The scale of a map is 1:500 000. The actual area of the lake in km is 3x10¹² km².
What is meant by the scaling on the map?The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult.
• If 1 centimeter on a map corresponds to 500 000 km on the earth, then 1 cm2 would be equivalent to 1 cm² = (500000km) 2
=25×10¹⁰ km²
• The lake's exact area may now be determined by multiplying 12 cm² by 25 × 10¹⁰ km² (3 × 10¹² km²)
As a result, the distance between the towns is 0.000344 cm on the map, while the lake's real area is 3x10¹² km².
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Un inversionista pierde en la bolsa el 10% de su capital, luego pierde el 20% de lo que le queda, vuelve a invertir y pierde el 10% de lo que quedaba, finalmente hace una última inversión, que resulta exitosa, ganando el 40% del resto. Si su capital inicial fue de $ 16 000. ¿Cuál fue el capital final resultante?
El capital final resultante es igual a $ 14 515,20.
¿Cómo determinar el capital final de un inversionista?
En este problema tenemos el caso de un inversionista que invierte cuatro veces, teniendo tres pérdidas y una ganancia sucesivas. Esta situación se puede modelar mediante una productoria que involucra el capital inicial y los porcentajes de ganancia y pérdida:
C' = C · Π (1 + r / 100) (1)
Donde:
C - Capital inicialr - Porcentaje de ganancia (la pérdida es un número negativo).C' - Capital finalEn consecuencia, el capital final resultante es el siguiente:
C' = 16 000 · (1 - 10 / 100) · (1 - 20 / 100) · (1 - 10 / 100) · (1 + 40 / 100)
C' = 14 515,20
El capital final resultante es igual a $ 14 515,20.
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515,060 to the nearest hundred thousand
Answer:
500,000
hope this helps
please help
maths geometry
Step-by-step explanation:
ABCD is a rectangle.
so, it has 2 pairs of equal and parallel sides.
all 4 angles are 90°.
both diagonals are equally long and intersect each other at their midpoint. so, all 4 half-diagonal segments are equally long.
(1)
2x + 4y = 4x - y = 36/2 = 18 cm
we can split this into 2 equations
2x + 4y = 4x - y
5y = 2x
x = 5y/2
and e.g.
4x - y = 18
now we use the first equation in the second
4(5y/2) - y = 18
20y/2 - y = 18
10y - y = 18
9y = 18
y = 2
x = 5y/2 = 5×2/2 = 5
(2)
I cannot draw here, but the shortest distance between a point and a line is always a height (a line segment from the point meeting it intersecting the line at a right angle, 90°).
(3)
e.g.
AE, AD/2 and the drawn height from E to AD create a right-angled triangle.
we know AD/2 = 15 cm
from (1) we know AE = 4x - y = 4×5 - 2 = 20 - 2 = 18 cm.
the height E to AD we get via Pythagoras
AE² = (AD/2)² + height²
height² = AE² - (AD/2)² = 18² - 15² = 324 - 225 = 99
height = sqrt(99) = sqrt(9×11) = 3×sqrt(11)
remember trigonometry ?
this height = sin(theta) × AE
sin(theta) = height / AE = 3×sqrt(11) / 18 = sqrt(11)/6 =
= 0.552770798...
theta = 33.55730976...° ≈ 34°
(4)
the diagonals of a square bisect the angles of the square, so that theta would become 90/2 = 45°.
Evaluate. Write your answer as a fraction in simplest form. 3/8 - 1/6 + 5/12
Answer:
5/8
Step-by-step explanation:
Get LCD of 24 and do the math
9/24 - 4/24 - 10/24
15/24
Divide top and bottom by 3
5/8
Shreya is training for a marathon. The graph shows the miles she ran each day of her training. Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. How far did Shreya run on day 5 of her training? Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.
She ran the distance on the day of 5 is 2miles.
Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.
