The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. suppose intensity is 8000 units at a distance of 2 miles. what will the intensity be at a distance of 11 miles? round your answer to the nearest unit. a. 247 units b. 228 units c. 264 units d. 290 units
Answer:
The ratio of the new distance to the old distance is (11/2) .
The intensity is inversely proportional to the square of the distance,
so the new intensity will be (2/11)² times the old intensity.
Intensity = 8,000 (2/11)² =
32,000 / 121 = 262.463 units
Rounded to the nearest whole unit: 262 units
Step-by-step explanation:
264 units of intensity came from a distance of 11 miles option (c) 264 units is correct.
It is given that the intensity is 8000 units at a distance of 2 miles.
It is required to find the intensity at a distance of 2 miles.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station.
Suppose the Intensity of the signal is I and the distance is d, then:
[tex]\rm I \propto\frac{1}{d^2}[/tex]
Intensity from the station [tex]\rm I_1=8000 \ units[/tex]
[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_1=2 \ miles[/tex]
Intensity from the station [tex]=\rm I_2[/tex]
[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_2=11 \ miles[/tex]
[tex]\rm \frac{I_2}{I_1} = \frac{d_1^2}{d_2^2}[/tex] (From the proportional relation)
[tex]\rm \frac{I_2}{8000} = \frac{2^2}{11^2}[/tex]
[tex]\rm I_2 =8000\times\frac{4}{121} \\\\\rm I_2 = 264.46 \ units[/tex] ≈ 264 units
Thus, the 264 units of intensity came from a distance of 11 miles.
Learn more about the fraction here:
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1. Convert 8cm³ into m³
2. Convert 0.7m³ into cm³
3. Convert 4000000cm³ into m³
1. Convert 8cm³ into m³
= 8.0E-6 m³
(divide the volume value by 1e+6)
2. Convert 0.7m³ into cm³
= 700000 cm³
(multiply the volume value by 1e+6)
3. Convert 4000000cm³ into m³
= 4 m³
(divide the volume value by 1e+6)
3. Two of the lines below are parallel. Which two? Justify your answer.
y= 3x - 5 y=-3x + 7 y - 3x = -12 y + 1/3x=8
Answer:
line 1 and 3
Step-by-step explanation:
Parallel lines have the same slope.
So if we're asked to identify a pair of parallel lines, we can just take a look at the slope (the number before x)
The first one is y=3x-5. Okay.
The second one is y=-3x+7. So the second line isn't parallel to the first line.
The third line is y-3x=12, or y=3x+12.
So the 3rd line is parallel to the 1st line :)
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
The lengths of a particular snake are approximately normally distributed with a given mean mu = 15 in. and standard deviation sigma = 0.8 in. what percentage of the snakes are longer than 16.6 in.?
The percentage of the snakes is longer than 16.6 in. with a mean of 15 in. and a standard deviation of 0.8 in. is 2.275%.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The lengths of a particular snake are approximately normally distributed with a given mean = 15 in. and standard deviation = 0.8 in.
Then the percentage of the snakes is longer than 16.6 in. will be
[tex]z = \dfrac{ x - \mu }{ \sigma }\\\\z = \dfrac{16.6-15}{0.8}\\\\z = 2[/tex]
Then we have
[tex]\rm P(x > 16.6) = P(z > 2) = 0.02275 \ or \ 2.275 \%[/tex]
More about the normal distribution link is given below.
https://brainly.com/question/12421652
Answer:
D, 5%
Step-by-step explanation:
edge
Which quadratic equation is equivalent itto * (x - 4) ^ 2 - (x - 4) - 6 = 0 ?
