Answer:
Equation: 2(357+30×5) = 580
x=4
Step-by-step explanation:
In one package, there is such a relationship:
357+30X5 = y
(Y is the price of a package)
The price of two parcels is 580:
then. 24=580
y= 290
x=4, so: equation: 2(35x+150) =580
Step-by-step explanation:
A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have cost Rs. 1 less. How many books did he buy?
A
8
B
16
Correct Answer
C
24
D
28
Medium
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Updated on : 2022-09-05
Solution

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Correct option is B)
Let the shopkeeper buy x number of books.
According to the given condition cost of x books =Rs80
Therefore cost of each book =x80
Again when he had brought 4 more books
Then total books in this case =x+4
So cost of each book in this case =x+480
According to Question,
x80−x+480=1
x(x+4)80(x+4)−80x=1
x2+20x−16x−320=0
(x−16)(x+20)=0
x=16orx=−20
Hence the shopkeeper brought 16 books
An assignment of probabilities to events in a sample space must obey which of the following? They must obey the addition rule for disjoint events. They must sum to 1 when adding over all events in the sample space. The probability of any event must be a number between 0 and 1, inclusive. All of the above
An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.
What is probability?Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.
The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.
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What is result of following operation(4623. 56)10+ (110011. 11)2whare (110011. 11(2 mean that 110011. 11as a number express in base 2
The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].
A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:
System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-
[tex](4623.56)_{10} , (110011.11)_{2}[/tex]
these are in decimal and binary system respectively.
now, we will express them in same system ( here we choose decimal system).
[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]
Now, addition is done below:-
4623.56+51.75= 4675.31.
hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]
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parabola a and parabola b both have the x-axis as the directrix. parabola a has its focus at (3,2) and parabola b has its focus at (5,4). select all true statements.
a. parabola A is wider than parabola B
b. parabola B is wider than parabola A
c. the parabolas have the same line of symmetry
d. the line of symmetry of parabola A is to the right of that of parabola B
e. the line of symmetry of parabola B is to the right of that of parabola A
In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.
The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.
Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.
Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.
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if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
Can someone help me with this please?
To solve the question asked, you can say: So, the other angle of the figure is 49 degree.
what are angles?In Euclidean geometry, an angle is a shape consisting of two rays, known as sides of the angle, that meet at a central point called the vertex of the angle. Two rays can be combined to form an angle in the plane in which they are placed. Angles also occur when two planes collide. These are called dihedral angles. An angle in planar geometry is a possible configuration of two rays or lines that share a common endpoint. The English word "angle" comes from the Latin word "angulus" which means "horn". A vertex is a point where two rays meet, also called a corner edge.
here the given angles are as -
107 + (180-156) + x = 180
as total angle sum of a triangle is 180
so,
x = 180 - 131
x = 49
So, the other angle of the figure is 49 degree.
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Pls read ss
PLS HELPP
The slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
What is slope?
Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.
1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,
=> slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]
2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,
=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]
3) The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,
=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]
4) The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,
=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]
5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,
=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]
Hence the slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
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Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)a. 81stb. 19thc. 76thd. 24the. 10 th
The percentiles for the standard normal distribution
a. 0.93
b. -0.88
c. 0.67
d. -0.65
e. -1.28
To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.
The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.
Step 1: Write down the given percentiles as a decimal and round to two decimal places.
For example, for the 81st percentile, 0.81 will be used.
Step 2: Use the standard normal distribution table to find the corresponding z-score.
Step 3: Round off the obtained answer to two decimal places.
a) 81st percentile:
The area to the left of the z-score is 0.81.
The corresponding z-score is 0.93.
Hence, the 81st percentile for the standard normal distribution is 0.93.
b) 19th percentile:
The area to the left of the z-score is 0.19.
The corresponding z-score is -0.88.
Hence, the 19th percentile for the standard normal distribution is -0.88.
c) 76th percentile:
The area to the left of the z-score is 0.76.
The corresponding z-score is 0.67.
