Hi, i need help quickly. I need the solution for
Estimate the value of
\( \sqrt{97.5 \div 1.96} \)
Please make it quick​

Answer:

14.

Step-by-step explanation:

The interquartile range (IQR) contains the second and third quartiles or the middle half of your data set.

Please give brainliest, will be appreciated.

Answer:

The interquartile range (IQR) measures the spread of the middle half of your data.

We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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After calculating the equation of the line that passes through the point (-3,-1) and has a slope of 2 we have come to find that the equation is

y - 2x - 5 = 0

An equation can be defined in a number of different ways. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." There are one or more variables in even the most fundamental and straightforward algebraic equations.

We know the point slope formula y-y1 = m (x-x1)

where (x1,y1) is the point through which the line passes and m is the slope

Here (x1,y1) is (-3,-1) and slope is 2

So, substituting the value, we get

y-(-1) = 2 (x-(-3))

y+1 = 2(x+3)

y + 1 = 2x + 6

y = 2x + 5

y - 2x - 5 = 0

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The average velocity when the position of an object is given by s(t) = - 18t² + 180t are:

(a) For interval [1, 10] = - 18 m/s.

(b) For interval [1, 9] = 0 m/s.

(c) For interval [1, 8] = 18 m/s.

(d) For interval [1, 1 + h] = (144 - 18h) m/s

We know that the average velocity is = (Initial velocity + Final velocity)/2

Given the function that represents the position of the object moving along the line is,

s(t) = - 18t² + 180t

Differentiating the above function with respect to 't' we get,

d/dt [s(t)] = d/dt [- 18t² + 180t]

s'(t) = - 36t + 180

v(t) = - 36t + 180

So at the time t the function of velocity is, v(t) = - 36t + 180

(a) For the interval [1, 10]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(10) = - 180

So the average velocity for [1, 10] = (144 + (-180))/2 = - 18 m/s.

(b) For the interval [1, 9]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(9) = - 324 + 180 = - 144

So the average velocity for [1, 9] = (144 + (-144))/2 = 0 m/s.

(c) For the interval [1, 8]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(8) = - 288 + 144 = - 108

So the average velocity for [1, 8] = (144 + (-108))/2 = 36/2 = 18 m/s.

(d) For the interval [1, 1 + h]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(1 + h) = - 36 - 36h + 180 = 144 - 36h

So the average velocity = (144 + (144 - 36h))/2 = (288 - 36h)/2 = (144 - 18h) m/s.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

8x-4

i remember being asked this question but i dont remember how to do it and i am sorry for that... but i know that it is 8x-4

The connection string for SQL Server using Windows Authentication is as follows:

Server=myServerAddress;Database=myDataBase;Trusted_Connection=True;

Specify the server address in the format "Server=myServerAddress". Replace "myServerAddress" with the name or IP address of the SQL Server instance you want to connect to.

Specify the name of the database you want to connect to in the format "Database=myDataBase". Replace "myDataBase" with the name of the database.

Use Windows Authentication by setting "Trusted_Connection=True". This means that the user running the application is authenticated using their Windows credentials, rather than a SQL Server login.

Use semicolons (;) to separate the different parts of the connection string.

Using Windows Authentication is a more secure and convenient way to connect to a SQL Server database, as it eliminates the need to store and manage login credentials in the application.

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There were initially 4 million bacteria in the culture.

To determine the initial number of bacteria in the culture, we can follow these steps:

Step 1: Identify the given data.
At the end of 6 hours, there are 5 million bacteria.
At the end of 9 hours, there are 8 million bacteria.

Step 2: Find the rate of bacterial growth.
Since the number of bacteria increased by 3 million (8 million - 5 million) over 3 hours (9 hours - 6 hours), the rate of bacterial growth is 1 million per hour (3 million ÷ 3 hours).

Step 3: Calculate the initial number of bacteria.
The number of bacteria increased by 5 million over the 6 hours. Therefore, if we divide this number by the rate of growth, we can determine the initial number of bacteria. Divide 5 million by 1 million per hour, which results in 5 hours.

Step 4: Subtract the time from the initial time.
Since we know that the culture was growing for 5 hours before reaching 5 million, we can subtract 5 hours from 6 hours, which equals 1 hour.

Step 5: Calculate the initial number of bacteria at 1 hour.
Since the bacteria grow at a rate of 1 million per hour, at the end of the 1st hour, there would be 1 million bacteria. Subtracting this number from the 5 million at the end of 6 hours will give us the initial number of bacteria: 5 million - 1 million = 4 million bacteria.

So, there were initially 4 million bacteria in the culture.

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Answer:

27

Step-by-step explanation:

(5+√2)²

you distribute the ² in the ()

so 5²+√2²

5²=25

√2²=2 because the √ and ² cancel each other out and you get 2

so now you have

25+2

which equals

27

Given expression:

             (5 + \(\sqrt{2}\))²

Now let us solve this problem by simplifying it;

    (5 + \(\sqrt{2}\))²:

   the power implies the expression in the bracket should be repeated twice:

        = (5 + \(\sqrt{2}\))  (5 + \(\sqrt{2}\))

  Then expand the bracket by distribution;

     =  (5 x 5) + 5(\(\sqrt{2}\)) + 5(\(\sqrt{2}\)) + 2

     = 25 + 10\(\sqrt{2}\) + 2

     =  27 + 10\(\sqrt{2}\)

False. A trigonometric equation with an infinite number of solutions is not necessarily an identity.

