Suppose an earthquake can be felt up to 80 miles from its epicenter. You are located at a point 60 miles west and 45 miles south of the epicenter. Do you feel the earthquake? If so, how many miles south would you have to travel to be out of the range of the earthquake?
Answers
Answer:
Yes (you are 75 mi from epicenter). Travel at least 7.91 mi south
Step-by-step explanation:
See the attached image.
The epicenter is the point at the upper right of the drawing. You are 60 miles west (left) and 45 miles south (down) from the epicenter. A right triangle is formed--apply the Pythagorean Theorem, (leg)^2 + (leg)^2 = (hypotenuse)^2.
[tex]x^2=60^2+45^2\\\\x^2=3600+2025\\\\x^2=5625\\\\x=\sqrt{5625}=75[/tex] This is within 80 mi, so you feel the quake.
Now (see image2) you go y miles south. You want the distance between you and the epicenter to be at least 80 mi. You have another right triangle with legs 60 and y + 45 and hypotenuse 80.
[tex](y+45)^2+60^2=80^2\\\\(y+45)^2+3600=6400\\\\(y+45)^2=2800\\\\y+45=\sqrt{2800}\\\\y=\sqrt{2800}-45 \approx 7.91 \rm mi[/tex]
Related Questions
a cylindrical jar of jam has a diameter of 6cm and a height of 8 cm. if the jar is 70% full of jam how many cubic centimeters of jam are in the jar? Please answer correctly
Answers
Answer: 158.26cm³
Step-by-step explanation:
First, we.need to calculate the volume of the cylinder and this will be:
Volume = πr²h
Volume = 3.14 × 3² × 8
Volume = 3.14 × 9 × 8
Volume = 226.08cm³
Since the jar is 70% full, the volume will be:
= 70% × 226.08cm³
= 0.7 × 226.08cm³
= 158.26cm³
Note:
Radius = Diameter/2 = 6cm/2 = 3cm
PLEASE HELP ME!!!!!!!! ASAP
Fill in the missing data labels on the histogram.
Answers
Answer:
0 - 9 = 1
10 - 19 = 2
20 - 29 = 2
30 - 39 = 4
40 - 49 = 6
Have a great day! :)
Which equations have 8 as a solution?
15-n=7 n + 3 = 12 4n = 32
64 : n = 8
Select all the equations that have 8 as a solution.
A. 15-n=7
B. n + 3 = 12
C. 4n = 32
D. 64:n = 8
Answers
Answers:
15 - n = 7
-15 -15
-n = -8
n = 8
4n = 32
n = 8
Select all the equations that have 8 as a solution.
Answers:
A and C
Explanation is above.
Hope this helps!
Answer:
The equations 15 - n = 7, 4n = 32, and 64 : n = 8 have 8 as a solution.
Step-by-step explanation:
Each equation will have work shown below :
15 - n = 7
For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to subtract and the inverse operation of that is addition. Since the original operation is subtraction, we need to add it by a negative sign to each side. In order to isolate the variables, we have to add -7 to both sides.
15 - n = 7
+ -7 + -7
8 = n
The right side has a sum of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.
4n = 32
For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to multiply and the inverse operation of that is division. In order to isolate the variables, we have to divide 8 to both sides.
4n = 32
/4 /4
n = 8
The left side has a quotient of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.
This is a ratio which is basically just the operation of division. For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to divide and the inverse operation of that is multiplication. Since the original operation is division, we need to multiply it by the reciprocal to each side. In order to isolate the variables, we have to multiply 1/8 to both sides.
64 : n = 8
* 1/8 * 1/8
8 = n
The right side has a product of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.
Which point would NOT be a solution to the system of linear inequalities shown below?
Answers
Answer:
(-1,1) would not be a solution to the system of linear inequalities presented in the problem. Simply substitute the x and y values in the coordinates provided to see if they would work as solutions.
Hope I helped, have a nice day :)
Answer:
(-1,1)
Step-by-step explanation:
If we try to substitute this values in the second inequality we have
1 > 4 (false)
which graph correctly represents
3x + y>72
A graph A
B. graph B
с graphic
D graph D
Answers
Answer:
The correct graph should have an x-intercept of 24, a y-intercept of 72, connected by a dashed line, with shading to the right
Step-by-step explanation:
y > -3x + 7
The correct graph should have an x-intercept of 7/3, a y-intercept of 7, connected by a dashed line, with shading to the right
A map of a highway has a scale of 2 inches equals 33 miles. The length of the highway on the map is 6 inches. There are 11 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch equals 30 miles. How far apart are the rest stops on the new map?
(nvm)
Answers
Answer:
The answer is "0.975"
Step-by-step explanation:
Please find the complete question in the attched file.
