Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)

Answers

Answer 1

It takes Bob 125.0633 seconds to cover the entire track.

Let the time taken by Bob to cover the track be x sec

Let the distance of the track be y m

Akira covers the whole track in 95 seconds

hence, his speed is y/95 m/s

Similarly, Bob's speed is y/x m/s

He has traveled to the Easternmost point in 22 seconds. Hence to meet Akira, he has to run for 4 more seconds.

In that time he will cover a distance of 4y/95 m

Similarly, in 26 seconds, Bob will cover

26 y/x m/s

Now Akira has started from the Northernmost point, and we all know that the distance between the Easternmost and Northernmost points of the track will be 1/4th of the whole track length.

Hence,

4y/95 + 26y/x = y/4

or, y(4/95 + 26/x) = y/4

or, 4/95 + 26/x = 1/4

or, (4x + 2470)/95x = 1/4

or, 4x + 2470 = 95x/4

or, 16x + 9880 = 95x

or, 79x = 9880

or, x = 125.0633 seconds

To know more about distance visit

https://brainly.com/question/20330990

#SPJ4


Related Questions

The perimeter of a square is equal to the perimeter of an equilateral triangle. the length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by x 1. which equation can be used to find the value of x? x = 3 (x 1) 3 x = 4 (x 1) 4 x = 3 (x 1) x = x 1

Answers

The equation used to determine the value of x for the length of a square side is:  4 x = 3 (x 1).

Explain the term equilateral triangle?An equilateral triangle, which is frequently referred to as a "regular" triangle, is a triangle with three equal-length sides. Because all three sides of an isosceles triangle are equal, an equilateral triangle is a particular case of just an isosceles triangle.

The given condition are-

A square's perimeter is the same as an equilateral triangle's perimeter.x determines the length of a square side, while x1 determines the length of an equilateral triangle side.

Perimeter of square = 4x

Equilateral triangle perimeter = 3(x 1)

Equating both by the condition-

4x = 3(x 1)

Thus, the equation used to determine the value of x for the length of a square side is:  4 x = 3 (x 1).

To know more about the equilateral triangle, here

https://brainly.com/question/2351368

#SPJ4

Solve the equation 1 - (-x + 3) =10

Answers

The Answer: x = 12
Hope this helps

a grocery store company wanted to know how well some of their local stores were doing. in order to find out, they hired 6 different reviewers to rate 15 local stores. what are the degrees of freedom?

Answers

The degrees of freedom here is 5.

Given,

A grocery store company wanted to know how well some of their local stores were doing.

The number of sample reviewers they hired to rate 15 local stores = 6

We have to find the degrees of freedom;

Degrees of freedom;-

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the number of items in the data sample.

Here,

Degrees of freedom = n - 1

n = 6

Then,

Degrees of freedom = 6 - 1 = 5

That is,

5 is the degrees of freedom in this case.

Learn more about degrees of freedom here;

https://brainly.com/question/16254305

#SPJ4

Find the equation that represents the proportional relationship in this graph, for y in terms of x.

Answers

The equation that represents the proportional relationship in this graph is y = 2 / 7 x.

How to find proportional relationship?

Two variables have a proportional relationship if all the ratios of the variables are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x if:  

y = kx

for some constant k , called the constant of proportionality .

Therefore, the variables in this case are y and x.

Hence, let's find k using the coordinates on the graph

(0.7, 0.2)

0.2 = k (0.7)

k = 0.2 / 0.7

k = 2 / 7

Hence,

y = 2 / 7 x

learn more on proportional relationships here: https://brainly.com/question/20213987

#SPJ1

translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative. a. a2b3 b. a22(b21c)2 c. (ab2)23c2 5 e

Answers

The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.

a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.

Then, a+a+b+b+b=2a+3b.

b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.

Then,

[tex]\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}[/tex]

c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.

Then,

[tex]\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}[/tex]

Also, the additive identity to e is zero. And, aⁿ=na.

Then,

(-2b-a)+(-2b-a)+(-2b-a)+2c=0

Simplifying we get,

-3(a+2b)+2c=0.

