Answer:
start by using the formula for the area of a rectangle:
Area = length × width
We know that the area of the farm is given as square miles, so we can write:
lw =
Solving for w, we can divide both sides by l:
w =
Therefore, the width of the rectangular farm is miles.
To simplify the expression, we can multiply the numerator and denominator by 2:
w =
So the width can also be expressed as the fraction __.
The given pie-chart represents the division of sports played by students during summer camp.
If the total number of students took part in the summer camp was 300
, then how many students played cricket more than basketball?
17 students played cricket more than basketball.
What is a Pie Chart?A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.
Pie chart showing the preference of the students is given below.
Total number of students = 300
We know that total degree of the circle = 360°
Students who played cricket = 90°
Number of students who played cricket will be (90° / 360°)th of 300.
Number of students who played cricket = (90° / 360°) × 300
= 75
Students who played basketball = 70°
Number of students who played basketball = (70° / 360°) × 300
= 58.33 ≈ 58
Students played cricket - Students played basketball = 75 - 58 = 17
Hence there are 17 students more in cricket than that in basketball.
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Oliver worked 9 months out of the year. What percent of the year did he work?
Answer:
75%
Step-by-step explanation:
We know
A year has 12 months
Oliver worked 9 months out of the year
What percent of the year did he work?
We take
9 divided by 12, time 100 = 75%
So, he works 75% of the year.
3. Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value. You can find it if you know the number of trials and the probability of success for an individual trial. Use the formula μx = np to find the expected value.
The probability of having a 4 in a 30 roll is 5 times
What is the probability distribution
The expected value, μ, of rolling a 4 on a fair number cube (with faces numbered 1 to 6) can be found by using the formula μ = np, where n is the number of trials (30 in this case) and p is the probability of success for an individual trial (rolling a 4).
The probability of rolling a 4 on a fair number cube is 1/6. Therefore, the expected value of rolling a 4 30 times can be calculated as follows:
μ = 30 * (1/6) = 5
So, Mr. Jackson can expect to roll a 4 approximately 5 times in 30 rolls of his number cube.
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There is a harvest festival each year on the planet Bozone. During that time, most of the Bozone residents sit down to rejoice and eat roast snig. Past history shows that a reasonable price-demand equation is: p= 300 – 20x where x is the number of kilograms of snig sold, and p is the price per kilogram of snig in the local currency, the Bozat. a. To sell an additional kilogram of snig, how much does the price need to decrease? Price needs to decrease by ______Bozats. b. Solve the price-demand equation for æ in terms of p. x =
x = (300 - p) / 20
According to the equation, the quantity of kilos (x) of snig that will be sold is equal to the difference between 300 and p, divided by 20.
The price-demand connection for roast snig at the harvest festival on the planet Bozone can be represented by the equation p=300 - 20x. The formula specifies that 300 minus 20 times the number of kilogrammes (x) of snig sold is the price per kilogramme of snig (p) in the local currency (Bozats).
Using this equation, one can determine how much of the price must be reduced in order to sell 1 extra kilogramme of snig. The equation can be rewritten to solve for x in terms of p in order to accomplish this. This can be done by taking 300 off of both sides of the equation, multiplying both sides by 20, and then solving for x = (300 - p) / 20. This rearrangement has the effect of dividing the number of kilogrammes of snig that will be sold in terms of price per kilogramme by the difference between 300 and p. This equation can be used to calculate the price reduction required to sell an extra kilogramme of snig.
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Calculate the expectation value of and for a particle in the state n = 5 moving in a one dimensional box of length 2.50 × 10−10. Is =2. Explain
The expectation values are <x> = 1.25 x 10⁻¹⁰ , <x²> = 2.07 x 10⁻²⁰
What is average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
We need to find expectation value of <x> and < x²>
average value for <x> is given by a/2 where a = length of box
hence <x> = ( (2.5 x 10⁻¹⁰) /2) = 1.25 x 10⁻¹⁰
hence <x²> = (1.25 x 10⁻¹⁰)² = 1.56 x 10⁻²⁰
<x²> = ( a/2 x 3.14 x n)² x ( 4 x 3.14² x n² /3 -2)
hence <x²> = ( 2.5 x 10⁻¹⁰ / 2 x 3.14 x 5)² x ( 4 x 3.14² x 5² /3 -2)
<x²> = 2.07 x 10⁻²⁰
<x²> is not equal to <x>²
The expectation values are <x> = 1.25 x 10⁻¹⁰, <x²> = 2.07 x 10⁻²⁰
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Consider the exponential function E(t)=6⋅1.02^t where t is measured in seconds. Find the amount of time it takes for E to increase by 10%.
it takes ____ seconds (give answer in exact form)
The amount of time it takes for E to increase by 10%. it takes 4.81 seconds.
