By the law of total probability,
[tex]P(A\cap B)=P[(A\cap B)\cap C]+P[(A\cap B)\cap C'][/tex]
but the events A, B, and C are mutually independent, so
[tex]P(A\cap B)=P(A)P(B)[/tex]
and the above reduces to
[tex]P(A)P(B)=P(A)P(B)P(C)+P(A\cap B\cap C')\implies P(A\cap B\cap C')=P(A)P(B)(1-P(C))=P(A)P(B)P(C')[/tex]
which is to say A, B, and C's complement are also mutually independent, and so
[tex]P(A\cap B\cap C')=0.5\cdot0.8\cdot(1-0.3)=0.12[/tex]
By a similar analysis,
[tex]P(A\cap B'\cap C)=P(A)P(B')P(C)=0.03[/tex]
[tex]P(A'\cap B\cap C)=P(A')P(B)P(C)=0.12[/tex]
These events are mutually exclusive (i.e. if A and B occur and C does not, then there is no over lap with the event of A and C, but not B, occurring), so we add the probabilities together to get 0.27.
Final answer:
The probability that exactly two of the independent events A, B, and C occur is 0.43, calculated by adding the probabilities of each possible pair of events occurring while the third does not.
Explanation:
The student is seeking the probability that exactly two out of the three events A, B, and C occur given their individual probabilities P(A) = 0.5, P(B) = 0.8, and P(C) = 0.3, and the fact that they are mutually independent events. To find this, we ned to consider the three scenarios where exactly two events occur: A and B, A and C, and B and C. The probability for each scenario is found by multiplying the probabilities of the two events occurring and then multiplying by the probability of the third event not occurring.
For example, the probability of A and B both occurring but not C is P(A) × P(B) × (1 - P(C)). To find the total probability that exactly two events occur, we sum up the probabilities of all three scenarios:
P(A and B but not C) = P(A) × P(B) × (1 - P(C))
P(A and C but not B) = P(A) × (1 - P(B)) × P(C)
P(B and C but not A) = (1 - P(A)) × P(B) × P(C)
We then calculate and sum these probabilities:
P(A and B but not C) = 0.5 × 0.8 × (1 - 0.3) = 0.5 × 0.8 × 0.7 = 0.28
P(A and C but not B) = 0.5 × (1 - 0.8) × 0.3 = 0.5 × 0.2 × 0.3 = 0.03
P(B and C but not A) = (1 - 0.5) × 0.8 × 0.3 = 0.5 × 0.8 × 0.3 = 0.12
Adding these probabilities together provides the final answer:
Σ P(exactly two events) = 0.28 + 0.03 + 0.12 = 0.43
Therefore, the probability that exactly two of the events A, B, and C occur is 0.43.
True or False: As long as the information reported follows the generally accepted accounting principles (GAAP) guidelines, accountants in a firm have the liberty to use personal judgment to report transactions in the firm’s financial statements.
Answer:
The given statement is true.
Step-by-step explanation:
Yes this is true.
GAAP is a collection of certain standard accounting rules for financial reporting.
Few general principles of GAAP guidelines are :
1. Principle of Regularity.
2. Principle of Sincerity.
3. Principle of Consistency.
4. Principle of Non-Compensation.
5. Principle of Continuity.
The number of visitors to a park is expected to follow the function v(x) = 8(x − 1), where x is the number of days since opening. On the first day, there will be a ceremony with 32 people in attendance. What is the function that shows total visitors, including the ceremony?
Answer:
[tex]v(x)=32+8(x-1)[/tex]
Step-by-step explanation:
We have been given that the number of visitors to a park is expected to follow the function [tex]v(x)=8(x-1)[/tex], where x is the number of days since opening. On the first day, there will be a ceremony with 32 people in attendance.
