Categories

## The table shows conversions of common units of length. Unit of Length Customary System Units Metric System Units 1 inch 2.54 centimeters 1 foot 0.3048 meters 1 mile 1.61 kilometers How many miles are equivalent to 800 meters? Round answer to the nearest hundredth. 0.50 miles 1.29 miles 2.62 miles 4.97 miles

The table shows conversions of common units of length. Unit of Length Customary System Units Metric System Units 1 inch 2.54 centimeters 1 foot 0.3048 meters 1 mile 1.61 kilometers How many miles are equivalent to 800 meters? Round answer to the nearest hundredth. 0.50 miles 1.29 miles 2.62 miles 4.97 miles

Categories

## On a vacation, DeVante and his family traveled 382 miles at 64 mph. How long did the trip take? (Round to the nearest hundredth)

On a vacation, DeVante and his family traveled 382 miles at 64 mph. How long did the trip take? (Round to the nearest hundredth)

Categories

## Melissa will rent a car for the weekend. She can choose one or two plans. The first plant has no initial fee but costs \$.80 per mile driven. That’s like a plan has an initial fee of \$75 in cost an additional \$.38 per mile driven. How many miles with Melissa need to drive for two plants to cost the same? NEED HELP ASAP PLEASE

If you equal both of the PLANS you will get
\$.80x=\$75+\$.38x
then you subtract .38x on both sides and get
\$.42x=\$75
once thats done you will divide .42 on both sides leaving the variable x by itself…
and then x=178.57miles
but to break even it would be 179 miles for both of the plans to cost the same

Categories

## How long will it take Karen to drive 975 miles, if her average speed is 65 miles per hour? how to write a formula

How long will it take Karen to drive 975 miles, if her average speed is 65 miles per hour? how to write a formula

Categories

## A construction crew is lengthening a road. The road started with a length of 59 miles, and the crew is adding 3 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 34 days. Equation: Total length of the road after 34 days: ____miles

A construction crew is lengthening a road. The road started with a length of 59 miles, and the crew is adding 3 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 34 days. Equation: Total length of the road after 34 days: ____miles

Categories

## Two for service watchtowers spot a fire in the distance the fire is 27 miles from tower to about how far apart are they to watch towers please help

Two for service watchtowers spot a fire in the distance the fire is 27 miles from tower to about how far apart are they to watch towers please help

Categories

## Which of the following represents a method by which one could convert inches into miles A. Multiply by 12, then multiply by 5,280 B. Divide by 12, then divide by 5,280 C. Add 12, then divide by 5,280 D. Multiply by 12, then divide by 5,280

To convert inches to miles, you would first have to convert inches to feet, and since there are 12 inches in a foot, the first step would be multiply by 12. After converting 12 inches to 1 foot, you would then have to take 1 and multiply by 5,280, since there are 5,280 feet in a mile, so the answer would be A, Multiply by 12, then multiply by 5,280.

Categories

## If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour

If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour

Categories

## Harley is on a trip with her dad. Her dad tells her that they've traveled 182.6 miles and they are 83% of the way to their destination. How many miles long is their trip?

Harley is on a trip with her dad. Her dad tells her that they’ve traveled 182.6 miles and they are 83% of the way to their destination. How many miles long is their trip?

Categories

## If a wheel with a radius of 30 inches spins at a rate of 500 revolutions per minute, find the approximate linear velocity in miles per hour.

30 inches @ 500 rpm = 15,000 inches per minute

15,000 inches per minute = 900,000 inches per hour (multiply by 60)

1 mile = 5,280 feet (google-able fact you shouldn’t have to memorize)
1 foot = 12 inches (you probably already know this)
900,000 inches = 75,000 feet (divide by 12)

75,000 feet = 14.20454545454545. . . miles (divide by 5280)

Linear velocity in miles per hour is 14.20454545454545. . . miles per hour.

Categories

## An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)? plzzz helpppp

Distance between plane and airport is 134.4 miles.

Step-by-step explanation:

Given : An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W.

To find : How far is the plane from the airport.

Solution : Distance from airport to west is 150 miles and then 170 miles in the direction south  and angle form is S 49.17° W

Refer the attached picture for clearance.

