Mathematics Middle School

if a ship sailed due south from iceland to antarctica, it would sail through an angle of rotation of about 140 degrees around Earth's center. Find this measure in radians. Then, using 3960 miles for Earth's radius, find how far the ship would travel

Answers

Answer 1

Sushbehshdbdjssosshshjsns

Answer 2

the ship would travel approximately 9685.82 miles from Iceland to Antarctica.

To convert the angle from degrees to radians, we use the conversion factor[tex]$ \pi $[/tex]radians = 180 degrees.

[tex]\[ \text{Angle in radians} = \frac{\text{Angle in degrees} \times \pi}{180} \][/tex]

In this case, the angle in degrees is 140 degrees:

[tex]\[ \text{Angle in radians} = \frac{140 \times \pi}{180} \]\[ \text{Angle in radians} = \frac{140}{180} \times \pi \]\[ \text{Angle in radians} = \frac{7}{9} \pi \][/tex]

Next, we'll find how far the ship would travel using Earth's radius. The distance traveled on a circle is given by the formula:

[tex]\[ \text{Distance} = \text{radius} \times \text{angle in radians} \][/tex]

Given Earth's radius as 3960 miles and the angle in radians as [tex]$ \frac{7}{9} \pi $[/tex], we can calculate the distance:

[tex]\[ \text{Distance} = 3960 \times \frac{7}{9} \pi \]\[ \text{Distance} = 3080 \pi \]\[ \text{Distance} \approx 9685.82 \text{ miles} \][/tex]

So, the ship would travel approximately 9685.82 miles from Iceland to Antarctica.

Related Questions

Stevens family traveled 240 miles in 4 hours. What was there average speed in miles per hour?

Answers

about 60 miles an hour

Answer:

60mph

Step-by-step explanation:

divide 240 by 4 it's easy that's

how I solve these types of questions so keep that in mind.

what are all the properties of a square

Answers

The sides and angles of a square:
square

The sides of a square are all congruent (the same length.)

The angles of a square are all congruent (the same size and measure.)

Remember that a 90 degree angle is called a "right angle." So, a square has four right angles.

Opposite angles of a square are congruent.
Opposite sides of a square are congruent.
Opposite sides of a square are parallel.

To find the perimeter of a square, just add up all the lengths of the sides.

To find the area of a square, multiply the lengths of two sides together.

To find the length of the diagonal of a square, multiply the length of one side by the square root of 2

The diagonals of a square intersect (cross) in a 90 degree angle. This means that the diagonals of a square are perpendicular.
The diagonals of a square are the same length (congruent).

A square is a rectangle, parallelogram, trapezoid, and rhombus.

Hope this helps!!!

A square is a quadrilateral defined by its properties of equal sides and right angles.

A square is a quadrilateral with four equal sides and four right angles.

Its properties include:

All sides are equal in length

All angles are right angles

The diagonals are equal in length and bisect each other at right angles

kathleen rolled a number cube that has sides labeled 1 to 6. What is the probability that she rolled a 2 or a 4

Answers

the probability would be 1/6 for each number but for this is would be 2/6

write as a numerical expression subtract 50 from the sum of 6 and 4 to the tenth power

Answers

[tex](6+4^{10})-50[/tex]

The numerical expression for 'subtract 50 from the sum of 6 and 4 to the tenth power' is written as[tex](6 + 4^{10}) - 50,[/tex] following the order of operations.

To write the statement "subtract 50 from the sum of 6 and 4 to the tenth power" as a numerical expression, you would first calculate 4 to the tenth power, then add 6 to this result, and finally subtract 50 from the total sum.

The expression would look like this:

[tex](6 + 4^{10) - 50[/tex]

It's important to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here, you calculate the exponent before adding 6 and then subtract 50 from the result.

The next step in the solution for which equation could use the distributive property?

A. 4(t-6)=3t+9

B. 4•(t•6)=3t+9

C. 4t-6+3t=9

D. 4•t•1/4=3t+9

Answers

Hello there!

The correct answer is option A, because:

4(t - 6)
Use the distributive property

(4)(t) + (4)(-6)

So yeah, this is how the distributive property works.

Option A is the only option that works with the distributive property.

Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!

use the graph of f(x)to find the solutions to the equation f(x)=0.

Answers

We want to solve the following equality:
f (x) = 0
For this case, the first thing you should see is the cut points of the graph with the x axis.
We then have the following computer pairs:
(-6, 0)
(2, 0)
Answer:
The solution for f (x) = 0 is:
(-6, 0)
(2, 0)

how many cube shaped boxes with 12-inch edges can fit into a box that is 4 feet tall 4 feet long and 5 feet wide
A-20
B-27
C-68
D-80

Answers

the answer is d because you would take 4 x 4 x 5 and then you divide and you get 80

Dimensions of bigger box = 4ft x 4ft x 5ft

or, 48 in x 48 in x 60 in (Because 1 ft = 12 inch)

We know that, volume of a cuboid is:

V = length x breadth x height

Volumeo f big box = 48 x 48 x 60

= 138240 cubic inch.

Edge length of cube shape box = 12 inch

For cube, volume = edge^3

Volume of cube = (12)^3

= 1728 cubic inch

Number of cube shaped box that can fit into big box = Volume of big box / Volume of cube shaped box

= 138240 / 1728

= 80

Hence, correct answer is D-80.

William invested $7000 in an account that earns 4.5% interest, compounded annually. The formula for compound interest is A(t) = P(1 + i)t. How much did William have in the account after 3 years? A. $21,340.38 B. $7988.16 C. $7094.93 D. $7945

Answers

Answer:

7988.16

Step-by-step explanation:

This is a matter of plugging in numbers.

P = 7000 (starting value)

l = 0.045 (rate)

t = 3 (number of years)

A(t) = 7000(1 + 0.045)^3

A(t) = 7000(1.045)^3

After three years, William will have 7988.16

The amount in William's account after 3 years with compound interest will be $7,988.16. Hence the correct option is B.

The compounded interest formula is:

A(t) = P(1 + i)^t

where P is the principal amount ($7000), i is the interest rate (4.5% or 0.045), and t is the time in years (3).

Calculate the total amount:

A(3) = 7000(1 + 0.045)^3

A(3) = 7000(1.045)^3

A(3) = 7000 * 1.144976125

A(3) = $7,988.16

Ebony wants to leave an 18% tip for a $19.82 restaurant bill. The tax is 6.25%, which is added to the bill before the tip.

Answers

if I understand correctly the price of the meal was 19.82 we need to then add tax and tip? If so here is how we go about it.
1. find the tax. we are told it is 6.25% in decimal form this is .0625. We need to multiply that by the total 19.82 to find the tax so
[tex]0.0625 \times 19.82 = 1.24[/tex]
so the tax is $1.24

2. Add the tax to the total
[tex]19.82 + 1.24 = 21.06[/tex]
3. calculate a 18% tip. we can do this in our head numerous ways (moving the decimal place to find 10% taking half of that for 5% and moving the decimal again for 1% multiply by 3 and add) but for space we will simply do the same as we did for tax
[tex]21.06 \times .18 = 3.79[/tex]
so our tip is $3.79
4. add the tip to the total
[tex]21.06 + 3.79 = 24 .85[/tex]
so with tax and tip her total is 24.85 However I have found it very common for people to tip just on the price before tax. if this is the case calculate the 18% based just on the original price and add that value plus the 1.24 tax

Ebony will pay a total of $24.85 for her meal after adding a 6.25% tax to the original price of $19.82 and then calculating an 18% tip on the resulting amount, which includes the tax.

The student, Ebony, needs to calculate the total cost of a restaurant bill which involves adding tax and a tip. The cost of her meal is $19.82, with a 6.25% tax to be added before calculating an 18% tip.

First, determine the sales tax amount by converting the percent to a decimal:
0.0625 × $19.82 = $1.24.

Add the sales tax to the meal's original cost to find the total before tip:
$19.82 + $1.24 = $21.06.

Next, calculate the tip amount by converting 18% to a decimal and multiplying by the post-tax total:
0.18 × $21.06 = $3.79.

To find the final amount Ebony will pay including the tax and tip, add the tip to the post-tax total:
$21.06 + $3.79 = $24.85.

