The volume of the solid obtained by rotating the region bounded by the given curves about the X-axis is 340978 vu.
Given curve is,
y = [tex]x^{3}[/tex] , y = 8, x = 0 about x = 7
we know the formula for cylindrical shell is
V = πR²h
where R² = f(x)₂-f(x)₁ ,
h = dx
here f(x)₂ = 8 and f(x)₁ = x³
⇒ V = π(8 - x³)²h
V = π(64 - 16x³+x⁶)dx
integrating on both sides,
[tex]\int dV[/tex] =π [tex]\int ({64 - 16 x^{2} + x^{6} }) \, dx[/tex]
= [tex]64 \int dx - 16 \int {x^{3} } \, dx + \int\ {x^{6} } \, dx[/tex]
V = π(64x - 4x⁴+[tex]\frac{x^{7} }{7}[/tex])
V = π(64 × 7 - 4(7)⁴ + [tex]\frac{7^{7} }{7}[/tex])
= π(448 - 9604 + 117649 )
= [tex]\frac{22}{7}[/tex](108493)
V = 340978 vu
Therefore volume of the cylindrical shells to the region y = x³, y = 8, x = 0 about x = 7 is 340978 vu.
Cylindrical shells are essential structural elements in offshore structures, submarines, and airspace crafts. They are often subjected to combined compressive stress and external pressure, and therefore must be designed to meet strength requirements.
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Julia get on the bus at 8:17am. She rides 22 minutes to downtown. When she arrives, she walks 3 minutes to the pet store and then spends 26 minutes in there. Julia leaves and Walk 2 minutes to the dry cleaner. She spends 8 minutes at the dry cleaner picking up her clothes. After the dry cleaner, she waits for bus for 6 minutes. On the bus, she rides for 12 minutes before getting off in another neighborhood. Julia walks from the bus stop for 3 minutes to the café where she spends 3 hours on the line, eating, and doing work on her laptop. She walk 3 minutes back to the bus stop where Julia waits 13 minutes for the bus. She ride the bus for 34 minutes back to her original bus stop, and then walks for 15 minutes to her apartment.
What time is it when she walks in her front door?
Answer:01:44 PM
Step-by-step explanation: Hope this helps!
Isosceles- i need help with this 2 problems
Answer:
Below
Step-by-step explanation:
See image below
T/F a calculus for computing filippov's differential inclusion with application to the variable structure control of robot manipulators
It is proved that T/F a calculus is used for computing filippov's differential inclusion with application to the variable structure control of robot manipulators.
In this we also get to know more about the calculus concepts and it also helps in paper to develops a calculus for computing Filippov's differential inclusion which simplifies the analysis of dynamical systems described by differential equations with discontinuous right-hand-side. In particular, when a slightly generalized Lyapunov theory is used, the rigorous stability analysis of variable structure systems is routine. As an example, a variable structure control law for rigid-link robot manipulators is described and its stability is proved.
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A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Al steps onto the start of the walkway and stands. Bob steps onto the start of the walkway two seconds later and strolls forward along the walkway at a constant rate of 4 feet per second. Two seconds after that, Cy reaches the start of the walkway and walks briskly forward beside the walkway at a constant rate of 8 feet per second. At a certain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle person.
The distance between the start of the walkway and the middle person is 52 feet.
It is given that a 100 foot long moving walkway moves at a constant rate 6 feet per second.
AI steps into the start of the walkway and stands this means speed of AI is 6 feet per second.
Bob steps onto the start of he walkway two second later and stolls forward along walkway 4 feet per second that means 10 feet [per seconds.
And CY reaches the starts of the walkway and walks briskly forward beside the walkway at a rate of 8 feet per second.
At the time s we gave that,
[tex]\frac{8(s-4)+10(s-2)}{2}[/tex] = 6s
[tex]\frac{8s -32 + 10s - 20}{2}[/tex] = 6s
18s - 52 = 12s
6s = 52
s = [tex]\frac{26}{3}[/tex]
At the time AI has travels,
6* [tex]\frac{26}{3}[/tex] = 52 feet.
Therefore distance between the start of the walkway and the middle person is 52 feet.
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There are 200 seats on a train. Forty-two percent of the seats are taken. About how many seats are empty? Show and explain your work.
Answer:
116
Step-by-step explanation:
42/100 (that's the percent) = 84/200
200-84=116
Sandra deposits $3000 at the beginning of each semi annual period for 12 years at 10% interest compounded semi annually determine the amount she will have in the account after 12 years 
The account balance in her account will be $9675.30 after 12 years.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
The formula of semi annual compound interest is
A = P [ 1 + r/n]^{nt}
P = principal
n = number of period
t = time
r = Rate of interest.
Given that Sandra open a bank account with $3000.
The semi annually compound interest is 10%.
She deposits it for 12 years.
Here P = 3000, n = 2, t = 12, r = 10% = 0.1
A = 3000 [ 1 + 0.1/2]^{24}
A = 9675.30
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Which figure has two sets of parallel sides?
Answer: Parallelogram
Step-by-step explanation: [Parallelogram definition]: A parallelogram is a quadrilateral with 2 pairs of parallel sides. In these figures, sides of the same color are parallel to each other. A shape with four sides of equal length.
To see a shape that is a parallelogram, look at the attachment down below:
the following results are from independent samples taken from two populations. sample 1 sample 2 n1
The t-statistic for these two sample is 3.80 with 73 df
T-value is a ratio of the difference between the mean of two samples sets an the variation exist within the sample sets .
The numerator value is difference of mean of two samples.
According to the question,
We have two different sample
Sample 1
n1 = 35 (sample size)
x1 = 13.6 (sample mean)
s1 = 5.8 (standard deviation)
Sample 2
n2 = 40
x2 = 10.1
s2 = 8.5
To calculate the t-value of difference of sample means
[tex]t = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{\frac{s_1^2}{n_1} - \frac{s_2^2}{n_2}}}[/tex]
Substituting all the values
=> [tex]t = \frac{13.6-10.1}{\sqrt{\frac{5.8^2}{35} - \frac{8.5^2}{40}}}[/tex]
Solving ,
=> t = 3.5 / 0.9192
=> t = 3.807
With degree of freedom = n1 + n2 - 2
=> df =73
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Why is it important to know what qualified ministerial service are
It is important to know what qualified ministerial service are because they are activities that are considered to be tax-exempt under Internal Revenue Service (IRS) rules. These activities are typically related to religious or spiritual work, and may include preaching, teaching, and leading worship services. Understanding what qualifies as ministerial service can help individuals and organizations ensure that they are in compliance with tax laws and can claim the appropriate tax exemptions. It can also help individuals understand their tax liability and plan their finances accordingly.
the zerodivisionerror exception is raised when the program attempts to perform the calculation x/y if y=0. True or False?
It's True because zero cannot divided by any number it is undefined.
In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0, where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by 0, gives a (assuming a ≠ 0); thus, division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst
It's True because zero cannot divided by any number it is undefined.
let us consider
x = 3
and y =0
x/y = 3/0 = undefined
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Question 4
According to a survey of 1,362 adult college students, the mean number of alcoholic beverages consumed
per week is 15, with a standard deviation of 3 beverages. What test statistic is calcuated for this scenario?
The test statistic calculated for this scenario is the test of the significance of the mean.
What is mean?
Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
For example, if there are 3 students getting numbers 10, 20, and 30 in math then their mean is 10 + 20 + 30 / 3 = 60 / 3 = 20.
Given:
According to a survey of 1,362 adult college students, n = 1362,
The mean number of alcoholic beverages consumed, μ = 15,
The standard deviation, σ = 3,
As you can see here the sample is greater than 30 i.e. n > 30 and the value of standard deviation is also present then,
The static test, z can be given as shown below,
z = (X - μ) / σ / √n
Here, z is the static test and X is the sample mean.
Thus, the test of the significance of the mean can be calculated for this scenario.
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TRUE/FALSE american television programs that cross cultural and linguistic frontiers are successful because they appeal to basic human values.
Answer: True
Step-by-step explanation:
They appeal to how humans are empathetic towards others who may not speak their language. Also, they are more inclusive and may talk about things considered "taboo".
