Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
(x- 9)² = 16 X x ... = ... (smaller value) x ... = ... (larger value)

Answer:

Methods including water divining, astrology, numerology, fortune telling, interpretation of dreams, and many other forms of divination, have been used for millennia to attempt to predict the future.

Step-by-step explanation:

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As describes in geometry the area of the rectangle = 288cm

what is geometry ?

The area of mathematics known as geometry is concerned with the characteristics of the surrounding space as well as the shapes of individual objects and their spatial relationships.

solution

radius of semicircle = 12

diameter will be = 24 and this is the length of rectangle s given in the question

area of the rectangle  = l*b

                                     = 24*12

area of the rectangle = 288cm

Hence the area of the rectangle = 288cm

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To determine whether there are differences between more than two population variances, utilise anova is True

What is Anova?

A statistical technique called analysis of variance, or ANOVA, divides observed variance data into various components for use in further testing. When there are three or more data groups, a one-way ANOVA is used to find out how the dependent and independent variables are related.

Concept:

One-way ANOVAs are typically used when there are three or more categorical independent groups, although they can also be employed when there are only two groups (but an independent-samples t-test is more commonly used for two groups)

A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

The absence of a difference in means is always the null hypothesis in an ANOVA. The alternative or research hypothesis, which is typically expressed in words rather than mathematical symbols, asserts that the means are not all equal. The research hypothesis involves any difference in means, such as when all four means are different from one another, one mean differs from the other three, two means differ, and so on. All scenarios other than the equality of all means described in the null hypothesis are covered by the alternative hypothesis, as it was previously illustrated.

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A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

Answer:

\(x=2,\\x=-2,\\x=\sqrt{3},\\x=-\sqrt{3}\)

Step-by-step explanation:

This is a quadratic in disguise. Let \(n=x^2\). We can rewrite the problem as a quadratic to solve:

\(n^2-7n+12=0,\\(n-3)(n-4)=0,\\n=3,\: n=4\).

Now plug in these values of \(n\) to solve:

\(\begin{cases}x^2=4, \:x=\pm 2\\\\x^2=3, x=\pm\sqrt{3}\end{cases}\).

Therefore, our solutions are \(x=\pm 2, \:x=\pm\sqrt{3}\).

The amount paid by the first place $60 when the second place pays $36.

According to the question,

We have the following information:

When the first place pays $100, the second place pays $60.

Now, we will first find the money to be paid by the first place when the second place pays $1.

So, we will find this value by dividing the money paid by the first place by the money paid by the second place.

$60 of second place = $100 of first place

$1 of second place = 100/60 of first place

$ 1 of second place = 5/3 of first place

Now, when the second place has paid $36, we have the following expression:

$36 of second place = 5*36/3

$36 of second place = $60 of first place

Hence, the first place pays $60 when the second place pays $36.

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A 0.25 = 25% probability of having three females and one guy is discovered using probability & sample space ideas (in any order ).

The set containing all potential outcomes is known as the sample space.

The proportion of intended results in the sample space multiplied by the total of possibilities is the probability estimated from the sample space.

The sample space for 4 kids is provided by:

B - B - B - B

B - B - B - G

B - B - G - B

B - B - G - G

B - G - B - B

B - G - B - G

B - G - G - B

B - G - G - G

G - B - B - B

G - B - B - G

G - B - G - B

G - B - G - G

G - G - B - B

G - G - B - G

G - G - G - B

G - G - G - G

There are 16 possibilities.

There are 3 girls and 1 guy in the four groups, which are B-G-G-G, G-B-G-G, G-G-B-G, & G-G-G-B.

In other words, the likelihood of having three girls & one male is 25% when p = D T = 4 16 = 0.25 0.25 (in any order).

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An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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A. The relative frequency of a class is computed by dividing the frequency of the class by the sample size. A graphical presentation of the relationship between two variables is c) either an ogive or a histogram, depending on the type of data.

To compute the relative frequency of a class, the frequency of the class is divided by the a)sample size. The sample size is the total number of observations in the data set. This gives the proportion of the observations that belong to the class.  

A graphical presentation of the relationship between two variables is either an ogive or a histogram, depending on the type of data. An ogive is a cumulative frequency graph, which shows the cumulative frequency of a data set.

A histogram is a bar chart that shows the frequencies of a data set. Depending on the type of data, either an ogive or a histogram may be used to present the relationship between two variables.

