Answer:
Point is at x = 4 m
Step-by-step explanation:
From the question, we can write the formula for intensity as;
I = strength/distance²
Now,
- Let x be the position from the stronger source
- Let k be the strength of the weaker light source
- 8k will be the strength of the stronger light source.
We are told that the two sources are 6 meters apart and one of them is 8 times stronger than the other.
Thus, the total illumination is;
I(x) = (8k/x²) + k/(6 - x)²
Using chain rule to get the critical points, let's find the first derivative and equate to zero;
I'(x) = -16k/x³ + 2k/(6 - x)³ = 0
Adding -16k/x³ to both sides, we have;
2k/(6 - x)³ = 16k/x³
Cross multiply to get;
2kx³ = 16k(6 - x)³
Dividing both sides by 16k to give;
x³/8 = (6 - x)³
Taking cube root of both sides to give;
x/2 = 6 - x
Multiply both sides by 2 to give;
x = 12 - 2x
x + 2x = 12
3x = 12
x = 12/3
x = 4 m
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Hello!
Answer:
(x + 1).
Step-by-step explanation:
Begin by using the rational root theorem to find possible factors of this equation.
We get the following:
±1, ±3, ±1/2, ± 3/2
We can use synthetic division to check numbers to see if they are a factor of the equation. After checking the possible numbers, -1 was found to produce a remainder of 0 when calculated:
-1 | 2 1 -4 -3
+ -2 1 3
2 -1 -3 0
Therefore, x = -1 is a possible root of this equation. Writing this as a factor would become:
x = -1
x + 1 = 0
(x + 1) is the factor.
I hope this helped you!
Can I get help with this problem?
Answer:
area of sector:
[tex] \frac{theta}{360} \times \pi \: {r}^{2} [/tex]
[tex] \frac{165}{360} \times \frac{22}{7} ( {8}^{2} )[/tex]
[tex] \frac{11}{24} \times \frac{1408}{7} [/tex]
[tex] \frac{1936}{21} [/tex]
[tex]92.19 \: {in}^{2} [/tex]
Answer:
the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]
Step-by-step explanation:
Use the fraction of the area of the circle associated with the red sector. Use a proportion to find the appropriate fraction knowing that a full circle [tex](360^o)[/tex] corresponds to the area:
[tex]Area=\pi\,R^2=\pi\, (8\,in)^2= 64\, \pi\,\,in^2[/tex]
then the proportion goes like:
[tex]\frac{64\,\pi\,\,in^2}{360^o} =\frac{sector}{165^o} \\ sector=\frac{64\,\pi\,165^o}{360^o}\,\,in^2\\sector\approx 92.15\,\,in^2[/tex]
Therefore, the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]
What is the measure of angle EFD? 37.5° 45° 47.5° 55°
Answer:
Step-by-step explanation:
Please try reposting with a picture so brainly users can help answer this question :)
The measure of angle < EFD = 47.5 degrees.
Option C is correct.
What is an Arc?An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference.
As, we know
The angle that an arc subtends at its centre is double that of its circumference.
In other words, the angle at the centre is twice as large as the angle at the perimeter.
So, <EFD = 95/2
or, <EFD = 47.5 degrees.
Learn more about Arc here:
https://brainly.com/question/18741430
#SPJ5
This month the company reported an increase in profit of 25%. If the company made $45,000 last month, how much did they make this month? A. $5,400 B. $5,625 C. $54,000 D. $56,250
Answer:
D. $56,250
Step-by-step explanation:
Calculate the increase.
45000 × (1 + 25%)
45000 × 1.25
= 56,250
They made $56,250 this month.
Answer:
D
Step-by-step explanation:
PLEASE HELP!!!
Fairview High School has an anime (Japanese animation) club that any
student can attend. The relative frequency table shows the proportion of
students in the high school who take Japanese and/or are in the anime club.
You have the correct answer.
=======================================================
Explanation:
Focus solely on the "in anime club" row. We do this because of the phrasing "given the student is in the anime club". We know for a fact that whoever is randomly picked, they are in the anime club. So we don't have to worry about other data values in the other rows.
Divide the value 0.13 which is in the "takes Japanese" column over 0.14, which is in the "total" column.