Find the remaining distance inside the original map
[tex]\to \frac{9}{6}=1.5 \ in[/tex]
Dividing the value by 6 because there are 7 rest stop:
[tex]\to \frac{2 \ inches}{39 \ inches} =\frac{1.5 \ inches}{x \ miles}\\\\\to x=39 \times \frac{1.5}{2}\\\\\to x=29.25 \ miles[/tex]
Finding the diatance of the rest stop in the new map
Using proportion:
[tex]\to \frac{1 \ inches}{30 \ miles} =\frac{x \ inches}{ 29.25 \ miles}\\\\\to x= \frac{29.25}{30}\\\\\to x=0.975 \ in[/tex]
Rachel rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that one number cube lands on a 1 and the other lands on an even?
Answers
Answer:
4/6. out of 1 2 3 4 5 6 only 3 number are even.but it says lands on 1 and the other lands on even. so 3 +1 = 4. sorry if it doesnt make sense
- A box of specialty baking flour holds 2 kilograms. How many angel food cakes can be made with a recipe that calls for 100 grams of flour?
Answers
Answer:
20
Step-by-step explanation:
1000g = 1 kil0
2 x 1000 = 2000g
Number of cakes = 2000 / 100 = 20
Evaluate. Write your answer as a fraction in simplest form.
Answers
Answer:
6/21
Step-by-step explanation:
2/3 x 2/3 x 2/3
6/21
Find the area of the figure.
Answers
Answer:
28.5 units²
Step-by-step explanation:
Shape 1 - ( length * width ) 3*5 = 15
Shape 2 - ( length * width ) 3*3 = 9
Shape 3 - ( height * base / 2 ) 3*1.5 = 4.5
2. The pitcher had 1 quarts of water. After Lena poured some of the water into
a bowl, the pitcher had') quart of water left How much water was poured in
the bowl?
Answers
Solve the problem.
The locations, given in polar coordinates, of two ships are (7 mi, 44°) and (8 mi, 104°). Find the
distance between the two ships.
A=3601 mi
B=10.63 mi
C=7.55 mi
D=4.00 mi
Answers
Show your work to solve me following. Will give Brainliest
Answers
Answer:
X = -32/11
Step-by-step explanation:
Help asap plz and thank you
Answers
Answer:
A
Step-by-step explanation:
z, duehdhdhd 2747 36veuend
Collete mapped her vegetable garden on the graph below. Each unit represents 1 foot. Collete plants an 8-foot row of lettuce in the garden. Which points could tell where the row of lettuce starts and ends?
Answers
Answer:
(-4,-1) and (-4,7)
Step-by-step explanation:
If Collete planted a row of lettuce, that means their coordinates must have the same vertical coordinate, or the same horizontal coordinate. Another important characteristic is that between those points, there must have 8 units of separation, because it's an 8-foot row.
Which number sentence is always true? Select all that apply.
negative + negative = negative
positive - negative = negative
negative + positive = positive
.positive - positive = positive
positive + positive = positive
.negative - positive = negative
Answers
2. true
3. false
4. true
5.true
6.true
Three statements that always hold true are,
negative + negative = negative.
positive + positive = positive.
negative - positive = negative.
What are some concepts related to arithmetic operations of odd and even numbers?Odd + Odd = Even.
Odd + Even = Even + Odd = )dd.
Even + Even = Even.
Odd × Odd = Even.
Even × Even = Even.
Odd × Even = Even × Odd = Odd.
Odd ÷ Odd = Even.
Even ÷ Odd = Even Or Odd.
Odd ÷ Even = Fraction/Decimal.
The true statement about positive and negative numbers are,
negative + negative = negative.
positive + positive = positive.
negative - positive = negative.
learn more about negative and positive numbers here :
https://brainly.com/question/17865861
#SPJ2
Which value of x is the solution to the equation 4(-3x+8)= -16?
answer choices:
1. -4
2. -2
3. 2
4. 4
explain
Answers
Answer:
x = 4
Step-by-step explanation:
4(-3x + 8) = -16
Divide both sides by 4
-3x + 8 = -4
Subtract 8 from both sides
-3x = -12
Divide both sides by -3
x = 4
. 4(-3x+8)=-16
-12x+32= -16
-12x=—48
X=4
CHECK:
4(-3(4)+8)=-16
4(-4)=-16
-16=-16
Approximate the distance between (0, -5) and (4, 1) to the nearest tenth, if necessary.
