Answer:
18
X + 12 = 30
-12. -12. Subtract 12
X = 18. Answer
Answer:
42
Step-by-step explanation:
What is the image point of (−8,−1) after a translation left 3 units and up 4 units?
Answer:
i think it is
( 3,-11) or
(-4,-4) as
the
answer
kingda ka in new jersey is the tallest and fastest roller coaster in the world. riders travel at an average speed of 61 feet per second for 3118 feet. They reach a maximum speed of 187 feet per second.
a. if x represents the total time that the roller coaster is in motion for each ride, write an expression to represent the situation.
b. how long is the roller coaster in motion?
Answer:
(a) 3118=61*t
(b) The amount of time the roller coaster is in motion is 51.11 seconds.
Step-by-step explanation:
Speed is a magnitude that expresses the relationship between the space traveled by an object, the time used for it and its direction. In other words, speed is associated with the change in position of a body over time and can be expressed as:
[tex]speed=\frac{distance}{time}[/tex]
Then the distance traveled can be expressed as:
distance=speed*time
(a) If x represents the total time that the roller coaster is in motion for each ride, the average speed is 61 feet per second and the distance is 3118 feet then the expression to represent the situation is:
3118=61*x
(b) To calculate the amount of time the roller coaster is moving, you simply need to solve the expression found in (a). Dividing 61 to both sides:
[tex]\frac{3118}{61} =\frac{61*x}{61}[/tex]
51.11 seconds=x
The amount of time the roller coaster is in motion is 51.11 seconds.
rose has a combined total of 25 nickels, dimes, and quarters that together have a value of $3.20. the number of dimes exceeds the number of nickels by 4. how many coins of each kind does she have?
Rose has 5 nickels, 9 dimes, and 10 quarters. To solve the problem, we used a system of equations, where the first equation was the sum of the number of nickels, dimes, and quarters, and the second equation was the value of the coins.
Let the number of nickels = x
Let the number of dimes = y
Let the number of quarters = z
According to the given question, rose has a combined total of 25 nickels, dimes, and quarters:
Therefore, x + y + z = 25
The total value of coins is $3.20.
So, the value of x nickels, y dimes and z quarters is:
$0.05x + $0.10y + $0.25z = $3.20
The number of dimes exceeds the number of nickels by 4. Therefore, y = x + 4
Now we have three equations: x + y + z = 25
$0.05x + $0.10y + $0.25z = $3.20y = x + 4
Solving for the equations: x + (x + 4) + z = 25
2x + 4 + z = 25
2x + z = 21$0.05x + $0.10(x + 4) + $0.25z = $3.20
0.05x + 0.10x + 0.40 + 0.25z = 3.20
0.15x + 0.25z = 2.80
Substituting 2x + z = 21 in 0.15x + 0.25z = 2.80, we get:
x = 11, y = 15, z = -1
This means that Rose has 11 nickels, 15 dimes and -1 quarters.
However, she can't have -1 quarters, so let's check again.
x = 11, y = 15, z = -1 (from 2x + z = 21)
5x + 10y + 25z = 800 (multiply by 100 to get rid of decimal places)
$0.05x + $0.10y + $0.25z = $3.20
$0.55x + $1.5y + $0.25z = $7.20
Add the equations: 5x + 10y + 25z = 800
$0.55x + $1.5y + $0.25z = $7.20
5.5x + 15y + 2.5z = 72
But we also know that: x + y + z = 25
If we add 10 to both sides, we get: x + y + z + 10 = 35
If we multiply both sides by 0.05, we get:
$0.05x + $0.10y + $0.25z + $0.50 = $1.75
But we know that: $0.05x + $0.10y + $0.25z = $3.20
Therefore, $3.20 + $0.50 = $3.70, which is the value of 10 quarters.
This means that z = 10, and we can substitute it into x + y + z = 25 to get:
y = x + 4y + x + z = 25
2x + 14 = 25
2x = 11
x = 5, y = 9
Therefore, Rose has 5 nickels, 9 dimes, and 10 quarters.
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What will be the ones place digit of the square of 269?
Answer:
hi
Step-by-step explanation:
it wuold be nine
Answer: The ones place digit would be 9
Triangle A B C is reflected across the line of reflection m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated about point B prime 270 degrees to form triangle A double-prime B double-prime C double-prime. Which rule describes the composition of transformations that maps ΔABC to ΔA"B'C"?
Answer: D
Step-by-step explanation: edge 2022
Answer:
B - a reflection across line n followed by a 270° rotation about point P
Step-by-step explanation:
got it correct on edge
the standard form of a linear equation -2x+3=4y
Answer:
ax+b=0
Step-by-step explanation:
linear equation
How to find 6x = 50 + x ?
Answer: 10
Step-by-step explanation:6x-50=x
6x-50-(x)=0
We add all the numbers together, and all the variables
5x-50=0
We move all terms containing x to the left, all other terms to the right
5x=50
x=50/5
x=10
the graph of the line x y=b is a perpendicular bisector of the line segment from (0,3) to (6,9). what is the value of b?
Answer:
Step-by-step explanation:
the graph of the line x y=b is a perpendicular bisector of the line segment from (0,3) to (6,9). what is the value of b?
Consider the following system of linear equation in three unknowns x1, x2, x3:
4x1+2x2-x3=9
-5x1+9x2+x3=0
2x1-2x2+10x3=12
Perform the LU decomposition of A i.e. A=LU, where A is the coefficient matrix of system (1) above, L is a lower triangular matrix with ones on the main diagonal, and U is upper triangular.
The LU decomposition of the given Matrix A is given as A = LU = [1 0 0][-5/4 1 0][1/2 -2/19 1][4 2 -1][-5 9 1][2 -2 10]
The LU Decomposition of a matrix is a way of representing it as the product of a lower triangular matrix L and an upper triangular matrix U. The process of LU Decomposition can be done in various ways.
One common method for LU Decomposition is called the Gaussian Elimination method or the Crout method.
The LU decomposition of a given matrix is a factorization of a matrix A into two matrices L and U such that L is a lower triangular matrix and U is an upper triangular matrix.LU Decomposition of the given system of linear equation in three unknowns x1, x2, x3 is performed as follows
:Given system of linear equations is:4x1+2x2−x3=9−5x1+9x2+x3=02x1−2x2+10x3=12The corresponding matrix form of the given system of equations is given by A x = B where A is the coefficient matrix, x is the column matrix of unknowns (x1, x2, x3) and B is the column matrix of constan ts.The coefficient matrix A of the given system of equations is given as follows:A = 4 2 -1 -5 9 1 2 -2 10We will perform the Gaussian elimination method to find the LU decomposition of matrix A.To find the LU decomposition, we will perform the following steps:
Step 1: Write the augmented matrix [A|B].
Step 2: Convert the matrix [A|B] to the upper triangular form using the Gaussian elimination method.
Step 3: Extract the lower triangular matrix L from the upper triangular matrix U, and rewrite the upper triangular matrix U.
Step 1: Augmented Matrix [A|B]The augmented matrix [A|B] of the given system of linear equations is given as follows:[4 2 -1 9 | 0][-5 9 1 0 | 0][2 -2 10 12 | 0]
Step 2: Upper Triangular FormUsing the Gaussian elimination method, we will reduce the augmented matrix [A|B] to the upper triangular form as follows:[4 2 -1 9 | 0][-5 9 1 0 | 0][2 -2 10 12 | 0]
We will multiply the first row by -5/4 and add it to the second row. Similarly, we will multiply the first row by 1/2 and add it to the third row. The resulting matrix is given as follows:[4 2 -1 9 | 0][0 19/4 3/4 45/4 | 0][0 0 101/19 39/19 | 0]We have obtained the upper triangular matrix U of the given matrix A. The corresponding lower triangular matrix L is obtained as follows:
Step 3: Lower Triangular Matrix LThe lower triangular matrix L is obtained as follows:L = [1 0 0][-5/4 1 0][1/2 -2/19 1]We have obtained the lower triangular matrix L and upper triangular matrix U for the given system of linear equations using the Gaussian elimination method.
