result, is 0.4%. It is important to remember that this number could vary depending on the accuracy and false positive rate of the test, as well as the number of people infected with HIV in the given area.

Assuming you tested positive for HIV, the chance of having the virus is higher than 2.5%, since the test has a false positive rate of 2.5%.

Out of the 10,000 people, 250 are likely to test positive, of which only one person actually has the virus. This means that the actual chance of having HIV, assuming a positive test result, is 1 in 250 or 0.4%.

It is important to note that this calculation only applies to the specific case of the 10,000 people in question, and the false positive rate of the test. Different tests have different levels of accuracy and false positive rate, which could alter the result. Furthermore, the number of people infected with HIV may differ significantly in different areas, which could also change the probability.

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Answer:

1

Step-by-step explanation:

(10-(-9)*-1)

Remember that 2 negative equal a positive. So -(-9) is positive.

(10+9*-1)

Then, PEMDAS is how you should finish this.

So, 9*-1 is -9

Then, 10-9 is 1

Answer:

Step-by-step explanation:

The equation of a line with slope of m and y-intercept of b is: y = mx + b

b = 2 and line contains the point (4, -9), so:

-9 = m×4 + 2          {subtract 2 from both sides}

-11 = 4m                   {divide booth sides by 4

m = -¹¹/₄

Using the empirical rule, approximately 68% of the scores will fall within one standard deviation of the mean.

According to the empirical rule (also known as the 68-95-99.7 rule), for a bell-shaped distribution (or a normal distribution), approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Given that the mean score is 75 and the standard deviation is 6, we can calculate the range within one standard deviation of the mean as follows:

Lower bound: 75 - 6 = 69

Upper bound: 75 + 6 = 81

Thus, approximately 68% of the scores will fall between 69 and 81. It's important to note that the empirical rule provides a rough estimate and assumes a perfectly normal distribution.

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The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.

95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean. The empirical rule is a statistical technique that allows you to estimate the percentage of data within a certain number of standard deviations from the mean.

Therefore, to find the percentage of scores between 69 and 81 on a competency test with a mean of 75 and a standard deviation of 6, we can use the empirical rule as follows: Z-score for 69 = (69 - 75) / 6 = -1Z-score for 81 = (81 - 75) / 6 = 1

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since the distance between 75 and 69 is one standard deviation (6), we know that approximately 68% of the scores fall between 69 and 81. Therefore, the percentage of scores between 69 and 81 on the competency test is approximately 68%.

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Answer: Round the number: 38.872601

get the result: 38.87

Step-by-step explanation: hope this helpsss!!!!

Step-by-step explanation:

the positions after the decimal point (to the right side of the decimal point) are

tenths

hundredths

thousandths

...

we round by looking at the next smaller position. is the digit there smaller than 5 we round down. is it greater or equal to 5 we round up.

so, the rounded number here is

38.87

Answer:

D

Step-by-step explanation:

Answer:

8/5

Step-by-step explanation:

The given differential equation represents an LCR circuit, which is a second-order linear time-invariant system. The mechanical analogue of this equation is the harmonic oscillator. The natural frequency of the circuit for this combination of C, R, and L is approximately 10000 rad/s.

(a) The given differential equation represents a second-order linear homogeneous differential equation. It is a type of system known as a damped harmonic oscillator. The mechanical analogue of this type of equation in physics is the motion of a mass-spring-damper system. In this analogue, the capacitor corresponds to the spring, the resistor corresponds to the damper, and the inductor corresponds to the mass. The charge flowing in the circuit represents the displacement of the mass, and the voltage across the circuit represents the force acting on the mass.

(b) To find the complementary function in the critically damped case for the LCR circuit, we need to solve the characteristic equation associated with the given differential equation.

The characteristic equation is obtained by setting the coefficient of the highest derivative to zero:

s² + (R/L)s + (1/LC) = 0

For the critically damped case, the roots of the characteristic equation are equal:

s₁ = s₂ = -R/(2L)

The complementary function can be written as:

q_c(t) = e^(s₁t)(A + Bt)

where A and B are constants to be determined from initial conditions.

(c) In the given LCR circuit with C = 6 µF, R = 102, and L = 0.5 H, we need to determine the type of damping and write the general solution for g(t) in this situation.

The damping factor, ζ, can be calculated as:

ζ = R/(2√(LC))

Substituting the values:

ζ = 102/(2√(0.5610^(-6)))

ζ ≈ 0.477

Since ζ is less than 1, the circuit exhibits underdamping.

The general solution for g(t) in the underdamped case can be written as:

g(t) = e^(-ζω₀t)(Acos(ωdt) + Bsin(ωdt))

where ω₀ is the undamped natural frequency and ωd is the damped natural frequency.

(d) To calculate the natural frequency of the circuit, we can use the formula:

ω₀ = 1/√(LC)

Substituting the given values of C and L:

ω₀ = 1/√(0.5610^(-6))

ω₀ ≈ 10000 rad/s

The natural frequency of the circuit for this combination of C, R, and L is approximately 10000 rad/s.

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(a) The logistic differential equation is dP/dt = kP(1 - P/5900).

(b) The estimated population after 50 years is 5616.

(c)  The formula for the population after t years, given an initial population of P0, is:
P(t) = (5900 * P0) / (P0 + (5900 - P0) * e^(-k*t))

(d) The population after 50 years is approximately 5612.3.

(a) The logistic differential equation is given by:

dP/dt = kP(1 - P/5900)

where P is the population, t is time in years, k is the growth rate constant, and 5900 is the carrying capacity.