Hope this helps! :)
Answer:
False
Step-by-step explanation:
Kate Sanders, a researcher in the department of biology at IPFW University, studied the effect of agriculture contaminants on the stream fish population in Northeastern Indiana (April 2012). Specially designed traps collected samples of fish at each of four stream locations. A research question was: did the differences in agricultural contaminants found at the four locations alter the proportion of the fish population by gender? Observed frequencies were as follows.
Excel file: data12-05.xls
assb12h_ch12_12.5.gif
a. Focusing on the proportion of male fish at each location, test the hypothesis that the population proportions are equal for all four locations. Use a .05 level of significance.
1. assb12h_ch12_ex05a1.gif
2. assb12h_ch12_ex05a2.gif
3. assb12h_ch12_ex05a3.gif
Choose correct answer from above choice
- Select your answer -123Item 1
Ha: - Select your answer -All population proportions are equalNot all population proportions are equalItem 2
The p-value is - Select your answer -less than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 3
What is your conclusion?
- Select your answer -The population proportion of male fish are equal in all four locations.The population proportion of female equal in all four locations.The population proportion of male not equal in all four locations.The population proportion of female not equal in all four locations.Item 4
b. Does it appear that differences in agricultural contaminants found at the four locations altered the fish population by gender?
- Select your answer -YesNoItem 5
From the following obeservation done by Kate, the hypothesis that the population proportions is equal for all four locations is not true. Also, the population of male fish are not equal in all four locations and the p-value is greater than 0.10
What is a p- value or chi square test?A chi square ( χ2) test is performed in order to find a co relation between two unrelated variables. The main objective of the test is to prove whether the relationship holds true or is just a product of mere chance. For example, if we are conducting a survey of two different paramters, first being the population of people who are married and the other about their educational qualififcation, we will get two distinct table of values without any significant corelation. But now if we wnt to establish a relationship, lets say that married people have less educational qualifications, we need to prove our statement by performing a chi square test. The final value can either be a null hypothesis which states that their is no convinving relationship betwwen the two paramters or can be a alternate hypothesis with significant corelation.
How de we tackle this specific problem with the test?For this problem lets focus on the male fish population alone and perform the test:
Population (Observed)
A B C D TOT
Male fish 49 44 49 39 181
Female fish 41 46 36 44 167
90 90 85 83 348
Population(Expected)
Male fish 46.81 46.81 44.20 43.16
Female fish 43.18 43.18 40.79 39.83
χ2 = ∑[tex]\frac{(Obsereved-Expected)^2}{Expected}[/tex];
=[tex]\frac{4.79}{46.81} +\frac{7.89}{46.81} +\frac{23.04}{44.20} +\frac{17.30}{43.16}[/tex]
= 0.10+0.16+0.52+0.40 = 1.18
Now to calculate degree of freedom= (coulmn-1)(row-1)= 3×1= 3.
Looking at the reference table at 0.05 significance level, the value shows 7.815
Thus as our value of 1.18 is less than the given value, null hypothesis cannot be rejected.
Hence the population proportions are not equal at all four locations. Whether this conclusive difference in gender proportions is due to varied contaminants cant be answered with this single observation and further tests are needed to be performed to construct a well found connection.
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Which of the following best describes a function?[A] A special type of relation that pairs each domain value with exactly one range value. [B] A special type of relation that pairs each range value with exactly one domain value.
Option A. A special type of relation that pairs each domain value with exactly one range value. This means that for each input value, there is only one corresponding output value.
Which of the following best describes a function?Option A. A special type of relation that pairs each domain value with exactly one range value.A function is a special type of relation that takes an input value (domain) and maps it to exactly one output value (range). This means that for each input value, there is only one corresponding output value.
This type of relation is often represented graphically, with the domain values on the x-axis and the range values on the y-axis. Functions are also commonly represented using equations, which allows for more precise calculations. In many cases, the output value of a function is determined by a mathematical operation that is performed on the input value. In this way, functions can be used to model real-world phenomena, such as population growth or the trajectory of a rocket.
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In addition to putting books on the shelves, Mandy wants to put CD's on the shelves as well. If each shelf is 28 inches long and each CD is 1 3/ inch thick, how many CD's can she place on a shelf?