A trigonometric identity is an equation that holds true for all values of the variables involved. It is a fundamental property of trigonometric functions. On the other hand, a trigonometric equation with an infinite number of solutions means that there are multiple values of the variables that satisfy the equation, but it doesn't imply that the equation is true for all values.

For example, the equation sin(x) = 0 has an infinite number of solutions, which are x = 0, π, 2π, 3π, and so on. However, this equation is not an identity because it is not true for all values of x. It is only true when x is an integer multiple of π.

Therefore, it is important to distinguish between trigonometric identities that hold true for all values and trigonometric equations that have an infinite number of solutions but may not be true for all values.

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Step-by-step explanation:

the 2 and the t were combined when they weren't like terms, combined your like terms first and then answer

There are 10,626  ways of selecting four members from a group of 24 members and a basic problem of combination .

Total ways of selecting k members from a group of n members is nCk(n combination k) ways which equates to  n!/(k!*(n-k)!)

where n! is also known as n factorial

n!= n*(n-1)*(n-2)*(n-2)*(n-3).....*2*1.

so in the given question n=24 and k=4

After putting these values in the above equation

the formula simplifes to 24!/(4!*20!) = 10,626

so there are 10,626 ways of selecting 4 members from group of 24 members.

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Answer:

0

Step-by-step explanation:

m=y2-y1

____

x2-x1

m=-3-(-3) =(-3+3)/(-36) =0/-36=0

_____

-16-20

Answer:

x - 7

Step-by-step explanation:

just add/substract like terms only

Let's call the length of the rectangle "L" and the width "W". We know that the width is 10 cm shorter than the length, so we can write.

W = L - 10
We also know that the area of the rectangle is 200 cm 2, so we can write:
A = L x W
Substituting W = L - 10, we get:
A = L x (L - 10)
Expanding the brackets, we get:
A = L^2 - 10L
Now we can substitute in A = 200 and solve for L:
200 = L^2 - 10L
0 = L^2 - 10L - 200
We can use the quadratic formula to solve for L:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -10, and c = -200. Plugging in these values, we get:
L = (10 ± sqrt(10^2 - 4(1)(-200))) / 2(1)
L = (10 ± sqrt(1100)) / 2
L = (10 ± 10sqrt(11)) / 2
L ≈ 19.9 or L ≈ -9.9
We can disregard the negative solution since we're dealing with lengths, so the length of the rectangle is approximately 19.9 cm.
Now we can use W = L - 10 to find the width:
W = 19.9 - 10
W ≈ 9.9 cm
Therefore, the length of the rectangle is approximately 19.9 cm and the width is approximately 9.9 cm.

To find the length and width of a rectangle whose width is 10 cm shorter than its length and whose area is 200 cm², follow these steps:
1. Define the variables: Let the length of the rectangle be L cm, and the width be W cm.
2. Use the given information: Since the width is 10 cm shorter than the length, we can write the equation W = L - 10.
3. Use the formula for the area of a rectangle: The area of a rectangle is given by the formula A = L × W.
4. Substitute the given area and the equation from step 2: In this problem, the area is 200 cm², so we have 200 = L × (L - 10).
5. Solve the equation for L: Expand the equation to get 200 = L² - 10L. Rearrange the equation to L² - 10L - 200 = 0.
6. Factor the quadratic equation or use the quadratic formula: (L - 20)(L + 10) = 0. This gives two possible values for L: L = 20 cm or L = -10 cm.
7. Discard the negative value: Since the length of a rectangle cannot be negative, we discard the value L = -10 cm. So, the length L is 20 cm.
8. Find the width using the equation from step 2: W = L - 10 = 20 - 10 = 10 cm.
Thus, the length and width of the rectangle are 20 cm and 10 cm, respectively.

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The requried solution of the respective complementary angles mentioned in the exercise has been given.

Complementary angles are two angles whose measures add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees.

Here,
Since in the whole exercise expression for the complementary angles are given we have to determine the unknowns.
As we know the sum of complementary angles is 90,
So.
1.
x + 45 = 90
x = 45

2.
72 + x = 90
x = 90 - 72
x = 18

Similarly,
3
x + 23 = 90
x = 67

4.

81 + x = 90
x = 9

5.
x + 17 = 90
x = 73

6..
x + 43 = 90
x = 47

7.
x + 77  = 90
x = 13

8.

x + 68 = 90
x = 22

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Seth must attend the move 17 times

The difference in price of matinee is

= price of matinee normally - price of matinee with movie pass

=  3.50 - 1

= 2.5

We divide to find the number of times

= 40 / 2.5

= 16

In other that Seth's father benefits Seth must attend at least 17 times

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Step-by-step explanation:

Do 99 / 12 = 8.25 Then to check if it works, do the opposite operation and multiply 8.25 x 4 = 33 so it works. The unit rate is $8.25 per hour.

