Using Arithmetic progression, There were 4,13,22,31 pupils chosen out of the applicants.
The professor desires to choose four students at random.
A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
The fourth student was chosen at random, followed by every ninth student.
The fourth student is chosen first.
Using the following term formula, which is
=>a + d(n-1) (n-1)
The second student is the one after that.
=>4 + 9(2-1) (2-1)
=>4 + 9(1) (1)
=>4 + 9
=> 13
The third pupil will be
=>4 + 9(3-1) (3-1)
=>4 + 9(2) (2)
=>4 + 18
=> 22
The fourth pupil will be
=>4 + 9(4-1) (4-1)
=>4 + 9(3) (3)
=> 4+ 27
=> 31
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A lighthouse 1 flaahes its light every 15 minutes. A lighthiuse 2 flaahes every 18 minutes. If the two lighthouse flaah togethwr at 1:00 A. M, what time they will next flash together
The next time they will flash together will be at 4:00 AM.If they flash together at 1:00 AM.
According to the given information we are trying to find the smallest time interval at which both the lighthouses will flash together.The first lighthouse flashes every 15 minutes, and the second lighthouse flashes every 18 minutes.
To find the LCM of 15 and 18, we can list out the multiples of each number and find the smallest multiple that is common to both.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, ...
As we can see, the smallest multiple that is common to both lists is 90. This means that the two lighthouses will flash together every 90 minutes.Since they both flash at 1:00 AM, we can add 90 minutes to 1:00 AM to find the next time they will flash together:
1:00 AM + 90 minutes = 4:00 AM
So, the next time they will flash together will be at 4:00 AM.
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PLEASE HURRY LIMITED TIME TEST QUESTION!!!!
Question Write the standard form equation of a circle given the center of (-7, -15) and an area of A = π. Show all work for your calculations using the equation editor.
The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.
What is the equation of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
The area of the circle is 9π. Then the radius of the circle is given as,
A = π
πr² = π
r² = 1
The center of the circle is at (-7, -15). Then the equation of the circle is given as,
(x + 7)² + (y + 15)² = 1
The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.
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Can y’all help me please on question 7-8 plssss I beg y’all homework’s due tommorow
The solution to the fractions are;
7. 5/6
8. 6/5
What is a fraction?A fraction can be described as the part of a whole variable, number or element.
There are several types of fractions, which includes;
Proper fractionsMixed fractionsImproper fractionsSimple fractionsComplex fractionsFrom the information given, we have that;
1 1/3 × 5/12
convert to improper fraction
4/3 × 5/12
Multiply the values
5/6
(7/10 + 1/5) ÷ ( 6/4 - 3/4)
find the lowest common denominators
( 7 + 2 /10) ÷ (6 - 3 /4)
subtract or add the numerators
9/10 ÷ 3/4
take inverse of the divisor and multiply
9/10 × 4/3
6/5
Hence, the values are 5/6 and 6/5 respectively.
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solve the equation:(x+5)^4 = 81
Answer:4√81=±3
Step-by-step explanation:
If (x+5)^4 = 81,
then (x+5)^2 = ± sqrt(81), so
(x+5)^2 = ±9
Focusing on (x+5)^2 = 9 for the two real roots, we have
(x+5)^2 = 9
x+5 = ± sqrt(9)
x+5 = ± 3
x+5 = 3 gives you x = -2
x+5 = -3 gives you x = -8
There are two complex roots too, but I'm not sure if you're studying that too. If so, then you'd solve (x+5)^2 = -9:
x+5 = ± sqrt(-9)
x+5 = ±3i
x = 5 ± 3i as the two complex roots.
The mass of a 45. 750 g piece of copper is measured four times on two different balances with the following results: Trial Balance 1 (g) Balance 2 (g) 1 45. 747 45. 76 2 45. 748 45. 74 3 45. 744 45. 73 4 45. 745 45. 77 a) Calculate the mean, deviation, % relative deviation, absolute error, and % relative error. Show all Work. B) Which balance is more precise
The mean of the copper measured is 45.747. when the mass of copper is 45.750.
