The length of the missing side is 15.
What is a theorem?
A statement that can be proven true using well-known mathematical procedures and arguments is known as a theorem. A theorem, in general, is an application of a general principle that joins it to a larger theory. Proof is a procedure used to demonstrate a theorem's correctness.
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
The hypotenuse is 17. The length of one leg is 8.
The length other leg is
√(17² - 8²)
= √(289 - 64)
= √(225)
= 15
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Iteration = 5000
Random: =RAND()
Demand: =ROUND ( NORM.INV ( RAND(), Mean, Standard Deviation),0)
Revenue: = Unit Price x MIN (Demand, Order Quantity)
Cost: = Order Quantity x Unit Cost
Refund: = Unit Refund x MAX(0, Order Quantity - Demand)
Profit: = Revenue - Cost + Refund
The Bin is the given, how should I get the chart that I had circled in the second picture with all these given?
To get the chart that you have circled in the second picture, you need to create a table using the given formulas and then create a chart using the table. Here are the steps:
1. Create a table with the following columns: Iteration, Random, Demand, Revenue, Cost, Refund, and Profit.
2. In the first row of the table, enter the given formulas in the respective columns. For example, in the first row of the Random column, enter =RAND(), in the first row of the Demand column, enter =ROUND ( NORM.INV ( RAND(), Mean, Standard Deviation),0), and so on.
3. Copy the formulas down to the 5000th row to get the values for all 5000 iterations.
4. Select the entire table and click on the Insert tab in the Excel ribbon.
5. In the Charts group, click on the type of chart that you want to create. In this case, it looks like you want to create a scatter chart.
6. In the Chart Design tab, click on the Select Data button in the Data group.
7. In the Select Data Source dialog box, click on the Add button in the Legend Entries (Series) section.
8. In the Edit Series dialog box, enter a name for the series, select the Profit column for the Series X values, and select the Demand column for the Series Y values.
9. Click on the OK button to close the Edit Series dialog box and then click on the OK button to close the Select Data Source dialog box.
10. Your chart should now be created and should look like the one that you have circled in the second picture.
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Solving a rational equatic Solve for v. (3)/(4v)+(7)/(v)=1 If there is more than one solution, If there is no solution, click on "No s
There is only one solution for this equation. v = 31/4 is the only solution to this equation.
To solve for v in the equation (3)/(4v)+(7)/(v)=1, we need to get a common denominator and then solve for v.
Step 1: Get a common denominator. The common denominator for 4v and v is 4v. So, we will multiply the second fraction by 4/4 to get a common denominator:
(3)/(4v)+(7*4)/(v*4)=1
Step 2: Simplify the fractions:
(3)/(4v)+(28)/(4v)=1
Step 3: Combine the fractions:
(3+28)/(4v)=1
Step 4: Simplify the numerator:
(31)/(4v)=1
Step 5: Cross-multiply to solve for v:
31=4v
Step 6: Divide both sides by 4 to get v:
v=31/4
The solution is v=31/4.
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Determine if the given function is linear, quadratic, or exponential.
f(x) = 5 (2.3)^x
The given function f(x) = 5 (2.3)^x is an exponential function.
The given function is f(x) = 5 (2.3)^x.
To determine if the function is linear, quadratic, or exponential, we need to examine the form of the function.
A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept.
A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
An exponential function has the form f(x) = ab^x, where a and b are constants.
The given function, f(x) = 5 (2.3)^x, is in the form of an exponential function, with a = 5 and b = 2.3. Therefore, the function is exponential.
In conclusion, the given function f(x) = 5 (2.3)^x is an exponential function.
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A chemist wants to make 54 ml of 18% acid solution by mixing 11% acid solution and a 20% acid solution how many ml should the chemist use
The chemist must use 12 ml of the 11% acid solution and 42 ml of the 20% acid solution to make a solution of quantity 54 ml of 18% concentration acid solution.
It is already given that the chemist wishes to make a solution of 54 milliliters of 18 percent concentration using two different solutions of concentration 11% and 20% each.