Basically we're computing [tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex] where A and B represent the events "takes Japanese" and "in anime club" respectively. The upside down U symbol represents intersection to indicate both events are happening at the same time.
So we end up with 0.13/0.14 = 0.92857142857142 which rounds to 0.93, then that converts to 93% when you move the decimal point over to the right two spots.
Answer:
Step-by-step explanation:
A survey of 900 randomly selected high school students determined that 422 play organized sports. (a) What is the probability that a randomly selected high school student plays organized sports? (b) Interpret this probability.
Answer:
P = 0.4688 = 46.88%
The probability that a randomly selected high school student plays organized sports is 0.4688.
Step-by-step explanation:
We are given that a survey of 900 randomly selected high school students determined that 422 play organized sports.
(a) What is the probability that a randomly selected high school student plays organized sports?
We know that the probability of an event is given by
P = Number of desired outcomes/total number of outcomes
For the given case, the desired outcomes are those students who play organized sports and the total number of outcomes are 900 randomly selected high school students who were surveyed.
So the probabilty is
P = 422/900
P = 0.4688
P = 46.88%
(b) Interpret this probability
There is a 46.88% chance of randomly selecting a high school student who plays organized sports or in other words, if we randomly choose a high school student then there is a 46.88% probability that the selected student plays organized sports.
. A law firm is run by four partners (A; B; C; D) . Each partner has one vote and decisions are made by majority rule, but in the case of a 2-2 tie, the coalition with A (the senior partner) wins.
Answer:
1) (ABCD) (ABC) (ABD) (ACD) (BCD) (AB) (AC) (AD)
2) A= 0.5000; B = 0.1667; C = 0.1667; D = 0.1667
Step-by-step explanation:
The questions are missing and should be
1) List all the winning coalitions in this voting system and the critical players in each.
2) Find the Banzhaf power index of this law firm.
1) Any combination of three partners, four partners, or a combination with two partners containing A is a winning coalition:
(ABCD) (ABC) (ABD) (ACD) (BCD) (AB) (AC) (AD)
2) The Banzhaf power index for each partner is given by the number of outcomes that said partner has a swing vote, divided by the number of possible swing vote situations.
Partners B, C, D will only have swing votes (change the outcome of the voting) when they are all in the same coalition, or when they are alone in a coalition with partner A:
[tex]B_B=2\\B_C=2\\B_D=2[/tex]
As for partner A, they will only be powerless to change the outcome when all of the other partners are in the same coalition (2 out of 8 possible combinations):
[tex]B_A=6\\[/tex]
The Banzhaf power index for each partner is:
[tex]B=\frac{2}{2+2+2+6}=0.1667\\C=\frac{2}{2+2+2+6}=0.1667 \\D=\frac{2}{2+2+2+6}=0.1667 \\A=\frac{6}{2+2+2+6}=0.5000[/tex]
What is the shape of the cross section of a sphere?
Rectangle
triangle
ellipse
circle
Answer:
the correct answer is circles
Step-by-step explanation:.
Suppose N coins lie heads up on a table. In one turn, you can turn over any (N−1) coins. Is it possible that N coins could lay tails up in any number of turns, if a N=15 ?
Answer:
The answer is no
Step-by-step explanation:
no
Ming took a cab across town. His fare was $ 2 2 $22dollar sign, 22, and he leaves an 1 8 % 18%18, percent tip. What is the total amount Ming pays the cab driver?
Answer: $25.96
Step-by-step explanation:
Fare = $22
Percent tip = 18%
Hi, to answer this question, first we have to multiply the fare paid by the tip percentage in decimal form (divided by 100 ):
Mathematically speaking:
22x (18/100) = 22 x 0.18 = $3.96 (tip amount)
Finally, we have to add the tip amount and the fare:
22 +3.96 = $25.96
Feel free to ask for more if needed or if you did not understand something.
