I State whether the roots of the following equations are real and unequal real and equal or imaginary and unequal 1. x - 6x +9= 0 4. x(x – 5) = 4(5 – x) 7. 5x – 6= 13x 10. x -0.6=1.7x - 5. x + 7x + 1 = 0 8. x-x=3(x+7) 11. 4x? - 12 = 13x 2. Sx-x= 4x + 2 2 3 3. -=-=X-4 4 3x 6. 2x + 9x + 3 = 0 9. - 11 - 12. 3x + 1 = 4x 2 4

Pls help me​

The length of the rectangle = 8 inches

The width of the rectangle, w = 15 inches

The diagonal, d = 17 inches

The length of the rectangle, l = ?

The diagram is drawn below

The diagonal of the rectangle forms a right triangle with the width and the length. Therefore, the length will be found using the Pythagora's theorem

The length of the rectangle = 8 inches

Answer:

the graph has two vertical asymptotes, line q intersects the line at -8 and is the more important one.

Step-by-step explanation:

This is visible based off of the picture.

Answer:

Step-by-step explanation:

The probability that their total completion time in the maze for all rats is between 5.75 and 6.25

To solve this problem, you would need to use the properties of the normal distribution and the central limit theorem. The central limit theorem states that the sum of a large number of independent and identically distributed random variables will tend to be normally distributed, regardless of the underlying distribution of the individual variables.

Since the completion time for each rat is normally distributed with a mean of 1.5 and a standard deviation of 0.35, the total completion time for 5 rats will also be normally distributed with a mean of 7.5 (5 x 1.5) and a standard deviation of 0.7 (√(5) x 0.35).

Then, you can use the cumulative distribution function (CDF) of the normal distribution to find the probability that the total completion time is between 5.75 and 6.25. This would involve finding the area under the normal distribution curve between those two values, which can be calculated using a table of the standard normal distribution or a calculator with the normal distribution function.

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Answer:

200

Step-by-step explanation:

Just took the test on edge.

The true statements about the functions are:

The function is given as:

f(x) = 25000 * 0.96^x

Set x = 0 to determine the initial value of the function

f(0) = 25000 * 0.96^0

Evaluate

f(0) = 25000

This means that the population of the city in 2010 is 25000 i.e. option (B) is correct

Also, we have:

f(x) = 25000 * 0.96^x

The rate at which the population decreases every year is calculated as:

r = 1 - 0.96

Evaluate the difference

r = 0.04

Express as percentage

r = 4%

This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct

The population after 5 and 10 years are:

f(5) = 25000 * 0.96^5

f(5) = 20384

f(10) = 25000 * 0.96^10

f(10) = 16621

Divide these populations by the initial population in 2010

20384/25000 = 82%

16621/25000 = 66%

This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.

So, options (d) and (e) are false

Lastly, because the population function is an exponential decay function;

The function value would approach 0 as it decreases

This means that option (f) is correct

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Answer:

Well like what? It could be anything, but what do you mean "like these"

Step-by-step explanation:

2. Ava has to buy two pounds of cheese and a box of cereal. How much money does she spend?

3. (I can't think of one here I am so sorry q-q)

4. Sam has $20 to spend at the market. He buys 2 loafs of bread, and a carton of eggs, and a box of cereal. How much money does he left?

The answer is that the 70% confidence interval for the slope of the regression line using the provided data is between 0.0019 and 0.0037.


To calculate the 70% confidence interval for the slope of the regression line, we need to use the t-distribution with degrees of freedom equal to n - 2, where n is the number of data points. In this case, n = 116, so we have 114 degrees of freedom.

Using a statistical software or calculator, we can find that the t-value for a 70% confidence interval with 114 degrees of freedom is approximately 1.648.

Next, we need to calculate the standard error of the slope, which is given by:

SE =√[ (SS_residuals / (n - 2)) / SS_x ]

where SS_residuals is the sum of squared residuals, SS_x is the sum of squared deviations of x from its mean, and n is the sample size.

Using the regression model provided, we can find that SS_residuals = 6.3574 and SS_x = 1484.9584. Plugging these values into the formula, we get:

SE = √[ (6.3574 / (116 - 2)) / 1484.9584 ] = 0.00044

Finally, we can calculate the confidence interval for the slope using the formula:

slope +/- t * SE

where slope is the estimated slope from the regression model.

Plugging in the values, we get:

slope +/- 1.648 * 0.00044 = 0.0028 +/- 0.0007

Therefore, the 70% confidence interval for the slope of the regression line is between 0.0019 and 0.0037, rounded to 4 decimal places.

