Answer:
The methods that are fair include __A, B and C__ because __D__ is flawed due to increased chances of winning based on one's skill, ___F___ is flawed due to poor randomization, and ___E___ is flawed due to unequal probabilities of winning and losing.
Step-by-step explanation:
A. Place both names in equal amounts into a hat and draw one without looking:
If you place both names in equal amounts into a hat, then the probability of picking any one of the names would be equal.
For example, if you put 20 pieces of paper containing each name in a hat, then,there will be 40 names in the hat. The probability of picking any one or the other randomly would be:
P = 20/40 =1/2
B. Ask a stranger to flip a coin:
A coin has only two faces, head and tail. Hence, if one person picks head and the other picks tail, the probability of landing on either head or tail is given as:
P = 1/2
C. Roll a die and evaluate the outcome as either even or odd:
A die has 6 faces with equal number of faces with equal number of even numbers and odd numbers, 3. Hence, the probability of rolling an even or odd number is given as:
P = 3/6 = 1/2
D. Throw a stone closest to an object:
This method is not fair because then it depends solely on who can throw the farthest i.e. the physical ability of the throwers.
E. Play a hand of blackjack
This method is flawed because it has unequal probabilities of winning and losing.
F. Ask a random stranger to select:
This method is unfair because it then depends solely on the random picker. The picker could have personal preferences or a bias based on maybe height, beauty, weight, basically anything characteristic. Hence, it is unfair.
Final answer:
Fair methods for deciding who gets the prize include placing both names in a hat, flipping a coin, and rolling a die as they provide equal chances of winning, while throwing a stone, playing blackjack, or asking a stranger can introduce bias or skill, making them unfair.
Explanation:
The methods that are fair include placing both names in a hat, asking a stranger to flip a coin, and rolling a die because these methods provide equal probabilities of winning or losing. Method D: Throwing a stone closest to an object is flawed due to increased chances of winning based on one's skill, which means it's not random. E: Playing a hand of blackjack is flawed due to poor randomization, as the cards dealt can create significantly different chances of winning. F: Asking a random stranger to select is flawed due to unequal probabilities of winning and losing if the stranger holds a bias, even if unintended.
Tossing a coin is a fair way to decide because both outcomes (heads or tails) have equal chances of occurring, which is a 50% chance each way. This is consistent with the principle of randomness and independent events, where the outcomes of past coin tosses do not influence the results of future tosses.
The perimeters of two 30-60-90 triangles are in the ratio 1:2. If the length of the hypotenuse of the larger triangle is 20 cm, find the length of the longer leg of the smaller triangle.
Answer:
The answer to your question is 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Data
Proportion 1:2
Hypotenuse of the larger triangle = 20
length of the longer leg of the smaller triangle = ?
Process
1.- Remember the proportions of a 30- 60 - 90 triangle
hypotenuse = 2x
short leg = x
long leg = x[tex]\sqrt{3}[/tex]
2.- Use the previous information to find the lengths of the larger triangle
hypotenuse = 20 = 2x
short leg = x = 10
large leg = 10[tex]\sqrt{3}[/tex]
3.- Use the previous information to find the lengths of the smaller triangle
Proportion 1:2
hypotenuse = 10
short leg = x = 5
long leg = 5[tex]\sqrt{3}[/tex]
Answer:
It’s 5 radical 3
Step-by-step explanation:
Consider a coordinate system in which the positive x axis is directed upward vertically. What are the positions of a particle (a) 5.0 m directly above the origin and (b) 2.0 m below the origin?
Answer:
a) (5,0)
b) (2,0)
Step-by-step explanation:
(a) A particle that lies 5.0 m directly above the origin would have its x-coordinate be 5 and its y-coordinate be 0. So (5,0).
(b) A particle that lies 2.0 m directly below the origin would have its x-coordinate be 2 and its y-coordinate be 0. So (2,0).
In a coordinate system with the positive x-axis directed upward, a particle located 5.0 m directly above the origin has a position of +5.0 m, and a particle 2.0 m below the origin has a position of -2.0 m.
