The measure of angle 1 is (10x+8)° and the measure of angle 3 is (12x- 10)°.
What is the measure of angle 2 in degrees?

9
98
82
16

The image of the inscribed circle is missing so i have attached it.

Answer:

x = 35

None of the given options are correct.

Thus, Option D is the answer.

Step-by-step explanation:

From the attached image, we can see that there are two lines projecting out of the centre of the circle with one having it's endpoint touching the edge of the hexagon while the other is perpendicular to the centre of a side of the hexagon and labeled x has it's endpoint touching both the circumference and the hexagon side.

Since line labeled x projects from the centre of the circle to the circumference, we can say that the radius is x.

The triangle formed is a right angled triangle with the other part touching only the hexagon as the hypotenuse.

We see the remaining part between the circle and the hexagon of this hypotenuse line given as 2.

Thus, hypotenuse = x + 2

This is because from the centre to the circumference is x as earlier discussed and this hypotenuse line crosses the circumference of the circle before touching the edge of the hexagon.

Using pythagoras theorem, we can find x:

x² + 12² = (x + 2)²

x² + 144 = x² + 4x + 4

x² will cancel out to give;

4x + 4 = 144

4x = 144 - 4

4x = 140

x = 140/4

x = 35

The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

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Answer:

3

Step-by-step explanation:

The answer is 3 because first you add -2 + 1 which is -1 then you multiply -3 by -1 and you get 3

In the Pythagorean theorem, a²+b²=c² is the formula for finding the missing side length in a right-angled triangle. This formula is useful for determining one of the missing side lengths of a right triangle if you know the other two.

However, the theorem also states that c is the length of the triangle's hypotenuse. So, if you have a right-angled triangle with all three sides provided, you may use the Pythagorean theorem to solve for any of the missing sides. You'll use the hypotenuse length as the c variable when the three sides are given, then solve for the missing side.

To apply the Pythagorean theorem, you must identify the hypotenuse, which is the side opposite the right angle. If you're given three sides, the longest side is always the hypotenuse. As a result, you can always use the Pythagorean theorem to solve for one of the shorter sides by using the hypotenuse length.

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The hexadecimal number 0x3d is equal to 61 in decimal (base 10).

To convert the hexadecimal number 0x3D to decimal (base 10), we need to understand the positional system of both bases. In hexadecimal, each digit represents a power of 16, starting from the rightmost digit. The digits range from 0 to 9, and then from A to F, where A represents 10 and F represents 15, In hexadecimal (base 16) representation, each digit can have values from 0 to 15. The digits from 0 to 9 represent their respective values, and the letters A to F represent the values 10 to 15.

To convert 0x3d to decimal, we can break down the number as follows:

0x3d = (3 * 16^1) + (13 * 16^0)

Simplifying the expression:

0x3d = (3 * 16) + 13

0x3d = 48 + 13

0x3d = 61

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The Central Limit Theorem is a fundamental concept in statistics that states that the sampling distribution of the mean of a random sample approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To validate the Central Limit Theorem, you can follow these steps in any computation language of your choice:

1. Define the population distribution: Choose a probability distribution, such as a uniform, exponential, or binomial distribution, to represent the population from which samples will be drawn.

2. Generate random samples: Use the chosen distribution to generate random samples of different sizes. For example, you can generate 100 samples of size 10, 100 samples of size 30, and so on. Make sure to record the means of these samples.

3. Calculate the sample means: For each sample, calculate the mean by summing up all the values in the sample and dividing by the sample size.

4. Plot the sampling distribution: Create a histogram or a density plot of the sample means. This plot will show the distribution of the sample means.

5. Compare with the theoretical distribution: Overlay the theoretical normal distribution on the plot of the sample means. The mean of the sample means should be close to the mean of the population, and the shape of the distribution should resemble a normal distribution.

6. Repeat the process: Repeat steps 2-5 with different sample sizes to observe how the shape of the sampling distribution changes as the sample size increases. The Central Limit Theorem predicts that the distribution of the sample means will approach a normal distribution as the sample size increases.

By following these steps and comparing the distribution of the sample means with the theoretical normal distribution, you can validate the Central Limit Theorem in your chosen computation language.

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It is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques.

