The state of Connecticut is approximated by a rectangle 100 mi by 50 mi.
Hartford is approximately at the center of Connecticut. If a meteor hit the
earth within 200 mi of Hartford, find the probability that the meteor landed in
Connecticut.
Answers
Answer:
4.0%
Step-by-step explanation:
If we assume that potential impact sites are uniformly distributed over the area, the probability of interest is the ratio of the area of Connecticut to the area of the circle within 200 miles of Hartford.
__
area of circleThe area of a circle with radius 200 miles is ...
A = πr²
A = π(200 mi)² = 40000π mi² ≈ 125,664 mi²
area of CTThe area of a rectangle 100 miles by 50 miles is ...
A = LW
A = (100 mi)(50 mi) = 5000 mi²
probabilityThe probability of interest is the ratio of these areas:
p(impact in CT) = (5000 mi²)/(125664 mi²) ≈ 0.03979
The probability the meteor landed in Connecticut is about 4.0%.
Related Questions
A right triangle has a 120° angle and 190° angle. What is the measure of the third angle?
Answers
Answer:
i measures of the third angle is 18degrees
Which of the sets of ordered pairs represents a function? (5 points) A = {(2, −2), (5, −5), (−2, 2), (−5, 5)} B = {(4, 2), (4, −2), (9, 3), (9, −3)} Group of answer choices Only A Only B Both A and B Neither A nor B
Answers
Answer:
A
Step-by-step explanation:
30. What is the length of XPY in terms of pie ?
675 m
225 m
457 m
15 m
Answers
Answer:
circumference = 2 x PI x r= 2 x 3.14 x 30 = 60 PIthe area from x to y = 90 degrees so XPY would be 360 - 90 = 270 degrees or 3/4 of a full circleso XPY = 60 x 3/4 = 45 PI meters
Complete the Proof Statements Reasons 1. ABCD is a given AC BD 2. AD BC 3. 4. AABC=ABAD 5 ZDAB=LCBA 6. 7. ABCD is a rectangle 1. 2. 3. 4. 5. 6. 7. Congruent supp. angles are right angles 8. Given: ABCD is a parallelogram AC = BD Prove: ABCD is a rectangle SSS Triangle Congruence Theorem mZDAB = 90° m/CBA = 90° Reflexive Property of Congruence ZDAB and ZCBA are supplementary Definition of Rectangle O B CPCTC If the quad is a both pairs of opposite sides are congruent Consecutive angles in a are supplementary AB = AB
Answers
1) ABCD is a parallelogram, [tex]\overline{AC} \cong \overline{BD}[/tex] (given)
2) [tex]\overline{AD} \cong \overline{BC}[/tex] (if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent)
3) [tex]\overline{AB} \cong \overline{AB}[/tex] (reflexive property of congruence)
4) [tex]\triangle ABC \cong \triangle BAD[/tex] (SSS Triangle Congruence Theorem)
5) [tex]\angle DAB \cong \angle CBA[/tex] (CPCTC)
6) [tex]\angle DAB[/tex] and [tex]\angle CBA[/tex] are supplementary (consecutive angles in a parallelogram are supplementary)
7) [tex]m\angle DAB=90^{\circ}, m\angle CBA=90^{\circ}[/tex] (congruent supplementary angles are right angles)
8) [tex]ABCD[/tex] is a rectangle (definition of rectangle)
All the missing statements with the respective reasons are given below.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Statement 1.
ABCD is a parallelogram,
AC ≅ BD
Reason: Given.
Statement 2.
AD ≅ BC
Reason: if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent.
Statement 3. AB ≅ AB
Reason: reflexive property of congruence.
Statement 4. ΔABC ≅ ΔBAD.
Reason: SSS Triangle Congruence Theorem
Statement 5. ∠DAB ≅ ∠CBA
Reason: CPCTC
Statement 6. ∠DAB and ∠CBA are supplementary
Reason: consecutive angles in a parallelogram are supplementary.
Statement 7. m∠DAB = 90° and m∠CBA = 90°
Reason: congruent supplementary angles are right angles.
Statement 8. ABCD is a rectangle.
Reason: definition of a rectangle.
Therefore, all the required points are given above.
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PLSS HELP ME WITH THIS !! 20 POINTSS
Answers
Answer: constant of proportionality = 2.5
What is the distance between the following points?