To calculate the mean of a set of values, the value of Σx is divided by a) n, the number of values in the set. If the value of Σx is zero, then the mean of the set will also be zero. The value of Σx can never be b) negative because it is the sum of all the values in the set. It can, however, be any positive value.

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Answer:

x = 20

Step-by-step explanation:

\(\frac{10}{x}\) = \(\frac{x}{40}\)

We cross-multiply and get

400 = \(x^{2}\)

\(\sqrt{400}\) = \(\sqrt{x^{2} }\)

x = 20

So, the answer is x = 20

Answer:

-20 1/3

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

Because right now 19 4/3 is positive, we need to make it negative for it to even be the opposite. So B would be the correct answer.

Answer:

0.5

Step-by-step explanation:

-1+3(10-12)^3/-16

-1+3(-2)^3/-16

-1+(-24)/-16

.5

Answer: 1/5

Step-by-step explanation:

The root of the equation 2x(x - 8) = (x + 1)(2x - 3) is x = -1/4. To find the root of the equation 2x(x - 8) = (x + 1)(2x - 3), we need to solve for the value of "x" that makes both sides of the equation equal.

First, let's expand both sides of the equation:

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

\(2x^2 - 16x = 2x^2 - x - 3x + 3\)

Now, combine like terms on the right-hand side:

\(2x^2 - 16x = 2x^2 - 4x + 3\)

Next, subtract \(2x^2\) from both sides to get the x terms on one side:

-16x = -4x + 3

Now, bring all the x terms to one side by subtracting -4x from both sides:

-16x + 4x = 3

Simplify the left-hand side:

-12x = 3

Finally, solve for x by dividing both sides by -12:

x = 3 / -12

x = -1/4

So, the root of the equation 2x(x - 8) = (x + 1)(2x - 3) is x = -1/4.

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{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)}, {(−8, −3), (−6, −5), (−4, −2), (−2, −7), (−1, −4)} and {(−6, 4), (−3, −1), (0, 5), (1, −1), (2, 3)} are the sets of ordered pairs considered as a function.

{(−4, −2), (−1, −1), (3, 2), (3, 5), (7, 10)} is not a function.

In mathematics, ordered pair is a pair of numbers that are written in a specific order. They are generally written in (x, y) form. For example (3, 5) is an ordered pair.

The function can also be represented by a set of ordered pairs. A function Is a set of ordered pairs in which no two different ordered pairs have the same value of x coordinate.

Option (a) : {(5, 2),(4, 2),(3, 2),(2, 2),(1, 2)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (b) : {(-4, -2),(-1, -1),(3, 2),(3, 5),(7, 10)}

Two ordered pairs have the same value of x coordinate (3, 2) and (3, 5).

So, it can not be considered a function.

Option (c) : {(-8, -3),(-6, -5),(-4, -2),(-2, -7),(-1, -4)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (d) : {(-6, 4),(-3, -1),(0, 5),(1, -1),(2, 3)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Therefore, Options (a), (c), and (d) are the functions.

Option (b) is not a function.

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The solution accurate to equation within \(10^{-2}\) for \(x^{4}-2x^{3} -4x^{2} +4x+4=0\) lies in [0,2].  

Given the equation  \(x^{4}-2x^{3} -4x^{2} +4x+4=0\) and range is  \(10^{-2}\).

We are required to find the interval in which the solution lies.

The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the mid point of the interval is found. The sign of its relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than \(10^{-2}\).

Interval:[0,2], signs [+,-],mid point:1, sign at midpoint +.

[1,2]                                                       3/2

[1,3/2]                                                    5/4

The rest is in the attachment. The listed table values are the successive interval mid points.

The final midpoint is 181/128=1.411406.

This solution is within 0.0002 of the actual root.      

Hence the solution accurate to equation within \(10^{-2}\) for \(x^{4}-2x^{3} -4x^{2} +4x+4=0\) lies in [0,2].

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The area of the square is 1/4inches² in square inches

The area of a square is calculated by multiplying its two sides, that is area = s × s, where, 's' is one side of the square.

The square has side of length = 6/12

this can be simplified as 1/2

so

area of the square = (1/2 × 1/2) inches ²

area of the square = 1/4inches²

Thus, the area of the square is calculated using area = s × s, as 1/4inches²

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(1) The relative humidity is 60%.