Average Absolute Deviation:
The average deviation is a statistic that measures the absolute difference of each measurement from the mean value and then gets its average.
It also includes both the mean absolute deviation and the median absolute deviation and also defines the data set as the average of the absolute deviations from a central point.
This is given by the formula:
Average Deviation=∑ni=1|x−¯x|
where:
x is the observed value
¯x is the mean value
n is the number of observations
Computing for the mean of balance 1:
¯x=45.747+45.745+45.748/3
¯x=45.747
Computing for the mean of balance 2:
¯x=45.76+45.77+45.74/3
¯x=45.79
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Can someone help me with this please? I need help ASAP
A: Classify the triangle above by its sides
B: Classify the triangle above by its angles
C: Explain your answer to part a and b
How much material would be required to make one triangular sail for a sailboat if the base is 420 centimetres and the altitude is 653 centimetres?
Answer:
Step-by-step explanation:
I don't know I'm just asking the question
John is starting a roofing business. He will need to buy a truck and some supplies to get his business going. The truck costs $13000 used. He gets three jobs right away. And hires 2 workers to help him. The materials for all three jobs cost $3000 total. The jobs will each take a week not including Saturday and Sunday and he pays his workers $125 per day per worker. How much will he have to charge for each job in order to break even at the end of the third job?
As per the unitary method, the charge for each job in order to break even at the end of the third job is $3,000
In math the term unitary method is known as a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Here we have given that John is starting a roofing business. He will need to buy a truck and some supplies to get his business going.
And here we we have also known as the truck costs $13000 used.
The value of truck is 13000 and material for all 3 jobs is 3000
Here we have also know that each job takes 5 days for a total of 15 days
workers get paid 125 dollars a day.
As we all know that each worker gets 125 a day.
Then here we have also know that each job requires 5 days so he pays each worker 625 per job.
Then he has them work on 3 jobs, and then he pays each worker 1875 for all 3 jobs.
Where here he has 2 workers so he pays out 3750 in total to the workers for all 3 jobs.
Then the total cost is calculated as,
=> $13,000 for the truck
=> $3,000 for the material
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a square is cut out of a circle whose diameter is approximately feet. what is the approximate area (shaded region) of the remaining portion of the circle in square feet? ( where )
The approximate area (shaded region) of the remaining portion of the circle in square feet is 55.94 ft².
We know that,
the side of square=2*[r*√2/2]=r*√2 that is being taken out.
diameter = 14 ft and radius , r = 7 ft.
the side of square=7*√2=9.89 ft
[area of the remaining portion of the circle]=[ area of a circle]-[area of a square]
[area of a square] = (7√2)²=98 ft²
[ area of a circle] = π*r²= π x 7^2 = 153.94 ft²
therefore,
[area of the remaining portion of the circle]=153.94 - 98=55.94 ft²
the answer is 55.94 ft².
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four players pick a real number from [0,1]. the players with the middle two numbers are paired together, while the players with the two extreme numbers are paired together. the pair with a lower sum has to each pay the difference to the pair with a higher sum. if you are allowed to choose your number (while everyone else draws uniformly at random), which number should you choose?
If the four players choose their numbers independently and uniformly at random from [0,1], then the expected value of the sum of the two middle numbers is 1/2, and the expected value of the sum of the two extreme numbers is 1/2. Therefore, in order to minimize the expected
One of the most straightforward methods for gathering information from the entire population is random sampling. Every member of the subset has an equal chance of being chosen as part of the sampling process when using random sampling. For instance, if an organization employs 300 people overall, a sample group of 30 workers will be chosen to participate in the survey. In this instance, the population is the entire workforce of the organization, and the sample is 30 employees. Since all of the employees who were picked to participate in the survey were chosen at random, every worker has an equal chance of getting chosen.