Now let us consider that the quantity of acid to be present in the final solution is (18/100)×54 = 9.72 ml
If we consider that x ml of 11% solution and y ml of 20% solution are added, then following relations can be obtained:
Total volume of x and y in the final solution = x + y = 54 ...(1)
Considering the concentration of acid and its volume, the following equation is formed:
0.11x + 0.2y = 9.72 ...(2)
Solving the equations (1) and (2) for the value of x and y, we get:
x = 54 - y
∴ 0.11(54 - y) + 0.2y = 9.72
⇒ 5.94 - 0.11y + 0.2y = 9.72
⇒ 0.09y = 3.78
⇒ y = 42 ml
Putting the value of y in equation (1), we get
x = 54 - y
x = 54 - 42 = 12 ml
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Question
What is the expanded form of this number?
204.017
⁰ (2 x 100) + (4 x 1) + (1 x 1/10) + (7 x 1/1000)
⁰ (2 x 100) + (4 x 1) + (1 x 1/100) + (7 x 1/1000)
⁰ (2 x 100) + (4 x 1) + (1 x 1/10) + (7 x 1/100)
⁰ (2 x 100) + (4 x 1) + (1 x 1/100) + (7 x 1/100)
Answer:
B
Step-by-step explanation:
2 is hundred = 2x100
0 is tens =0x10
4 is unit =4 x 1
All numbers after the decimal point to the right are fractions
0 is tenth = 0/10 =0
1 is hundredth =1/100
7 is thousandth 7/1000
Now you can choose the right answer
if there are 578 coyotes in 2003 with initial growth of 1.52. How many coyotes in 2028
If there are 578 coyotes in 2003 with initial growth of 1.52, there will be approximately 336113 coyotes in 2028.
The number of coyotes in 2028 can be found by using the formula for exponential growth:
[tex]A = P(1 + r)^t[/tex]
Where:
A = final amount
P = initial amount
r = growth rate
t = time in years
Plugging in the given values:
[tex]A = 578(1 + 1.52)^25[/tex]
Using a calculator, we get:
[tex]A = 578(1.52)^25[/tex]
[tex]A = 578(581.68)[/tex]
[tex]A = 336112.64[/tex]
Therefore, there will be approximately 336113 coyotes in 2028.
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Which equation can be used to find the area of the figure below?
F.A = (10⋅82
)+
(16⋅8
)
G.A = (6⋅82
)+
(10⋅8
)
H.A = (6⋅82
)+
(6⋅8
)
J.A = (6⋅8
)+
(10⋅8
)
The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
What is area of composite figure?The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.
A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.
The area of the rectangle is given as:
A = (l)(w)
A = 10(8)
A = 80 sq. units
The area of the triangle is:
A = 1/2(b)(h)
In the figure:
b = 16 - 10 = 6 and h = 8.
A = 1/2(6)(8)
A = 24 sq. units
The total area of the figure is:
Area = area of rectangle + area of triangle
Area = 80 + 24
Area = 104 sq. units
Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
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Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm 1.2 Hence, determine the circumference of the base of the tin in mm. You may us the formula: CС = 2πr Hint: radius = half of diameter MATHEMATICAL LITERACY GRADE 11, 2023 SBA GUIDELINE π = 3,142 Page 2 (3) (3)
Answer: 1.1 The diameter of the tin on the picture is approximately 90 mm.
1.2 The circumference of the base of the tin is approximately 565 mm (2πr = 2π(45) = 565).
Step-by-step explanation: math is stressful fr
We can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumferance as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
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HELP MEEEEEE 20 EASY PONTSSSSS
The function that represents exponential growth is C. Of(x) = 0.3(1.05)^(x), where x is the input variable.
Exponential growth occurs when a quantity increases at a constant percentage rate over time, which is exactly what happens in the function C. As x increases, the term (1.05)^(x) grows larger and larger, leading to a corresponding increase in the value of the function. The coefficient 0.3 scales the rate of growth so that it starts at a manageable level.
Functions A, B, and D do not represent exponential growth. Function A decreases over time as the base is less than 1, function B represents a linear growth, and function D represents linear growth as well.
The function with Exponential growth is f(x) = 0.3 [tex](1.05)^x[/tex].
What is Exponential Function?An exponential function is a nonlinear function with the formula y = [tex]a(b)^x[/tex], where a = 0 and b = 1.
