Solve the radical equation.
x+1=7-6x-6
Which solution is extraneous?
The solution x=-1 is an extraneous solution.
Both x=-1 are x=-7 true solutions.
O The solution x=-7 is an extraneous solution.
O Neither x=-1 nor x=-7 is a true solution to the equation.

Answer:

Final cost is 817.76

Step-by-step explanation:

First find the amount of the tax

760 * 7.6%

760 * .076

75.76

Add this to the cost of the bike

760+57.76

817.76

Answer:

uhhhhhhhhhh

Step-by-step explanation:

hiiii

The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.

Hence option D is the correct option.

Mean is the average value of a given set of data. It is calculated by the formula,

Mean =  {Summation of all the values in the data set} / {Number of observations is the data set}

That is, Mean = {Σ all values in the data set} / {number of observations}

The given data set is as follows,

0,5,30,25,16,18,19,26,0,20,28

The number of observations in the data set is 11.

The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187

Therefore, by applying  the formula of Mean we get

Mean = 187/ 11 = 17

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Answer:

dogs sold = 6

burgers sold = 11

Step-by-step explanation:

B = 2H-1

1.50H + 2.00B = 31.00

substitute for B

1.5H + 2(2H-1) = 31

1.5H + 4H-2 = 31

5.5H = 33

H = 6

B = 11

The function \(f(x) = (x^2 - 1)/(x - 1)\) is continuous for all x except at x = 1, where there is a point of discontinuity. The point of discontinuity is (1, 2).

To determine the continuity of the function \(f(x) = (x^2 - 1)/(x - 1)\) for all the domain of the function, we need to check if it is defined at x = 1 and if the limit exists as x approaches 1.

At x = 1, the denominator of the function becomes 0, which results in an undefined value. Therefore, there is a potential point of discontinuity at x = 1.

To analyze the limit as x approaches 1, we can simplify the function by factoring the numerator:

f(x) = ((x - 1)(x + 1))/(x - 1).

Canceling out the common factor (x - 1), we get f(x) = x + 1.

The limit of f(x) as x approaches 1 is then lim(x->1) (x + 1) = 1 + 1 = 2.

Since the limit exists and is equal to the value of the function at x = 1, the function is continuous at all points except x = 1.

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To learn abount the students opinion about nutritional quality of school lunch the cashier asked each every fifth student as they pay for their lunch.

This type of sampling method is when you take the sample using a fixed and periodic interval and is called systematic sampling

We want to solve the following inequality:

11.22x - 200 < 347.96

In order to solve these type of expressions, we just have to "leave alone" the x on one side of the inequality (left side in this case).

In order to do that, we must remember two simple rules:

We want to take to the right side the -200 and 11.22.

Step 1: taking -200 to the right side

11.22x - 200 < 347.96

↓ adding 200 both sides

11.22x - 200 + 200 < 347.96 + 200

↓ left: since 11.22x - 200 + 200 = 11.22x

11.22x < 347.96 + 200

↓ right: since 347.96 + 200 = 547.96

11.22x < 547.96

Step 2: taking 11.22 to the right side

11.22x < 547.96

↓ dividing 11.22 both sides

11.22x/11.22 < 547.96/11.22

↓ left: since 11.22x/11.22 = x

x < 547.96/11.22

↓ right: since 547.96/11.22 = 48.8377

x < 48.8377

We want to round it to the nearest hundredth (number with two digits after the decimal point).

Since 48.8377 is nearer to 48.8400 than to 48.8300

then

48.8377 ≅ 48.8400 = 48.84

Answer: A. 48.84

\(\begin{align}\text{Time elapsed} &= 5:30\text{ a.m.} - 11:30\text{ p.m.} \ &= 6\text{ hours}\end{align}\)

\(\begin{align}\text{Average speed} &= \frac{\text{Distance traveled}}{\text{Time elapsed}}\end{align}\)

\(\begin{align}&= \frac{4{,}415\text{ km}}{6\text{ hours}} \ &\approx 736.67\text{ km/h}\end{align}\)

