a. Write the function if Cecily releases the ball 40 feet above the ground at a velocity of 64 feet per second

Many times referred to as "story issues," word problems can range in the amount of technical terminology utilized and typically incorporate some form of narrative.

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Let's use v1(t) and v2(t) to represent the speed of the first and second runners, respectively, at time t. The functions v1 and v2 must both be continuous in the time variable t, hence this assumption must be made.

So, their difference, a(t), is similarly a continuous function in the variable t, with the formula a(t) = v1(t)-v2(t).  

Now, using the principle of contradiction, one may demonstrate that t1, t2, such that a(t1) is less than or equal to 0 and a(t2) is higher than or equal to 0, exist because the overall average speed of both runners is identical.

Now, we may utilize the continuous function a's Intermediate Value Property to locate a t0 between t1 and t2, where a(to)=0 and the runners are moving at the same speed at this point.

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The percentage of the variation in height that is explained by a regression on age is 0.64, which is the right answer.

from the aforementioned case, The relationship between children's age and height is strongly correlated, as evidenced by the correlation coefficient R of 0.8. Given the correlation coefficient value, we can calculate the coefficient of determination (R2), which indicates the proportion of variation that the regression model can account for.

Therefore, R2 = 0.82 = 0.64, which is the coefficient of determination. Therefore, the proportion of the variation in children's height that can be attributed to age is 0.64 and the remaining 0.36 can be attributed to other factors.

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The number of different votes that are possible are = 120

Permutation is defined as the expression that shows the number of ways a data can be arranged.

The permutation of the the list of 5 bands will determine the number of different votes that are possible which is as follows:

5!= 5×4×3×2×1 = 120

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We can start solving the problem by using algebra. Let's call the first number x and the second number y. From the problem statement, we know that:

y = 4x + 6 (because the second number is 6 more than 4 times the first number)

x + y = 71 (because the sum of the two numbers is 71)

We can substitute the first equation into the second equation:

x + (4x + 6) = 71

5x + 6 = 71

5x = 65

x = 13

Now that we know the value of x, we can substitute it back into the first equation to find the value of y:

y = 4(13) + 6

y = 54

So the two numbers are 13 and 54.

Answer:

6--(3x+5)

Step-by-step explanation:

Answer:

Translation: -3x + 5 - 6

Area of the blue region = A - B = (2+ 2*√(2))/2 * (side length)^2 - 48 square units.

What is the area of congruent right triangles?

Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle.

The blue region is a square, and the four red regions are congruent right triangles.

The blue square is formed by connecting the midpoints of the four sides of the octagon. Since it is an octagon, each of its angles is 135 degrees, and the four red regions are 45-45-90 triangles.

Thus the area of the blue region is equal to the area of the square which is (side length)^2.

The four red regions have a combined area of 124 = 48 square units.

Since the octagon is a regular polygon, all its sides are congruent.

The area of the octagon can be found by multiplying the square of the length of one side by (2+ 2√(2))/2.

If we call the area of the octagon A, and the area of the four red regions B then:

A = B + 4 * 12

Now we can solve for the area of the blue region (A - B)

Area of the blue region = A - B = (2+ 2*√(2))/2 * (side length)^2 - 48 square units

Since we know the area of the red regions we can find the area of the blue region.

Hence, the Area of the blue region = A - B = (2+ 2*√(2))/2 * (side length)^2 - 48 square units.

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The value of the third quartile was then found to be 4.0, which is the 12th entry in the ordered data.

below is a stem and leaf plot of the magnitude of earthquakes on sept. 4th, 2012 in the philippine islands region. this data was collected by the general social survey. find the third quartile.

Stem|Leaf

2 | 0 2 3 6 8 9

3 | 0 1 3 4 6 7 8

4 | 0 1 2 4 5

Third Quartile = 4.0

Step 1: Order the data from least to greatest:

2.0, 2.3, 2.6, 2.8, 2.9, 3.0, 3.1, 3.3, 3.4, 3.6, 3.7, 3.8, 4.0, 4.1, 4.2, 4.4, 4.5

Step 2: Count the data points:

There are 16 data points.

Step 3: Calculate the index of the third quartile:

Index of third quartile = (3/4) x (16) = 12

Step 4: Find the value of the third quartile:

The value of the third quartile is the 12th entry in the ordered data, which is 4.0.

The third quartile of the magnitude of earthquakes in the Philippine Islands region on September 4th, 2012 is 4.0. This data was collected by the General Social Survey. To calculate the third quartile, the data points were ordered from least to greatest and the index of the third quartile was calculated. The value of the third quartile was then found to be 4.0, which is the 12th entry in the ordered data.

