Based on the information given, there are a total of 118 solutions.
How many possible solutions are there?This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:
x1 + x2 + x3 + y4 = 20
Subject to the following conditions:
0 ≤ x1 < 3
0 ≤ x2 < 4
0 ≤ x3 < 5
0 ≤ y4 < 6
We can solve this problem using the technique of generating functions. The generating function for each variable is:
(1 + x + x^2) for x1
(1 + x + x^2 + x^3) for x2
(1 + x + x^2 + x^3 + x^4) for x3
(1 + x + x^2 + x^3 + x^4 + x^5) for y4
The generating function for the equation is the product of the generating functions for each variable:
(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)
We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118
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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.
Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:
**|**||
then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.
In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).
Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:
C(20+4-1, 4-1) = C(23, 3) = 1771
However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.
Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:
A = A₀ ∩ A₁ ∩ A₂ ∩ A₃
where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.
To find the cardinality of A₀, we use the formula above and obtain:
C(20+4-1, 4-1) = 1771
To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:
C(20-4+3-1, 3-1) = C(18, 2) = 153
Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:
|A| = |A₀| - |A
Step-by-step explanation:
. Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance. Because a clerk mistakenly discarded some labor records, however, Ellen has only partial data for April. She knows that the total direct-labor flexible-budget variance was $1,643 favorable. Moreover, a recent pay raise produced an unfavorable labor price variance for April of $1,157. The actual hours of input were 1,780 and the standard labor price was $20 per hour. 1. Find the actual labor rate per hour 2. Determine the standard hours allowed for the output achieved.
Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance, the actual labor rate per hour for April was $19.35.
1. Actual Labor Rate per Hour:
The labor price variance formula is:
Labor Price Variance = (Actual Labor Rate - Standard Labor Rate) x Actual Hours
We are given that the labor price variance for April was unfavorable and equal to $1,157. We also know that the standard labor rate was $20 per hour. Using the formula above and plugging in the known values, we can solve for the actual labor rate:
-1,157 = (Actual Labor Rate - 20) x 1,780
-1,157 = 1,780Actual Labor Rate - 35,600
1,780Actual Labor Rate = 34,443
Actual Labor Rate = 19.35
Therefore, the actual labor rate per hour for April was $19.35.
2. Standard Hours Allowed for the Output Achieved:
The flexible-budget variance formula is:
Flexible-Budget Variance = (Actual Hours - Standard Hours) x Standard Labor Rate
We are given that the flexible-budget variance for April was favorable and equal to $1,643. We also know that the standard labor rate was $20 per hour.
Using the formula above and plugging in the known values, we can solve for the standard hours allowed:
1,643 = (1,780 - Standard Hours) x 20
1,643 = 35,600 - 20Standard Hours
20Standard Hours = 33,957
Standard Hours = 1,697.85
Therefore, the standard hours allowed for the output achieved in April was 1,697.85.
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Question 7 (3 points)
The graph and table below represent the constant rate for the amount of time it takes for a given
number of gallons of water to flow from a hose.
a. Find the rate of both the graph and table. Be sure to show all work.
b. Which one has the greater rate? Explain how you know.
The rate of water flow is 6 gallons per unit of time.
What is slope?
Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.
a. To find the rate, we need to calculate the amount of water that flows per unit of time.
Method 1: Using the Graph
First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.
From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.
So, the slope of the line is:
slope = change in y-values / change in x-values
= (60 - 30) / (10 - 5)
= 6
Therefore, the rate of water flow is 6 gallons per unit of time.
Method 2: Using the Table
We can also find the rate by calculating the differences in y-values and x-values in the table.
x y Difference in y Difference in x Rate (y/x)
-------------------------------------------------------
5 30 - - -
7 42 12 2 6
10 60 18 3 6
From the table, we can see that the rate of water flow is 6 gallons per unit of time.
b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.
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The radius of the wheel is 1.2 feet. What is the distance traveled when the wheel turns 20 time?
The distance traveled by the wheel when it turns 20 times is 150.7964 feet.
What is circumference?
The circumference of a wheel can be calculated as:
Circumference = 2 x π x radius
where π (pi) is a mathematical constant approximately equal to 3.14159.
The distance traveled by a wheel when it turns is equal to the circumference of the wheel multiplied by the number of times it turns.