Answers
Answer:
7.615773105864
Step-by-step explanation:
[tex]\text{let A and B be the points of coordinates} \ A\left( 3,-9\right) \text{and} \ B\left( 6,-2\right)[/tex]
[tex]AB=\sqrt{\left( 6-3\right)^{2} +\left( -2-(-9)\right)^{2} }[/tex]
[tex]=\sqrt{\left( 3\right)^{2} +\left( 7\right)^{2} }[/tex]
[tex]=\sqrt{58} =7.615773105864[/tex]
whats the next term of arithmetic sequence 24,16,8,0
Answers
Answer:
-8, 16, ...
Step-by-step explanation:
You are subtracting 8 everytime. Therefore, you would go into negatives from here.
Answer:
24, 16 , 8 , 0
\/ \/ \/
-8 -8 -8
Step-by-step explanation:
for you to get 8 you subtract the first term with the second term
Three trends each have a balance of $5,000 on their credit cards with a 25%APR. They've
decided that they will not make any other purchases on the cards until they pay of the debt
and make varying amounts of monthly paymentes
• Sharon can only make the credit card minimum payment, $150 per month
• Ceollia can set aside $400 per month to pay back her dett
• Alexander can pay $800 per month for his credit card
After 5 months, how much will each person have paid in interest so far and how large will
their remaining balance be? Use the formulas below to calculate their interest and balance
for each month
Hint Credit card interest is typically compounded daily so n=365Time here is in years, so
make sure you use a fraction for your t value. Need to show monthly interest and balance paid monthly for first 5 months on each person.
Answers
here i hope this exaple helps but for the time being while i solve it heres this example
if you currently owe $500 on your credit card throughout the month and your current APR is 17.99%, you can calculate your monthly interest rate by dividing the 17.99% by 12, which is approximately 1.49%. Then multiply $500 x 0.0149 for an amount of $7.45 each month.
which value make the inequality c+10<17
Answers
Answer:
c < 7
Step-by-step explanation:
Given inequality:
c + 10 < 17
Subtract 10 from both sides:
⇒ c + 10 - 10 < 17 - 10
⇒ c < 7
Let's solve
c+10<17c<17-10c<7The solution set is
(-oo,7)
XYZ is a right triangle If XY = 8, what is XZ?
Answers
Answer:
square root of 64 minus yz square
Order the following from least to greatest.
0.98, 3/5, 4, 1/2, 0.4
Answers
Answer:
.4, 1/2, 3/5, .98, 4
Step-by-step explanation:
give me brainliest please
Suppose Marco draws a cross-section of the cube shown below and the result is a triangle. Describe how Marco could have sliced the cube to produce a triangular cross-section.
Answers
The biggest triangle he can get is by cutting along the diagonals of the three visible faces.
Given the equation y= 3x + 8, what would be the value of y be when x = 3?
A. 17
B. 14
C. 1
D. 15
Answers
Answer:
[tex]y = 17[/tex]
Step-by-step explanation:
We were given the equation
[tex]y = 3x + 8[/tex]
and we were told that x = 3, therefore y would be
[tex]y = 3x + 8 \\ y = 3(3) + 8 \\ y = 9 + 8 \\ y = 17[/tex]
Determine which expressions represent purely real numbers and which expressions represent non-real complex numbers. -i^2+i^3 7-5i √ 6 0+9i √(-5)^2 -12 2 -7i^2
purely real number
non-real complex number
Answers
Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
What are Purely real numbers and Non-real complex numbers?Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
The given expressions can be simplified in the following manner,
[tex]-i^2+i^3 = -(\sqrt{-1})^2+(\sqrt{-1} \times \sqrt{-1} \times \sqrt{-1}) = 1 -i[/tex] 7-5i [tex]\sqrt{-6} = \sqrt{-1 \times 6} = \sqrt{-1} \times \sqrt{6} = 0+ i\sqrt{6}[/tex]i⁶ = (i²)³ = (-1)³ = -1 = -1 +0i0+9i [tex](\sqrt{-5})^2 = (\sqrt{-1 \times 5})^2 = -1 \times 5 = -5+0i[/tex] -12 = -12+0i[tex]2 -7i^2 = 2-7(-1) = 2+7 = 9+0i[/tex]Purely real numbers (a+0i)
-1 +0i-5+0i-12+0i9+0iNon-real complex number (0+bi)
1-i7-5i0+i√60+9iLearn more about Purely real numbers and Non-real complex numbers:
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Answer:
Step-by-step explanation:
go to BYJU's learning app and get to expert answer
If JK = 20, KL = x + 9, and JL = 6x + 9, what is KL?
Answers
[tex]\underset{\leftarrow ~~ 6x+9 ~~ \to }{J\stackrel{20}{\rule[0.35em]{15em}{0.25pt}} K\stackrel{x + 9}{\rule[0.35em]{10em}{0.25pt}} L} \\\\\\ \stackrel{JL}{6x+9}~~ = ~~\stackrel{JK}{20}+(\stackrel{KL}{x+9})\implies 6x+9=29+x\implies 5x+9=29 \\\\\\ 5x=20\implies x=\cfrac{20}{5}\implies x=4\hspace{5em}\boxed{\underset{KL}{\stackrel{(4)~~ + ~~9}{13}}}[/tex]
What is the volume?
2 mm
4 mm
2 mm
Answers
Answer:
16mm
Step-by-step explanation:
that's because volume is lwh ( length X width X height)
a regular number cube is rolled. What is the probability that a 3 will not be rolled?
•1/6
•1/2
•4/5
•5/6
Answers
Answer:
5/6
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
probability(event) = (number of desired outcomes)/(total number of outcomes)
The total number of outcomes is 6 since there are 6 different sides on the cube.
The number of desired outcomes is 6 minus 1 for rolling a 3, so it is 5.
p(not 3) = 5/6
The probabilities for four different simple events are given. Of the four, which is LEAST LIKELY to occur?
Question 1 options:
0.01
0.35
0.5
0.9
Answers
Answer:
Step-by-step explanation:
We are supposed to find the least likely, which means we are looking for the smallest number.
.9 is the largest
.5 is next
.35 is second to smallest
A is the answer 0.01
Still stuck? Get 1-on-1 help from an expert tutor now.
Students measured the length of different earthworms using centimeters (cm).The lengths were:
14 cm, 12.5 cm, 13 cm, 18 cm, 17 cm, 16.75 cm, 19 cm, 12.5 cm, 15 cm
If the students were asked to describe the difference in length of the worms, which answer would be best and why? (5 points)
Group of answer choices
6.5 cm; this is found by determining the range which is found by finding the difference between the greatest length and the least length
12.5 cm; this is found by determining the mode which is found by finding the number that occurs most frequently in a data set
15 cm; this is found by determining the median which is found by ordering the numbers from least to greatest and finding the middle number
15.3 cm; this is found by determining the mean which is found by finding the sum of all of the lengths and dividing by the total number of worms
Answers
The correct option regarding the difference in the length of the worms is given by:
6.5 cm; this is found by determining the range which is found by finding the difference between the greatest length and the least length.
What is the range of a data-set?It is given by the difference of the highest value by the lowest value in the data-set.
In this problem, the difference is exactly what we want to estimate, hence we need to consider all measures(which removes the mode and the median), and find the largest lowest and the highest, which is the range, hence:
19 cm - 12.5 cm = 6.5 cm.
Which means that the correct option is given by:
6.5 cm; this is found by determining the range which is found by finding the difference between the greatest length and the least length.
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HELP ASAP!! AND PLEASE EXPLAIN! The pyramid has a square base of 230 meters on each side and a height of 147 meters. Find the volume of the pyramid if the slant height is 186.63 meters.
Answers
Answer:
2,592,100 m³
Step-by-step explanation:
Volume of Square Pyramid
V = 1/3a²hV = 1/3(230)²(147)V = 49 x 52900V = 2,592,100 m³Stanley walks a round-trip of 1.75 miles to work every day. How many miles will he walk in 5.5 days
A. 9.625 miles
B. 96.25 miles
C. 962.5 miles
D. 9625 miles
Answers
Multiply miles per day by number of days
5.5 x 1.75 = 9.625
answer: A. 9.625 miles
Explanation: 1.75 x 5.5 = 9.625
Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.
Long beakNot a long beakTotalFlies11719Does not fly31315Total142034
Answers
The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.
What is an odds ratio?An odds ratio is a measure of the strength of an association with the exposure and outcome.
The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).