Hence, the 76th percentile for the standard normal distribution is 0.67.
d) 24th percentile:
The area to the left of the z-score is 0.24.
The corresponding z-score is -0.65.
Hence, the 24th percentile for the standard normal distribution is -0.65.
e) 10th percentile:
The area to the left of the z-score is 0.10.
The corresponding z-score is -1.28.
Hence, the 10th percentile for the standard normal distribution is -1.28.
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The summaries of data from the balance sheet, income statement, and retained earnings statement for two corporations, Walco Corporation, and Gunther Enterprises, are presented below for 2017.
Determine the missing amounts. Assume all changes in stockholders equity are due to changes in retained earnings
Walco Corporation Gunther Enterprise
Beginning of year Total assets $100,000 $159,000
Total liabilities 73,000 $_____ (d)
Total stockholders' equity $_____ (a) 67,500
End of year Total assets $_____ (b) 190,000
Total liabilities 128,000 50,000
Total stockholders' equity 54,000 $_____ (e)
Changes during year in retained earnings Dividends $_____ (c) 4,900
Total revenues 219,000 $_____ (f)
Total expenses 167,000 79,000
The missing amounts for Walco Corporation and Gunther Enterprises assuming all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.
a) Total liabilities + Total stockholders' equity = Total assets
Total liabilities + $54,000 = $100,000
Total liabilities = $46,000
(b) Total assets = Total liabilities + Total stockholders' equity
Total assets = $128,000 + $54,000
Total assets = $182,000
(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $167,000 - $4,900
Changes during year in retained earnings = $47,100
The missing values for Gunther Enterprises:
(d) Total liabilities + Total stockholders' equity = Total assets
$67,500 + $(e) = $159,000
$(e) = $91,500
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $(f) - $79,000 - $4,900
Changes during year in retained earnings = $(f) - $83,900
Using the balance sheet equation, we can find the missing values:
(d) Total liabilities = Total assets - Total stockholders' equity
Total liabilities = $159,000 - $67,500
Total liabilities = $91,500
(e) Total stockholders' equity = Total assets - Total liabilities
Total stockholders' equity = $190,000 - $50,000
Total stockholders' equity = $140,000
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $79,000 - $4,900
Changes during year in retained earnings = $135,100
Therefore, the missing amounts are:
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
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Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.
Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
write the equation in standard form for the circle with center (5,0) passing through (5, 9/2)
The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0
Calculating the equation of the circleGiven that
Center = (5, 0)
Point on the circle = (5. 9/2)
The equation of a circle can be expressed as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
So, we have
(x - 5)² + (y - 0)² = r²
Calculating the radius, we have
(5 - 5)² + (9/2 - 0)² = r²
Evaluate
r = 9/2
So, we have
(x - 5)² + (y - 0)² = (9/2)²
Expand
x² - 10x + 25 + y² = 81/4
Multiply through by 4
4x² - 40x + 100 + 4y² = 81
So, we have
4x² + 4y² - 40x + 19 = 0
Hence, the equation is 4x² + 4y² - 40x + 19 = 0
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f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f.
The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x)) is 1
Calculating the inverse of g(x)Given that
f(x) = 3 - 2x
Rewrite as
g(x) = -x² + x + 1
Express as vertex form
g(x) = -(x - 0.5)² + 1.25
Express as equation and swap x & y
x = -(y - 0.5)² + 1.25
Make y the subject
y = 0.5 + √(1.25 - x)
So, the inverse is
g⁻¹(x) = 0.5 + √(1.25 - x)
Calculating the value of xHere, we have
f(g(x)) = g(f(x))
This means that
f(g(x)) = 3 - 2(-x² + x + 1)
g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1
Using a graphing tool, we have
f(g(x)) = g(f(x)) when x = 1
Hence, the value of x is 1
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Complete question
f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers
Find the inverse of G and the value for x for which f(g(x)) = g(f(x)).
c) assume that 25% of the defendants in the state are innocent. in a certain year 200 people put on trial. what is the expected value and variance of the number of cases in which juries got the right decision?