The answers are  (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

The complete question is -

Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative

a. a²b³

b. a⁻²(b⁻¹c)²

c. (ab²)⁻³c²=e

To know more about commutative:

https://brainly.com/question/778086

#SPJ4

A study obtained data on the amount of time 32 randomly selected young adults spent on their cell phones pre-pandemic and then during the lockdown phase of the pandemic. The investigator is interested in determining whether there is evidence that the amount of time young adults spent on their cell phone during the lockdown increased when compared to pre-pandemic times. Let
L=
time spent on phone during lockdown;
P=
time spent on phone prepandemic time; and
d=L−P
Question 4 (1 point) The data are paired because: The conclusion pertains to a mean difference. All of these are true Each element in the sample is measured twice: once pre-pandemic and once in lockdown There is only one sample

Answers

The Null hypothesis and alternative hypothesis for the given sample of cell phone spent time data of 32 randomly selected adults during lockdown and pre-pandemic times are,

                           H₀ : μd = 0 and Hₐ : μd > 0

Correct option is option (d).

What is hypothesis testing?

To decide whether a hypothesis should be accepted or rejected, statisticians utilize formal, planned procedures known as hypothesis testing. Hypothesis testing is the process of choosing hypotheses for a specific probability distribution based on observable evidence.

Given:

A study obtained time data of 32 randomly selected young adults spent on their cell phones pre-pandemic and then during the lockdown phase of the pandemic. let us consider,

L --> time spent on cell phone by adults during lockdown

P --> time spent on cell phone by adults at pre pandemic time

and                       d = L- P

we want to perform a hypothesis testing on this sample .

The samples are dependent because same adults are being sampled before and after the lockdown.

Also, we need to test if mean time after is higher than mean time before so this is a right tailed test. Hence,

The correct hypotheses will be:

                                   H₀ : μd= 0

                                     Hₐ : μd> 0

Hence, option D is the correct option.

To learn more about Hypothesis testing :

brainly.com/question/29690266

#SPJ4

convert 37 base ten to base five​

Answers

Answer : 122 base five

A gas station is open 365 day a year, 24 hours a day. The store owner estimates that they served 40,000 cups of coffee last year. This quantity can also be expressed as
functions
equation editor
cups of coffee per hour (round to the nearest whole cup). This is a ? reasonable not reasonable estimate.

Answers

A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.

The problem can be solved using the average value approach.

Average value = total amount or sum of data / number of data

In the given problem,

total amount = total coffee served last year

total amount = 40,000

number of data = number of hours in a year

number of data = 365 day/year x 24 hours/day = 8760 hours

Hence,

Average value = total amount or sum of data / number of data

                         = 40000 / 8760

                         = 4,6 ≈ 5 (round to the nearest whole cup)

Hence, the average coffee served is 5 cups per hour.

Learn more about average here:

https://brainly.com/question/28254231

#SPJ4

what is the simplified product of 2/5+2/3​

Answers

[tex] \frac{2}{5} + \frac{2}{3} = \\ lcm \: of \: 5 \: and \: 3 \: is \: 15 \: so \\ \frac{6 + 10}{15} = = \: \frac{16}{15} [/tex]

Therefore, the answer is

[tex]{ \red{ \sf{ \frac{16}{5}}}}[/tex]

[tex]\colorbox{pink}{\blue{ \boxed{ \tt{ hope \: it \: helps \: you}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \sf{ \frac{2}{5} + \frac{2}{3}}}}[/tex]

If you take the Lowest Common Multiple (L.C.M.) you will get 15.

[tex]{ \blue{ \sf{ \frac{6+10}{15}}}}[/tex]

[tex]{= \blue{ \sf{ \frac{16}{15}}}}[/tex]

Amber is given a Stanford-Binet intelligence test. Her mental age is determined to be 14, and her chronological age is 10. Which of the following is true of Amber? A) Her IQ score is 86. B) Her IQ score is about average. C) Her IQ score is below the majority of the population. D) Her IQ score is above the majority of the population types of intelligence.

Answers

The correct option is . D) Her IQ score is above the majority of the population types of intelligence.

IQ is an abbreviation for intelligence quotient. IQ tests are used to assess people's intellectual abilities and potential. They are intended to test a wide range of cognitive abilities, including reasoning, logic, and problem-solving.

It's a test of intelligence, which you're born with. It is not a test of knowledge that represents what you learn in school or through life experience.

Amber's mental age = 14

Amer's age = 10

Then her IQ can be calculated by

[tex]IQ=\frac{mental\ age}{chronological\ age}*100=\frac{14}{10}*100=140[/tex]

Average IQ of majority of population is between 85 to 115.

Only small percentage of population has IQ score higher than 130.

It means Amber's IQ score is above the majority of the population.

To learn more about fractions refer here

https://brainly.com/question/10354322

#SPJ4

a research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 60,139.7 and 3517.57 kilometers. can you conclude, using ????

Answers

There is no sufficient evidence to indicate the true standard deviation is less than 4000

What is standard deviation ?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

given that n = 16

x = 60139.7

s = 3718.06

∝ = 0.05

To test the hypothesis

H0 : = 4000

H1 :  < 4000 (claim)

test statistics

x² = ((n-1)s²) / H0²

   = (15 * 13823970.16) / (16000000)

   = 12.96

P- value = P [x² < 12.96]           DF = n-1 = 15

             = 0.3946

0.1 < P-value <0.5

To learn more about standard deviation from the given link  

https://brainly.com/question/475676

#SPJ4

Given the least-squares regression line, In(Element) = 2.305 -0.101(Time), what is the predicted amount of an
unstable element that is left after 6 years?
and explanation

Answers

The predicted amount of an unstable element that is left after 6 years is 5.46 grams.

Explain the least-squares regression line?A least-squares regression line, that minimizes the vertical distance between the data points and the regression line, is the line that best fits a linear relation between two variables when the data indicates such a relationship.

For the stated question-

The equation for the least-squares regression line, is;

In(Element) = 2.305 -0.101(Time)

Amount of unstable element left after time t = 6 years.

In (Element) = 2.305 -0.101(6)

ln (Element) = 1.699

(Element) = e¹°⁶⁹⁹

(Element) = 5.46

Thus, the predicted amount of an unstable element that is left after 6 years is 5.46 grams.

To know more about the least-squares regression line, here

https://brainly.com/question/14563186

#SPJ1

The bag contained red marbles and blue marbles.red marbles to blue marbles was 5 to 3 what fraction of the marbles were blue

Answers

Answer:

53

Step-by-step explanation:

Solve for h:
2h-4x=-6y
Please provide steps also

Answers

h=3y+2x
That’s ur answer because you have to add 2x to the other side where 6y and then you divide the 2 from both sides and then 4 divided by 2=2 and then 6 divided by 2=3

Answer:

h = -3y + 2x

Step-by-step explanation:

Add 4x to both sides of the equation.

2h = −6y + 4x

Divide each term in 2h = −6y + 4x by 2 and simplify.

Divide each term in 2h = −6y + 4x by 2.

2h/2 = -6y/2 + 4x/2

Simplify the left side.

h = −6y/2 + 4x/2

Simplify the right side.
Simplify each term.
Cancel the common factor of −6 and 2.

h = -3y+2(2x)/2

Cancel the common factors.
Factor 2 out of 2.

h = -3y+2(2x)/2(1)
Cancel the common factor

h = -3y+2(2x)/2(1)
Rewrite the expression
h = -3y + 2x/1

Divide 2x by 1.
h = -3y + 2x

hopefully its right LOLZ

john drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. what was his average speed for the whole journey?

Answers

The average speed is 54 miles per hour.

What is average ?

In plain English, an average is one number chosen to represent a list of numbers. It is often calculated by dividing the total number of numbers in the list by the number of numbers in the list. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.

The definition of the average is the mean value, which is the ratio of the sum of the values in a given set to the total number of values in the set.

The formula for distance is

Distance = Rate × Time

Total distance = 50 × 3 + 60 × 2 = 270

Total time = 3 + 2 = 5

Using the formula:

[tex]Speed = \frac{Distance}{Time}[/tex]

       = 270 / 5

       = 54

To learn more about average from the given link

https://brainly.com/question/20118982

#SPJ4

Please help with this question

Answers

Blank 1: Corresponding because All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

Blank 2:

Blank 3: x= 46 as 180-134 = 46

Q(t)=4000(4)t^3
. Write an equivalent function of the form Q(t)=ab^t.Q(t)=abt

Answers

The equivalent form of the function is [tex]Q(t)=4000(64)^t[/tex]

How to determine the equivalent form of the function?

The equation of the function, according to the question is given as

Q(t)=4000(4)3t

This equation can be properly rewritten as

Q(t)=4000(4)³⁺

Express 4 as a radical expression

So, we have the following representation

Q(t)=4000(4³)⁺

Evaluate the exponent in the above expression

Q(t)=4000(64)⁺

The above expression cannot be further simplified

Hence, the solution to the exponential expression is Q(t)=4000(64)⁺

Read more about exponential expressions at

https://brainly.com/question/2456547

#SPJ1

Complete question

Q(t)=4000(4)3t.

Write an equivalent function of the form Q(t)=ab^t.

3. Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours? Show your work

Answers

The number of bacteria in the petri dish after 24 hours will be y = 125 + 24x

What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

Given is Gina was working in the laboratory on an experiment involving the population of bacteria. Her initial starting amount in a petri dish was 125 bacteria.

Assume that each hour the bacteria rises by [x] bacteria per hour. Then,

the number of bacteria in the petri dish after 24 hours will be -

y = 125 + 24x

Therefore, the number of bacteria in the petri dish after 24 hours will be y = 125 + 24x.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ1

A set of shirt prices are normally distributed with a mean of 454545 dollars and a standard deviation of 555 dollars. What proportion of shirt prices are between 373737 dollars and 59. 3559. 3559, point, 35 dollars?.

Answers

The total proportion of shirts between two prices is 0.9431, which is obtained using the knowledge of proportion and statistics.

What is proportion?

In mathematics, a proportion is defined as the comparison between two numerical quantities. If both possess the same nature, they are called directly proportional, or else called inversely proportional.

Calculation of the proportion based on the problem

The mean and standard deviation are given to be 45 and 5 respectively

Calculate standard normal variate using the formula, z = (x - 45) / 5

Taking x = 37, we get,

z1 = (37 - 45) / 5

= -1.6

Using the z table, we get the value, z1 = 0.0548

Now, taking x = 59.35, we get,

z2 = (59.35 - 45) / 5

= 2.87

Using the z table, we get the value, z2 = 0.9979

The proportion between two prices is given by z = z2 - z1

z = 0.9979 - 0.0548

= 0.9431

Hence, the proportion of shirts between the two prices is 0.9431.

learn more about proportion here:

brainly.com/question/870035

#SPJ4

write a congruence statement for the polygons. identify all pairs of congruent corresponding parts


Please help. problem #1

Answers

The polygon ABCD and polygon EFGH are congruent polygons.

What is a polygon?

A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons, etc

Here,
Consider two polygons,
ABCD and EFGH,
As given in the figure,
AB = EF,
AD = EH
∠A = ∠E
∠D = ∠H
ABCD ≅ EFGH,

Thus, Congruent polygons are polygons ABCD and EFGH.

Learn more about polygon here:
https://brainly.com/question/24464711
#SPJ1


These figures are similar. The perimeter and
area of one are given. The area of the other
is also given. Find its perimeter and round
to the nearest tenth.
Perimeter = 21.3 m
Area = 16 m²
Perimeter [? ]m
Area = 25 m²
Enter

Answers

Check the picture below.

bearing in mind that the ratio of the sides of similar figures is the same as the ratio of their perimeters

[tex]\stackrel{\textit{\Large perimeters}}{21.3\hspace{5em}p}\hspace{5em}\stackrel{\textit{\Large areas}}{16\hspace{5em}25} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(21.3)^2}{(p)^2}~~ = ~~\cfrac{16}{25}\implies \left( \cfrac{21.3}{p} \right)^2=\cfrac{16}{25}\implies \cfrac{21.3}{p}=\sqrt{\cfrac{16}{25}}\implies \cfrac{21.3}{p}=\cfrac{\sqrt{16}}{\sqrt{25}} \\\\\\ \cfrac{21.3}{p}=\cfrac{4}{5}\implies 106.5=4p\implies \cfrac{106.5}{4}=p\implies {\Large \begin{array}{llll} 26.625=p \end{array}}[/tex]

