A cyclist travels north along a road at a constant speed of 28 miles per hour. At 1:00 pm a runner is 68 miles away, running south along the same road at a constant speed. They pass each other at 3:00 pm. What is the speed of the runner?

2 pounds 6 ounces in ounces is equivalent to 38 ounces.

The given measurement is -

2 pounds 6 ounces

In 1 pound, there are 16 ounces.

So, we can write that -

2 pounds 6 ounces = 2 x 16 + 6

2 pounds 6 ounces = 38 ounces

So, 2 pounds 6 ounces in ounces is equivalent to 38 ounces.

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The equation of the least-squares line predicting wins from payroll is:

y = -6.37 + 0.1*x

The equation of the least-squares line predicting wins from payroll can be calculated using the following formula:

y = b0 + b1*x

where y is the dependent variable (number of wins), x is the independent variable (payroll in millions of dollars), b0 is the y-intercept of the line, and b1 is the slope of the line.

To calculate the values of b0 and b1, you can use the following formulas:

b1 = r*(\(\frac{sy}{sx}\))

b0 = mean(y) - b1*mean(x)

where r is the correlation coefficient between x and y, sx is the standard deviation of x, and sy is the standard deviation of y.

Using the values provided in the table, we can calculate the equation of the least-squares line as follows:

b1 = 0.393*(\(\frac {3.12}{12.34}\)) = 0.1

b0 = 7.75 - 0.1*142.1 = -6.37

Therefore, the equation of the least-squares line predicting wins from payroll is:

y = -6.37 + 0.1*x

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The sale price (p) is $1,518.00 in $2530 dining room set.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that Price = 2530

The Final Sale Price = 40% of 2530 or % of Price

The Final Price = Price - % off

Final Price = ( 2530 ) - ( 40/100 × 2530 )

Final Price = 2530 - 1012

Final Price = $1,518.00

Hence, the sale price (p) is $1,518.00 in $2530 dining room set.

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The distance from Cuba to Key West is 145 km, and if Hurricane Charles is travelling at 20.80 km per hour, it will take 6.97 hours to travel that distance. To calculate this, use the following equation: 145 km / 20.80 km/h = 6.97 hours.

The time it takes for Hurricane Charles to travel from Cuba to Key West can be calculated using the formula time = distance / speed. In this case, the distance is 145 km and the speed is 20.80 km per hour. Plugging in these values gives:

Time = 145 km / 20.80 km per hour

Time = 6.97 hours

Therefore, it will take Hurricane Charles approximately 6.97 hours to travel from Cuba to Key West.

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Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

Answer:

4, 2, 9, 3, 6

Step-by-step explanation:

756/4= 189

756/2= 378

756/9= 84

756/25= 30.24

756/5= 151.2

756/8= 94.5

756/10= 75.6

756/3= 252

756/6= 126

Answer:

let me calculate it

Step-by-step explanation:

and then i will tell you if i can answer it

The points b, c, and a contains 3 planes.

Here,

Given that;

The figure is shown.

We have to find number of planes contains points b, c and a.

What is Planes?

Plane is a flat, two-dimensional surface that extends infinitely far.

Now,

The point b contain planes ABGD, ABCL and BLD.

The point c contain planes ACG, ABLC and CGDL.

The point a contain planes ACLB, ABDG and ACG.

Hence, The points b, c, and a contains three planes.

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Answer:

D

Step-by-step explanation:

Answer: 15 min each chore

Step-by-step explanation: 60 divided by 4 = 15

Answer:

15 minutes per chore.

Step-by-step explanation:

An hour is made up of 60 minutes. 60 divided by 4 is 15. 15 minutes can also be referred to as "a quarter of an hour".

Answer:

  A, B, C

Step-by-step explanation:

The variables in a polynomial term are non-negative integers.

  A: x is to 1/2 power (square root) . . . not a polynomial

  B: x is to -2 power . . . not a polynomial

  C: x is to -2 power . . . not a polynomial

  D: x is to powers of 2 and 1 . . . is a polynomial

The choices A, B, and C are not polynomials

Answer:

B, C, G

Step-by-step explanation:

If we look at the graph, it shows that if an employee works for 5 hours, then they will earn $36.25.

We can take 36.25 and divide that by 5 to get the hourly wage.

36.25 ÷ 5 = 7.25

We now know that employees get $7.25 every hour.

Using this we can look back to the graph.

'A' says that if an employee does not work, they will earn $7.25.

We know that this is wrong because if you do not work, then you do not earn money.

Let's look at 'B'.

If employees work for one hour, they will earn $7.25

We know this is correct because we now know the hourly wage.

Let's look at 'C'

If employees work for 4 hours, then they will get a revenue of $29.

We can figure this out by using this equation.

number of hours × hourly wage = total payment

4 × 7.25 = 29

Then this means that this is correct.

Let's look at 'D'

It says that if employees work for 10 hours, they will earn $73

Let's use that same equation again.

10 × 7.25 = 72.5

Employees earn $72.5 for working 10 hours, not $73.

So, this is obviously incorrect.

Let's look at 'E'

It says that if employees work for 3.5 hours, they will get a revenue of $21.75.

3.5 × 7.25 = 25.375

Therefore, this is incorrect.

Now let's take a look at 'F'.

It says that if employees work for 7.25 hours, then they earn $1.

This is incorrect.

And lastly, 'G'.

We know that if you do not work, then you do not earn money.

Therefore, A, B and G are the correct answers.

Answer:

44

Step-by-step explanation:

20+36+40+80= 176

176/4= 44

The x-intercepts are the points on the plot of a function f(x) where the graph crosses the x-axis. In other words, they're the values of x that make f(x) = 0.

In this case, the x-intercepts are the two roots of the parabola,

(x - 4) (x - 5) = 0 … … … (this is what the hint is referring to)

==>   x - 4 = 0   or   x - 5 = 0

==>   x = 4   or   x = 5

The intercepts themselves are points (x, f(x)), so you can report them as (4, 0) and (5, 0).

The input value x when the output value f( x ) = 4 in the function f( x ) = 5x - 7 is 11/5.

A function is simply a relationship that maps one input to one output, each x-value can only have one y-value.

Given the data in the question;

To determine the input value x when the output value f( x ) = 4, replace f( x ) by 4 in the function and solve for x.

f( x ) = 5x - 7

4 = 5x - 7

Collect like terms

4 + 7 = 5x

5x = 11

Divide both sides by 5

5x/5 = 11/5

x = 11/5

Therefore, the input value x is 11/5, this forms an ordered pair of ( 11/5, 4 ).

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Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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Answer:

given

Step-by-step explanation:

Answer:

statement - reason

BC||AD, <BAD is congruent to <DCB - given

<CBD is congruent to <ADB - alternate interior angles

BD is congruent to BD - reflexive (?)

triangle ADB is congruent to triangle CBD - AAS

AB is congruent to CD - CPCTC (corresponding parts of congruent triangles are congruent)

∠LMN is an obtuse angle.

==========================================

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer and Step-by-step explanation: The critical value for a desired confidence level is the distance where you must go above and below the center of distribution to obtain an area of the desired level.

Each sample has a different degree of freedom and critical value.

To determine critical value:

1) Calculate degree of freedom: df = n - 1

2) Subtract the level per 100%;

3) Divide the result by 2 tails;

4) Use calculator or table to find the critical value t*;

For n = 5 Level = 90%:

df = 4

t = \(\frac{1-0.9}{2}\) = 0.05

Using t-table:

t* = 2.132

n = 13 Level = 95%:

df = 12

t = \(\frac{1-0.95}{2}\) = 0.025

Then:

t* = 2.160

n = 22 Level = 98%

df = 21

t = \(\frac{1-0.98}{2}\) = 0.01

t* = 2.819

n = 15 Level = 99%

df = 14

t = \(\frac{1-0.99}{2}\) = 0.005

t* = 2.977

The critical values and degree of freedom are:

sample size          level           df              critical value

     5                      90%           4                   2.132

   13                       95%            12                 2.160

   22                      98%            21                 2.819

   15                       99%            14                 2.977

Answer:

a. 36

b. 8.5 (8 1/2)

c. 2/5

d. 6

e. 9

f. 8

Step-by-step explanation:

a. 36

b. 8.5 (8 1/2)

c. 2/5

d. 6

e. 9

f. 8

Answer:1.6

Step-by-step explanation:

By looking at the graph we can see that the triangle is formed by 2 triangles.

1 triangle has the measures of the sides:

vertical side = 4

Horizontal side= 3

triangle2 :

vertical side: 5

horizontal side: 3

We have to find the hypotenuse of each one:

c^2 = a^2+b^2

where x is the hypotenuse and a and b are the know lengths:

Triangle 1:

c^2 = 4^2+3^2

c^2 = 16+9

c^2= 25

c= √25

c= 5

Triangle 2

C^2 = 5^2+3^2

C^2 = 25+9

c = √34

c= 5.83

Now we have the 3 sides of the big triangle:

5,5.83, 9

To find the perimeter we simply add the side lengths:

Perimeter: 5+5.83+9 = 19.8 inches

For the area we have that:

Area of a triangle: (base x height )/2

Looking it by the y axis:

A = (9 x 3)/2 = 13.5 in2

Answer:

The answer is 216

Step-by-step explanation:

if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.

The given statement is true, The set of all possible outcomes during the course of an experiment is called a sample-space.

Sample-space, in probability, is referred to as the collection of all possible outcomes in any random experiment. It is denoted by "S".

Since it is a set, it is shown within the braces.

Given statement,

The set of all possible outcomes during the course of an experiment is called a sample-space.

By the definition of sample space, statement is true.

Example: Toss a coin

Sample-space, S={H,T}

H= head

T= tail

Hence, The set of all possible outcomes of any experiment is called sample-space.

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Answer:

-15

Step-by-step explanation:

4b - 3(6 + 2b) = 12

4b - 18 - 6b = 12

4b - 6b = 12 + 18

-2b = 30

b = 30/-2

b = -15

In a case whereby Anu was checking her emails and she casually told her friend siting next to her the ratio of unread emails in my inbox is ratio 4:1 where the total number of emails is 120  then the number of unread emails in her inbox is 96mails.

The concept that will be used here is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The total mails in her box is 120

The we can represent the unread mails  as 4x and read mails be 1x

This can be expressed as :

(4x+1x)=120mails

5x=120mails

x=120/5

x=24

This implies that the uread mails(4×24)

=96mails

Then the number of the read mail =(1×24)=24mails

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It sure looks like a linear function to me.

You can confirm this by finding the slope of "down 10/right 2" to give you a slope of -5.