The expected value of cases in which juries got the right decision is 150, and the variance is 375.
1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.
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4. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?
Answer:
a=1/3
Step-by-step explanation:
First, expand the brackets by doing multiplication:
2+6a+3=3a+6
Then, move the unknown to the left and the numbers to the right:
3a=6-5
3a=1
a=1/3
The solution to the given equation is -1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 2+3(2a+1)=3(a+2)
2+6a+3=3a+2
6a+5=3a+2
6a-3a=2-5
3a=-3
a=-1
Therefore, the solution to the given equation is -1.
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A+9 as a verbal expression
Answer:
"9 more than A" is a verbal expression.
Operación de vectores
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Step-by-step explanation:
two people standing at different locations are looking at a tall building. person a angle of elevation to the building is 35 degrees. person b angle of elevation is 77 degrees. the building is 8 miles away from person b. how far away is person a from the building?
Therefore, Person A is approximately 95.17 miles away from the building.
To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.
Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.
Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.
First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:
height = 8tan(77) ≈ 61.23 miles.
Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:
x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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Seven bags of cement weighs 3kg 52g what Is the weight of the each?
Answer:
436g
Step-by-step explanation:
1kg=1000g
3kg=3000g
3000+52=3052
3052÷7=436
Enter the correct answer in the box.
Write this expression in simplest form.
Don’t include any spaces or multiplication symbols between coefficients or variables in your answer.
16h^(10/2) *remove the root sign
16h^5 *simplify the exponent
Answer: 16h^5
Step-by-step explanation: im correct
To compare the pain control offered by two different analgesics in pediatric patients, the authors selected the Wong-Baker FACES pain rating scale as the primary end point. Before beginning the clinical trial, the authors sought to validate this ordinal scale by showing a correlation with a previously validated visual analog scale. Which one of the following statistical test is most appropriate to assess whether a correlation exists between these two measurements?
A. Pearson correlation
B. Analysis of variance (ANOVA)
C. Spearman rank correlation
D. Regression analysis
The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.
What is correlation?Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.
Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".
The formula for Spearman's rank correlation coefficient:
Rs = 1 - {6Σd₂}/{n(n₂-1)}
Where, Σd₂ = the sum of the squared differences between ranks.
n = sample size
Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.
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a pastry chef accidentally inoculated a cream pie with six s. aureus cells. if s. aureus has a generation time of 60 minutes, how many cells would be in the cream pie after 7 hours?
After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.
How many cells would be in the cream pie after 7 hours?Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.
The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.
If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.
The number of generations (n) in seven hours is calculated as:
n = t/g
n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations
The number of cells in the cream pie after 7 hours is calculated as :
N = N₀ × 2ⁿ
N = 6 cells × 2⁷
N = 768 cells
Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.
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Your monthly take-home pay is $900. Your monthly credit card payments are about $135. What percent of your take-home pay is used for your credit card payments?
i came up with $765
Answer:15 percent
Step-by-step explanation:
In ΔJKL, the measure of ∠L=90°, JK = 7. 3 feet, and KL = 4. 7 feet. Find the measure of ∠J to the nearest tenth of a degree
The measure of ∠J in ΔJKL is approximately 57.5 degrees.
The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.
The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.
tan(∠J) = JK/KL
tan(∠J) = 7.3/4.7
∠J = arctan(7.3/4.7)
∠J = 57.5 degrees (rounded to the nearest tenth of a degree)
Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.
How to determine the true statement from the optionsBy comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.
Comparing the probabilities of the three players, we can see that:
Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.
Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.
Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.
Therefore, the statement that is true is: Player 2 has the of getting a hit in their at-bats.
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Mrs Smith walks a half a mile a day after work. She works five days a week. How many yards will she have walked for the week by Friday morning?
The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.
One week has seven days in total.