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The statistics class was where the data were gathered. The variable is indicated by the column headers, along with each row's Eye Shoe Height 9.

5 different variables are present. Category-specific characteristics include gender, handedness, and field side. Quantitative factors include height and the distance covered when walking. Numbers are used to express variables like the number of siblings and student height. It is discrete since it is a count of siblings. As a continuous numerical variable, height varies throughout time.

There are three primary types of variables: controllable, dependent, and independent. His realization that shoe size is an interval variable came later. Eureka! There is no zero point in an interval variable, but there is a defined range between values. If we take shoe sizes into consideration,

we can conclude that the difference between

a size 2 and a size 3 = size 8 - a size 7

Two major categories—categorical and numeric—can be used to group variables.

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Full question:

Yes, there is an association between food ordered and drink ordered because the distributive property of drinks ordered differs among the food groups.

Yes, there is an association between food ordered and drink ordered, as evidenced by the graph. The graph shows the distribution of drinks ordered among the various food groups, and it can be seen that the distribution differs among the food groups. For example, beer is the most popular drink ordered when burgers are the food ordered, while soda is the most popular drink when salads are the food ordered. This indicates that customers are more likely to order certain drinks depending on the type of food they are ordering, showing an association between food ordered and drink ordered.

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The values of the variance and expected value expressions are

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

E(Y1) = 10

E(Y2) = 2

The above parameters are calculated as follows:

a. Expected value

E(4Y1 – 2Y2 + 6) = 4E(Y1) – 2E(Y2) + 6

= 4(10) – 2(2) + 6

= 40 - 4 + 6

= 42

So E(4Y1 – 2Y2 + 6) = 42

b. Variance

V(4Y1 – 2Y2 + 6) = 4^2 * V(Y1) + (-2)^2 * V(Y2)

= 16 * V(Y1) + 4 * V(Y2)

The variances of Y1 and Y2 are not given

This means that the value of the expression cannot be calculated

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The expression 12 *3/4 is 9.

Explanation:

12 * 3/4 = 91 = 9.

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The expression 12 *3/4 is 9.

By multiplying both sides of the equation by the least common denominator (LCD) of each term, a fractional equation can be solved by first eliminating the fractions. This is possible because an equation cannot become unbalanced when both sides are multiplied by the same number, in this case, the LCD.

Using mathematical operations like subtraction, addition, multiplication, and division, terms are joined to form an expression. Mathematical expressions contain the following terms: Constant: An absolute number is a constant.

12 * 3/4 = 91 = 9.

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The required quadratic polynomial is  [tex]x^{2} - 8x + 12 =0[/tex] and roots of this quadratic polynomial are 2 and 6.

Let the roots of the quadratic equation be  [tex]\alpha[/tex] and [tex]\beta[/tex] .

Given,  

          Sum of zeroes,  [tex]\alpha +\beta = 8[/tex]

           Product of Zeroes, [tex]\alpha *\beta = 12[/tex]

we know that,

      Quadratic Equation can be written as :

                     [tex]x^{2} - (\alpha + \beta )x + \alpha \beta =0[/tex]

     Substituting the values in the above Equation,

                    [tex]x^{2} - (8)x + (12) =0[/tex]

                    [tex]x^{2} - 8x + 12 =0[/tex]

Hence, The required quadratic equation is [tex]x^{2} - 8x + 12 =0[/tex] .

Now, let's factorize the equation to find its root:

                    [tex]x^{2} - 8x + 12 =0[/tex]

                    [tex]x^{2} - 6x -2x+ 12 =0[/tex]

                    [tex]x(x-6) -2(x-6)=0[/tex]

                     [tex](x-6)(x-2)=0[/tex]

                    ⇒ [tex]x= 2,6[/tex]

Therefore roots of the quadratic equation [tex]\alpha ,\beta[/tex] are [tex]2,6[/tex] .

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The correct function notation when x = 3 is

D. ƒ(3) = 12

This is because ƒ(3) represents the output of the function when the input is 3. The equation states that when the input is 3, the output is 12.

A, B and C are not correct because the input is not 3 in those equations.

The angular size of the minor arc AB can be calculated using the formula: Angular size = Arc length/Radius. Therefore, the angular size of the minor arc AB is 16 cm/12 cm = 1.333 radians.

The angular size of the minor arc AB can be calculated using the formula: Angular size = Arc length/Radius. To calculate the angular size of the minor arc AB, we need to know the length of the chord AB and the radius of the circle. In this case, the chord AB is 16 cm long and the radius of the circle is 12 cm. Therefore, we can calculate the angular size of the minor arc AB by dividing the length of the chord AB by the radius of the circle, which is 16 cm/12 cm = 1.333 radians. The angular size of the minor arc AB is 1.333 radians.

