Answer:
93.5 inches
Step-by-step explanation:
Length times width
The guidance counselor of a large high school reports that 48.5% of Junior Pre-Calculus students signed up to take AP Statistics next year, 52.5% signed up to take AP Calculus next year and 10% of Junior Pre-Calculus students signed up to take both AP Statistics and AP Calculus next year.
If one Junior Pre-Calculus student is selected at random, what is the probability that they did not sign up to take AP Statistics or AP Calculus next year?
(A) 0.09
(B) 0.11
(C) 0.19
(D) 0.91
(E) Not enough information is given to determine the probability
Answer:
A. 0.09
Step-by-step explanation:
Bethany sells roses and petunias. The expression
3
r
+
2.5
p
3r+2.5p3, r, plus, 2, point, 5, p gives the cost (in dollars) of
r
rr roses and
p
pp petunias.
What is the cost of
7
77 roses and
8
88 petunias?
Answer:
$41
Step-by-step explanation:
Fill in the values of the variables and do the arithmetic.
3r +2.5p = 3(7) +2.5(8) = 21 +20 = 41
7 roses and 8 petunias cost $41.
Your bank offers free access to online banking, but they charge you $.02 for each online e-check you send. They charge you $.10 for each paper check you write. You have chosen to write all future checks online. Over the year you have sent an average of 18 checks per month. What have you saved in a year with online checking?
Answer: 17.28
Step-by-step explanation:
18*12 =216*.02=4.32
18*12=216*.10=21.6
21.6-4.32=17.28
In a year, by opting for online e-checks at a rate of $.02 per check instead of paper checks at $.10 per check for an average of 18 checks per month, your savings amount to $17.28.
Explanation:The subject of your question is a practical application of mathematics, specifically an area often referred to as personal finance. To find out how much you've saved over a year by sending e-checks online instead of writing paper checks, we first need to calculate the cost of each method and then compare the two.
First, let's calculate how much it would cost for the e-checks. The bank charges you $0.02 for each e-check you send. If you send an average of 18 checks per month over a year (12 months), that's 18 checks/month x 12 months/year = 216 checks/year. At $0.02 a check, that comes out to 216 checks/year x $0.02/check = $4.32/year.
Now let's calculate the cost if you were writing paper checks. The bank charges $0.10 for each paper check you write, so that would have been 216 checks/year x $0.10/check = $21.60/year.
So, by choosing to send e-checks online instead of writing paper checks, you've saved $21.60/year - $4.32/year = $17.28/year.
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Please help me !!☹️❤️
Answer:
(x-10) (x+1) =0
x=10 x=-1
Step-by-step explanation:
x^2 -9x-10 =0
Factor
What two numbers multiply to -10 and add to -9
-10*1 = -10
-10+1=-9
(x-10) (x+1) =0
Using the zero product property
x-10 = 0 x+1=0
x-10+10=0+10 x+1-1=0-1
x=10 x=-1
These are the x intercepts
7/10 = 350/x
Please help cross multiply
Answer:
x=500
Step-by-step explanation:
7/10=350/x
cross-multiply by multiplying 350 to 10 and multiply 7 to x.
example:
7•x
350•10
7x=3500
divide both sides by 7
-------------
x=500
-------------
In the number 49,869 there are how many tens?
Answer:
The number at tenth place is 6. Therefore, I guess there's 6 tens.
Step-by-step explanation:
There are 6 tens in the number 49,869.
To find the number of tens, we look at the digit in the tens place, which is the second digit from the right.
4 is in ten thousand place.
9 is in thousand place.
8 is in hundred place.
6 is in ten place.
As the digit in the tens place is 6.
The digit 6 represents six groups of ten in the number.
So, in the number 49,869, there are 6 tens.
Therefore, the correct answer is that there are 6 tens in the number 49,869.
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What is the quotient?
StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction
Answer:
3/2
Step-by-step explanation:
StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction
I think you mean:
(2m + 4) / 8 divided by (m + 2)/6
=
(2m + 4)/8 times (6 / (m + 2) )
= (m + 2)/4 times 6/(m + 2)
= 6/4 = 3/2
The quotient of the given (2m + 4)/8 divided by (m +2)/6 will be 3/2.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers but the division is not wholly complete.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and a lower word is called the denominator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
Given that
(2m + 4)/8 ÷ (m +2)/6
⇒ (2m + 4)/8 × 6/(m +2)
⇒ 2 ×6 ÷8
⇒3/2 hence it will be the correct answer.
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La suma de tres términos consecutivos a partir a 55(sin incluirlo) vale 738.Encontrar n
The first of three consecutive terms after 55, which sum up to 738, is found to be 245 by setting up an equation and solving for n.
Explanation:The student's question involves finding a variable, n, which represents the first of three consecutive terms, given that the sum of the three terms is 738 and that the sequence starts with a term after 55.
Let's denote the three consecutive terms as n, n+1, and n+2, where n is the first term that comes after 55. Since the sum of the terms is given as 738, we can formulate the following equation:
\(n + (n+1) + (n+2) = 738\)
Combining like terms, we get:
\(3n + 3 = 738\)
To find n, we'll subtract 3 from both sides of the equation and then divide by 3:
\(3n = 738 - 3\)
\(3n = 735\)
\(n = 245\)
Therefore, the first of the three consecutive terms is 245.
Integrate both sides of the differential equation you found for dp to obtain an equation for p. Your equation should then include a constant that depends on initial conditions. Determine the value of this constant by assuming that the pressure at some reference height y0 is p0. Express your answer in terms of quantities given in the problem introduction along with y0 and p0.
Answer:
Step-by-step explanation:
FIND THE SOLUTION BELOW
38:27
The cost table shows the average cost, a(x), of producing x
number of earbuds.
When verifying that a function represented in another table
is the inverse of the given cost function, which ordered pair
can be expected?
x
a(x)
20 25
52 67.5
30
84
(20, 20)
(52, 20)
(20,52)
(52, 52)
What’s the answer
Answer:
(52,20)
Step-by-step explanation:
Answer: B
(52, 20)
Step-by-step explanation:
1. In a study on the likability of comedians, 10 participants observed one of two comedians (one who was humorous and one who was not humorous), and rated how likeable these comedians were on a 9-point scale from 1 (not likeable at all) to 9 (very likeable). The ratings are the data below. Test to see if the humorous comedian was liked more or less than the nonhumorous comedian, using alpha = .05 and four steps. Also calculate and interpret effect size and explained variance if appropriate.]
Answer:
a. 84 < n + (n + 2) + (n + 4) < 96
b. 26 < n < 30
step-by-step explanation:
using 'n' to represent the smallest even number, the next even number would be 'n + 2' and the next even number would be 'n + 4'. so, the expression to represent three consecutive even numbers is: n + (n + 2) + (n + 4).
since the sum of the these numbers needs to be between 84 and 96, we can set up the following inequality:
84 < n + (n + 2) + (n + 4) < 96
in order to solve for 'n', we must first combine like terms:
84 < 3n + 6 < 96
subtract 6 from all sides: 84 - 6 < 3n + 6 - 6 < 96 - 6 or 78 < 3n < 90
divide 3 by all sides: 78/3 < 3n/3 < 90/3 or 26 < n < 30.
What is the equation of the circle with center (0, 0) that passes through the point (-3, -5)
A) x2+y2=34
B) x2+y2=64
C) x2+y2=16
D) x2+y2=31
Answer:
A
Step-by-step explanation:
(x - h)² + (y - k)² = r²
x² + y² = r²
(-3)² + (-5)² = r²
r² = 34
x² + y² = 34
(b) 3m - 2n=19
5m + 7n=11
3m-2n=19
5m+7n=11
21m-14n=133
10m+14n=22
Now add equations
31m=155
m=5
Now let's find n
3×5-2n=19
-2n=4
n=-2
Answer: (5; -2)
The question is about solving a system of two linear equations with two variables, m and n, using substitution method. First, solve one of the equations for one variable and substitute this into the other equation. Solve the resulting equation to find the value of one variable and substitute this value into the first equation to find the value of the second variable.
Explanation:The question represents a system of linear equations. Such system contains two equations with two variables, namely m and n. To solve such a system, we can use various methods, such as substitution, elimination, or matrix methods. Let's use the substitution method in this case.
From the first equation, isolate variable m: m = (19 + 2n) / 3. Substitute m into the second equation: 5 * ((19 + 2n) / 3) + 7n = 11. Solve the second equation, you will find the value of n. Substitute the value of n into the first equation to find the value of m. Learn more about System of Linear Equations here:
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Tim has to mow his lawn in under two hours. If "t" represents the time it takes to mow the lawn, how can you express this as an inequality? At > 2 incorrect answer Bt < 2 incorrect answer C2 ≠ t incorrect answer Dt = 2
Answer:
B. t<2 hours
Step-by-step explanation:
If Tim has to mow his lawn in under two hours.
It means:
Tim cannot spend more than two hours mowing the lawn, therefore t>2 is not correct.2[tex]\neq[/tex]t means that Tim can spend less or more than 2 hours which is not what is required.Tim cannot spend exactly two hours mowing the lawn, therefore t=2 is not correct.Tim must finish mowing the lawn before two hours, therefore t<2 is the correct option.
To express that Tim must mow his lawn in under two hours, the correct inequality is t < 2. This indicates that the time, t, must be less than two hours to complete the task. Option B.
To express the condition that Tim has to mow his lawn in under two hours as an inequality, we represent the time it takes to mow the lawn with the variable t. The inequality that represents the situation is t < 2, meaning the time must be less than two hours. This is conveyed using the less than symbol (<).
In the context of other example inequalities, such as t=0, which represents a starting time, and t=t+1, which indicates an increment of time, these are used to express discrete points or changes in time. However, to represent a range of time under a specific amount, we use an inequality like t < 2 to denote that the time taken should not exceed two hours, option B.
Complete the sentence below. The standard deviation of the sampling distribution of x overbar, denoted sigma Subscript x overbar, is called the _____ _____ of the _____. The standard deviation of the sampling distribution of x overbar, denoted sigma Subscript x overbar, is called the ▼ standard population sample ▼ mean error deviation distribution variance of the ▼ mean. sample. error. distribution.
Answer:
The standard deviation of the sampling distribution of x overbar, denoted sigma subscript x overbar, is called the Standard Error of the Mean.
Step-by-step explanation:
Standard deviation of the sampling distribution, or sigma Subscript x overbar, is also known as the standard error of the mean. It represents how much the sample means deviate from the population mean. The standard error can be calculated by dividing the population standard deviation by the square root of the sample size.
Explanation:The standard deviation of the sampling distribution, represented by the symbol sigma Subscript x overbar is also known as the standard error of the mean. This term refers to the standard deviation of the population of all possible sample means from samples of a specific size.
The basic formula to calculate the standard deviation is Σ(x – μ)2 / N for the population and Σ(x – x)² / (n-1) for the sample. Greek symbol µ represents the population mean while 'x' is the sample mean.
The standard error can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). Thus, lesser the standard error, closer are the sample means to the population mean and vice versa. This is a very important concept in statistics as it allows one to estimate an unknown population parameter using sample data.
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Which unit rate is the lowest price per ounce? 5 ounces for $1.49 or 12 ounces for $3.59.
Answer:
5 ounce for $1.49 is you're answer.
Step-by-step explanation:
1.49/6 = 0.248 per oz
3.59/13 = 0.276 per oz
NEED HELP ASAP PLZ
which of the following are rational numbers select three that apply
Square root 3
Square root 9
Square root 5
Square root 4
Square root 8
Square root 1
Find the probability of rolling factors of 8
The probability of rolling a factor of 8 with a six-sided die is 0.5 or 50%, as there are 3 favorable outcomes (1, 2, 4) out of 6 possible outcomes when rolling the die.
Explanation:To find the probability of rolling factors of 8 with a fair, six-sided die, we first need to identify the factors of 8, which are 1, 2, 4, and 8. Of these, only 1, 2, and 4 are possible outcomes on a six-sided die. There are six possible outcomes when rolling a die (1, 2, 3, 4, 5, 6), so the probability of rolling a factor of 8 is the number of favorable outcomes (where the result is a factor of 8) divided by the total number of possible outcomes.
The favorable outcomes for this probability event are {1, 2, 4}, hence there are 3 favorable outcomes. Thus, the probability of rolling a factor of 8 is:
P(rolling a factor of 8) = Number of favorable outcomes / Total number of possible outcomes
P(rolling a factor of 8) = 3 / 6
P(rolling a factor of 8) = 0.5
Therefore, the probability of rolling a factor of 8 is 0.5 or 50%.