What is exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Given that,
Let the amount of time it takes for E to increase by 10% be x.
Thus, after (t + x) seconds, E is increased by 10%.
E(t + x) = E(t) + 10% of E(t)
= E(t) + 10/100 E(t)
= E(t) + 0.1 E(t)
E(t + x) / E(t) = 1.1
As,
[tex]E(t) = 6(1.02)^t\\\\E(t + x) = 6(1.02)^{t + x}\\\\\frac{E(t + x)}{E(t)} = \frac{6(1.02)^{t + x}}{6(1.02)^{t}}\\\\\frac{E(t + x)}{E(t)} = (1.02)^{t + x - t}\\\\(1.02)^x = 1.1[/tex]
Taking log on both sides:
x = log (1.1) / log (1.02)
x = 4.81 seconds.
Hence, the amount of time it takes for E to increase by 10%.
it takes 4.81 seconds.
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I don’t think 53/63 is in lowest terms haha so help is def needed
Answer:
53/63
Step-by-step explanation:
It is already in simplest form
Help please I dont understand thank uuuu
A. The velocities are given as follows:
Devron: 45 miles per hour.Avery: 60 miles per hour.B. The graph is given by the image presented at the end of the answer.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
From the table, Devron's rate is given as follows:
k = 180/4
k = 45 miles per hour.
Hence the equation is of:
y = 45x.
For Avery's equation of y = 60x, the rate is of 60 miles per hour.
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A square plastic tarp has sides that are 13 meters long. What is the tarp’s perimeter?
A newly hired lawyer receives a $15,000 signing bonus from a law firm and invests the money in a savings account at 4.75% interest. After 42 months, the lawyer checks the account balance. Part A: Calculate the interest earned, to the nearest dollar, if the interest is compounded quarterly. Show all work. (2 points) Part B: Calculate the interest earned, to the nearest dollar, if the interest is compounded continuously. Show all work. (2 points) Part C: Using the values from Part A and Part B, compare the interest earned for each account by finding the difference in the amount of interest earned. (1 point)
The amount when compounded quaterly and compounded continuously will be $16,979.44 and $17,713.02. And the difference is $733.58
What is continuous compounding?Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.
The equation is given as,
[tex]\rm P=P_o \times e^{rt}[/tex]
The initital amount is $15,000 and the interest rate is 4.75% annually.
A. If the interest is compounded quarterly. Then the amount is given as,
[tex]\rm A = \$15,000 \times \left (1 + \dfrac{0.0475}{4} \right)^{42/4}[/tex]
A = $15,000 x 1.1319
A = $16,979.44
B. if the interest is compounded continuously. Then the amount is given as,
[tex]\rm A = \$ 15,000 \times e^{0.0475 \times (42 / 12)}[/tex]
A = $15,000 x 1.1808
A = $17,713.02
C. The difference in the amount of interest earned is given as,
Differenece = $17,713.02 - $16,979.44
Differenece = $733.58
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Last night, the Dallas Mavs made 12 free throws. If
their free throw percentage is 75%, how many free
throws were attempted?
A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation y = 4.9x + 15.2, where x represents the attendance (in thousands) and y is the predicted number of wins. What is the predicted number of wins for a team that has an attendance of 17,000?
A. 83.3 wins
B. 98.5 wins
C. 258.4 wins
D. 263.3 wins
Notably, this response comes the nearest to choice A (83.3 wins). The right response is thus A.
What kind of a equation is that?A mathematical statement that shows the equivalence of two mathematical equations is what a solution in algebra means. For instance, the two numbers 3x + 5 and 14 make up the expression 3x + 5 = 14, which is separated by the sign "equal."
We can change x to 17 in the regression model y = 4.9x + 15.2 and calculate for y to get the number of victories for a squad with 17,000 spectators: y = 4.9(17) + 15.2 = 83.5
Consequently, 83.5 victories are expected for a squad with a 17,000-fan attendance.
To predict the number of wins for a team with an attendance of 17,000, we can substitute x = 17 into the regression equation y = 4.9x + 15.2 and solve for y:
y = 4.9(17) + 15.2 = 83.5
Therefore, the predicted number of wins for a team with an attendance of 17,000 is 83.5 wins.
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Find a basis {p(x),q(x)} for the vector space {f(x) € P3[x] | f'(1) = f(1)} where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) = =
A basis {p(x),q(x)} for the vector space {f(x) € P3[x] | f'(1) = f(1)} where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) = is {p(x) = x² - 1, q(x) = x² + x - 2}
Polynomial Space Basis SearchThe vector space {f(x) € P3[x] | f'(1) = f(1)} consists of polynomials of degree less than 3 with the property that their derivative at x = 1 is equal to the polynomial itself evaluated at x = 1. To find a basis for this space, we can start by finding a set of two polynomials that satisfy this property, and that are linearly independent.