There are 9 CD's can she place on a shelf.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Each shelf is 28 inches long and each CD is 1 3/ inch thick.
Now,
Since, Each shelf is 28 inches long and each CD is 1 3/ inch thick.
Hence, The number of CD's = 28 x 1/3
= 9.33
= 9
Thus, There are 9 CD's can she place on a shelf.
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TRUE/FALSE. A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants.
The given statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants." is true.
The term probability refers the occurrence of a random event.
Here we have given the statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants."
And we have to identify whether this one is true or not.
While looking into the given question, we have identified the value like the following,
level in factor A = 2
levels in factor B = 3
Number of participants = 5
Then the total number of participants is calculated as,
=> (3 + 2) x 5
Now, we have to expand the given equation, then we get,
=> 5 x 5
Then the total number of participants is 25.
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In an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books. (a) How many ways can you select and arrange 10 of the 17 books on the shelf? Notice that here we will allow the books to end up in any order. Explain. (b) How many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author? Explain. 6. How many triangles are there with vertices from the points shown below? Note, we are not allowing degenerate triangles - ones with all three vertices on the same line, but we do allow non-right triangles. Explain why your answer is correct. 14. We have seen that the formula for Pln,k) is Your task here is to explain why this is the right formula. (a) Suppose you have 12 chips, each a different color. How many different stacks of 5 chips can you make? Explain your answer and why it is the same as using the formula for P(12,5). (b) Using the scenario of the 12 chips again, what does 12! count? What does 7! count? Explain. (c) Explain why it makes sense to divide 12! by 7! when computing P(12,5) (in terms of the chips). (d) Does your explanation work for numbers other than 12 and 5? Explain the formula P(n,k) = using the variables n and k.
(a) In 70,572,902,400 ways can you select and arrange 10 of the 17 books on the shelf.
(b) In 19,448 ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author.
In the given question, in an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books.
Total number of books = 17
Number of books which self hold = 10
We have to find the following.
(a) We have to find how many ways can you select and arrange 10 of the 17 books on the shelf.
Number of ways to select the 10 books out of 17 books = [tex]^{17}C_{10}[/tex]
Now,
The number of ways of arranging the 10 books = [tex]10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]^{17}C_{10}\times10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]\frac{17!}{10!(17-10)!}\times10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]\frac{17!}{10!7!}\times10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]\frac{17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7!}{7!}[/tex]
Total number of ways of selecting and arranging 10 books out of 17 = 17×16×15×14×13×12×11×10×9×8
Total number of ways of selecting and arranging 10 books out of 17 = 70,572,902,400
Hence,
Total number of ways of selecting and arranging 10 books out of 17
(b) We have to find how many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author.
Number of ways to select the 10 books out of 17 books = [tex]^{17}C_{10}[/tex]
Number of ways of arranging the 10 books alphabetically = 1
Total number of ways of arranging 10 books out of 17 in the shelf = [tex]^{17}C_{10}[/tex]
Total number of ways of arranging 10 books out of 17 in the shelf = [tex]\frac{17\times16\times15\times14\times13\times12\times11\times10!}{10!\times7\times6\times5\times4\times3\times2\times1}[/tex]
Total number of ways of arranging 10 books out of 17 in the shelf = 19,448
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A basketball player has a constant probability of 0.4 of making any given shot, independent of previous shots. Let an be the ratio of shots made to shots attempted after n shots. The probability that a10 = 0.4 and an ≤ 0.4 for all n such that 1 ≤ n ≤ 9 is given to be p^aq^br/s^c where p,q,r and s are primes, and a, b, and c are positive integers. Find (p+q+r+s)(a+b+c)
The value of (p+q+r+s) / (a+b+c) is 3.66 if the basketball player has probability 0.4 to make a perfect shot.
We know that if probability is given for r distribution and if question is asking distribution for n terms, we need to use binomial probability distribution which is given by [tex]^nC_r[/tex][tex]p^r[/tex][tex]q^r[/tex] where p is defined as the success probability and q is called as failure probability.