Explanation:In this coordinate system, the position of a particle is indicated by its vertical position relative to the origin. Therefore:
Directly above the origin: If a particle is 5.0 m directly above the origin, this is represented as a positive number in this coordinate system. Thus, its coordinate is +5.0 m.Below the origin: If a particle is 2.0 m below the origin, this is represented as a negative number in this coordinate system. Thus, its coordinate is -2.0 m.Learn more about Coordinate System here:https://brainly.com/question/32885643
#SPJ3
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3{,}200\text{ m}3,200 m3, comma, 200, start text, space, m, end text. How many kilometers did Issa travel from school to his house? kilometers
Answer:
9.6
Step-by-step explanation:
The question is :
Solution;
Let total distance from school to home = 'x' meters
Issa jogged 2/3rd of 'x'= [tex]\frac{2x}{3}[/tex]
So total distance from school to home = [tex]\frac{2x}{3} +3200[/tex]
But total distance from school to home = [tex]x[/tex]
[tex]==> \frac{2x}{3} + 3200 = x[/tex]
[tex]==> 3200= \frac{x}{3}[/tex]
[tex]==> 9600=x[/tex]
So total distance from school to home is 9600 meters
We convert it into km now
we know 1000 meters = 1km
==> 9600 meters = 1/100 x 9600= 9.6 km
Answer:
9.6 or (48\5
Step-by-step explanation:
What is the value of n?
Enter your answer in the box.
n =
m
Circle with two intersecting chords forming an x shape in the circle. The top left side of the x shape is labeled 5 meters. The top right side of the x shape is labeled 2 meters. The bottom left side of the x is labeled 15 meters.The bottom right side of the x is labeled n.
Answer:
6 meters
Step-by-step explanation:
Intersecting Chord Theorem: When two chords intersect each other inside a circle, the products of their segments are equal.
One chord is divided into two segments with lengths of 15 m and 2 m.
Anothe chord is divided into two segments with measures of 5 m and n m.
Therefore,
[tex]5\cdot n=15\cdot 2\\ \\5n=30\\ \\n=6\ m[/tex]
Answer:
6 m
Step-by-step explanation:
just took the test
Dan's business loses $9 each day. Which equation would be used to show how much money Dan's business has lost in a week? A. -9 × 7 B.-9 × (-7) C.9 × 7 D.9 × (-7)
Answer:
[tex]C. \: 9 \times 7[/tex]
Donata bought 3 Apples and 5 Pomegranites at the local supermarket for a total of $16.50 Meaghan bought 6 Apples and 11 Pomegranites at the same store for a total of $35.70 How much does one Apple cost?
Answer: the cost of one apple is $1
Step-by-step explanation:
Let x represent the cost of one apple.
Let y represent the cost of one Pomegranate.
Donata bought 3 Apples and 5 Pomegranates at the local supermarket for a total of $16.50. This means that
3x + 5y = 16.5 - - - - - - - - - - - - -1
Meaghan bought 6 Apples and 11 Pomegranates at the same store for a total of $35.70. This means that
6x + 11y = 35.7- - - - - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 1, it becomes
6x + 10y = 33
6x + 11y = 35.7
Subtracting, it becomes
- y = - 2.7
y = 2.7
Substituting y = 2.7 into equation 1, it becomes
3x + 5 × 2.7 = 16.5
3x + 13.5 = 16.5
3x = 16.5 - 13.5 = 3
x = 3/3 = 1
A windshield wiper blade turns through an angle of 135°. The bottom of the blade traces an arc with a 8-inch radius. The top of the blade traces an arc with a 24-inch radius. To the nearest inch, how much longer is the top arc than the bottom arc? Round to the nearest whole number.
Answer:142
2
+2
Step-by-step explanation:
A study found that a driver’s reaction time A(x) to audio stimuli and his or her reaction time V(x) to visual stimuli (both in milliseconds) can be modeled by
A(x) = 0.0051x² - 0.319x + 15, 16 ≤ x ≤ 70,
V(x) = 0.005x² - 0.23x + 22, 16 ≤ x ≤ 70
where x is the driver's age (in years). Write an inequality that you can use to find the x-values for which A(x) is less than V(x).
Answer:
The required inequality is [tex]0.0001 x^2 - 0.089 x - 7<0[/tex].
Step-by-step explanation:
The given inequalities are
[tex]A(x) = 0.0051x^2 - 0.319x + 15[/tex]
[tex]V(x)= 0.005x^2 - 0.23x + 22[/tex]
where, x is the driver's age (in years), A(x) is driver’s reaction time to audio stimuli and V(x) is his or her reaction time to visual stimuli, 16 ≤ x ≤ 70.
We need to find an inequality that can be use to find the x-values for which A(x) is less than V(x).
[tex]A(x)<V(x)[/tex]
[tex]0.0051x^2 - 0.319x + 15< 0.005x^2 - 0.23x + 22[/tex]
[tex]0.0051x^2 - 0.319x + 15- 0.005x^2 + 0.23x- 22<0[/tex]
Combine like terms.
[tex]0.0001 x^2 - 0.089 x - 7<0[/tex]
where, 16 ≤ x ≤ 70.
Therefore, the required inequality is [tex]0.0001 x^2 - 0.089 x - 7<0[/tex].
