Answers
It would take 21 weeks for the population to surpass 16,000.
The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.
For the population to surpass 16,000, we can set up the following equation:
15,000 + 2500 sin(πt/52) = 16,000
Subtracting 15,000 from both sides, we get:
2500 sin(πt/52) = 1000
Dividing both sides by 2500, we get:
sin(πt/52) = 0.4
We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:
πt/52 = sin⁻¹(0.4)
Multiplying both sides by 52/π, we get:
t = (52/π) sin⁻¹(0.4)
Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.
t = (52/π) (0.4115)
t = 21.02
Therefore, it would take 21 weeks for the population to surpass 16,000.
Learn more about Trigonometric functions here:
brainly.com/question/6904750
#SPJ1
Related Questions
Bill checked out 5 books from the library. Hazel checked out b fewer books than Bill. Choose the expression that shows the number of books Hazel checked out.
Answers
The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
Here, we have,
given that,
Bill checked out 5 books from the library.
Hazel checked out b fewer books than Bill.
now, we have to find the expression that shows the number of books Hazel checked out.
let,
that shows the number of books Hazel checked out = x
so, we have,
that shows the number of books Hazel checked out = b fewer books than Bill.
as, Bill checked out 5 books from the library.
so, we get,
the number of books Hazel checked out = 5 - b
so, we have,
x = 5-b
Hence, The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
To learn more on Expression click:
brainly.com/question/14083225
#SPJ1
Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.
Answers
Our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use a proof by contradiction.
Assume that for every vertex u in T, the distance between u and v is greater than (n-1)/2.
Since T is a tree with n vertices, it has n-1 edges. We can select a longest path P in T, which has a length of at least n-1. Let's denote the endpoints of this path as u and w, where u is the starting vertex and w is the ending vertex.
Now, consider the distance between u and v. Since we assumed that the distance between any vertex u and v is greater than (n-1)/2, the distance between u and v must be greater than (n-1)/2.
However, let's consider the distance between w and v. Since the path P is the longest path in the tree, the distance between w and v must be greater than or equal to the length of path P, which is at least n-1.
Now, let's consider the total number of vertices in the tree, which is n. Since n is an odd integer, (n-1)/2 is an integer as well.
If the distance between w and v is greater than or equal to n-1, and (n-1)/2 is an integer, then there must be a contradiction. This is because the distance between w and v is greater than (n-1)/2, violating our assumption.
Therefore, our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
for such more question on vertex
https://brainly.com/question/18274774
#SPJ11
2/5 of Jim's savings is equal to 4/9 of Max's savings. Jim has $30 more than Max. 5 How much money does Max have?
Answers
As Jim has $30 more than Max, as per this, Max has $270.
Let's assume Max's savings as 'x' dollars.
We have:
2/5 of Jim's savings is equal to 4/9 of Max's savings.
(2/5) * Jim's savings = (4/9) * Max's savings
We also know that Jim has $30 more than Max.
Jim's savings = Max's savings + $30
So,
(2/5) * Jim's savings = (4/9) * Max's savings
(2/5) * (Max's savings + $30) = (4/9) * Max's savings
To solve for Max's savings, we can solve this equation:
(2/5) * (x + $30) = (4/9) * x
So, for x:
(2/5) * (x + $30) = (4/9) * x
Multiplying both sides by 45 (the least common denominator of 5 and 9) to eliminate the fractions:
18(x + $30) = 20x
18x + 540 = 20x
540 = 20x - 18x
540 = 2x
x = 270
Therefore, Max has $270.
For more details regarding savings, visit:
https://brainly.com/question/7965246
#SPJ1
Hii please answer i would appreciate it thankssss
Answers
a) The triangles are congruent by the AAA criterion.
b) The triangles are congruent by the SAS criterion.
a) In the first triangle the interior angles are 40 degrees and 30 degrees.
The other interior angle would be 180 - (40 + 30) = 110 degrees.
As per the diagram, the triangles have equal proportionate-sized side lengths.
Therefore, the triangles are congruent by the AAA criterion.
b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.
Therefore, the triangles are congruent by the SAS criterion.
To learn more about the congruent;
https://brainly.com/question/12413243
#SPJ1
Fractions such as
12 in.