99 / 12 = p or 99 / 12 = 8.25

Answer:

-8x-36

Step-by-step explanation:

-4(2x+9)

distribute: -4(2x+9)= -8x-36

Answer:

a, b ,e

Step-by-step explanation:

The solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a value or a set of values, when substituted for the unknowns, the equation becomes true."

For given question,

We have been given the graph of a quadratic function f(x) and an absolute value function g(x).

We need to find the x-values that are approximate solutions to the equation f(x) = g(x).

To solve the equation f(x) = g(x), we look for the points where the graphs of f(x) and g(x) intersect.

The intersection point of f(x) = g(x) appears to be at point which lie in the second quadrant and the x-value lie between -2 and -4.

Also,  the second intersection point lie in the fourth quadrant where x value is in between 4 and 6.

So, the solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

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To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).

The key combination [Ctrl]+[] is used to display formulas.

This is a useful feature for checking and editing formulas without altering the calculated values.

By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.

This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.

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The radius of curvature of a particle's path in the x-y plane at t=2.2 sec is 94.25 inches, found using velocity and acceleration vectors. Sketch shows velocity and curvature vectors.

To find the radius of curvature rho, we need to first find the velocity vector v and the acceleration vector a at t=2.2 sec.

The position vector of the particle is given by:

r = 1.35t^2 i + 1.22t^3 j

Differentiating this with respect to time t gives the velocity vector:

v = dr/dt = 2.7t i + 3.66t^2 j

Differentiating again with respect to time t gives the acceleration vector:

a = dv/dt = 2.7 i + 7.32t j

Now, to find the radius of curvature rho, we use the formula:

rho = |v|^3 / |a|*sin(theta)

where |v| is the magnitude of the velocity vector, |a| is the magnitude of the acceleration vector, and theta is the angle between v and a.

At t=2.2 sec,

|v| = |2.7(2.2) i + 3.66(2.2)^2 j| = 11.209 in/sec

|a| = |2.7 i + 7.32(2.2) j| = 16.416 in/sec^2

theta = angle between v and a

To find theta, we can use the dot product:

v . a = |v| |a| cos(theta)

cos(theta) = (v . a) / (|v| |a|)

cos(theta) = (2.7)(2.7) + (3.66)(2.2)^2 / (11.209)(16.416)

cos(theta) = 0.503

theta = cos^-1(0.503) = 1.042 radians

Substituting these values into the formula for rho, we get:

rho = (11.209)^3 / (16.416)(sin(1.042))

rho = 94.25 in

Therefore, the radius of curvature of the path for the position of the particle when t=2.2 sec is 94.25 inches.

To sketch the velocity vector v and the curvature of the path at this instant, we can draw the vectors at the position of the particle for t=2.2 sec. The velocity vector v has a magnitude of 11.209 in/sec and is directed at an angle of approximately 67 degrees above the x-axis. The curvature vector points towards the center of curvature of the path and has a magnitude of 1/rho.

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Answer:

Step-by-step explanation:

8(2+3)

Answer:

17.7 meters

Step-by-step explanation:

x = 30

15 + 0.09*30

0.09*30 = 2.7

2.7 + 15 = 17.7 meters

a) The polynomial written in standard form is -4x^3 + x + 7.

b) It is a cubic polynomial because it has three terms and a degree of 3.

A polynomial is an expression consisting of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants. The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial -4x^3 + x + 7, the degree is 3 because the highest power of x is 3.

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. This means that the term with the highest power of the variable is written first, followed by the next highest power, and so on, until the constant term is written last. In the case of -4x^3 + x + 7, we rearranged the terms so that the -4x^3 term is first, followed by the x term, and then the constant term of 7.

Finally, we can name the polynomial based on its degree and number of terms. In this case, we have a polynomial with three terms and a degree of 3, so it is called a cubic polynomial.

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The given question is incomplete, the complete question is:

Write the polynomial in standard form then name the polynomial based on its degree and number of terms. x+ 7 - 4x^3

To construct a box plot from the given data, which represents the diameters of cans in an assembly line, we need to determine the five-number summary and plot the corresponding box and whisker plot.

The five-number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.

To construct the box plot, we start by arranging the data in ascending order: 5.1, 5.2, 5.2, 5.2, 5.3, 5.5, 5.5, 5.5, and 5.6. The minimum value is 5.1, and the maximum value is 5.6. The median is the middle value, which in this case is 5.3.

To find the first quartile (Q1) and the third quartile (Q3), we divide the data into two halves. Q1 is the median of the lower half, which consists of 5.1, 5.2, 5.2, and 5.2. Q3 is the median of the upper half, which consists of 5.5, 5.5, 5.5, and 5.6. The box plot will show the minimum value, Q1, Q2 (median), Q3, and the maximum value, giving us a visual representation of the distribution and variability of the data.

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