The number of hours Nadeem will be riding her bike can vary depending on her rate. It can range from 4 to 7.5 hours.
To find how many hours Nadeem will be riding her bike, we can use the formula:
distance = rate x time.
Let's assume Nadeem's rate is r mi/hr and the time she will be riding is t hours.
Given that Nadeem plans to ride her bike between 12 mi and 15 mi, we can set up the following inequality:
\(12 \leq r \times t \leq 15\)
To solve for t, we can divide both sides of the inequality by r:
\(12/r \times t \leq 15/r\)
Now, let's consider a few examples:
Example 1:
If Nadeem's rate is 3 mi/hr, we can substitute r = 3 into the inequality:\(12\leq r \times t \leq 15\)
\(12/3 \leq t\leq15/3\\4 \leq t \leq 5\)
This means Nadeem will be riding her bike for a duration between 4 hours and 5 hours.
Example 2:
If Nadeem's rate is 2 mi/hr, we can substitute r = 2 into the inequality:
\(12/2\leq t \leq 15/2\\6 \leq t \leq 7.5\)
Since time cannot be negative, Nadeem will be riding her bike for a duration between 6 hours and 7.5 hours.
Therefore, the number of hours Nadeem will be riding her bike can vary depending on her rate. It can range from 4 to 7.5 hours.
Complete question:
Nadeem plans to ride her bike between 12mi and at most 15mi. Write and solve an inequality to model how many hours Nadeem will be riding.
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What is the scale factor from abc to def?
Answer:
the answer is 8 because DEF is 8 times larger than ABC.
Step-by-step explanation:
hope that helps>3
Answer:
3
Step-by-step explanation:
To find scale factor, you need to divide two of the given sides. Meaning you can do any corresponding sides. So, for now, I will do 12 from DEF and 4 from ABC.
12 ÷ 4 = 3
To check if it is accurately 3, you will do it again (optional). You can use 15 from DEF and 5 from ABC
15 ÷ 5 = 3
Since both are 3, that will be the scale factor.
The answer is 3.
Please help me with this
Answer:
A and F
Step-by-step explanation:
PLEASE HELP! Thank you!!!
a student wants to make a short playlist that consists of music from both artist a and artist b. artist a has 10 songs and artist b has 15 songs. the student wants the playlist to consist of 6 songs. for each of the following conditions, count the number of ways to build the playlist. each song is unique and the order of the playlist matters. (a) no conditions. the playlist can consist of any 6 songs. (b) the playlist must consist of exactly 3 songs from each artist. (c) the playlist must consist of at least 2 songs from each artist.
(a) No conditions. (b) The playlist must consist of exactly 3 songs from each artist. (c) The playlist must consist of at least 2 songs from each artist.
Working:
To build a playlist of 6 songs from 25 unique songs, we can use the formula for combinations:
nCr = n! / r!(n-r)!
where n is the total number of songs and r is the number of songs we want to include in the playlist.
So the number of ways to build the playlist is:
25C6 = 25! / 6!(25-6)! = 177,100
Therefore, there are 177,100 ways to build the playlist without any conditions.
(b) The playlist must consist of exactly 3 songs from each artist.
To build a playlist of 6 songs with exactly 3 songs from each artist, we can use the formula for combinations again:
nCr = n! / r!(n-r)!
We need to choose 3 songs from artist A and 3 songs from artist B, so we can calculate the number of ways to do this separately:
Number of ways to choose 3 songs from artist A:
10C3 = 10! / 3!(10-3)! = 120
Number of ways to choose 3 songs from artist B:
15C3 = 15! / 3!(15-3)! = 455
To get the total number of ways to build the playlist, we can multiply these two numbers together:
120 * 455 = 54,600
Therefore, there are 54,600 ways to build the playlist with exactly 3 songs from each artist.
(c) The playlist must consist of at least 2 songs from each artist.
To build a playlist of 6 songs with at least 2 songs from each artist, we can break this down into cases:
Case 1: 2 songs from artist A and 4 songs from artist B
Number of ways to choose 2 songs from artist A:
10C2 = 10! / 2!(10-2)! = 45
Number of ways to choose 4 songs from artist B:
15C4 = 15! / 4!(15-4)! = 1,386
Total number of ways for case 1:
45 * 1,386 = 62,370
Case 2: 3 songs from artist A and 3 songs from artist B
We already calculated the number of ways for this case in part (b):
54,600
Case 3: 4 songs from artist A and 2 songs from artist B
Number of ways to choose 4 songs from artist A:
10C4 = 10! / 4!(10-4)! = 210
Number of ways to choose 2 songs from artist B:
15C2 = 15! / 2!(15-2)! = 105
Total number of ways for case 3:
210 * 105 = 22,050
Total number of ways to build the playlist with at least 2 songs from each artist:
62,370 + 54,600 + 22,050 = 139,020
Therefore, there are 139,020 ways to build the playlist with at least 2 songs from each artist.