HELP I NEEEEED ANSWER PLEASEEEEE
Answer:
6
Step-by-step explanation:
8^2*(TS)^2=10^2
(TS)^2=36
TS=6
Answer:
Step-by-step explanation:
Triangle RST is a right angle triangle.
From the given right angle triangle,
RS represents the hypotenuse of the right angle triangle.
With m∠R as the reference angle,
RT represents the adjacent side of the right angle triangle.
ST represents the opposite side of the right angle triangle.
To determine m∠R, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos m∠R = 8/10 = 0.8
m∠R = Cos^-1(0.8)
m∠R = 36.9 to one decimal place.
Miguel orders 595 candy bars. They come in 7 boxes. How many candy bars are in each box? How many candy bars will he have left if he gives 3 boxes to his friend?
There are 85 candy bars in each box, and he will have 340 candy bars left after he gives three boxes to a friend.
Answer: he has 340 candy bars left.
Step-by-step explanation:
The total number of candy bars that
Miguel ordered is 595.
They come in 7 boxes. Assuming each box contains equal number of candy bars. This means that the number of candy bars in each box would be
595/7 = 85 candy bars
If he gives 3 boxes of candy bars to his friend, it means that the number of candy bars that he gave to his friend is
85 × 3 = 255 candy bars
Therefore, the number of candy bars that he has left is
595 - 255 = 340
Jim's work evaluating 2 (three-fifths) cubed is shown below. 2 (three-fifths) cubed = 2 (StartFraction 3 cubed Over 5 EndFraction) = 2 (StartFraction 3 times 3 times 3 Over 5 EndFraction) = 2 (StartFraction 27 Over 5 EndFraction) = StartFraction 54 Over 5 EndFraction Which statement best describe Jim's first error? He did not multiply Three-fifths by 2 before applying the power. He did not apply the power to the denominator of Three-fifths. He did not evaluate 33 correctly. He did not multiply StartFraction 27 Over 5 EndFraction by 2 correctly.
Jim's first error occurred when he incorrectly applied the cube to three-fifths. He made the mistake of not applying the power to the denominator of the fraction. The answer is 54/125
Explanation:The question revolves around a mathematical operation where Jim is attempting to determine the cube of 2 times three-fifths. Jim's first error lies in how he applied the power of three. According to the rules of exponentiation for fractions, you should apply the power to both the numerator and denominator. Hence, Jim's first mistake was that he did not apply the power to the denominator of three-fifths. Instead of merely cubing the numerator (3), Jim should have also cubed the denominator (5). He should have performed the calculation as follows:
= 2 x (3/5)^3
= 2 x (3^3/5^3)
= 2 (27/125).
= 54/125
Learn more about Exponentiation here:
https://brainly.com/question/32448437
#SPJ3
Jim first errored by failing to apply the exponent to both the numerator and denominator of the fraction before multiplying by two. The correct calculation for cubing a fraction should involve cubing both the numerator and the denominator, which would have resulted in 54/125 instead of 54/5.
The first error that Jim made was not applying the power to both the numerator and the denominator of the fraction before multiplying by two. When cubing a number in fractional form, such as three-fifths, one must cube both the numerator (33) and the denominator (53) to correctly apply the exponent to the entire fraction. The correct method is to first cube three-fifths, which results in 27/125, and then multiply that result by 2, leading to the final answer of 54/125, not 54/5 as Jim calculated.
It's important to follow the correct order of operations and apply exponents before multiplication. In this case, to find the value of 2 × (three-fifths) cubed, the calculation should be 2 × (3/5)3, which simplifies to 2 × (27/125), and then to 54/125.
Sam eats 1/2 of a chocolate bar. Jack eats 1/4 of the remaining chocolate bar. After both Jack and Sam eat their portions of the chocolate bar how much is left uneaten of the original whole chocolate bar?
Final answer:
After Sam eats 1/2 and Jack eats 1/4 of the remaining chocolate bar, 3/8 of the original chocolate bar is left uneaten.
Explanation:
Sam eats 1/2 of a chocolate bar. Jack then eats 1/4 of the remaining chocolate bar. To determine how much of the chocolate bar is left, we need to perform a couple of simple calculations. After Sam eats his portion, 1/2 of the bar is left. Jack eats 1/4 of what remains after Sam, which is 1/4 of 1/2, or 1/2 * 1/4 = 1/8 of the original bar.
This means that Jack's portion is 1/8 of the entire chocolate bar. Now, the total amount eaten by Sam and Jack together is 1/2 (Sam's portion) + 1/8 (Jack's portion). To add these fractions, they need to have a common denominator, which in this case is 8. This makes Sam's portion 4/8 when expressed with the common denominator. Now, add 4/8 (Sam's adjusted portion) + 1/8 (Jack's portion) = 5/8.