Ebony will pay $24.85 at the restaurant's register, using either cash or a credit card, to cover her $19.82 meal with tax and tip.

Read the complete problem before answering. Teresa bought 2 1/2 gallons of chocolate milk at the dairy farm. Chocolate milk cost $4.50 a gallon. How much did Teresa spend on the milk? A student solved the problem this way. gallons 2 1/2 = 2.5 gallons Let n represent the amount Teresa spent on the milk. n = 2.5 × $4.50 n = $11.25 Teresa spent $11.25. Use a similar strategy to solve this problem. Pedro bought 1 1/4 lb of red sand and 5 1/2 lb of brown sand to refill his sand box. Both types of sand cost $4.60 a pound. How much did Pedro spend on the sand?

Answers

he spent $5.75 on the red sand and $25.30 on the brown sand he spent a total of $31.05 on sand to fill his sand box! Hope this helps you :)

turn 0.43,0.50 into a median
20 points

Answers

0.47 is the answer. Because it's in the middle of 0.43 and 0.50. I answered this on your last question =p

THE ANSWER IS 0.47

HOPE THIS HELPS

the product of 3/4 and a number s is 3/5

Answers

Product= multiplication
s= a number
is= equal sign

3/4s= 3/5
divide both sides by 3/4

s= (3/5) / (3/4)
to divide fractions, multiply by the reciprocal/inverse of 3/4

s= 3/5 * 4/3
multiply numerators; multiply denominators

s= (3*4)/(5*3)
multiply within parentheses

s= 12/15
simplify by 3

s= 4/5

ANSWER: 4/5

Hope this helps! :)

Traci plans to conduct a coin-flipping experiment to see if the probability of landing on "heads" or "tails" is close to the theoretical probability of 1 2 . Which experiment is likely to yield a result FARTHEST from the theoretical probability?

Answers

Traci's coin-flipping experiment is more likely to yield results farthest from the theoretical probability of 1/2 if she conducts the experiment with only a few flips, due to the law of large numbers.

Traci wants to investigate the probability of landing on heads using a coin-flipping experiment. To find the result furthest from the theoretical probability, Traci should plan an experiment with fewer flips. The law of large numbers implies that as the number of trials increases, the experimental probability will converge closer to the theoretical probability. Hence, if Traci flips the coin only a few times, there's a greater chance that the experimental results will diverge significantly from the expected outcome of 50% heads and 50% tails. On the other hand, flipping the coin many times, such as in Pearson's experiment with 24,000 flips, is likely to yield a result very close to the theoretical probability. This is because individual variations have less impact on the overall outcome as the sample size increases.

please help solve 13 + m = 10
m = _____

Answers

-3 hope this helps ^_^

Hello there, and thank you for asking your question here on brainly.

Short answer: -3

Why?

To find out what m is, we have to subtract the two numbers. 10 - 13 => -3

Hope this helped you! ♥

HURRY PLZ!!!!!!!!!!!The cafeteria uses rectangular trays with a raised edge around them. The area of the flat surface of each tray is 228 and its length is 19 inches. What is the perimeter of the tray, where the raised edge is? To find the width, use the formula , where w represents the width, A represents the area and l represents the length. To determine the perimeter, use the formula , where P represents the perimeter, l represents the length, and w represents the width

Answers

62 inches.

2*(19+228/19)=62

Hope this helps!

Answer:

62 inches

Step-by-step explanation:

plz mark brainliest

what is greater 3 x 1/10 plus 4 x 1/100 plus 8x 1/1000 greater than one and two tenths

Answers

So, first let's change these numbers into decimal form:
3*0.1 + 4*0.01 + 8*0.001 ? 1.2
Multiply:
0.3 + 0.04 + 0.008 ? 1.2
0.348 < 1.2
One and two tenths is larger.
Hopefully this is what you're asking, as this question is unclear

3*0.1 + 4*0.01 + 8*0.001 ? 1.2

Multiply:

0.3 + 0.04 + 0.008 ? 1.2

0.348 < 1.2

One and two tenths is larger

Help please........................