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There are 24 baseball cards In 4 packs complete the table to find the rate that gives the number of cards in 2 packs. Write this rate in three different ways.
2 packs include 12 baseball cards, and there are 6 baseball cards per pack.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
given, There are 24 baseball cards In 4 packs complete the table to find the rate that gives the number of cards in 2 packs.
Since
There are baseball cards in 4 packs = 24
Thus,
Baseball cards in 1 pack = 24 / 4
Baseball cards in a pack = 6
Baseball cards in 2 packs = 12
therefore, there are 12 baseball cards in 2 packs also the rate of baseball cards per pack is 6.
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Complete question:
pls pls pls help the second photo is the answer choices given
Answer
see attached
Step-by-step explanation:
x-2y = 8 means x = 8+2y. so when y =0, x = 8; when y=1, x =10. draw a line with these 2 points.
Same with x - 2y = 4 ==> x = 4+2y. so when y=0, x = 4, when y=1, x=6, draw a line with these 2 points.
In a grade 7 class,There are 30 students in a class 18 of them own at least one pet.What percent of them have pets.Answer is 60 percent but how do i do the work.NEED URGENT RESPONSE
Answer: Use cross product property
Step-by-step explanation:
I solved it out for you below! I hope it helps! If you need a better explanation maybe ask your teacher? :)
Solve for x and the missing angles in the diagram below: x = The missing angles are °, ° and °.
The measure of {x} equals to 8 and ∠WYZ is 32°.
What is a radian?The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics
Given is the figure as shown in the image.
It is given that ∠XYZ = 106°. We can write -
∠XYZ = ∠XYW + ∠WYZ
106 = 70 + 5x - 4
5x + 66 = 106
5x = 40
x = 8
∠WYZ = 5x - 8 = 5 x 8 - 8 = 32°.
Therefore, the measure of {x} equals to 8 and ∠WYZ is 32°.
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Write a function g that determine's the point's x-coordinate in terms t.
g(t)=
A function g that determine the point's x-coordinate in terms t.
g(t) = r .cos (2.t).
Now, According to the question:
The input variable and output variable are also called the domain and the range. The domain of a function is the set of all values that will work in the function, which are the inputs. The range of a function is the set of all possible outputs produced by the function. In the example above, the 3 would be part of the range and the 8 would be part of the domain.
Input data
A point started at the location (-4, 0)
and, moves CCW along a circle centered at (0, 0)
angular speed = 2 rad/s
Procedure
The value of x is equal to the cosine of the swept angle time radius.
We can calculate the swept angle as 2×t
g(t) = r .cos (2.t).
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The given question is incomplete.
For the complete question, To see the attachment.
the equation above can be used to model the population, in thousands, of a certain city t years after 2000. according to the model, the population is predicted to increase by 0.5% every n months. what is the value of n ?
The value of n=36 months.
It is given that the population is predicted to increase by 0.5%. To know the value after the increment, 215 has to be multiplied by (1 + 0.005) or 1.005.
In the equation P = 215(1.005)t/3, the value of t/3 has to be equal to 1 for a 0.5% increase.
The population increases by 0.5 % every n month.
Initial Population = 215
Final Population:
=215+215*0.5/100
=215.1.074
=216.074
Substituting the value of, Initial and final Population
[tex]216.075=215*(1.005)^\frac{t}{3} \\\\(1.005)^\frac{t}{3} =\frac{216.075}{215}\\ \\(1.005)^\frac{t}{3}(1.005)^1\\\\\\frac{t}{3} =1[/tex]
t=3 years=>36 months.
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This figure consists of two squares. The length of each side is a whole number of feet. The combined area of the squares is 100 feet. What is the perimeter of the entire figure in inches?
The perimeter of the entire figure is 40 inches
How to determine the perimeter of the figureIt is important to note that the formula for area of a figure is expressed as;
A = a²
Where;
A is the area of the squarea is the length of side of the squareThe total area is 100 feetA + A = 100
a² = 100
Take the square root of both sides
a = √100
a = 10 inches
The formula for calculating the perimeter of a square is expressed as;
Perimeter = 4a
Substitute the value of a, we have;
Perimeter = 4(10)
expand the bracket
Perimeter = 40 Inches
Hence, the perimeter is 40 Inches
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please help this is for geometry
how would i solve for x here
Using the leg rule, the value of x in the right triangle is: 42.
What is the Leg Rule?The leg rule gives the relationship between the lengths of the segments formed on the hypotenuse of a right triangle by its altitude.
The leg rule is given as:
Hypotenuse/leg = leg/part.
In the image given, we have:
Hypotenuse = x + 8
Leg = 20
Part = 8
Plug in the values:
x + 8 / 20 = 20 / 8
8(x + 8) = (20)(20)
8x + 64 = 400
8x = 400 - 64
8x = 336
x = 336/8
x = 42
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I need help. need answer I have one more try
Answer:
1/7
Step-by-step explanation:
5/7 was already traveled so that leaves 2/7.
Thye traveled 1/2 of 2/7 so we multiply them.
1/2 x 2/7 = 2/14
We can simplify this by dividing both sides by 2.
1/7 is the final answer.
Someone please help! I'm in Algebra 1 and this is supposed to be a puzzle.
a^x a^y = a^88 x and y differs by 32
The solution of the system is x = 60 and y = 28.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
An algebraic equation,
[tex]a^{x} a^{y} = a^{88}[/tex]
When the base value is the same, we can add the exponents.
x + y = 88
And x - y = 32
Now, we have the system of equations,
Adding both the equations,
2x = 120
x = 60
And y = 28.
Therefore, the values are x = 60 and y = 28.
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Which of the following is a statistical question that can result in numerical data?
A. How many miles do you ride your bike each week?
B. How many miles do the students in your class run each week?
C. Who is the dentist at Uptown Dentistry?
D. How many pets do your grandparents have?
The option that is a statistical question is how many miles do the students in your class run each week? (option b)
What is a statistical question?A statistical question is a question that can be answered by collecting data that have varying values.
For example, the number of miles that the students in your class run each week is statistical question because each student would run. This is because data would be collected from more than one student and the students would have varying miles that they run.
The number of pets your grandparents have is not a statistical questions because they can only have a set number of pets.
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Answer:
B. How many miles do the students in your class run each
Step-by-step explanation:
Jackson is working two summer jobs, making $10 per hour washing cars and $12 per hour landscaping. Last week Jackson worked a total of 14 hours and earned a total of $152. Determine the number of hours Jackson worked washing cars last week and the number of hours he worked landscaping last week
The number of hours Jackson worked washing cars last week is 8 hours
The number of hours Jackson worked landscaping cars last week is 6 hours
How to write the required equationThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
Jackson worked a total of 14 hours
let the washing cars be x and landscaping be yx + y = 14
Jackson earned a total of $152
$10 per hour washing cars and $12 per hour landscaping
10x + 12y = 152
The simultaneous equation
x + y = 14
10x + 12y = 152
using calculator to solve the equation we have that
x = 8 and y = 6
hence hours of washing cars is 8 hours while hour s of landscaping is 6 hours
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Bobs gift shop sold a record number of cards for Mother’s Day. One salesman sold 36 cards, which was 4% of the cards sold for Mother’s Day. How many cards were sold for Mother’s Day
The number of cards were sold for mother's day is 900 cards.
How to calculate total number using percentage?To calculate a total number using a percentage, first identify the percentage and the total number. Then divide the percentage by 100 to convert it to a decimal fraction. Finally, multiply the total number by the decimal fraction to calculate the total number.
For example, if the percentage is 10% and the total number is 200, first divide 10% by 100 to get 0.1. Then multiply 0.1 by 200 to get 20. The total number is 20.
