The Perimeter of the Pathway around the pool is 38.4m
What is Perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.
Solution:
Length of the Pathway = 12m + 80cm + 80cm = 12m + 1.6m = 13.6m
Breadth of the Pathway = 4m + 80cm + 80 cm = 4m + 1.6m = 5.6m
Perimeter of Rectangle = 2(l+b)
Perimeter = 2(13.6 + 5.6)
Perimeter = 2(19.2)
Perimeter = 38.4m
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there are 8 people participating in a focus group for a new software product related to the health system, 3 of them are software engineers, 2 of them are nurses, 1 of them is a doctor, and the remaining 2 people are technicians. in how many ways they can be seated in a row so that no two software engineers are together?
Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.
What is combination?An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol [tex]^nC_{r}[/tex].
There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.
So the 3 software engineers =3! ways, 2 nurses =2! ways,
doctor =1! way , 2 technicians =2! ways.
We must determine how many different configurations are possible so that no two pieces of software may coexist.
In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.
[tex]We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.[/tex]
Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.
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The diameter of a hat is 6.8 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
Answer:
21.35 inches
Step-by-step explanation:
You want to know the circumference of a hat that has a diameter of 6.8 inches.
CircumferenceThe circumference is given by ...
C = πd
C = 3.14 × 6.8 in = 21.352 in
C ≈ 21.35 in
The distance around the hat is about 21.35 inches.
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Write a triangle congruence statement
Please answer this question ty
Answer:
m<1 = 45 M<2 = 135 M<3 = 45
Step-by-step explanation:
Answer: M<1 = 45, M<2 = 135, m<4 = 45
Step-by-step explanation:
Angles such as 1 to 4 and 2 to 3 have the same angle, so you take the total of 3 and 2 (270) and subtract it from 360 to to get the values of angles 1 and 4 combined. divide this in half to separate the two angles to get 45 degrees.
135+135=270
360-270=90
90/2=45
Janet is shopping for silver as an investment. At her local silver shop she is presented with two options: round coins and rectangular bars. She looks at the
prices for each.
●
The silver shop will sell her round silver coins according to the equation p=
27s which shows the relationship between s, the number of ounces of silver
she buys, and p. what she will pay for the round coins.
The silver shop will sell her rectangular silver bars but they are more popular
so she has to pay a premium to acquire the rectangular bars. The equation p
= 27.5s +50 shows the relationship between s, the number of ounces of
silver she buys, and p, what she will pay for the rectangular bars.
Janet intends to buy 40 ounces of silver at the silver shop. How much money will
she save by purchasing only round coins instead of rectangular bars?
Answer:
To determine how much money Janet will save by purchasing round coins instead of rectangular bars, we need to find the difference in cost between the two options.
First, we can find the cost of the round coins by plugging 40 ounces into the equation p=27s:
p = 27 * 40 = 1080
Next, we can find the cost of the rectangular bars by plugging 40 ounces into the equation p = 27.5s + 50:
p = 27.5 * 40 + 50 = 1100
The difference in cost between the two options is 1100 - 1080 = $<<1100-1080=20>>20. Therefore, Janet will save $20 by purchasing round coins instead of rectangular bars.
Step-by-step explanation:
SELF EXPLANATORY
How many solutions are there to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers?
There are 66 solutions to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers.
To solve this inequality, we must find all the possible combinations of nonnegative integers x₁, x₂, and x₃ that add up to 11 or less. This can be done by breaking down the problem into a series of nested loops. The outermost loop will iterate through all possible values of x₁, while the two inner loops will iterate through all possible values of x₂ and x₃ that add up to the remaining value of 11 minus x₁. We know that the maximum value of x₁ is 11, so the outermost loop will run from 0 to 11. For each value of x₁, the inner loops will run from 0 to (11 - x₁), incrementing by 1 each time. This will ensure that all possible combinations of x₂ and x₃ that add up to 11 minus x₁ are tested. Once we have all the combinations, we can count them to get the total number of solutions. In this case, there are 66 solutions to the inequality.
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between 2 p.m. and 4 p.m. on wednesday, patient insurance inquiries arrive at blue choice insurance with a mean rate of 3.6 calls per minute. what is the probability of waiting more than 0.5 minutes to get the next inquiry call?
The probability of waiting more than 0.5 minutes to get the next inquiry call is .165 seconds.
Probability is given by the number of possible outcomes ÷ number of total outcomes
Rate of phone calls = 3.6 per minute
Total number of calls between 2:00 p.m and 4:00 p.m (120 minutes) = 3.6 × 120 = 432
Number of calls in 0.5 minutes = 3.6 × 0.5 = 1.8
The probability that the number of calls in 0.5 minutes = 1.8/432 = 1/240.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X=x) =[/tex] e^-μ * μ^[tex]x[/tex]
[tex]x[/tex]!
