The number of hours people spent jogging last week is shown in the histogram below.
Hours Spent Jogging
Number of People
12
10
8
S SP
2-
0 1 2 3 4 5
Number of Hours
Which of the following statements is true for the data?
A. The majority of people jogged between 1 hour and 4 hours.
CB. The majority of people jogged between 1 hour and 2 hours.
C. The majority of people jogged between 2 hours and 3 hours.
The majority of people jogged between 3 hours and 5 hours.
Copyright

Hey there!

Answers;

For part (a):

[tex]v=669,883[/tex]  [tex]miles/day[/tex]

[tex]r=44,423[/tex] [tex]miles[/tex]

[tex](a)V=rw[/tex]

[tex]w=\frac{v}{r}[/tex] [tex]=\frac{669883}{44423}[/tex][tex]=15.0796[/tex] [tex]radians/day[/tex]

[tex]15[/tex] [tex]radians/day[/tex]

For part (b):

[tex]Circumference=2\pi r[/tex]

[tex]2*3.14*44423[/tex]

[tex]278976*44[/tex]

Number of rotations = [tex]\frac{669883}{278976*44}[/tex] =  [tex]2*40[/tex] ⊥ ≈ [tex]2[/tex]

Hence:

(a) [tex]15[/tex] [tex]radiations/day[/tex]

(b) Number of rotations = [tex]2[/tex]

___________________________________________

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Answer:

18.

3.25

19.

3.125

20.

-26.36

Step-by-step explanation:

Out of the given vectors is in the span of the other vectors,  b. One of the vectors is in the span of the other vector. Since u and v have the same last component, they are linearly dependent, so u is in the span of v and w.

If a set of vectors is linearly dependent, then one of the vectors can be expressed as a linear combination of the other vectors. This means that one vector is in the span of the other vectors. In this case, u can be expressed as a linear combination of v and w, so u is in the span of the other vectors.  

To check for linear dependence, we can first check for a zero row in the matrix formed by the vectors. If there is a zero row, then the vectors are linearly dependent. In this case, the last row of the matrix formed by the vectors is [3,3,0], which is a zero row, so the vectors are linearly dependent.  We can also check for linear dependence by computing the determinant of the matrix formed by the vectors.

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A two variable linear equation means an equation having two variables. It is usually represented as ax+by =c. We can solve a two variable linear equation in many ways.

If the linear equation is only given, to solve it we have to calculate the x-intercept and y-intercept. It is one way of solving a two variable linear equation. Lets look into an example.

 2x+5y = 19

The x intercept is when y=0,

then, 2x+ (5×0) = 20

          2x = 20, x=10

y intercept is when x=0, then

2×0 + 5y = 20

   5y = 20,  y= 20/5 =4

So, by solving the equation, we get x=10 at x intercept and y=4 at y intercept.

If one the values are given , we can substitute it in the equation to calculate the other variable.

In the equation, 2x+3y= 12, if y=2, we can calculate by substituting.

    2x + (3×2) = 12

     2x = 12-6

     2x = 6

      x =3

So when y=2 then x=3.

Constraints are the restrictions on the domain of a linear equation, like a number of days or students should be a positive integer.

So, we can solve a two variable linear equation through different ways.

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The position of the value is shown on the number line attached to this answer.

A number line is a ray which extends from -∞ to +∞ as its two extreme ends. Thus all number fall within this range such that all directed numbers can be located on the number line.

A directed number is a any number which has either a positive or negative sign. This implies that the position of all numbers can be shown on the line.

Thus, from the question to show 2/3 of 4 on the number line;

2/3 of 4 = 2/3 x 4

             = 8/ 3

             = 2 2/3

The position of 2 2/3 is shown on the number line attached to this answer.

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The numbers that correctly complete the two-way table are 100,70, 170, 80, 130, 210, 180,200, and 380 as shown in the attached chart.

Total of sweatshirts= 380

Total with no hood= 210

Green sweatshirts= 180

Purple sweatshirts with no hood= 70

Based on this information we can conclude:

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The critical values for a one-sample t test given the following conditions are  +1.796, -1.796 2. -2.60 3. +2.576, -2.576 4. +1.729.

Value is a term used in many different contexts to refer to the worth or importance of something. It is used to describe the worth of an item or service in terms of its utility, its ability to satisfy a need or desire, or its usefulness in exchange. Value can also refer to the worth of an individual or group in terms of their contribution to society or their inherent worth. Value is subjective and can vary greatly from one person or group to another.