Answer:
ur answer is in the calculator
$25.96
Step-by-step explanation:
multiply $22 by 1.18 or 118 percent
Joe and Nate went for a walk. The system representing each boy’s progress is graphed below. A graph titled Joe and Nate's progress has minutes since noon on the x-axis and miles from Joe's house on the y-axis. A line labeled Joe's progress goes through (10, 1) and (20, 2). A line labeled Nate's Progress goes through (0, 5) and (30, 3). Which statements about the system and scenario are true? Check all that apply. Nate starts 5 miles away from Joe’s house and gets closer as he walks because the y-intercept is 5 and his distance is decreasing. Nate walks at a negative speed because the slope of his line is negative. Joe walks at 1 mile per hour because the line representing his progress rises 1 for every 1 it runs. Nate walks at rate of 2 miles every 30 minutes because the difference in distance is 2 miles for every 30 minutes of time. Joe is walking faster than Nate because his line is steeper, meaning the distance he travels is changing more quickly.
Answer:
A,D E
Step-by-step explanation:
I took the quiz-ur welcome.
Dont forget to rate and thanks!
Answer:
A,D E
Step-by-step explanation:
If a candy box has a base which is 10 cm long and 8 cm wide, with a height of 5 cm, find out how much cardboard is needed to make the box.
Answer:
400cm³ of cardboard is required to make the box
Step-by-step explanation:
Hello,
To find the the size of cardboard required to make the box we need to know the shape of the box. This is to enable us calculate the volume of the box.
Data;
Length = 10cm
Width = 8cm
Height = 5cm
This dimension corresponds to that of a cubiod.
Volume of a cubiod = length × width × height
Volume of the box = 10 × 8 × 5
Volume of the box = 400cm³
The volume of the box is 400cm³
About 400cm³ of cardboard is needed to make the box
Find the surface area of a cylinder with radius r = 6 and height h = 14.8 to the nearest tenth of a square cm. Use π = 3.14
Answer:
783.7 square units
Step-by-step explanation:
The formula for the surface area of a cylinder is ...
A = 2πr^2 + 2πrh = 2πr(r +h)
Using the given numbers, the area is ...
A = 2(3.14)(6)(6 +14.8) = 783.7 . . . square units
Answer:
About 783.7 square cm.
Step-by-step explanation:
The formula for the surface area of a cylinder is (2 * pi *r^2) + (2 * pi * r * h).
(2 * 3.14 * 6^2) + (2 * 3.14 * 6 * 14.8) = (2 * 3.14 * 36) + (2 * 3.14 * 6 * 14.8) = 6.28 * 36 + 6.28 * 88.8 = 226.08 + 557.664 = 783.744.
So, the surface area of the cylinder is about 783.7 square centimetres.
Hope this helps!
Evaulate 9^sqrt{3} in it to the nearest ten thousandth
Answer:
44.957
Step-by-step explanation:
All we can do is estimate √3 and then exponent 9 by it.
Alternatively, plug it into a calc and calculate.
While calculating HCF using index notation, we choose ____________ index of common prime factors.
Answer:
power index
Step-by-step explanation:
Prime factor index form is expression of a number as product of its prime number. Here the prime factor is listed only once. It is necessary to insert the required power index to solve for the HCF
Describe the follow scenario involves a permutation or combination. Then find the number of possibilities. Cody and Aaliyah are planning trips to two countries this year there in 15 countries they would be interested in visiting one trip will be one week long another two weeks
Answer:
This is a permutation problem because the order of their choice is important.
There are 210 ways in which this choice can be made.
Step-by-step explanation:
Complete Correct Question
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities. Cody and Aaliyah are planning trips to two countries this year. There are 15 countries they would be interested in visiting. One trip will be one week long and the other two weeks.
Solution
Permutation is used to calculate the number of possibilities or number of ways k choices can be made from n options given that the order of picking the choices is important. If there are choices A, B and C, picking ABC is different from CAB if order of picking is important like permutation preaches.
Combination on the other hand, is used to calculate the number of possibilities or number of ways k choices can be made from n options given that the order of picking the choices is unimportant. If there are choices A, B and C, picking ABC is the same as picking CAB if order of picking is unimportant like combination preaches.
So, in this question, Cody and Aaliyah want to pick 2 countries to visit, out of 15. They plan to spend 2 weeks in one country and 1 week in the other country.