A company that produces laundry detergent is interested in the level of consumer awareness concerning the unique properties of their product. Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. The marketing manager feels that decreases in the TV advertising budget over the years has caused a decrease in sales. She decides to conduct a survey to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV. What is the value of the test statistic for the test described above and what is the type of alternative hypothesis?
Answer:
The value of test statistic is -2.736.
The type of alternate hypothesis is Left- tailed.
Step-by-step explanation:
We are given that Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV.
We have to test the hypothesis to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80.
Let p = population proportion of people who purchased the detergent because they had seen it advertised on TV.
SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 0.80 {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is greater than or equal to 0.80}
Alternate Hypothesis, [tex]H_a[/tex] : p < 0.80 {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80}
The test statistics that will be used here is One-sample z-proportion test;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = proportion of people who bought detergent because they saw it advertised on TV in a sample of 400 customers = [tex]\frac{296}{400}[/tex] = 0.74
n = sample of customers = 400
SO, test statistics = [tex]\frac{0.74-0.80}{\sqrt{\frac{0.74(1-0.74)}{400} } }[/tex]
= -2.736
Therefore, the value of the test statistic for the test described above is -2.736.
And the type of alternative hypothesis is left-tailed because we have to determine whether the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80.
Final answer:
To test if the population proportion is less than 0.80, a hypothesis test can be conducted using the sample data. The test statistic can be calculated using the formula (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size). Using the given information, the test statistic is approximately -5.00.
Explanation:
To test whether there is sufficient evidence to conclude that the population proportion of consumers who purchased the detergent because of TV advertisements is less than 0.80, we can conduct a hypothesis test using the sample data.
Null Hypothesis:
The proportion of consumers who bought the detergent because of TV advertisements is 0.80 or higher.
Alternative Hypothesis:
The proportion of consumers who bought the detergent because of TV advertisements is less than 0.80.
We can calculate the test statistic, which is also known as the z-score, using the formula:
test statistic = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)
Using the given information, the sample proportion is 296/400 = 0.74. The hypothesized proportion is 0.80, and the sample size is 400.
Plugging these values into the formula, we get:
test statistic = (0.74 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 400)
Calculating this expression, we find that the test statistic is approximately -5.00.
Several years ago, Dirk bought some gold at a price of $710 per ounce. When he went to sell it, the gold was worth 60% more than it was when he purchased it. What was the new value of the gold?
Answer:
$1,136 per ounce.
Step-by-step explanation:
To find the new value of gold, you have to find what 60% of 710 is. You do this by converting 60% into a decimal and multiplying it by 710. This results in 0.6*710. 60% of 710 is 426. 426 + the original price of 710 is equal to 1,136.
You can also solve this problem in a condensed manner by multiplying 710 by 1.6: the 1.0 stands for the original price (710) so you don't have to add it later. The 0.6 stands for the 60% more. Multiplying 710 by 1.6 gets you 1,136, which is the new value of gold/ounce.
What is the ratio of our solar system's radius to the Milky Way's radius given that the distance from Pluto to the sun is 5.9 * 10^12 meters; and the Milky Way's disk radius is 3.9 * 10^20 meters. Round the coefficient to the nearest tenth.
Answer:
Just divide the sun-pluto distance by the milky way radius and you get the following ratio:
6.6 x 10^7 : 1
How can models and equation help me subtract like fractions?
Answer:
You don't need "models and equations"; if the denominator is the
same, just subtract the numerators.
Step-by-step explanation:
Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured. A different random sample of 1,100 drivers found 96.9% compliance.
(2 Points) State an appropriate null and alternative hypothesis for testing whether or not there is any statistical difference (i.e., a two-sided test) in these two proportions measured initially and then one year later. Conduct the test of hypothesis using a significance level of α= 0.05. Be sure to check the assumptions and conditions for your test. State the P-value of your test and also state your conclusion. (Feel free to use R in showing your work - and show your commands and output if using R.)
(2 points) Develop a 95% confidence interval for the true difference in proportions between the first survey and the second survey and explain what this confidence interval means in context of this problem. (Feel free to use R in showing your work - and show your commands and output if using R.
