Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?
Answers
Kate can see across the horizon by 3.33 times further than Paul.
What is the shape of the horizon?The assumed shape of the horizon shows that it forms a cone shape. The volume of the cone can be used to determine how far they can see.
The volume of the cone [tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
For Kate:
Height (h) = 50 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]
V = 2.12526863 × 10¹⁵ m³
For Paul
Height (h) = 15 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]
V = 6.3758059 × 10¹⁴ m³
To determine how much further can kate see across the horizon than Paul, we have:
= Volume of Kate/Volume of Paul
= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³
= 3.33 times further.
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Related Questions
solve the system using substitution. show all work
Answers
Step-by-Step Explanation:
=> 4x + 5y = 7 (Eq. 1)
=> y = 3x - 10 (Eq. 2)
Substitute value of ‘y’ from Eq. 2 in 1 :-
4x + 5y = 7
4x + 5(3x - 10) = 7
4x + 15x - 50 = 7
19x - 50 = 7
19x = 7 + 50
19x = 57
=> x = 57/19 = 3
Therefore, x = 3
Substitute value of ‘x’ in Eq. 2 :-
y = 3x - 10
y = 3(3) - 10
y = 9 - 10
=> y = -1
Therefore, y = -1
A prism is completely filled with 270 cubes that have edge length of 1/3in.
what is the volume of the prism?
Answers
If the volume of the cube is 1/27 cubic inches. Then the volume of the prism will be 10 cubic inches.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
A prism is completely filled with 270 cubes that have an edge length of 1/3in.
Then the volume of the prism will be given as
Volume of prism = 270 (volume of the cube)
Then the volume of the cube will be
Volume of cube = (edge)³
Volume of cube = (1/3)³
Volume of cube = 1/27 cubic inches
Then the volume of the prism will be
Volume of prism = 270 × (1/27)
Volume of prism = 10 cubic inches
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Which explicit function defines this arithmetic sequence?
-351, -343, -335, -327, -319
A.
f(n) = 8n − 351
B.
f(n) = -8n − 351
C.
f(n) = 8n − 359
D.
f(n) = -8n + 359
Answers
Answer:
C. f(n) = 8n − 359
Step-by-step explanation:
The given arithmetic sequence has first term -351, and common difference (-343 -(-351)) = 8. The common difference will be the multiplier of n in the explicit function.
__
You can identify the appropriate explicit function by finding the one that correctly describes the sequence. Evaluating each for n=1 is sufficient. (You will note that choices B and D have the wrong sign on the multiplier of n.)
A f(1) = 8 -351 = -343
B f(1) = -8 -351 = -359
C f(1) = 8 -359 = -351 . . . . correctly gives the first term
D f(1) = -8 +359 = 351
The sequence is defined by the explicit function ...
f(n) = 8n -359
Answer:A:f(n)=8n-359
Step-by-step explanation:
Find (a) the range and (b) the standard deviation of the data set 141,116,117,135,126,121. round to the nearest hundredth if necessary.
Answers
a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
The given data set is 141, 116, 117, 135, 126, 121.
a) The range is the difference between the highest and lowest values within a set of numbers.
Range = Highest value - Lowest value
= 141-116
= 25
So, the range is 25.
b) Set up the formula for sample standard deviation. The standard deviation of a set of values is a measure of the spread of its values.
[tex]s=\sqrt{\frac{(x_i-\bar x)^2}{n-1} }[/tex]
Here, mean ([tex]\bar x[/tex]) = [tex]\frac{141+116+117+135+126+121}{6}[/tex]
= 126
[tex]s=\sqrt{\frac{(141-126)^2+(116-126)^2+(117-126)^2+(135-126)^2+(126-126)^2+(121-126)^2}{6-1}}[/tex]
[tex]s=\sqrt{\frac{(15^2+(-10)^2+(-9)^2+(9)^2+(0)^2+(-5)^2}{5}}[/tex]
[tex]s=\sqrt{\frac{(225+100+81+81+25)}{5}}[/tex]
[tex]s=\sqrt{\frac{512}{5}}[/tex]
s=10.1
So, the standard deviation is 10.1.