In another example, if the percentage is 25% and the total number is 500, divide 25% by 100 to get 0.25. Then multiply 0.25 by 500 to get 125. The total number is 125.
It is important to remember that percentages are based on a whole, which is usually 100. Therefore, to use percentages to calculate a total number, it is necessary to first convert the percentage to a decimal fraction by dividing it by 100. Then, multiply the total number by the decimal fraction to calculate the total number.
36 cards is 4% of the total cards sold for Mother's Day.
Total number of cards = 36 / 4%
Total number of cards = 36 x 100/4
Total number of cards = 900 cards.
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To indirectly measure the distance across a river, Fatoumata stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Fatoumata draws the diagram below to show the lengths and angles that she measured. Find PR, the distance across the river. Round your answer to the nearest foot.
The distance PR across the river is 177 feet
How to determine the distance PRThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The equivalent ratio represented as
PR : 125 = PR + 170 : 245
Express the ratio as a fraction
So, we have the following representation
PR/125 = (PR + 170)/245
Cross multiply
This gives
245PR = 125PR + 21250
Evaluate the like terms
120PR = 21250
Divide both sides by 120
PR = 177
Hence, the distance is 177 feet
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The Students Athletes Club has a monthly budget ofxdollars. Every month $500 is spent on transportation. One-fourth the remaining budget is spent on monthly activities. Which function can be used to find the amount in dollars spent on monthly activities?
The function to find the amount in dollars spent on monthly activities can be represented as: A(x) = (x - 500) * 1/4
Let x be the total monthly budget in dollars and A(x) be the function of x that determines the amount in dollars spent on monthly activities.
To find the value of A(x), we follow the steps:
First, we subtract the fixed monthly transportation cost of $500 from the total budget.
The remaining budget is then divided by 4 to find the amount spent on monthly activities.
Therefore, the function A(x) can be written as: A(x)= (x-500)/4
Thus, the function (x - 500) * 1/4 can be used to find the amount in dollars spent on monthly activities.
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A turtle traveled 1/10 miles in 1/2 hour. What was the turtles rate in miles per hour?
Answer: 0.2m/h
Step-by-step explanation: We can say when the turtle travels 1/10 of a mile in 1/2 of an hour, he's traveled 0.1 miles in 30 minutes.
If you're looking for the turtle's rate in miles per hour, just double both the time and the distance traveled.
You will end up with 0.2 miles per hour or 2/10 of a mile per hour.
a coin with a head on one side and a tail on the other is tossed, followed by a six sided die with faces marked 1 through 6 being rolled. if each outcome is equally likely, what is the probability of each outcome?
can i please receive an explanation
What is the length of the unknown side on the following right triangle?
Answer: c=√202
Step-by-step explanation:
c = √(9² + 11²)
which also simplifies to 23.769729
I hope this helps!
Answer:
Step-by-step explanation:
DE is
midsegment of AABC. Find the value of x
B
X
The value of x in the triangle is 8 units.
How to find the mid segment of a triangle?The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle.
It is parallel to the third side and it is half the length of the third side.
Therefore, DE is the mid segment of the triangle ABC. The value of x can be found as follows:
Using the mid segment rule,
BE = EC
BD = DA
Therefore,
x = 8 units
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How do you eliminate the parameter to find a cartesian equation of the curve?
A horizontal parabola with a right-facing opening and a vertex at (1,1) is we have positive direction.
In order to make the coefficients of either the variable x or the variable y numerically equal, first multiply both of the following equations by any suitable non-zero constants.
Finding the single equation of a curve in standard form with only the variables xs and ys constitutes the cartesian equation of that curve. You must simultaneously solve the parametric equations in order to arrive to this equation.
X and Y both
are t-related functions.
We have t=y1 after solving y=t+1 to get t as a function of y.
Thus, given x=t2+1, we have x=(y1)2+1x1=(y1) by substituting t=(y1).
A horizontal parabola with a right-facing opening and a vertex at (1,1) is what we have positive direction.
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