The total number of visitors including the ceremony would be number of people on ceremony plus people at x number of days since opening that is:
[tex]v(x)=32+8(x-1)[/tex]
Therefore, the function [tex]v(x)=32+8(x-1)[/tex] total visitors, including the ceremony.
asap asap asap plzzzz help
Answer: x=7
Step-by-step explanation:
Ok, so first put SR/ML=QR/KL (not dividing)
Then, fill in the blanks, x/5=4.2/3
Then, cross multiply leaving the equals sign there
x*3=4.2*5
Then, solve for x
3x=21
— —
3. 3
Lastly you get your answer of
X=7
Hope I helped
Answer:
The value of x is 7.
Step-by-step explanation:
Consider the provided figure.
It is given that both the pentagons are similar.
That means the ratio of the sides will be same and we need to find the value of x.
[tex]\frac{NM}{TS}=\frac{ML}{SR}[/tex]
Substitute the respective values in the above formula.
[tex]\frac{4}{5.6}=\frac{5}{x}[/tex]
[tex]4x=5\times 5.6[/tex]
[tex]x=\frac{28}{4}[/tex]
[tex]x=7[/tex]
Hence, the value of x is 7.
The function -6t^2+5t+56=h is used to calculate the amount of time (t) in seconds it takes for an object to reach a certain height (h). According to this function, how many seconds will it take for the object to hit the ground?
Answer:
3.5 seconds
Step-by-step explanation:
h(t) is a quadratic function, it indicate that the object start with initial height (56).
If you want to know when the object hit the ground (h=0) you have to use the quadratic formula [tex](-b +- \sqrt{b^{2}-4ac } )/2a[/tex] and take the positive root (the negative shows a negative time, so we have to discard it).
In this case: a=-6, b=5 and c=56, then the solve is 7/2=3.5
Jose is applying to college. He receives information on 7 different colleges. He will apply to all of those he likes. He may like none of them, all of them, or any combination of them. How many possibilities are there for the set of colleges that he applies to?
Answer:
128 posibilities
Step-by-step explanation:
We have 7 colleges (A,B,C,...,H) which form a set with seven elements.
What you are asking is the number of elements (or cardinality) of the set that contains all possible sets formed by those 7 elements (or the "power set").
It is known that if n is the number of elements of a given set X, then the cardinality of the power set is [tex]2^n[/tex].
Therefore, there are [tex]2^7[/tex] or 128 possibilities (or elements) for the set of colleges that he applies to.
Final answer:
The number of possible combinations of colleges that Jose can apply to from 7 options is 128. This includes the possibility of not applying to any college as well.
Explanation:
The question asks how many different combinations of colleges Jose may apply to given 7 different options.
This is a problem related to the field of combinatorics in mathematics, specifically the concept of the power set, where each college can either be chosen or not, resulting in 2⁷ possible combinations.
Since he can like none, some, or all colleges, we include the possibility of an empty set, leading to a total of 2⁷ = 128 possibilities.
In each case, Jose has two options for every college - to apply (like) or not to apply (dislike).
Therefore, the number of combinations is calculated by raising 2 (the number of options for each item) to the power of 7 (the number of items).
4. Find x if PQ = RS,
PQ = 9x - 7, and RS = 29.
Answer:
x=4
Step-by-step explanation:
Because we know that PQ = RS, we can use the transitive property to replace PQ in the first equation with 29:
9x-7=29
1) Add 7 to both sides:
9x=36
2) divide by 9 on both sides:
x=4
Final answer:
To find x, set the given equations equal to each other. Simplify the equation and solve for x. The solution is x = 4.
Explanation:
To find x, we can set the given equations equal to each other:
9x - 7 = 29
Adding 7 to both sides, we get:
9x = 36
Dividing both sides by 9, we find:
x = 4
So, x is equal to 4.
Jay has a part time job, and he earns $6.80 per hour. The taxes withheld from his weekly paycheck are 28% of his total earnings:if he works 10 hours in one week,how much I withheld for taxes.