We have success probability =0.4
Failure probability(q) = 1-p=1-0.4=0.6
From 9 terms, we need to choose single term having success probability =0.4 and failure probability=0.6
So, this can be given by =[tex]^9C_1[/tex] × (0.4)¹ ×(0.6)⁹⁻¹
which is equivalent to =9 × (0.4) × (0.6)⁸
On comparing with the given equation =([tex]p^a[/tex] × [tex]q^b[/tex]×[tex]r^d[/tex]) / [tex]s^c[/tex] ,we get
p=9,a=1,q=0.4,b=1,r=0.6,d=8,s=1,c=1.
So,value of p+q+r+s = 9+0.4+0.6+1=11
and value of a + b + c = 1+1+1=3
So, value of (p + q + r + s) / (a + b + c)= 11 / 3=3.66
Hence, required value is 3.66
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Determine if (x-1) is a factor of g(x)=-2x^4+4x^3-x+9
No, the expression ( x - 1 ) as required to be checked is not a factor of the given polynomial function g ( x ) = -2x⁴ + 4x³ - x + 9.
Factor of a polynomial functionIt follows from the task content that the expression ( x - 1 ) is required to be checked if it's a factor of the given polynomial function.
Since the given factor can be equated to 0 so that we have; x - 1 = 0; x = 1.
On this when g (1) is evaluated, the result must be zero in order to confirm ( x - 1 ) is a factor of g ( x ) = -2x⁴ + 4x³ - x + 9.
Hence; g ( 1 ) = -2 ( 1 )⁴ + 4 ( 1 )³ - 1 + 9.
g (1) = -2 + 4 - 1 + 9
g (1) = 10
Ultimately, since g (1) ≠ 0; the expression ( x - 1 ) is not a factor of the given expression; g ( x ) = -2x⁴ + 4x³ - x + 9.
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what is the answer to -25g greater than or equal to 150
Answer:
g ≤ - 6 or g ∈ (- ∞, - 6]---------------------------------------
Given inequality:
-25g greater than or equal to 150-25g ≥ 150Divide both sides by -25:
-25g / (-25) ≥ 150 / (-25)g ≤ - 6 Division by a negative number flips the inequality signHow to Multiple fractions with different denominators?
Please explain step by step on what I need to understand. And rules that I may need to follow
Answer:
multiplying numerator by denominator, as in number times number equals = A = answer
Step-by-step explanation:
A town park has two paths leading to the playground. One path is 2 miles from the road and the other path makes a right angle with the road. The two paths intersect at an angle of . What is the approximate distance from the playground to the road along the other path?
The picture shows an upside-down right-angle triangle. The angle of the top vertex is 50 degrees. The length of the hypotenuse is 2 mi and the swing stands on the downside of the triangle
A.
3.1 mi
B.
1.5 mi
C.
1.3 mi
D.
2.6 mi
The approximate distance from the playground to the road along the other path is 1.3 miles.
How to find the distance between the road and the playground?A town park has two paths leading to the playground. One path is 2 miles from the road and the other path makes a right angle with the road. The two paths intersect at an angle of 50 degrees.
The approximate distance from the playground to the road along the other path can be calculated as follows;
using trigonometric ratios,
cos 50° = adjacent / hypotenuse
let
x = distance from the playground to the road along the other path
Hence,
cos 50 = x / 2
cross multiply
x = 2 cos 50°
x = 2 × 0.64278760968
x = 1.28557521937
x = 1.3 miles.
Therefore,
distance form play ground to the road = 1.3 miles.
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To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term. group of answer choices true false
It is true that an interaction term can be used to properly examine the effect of a categorical independent variable in a multiple linear regression model.
How to examine the effect of a categorical independent?In a multiple linear regression model, an interaction term is a product of two or more independent variables. It allows the model to capture the effect of the interaction between the variables on the dependent variable.
For example, suppose you are using a multiple linear regression model to examine the relationship between income, education level, and job satisfaction. You might include an interaction term for education level and income, which would allow the model to capture the effect of the interaction between these two variables on job satisfaction.
Using an interaction term can be especially useful when you want to examine the effect of a categorical independent variable on the dependent variable since it allows you to control for the effects of other variables in the model.
Therefore, it is true
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state university uses thousands of fluorescent light bulbs each year. the brand of bulb it currently uses has a mean life of 1000 hours. a competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 1000 hours. the university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .05 significance level. suppose 64 bulbs were tested with the following results: conduct the test using
Therefore, the solution to the question is T = 2.5 is the test statistic and the manufacturer's claim is supported by the data at the.05 significance level, according to the test's p-value of 0.007 <0.05.
What is test statistics?In statistical hypothesis testing, a test statistic is a statistic that is employed. A hypothesis test is often defined in terms of a test statistic, which is a numerical summary of a data set that can be used to execute the test and reduces the data to one value.
Here,
The test's p-value was 0.007 0.05, indicating that the evidence at the.05 level of significance supports the manufacturer's claim.
1000 hours on average. See if there is more.
We examine the null hypothesis, that is, whether the mean is 1000 hours, by asking:
[tex]H_{0}[/tex]: u=1000
If the mean is greater than1000 hours, we test the alternative hypothesis, which is:
[tex]H_{A}[/tex] : u > 1000
Test statistics:
t= [tex]\frac{X-u}{\frac{S_{d} }{\sqrt{n} } }[/tex]
t= [tex]\frac{X-u}{\frac{S_{d} }{\sqrt{n} } }[/tex]
t=[tex]\frac{1025-1000}{\frac{310 }{\sqrt{1000} } }[/tex]
t=25/9.80
t≈2.5
The test statistic is t = 2.5
P-value for the test and judgment
The right-tailed test's p-value, which has t = 2.5 and 100 - 1 = 99 degrees of freedom, measures the likelihood that a sample mean will be higher than 1025 hours.
This p-value is 0.007 according to a t-distribution calculator.
The manufacturer's claim is supported by the data at the.05 significance level, according to the test's p-value of 0.007 <0.05.
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Value of x on 10x+12=2
Answer:
[tex]x = -1[/tex]
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Addition
Subtraction
~
First, subtract 12 from both sides of the equation:
[tex]10x + 12 = 2\\10x + 12 (-12) = 2 (-12)\\10x = 2 - 12\\10x = -10[/tex]
Next, divide 10 from both sides of the equation:
[tex]10x = -10\\\frac{(10x)}{10} = -\frac{(10)}{10}\\ x = -\frac{10}{10} = -1\\ x = -1[/tex]
[tex]\textbf {x = -1}[/tex] is your answer.
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40 POINTS PLS HELP!!
These items are all on sale with one-third off. What was the full price of each?
Sale price: Original full price:
£32.24 £_________
£86.08 £_________
£105.48 £_________
£230.62 £___________
The full price when the sales price is £32.24 is £96.72
The full price when the sales price is £86.08 is £258.24
The full price when the sales price is £105.48 is £316.44
The full price when the sales price is £230.62 is £691.86
What are the full prices?The sales price is one third of the full price of the items. Thus, in order to determine the full price, multiply the sales price by 3.
Full price = sales price x 3
Full price when the sales price is £32.24 = 3 x £32.24 = £96.72
Full price when the sales price is £86.08 = 3 x £86.08 = £258.24
Full price when the sales price is £105.48 = 3 x £105.48 = £316.44
Full price when the sales price is £230.62 = 3 x £230.62 = £691.86
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Eli wants to combine 0.5 gallons of a 10% acid solution with a 35% solution to make a 15% acetic acid solution. He needs to determine how many gallons of 35% solution are needed.
Eli decides to let v represent the volume of the 35% solution and makes a table to help solve the problem.
Help Eli by completing the table.
Drag each tile to the correct cell in the table.
The required volume of the 35% acetic acid solution that will combine with the 0.5 gallons of the 10% acetic acid solution to make a solution that is 15% acetic acid solution is 0.125 gallons, which indicates, using the dilution formula, that the correct options for the completed table are;
[tex]{}[/tex] Amount of Solution Acid Concentration Amount of Acid
10% Acid[tex]{}[/tex] 0.5 0.10 (0.10)·(0.5)
35% Acid [tex]{}[/tex] v 0.35 0.35·v
Mixture v + 0.5 [tex]{}[/tex] 0.15 0.15·(v + 0.5)
What is the dilution formula?The dilution formula indicates that the product of the concentration and volume of the initial solution is equivalent to the product of the concentration and volume of the intended solution to be made.