Answer:
[tex]x2 - 9x + 14 = 0[/tex]
Step-by-step explanation:
x2 - 9x + 14 = 0
tan x * csc x = sec x
Answer:
see explanation
Step-by-step explanation:
using the identities
tanx = [tex]\frac{sinx}{cosx}[/tex] , cscx = [tex]\frac{1}{sinx}[/tex] , secx = [tex]\frac{1}{cosx}[/tex]
consider left side
tanx × cscx
= [tex]\frac{sinx}{cosx}[/tex] × [tex]\frac{1}{sinx}[/tex] ( cancel sinx on numerator/ denominator )
= [tex]\frac{1}{cosx}[/tex] × 1
= secx = right side
4/8 + 8 7/8 (this is fractions)
Answer:
9 3/8 as a fraction or 9.375 as a decimal
Step-by-step explanation:
4/8 + 8 7/8 = 75/8= 9 3/8= 9.375
Why would neighborhoods with more station wagons tend to have more
playgrounds?
A. Adoring crowds of children like to follow station wagons to the
nearest playground.
B. Playground equipment dealers tend to buy station wagons and
then have kids to fill them.
C. Families with children tend to own station wagons and move to
neighborhoods with playgrounds.
D. Playgrounds are made from former used car lots (which used to
sell station wagons).
O E. Station wagon owners like to build playgrounds.
Answer:
C
Step-by-step explanation:
Based on my knowledge, thast what i think it is, but im not sure
divide and simplify. − 8/ 15 ÷ − 3/ 5
What is 2x+3+8x=3x+9x+7
Answer:
x=-2
Step-by-step explanation:
Hey there!
In order to solve this equation, you need to combine like terms
The equation after combining the x terms and the contants will look like this
10x+3=12x+7
Now you have to take 10x away from both sides
3=2x+7
Now bring all the constants to the left side
3-7=2x
Simplify
-4=2x
divide 2 on both sides to get x by itself
x=-2
So, the answer is x=-2
7.9, 7.8, 7.7, 8.8, 9.2, 8.7, 7.3, 8.0, 7.9, 7.6
What is the Mean??
Answer:
8.09
rounded to the nearest tenth ; 8.1
Step-by-step explanation:
Mean is adding all the data together than dividing by the number of data points
7.9 + 7.8 =
15.7 + 7.7 =
23.4 + 8.8 =
32.2 + 9.2 =
41.4 + 8.7 =
50.1 + 7.3 =
57.4 + 8.0 =
65.4 + 7.9 =
73.3 + 7.6 =
80.9
80.9 / 10 = 8.09
rounded to the nearest tenth = 8.1
Solve the following system of linear equations algebraically.
3x + y = 5
5x – 4y = -3
3x+y=5 & 5x-4y=-3
3x+5x=8x+y-4y=-3
8x+y-4y=-3
8x+3y=-3
-3 -3
8x=-6
x = 1 and y = 2.
Step-by-step explanation:
to do this, i changed the form of one of the equations so it was in the y= form then plugged it into the pther equation to solve for x. once i had x i plugged it into one of the equation to get y! hope this helps
Given that a+b=7; and a-b=3.. find the following, 2^a*2^b ( 2 to the power of a * 2 to the power of b) Please help asap, Thanks! :)
Answer:
128
Step-by-step explanation:
first solve the equations. a+b=7. a-b=3. a=3+b .Hence a(3+b)+b=7. 3+b+b=7. 3+2b=7. 2b=7-3. 2b=4. b=2. a-2=3. a=5. 2^5×2^2=128You received your $1,200 stimulus check from the government due to the coronavirus. If you choose to invest this into an investment account that pays 5.25% compounded continuously (rather than spending it), how long will it take to double your money?
Answer: IRS has sent $6 billion in stimulus payments just in June. Here's how to track your money Your stimulus check could be on its way, along with child tax credit money and unemployment tax refunds.
Step-by-step explanation:
Maryam scored an 8 out of 10 on her spelling test one week. The next week, her score decreased by 25%. What was her score for the second week?
a.) 5 out of 10
b.) 6 out of 10
c.) 7 out of 10
d.) 4 out of 10
Emma buys a game for $26.84 she gives the clerk $30.00. List Emma’s change using the least amount of dollar bills and coins
Answer:
4 dollars, a dime, a nickel, and a penny
Answer:
4 dollars
1 dime
1 nickel
1 penny
Step-by-step explanation:
what are the guidlines
Answer:
A guideline is a statement by which to determine a course of action. A guideline aims to streamline particular processes according to a set routine or sound practice.
100 points !! 3 answers !!
Instructions: Find the missing side. Round your answer to the nearest tenth.
#1
cos28=x/25x=25cos28x=22.1#2
cos26=x/15x=15cos26x=16.7#3
tan41=x/16x=16tan41x=14Answer:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuseGiven:
[tex]\theta[/tex] = 28°A = xH = 25[tex]\implies \sf \cos(28^{\circ})=\dfrac{x}{25}[/tex]
[tex]\implies \sf x=25cos(28^{\circ})[/tex]
[tex]\implies \sf x=22.1\:(nearest\:tenth)[/tex]
Given:
[tex]\theta[/tex] = 26°A = 15H = x[tex]\implies \sf \cos(26^{\circ})=\dfrac{15}{x}[/tex]
[tex]\implies \sf x=\dfrac{15}{\cos(26^{\circ})}[/tex]
[tex]\implies \sf x=16.7\:(nearest\:tenth)[/tex]
Given:
[tex]\theta[/tex] = 41°O = xA = 16[tex]\implies \sf \tan(41^{\circ})=\dfrac{x}{16}[/tex]
[tex]\implies \sf x=16\tan(41^{\circ})[/tex]
[tex]\implies \sf x=13.9\:(nearest\:tenth)[/tex]
A pharmacist orders medications for a total of $6,439.65.a 6 44% discount is given if payment is made within
15 days, and a 2.5% discount is given if payment is made within 30 days. how much money can be saved by paying in 15 days instead of 30 days?
Answer:
2,672.45475 (round if needed)
Step-by-step explanation:
44 percent to a decimal is 0.44
2.5 percent to a decimal is 0.025
6,439.65 × 0.44 = 2833.446 (within 15 days)
6,439.65 × 0.025 = 160.99125 (within 30 days)
2833.446 - 160.99125 = 2,672.45475
HELP PLEASE?!!
Taking post test: exponential and logarithmic functions
Answer:
k = 2
Step-by-step explanation:
f(2) = 1
g(2) = 2
g(x) is double of f(x)
CHOOSING BRAINLIEST
A counselor determined that 60% of the senior class had taken a precalculus course and that 15% of the senior class had taken both a precalculus course and a statistics course?
What percentage of seniors who took a precalculus course also took a statistics course?
Using conditional probability, it is found that 25% of seniors who took a precalculus course also took a statistics course.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Senior student took a precalculus course.Event B: Senior student took a statistics course.The probabilities given are [tex]P(A) = 0.6, P(A \cap B) = 0.15[/tex].
The desired probability is P(B|A), hence:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.6} = 0.25[/tex]
0.25 = 25% of seniors who took a precalculus course also took a statistics course.
More can be learned about conditional probability at https://brainly.com/question/14398287
Answer the statistical measures and create a box and whiskers plot for the following set of data. 4,4,5,5, 6, 6, 8, 10, 11, 11, 12, 14 Min: Q1: Med: Q3: Max: Create the box plot by dragging the lines: 2 3 4 b 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Answer:
Step-by-step explanation:
First you take your smallest number, which in this case is 4 - then you find your maximum number which is 14. Then we can list these numbers on a piece of paper and cross a number out from each side until you reach the middle number which would be 8. Then you go from the min to the middle number which would be 5. Then you repeat between the max number and the middle number which is 11. So your minumum would be 4, max would be 14, Q1 would be 5 Median would be 8 and Q3 would be 11. Let me know if I got it right! I haven't done it for a while, but I am pretty sure this is correct..
The missing values are:
Minimum value = 4 ,
Q₁ = 5 ,
Median = 6,
Q₃ = 11
Maximum value = 14.
What are Quartiles?The set of values known as quartiles divides a batch of data into four equal portions.