Answer:
Tax = $19.04
Step-by-step explanation:
Hourly wage = $6.8/hr
hours worked = 10
Tax = 28%
[tex]total \: earnings =6.8 \times 10 = 68 \\ amount \: of \: tax = 68 \times 28\% = 68 \times \frac{28}{100} \\ = 19.04[/tex]
Bobby decides to sell lemonade on a hot summer day. If Bobby sells 20 glasses of lemonade for $0.20 per cup, and his average total cost is $0.17, what are Bobby's economic profits for the day? a. $0.60 b. $0.00 c. $0.20 d. $0.80
Bobby's economic profit for the day is $0.60, calculated by subtracting his total cost of $3.40 from his total revenue of $4.00. Here option A is correct.
To calculate Bobby's economic profits, we first need to understand the concept of economic profit.
Economic profit is calculated as total revenue minus total cost. Total revenue (TR) is the total amount of money earned from selling a product, which is calculated by multiplying the quantity sold (Q) by the price per unit (P). Total cost (TC) is the total expense incurred in producing a product.
In this case, we have the following information:
Bobby sells 20 glasses of lemonade at $0.20 per cup, so his total revenue is:
TR = 20 cups * $0.20/cup = $4.00
Bobby's average total cost is $0.17 per cup. Since he sold 20 cups, his total cost is:
TC = 20 cups * $0.17/cup = $3.40
Now, we can calculate Bobby's economic profit:
Economic Profit (π) = Total Revenue (TR) - Total Cost (TC)
= $4.00 - $3.40
= $0.60
So, Bobby's economic profit for the day is $0.60.
The correct option is:
a. $0.60
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What are the coordinates of point Q.
The coordinates of point Q are (0, 3).
Option C is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph,
Point Q is at y = 3 on the y-axis and 0 on the x-axis.
So,
The coordinates of point Q are (0, 3).
Thus,
The coordinates of point Q are (0, 3).
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Discribe the difference between simple interest and compound interest?
Answer:
Compound interest the interest changes annually and with simple interest the interest is the same annually
The main difference between simple interest and compound interest is that simple interest is calculated only on the initial investment, whereas compound interest is calculated on the initial principal and also on the accumulated interest of previous periods.
Explanation:The primary difference between simple interest and compound interest lies in the way they are calculated. Simple interest is calculated only on the initial amount (principal) that you invested. For example, if you invest $1000 at a simple interest of 5% per annum, your interest for the first year will be $50, and it will remain the same for all the years the money is deposited.
Compound interest, on the other hand, is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit. So, in a scenario where you invest $1000 at a compound interest of 5% per annum, your interest for the first year will be $50, but for the second year, the interest will be calculated on $1050 (Principal + Interest of first year), making the interest for the second year $52.5 rather than $50.
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this is all the question gave me 6 C 2 = _______ a0
Answer:
15
Step-by-step explanation:
Using the definition of n[tex]C_{r}[/tex]
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n! = n(n - 1)(n - 2) × 3 × 2 × 1
Hence
6[tex]C_{2}[/tex]
= [tex]\frac{6!}{2!(4!)}[/tex]
= [tex]\frac{6(5)(4)(3)(2)(1)}{2(1)4(3)(2)(1)}[/tex]
Cancel 4(3)(2)(1) on numerator/ denominator, leaving
= [tex]\frac{6(5)}{2(1)}[/tex] = [tex]\frac{30}{2}[/tex] = 15
The _____________ is the most important descriptive statistic for a categorical variable. It is calculated by dividing the number of observations in the category of interest by n, the total number of observations in all categories combined.
Answer:
Proportion
Step-by-step explanation:
Proportion is just the division of the data that meets the description, between the total number of data present in the study.
For example, let's suppose that we have a tiger, a lion, a sheep, a cow and a horse, and we want to know the proportion of animals that eat meat, then, only 2 out of 5 of those eat meat, the tiger and the lion, meaning [tex]\frac{2}{5}[/tex], which would be the proportion, or 0.40
How to find the probability? Please show your work. Thanks!
The event of the machine working is [tex]A\cap B\cap C\cap D[/tex], and since the components operate independently, we have
[tex]P(A\cap B\cap C\cap D)=P(A)P(B)P(C)P(D)[/tex]
so just multiply the given probabilities together,
[tex]P(A\cap B\cap C\cap D)=0.99^2\cdot0.94\cdot0.93\approx0.8568[/tex]
Christina is tying tow pieces of string together to make a single piece. Her knot will reduce the lenght of each piece by 1/4 inch. If one piece is 3 1/4 inches long and the other is 5 1/2 inches long, what will be the length of the single piece of string?