1 ft
and
1 yd
3 ft
are called
fractions.
Answers
Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called unit conversion fractions
Unit conversion fractions are used to convert between different units of measurement within the same quantity.
The fraction 12 in/1 ft represents the conversion factor from inches to feet, where 12 inches is equivalent to 1 foot.
This fraction allows us to convert a certain length measured in inches to an equivalent length in feet.
Similarly, the fraction 1 yd/3 ft represents the conversion factor from yards to feet, where 1 yard is equivalent to 3 feet.
This fraction allows us to convert a certain length measured in yards to an equivalent length in feet.
To learn more on Fractions click:
https://brainly.com/question/10354322
#SPJ1
Fill in each blank so that the resulting statement is true
Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called _________fractions
Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.
Answers
a) The given symbolic logic statement can be translated into English as follows:
"Not exists x such that (P(x) and Q(x)), and for all y, if R(y) then P(y)."
b) Potential ambiguities in the translated statement:
The scope of the negation symbol "¬" is not explicitly defined. It can be interpreted as applying only to the first part of the statement or to the entire statement.
The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which parts of the statement they apply to.
c) To eliminate ambiguities while maintaining the original meaning, the statement can be rewritten as follows:
"(∀x)(¬(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y))"
How to explain the informationIn the revised statement: The negation symbol "¬" applies to the entire first part of the statement, indicating that there does not exist any x for which both P(x) and Q(x) are true.
The quantifiers (∀x) and (∀y) explicitly indicate that the following predicates apply universally to all values of x and y.
Learn more about logic statement
https://brainly.com/question/24912495
#SPJ1
a) The monthly basic salary of the married Chief of Army Staffs (COAS) General is Rs 79,200 with Rs 2,000 dearness allowance. He gets Dashain allowance which is equivalent to his basic salary of one month. He contributes 10% of his basic salary in Employee's Provident Fund (EPF) and he pays Rs 50,000 as the premium of his life insurance. Given that 1% social security tax is levied upon the income of Rs 6,00,000, 10% and 20% taxes are levied on the next incomes of Rs 2,00,000 and up to Rs 3,00,000 respectively. Answer the following questions. What is his monthly basic salary? (ii) Find his taxable income. (iii) Find the total income tax paid by him.
Answers
i) The monthly basic salary of the married COAS General is Rs 79,200.
ii. Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480
iii. The total income tax paid by him is Rs 24.8.
How to calculate the valueHis taxable income can be calculated as follows:
Total Monthly Income = Rs 79,200 + Rs 2,000 + Rs 79,200 = Rs 1,60,400
EPF Contribution = 10% of Basic Salary = 10% of Rs 79,200 = Rs 7,920
Life Insurance Premium = Rs 50,000
Total Deductions = EPF Contribution + Life Insurance Premium = Rs 7,920 + Rs 50,000 = Rs 57,920
Taxable Income = Total Monthly Income - Total Deductions
Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480
For income up to Rs 6,00,000: No income tax
For income between Rs 6,00,001 and Rs 8,00,000: 1% of the amount exceeding Rs 6,00,000
Taxable Income in this slab = Rs 2,480 (Rs 1,02,480 - Rs 6,00,000)
Income tax for this slab = 1% of Rs 2,480 = Rs 24.8
Therefore, the total income tax paid by him is Rs 24.8.
Learn more about income on
https://brainly.com/question/25745683
#SPJ1
Li Wei and Colleen have the same reading assignment. After one week Li Wei has read 90 pages and Colleen has read 126 pages. If Li Wei can you read 30 pages in an hour and Colleen henry 24 pages an hour, when will they be on the same page 
Answers
Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.
What are equivalent expressions?Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.
In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.
The number of pages Li Wei can read in a week = 90
The number of pages Collen can read in a week = 126
Li Wei's reading rate per hour = 30 pages
Collen's reading rate per hour = 24 pages
Let the hours that Li Wei and Colleen can be on the same page= x
Expressions:The total number of pages Li Wei can read = 90 + 30x
The total number of pages Colleen can read = 126 + 24x
For Li Wei and Colleen to be on the same, the two expressions are equated.