Therefore, the total amount eaten by both is 5/8 of the bar, leaving 3/8 of the original chocolate bar uneaten.
Determine, in degrees, the measure of each interior angle of a regular octagon
Please show all work on how you got your answer
Answer:
Each interior angle = 135 degrees,
Step-by-step explanation:
The exterior angles of all convex polygons add up to 360 degrees.
So for a regular octagon each exterior angle = 360 / 8
= 45 degrees.
Therefore each interior angle = 180 - 45 = 135 degrees,
A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends).
A. What is the probability that a player defeats all four opponents in a game?
B. What is the probability that a player defeats at least two opponents in a game?
C. If the game is played three times, what is the probability that the player defeats all four opponents at least once?
Answer:
(a) 0.4096
(b) 0.64
(c) 0.7942
Step-by-step explanation:
The probability that the player wins is,
[tex]P(W)=0.80[/tex]
Then the probability that the player losses is,
[tex]P(L)=1-P(W)=1-0.80=0.20[/tex]
The player is playing the video game with 4 different opponents.
It is provided that when the player is defeated by an opponent the game ends.
All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)
(a)
The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.
The probability that the player defeats all four opponents in a game is,
P (Player defeats all 4 opponents) = [tex]P(W)\times P(W)\times P(W)\times P(W)=[P(W)]^{4} =(0.80)^{4}=0.4096[/tex]
Thus, the probability that the player defeats all four opponents in a game is 0.4096.
(b)
The probability that the player defeats at least two opponents in a game is,
P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) = [tex]1-P(L)-P(WL)[/tex]
[tex]=1-(0.20)-(0.80\times0.20)\\=1-0.20-0.16\\=0.64[/tex]
Thus, the probability that the player defeats at least two opponents in a game is 0.64.
(c)
Let X = number of times the player defeats all 4 opponents.
The probability that the player defeats all four opponents in a game is,
P(WWWW) = 0.4096.
Then the random variable [tex]X\sim Bin(n=3, p=0.4096)[/tex]
The probability distribution of binomial is:
[tex]P(X=x)={n\choose x}p^{x} (1-p)^{n-x}[/tex]
The probability that the player defeats all the 4 opponents at least once is,
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
[tex]=1-[{3\choose 0}(0.4096)^{0} (1-0.4096)^{3-0}]\\=1-[1\times1\times (0.5904)^{3}\\=1-0.2058\\=0.7942[/tex]
Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.
Final answer:
The probability of defeating all four opponents in one game is 40.96%. The probability of defeating at least two opponents is 87.04%. Playing the game three times, the probability of defeating all four opponents at least once is 88.47%.
Explanation:
To calculate the probability of different outcomes when playing a video game against four opponents, we'll use basic probability rules and assumptions given in the question.
A. Probability of Defeating All Four Opponents
The probability of defeating each opponent is 80% or 0.8. Since the fights are independent, to find the probability of defeating all four, we multiply the probabilities together:
0.8 × 0.8 × 0.8 × 0.8 = 0.4096 or 40.96% chance of defeating all four opponents.
B. Probability of Defeating At Least Two Opponents
To find the probability of defeating at least two opponents, we must consider all possible combinations of winning 2, 3, or 4 opponents' fights, and add those probabilities together. Let W represent a win and L represent a loss:
P(WWLL) + P(WLWL) + P(WLLW) + P(LWWL) + P(LWLW) + P(LLWW)We already calculated P(WWWW) as 0.4096. The other probabilities can be calculated using similar multiplication of respective individual probabilities (0.8 for W, 0.2 for L). After calculation, we sum these to find the cumulative probability, which is 0.8704 or 87.04%.
C. Probability of Defeating All Four Opponents At Least Once Over Three Games:
The probability of not defeating all four opponents in one game is 1 - P(WWWW) = 0.5904. The events in each game are independent, so the probability of not defeating all four opponents in all three games is (0.5904)^3. Therefore, by subtracting this result from 1, we get the probability of defeating all opponents at least once: 1 - (0.5904 × 0.5904 × 0.5904) = 0.8847 or 88.47%.
How high is a tree that casts a 2222-ftft shadow at the same time a 44-ftft postpost casts a shadow which is 77-ftft long?
Answer: The height of the tree is 12.57 ft.
Step-by-step explanation:
The height of a thing is proportional to the its shadow.
Let H = Height and S = length of shadow
Then by equation direct proportion , [tex]\dfrac{H_1}{S_1}=\dfrac{H_2}{S_2}[/tex] (i)
Given : A tree that casts a 22 ft shadow at the same time a 4 ft postpost casts a shadow which is 7-ft long.