Answer:
8 1/4 inches
Step-by-step explanation:
(3 1/4 - 1/4) + (5 1/2 - 1/4) = 3 + 5 1/4 = 8 1/4 . . . inches
Find the least common denominator of the fractions: 3/5 and 2/7
Answer:
35
Step-by-step explanation:
5 and 7 are both prime numbers, so the least common multiple of 5 and 7 is their product, 5 * 7 = 35
The least common denominator of the fractions 3/5 and 2/7 is found by determining the least common multiple of the denominators 5 and 7. Since they are prime numbers, their LCM is their product, which is 35.
Explanation:To find the
least common denominator
(LCD) of the given
fractions
, 3/5 and 2/7, we must find the least common multiple (LCM) of the two
denominators
5 and 7. The LCM of any two numbers is the smallest number that both numbers can divide evenly into. Since 5 and 7 are prime numbers, the LCM is simply their product, which is 35. Therefore, the least common denominator of 3/5 and 2/7 is 35.
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After creating a hypothesis, Janis decides how to best measure the impact of her manipulation. This variable that is impacted by manipulating the independent variable is known as _____
Answer:
This variable that is impacted by manipulating the independent variable is known as dependent variable
Step-by-step explanation:
One of the methods to test a hypothesis is the use of independent variable. The independent variable is manipulated to know if the change will be effective or not.
The variable which will be impacted by the independent variable is called dependent variable. The researcher manipulated the values for independent variable to check if the dependent variable changes or not ..
You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324π cubic inches. What is the least possible height of the container?
Answer:
The answer to your question is: h = 9 in
Step-by-step explanation:
Data
radius = 6 inches
V = 324 π in³
h = ?
Formula
V = πr²h
Then, we solve it
324π = πr²h cancel π
324 = r²h substitution
324 = 6² h
h = 324 /6² simplify
h = 324/36
h = 9 in result
Utilizing the volume formula for a cylinder, we can calculate the minimum height required for a volume of 324π cubic inches. Given a radius of 6 inches, we solve the formula to find a minimum cylinder height of 9 inches.
Explanation:The subject of this question is mathematics, specifically geometry focusing on the properties of cylinders. In this instance, we want to calculate the minimum height of a cylinder that can hold a specified volume. The formula to find the volume of a cylinder is V = πR²h, where 'R' is the radius and 'h' is the height.
Given that the radius is 6 inches and the desired volume is 324π cubic inches, we can insert these values into our formula. So, 324π = π*(6)²*h which simplifies to 324 = 36h. Then, we need to solve for 'h', which involves dividing 324 by 36. The result shows that the minimum height 'h' of the cylinder is 9 inches.
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20 POINTS AND BRAINLIEST PLZ HELP
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
A. −4
B. −2
C. 2
D. 4
Answer:
4
Step-by-step explanation:
Recall that for a function f(x) and for a constant k
f(x+k) represents a horizontal translation for the function f(x) by k units in the negative-x direction.
Hence f(x+k) is simply the graph of f(x) that has been moved left (negative x direction) by k units.
From the graph, we can see that g(x) = f(x+k) is simply the graph of f(x) that has been moved 4 units in the negative x-direction.
hence K is simply 4 units.
Answer:
Step-by-step explanation:
Yes I'd have to agree with @previousbrainliestperson
I'd go with solid 4
One of your household chores is to do the dishes every night after dinner.Your parents come to you with two choices about how you want to earn your allowance. Option one: is that you will be paid $250.00 at the end of every month for the work you do Option two: is that they will pay you a penny the first day and double your play each day for the rest of the month Which method of payment is the better deal? Use a problem solving strategy to determine your answer. Explain, in clear sentences, why your decision is the best one. Your explanation must prove why the method you chose is the better option
Answer:
the penny option is the much better deal
Step-by-step explanation:
The sequence of pay amounts for the "penny option" is ...
$0.01, $0.02, $0.04, $0.08 ...
For day n, the amount of pay is $0.01·2^(n-1). For day 30, the amount of pay is ...
$0.01·2^29 = $5,368,709.12
In case you can't tell, the "penny option" is a much better deal than $250.00. (You might need to credit check your parents before accepting this deal. I know my parents could not make good on this "penny option" offer.)
The total amount for the 30 days will be double this amount, less one cent, or ...
$10,737,418.23
_____
Sum of a geometric sequence
The daily payments of the penny option are a geometric sequence. The sum of n terms of such a sequence is given by ...
Sn = a1(r^n -1)/(r -1)
where a1 is the first term ($0.01) and r is the common ratio (2). In our case, the sum for n days is ...
Sn = $0.01·(2^n -1)
On day 15, this will already be more than $250. The accumulated pay on that day will be $0.01·(2^15-1) = $327.67.
Two angles are supplementary. the measure of one angle is 4 more than 2 times the measure of teh other andgle. Write an equation that can be used to find the measures?
Answer:
[tex]y=58.67^{\circ}[/tex]
[tex]x=121.33^{\circ}[/tex]
Step-by-step explanation:
We are given that two angles are supplementary .
We have to write an equation that can be used to find the measures.
Let x and y are supplementary
According to question
[tex]x+y=180^{\circ}[/tex]( by definition of supplementary angles)
[tex]x=2y+4[/tex]
Substitute the value then we get
[tex]2y+4+y=180[/tex]
[tex]3y=180-4[/tex]
[tex]3y=176[/tex]
[tex]y=\frac{176}{3}[/tex]
[tex]y=58.67^{\circ}[/tex]
Substitute the value then, we get
[tex]x+58.67=180[/tex]
[tex]x=180-58.67[/tex]
[tex]x=121.33^{\circ}[/tex]
Anthony leaves Kingstown and drives 160 miles to Albany. He leaves at 2:00 p.m. At 2:15p.m., Emily leaves Albany and drives to Kingstown at 40 m.p.h. If Anthony is driving 45 m.p.h., at what time do they pass each other on the road?
Answer:
The time at which the pass each other on the road is 4:00 pm
Step-by-step explanation:
The first step is to write the equations that give us the position of Emily and Anthony, these are give by:
[tex]x_A = x_{A0}+v_At[/tex] for Anthony
[tex]x_E=x_{E0}+v_Et[/tex] for Emily
Since Antony drives 160 miles to Albany, we can claim that the distance from Kingstown to Albany is 160 miles.
Let us set the initial position of Antony in Kingstown and consider it as the origin of our coordinate system. In this way, [tex]x_{A0}=0[/tex].
This automatically tells us that Emily initial position, in Albany, is 160 miles from our origin, hence [tex]x_{E0} = 160 miles[/tex].
Now, we need to define where to start counting the time. In this problem, it is easier to set time zero when Emily leaves. The reason for this is that now, we can say that when Emily left, Anthony was already traveling during 15 mins (remember Emily departing time was 2:15 pm and Anthony's time was 2:00 pm) and Anthony's initial position was from Emily's point of view was different from zero. We can calculate this distance as the multiplication of the time Anthony was traveling times the speed at which he was driving. This is:
[tex]x_{A0}=v_At[/tex]
being [tex]t[/tex] the 15 mins he traveled before Emily started and [tex]v[/tex] the 45 m.p.h given by the problem. We also need to convert 15 mins to hours, which gives 0.25 hours. Thus:
[tex]x_{A0}=45*0.25\\x_{A0}=11.25[/tex] miles
and the position equations are now:
[tex]x_A= 11.25 + v_At[/tex] for Anthony
[tex]x_E=160 + v_Et[/tex]
Since we are asked the time at which the pass each other on the road we need to equals their positions, [tex]x_A=x_E[/tex]:
[tex]11.25+v_At=160-v_Et[/tex]
Notice here that Emily's position is negative since she is moving towards the origin of our system, meaning in the negative direction. Solving for [tex]t[/tex]:
[tex]11.25+v_At=160-v_Et\\v_At+v_Et=160-11.25\\t(v_A+v_E)=148.75\\t = \frac{148.75}{v_A+v_E}[/tex]
Substituting the values of [tex]v_A=45[/tex] and [tex]v_E=40[/tex]:
[tex]t = \frac{148.75}{45+40}=\frac{148.75}{85}\\t=1.75 h[/tex]
What we have calculated is the time interval from where we start counting the time and remember this was set at 2:15 pm when Emily left. Since the exercise asks for the hours of the day we need to add the time interval to 2:15 pm and:
[tex]1.75 h = 1 h+45 min[/tex]
And 2:15 pm + 1 h is 3:15 pm + 45 mins is 4:00 pm which is the time at which the pass each other on the road.