One possible choice for p(x) is x² - 1, and one possible choice for q(x) is x² + x - 2. These polynomials satisfy the required property (i.e., their derivatives at x=1 are equal to the polynomials themselves evaluated at x=1), and they are linearly independent because their leading terms (x² in both cases) are distinct.
Thus, {p(x) = x² - 1, q(x) = x² + x - 2} is a basis for the vector space {f(x) € P3[x] | f'(1) = f(1)}.
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Please answer this.
Help Me
1. The two equations have different slopes.
2. The two equations have different intercepts.
3. The system of equations has one solution.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the initial amount.The number of solutions for a system of two linear functions is defined as follows:
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Let f(x) = -3x + 2, g(x) = g(x)=x/5 h(x)= -2x^2+9 j(x)= 5-x
Find each value or expression.
I need help on # 5, which is #12, # 7, which is# 13, and # 9, which is 14. See attached photo below
Let f(x)=-3x+2, g(x)=5 h(x) = -2x+9, and j(x) = 5-x. Find each value or expression.
1. (f +j)(3) = -5
3. (h + g)(-5) = 10
5. (f + g)(2) = 1
7. (g f)(-5) = 22
9. f((5)) = -11
How did we get the values?1. (f + j)(3) = f(3) + j(3) = (-3(3)+2) + (5-3) = -7 + 2 = -5
3. To find the value of (h + g)(-5), we need to first add the functions h(x) and g(x), then evaluate the result at x = -5.
h(x) = -2x + 9
g(x) = 5
h(x) + g(x) = -2x + 9 + 5 = -2x + 14
So, (h + g)(-5) = -2(-5) + 14 = 10.
The answer is 10.
5. To find the value of (f + g)(2), we need to first add the functions f(x) and g(x), then evaluate the result at x = 2.
f(x) = -3x + 2
g(x) = 5
f(x) + g(x) = -3x + 2 + 5 = -3x + 7
So, (f + g)(2) = -3(2) + 7 = 1.
The answer is 1
7. (To find the value of (g + f)(-5), we need to first add the functions g(x) and f(x), then evaluate the result at x = -5.
f(x) = -3x + 2
g(x) = 5
f(x) + g(x) = -3x + 2 + 5 = -3x + 7
So, (g + f)(-5) = -3(-5) + 7 = 22.
The answer is 22
9. f(5) = -3(5) + 2 = -13 + 2 = -11
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Help me pleaseeeeeeeee
Answer:
61
Step-by-step explanation:
√(2+3)^2+(2+4)^2
=√5^2+6^2
=√25+36
=√61
So the number is 61
Suppose that you have at your disposal a software package that solves a square nonsingular system of equations Cx=d. Assume that the package either finds the unique solution of Cx=d or terminates with an error message if C is singular. Given an m×n matrix A of rank n and an m -vector b, briefly describe in words how you would use the package to find whether or not the equations Ax=b are compatible, and if they are, compute a solution x. Comment briefly on the uniqueness of a solution if one exists.
The equations Ax = b are not compatible.
What do you mean by equation?It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
To determine whether the equations Ax = b are compatible and to compute a solution x, you would first form the augmented matrix [A|b]. Then, you would perform row operations on [A|b] to reduce it to an upper triangular matrix [C|d]. Finally, you would use the software package to solve the square system of equations Cx = d.
If the software terminates with an error message, it means that C is singular, and the equations Ax = b are not compatible. If the software finds the unique solution of Cx = d, it means that the equations Ax = b are compatible and that the solution x is unique. However, it is important to note that the uniqueness of the solution depends on the rank of A being equal to n. If the rank of A is less than n, the equations are not compatible, and if the rank of A is greater than n, the equations have infinitely many solutions.
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When making chocolate chip cookies, Jesse uses 2 1/4 cups of flour for every 5 dozen cookies. Enter the number of cups of flour Adriana uses for 10 dozen cookies. Show your work.
HELP ASAP
Michaela makes $5.50 per hour at her job, How much does she make in an average eight-hour day?
Answer:
$44
Step-by-step explanation:
What we know:
$5.50 = 1 hour
average day's work = 8 hours
Question: How much money for eight hours?
To figure this out, 5.50 and multiply it by 8.
This gives us 44.
So, Michaela makes $44 dollars in an average eight-hour day.
What is the rise-over-run value for the relationship represented in the graph?
1/35
2/17
35
40
Answer:
Below
Step-by-step explanation:
Pick any two points on the graph say 2,70 and 3 , 105
rise is 70 to 105 = 35 run is 2 to3 = 1
rise/run = 35/1 = 35
Answer:
35
Step-by-step explanation:
gradient= rise/run
= 70-35/2-1
= 35
Marip has a piece of string. He cuts off six -eights of its length. How much is left?