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The function F is defined by F(x)= 12/x + 1/2 . Use this formula to find the following values of the function. F(k)
So the value of the function F at k is 12/k + 1/2.
What is function?In mathematics, a function is a relationship between two sets of values, where each input value in the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function can be represented in several ways, including as a set of ordered pairs, a graph, an equation, or a verbal description. Functions are widely used in mathematics and many other fields, such as physics, engineering, and computer science, to model and analyze real-world phenomena.
Here,
To find F(k), we simply substitute k for x in the formula for F:
F(k) = 12/k + 1/2
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Complete question:
The function F is defined by F(x)= 12/x + 1/2 . Use this formula to find the following values of the function: F(k)
In square ABCD, points E and F are on sides AD and CD, respectively, such that 3DE=3FC=AB, Segments BF and CE intersect at point G. If the area of the square is 180 cm², what is the area (in cm²) of quadrilateral EDFG?
The area of quadrilateral EDFG is approximately 107.38 cm².
As 3DE = 3FC = AB, we can divide square ABCD into nine congruent smaller squares, each with an area of 20 cm² (since the total area of the square is 180 cm²). We can see that quadrilateral EDFG consists of two of these smaller squares and two right triangles.
The area of each of the smaller squares is 20 cm², so the area of both of them together is 40 cm². To find the area of the two right triangles, we need to first find the length of the diagonal of each of these squares. Using the Pythagorean theorem, we can see that the diagonal of each square is:
√(AB² + AB²) = √(2AB²) = AB√2 = 3DE√2
So the diagonal of each square is 3 times the length of DE (or FC), multiplied by the square root of 2. Since DE = FC = AB/3 = 6 cm, the diagonal of each square is:
3DE√2 = 3(6)√2 = 18√2 cm
The height of each right triangle is DE, which is 6 cm, and the base is half of the diagonal of each square, or (18√2)/2 = 9√2 cm. So the area of each right triangle is:
(1/2) × base × height = (1/2) × (9√2) × 6 = 27√2 cm²
Therefore, the area of quadrilateral EDFG is:
2 × area of small squares + 2 × area of right triangles
= 2(20 cm²) + 2(27√2 cm²)
= 40 cm² + 54√2 cm²
≈ 107.38 cm² (rounded to two decimal places)
Therefore, the area of quadrilateral EDFG is approximately 107.38 cm².
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When x=-3, then y=______
Answer:-1
Step-by-step explanation:
Answer: -6
Step-by-step explanation:
the line pass through (-3,-6)
answer the following here
Answer:
hi
Step-by-step explanation:
Answer:
y=4 and boundary point
Step-by-step explanation:
one student from the school will be selected at random. what is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy?
Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:
Step 1: 89 pupils out of a possible 200 answered with joy, as shown in the table.Step 2 - It is also stated that there were a total of 28 students in the age range of 6 to 8 years who answered positively.Step 3 - Accordingly, the likelihood that the pupil belongs to the 6 to 8-year-old age range is:P = 28/89
Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
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The complete question is given below:
Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?
For an acceptance sampling plan with n = 27 and c = 0, find the probability of accepting a lot that has a defect rate of 4%. (Round your answer to four decimal places.)
To find the probability of accepting a lot with a defect rate of 4% using an acceptance sampling plan with n = 27 and c = 0, we need to calculate the binomial probability of having zero defects in a sample of 27 items.
The probability of accepting a lot is equal to the probability of having zero defects, which can be calculated using the binomial probability formula. The formula is P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where P(X = k) is the probability of getting k successes, n is the sample size, p is the probability of success (defect rate), and C(n, k) is the binomial coefficient.
In this case, we want to find P(X = 0) where n = 27 and p = 0.04 (4% defect rate). Substituting these values into the binomial probability formula and calculating it will give us the desired probability of accepting the lot with zero defects.
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Use the change of base formula to compute logo 4.
Round your answer to the nearest thousandth. Yea
Answer:
\(\log_{9}4\approx 0.631\)
Step-by-step explanation:
The change of base formula we can use is
\(\log_{b}a=\frac{\log{a}}{\log{b}}\)
Not all calculators will allow the user to directly enter the logarithms with a given base, so the change of base can be used for all calculators, which use the common log.
Common logs have a base of 10.