90 + 30x = 126 + 24x
6x = 36
x = 6
Learn more about equivalent expressions at https://brainly.com/question/2972832.
#SPJ1
#1 Write a positive or negative integer that represents the situation.
You run up 24 steps.
© 24
0-24
Answers
The integer number that represents the situation running up 24 steps is given as follows:
+24.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For altitudes, the signs are given as follows:
Gain of altitude: positive integer.Loss of altitude: negative integer.In this problem, we have an increase of altitude of 24 steps, hence the integer number is given as follows:
+24.
More can be learned about integer numbers at brainly.com/question/17695139
#SPJ1
Dana had to pay her friend $900, 3 months ago and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month, what single payment would settle both payments today?
Answers
Dana had to pay her friend $900, 3 months ago, and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month. $1499.45, single payment would settle both payments today.
Given:
The principal of a loan is the original sum borrowed.The interest rate per period is known as rate.The loan's duration is expressed in terms of time.Simple interest = Principal × Rate × Time
Simple interest = $900 × 0.015 × 3
Simple interest = $40.50
Present Value = Future Value / (1 + Rate x Time)
Present Value = $580 / (1 + 0.015 × 3)
Present Value = $580 / 1.045
Present Value = $558.95
Total amount $580 loan is $558.95.
Total amount owed = $940.50 + $558.95
Total amount owed = $1499.45
Learn more about on single payment, here:
https://brainly.com/question/27961161
#SPJ1
Kenya wants to open a savings account at a bank. The bank offers a savings account that pays
out 8% annual interest. If Kenya wants at least $7,000 in his account after 15 years, how much does
Kenya need to put in the account initially?
Answers
Kenya needs to initially put in the amount of $2,208.2in the account to have at least $7,000 after 15 years.
We can use the formula for compound interest:
A = P(1 + r/n)ⁿ
where A is the amount of money in the account after t years, P is the initial principal, r is the annual interest rate (as a decimal), and n is the number of times per year the interest is compounded.
Here, we want to find P, so we can rearrange the formula as:
P = A / (1 + r/n)ⁿ
We are given that r = 0.08 (8% interest) and n = 1 (interest is compounded annually).
We also know that A = $7,000 and t = 15 years.
So we can plug in these values and solve for P:
P = 7000 / (1 + 0.08/1)¹⁵
P = 7000 / (1.08)¹⁵
P ≈ $2,208.2
Therefore, Kenya needs to initially put in approximately $2,208.2in the account to have at least $7,000 after 15 years.
To learn more about Compound interest click here:
brainly.com/question/25857212
#SPJ1
MA.7.AR.4.1
Johnny and Eleanor went to their local gas station to collect information about the cost of
fuel for compact cars. They observed both regular and premium gas purchases that day and
recorded their data in the table below.
Gallons Purchased 11.5 7.2
10
14.3 6.8
9.7
Cost
$25.23 $15.80 $21.94 $40.63 $14.92 $27.56
Part A. Is there a proportional relationship between the number of gallons of gas sold and
the cost? Explain your answer.
Part B. If the relationship is not proportional, which data value or values should be
changed to make the relationship proportional? What could explain this
difference?
Answers
a) The fourth and sixth data points have significantly different ratios.
a) Let's calculate the ratios:
For the first data point:
= 11.5 gallons / $25.23 = 0.4555 gallons per dollar
For the second data point:
= 7.2 gallons / $15.80 = 0.4557 gallons per dollar
For the third data point:
= 10 gallons / $21.94 = 0.4556 gallons per dollar
For the fourth data point:
= 14.3 gallons / $40.63 = 0.3519 gallons per dollar
For the fifth data point:
= 6.8 gallons / $14.92 = 0.4555 gallons per dollar
For the sixth data point:
= 9.7 gallons / $27.56 = 0.3517 gallons per dollar
However, the fourth and sixth data points have significantly different ratios.
b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.
The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.
To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.
Learn more about Ratio here:
https://brainly.com/question/31945112
#SPJ2
Find the simple interest owed if $340 is borrowed at 6.6% for 9 years
Answers
The simple interest owed on a $340 loan at 6.6% interest for 9 years is $201.96.
