two balls undergo a perfectly elastic head-on collision, with one ball initially at rest. if the incoming ball has a speed of 200 m/s .

the 95% confidence interval contains the value of 0. This is expected since the result from the chi-square test and the result from the normal approximation test were both significant.

a) The chi-square test statistic is 15.95 and is significant at the 0.005 level. This indicates that the population proportions of students who drove while drinking are not the same in the two calendar years.

b) The behavior of college students regarding driving while drinking changed between 2013 and 2017.

c) The test based on the normal approximation to the binomial distribution also yields a significant result (p-value = 0.0045), indicating that the population proportions of students who drove while drinking are not the same in the two calendar years.

d) The 95% confidence interval for the true difference in population proportions is [-0.072, -0.023].

e) Yes, the 95% confidence interval contains the value of 0. This is expected since the result from the chi-square test and the result from the normal approximation test were both significant.

Chi-square test statistic:

X2 = 15.95

Normal approximation test statistic:

P-value = 0.0045

95% confidence interval:

[-0.072, -0.023]

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The option a is giving the same value according the table. So the option a is correct answer.

In the given question, the table represents some points on the graph of linear function f.

We have to find which function represents f.

(a) f(x)= 32(3x-1)

(b) f(x)= -32(x-3)

(c) f(x)= -2(32x-3)

(d) f(x)= 16(2x-1)

We find the pattern we firstly observe the given table closely.

So from the given table;

f(-2) = -224, f(1) = 64, f(5) = 448, f(10) = 928

To check which option is giving the value of f(x) right according to table, we put the value in each option.

Firstly taking the option a.

f(x)= 32(3x-1)

Now checking the option 1.

Putting x=-2, if the value of f(-2) = -224, then the option is correct.

f(-2)= 32(3(-2)-1)

f(-2)= 32(-6-1)

f(-2)= 32*(-7)

f(-2)= -224 (True)

Now putting x=1 in the same option to cross check, if the value of f(1) = 64, then the option is correct.

f(1)= 32(3(1)-1)

f(1)= 32(3-1)

f(1)= 32(2)

f(1)= 64

Now the option a is giving the same value according the table. So the option a is correct answer.

We find the right answer so we don't check the further option. To check next option you can use the same way.

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Answer:

The solution to the system of equations is x = 28, y = -40.

Step-by-step explanation:

3x + 2y = 4

-2x + 2y = 24

---------

x = 28

3x + 2y = 4

3(28) + 2y = 4

84 + 2y = 4

2y = -80

y = -40

the solution to the system of equations is x = 28, y = -40.

In view of Molly's three types of bills

Therefore the first equation is    [tex]1x+5y+10z=96[/tex]

Therefore the second equation is [tex]x+1=y+z[/tex]

Therefore the third equation is [tex]x+y+z=23[/tex]

As per the details share in the above question as as follow,

x for the no, of $1 bills

y for the no. of $5 bills.

z for the no. of $10 bills.

We have to find the first, second and third equations.

Therefore worth of x $1 bills is [tex]1 \times x[/tex]

So of y for the no. of $5 bills is [tex]5 \times y[/tex]

And z for the no. of $10 bills is [tex]10 \times z[/tex]

The total worth in molly wallet is $96.

So the equation will be,

[tex]1x+5y+10z=96[/tex]

Now further is molly has one more  $1 bill then the number of $1 bill will be same as.

Therefore the second equation is [tex]x+1=y+z[/tex]

Now she had 23 bills,

We also know that she has one-dollar, five-dollar, and ten-dollar notes, with x denoting the quantity of each, Y the number of the five-dollar bill, and Z the number of the ten-dollar bill.

Therefore the third equation is [tex]x+y+z=23[/tex]

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As per the polar coordinates, the limits of the integration is written as ∬Df(rcos⁡(θ),rsin⁡(θ))rdrdθ.

What is meant by polar coordinates?

In math, polar coordinates refer a pair of coordinates locating the position of a point in a plane, the first being the length of the straight line ( r ) connecting the point to the origin, and the second the angle ( θ ) made by this line with a fixed line.

Here we have  the limits of integration and evaluate the integral to find the volume. for the polar coordinates.

Here we have the polar representation of a point P is the ordered pair (r,θ) where r is the distance from the origin to P and θ is the angle the ray through the origin and P makes with the positive x-axis.