Answer:
Step-by-step explanation:
* The Null hypothesis was rejected.
* The confidence interval for the true difference in proportions between the first and second survey are:
0.008238357 and 0.003176164 respectively in 95% situations.
Please kindly go through the attached files for a step by step explanation of how these answer are gotten.
What the value 0 in degrees
Answer:
45 degrees
Step-by-step explanation:
A new concert venue just opened in downtown Atlanta and they are in the process of deciding how many tickets they can sell for each show. The venue has three levels, two general admission levels that only have standing room, and one level with 180 seats. The first level of standing room is a square with one side measuring 75’. The second level, also standing room, is a rectangle measuring 130’ by 60’ ft. The third level has 180 seats. The venue thinks each person will occupy 2.25 square feet.
(A) How many tickets should they sell?
Answer:
[tex]6147\:Tickets[/tex]
Step-by-step explanation:
Area of the first level [tex]=75 X 75=5625 \:ft^2[/tex]
Area of the second level [tex]=130 X 60=7800 \:ft^2[/tex]
Total Area of Standing Room [tex]=5625+7800=13425 \:ft^2[/tex]
Since each person will occupy 2.25 square feet.
Number of Persons that will occupy the standing room
[tex]= 13425 \div 2.25\\=5966.7 \approx 5767\:persons[/tex]
Therefore the number of Tickets that should be sold
=Number of seats + Number for standing Room
=180+5967
[tex]\approx 6147\:tickets[/tex]
Therefore, the concert venue should sell 6,147 tickets.
By calculating the total square footage available in the venue, and then dividing by the space each person occupies, it's determined that the venue can sell roughly 6046 tickets per show.
Explanation:The main task is to calculate the total available space, in square feet, in the concert venue. For the standing room areas, we first calculate the total square footage of each level by multiplying the dimensions of each space. For the first level, the area of a square is calculated by squaring the side length, so 75' x 75' = 5625 sq. ft. For the second level, the area of a rectangle is calculated by multiplying the length by the width, so 130' x 60' = 7800 sq. ft. The seated area already specifies the number of people it can accommodate, so no calculation for square footage is needed. Altogether, the venue has 5625 + 7800 + 180 = 13605 sq ft. available.
The next step is to divide the total square footage by the space taken up by each person to find out how many people can be accommodated. We divide 13605 by 2.25, obtaining 6046.67, but since we can't sell a fraction of a ticket, we should round down to the nearest whole number. Therefore, the venue can sell roughly 6046 tickets per show.
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The length of life (in days) of an alkaline battery has an exponential distribution with an average life of 340 days. (Round your answers to three decimal places.) (a) What is the probability that an alkaline battery will fail before 185 days? (b) What is the probability that an alkaline battery will last beyond 2 years? (Use the fact that there are 365 days in one year.)
The probability that an alkaline battery will fail before 185 days is approximately 0.457, or 45.7%. The probability that an alkaline battery will last beyond 2 years is approximately 0.228, or 22.8%.
Explanation:To answer part (a), we need to find the probability that an alkaline battery will fail before 185 days. Since the length of life of an alkaline battery follows an exponential distribution with an average life of 340 days, we can use the formula for the exponential distribution to calculate the probability. The formula is:
P(X < t) = 1 - e^(-t/μ)
Where X is the random variable representing the length of life of the battery, t is the time (in days) we are interested in, and μ is the average life of the battery. Plugging in the values, we have:
P(X < 185) = 1 - e^(-185/340)
Solving this equation gives us a probability of approximately 0.457, or 45.7%.
For part (b), we want to find the probability that an alkaline battery will last beyond 2 years. Since there are 365 days in a year, 2 years is equal to 730 days. Using the same formula as before, we have:
P(X > 730) = 1 - P(X < 730) = 1 - (1 - e^(-730/340))
Solving this equation gives us a probability of approximately 0.228, or 22.8%.
At a candy store, 3 giant lollipops sell for $7.59 and 2 small packets of bubblegum cost $4.82. Which is a better buy?
I am not understanding this question.
Answer:
boardgamegeek.com/boardgame/245655/kings-dilemma
Step-by-step explanation:
A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the cost to make the can if the metal for the sides will cost $1.25 per 2 cm and the metal for the bottom will cost $2.00 per 2 cm ?
Answer:
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
Step-by-step explanation:
Given that, the volume of cylindrical can with out top is 25 cm³.
Consider the height of the can be h and radius be r.
The volume of the can is V= [tex]\pi r^2h[/tex]
According to the problem,
[tex]\pi r^2 h=25[/tex]
[tex]\Rightarrow h=\frac{25}{\pi r^2}[/tex]
The surface area of the base of the can is = [tex]\pi r^2[/tex]
The metal for the bottom will cost $2.00 per cm²
The metal cost for the base is =$(2.00× [tex]\pi r^2[/tex])
The lateral surface area of the can is = [tex]2\pi rh[/tex]
The metal for the side will cost $1.25 per cm²
The metal cost for the base is =$(1.25× [tex]2\pi rh[/tex])
[tex]=\$2.5 \pi r h[/tex]
Total cost of metal is C= 2.00 [tex]\pi r^2[/tex]+[tex]2.5 \pi r h[/tex]
Putting [tex]h=\frac{25}{\pi r^2}[/tex]
[tex]\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}[/tex]
[tex]\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}[/tex]
Differentiating with respect to r
[tex]C'=4\pi r- \frac{62.5}{ r^2}[/tex]
Again differentiating with respect to r
[tex]C''=4\pi + \frac{125}{ r^3}[/tex]
To find the minimize cost, we set C'=0
[tex]4\pi r- \frac{62.5}{ r^2}=0[/tex]
[tex]\Rightarrow 4\pi r=\frac{62.5}{ r^2}[/tex]
[tex]\Rightarrow r^3=\frac{62.5}{ 4\pi}[/tex]
⇒r=1.71
Now,
[tex]\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0[/tex]
When r=1.71 cm, the metal cost will be minimum.
Therefore,
[tex]h=\frac{25}{\pi\times 1.71^2}[/tex]
⇒h=2.72 cm
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
The radius should be approximately 1.7 cm, and the height should be approximately 2.77 cm.
We are to find the dimensions of a cylindrical can without a top that will minimize the cost while containing 25 cubic centimeters (cm³) of liquid.
The volume of a cylinder is given by the formula:
V = πr²h
where r is the radius and h is the height.
Given V = 25 cm³, we can express the height h in terms of the radius r:
h = V / (πr²) = 25 / (πr²)
The cost involves the lateral surface area (sides) and the bottom area:
Lateral surface area: As = 2πrh
Bottom area: Ab = πr²
Cost of the sides: $1.25 per square cm (let's denote the lateral cost by Cs)
Cs = 1.25 * 2πrh = 2.5πrh
Cost of the bottom: $2.00 per square cm (let's denote the bottom cost by Cb)
Cb = 2.00 * πr² = 2πr²
Total cost C is given by:
C = Cs + Cb = 2.5πrh + 2πr²
Substituting h = 25 / (πr²) into the total cost formula,
C = 2.5πr(25 / πr²) + 2πr² = 62.5 / r + 2πr²
To minimize the cost, we take the derivative of C with respect to r and set it to zero:
dC/dr = -62.5 / r² + 4πr = 0
Simplifying, we get:
4πr³ = 62.5
r³ = 62.5 / 4π = 4.978
r = ∛(4.978) ≈ 1.7 cm
Now, calculate the height h:
h = 25 / (π * 1.7²) ≈ 2.77 cm
Thus, the dimensions of the can that minimize the cost are approximately: radius = 1.7 cm and height = 2.77 cm.
If tan0= 3/4, find csc0
Answer: 5/3
Step-by-step explanation:
This is a trigonometry ratio. Tangent of a right angle triangle
Tan0° = opposite
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adjacent.
Now from the question
Tan0° = 3/4 meaning that the opposite side is 3 while the adjacent side is 4. Going by the triple coordinate, when two of the sides of a right angle triangle are, 3 and 4, the third side should be 5, in other words you could as well use the Pythagoras theorem to find the other side which I believed you should be familiar with. Since the third side is known, the cosec could be calculated.
Cosec of an angle =
1/sine. From the question now,
Sine0° = opposite side
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Hypothesis
= 3/5
Therefore
Cosec0° = 1/3/5
= 1
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3/5
= 5/3