please help with this practice question, thank you

While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

For more such questions on dedication, click on:

https://brainly.com/question/30160240

#SPJ8

Rita would need to rent at least 37 movies in a year for Option B to be cheaper than Option A.

To determine the number of movies Rita would need to rent for Option B to be cheaper than Option A, we can set up an equation and solve for the unknown variable.

Let's assume Rita rents "x" number of movies in a year.

For Option A:

Yearly fee = $40

Cost per movie rental = $3

Total cost for Option A = Yearly fee + (Cost per movie rental * Number of movie rentals)

Total cost for Option A = $40 + ($3 * x) = $40 + $3x

For Option B:

Yearly fee = $150

Cost per movie rental = $0 (unlimited movie rentals)

Total cost for Option B = Yearly fee + (Cost per movie rental * Number of movie rentals)

Total cost for Option B = $150 + ($0 * x) = $150

We want to find the number of movies (x) at which Option B becomes cheaper than Option A. So we can set up the inequality:

$150 < $40 + $3x

Now, we can solve the inequality:

$150 - $40 < $3x

$110 < $3x

Dividing both sides of the inequality by $3:

($110 / $3) < ($3x / $3)

Approximately 36.67 < x

Since the number of movies must be a whole number, we round up to the nearest whole number:

x ≥ 37

Therefore, Rita would need to rent at least 37 movies in a year for Option B to be cheaper than Option A.

for such more question on number

https://brainly.com/question/859564

#SPJ8

Answer:

/_ b = /_ e

2x + 31 = 7x - 24

5x = 55

x = 11

Step-by-step explanation:

The solutions to the simultaneous equations are approximately (2.18, -2.45) and (-0.18, 3.45).

To solve the simultaneous equations:

Begin by rearranging the second equation to solve for one variable in terms of the other. In this case, we'll solve for y:

5x + 2y = 6

2y = 6 - 5x

y = (6 - 5x)/2

Substitute the expression for y in terms of x into the first equation:

\(2x^2 + y^2 = 12\)

\(2x^2 + ((6 - 5x)/2)^2 = 12\)

Simplify the equation by expanding and combining like terms:

\(2x^2 + (6 - 5x)^2/4 = 12\)

\(2x^2 + (36 - 60x + 25x^2)/4 = 12\)

Multiply through by 4 to eliminate the fraction:

\(8x^2 + 36 - 60x + 25x^2 = 48\)

Rearrange the equation to form a quadratic equation:

\(33x^2 - 60x - 12 = 0\)

Solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula here:

\(x = (-b ± √(b^2 - 4ac)) / (2a)\)

Plugging in the values from the quadratic equation, we have:

\(x = (-(-60) ± √((-60)^2 - 4 * 33 * -12)) / (2 * 33)\)

x = (60 ± √(3600 + 1584)) / 66

x = (60 ± √5184) / 66

x = (60 ± 72) / 66

Calculate the values of x:

For x = (60 + 72) / 66: x ≈ 2.18

For x = (60 - 72) / 66: x ≈ -0.18

Substitute the x values back into the second equation to find the corresponding y values:

For x ≈ 2.18:

5(2.18) + 2y = 6

10.9 + 2y = 6

2y = 6 - 10.9

2y ≈ -4.9

y ≈ -2.45

For x ≈ -0.18:

5(-0.18) + 2y = 6

-0.9 + 2y = 6

2y = 6 + 0.9

2y ≈ 6.9

y ≈ 3.45

Therefore, the solutions to the simultaneous equations are approximately (2.18, -2.45) and (-0.18, 3.45).

For such more questions on Simultaneous Equations Solution

https://brainly.com/question/15165519

#SPJ8

Answer:

10, 11, 4, 5, 0, 8, 6, 9, 1, 7, 2

Step-by-step explanation:

Mode is the number that is most repeated but since all them are repeated only once, the answer would contain all the numbers.

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

To know more about PEMDAS, visit:

https://brainly.com/question/345677

#SPJ1

Answer:

fart

Step-by-step explanation:

Answer:

About $1627.5

Step-by-step explanation:

15.50 x 35 = 542.5

542.5 x 3 (the amount of weeks in a month) = $1627.5

Answer:

c

Step-by-step explanation:

Answer:

It would be c

Step-by-step explanation:

Have a nice day!

Answer:

See Below

Step-by-step explanation:

We are given 3 equations.

3x + 8

5x - 20

and

5x + 4y

First lets solve for x using the first two

3x + 8 = 5x -20

Move the variables to one side

3x + 8 = 5x -20

-3x        -3x

8 = 2x -20

+20     +20

28 =2x

28/2 =2x /2

14 = x

Now we have x = 14

Lets plug this into the second equation to solve for the angle

3(14) + 8

42 + 8 = 50

5(14) - 20

70 - 20 =50

Now, lets plug the x and the angle into the third equation to find y

5 (14) +4y = 50

70 + 4y = 50

-70           -70

4y = -20

4y/4 = -20/4

y = -5

So now we have:

x = 14

y = -5

and the angle = 50

Hope this helps!

Answer:

7 votos

Answer:12Step-by-step explanation:For each of the four triangles you multiply the base (2) by the height (2) and then divide it by 2 which equals 2.

Answer:

x = 70

c = 72

Step-by-step explanation:

Answer:

they are the same

Step-by-step explanation:

6x - 2x + 4 ← collect like terms

= 4x + 4

and

4(x + 1) ← distribute parenthesis by 4

= 4x + 4

The 2 expressions are equivalent to 4x + 4

Answer:

No, Jamie is incorrect

Step-by-step explanation:

No, because in the expression 4(x+1)  you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.

Also in the expression 6x-2x+4  ,you will first need to subtract 2x from  6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4

Our final answer is:

6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4

The original data is:

405, 1108, 84, 315, 495, 609, 362, 428, 224, 338, 700, 790, 814, 767, 633

To find the required percentiles, we need to sort the dataset from lowest to highest.

84, 224, 315, 338, 362, 405, 428, 495, 609, 633, 700, 767, 790, 814, 1108

The total number of data is 15.

a) The 25th percentile is the element located at the position:

25/100 * 15 = 3.75

Rounding down, the position is 3, so the 25th perc

After dividing and simplifying the given cοmplex numbers 5-3i and

7+8i, the answer is \($\frac{59}{113} - \frac{77}{113}i$\).

Cοmplex numbers are a type οf number that includes bοth a real cοmpοnent and an imaginary cοmpοnent. They are written in the fοrm

a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square rοοt οf -1.

The real cοmpοnent, a, represents the hοrizοntal axis οn a cοmplex plane, while the imaginary cοmpοnent, bi, represents the vertical axis. The cοbmplex plane is a twο-dimensiοnal graph where the hοrizοntal axis represents the real cοmpοnent and the vertical axis represents the imaginary cοmpοnent.

Tο divide twο cοmplex numbers, we use the fοllοwing fοrmula:

\($\frac{a+bi}{c+di} &= \frac{(a+bi)(c-di)}{(c+di)(c-di)} \\)

&= \($\frac{(a+bi)(c-di)}{c^2 + d^2}\)

where \($a,b,c,d$\)  are reaL numbers, \($i$\) is the imaginary unit, and we assume that  \($c+di \neq 0$\)  . Using this formula, we can simplify:

\($\frac{5-3i}{7+8i} &= \frac{(5-3i)(7-8i)}{(7+8i)(7-8i)} \\)

&=   \($ \frac{35 - 56i - 21i - 24i^2}{7^2 - (8i)^2} \\)

&= \($ \frac{35 - 77i + 24}{49 + 64} \\)

&=  \($\frac{59 - 77i}{113} \\)

&=  \($\frac{59}{113} - \frac{77}{113}i\)

After simpIification the needed final answer is

\($\frac{59}{113} - \frac{77}{113}i$\).