We have,
Minimum value = 4
Now, arrange the data in ascending order
4,4,5,5, 6, 6, 8, 10, 11, 11, 12, 14
Then, Quartiles
Q₁ = [ (n+1)/4]th term
= (12+1) / 4
= 3.25th term
= 3rd term + 0.25 ( 4th term - 3th term)
= 5 + 0.25 (5 -5)
= 5
Now, Median = (N/2)th term
= 12 /2
= 6th term
= 6
and, Q₃ = [3(n+1)/4]th term
= 3 × 3.25
= 9.75
= 9th term + 0.75( 10th term - 9th term)
= 11 + 0.75 (10 -10)
= 11
and, Maximum value = 14
Learn more about Quartiles here:
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#SPJ2
Is (10, 8) a solution to this system of equations?
2x - 5y = -20
X + 9y = 14
A
O a. Yes
b. No
Answer: No, there isn't anything showing that it is.
No
Step-by-step explanation:
Substitute value of x (10) & y (8) in both equation
x + 9y =14
10 + 9 x 8 = 82
(doesn't give us the output of 14)
2x - 5y = -20
2 x 10 - 5 x 8 = - 20
(this does, but both have to work)
Solution is at (-4.8,2.1):
2x +18y =28
2x - 5y = -20
(minus)
(18 - - 5 & 28 - - 20 those minus becomes a + )
23y = 48
÷23
y= 48/23
(2.1 to 1d.p)
Substitute y to find x
2x - 5y = -20
2x - 5 x 48/23 = - 20
2x - 240/23 = - 20
+240/23
2x = -220/23
÷2
x = - 110/23
X= -4.8 to 1d.p
(-110/23, 48/23)
Hope this helps!
Each week Samantha can pay as much $15 for her school at lunch. Write an inequality showing how much Samantha spends at lunch. Please help me!! I need an answer fast!
Answer:
To represent all the possible amounts that Samantha can pay, you will write that x is less than or equal to 15.
This means that any amount up to and including 15 is a possibility.
Step-by-step explanation:
Answer:
x≤15
Step-by-step explanation:
x means how much samantha is able to spend on lunch each week. she can spend only 15 dollars or less. -Crispin
How many milliliters are in 12.9 liters?
Answer:
12,900
Step-by-step explanation:
12.9 x 1000 = 12,900
Answer:
12,900. That is because you must multiply the amount to find the converted value, in this case, 12,900.
What is the difference between 1.1 and 1.10
Answer:
They are the same.
Step-by-step explanation:
1.1 and 1.10 are both the same, actually. There is just an extra 0 at the end. For example, 2 and 2.0 are the same, because 0 is 0, and it doesn't change your answer. The 0 could go on as in 1.100000000 but it will still equal 1.1 .
Hope this helped :)
Find the surface area of this figure.
Answer:
592 in²
Step-by-step explanation:
The surface area is the sum of the areas of the rectangles shown in the figure.
__
The light blue central rectangle is 12 in wide and a total of 36 in tall. Its surface area is ...
A = LW = (12 in)(36 in) = 432 in²
The two identical darker blue rectangles on the sides are each 8 in by 10 in, so their total area is ...
A = 2(LW) = 2(8 in)(10 in) = 160 in²
The total surface area of the figure is (432 +160) in² = 592 in².
The manager of a sporting goods store ordered 256 packages of football cards. There are 24 cards in each package how many cards did the manager order?
Answer:
6144
Step-by-step explanation:
The answer is 6144 because if you do 256×24 you will get 6144
NEED HELP ASAP!!! 100 POINTS!!!!!!! look at pic
Answer:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 3
Step-by-step explanation:
the coordinates of the points are
(1, - 6 ), (2, - 3 ), (3, 0 ), (4, 3 ), (5, 6 )
consider the values of y
- 6, - 3, 0, 3, 6
there is a common difference between consecutive terms, that is
- 3 - (- 6) = 0 - (- 3) = 3 - 0 = 6 - 3 = 3
this indicates the sequence is arithmetic with recursive rule
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + d ( d is the common difference )
here d = 3 , then recursive formula is
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 3 ; with a₁ = - 6
..............................................................
Answer:
yes
Step-by-step explanation:
yes
