The probability of any one person visiting a particular station is 1/3. Since there are three people in the family, the probability that they would all visit the same station is 1/3 x 1/3 x 1/3, which is equal to 1/27.
The probability that all three members of the family visit the same station at the medical clinic is 1/27 (1/3 x 1/3 x 1/3). This is because each person has an equal chance of being assigned to any of the three stations and since there are three people in the family, the probability that they would all visit the same station is 1/3 multiplied by itself three times, which is equal to 1/27. The experiment is recording the station number for each member and since the incoming individuals are assigned to any of the three stations randomly, the probability that all three members visit the same station is 1/27.
The complete question is :
A family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that all three members visit the same station?
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
A train leaves the station at time t=0. Traveling at a constant speed, the train travels 380 kilometers in 3 hours. The function that relates the distance traveled d to the time t is?
Answer:
.
Step-by-step explanation:.
an had 480 mangoes. He gave Lucy 25% and John 10% of the remainder. He est. How many did he keep?
Answer: 324
Step-by-step explanation: Take 25% and enter it into a calculator with the percentage sign and times it by 480 and then subtract the number you get from 480, which is 360. Take 10% and enter it and times it by 360 and subtract that number from 360 and you should get 324. :)
Candice is taking a group nature hike in a park. There is a $15.00 fee just to enter the park. I’m addition the tour group charges $0.31 per mile they hike. She brought $93.00 with her. Which equation can be used to determine how many miles can she hike
Answer:
Step-by-step explanation:
15+.31x ≤ 93
3x−8 /2=x−6
Enter your answer in the box.
x =
Step-by-step explanation:
[tex]3x - \frac{8}{2} = x - 6[/tex]
[tex] \frac{8}{2} = 4[/tex]
[tex]3x - 4 + 4 = x - 6 + 4[/tex]
[tex]3x = x - 6 + 4[/tex]
[tex]3x - x = - 6 + 4 - x[/tex]
[tex]3x - x = - 6 + 4[/tex]
[tex]2x = - 2[/tex]
[tex] \frac{2x}{2} = \frac{ - 2}{2} [/tex]
[tex]x = - 1[/tex]
I need help in this activities, please
The option that would give the most money after 2 years would be Option 1.
How to find the better option ?The amount that Option 1 would give after 2 years is:
= Amount invested x ( 1 + rate / number of periods ) ^ number of periods in quarters
= 1, 000 x ( 1 + 12 % / 4 ) ⁴ ˣ ²
= $ 1, 267
The amount Option 2 would give after 2 years with continuous compounding is:
= Amount to invest x e ^ ( rate x number of periods)
= 1, 000 x e ^ ( 6 % x 2 years )
= $1, 127 .50
Option 1 is the better option.
Find out more on compounding continuously at https://brainly.com/question/14303868
#SPJ1
HELP pls will mark you the brainliest
An equation for the total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:
Let the variable x represent the number of kites purchased.Let the variable s represent the total cost.Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:
y = 2x + 20
When x = 4, the total cost for Wendy kites is given by:
y = 2(4) + 20
y = $28.
When x = 7, the total cost for Wendy kites is given by:
y = 2(7) + 20
y = $34.
When x = 10, the total cost for Wendy kites is given by:
y = 2(10) + 20
y = $40.
Read more on equation here: brainly.com/question/19855458
#SPJ1
Help me with this……..
Answer:
3239609472 Km
Step-by-step explanation:
I need help with this question
The value of x is equal to 16
What is the Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².
Given here: A right angle triangle
let the triangle be ABC with AC as the hypotenuse and AB is the perpendicular and BC is the base of the triangle. And D be a point on AC with AD=32 and DC=8 .Clearly the perpendicular using the pythagoras theorem
AB=[tex]\sqrt{x^2+32^2}[/tex]
Now in triangle BDC we have BC= [tex]\sqrt{x^2+64}[/tex]
Again a triangle ABC we have
AC²=BC²+AB²
[tex]40^2=x^2+64+x^2+32^2\\2x^2=40^2-32^2-64\\2x^2=512\\x^2=256\\x=16[/tex]
Thus x is equal to 16
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ1
Solve the following expression if x = 6 1/2 x + 7.5 (x) + 11.4 + 2.6
The expression is solved with x = 6 to 62
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, factors and constants.