Multicollinearity is a statistical phenomenon where two or more independent variables in a regression model are highly correlated with each other. This can cause problems in the regression model as it becomes difficult to distinguish the individual effects of the independent variables on the dependent variable.
When multicollinearity is present in a regression model, the p-values of the slopes of the independent variables are affected. The p-value measures the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. The null hypothesis in a regression model is that the slope of the independent variable is zero, meaning that there is no relationship between the independent variable and the dependent variable.
Multicollinearity can cause the standard errors of the slopes to increase, leading to inflated p-values. In other words, the significance of the relationship between the independent variable and the dependent variable may be underestimated. This is because the highly correlated independent variables are both trying to explain the same variation in the dependent variable, leading to an unreliable estimate of the effect of each independent variable on the dependent variable.
Therefore, it is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques. This can help to ensure that the regression model produces reliable estimates of the effects of the independent variables on the dependent variable.

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Answer:

69/195

Step-by-step explanation:

So u add 24 and 16 to find the total number of people who are there

The total is 40

If they want at least 2 girls

So one of the probability for one girl is 24/40 which is 3/5

The other probability of another girl is 23/39

So u multiply 23/39 by 3/5 which is 69/195

Correct me if this is wrong

Sorry

Answer:

30.77%.

Step-by-step explanation:

There are a total of 40 members.

24 girls 16 boys.

Prob( 0 girls being chosen - so all boys ) =  16/40 * 15/39*14/38*  13/37*12/36 = 0.0063956

Prob( first one to be chosen is a girl  then all boys) = (24/40*16/39*15/38*14/37*13/36) = 0.013276

There are 5 ways of 1 girl being chosen so

Prob(1 girl out of 5 chosen) = 0.013276 * 5 = 0.06638

Prob( First 2  chosen are girls then all boys) = 24/40 * 23/39 * 16/38*15/37*14/36

= 0.023489

Number of ways of 2 girls being chosen is 5C2 and so the probability of 2 girls

= 0.023489 * 5C2

= 0.023489 * 10

= 0.23489.

Required probability = 0.23489 + 0.06638 + 0.0063956.

= 0.3076656

= 30.77% to the nearest hundredth.

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

We have,

a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:

P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))

Where:

P(t) = Pressure at time t

Pi = Initial reservoir pressure

Q = Flow rate

K = Permeability

h = Reservoir thickness

ϕ = Porosity

μ = Viscosity

Ct = Total compressibility

t = Shut-in time (12 hours)

Δt = Time since the start of the flow period

Bo = Oil formation volume factor

ΔP = Pressure drop during the flow period

Given:

Pi = 3100 psi

Q = 200 STB/day

K = 45 md

h = 60 ft

ϕ = 15%

μ = 1.2 cp

Ct = 15x10^-6 psi^-1

Bo = 1.3 bbl/STB

t = 12 hours

Δt = 48 hours

ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))

Substituting the given values into the equation:

ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))

After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.

b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.

It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.

The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.

Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.

It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.

Thus,

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

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Answer: σ: 2.76

Step-by-step explanation:

Count, N: 5

Sum, Σx: 125

Mean, μ: 25

Variance, σ2:  7.6

Steps

look at attached pic for formula

σ^2 = \(\frac{Σ(xi - μ)^{2} }{N}\)

\(\frac{(21 - 25)2 + ... + (29 - 25)2}{5}\)

⇒ \(\frac{38}{5}\)

⇒ 7.6

σ =  \(\sqrt{7.6}\)

⇒   2.756809750418

⇒ or 2.76

The chords in the circle L are illustrations of intersecting chords

The lengths that are even numbers are FJ and GJ

The length AD is given as:

AD = 10

From the circle, we have:

AD = AH + HK + KD

Where:

AH = 3 and KD = 2

So, we have:

10 = 3 + HK + 2

Solve for HK

HK = 5 ---- odd length

Next, we calculate length FH using the following intersecting chord theorem

FH * HB = AH * HD

This gives

(FJ + 3) * 3 = 3 * (2 + 5)

Divide by 3

FJ + 3 = 7

Subtract both sides by 3

FJ = 4 --- even length

Next, we calculate length KE using the following intersecting chord theorem

KE * KC = KD * KA

This gives

KE * 3.2 = 2 * (5 + 3)

Evaluate the product

KE * 3.2 = 16

Divide by 3.2

KE = 5 --- odd length

Next, we calculate length GJ using the following intersecting chord theorem

GJ * JE = FJ * JB

This gives

GJ * 4.5 = 4 * (6 + 3)

Evaluate the product

GJ * 4.5 = 36

Divide by 4.5

GJ = 8 --- even length

Hence, the lengths that are even numbers are FJ and GJ

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Answer:

Since the line is not filled in it has to be greater than or less than it cannot be equal to so x<-1.