Put [tex]S_1=22 ,\ H_2= 4,\ \ S_2=7[/tex] in (i), we get
[tex]\dfrac{H_1}{22}=\dfrac{4}{7}\\\\ H_1=\dfrac{4}{7}\times22\approx12.57[/tex]
Hence, the height of the tree is 12.57 ft.
What the user said above!
25 Points.
The function f(x) = 4x + 3 represents the length of a rectangle. The function g(x) = 2x − 5 represents the width of the rectangle. Use (f • g)(4) to determine the area of the rectangle.
57
19
16
3
Answer:
57
Step-by-step explanation:
(f•g)(x) = f(x)•g(x)
= (4x+3)(2x-5)
= 8x²-20x+6x-15
= 8x²-14x-15
(f•g)(4) = [4(4)+3] [2(4)-5]
= (16+3)(8-5)
= 19 • 3
= 57
Answer:
57
Step-by-step explanation:
got it correct on test. :)
The 1985 1985 explosion at a nuclear lab sent about 1000 kilograms of a radioactive element into the atmosphere. The function f left parenthesis x right parenthesis equals 1000 left parenthesis 0.5 right parenthesis Superscript StartFraction x Over 30 EndFraction f(x)=1000(0.5) x 30 describes the amount, f(x), in kilograms, of a radioactive element remaining in the area x years after 1985 1985. If even 100 kilograms of the radioactive element remains in the atmosphere, the area is considered unsafe for human habitation. Find f( 40 40) and determine if the area will be safe for human habitation by 2025 2025.
Answer:
Step-by-step explanation:
If I'm understanding this correctly, the rate of decay function is
[tex]f(x)=1000(.5)^{\frac{x}{30}}[/tex]
and we want to solve for the amount of element left after x = 40 years. That would make our equation
[tex]f(40)=1000(.5)^{1.33333333333}[/tex]
Multiply the repeating decimal by .5 to get
f(40) = 1000(.3968502631)
and f(40) = 396.85
So no, it's not safe for human habitation.
f(40) ≈ 793.7 kilograms. The area will not be safe for human habitation by 2025.
Explanation:For the decay, to find f(40), we substitute x=40 into the function f(x)=1000(0.5)x/30.
f(40)=1000(0.5)40/30
f(40)=1000(0.5)4/3
f(40) ≈ 1000(0.7937)
f(40) ≈ 793.7 kilograms
Since the question asks if the area will be safe for human habitation by 2025, we need to check if f(40) is less than or equal to 100 kilograms.
But the value of f(40) is about 793.7 kilograms, which is greater than 100 kilograms.
Therefore, the area will not be safe for human habitation by 2025.
Learn more about Radioactive decay here:https://brainly.com/question/1770619
#SPJ2
NASA is sending a probe to Alpha Centauri and then to Sirius. A problem with the probe is noticed while it is at Alpha Centauri, so it must go back to Erth before going to Sirius. Alpha Centauri is 4.3 light-years away from Earth and Sirius is 8.6 light-years away. The probe is traveling at 18.03 km/s, there are 1.58125 x 10-5 light-years in one astronomical unit. How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?
Answer:
Time = 9.0252 *10^12 s
Step-by-step explanation:
Given:
- The distance from Earth to Alpha Centauri = 4.3 light years
- The distance from Earth to Sirius = 8.6 light years
- Speed of the probe is V = 18.03 km/s
- 1 AU = 1.58125 x 10-5 light-years
Find:
How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?
Solution:
- We will track probe for each destination it reaches one by one:
Earth ------> Alpha Centauri d_1 = 4.3 light years
Alpha Centauri ------> Earth d_2 =4.3 light years
Earth ------> Sirius d_3 = 8.6 light years
Total distance D = 17.2 light years.
- Now we know the total distance traveled by the probe is D. We will convert the distance into km SI units:
1 AU ------------------> 1.58125 x 10-5 light-years
x AU ------------------> 17.2 light years.
- Using direct proportions
x = 17.2 / (1.58125 x 10-5) = 1087747.036 AU
Also,
1 AU ---------------------> 149597870700 m
1087747.036 AU ----> D m
- Using direct proportions
D = 1087747.036*149597870700 = 1.62725*10^17 m
- Now use the speed - distance - time formula to compute the total time taken:
Time = Distance traveled (D) / V
Time = 1.62725*10^17 / 18.03*10^3
Answer: Time = 9.0252 *10^12 s
WHAT IS 5/12 X - 1/2= 1/3
A. -1/72
B. 5/72
C. 2
D. 2/5
Answer:
C. 2
Step-by-step explanation:
Given:
[tex]\frac{5}{12}x-\frac12=\frac13[/tex]
We need to solve the equation to find the value of x.