The function is an exponential growth function for a > 0 and b > 1. The function is an exponential decay function when a > 0 and 0 b 1.
First function, f(x) = 134 [tex](0.75)^x[/tex]
Here the value of b < 1 then it Exponential Decay.
Now, f(x) = 513 + 0.2x is linear function.
Now, f(x) = 0.3 [tex](1.05)^x[/tex]
Here the value of b > 1 then it Exponential Growth.
Now, f(x) = 15+ 1.6x is linear function.
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Damion is building a pool in his backyard. He needs the pool to have a length of 12.5 meters (m) and a width of 5.7 m. He also needs the volume of the
pool not to exceed 114 cubic meters (m³).
12.5 m
The Height of the pool should be 1.6 m.
What is Volume?Every three-dimensional item requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object inside the confines of three-dimensional space. It is also known as the object's capacity.
Given:
length of pool= 12.5 m
width of pool = 5.7 m
and, Maximum volume of pool = 114 m³
So, Volume= l w h
114 = 12.5 x 5.7 x h
114 = 71.25 h
h = 114/ 71.25
h = 1.6 m
Thus, the height can be 1.6 m.
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iven the polynomial 4x^(2)y^(4) - 9x^(2)y^(6), rewrite as a product of polynomials
The polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials as:
x^(2)y^(4)(2y + 3)(2y - 3)
The polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials by factoring out the common factor of x^(2)y^(4). This leaves us with:
x^(2)y^(4)(4 - 9y^(2))
Now, we can factor the polynomial inside the parentheses as a difference of squares:
x^(2)y^(4)(2y + 3)(2y - 3)
Therefore, the polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials as:
x^(2)y^(4)(2y + 3)(2y - 3)
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Math Recommendations If h(v)=2v^(3)-25v+4, use synthetic division to find h(-4). Submit
Using synthetic division, the value of h(-4) is - 24.
To find h(-4) using synthetic division, we will use the following steps:
1. Set up the synthetic division grid with the divisor (-4) in the top left corner and the coefficients of the polynomial in the top row.
-4 | 2 0 -25 4
2. Bring down the first coefficient to the bottom row.
-4 | 2 0 -25 4
|
2
3. Multiply the divisor (-4) by the first number in the bottom row (2) and put the result (-8) in the second column of the top row.
-4 | 2 0 -25 4
| -8
2
4. Add the numbers in the second column (0 and -8) and put the result (-8) in the second column of the bottom row.
-4 | 2 0 -25 4
| -8
2 -8
5. Repeat steps 3 and 4 for the remaining columns.
-4 | 2 0 -25 4
| -8 32 -28
2 -8 7 -24
6. The last number in the bottom row (-24) is the remainder and the value of h(-4). The other numbers in the bottom row (2, -8, 7) are the coefficients of the quotient polynomial.
Therefore, h(-4) = 24.
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Landon has a jar of coins. He chooses a coin at random, notes what type of coin it is, and returns it to the jar. After 12 trials, he calculates the experimental probabilities shown in the table.
On the 13th trial, Landon chooses a nickel.
What is the experimental probability of choosing a nickel based on the 13 trials?
Coin
Penny
Nickel
Dime
Quarter
Experimental
Probability
1/2
1/4
1/6
1/12
The experimental probability of choosing a nickel based on the 13 trials is 4/13.
What is probability ?
Probability can be defined as ratio number of favourable outcomes, total number of outcomes.
Based on the experimental probabilities shown in the table, we can calculate the probability of choosing a nickel on the 13th trial using the following steps:
Calculate the total number of trials: 12 + 1 = 13
Calculate the total number of times a nickel was chosen in the 12 trials: 12 * 1/4 = 3
Add 1 to the total number of times a nickel was chosen to account for the 13th trial: 3 + 1 = 4
Calculate the experimental probability of choosing a nickel based on the 13 trials: 4/13
Therefore, the experimental probability of choosing a nickel based on the 13 trials is 4/13.
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Hi, Could you please show and explain the methods for
calculating Mean, Median and Mode?
Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set.
Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order.
Mode: The mode is the number that appears most frequently in a set of numbers.
Hi there! Yes, I can certainly show and explain the methods for calculating Mean, Median, and Mode. These are all measures of central tendency, which are used to describe the center of a data set.
Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set. For example, if you have the numbers 2, 4, 6, 8, and 10, the mean would be (2 + 4 + 6 + 8 + 10) / 5 = 6.
Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. For example, if you have the numbers 2, 4, 6, 8, and 10, the median would be 6. If you have the numbers 2, 4, 6, 8, 10, and 12, the median would be (4 + 6) / 2 = 5.
Mode: The mode is the number that appears most frequently in a set of numbers. If there is more than one number that appears the same number of times, there can be more than one mode. For example, if you have the numbers 2, 4, 6, 8, 10, and 10, the mode would be 10 because it appears twice and the other numbers only appear once.
I hope this helps! Let me know if you have any other questions.
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Exercise 3. Let \( n \in \mathbb{N} \) with \( n>2 \). Prove that there exists \( a \in \mathbb{Z}_{n} \) such that \( a^{2}=[1] \in \mathbb{Z}_{n} \) and \( a \neq[1] \).
\(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\)
Let \(n \in \mathbb{N}\) with \(n>2\). We consider the set \( S = \{a \in \mathbb{Z}_{n} \ | \ a^{2} = [1] \in \mathbb{Z}_{n}\} \). We have to prove that \( S \neq \emptyset \).
We prove by contradiction. Suppose \( S = \emptyset \). This implies that for all \( a \in \mathbb{Z}_{n}, \ a^{2} \neq [1] \in \mathbb{Z}_{n}\). Thus, \( [1] \) is not a square in \(\mathbb{Z}_{n}\). But since \(n >2\), \([1]\) has at least two square roots in \(\mathbb{Z}_{n}\) which implies that \( S \neq \emptyset \).
Therefore, \(S \neq \emptyset\) and thus there exists \(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\).
This proves that there exists an \(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\).
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Find the values of a and b to express this recurring decimal as a fraction.
Simplify this fraction as much as possible before entering your answer.
0.727272... = [tex]\frac{a}{b}[/tex]
a=
b=
Answer: Let x = 0.727272...
Then, 100x = 72.727272...
Subtracting x from 100x gives:
100x - x = 72.727272... - 0.727272...
99x = 72
x = 72/99
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 9. Therefore:
x = (72/9) / (99/9) = 8/11
So, a = 8 and b = 11. Therefore, the recurring decimal 0.727272... can be expressed as the fraction 8/11.
Step-by-step explanation:
Use simple interest to find the ending balance.
$7,900 at 1.9% for 2 & 3/4 years
Answer:
To calculate the ending balance, we can use the following formula:
Ending Balance = Principal x (1 + Interest Rate x Time)
Given:
Principal = $7,900
Interest Rate = 1.9%
Time = 2 3/4 years
Therefore,
Ending Balance = $7,900 x (1 + 0.019 x 2.75) = $8,084.60
Answer: 8319.66994
Step-by-step explanation:
your initial x your interest all raised to your time interval.
7,900(1+.019)^2.75
What does it equal?
-8=z/14
If you are solving for z:
-8=z/14
multiply by 14 on both sides:
z = -112
If 1/6 of a gallon of milk is shared equally between three friends how much milk will each friend get
the friends receive one eighteenth each
A pilot flies in a straight path for 1.5 hrs. She then makes a course correction, heading 20 degrees to the right of her original course, and flies 2 hrs in the new direction. If she maintains a constant speed of 685 mi/h, how far is she from her starting position?
Ans - The pilot is 1868.08 mi from her starting position, To find the distance the pilot is from her starting position, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite side c:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
In this case, the pilot's original path is one side of the triangle (a), her new path after the course correction is another side of the triangle (b), and the distance she is from her starting position is the third side of the triangle (c). The angle between the two paths is 20 degrees (C).
First, we need to find the length of sides a and b. The pilot flew for 1.5 hrs at a speed of 685 mi/h on her original path, so:
a = 1.5 hrs * 685 mi/h = 1027.5 mi
She then flew for 2 hrs at the same speed on her new path, so:
b = 2 hrs * 685 mi/h = 1370 mi
Now we can plug these values into the law of cosines to find the distance the pilot is from her starting position (c):
[tex]c^2 = 1027.5^2 + 1370^2 - 2*1027.5*1370*cos(20)[/tex]
[tex]c^2 = 3,488,806.25[/tex]
[tex]c = sqrt(3,488,806.25)[/tex]
[tex]c = 1868.08 mi[/tex]
Therefore, the pilot is 1868.08 mi from her starting position.