Final answer:
Anthony and Emily will cross paths at 4:00 p.m. after calculating the distance covered by Anthony and the remaining distance between them when Emily starts driving, with their combined speed taken into consideration.
Explanation:
To solve this question, we need to calculate the time when Anthony and Emily will cross paths on the road, given that they are traveling towards each other from Kingstown to Albany and vice-versa. Anthony drives at 45 mph whereas Emily drives at 40 mph
Let's first find out how far apart they are when Emily starts her journey at 2:15 p.m. Since Anthony left at 2:00 p.m. and drives for 15 minutes until Emily starts her journey, we calculate the distance he has covered as:
Distance = Speed × Time = 45 mph × 0.25 hours (since 15 minutes is 0.25 of an hour) = 11.25 milesNow, the remaining distance between them is:
160 miles - 11.25 miles = 148.75 milesThe combined speed at which they're closing the distance is:
45 mph + 40 mph = 85 mphTo find the time it takes for them to meet, we use the formula:
Time = Distance / Speed = 148.75 miles / 85 mph ≈ 1.75 hoursSince 1.75 hours is 1 hour and 45 minutes, they will meet at:
2:15 p.m. + 1 hour and 45 minutes = 4:00 p.m.Therefore, Anthony and Emily will cross paths at 4:00 p.m.
A park ranger uses exponential functions to model the population of two species of butterflies in a state park.
The population of species A, x years from today, is modeled by function f.
f(x) = 1,400(0.70)x
The population of species B is modeled by function g, which has an initial value of 1,600 and increases by 20% per year.
Which statement correctly compares the functions modeling the two species?
A.
The populations of both species are increasing, but the population of species B is growing at a faster rate than species A.
B.
The population of species A is decreasing, and it had the greater initial population.
C.
The populations of both species are increasing, but the population of species A is growing at a faster rate than species B.
D.
The population of species A is decreasing, and it had the smaller initial population.
Answer:D
THE POPULATION OF SPECIES A IS DECREASING. AND IT HAD THE SMALLER INITIAL POPULATION
The statement that correctly compares the given functions is - 'The population of species A is decreasing, and it had the smaller initial population.'
The correct answer is an option (D)
What is an exponential function?"A function of the form [tex]f(x)=b^x[/tex] where b is constant."
What is exponential growth formula?" [tex]f(x) = a (1 + r)^x[/tex]
where a is the initial value
r is the growth rate
x is time"
For given question,
We have been given a exponential function [tex]f(x) = 1400(0.70)^x[/tex]
This function represents the population of species A, x years from today.
The population of species B is modeled by function g, which has an initial value of 1,600 and increases by 20% per year.
a = 1600
r = 20%
= 0.2
Using the exponential growth formula the exponential function that represents the population of species B would be,
[tex]g(x) = 1600 (1 + 0.2)^x\\\\g(x)=1600(1.02)^x[/tex]
We know that, if the factor b ([tex]f(x)=a\bold{b}^x[/tex]) is greater than 1 then the exponential function represents the growth and if b < 1 then the exponential function represents the decay of population.
From functions f(x) and g(x) we can observe that, the population of species A is decreasing, and it had the smaller initial population.
