Answer:
9
Step-by-step explanation:
Radius = x
The triangle in the given image is a right angled triangle.
By Pythagoras theorem,
x² + 12² = ( x + 6 )²
x² + 144 = x² + 36 + 12x
x² - x² = 36 - 144 + 12x
0 = - 108 + 12x
12x = 108
x = 108 / 12
x = 9
Jakim deposited $10,000 in an account that earned simple interest annually.
- He did not make additional deposits nor withdrawals.
-At the end of 7 years, the balance was $12,100.
What is the interest rate on this account?
Answer:
Step-by-step explanation:
Simple interest is a method for calculating the percentage of interest paid on a sum over a predetermined time period at a predetermined rate. The annual simple interest rate on the principal amount of 10000 at the end of 7 years would be 3%.
What exactly is simple interest?In simple interest, the principal amount doesn't change. Simple interest is a clear-cut and simple method for figuring out how much money has earned interest. It is a way to figure out how much interest will be charged.
Simple interest can be computed by multiplying the principal amount by the rate multiplied by the time period. In banks and other financial institutions, simple interest is frequently used to complete a variety of calculations. The total amount of cash that was spent on interest during the course of the loan is described.
Simple Interest = ( Principal × Rate × Time ) / 100
First, we need the Simple Interest (S.I)
Total = Principal + Simple Interest
T = P + S.I
$10,000 = $12,100. + S.I
S.I = $12,100 - $10,000
S.I = 2100
Simple Interest = (Principal × Rate × Time) / 100
S.I = (P × R × T) / 100
2100 = (10000 × R × 7) / 100
2100 = 70000R / 100
2100 = 700R
R = 2100 / 700
R = 3
Thus, The annual interest rate is 3%
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The following table shows the breakdown of opinions for both faculty and students in a recent survey about the new restructuring of the campus to include an honors college. find the probability that a randomly selected person is either in favor of or opposed to the restructuring. express your answer as a fraction.
Given:
The number of people are in the favor of restructuring is 50.
The number of people are in the oppose of restructuring is 82 .
The total number of persons is 182.
The probability of persons is in the favor of restructuring is,
\(\begin{gathered} \text{Probability}=\frac{Desired\text{ outcomes}}{t\text{otal outcomes}} \\ P_F=\frac{50}{182} \end{gathered}\)The probability of persons is in the oppose of restructuring is,
\(P_O=\frac{82}{182}\)To find the probability that a randomly selected person is either in favor of or opposed to the restructuring,
\(\begin{gathered} P(\text{Favor or oppose)=}P_F+P_O \\ =\frac{50}{182}+\frac{82}{182} \\ =\frac{50+82}{182} \\ =\frac{132}{182} \\ =\: \frac{66}{91} \end{gathered}\)Answer:
\(P=\frac{66}{91}\)Find the volume of the sphere:
A. 452.4 cubic meters
B. 904.8 cubic meters
C. 150.8 cubic meters
D. 36 cubic meters
Work Shown:
r = 6 = radius
V = volume of a sphere of radius r
V = (4/3)*pi*r^3
V = (4/3)*pi*6^3
V = 904.77868423386
V = 904.8
I used my calculator's stored version of pi (instead of something like pi = 3.14)
The units "cubic meters" can be abbreviated to m^3 or \(m^3\)
The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.
The volume of a sphere can be calculated using the formula:
V = \(4/3 * \pi * r^3\),
Where V is the volume and r is the radius of the sphere.
\(\pi\) = 3.14
The radius of the sphere (r) = 6m
Plugging in the given radius of 6m into the formula, we get:
V = (4/3) * \(\pi\) * (6^3)
V = 1.333 * \(\pi\) * 216
V = 1.333 * 3.14 * 216
V = 4.1866 * 216
V = 904.8 cubic meters
Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8 cubic meters.
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3. Han and Tyler are following a polenta recipe that uses 5 cups of water for every 2
cups of cornmeal.
• Han says, "I am using 3 cups of water. I will need 1 1
- cups of cornmeal."
o Tyler says,"I am using 3 cups of cornmeal. I will need 7> cups of water."
Do you agree with either of them? Explain your reasoning.
Simplify (-5)^4•[(-5)²]5• (-5)^4
Answer:
\((-5)^{4}.[(-5)^{2}]^{5}.(-5)^{4}=(-5)^{4}.(-5)^{10}.(-5)^{4}=(-5)^{18}\)
Step-by-step explanation:
Answer:
(-5)^18
Step-by-step explanation:
The equation will look like this after you simplify[(-5)^2)^5]
(-5)^4 x (-5)^10 x (-5)^4
Now you add up all the exponents and keep it the same:
(-5)^18
Hope this helps!
Data where the difference between data values has meaning but there is no defined starting point
Examples of such data include stock prices, economic indicators, and meteorological data such as temperature, wind speed, and barometric pressure.
These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.
1. Data where the difference between data values has meaning but there is no defined starting point can be defined as data that is not linearly dependent.
2. Examples of such data include stock prices, economic indicators, and meteorological data. These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.
3. Stock prices, economic indicators, and meteorological data all have different scales and can move in different directions, making it difficult to track the exact difference between data points.
4. Despite this, these types of data still allow for meaningful analysis and can be used to make predictions and draw conclusions.
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Write an equation for the following:
A number increased by 6 is 22.
Its in the form of a picture
The equations that are parallel to the given line are C. 6x + 2y = -4 and D. 6x - 2y = -4.
What is the slope-intercept form?
The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
Two lines are parallel if they have the same slope. The given line y = 3x - 5 is in slope-intercept form, which means its slope is 3.
