If a 12-ft-by-15-gt rectangular swimming pool has a 3-ft-wide no-slip surface around it. The outer perimeter of the no-slip surface around the rectangular swimming pool is 78 feet.
The key idea in this problem is to recognize that the no-slip surface around the pool consists of a rectangular strip of uniform width that runs parallel to the edges of the pool. To find the outer perimeter of this strip, we need to add up the lengths of all four sides of the rectangle formed by the outermost edges of the no-slip surface.
Let's start by finding the length of the no-slip surface that runs along the length of the pool. Since the pool is 12 feet long and the no-slip surface extends 3 feet beyond each end of the pool, the total length of the no-slip surface is:
12 + 2(3) = 18 feet
The "2(3)" term in this equation represents the 3-foot-wide extension on each end of the pool. Next, we need to find the length of the no-slip surface that runs along the width of the pool. Since the pool is 15 feet wide and the no-slip surface extends 3 feet beyond each side of the pool, the total width of the no-slip surface is:
15 + 2(3) = 21 feet
Now we have the lengths of the two parallel sides of the rectangle formed by the outermost edges of the no-slip surface. To find the lengths of the other two sides, we simply add up the lengths of the corresponding sides of the pool.
Therefore, the length of the rectangle is 12 + 2(3) = 18 feet, and the width of the rectangle is 15 + 2(3) = 21 feet.
Finally, we can add up the lengths of all four sides of the rectangle to find the outer perimeter of the no-slip surface:
2(18) + 2(21) = 36 + 42 = 78 feet.
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903-814 with solution
Answer:
89
Step-by-step explanation:
903 - 814 =
= (900 + 3) - (800 + 14) =
= 900 + 3 - 800 - 14 = 100 - 11 =
= 89
If Sullivan got 32 pieces of candy, how many did Carter get? Answer
Sullivan received half as many candy as Carter did, or half as many candies as Sullivan received.
What is an amount?aggregate means the complete amount or quantity. attempting to estimate the time required. the amount on hand or being considered. mutable noun How much of something there is, how much you possess, require, or receive, is known as its amount. He is dependent on that sum of money to get by.Therefore, a number only refers to things that we can count. Contrarily, quantity relates to how much of something there is, such as how much liquid, resistance, or stimulation. In actuality, the term "amount" refers to amounts that we can measure but not count individually." Amount is defined as the representation of total quantity of given object."
According to the question,
Number of candies Sullivan got = s
Number of candies Carter got = 2s
Compare the given amount of data we get,
Number of candies Carter got = 2(Number of candies Sullivan got )
This shows Carter got twice number of candies comparison to Sullivan.
or
Number of candies Sullivan got = 1/2 (Number of candies Carter got)
Sullivan got half number of candies compare to Carter.
Hence, we conclude Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.
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1. What is the rule for the following geometric sequence? 64, -32, 16, -8...
an=64(-2)n-1
an = 64(1)-1
an=64(-1)-1
an=64(2)-1
The rule for the given geometric sequence as required to be determined is; a (n) = 64 (-1/2)^(n-1).
Which rule represents the geometric sequence?By observation, the first term of the sequence is; 64.
Also, the common ratio of each successive terms is as follows;
-32 / 64 = 16 / -31, -8 / 16 = -1/2.
On this note, the ratio is; -1/2.
Consequently, it follows that the answer choice which correctly represents the rule for the geometric sequence is; an = 64(-1/2)^n-1.
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cover all material from the lessons but will hopefully remind you of key points. To be prepared,
you must study all packets from Unit 1.
A salesman tracks the number of cars he sells through the model c, where c(m) is number of cars sold
and m is the month for 0 ≤ m ≤ 24.
1. What does c(10) represent?
2. What does
c(16)-c(8)
16-8
represent? 3. What does
represent?
c(7)-c(6.999)
7-6.999
a. It should be noted that c(10) represents the number of cars sold in the 10th month.
b. c(16) - c(8) represents the number of cars sold in the 16th month minus the number of cars sold in the 8th month. This difference could represent the net change in the number of cars sold between those two months.