Rounding to the nearest whole number, we get the average speed of the aeroplane in km/h as $\boxed{737\text{ km/h}}$

\(\begin{align}\huge\colorbox{black}{\textcolor{yellow}{I hope this helps !}}\end{align}\)

\(\begin{align}\colorbox{purple}{\textcolor{lime}{Please mark as brillinest !}}\end{align}\)

\(\textcolor{cyan}{\small\textit{If you have any further questions, feel free to ask!}}\)

The slope of the line represents the ratio of the change in y to the change in x, indicating that for every increase of 5 units in x, the y-coordinate increases by 2 units. The y-intercept (-4) is the value of y when x is zero.

The equation of a line in standard form is given by Ax + By = C, where A, B, and C are constants. In this case, the slope of the line is 2/5, which means that for every increase of 5 units in x, the y-coordinate increases by 2 units. This can be represented as the fraction 2/5 or the decimal 0.4. The y-intercept is given as (0, -4), which means that when x is zero, the y-coordinate is -4.

To find the equation, we substitute the slope and y-intercept into the standard form equation. Plugging in the slope, we have 2x - 5y = C. We can use the y-intercept to determine the value of C. Substituting x = 0 and y = -4 into the equation, we get 2(0) - 5(-4) = C, which simplifies to 20 = C. Therefore, the equation of the line is 2x - 5y = 20. However, to express the equation in standard form, we need to make sure the coefficients are integers and the constant term is on the opposite side of the equation. By multiplying the entire equation by -1, we get -2x + 5y = -20, which is the final equation in standard form.

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a. The mean of the sample is 31

b. The standard deviation remains the same = 2

The formula for calculating mean of sample is expressed as;

Mean = (Sum of all measurements) / (Number of measurements)

Sum of measurements would be 12(31) = 372.

The addition of two measurements with a common value of 31.

Then, we have;

= 372 + 31 + 31 = 434.

Mean = 434 / 14

Mean = 31.00

B. The formula for calculating standard deviation is;

Standard Deviation = √((Sum of (each measurement - mean)²) / (Number of measurements))

Substitute the values, we have;

The sum of squared deviations= (31 - 31)² + (31 - 31)² = 0.

Then, we can say that there is no change in the standard deviation of the sample

Standard Deviation = 2.

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The standard deviation of the sample of 14 measurements is 1.48 (approx).

A sample of 12 measurements has a mean of 31 and a standard deviation of 2. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 31 each.

The mean of the sample of 14 measurements:

In order to find the new mean of 14 measurements we first need to find out the total sum of the 14 measurements.

Total sum of 12 measurements = 12 x 31

                                                    = 372

The additional 2 measurements that have a common value of 31, contribute to the total sum 2 x 31 = 62

Total sum of 14 measurements = 372 + 62

                                                    = 434

Therefore, the new mean of the sample of 14 measurements will be the total sum of all measurements divided by the total number of measurements = 434 / 14

                                                    = 31.

The mean of the sample of 14 measurements is 31..

The standard deviation of the sample of 14 measurements:

Standard deviation of the sample of 14 measurements is given by:

σ =  sqrt[ Σ ( Xi - µ )² / N ]

Where Xi is the individual data points, µ is the mean, and N is the total number of data points.

Let's calculate this by adding the additional two measurements to the original 12 measurements.

σ =  sqrt[ ((12-1) x 2² + (31-31)² + (31-31)²) / 14 ]

σ =  sqrt[ (44) / 14 ]

σ =  sqrt[ 22/7 ]

   = 1.48

Therefore, the standard deviation of the sample of 14 measurements is 1.48 (approx).

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Therefore, a factor of the given expression 27x³ - 22x² - 250x + 2574 is 9x - 14 or 3x + 13.

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.

Here,

One possible way to find a factor of 27x³- 22x² - 250x + 2574 is to use synthetic division with a possible root of the polynomial. We can try x = 2, since it is a common factor of the constant terms 22 and 2574. Using synthetic division with x = 2, we get:

2  |  27  -22  -250  2574

  |     54    64  -372

  |------------------

     27   32  -186  2202

The remainder is 2202, which means that x - 2 is not a factor of 27x³ - 22x² - 250x + 2574. However, the quotient is 27x² + 32x - 186, which we can factor further using the quadratic formula or factoring by grouping:

27x² + 32x - 186 = (9x - 14)(3x + 13)

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The 3 ways to prove similarity are Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).