Answers
Answer:
7.7
Step-by-step explanation:
To solve this question we must use Pythagoras (a²+b²=c²) Let those two dots be A and B respectively.Imagine a line is drawn that pases through both dots,
Imagine that the line given is the hypotenuse (the longest side of a right-angled triangle) of a right-angled triangle and the other sides as a line from A going to the right, and a line from B going downwards, making the final vertexes for the triangle at coordinates: 0,-5 4,1 and 4,-5 (the vertex we made). now we find the lengths for the sides: 4 and 6 so we use these to plug them into pythagoras's equation:
4²+6²=c²
24+36=c²
√60=c
c=7.74....
But all we need is until the tenths so the answer is 7.7 (as the hundredths digit, 4, rounds down)
PLEASE HELP!!!!!!!!!!!
Answers
What expression is equivalent to -3z + 6y + 7z - 14?
Select all correct answers.
A. -10z - 14
B. 2(2z + 3y - 7)
C. 4z -6y +14
D. 4z + 6y - 14
E. 10z + 6y - 14
Answers
Answer:
immma send you the link friend me on hereStep-by-step explanation:
100
75
50
25
what is the slope of this image
Answers
Answer:
50
Step-by-step explanation:
Alright, so two of the points are: (0,25) (1,75)
Now we line them up:
(0,25)
(1, 75)
And, 0 to 1 has "1" as a difference.
That'll go on the bottom.
25 to 75 has a "50" difference.
That goes on top.
And then we get the slope of 50.
Hope this helped! :)
Answer:
Slope = 50
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
(1,75) (2,125)
125 - 75/2-1
125-75 = 50
2-1 = 1
50/1 = 50
What is the area of the sector?
Answers
Answer:
d
Step-by-step explanation:
100pi
Estimate 12.32+7.636 by first rounding each number to the nearest tenth.
pls help need the right answer thank u
Answers
===========================================================
Explanation:
12.32 rounds to 12.3 when rounding to the nearest tenth (aka one decimal place). The digit in the tenths place stays the same because the next digit over is not 5 or larger.
7.636 rounds to 7.6 when following the same rule
Adding those two rounded values gets us 12.3+7.6 = 19.9
hi! please help i’ll give brainliest
Answers
Answers:
deposition of eroded materials
Step-by-step explanation:
The heights of the pine trees in a certain forest are normally distributed, with a mean of 86 feet and a standard deviation of 8 feet.
Approximately what percentage of the pine trees in this forest are taller than 100 feet?
Answers
Answer:
4%
Step-by-step explanation:
We solve this question using z score formula
z = (x-μ)/σ,
where
x is the raw score = 100 feet
μ is the population mean = 86 feet
σ is the population standard deviation = 8 feet
Hence,
x > 100 feet
z = (100 - 86)/8
z = 1.75
Probability value from Z-Table:
P(x<100) = 0.95994
P(x>100) = 1 - P(x<100) = 0.040059
Converting to Percentage
= 0.040059 × 100
= 4.0059%
Approximately = 4%
Therefore, the percentage of the pine trees in this forest are taller than 100 feet is 4%
What is the Ka of a solution of 0.025M formic acid, if the pH 10 points
is 2.60? Answers
Ka = 0.025
Ka = 2.5x10^-4
Ka = 2.8x10^-4
Ka = 2.8x10^-2
Answers
Answer:
ka=2.8×10>4
Step-by-step explanation:
.$%_&<</___/%$
taylor's little sister is 3 feet and 4 inches tall. there are 2.54 centimetres in one inch. what is the height of taylor's sister in centimetres
Answers
Answer:
101.6 cm
Step-by-step explanation:
3 ft = 36 in
36 in + 4 in = 40 in
40 * 2.56 = 101.6 cm
5)
You are told that the median score on
these four cards is 9.5
Work out what the number is on the
bottom card.
7
15
8
Answers
Answer:
11
Step-by-step explanation:
7 8 11 15
median (8+11)/2=19/2=9.5
Which equation does the graph below represent
Answers
Answer:
4) y=-4x
Step-by-step explanation:
The lines goes down 4 units as it moves 1 unit right.
How many cubes with side lengths of
1
2
cm
2
1
cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text does it take to fill the prism?
Answers
question:
How many cubes with side lengths of \dfrac12 \text{ cm} 2 1 cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text does it take to fill the prism?
Step-by-step explanation:
81 cubes are needed to fill the prism
Step-by-step explanation:
Volume of prism = 3 cubic units
Side lengths of cube = 1/3
Therefore the volume of the cube is,
V = a³ (a = side of the cube)
V = 1/3 × 1/3 × 1/3
= ( 1/3 )³
= 1/27 cubic units
To find the number of cubes needed to fill the prism, we need to divide the volume of cube by volume of the prism.
Number of cubes to fill the prism= Volume of prism / Volume of cube
= 3÷1/27
=3×27/1
= 81
Therefore, 81 cubes are needed to fill the prism