This last sentence makes the order in which they pick the countries to visit important. If they chose to spend two weeks in country A and one week in country B, it is now a different possibility from spending two weeks in country B and one week in country A.
Hence, this is a permutation problem
The number of possibilities of picking 2 countries out of 15 countries to spend 2 weeks in first country and spend 1 week in the other country is ¹⁵P₂ = 15! ÷ (15 - 2)!
= 210 ways in which this choice can be made.
Hope this Helps!!!
Which figures have more than one base? Select three options.
O cone
cylinder
rectangular prism
rectangular pyramid
triangular prism
Answer:
cylinderrectangular prismtriangular prismStep-by-step explanation:
The figures that come to a point (cone, pyramid) only have one base. The others have two:
cylinder
rectangular prism
triangular prism
Answer:
B-cylinder
C-rectangular prism
E-triangular prism
Step-by-step explanation:
Got it right on edge unit test
3(4-2) help please thank you
━━━━━━━☆☆━━━━━━━
▹ Answer
6
▹ Step-by-Step Explanation
Follow PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
3(4 - 2)
3(2)
= 6
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Write these as normal numbers.
a)
5.1 x 108
b)
9.6 x 10°
c)
2.44 10
d)
5.023 1010
Answer:
Step-by-step explanation:
5.1 × 108 = 550.8
9.6 × 10^0
10^0 = 1
9.6 × 1 = 9.4
2.44 × 10 = 24.4
5.023 × 1010 = 5073.23
Please answer this fast there can be more than one option answer in two minutes
Answer:
Options (1) and (2)
Step-by-step explanation:
In 3-dimensional geometry,
Skew lines are lines which do not intersect and are not parallel.
From the given triangular prism,
Option (1). RS and TU
Sides RS and TU are neither parallel nor intersect each other.
Therefore, these lines are skew lines.
Option (2).QR and SV
Since QR and SV neither intersect nor parallel,
These lines are the skew lines.
Option (3) RS and RU
Since RS and RU intersect at R therefore, they are not the skew lines.
Option (4).RS and UV
Since RS and UV are the parallel lines therefore, they are not the skew lines .
If you vertically stretch the quadratic parent function, f(x) = 2^x, by a factor of 3, what is the equation of the new function?
If you stretch on the y-axis then you are increasing/decreasing values at a every x.
The new function is therefore:
[tex]g(x)=3\cdot2^x[/tex]
Hope this helps.
not sure what to do here
Answer:
P(-2 ≤ x ≤ 2) = .6
Step-by-step explanation:
Given
The data in the above table
Required
Find P(-2 ≤ x ≤ 2)
To solve for P(-2 ≤ x ≤ 2); we have to consider the boundary covered by the interval
The interval -2 ≤ x ≤ 2 according to the table is -2 , 0 and 2
Solving further;
P(-2 ≤ x ≤ 2) = P(-2) + P(0) + P(2) ----- (1)
From the table;
P(-2) = .33
P(0) = .16
P(2) = .11
Substitute these values in (1) above
P(-2 ≤ x ≤ 2) = P(-2) + P(0) + P(2) becomes
P(-2 ≤ x ≤ 2) = .33 + .16 + .11
P(-2 ≤ x ≤ 2) = .6
1. Solve 2r - 15 = -9r + 18.
a.) r = -0.3
b.)r = -3
c.)r = 0.3
d.)r = 3
Answer:
D
Step-by-step explanation:
11r = 33
r = 3
Answer
D
Step-by-step explanation:
cancel out -9r on the right side by adding it to the left side. so then you get 11r-15=18 . then add 15 to the right to get 11r by itself . you'll get 11r=33 . divide both sides by 11 and you'll get r=3 ! :)
This grid follows two rules.
Rule 1 The sums of each row are equal.
Rule 2 The products of each column are equal.
The grid below follows the same two rules.
Work out the missing numbers.
a =
b =
c =
d =
Answer:
a = 4,
b = 12
c = 10
d = 15
Step-by-step explanation:
Since the product of each column is equal, therefore,
b*5 = 60
b = 60 ÷ 5 = 12
c*6 = 60
c = 60 ÷ 6 = 10
Since the sum of each column are equal, therefore,
12 + 10 + a = 5 + 6 + d
22 + a = 11 + d
Think of a number you can add to 22, and another number you can add to 11, which will make both sides equal. Add both numbers, whenmultiplied together should give you 60.