The three theorems are as follows :

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Answer:

idk

Step-by-step explanation:

Answer:

We can start by simplifying both sides of the equation:

5x² + 18x = 25x + 15 + 3x²

2x² - 7x - 15 = 0

Now we need to factor this quadratic equation:

2x² - 7x - 15 = (2x + 3)(x - 5)

Setting each factor equal to zero gives us the solutions:

2x + 3 = 0 or x - 5 = 0

Solving for x, we get:

x = -3/2 or x = 5

Therefore, the solutions to the quadratic equation are x = -3/2 and x = 5.

So, the correct answer is (x - 5)(2x+3).

Multiples of a number are the numbers that a number can be divided by without any remainder.

The buses X and Y will leave at the same time by 8:40 am

To calculate when buses X and Y will leave at the time, we would have to find the Lowest Common Multiple of 20 and 25 minutes.

Find and list multiple until the first common multiple is found. This is the lowest common multiple.

Multiples of 20:

20, 40, 60, 80, 100, 120, 140

Multiples of 25:

25, 50, 75, 100, 125, 150

Therefore,

LCM(20, 25) = 100

The LCM is 100 minutes

Converting 100 minutes

60 minutes = 1 hour

100 minutes = ?

Cross Multiply

100 minutes x 1 hour / 60 minutes

= 1 2/3 hours.

This can be rewritten as :

= 1 hr 40 minutes

Adding this to 7am

7 am + 1 hr 40 minutes = 8 : 40am

Therefore, the buses X and Y will leave at the same time by 8:40 am

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Answer: 2 year

Step-by-step explanation: After 3 years scheme B would be 80$ while Scheme A would be 75$

A) The two possibilities for the x component are approximately +58.12 units and -58.12 units. B) The magnitude of the vector that, when added to the original one, would give a resultant vector that is 80.0 units long and points entirely in the +x direction is 0 units. c) The direction of the vector is approximately -42.29 degrees relative to the positive x-axis.

Part A:

Given that the magnitude of the vector is 80.0 units and the y component is -55.0 units, we can use the Pythagorean theorem to find the two possibilities for the x component.

The Pythagorean theorem states that the magnitude of a vector can be calculated as:

|V| = √(x² + y²)

Where |V| is the magnitude of the vector, x is the x component, and y is the y component.

In this case, we have:

|V| = 80.0 units

y = -55.0 units

Substituting these values into the equation, we can solve for x:

80.0 = √(x² + (-55.0)²)

Squaring both sides of the equation, we get:

6400.0 = x² + 3025.0

Rearranging the equation, we have:

x² = 6400.0 - 3025.0

x² = 3375.0

Taking the square root of both sides, we find:

x = ±√3375.0

Calculating the square root, we get two possibilities for the x component:

x₁ ≈ +58.12 units

x₂ ≈ -58.12 units

Part B:

Assuming the x component is known to be positive, we need to find the magnitude of the vector that, when added to the original one, would give a resultant vector that is 80.0 units long and points entirely in the +x direction.

To achieve this, we need to subtract the magnitude of the original vector (80.0 units) from the desired magnitude (80.0 units). Since the resultant vector points in the +x direction, the magnitude of the additional vector should be zero.

Therefore, the magnitude of the vector that, when added to the original one, would give a resultant vector that is 80.0 units long and points entirely in the +x direction is 0 units.

Part C:

The direction of the vector can be determined by using trigonometric functions. We can calculate the angle θ between the vector and the positive x-axis using the inverse tangent function:

θ = arctan(y / x)

Given that the y component is -55.0 units and the x component is +58.12 units (assuming positive x), we have:

θ = arctan(-55.0 / 58.12)

Calculating this angle, we find:

θ ≈ -42.29 degrees

The negative sign indicates that the vector points below the negative x-axis.

So, the direction of the vector is approximately -42.29 degrees relative to the positive x-axis.

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Answer:

x = -13

Step-by-step explanation:

Multiply:

1x+16=31

+16=3

Subtract them

x+16=3

+16 - 16 = 3 - 16

Simplifying:

x+16−16=3−16

x = 3 - 16 =

-13.

Answer x = - 13

Good or bad?

The cost of covering the field with grass pallets is $40996.58.

Given that the rectangular field measures 90 m and 162 m.

Hence, the area of the field is 90 X 162 m²

The grass pallets are sure in shape with an area covering 90 square yards.

1 m = 1.09 yards

Hence,

1 m² = 1.09² square yards

Hence,

90 X 162 m² = 90 X 162 X 1.09² square yards

Hence the number of pallets to be used is

(90 X 162 X 1.09²) / 90

= 162 X 1.09² pallets.

= 192.4722 pallets.

1 pallet costs $213

Hence,

192.4722 pallets cost

192.4722 X 213

= $40996.58

Therefore we get the cost of covering the field with grass is  $40996.58.

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The rate at which a point object revolves around a fixed origin is referred to as orbital angular velocity.

The speed of a point on its rim = 3150 cm / min.

angular velocity \(\omega\) = 7 rad/sec.

diameter = 15 cm ;

Radius = 7.5 cm.

The speed of a point on its rim = r \(\omega\) = 7.5 x 7 =52.5 cm/s =3150 cm / min

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Answer: B, the index fossils in the area of the bones.

(I do need 1 more brainliest to rank up, so if my answer is correct, that would be great, sorry if I sound rude.)

The 95% confidence interval for the slope is a) y = 0.720x - 91.030, [0.628, 0.812]

The equation of the least squares regression line can be found using the coefficients given in the summary.

The equation is y = 0.720x - 91.030.
To find the 95% confidence interval for the slope, we can use the t-value and standard error given in the summary.

Using a t-distribution with n-2 degrees of freedom (where n is the sample size), we can find the critical value for a 95% confidence interval.
In this case,

The t-value is 15.929 and the standard error is 0.045. With a sample size of n=1 (since we only have one predictor variable), the degrees of freedom are n-2 = -1, which is not possible.

Therefore,

We cannot calculate a valid confidence interval for the slope.
This equation represents the least squares regression line, and the 95% confidence interval for the slope is [0.628, 0.812].
The correct answer is a) y = 0.720x - 91.030, [0.628, 0.812]

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Answer:i think its 115 degres

Step-by-step explanation:

Given that,

Therefore,

Hence,

The value of x =9

Step-by-step explanation:

here is your answer bro..just use the formula and keep the value

He stands 6 feet tall, and his shadow extends 9 feet. if the building's shadow extends for 322.5 feet.

Now 6/9 = X/322.5

9X = 1935

X = 215ft

The Height of the building = 215ft

Consider an object AB of height h such that its shadow of length s is formed and angle of elevation is θ.

The object AB depicts a right triangle in which ∠ABO = 90o.

Now we know that in trigonometry, the tangent ratio for an angle is equal to the opposite side to that angle divided by its adjacent side.

So, for the angle of elevation θ, we have

=> tan θ = AB/OB

Putting AB = h and OB = s, we get

=> tan θ = h/s

=> s/h = 1/tan θ

=> s = h/tan θ

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Answer:

We need 144 birthday candles do you need for the 12 parties.

Step-by-step explanation:

We are given that you are a caterer specializing in children's birthday parties. You have 12 birthdays to cater to next week. You must bake 2 cakes for each party. Each cake will have 6 candles on it.

And we have to find the birthday candles we need for the 12 parties.

AS it is stated that next week you have 12 birthday parties and for each birthday party you must bake 2 cakes.

This means that for 12 birthday parties you have to make = \(12 \times 2\) = 24 cakes.

Also, each cake has 6 candles on it. This means that the total number of candles for 24 cakes = \(24 \times 6\) = 144 candles.

Hence, we need 144 birthday candles for the 12 parties.

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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