In which
x is the number of successes
e = 2.71828 is the Euler number
μ is the mean in the given time interval.
The probability of waiting more than 0.5 minutes to get the next inquiry call is according to a Poisson process.
Each minute has 60 seconds.
Rate of phone calls = 3.6 per minute
So a rate of 1 call every 50/3 seconds.
The probability that it takes more than 0.5 minutes for the first inquiry to arrive is approximate.
Mean of 1 call every 50/3 seconds, so for 0.5 minutes, μ = 0.5*60/50/3 = 1.8.
This probability is P(X = 0).
[tex]P(X=x) =[/tex] e^-μ * μ^[tex]x[/tex]
[tex]x[/tex]!
P(X=0) = e^-1.8 * 0.03^0
0!
= 0.165
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Three students are participating in a walkathon. The data for each student is shown.
Student A: The equation y = 13x represents the amount of money raised (y) for walking (x) miles.
Student B: $36 is raised after walking 3 miles.
Student C:
Miles Walked 4 5
Money Raised $52 $65
Determine which student raised the least amount of money after walking 7 miles.
Student A
Student B
Student C
All three students raised the same amount of money after walking 7 miles.
The student C raised the least amount of money after walking 7 miles .
What is meant by mathematical equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
A mathematical sentence with an equals sign is referred to as an equation. It informs us that two expressions that represent the same number or have the same meaning are equivalent. Constants and variables can both be found in an equation. Equations allow us to quickly solve problems and express math facts in condensed, easy-to-remember forms.
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Wendy spent 1/4of her paycheck on Monday and
3/7of it on Tuesday. She spent the rest of her
paycheck over the next 3 days. If Wendy spent $18 on each of the 3 days, what was the amount of
her paycheck
Answer:
$56.00
Step-by-step explanation:
Check:
1/4(56) + 3/7(56) + 18 =
14 + 24 + 18 = 56
See the picture below. I wanted to figure out what fraction of the paycheck was the 18.
I took 1 which is the whole pay check and subtracted out the fractions that I knew were spent 1/4 and 3/7. That left me with 9/28. So I knew 9/28 of the paycheck was 18 dollars. I drew out 28 squares. 9 of those squares was worth $18. That meant that each square was worth $2. 2 x 28 = 56
a) 3-8=
b) -6-4=
c) -2 + 6 =
Answer:
A= -5
B= -10
c= 4
Step-by-step explanation:
hope this helps
Answer:
a) -5
b)-10
c) 4
Hope this helps!
Compute 5/6(43)+1/2(43)+2/4(43)
The value of the equation A = 5/6(43) + 1/2(43) + 2/4(43) is A = 78.83 and the improper fraction of the number A = 473/6
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the value of the equation be A
Now , the equation A is given as
A = 5/6(43) + 1/2(43) + 2/4(43)
So , on simplifying the equation , we get
Taking 43 as the common term of the expression , we get
The value of A = 43 [ 5/6 + 1/2 + 2/4 ]
The value of A = 43 [ 5/6 + 1/2 + 1/2 ]
The value of A = 43 [ 5/6 + 1 ]
So , on further simplification , we get
The value of A = 43 [ 11/6 ]
So , the value of A is A = ( 43 x 11 ) / 6
The value of A = 473/6
The value of A in decimal form is A = 78.83
Therefore , the value of A is 78.83
Hence ,
The value of the equation A = 5/6(43) + 1/2(43) + 2/4(43) is A = 78.83
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Answer:70.83 I think..
Step-by-step explanation:
24+6k<-6(-4-k) please help me :(
inequality will not be use in the given expression.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
The given information,
24+6k<-6(-4-k)
24+6k < 24+6k
It's can be seen that both expressions are equal, but in the question, it is given that the inequality which is not valid.
Hence, inequality will not be use in the given expression.
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determine if a-1 c = c a–1 given
CA ⁻¹ is undefined because there are more columns in A ⁻¹ than there are rows in C.
What is matrix?A matrix is a numerical arrangement that is divided into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a rectangular organization of a collection of integers into a defined number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.
CA⁻¹ is undefined because A⁻¹ contains more columns than rows in C.
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a car is sold for $18,000. after one year, the value of the car is $11,700. write an exponential function y to determine the value of the car after x years if the rate of decrease is the same each year.
The exponential function that determines the value of the car after x years is y = 18000(0.65)ˣ. Here the rate of decrease is the same each year.
What is the exponential function?The exponential function is the function that gives the relationship between the input and the output with a rate of increase or decreases exponentially. It is given by the formula,
y = abˣ
Where 'a' is the initial value, 't' is the time, and 'b' is the rate. If b > 1, then the function is said to be the exponential growth function, and if b < 1, the function is said to be the exponential decay function.
Calculation:Given that, a car is sold for $18,000.
So, the initial value a = 18000.
After one year (x = 1), the value of the car is $11,700 i.e., y = 11700. So we can write the exponential function as
11700 = 18000(b)¹
⇒ b = 11700/18000 = 0.65
Since b < 1, the function is exponentially decaying.
Then, the value of the car after 'x' years is given by the exponential decay function as
y = 18000(0.65)ˣ
(It is given that, the rate of decrease is the same each year).
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Justin, age 52, wants to pay no more than S800 a year in lite insurance. If the annual life insurance premium rate (per $1000 of face value) is $5.38, what is the largest 15-year term policy he ca
buy without spending more than S800 annually?
If Justin, age 52, wants to pay no more than S800 a year in lite insurance. The largest 15-year term policy he ca buy without spending more than S800 annually is:$148,700
What is insurance?Insurance can be defined as the coverage that help to cover the cost or expense of those that enroll under the insurance plan.
Now let find the largest 15-year term policy he can buy using this formula
Largest 15-year term policy = Lite insurance amount / Annual life insurance premium × Face value
Let plug in the formula
Largest 15-year term policy = $800 / $5.38 × $1,000
Largest 15-year term policy = $148,698.9
Largest 15-year term policy = $148,700 (Approximately)
Therefore the Largest 15-year term policy is $148,700.
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How many meters tall is the tree?
Nate heard stories about the massive Sierra redwoods in California and looked forward to seeing one of these trees for himself. On his first actual encounter with one of the trees, Nate wants to know just how tall the tree is. He places a mirror on the ground and experiments several times until he determines the correct distance from the base of the tree as well as the correct angle of incidence that allows him to see the top of the tree.
Answer:
95 meters
Step-by-step explanation:
Given the dimensions of the triangles shown in the figure, you want the height of the tree.
Similar trianglesThe ratio of the height of the triangle to the base is the same for both triangles shown. That means ...
1.9/0.75 = x/(38.25 -0.75)
where x represents the height of the tree.
Multiplying by (38.25 -0.75), we have ...
[tex]x=\dfrac{(38.25-0.75)\cdot1.9}{0.75}=1.9\left(\dfrac{38.25}{0.75}-1\right)=95[/tex]
The height of the tree is 95 meters.
Which of the following pair of linear equations are consistent or inconsistent x - y = 8, 3x - 3y = 16?
Answer:
the equations listed are inconsistent because the do not intersect or overlap.
Step-by-step explanation:
use the desmos graphing calculator website to graph the two equations. if they are parallel then they are inconsistent. if the cross or overlap then they are consistent
suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. what is the probability that the penny and nickel both come up heads?
The probability of the coins penny and nickel both should show heads when four coins flip simultaneously is equal to 1/4.
As given in the question,
Number of coins flip simultaneously = 4
Possible outcomes on flipping a outcome = { head , tail}
Total outcomes = 2
Probability of getting a head for each coin = 1 /2
Probability of getting heads on both the coins penny and nickel
= ( 1 / 2 ) × ( 1 / 2 )
= ( 1 / 4 )
Therefore, the probability of getting heads on both the coins penny and nickel is equal to 1 / 4.
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9. The population of a city increases by 25% each year, and that city's initial population is 1250. Which function provides a model for P(t), this city's population after t years? A. P(t) = 1250(25)* B. P(t) = 1250(0.25)* C. P(t) = 1250+ (25)* D. P(t) = 1250(1.25)* 1
The function that provides a model for the function p(t) for the population of a city is
D. P(t) = 1250(1.25)*tHow to write an exponential function to model the dataThe given problem is solved using, f(x) = a (b)^x
the starting = a
the base = b
the exponents = x
considering the given problem
p(t) = a (b)^t
a = 1250
rate, r = 25%
r = 25 / 100
r = 0.25
for increasing rate, b = 1 + r = 1 + 0.25 = 1.25
substituting known variables
p(t) = 1250 (1.25)^t
the equation that models the population of a city is p(t) = 1250 (1.25)^t
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Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop. How much she make in a workweek if she sold $4,800 worth of merchandise?
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.
How to calculate the value?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:
= $365 + (5% × $4800)
= $605
The amount is $605.
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a concesquence can be defined as
Answer:
an outcome
Step-by-step explanation:
how do i solve 4( К-8 ) = -3+4к
Answer:
No solutions, there is nothing that will make the equation true
Step-by-step explanation:
You need to isolate the variable
4(K-8) = -3+4K
First get ride of the parenthesis by distributing
(4 x k) - (4 x 8) =-3+4k
4k-32 = -3+4k
next rearrange the equation to have the variable on only one side
4k-32 = -3+4k (subtract 4k from one side)
-32 = -3
The variables canceled out, leaving an equation. If the equation is true there are infinite equations while if the equation is false there are no solutions
-32 is NOT equal to -3, meaning there are no solutions
What is the value(s) of x in the equation below? Simplify if necessary.
x² +5=30
Answer: x=25
Step-by-step explanation:
x²+5=30
30-5=25
x²=25
[tex]\sqrt{x^2}=\sqrt{25}[/tex]
x=25
Answer:
x = -5 or 5
Step-by-step explanation:
1. subtract 5 from both sides
x^2 = 25
2. take the square root of both sides and remember to use positive and negative roots
x = ± 5
3. separate both solutions
x = -5 or x = 5
Find the value of x. Show all work.
Area of the rectangle is 30 sq. Ft
Answer:
The answer is 3 ft
Step-by-step explanation:
Given;Area of rectangle (A) = 30 sq ft.Length (l) = xWidth (w) = 3x + 1To Find;Value of xNow, we know that
A = l × w
30 = (x) × (3x + 1)
30 = 3x² + x
3x² + x = 30
3x² + x - 30 = 0
3x² - 9x + 10x - 30 = 0
3x(x - 3) + 10(x - 3) = 0
(x - 3) (3x + 10) = 0
x = 3 ft
Thus, The value of x is 3
For Verification Only ;
30 = (x) × (3x + 1)
30 = (3) × (3*3 + 1)
30 = 3 × 10
30 = 30
Hence, L.H.S = R.H.S
Thinking and Reasoning Choose Efficient Methods What are two different ways to simplify the expression 4(3x + 7x + 5) so that it equals 40x - 20? Explain.
What is the volume of the figure below if a = 9 units and b = 7 units?
A.
760.5 cubic units
B.
1,296 cubic units
C.
1,012.5 cubic units
D.
364.5 cubic units
Base (cube): [tex]V=s^3[/tex]
[tex]V=9\cdot9\cdot9=729[/tex]
Top (triangular prism): [tex]V=\frac{1}{2}bhl[/tex]
[tex]V = \frac{1}{2}(9\cdot7)\cdot9=283.5[/tex]
Together:
[tex]V = 729+283.5 =1012.5[/tex]
C.
1012.5 cubic units.
The purchase price of a large 4K LED TV, including finance charges, was $1230. A down payment of $300 was made, and the remainder was paid in 12 equal monthly installments. Find the monthly payment.
The monthly installment is $ 77.5. We have to divide the annual rate by 12 to find monthly installments.The number of equated monthly installment is equal to the number of month in the repayment tenure.
What is finance purchase charges?
A purchase finance charge is a fee applied to purchase a credit account like a credit card .This typically takes the form of an interest charge, although some accounts have may other terms.
How do we made monthly installment?The installment is generally in equal month payments that include interest and portion of the principle.We schedule to be created by the lender detailing payment throughout the loan duration.
By solving :
1230=300+12 x
1230-300=12 x
x= $ 77.5 monthly payment
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what is the probability that a particle in the state of the finite potential well will be found at the center of the well? explain.
There is a non zero probability of the particle in the state of finite potential .
It is an extension of the infinite potential well, in which a particle is confined to a "box", but one which has finite potential "walls". Unlike the infinite potential well, there is a probability associated with the particle being found outside the box. The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than the potential energy barrier of the walls it cannot be found outside the box. In the quantum interpretation, there is a non-zero probability of the particle being outside the box even when the energy of the particle is less than the potential energy barrier of the walls (cf quantum tunnelling).
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an engineering research center claims that through the use of a new computer control system, automo- biles should achieve, on average, an additional 3 miles per gallon of gas. a random sample of 100 automo- biles was used to evaluate this product. the sample mean increase in miles per gallon achieved was 2.4, and the sample standard deviation was 1.8 miles per gallon. test the hypothesis that the population mean is at least 3 miles per gallon. find the p-value of this test, and interpret your findings.
The test is proved that hypothesis that the population mean is atleast 3-miles per gallon.
What is hypothesis?A hypothesis is the proposed explanation for any kind of phenomenon.
So here are the values of X BAR i=2.4. S is 1.8.
Our sample n =100.
The null hypothesis here is that mu is greater than or equal to 3.
Against the alternative hypothesis that is less than three. Now the calculated value for the test statistic is going to be the equal to X bar is in (-) knots. That's 2.4 -3. divided by S over 2^2 of end. So 1.8 divided by the square root of the 100 gives us negative 3.33. So we can refer to that box of the T distribution and we are get the value. The p value for the test is going to be less than 0.5. Therefore we have the strong evidence that the not hypothesis is going to be the read checked it. So therefore we can reject to the null hypothesis and then it can accept the alternative by the hypothesis that is less than three. Where it is here is the mean of the population, the noting the average increase per gallon.
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-4(n-6)= 12
What is the value of n?
Step-by-step explanation:
-4(n-6)=12
-4n+24=12
-4n=-36
4n=36
n=36/4