⇒ (8-6-3-7)/5
⇒ (-8)/5
⇒ 1.8
⇒ 2 miles
The fraction whose numerator is 8 minus 6 minus 3 minus 7, whose denominator is 5 which is equal to the fraction of 2 miles.
Hence, Shreya ran on the day of 5 in her training is 2 miles.
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The line y=kx + 4 goes through the point (2,-2)
Find the value of K
Please answer quickly
You want to plug in the coordinate pair to solve this.
x = 2
y = -2
y = kx + 4
-2 = 2k + 4
-6 = 2k
k = -3
Lucie works out 25 x 12.2 without a calculator.
Here is her working.
10 × 12.2 = 12.20
20 × 12.2 = 24.40
5 x 12.2 = 61
25 x 12.2 = 24.40 +61 = 85.40
Lucie's working is incorrect.
Identify and (only) correct the lines containing a mistake
to work out the correct answer.
122
244
Answer:
[tex]25 \times 12.2 = 305.00[/tex]
Step up an inequality for this situation below. Define your variable, but do not solve.
Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?
The student can take 5 number of lessons if they pay no more than $175
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of music lessons. The student can pay no more than $175, hence:
25x + 50 ≤ 175
x ≤ 5
The student can take 5 number of lessons if they pay no more than $175
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if two angles are not adjacent, then they are not a linear pair
False, if two angles are not adjacent, then they are not a linear pair.
Given that,
To justify that if two angles are not adjacent, then they are not a linear pair.
The angle can be defined as the one line inclined over another line. The measure of angle is in degrees and radians.
Here,
When two angles are not adjacent can be linear pairs,
But pair can be linear pair whether the angle is not adjacent.
Thus, the statement is false False, if two angles are not adjacent, then they are not a linear pair.
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A department store advertises a sale where the customer chooses the discount. A customer may choose a flat discount of $20 off any purchase or 20% off the total purchase price. The final purchase price of an item was $175.
a. What are the possible prices of the item before each discount?
b. Which discount represents a bigger savings in cost for the customer?
The answers will be :
A. The possible prices at flat discount of $ 20 will be $195 and at flat discount of 20% will be $218.75
B. The discount of flat 20 % gives a bigger savings in cost for the customer.
What do you mean by discount ?
The discount is the difference between the purchase price and the item's par value or simply deduction from the cost price of a good.
It is given that the final purchase price of the item is $175.
A.
Let's try to find out the possible price of item before each discount.
So , price before discount can be calculated by using formula which is :
Price before discount = Discount + Final purchase price
As in first case the flat discount is of $20 , so :
Price before discount = $20 + $ 175
Price before discount = $195
Now as per the question , there is a flat discount of 20% off the total purchase price .
So , let's assume if price before discount is P then :
[ P - ( 20P / 100) ] = 175
P - 0.2 P = 175
0.8 P = 175
or
P = $ 218.75
B.
From the above calculations which we have done , we can conclude that the discount of 20 % represents a bigger savings in cost for the customer because customer is saving an amount of $218.75 which is greater than $195.
Therefore , the answers will be :
A. The possible prices at flat discount of $ 20 will be $195 and at flat discount of 20% will be $218.75
B. The discount of flat 20 % gives a bigger savings in cost for the customer.
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Solve each system by substitution
What is the slope of a line graphed below?
Answer:
Undefined
Step-by-step explanation:
The slope of a horizontal line is zero. The slope of a vertical line is undefined.
The florist makes the greatest number of identical arrangements with the carnations and asters. She has 72 carnations and 42 asters. How can she decide how many carnations to place in each arrangement?
The carnations to place in each arrangement is 6.
How to calculate the value?It should be noted that from the information, the florist makes the greatest number of identical arrangements with the carnations and asters and she has 72 carnations and 42 asters.
In order to know the carnations to place in each arrangement, this can be done by finding the common factor. This will be illustrated that the numbers have a highest common factor of 6.