They are also composed of mathematical operations
From the information given, we have that;
1/2 x + 7.5 (x) + 11.4 + 2.6
Now, expand the bracket
1/2x + 7.5x + 11.4 + 2.6
Substitute the value of x as 6 , we get;
1/2(6) + 7.5(6) + 11.4 + 2.6
Multiply the values
3 + 45 + 11.4 + 2.6
Add the values
62
Hence, the value is 62
Learn about algebraic expressions on:
https://brainly.com/question/4344214
#SPJ1
Ms. Williams counted students by eye color. The table shows how many students had each eye color.
Brown 21
Blue 6
Green 3
Write a ratio to compare blue eyes to green eyes.
6:21
one half
2:1
6 to 30
Answer: One Half
Step-by-step explanation: 3 is half of 6 and I took the test ;)
13 and 8/9 rounded to the nearest whole number
Answer:
14
Step-by-step explanation:
8/9 = 0.888888888......
<5 round down
[tex]\geq[/tex]5 round up
8/9 = 0.888888888....
larger than 0.5
the answer is 14
Pls does anyone know what I need to do to move on I've tried plotting another point but it won't let me? Pls if anyone knows tell me asap! I'll give 80 points!
A graph of the solution (4, 4) for the system of linear equations is shown in the image attached below.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
In this context, we would replace the y-value of the first equation 4x - 2y = 8 with zero (0) as follows;
4x - 2(0) = 8
4x = 8
x = 2 ⇒ (2, 0).
For the y-intercept of the first equation 4x - 2y = 8, we would substitute the x-value with zero (0) as follows;
4(0) - 2y = 8
2y = -8
y = -4 ⇒ (0, -4).
For the y-intercept of the first equation y = 3x/2 - 2, we would substitute the x-value with zero (0) as follows;
y = 3(0)/2 - 2
y = -2 ⇒ (0, -2).
Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of linear equations is at the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is equal to the ordered pair (4, 4).
Read more on equation here: brainly.com/question/19855458
#SPJ1
Last question and its below
The correct option for the true proportion is AB/EF = CD/GH (option D)
What are similar figures?Two figures are called similar if they have equal corresponding angles and their side are in same ratios,
Given that, there are two similar polygons, ABCD and EFGH, we need to find the true proportion for the side of the polygons,
We know that, similar figure have equal ratios of the corresponding sides,
Therefore, we get,
AB/EF = CD/GH = BC/FG = AD/EH
From the options given, the true proportion is
AB/EF = CD/GH (option D)
Hence, the correct option for the true proportion is AB/EF = CD/GH (option D)
Learn more about similar figures, click;
https://brainly.com/question/23637627
#SPJ1
What is the probability exactly one card drawn is a heart when playing cards
If you draw 2 cards, the probability of drawing 1 heart and 1 non-heart card are: 26/676.
How is the probability determined?It's crucial to keep in mind that your chances may change depending on the particular rules of the card game you're playing. B. The quantity of cards in the deck, the number of cards drawn, and whether or not the cards drawn after play were replaced.
A regular deck of 52 cards has a chance of producing exactly one heart depending on how many cards are drawn.
The likelihood of drawing a heart if you only draw one card is 13/52, or 1/4.
The probabilities of getting a card with a heart and a non-heart are:
(13/52) × (39/51) + (39/52) × (13/51) = 26/676
And if more cards are drawn, the odds of drawing exactly one heart are different.
To know more about probability visit:
brainly.com/question/30034780
#SPJ1
Are the two triangles similar? If so, how do you know *
Not Similar
Similar by AA~
Similar by SAS~
Similar by SSS~
Answer:
Similar by AA/SAS
Step-by-step explanation:
20.8/8 = 23.4/9 = 2.6
So, the bottom of the smaller triangle is parallel the bottom of the larger one (Thales' theorem)
So, corresponding angles are equal and hence, they are similar by AA similarity.