What is a function about?The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. The process of evaluating a function is typically straightforward when we have the function in the form of a formula.
In this case, c(10) represents the number of cars sold in the 10th month.
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The accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency. a) Which would you expect to be larger: the median or the mean? Explain briefly. b) Which would you report: the median or the mean? Explain briefly.
Shawn's retirement party will cost $6 if he invitês 3 guests. If there are 8 guests, how much
will Shawn's retirement party cost? Assume the relationship is directly proportional.
Step-by-step explanation:
Shawns party will cost $16 if there are 8 guest
Is 96 the lowest common multiple of 4 and 24?
no
4x6=24
24x1=24
hence 24 is the lowest common multiple , i hope this helped xx
The taj Mahal in India is a square about 95.4 on each side.What is the area of the taj mahal?
The area of the Taj Mahal is 9092.16 square meters (97,890.56 square feet).
What is area of a square?The quantity of square units required to completely cover a square is known as the area of a square. The territory that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square meters serving as the standard unit.
The Taj Mahal has an area of 9092.16 square meters (97,890.56 square feet). We utilise the formula for calculating the area of a square, which is length x width. The Taj Mahal's length and width are both 95.4 metres, therefore we just multiply these two values together. 9092.16 square meters = 95.4 × 95.4 square meters (97,890.56 square feet). This is the Taj Mahal's area.
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What is the answer to this equation (5+12i)+(7-5i)
The answer to the equation (5+12i) + (7-5i) is found to be 12-7i.
The provided equation is a simple algebraic relation between two complex numbers.
The given complex numbers are 5+12i and 7-5i.
We have to add these two complex numbers.
We will add the real part of the complex number to the real part and complex part of one complex number to the complex part of the complex number.
Sum of number = (5+12i) + (7-5i)
Sum of number = 12-7i
The sum of the two complex numbers is also complex number that has a real part has 12 and the imaginary or the complex part as -7.
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in a shipment of 66 vials, only 14 do not have hairline cracks. if you randomly select 4 vials from the shipment, what is the probability that all 4 of the selected vials have hairline cracks?
that the probability of selecting 4 vials with hairline cracks is approximately 0.0375, or 3.75%
We can solve this problem using the hypergeometric distribution, which is used when sampling without replacement from a finite population. In this case, we have a population of 66 vials, out of which 14 are good (do not have hairline cracks) and 52 are bad (have hairline cracks). The probability of selecting all 4 bad vials (with hairline cracks) can be calculated as follows: P(4 bad vials) = (number of ways to choose 4 bad vials) / (total number of ways to choose 4 vials)
The number of ways to choose 4 bad vials from 52 is: C(52,4) = 52! / (4! × (52-4)!) = 270725
The total number of ways to choose 4 vials from 66 is: C(66,4) = 66! / (4! × (66-4)!) = 7219420
Therefore, the probability of selecting all 4 bad vials is: P(4 bad vials) = 270725 / 7219420 = 0.0375
This means that the probability of selecting 4 vials with hairline cracks is approximately 0.0375, or 3.75%
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What is the area of this compound figure?
Answer:
177 mi²
Step-by-step explanation:
are two rectangles, one has sides of 6 and 19 and one has sides of 9 and 7, we find the two areas with the formula A = L x W and add them, all as in the expression:
remember PEMDAS
6 × 19 + 9 × 7 =
114 + 63 =
177 mi²
What is the solution to 3 (2k + 3) = 6 - (3k - 5)?
Move the correct answer to each box. Not all answers will be used.
k
-8 -2 2
3 8
9
Answer: 22k
Step-by-step explanation:
The solution to the equation is k = 2/9
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 equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
3 ( 2k + 3 ) = 6 - ( 3k - 5 ) be equation (1)
On simplifying , we get
3 ( 2k ) + 9 = 6 - 3k + 5
6k + 9 = 11 - 3k
Adding 3k on both sides , we get
9k + 9 = 11
Subtracting 9 on both sides , we get
9k = 2
Divide by 9 on both sides , we get
k = 2/9
Therefore , the value of k is 2/9
Hence , the solution is k = 2/9
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David biked 12\frac{7}{8}12
8
7
miles on Tuesday and 5\frac{3}{8}5
8
3
miles on Wednesday.
How much farther did David bike on Tuesday than on Wednesday?
David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.
We are given that David biked [tex]12\frac{7}{8}[/tex] miles on Tuesday and [tex]5\frac{3}{8}[/tex] miles on Wednesday.
In order to find the number of miles David biked farther on Tuesday than on Wednesday, we will subtract the miles biked by him on Wednesday from the miles biked by him on Tuesday as follows -
[tex]12\frac{7}{8} - 5\frac{3}{8}[/tex]
So, first, we will subtract the whole number of parts as follows -
12-5 = 7
Then, we will subtract the fractional parts as follows -
7/8 - 3/8 = 4/8 = 1/2
so we get,
[tex]12\frac{7}{8} - 5\frac{3}{8} = 7\frac{1}{2}[/tex]
Therefore, David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.
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please help me with this
Answer: 1 [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Make it a mixed number then simplify if you can. I hope this helps.
find the lower quartile and the upper quartile of the data set
Answer:
Lower Quartile = 13 min; Upper Quartile = 27 min
Step-by-step explanation:
Since we have the median, we now separate the data equally to the left and right of the median.
Thus, on the left (lower) portion we have 10, 11, 13, 18, and 19. We see 13 is the middle term of these 5 values so 13 is the lower quartile (Q1).
Similarly, one the right (upper) portion, we have 22, 25, 27, 30, and 32. We see 27 is the middle term of these 5 values so 27 is the upper quartile (Q3)
A trail map has a scale of 3 in. : 2 mi. On the map,
a trail is 5 in. long.
How long is the actual trail?
0 1/mi
O2 mi
O O
12
3-mi
O 07 mi
Answer:
Step-by-step explanation:
in: mi
3:2
5:x
3*1.6667=5
2*1.6667=3.3334/
becaus the first answer was rounded up, the last one needs to be rounded down.
so the answer, rounded up to the nearest hundredth is 3.34
(rounded up to the nearest whole number is 3)
Write 60.9% as a decimal.
A.0.0609
B.0.609
C.0.00609
D.6.0900
To convert a percentage to a decimal, divide the percentage by 100, The correct answer is B. 0.609.
What is Decimal number?When the decimal places in the factors are tallied together, they equal the number of decimal places in the product. A decimal number is one with a whole and a fraction part separated by a decimal point.
A base-10 representation of numeric values is used in the decimal numbering system. The system is widely used in daily life to complete routine tasks like grocery shopping, stock trading, keeping track of football scores, or scrolling through cable channels. Decimal numbers include 7, 28, 199, and 532.11.
To convert a percentage to a decimal, divide the percentage by 100.
So, 60.9% as a decimal would be:
60.9 / 100 = 0.609
Therefore, The correct answer is B. 0.609.
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Liz is recording what kinds of shoes people are wearing at the mall. sandals 2 sneakers 12 high heels 6 Considering this data, how many of the next 10 people Liz sees would you expect to be wearing sandals?
10% of the next 10 people Liz sees would be expected to be wearing sandals.
Liz is recording what kinds of shoes people are wearing at the mall. sandals 2 sneakers 12 high heels 6 Considering this data.
We have to determine how many of the next 10 people Liz sees would you expect to be wearing sandals.
Since 12 out of the 20 people Liz has seen were wearing sneakers, and 6 were wearing high heels, then 2 must have been wearing sandals.
Then, Expect to be wearing sandals = Number of people wearing sandals/Total number of records
Expect to be wearing sandals = 2/20 × 100
Expect to be wearing sandals = 1/10 × 100
Expect to be wearing sandals = 10%,
So 10% of the next 10 people Liz sees would be expected to be wearing sandals.
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one way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. for example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. in this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. throughout the study, the health status of the participants is monitored closely. suppose that you are a researcher designing an experimental feeding trial. how would you set up your study and what limitations would you face? drag the labels onto the flow chart to identify the elements and limitations of your experimental design.
The steps to set up the study and the limitations that would be faced are explained below .
The Steps to setup the study are :
(i) Recruit a large and diverse group of participants who are willing to stick to the prescribed diets for the duration of the study.
(ii) Divide the participants randomly into two or more groups. One group would be given a diet high in trans fats, and the other group(s) would be given a diet low in trans fats.
(iii) Monitor the health status of the participants closely throughout the study .
(iv) At the end of the study, compare the health outcomes of the different groups of participants to determine whether there is a significant difference in health outcomes .
The Limitations of this type of study include :
⇒ the difficulty of controlling all aspects of participants' diets, since participants may consume other foods outside of what is provided to them.
⇒ the study may not be long enough to detect long-term effects of trans fats on health.
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The given question is incomplete , the complete question is
One way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. For example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. In this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. Throughout the study, the health status of the participants is monitored closely.
Suppose that you are a researcher designing an experimental feeding trial. How would you set up your study and what limitations would you face ?
The Son has got his Crown On The pharaoh’s outfitters, ‘Cloaks and Crowns’, sell Cloaks and Crowns in 3 sizes – prince, king and emperor (in increasing size order). He wants to kit out his three sons for the forthcoming festival of Ra. Ahmose chooses a bigger cloak than Kamose, but a smaller crown than Thutmose. Both Thutmose’s cloak and crown are larger than Kamose’s, but the size of Thutmose’s crown matches the size of Kamose’s cloak. Which sizes did the pharaoh’s sons each get?
The only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Let's us consider the sizes of the cloaks by C (prince), B (king), and A (emperor)
The sizes of the crowns by 1 (prince), 2 (king), and 3 (emperor).
Now let us write the following system of inequalities:
B > C
A > B
3 = C (Thutmose's crown matches Kamose's cloak)
2 > C
A > 3
A > 2 (Thutmose's crown is larger than the king size crown)
From the fifth inequality, we know that Thutmose's cloak is the largest of all three cloaks, so A must equal C.
Therefore, we can simplify the system of inequalities to:
B > C, A > B, C = 3, 2 > C, A > 3 and A > 2
Hence, the only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
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Como puedo resolver esto?
- x - y = 4
The points on the graph of the equation represent the solution set to the equation.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the equation as -
- x - y = 4
The given equation is -
- x - y = 4
x + y = 4
The graph of the given equation will represent a straight line. All the points on the line represent the solution set to the equation.
Therefore, the points on the graph of the equation represent the solution set to the equation.
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{Question in english -
How can i solve this?
- x - y = 4}
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
11, 20, 29, ...
Find the 43rd term.
The given sequence appears to be an arithmetic sequence, as the difference between consecutive terms is 9. To find the 43rd term, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term (11 in this case), n is the term number (43 in this case), and d is the common difference (9 in this case).
Plugging in the values, we get:
a_43 = 11 + (43 - 1) * 9
a_43 = 11 + 42 * 9
a_43 = 11 + 378
a_43 = 389
So the 43rd term of the sequence is 389.
Your school is going to start offering afterschool clubs they will be nine clubs to choose from to have clubs at least 23 students we will need to sign up for each one what is the least number of students that must sign up to have all nine clubs
At least number of students who must have signed up to have all nine clubs is equal to 207.
Number of clubs school going to start after school = 9 clubs
At least number of students need to sign up in each one of the club is equal to 23 students.
At least number of students need to sign up to have all in nine clubs is equal to :
At least number of student in 1 club > 23
⇒ At least number of student in 9 club > 23 × 9
At least number of student in 9 club > 207
Therefore, at least number of students need to signed up to have in all nine given clubs are 207 students.
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Please help meeh:
Find the first four terms and stated term given the arithmetic sequence, with a, as the 1" term.
an = 25 - 10n, a5
an = 11 + 9n, a6
an = 65 - 35n, a9
The first four terms and the stated term, with an as the first term, are given the arithmetic sequence: 11 + 9n, a6.
What is an arithmetic sequence?The difference between any succeeding term and its preceding term remains constant throughout an arithmetic progression or arithmetic sequence, which is a set of numbers. That arithmetic progression's common difference is the constant difference. A series of numbers in the following format is an arithmetic sequence: a, a + d, a + 2 d, a + 3 d, a + 4 d,... The common difference between the terms in the sequence is d, and number an is the first term. An = a + (n - 1)d gives the nth term of an arithmetic series. A sequence is considered to be arithmetic if there is a constant difference between each subsequent term.To learn more about arithmetic sequence refer to:
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Somebody please look at this picture and help me pleaseeeeeee
Answer:
I think it's
Step-by-step explanation:
usually involves reading the pattern on the table while keeping in mind that x goes on top and y on
−2x+y = 0 - −7x+3y = 2
To solve this system of linear equations, we need to find the values of x and y that make both equations true at the same time. One method to solve this is to use elimination or substitution.
First, let's rearrange the first equation:
y = 2x
Next, we can substitute y = 2x into the second equation:
-7x + 3y = 2
-7x + 3(2x) = 2
-7x + 6x = 2
-x = -2
So, x = 2.
Finally, we can use the first equation to find y:
y = 2x
y = 2 * 2
y = 4
So, the solution to the system of equations is (x, y) = (2, 4).
Lillian needed
2 bottle of glue to make 8 Halloween Decorations. How many can she make
10
with 1 bottle of glue?
Please Help Me! I really need this question answered. I am behind in my work!!!!!
Answer:
The flagpole is 15 ft tall.
Step-by-step explanation:
In this problem, we are asked to create a proportion of similar triangles to solve for the height of a flagpole.
1) Setting up the ProportionWe are given an equation with the proportion:
[tex]\dfrac{h}{6\text{ft}}=\dfrac{\square}{\square}[/tex]
We can fill in the blanks as follows:
[tex]\dfrac{h}{6\text{ft}}=\dfrac{25 \text{ft}}{10 \text{ft}}[/tex]
Notice that the heights of the triangles compared are both in the numerator, and the lengths of both triangles are in the denominator.
2) Solving the ProportionThen, to solve for the height of the flagpole, we can isolate the variable h in the proportion.
[tex]\dfrac{h}{6}=\dfrac{25}{10}[/tex]
↓ multiply both sides by 6
[tex]h = \dfrac{150}{10}[/tex]
↓ simplify the fraction
[tex]h = 15 \text{ ft}[/tex]
So, the flagpole is 15 ft tall.
Calculate the volume of this cylinder, giving your answer to 1 decimal point
The volume of the cylinder is approximately 1413.7 cubic centimeters.
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height or length of the cylinder.
Since the base of the cylinder has a diameter of 9cm, the radius is half of that, or r = 4.5cm.
The length of the cylinder is given as 20cm.
Therefore, the volume of the cylinder is:
V = πr²h
= π(4.5)²(20)
= 1413.72 cubic centimeters (rounded to 1 decimal place)
Thus, the volume of the cylinder is approximately 1413.7 cubic centimeters.
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Complete question:
Calculate the volume of this cylinder. give your answer to 1 decimal place. Base is 9cm. Length is 20cm.
Say you have a 92% in a class and you do 2 assignments and they are both worth 50% of your grade. And you get a 2/5 on one of them and a 5/5 on the other. Whats the resulting grade?
Answer:
70%
Step-by-step explanation:
