Mathematics Middle School

The scale on a map is 1:500000

Two towns are 7cm apart on the map

work out the actual distance between the map
Give your answer in kilometres

Answers

Answer 1
1:500000
it mean:
1cm : 500000 cm
(500000×7) cm = 3500000 cm (real distance between the two towns, in cm)
 if
 1 Km = 100000 cm
3500000 /100000 = 35 Km (real distance between the two towns, in Km)
Answer 2
Final answer:

The actual distance between the two towns, considering that they are 7cm apart on a map with a scale of 1:500000, is 35 kilometers.

Explanation:

In the given scenario, you're being asked to find the actual distance between two towns based on their distance on a map, using the map's scale, which is 1:500000. This means 1 cm on the map is equivalent to 500000 cm on the ground.

Since the towns are 7 cm apart on the map, the actual distance on the ground will be 7 (distance on the map) multiplied by 500000 (scale of the map), i.e., 3500000 cm. Since there is 100000 cm in 1 km, you convert the distance to kilometers by dividing by 100000. Hence, the actual distance is 3500000/100000 = 35 km.

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Related Questions

when 4 is added to the difference between 5 times a number and 9 the result is greater than 10 * to 4 times the number what's the number

Answers

5x - 9 > x*10^4
5x - 9 > x * 10000 I hope I'm reading the question correctly.
5x > 10000 x + 9
x > 10000/5 x + 9/5
x > 2000x + 1.8
0 > 1999x + 1.8
- 1.8 > 1999x
- 1.8 / 1999 > x
- 0.0009004 > x

a tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum. About how much did the tyrannosaurus rex weigh?

A Patagonian mayorum was a tyrannosaur that weighed about 76 tons

Answers

This is a very easy question here.

You have two dinosaurs. Let's just label them as Dinasour A (the Tyrannosaurus Rex), and Dinosaur B (the Patagonian Mayorum)

Dinasoar A weighs in at 1.4 tons more than a TENTH of Dinasoar B's weight
We know that Dinosaur B weighs in at 76 tons.

A tenth means exactly what it sounds like, 10/100. If it helps, you can think of it in terms of money, where a single Dime is a TENTH of a Dollar, because it takes 10 total Dimes to make $1

So, to fine a tenth of anything, you have to divide it by 10! 
76/10=7.6

7.6 is the tenth of the weight of Dino B. However, the question states that dino A weighs in at 1.4 tons MORE than a tenth, meaning addition.

So, 7.6+1.4=9

Dinosaur A, AKA the Tyrannosaurus Rex, weighs in at 9 Tons.

~Hope this helps!
Final answer:

The Tyrannosaurus rex weighed approximately 9 tons.

Explanation:

To determine the weight of the Tyrannosaurus rex, we need to find one tenth the weight of Patagotitan mayorum, which is 76 tons. One tenth of 76 tons is 7.6 tons. We then add 1.4 tons to this, as the Tyrannosaurus rex weighs about 1.4 tons more than one tenth the weight of Patagotitan mayorum. Therefore, the weight of the Tyrannosaurus rex is approximately 9 tons.

Which are equivalent ratios to 4:9?
Check all that are true.

9:28

20:45

12:27

4:24

8:18

Answers

The second, third, and fifth are equal to 4:9.

Final answer:

The equivalent ratios to 4:9 are 20:45, 12:27, and 8:18 because they all simplify proportionally to 4:9.

Explanation:

To determine which of the given ratios are equivalent to 4:9, we need to have ratios that can be simplified to 4:9 or for which 4:9 can be scaled up proportionally. We check each given ratio by either simplifying it or finding a common multiplier that would lead us back to 4:9.

9:28 is not equivalent because it does not simplify to 4:9 or scale from 4:9.20:45 simplifies to 4:9 when both numbers are divided by 5.12:27 simplifies to 4:9 when both numbers are divided by 3.4:24 is not equivalent because it simplifies to 1:6, not 4:9.8:18 simplifies to 4:9 when both numbers are divided by 2.

Therefore, 20:45, 12:27, and 8:18 are equivalent ratios to 4:9.

A right triangular prism is shown. Find (A) the total surface area and (B) the volume. You must show formulas and your work.
10m height
8m width
10.77m

Answers

Hello!

We are going to use the rectangular prism of the image as a guide:

First of all, the AC segment is calculated using the Pythagoras' theorem:

[tex]AC= \sqrt{ AB^{2}+ BC^{2} } =\sqrt{ 10^{2}+ 8^{2} }=12,81 m[/tex]

(A) The surface area of a prism is the sum of the surface areas of each face. 

For the 2 triangles  ABC and DEF

[tex]A=2*(1/2*b*h)=2*(1/2*8m*10m)=80m[/tex]

For the ABEF Rectangle

[tex]A=w*l=10,77m*10m=107,7m^{2}[/tex]

For the ACDE Rectangle

[tex]A=w*l=10,77m*12,81m=137,96 m^{2}[/tex]

For the BCDF Rectangle 

[tex]A=w*l=10,77m*8m=86,16 m^{2}[/tex]

To finish you need to sum up the areas of each face:

[tex]SA=2A_{ABC}+ A_{ABEF}+A_{ACDE}+A_{BCDF}= \\ 80 m^{2} +107,7m^{2} +137,96m^{2} +86,16m^{2} =411,82m^{2} [/tex]

(B) The volume of a prism is the product of the area of its base and the height of the prism. In this case, the base is a triangle so the formula and the calculations for the volume are as follows

[tex]V= \frac{1}{2} *w*h*l= \frac{1}{2}* 8m*10m*10,77m=430,8m^{3} [/tex]

23=30-g;6,7,8 what is the solution

Answers

7
30-7=23
7=g
Solve the equaton backwards to get the answer

Shauna bought a flat cardboard box

Answers

and? what about it?????

A model car has a windshield with dimensions 1/18 the size of a real car windshield. They rectangular windshield of the real car has an area of about 2318 square inches, with a width of 61 inches. What are the side lengths of the model car's windshield? Round to the nearest hundredth. Justify your answer

Answers

We know the model car is 1/18 the size of all values of the real car. This means that the model car has an area that is 1/18 the area of the real car, a length that is 1/18 the size of the real car, and a width that is 1/18 the size of the real car.  To get rid of the fraction, we can simply divide by 18.

The first step here is to figure out the missing length of the real car. We know the area is 2318 square inches, and the width is 61 inches. Since the area of a rectangle is length x width, we can find the length by doing the opposite of multiplication which is division. 

2318 ÷ 61 = 38 

So the dimensions of the real car windshield is 61 and 38. 

Now, we have to find what 1/18 of 61 is, and what 1/18 of 38 is. We can divide 61 and 38 by 18 to find these values. 

The attached image shows that division process, and how we can take it a step further to find the area of the model car windshield. 

Answer:

A. 2375 inches

Step-by-step explanation:

just did it lol

If postage costs $.54 the 1st ounce and $.22 for each additional ounce calculate the cost of mailing a 10 ounce envelope.

A. $5.40
B. $2.20
C. $5.08
D. $2.52

Answers

0.54+(0.22*9) is equal to 2.52

How can you determine if a piece-wise relation is a function?

Answers

use the vertical line rule to test. 
Imagine you are drawing lines parallel to the y axis, if any of your lines touches the graph twice, the graph does not represent a function. otherwise, it does. 

A hollow ball is made up of rubber that is 2 centimeters thick. The ball has a radius to the outside surface of 6 centimeters. What is the approximate volume of rubber used to make the ball? Use 3.14 for pi.

a. 33.5cm^3

b. 267.9cm^3

c. 636.4cm^3

d. 994.3cm^3

Answers

The volume of rubber used to make the hollow ball is approximately 636.4 cm^3, which is calculated by subtracting the inner space volume from the total volume of the ball.

To find the volume of rubber used to make a hollow ball, we need to calculate the volume of the entire ball and then subtract the volume of the inner empty space. The ball's external radius is 6 centimeters, and the rubber thickness is 2 centimeters, which makes the inner radius 4 centimeters (6cm - 2cm).

The formula to calculate the volume of a sphere is V = (4/3)
y. Using
for pi and plugging in the numbers, we get:

Volume of the entire ball (outer radius of 6cm): V = (4/3)
(6)
= 904.32 cmVolume of the inner space (inner radius of 4cm): V = (4/3) 3.14 (4)
= 268.08 cm

To find the volume of the rubber used, we subtract the smaller volume from the larger volume:

904.32 cm - 268.08 cm = 636.24 cm

Therefore, option c. 636.4cm is the approximate volume of rubber used to make the ball.

WILL GIVE 99 POINTS IF ANSWERED ASAP PLEASE

Answers

Answer:

Part A

1.  Perimeter of the outside edges = 24 inches

2.  One possibility is: length = 8 in. and width = 8 in.

second possibility is: length = 16 in. and width = 4 in.

3.  Area of the wood portion = 11 [tex]inches^{2}[/tex]

4.  New dimensions are:

Length = 17.5 ft.

Width = 12.5 ft.

Part B

Area of the picture = 24 [tex]inches^{2}[/tex]

Area of the frame = 35 [tex]inches^{2}[/tex]

Step-by-step explanation:

Part A

1.  Perimeter of the outside edges = 2(length + width)

= 2(7 + 5)

= 2(12)

= 24 inches


2.  If the area of the frame was 64 [tex]inches^{2}[/tex], then the two possible dimensions are:

8 × 8 and 16 × 4

i.e., one possibility is: length = 8 in. and width = 8 in.

second possibility is: length = 16 in. and width = 4 in.


3.  Area of the wood portion = Area of the frame - Area of the picture

= (5 × 7) - (4 × 6)

= 35 - 24

= 11 [tex]inches^{2}[/tex]


4.  The scale factor is:

1 in. = 2.5 ft.

So, its length = 7 in. = 7(2.5) = 17.5 ft.

width = 5in. = 5(2.5) = 12.5 ft.


Part B:

Length of the picture = 6in.

Width of the picture = 4 in.

Area of the picture = Length × Width

= 6 × 4

= 24 [tex]inches^{2}[/tex]

Length of the frame = 7in.

Width of the frame = 5 in.

Area of the frame = 7 × 5 = 35 [tex]inches^{2}[/tex]

Part A

1) Perimeter of the outside edges

24 inches



2) One possibility is:

length- 8 inches

and width - 8 inches


3) Area of the wood portion

= 11


4) New dimensions are:

Length - 17.5 feet

Width - 12.5 feet




Part B

Area of the picture

- 24

Area of the frame

- 35


Step-by-step explanation:

first part-


1) Perimeter of the outside edges = 2(length + width)

= 2(7 + 5)

= 2(12)

= 24 in



2) if the area of the frame was 64 then there are two possible dimensions

8 × 8 and 16 × 4

the first possibility

length = 8 inches

width = 8 inches


the second possibility

length = 16 inches

width = 4 inches



3) Area of the wood portion= Area of frame - Area of picture

= (5 × 7) - (4 × 6)

= 35 - 24

= 11



4)The scale factor

1 inches = 2.5 feet

length = 7 inches

= 7(2.5)

= 17.5 feet



width = 5 inches

= 5(2.5)

= 12.5 feet



Second part-

Length of picture

= 6 inches


Width of picture

= 4 inches



Area of the picture

(Length × Width)

= 6 × 4

= 24


Length of frame = 7 inches

Width of frame = 5 inches

Area of frame = 7 × 5 = 35




If this helped you please say thanks and mark brainliest



Sharon has a balance of $3,825 on her credit card. If the card has an annual rate of 20.99% how much is the finance charge for this month? $802.87 $219.96 $66.96 $20.99

Answers

20.99%/12 = 1.7492% which is the monthly rate (or at least the way my credit card does it)

1.7492/100 * 3825 = 66.91 
66.91 is just a rounding error. <<<=== answer.

Find the next three terms of the sequence.

–6, –24, –96, –384, . . .

Answers

-1,536, -6,144, -24,576

You multiply by 4 each time
-1536, -6144, -24576
HOPE THIS HELP!

20 POINTS, PLZ HELP!

The circumference of a circular tabletop is 72 π inches. What is the area, in square inches, of the tabletop?


144π

5185 π

1296 π

36π

WILL MARK BRANLIEST 20 POINTS!

Answers

Hi,

] The circumference=72π, this the radius will be found as follows:
C=2πr
therefore radius r will be:
2πr=72ππ
r=(72ππ)/(2π)
r=36
hence:
Area=πr²=π(36)²=1296π



Please help me with this compound interest.

Answers

6,300 x (1+0.06) ^3=

6300 x 1.191016 =

7503.40

A grasshopper coved a distance of 5 yards in 9 equal hops. How many yards did the grasshopper travel on each hop.

Answers

He covered 5 yards in 9 hops.
So you would do 5 divided by 9, which is 0.555555555555556, rounded, it would be about 0.6 yards. Hope this helps.
Hello!