How to find simple interest?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given that:
Principal P = $340
Interest Rate r = 6.6%
Time t = 9 years
First convert the interest rate from percent to decimal:
Rate = r/100
Rate = 6.6/100
Rate = 0.066
Now, plug the values into the above formula and solve for interest.
I = P × r × t
I = $340 × 0.066 × 9
I = $201.96
Therefore, the simple interest is $201.96.
Learn more about simple interest here: brainly.com/question/25845758
#SPJ1
.....................................................................
Answers
Answer:
b
Step-by-step explanation:
Answer:
The correct statement is: The temperature of the object is decreasing exponentially by 0.007% each minute.
Step-by-step explanation:
The exponential term in the function, [tex]e^{0.007 h}[/tex], is greater than 1. This means that the temperature is increasing over time.
However, the exponent is very small, so the increase in temperature is very slow. In fact, the temperature is increasing by only -0.007% each minute.
We can use the following formula to calculate the percent change in temperature each minute.
[tex]\boxed{\bold{Percent\: change = \frac{(new \:value - \:old \: value) }{ old\:value }* 100\%}}[/tex]
In this case, the new value is the temperature after one minute, and the old value is the temperature at the start of the minute.
So, the percent change in temperature is:
[tex]= \frac{10 + 160e^{-0.007 * 1} - 10) }{ 10} * 100\%[/tex]
≈ -0.007%
Therefore, the temperature of the object is decreasing exponentially by 0.007% each minute.
An urn contains 11 red balls numbered 1 through 11, 11 yellow balls numbered 1 through 11, 11 green balls numbered 1 through 11, and 11 black balls numbered 1 through 11. If 4 balls are randomly selected, find the probability of getting
(a) a flush (i.e., all balls the same color).
(b) three of a kind. (Three of a kind is 3 balls of one denomination and a fourth ball of a different denomination. e.g., 5,5,5,2)
(c) two pairs. (A pair is two balls of the same denomination. e.g., 3,3. Two pairs is something like 3,3,5,5, i.e., a pair of one denomination and a second pair of a different denomination.)
please write the steps as well!! thank you so much
Answers
(a) Probability of getting a flush is 0.000546.
(b) Probability of getting three of a kind is 0.00451.
(c) Probability of getting two pairs is 0.0150.
We have,
(a)
To calculate the probability of getting a flush, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of balls = 11 (red) + 11 (yellow) + 11 (green) + 11 (black) = 44 balls
The number of ways to choose 4 balls (without replacement)
= 44C4 = 44! / (4! x (44 - 4)!) = 44! / (4! x 40!)
= 44 x 43 x 42 x 41 / (4 x 3 x 2 x 1)
= 7315
The number of favorable outcomes:
There are 4 different colors of balls, so we have 4 possible flushes (all red, all yellow, all green, all black).
Probability of getting a flush = Number of favorable outcomes / Total number of outcomes = 4 / 7315 ≈ 0.000546
(b)
To calculate the probability of getting three of a kind, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).
Number of ways to choose 3 balls of the same denomination: We have 11 denominations, so we can choose 3 balls of the same denomination in 11C1 = 11 ways.
Number of ways to choose the fourth ball of a different denomination: After choosing 3 balls of the same denomination, we have 3 denominations left from which we can choose the fourth ball. So, the number of ways to choose the fourth ball = 3.
Number of favorable outcomes = Number of ways to choose 3 balls of the same denomination x Number of ways to choose the fourth ball of a different denomination
= 11 x 3
= 33
Probability of getting three of a kind = Number of favorable outcomes / Total number of outcomes = 33 / 7315 ≈ 0.00451
(c)
To calculate the probability of getting two pairs, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).
Number of ways to choose the first pair: We have 11 denominations, so we can choose the first pair in 11C1 = 11 ways.
Number of ways to choose the second pair: After choosing the first pair, we have 10 denominations left from which we can choose the second pair. So, the number of ways to choose the second pair = 10.