1. +1.796, -1.796
2. -2.60
3. +2.576, -2.576
4. +1.729

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Answer:

your question is 6=1/v+2

Step-by-step explanation:

6-2=1/v

4v=1

v=1/4

The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π

When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.

Thus, since we want to find the radian measure of 170 degrees, it means that;

If 180° = π radians,

then; 170° = (170 * π)/180

= ¹⁷/₁₈π

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The standard deviation of the data is  2.41 smartphones.

Data refers to the elements that make up persons, things, events, and ideas. It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics. The presentation of data is the name given to such a configuration.

Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.

Given, The number of smartphones sold at an electronic store each day

is represented by the table with two columns and 5 rows.

The mean of the data set is,

= (8 + 13 + 12 + 10 + 15)/5.

= 11.6.

We know the formula for the standard deviation of a data set is,

= [tex]\frac{1}{\sqrt{n}}\sqrt{\sum_{i =1}^{n} (x_i - \overline{x}{}})^2[/tex].

= (1/√5)×√[(-3.6)² + (-1.4)² + (-0.4)² + (-1.6)² +(-3.4)²].

= (1/√5)×[√29.2].

= 2.41.

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Answer:

2.7 Smartphones

Step-by-step explanation: Just did it

Answer:

A

Step-by-step explanation:

this is a college level question ? oh my ...

to get the total area we need to add the area of the rectangle and the area of the half-circle.

the area of the rectangle is

length × width = 15 × 5 = 75 ft²

the area of the half-circle is

pi×r² / 2

how do we get r (radius) ?

we know, both lengths of the rectangle must be equally long. so, 15 ft.

we see that the remaining length after the half-circle is 9 ft.

so, the diameter of the half-circle is 15 - 9 = 6 ft.

the radius is half the diameter, so r = 6/2 = 3 ft.

the area is therefore

pi×3² / 2 = 9pi /2 = 14.13716694... ft²

in total that makes

75 + 14.13716694... = 89.13716694... ft²

the closest of your answer options is A : 88 ft²

Answer:

Step-by-step explanation:

Quarter implies 4. If there were 20 items, and you broke them into quarters, each quarter would have 5 items.

The charge of each company will be the same at 40 miles.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let us suppose the miles travelled as x.

Given that:

Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00, this is represented as:

C = 0.10(x) + 40

Carnuba's Car rental charges $.15 per mile and has a service of $20.

D = 0.15(x) + 20

The charge of both the companies would be equal when C = D:

0.10(x) + 40 = 0.15(x) + 20

40 -20 = 0.15x = 0.10x

20 = 0.5x

x = 20/ 0.5

x = 40

Hence, the charge of each company will be the same at 40 miles.

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The mean birthweight of the obstetrician's own patients is higher than the national mean.

In the first description, 84% is a parameter, since it describes the population as a whole. The survey of 100 residents in Pleasant Valley yields a statistic of 75%, since it is a sample of the population.

In the second description, the mean birthweight of infants in the United States in 2006 of 3.3 kg and the standard deviation of 0.57 kg are both parameters. The mean birthweight of the obstetrician's own patients of 3.6 kg is a statistic. To calculate the difference between the two means, we can subtract the two values: 3.6 kg - 3.3 kg = 0.3 kg. This 0.3 kg difference indicates that the mean birthweight of the obstetrician's own patients is higher than the national mean.

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Answer:

see attached

Step-by-step explanation:

Method 2 is the best option for estimating the average yearly income of the class of 2005.

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So, the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.

To find the height of the pedestal, we can use the concept of angles of elevation. The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal.

From the given information, we know that the angles of elevation of the top and bottom of the statue from a point h2 metres above the ground level are α and β respectively.

We can use the tangent of the angle of elevation to find the height of the object. The tangent of the angle of elevation is equal to the height of the object divided by the distance from the base of the object to the point of observation.

Let's call the height of the pedestal as "h3"

So we can write the following equations:

h1/((h3+h1)-h2)= tan(α)

h1/((h3)-h2)= tan(β)

By solving the above equations we can get the value of h3 which is the height of the pedestal.

((h1−h2)tanβ+h2tanα)/tanα−tanβ

This is the final equation which gives the height of the pedestal.