Therefore,
a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
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pls help, full explanation pls
Answers
Step-by-step explanation:
Apply exponent rule: (a. b)^n= a^n b^n
=3²(x¹⁰)²(y⁴)²
3²=9
=9(x¹⁰)²(y⁴)²
break =9(x¹⁰)²(y⁴)² into two
simplify (X¹⁰)² = (x²⁰)
simplify (y⁴)²=(y⁸)
=9(x²⁰)(y⁸)
Which is the graph of the inequality?
3y−9x≥9
Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A solid line passes through (zero, negative fourteen) and (two, zero). The area to the right of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A dotted line with a positive slope is drawn in the fourth quadrant of the graph. The area above the line is shaded gray.
Answers
A solid line passes through (-1, 0) and (0, 3). The area to the left of the line is shaded gray.
How to get the graph of the inequality?
Here we have the inequality:
3y - 9x ≥ 9
First, we should isolate y on one side of the inequality.
3y ≥ 9x + 9
y ≥ 3x + 3
Then, the graph will be a solid line of the form:
y = 3x + 3
Where the line is solid because the points on the line are solutions, and we need to shade all the region above the line.
Also, notice that for the line:
y = 3x + 3
if x = -1 we have:
y = 3*(-1) + 3 = 0
if x = 0 we have:
y = 3*0 + 3 = 3
Then the line passes through (0, 3) and (-1, 0). So the correct option is the second one.
"Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray."
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Hugo lives in the northwest corner of Greene County, Lena lives 29 miles away in the southeast corner, and the office where they work is directly between them. On Monday, Hugo took the bus into work, taking a direct route at 32 miles per hour. Lena left at the same time, taking her car along a direct route at a speed of 36 miles per hour. The two coworkers arrive at the office at the same time. How long did the commute take? If necessary, round your answer to the nearest minute.
Answers
Using the relation between velocity, distance and time, it is found that the commute took 48 minutes.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
For Lena, we have that d = 29, v = 36, hence the time in hours is given by:
[tex]t = \frac{d}{v} = \frac{29}{36} = 0.8056[/tex]
In minutes, the time is given by:
tM = 0.8056 x 60 = 48.
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A 15-foot ladder rest against a wall, The base of the ladder is 8 feet from the wall.
How far is the top of the ladder from the ground, Enter your answer as a decimal to the nearest tenth.
Can someone help I’ve been stuck on this question for almost a hour (please help).
Answers
Answer:
12.7
Step-by-step explanation:
Its a pythagerous question question
so if the ladder is 8 feet from the wall the base is 8
and the ladder is 15 foot and is the hypotemuse
so 15^2-8^2=161^2
The root of 161 = 12.69 rounded to 2 dp
so 12.7
The distance far the top of the ladder from the ground is 12.7 feet
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
We are given that;
Length= 15foot
Base= 8feet
Now,
In this case, the ladder is the hypotenuse, and the base and the height are the legs. So, we can write:
15^2 = 8^2 + h^2
where h is the height of the ladder from the ground. Solving for h, we get:
h^2 = 15^2 - 8^2
h^2 = 225 - 64
h^2 = 161
h = sqrt(161)
h = 12.688
Therefore, by Pythagoras theorem the answer will be 12.7 feet.
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find the height of a right circular cone if the slant height is 4 units and the radius is 2 units
Answers
The slant height of the right circular cone will be [tex]l=2\sqrt5}[/tex]
What is slant height of cone?The formula for the slant height of the cone is given as:
[tex]l^2=r^2+h^2[/tex]
Here we have
r=2 units
h=4 units
By putting the values we will get
[tex]l=\sqrt{4^2+2^2[/tex]
[tex]l=\sqrt{16+4[/tex]
[tex]l=\sqrt{20}[/tex]
[tex]l=2\sqrt{5}[/tex]
Hence the slant height of the right circular cone will be [tex]l=2\sqrt5}[/tex]
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Line segment AB has vertices A(-3, 4) and B(1, -2). A dilation centered at the orgin is applied to AB. The image has vertices A(-1, 4/3) and B(1/3, -2/3). What is tjr scale factor of the dilation?
1. 1/6
2. 1/3
3. 3
4. 6
Answers
Answer:
option 2
Step-by-step explanation:
consider the coordinates A (- 3, 4 ) and A' (- 1, [tex]\frac{4}{3}[/tex] )
since the dilatation is centred at the origin, then corresponding coordinates are multiples/ divisors of each other, then image to original gives scale factor.
scale factor = [tex]\frac{A'}{A}[/tex] = [tex]\frac{-1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] and [tex]\frac{\frac{4}{3} }{4}[/tex] = [tex]\frac{1}{3}[/tex]
similarly B (1, - 2 ) and B' ([tex]\frac{1}{3}[/tex], - [tex]\frac{2}{3}[/tex] )
[tex]\frac{\frac{1}{3} }{1}[/tex] = [tex]\frac{1}{3}[/tex] and [tex]\frac{-\frac{2}{3} }{-2}[/tex] = [tex]\frac{1}{3}[/tex]
Find the missing value (x)
Answers
Answer:
y=14; x=72
Step-by-step explanation:
y=(21×2)/3; x=(48×21)/14
Two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
Create an organized list showing all the possible outcomes after both spinners are spun. Use R to represent red, G to represent green, W to represent white, and B to represent blue. Explain how to find the total number of outcomes from the list.
Answers
The total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
What are permutation and combination?A permutation can be defined as the number of ways a set can be arranged, order matters, but in combination, the order does not matter.
Total number of outcomes on the first spinners = 4 (red, green, white, blue)
Total number of outcomes on the second spinners = 4 (red, green, white, blue)
Total number of outcomes = 4×4 = 16
Total outcomes:
RR RG RW RB
GR GG GW GB
WR WG WW WB
BR BG BW BB
Thus, the total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
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Marcus states that the polynomial expression 3x3 – 4x2y y3 2 is in standard form. ariel states that it should be y3 – 4x2y 3x3 2. explain which student is correct and why.
Answers
The correct student is Marcus because the power of the polynomial decreases till 0
How to determine the correct student?The polynomial expressions are given as:
Marcus: 3x³ - 4x²y + y³ + 2
Ariel: y³ - 4x²y + 3x³ + 2
The standard form of a polynomial with the variable x is:
P(x) = ax³ + bx² + cx + d
This means that the power of the polynomial decreases till it gets to 0
Using the above form as a guide, the correct student is Marcus.
Marcus is correct because the power of the polynomial decreases till it gets to 0
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What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answers
in the exponent of 3.
So, the given function is actually f(x) = 3^x +9
Now, we need to find the range of given
function.
We can see that first term is and exponential
term 3^x and second term is 9
We know that 3^x will always be greater than
O.
Therefore, 3^x +9 would always be greater
than 9.
Therefore, range would be y>9.
So, the correct option is B) (y | y > 9}.
The egg delivery truck arrives to savers supermarket with 250 dozen eggs. how many total eggs are in that truck.
Answers
Answer:
3000
Step-by-step explanation:
12x250=3000
Match each equation with the number that makes it true.
Answers
the first equation is 15
the second equation is 3
the third equation is 17
the fourth equation is 7
the fifth equation is 6
the sixth equation is 50
the seventh equation is 2
the eighth equation is 5
the ninth equation is 11
the tenth equation is 31
Please can i have brainliest I did all answers correct I hope this helps you
I need help finding the slope and what m=
Answers
Apply the means-extremes property to the ratios of the corresponding sides to determine if the polygons are similar. has sides of length 2 cm, 3 cm, and 3.5 cm. has sides of length 4 cm, 6 cm, and 7 cm.
Answers
The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangles are given below.
The ratio of the sides of the triangles ΔABC and ΔDEF will be
AB / DE = BC / EF = CA / FD
2 / 4 = 3 / 6 = 3.5 / 7
1 / 2 = 1 / 2 = 1 / 2
The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.
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This is a substitution problem
Julianna has thirty two pieces of candy in a candy jar. Julianna only has two kinds of candy,
jolly rangers and twix. For every four twix bars, she has two pieces of jolly rangers. How many
pieces of each candy are in the candy jar?
Answers
a. The number of twix bars is 21
b. The number of jolly rangers is 11.
Julianna has thirty two pieces of candy and has four twix bars for every two jolly rangers, we need to find the ratio of candy bars.
What is the ratio of candy bars?Let
x = number of twix bars and y = number of jolly rangers.Since for every four twix bars, she has two pieces of jolly rangers, the ratio of candy bars is
x:y = 4:2 = 2:1
a. Number of twix barsThe number of twix bars is 21
The number of twix bars x = ratio of twix bars/total ratio × total number of candy bars
So, x = 2/(1 + 2) × 32
= 2/3 × 32
= 64/3
= 21.33
≅ 21
So, the number of twix bars is 21
b. Number of jolly rangersThe number of jolly rangers is 11.