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The value of expression after simplify is,

⇒ (w⁻⁴ x³⁶ y⁻⁶ z²⁰) / 9

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ (6w³x⁻⁸y⁻¹z⁻¹⁰ / 2wx³y⁻⁴x⁷) ⁻²

Now, We can simplify as;

⇒ (6w³x⁻⁸y⁻¹z⁻¹⁰ / 2wx³y⁻⁴x⁷) ⁻²

⇒ ( 3 w³⁻¹ x⁻⁸⁻³⁻⁷ y⁻¹⁺⁴ z⁻¹⁰ )⁻²

⇒ ( 3 w² x⁻¹⁸ y³ z⁻¹⁰ )⁻²

⇒ (3⁻² w⁻⁴ x³⁶ y⁻⁶ z²⁰)

⇒ (w⁻⁴ x³⁶ y⁻⁶ z²⁰) / 9

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The average four-digit number 7254 is the only one that is a multiple of another one, as it is composed of the digits 2, 4, 5 and 7 used exactly once.

To find the four-digit number that is a multiple of another one using the digits 2, 4, 5 and 7, we can list all the possible combinations of these digits:

2457, 2475, 2547, 2574, 2745, 2754, 4257, 4275, 4527, 4572, 4725, 4752, 5247, 5274, 5427, 5472, 5724, 5742, 7245, 7254, 7425, 7452, 7524, 7542. as it is composed of the digits 2, 4, 5 and 7 used exactly once.

Next, we can check to see which of these numbers is a multiple of another one. 7254 is the only one that is a multiple of another one, as it can be divided by 2, 4, 5 and 7. Therefore, the answer is 7254.

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The area of the square A would be calculated for the area of the given square B which would be = 768cm². That is option B.

A square is defined as the quadrilateral that has equal four sides with a total of four equal 90° angles.

The dimensions of square A = 3× dimensions of square B

The given area for B = 256 cm2

Area of A = 3× 256

= 768cm²

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Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

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The average rate of growth between each pair of years was calculated in part (a). The instantaneous rate of growth for 2006 was estimated in part (b) and (c), and the instantaneous rate of growth for 2007 was estimated in part (d). Comparing the growth rates from parts (c) and (d), it can be concluded that the rate of growth is constant.

In part (a), the average rate of growth between each pair of years was calculated by dividing the difference between the number of locations in two consecutive years by the number of years between them. For example, to find the average rate of growth between 2005 and 2006, the difference in the number of locations (12441-10236) was divided by the number of years (1). The result was 22.05 locations/year. In part (b), the instantaneous rate of growth in 2006 was estimated by taking the average of the last two rates of change from part (a). This was done by adding the rates of growth from 2005 to 2006 (22.05 locations/year) and 2006 to 2007 (27.64 locations/year) and then dividing by two. The result was 24.85 locations/year. In part (c), the instantaneous rate of growth in 2006 was estimated by measuring the slope of the tangent line through (2005, 10236) and (2007, 15005). This was done by finding the difference in the number of locations (15005-10236) and dividing by the number of years (2). The result was 22.85 locations/year. In part (d), the instantaneous rate of growth in 2007 was estimated by measuring the slope of the tangent line through (2006, 12441) and (2008, 16683). This was done by finding the difference in the number of locations (16683-12441) and dividing by the number of years (2). The result was 22.21 locations/year. Comparing the growth rates from parts (c) and (d), it can be concluded that the rate of growth is constant.

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The probability that at least two of the students were born on the same day of the week is 0.6501.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total students = 4

So, Total number of possible outcomes = 7 x 7 x 7 x 7

Number of ways of choosing 4 from 7 = C(7, 4) = 35

So, number of outcomes in which no day is repeated

= 4! x 35 = 840

P(girls all born on different days) = 840/(2401) = 0.3498

P(at least two born on same day) = 1 - 0.3498

                                                       = 0.6501

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trignometry of  secx * cscx= 1/ cosx*sinx  = sin^2 x+ cos ^ 2 x/ cos x * sin x   = cotx + tan x

What is the formula of sin?

The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as: sin θ = Perpendicular / Hypotenuse.

secx = 1/cosx

and cscx= 1/sin x

then secx * cscx= 1/ cosx*sinx

                         = sin^2 x+ cos ^ 2 x/ cos x * sin x

                          = cotx + tan x

Hence trignometry of  secx * cscx= 1/ cosx*sinx  = sin^2 x+ cos ^ 2 x/ cos x * sin x   = cotx + tan x

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The domain of the function is all real numbers[tex]$\{x|x\in \mathbb{R}\}$[/tex] greater or equal to 0, because the number of players $n$ can not be negative.