Given that the radius of the wheel is 1.2 feet, the circumference of the wheel is:
Circumference = 2 x π x radius
Circumference = 2 x 3.14159 x 1.2
Circumference = 7.53982 feet (rounded to 5 decimal places)
Therefore, each time the wheel turns, it travels a distance of 7.53982 feet. To find the distance traveled when the wheel turns 20 times, we can multiply the distance traveled each time by the number of times the wheel turns:
Distance traveled = Circumference x Number of turns
Distance traveled = 7.53982 feet x 20
Distance traveled = 150.7964 feet (rounded to 4 decimal places)
Therefore, the distance traveled by the wheel when it turns 20 times is 150.7964 feet.
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how do I find the IQR for the numbers 7,9,8,9,6
Answer:
There are three steps to find IQR
1. Know how the IQR is used. Essentially, it is a way of understanding the spread or "dispersion" of a set of numbers. The interquartile range is defined as the difference between the upper quartile (the highest 25%) and the lower quartile (the lowest 25%) of a data set.
2. Understand quartiles. To visualize a quartile, chop a list of numbers into four equal parts. Each of these parts is a "quartile."[2] Consider the set: 1, 2, 3, 4, 5, 6, 7, 8.
1 and 2 are the first quartile, or Q1
3 and 4 are the second quartile, or Q2
5 and 6 are the third quartile, or Q3
7 and 8 are the fourth quartile, or Q4
3. Learn the formula. In order to find the difference between the upper and lower quartile, you'll need to subtract the 25th percentile from the 75th percentile.
The formula is written as: Q3 – Q1 = IQR.
Answer:
the answer would be 2.5
Explanation:
The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data).
Find the surface area for the figure ( on photo )
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?The diagram above is a typical example of the square based pyramid which has four triangles connected to a vertex.
To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where b = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
Therefore the surface area of the square based pyramid given above would be = 400ft².
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Solve for x:-
2^x=32
Answer:
x=5
Step-by-step explanation:
2^x= 32
2^x=2^5
(comparing, common denominator)
therefore x=5.
find the surface area of the figure
Answer:
The answer for Surface area is 332m²
Step-by-step explanation:
S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle
S.A=2×1/2×4×3 + 2(20×5) + 20×6
S.A=12+2(100)+120
S.A=12+200+120
S.A=212+120
S.A=332m²
How many gallons of a 80% alcohol solution and a 20% alcohol solution must be mixed to get 9 gallons of 60% alcohol solution?
In linear equation, x = 6 gallons (of 80% alcohol)
y = 3 gallons (of 20% alcohol)
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Let
x = liters of 80% alcohol
y = liters of 20% alcohol
There are two unknowns, we need two equations
x + y = 9. (1)
0.80x + 0.20y = 0.60(x+y) (2)
From (1)
x + y = 9
y = 9-x
Substitute the value of y into (2) and solve for x:
0.80x + 0.20y = 0.60(x+y)
0.80x + 0.20(9-x) = 0.60(x+9-x)
0.80x + 1.8 - 0.20x = 0.60(9)
0.80x + 1.8 - 0.20x = 5.4
0.6x = 3.6
x = 6 gallons (of 30% alcohol)
Substitute x=6 into (1) and solve for y:
x + y = 9
6 + y = 9
y = 3 gallons (of 60% alcohol)
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It took a crew 1 h 30 min to row 5 km upstream and back again. If the rate of flow of the stream was 8 km/h, what was the rowing speed of the crew in still water? km/h
The rowing speed of the crew in still water is:
x = 12 km/h.
What is meant by speed?
Speed is a measure of how fast an object is moving. It is usually expressed in units of distance per unit of time, such as miles per hour or meters per second. Speed can be calculated using the formula speed = distance/time.
According to the given information
We can use the formula:
distance = rate × time
to set up two equations based on the information given.
When the crew rows upstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x - 8)
When the crew rows downstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x + 8)
The total time for the round trip is 1 hour 30 minutes, or 1.5 hours:
total time = time upstream + time downstream
1.5 = 5/(x-8) + 5/(x+8)
To solve for x, we can start by multiplying both sides of the equation by (x - 8)(x + 8) to clear the denominators:
1.5(x - 8)(x + 8) = 5(x + 8) + 5(x - 8)
Expanding and simplifying, we get:
1.5x^2 - 72 = 10x
Bringing all the terms to one side of the equation, we get:
1.5x^2 - 10x - 72 = 0
We can factor this quadratic equation by first dividing both sides by 1.5:
x^2 - (10/1.5)x - 48 = 0
We can then factor this expression as:
(x - 12)(x + 4) = 0
This gives us two possible values of x: x = 12 and x = -4.
Since we are looking for a rowing speed (which is a positive quantity), we can discard the negative solution and conclude that the rowing speed of the crew in still water is:
x = 12 km/h.
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and area of the original figure to
of the reduced figure using the
3
6
Which statements are true about the comparison
between the two figures? Check all that apply.
The scale factor is 2.
The scale factor is
2
The perimeter of the model is the product of the
scale factor and the perimeter of the original
rectangle.
The area of the reduced figure is half the area of
the original figure.
The area of the reduced figure is
area of the original figure.
(94
times the
The scale factοr is οne-half. The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle. The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure
What is the scale factοr?The ratiο between cοmparable measurements οf an οbject and a representatiοn οf that οbject is knοwn as a scale factοr in mathematics.
Here,
We have tο cοmpare the perimeter and area οf the οriginal figure tο the perimeter and area οf the reduced figure using the scale factοr.
The ratiο οf the length οf the οriginal rectangle tο that οf the reduced rectangle is 6 tο 3 οr a factοr οf 1/2.
The ratiο οf the width οf the οriginal rectangle tο that οf the reduced rectangle is 2 tο 1, οr, again, a factοr οf 1/2. Sο, because this ratiο οf 1/2 is cοnstant, we knοw the tοtal scale factοr is 1/2, making B cοrrect.
16 ×(1/2) = 8, which means that the perimeter οf the scale-factοred, reduced rectangle is "the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle". Sο, C is cοrrect.
Hence, The scale factοr is οne-half.
The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle.
The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure.
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Question 10
Find a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36.
a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36 is
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
How to find the 5 degree polynomial?Let us begin by writing the polynomial factors using the supplied zeros:
Because -2 is a zero, the polynomial has a component of (x + 2).
Because [tex]\sqrt{ 3i }[/tex] is a zero, its conjugate -[tex]\sqrt{ 3i }[/tex] is likewise a zero, implying that the polynomial has a component of (x - [tex]\sqrt{3i}[/tex])(x + [tex]\sqrt{3i}[/tex]) = (x2 + 3).
Similarly, because [tex]\sqrt{2i}[/tex] is a zero, its conjugate -[tex]\sqrt{ 2i }[/tex] is also a zero, implying that the polynomial has a component of (x - [tex]\sqrt{ 2i }[/tex])(x + [tex]\sqrt{ 2i }[/tex]) = (x2 + 2).
Finally, we know that the y-intercept is 36, which means that the polynomial's constant term is 36 when x=0.
When we add these components together, we get:
[tex]f(x) = (x + 2)(x^2 + 3)(x^2 + 2) + 36[/tex]
Extending on this, we get:
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
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HELP ME PLEASE! And I already did the first part I need help on the second. (Give me a full explanation NO DECIMALS! Just fractions.)
The amount of chalk that is greater is yellow.
Michelle is correct because more than 1/2 the chalk in the bucket is blue.
How to determine which amount of chalk is greater?In order to determine the amount of chalk that is greater between the amount of yellow chalk and amount of green chalk, we would have to find the difference between them as follows;
Difference = 2/6 - 3/12
Difference = (4 - 3)/12
Difference = 1/12 (positive value)
Similarly, we can determine the greater amount of chalk as follows;
2/6 × 2/2 = 4/12
4/12 > 3/12
Total number of chalks = 2/6 + 5/12 + 3/12
Total number of chalks = (4 + 5 + 3)/12
Total number of chalks = 12/12
Total number of yellow and green chalks = 2/6 + 3/12
Total number of yellow and green chalks = (4 + 3)/12
Total number of yellow and green chalks = 7/12 chalks.
1 - 7/12 = 5/12
7/12 - 1/2 = 6/12 (Michelle is correct).
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NO LINKS!! URGENT HELP PLEASE!!