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The focal length of the lens is mathematically given as

f = 17.15cm

Generally, the equation for focal length is mathematically given as

1/f = (n-1)(1/R1 -1/R2)

f: focal length of the lens

n: refractive index of the lens

R1 radius of the front surface

R2 radius of the back surface

R1(front surface) = 20cm

R2(back surface) = 30cm

n = 1.70

therefore,

1/f = (1.70-1)(1/20 -1/-30)

1/f = 0.70 * 0.083

1/f = 0.0581

f = 17.15cm

In conclusion, the focal length of the lens

f = 17.15cm

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The Analyst can use COALESCE function to eliminate the null values from the results.

The SQL Coalesce functions is used to handle NULL values. During the expression evaluation process the NULL values are replaced with the user-defined value. It  returns the first non-NULL value from a series of expressions.

The SQL Coalesce function evaluates the arguments in order and always returns first non-null value from the defined argument list.

Few Properties of COALESCE Function

SYNTAX -

COALESCE ( expression [ ,...n ] )  

Hence, the analyst can use COALESCE function to eliminate the null values from the results.

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Step-by-step explanation:

\( {30.5}^{2} = {x}^{2} + {19.1}^{2} \\ 930.25 = {x}^{2} + 364.81 \\ {x}^{2} = 930.25 - 364.81 \\ {x}^{2} = 565.44 \\ x = \sqrt{565.44} \\ \\ x = 23.78\)

The changes in the volume of the spherical balloon is approximately o.3351-meter cube.

the volume of the sphere =\(v=\frac{4}{3}\pi r^3\)

using the definition of differential to find the change we write

                                          \(dv=\frac{4}{3}\pi (dr)^3\)

where,                               \(dr\)=\(r_{2}-r_{2}\)

                                         \(dr\)=\(2-1.8\\\)

                                         \(dr\) \(=0.2\)

                                         \(dv=\frac{4}{3}\pi (0.2)^3\)

                                         \(dv=0.3351\) approx.

where dr and dv represent the differential or change with respect to radius and volume in the above calculation. so first we apply differential on both sides of the formula of the sphere then we find its approximation by the next coming equation. so, the volume of the sphere is approximately 0.3351-meter cube here approximation represents that it is not the exact solution it is basically approximated solution.

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Answer:

3.2 π

Step-by-step explanation:

The volume V of a sphere with radius r is given by the formula V = (4/3) * π * r^3.

Taking the derivative with respect to r, we get dV/dr = 4 * π * r^2.

Let dr be the change in radius, which is 1.8 - 2 = -0.2.

The differential dV is given by dV ≈ (dV/dr) * dr = 4 * π * r^2 * dr.

Substituting r = 2 and dr = -0.2, we get dV ≈ 4 * π * 2^2 * (-0.2) = -3.2 * π.

So, using differentials, we estimate that the volume of the balloon decreases by approximately 3.2 * π cubic meters as it deflates from a radius of 2 meters to a radius of 1.8 meters.

Answer:

D. 13.79

Step-by-step explanation:

74.6-50.25-10.56=13.79

13.79 seconds Jodie left to match the record.

Jodie wanted to match Mandy's obstacle course record of 74.6 seconds. She had already spent fifty and one fourth seconds on wall climbing and 10.56 seconds on the ropes. We have to find the time she left to match the record

Two expressions with equal sign is called as equation.

The time for climbing wall is fifty and one fourth seconds=50.25 seconds

The time on ropes is 10.56 seconds

The total time she spent is 50.25+10.56=60.81

Left time = Record Time-Spent time

=74.6-60.81=13.79

Therefore 13.79 seconds she have left to match the record

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If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point  of view,

Toss a coin twice, and then then roll a 6-sided number cube.

How can he play a statistically fair game to get exactly 24 outcomes?

The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.

The first of the alternatives is the only one with a sample space of 24 elements.

Flip two coins, then roll a D6.

The results of each coin toss are 2:  (tails and heads).

There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)

The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:

C = 2 × 2 × 6

C = 24

Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.

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The interquartile range is the same for the eighth grade and the seventh grade.

From the box plot - I

Minimum= 15

Q1 = 20

Median = 25

Q3 =30

Maximum = 60

So, IQR = 30-20 = 10

From the box plot - II

Minimum= 20

Q1 = 30

Median = 35

Q3 = 40

Maximum = 90

So, IQR = 40-30= 10

Thus, The interquartile range is the same for the eighth grade and the seventh grade.

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We can either round off 11.75 to 12 or to 11, depending on whether we want to overestimate or underestimate the number of cups of coffee sold. In the former case, the solution is (12, 31), and in the latter case, the solution is (11, 32).

Let the number of cups of coffee sold be x and the number of cups of tea sold be y. The ordered pair representing the solution will be (x, y).Given, a total of 43 cups were sold. Therefore, we have:

x + y = 43 ..... (1)

Also, the money collected was $140. Since cups of coffee are sold for $5 and cups of tea are sold for $2, we can write the total amount of money as:

5x + 2y = 140 ..... (2)

We have two equations (1) and (2) in two unknowns x and y. We can solve them to find the values of x and y.