The graph of the function is a line with a slope of 1.5 and a y-intercept of 2.5. This can be seen by considering the equation c(n) = 1.5n + 2.5. As the number of new players n increases, the cost c increases by 1.5 for each new player added. For example, if you add 3 new players, the total cost c is 1.5(3) + 2.5 = 6.5. Similarly, if you add 5 new players, the total cost is 1.5(5) + 2.5 = 8.5.

For example, if you want to add 10 new players, the cost will be $c=1.50\times10+2.50=17.50$. Substituting $n=10$ into the function gives $c=17.50$. The graph of this function is a straight line that passes through the origin and has a positive slope of 1.50.

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The percentage of speakers that were sold is equal to 24%.

First of all, we would determine the total number of products that were sold by this electronic store. From the information provided in the table shown in the image attached below, we can logically deduce the following sales for products sold at an electronic store;

Product             Unit sold

Cables                   180

Computers            1,180

Televisions            540

Speakers               600

Total number of products = 180 + 1,180 + 540 + 600

Total number of products = 2,500

Now, we can calculate the percentage of speakers that were sold:

Percentage of speakers = 600/2500 × 100

Percentage of speakers = 0.24 × 100

Percentage of speakers = 24%.

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The following statements are true:

BC║B'C'

AC ⊥ line C'D'

D' and C have the same coordinates

C' lies on line OC

What is dilation?

In mathematics, dilation refers to the process of scaling a geometric figure by a certain factor. This factor is called the scale factor or dilation factor, and it can be either greater than or less than 1. A dilation that enlarges an object is called a magnifying dilation and a dilation that reduces an object is called a shrinking dilation.

Dilation does not change angles or directions. Every image point X' lies on the line containing the center of dilation and the pre-image point X. If the scale factor is other than 1, no image segment will be congruent to its pre-image segment.

Hence, the following statements are true:

BC║B'C'

AC ⊥ line C'D'

D' and C have the same coordinates

C' lies on line OC

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It takes 95.75 minutes to fill a 270-gallon hot tub​.

Given,

A hose fills a hot tub in 1 minute =  2.82 gallons

Time taken to fill a 270-gallon hot tub​,

[tex]= \frac{270}{2.82}[/tex]

= 95.75 minutes

Therefore, It takes 95.75 minutes to fill a 270-gallon hot tub​.

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The numeric value of f(x) = x - 3 at x = 7 is given as follows:

f(7) = 4.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = x - 3.

To obtain the numeric value of the function at x = 7, we replace the lone instance of x by 7, hence:

f(7) = 7 - 3 = 4.

The function for this problem is defined as follows:

f(x) = x - 3.

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Answer:

Step-by-step explanation:

Let's assume the number of soft-cover books Mrs. singh purchased as y.

let's assume the number of hard-cover books Mrs. singh purchased as x.

Total number of books purchased = 29 (given)

i.e. (hardcover books) + (softcover books) = 29

x + y = 29 ........................(i)

Total amount spent on books =  Rs.205.50

i.e. (cost of hardcover books) + (cost of softcover books) = 205.50

(price * no. of hardcover books) + (price * no. of softcover books) = 205.50

(11.50*x) + (3.50*y) = 205.50 ......................(ii)

from eq(i),

we find x,

x = 29-y

putting the value of x in eq(ii),

(29-y)11.50 + 3.50y = 205.50

333.50 - 11.50y + 3.50y = 205.50

8y = 128

y = 16

so, x = 29 - 16 = 13

Therefore, the number of soft cover books purchased by Mrs. Singh is 16 and the number of hardcover books purchased by Mrs. Singh is 13.

Answer:

Solve the formula firnthebspecified variable

I= Prt

P=

The volume of the cube with side of (4m⁸n⁴) unit is (64m²⁴n¹²) unit³

An equation is an expression showing two or more numbers and variables linked together by a mathematical operation. Types of equations are linear, quadratic, cubic and so on depending on the degree of the variable.

Volume is the amount of space that a three dimensional object occupies. For a cube, all the sides are equal, that is length = width = height

The volume of the cube is:

Volume = length³

Given that length = 4m⁸n⁴

Hence:

Volume = length³ = (4m⁸n⁴)³ = 64m²⁴n¹²

The volume of the cube is (64m²⁴n¹²) unit³

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