Select all that apply
b. Symmetric with respect to the x-axis
The ones that are symmetric with respect to the x-axis is:
y = -7x^2Checking the symmetric for all equationsA function is symmetric with respect to the x-axis if replacing y with -y in the equation does not change the equation. In other words, if the graph of the function is the same when reflected across the x-axis.
y = -7x^2 is symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y and the equation remains the same.y = 6x² - 9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = 6x² - 9, which is not the same as the original equation.x=1/4y^2 is not a function, since it does not pass the vertical line test and has multiple values of x for some values of y.y=x^3-1 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = x^3 - 1, which is not the same as the original equation.x=-y^2+9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to x = -(-y)^2 + 9, which is not the same as the original equation.y=sqrt(x) is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x), which is not the same as the original equation.y=sqrt(x)-6 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x) - 6, which is not the same as the original equation.Therefore, only the equation y = -7x^2 is symmetric with respect to the x-axis.
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Suppose we are given the following....(picture below)
Line 1: slope = 1/4
Line 2: slope = -4
Line 3: slope = -1/12
Line 1 and Line 2: perpendicular
Line 1 and Line 3: neither
Line 2 and Line 3: neither
How to find the slope of the lines?Slope is the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Mathematically, the slope is the change in y divided by the change in x. That is:
Slope = (y₂-y₁) / (x₂-x₁)
Line 1:
(4, -1) and (8, 0)
Slope = (0--(-1)) / (8-4)
= 1/4
Line 2:
(2, -6) and (0, 2)
Slope = (2-(-6)) / (0-2)
= 8/(-2)
= -4
Line 3:
(3, -6) and (6, -7)
Slope = (-7-(-6)) / (6-(-6))
= -1/12
Remember:
1. When the two lines are parallel, they have the same (equal) slope.
2. When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ * m₂ = -1. Where m₁ and m₂ represent the slope of the lines.
Let's check:
Line 1 and Line 2:
They are not parallel but they are perpendicular (i.e. 1/4 * (-4) = -1).
Line 1 and Line 3:
Neither
Line 2 and Line 3:
Neither
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find the surface area of the figure
The surface area of the square pyramid is 416.23 ft²
How to find the surface area of a square pyramid?
The surface area of a square pyramid is given by the formula:
A = a² + 2a√(a²/4 + h²)
Where a is the base length of the square pyramid and h is the height of the square pyramid.
From the figure, we have: a = 10 ft and h = 15 ft
A = a² + 2a√(a²/4 + h²)
A = 10² + 2*10√(10²/4 + 15²)
A = 100 + 20√(100/4 + 225)
A= 100 + 20√250
A = 416.23 ft²
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Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run? A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by. Select all that apply. You know the difference in the distances the boys ran, so this is a subtraction problem. You are finding the total distance the boys ran, so this is an addition problem. Dean ran part of the distance Sam ran, so this is a multiplication problem. The correct equation is s + 2.3 = 6.8. The correct equation is s – 2.3 = 6.8. The correct equation is 2.3s = 6.8.
The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.
What is distance?Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.
According to question:The Situation column should have two entries: "finding part of a total" and "difference".
The Operation column should have only one entry: "minus".
The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.
To solve for s, we can add 2.3 to both sides of the equation:
s - 2.3 + 2.3 = 6.8 + 2.3
s = 9.1
Therefore, Sam ran 9.1 kilometers.
So, the Situation entries are: "difference" and "finding part of a total".
The Operation entry is: "minus".
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Find LM
A. 18
B. 24
C. 28
D. 36
Applying the Two-Tangent Theorem, the length of segment LM in the circle is: A. 18.
What is the Two-Tangent Theorem?
If two tangent segments are drawn to one circle from the same external point, the Two-Tangent Theorem states that both segments are congruent together.
Applying the theorem, we have:
4x - 2 = 3x + 3
Find the value of x:
4x - 3x = 2 + 3
x = 5
Find the length of LM:
LM = 3x + 3
Plug in the value of x:
LM = 3(5) + 3
LM = 18
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or 1/2 x + 3/4 - 5/8 x - 7/8 and 1/8 ( x + 1 ( equivalent expressions show your work
To simplify the expression 1/2 x + 3/4 - 5/8 x - 7/8 + 1/8 (x + 1), we'll need to combine like terms.
First, let's distribute the 1/8 to the expression in parentheses:
1/2 x + 3/4 - 5/8 x - 7/8 + 1/8 x + 1/8
Next, we can combine like terms:
(1/2 - 5/8 + 1/8) x + (3/4 - 7/8 + 1/8)
Simplifying the coefficients of x, we get:
(1/2 - 4/8 + 1/8) x + (3/4 - 6/8 + 1/8)
(1/2 - 1/8) x + (3/4 - 5/8)
(4/8 - 1/8) x + (6/8 - 5/8)
3/8 x + 1/8
Therefore, the expression 1/2 x + 3/4 - 5/8 x - 7/8 + 1/8 (x + 1) simplifies to the equivalent expression 3/8 x + 1/8.
I was a bit confused about what you were asking, please correct me if I am wrong!
The factorization of x2 – 6x – 72 is:
Step-by-step explanation:
x^2 -6x - 72 = ( x-12)(x+6)
If you can't do this 'in your head' you can always use Quadratic Formula
with a = 1 b= - 6 and c= -72
to find roots x = 12 and -6 then write the equation as above
I don’t know how to solve
Answer:
5.6
Step-by-step explanation:
180/50 is 5.6
What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic centimeters? 3,600,000 cm 3 3,600 cm 3 36,000 cm 3 3.6 cm 3
The volume of the rectangular prism in cubic centimeters is 3,600,000
What is the volume of the rectangular prismFrom the question, we have the following parameters that can be used in our computation:
Dimension = 120 centimeters by 2 meters by 1.5 meters
The volume of the rectangular prism is the product of the dimensions
i.e.
Volume = Length * width * height
Substitute the known values in the above equation, so, we have the following representation
Volume = 120 * 2 * 1.5
Convert to cm
Volume = 120 * 200 * 150
Evaluate
Volume = 3600000
Hence, the volume in cubic centimeters is 3,600,000
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Solve for AB using the given info.
#11
The length of AB of the parallelogram is determined as 14.36 inches.
What is the length AB?The length of AB of the parallelogram can be determined by applying cosine rule as shown below:
The cosine rule, also known as the law of cosines, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is commonly used to find the length of an unknown side or the measure of an unknown angle in a triangle when the lengths of two sides and the measure of the included angle are known.
Length AB = Length AD = x
DB² = AB² + AD² - 2(AB x AD) cos (A)
22² = x² + x² - 2x²(cos 100)
484 = 2x² + 0.347x²
484 = 2.347x²
x² = 484/2.347
x² = 206.2
x = √206.2
x = 14.36 inches
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PLEASE HELP FOR 100 POINTS Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)
Answer: a
Step-by-step explanation:
A square pyramid has a base with an area of 225 centimeters squared if the volume is 300 centimeters cubed how tall is the pyramid
The height of the square pyramid with base area 225 cm² and volume 300cm³ is equal to 4 centimeters.
Area of the base of square pyramid = 225 centimeters squared
Volume of the square pyramid = 300 centimeters cubed
Using the formula for the volume of a square pyramid,
V = (1/3) × B × h
where V is the volume,
B is the area of the base,
and h is the height of the pyramid.
Substitute this value into the formula we have,
⇒ 300 = (1/3) × 225 × h
Simplifying the equation , we get,
⇒ 900 = 225 × h
Dividing both sides by 225, we get,
⇒ h = 4
Therefore, the height of the square pyramid is 4 centimeters.
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Find the indefinite integral.
The indefinite integral, given the integral can be found to be √14x + C.
How to find the indefinite integral ?An indefinite integral is an antiderivative of a function. More specifically, if f(x) is a function, then an antiderivative of f(x) is a function F(x) such that F'(x) = f(x), where F'(x) represents the derivative of F(x) with respect to x.
To find the indefinite integral of a constant (in this case, √14) with respect to x, simply multiply the constant by x and add a constant of integration (C):
∫√14 dx = √14 × ∫dx = √14 × x + C
So, the indefinite integral of √14 with respect to x is:
√14x + C
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ANALYSIS
Graphs and tables not only represent data, but they also allow you to answer questions about the data. Use your tables and graphs on the resource pages from problem 1-13 to answer the questions below.
Which data appears to be linear? That is, when graphed, which data can be modeled best using a line? Explain why it makes sense for this situation to have a linear graph.
Now that Perry knows his options for the design of his hot tub, he wants to pick the hot tub that has the smallest perimeter (without cutting any tiles). What do you recommend?