The number of jolly rangers y = ratio of jolly rangers/total ratio × total number of candy bars
So, y = 1/(1 + 2) × 32
= 1/3 × 32
= 32/3
= 10.66
≅ 11
So, the number of jolly rangers is 11.
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see attached question please please help!!
Answers
Based on the size of the pool that Mr. DelGrande wants to build, the ratio of the Olympic pool to the smaller pool is 2.5:1 and the area of an Olympic pool is 1,250 m².
What is the ratio of the length of an Olympic pool to Mr. DelGrande's pool?The ratio of the pools is:
Olympic pool length : Mr. DelGrande pool
50 : 20
Simplest terms give:
50 / 20 : 20 / 20
2.5 : 1
What is the area of a regulation Olympic Pool?Given the area of Mr. DelGrande's pool, the area of an Olympic pool is:
= Ratio ² x Area of Mr. DelGrande pool
= 2.5² x 200
= 1,250 m²
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a magnifying glass makes objects appear 2.54 times largers than their actual size. How large does a 6-millimeter seed appear in the magnifying glass
Answers
Answer:
15.24 millimeters
Step-by-step explanation:
6 * 2.54 = 15.24 mm.
Answer: should be 15.24
Step-by-step explanation: quick maths
Round 7.09 to the nearest tenth
Answers
Answer:
7.1
Step-by-step explanation:
To round 7.09 to the nearest tenth, you must use the hundredths' place value of 7.09, which is 9 and equal or more than 5. Therefore, the tenths value of 7.09 increases by 1 to 7.1.
ok im super confused bc like it ask me put i dont know what to put.............pls help me
Answers
Answer:
u drag the green dot thing over to the coordinate (6,8)
Step-by-step explanation:
i put a black dot where i think ur supposed to drag the green dot to
The table below represents a breakdown of food costs for Eddie, a traveling
salesman. How much did he spend in total for food on Tuesday?
Mon.
Tue.
Wed.
Thurs.
Fri.
Breakfast $7.88
$12.02
$9.64
$6.98
$13.30
Lunch
$13.41
$11.79
$14.55
$16.09
$10.76
Dinner
$18.80
$22.13
$20.79
$24.82
$16.74
OA. $40.09
OB. $42.56
OC. $41.23
OD. $45.94
SURMIT
Answers
The total amount of money that was spent on lunch on Tuesday is $45.94.
What is the total amount spent on food?
The total amount that was spent on food on Tuesday can be determined by adding the amount spent on breakfast, lunch and dinner. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Total amount spent = 22.13 + 12.02 + 11.79 = $45.94
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THIS IS EASY BUT PLEASE HELP ME IM BIT SLOW
Answers
Answer:
A: Isosceles (two sides the same)
B: Equilateral (all sides the same)
C: Scalene (all sides different)
Step-by-step explanation:
2. equilateral
3. scalene
What is the value of y?
2
5
7
8
Answers
confused by your question
Wyatt has a loyalty card good for a discount at his local hardware store. To find the
total he has to pay, before tax, he multiplies the prices by 0.8. What percent discount
does the card give?
Answers
Answer:
80%
Step-by-step explanation:
You multiple .8 by 100 to find percentage, giving you 80%.
Answer:
i don’t know
Step-by-step explanation:
I don’t know
what is 40% of 526,367.50
Answers
Answer:
[tex]210547[/tex]
Hope this helps. :)
Answer:
210547
Step-by-step explanation:
Multiply 526, 367.50 by 40 percent than the answer you get from that subtract from 526,367.50 then you get 210547.
Hope this Helps!
:D
You travel 10 miles north and then 3 miles west.
How many miles are you from your starting location?
Round your answer to the nearest tenth.
Answers
It’s just the Pythagorean theorem 10 squared plus 3 squared is 109
The square root of 109 is approximately 10.4
Help please
5x-2y=-10
Answers
Answer:
[tex]5x - 2y = - 10 \\ 5x = - 10 + 2y \\ x = \frac{ - 10 + 2y}{5} \\ \\ [/tex]
when y=0,-5,5,-10,10
then x=-2,-4,0,-6,2