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Joey bought 5 plates of nachos and 2 2-liter sodas for him and his friends. The total bill came to $67.87 (before tax). The next day he bought one 2-liter of soda and 2 plates of nachos for him and his dad. That total bill came to $27.94 (before tax). How much does a plate of nachos cost? How much does a 2-liter of soda cost?
Therefore , the solution of the given problem of unitary method comes out to be a 2-liter soda costs $4.98 and a platter of nachos costs $11.99.
What is unitary method ?The measurements taken from this femtosecond section must be multiplied by two in order to complete the task using the unitary variable technique. In essence, the characterised by a group and the hue groups are both removed from the unit approach when a desired object is present. For example, 40 pens with a expression price will indeed cost Inr ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.
Here,
Let's use "N" for the price of a platter of nachos and "S" for the price of a 2-liter soda.
The first aspect of the issue reveals that:
=> 5N + 2S = 67.87
The second component of the issue reveals the following to us:
=>2N + S = 27.94
=> S = 27.94 - 2N
When we use this expression in place of S in the first equation, we obtain:
=> 5N + 2(27.94 - 2N) = 67.87
When we simplify and account for N, we obtain:
=> 5N + 55.88 - 4N = 67.87\sN = 11.99
We can determine S by substituting this number for N in the second equation:
=> 2(11.99) + S = 27.94\sS = 4.98
As a result, a 2-liter soda costs $4.98 and a platter of nachos costs $11.99.
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One lap of a race track is 1 km.
Work out the total distance, in kilometres (km), of 2 laps of the race
track.
Give your answer as an integer or as a mixed number in its simplest form.
The total distance of 2 and 1/7 laps of the race track is given as follows:
[tex]3\frac{39}{42}[/tex]
How to obtain the total distance?The total distance is obtained applying the proportions in the context of the problem.
The length of one lap, as a fraction, is given as follows:
1 and 5/6 km = (6 + 5)/6 = 11/6 km.
The number of laps is given as follows:
2 and (1/7) = (14 + 1)/7 = 15/7 laps.
Hence the total distance is given as follows:
11/6 x 15/7 = 165/42.
165 divided by 42 has a quotient of 3 with a remainder of 39, hence the mixed number representing the number of laps is given as follows:
[tex]3\frac{39}{42}[/tex]
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A die is rolled ten times. What is the probability that a prime
number will be rolled every time?
The probability of rolling a prime number every time
The probability of rolling a prime number on a single die is 3/6 or 1/2, since there are three prime numbers (2, 3, 5) out of six possible outcomes.
To find the probability of rolling a prime number ten times in a row, we need to multiply the probabilities together. This is because each roll is independent of the others, so the probability of rolling a prime number on each roll is the same.
So the probability of rolling a prime number ten times in a row is:
(1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 1/1024
Therefore, the probability of rolling a prime number every time a die is rolled ten times is 1/1024.
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if you have any more questions let me know i need help
Answer:
x=6
My best attempt
Step-by-step explanation:
The ratio is 4:5.6 from top to bottom.
We have a ratio of x:8.4
We will make an equation.
4:5.6=x:8.4
Cross multiply:
5.6x=4x8.4
5.6x=33.6
Divide both sides by 5.6:
x=6
Wyatt plays a vides game called Rock Climber. He starts with 100 points. He loses 7 points each time he falls off a rock. Wyatt has fallen off 6 rocks. How many points does he have left? points Submit
The number of points Wyatt has left is 58.
If Wyatt loses 7 points every time he falls off a rock and he falls off 6 rocks, he will lose a total of 42 points (7 x 6 = 42). To find out how many points he has left, we can subtract 42 from his starting points of 100:
100 - 42 = 58
Therefore, Wyatt has 58 points left after falling off 6 rocks in the Rock Climber video game.
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PLEASE HELP ME IM TIMED
Answer:
12
Step-by-step explanation:
g(-4)=2(-4)^2+4(-4)-8
g(-4)=8
f(8)=2(8)-4
f(8)=12
a printer makes more than three copies of labels every hour graph the number of books made in 2 hours.