Factors of 60 are:
(a, d)
(1, 60) => 22 + a = 11 + d => 22+1 = 11+60 (incorrect)
(2, 30) => 22 + a = 11 + d => 22+2 = 11+30 (incorrect)
(3, 20) => 22 + a = 11 + d => 22+3 = 21+20 (incorrect)
(4, 15) => 22 + a = 11 + d => 22+4 = 11+15 => 26 = 26 [CORRECT]
(5, 12) => 22 + a = 11 + d => 22+5 = 11+12 (incorrect)
(6, 10) => 22 + a = 11 + d => 22+6 = 11+10 (incorrect)
Therefore,
a = 4,
d = 15
ABCDEFGHI is a regular 9-sided polygon.
B
Diagram NOT
accurately drawn
H
o
G
D
F
E
The vertices B and E are joined with a straight line.
Work out the size of angle BEF.
(4 marks)
angle BEF
Answer:
angle BEF = 100 degrees
Step-by-step explanation:
For a regular 9-sided polygon (nonagon),
each exterior angle = 360/9=40 degrees
each interior angle = 180-40 = 140 degrees.
Referring to diagram, in the trapezoid (trapezium) BCDE, the base angles are 180-140 = 40 degrees.
Therefore angle DEB = 40 degrees
that leaves BEF = 140-40 = 100 degrees
On a map, 1 cm represents 4 km.
The real-life distance between two towns is 28 km.
What is the distance between these two towns on a map?
The conversion rate is 1cm to 4km, or 1:4.
Because we know the conversion rate, we can use this ratio to calculate the map distance.
If the distance between the two towns is 28km, then we can use the conversion rate to calculate the distance on the map.
28 / 4 = 7
Therefore, the distance between the two towns on a map is 7cm.
Hope this helped! :)
Answer:
7 cmStep-by-step explanation:
1cm……..4km
x…………28km
x=28km*1cm/4km
x=7cmFirst, he needs to run to the store. To get to the store from his apartment, he can walk 1.2 miles North and 0.5 miles East along the sidewalks. Or, he can cut through the city to get from his apartment to the store along a single straight line. Walking on the sidewalks, Henry walks 6 miles/hour. Cutting through the city, Henry can only walk 3.5 miles/hour.
Answer:
If Henry walks along the sidewalks, he will walk 1.7 miles in total. It will take him 17 minutes to reach the store and another 17 minutes to come back.
If Henry cuts through the city, he will walk √(1.2² + 0.5²) = 1.3 miles in total. It will take him 22.3 minutes to reach the store and another 22.3 minutes to come back.
Even though Henry will need to walk a longer distance if he walks along the sidewalks, he will be able to reach the store and back back in a shorter time than if he cuts through the city.
Below is the graph of a polynomial. which statement about this graph is true?
Answer:
c: the point -2,-4 is minimum
Step-by-step explanation:
Please answer this what is the answer to this question now
Answer:
19
Step-by-step explanation:
M is the center of the triangle, means that MR=MQ=PM
and M is the in center of the triangle=MS=MT=MU=19
The table below shows the possible outcomes of rolling a six-sided number cube and flipping a coin. What is the probability of getting a number less than 3 and a tails?
Answer: the probability of getting a number less than 3 and tails is P 1/6
Step-by-step explanation:
Assuming that the dice and the coin are normal ones, we can expect that the probability for each outcome is about the same.
For the coin we have 2 outcomes, heads and tails, then each outcome has a probability of 1/2
The dice has 6 outcomes, and each outcome has a probability of 1/6.
Then the probability of rolling a number less than 3 is equal to the probability of rolling a 1 plus the probability of rolling a 2.
P1 + P2 = 1/6 + 1/6 = 2/6 = 1/3.
The probability of getting tails with the coin is 1/2.
Now, the joint for both events is equal to the product of the probabilities of each event, this is:
P = (1/3)*(1/2) = 1/6
Answer:
1/6
Step-by-step explanation:
got it right on edge