Let's convert your expression:
\(\log_{9}4=\frac{\log4}{\log9}\)
Using our calculator, we will compute log 4 divided by log 9:
\(\frac{\log4}{\log9}\approx0.631\).
If the combination r = 5% and Y = $100 billion is on the Fed rule line, we know that the combination r = 7% and Y = $100 billion would represent Select one: a. the Fed rule shifting to the left. b. a movement down the Fed rule. c. a movement up the Fed rule. d. the Fed rule shifting to the right.
If the combination r = 5% and Y = $100 billion is on the Fed rule line, and the combination r = 7% and Y = $100 billion is considered, it would represent a movement up the Fed rule.
The Fed rule represents the relationship between the interest rate (r) and the level of real GDP (Y). As the interest rate increases from 5% to 7% while keeping the level of real GDP constant at $100 billion, it indicates a movement along the Fed rule line in an upward direction.
This implies that as the interest rate increases, the recommended level of real GDP decreases, based on the Fed rule. Therefore, the combination r = 7% and Y = $100 billion represents a movement up the Fed rule.
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a study was conducted on the effects of long-term marriage (more than 10 years). researchers gathered data from a sample of 4,563 adults in one small town and measured quite a few variables, in addition to the explanatory variable of marriage and the response variable of longer life span. according to a newspaper article summarizing the study, everyone in long-term marriages is more likely to be more physically active, at a healthy weight, and nonsmokers. all those who are not married are about 20% more likely to be deceased. was this a valid conclusion? explain. this is a valid conclusion because the sample was large. this is a valid conclusion because an observation was conducted. this is not a valid conclusion because the sample was not random. this is not a valid conclusion because there was no control group.
We cannot infer a cause and effect relationship because the treatments imposed were not blocked correctly.
What is cause and effect relationship?Cause-and-effect describes a relationship between actions or events in which at least one action or event is a direct result of the others.
Cause and effect is the relationship between two things when one thing makes something else happen.
For example, if we eat too much food and do not exercise, we gain weight. Eating food without exercising is the “cause;” weight gain is the “effect.” There may be multiple causes and multiple effects.
The treatments given to the groups given in the question where not assigned proper treatments to establish proper randomized block design.
Thus, we can say the conclusion is that we can't truly infer a cause and effect relationship as the blocks were not properly done.
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A survey was run by a high school student in order to determine what proportion of mortgage-holders in his town expect to own their house within 10 years. He surveyed 178 mortgage holders and found that the proportion of these that did expect to own their house within 10 years is 0.69.
The student decides to construct a 95% confidence interval for the population proportion. You may find this standard normal table useful for the following questions.
a)Calculate the margin of error that the high school student will have. Give your answer as a decimal to 3 decimal places.
Margin of error =
A different high school student sees this survey and decides to try and repeat it. This second high school student also surveys 178 mortgage holders, but this student finds that the proportion of these that do expect to own their house within 10 years is 0.83. This student also constructs a 95% confidence interval for the population proportion.
b)Calculate the margin of error that the second student will have. Give your answer as a decimal to 3 decimal places. Margin of error =
Margin of error = 1.96 * 0.038 = 0.0745 ≈ 0.075 (to 3 decimal places)
a) To calculate the margin of error for the first high school student, we can use the formula:
Margin of error = z* (standard error)
where z* is the critical value of the standard normal distribution corresponding to the desired level of confidence, and the standard error is given by:
standard error = sqrt[(p-hat * (1-p-hat))/n]
where p-hat is the sample proportion, and n is the sample size.
Given that the sample size is n=178, and the sample proportion is p-hat = 0.69, the standard error is:
standard error = sqrt[(0.69*0.31)/178] = 0.042
To find the critical value z* for a 95% confidence interval, we can look up the value in the standard normal table. Since we want a two-tailed confidence interval, we need to divide the level of significance (1 - 0.95 = 0.05) by 2, resulting in an alpha level of 0.025. Looking up the corresponding z-score, we find:
z* = 1.96
Therefore, the margin of error for the first high school student is:
Margin of error = 1.96 * 0.042 = 0.0828 ≈ 0.083 (to 3 decimal places)
b) To calculate the margin of error for the second high school student, we can follow the same procedure as above, using the sample size n=178 and the sample proportion p-hat = 0.83. The standard error is:
standard error = sqrt[(0.83*0.17)/178] = 0.038
The critical value z* for a 95% confidence interval is still 1.96, so the margin of error is:
Margin of error = 1.96 * 0.038 = 0.0745 ≈ 0.075 (to 3 decimal places)
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A survey asked 100 adults about car ownership and ride-sharing apps. Of the 38 people without a car, 29 have ride-sharing app on their phone. A total of 47 people have a ride-sharing app on their phone.