So, the correct answer is an option (D)
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A person stands 10 meters from a lamppost at night. If the person is 2 meters tall and the lamppost is 6 meters tall, how long is their shadow cast by the lamp?
Answer:
5 meters
Step-by-step explanation:
The height of the lamppost above the person is twice the height of the person, so the distance between the lamppost and person is twice the length of the person's shadow. (A diagram can help you see this.)
The person's shadow is (10 m)/2 = 5 m long.
___
Check
The tip of the shadow is 15 m from the lamppost, 2.5 times the height of the lamp. The tip of the shadow is also 5 m from the person, 2.5 times the height of the person. The triangles involved are similar.
Final answer:
To find the length of the person's shadow, we use the properties of similar triangles defined by the person and the lamppost. By setting up a proportion between the person's and the lamppost's height to their respective shadow lengths and solving, we find the person's shadow is 5 meters long.
Explanation:
To solve the problem of determining the length of the shadow cast by the person standing 10 meters from the lamppost at night, we can use the concept of similar triangles.
Since the light source (lamppost) is above ground level, the triangle formed by the lamppost, the end of the shadow, and the top of the person's head is similar to the triangle formed by the person, their shadow, and the ground. Using the properties of similar triangles, the ratios of corresponding sides are equal.
Let's denote the length of the person's shadow as s. The triangles' corresponding sides' ratios would be:
The person's height (2 meters) to the length of their shadow (s meters)The lamppost's height (6 meters) to the distance from the lamppost to the end of the shadow (10 + s meters)Setting up the proportion, we have:
2 / s = 6 / (10 + s)
By cross-multiplying and solving for s, we get:
2(10 + s) = 6s
20 + 2s = 6s
4s = 20
s = 5
Hence, the length of the person's shadow is 5 meters.
A point is rotating with uniform circular motion on a circle of radius r. Find ω if
r = 9 cm and v = 3 cm/sec.
Answer:
w = 0.333
Step-by-step explanation:
In circular motion you have:
v = wr
replacing:
3 = 9w
0.333 = w
The angular speed of a point with r = 9 cm and v = 3 cm/sec is 0.33 rad/s
The angular speed?
The angular speed (ω) is given by:
ω = v/r
Where v is the linear speed and r is the radius.
Given that v = 3 cm/sec = 0.03 m/s, radius = 9 cm = 0.09 m, hence:
ω = v/r = 0.03/0.09 = 0.33 rad/s
The angular speed of a point with r = 9 cm and v = 3 cm/sec is 0.33 rad/s
Find out more on angular speed at: https://brainly.com/question/6860269
How many phone numbers are possible in the (770) area code if: For the form ABC-XXXX, A is restricted to numbers 2-9. B, C, and X can be any digit 0-9. Also, the number 867-5309 is not used.
a. 6,999,999 c.7,999,999
b. 7,000,000 d.8,000,000
Answer:
c.7,999,999
Step-by-step explanation:
The phone number is of the form ABC - XXXX
A can be any number from 2 - 9. This means number of possible values for A are 8.
The rest of the places B,C and X can be any digit from 0 - 9. This means there are 10 possible values for each of these.
Since, value to A can be assigned in 8 ways, and to the rest of the 6 positions in 10 ways, according to the fundamental rule of counting, the total number of possible phone numbers that can be formed will be equal to the product of all the individual ways:
Total possible phone numbers = 8 x 10 x 10 x 10 x 10 x 10 x 10
Since, 1 of the given number: 867-5309 is not used, the total possible phone numbers will be:
Total possible phone numbers = [tex]8 \times 10^{6} - 1 = 7999999[/tex]
Hence, option C: 7,999,999 give the correct answer.
Final answer:
The answer calculates the possible phone numbers in the (770) area code with given restrictions, ending up with 7,999 possible phone numbers.
Explanation:
To calculate how many phone numbers are possible in the (770) area code with the given restrictions, we first determine the possibilities for each digit:
A (restricted to 2-9): 8 optionsB, C, X (0-9 for each digit): 10 options each
So, the total number of possible phone numbers is: 8 (A) * 10 (B) * 10 (C) * 10 (X) = 8,000. However, we need to exclude the number 867-5309, so the final count is 8,000 - 1 = 7,999.
elley is mixing blue and yellow food coloring to make green food coloring for her bakery. The relationship between the amounts of food coloring she mixes can be modeled by the equation b=2/3y, where b represents the amount of blue food coloring and y represents the amount of yellow food coloring. Which of the following statements is true?
A.
Kelley uses 2 parts blue for every 3 parts yellow.
B.
Kelley uses 3 parts blue for every 2 parts yellow.
C.
Kelley uses 2 parts blue for every 5 parts yellow.
D.
Kelley uses 5 parts blue for every 2 parts yellow.
Answer:
A. Kelley uses 2 parts blue for every 3 parts yellow.
Step-by-step explanation:
Given equation that shows the amount of blue food coloring,
[tex]b=\frac{2}{3}y[/tex]
Where,
y = amount of yellow food coloring,
If y = 2,
[tex]b=\frac{2}{3}\times 2=\frac{4}{3}[/tex]
i.e. [tex]\frac{4}{3}[/tex] parts of blue for every 2 parts yellow.
If y = 3,
[tex]b=\frac{2}{3}\times 3=2[/tex]
i.e. 2 parts of blue for every 3 parts yellow.
If y = 5,
[tex]b=\frac{2}{3}\times 5=\frac{10}{3}[/tex]
i.e. [tex]\frac{10}{3}[/tex] parts of blue for every 5 parts yellow.
Hence, OPTION A is correct.
declaration a plane at the uniform rate of 8.0 meter/second ^2 , a pilot stops the plane in 484 meters. how fast was the plane going before breaking began ?
Answer:
88 m/s
Step-by-step explanation:
The appropriate formula relating initial speed v, acceleration a, and distance d is ...
v² = 2ad
v² = 2(8 m/s²)(484 m) = 7744 m²/s²
Taking the square root gives ...
v = √7744 m/s = 88 m/s
Using an independent-measures t, the 90% confidence interval for the difference between two population means ranges from 19 to 23. Based on this confidence interval, you can conclude that the difference between the two sample means is ____.a) 4 pointsb) 19 pointsc) 21 pointsd) 23 points
Answer:
b
Step-by-step explanation:
We must determine the the x value at 90% confidence interval. We find this from a table relating confidence intervals and x values. For 90%, z is 1.645.
WE must determine the mean of 19 and 23:
[tex]=(19+23)/2=21[/tex]
We must determine the standard deviation. We let n be the number of population which is 2. We need to take the numbers 19 and 23 and subtract each by the mean and square the answer:
[tex](19-2)^2=289[/tex]
[tex](23-2)^2=441[/tex]
We then determine the mean of these two values as:
[tex](289+441)/2=365[/tex]
Now we take the square root of 365:
[tex]\sqrt{365}=19.1[/tex]
The standard deviation is 19.1
The answer is b
The total number of eggs, T, collected in one day from a chicken coop is proportional to the number of chickens, C, in the coop. If each chicken laid the same number of eggs, 4, which equation could be used to find the total number of eggs collected from the coop?
Answer:
T = 4C.
Step-by-step explanation:
T = 4C.
Total number of eggs = 4 * number of chickens.
At the beginning of this month, Diego had $272.79 in digital money. So far
this month he has made deposits of $26.32, $91.03, and $17.64 into his
account, while he has made withdrawals of $31.08, $29.66, and $62.19. How
much digital money does Diego have now?
O
A. $530.71
B. $14.87
O
c. $284.85
O
D. $260.73
SUSMIT
Answer:
Option c. $284.85
Step-by-step explanation:
we know that
The amount of money Diego now has is equal to the amount of money he originally had plus deposits minus withdrawals.
so
[tex]272.79+(26.32+91.03+17.64)-(31.08+29.66+62.19)\\272.79+134.99-122.93\\\$284.85[/tex]