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The average velocity (in m/s) over the given time intervals is [1,2]

Part A.

Keep in mind that the formula for average velocity is

(Y2 - Y1)/V avg = displacement/time interval (t2 - t1)

Given that the rock's position at time t is determined by:

y = 16t - 1.86*t^2

Part 1

for the time period [1, 2]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*2 - 1.86*22 = 24.56 m when t2 = 2 sec.

So

average Velocity = (24.56 - 14.14)/(2 - 1) (2 - 1) = 10.42 m/s V avg

Part 2.

for the time period [1, 2]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.5 - 1.86*1.52 = 19.815 m when t2 = 1.5 sec.

So,

average Velocity  = (19.815 - 14.14)/(1.5 - 1) (1.5 - 1) = 11.35 m/s V avg

Part 3.

During the period [1, 1] .1]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.1 - 1.86*1.12 = 15.3494 m when t2 = 1.1 sec.

So,

average Velocity  = (15.3494 - 14.14)/(1.1 - 1) (1.1 - 1)

average Velocity = 12.094 m/s and equals 12.09 m/s (In two decimal places)

Part 4.

During the period [1, 1] .01]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.01 - 1.86*1.012 = 14.262614 m when t2 = 1.01 sec.

So,

average Velocity = (14.262614 - 14.14)/(1.01 - 1) (1.01 - 1)

12.26 m/s and V avg = 12.2614 m/s (In two decimal places)

Part 5.

During the period [1, 1] .001]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.001 - 1.86*1.0012 = 14.15227814 m when t2 = 1.001 sec.

So,

average Velocity = (14.15227814 - 14.14)/(1.001 - 1) (1.001 - 1)

12.28 m/s V avg = 12.27814 m/s (In two decimal places)

Part B.

Rock's immediate velocity will be determined by:

d[16t - 1.86t2]/dt = V= dy/dt

Velocity = 16*1 - 2*1.86*t

time = 1 second,

Velocity = 16 - 2*1.86*1

average velocity at time t is equal to V = 12.28 m/s.

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The magnitude of the electric flux through the sheet will be 6.1 N.m²/C.

What is Electric flux?

The amount of electric lines of force (or electric field lines), which cross a specific area, is referred to as electric flux, a feature of an electric field. According to this theory, electric field lines begin with positive electric charges and end with negative charges.

The following formula can be used to get the electric flux:

∅ = EAcosФ

where,

∅ = Electric flux

E is the Electric field which is 73.9 N/C.

A is Area of the plate which is =  (0.4 m)(0.6 m) = 0.24 m²

θ is the angle between normal to the area and electric field lines = 90° - 20° = 70°.

Putting these values in our formula, we get:

∅ = (73.9)(0.24)cos(70°)

∅ = 6.1 N.[tex]m^{2}[/tex]/c.

Therefore the Magnitude of the electric flux through the sheet is 6.1 N.m²/C.

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After divide, the value of quotient is 0.133.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 10 divided by 75.10.

Now, We get;

⇒ 10 divided by 75.10

⇒ 10 ÷ 75.10

⇒ 0.133

Thus, The value of quotient after divide = 0.133

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Step-by-step explanation:

x² - y² = (x + y)(x - y)

3x - 3y = 3(x - y)

(x + y)(x - y) / (3(x - y)) = (x + y)/3

Answer:

x^2 - y^2

_______

3x - 3y

(x+y) (x-y)

_______ { (x-y) (x-y) cancels out}

3(x-y)

(x+y)

____

3

Hope this will help you...!!!!

The market share of the vape machine market had sales of $1.4M is given as 63.57%.

To calculate the brand's market share, you would need to divide the brand's sales by the total sales of the market and then multiply by 100 to get the percentage.

In this case, the brand's sales are 10000 units x $89/unit = $890,000.

So the market share would be:

$890,000 / $1,400,000 x 100 = 63.57%.

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The population after 12 years is 98448 and the formula is[tex]P(t) = 25000(1.121)^{t}[/tex].

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the population of the town is 25000 and increasing at the rate of 1.121.

The expression will be written as:-

[tex]P(t) = 25000(1.121)^{t}[/tex]

[tex]P(12) = 25000(1.121)^{12}[/tex]

P(12) = 98448

Hence, the population after 12 years will be 98448.