Solution:
[tex]\frac{5}{12}x-\frac12=\frac13[/tex]
Combining like terms we get;
[tex]\frac{5}{12}x=\frac13+\frac12[/tex]
Now Using LCM for making the denominators same we get;
[tex]\frac{5}{12}x=\frac{1\times2}{3\times2}+\frac{1\times3}{2\times3}\\\\\frac{5}{12x}=\frac{2}{6}+\frac{3}{6}[/tex]
Now Denominators are common so we solve the number we get;
[tex]\frac{5}{12}x=\frac{2+3}{6}\\\\\frac{5}{12}x=\frac{5}{6}[/tex]
Now Dividing both side by [tex]\frac{12}{5}[/tex] we get;
[tex]\frac{5}{12}x\times \frac{12}{5}=\frac{5}{6}\times \frac{12}{5}\\\\x=2[/tex]
Hence the value of x is 2.
If the eyepiece of a compound microscope has a magnification power of 10X and the objective lense has a magnification power of 4X, what is the total magnification of the microscope at this setting?
Answer:
Total magnification of microscope at this setting is 40X
Step-by-step explanation:
Total magnification of microscope is determined by multiplying the magnification power of individual lenses.
So if eyepiece has magnification power of 10X and objective lense has magnification power of 4X , the total magnification of microscope would be
10 × 4 = 40
which means the object will appear 40 times larger than actual object.
The total magnification of the microscope at this setting is 40X.
To determine the total magnification of a compound microscope, one needs to multiply the magnification power of the eyepiece by the magnification power of the objective lens. In this case, the eyepiece has a magnification power of 10X and the objective lens has a magnification power of 4X.
The formula for the total magnification [tex]\( M_{total} \)[/tex] is given by:
[tex]\[ M_{total} = M_{eyepiece} \times M_{objective} \][/tex]
Substituting the given values:
[tex]\[ M_{total} = 10X \times 4X \][/tex]
[tex]\[ M_{total} = 40X \][/tex]
Therefore, the total magnification of the microscope when using the 10X eyepiece and the 4X objective lens is 40X. This means that the image seen through the microscope will appear 40 times larger than its actual size.
the parallelogram shown below has an area of 54 units. find the missing height
Answer:
h = 6 units.
Step-by-step explanation:
Given:
Area of the parallelogram = [tex]54\ units^2[/tex].
Base = 9 units.
We need to find the missing height.
Solution:
We know that the area of the parallelogram is represented by below formula.
[tex]A = bh[/tex] -----------(1)
Where:
A = Area of the parallelogram.
h = height of the parallelogram.
b = Base
Since, base and area is known. So, we substitute these values in equation 1.
[tex]54 = 9\times h[/tex]
[tex]h = \frac{54}{9}[/tex]
h = 6 units.
Therefore, height of the parallelogram h = 6 units.
The average weight of 5 items is 24 pounds. If the total weight of 3 blue items is 39 pounds, what is the average weight of the remaining 2 non-blue items?
Answer: the average weight of the remaining 2 non-blue items is 81 pounds
Step-by-step explanation:
The formula for determining average is expressed as
Average = sum of each item/ total number of items
Let x represent the average weight of the remaining 2 non-blue items.
The average weight of 5 items is 24 pounds. If the total weight of 3 blue items is 39 pounds, it means that
(x + 39)/5 = 24
x + 39 = 5 × 24 = 120
x = 120 - 39
x = 81
A variable that is systematically linked with the factor you believe is causing the overall effect in your research is called the ________ variable. The presence of such a variable can prevent you from knowing what is really causing the effect.
Answer: Extraneous variable
Step-by-step explanation:
In an experiment , Independent variable can be manipulated by the experimenter to see the change in the dependent variable or response variable. But there are some variable known as extraneous variable that is attached to independent variable and make experimenter confuse.
Extraneous variables is defined as :
A variable that is not intentionally involved in any study.It is systematically linked with the independent variable.It can cause effect in research.∴ A variable that is systematically linked with the factor you believe is causing the overall effect in your research is called the extraneous variable variable. The presence of such a variable can prevent you from knowing what is really causing the effect.
I WILL GIVE BRAINLIEST! 30 POINTS!
Koji is installing a rectangular window in an office building. The window is 823 feet wide and 534 feet high.
The formula for the area of a rectangle is A=bh.
What is the area of the window?
Enter your answer as a mixed number in simplest form in the box.
$$
ft2 ( ? ) ( ? )
-------
( ? )
Answer:
Area = 823 * 534 = 439,482 ft^2
Step-by-step explanation:
What’s the value of x?
Answer:
98 degrees
Step-by-step explanation:
m<H = 45, m<F = 53
180 = 45 + 53 + (180-x)
82 = 180-x
x+82 = 180
x = 98
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is 180 degrees. This means that
Angle F + angle G + angle H = 180
Therefore,
53 + 45 + angle G = 180
98 + angle G = 180
Subtracting 98 from the left hand side and the right hand side of the equation, it becomes
98 - 98 + angle G = 180 - 98
angle G = 82 degrees
The sum of angles on a straight line is 180 degrees. Therefore,
x + 82 = 180
Subtracting 82 from the left hand side and the right hand side of the equation, it becomes
x + 82 - 82 = 180 - 82
x = 98 degrees
A ball is dropped from a height of 16 feet. The function f(x)=16(0.67)^x gives the height in feet of each bounce, where x is the bounce number. What will be the height of the second bounce rounded to the nearest tenth of a foot?
Answer:
Step-by-step explanation:
This is an exponential function:
[tex]y=16(\frac{2}{3})^x[/tex] that tells us that the initial height of the ball is 16 feet and that after each successive bounce the ball comes up to 2/3 its previous height. We are looking for y when x = 2, so
[tex]y=16(\frac{2}{3})^2[/tex] and
[tex]y=16(\frac{4}{9})[/tex] and
[tex]y=\frac{64}{9}[/tex] so
y = 7.1 feet
Which of the following functions has the same horizontal asymptote and
range as the function graphed below?
A. f(x) = 2^x+2 + 3
B. f(x) = 2^x+2 + 2
C. f(x) = 2^x+2 - 2
D. f(x) = 2^x+2 - 3
Answer:
C. f(x) = 2^x+2 - 3
Step-by-step explanation:
Looking at the graph and answer choices, it's obvious that the only change is the vertical shift. Since we know that the smallest value of 2^x+2 is 0, we can infer that the vertical shift will be -3 to match the horizontal asymptote of y=-3.
A box with a square base and an open top is being constructed out of A cm2 of material. If the volume of the box is to be maximized, what should the side length of the base be? What should the height of the box be? What is the maximal volume of the box? Your answers should be in terms of A.
FInd: Side length(cm), Height(cm), and Volume(cm)
Answer:
Side length = [tex]\sqrt{\frac{A}{3} }[/tex] cm , Height = [tex]\frac{1}{2} \sqrt{\frac{A}{3} }[/tex] cm , Volume = [tex]\frac{A\sqrt{A}}{6\sqrt{3} }[/tex] cm³
Step-by-step explanation:
Assume
Side length of base = x
Height of box = y
total material required to construct box = A ( given in question)
So it can be written as
A = x² + 4xy
4xy = A - x²
[tex]y = \frac{A - x^{2} }{4x}[/tex]Volume of box = Area x height
V = x² ₓ y
V = x² ₓ ( [tex]\frac{A - x^{2} }{4x}[/tex] )
V = [tex]\frac{Ax - x^{3} }{4}[/tex]
To find max volume put V' = 0
So taking derivative equation becomes
[tex]\frac{A - 3 x^{2} }{4} = 0[/tex]
A = 3 [tex]x^{2}[/tex]
[tex]x^{2}[/tex] = [tex]\frac{A}{3}[/tex]
x = [tex]\sqrt{\frac{A}{3\\} }[/tex]
put value of x in equation 1
y = [tex]\frac{A - \frac{A}{3} }{4\sqrt{\frac{A}{3} } }[/tex]
y = [tex]\frac{2 \sqrt{\frac{A}{3} } }{4 \sqrt{\frac{A}{3} } }[/tex]
y = [tex]\frac{1}{2} \sqrt{\frac{A}{3} }[/tex]
So the volume will be
V = [tex]x^{2}[/tex] × y
Put values of x and y from equation 2 & 3
V = [tex]\frac{A}{3} (\frac{1}{2} \sqrt{\frac{A}{3} } )[/tex]
V = [tex]\frac{A\sqrt{A}}{6\sqrt{3} }[/tex]
The side length is [tex]\mathbf{l =\sqrt{ \frac A3}}[/tex], the height is [tex]\mathbf{h = \frac{1}{2}\sqrt{\frac A3}}[/tex] and the maximal volume is [tex]\mathbf{V = \frac A6 \sqrt{\frac A3}}[/tex]
Let the dimensions of the box be l and h, where l represents the base length and h represents the height.