Applying law of cosines

where a= 150 miles

b=170 miles

C=   49.17° angle in degree

c = distance between plane from the airport

Put values in the formula,

Therefore, Distance between plane and airport is 134.4 miles.

Categories

## A sailboat travels a distance of 2 1/2 miles in 1/6 of an hour. Which complex fraction represents the unit rate in miles per hour?

Rewrite “2 1/2 miles” as the improper fraction (5/2) miles.
Divide this by (1/6) hour:

5

2

——– (miles/hour)
1

6

To divide by the fraction 1/6, invert it and multiply.  We get

5                  6
— (miles) * ———— = (30/2) mph = 15 mph
2                  1 hour

Categories

## Which is the best way to rewrite these sentences? They had to walk over 1,000 miles of rough terrain, as thousands of men, women, and children went from their Georgia homelands to Oklahoma. Forced to march over 1,000 miles of rough terrain, thousands of men, women, and children abandoned their Georgia homelands for Oklahoma. Forced to march over 1,000 miles of rough terrain, as thousands of men, women, and children walked from their Georgia homelands for Oklahoma.

Which is the best way to rewrite these sentences? They had to walk over 1,000 miles of rough terrain, as thousands of men, women, and children went from their Georgia homelands to Oklahoma. Forced to march over 1,000 miles of rough terrain, thousands of men, women, and children abandoned their Georgia homelands for Oklahoma. Forced to march over 1,000 miles of rough terrain, as thousands of men, women, and children walked from their Georgia homelands for Oklahoma.

Categories

## Which is the best way to rewrite these sentences? They had to walk over 1,000 miles of rough terrain, as thousands of men, women, and children went from their Georgia homelands to Oklahoma. Forced to march over 1,000 miles of rough terrain, thousands of men, women, and children abandoned their Georgia homelands for Oklahoma. Forced to march over 1,000 miles of rough terrain, as thousands of men, women, and children walked from their Georgia homelands for Oklahoma.

Which is the best way to rewrite these sentences? They had to walk over 1,000 miles of rough terrain, as thousands of men, women, and children went from their Georgia homelands to Oklahoma. Forced to march over 1,000 miles of rough terrain, thousands of men, women, and children abandoned their Georgia homelands for Oklahoma. Forced to march over 1,000 miles of rough terrain, as thousands of men, women, and children walked from their Georgia homelands for Oklahoma.

Categories

## In a race that consist of three parts,the cycling 12 1/2 miles long,the running part of the race was 1/4 the distance of cycling,the kayaking is 1/2 the distance running.what is the entire distance in miles of the race

In a race that consist of three parts,the cycling 12 1/2 miles long,the running part of the race was 1/4 the distance of cycling,the kayaking is 1/2 the distance running.what is the entire distance in miles of the race

Categories

## A ship traveled for 4 hours heading west and for 5 hours heading north. If the total distance traveled was 119 miles, and the ship traveled 5 miles per hour faster west, at what speed was the ship traveling west

To answer this problem, we will use the formula of
hypotenuse:

c^2 = a^2 + b^2

Where,

c = total distance traveled / displacement = 119 miles

a = distance traveled north = 5 hours * x mph =  5 x

b = distance traveled west = 4 hours * (x + 5) mph = 4 (x
+ 5)

Substituting to the equation:

119^2 = (5 x)^2 + [4(x + 5)]^2

14,161 = 25 x^2 + 16 (x + 5)^2

14,161 = 25 x^2 + 16 (x^2 + 10 x + 25)

14,161 = 25 x^2 + 16 x^2 + 160 x + 400

0 = 41 x^2 + 160 x – 13,761

x =[ – b ± sqrt (b^2 – 4ac)]/ 2a

x = [- 160 ± sqrt (160^2 – 4 * 41 * (– 13,761))] / 2 * 41

x = – 1.95 ± 18.42

x = -20.37 , 16.47

Since speed cannot be negative, therefore x = 16.47

Therefore the speed of the ship travelling west is:

x +

Categories

## A loaded moving truck is traveling 30 mph faster than a freight train. in the time it takes the train to travel 135 miles, the truck travels 225 miles. find the speed of the truck

Speed of truck= x
speed of train=x-30
A loaded moving truck is traveling 30 mph faster than a freight train. in the time it takes the train to travel 135 miles, the truck travels 225 miles. find the speed of the truck.

A loaded moving truck is traveling 30 mph faster than a freight train…
(x-30)=speed of train
the time it takes the train to travel 135 miles, the truck travels 225 miles…
135/(x-30)=225/x
the you multiply on both sides the x values and get…
135x=225x-6750
then you subtract 225x on both sides…
-90x=-6750
then you divide -90 on both sides…
x=75
the speed of the truck is 75mph
i hope this helped give me a thanks and a 5 star rating if it helped! c:

Categories

## If you travel 40 miles east and then turn around and drive 12 miles west, the displacement is?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

Categories

## LAW ENFORCEMENT: A police accident investigator can use the formula S=25L‾‾‾√S=25L to estimate the speed s of a car in miles per hour based on the length l in feet of the skid marks it left. How fast was a car traveling that left skid marks 109 feet long?

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=   …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

Subtract [2] and [3]

……….[4]

Add equation [1] and [4], to get values of x and y

Substitute x in [1]

Substitute value of x in equation [2], to get z

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

Categories

## The police department is very proud of their new police cars. They announced that they are able to go from a stopped position to 80 miles per hour in 6 seconds. They are describing their cars’ velocity. direction. speed. acceleration.

The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h.

So the time for the pencil and eraser to touch is T=1.3449 hours.

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

Categories

## A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?

A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?

Categories

## Each week you drive 150 miles your car gets 25 miles to the gallon and gas prices are three dollars per gallon how much gas money would you spend on gas each week

Number of copy machines must be made to minimize the unit cost=160.

Step-by-step explanation:

We are given that the unit cost function C ( the cost in dollars to make each copy machine)

Then the unit cost function is given by

We have to find the number of copy machines for  minimize the unit  cost

Differentiate with respect to x

Then we get

……(equation I)

To find the value of x then we susbtitute is equal to zero

By using division property of equality

Again differentiate the equation I with respect to x then we get

Hence, the unit cost is minimize for x=160

Therefore, the number of copy machines must be made to minimize the unit cost =160

Categories

## 1. 7.2 aliens =1 monster. 1 monster= 15.5 oranges. Using the conversion above, about how many oranges are equal to 1 alien? 2. In a scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represents 1 square meters? 3. While driving with his father, Amit holds his breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds that he holds his breath, on average for about 8 seconds. If his father drives the car at 60 mph through the tunnel, according to the average time, Amit holds his breath, about how long is the tunnel. 4. Lea’s car travels on average of 30 miles per gallon of gas. If she spent \$20.70 on gas for a 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?

127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

Categories

## The Gonzales family drove 300 miles on the first day of their vacation and 250 on each day after that. If d represents the number of days they drove after the first day, which expression gives the total distance driven?

Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       \$6,800   \$10,500  \$8,400    \$66,000   \$4,700

Pay subject to FICA S.S.         \$421.60  \$651.00  \$520.80 \$4092.00 \$291.40
6.2%, (First \$118,000)

Pay subject to FICA Medicare \$98.60 \$152.25    \$121.80    \$957.00    \$68.15
1.45% of gross

Pay subject to FUTA Taxes      \$40.80  \$63.00     \$50.40    \$396.00  \$28.20
0.6%

Pay subject to SUTA Taxes   \$367.20  \$567.00  \$453.60  \$3564.00 \$253.80
5.4% (First \$7000)

Totals                                     \$928.20 \$1,433.25 \$1,146.60 \$9,009.00 \$641.55

Categories

## Smitty’s car breaks down on a country road. He starts walking toward home at a rate of 1.25 miles an hour. After 0.75 hours, he is 3 miles from home. What is the point-slope formula for this information.

(A)

Step-by-step explanation:

It is given that lines v and w are parallel, then from the given figure, ∠2 and ∠6 form corresponding angle pair, therefore ∠2=∠6.

A.∠2+∠6=180°, his is incorrect because ∠2 and ∠6 form corresponding angle pair and are equal.

B.∠5≅∠8 because ∠5 and ∠8 form vertically opposite angle pair. Thus, this option is correct.

C.Since, sum of interior angles on the same side of transversal is 180°, therefore ∠3+∠5=180°, thus this option is correct.

D.∠1≅∠5 because ∠1 and ∠5 form the corresponding angle pair and are equal. Thus, this option is correct.