The town of Parsnipville will have a flu vaccine available on Day 7. Only people who have not yet gotten the flu will need to be vaccinated. Since the town has
citizens, how many people will need the vaccine on that day? Is it easier to answer this question using your graph or using your table? Explain.
Certain legal documents, such as those used when buying property, sometimes require up to
signatures! How long do you think it might take to sign all the documents?
Considering each situation (lab), which of your graphs could have a point where
? Explain.
Assume that Perry’s hot tub tiles measure one foot on a side. If Perry could cut his tiles, what is the longest hot tub he could possibly build?
The data that appears to have a consistent rate of change over time or with respect to another variable often appears to be linear.
When data is graphed, which data can be modeled best using a line?The data that has a clear trend or pattern that can be represented by a straight line is best modeled using a line.
Why does it makes sense to have a linear graph?Linear graphs are useful because they allow us to easily visualize and analyze trends or patterns in data. The equation of a line can also be used to make predictions or forecasts based on the data. Linear graphs can be used to identify correlations between variables and to assess the strength and direction of those correlations.
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Downtown Mathville is laid out as a 6 x 6 square grid of streets (see diagram below). Your apartment is located at the southwest corner of downtown Mathville (see point H). Your math classroom is located at the northwest corner of downtown Mathville (see point M). You know that it is a 12-block walk to math class and that there is no shorter path. Your curious roommate (we’ll call her Curious Georgia) asks how many different paths (of length 12 blocks – you don’t want to back track or go out of your way) could you take to get from your apartment to the math class. It should also be clear that no shorter path exists. Can you solve Curious Georgia’s math problem?
Yes, we can solve Curious Georgia's math problem using the concept of combinations.
There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.
We have,
Yes, we can solve Curious Georgia's math problem using the concept of combinations.
Since we cannot backtrack or go out of our way, we need to take exactly 6 blocks to the north and 6 blocks to the east to reach the math classroom.
This means that we need to choose 6 out of the 12 blocks to go north, and the remaining 6 blocks will be used to go east.
The total number of paths we can take is the number of ways we can choose 6 blocks out of the 12 blocks.
This can be calculated using the combination formula:
[tex]^nC_r[/tex] = n! / r!(n-r)!
where n is the total number of objects, r is the number of objects to choose, and ! represents the factorial function
In this case,
we have n = 12 and r = 6.
The number of paths.
= [tex]^{12}C_6[/tex]
= 12! / 6!(12-6)!
= 924
Therefore,
There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.
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help! please help me with this math
The only function that represents a range as less than zero only is: Option C: 1/(x - 2)²
How to find the range of the function?The range of a function is defined as all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.
Now, we want to find the function for which the range is a set of all real numbers less than zero. This means that the range is made up of only negative numbers.
The only option that denotes the range to be less than zero is option C because no matter the domain value, the range will remain a negative number.
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18
If the mean for a data set was 8 and the standard deviation was 1.5, where would most of the data points be located?
A) Above 9.5
B) Between 6.5 and 9.5
Above 12
D) None of these answer choices are correct.
the correct answer is B, between 6.5 and 9.5.The solution of given standard deviations Problem isit is unlikely that most of the data points would be located there.
what is standard deviations?Standard deviation is a statistical measure of the amount of variation or dispersion in a set of data values. It represents the average distance of each data point from the mean of the data set.
According to given informationThe answer to this question can be found using the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.
Given that the mean is 8 and the standard deviation is 1.5, one standard deviation above the mean would be 8 + 1.5 = 9.5, and one standard deviation below the mean would be 8 - 1.5 = 6.5. Therefore, approximately 68% of the data would be expected to fall between 6.5 and 9.5.
Based on this information, we can eliminate answer choices A and D. Answer choice C is more than two standard deviations above the mean, so it is unlikely that most of the data points would be located there. Therefore, the correct answer is B, between 6.5 and 9.5.
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which of the following equations can be used to find the misssing angle x in triangle 42
The equation in the triangle to find x is x + 84 = 180.
Option B is the correct answer.
We have,
The sum of the angles in a triangle is 180.
And,
42 + 42 + x = 180
84 + x = 180
x = 180 - 84
x = 96
Thus,
The equation in the triangle to find x is x + 84 = 180.
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