Number of favorable outcomes
= Number of ways to choose the first pair x Number of ways to choose the second pair
= 11 x 10
= 110
Probability of getting two pairs = Number of favorable outcomes / Total number of outcomes = 110 / 7315 ≈ 0.0150
Thus,
(a) Probability of getting a flush = 4/7315 ≈ 0.000546
(b) Probability of getting three of a kind = 33/7315 ≈ 0.00451
(c) Probability of getting two pairs = 110/7315 ≈ 0.0150
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ1
10A34594-4103-466C-A0CC-22EBA
9EB47A6.jpeg
Answers
The total surface area of the cylinder is 414.7 cm².
What is the curved surface area of the cylinder?The curved surface area of the cylinder is calculated as follows;
C.S.A = 2πrh
where;
r is the radius of the cylinderh is the height of the cylinderThe curved surface area of the cylinder is calculated as;
C.S.A = 2π(6 cm) x (5 cm)
C.S.A = 188.5 cm²
The total surface area of the cylinder is calculated as follows;
T.S.A = 2πrh + 2πr²
circular area = 2πr² = 2π x (6cm)² = 226.2 cm²
The total surface area = 188.5 cm² + 226.2 cm² = 414.7 cm²
Learn more about total surface area here: https://brainly.com/question/28178861
#SPJ1
Based on the picture above, what is the solution to the system of equations?
Type a response
Answers
Step-by-step explanation:
The 'solution ' is the point where the two lines intersect : ( 0,-1)
HELP PLS !% POINTS!!
Answers
Answer:
149 sq. ft
Step-by-step explanation:
For the triangle:
Base = 16-9 = 7 ft
Area of Triangle = 1/2 of b.h
= 1/2 of 7 * 6
= 21 sq. ft
Area of Rectangle = l.b
= 5 * 16
= 128 sq. ft
Total Area = 149 sq. ft
Which graph represents the solution to the following problem? y < |x+3|
Answers
The graph that shows the solution set of the inequality is the second one.
Which graph represents the solution set of the inequality?Here we have the following inequality:
y < |x + 3|
Notice that we have the symbol "<", then we know that the graph of the absolute value must be with dashed lines (because the points that lie on the graph aren't solutions).
Also, y is smaller than that, then the shaded region must be below the graph.
With that in mind, we conclude that the correct option is the second one.
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
A sales person starts working 40 hours per week at a job with 2 options for being paid . Option A is an hourly wage of $19. Option B is a commission rate of 8% on weekly sales.
How much does the sales person need to sell in a given week to earn the same amount with each option?
A. $9,500
B. $4,750
C. $760
D. $320
Answers
Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week [tex]\sf = 19 \times 40 = \$760[/tex]
Now, according to option b, he will get 8% commission on weekly sales.
Let. x = the amount of weekly sales.
To earn the same amount of option A, he will have to equal the 8% of x to $760
So, [tex]\sf \dfrac{8x}{100}=760[/tex]
Or, [tex]\sf 8x= 76000[/tex]
Or, [tex]\sf x= \dfrac{76000}{8}=9500[/tex]
the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.
Help !!
centimeters and millimeters <3
Answers
1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .
How to compare centimeters and millimeters ?The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.
The length of my book in when measured in millimeters is 280 mm.
In centimeters, this is therefore:
= 280 mm / 10 cm /mm
= 28 cm
Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.
Find out more on centimeters at https://brainly.com/question/22462126
#SPJ1
This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =[tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
For similar questions on water bill
https://brainly.com/question/31119915
#SPJ11
are the side lengths of triangle Graph shows a triangle plotted on a coordinate plane. The triangle is at A(minus 7, 3), B(minus 3, 6), and C(5, 0). Type the correct answer in each box. If necessary, round any decimal to the nearest tenth. units units units
Answers
The side lengths for the triangle are given as follows:
AC = 12.4.AB = 5.BC = 10.How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Then the length AC is given as follows:
[tex]AC = \sqrt{(5 - (-7))^2 + (0 - 3)^2}[/tex]
AC = 12.4.
The length AB is given as follows:
[tex]AB = \sqrt{(-3 - (-7))^2 + (6 - 3)^2}[/tex]
AB = 5.
The length BC is given as follows:
[tex]BC = \sqrt{(5 - (-3))^2 + (6 - 0)^2}[/tex]
BC = 10.