Subtracting equation (1) from twice equation (2), we get:

8x = 94 => x = 11.75

Substituting this value of x in equation (1), we get:

11.75 + y = 43 => y = 31.25

The solution is the ordered pair (x, y) = (11.75, 31.25).

However, we need to remember that the number of cups must be integers and not fractions. We can see that 11.75 is not an integer. Therefore, we need to adjust our solution by rounding off appropriately.

We can either round off 11.75 to 12 or to 11, depending on whether we want to overestimate or underestimate the number of cups of coffee sold. In the former case, the solution is (12, 31), and in the latter case, the solution is (11, 32).

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The set of ordered pairs share the same reference angle is (- 1/2, -√3/2 ), (1/2,√3/2 )

The term ordered pair in math is defined as  a composition of the x coordinate  and the y coordinate by having two values written in a fixed order within parentheses.

Here we have know that the reference angle of x is obtained by either 180-x, 180+x. or 360-x depending on the position of terminal whether II quadrant or iv quadrant, or iii quadrant, etc.

So, based on these condition in order to find the reference angles here we must define that cos will remain cos only and sin will remain sin only there may be only changes in sign.

On the other hand all the ordered pairs given, here we find that I, II, and Iv there is a switch over form cos to sine and sin to cos.  

Based on these condition option (3) is correct one.

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Answer:

two plus two equals five

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

The answer is 42 because -3.5 multiplied by -12 is 42

Answer:

-3.5 * -12 = 42

Step-by-step explanation:

Hope this helps

Answer:

The first is (-1, 1) and the second is (2, -2)

Step-by-step explanation:

Answer:

28x

Step-by-step explanation:

7×3x=21x+x×7=7x

21x+7x×28x

SOLUTION

We want to simplify (3xy³)⁴ (x²)⁵

This becomes

So we have

Hence the answer is

Answer:

Step-by-step explanation:

12.6 + 0.1x = 0.15x + 8

(subtract 0.1 x both sides and subtract 8 both sides)

4.6 = 0.05x

(divide 0.05 both sides)

x = 92

Answer:

hakkubvacfauaiijsbbs

Step-by-step explanation:

gajajffjdjjfaa

Answer:

2x + 6 = or > than 3

The given function f, with the provided set of ordered pairs, has a domain of {10, 17, 45, 51} and a range of {-6, 1, 5}.

The domain of a function refers to the set of all possible input values or x-values for which the function is defined. In this case, the given set of ordered pairs determines the domain. Looking at the x-values in the set {10, 17, 45, 51}, these are the unique inputs for which the function f is defined. Hence, the domain of f is {10, 17, 45, 51}.
On the other hand, the range of a function refers to the set of all possible output values or y-values that the function can take. By examining the y-values in the set {-6, 1, 5}, we can observe the distinct outputs generated by the function f. Thus, the range of f is {-6, 1, 5}.
In summary, the domain of the function f is {10, 17, 45, 51}, and the range of f is {-6, 1, 5}.

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Only possibility for the number written on the 21st card is 2.7.

In order to make a 4x5 rectangle, Ted needs to select 20 cards out of 21. Since the sums of numbers in all rows should be equal, we can find the sum of numbers in each row by dividing the sum of all selected numbers by 5.

For this problem, the sum of all selected numbers is: 41 + 22 + 73 + 84 = 4 + 4 + 21 + 32 = 61

So, the sum of numbers in each row should be 61/5 = 12.2

Now, we can find the sum of numbers in each column by adding the number of times each number appears on the cards.

For example, the sum of number 1's in each column should be 4/4 = 1.

The sum of number 2's in each column should be 2/4 = 0.5.

And so on.

The sum of numbers in each column should be: 1+2.5+3+3 = 9.5

So, to make all rows have the same sum, the 21st card should be a number that when added to 9.5 will give 12.2.

Therefore, the number written on the 21st card could be 2.7.

So the only possibility for the number written on the 21st card is 2.7.

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The correlation between the ages of men and women in this situation would be +1. This means that for every one-year increase in the age of the man, the age of the woman would increase by one year as well. The correlation coefficient of +1 signifies a perfect positive linear correlation between the two variables.

In other words, if a man is 40 years old, the woman he is married to would be 37. If the man was 50, then the woman would be 47, and so on. This would remain true for any age, regardless of the difference in their ages. Therefore, the correlation between their ages would always remain +1.

It is important to note that this correlation coefficient is not necessarily reflective of  traditional or even natural social or biological behavior. Rather, it is simply a mathematical relationship that would exist in this specific situation. In reality, the age gap between married couples can vary widely depending on various social and cultural factors.

To summarize, the correlation between the ages of men and women in this scenario would be +1, signifying a perfect positive linear correlation. This means that for any given age of the man, the age of the woman would be exactly three years younger.

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