Mr. Naxvip wrote the expression below to represent the number of
people in his extended family based on the number of brothers, b, and
sisters, s, that he has.
b x 3 + 5 - 1
If Mr. Naxvip has 5 brothers and 2 sisters, how many total people are
in his family?

The exact value of the given expression is:(sqrt(15) + 2)/8.We are given that sin(theta) = 1/4 and tan(theta) > 0, where 0 ≤ theta ≤ 2pi. We need to find the exact value of cos(theta/2).

From the given information, we can find the value of cos(theta) using the Pythagorean identity:

cos(theta) = sqrt(1 - sin^2(theta)) = sqrt(15)/4.

Now, we can use the half-angle formula for cosine:

cos(theta/2) = sqrt((1 + cos(theta))/2) = sqrt((1 + sqrt(15)/4)/2) = sqrt((2 + sqrt(15))/8).

Therefore, the exact value of cos(theta/2) is:

cos(theta/2) = sqrt((2 + sqrt(15))/8).

Alternatively, if we rationalize the denominator, we get:

cos(theta/2) = (1/2)*sqrt(2 + sqrt(15)).

Thus, the exact value of cos(theta/2) can be expressed in either form.In the second part of the problem, we are given an expression:

sqrt(10)/4 * sqrt(6)/4 + sqrt(8 + 2sqrt(15))/4 * sqrt(8 - 2sqrt(15))/4.

We can simplify this expression by recognizing that the second term is of the form (a + b)(a - b) = a^2 - b^2, where a = sqrt(8 + 2sqrt(15))/4 and b = sqrt(8 - 2sqrt(15))/4.

Using this identity, we get:

sqrt(10)/4 * sqrt(6)/4 + sqrt(8^2 - (2sqrt(15))^2)/16

= sqrt(10*6)/16 + sqrt(64 - 60)/16

= sqrt(15)/8 + sqrt(4)/8

= (sqrt(15) + 2)/8.

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Answer:

Step-by-step explanation:

2k^2 + k – 3

Answer:

600

Step-by-step explanation:

Area of Square:

= l*w

= 20x20 = 400

Area of Triangle:

= b*h/2

= 20*20/2

= 200

400 + 200 = 600

Good luck! <3

Answer:

The total area of the shape is 600 square centimetres.

Step-by-step explanation:

You can solve this by finding the area of the square and the triangle separately.

The area of any rectangle, including squares, is width times height. The bottom square then has an area of 20cm × 20cm, which equals 400cm²

The area of a triangle is have of its base width times its height.  It too has a width of 20cm and a height of 20cm, so its area is 20cm × 20cm ÷ 2, which equals 200cm²

Add them together for the full area of the shape:

400cm² + 200cm² = 600cm²

Answer:

71.5556 but since you cant have half a pizza its only 71

Step-by-step explanation:

You can rent time on computers at the local copy center for 35 minutes with $25.

To find out how much time you can rent for $25 at the local copy center, follow these steps:

1. Subtract the $10 setup charge from the total amount you have: $25 - $10 = $15.
2. Now you have $15 left for renting time on the computers. Since it costs $2 for every 5 minutes, you need to find out how many 5-minute increments can be covered by $15.
3. Divide the remaining amount by the cost per 5-minute increment: $15 / $2 = 7.5. Since you can't have half an increment, round down to 7.
4. Multiply the number of 5-minute increments by the time per increment: 7 * 5 = 35 minutes.

So, you can rent time on computers at the local copy center for 35 minutes with $25.

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Answer:

x is 60 and y is 50

hope it helped have a good day mate

The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral \(\( \int_{1}^{2} x \ln x \, dx \)\) is approximated using \(\( n = 4 \)\)subintervals. In part (b), the integral\(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) is given with incorrect limits, so it cannot be evaluated.

To approximate \(\( \int_{1}^{2} x \ln x \, dx \)\) using the Composite Trapezoidal rule, we divide the interval \(\([1, 2]\) into \( n = 4 \)\) subintervals. The step size, \(\( h \)\), is calculated as\(\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)\). Then, we evaluate the function \(\( x \ln x \)\)at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: \(\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\]\)

Using this formula, we can calculate the approximation for the given integral. The limits of the integral \(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) are given as \(\( 2 \)\) to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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Answer:

i think its C

Step-by-step explanation:

It may be d though

Answer: 56

Step-by-step explanation: :)

a) To obtain the potential pressure drop in the wellbore, we can use the hydrostatic pressure equation.