What percentage of people surveyed who own a car have a ride-sharing app on their phone? Round to the nearest whole percent.
Enter the correct answer in the box.
Answer:
it should be 18%
Step-by-step explanation:
3) The road centerline asignment below: Given: the distance from Point A to Pls is 222.841 the distance from Point Ply to Ply is 345.036 the distance from Point Pl
2
to b is 214.761 If the station of Point A is 3+ def ghi, determine the station of BC1,EC
1
,BC, and EC
2
The stationing of BC1, EC1, BC, and EC2 can be determined by adding the respective distances to the station of Point A.
To determine the station of BC1, EC1, BC, and EC2, we need to understand the concept of stations in road centerline alignment. In road design and construction, stations are used to measure distances along the centerline of the road. The station of a point refers to its distance from a reference point, typically the starting point of the road.
Given that the station of Point A is 3+ def ghi, we can assume that the stationing system used is based on chainage, where the main stations are represented by whole numbers and the sub-stations are represented by decimals or fractions.
Let's break down the given distances:
The distance from Point A to Pls is 222.841.
The distance from Point Ply to Ply is 345.036.
The distance from Point Pl2 to b is 214.761.
Based on the given information, we can determine the stations as follows:
Station of Point A: 3+ def ghi (given).
Station of BC1: Station of Point A + Distance from Point A to Pls = 3+ def ghi + 222.841.
Station of EC1: Station of BC1 + Distance from Point Ply to Ply = (3+ def ghi + 222.841) + 345.036.
Station of BC: Station of EC1 + Distance from Point Pl2 to b = ((3+ def ghi + 222.841) + 345.036) + 214.761.
Station of EC2: Station of BC + Distance from Point Pl2 to b = ((3+ def ghi + 222.841) + 345.036 + 214.761) + 214.761.
The above equations represent the stationing along the road centerline from Point A to BC1, EC1, BC, and EC2, respectively. By substituting the given station of Point A and the distances into the equations, we can calculate the stations of BC1, EC1, BC, and EC2.
Please note that the specific numerical values for def, ghi, and the distances are not provided in the question, so the actual station values cannot be determined without those values. However, you can substitute the known values into the equations to calculate the stations once you have the complete information.
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Suppose that the price of a pair of shoes is $5 and the price of a box of tea is $3. What is the relative price of a pair of shoes? What is the relative price of a box of tea?
The relative price is a useful measure for comparing the prices of different products or services, especially in the context of consumer preferences and demand.
Relative price refers to the price of a particular product or service in relation to other goods or services in the market.
It is calculated as the ratio of the price of a given product or service to the price of a reference product or service, commonly referred to as a base good or service.
Let the price of a pair of shoes be $5 and the price of a box of tea be $3.
Then the relative price of a pair of shoes is given by:
Relative price of shoes = Price of shoes / Price of tea
= $5 / $3
= 1.67
Thus, the relative price of a pair of shoes is 1.67.
Similarly,
The relative price of a box of tea can be calculated as follows:
Relative price of tea = Price of tea / Price of shoes
= $3 / $5
= 0.6
Therefore, the relative price of a box of tea is 0.6.
This means that the price of tea is relatively cheaper than that of shoes, as its relative price is less than one.
The relative price of shoes is greater than one, which indicates that shoes are relatively more expensive than tea.
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You are given a bag of jelly beans there are 7 red, 8 blue, 4 yellow, and 10 pink. Find the probability of drawing two blue in a row with replacement
Answer:
8 / 29 = .276
Step-by-step explanation:
29 is the total number of jelly beans
When we have replacement, we do not reduce the number of total jelly beans, so the probably of drawing blue stays the same.
Answer:
.276
Step-by-step explanation:
Find the surface area of the cube.
3/5 inches
Step-by-step explanation:
Area of the cube : 6a²
6 ( 3/5)²
6 (9/25)
54/25
54/25 = 2.16
Show that w is in the subspace of R4 spanned by V1, V2, and V3, where these vectors are defined as follows. 1 -4 -9 -4 6 3 5 W= -2 - 1 - 1 -2 4 11 -8 - 15 To show that w is in the subspace, express was a linear combination of V1, V2, and V3. Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice. O A. The vector w is in the subspace spanned by V1, V2, and V3. It is given by the formula w= (v1+ 2+ 3. (Simplify your answers. Type integers or fractions.) B. The vector w is not in the subspace spanned by V1, V2, and V3.
To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:
w = c1V1 + c2V2 + c3V3
We can write this as a matrix equation:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
We can solve this system of equations using row reduction:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
R2 = R2 - 6R1
R3 = R3 - 2R1
R4 = R4 + 15R1
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 -23 67 -59 | | -32 |
R4 = R4 + 23R2
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 0 174 -294 | | 225 |
R3 = R3 - (12/27)R2
R4 = (1/174)R4
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 0 -1 22/3 | | c3 | | -13/3 |
| 0 0 1 -98/87 | | 25/58 |
R1 = R1 + 4R3
R2 = R2 - 59R3
R4 = R4 + (98/87)R3
| 1 0 -13 -10/3 | | c1 | | 21/29 |
| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |
| 0 0 1 -98/87 | | c3 | | 25/58 |
| 0 0 0 1390/2391 | | 1009/2391 |
R1 = R1 + (13/1390)R4
R2 = (1/27)R2
R3 = R3 + (98/1390)R4
| 1
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-6(a+8)
simplify the expression with distributive property
Answer:
-6(a+8) simplified using distributive property would equal -6a+-120
Step-by-step explanation:
Which of these sets of ordered pairs would define a line with a positive slope?
a. (5, 1) and (0, 5)
b. (2, 3) and (-4, 8)
c. (3, 6) and (5, 1)
d. (2, 3) and (7, 6)
Part A: A statement about rational numbers is shown.
The product of two negative rational numbers is greater than either factor. Is the statement always true, sometimes true, or never true? Explain your answer. Provide at least two examples to support your answer.
Part B: A different statement about rational numbers is shown.
The product of two positive rational numbers is greater than either factor. Provide at least two examples to show that this statement is only sometimes true.
i didn’t realize u were chill like that
There are 24 hours in 1 day. If you sleep 30% percent of the day how many hours do you sleep
Step-by-step explanation:
30%of24
30÷100×24
7.2
For the geometric sequence 3,9/4,27/16,81/64, 1. What is the common reason? 2. What is the fifth term of the sequence? 3 What is the nth term of the sequence"
For the given geometric sequence we have:
a) R = 3/4
b) 243/256
c) Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾
What is the common reason?The common reason is given by the quotient between two consecutive terms, so using the first two, we will get:
R = (9/4)/3
R = 3/4
That is the common reason.
b) To find the fifth therm, we need to take the fourth one and multiply it by the common reason, so we will get:
81/64*(3/4) = 243/256
c) The n-th term of the sequence is the first term of the sequence multiplied by the common reason (n - 1) times, it gives:
Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾
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Please solve
1/3 (b+6)=1/4b +8
Find the 46th term of 15. 30, 60
Answer:
5.2776558e+14
Step-by-step explanation:
\(a_{n} =a_{1} *r^{n-1}\)
15, 30, 60
\(a_{46} =15(2)^{46-1}\)
\(a_{46}\) = 5.2776558e+14
hope it helps :)
mark brainliest!
Shaundra went to 4 stores and found these prices for cases of water.
Super Buy: 12 bottles for $3.96
Fresh Grocers: 8 bottles for $2.08
Saveway: 24 bottles for $5.52
Shop and Go: 36 bottles for $7.56
Lod
Which store charges the least amount per bottle?
Answer:
Step-by-step explanation:To determine which store charges the least amount per bottle, you need to calculate the price per bottle for each store. You can do this by dividing the total price of the cases by the number of bottles in each case.
For Super Buy, the price per bottle is $3.96 / 12 bottles = $0.33 per bottle.
For Fresh Grocers, the price per bottle is $2.08 / 8 bottles = $0.26 per bottle.
For Saveway, the price per bottle is $5.52 / 24 bottles = $0.23 per bottle.
For Shop and Go, the price per bottle is $7.56 / 36 bottles = $0.21 per bottle.
Based on these calculations, it looks like Shop and Go charges the least amount per bottle at $0.21.
if the circumference is 21 pi what is the area
Answer:1386cm2
Step-by-step explanation:
Please explain it. and no links.
thanks.
Answer: 4*sqrt(66)
This is the same as saying \(4\sqrt{66}\)
===========================================================
Explanation:
x = length of segment BD
Because BD is an altitude of triangle ABC, this means the triangle is split into two smaller right triangles which are similar to the original. All three right triangles are similar to one another.
What this leads to is the proportion
CD/BD = BD/AD
Apply substitution and solve for x.
24/x = x/44
24*44 = x*x .... cross multiply
1056 = x^2
x = sqrt(1056)
x = sqrt(16*66)
x = sqrt(16)*sqrt(66)
x = 4*sqrt(66)
Notice how I factored 1056 in such a way that I pulled out the largest perfect square factor (16). Then I used the rule \(\sqrt{x*y} = \sqrt{x}*\sqrt{y} \) to break up the root.