Note: As sides are given, similarity can also be proven by SAS.
data with 320 observations are drawn from a bell-shaped distribution with a mean of 62 and a standard deviation of 15. approximately how many observations are more than 92? (round your answer to the nearest whole number.)
Answer:
as 92 is 2 std deviaiton above mean ; th
Step-by-step expla
Question 12 (Essay Worth 10 points)
(Comparing Types of Interest MC)
Asmall business owner is applying for a small business loan and has been approved for a $50,000 loan with 5.25% annual interest. The first loan is a simple interest rate, the second loan compounds interest quarterly, and the third loan compounds
interest continuously. The small business owner plans to pay off the loan in 3 years and 8 months
Part A: Determine the total value of the loan with the simple interest Show all work and round your answer to the nearest hundredth (3 points)
Part B: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth (3 points)
Part C: Determine the total value of the loan with the continuously compounded interest Show all work and round your answer to the nearest hundredth (2 points)
Part Di Using the values from Parts A, B, and C, explain which loan option is the best choice for the small business owner (2 points)
The total value of the loan in simple interest is $59,625, which is the lowest amount and hence is the best option.
What is Simple and Compound Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Compound interest is defined as the amount of interest which has been calculated on the principal amount and the amount accumulated over the previous period.
Principal amount, P = $50,000
Rate of interest, r = 5.25% = 0.0525
Time,t = 3 years 8 months = 3 + 0.6667 years = 3.6667 years
Part A :
For simple interest, total amount is,
A = P (1 + rt) = 50,000 ( 1 + (0.0525 × 3.6667 ))
= $59,625
Part B :
For compounded interest. total amount is,
A = P (1 + [tex]\frac{r}{n}[/tex])^(nt), where n is the number of times compounding is done in an year.
Here, n = 4, since compounding is quarterly
A = 50,000 [ 1 + [tex]\frac{0.0525}{4}[/tex]] ^(4 × 3.6667)
= $60,537.9639 ≈ $60,537.96
Part C :
For continuously compounded interest, final amount is,
A = P [tex]e^r^t[/tex]
= 50,000 [tex]e^{0.0525*3.6667[/tex]
≈ 60,613.83
Part D :
The option of simple interest is best for the small business owner since the total value of the loan is lowest for it.
Hence the value of the loan for simple interest is $59,625, value of the loan when compounded quarterly is $60,537.96 and the value of the loan when continuously compounded is 60,613.83. Simple interest is the best option since the value of the loan is lowest for it.
Learn more about Simple and Compound Interest here :
https://brainly.com/question/22621039
#SPJ1
the person swims at 5 kilometers per hour and runs at 20 kilometers per hour. for what distance x is the total time for swimming and running 3 hours? round to the nearest tenth of a kilometer. (hint: time swimming time running
The total distance covered while swimming and running for a total of 3 hours is 45 kilometers.
In mathematics, the term "total" refers to the sum of two or more values. It is used to describe the combined or complete amount of a quantity. The total can be calculated by adding together all the individual values in a set or series.
The distance x can be calculated by using the formula:
distance = rate * time
For swimming, the rate is 5 kilometers per hour, and the time is t₁. So, the distance covered while swimming is:
d₁ = 5 * t₁
For running, the rate is 20 kilometers per hour, and the time is t2. So, the distance covered while running is:
d₂ = 20 * t2
The total time for swimming and running is 3 hours, so:
t₁ + t₂ = 3
The total distance covered while swimming and running is x, so:
x = d₁ + d₂
Substituting the values of d₁ and d₂, we get:
x = 5 * t₁ + 20 * t₂
Now, substituting the value of t₁ + t₂ = 3, we get:
x = 5 * t₁ + 20 * (3 - t₁)
Expanding the equation, we get:
x = 5 * t₁ + 60 - 20 * t₁
Combining the like terms, we get:
x = -15 * t₁ + 60
Substituting the value of t₁ = 3 - t2, we get:
x = -15 * (3 - t2) + 60
Expanding the equation, we get:
x = 45 - 15 * t₂
Now, we have to find the value of t₂ such that x is maximum.