Therefore, the LU decomposition of the given matrix A is given as A = LU = [1 0 0][-5/4 1 0][1/2 -2/19 1][4 2 -1][-5 9 1][2 -2 10]
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The sum of three consecutive integers is 201. Find the integers
Answer:
66 67 68
Step-by-step explanation:
to solve for x youfirst add the integer together and the x variable together then u subtract 3from each side followed by dividing 3in each side
The three integers are 66, 67 and 68.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
We have,
The sum of three consecutive integers is 201.
let the three consecutive integers are x, x+1 and x+2.
So, x + x + 1 + x +2=201
3x + 3 = 201
3x = 198
x = 66
Thus, the three numbers are 66, 67 and 68.
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Why
is i= 0.058?
17. A business owner wants to build a reserve fund. To have \( \$ 50,000 \) in the fund at the end of 10 years, the amount the owner will need to invest annually, assuming an annual return of \( 5 \%
The annual investment amount required to accumulate a reserve fund of $50,000 in 10 years, assuming an annual return of 5%, is approximately $3,720.
To calculate this, we can use the formula for the future value of an ordinary annuity: \[FV = P \times \left( \frac{{(1 + r)^n - 1}}{r} \right),\] where \(FV\) is the future value (desired reserve fund amount), \(P\) is the annual investment amount, \(r\) is the annual interest rate (in decimal form), and \(n\) is the number of years. Rearranging the formula to solve for \(P\), we have: \[P = \frac{{FV \times r}}{{(1 + r)^n - 1}}.\]Substituting the given values into the formula, we get: \[P = \frac{{50000 \times 0.05}}{{(1 + 0.05)^{10} - 1}} \approx 3720.\]Therefore, the business owner would need to invest approximately $3,720 annually to accumulate a reserve fund of $50,000 at the end of 10 years, assuming a 5% annual return.
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A truck is hauling earth from a construction site. The truck has the following specifications: T
Bank density
Loose density
110 pcf
100 pef
The productivity, in bank measure (yd
3
/hr), of this operation is most nearly: (A) 38.8 (B) 35.3 (C) 32.3 (D) 29.5
The productivity of the truck in bank measure is most nearly 32.3 (option C).
To calculate the productivity of the truck in bank measure, we need to convert the loose density to bank density. Bank measure refers to the volume of material when it is compacted or in its natural state, while loose measure refers to the volume of material when it is loose or not compacted.
The formula to convert loose density to bank density is as follows:
Bank Density = Loose Density / (1 + Moisture Content)
Since the moisture content is not provided in the question, we assume it to be zero for simplicity. Therefore, the bank density is equal to the loose density.
Next, we need to calculate the truck's productivity in bank measure. The formula for productivity is:
Productivity = Truck Capacity / Cycle Time
However, the truck capacity and cycle time are not provided in the question. Therefore, we cannot directly calculate the productivity.
Given that we have the specifications of the truck's density, we can make an estimation based on industry standards. A common truck capacity for earth hauling is around 20 cubic yards. The cycle time can vary depending on factors such as loading and dumping time, travel distance, and road conditions. For estimation purposes, let's assume a cycle time of 30 minutes (0.5 hours).
Using these values, we can calculate the productivity as follows:
Productivity = Truck Capacity / Cycle Time
Productivity = 20 / 0.5
Productivity = 40 cubic yards per hour
However, the productivity is measured in bank measure (yd³/hr), so we need to adjust the result based on the bank density.
Adjusted Productivity = Productivity * (Loose Density / Bank Density)
Adjusted Productivity = 40 * (100 / 110)
Adjusted Productivity ≈ 32.3 cubic yards per hour (bank measure)
Therefore, the productivity of the truck in bank measure is most nearly 32.3 (option C).
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Which of these ordered pairs is a solution of 3x−y=12? Choose all that apply.
The height of a plant was 133 centimeters. After one week, it grew by 37 centimeters, and after three more weeks, the new height was 238 centimeters.
How much did the plant grow in three weeks?
______ centimeter(s)
The plant grew by approximately 41.75 centimeters in the following three weeks.
The initial height of the plant was 133 centimeters. After one week, it grew by 37 centimeters, so its height became:
133 + 37 = 170 centimeters
After three more weeks, the new height was 238 centimeters. If we subtract the initial height (133 centimeters) from the final height (238 centimeters), we can find the total growth in four weeks:
238 - 133 = 105 centimeters
We can then subtract the growth in the first week (37 centimeters) to find the growth in the following three weeks:
105 - 37 = 68 centimeters
Therefore, the plant grew by 68 centimeters in three weeks.
Alternatively, we can find the average growth rate per week by dividing the total growth in four weeks by the number of weeks:
(238 - 133) / 4 = 26.25 centimeters per week
Multiplying the growth rate by the number of weeks in the following three weeks, we can find the expected growth in that period:
26.25 * 3 = 78.75 centimeters
Subtracting the initial growth from the expected growth, we can find the growth in the following three weeks:
78.75 - 37 = 41.75 centimeters
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American Heart Association Recipes >... Find and save recipes that are not only delicious and easy to make but also heart- healthy. All of our recipes are lower in sodium, lower in fa
The American Heart Association provides a variety of delicious and easy-to-make recipes that are not only tasty but also heart-healthy.
These recipes are designed to be lower in sodium and lower in fat, making them a great choice for maintaining a healthy heart.
To find and save these recipes, you can visit the American Heart Association's official website or use their mobile application. They offer a wide range of recipes in various categories, including breakfast, lunch, dinner, snacks, and desserts. You can search for recipes based on your dietary preferences, ingredients, and cooking time.
By incorporating heart-healthy recipes into your meal planning, you can enjoy flavorful and nutritious meals while taking care of your cardiovascular health.
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How do you convert 0.67(7 repeating) to a fraction
Answer:
Step-by-step explanation:
The answer is 67%.
To turn a decimal into a fraction you must move the decimal over two places to the left.
For example: .87% = 87%
24 lb turkey for 15 people
Answer:
Each person gets 1.6 of the turkey
Step-by-step explanation:
24/15 = 1.6
HELP I WILL GIVE BRAINLIEST HELP HELP
Answer:-3/2
Step-by-step explanation:
3. An hollow metallic ball is created that has an outer diameter of 10 centimeters and a thickness of 1 centimeter in all directions. Which of the following expressions could be used to calculate the volume of metal used in units of cubic centimeters? (1) 47 (10³-8³) 4 (2) ½-½π(10³ −8³) 3 (3) 4π(5³ −4³) (4) — π(5³-4²³) A spherical baseball has a radius of 1.47 inches and weighs 11 grams per cubic inch. Which of the following is closest to the weight of the entire baseball? (1) 128 grams (3) 146 grams (2) 135 grams (4) 158 grams
The expression that can be used to calculate the volume of metal used in the hollow metallic ball is (3) 4π(5³ - 4³). The weight of the entire baseball is closest to (4) 158 grams.
To calculate the volume of metal used in the hollow metallic ball, we need to find the difference between the volumes of two spheres: the outer sphere and the inner sphere. The outer diameter of the ball is 10 centimeters, so its radius is 5 centimeters. The inner diameter is obtained by subtracting the thickness from the outer diameter, which gives us 8 centimeters for the inner diameter and a radius of 4 centimeters.
The expression (3) 4π(5³ - 4³) represents the volume of metal used. Here, (5³ - 4³) calculates the difference between the volumes of the two spheres, and 4π multiplies this difference by 4π to obtain the final volume in cubic centimeters.
For the weight of the baseball, we are given that it weighs 11 grams per cubic inch, and we need to find the weight of the entire baseball. The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius.
The radius of the baseball is given as 1.47 inches. Using the formula for the volume of a sphere, we can calculate the volume of the baseball. Multiplying the volume by the weight per cubic inch, which is 11 grams, will give us the weight of the entire baseball.
Among the given options, (4) 158 grams is the closest value to the weight of the entire baseball.
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A carton has a length of 1 2/3 feet, width of 1 1/6 feet, and height of 1 1/5 feet. What is the volume of the carton?
Answer:
Step-by-step explanation:
Volume= (length)(width)(height)
step 1: make sure all the measurements have the same unit (ft)
step 2: convert mixed fractions to improper fractions
1 2/3= 5/3 1 1/6= 7/6 1 1/5 = 6/5
multiply the length by width and height
(5/3)(7/6)(6/5)
=7/3 ft^3
What is the product?
Answer:
d. is the correct answer
You want to estimate how many fish there are in a pond. Suppose you cature 135 fish, tag them, and throw them back into the pond. After a couple of days, you go back to the pond and capture 540 fish, of which 27 are tagged.
An estimate for the number of fish in the pond is ............................... fish.
One of the common methods of estimating the number of individuals in a particular population is called the Mark-Recapture method. The method is also known as the capture-mark-recapture method, or CMR, and is widely used in ecology, population biology, and wildlife management.
In order to apply the Mark-Recapture method, the following conditions have to be met:
Marking or tagging of individuals must not cause any harm or effect on their behavior. The marking or tagging of individuals must be permanent, and the marks must remain visible or detectable until the end of the study.
The population must be closed or well-mixed, meaning that no immigration or emigration occurs within the period of the study. The probability of capturing a marked individual in the second sample must be the same as the probability of capturing an unmarked individual. After the sample capture, the marked and unmarked individuals must be thoroughly mixed and distributed before the second sample is taken.
To estimate the total population size, the following equation is used:
N = (n1 * n2) / m
where N is the estimated population sizen1 is the number of individuals marked in the first samplen2 is the number of individuals in the second sample m is the number of marked individuals recaptured in the second sample.
Using the values provided in the problem:
First sample: 135 individuals tagged
Second sample: 540 individuals captured, 27 of which are taggedn1 = 135n2 = 540m = 27
Using the formula:
N = (n1 * n2) / m
N = (135 * 540) / 27
N = 2,700
Therefore, an estimate of the total population size in the pond is 2,700 fish.
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the volume of the parallelepiped determined by the three-dimensional vectors $\bold{a}$, $\bold{b}$, and $\bold{c}$ is 11. find the volume of the parallelepiped determined by the vectors $\bold{a} 2 \bold{b}$, $\bold{b} 2 \bold{c}$, and $\bold{c} 2 \bold{a}$.
The volume of the parallelepiped determined by the vectors \boldsymbol{a} 2 \boldsymbol{b}, \boldsymbol{b} 2 \boldsymbol{c}, and \boldsymbol{c} 2 \boldsymbol{a} is 121.
To find the volume of the parallelepiped determined by the vectors \boldsymbol{a} 2 \boldsymbol{b}, \boldsymbol{b} 2 \boldsymbol{c}, and \boldsymbol{c} 2 \boldsymbol{a}, we need to use the scalar triple product formula. The scalar triple product is the dot product of the vector \boldsymbol{a} 2 \boldsymbol{b} with the cross product of vectors \boldsymbol{b} 2 \boldsymbol{c} and \boldsymbol{c} 2 \boldsymbol{a}.