(b) Using Euler's method with step size h=1, the population after 50 years can be estimated as follows:

P(0) = 1000 (initial population)
P(1) = P(0) + h * dP/dt = 1000 + 1 * 0.0017 * 1000 * (1 - 1000/5900) = 1041 (rounded to nearest whole number)
P(2) = P(1) + h * dP/dt = 1041 + 1 * 0.0017 * 1041 * (1 - 1041/5900) = 1083 (rounded to nearest whole number)
...
P(50) = 5616 (rounded to nearest whole number)

Therefore, the estimated population after 50 years is 5616.

(c) The formula for the population after t years, given an initial population of P0, is:

P(t) = (5900 * P0) / (P0 + (5900 - P0) * e^(-k*t))

(d) Using P0 = 1000 and t = 50, the population after 50 years is:

P(50) = (5900 * 1000) / (1000 + (5900 - 1000) * e^(-0.0017*50)) = 5612.3 (rounded to one decimal place)

Therefore, the population after 50 years is approximately 5612.3.

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Answer:

d ≥ - 14

Step-by-step explanation:

6d ≥ - 84

Divide by 6 both sides

6d/6 ≥ - 84/6

d ≥ - 14

The given inequality 6 > x + 1 > 3 is an "and" inequality.

Compound inequalities are kind of inequality expressions which consists of two or more simple inequalities.

"And" inequality represents that both the inequalities are true.

"Or" inequality represents that either of the statement is true.

Given inequality is,

6 > x + 1 > 3

Subtracting 1 from throughout the inequality,

6 - 1 > x > 3 - 1

5 > x > 2

This implies that x is less than  and x is greater than 2, for which the value of x are 3 and 4.

Hence the given inequality is an "and" inequality.

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Answer:

180000

by multiplying 1.8 by 10^5 you have to move the decimal point 5 spots to the right since the power is a positive number. 1.8 turns into 180000

The domain and range is  [-4, 4] and [0, 4]

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

x² + y² = 16

y = √16 - x²

For domain under root should not be negative quantity,

16 - x²≥0

16≥x²

So, x≤4 or x≥4

Thus, the domain is  [-4, 4]

Range:

y is maximum at x=0, y=4

y is minimum at x=4, y=0

Thus, range = [0, 4]

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Answer:

we know that given triangle is right angled triangle.

➢ By using Phythagoras Theorem:-

\( \sf \longrightarrow \: (AC)^2 = (AB)^2 + (BC)^2\)

\( \sf \longrightarrow \: ( \sqrt{80} )^2 = (x)^2 + (8)^2\)

\( \sf \longrightarrow \: 80 = (x)^2 + (8)^2\)

\( \sf \longrightarrow \: 80 \: = x^2 \: + \: 8^2\)

\( \sf \longrightarrow \: 80 \: = x^2 \: + \: 64\)

\( \sf \longrightarrow \: 80 \: - 64 = x^2 \:\)

\( \sf \longrightarrow \: 16 = x^2 \:\)

\( \sf \longrightarrow \: x^2 \: = 16\)

\( \sf \longrightarrow \: x \: = \sqrt{16} \)

\( \sf \longrightarrow \: x \: = 4 \: units \)

Answer:

Step-by-step explanation:

Answer:

sorry but I actually don't know about it sorty

Answer:

460 miles/hour

Step-by-step explanation:

Distance = Speed x Time

We want the Speed, so let's rearrange the equation:

Speed = Distance/Time

We are given Distance = 2070 miles

and Time of 4.5 hours

Speed = (2070 miles)/(4.5 hours)

Speed = 460 miles/hour

The quantity of bread that Debbie uses each week on the average is = 54 loaves of bread

The number of days the restaurant opens per week = 6 days.

The number of bread she uses everyday is = 9 loaves.

Therefore, the quantity of bread that Debbie uses each week on the average is = 6×9 = 54 loaves of bread.

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In the binomial expansion (2x + 3)^5 , there are 6 terms.

According to the question, given that

Binomial expansion  (2x + 3)^5

Number of terms in a binomial expansion of (x + y)^n is

N = n + 1 words in total

In the binomial expansion (2x + 3)^5

n = 5

N = 5 + 1 = 6

Therefore, In Binomial expansion  (2x + 3)^5 there are 6 terms.

The algebraic expression (x + y)n can be expanded according to the binomial theorem, which represents it as a sum of terms using separate exponents of the variables x and y. Each word in a binomial expansion has a coefficient, which is a numerical value.

The formula for expanding the exponential power of a binomial expression is provided by the binomial theorem, sometimes referred to as the binomial expansion. The following is the binomial expansion of (x + y)n using the binomial theorem:

\((x+y)^n = n_C_{0} * n_y_{0} + n_C_{1} * n-1_y_{1} + n_C_{2} * n-2_ y_{2} + ... + n_C_{n-1} * 1_y_{n-1} + n_C_{n} * 0_y_{n}\)

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Answer:D

Step-by-step explanation:

you plug 4 in for x

f(4)=4^2+2(4)-3

=16+8-3

=24-3

=21

Step-by-step explanation:

perpendicular slope is negative reciprocal. -1/-1 = 1

y - 4 = x +3

y = x + 7

To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is recommended to add the numbers in ascending order (from smallest to largest) to minimize the accumulation of rounding errors and maintain higher precision during intermediate calculations. Thus, starting with 0.01 and ending with 1.00 would provide better accuracy.

To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is generally recommended to use an order that minimizes the accumulation of rounding errors. In this case, it is advisable to start with the smaller numbers and progress towards the larger ones.

By adding the numbers in ascending order (from 0.01 to 1.00), the rounding errors at each step will have a smaller impact on the overall result. This is because adding smaller numbers together first helps maintain a higher level of precision during intermediate calculations.

Therefore, to achieve better accuracy, you should add the numbers in ascending order, starting with 0.01 and ending with 1.00.

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