Taking the derivative of x with respect to t₂, we get:
dx/dt₂ = -15
So, t₂ is a decreasing function of x. Hence, when t₂ is maximum, x is also maximum.
As t₂ cannot be negative, the maximum value of t₂ is 0. Hence,
t₂ = 0
Substituting the value of t₂ = 0 in the equation x = 45 - 15 * t₂, we get:
x = 45
To know more about total here
https://brainly.com/question/14286201
#SPJ4
for the 5 days shown in the graph, how many kilowatt-hours greater was the median daily electricity use than the average (arithmetic mean) daily electricity use?
The median daily electricity use is 1 kW-hr than the average (arithmetic mean) daily electricity use.
The median is the middle value of a set of data when the data is arranged in order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.
The data in ascending order is : 19 24 27 29 31
The median of the data is 27.
The mean, or average, is calculated by summing all the values in a set of data and dividing by the total number of observations.
Average of the data is
= ( 19 + 24 + 27 + 29 + 31)/ 5
= 26
The difference is therefore
= 27 - 26
= 1
To know more on median
https://brainly.com/question/28060453
#SPJ4
Shelley bought cupcakes for her sister's birthday party. 25% of the 64 cupcakes had sprinkles on top. How many cupcakes had sprinkles?
Answer:
16
Step-by-step explanation:
You need to find 25% of 64.
To find a percent of a number, multiply the percent by the number.
25% of 64 = 25% × 64
To multiply a percent by a number, change the percent to a decimal by dividing the percent by 100. Move the decimal point two places to the left.
25% × 64 = 0.25 × 64 = 16
Jessica locates her garden using a coordinate grid with yards as the units. The two points (8, -2) and (5, -3) represents the two corners of the garden. Approximately how far apart are the two corners?
The distance between the two corners of the garden is approximately equal to 3 units.
How to calculate the distance between the two corners?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given parameters into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(5 - 8)² + (-3 - (-2))²]
Distance = √[(-3)² + (-3 + 2)²]
Distance = √[(-3)² + (-1)²]
Distance = √(9 + 1)
Distance = √10
Distance = 3.1623 ≈ 3 units.
Read more on distance here: brainly.com/question/12470464
#SPJ1
If Quadrilateral ABCD is dilated about the origin using a scale factor of 12 to make Quadrilateral A′B′C′D′, what will be the coordinates of A′, B′, C′, and D′?
The coordinates of A', B', C' and D' are obtained as follows:
A': each coordinate of A(x-coordinate and y-coordinate) is multiplied by the scale factor of 12.B': each coordinate of B is multiplied by the scale factor of 12.C': each coordinate of C is multiplied by the scale factor of 12.D': each coordinate of D is multiplied by the scale factor of 12.What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Hence the coordinates of the dilated figure are obtained multiplying it's respective coordinates on the original figure by the scale factor.
Missing Information
The problem is incomplete, hence the answer was given in general terms.
More can be learned about dilation at brainly.com/question/3457976
#SPJ1
In Jess's swimming club there are 16 members who prefer apples, 12 who prefer strawberries and 22 who prefer oranges. Jess chooses a member from the club at random. Find the probability that Jess chooses a member who prefer apples.
Answer:
34/50 or 68% or 0.68
Step-by-step explanation:
S= {16, 12, 22}
16 + 12 + 22 = 50
50 - 16 = 34
34/50
or
68%
or
0.68
Brett baked 36 cookies with 3 scoops of flour. With 4 scoops of flour, how many cookies can Brett bake? Solve using unit rates.
Answer:
Step-by-step explanation: what you have to do is 36 divided by 3 because he used 3 scoops = 12 now 12 x 4( amount of how many scoops he used)= 48
* you times 4 by 12 because that's the amount he makes with 1 scoop
which triangle does not belong with the other three triangles?