(2) The temperature of the air parcel is Tdp ≈ 51.0 °F.

(3) LCL ≈ 1.82 km or 1820 meters

(4) The temperature at 6000 meters is 52.63 °F.

(5) SH at 6000 meters is 3.58 g/kg.

(6) Parcel temperature at 1000 meters is 35.13 °F.

Given data at sea level (ground):

(1) Calculate the Relative Humidity (RH) on the ground.

To calculate RH, we need to know the saturation-specific humidity at the given temperature.

The saturation-specific humidity (5Hs) at 59.0 °F can be found using a particular table of humidity or formula. However, since I don't have access to the internet for real-time calculations, let's assume the specific humidity at saturation is 9 g/kg at 59.0 °F.

Now we can calculate the RH on the ground:

RH = (SH / SHs) x 100

RH = (5.4 g/kg / 9 g/kg) x 100

RH ≈ 60%

(2) Calculate the Dew Point Temperature (Tdp) on the ground.

To calculate the dew point temperature, we can use the following approximation formula:

\(Tdp = T - (\dfrac{(100 - RH)} { 5}\)

Where Tdp is in °F, T is the temperature in °F, and RH is the relative humidity in percentage.

\(Tdp = 59.0 - \dfrac{(100 - 60) }{5}\\Tdp = 59.0 - \dfrac{40} { 5}\\Tdp = 59.0 - 8\\Tdp = 51.0 ^oF\)

(3) Calculate the Lifted Condensation Level (LCL) on the ground.

The LCL is where the air parcel would start to condense if lifted.

\(LCL = \dfrac{(T - Tdp)} { 4.4}\\LCL = \dfrac{(59.0 - 51.0)} { 4.4}\\LCL = \dfrac{8.0} { 4.4}\\LCL = 1.82 km or 1820 meters\)

(4) Lift the air parcel to 6000 meters (approximately 19685 feet).

The temperature decreases with height at a rate of around 3.5 °F per 1000 feet (or 6.4 °C per 1000 meters) in the troposphere. Let's calculate the temperature at 6000 meters.

Temperature at 6000 meters ≈ T on the ground - (LCL height / 1000) x temperature lapse rate

\(T= 59.0 - \dfrac{1820} { 1000} \times 3.5\\T= 59.0 - 6.37\\T= 52.63 ^oF\)

(5) Calculate the specific humidity (5H) at 6000 meters.

Assuming specific humidity decreases linearly with height, we can calculate it using the formula:

SH at 6000 meters ≈ SH on the ground - (LCL height / 1000) * specific humidity lapse rate

Let's assume a specific humidity lapse rate of 1 g/kg per 1000 meters.

\(SH = 5.4 - \dfrac{1820} { 1000} \times 1\\SH = 5.4 - 1.82\\SH = 3.58 \dfrac{g}{kg}\)

(6) The parcel descends from 6000 meters to 1000 meters.

We will assume the dry adiabatic lapse rate, which is 3.5 °F per 1000 feet (or 6.4 °C per 1000 meters).

Temperature change during descent ≈ (6000 - 1000) * temperature lapse rate

\(\Delta T= 5000 \times \dfrac{3.5} { 1000}\\\Delta T= 17.5 ^oF\)

Parcel temperature at 1000 meters ≈ Temperature at 6000 meters - Temperature change during descent

Parcel temperature at 1000 meters ≈ 52.63 - 17.5

Parcel temperature at 1000 meters ≈ 35.13 °F

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Answer:d.

explanation:brainleist please tysm☻

Rental: $15

Cost per hour: $6

total rental cost =15+6x

Where x is the number of hours

Using Kepler's Third Law, we can find the distance of the exo-planet from its star. The formula is P^2 = a^3, where P is the orbital period in years and a is the average distance from the planet to the star in astronomical units (AU).

the average distance of Le Grosse Homme from its star is approximately 2 AU, which is answer choice b).

To determine the distance of the exo-planet Le Grosse Homme to the star, we will use Kepler's Third Law, which states that the square of the orbital period (P) of a planet is proportional to the cube of the semi-major axis (a) of its orbit. The formula is given as:

P² = a³

In this case, the orbital period P is 2.8284 years. We can now solve for the semi-major axis (a), which represents the distance from the planet to the star in astronomical units (AU).