The potential pressure drop is equal to the pressure gradient multiplied by the length of the wellbore. The pressure gradient can be calculated using the equation: Pressure gradient = (density of oil × acceleration due to gravity) × sin(θ), where θ is the deviation angle of the wellbore from horizontal flow. In this case, the pressure gradient would be (48 lbm/ft^3 × 32.2 ft/s^2) × sin(15°). Multiplying the pressure gradient by the wellbore length of 6,000 ft gives the potential pressure drop.

b) To determine the frictional pressure drop in the wellbore, we can use the Darcy-Weisbach equation. The Darcy-Weisbach equation states that the pressure drop is equal to the friction factor multiplied by the pipe length, density, squared velocity, and divided by the pipe diameter. However, to calculate the friction factor, we need the Reynolds number. The Reynolds number can be calculated as (density × velocity × diameter) divided by the oil viscosity. Once the Reynolds number is known, the friction factor can be determined. Finally, using the friction factor, we can calculate the frictional pressure drop.

c) To calculate the in-situ oil velocity, we need to consider the total volume of the pipe, including both oil and gas. The total pipe volume is calculated as the pipe cross-sectional area multiplied by the wellbore length. Subtracting the gas volume from the total volume gives the oil volume. Dividing the oil volume by the total time taken by the oil to flow through the pipe (converted to seconds) gives the average oil velocity.

d) The flow regime of the two-phase flow can be determined based on the oil and gas mixture properties and flow conditions. Common flow regimes include bubble flow, slug flow, annular flow, and mist flow. These regimes are characterized by different distribution and interaction of the oil and gas phases. To determine the specific flow regime, various parameters such as gas and liquid velocities, mixture density, viscosity, and surface tension need to be considered. Additional information would be required to accurately determine the flow regime in this scenario.

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Answer:

Base:3

Height:5

Area= 15

Step-by-step explanation:

Formula=BxH

3x5=15

Answer: a^3

Step-by-step explanation:

The gcf of 2a^3 and a^6 is a^3 because a is seen both in the two numbers. and also a^3 can go in both numbers(2a^3) and (a^6)

Answer: True

Step-by-step explanation:

Answer

x = 6°

Explanation

The key to solving this is shown in the attached image below

So, we can see that the relation between all of this is that

5x + 17 = ½ [(37x + 5) - (23x - 5)]

5x + 17 = ½ (37x + 5 - 23x + 5)

5x + 17 = ½ (37x - 23x + 5 + 5)

5x + 17 = ½ (14x + 10)

5x + 17 = 7x + 5

5x - 7x = 5 - 17

-2x = -12

Divide both sides by -2

(-2x/-2) = (-12/-2)

x = 6°

Hope this Helps!!!

Answer:

  x = 70°

  y = 35°

Step-by-step explanation:

Given one angle of a triangle is 75° and the other two are 'x' and 'y', you want to find the possible values of 'x' and 'y' when x = 2y.

The angle sum theorem and the given relation give rise to two equations:

  75 +x +y = 180

  x = 2y

Using the second equation to substitute for x in the first equation, we have ...

  75 +(2y) +y = 180

  3y = 105 . . . . . . . . . subtract 75 and simplify

  y = 105/3 = 35

  x = 2y = 2(35) = 70

The measures of angles x and y are 70° and 35°, respectively.

Answer:

Step-by-step explanation:

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).
Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.
Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.
So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.
To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.
We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.
Using these estimates, we can calculate the z-scores as follows:
z1 = (35 - 48)/17 = -0.76
z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.
To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:
0.3514 * 380 ≈ 133.7
So, the answer is not one of the choices given.

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The answer is not one of the choices given.0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).

Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.

Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.

So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.

To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.

We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.

Using these estimates, we can calculate the z-scores as follows:

z1 = (35 - 48)/17 = -0.76

z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.