The volume of the 10% acetic acid solution in the mixture = 0.5 gallons
The volume of the 35% acetic acid solution = v
The concentration of the acetic acid solution Eli wants to make = 15%
The dilution formula for mixtures is; C₁·V₁ = C₂·V₂
Therefore; 0.1 × 0.5 + 0.35 × v = (v + 0.5) × 0.15
0.35 × v - (v + 0.5) × 0.15 = -0.1 × 0.5 = -0.05
0.2·v - 0.075 = -0.05
v = (0.075 - 0.05)/0.2 = 0.125
The volume of the 35% solution required, v = 0.125 gallons
The completed table is therefore;
[tex]{}[/tex] Amount of Solution Acid Concentration Amount of Acid
10% Acid [tex]{}[/tex] 0.5 0.10 (0.10)·(0.5)
35% Acid [tex]{}[/tex] v 0.35 0.35·v
Mixture v + 0.5 [tex]{}[/tex] 0.15 0.15·(v + 0.5)
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John, Sally and Jane form a partnership. They agree to distribute profits by paying Sally a $50,000 salary and distributing the balance using a 2:1:2 ratio respectively. Profits for the year are $70,000. John’s share of the profits is:
Multiple Choice
$4,000
$8,000
$14,000
$54,000
The required share of John in the profit is given as $8000. Option B is correct.
Given that,
John, Sally, and Jane form a partnership. They agree to distribute profits by paying Sally a $50,000 salary and distributing the balance using a 2:1:2 ratio respectively. Profits for the year are $70,000.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
here,
total profit = 70000
Sally is salary = 50000
remaining profit = 70000 - 50000 = $20000
Now,
total share as of the proportions is 2 + 1 + 2 = 5
Jhon proportion for the share of the profit = 2 / 5
Now,
John share = 2 / 5 [20000] = $8000
Thus, the required share of John in the profit is given as $8000. Option B is correct.
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prove: if a quadrilateral has consecutive angles that are supplementary, then it is a parallelogram.
A quadrilateral is a parallelogram if its adjacent angles are supplementary.
We are expected to demonstrate that a quadrilateral is a parallelogram if its adjacent angles are supplementary. Writing down what is given and needs to be supported will be our first step.
1) An ABCD quadrilateral is a given.
2) ∡A supplements ∡B, ∡B supplements ∡C, ∡C supplements ∡D and ∡D supplements ∡A.
To demonstrate: Parallelogram ABCD is a quadrilateral.
Consider AC and BD as evidence. The intersection of AC and BD is AB.
Two angles on the same side of the transversal AB are ∡A and ∡B.
A property states that two lines are parallel if a transversal cuts them and the interior angles on the same side of the transversal are additional.
Here, it is given that ∡A supplements ∡B.
⇒∡A+∡B=180∘
The lines AC and BD are therefore parallel to one another.
Now think about AB and CD. The intersection of AB and CD is AC.
Two angles on the same side of the transversal AB are ∡A and ∡D .
A property states that two lines are parallel if a transversal cuts them and the interior angles on the same side of the transversal are additional.
Here, it is given that ∡D supplements ∡A.
⇒∡A+∡D=180∘
The lines AB and CD are therefore parallel to one another.
Now, since both the pairs of opposite sides are parallel, ABCD is a parallelogram.
Hence proved.
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If f(a)=3a+5 and g(a) =a^2+4, find f(-2)-g(-2)
The value of find f(-2)-g(-2), if f(a) = 3a + 5 and g(a) = a² + 4 is -9.
What is function?In the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and co-domain are respectively referred to as the sets X and Y as a whole.
Given function:
f(a) = 3a + 5 and g(a) = a² + 4
Calculate the f(-2) - g(-2) by putting value -2 in both function
f(-2) = 3(-2) + 5 = -6 + 5
f(-2) = -1
g(-2) = (-2)² + 4
g(-2) = 4 + 4
g(-2) = 8
Hence, f(-2) - g(-2) = -1 - 8 = -9
Therefore, the value of find f(-2)-g(-2), if f(a) = 3a + 5 and g(a) = a² + 4 is -9.
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