Which of the following has the same value as -5 - 15?
A -15 - (-5)
B-5 + 15
C-5 + (-15)
D-15 + 5

Answers

Answer:

C -5 + (-15)

Step-by-step explanation:

-5 - 15 = -20

A -15 - (-5) = -15 + 5 = -10

B -5 + 15 = 10

C -5 + (-15) = -20

D -15 + 5 = -10

Answer:

c; -5+(-15)

Step-by-step explanation:

-5-15=-20

adding a negative number is subtraction, which means;

-5+(-15)=-20

therefore

-5-15=-20=-5+(-15)

[tex]2x^2-4x+3=0[/tex]

Solve the quadratic equation using the quadratic formula or completing the square. Show exact answers in simplified, radical form; no rounded decimals.

**Show steps

Answers

The solution to the quadratic equation using quadratic formula is X has a negative value x is undefined with no real solution.

    x= [tex]\frac{4 + 3.41i}{4}[/tex]  or  x=  [tex]\frac{4 - 3.14i}{4}[/tex]

Using quadratic formula to solve the equation

[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]

2x^2-4x +3 = 0

All equations of the form ax^2+bx+c=0 can be solved using the quadratic formula:  

The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

we need to identify a, b and c

from the quadratic equation a = 2, b= -4 and c=3

[tex]x = \frac{-b +or - \sqrt{b^{2}-4ac } }{2a}[/tex]

Substitute the value of a, b and c into the equation

[tex]x = \frac{-(-4) ± \sqrt{(-4^{2} - 4(2)(3)} }{2(2)}[/tex]

[tex]x=\frac{ 4 ± \sqrt{16 -28} }{4}[/tex]

x= [tex]\frac{4+\sqrt{-12} }{4}[/tex] or  x= [tex]\frac{4-\sqrt{-12} }{4}[/tex]

x= [tex]\frac{4 + 3.41i}{4}[/tex]  or  x=  [tex]\frac{4 - 3.14i}{4}[/tex]

Since X has a negative value x is undefined with no real solution.

Learn more about quadratic equation here: https://brainly.com/question/1214333

#SPJ1

Answer:

[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]2x^2-4x+3=0[/tex]

When completing the square for a quadratic equation in the form ax²+bx+c=0, first move the constant to the right side of the equation:

[tex]2x^2-4x=-3[/tex]

Divide both sides of the equation by the coefficient of x²:

[tex]x^2-2x=-\dfrac{3}{2}[/tex]

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]x^2-2x+\left(\dfrac{-2}{2}\right)^2=-\dfrac{3}{2}+\left(\dfrac{-2}{2}\right)^2[/tex]

Simplify:

[tex]x^2-2x+1=-\dfrac{3}{2}+1[/tex]

[tex]x^2-2x+1=-\dfrac{1}{2}[/tex]

Factor the perfect square trinomial on the left side:

[tex](x-1)^2=-\dfrac{1}{2}[/tex]

Square root both sides:

[tex]\sqrt{(x-1)^2}=\sqrt{-\dfrac{1}{2}}[/tex]

[tex]x-1=\pm\sqrt{-\dfrac{1}{2}}[/tex]

Simplify:

[tex]x-1=\pm\sqrt{\dfrac{1}{2} \cdot -1}[/tex]

[tex]x-1=\pm\sqrt{\dfrac{1}{2}} \sqrt{-1}[/tex]

[tex]x-1=\pm\dfrac{1}{\sqrt{2}} i[/tex]

[tex]x-1=\pm\dfrac{\sqrt{2}}{2} i[/tex]

Add 1 to both sides:

[tex]x=1\pm\dfrac{\sqrt{2}}{2} i[/tex]

[tex]x=\dfrac{2}{2}\pm\dfrac{\sqrt{2}}{2} i[/tex]

[tex]x=\dfrac{2\pm\sqrt{2}\: i}{2}[/tex]

Therefore, the solutions of the given quadratic equation using the method of completing the square are:

[tex]x=\dfrac{2+\sqrt{2}\: i}{2}, \quad x=\dfrac{2-\sqrt{2}\: i}{2}[/tex]

Learn more about completing the square here:

brainly.com/question/28819535

A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (2, 5) and the stadium in Columbus is at point (8, 13). The map shows a highway rest stop halfway between the cities. What is the distance between the high school and the stadium? (One unit = 8.6 miles.)

Answers

To find the distance between the high school and the stadium, we need to use the distance formula. The distance formula is given by the following equation:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the coordinates of the starting point, and (x2, y2) is the coordinates of the ending point.

In this case, the starting point is the high school, which is located at the coordinates (2, 5), and the ending point is the stadium in Columbus, which is located at the coordinates (8, 13). Plugging these values into the distance formula, we get:

d = sqrt((8 - 2)^2 + (13 - 5)^2)

d = sqrt(6^2 + 8^2)

d = sqrt(36 + 64)

d = sqrt(100)

d = 10

Therefore, the distance between the high school and the stadium is 10 units. Since 1 unit is equal to 8.6 miles, the distance between the high school and the stadium is 86 miles.

It's worth noting that the rest stop is located halfway between the high school and the stadium. This means that the distance from the high school to the rest stop is 86/2 = 43 miles, and the distance from the rest stop to the stadium is also 43 miles. This can be verified by using the distance formula to find the distance between the rest stop and the high school, and then between the rest stop and the stadium.

What percent

of 60 is 51?
↓ ↓ ↓
X 60 = 51

Answers

Answer:85%

Step-by-step explanation:

51 is what percent of 60 is equal to (51 / 60) x 100 = 85%. So if you buy an item at $60 with $51 discounts, you will pay $9 and get 85% discount cashback rewards. So 51 out of 60 as a percentage is 85%

The table shows the last holiday destination of 60 people.Holiday
destinations
Frequency | Angle in º
France
25
Spain
18
Greece
15
Other
2
Complete the table and draw a pie chart
to represent this information.
Note: Please draw your pie chart in a 'clockwise' direction from the line already drawn
and follow the order from the table (France, then Spain etc...).

Answers

The required answer are according to the following order,

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

What do you mean by sum of angles?

We know that the sum of angles in a triangle is 360°. The question requires us to find the angle that corresponds to each of the given holiday destinations. We shall now proceed as follows:

The angle subtended is obtained from number of people that chose a particular location.

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

To learn more about sum of angles, visit:

https://brainly.com/question/28448363?referrer=searchResults

#SPJ4

You deposit $200 in an account that earns simple interest at an annual rate of 3%. How much money is in the account after 3 years?

Answers

The account balance after 3 years will be $218.

What is simple interest?

The crediting of cash flows connected with an investment or deposit is referred to as "simple" interest.

Given that you deposit $200 in an account that earns simple interest at an annual rate of 3%.

The formula to calculate the simple interest is given below,

SI = ( P x R x T ) / 100

SI = ( 200 x 3 x 3 ) / 100

SI = 2 x 3 x 3

SI = $18

Total account balance = 200 + 18 = $218

Therefore, the account balance after 3 years will be $218.

To know more about simple interests follow

https://brainly.com/question/25793394

#SPJ1

Find the slope of the line going through the points (2,4) and (12)

Answers

Step-by-step explanation:

If there are 2 points (a,b) and (c,d),

then the slope = (d - b)/(c - a) = (b - d)/(a - c)

Therefore slope = (10 - 4)/(4 - 2) = 6/2 = 3

The point-slope form of a line is

y = mx + b, where m is the slope and b is the y-intercept Substituting either point (2,4) or (4,10) into the equation is fine.

(4) = (3)(2) + b

4 = 6 + b

b = 4 - 6 = -2

y = 3x - 2

Or

(10)=(3)(4) + b

10 = 12 + b

b = 10 - 12 = -2

y = 3x - 2

A line has a slope of 8 and includes the points (9, u) and (10, –1). What is the value of u?

Answers

Answer: -9

Step-by-step explanation: To find the value of u, we can use the slope formula to calculate the slope of the line that goes through the points (9, u) and (10, -1). The slope formula is: slope = (y2 - y1)/(x2 - x1). In this case, we have: slope = (-1 - u)/(10 - 9) = (-1 - u)/1. Since the slope of the line is given as 8, we can set this equal to the value we calculated above and solve for u. This gives us: 8 = (-1 - u)/1. Multiplying both sides by 1 gives us: 8 = -1 - u. Adding 1 to both sides gives us: 9 = -u. Finally, negating both sides gives us: u = -9. Therefore, the value of u is -9.

"write the equation in fully simplfied slope - intercept form" Can someone provide a step by step answer pls.​

Answers

Step-by-step explanation:

y=Mx+b

M- slope

B- y intercept


1. find slope by choosing 2 point(any 2)

Once you’ve picked 2 point- (X1, y1) (x2, y2) set up the equation to calculate slope


y2-y1 / x2-x1 = m

2. Solve for b

Take any point and plug in the x and y value


Plug in y= (the slope you solved for)(x intercept) + b


3. then write the equation

Y= (slope)x + b

Other Questions
Which of the following is a good piece of advice to give to individuals who have multiple bosses in a matrix structured organization?a) Make sure all managers are familiar with your overall workload.b) Keep conflicts you are experiencing to yourself.c) Avoid situations where you have multiple managers as they produce more conflict than benefits.d) Set a schedule so that you work with one manager on certain days and the other manager on the other days. hearth company uses the units-of-production method to estimate depreciation. the company purchased a new machine for $50,000 that will produce an estimated 350,000 units over its useful life. the estimated residual value of the machine is $3,000. what is the depreciation rate per unit? professionals are required to deliver services but the competency of the services is never an issue. true false when 11.8 g of c8h18 underwent a combustion reaction with 8.84 g of o2, it produced 1.15 g of h2o. balance the reaction and answer the following questions. what is the mass (in g) of remaining oxygen gas? the iranians ruled for a thousand years and did not need us arabs even for a day. we have been ruling then for one or two centuries and cannot do without them for an hour A display that needs to be present throughout the entire game should be small enough that it doesnt interfere with the game itself but large enough that the user is able to do what? A. read the display easily out of the corner of their eye B. see it from across the room if need be C. see it and understand what its trying to communicate D. move their avatar over the display box without interfering with the text design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used. when conducting a one-way independent anova with three levels on the independent variable, an f-ratio that is large enough to be statistically significant tells us: Question 1-4A punch bowl contained 4 liters of soda, 5 liters of orange juice, and 2 liters of raspberry juice.Select the statements that are true.The ratio of the entire punch bowl to the juices is 9: 11.The ratio of the entire punch bowl to the orange juice is 11 to 5.The ratio of orange juice to soda is 4 to 5.4The ratio of soda to the entire punch bowl is11The ratio of orange juice to raspberry juice is 5 : 2. Which principle of law do you think has been Romes greatest contribution to modern legal systems? Think about: equality before the law, innocent until proven guilty, unfair laws could be set aside. we learn two exceptions to the general rule that offers may be revoked any time prior to acceptance in this class. what are they called? Amelia thinks of a number. Her number is a factor of both 18 and 12. Her number is odd. What is the largest number she could be thinking of? if you decide to use alcohol you should use it blank 1. What symptoms is Nicholas experiencing? The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?. if the cost of 1kg of apples is $12 what is the cost of 500g of apples o develop mrp report, you need three piece of information as direct inputs. what are the three key inputs (refer to exhibit 9.5)? Jenna made an electric circuit as seen in the picture. She placed a thermometer near her light bulb. The light bulb was turned on for an hour. Select the most likely observation. Mia buys a t-shirt online for $15.. If shipping andhandling are an additional 30% of the price, howmuch shipping and handling will Mia pay? question at position 6 a three-phase transformer connection has a delta-connected primary and a wye-connected secondary. the center tap of the wye is used as a neutral conductor. if the line-to-line voltage is 480 v, what is the voltage between any one phase conductor and the neutral conductor?