The solution to the differential equation y" + 2y + 10y=0 with the given initial conditions is given by:

y = e^(-t)(7cos(3t) - (7/3)sin(3t)).

Given the differential equation: y" + 2y +10y=0

We have to find the solution to the differential equation such that the initial values are:

y(0) = 7 and y'(0) = 2.

To solve the above differential equation, we first find the characteristic equation whose roots are given as follows: r² + 2r + 10 = 0

Applying the quadratic formula, we have:

r = (-2 ± √(4 - 40))/2

r = -1 ± 3i

Since the roots are complex, the solution is given as follows:

y = e^(-1t)(c₁cos(3t) + c₂sin(3t))

Differentiating the above equation, we get:

y' = e^(-1t)(-c₁sin(3t) + 3c₂cos(3t))

Differentiating the above equation again, we get:

y" = e^(-1t)(-3c₁cos(3t) - 9c₂sin(3t))

Substituting the values of y(0) and y'(0) in the solution equation, we get:

7 = c₁1 + c₂0 and 2 = -c₁3 + c₂0

Solving the above two equations, we get:

c₁ = 7 and c₂ = -21/3

The final solution to the differential equation is given by:

y = e^(-t)(7cos(3t) - (7/3)sin(3t))

Therefore, the solution to the differential equation y" + 2y + 10y = 0 with the given initial conditions is:

y = e^(-t)(7cos(3t) - (7/3)sin(3t))

Answer:

Thus, the solution to the differential equation y" + 2y + 10y=0 with the given initial conditions is given by:y = e^(-t)(7cos(3t) - (7/3)sin(3t)).

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Answer:

3 : 2

Step-by-step explanation:

Number of students in the class = 15

Number of boys in class  = 9

To describe ratio;

  We know that the number girls in the class will be

          15 - 9 = 6 students.    

Simply in this class, the ratio of boys to girls:

            9 : 6  = 3 : 2

In the class, we have 3 boys to 2 girls.

Answer:

16

Step-by-step explanation:

the quadratic equation –3 = –x2 + 2x can be changed into :

x²-2x-3= 0

a=1, b= -2 , and c = -3

so, the discriminant = (-2)²-4(1)(-3)

= 4 + 12 = 16

To calculate the net present value (NPV) at Time 0, we need to discount the cash flows from Years 2 through 6 to their present value, and then compare it to the initial investment at Time 0.

Let's break down the calculation step by step:

Calculate the present value of cash flows from Years 2 to 6:

The cash flow for each year is $543,000.

Since the cash flows are received annually, we need to discount them by the appropriate discount rate for each year.

The discount rate is 11 percent.

Using the formula for the present value of a cash flow, we can calculate the present value for each year:

PV = CF / (1 + r)^n

Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the year.

Calculating the present value for each year:

PV2 = $543,000 / (1 + 0.11)^2

PV3 = $543,000 / (1 + 0.11)^3

PV4 = $543,000 / (1 + 0.11)^4

PV5 = $543,000 / (1 + 0.11)^5

PV6 = $543,000 / (1 + 0.11)^6

Calculate the probability-weighted present value of cash flows from Years 2 to 6:

The probability of a successful test and investment is 70 percent.

Multiply each present value by the probability to get the probability-weighted present value.

PWPV2 = 0.7 * PV2

PWPV3 = 0.7 * PV3

PWPV4 = 0.7 * PV4

PWPV5 = 0.7 * PV5

PWPV6 = 0.7 * PV6

Calculate the total present value of cash flows:

Add up the probability-weighted present values.

Total PV = PWPV2 + PWPV3 + PWPV4 + PWPV5 + PWPV6

Calculate the net present value at Time 0:

Subtract the initial investment at Time 0 from the total present value.

NPV = Total PV - $159,000

Now, let's perform the calculations:

PV2 = $543,000 / (1 + 0.11)^2 = $543,000 / 1.2321 ≈ $441,648.60

PV3 = $543,000 / (1 + 0.11)^3 = $543,000 / 1.3676 ≈ $397,431.88

PV4 = $543,000 / (1 + 0.11)^4 = $543,000 / 1.5162 ≈ $358,262.97

PV5 = $543,000 / (1 + 0.11)^5 = $543,000 / 1.6782 ≈ $323,335.62

PV6 = $543,000 / (1 + 0.11)^6 = $543,000 / 1.8550 ≈ $292,290.66

PWPV2 = 0.7 * $441,648.60 ≈ $309,154.02

PWPV3 = 0.7 * $397,431.88 ≈ $278,202.32

PWPV4 = 0.7 * $358,262.97 ≈ $250,784.08

PWPV5 = 0.7 * $323

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The net present value at Time 0, given an 11 percent discount rate, is $374,432.84.