Data and Calculations:Contingency Table
Flies Does not fly Total
Long beak 11 7 19
Not a long beak 3 13 15
Total 14 20 34
Probability of long beaks flying = 0.79 (1/14)
Probability of not having long beaks flying = 0.21 (3/14)
Odds ratio = 3.76 (0.79/0.21)
Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.
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Answer:
Step-by-step explanation:
6.81
URGENT! please answer. i'll give 5 stars + brainilest if correct
To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level)
b
=
560
meters from the base of the mountain to the top of the mountain is
β
=
51
∘
. The students then walk
a
=
1850
meters straight back and measure the angle of elevation to now be
α
=
34
∘
. If we assume that the ground is level, use this information to estimate the height of the mountain.
The height of the mountain is
_____ meters.
Answers
Answer:
times the nimbers
Step-by-step explanation:
240
Margot has 8 kilograms of apples.how many liters Of apple juice can Margot make. How do l do this?????
Answers
Answer:
so about 4?
Step-by-step explanation:
1 kilogram = 1,000 grams
2 kilograms = 2 times 1,000 which equals 2,000 grams
2,000 grams makes one liter
uhh this is just an educated guess...
Bell sells pies each week at the farmers market. She spends $65 on materials and charges $10 per pie. She hopes to make a profit of at least $15 per hour. What constraints might bell want to set?
Answers
Answer:
43.33
Step-by-step explanation:
You will start out by putting 65 in time 10 divide by 15 and that will give you your answer
Answer:
43.33
Step-by-step explanation:
You will start out by putting 65 in time 10 divide by 15 and that will give you your answer
Find the standard deviation of the data, 12, 19, 9.
Answers
Answer:
4.19
Step-by-step explanation:
Find the mean:
[tex]\text{Mean}=\frac{12+19+9}{3}=\frac{40}{3}[/tex]
Find the standard deviation:
[tex]\text{Standard Deviation}=\sqrt{\frac{(12-\frac{40}{3})^2+(19-\frac{40}{3})^2+(9-\frac{40}{3})^2}{3}}=\sqrt{\frac{158}{9}}\approx4.19[/tex]
3 What is the solution to ža>-16? o a O a>-21 a 21 O a
Answers
Answer: The answer is the first option: [tex]a > -21\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] × [tex]a > -16[/tex]
[tex]\frac{3}{4}a\cdot \frac{4}{3} > -16\cdot \frac{4}{3}[/tex]
[tex]\frac{3}{4}\cdot \frac{4}{3}a > -16\cdot \frac{4}{3}[/tex]
[tex]a > -16\cdot \frac{4}{3}[/tex]
[tex]a > \frac{-16\cdot 4}{3}[/tex]
[tex]a > \frac{-64}{3}[/tex]
Find the area of the figure. Round to the nearest hundredth where necessary.
55 mm
32.5 mm
12.5 mm
12.5 mm
Answers
[tex]\bold{ANSWER:}[/tex]
746 mm^2
[tex]\bold{SOLUTION:}[/tex]
Write the equation of the line that passes through the point
(1,−5) and with the slope of −3. Write the in slope-intercept form.
Answers
Answer:
y = -3x -2
Step-by-step explanation:
Hi there!!
We're given that a line has a slope of -3 and it contains the point (1, -5)
We want to write the equation of this line in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
As we are already given the slope, we can immediately plug it into the equation.
Replace m with -3 in y=mx+b.
y = -3x + b
Now we need to find b
As the equation passes through the point (1, -5), we can use its values to help solve for b.
Substitute 1 as x and -5 as y:
-5 = -3(1) + b
Multiply
-5 = -3 + b
Add 3 to both sides
-2 = b
Substitute -2 as b into the equation
y = -3x - 2
Hope this helps!
Topic: finding the equation of a line
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Given that 5 cos (x+8.5)° - 1 = 0
0° ≤x≤ 90, calculate correct to the nearest degree, the value of x.
Answers
Answer:
x = 70
Step-by-step explanation:
To solve for x, use inverse operations to undo the operations performed on x.
__
5cos(x +8.5)° -1 = 0 . . . . given
5cos(x +8.5)° = 1 . . . . . . add 1
cos(x +8.5)° = 1/5 . . . . . divide by 5
x° +8.5° = arccos(1/5) . . . . take the inverse cosine
x° = arccos(1/5) -8.5° ≈ 70° . . . . evaluate the expression
The value of x is 70.