Then the polar coordinates r and θ of a point (x,y) in rectangular coordinates satisfy

=> r=x² + x²      and      tan⁡(θ)=yx;

Here the rectangular coordinates x and y of a point (r,θ) in polar coordinates satisfy and x=rcos⁡(θ) and y=rsin⁡(θ).

Then the area element dA in polar coordinates is determined by the area of a slice of an annulus and is given by dA=rdrdθ.

Here we have to convert the double integral ∬Df(x,y)dA to an iterated integral in polar coordinates,

Now, we have to substitute rcos⁡(θ) for ,x, rsin⁡(θ) for ,y, and rdrdθ for dA to obtain the iterated integral

=> ∬Df(rcos⁡(θ),rsin⁡(θ))rdrdθ.

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The interval is [4, 6], and the compound inequality equals 4 ≤ x < 6 as indicated on the number line.

Given,

The number line;

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Here,

The blue line runs from 1 to 4 and then to 6.

The solid dot at position 4 denotes inclusion, whereas the hollow dot at position 6 denotes exclusion.

Then,

x  ≥ 4 and x < 6

Combindlly  4 ≤ x < 6

Hence "The interval is [4, 6], and the compound inequality on the number line is 4 ≤ x < 6 ."

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The required area of the regular 12-gon is obtained as 3 square units.

A regular polygon can be defined as a polygon having all of its sides and angles equal to one another. The expression for each angle of a regular polygon is 180(n - 2)/n.

The angle between two sides of regular 12-gon is given as below,

180(12 - 2)/12 = 150°.

Now, the area of regular 12-gon is equivalent to the area of sum of 12 triangles.

The angle for the triangle will be 150/2 = 75°.

The diagram for such a triangle is given as below,

Now, OC = 1 × Sin B

⇒ OC = Sin 75°

And, BC =  1 × Cos B

⇒  BC = Cos 75°

Then, AB = 2BC = 2Cos 75°

Area of the triangle is given as,

1/2 × base × height

⇒ 1/2 × Sin 75° × 2Cos 75°

⇒ 0.25

Now, the area of the regular 12-gon inscribed in a unit circle is given as,

12 × 0.25 = 3 square units.

Hence, the area of a regular 12-gon inscribed in a unit circle is 3 square units.

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Answer:

The number is:

321/7

Step-by-step explanation:

a + a/6  + 7 = 121/2

6a/6 + a/6 + 42/6 = 363/6

6a + a + 42 = 363

7a = 363 - 42

7a = 321

a = 321/7

Check:

321/7 + (321/7)/6 + 7 = 121/2

321/7 + 321/42 + 7 = 121/2

1926/42 + 321/42 + 294/42 = 2541/42

1926 + 321 + 294 = 2541

The reasonable range for the total cost of the tickets the groups

would pay  is {84, 126, 2163}.

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

Given:

The Function modeled for the situation is

f(x) = 21 x where x is the number of tickets sold.

So, For x= 4 Tickets

Fare, F(x) = 21 x 4= $84

and, For x= 6 Tickets

Fare, F(x) = 21 x 6 = $126

and, For x= 103 Tickets

Fare, F(x) = 21 x 103 = $2163.

Hence, the range is {84, 126, 2163}.

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To express the set of real numbers x that satisfies the inequality -2 ≤ x < 5, we used the Interval notation method and got the solution set as [-2,5).

Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers. We can use this notation to express inequalities.

Generally, we read about the three types of intervals :

We have given an inequality as -2 ≤ x < 5

We have to express the set of real numbers x that satisfies the given inequality.

Let's started, The first thing we'll want to ask ourselves is if we're going to use parentheses or brackets when we write this.

y = { x | -2 ≤ x < 5 }

We see that the lower value of x is -2 or greater than -2 and higher value of x is less than 5. We're just going to write it down. Using the interval notation, the lower side x is greater than and equal to -2 so, we use closed bracket here and the upper side x is less than 5 that is we use parentheses or open bracket here.

Thus, in interval notation y = x , x∈[-2, 5)

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Answer:

1. 2 pounds of beans and 1 pound of rice

2. 0.6 pounds of beans and 9 pounds of rice

3. b pounds of beans and (12-b)/2 pounds of rice

Step-by-step explanation:

1. You know that 2 pounds of beans costs 2*5 so $10. Then you subtract 12-10 to get 2.

2 pounds of rice

2. You multiply 0.6 by 5, and then you subtract that from 12, getting 9. then you divide by 2 (cost of rice per pound) getting 4.5 pounds of rice

Answer:

17.5 or 17 minutes and 30 seconds

Step-by-step explanation:

The value of the brand new Ford F-150 after five years is approximately 32,435 dollars. Rounded to the nearest dollar, the value of the Ford F-150 after five years is 32,000 dollars.

The value of a new vehicle after the first 12 months of ownership is given by the equation:

value after 12 months = value at time of purchase × (1 - depreciation rate)

In this case, the value of the vehicle at the time of purchase is 63,580, and the depreciation rate is 20%. Plugging these values into the equation gives us:

value after 12 months = 63,580 × (1 - 0.20) = 50,864

The value of the vehicle after five years is given by the equation:

value after 5 years = value after 12 months × [tex](1 - depreciation rate)^n[/tex]

where n is the number of years after the first 12 months of ownership. In this case, n is 4 (5 years - 1 year).

Plugging the values for the value after 12 months, the depreciation rate, and n into the equation gives us the following:

value after 5 years = 50,864 × [tex](1 - 0.10)^4[/tex] = 32,435

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something noteworthy is that, the y-coordinate for Line 1 is the same, well that simply means that Line 1 is a horizontal line, anything perpendicular to a horizontal line is simply a vertical line, Check the picture below.

the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

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The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder.

The total volume of the solid is 10 cubic centimeters.

The volume of a cylinder is given by:

V = πr²h

The total volume of the two hemispheres is given by:

V = 2 x 2/3 πr³

Now, the total volume of the solid is given by:

V total = πr²h + 2 x 2/3πr³

Now, substitute the value of the total volume in the above expression and then solve for h.

10 =  πr²h + 4/3πr³

h = 10/πr² + 4r/3

Now, the surface area of the curved surface is given by:

A = 2πrh

Now, the surface area of the two hemispheres is given by:

A' = 2 x 2πr²

A' = 4πr²

Now, the total area is given by:

A total = 2πrh + 4πr²

Now, substitute the value of 'h' in the above expression.

A total = 2πr(h = 10/πr² + 4r/3) + 4πr²

Simplify the above expression.

dA = -20/r + 4πr²/3

Now, differentiate the total area with respect to 'r'.

dA/dr =  20/r + 8πr/3

Now, equate the above expression to zero.

0 = -20/r² + 8πr/3

Simplify the above expression in order to determine the value of 'r'.

8πr³ = 60

r = 1.34 cm

Therefore, the radius of the cylinder that produces the minimum surface area is 1.34cm

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All statements that are true from the options are:

i. To circumscribe a given shape implies drawing a  circle outside the a given shape. While to inscribe a given shape means to draw a circle within the boundaries of the shape.

ii. A tangent is a straight line which intersect the the circumference of a circle at a point externally.

iii. A perpendicular bisector is a straight line that divides a given line into two equal halves. And it is at right angle to the given line.

iv. The circumcenter of a triangle is the middle point/ center of the triangle.

Therefore, the statements that are true are:

Thus all the given statements are true.

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c) Shane’s overall average number of jumps completed is of 2.458275.

d) As Shane's overall average number is greater than one half, then the eight graders will be awarded the 50 points.

The jumps that Shane takes are given as follows:

Then the probabilities for each number are given as follows:

Then the distribution of the number of jumps completed is given as follows:

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability, hence:

E(X) = 1 x 0.1667 + 2 x 0.208325 + 3 x 0.624975 = 2.458275.

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Answer:

The answer 700 centimeters cubic.

The percentage of students graduating from engineering or business

is ~50%

as per given in the questions

An university is divided into 6 colleges

with which the most of the students graduating from the four of the colleges given in the graph below

the percentage of students who are interested in biological science colleges are  20%

the percentage of students who are interested in mathematics  colleges are 10%

the percentage of students who are interested in Engineering colleges are  20%

the percentage of students who are interested in business colleges

are 30%

from the graph, graduating from either Engineering or Business

is = 20% + 30% = 50%

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0.0405 is the number that contains the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

based on data gathered from the sources

Suppose the information as shown by

How many eight-digit numbers have more 5s than 3s and contain the digits 2 exactly once, 3 exactly twice, and 4 precisely three times

Let there be more 5s than 3s and more 8-digit numbers with the digits 2 once, 3 twice, 4 three times, and 5s than 3.

2,3,3,4,4,4

after that:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now, 0.405, followed by a digit 2 and 3 make up the eight-digit number.

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y-6=-1/2(x+1)

1. the point-slope form is y-y1=m(x-x1)

x1 and y1 are the coordinates of the point (-1,6) because the line we are looking for its equation passes through it. "m" is the slope.

2. plug in the point (-1,6) in the form from step 1

y-6=m(x+1)

3. to find the slope of this line, the question tells us that this line is parallel to another line that passes through two given points. Any parallel lines, their slopes are the same. That means we have to find the slope of the 2nd line and use it for the 1st line.

The slope formula is m=(y2-y1)/(x2-x1)

plug in the two points m=(4-2)/(2-6), which is equal to -1/2

4. plug in "m" value in the equation from step 2.

Done

The equation of the line in fully simplified slope-intercept form is y = -x/3 -1

The slope-intercept form of a straight line is used to find a line's equation. We need to know the slope of the line and the intercept where the line crosses the y-axis in order to use the slope-intercept formula.

Consider a straight line with y-intercept b and slope m. For a straight line with slope "m" and y-intercept "b,"

The slope intercept form equation is: y = mx + b.

According to the question,

The line is passing through (3,-2) and (-3 ,0)

Slope of any line passing through two points = y2-y1 / x2-x1

Slope of required line: m = 0 - (-2) / -3 - 3

=> m = -2/6

=> m = -1/3

Equation of line => y = -1/3 x + b -----(1)

As we know this line is passing through (-3,0)

Substituting the value in equation(1)

=> 0 = 1 + b

=> b = -1

Hence , The equation of line is y = -1/3 x -1

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If a linear function is increasing, the reciprocal function must be decreasing, mathematically because the reciprocal function is the inverse of the linear function

The reciprocal function of a linear function is given by the formula:

f(x) = 1/x

If a linear function is increasing, then its slope (m) is positive. This means that the slope of the reciprocal function must be negative. The slope of the inverse of a linear function is the negative reciprocal of the slope of the linear function, meaning that the slope of the reciprocal function must be negative for the linear function to be increasing.

To illustrate this, we can consider a simple example of a linear function, f(x) = 2x. This linear function has a positive slope (2), so its reciprocal function, f(x) = 1/x, must have a negative slope (-1). This means that the reciprocal function is decreasing.

In general, if a linear function is increasing, then its reciprocal function must be decreasing, as the slope of the reciprocal function must be the negative reciprocal of the slope of the linear function.

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If  there are 40 school days in a 2-month period. The number of times can a boy be expected to take attendance is: B. 20.

Given data:

Number of school days = 40

Number of month = 2

Now let find the number of attendance times

Number of attendance times =  Number of school days/ Number of month

Number of attendance times = 40/2

Number of attendance times = 20

Therefore the correct option is B.

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The expression of the statement 40 divided by m is 40/m

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

40 divided by m

The above statement is a mathematical statement

The mathematical statement can be expressed as an expression

Recall that, we have

40 divided by m

The term "divided by" means a quotient expression

To divide is represented as / i.e. quotient

So, the expression that represents 40 divided by m is 40/m

Hence, the complete expression is 40/m

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A- The fitted line or the fitted linear regression model is:[tex]y=2625.385462-36.96179663*x[/tex]

B- [tex]s^{2} = 9811.21237[/tex]

C- [tex]y_{20} = 1886.14953[/tex]

A fundamental and widely used form of predictive analysis is linear regression. Regression analysis' main goal is to look at two things: (1) Is it possible to accurately forecast an outcome (dependent) variable using a set of predictor variables? (2) Which individual variables—as shown by the size and sign of the beta estimates—are highly important predictors of the outcome variable, and how do they affect the outcome variable? The link between one dependent variable and one or more independent variables is explained using these regression estimations.

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Answer:

B. 0

Pls choose me as brainliest!

Answer:

One

Step-by-step explanation:

The equation 9x+7=8x+7 has only one solution. This can be seen by setting the two sides of the equation equal to each other and then solving for x.

First, we set the two sides equal to each other by canceling out the 7 on the right side of the equation:

9x+7 = 8x+7

Then, we move all of the terms that have an x on the same side of the equation, and all of the constant terms on the other side:

9x - 8x = 7 - 7

Next, we combine like terms on the left side of the equation:

x = 0

Finally, we solve for x to find the value of x that makes the equation true:

x = 0

Therefore, the only solution to the equation 9x+7=8x+7 is x=0.