Therefore, the number of carnation is 6.
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST please explain how u got ur answer too..
Answer: yes the graph and the table represents the same relationship between x and y.
Step-by-step explanation: the table "x" is going up by X1 and y is going by x2 for each number meaning it does have a relationship, and the graph also has a relationship because is going (1,2) then (2,4) then (3,8) then (4,16) just like the table so yes it does have a relationship.
According to a recent survey, 62 % of the population owns a cat. 37 Percent of cat owners are married, while 44 % of non-cat owners are married. If you randomly select a person, what is the probability that she/he is married?
Answer:
There are two possibilities that you need to take into account:
1) having a cat and being married
2) not having a cat and being married
P(having a cat) = 0.19
P(no cat) = 1 - P(having a cat) = 1 - (0.19) = 0.81
Since 9% of cat owners are married: (0.19)(0.09) = 0.0171
Since 11% of non-cat owners are married: (0.81)(0.11) = 0.0891
Probability of randomly selected person being married = 0.0171 + 0.0891 = 0.1062
Write the number for 160,060 in expanded form and using number names
A taxi company charges an initial fee
of $2.80 plus $3.50 per mile traveled.
a. Does the situation represent a function? If so, identify
the independent and dependent variables.
b. You have enough money to travel at most 20 miles
in the taxi. Find the domain and range.
The situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively
a. Does the situation represent a function? If so, identify the independent and dependent variables.The given parameters are
Initial Fee = $2.80
Rate = $3.50 per mile
Let the number of miles be x and the total fee be y
So, we have
Total fee = Initial Fee + Rate * Number of miles
This gives
y = 2.8 + 3.5x
This means that the situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively
b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range.Here, we have
Maximum number of miles = 20
This means that the domain is 0 <= x <= 20
Substitute 20 for x in y = 2.8 + 3.5x
y = 2.8 + 3.5 x 20
Evaluate
y = 72.8
This means that the range is 0 <= x <= 72.8
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PLEASE ANSWER! WILL GIVE BRAINLIEST
Owen draws the cube shown. Pat draws a cube with a side length that is 3 units greater than the side length of Owen's cube, show an equation and answer to represent the volume of Pat's cube.
Volume = side³.
Cube drawn by Owen From the drawing:Side = 7 in.
Cube drawn by PatSide length is 3 units greater than the side length of Owen’s cube:Side = 7in + 3in = 10 in
So the 3 sides= 10 you multiply 10 x 10 x 10 and would give you 1000
Answer this!!!!!!!!!!!!!!!!!!!!!!!!
Based on the distance between the park bench and the basketball court, the distance between the park bench and the pond is 57¹/₈ feet
What is the distance between the park bench and pond?The distance between the park bench and the basketball is the sum of the distance between the park bench and the pond and the pond and the basketball court.
The distance between the park bench and the pond is therefore:
= Distance between park bench and basketball court - Distance between pond and basketball court
Solving gives:
= 75³/₄ - 18⁵/₈
= 75.75 - 18.625
= 57.125
= 57¹/₈ feet
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Answer:h
el]lo you commented on a post that helped me alot
Step-by-step explanation:
A box is launched upward from the ground at a speed of 69 feet per second. Calculate the height, in feet, of the box at 2 seconds if the height is given by h(t)=−16t2+69t where t is seconds.
According to the solving the Hight in feet at 2 second is 74.
What is the link between height and time, as well as height and velocity?This asserts that the height (h) of a projectile is equal to the combination of two products: its initial velocity and time in the air, and indeed the acceleration constant as well as half of the time squared.
What is the Max height formula?max = h plus V02 / (4 * g) When launching from the ground, the range is maximized (h = 0). If = 0°, therefore vertical velocity becomes equal to zero (Vy = 0), indicating horizontal projectile motion.
According to the given data:Given h(t)=−16t²+69t
t = 2 sec
substituting the value of t = 2.
h(2)=−16(2)²+69(2).