Mrs. Smith walks half a mile each day after work, she walks a total of
0.5 miles/ day × 7 days/ week = 3.5 miles/ week
Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.
Therefore,
0.5 miles/ day × 4 days = 2 miles
To convert miles to yards, we can use the fact that there are 1760 yards in one mile:
2 miles/week × 1760 yards/mile = 3520 yards/week
Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.
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Triangle lmn will be dilated with respect to the origin by a scale factor of 1/2
what are the new coordinates of L’M’N’
The triangle LMN, with vertices L(6, −8), M(4, −4), and N(−12, 2), dilated with respect to the origin by a scale factor of 1/2, results in triangle L'M'N', with vertices L'(3, -4), M'(2, -2), and N'(-6, 1)
To dilate a triangle with respect to the origin, we need to multiply the coordinates of each vertex by the scale factor. In this case, the scale factor is 1/2, so we multiply each coordinate by 1/2.
The coordinates of L' are obtained by multiplying the coordinates of L by 1/2:
L'((1/2)6, (1/2)(-8)) = (3, -4)
The coordinates of M' are obtained by multiplying the coordinates of M by 1/2:
M'((1/2)4, (1/2)(-4)) = (2, -2)
The coordinates of N' are obtained by multiplying the coordinates of N by scale factor 1/2:
N'((1/2)×(-12), (1/2)×2) = (-6, 1)
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The given question is incomplete, the complete question is:
Triangle LMN with vertices L(6, −8), M(4, −4), and N(−12, 2) is dilated with respect to origin by a scale factor of 2 to obtain triangle L′M′N′. What are the new coordinates of L′M′N′ ?
a rectangular swimming pool 50 ft long, 30 ft wide, and 8 ft deep is filled with water to a depth of 6 ft. use an integral to find the work required to pump all the water out over the top. (take as the density of water lb/ft. )
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
We have,
To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.
First, let's calculate the weight of the water in the pool.
The weight of an object is given by the formula:
Weight = mass x gravitational acceleration
Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.
The volume of the pool is given by the formula:
Volume = length x width x depth
Volume = 50 ft x 30 ft x 6 ft = 9000 ft³
Now, let's calculate the weight of the water:
Weight = density x volume x gravitational acceleration
Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb
To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.
The work required to pump the water out is given by the formula:
Work = weight x height
Work = 290,400 lb x 8 ft = 2,323,200 ft-lb
Therefore,
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
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50 POINTS
A bathroom heater uses 10.5 A of current when connected to a 120. V potential difference. How much power does this heater dissipate?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit
The power dissipated by the heater is 1260 watts (W).
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.
Given:
Current (I) = 10.5 A
Potential Difference (V) = 120 V
Unknown:
Power (P) = ?
The formula to calculate the power is:
P = VI
Substituting the given values:
P = 120 V × 10.5 A
P = 1260 W
It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:
P = 1260 W (rounded to three significant digits).
Therefore, the power dissipated by the heater is 1260 watts (W).
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Find the first 4 terms of the sequence represented by the expression 3n + 5
The first 4 terms of the sequence represented by the expression 3n + 5
is 8, 11, 14 and 17.
Sequence:
In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.
According to the Question:
Given, aₙ = (3n+5).
First four terms can be obtained by putting n=1,2,3,4
a 1=(3×1+5) = 8
a 2 =(3×2+5) = 11
a 3 =(3×3+5) = 14
a 4 =(3×4+5) = 17
First 4 terms in the sequence are 8, 11, 14, 17.
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cosθ(1+tanθ)=cosθ+sinθ
Answer:
Starting with the left side of the equation:
cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)
= cosθ + sinθ
Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.
Write the line equation of (5,-12) and (0,-2)
Answer:
To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:
slope = (change in y) / (change in x)
slope = (-2 - (-12)) / (0 - 5)
slope = 10 / (-5)
slope = -2
Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is one of the given points on the line.
Let's use the point (5,-12):
y - (-12) = -2(x - 5)
y + 12 = -2x + 10
y = -2x - 2
Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.