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Answer: THE CORRECT ANSWER IS 30  

Step-by-step explanation:

A line that is parallel to y = -4x + 11 and goes through the point (2, 1) in point slope form is: A. y - 1 = -4(x - 2).

Mathematically, the point-slope form of a line is modeled by this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the given linear equation y = -4x + 11, the slope is given by:

y = -4x + 11

m₁ = -4

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ (m represents the slope.)

At point (2, 1), an equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -4(x - 2)

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Yes, these numbers meet the triangular inequalities, then these can be the measures of the sides of a triangle.

Remember that if A, B, and C are the sides of a triangle, then the triangle inequality says that:

A + B > C

A + C > B

C + B > A

As long as 3 values are solutions of the inequalities, then these can be the sides of a triangle.

if we use:

A = 7

B = 10

C = 10

Then we get:

7 + 10 > 10 ---> 17 > 10

7 + 10 > 10 ---> 17 > 10

10 + 10 > 7 ---> 20 > 7

All the ienqualities are true, thus, these can be the measures of the sides of a triangle.

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The measure of the side length n is equal to 14 for the right triangle.

Considering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent m and hypotenuse 28+7= 35;

cosθ = m/35

for the smaller right triangle with adjacent 7 and hypotenuse m

cosθ = 7/m

m/35 = 7/m

m² = 245 {cross multiplication}

m = √245 = 7√5 {take square root of both sides}

(√245)² = 7² + n² {by Pythagoras rule for the smaller right triangle}

245 = 49 + n²

n² = 245 - 49 {collect like terms}

n² = 196

n = √196 {take square root of both sides}

n = 14

Therefore, the measure of the side length n is equal to 14 for the right triangle

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One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.

In sports, there are typically opponents or teams competing against each other to achieve a goal or win a match.

This competitive aspect is not present in play or dramatic spectacles, where the focus is typically on individual or group performance rather than competition against others.

Sports are defined as physical activities that involve a set of rules and are typically competitive in nature. They are typically organized and played by people in order to achieve a goal or win a match. Examples of sports include football, basketball, soccer, tennis, baseball, and golf.

Sports are also a form of recreation, entertainment, and physical activity. They can be played individually or in teams. They help to improve physical fitness, and mental health and also promote teamwork and social interaction.

Therefore, One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.

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the equation of the required line is 3xâ2y+1=3x1â2y1+1.

(i) We are given the parallel line of the given equation, that is yâ2x=0.

So, the equation of the required line will be yâ2x=c, where c is a constant.

Let the point of intersection of the two lines be (x1, y1).

Then, substituting the values of x1 and y1 in the equation yâ2x=c, we get

y1â2x1=c

or, c=y1â2x1

Hence, the equation of the required line is yâ2x=y1â2x1.

(ii) We are given the perpendicular line of the given equation, that is 2x+yâ5=0.

So, the equation of the required line will be 3xâ2y+1=c, where c is a constant.

Let the point of intersection of the two lines be (x1, y1).

Then, substituting the values of x1 and y1 in the equation 3xâ2y+1=c, we get

3x1â2y1+1=c

or, c=3x1â2y1+1

Hence, the equation of the required line is 3xâ2y+1=3x1â2y1+1.

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The comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.

Suppose that [tex]$\sum_{n=1}^{\infty} a_{n}$ and $\sum_{n=1}^{\infty} b_{n}$[/tex] are series with positive terms. We assume that does not exist and that [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex]diverges.

To prove that [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] also diverges, we will use the comparison test. Since [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex] diverges, we can find a number M such that [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges. Since [tex]$\lim_{n\rightarrow \infty} \frac{a_{n}}{b_{n}}$[/tex] does not exist, we can find a number N such that for all [tex]$n \geq N$, $\frac{a_{n}}{b_{n}} > 1$[/tex].

Now, for any [tex]$n \geq \max \{M,N\}$[/tex], we have [tex]$\frac{a_{n}}{b_{n}} > 1$[/tex]. Thus, [tex]$a_{n} > b_{n}$[/tex]. By the comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.If the ratio of two series with positive terms,[tex]$\sum_{n=1}^{\infty}a_n$[/tex]  and [tex]$\sum_{n=1}^{\infty}b_n$[/tex], does not converge to a limit as n approaches infinity and [tex]$\sum_{n=1}^{\infty}b_n$[/tex] diverges, then [tex]$\sum_{n=1}^{\infty}a_n$[/tex] must also diverge.

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