To know mοre about complex numbers,

brainly.com/question/20566728

#SPJ1

The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

learn more about trig ratios here :

https://brainly.com/question/14977354

#SPJ1

Answer:

165

Step-by-step explanation:

In 165 ways i can select 3 books to bring on vacation from a group of 11 books.

A combination is when you choose data from a group without any order or sequence. If the group of data is relatively lesser, you can calculate the number of possible combinations.

According to the question

Select 3 books to bring on vacation from a group of 11 books.

By using combinations formula

\(^{n} C _{r}=\frac{n!}{r!(n-r)!}\)

\(^{11} C_{3}\) = \(\frac{11!}{3!(11-3)!}\)

= \(\frac{11.(10)(9)(8!)}{3!.8!}\)

Cancelling out 8! from denominator and numerator

= \(\frac{11(10)(9)}{3(2)(1)}\)

= 165

Thus, In 165 ways i can select 3 books to bring on vacation from a group of 11 books.

Find out more information about combinations here

https://brainly.com/question/13387529

#SPJ3

Answer:

A. Margin of error=0.0346

B. Confidence interval=0.4854 to 0.5546

Step-by-step explanation:

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let plug in the formula

Confidence level= 1-0.95

Confidence level= 0.05

Second step is to find Z using this formula

Zα/2

Let plug in the formula

Z= 0.05/2

Z=0.025

Third step is to find the Z score of Z=0.025

Zα/2=1.96

Now let calculate the margin of error using this formula

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Computation for the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009

Computation for the boundaries of confidence interval

Using this formula

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

Therefore the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009 is 0.4854 to 0.5546

Answer:

Here is the answer

Step-by-step explanation:

36 = 3x2x3x2

8 = 2x2x2

42 = 7x3x2

In 20 days was the whole job done.

Let efficiency of each worker is 1 unit / day .

So, Total work = 10 x 1 x 15 = 150 units .

Now, in first 5 days 6 worker completes

= 5 x 6 x 1 = 30 units .

and, in next 3 days 8 workers completes

= 3 x 8 x 1 = 24 units .

Now, 4 more workers joined then total workers are = 12 workers .

So, amount of work left = 150 - 30 - 24 = 96 unit

Thus, the time taken by 12 workers to complete remaining work

= 96/12

= 8 days .

So, the Whole job was done in = 5 + 3 + 12 = 20 days

Learn more about Work done problem here:

https://brainly.com/question/32738245

#SPJ1

The question attaches here seems to incomplete the complete question is

10 workers can finish the job in 15 days. For the first 5 days, only 6 workers worked on the job. Then for the next 3 days 2 more workers joined them. To finish the job, 4 more workers joined them. After how many days was the whole job done?

Answer:

Given that 1minute =3/7of the vessel

let the time taken in minutes to fill the whole of the vessel be' x' minute.

1min =3/7

xmin =whole vessel =1=7/7

=3x/7=1=x=7/3=2.3min=2min.3sec

Answer:

145% increase

Step-by-step explanation:

343 - 140 = 203

203/140 = 1.45

1.45 x 100 = 145

He can use the sine rule

Answer:

x = 1

Step-by-step explanation:

5 = 2 + 3x

=> 5 - 2 = 3x

=> 3 = 3x

=> 3/3 = x

=> 1 = x

Answer:

x=1

Step-by-step explanation:

5=2+3x

5=3x+2

-2   -2

3=3x

/3  /3

x=1

hope this helps

brainliest pls?

An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

Read more on absolute value function here: brainly.com/question/28308900

#SPJ1

Answer:

Below

Step-by-step explanation:

20x to the power of three y ÷ by 5 will equal the same as

40x10

You have the right one selected.

The answer is 2:1

To find this take each side of ABC and its corresponding side on DEF, then simplify. You can treat ratios just like fractions, so simplify them in the same way.

20:10 becomes 2:1

12:6 becomes 2:1

16:8 becomes 2:1

=

Step-by-step explanation:

the numbers are equal n if u work out all of them ull get the same answer

Answer:

the value of √7=2.645751311065 and value of 14/5=2.8

so.......

√7<14/5