The net present value (NPV) is a financial metric that measures the profitability of an investment by calculating the present value of expected cash flows. It takes into account the time value of money, which means that future cash flows are discounted to their present value.

Step 1: To calculate the NPV, we need to discount the expected cash flows to Time 0 using the given discount rate of 11 percent. The cash flows include the initial testing cost, production cost, and aftertax cash flows for Years 2 through 6.

Step 2: By discounting the cash flows, we find that the NPV at Time 0 is $374,432.84.

Step 3: The NPV represents the expected profitability of the investment. A positive NPV indicates that the investment is expected to generate more value than the initial cost. In this case, the positive NPV of $374,432.84 suggests that the investment is likely to be profitable, considering the expected cash flows and the discount rate.

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Answer:

1/root(3)

Step-by-step explanation:

the steps are in the pic above.

The value of tan pi/6 is 0.5773502.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Given that, what is the exact value of tan pi/6,

To find the value of tan π/6 using the unit circle:

Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.

The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence, the value of tan pi/6 = y/x = 0.5774 (approx)

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Answer:

Derek

Step-by-step explanation:

15/25

8/14

find common factor:

350 is the lcm for both of them

Derek: 15/25= 210/350

Meredith: 8/14= 200/350

So, Derek got a better score

Answer:

derek

Step-by-step explanation:

if u simplify them, meredith in simplest form in decimal is .571428

and derek when you simplify his in simplest form in decimal is .6

so therefore derek has a higher or better score

plz give me brainliest

Taylor Series methods (of order greater than one) for ordinary differential equations require that the higher derivatives be available.

An autonomous ordinary differential equation is one in which the derivative depends only on x.

Taylor series method is a numerical technique used to solve ordinary differential equations. Higher order Taylor series methods require the availability of higher derivatives of the solution.

For example, a second order Taylor series method requires the first and second derivatives, while a third order method requires the first, second, and third derivatives. These higher derivatives are used to construct a polynomial approximation of the solution.

An autonomous ordinary differential equation is one in which the derivative only depends on the independent variable x, and not on the dependent variable y and the independent variable t separately.

This means that the equation has the form dy/dx = f(y), where f is some function of y only. This type of equation is also known as a time-independent or stationary equation, because the solution does not change with time.

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Answer: 4.25 meters of rope

Step-by-step explanation:

Because Donna is losing 7.75 meters of rope from her original 12 meters, this problem can simply be represented as 12 - 7.75, which equals 4.25.

Hope it helps :) and let me know if you want me to elaborate.

For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.

In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L

x→a⁻ x→a⁺

We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.

So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)

= 16+ 3h

Now, lim [ f(5 + h) − f(5)]/ h

h→0

= lim [(16 + 3h) − (16) ]/ h

h→0

= lim [ 16 + 3h - 16 ]/ h

h→0

= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]

h→0 h→0

= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]

h→0 h→0

= lim 3 (1) = 3 ( since, x⁰ = 1 )

h→0

Hence, the required limit value is 3.

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It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.

Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40

Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60

Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60

The amount of swimming pool filled in 1 minute = (60 - 40)/2400

The amount of swimming pool filled in 1 minute = 20/2400

The amount of swimming pool filled in 1 minute = 1/120

Total time taken to fill swimming pool = 1 ÷ (1/120)

Total time taken to fill swimming pool = 120 minutes

Thus, 120 minutes are required.

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Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

Step-by-step explanation:

try use ruler for AB , AC , & BC ,

then find the area of

A line is vertical, then all points lie on it have the same x-coordinates

If line L is a vertical line and passes through the point (a, b), then its equation is

Since the given line is a vertical line and passes through the point (-5, -3)

That means a = -5

Then its equation is

Answer:

\(1 \frac{2}{5} \)

Step-by-step explanation:

\(4 - 2 \frac{3}{5} \)

\( = 4 - \frac{13}{5} \)

\( = \frac{20 - 13}{5} \)

\( = \frac{7}{5} \)

\( = 1 \frac{2}{5} \)