More can be learned about the distance between two points at https://brainly.com/question/7243416
#SPJ1
PLEASE HELP!!!!!!
it’s a division equation
Answers
Answer:
x+1
Step-by-step explanation:
you have to rewrite the equestion, factor the expression, and than reduce it
Pls help I’m stuck Tysm I really thankful
Answers
Answer:
23/41
Step-by-step explanation:
You want to know the fraction who failed, given they predicted they would fail.
StatsThe attached 2-way table shows the given numbers (black) and the numbers that make the totals correct (blue).
It shows 23 of the 41 who thought they would fail actually did. That fraction is ...
23/41 . . . . failed who thought they would
<95141404393>
Suppose a website has about 1,500,000 users. When each member signs up,
he or she is assigned an account number.
A sample of users is to be chosen to take a survey. Using systematic
sampling of account numbers, which of these will result in the smallest
sample size?
OA. Choosing every 1500th account number
OB. Choosing every 15th account number
OC. Choosing every 150th account number
D. Choosing every 15,000th account number
Answers
Systematic sampling involves selecting every kth element from a population. In this case, since there are 1,500,000 users and we want the smallest sample size, selecting every 1500th account number will result in a smaller sample size compared to the other options.
I need help please with this question
Answers
The approximation of [tex]\sqrt{44}[/tex], to the hundredths place, is given as follows:
[tex]\sqrt{44} = 6.63[/tex]
How to estimate a non-exact square root?The estimate of a non-exact square root of x is done finding two numbers, as follows:
The greatest number less than x that is a perfect square, which we call a.The smallest number greater than x that is a perfect square, which we call b.For this problem, we want to estimate the root to the hundredth's place, hence the number that we must compare is:
44 x 10^4 = 440000.
(as each 10² is equivalent to the square root of a decimal digit).
Then the numbers are:
663² = 439569 < 440000.664² = 440896 > 440000.Hence the square root is approximated as follows:
663/100 = 6.63.
More can be learned about the estimation of the square root of a number at brainly.com/question/28734995
#SPJ1
What is the X intercepts of f(x) =-2x^2 + 10x - 7
Answers
Exam the following data set.
{8,19,11,20,2,14,17,9,15}
Which answer shows the five number summary that could be used to create a box plot for this data?
Answers
The five number summary of the data set for the box plot would be :
Minimum value: 2Q1 : 9Median : 14Q3 : 19Maximum value: 20How to find the five number summary ?First, order the numbers in ascending order:
2, 8, 9, 11, 14, 15, 17, 19, 20
The minimum is the smallest number which is 2. The maximum is the largest number which is 20.
The median is the number in the middle which is 19. The Q1 is the number in the middle of the first half of the numbers which is 9. The Q3 is the number in the middle of the second half which is 19.
Find out more on five number summary at https://brainly.com/question/24809873
#SPJ1
Answer:
min=2
1st quartile= 8.5
median=14
3rd quartile=18
max=20
Step-by-step explanation:
The mean of three test is 74 what must be the the 4th score to get a mean of 78?
Answers
To achieve a mean of 78 with four scores, the fourth score must be 90.
We need to consider the current mean, the number of tests, and the desired mean in order to find the fourth score needed to achieve a mean of 78
Let's assume the three test scores are x1, x2, and x3.
We know that the mean of these three scores is 74. So we can assume that
The sum of these numbers is 74 or
(x1 + x2 + x3)/3 = 74
Let's denote it as x4 ,to find the fourth score we will use the formula to calculate the mean:
(x1 + x2 + x3 + x4)/4 = 78
To solve for x4, we can rewrite it as:
x1 + x2 + x3 + x4 = 78 * 4
Now, we can substitute the value of the mean of the first three scores into the equation:
(x1 + x2 + x3) + x4 = 312
we know that,
(x1 + x2 + x3) = 3 * 74
or,
3 * 74 + x4 = 312
Simplifying this, we get:
222 + x4 = 312
Subtracting 222 from both sides:
x4 = 312 - 222
x4 = 90
Therefore, to achieve a mean of 78 with four scores, the fourth score must be 90.
Learn more about mean in mathematical expressions:
https://brainly.com/question/14532771