The following linear system of equations is given x1, x2 and x3 are unknowns.
3x1-x3 = 3
x1-x2+x3 = 6
-x1+34+2x3 = 0
a) Apply Gaussian elimination to solve for the unknowns
b) Apply Gauss-Jordan elimination to solve for the unknowns.
c) Apply LU decomposition to solve for the unknowns
d) Use matrix-inverse based solution (x=A^-1b) to solve for the unknowns. Use elimination approach to identify matrix inverse.
a) To solve for the unknowns using Gaussian elimination, follow these steps:
1. Multiply the first equation by -1 and add it to the second equation to get x2 = 7 + x3.
2. Multiply the first equation by -3 and add it to the third equation to get x3 = 3.
3. Substitute x3 = 3 into the first equation to get x1 = 2.
b) To solve for the unknowns using Gauss-Jordan elimination, follow these steps:
1. Multiply the first equation by -1 and add it to the second equation to get x2 = 7 + x3.
2. Multiply the first equation by -3 and add it to the third equation to get x3 = 3.
3. Substitute x3 = 3 into the second equation to get x2 = 4.
4. Substitute x3 = 3 and x2 = 4 into the first equation to get x1 = 2.
c) To solve for the unknowns using LU decomposition, follow these steps:
1. Compute the LU decomposition of the coefficient matrix A.
2. Solve Ly = b using forward substitution to get y = [1, 4, 3]^T.
3. Solve Ux = y using backward substitution to get x = [2, 4, 3]^T.
d) To solve for the unknowns using matrix-inverse based solution, follow these steps:
1. Compute the inverse of the coefficient matrix A.
2. Multiply the inverse of A with b to get x = [2, 4, 3]^T.
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A construction crew is lengthening a road that originally measured 51 miles. The crew is adding one mile to the road each day. The length, L (in miles), after d days of construction is given by the following.
L= 51+d
What is the length of the road after 38 days?
Answer: 89 miles
Step-by-step explanation:
Well, if the construction crew added one mile every day for 38 days, then the formula would look like this.
L = 51 + (38)
51 + 38 = 89
L = 89 miles
1. he marks of Calculus I in the final examination in a private college are normally distributed with a mean of 45 marks and a standard deviation of 10 marks. (a) If a student is chosen at random, find the probability that his/her mark is less than 52. 0.75$ (b) If the college has 220 students who sat for the examination, find the number of students whose marks are between 45 and 55. 75 (c) Find the percentage of students whose marks exceed 40. 69.15%
2. A survey on the study habits of 1000 HSM students shows that 550 use reference books, 750 have regular study times and all those who use reference books have regular study time. A HSM student is chosen at random; what is the probability that the student
a) only has regular study time?
b) either has a regular study time or uses
reference books?
c) neither studies regularly nor uses reference
books?
1. (a) Using a z-table, we can find the probability corresponding to this z-score, which is 0.758. Therefore, the probability that a student's mark is less than 52 is 0.758. (b) To find the number of students whose marks are between 45 and 55, we need to calculate the z-scores for 45 and 55 . The z-score for 45 is (45 - 45) / 10 = 0, and the z-score for 55 is (55 - 45) / 10 = 1. (c) The probability corresponding to this z-score is 0.3085. Therefore, the percentage of students whose marks exceed 40 is 1 - 0.3085 = 0.6915, or 69.15%. 2. (a) So, the probability that a student only has regular study time is 750/1000 - 550/1000 = 200/1000 = 0.2. (b) The probability that a student either has a regular study time or uses reference books is 750/1000 + 550/1000 - 550/1000 = 750/1000 = 0.75. (c) The probability that a student neither studies regularly nor uses reference books is 1 - 0.75 = 0.25.
Therefore, the probability that a student's mark is between 45 and 55 is 0.8413 - 0.3413 = 0.5. Since there are 220 students in the college, the number of students whose marks are between 45 and 55 is 0.5 * 220 = 110.
To find the probability that a student's mark is less than 52, we need to calculate the z-score for 52 using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. So, z = (52 - 45) / 10 = 0.7.
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