To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:

0.3514 * 380 ≈ 133.7

So, the answer is not one of the choices given.

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To find a 98% confidence interval for the difference between the population means using MATLAB, we can follow the steps below:

Step 1: Enter the data into MATLAB. We can create two vectors for the sample data, x for sample 1 and y for sample

2.x = [3 12 1.25 0.082]; % sample

= [14 1.32 0.326]; % sample 2

Step 2: Calculate the sample means, standard deviations, and sample sizes. We can use the mean, std, and length functions in MATLAB to calculate these statistics. xbar = mean(x); % sample mean for sample 1ybar = mean(y); % sample mean for sample 2s1 = std(x); % standard deviation for sample 1s2 = std(y); % standard deviation for sample

2n1 = length(x); % sample size for sample 1n2 = length(y); % sample size for sample 2

Step 3: Calculate the degrees of freedom and the t-value for the confidence interval. We can use the vartest2 function in MATLAB to calculate the degrees of freedom and the t-value for the confidence interval.[~, df] = vartest2(x, y); % degrees of freedomt = tinv(0.99, df); % t-value for 98% confidence interval

Step 4: Calculate the confidence interval. We can use the formula below to calculate the confidence interval. We should enter the smaller of the confidence interval in the answer input

window.lower = (xbar - ybar) - t*sqrt((s1^2)/n1 + (s2^2)/n2);upper

= (xbar - ybar) + t*sqrt((s1^2)/n1 + (s2^2)/n2);CI = [lower, upper]

The 98% confidence interval for the difference between the population means is [-0.1327, 9.8827]. We should enter the smaller value, which is -0.1327, in the answer input window.

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According to the information, we can infer that the volume of the solid generated by revolving the region bounded by the graphs of the equations is \(\frac{448}{3} \pi\) cubic units, which is equivalent to \(\frac{448}{15} \pi\)

To find the volume of the solid we have to use he method of cylindrical shells by revolving the region bounded by the graphs of the equations \(y=2x^2\), \(y=0\), and \(x=2\) about the line \(y=8\) as follows:

The line y=8 is the axis of rotation, which means the distance from the axis to the point (2,0) is 8. So, the equation of the line that we are revolving the region around is x=10.

The region bounded by \(y=2x^2\), \(y=0\), and\(x=2\) is a right triangle with base 2 and height 4, which means its area is \((\frac{1}{2} )(2)(4) = 4.\)

Now, to find the volume of the solid, we integrate the product of the height of the cylinder and the circumference of the shell over the region of integration. The height of the cylinder is 8 minus the height of the triangle at a given x-value. The circumference of the shell is 2\(\pi\) times the distance from the axis of rotation to the shell, which is x-10. So, the integral is:

\(V =\) ∫\([0,2] 2\pi (x-10)(8-2x^2) dx\)

Simplifying the integrand, we get:

\(V =\)∫\([0,2] (-4\pi x^3 + 16\pi \pix^2 - 160\pi x + 1600\pi ) dx\)

Integrating, we get:

\(V = [-\pi x^4 + (16/3)\pi x^3 - 80\pi x^2 + 1600\pi x]\) evaluated from 0 to 2

\(V = (448/3)\pi - (896/3)\pi + (640/3)\pi\)

\(V = (448/3)\pi\)

According to the above, the correct answer is \(\frac{448}{15}\)\(\pi\)

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The derivative of H(z) is H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)].

To differentiate the function H(z) = ln[(d^2-z^2)/(d^2+z^2)]^(1/2), we will use the chain rule and the power rule of differentiation.

First, we can simplify the expression inside the natural logarithm using the laws of exponents:

[(d^2-z^2)/(d^2+z^2)]^(1/2) = [(d^2-z^2)^(1/2)/(d^2+z^2)^(1/2)]

Now we can differentiate H(z) as follows:

H'(z) = d/dz [ln[(d^2-z^2)/(d^2+z^2)]^(1/2)]

= (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * d/dz [(d^2-z^2)/(d^2+z^2)]

Using the quotient rule, we can simplify the derivative:

d/dz [(d^2-z^2)/(d^2+z^2)] = [(2z)(d^2+z^2) - (d^2-z^2)(2z)]/(d^2+z^2)^2

= -4zd^2/(d^2+z^2)^2

Substituting this back into H'(z), we get:

H'(z) = (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * (-4zd^2/(d^2+z^2)^2)

= -2zd^2/[(d^2-z^2)(d^2+z^2)]

Therefore, the derivative of H(z) is:

H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)]

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The nearest integer 136,043 people. To find the total population within a 3-kilometer radius of the city center, we need to integrate the population density function (∂(x, y)) over the circular region with a radius of 3 kilometers.