The first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
The base lengths 12, 6, and 18 of the first three triangles corresponds in proportion but does not for the last triangle with 8.
The side 6, 3, and 9 corresponds in proportion but does not for the side 4 of the last triangle
And lastly, the side 8, 4, and 12 of the first three triangles corresponds in proportion but does not for the last triangle with side length 6.
Therefore, the first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.
Know more about similar triangles here:https://brainly.com/question/14285697
#SPJ1
A question for the nerds
Could Brittany be 27 years old and Nate 26? Why or why not?
If twice Brittany's age is less than the age of Abraham Lincoln when he died, then the answers are;
2b < 56
n = b - 2
b = n + 2
b < 28
n = b - 2 < 26
Yes, Brittany could be 27 years old and Nate 26
How to express inequality?Let Brittany's age = b
Twice Brittany's age = 2 × b = 2b
Lincoln's age = 56
Inequality to represent Brittany's age: 2b < 56
b < 56/2 = 28
Nate's age = n
in terms of Brittany's age: n = b - 2
Isolating b: b = n + 2
Substituting b: b < 28
Solving for b: b < 28 and n = b - 2 < 26
Could Brittany be 27 years old and Nate 26? Yes, Brittany could be 27 years old and Nate 26 as both are within the range defined by the inequality (b < 28 and n < 26).
Learn more on inequality here: https://brainly.com/question/25275758
#SPJ1
The complete question is:
Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death. Write an inequality to represent Brittany’s age, b. Brittany’s brother, Nate, is two years younger than Brittany. Write an equation for Nate’s age, n, in terms of Brittany’s age, b. Rewrite the expression from Part B to get the variable b alone on one side of the equation. (This is also called isolating b.) Substitute the value of b from Part C into the inequality you found in Part A. Solve the inequalities from parts A and D for the variables b and n, respectively. Could Brittany be 27 years old and Nate 26? Why or why not?
Does the value of the standard deviation depend on the value of the mean?
The value of the standard deviation depends on the value of the mean.
As per the given data, we have to determine that the value of the standard deviation depends on the value of the mean
Yes, the value of the standard deviation depends on the value of the mean.
Because you have to know the mean to calculate the standard deviation.
The size of the standard deviation of a data set depends on what the mean is because the calculation of the mean is essential for calculating Standard Deviation.
The standard deviation determines how much the values deviate from the mean.
Besides, Standard deviation in simple terms means the deviation of data from the Mean.
The most popular way to assess dispersion is standard deviation, which is based on all values. As a result, even a small change in one value can modify the standard deviation's value.
Hence, Standard Deviation depends on the Mean.
For more questions on Standard Deviation and Mean
https://brainly.com/question/11965406
#SPJ4
How do you guys convert fractions into trigonometry like the picture below?
The value of an angle in radians that corresponds to a given trigonometric function value can be found using the inverse trigonometric functions.
What is Trigonometry?In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.
In this case, since sinθ = 1/2, we can use the inverse sine function, denoted as sin^-1, to find the value of θ:
θ = sin^-1 (1/2)
Note that the inverse sine function returns an angle in the range of [−π/2, π/2].
The actual value of the angle may also lie in other ranges, depending on the context in which it is used.
Read more about trigonometry here:
https://brainly.com/question/24349828
#SPJ1
What is the reasonable difference after estimating
13 9/20 - 6 7/8
• 6
• 7
• 7 1/2
• 6 1/2
Answer:
6 1/2
Step-by-step explanation:
The difference between 13 9/20 and 6 7/8 can be found by converting both fractions to decimals and subtracting the two values.
13 9/20 can be expressed as a decimal as 13.45.
6 7/8 can be expressed as a decimal as 6.875.
So, the difference between 13 9/20 and 6 7/8 can be expressed as:
13.45 - 6.875 = 6.575
So the reasonable difference between 13 9/20 and 6 7/8 is 6.575.
what divided by (-2) = -7
Answer:
14
Step-by-step explanation:
14 divided by -2 = -7