Let's denote the volume of the original parallelepiped as [tex]V_1[/tex] and the volume of the new parallelepiped as [tex]V_2[/tex].
According to the given information,[tex]V_1[/tex] = 11. We want to find [tex]V_2[/tex].
The formula for the scalar triple product is:
\boldsymbol{a} \cdot (\boldsymbol{b} \times \boldsymbol{c}) = [tex]V_1[/tex]
Now, let's calculate the scalar triple product for the new parallelepiped:
(\boldsymbol{a} 2 \boldsymbol{b}) \cdot ((\boldsymbol{b} 2 \boldsymbol{c}) \times (\boldsymbol{c} 2 \boldsymbol{a})) = [tex]V_2[/tex]
We can simplify this expression further using properties of scalar triple product and dot product:
(\boldsymbol{a} \cdot (\boldsymbol{b} \times \boldsymbol{c}))^2 = [tex]V_2[/tex]
Substituting the value of [tex]V_1[/tex]:
[tex](V_1)^2 = V_2[/tex]
Substituting [tex]V_1 = 11[/tex]:
[tex](11)^2 = V_2\\121 = V_2[/tex]
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Question
The volume of the parallelepiped determined by the three-dimensional vectors $\bold{a}$, $\bold{b}$, and $\bold{c}$ is 11. find the volume of the parallelepiped determined by the vectors $\bold{a} 2 \bold{b}$, $\bold{b} 2 \bold{c}$, and $\bold{c} 2 \bold{a}$.I know that you can take the determinant and alter it, and I know that the parallelepiped volume is determined by a determinant. However, I can't figure this out. Any solutions?
A bottle of water of 34 liters of capacity, has only half of liquid, what amount of liters of water has the bottle?
f(x)= sin(x-90°)
circle the value of f(0°)
a= 1
b= 0
c= -1/2
d= -1
Answer:
d = -1
Step-by-step explanation:
Step 1: Define
f(x) = sin(x - 90°)
f(0) is x = -
Step 2: Substitute and Evaluate
f(0) = sin(0° - 90°)
f(0) = sin(-90°)
We know from the unit circle that -90° is equal to 270° or 3pi/2. The value of 3pi/2 is (0, -1). sin is always y, so our answer is -1.
What is the y-intercept "b" of the linear function y= -1x - 3?
Answer:
y=3-1x not answering to question
What is an angle with no point?
Answer:
Adjacent angles
Step-by-step explanation:
The following table shows the time it takes to ride the elevator to three different floors of a skyscraper.
Answer:
the answer would be no hope this helps
Answer: it is proportional
Step-by-step explanation:
I got it right on khan
8x + 4y = 3x - 6 is a Linear equation or not?
Yes, it is, as it has variables with the degree one, and a linear equation only has variables that are of degree one.
Answer:
No it's not linear equation
Find the seventh term of the geometric sequence from the given information. Express the term as an integer or simplified fraction.
a2 = -7 and r = 1/2
The seventh term of the geometric sequence is -7/32. The nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term
To find the seventh term of a geometric sequence, we can use the formula:
[tex]an = a1 * r^(n-1),[/tex]
where an represents the nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.
In this case, we are given a2 = -7 and r = 1/2.
Using the formula, we can find a1 by substituting n = 2:
a2 = a1 * (1/2)^(2-1).
We know that a2 = -7, so we can rewrite the equation:
-7 = a1 * (1/2)^1,
-7 = a1 * (1/2).
Now, let's solve for a1:
a1 = -7 * (2/1),
a1 = -14.
We have found that the first term, a1, is equal to -14.
Now, we can find the seventh term, a7, by substituting n = 7 into the formula:
a7 = (-14) * (1/2)^(7-1),
a7 = (-14) * (1/2)^6,
a7 = (-14) * (1/64),
a7 = -14/64,
a7 = -7/32.
Therefore, the seventh term of the geometric sequence is -7/32.
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