Given that the population density (∂) is defined as 7000 (x^2 + y^2)^-0.2 people per square kilometer, we can express the population density as a function of the distance from the origin (r).

Let's perform the integration using polar coordinates, where x = rcos(θ) and y = rsin(θ):

∂(r) = 7000\((r^2)^-0.2\)

∂(r) = 7000\(r^(-0.4)\)

Now, we need to integrate this population density function (∂(r)) over the circular region with a radius of 3 kilometers.

To do this, we integrate from 0 to 2π for the angle (θ), and from 0 to 3 kilometers for the radius (r).

Total population = ∫∫R ∂(r) r dr dθ

Total population = ∫[0 to 2π] ∫[0 to 3] 7000 \(r^(-0.4)\) r dr dθ

Simplifying the integral:

Total population = 7000 ∫[0 to 2π] ∫[0 to 3] \(r^(0.6)\) dr dθ

Total population = 7000 ∫[0 to 2π] [(\(r^(1.6)\))/(1.6)]|[0 to 3] dθ

Total population = 7000 \((1.6)^(-1)\)∫[0 to 2π] [(\(3^(1.6))\)/(1.6)] dθ

Total population = (7000/1.6) \((3^(1.6))\) ∫[0 to 2π] dθ

Total population = (7000/1.6) \((3^(1.6)\)) (θ)|[0 to 2π]

Total population = (7000/1.6) (\(3^(1.6)\)) (2π)

Now, let's evaluate this expression:

Total population ≈ (7000/1.6) (\(3^(1.6)\)) (2π)

Total population ≈ 136042.195 people

Rounding up to the nearest integer, the total population within a 3-km radius of the city center is approximately 136,043 people.

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Step-by-step explanation:

y=1/2x+4 y=_2x_3

y=y

1/2x+4= _2x_3

2x+2x=_3+4

4x=1

x=1/4

Answer:

2(lb+bh+hl)

Step-by-step explanation:

this the the formula

mark me brainliest

Answer:

=

Step-by-step explanation:

1. The square root of 4 is 2 because \(2^2\) = 4.

2. The cube root of 8 is 2 because \(2^3 = 2* 2 * 2\) = 8.

3. 2 and 2 are equal.

Therefore, the correct symbol is =.

Answer:

500

Step-by-step explanation:

g (10) = 20(x+15)

= 20 (10+15)

= 20 (25)

= 500

Based on the given information, the possible lengths of Pine Avenue are from 7 miles to 9 miles, because Main St. and Hill St. are located in that area. So, Pine Avenue must be longer than 7 miles and shorter than 9 miles.

The prompt mentions that Pine Avenue should be longer than seven miles, and shorter than nine miles. The distance between Hill Street and Pine Avenue is unknown and hence, it cannot be used to determine the length of Pine Avenue.

But, the distance between the house and Pine Avenue, or the distance between Pine Avenue and the movie theatre, or the distance between Pine Avenue and the beach are irrelevant to determine the possible lengths of Pine Avenue. Therefore, the answer to the given question is, Pine Avenue must be longer than 7 miles and shorter than 9 miles.

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Answer: (x +4)(x - 4)

Step-by-step explanation: Since x² - 16 represents the difference of two squares, it can be factored as the product of two binomials, one that has a plus in it and one that has a minus in it.

The first position in each binomial is filled by

the factors of x² that are the same, x times x.

The second position in each binomial is filled

by the factors of 16 that are the same, 4 times 4.

The answer therefore is (x + 4)(x - 4).

Answer:

1

Step-by-step explanation:

you cant fit more than one 2/3's in 1