Answers

Remark
(0,0) does not change with the rotation, nor does it change with the dilation.
(2,0) will become (-2,0) with the rotation and (-6,0) with the dilation.
(0,4) goes right around to the - y axis. It become (0,-4) with the rotation. and (0,3*-4) = (0,-12) with the dilation.

There is no way that these triangles are congruent. I could have said that right at the very beginning. But there is a way that they are similar. The angles between them remain unaltered. You can test that out with (0,4) to (0,0) to (2,0) which is a right angle (labeled CAB). No matter what you have done in these two steps, that right angle remains. Dilation other than a dilation of 1 will not produce congruence.

B . <<<< Answer.

For questions 1 and two find the volume of the given prism. Round to the nearest tenth if necessary.

Answers

1)D 2)B 3)A 4)B 5)B 6)D 7)C 8)A 9)A 10)B 11)B 12)B

The volume of the rectangular and triangular prisms are 269.3 cubic centimeters and 1756.3 cubic yards respectively

How to calculate the volume of the prism?

The formula for calculating the volume of a prism is given as;

V = lwh

l is the length

w is the width

h is the height

1) The volume of the prism is expressed as;

V = 12.1 * 5.3 * 4.2
V = 269.3 cubic centimeters

2) Volume of the triangular based prism = BH

Base area = 1/2(13)(13)sin60
Base area = 84.5(0.8660)
Base area = 73.177 square yard

Height H = 24 yards

Volume of the prism = 24 * 73.177

Volume of the prism = 1756.3 cubic yards

Hence the volume of the rectangular and triangular prisms are 269.3 cubic centimeters and 1756.3 cubic yards respectively

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You ran 4 miles. Rob ran half as far as you. Tim ran half as far as rob. Nicole ran half as far as tim. Write an expression for how far Nicole ran

Answers

4×(1/2)×(1/2)×(1/2)=0.5

Final answer:

Nicole ran 0.5 miles. The expression for Nicole's running distance, starting from your 4 miles run, is (4 / 2^3) or 4 / 8, which simplifies to 0.5 miles.

Explanation:

Expression for Nicole's Running Distance

The expression to find out how far Nicole ran is based on a sequence of halving distances starting from the original distance you ran. You ran 4 miles. Rob ran half as far as you, so Rob ran 4 miles / 2 = 2 miles. Tim ran half as far as Rob, therefore Tim ran 2 miles / 2 = 1 mile. Finally, Nicole ran half as far as Tim. Hence, Nicole ran 1 mile / 2, which is equal to 0.5 miles.

In a form of an expression, the distance Nicole ran can be represented as:

(4 / 2) / 2) / 2

Or simplified to:

(4 / 2^3)

Or,

4 / 8 = 0.5 miles

A boat traveling upstream goes 84 kilometers in 7 hours. If the return trip takes only 3 hours, what is the speed (in kilometers per hour) of the boat still in water?

Answers

Speed = Distance ÷ time

Speed upstream = 84 ÷ 7 = 12 km/h

Speed downstream = 84 ÷ 3 = 28 km/h

Speed in still water = 1/2(28 + 12) = 20 km/h

Answer: 20 km/h

The graph below displays the wrist circumferences and heights of six students in Alyssa’s classroom.

Is the height of these students a function of their wrist circumference?

A(Yes because as wrist circumference increases height also increases
B(Yes because a line can be fit to these data to predict other pairings.
C(No because the height of 151 cm is paired with two wrist circumferences.
D(No because the wrist circumference of 16 cm is paired with two heights.

Answers

Answer:

Option D(No because the wrist circumference of 16 cm is paired with two heights.

Step-by-step explanation:

In the given graph we have set of points representing the wrist circumferences and heights of six students in Alyssa’s classroom.

x axis represents the wrist circumference while y axis represent the height.

Any relation is called a function if for one value of x we have only one value of y. If the graph passes the vertical line test that is if a vertical line drawn touches the graph at only one point then the graph is called a function.In the given graph for x value x=16 there are two y values 162 and 165.So the graph is not a function.

Among all the options Option D(No because the wrist circumference of 16 cm is paired with two heights.) is the right answer.

Eight times the sum of a number and one is -8

Answers

x= a number
times= multiply
sum= add

8(x + 1)= -8
multiply 8 by parentheses

(8*x) + (8*1)= -8

8x + 8= -8
subtract 8 from both sides

8x= -16
divide both sides by 8

x= -2

CHECK:
8(x + 1)= -8
8(-2 + 1)= -8
8(-1)= -8
-8= -8

ANSWER: The number is -2.

Hope this helps! :)

how do I solve for x?

Answers

So it states that the area of the rectangle is 56 cm, so all of it.
Given: 56 cm of rectangle
Unknown: find x
Length: 2 + x or x + 2
Width: 2x-5
Area = l * w
(x+2)(2x-5)
set x equal to 0
x+2=0 --> x=-2 2x-5=0 --> 2x=5 --> x = 5/2
so the answer we got was x=-2,5/2
we know that x cannot be negative because you can't measure with negative numbers, therefore, 5/2 is your answer

length = a
width = b

ab = 56 ---- first equation
a = 2 + x ---- second equation
b = 2x - 5 ---- third equation

substitude second and third equation into the first equation

(2+x)(2x-5) = 56
4x - 10 + 2x^2 - 5x = 56
2x^2 - x - 10 - 56 = 0
2x^2 - x - 66 = 0
(x-6)(2x+11) = 0
x1 = 6 , x2 = - 11/2 ---> - 5.5 (nearest whole num)

I dont know how to set it up. #20 solving equations with variables on both sides.

Answers

First lets create an equation for each:

1) Cost = 5x + 60
2) Cost = 11x

Where x is the number of lessons.

Since we want to find the value of x (the number of lessons), we can set both equations equal to each other:

5x + 60 = 11x

Subtract 5x from both sides:

60 = 6x

Divide by 6:

x = 10
So it will take 10 lessons till a member and a nonmember pay the same amount.

Jason ran 325 meters farther than Kim.Kim ran 4.2 kilometers.How many meters did Jason run?Estimate to check your answer

Answers

4.2 km=4.2*1000=4200 m Kim ran
Jason 4200+325=4525 m Jason ran

Convert km to m
4.2km = 4.2 x 1000 = 4200m

Jason ran 325m farther than Kim
⇒ 4200 + 325 = 4525m

Answer: Jason ran 4525m

The answer for number 32

Answers

8% write left handed.
90+60=150
9+3=12
12/150=.08

Question 7 Unsaved A couch cost $825. If the state has a 10% sale's tax. What was the price of the couch before taxes?

Question 7 options:

$785
$750
$735
$700

Answers

Let the price be p. Then 1.10p = $8.25. Solving for p, p = $750 (answer)

The equation can be framed as follows:

Before tax cost *(1+tax rate) = Final cost

Given tax rate = 10% = 0.1

Final cost = $825

Before tax cost *(1+0.1) = 825

Before tax cost * 1.1 = 825

Before tax cost = 825/1.1

Before tax cost = $750

Price of the couch before taxes = $750

find the missing measure in each triangle with the given angle measure ? 45° , 35°,x°

Answers

45 + 35 + x = 180
80 + x = 180
80-80 = 0
180-80 = 100

The answer is x = 100°

Answer:

X=100

Step-by-step explanation:

ASAP pleaseeeeee!!!!!!

Answers

The answer to the question is C

C is the answer hope this helpsss

you spin a spinner the has 8 equal sized sections numbered. one to eight. Find P( 1 or 2 )

Answers

There is a 1/8 chance you'll land on 1, and a 2/8 chance you'll land on either 1 or 2.
This wasn't really a complete question but i hope i answered it!!
Fell free to ask questions :)

Final answer:

The probability of spinning a 1 or 2 on a spinner with eight equally sized sections can be calculated using the formula for probability, resulting in a probability of 0.25.

Explanation:

The question asks to find the probability of spinning a 1 or 2 on a spinner with eight equally sized sections, each numbered from 1 to 8. The problem is a straightforward application of the concept of probability in mathematics, which can be calculated by the formula P(E) = Number of favourable outcomes / Total number of outcomes.

In this case, the number of favourable outcomes (spinning a 1 or 2) is 2, and the total number of outcomes is the total number of sections on the spinner, which is 8. Therefore, the probability P(1 or 2) is computed as 2 / 8 = 0.25.

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