The volume is calculated as:
[tex]\mathbf{V = l^2h}[/tex]
The surface area is:
[tex]\mathbf{A= l^2 + 4lh}[/tex]
Make h the subject
[tex]\mathbf{h = \frac{A- l^2}{4l}}[/tex]
Substitute [tex]\mathbf{h = \frac{A- l^2}{4l}}[/tex] in [tex]\mathbf{V = l^2h}[/tex]
[tex]\mathbf{V = l^2 \times \frac{A- l^2}{4l}}[/tex]
[tex]\mathbf{V = l \times \frac{A- l^2}{4}}[/tex]
[tex]\mathbf{V = \frac{Al- l^3}{4}}[/tex]
Split
[tex]\mathbf{V = \frac{Al}{4}- \frac{l^3}{4}}[/tex]
Differentiate
[tex]\mathbf{V' = \frac{A}{4}- \frac{3l^2}{4}}[/tex]
Set to 0
[tex]\mathbf{\frac{A}{4}- \frac{3l^2}{4} = 0}[/tex]
Multiply through by 4
[tex]\mathbf{A- 3l^2 = 0}[/tex]
Add 3l^2 to both sides
[tex]\mathbf{3l^2 = A}[/tex]
Divide both sides by 3
[tex]\mathbf{l^2 = \frac A3}[/tex]
Take square roots
[tex]\mathbf{l =\sqrt{ \frac A3}}[/tex]
Recall that: [tex]\mathbf{h = \frac{A- l^2}{4l}}[/tex]
So, we have:
[tex]\mathbf{h = \frac{A - \frac{A}{3}}{4\sqrt{A/3}}}[/tex]
[tex]\mathbf{h = \frac{\frac{2A}{3}}{4\sqrt{A/3}}}[/tex]
Divide
[tex]\mathbf{h = \frac{2\sqrt{A/3}}{4}}[/tex]
[tex]\mathbf{h = \frac{\sqrt{A/3}}{2}}[/tex]
Rewrite as:
[tex]\mathbf{h = \frac{1}{2}\sqrt{\frac A3}}[/tex]
Recall that:
[tex]\mathbf{V = l^2h}[/tex]
So, we have:
[tex]\mathbf{V = \frac A3 \times \frac{1}{2}\sqrt{\frac A3}}[/tex]
[tex]\mathbf{V = \frac A6 \sqrt{\frac A3}}[/tex]
Hence, the side length is [tex]\mathbf{l =\sqrt{ \frac A3}}[/tex], the height is [tex]\mathbf{h = \frac{1}{2}\sqrt{\frac A3}}[/tex] and the maximal volume is [tex]\mathbf{V = \frac A6 \sqrt{\frac A3}}[/tex]
Read more about volumes at:
https://brainly.com/question/11599887
A baby otter was born 3/4 of a month early at first it's weight was 7/8 kg which is 9/10 kg less than the average weight of newborn otter in the aquarium what is the average weight of a newborn otter
Answer:
The average weight of the newborn otter is [tex]\frac{71}{40}\ kg.[/tex]
Step-by-step explanation:
Given:
A baby otter was born 3/4 of a month early at first it's weight was 7/8 kg which is 9/10 kg less than the average weight of newborn otter in the aquarium.
Now, to find the average weight of the newborn otter.
Let the average weight of the newborn otter be [tex]x.[/tex]
It's weight was = [tex]\frac{7}{8} \ kg.[/tex]
It's weight is less than the average weight of newborn by = [tex]\frac{9}{10} \ kg.[/tex]
According to question:
[tex]x-\frac{9}{10}=\frac{7}{8}[/tex]
Adding both sides by [tex]\frac{9}{10}[/tex] we get:
[tex]x=\frac{9}{10} +\frac{7}{8}[/tex]
[tex]x=\frac{36+35}{40}[/tex]
[tex]x=\frac{71}{40} \ kg.[/tex]
Therefore, the average weight of the newborn otter is [tex]\frac{71}{40}\ kg.[/tex]
Hi does anyone know how to solve this question if so please show the working out.
Explanation:
The Law of Sines is your friend, as is the Pythagorean theorem.
Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.
Then we have from the Pythagorean theorem ...
b² = 4² +(2√2)² = 24
b = √24
From the Law of Sines, we know that ...
b/sin(60°) = a/sin(θ)
y/sin(45°) = a/sin(φ)
Solving the first of these equations for "a" and the second for "y", we get ...
a = b·sin(θ)/sin(60°)
and ...
y = a·sin(45°)/sin(φ)
Substituting for "a" into the second equation, we get ...
y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)
So, we need to find the value of the coefficient ...
b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)
= √(24·2/3) = √16 = 4
and that completes the development:
y = 4·sin(θ)/sin(φ)