To calculate how many yards the grasshopper traveled on each hop, we must divide the number of yards (5) by the number of hops (9):

5 ÷ 9 = 0.5556 (Repeating decimal)

Answer:

The grasshopper traveled about 0.6 yards on each hop.

HELPPPPPP
Safety standards require a pool to add 3 chlorine tablets to every 2,000 gallons of water. Today, the lifeguards at Park Pool added 8 chlorine tablets to their pool's 10,000 gallons of water. How does Park Pool's chlorine compare to the safety standards?

Answers

They have less chlorine than the safety standards require.

Answer: With the help of Ratio we can compare Park Pool's chlorine to the safety standards.

Step-by-step explanation:

Since we have given that

Safety standards requires a pool to add 3 chlorine tablets to every 2,000 gallons of water.

Number of chlorine tablets = 3

Volume of water = 2000 gallons

So, Ratio will be

[tex]3:2000\\\\=1:\frac{2000}{3}\\\\=1:666.67[/tex]

Now, According to question, the lifeguards at Park Pool added 8 chlorine tablets to their pool's 10000 gallons of water.

So, Number of chlorine tablets = 8

Volume of water = 10000 gallons

So, Ratio will be

[tex]8:10000\\\\1:1250[/tex]

Hence, with the help of Ratio we can compare Park Pool's chlorine to the safety standards.


Evaluate m 0 - n 2 for m = 2 and n = -1.

-1
0
1

Answers

the answer is 1 because anything the zero power is 1

Answer:

the answer is -1

Step-by-step explanation:

In the figure, lines a, b, and c are parallel and m∠4=156° . Drag and drop the correct angle measure for each angle.

Answers

those are the perfect answer
well done:)

but please Brainliest mark me as the answer and thank me
and all the best

Answer:

[tex]m<1=156\°[/tex]

[tex]m<2=24\°[/tex]

[tex]m<3=24\°[/tex]

[tex]m<5=156\°[/tex]

Step-by-step explanation:

Part 1) If line a is parallel to line b

then

[tex]m<1=m<4[/tex] -----> by alternate exterior angles

so

we have

[tex]m<4=156\°[/tex]

therefore

[tex]m<1=156\°[/tex]

Part 2) we know that

[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles

we have

[tex]m<1=156\°[/tex]

substitute

[tex]156\°+m<2=180\°[/tex]

[tex]m<2=180\°-156\°=24\°[/tex]

Part 3) If line a is parallel to line b

then

[tex]m<3=m<2[/tex] -----> by alternate interior angles

so

we have

[tex]m<2=24\°[/tex]

therefore

[tex]m<3=24\°[/tex]

Part 4) If line b is parallel to line c

then

[tex]m<5=m<4[/tex] -----> by corresponding angles

so

we have

[tex]m<4=156\°[/tex]

therefore

[tex]m<5=156\°[/tex]

Picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts.

Answers

If you dealing with probability.


You got ten shirts 8 are blue 2 are white.

So you have an 80% chance of grabbing blue and 20% of white.

And 8:2 ratio

The probability of picking a blue shirt from the drawer is 4/5 or 0.8

The probability of picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts can be calculated as follows:

Probability of picking a blue shirt = Number of blue shirts / Total number of shirts

Probability of picking a blue shirt = 8 / (8 + 2)

Probability of picking a blue shirt = 8/10

Probability of picking a blue shirt = 4/5

Therefore, the probability of picking a blue shirt from the drawer is 4/5 or 0.8.

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A rope is 72 feet long. What is the length of the rope in yards

Answers

24 yards hop this helps
The answer is 24 you find how many yards are in a foot =3 72÷3=24

Describe two ways that an exterior angle of a triangle is related to one or more of the interior angles

Answers

Both sums of the exterior and interior have to add up to 180, and both are straight lines. That's what I remember

What is the distance between points S and U?

Round to the nearest tenth of a unit.

3.3 units
6.4 units
8.1 units
12.0 units

Answers

distance = sqrt((6-2)^2 +(8-1)^2)
sqrt(16 +49)
sqrt(65)
8.06
round to 8.1 units
ANSWER

The correct answer is C.

[tex] |SU| = 8.1units[/tex]


EXPLANATION

The given points are,
[tex]S(2,1) \: \: and \: \: U(6,8).[/tex]


We use the distance formula to determine the distance between the two points.