Answer:
if marip has a piece of string. He cuts off six-eights of it's length. how much is left it's 2
when the two countries did not specialize, the total production of chinos was 23 million pairs per day, and the total production of pistachios was 68
The total production of both countries when they did not specialize was 91 million / day.
Given the information that when the two countries did not specialize, the total production of chinos was 23 million pairs per day, and the total production of pistachios was 68, we can calculate the total production of both countries with the following equation:
Total Production = Chinos (23 million pairs / day) + Pistachios (68 million / day)
Therefore, the total production of both countries when they did not specialize was 91 million / day. This can be calculated as:
Total Production = 23 million pairs + 68 million = 91 million / day
Hence, the total production of both countries when they did not specialize was 91 million / day. This calculation can be represented by the following formula:
Total Production = Chinos (x) + Pistachios (y)
Where x = 23 million pairs and y = 68 million.
Therefore, the total production of both countries when they did not specialize was 91 million / day.
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help me please!!!!!!!
Answer:
see explanation
Step-by-step explanation:
W(2) = 5 , means
a puppy of 2 months has a weight of 5 pounds.
W(6) > W(4) , means
a puppy at 6 months has a greater weight than a puppy of 4 months
W(12) = W(15) , means
a puppy at 12 months is the same weight as a puppy of 15 months
The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 38 liters, and standard deviation of 4.3 liters.
A) What is the probability that daily production is between 28 and 45.9 liters? Do not round until you get your your final answer.
The probability that daily production is between 28 and 45.9 liters is 0.024.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Given that, x₁=28, x₂=45.9, μ=38 and σ =4.3
We know that, Z=(x-μ)/σ
Z=standard score, x=observed value, μ=mean of the sample and σ=standard deviation of the sample
z =(38-28)/4.3= 2.32 and probability on the z-table is 0.9896
z = (38-45.9)/4.3 = -1.83 and probability on the z-table is 0.9656,
Now, P(2.32<z<-1.83) = 0.9896-0.9656
= 0.024
Therefore, the probability that daily production is between 28 and 45.9 liters is 0.024.
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PLEASE HELP!! MATH PROBLEM!!
please answer and explain
To find the average speed of an object, we find the change in distance divided by the time over which that change occurs. For the instantaneous speed, we must make the time interval very _______, so that the speed does not change appreciably.
To find the instantaneous speed of an object, we must make the time interval very small, so that the speed does not change appreciably.
How to find the speed?
Speed is a scalar quantity which tells how fast an object is moving, regardless of its direction.
To find the instantaneous speed of an object, we must make the time interval very short, so that the speed does not change appreciably. The formula for the instantaneous speed of an object is given by the limit as time approaches zero of the change in distance divided by the time over which that change occurs. The formula for average speed is simply the total distance traveled divided by the total time elapsed.
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The polygon in the diagram is a square with center P. The length from the center to the vertex is 6sqrt(2) in. Find the area of the square to the nearest tenth of an inch.
A) 24.0 in^2
B) 72.0 in^2
C) 36.0 in^2
D) 144.0 in^2
A tree casts a shadow that is 180 feet long. At the same time, a person standing
nearby who is 5 feet 10 inches tall casts a shadow that is 60 inches long. How tall
is the tree?
Answer: 154.28 feet
Step-by-step explanation:
there exist two complex numbers $c$, say $c 1$ and $c 2$, so that $3 2i$, $6 i$, and $c$ form the vertices of an equilateral triangle. find the product $c 1 c 2$ in rectangular form.
(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.
What is triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.
Here,
An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.
The distance between two complex numbers a + bi and c + di can be found using the formula:
√((c - a)² + (d - b)²)
So, the distance between 3-2i and 6-i is:
√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10
And the distance between 3-2i and c is:
√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)
Since these distances must be equal, we have:
√((c - 3)² + (c + 2)²) = √10
Squaring both sides:
(c - 3)² + (c + 2)² = 10
Expanding both sides:
c² - 6c + 9 + c² + 4c + 4 = 10
Combining like terms:
2c² + 10c + 5 = 10
Subtracting 10 from both sides:
2c² + 10c - 5 = 0
This is a quadratic equation, which can be solved using the quadratic formula:
c = (-b ± √(b² - 4ac)) / 2a
Where a = 2, b = 10, and c = -5. Plugging these values into the formula:
c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2
c = (-10 ± √(100 + 40)) / 4
c = (-10 ± √(140)) / 4
c = (-10 ± 10√2) / 4
So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.
The product of these two solutions is:
c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)
= (100 - 100√2 + 100) / 16
= (200 - 100√2) / 16
(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.
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What does 100 liters equal to 1
Answer:
100 liters is equal to 100,000 milliliters.
Step-by-step explanation: