8
1
6
+
-7
² – 50 – 14 V - 50 - 14

The solution to the quadratic equation is ±6

From the question, we have the following steps that can be used in our computation:

2x^2 - 20 = 52

2x^2 = 32x^2

16x = ±4

The error in the above steps is appending x^2 to 32 after collecting the like terms.

Also, the like terms are not properly added

The correct solution is as follows

2x^2 - 20 = 52

Collect the like terms

2x^2 = 72

Divide by 2

x^2 = 36

Take the square root of both sides

x = ±6

Hence, the solution is ±6

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

2 3/10 ÷ 2 2/9

Step 02:

division:

The total amount accumulated after 4 years of $2,000 at 4% Interest (compounded annually) is approximately $2,169.86.

The total amount accumulated after 4 years of $2,000 at 4% interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, the principal amount (P) is $2,000, the annual interest rate (r) is 4% or 0.04 (expressed as a decimal), the number of times the interest is compounded per year (n) is not specified, and the number of years (t) is 4.

Let's assume that the interest is compounded annually (n = 1). Plugging the values into the formula, we have:

A = $2,000(1 + 0.04/1)^(1*4)

A = $2,000(1 + 0.04)^4

A = $2,000(1.04)^4

A ≈ $2,169.86

Therefore, the total amount accumulated after 4 years of $2,000 at 4% interest (compounded annually) is approximately $2,169.86.

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The total monetary amount of song downloads is $1080190

The percentage of amount paid for  video online sales = 15%

Number of times the songs downloaded in last year = 991000 times

Number of times the video downloaded in last year = 550000 times

The cost for each download of song = $1.09

The cost for each download of video = $9

The total monetary amount of song downloads = Number of times the songs downloaded in last year × The cost for each download of song

Substitute the values in the equation

Here we have to use multiplication

The total monetary amount of song downloads  = 991000 × 1.09

= $1080190

Therefore, the total amount for song download is $1080190

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We have found two quadratic functions with x-intercepts (-5,0) and (5,0): f(x) =\(x^2 - 25\), which opens upward, and g(x) = \(-x^2 + 25\), which opens downward.

For the quadratic function that opens upward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

f(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens upward, then a must be positive. Expanding the equation, we get:

f(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open upward, we need the coefficient of x^2 to be positive, so we can set a = 1:

f(x) = x^2 - 25

For the quadratic function that opens downward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

g(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens downward, then a must be negative. Expanding the equation, we get:

g(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open downward, we need the coefficient of x^2 to be negative, so we can set a = -1:

g(x) = -x^2 + 25

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Maximum 8A/144 people are allowed to entire the park.

The entire space taken up by the surface of the park is called area.

If the park is rectangular shaped, then the area is the product of length and breadth. If it is square shaped, area can be determined by the square of the side length.

Given, length of unused space = 12 foot

    breadth of unused space = 12 foot

Area of unused space = 12 x 12 = 144 square feet

Maximum 8 people is allowed for every 144 squares feet space

Let, area of the entire park is A square feet

Now maximum number of people allowed = (8 × A)/ 144

hence, 8A/144 people is allowed.

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Answer:

n = 5/8

Step-by-step explanation:

-2n = -1 1/4

-1 1/4 = -5/4

So, our equation is

-2n = -5/4

Divided both sides by -2

n = 5/8

So, the answer is

n = 5/8

Answer:

17

Step-by-step explanation:

well with the order of operations in this case you would do division first so it would be 72/8 = 9 then next you would add the 9+8 and that would leave you with 17

therefore c is the correct answer

hope this helped

have a good day :)

The new price after a 35% markup on a cost of $20 is $27.

The amount of money saved with a 15% discount on a cost of $36 is $5.4.

1. New Price = Cost + Markup

New Price = $20 + 0.35*$20

New Price = $20 + $7

New Price = $27

Therefore, the new price after a 35% markup on a cost of $20 is $27.

In order to calculate the amount of money saved with a 15% discount on a cost of $36, we need to find 15% of the cost and then subtract it from the original cost:

Discount = 15% * Cost

Discount = 0.15 * $36

Discount = $5.4

Amount saved = Discount = $5.4

Therefore, the amount of money saved with a 15% discount on a cost of $36 is $5.4.

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1. Cost: $20

Markup: 35%

What is the new price ?

2. Cost: $36

Discount: 15%

How much money would you

save ?

Yosef finished the mile in 9 minutes.

Distance = 1 mile

Demetrius' speed = 7.5 miles per hour

Demetrius' time = Distance/speed

= 8 minutes

Demetrius finished the mile first by taking 1 minute less than Yosef's finishing time.

Answer:

Step-by-step explanation:

We know that:

Let's see how much time Yosef take in 7.5 miles.

Solution:

After working on this problem, we can conclude that Demetrius wins the race by 7.5 minutes.

Answer:

You will have the same balance after 5 weeks.

Step-by-step explanation:

x represents number of weeks.

140 + 10x = y

95 + 19x = y

Answer: you will have the same amount after five weeks

Step-by-step explanation: because you have to think and do the equation

Answer:

the answer to your question is 'b'

Answer:

X + 6

Step-by-step explanation:

Think of it as (3x + 5) + (-1 x 2x) + (-1 x -1)

3x + 5 - 2x + 1

Combine like terms

3x - 2x = x + 5 + 1 = x + 6

The measure of hypotenuse length x would be 17.67 cm

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|² = |AB|² + |BC|²  

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Now, Using the Pythagoras' identity in the right angled triangle.

hypotenuse²  = perpendicular²  + base²

x² = 16² + 7.5²

x²= 256 + 56.25

x²= 312.25

Now , take the square root of both sides;

x = √312.25

x ≈ 17.67

Therefore, The measure of hypotenuse length x would be, 17.67 cm

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Answer:

Step-by-step explanation:

m

Answer:

6 × 36 = 216

Step-by-step explanation:

one ticket price: 216 ÷ 6 = $36

The density function of the sample means, Y, can be found using the central limit theorem. According to the central limit theorem, as the sample size increases, the distribution of the sample mean approaches a normal distribution.

With mean equal to the population means, µ, and variance equal to the population variance divided by the sample size, σ^2/n. Thus, the density function of Y = 1/n * ∑ (Yi) is given by:

f(y) = (1 / (σ * √(n)) ) * exp( - ((y - µ)^2) / (2 * (σ^2/n)) )

B) If σ^2 = 16 and n = 25, the variance of the sample mean is 16 / 25 = 0.64. Thus, the standard deviation of the sample mean is the square root of 0.64, which is approximately 0.8.

The probability that the sample mean, Y, takes on a value that is within one unit of the population mean, µ, is given by the cumulative density function of a normal distribution with a mean equal to µ and standard deviation equal to 0.8, evaluated at y = µ + 1 and y = µ - 1.

Using a standard normal table or a calculator with normal distribution functions, we can find that:

P(|Y - µ| ≤ 1) = P(µ - 1 < Y < µ + 1) = P(-1 < (Y - µ) / 0.8 < 1) = P(-1.25 < Z < 1.25)

Where Z is a standard normal random variable.

From a standard normal table or using a calculator with normal distribution functions, we find that P(-1.25 < Z < 1.25) = 0.8944.

C) If σ^2 = 16 and n = 36, the variance of the sample mean is 16 / 36 = 0.4444, and the standard deviation of the sample mean the square root of 0.4444, which is approximately 0.6667.

Similarly, if n = 64, the variance of the sample mean is 16 / 64 = 0.25, and the standard deviation of the sample mean the square root of 0.25, which is approximately 0.5.

And if n = 81, the variance of the sample mean is 16 / 81 = 0.1981, and the standard deviation of the sample mean the square root of 0.1981, which is approximately 0.44504.

In all three cases, the probability that the sample mean, Y, takes on a value within one unit of the population means, µ, can be found as described in part B. As the sample size increases, the variance of the sample mean decreases, and the standard deviation of the sample mean becomes smaller. This means that the sample is less variable, and the probability that it falls within one unit of the population mean increases.

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The slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is \(y=-\frac{9}{8}x+\frac{11}{4}\)

We know that the slope-intercept form of the line is y =  mx + c, where m is the slope of the line and c is the y-intercept of the line.

For given question we have been given two points (-2,5) and (6,-4)

We need to find the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4).

Using two-point form the equation of the line is,

\(\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}\)

Let (x1, y1) = (-2,5) and (x2, y2) = (6,-4)

So, the equation of the line is,

\(\frac{y-5}{-4-5} =\frac{x-(-2)}{6-(-2)}\\\\ \frac{y-5}{-9} =\frac{x+2}{6+2}\\\\\frac{y-5}{-9} =\frac{x+2}{8}\\\\ 8(y-5)=-9(x+2)\\\\8y-40=-9x-18\\\\8y=-9x-18+40\\\\8y=-9x+22\\\\y=-\frac{9}{8}x+\frac{11}{4}\)

above equation is in the slope-intercept form.

Therefore, the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is \(y=-\frac{9}{8}x+\frac{11}{4}\)

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Answer:

f(x)=3/2 x

Step-by-step explanation:

it starts at 0 and rise 3 and goes over 2

The answer is \(f(x)=\frac{3}{2}x\)

First, you must find 2 points.

(0,0)   (2,3)

Then, you must use the slope equation

\(\frac{3-0}{2-0}=\frac{3}{2}\)

The line crosses the y axis at 0, so there is no y intercept

\(f(x)=\frac{3}{2}x\)

The sampling distribution of difference between means approximates a normal curve whose mean is zero.

The sampling distribution means the probability distribution based on the large number of samples of size n from the given population

Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.

Here they used the normal curve, sot its mean value is zero

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Answer:

Step-by-step explanation:

Given :    shape 14cm 11cm 9cm 20cm

To Find : Find area

Solution:

20 - 1 1 = 9 cm

We can divide figure in 2 parts

rectangle = 14 cmx 11 cm

square = 9 cm x 9  cm

Area of rectangle = 14 * 11 = 154 cm²

Area of square = 9 * 9 = 81 cm²

Total area = 154 + 81

= 235 cm²

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Find the area of the given figure withTU = 6 cm, SR = 8 cm, UR = 15 ...

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In the figure, triangle ABC in the semi circle . Find the area if the ...

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Answer:

Area = 235 square cm

Step-by-step explanation:

Given :    shape 14cm 11cm 9cm 20cm

To Find : Find area

Split the figure into rectangle and square:

Rectangle : 14 x 11

Square : 9 x 9

\(Area \ of \ rectangle : 14 \times 11 = 154 \ cm^2\)

\(Area \ of \ square = 9 \times 9 = 81 \ cm^2\)

\(Total \ area = 154 + 81 = 235 \ cm^2\)

Answer:

they want u to replace the letters with the numbers and then solve the equation. so instead of having c/a+2b they want you to write 6/3+2(-4)

then they want u to solve it. 6/3=2 and 2(-4)=-8 finally add 2 and -8 to get the answer -6. (you probably need to write it step by step not just say what the answer is)

Step-by-step explanation:

Answer:

A.{7}^{15}

\(4.7475615 {}^{12}\)

Step-by-step explanation:

\(( {7}^{5} ) {}^{3} = {7}^{5} =(16807) {}^{3}=4.7475615 {}^{12} \)

Hope this helps ;) ❤❤❤

(−3.7x)(5.1y)

= −18.87xy

Answer:

  x = 4

Step-by-step explanation:

You want the equation of a line that goes through point (4, 0) and has an undefined slope.

The slope of a line is the ratio of "rise" to "run." When the "run" is zero, the ratio involves division by zero, which results in the value "undefined." That is, a line with undefined slope has a "run" of zero, meaning it is a vertical line.

The equation for a vertical line is ...

  x = c . . . . . where c is some constant

We want the line to go through a point that has x-coordinate = 4, so that constant must be 4.

The equation is x = 4.

The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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The solutions of a nonlinear system x' = F(x) near a critical point xC can be approximated by the linearized solutions of this system, in the case that the Jacobian matrix at the critical point, DF(XC), has eigenvalues with negative real part.

To be more specific, the linearized system near xC is given by:

x' = DF(XC)(x - xC)

where DF(XC) is the Jacobian matrix of F(x) evaluated at xC. The eigenvalues of DF(XC) determine the stability of the critical point xC. If all the eigenvalues have negative real part, then xC is a stable node or focus, and the solutions of the linearized system approach xC exponentially fast.

Moreover, the nonlinear solutions of the original system also approach xC as t goes to infinity.

On the other hand, if at least one eigenvalue has positive real part, then xC is an unstable node or focus, and the solutions of the linearized system diverge from xC exponentially fast. In this case, the nonlinear solutions of the original system may exhibit complex behavior, such as limit cycles or chaotic oscillations.

In summary, the stability of a critical point xC depends on the eigenvalues of the Jacobian matrix DF(XC). If all the eigenvalues have negative real part, then xC is a stable node or focus, and the solutions of the nonlinear system approach xC exponentially fast. Otherwise, xC is an unstable node or focus, and the solutions of the nonlinear system may exhibit complex behavior.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

The 2nd dot plot in the attachment represents the dot plot that has the same sample mean as the population mean

The dot plot that completes the question is added as an attachment.

Start by calculating the mean of the data plot using:

\(\bar x = \frac{\sum fx}{\sum f}\)

Substitute the values on the dot plot

\(\bar x = \frac{2*1+3*3+4*2+5+6*3+7*5+8*2+9*4+11*2+12*2}{25}\)

\(\bar x = 7\)

This means that the population mean of the dot plot is 7

Next, we create another dot plot that has the same mean as 7.

There are no direct rules to this, so we make use of the trial by error method.

After several attempts, we have the following frequency table:

Data point      Frequency

2                                  1

3                                  2

4                                  0

5                                  4

6                                  5

7                                  2

8                                  5

9                                  0

10                                 2

12                                 3

The mean of the frequency table is:

\(\bar x = \frac{2 * 1 + 3 * 2 + 4 * 0 + 5 * 4 + 6 * 5 + 7 * 2 + 8 * 5 + 9 * 0 + 10 * 2 + 12 * 3}{1+2+0+4+5+2+5+0+2+3}\)

Evaluate

\(\bar x = \frac{168}{24}\)

Evaluate the quotient

\(\bar x = 7\)

This means that the sample mean is 7 (same as the population mean)

Lastly, we represent the frequency table using a dot plot (the 2nd dot plot in the attachment)

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