[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]


We substitute the points to obtain,

[tex] |SU| = \sqrt{(6- 2) ^{2} + (8 - 1) ^{2} } [/tex]

We simplify to obtain,

[tex] |SU| = \sqrt{(4) ^{2} + (7) ^{2} } [/tex]



We further simplify this to obtain,

[tex] |SU| = \sqrt{16 + 49} [/tex]



[tex] |SU| = \sqrt{65} [/tex]

This evaluates to,

[tex] |SU| = 8.062[/tex]



We round to the nearest tenth to get,

[tex] |SU| = 8.1units[/tex]


If 5 pounds of broccoli cost is $12 then how much will 7 pounds of broccoli cost?

Answers

7 pounds costs $16.4 I think


Ok so, 5 pounds is 12$, since we can't count by 5's to get our answer we can divide 12 by 5 to see how much one pound would cost.

12 / 5 = 2.4

One pound of broccoli costs $2.40, SO. To find how much 7 pounds would cost we multiply 7 by 2.4.

7 x 2.4 = 16.8

So, 7 pounds of broccoli costs $16.80

Plies sambedy help problem 5.

Answers

no she wont because it starts the 5th and every 10 days she has practice. she will have it on the 25 and 35

a) A square has an area of 121 cm^2. What is the length of each side?

b) A square has a perimeter of 28m . What is the length of each side?

Answers

A square has equal sides. To find the area, you multiply the length and the height.
x*x=121
x^2=121
x=11
The length of each side is 11

A square has equal sides. To find the perimeter, you add all the sides together.
x+x+x+x=28
4x=28
x=7
The length of each side is 7

Jose creates a scale drawing of a character from one of his comic books using a scale factor of 40%. Caroline wants to use Jose’s scale drawing to create the original-size image of the comic book character. What scale factor will Caroline need to use to draw the original-size image?

Answers

Going from the original to the drawing had a scale factor of 40%=0.4=4/10.  Reversing this process, going from the drawing back to the original, would use the reciprocal of this, or 10/4=2.5=250%.

250% is scale factor will Caroline need to use to draw the original-size image.

What is Scale Factor?

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.

Given:

Scale Factor= 40%

As, Jacob use the scale factor= 40%

So, the new image size

= 100 x 40/100

= 40

let Caroline use x% scale factor

then, 40x/100= 100

x= 100 x 100 /40

x= 250%

Hence,  250% is scale factor will Caroline need to use to draw the original-size image.

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What is the range of this dot plot? I'm stuck between the answers 8 and 9.

Answers

Lowest value dots are plotted at 0. Highest-value dots are plotted at 9.
The range is the difference between these extremes.
.. 9 - 0 = 9

Rewrite the following expression in standard form by finding common denominator and collecting like terms

Answers

We have the expression [tex] \frac{2h}{3} - \frac{h}{9} + \frac{h-4}{6} [/tex]; to find the common denominator we are going to decompose each one of the denominators into prime factors, and then we are going to multiply the common factors raised to the highest power and all the non common factors.

The denominators of our fractions are 3, 6, and 9. 3 is already a prime, so we are going to let that one alone. 6 on the other hand is divisible by tow, so it can be decomposed into tow prime factors 2 and 3: [tex]6=(2)(3)[/tex].
9 is divisible by 3, so it can also be decomposed into tow prime factors 3 and 3: [tex]9=(3)(3)=3^{2} [/tex].
We have a common factor 3 in all our denominators, and among them the one raised to the highest power is [tex]3^{2} [/tex]. On the other hand we only have one non-common factor, 2. So, our common denominator will be:
[tex]common.denominator=(3^{2} )(2)=(9)(2)=18[/tex] 

Now we know that the common denominator of our standard form fraction is 18, the only thing left is convert the denominators of each one of our fractions to 18 and simplify. To do that we are going to divide the common denominator by the denominator of each fraction, and then multiply the quotient by each one of the numerators:
[tex] \frac{2h}{3} - \frac{h}{9}+ \frac{h-4}{6} = \frac{(6)(2h)-(2)(h)+3(h-4)}{18} [/tex]
[tex] \frac{12h-2h+3h-12}{18} [/tex]
[tex] \frac{13h-12}{18} [/tex]

Answer: [tex] \frac{13h-12}{18} [/tex]

The figure shows triangle ABC and a rotation of the triangle about the origin
a. How would you describe the rotation?
b. What are the coordinates of the image?

Answers

That is an anticlockwise rotation of 90 degrees about the origin

A'  is (3,1), B' is (2,3) and C' is (-1, 4)
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