= -64 + 138
= 74
According to the solving the height and time in feet at 2 second is 74.
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Which is a true statement? Question 3 options:
–4 > 0
–12 < –3
–15 > –5
2 < –5
Answer:
-12<-3
Step-by-step explanation:
-3 is bigger than -12 and is closer to 0
represent the expression please help
Answer:
10,350.98
Step-by-step explanation:
The decimal number is the sum of the terms of the expression.
Sum(1×10,000) +(3×100) +(5×10) +(9×1/10) +(8×1/100)
= 10,000 +300 +50 +0.9 +0.08
= 10,350.98
__
Additional comment
If you can't do this in your head, you can input the expression to your calculator, and it will give this same result.
example of a vertical line test
Answer:
The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of a relation, and then observe the points of intersections.
Step-by-step explanation: hope this helps
1 .If m∠SUT = 3x + 6 and m∠RUS = 5x – 4, find x
2.If m∠SUT = 3x + 6 and m∠RUS = 5x – 4, find m∠SUT.
same pic for both
*
Answer:
1.If you are to check the figure you will find that it is a rectangles. You should know the properties of a rectangle.
we are goin to use the property: Each vertex of a rectangle has angle equal to 90 degreesmeaning since m∠SUT and m∠ RUS form the vertex when added they give 90°3x+6+(5x-4)=90°
3x+5x+6°-4°=90°
8x+2°=90°
8x=90°-2°
8x=8°
[tex]\frac{8x}{8} =\frac{88}{8} \\x=11[/tex]
2.m ∠SUT is donated by 3x+6
and now we know the value of x=11°
m∠SUT=3(11°)+6
m∠SUT=33°+6°
m∠SUT=39°
if a ball is thrown into the air with a velocity of 20 ft/second it's height in feet and seconds is given by f(t) = 20t - 10t^2. find average velocity for the time period t0 = 1 to t=2
The average velocity is -10 ft/s.
What is Average velocity?Average velocity is just the average speed with a direction. If a trip starts and ends at the same point, the total displacement is zero, so the average velocity is zero.
For example, someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph).
Given:
f(t) = 20t - 10t²
Now, from t=1 to t=2
f(1)= 20*1 - 10 * 1*1
f(1)= 10
and, f(2)=20*2-10*2*2
f(2)= 40-40
f(2)=0
Now,
Average velocity:
v = ( 0-10 ) / ( 2- 1 )
= -10 ft/s
hence, the average velocity is -10 ft/s.
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All you have two unmarked cups 6 ounces and 10 ounces respectively how can you use the two cups to obtain exactly 8 ounces of liquid in the 10 ounce cup
need to find the value of x
Answer:
(6x+10)+(10x+10)=180
16x+20=180
16x=160
x=10
Step-by-step explanation: Due it being a supplementary angle which means 180 degrees in total.
Which number set is the most reasonable to describe a baby’s weight at birth?
Whole numbers
Rational numbers
Irrational numbers
Integers
the circle below centred at O has a radius of 12cm
Answer:
x = 9.7 cmStep-by-step explanation:
OB is perpendicular bisector of AC (since AB = BC) so triangle OBC is right triangle.
We have:
OB = x,OC = 12 cm,BC = 7 cmUse Pythagorean to find the missing value:
x² + BC² = OC²x² = OC² - BC²x² = 12² - 7²x² = 144 - 49x² = 95x = √95x = 9.7 cm (rounded)Name all segments on the line that contain point c
The name of all segments on the line that contain point c are AD, BD, AE, BE
How to name all segments on the line that contain point c?The points on the number line are given as:
A, B, C, D and E
On this number line, the point either sides of point C are
A and B & D and E
This means that the point C is on the lines AD, BD, AE, BE
Hence. the name of all segments on the line that contain point c are AD, BD, AE, BE
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