Step 1: Square the orbital period
(2.8284)² = 7.99968336

Step 2: Find the cube root of the squared orbital period to get the distance (a)
a = ∛(7.99968336) ≈ 2.0 AU

So, the distance of the exo-planet Le Grosse Homme to the star is approximately 2.0 AU. The correct answer is option (b) ~2.0 AU.

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Step-by-step explanation:

bodmas

7-4/4+12-10

7-4/16-10

3/4

0.75

The ferryman should transport the goat first, then return alone to bring the wolf, leaving the goat on the right bank. Finally, he should transport the cabbage and leave it with the wolf.

In order to solve this puzzle, the ferryman must make a series of careful moves to ensure the safety of the wolf, goat, and cabbage. The first step is to transport the goat to the right bank, leaving it there. The ferryman then returns to the left bank alone.

He takes the wolf across the river, but before leaving it on the right bank, he brings the goat back to the left bank. Now, the goat and cabbage are on the same side, while the wolf remains on the right bank.

The ferryman transports the cabbage to the right bank, leaving it there, and then returns alone to the left bank. Finally, he takes the goat across the river one last time, completing the puzzle. This sequence of moves ensures that the wolf and goat are never left alone together, nor are the goat and cabbage.

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The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Given four measurements:

We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.

A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as \(e^{-x}\).

We know that exponent shows continuous growth or continuous decay.

Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.

Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

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In a multiple regression model, the error term (often denoted as ε or e) is assumed to be a random variable with a mean of zero.

This assumption is a key component of the regression model and is often referred to as the assumption of zero conditional mean or the assumption of homoscedasticity. The assumption of a mean of zero for the error term means that, on average, the errors have no systematic bias or tendency to overestimate or underestimate the predicted values. It implies that the model's predictions are unbiased and that any deviations from the true values are due to random chance or other factors not captured by the model. The other options presented in the answer choices (B) -1, (C) 1, and (D) any value are incorrect. The mean of the error term is specifically assumed to be zero, as it represents the average deviation of the observed values from the predicted values in the model.

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Using a branch-and-bound algorithm combined with an effective search strategy and an appropriate selection of branching rules you can find the optimal solution for an optimization model with integer decision variables.

Solving an optimization model with integer decision variables requires a branch-and-bound algorithm, which recursively partitions the feasible region into smaller sub-regions until the optimal solution is found or proven to be infeasible. An effective search strategy, such as depth-first or best-first search, is used to explore the sub-regions efficiently.

The selection of branching rules is critical to the performance of the algorithm, as it determines the order in which variables are selected for partitioning. Effective branching rules, such as the most constrained variable or the strongest branching rule, can significantly reduce the number of nodes explored and improve the chance of finding the optimal solution. Additionally, using advanced techniques, such as domain reduction and cutting planes, can further enhance the performance of the algorithm.

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Answer:

(7,2)

Step-by-step explanation:

(7,-2) are the original coordinates, so you flip it over the x-axis, or you can flip the sign of the y value in the pond coordinates to get over the x-axis.

Answer: Factor

4xy out of 16xy2−28x2y.4xy(4y−7x)

Step-by-step explanation:

Answer:

y intercept is 2

x intercept is -2.6

Step-by-step explanation:

4y=3x-8

4y-3x=8

y/2-x/2.6=1

y intercept is 2

x intercept is -2.6

intercept formula

y/B+x/A= 1

where B and A are intercepts

Answer:

7x + 4y = 11,200

Step-by-step explanation:

Let

Number of Admission tickets A = x

Number of Admission tickets B = y

Cost of Admission tickets A = $7

Cost of Admission tickets B = $4

Total cost = $11,200

The equation is:

7x + 4y = 11,200

Answer:

option D. Car A has the same speed as car B.

The solution to the equation in this problem is given as follows:

y = -4.

The equation for this problem is defined as follows:

\(\frac{y - 6}{y^2 + 3y - 4} = \frac{2}{y + 4} + \frac{7}{y - 1}\)

The right side of the equality can be simplified applying the least common factor as follows:

[2(y - 1) + 7(y + 4)]/[(y + 4)(y - 1)] = (9y + 26)/(y² + 3y - 4)

The denominators of the two sides of the equality are equal, hence the solution to the equation can be obtained equaling the numerators as follows:

9y + 26 = y - 6

8y = -32

y = -32/8

y = -4.

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