A line in slope-intercept form has the equation y = mx + b, where m is the slope and b is the y-intercept. Therefore, any line of the form y = 3x + c, where c is a constant, will have a slope of 3 and be parallel to the given line.
Let's check each of the given equations to see which ones are of this form:
A. y = 3x - 7: This equation has the same slope as the given line, but it is not in the form y = 3x + c. Therefore, it is not parallel to the given line.
B. y = -3x - 5: This equation has a slope of -3, which is not the same as the slope of the given line. Therefore, it is not parallel to the given line.
C. 6x + 2y = -4: We can rearrange this equation to slope-intercept form by solving for y:
2y = -6x - 4
y = -3x - 2
This equation has the same slope as the given line, so it is parallel to the given line.
D. 6x - 2y = -4: We can rearrange this equation to slope-intercept form by solving for y:
-2y = -6x - 4
y = 3x + 2
This equation has the same slope as the given line, so it is also parallel to the given line.
Therefore, the equations that are parallel to the given line are C. 6x + 2y = -4 and D. 6x - 2y = -4.
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What is the Quadratic Equation of x^2-6x+9=0 A) (x+6) (x+6) B)(x-9) (x+9) C) (x-2)(x+3) D)(x-3) (x-3)
The quadratic equation of x2-6x+9=0 is C) (x-2)(x+3).
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
This equation is an example of a quadratic equation, which is an equation of the form ax2+bx+c=0, where a, b, and c are real numbers, and a is not equal to 0. In this equation, a is equal to 1, b is equal to -6, and c is equal to 9. To solve this equation, we need to use the quadratic formula, which states that the solutions to the equation are x= -b ± √b2-4ac / 2a. Therefore, the solutions to this equation are x= -(-6) ± √(-6)2-4(1)(9) / 2(1), which simplifies to x=3 ± √3 /2, or x=3 ± √9 /2. This simplifies to x=3 ± √3, or x=3 ± 1. Therefore, the solutions to this equation are x=2 and x=4. The factored form of this equation is (x-2)(x+3), which is option C.
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find the inverse of 5/9(F-32)?
Answer:
inverse of 5/9(F-32)
Step-by-step explanation:
Which of the following is a member of the solution set of -6 < x ≤ -1
A. -7
B. -6
C. -1
D. 3
pls help
Solve the following system of equations for x using elimination:
4x + y = 2
x - y = 3
-2.
3
Using the information in the diagram, what is the height of the tree to the nearest foot?
45 ft
54 ft
60 ft
135 ft
Answer:
60 ft
Step-by-step explanation:
a = 90
b = 108ft
the base angle can be found by using sin(x) = 120/108x2
=> x = 33.7 degrees
To find height, use tan(33.7) = Opp/ Adjacent = x / 90
=> x = 60.02 or 60 ft
anthony runs a bicycle courier company that charges $3 for delivery plus $0.50 per mile. Which equation matches this relationship
Answer:
c = .5m + 3
Step-by-step explanation:
i need help with this question asap
If triangle ABC is a 30-60-90 degree triangle and we know the following
point A is (-4,-2)
point B is (4,-2)
then we must find point C.
if the angle of C is 90 degrees and point C is in quadrant 1 then where is point C?
Therefore , the solution of the given problem of triangle comes out to be Point C has coordinates. (4,0).
What precisely is a triangle?A polygon is a hexagon if it has two or more extra parts. It is shaped like a simple square. A and B are the only sides of something like this arrangement that can set it apart from a regular triangle. The boundaries remain exactly collinear, nevertheless Euclidean geometry only produces a section rather than a complete cube. Three edges and three angles make up a triangle.
Here,
By using the edge that faces a 60-degree angle, or AB, we can determine the length of BC.
We possess Points A and B are on the same horizontal axis at (-4, -2) and (4, -2), respectively, so AB = 8 (their separation is 8 units).
=>BC = (AB/2) * √(3) = 4 * √(3)
We now need to determine location C's coordinates. As a result, the equation for line BC can be expressed as follows:
=> y - (-2) = -√(3) * (x - 4)
When we simplify this solution, we obtain:
=> y = -√(3)x + 4√(3)
We fix y = 0 and solve for x to locate this point:
=> √(3)x = 4√3 x = 4;
=> 0 = -√3)x + √(3)x
Thus, Point C has coordinates. (4,0).
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What does the complement rule state? Multiple Choice a P(A) = 1 - P(not A) b P(A) = P(A) x P(B) c P(A) = P(A)- P(B) d P(A) = P(A)X + P(B)
The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring.
In other words, the complement rule states that P(A) = 1 - P(not A). Therefore, the correct answer to this question is option a. P(A) = 1 - P(not A).
To summarize, the complement rule is a useful tool for calculating the probability of an event occurring when it is easier to calculate the probability of the event not occurring. By the probability of the event not occurring from one, we can find the For example, if the probability of an event A occurring is 0.6, then the probability of not A occurring (the complement of A) is 1 - 0.6 = 0.4.
So, the complement rule states that the probability of event A occurring is equal to 1 minus the probability of not A occurring subtracting of the event occurring. For example, if the probability of an event A occurring is 0.6, then the probability of not A occurring (the complement of A) is 1 - 0.6 = 0.4.
So, the complement rule states that the probability of event A occurring is equal to 1 minus the probability of not A occurring.
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What is equation easy?
A mathematical equation can be defined in a variety of ways.
Equation that is linear.A quadratic equation.Cubic Formula.Define the term equation?A mathematical equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Equation that is linear.
There could be multiple variables in a linear equation. If a variable's highest power is always 1, an equation is said to be linear. A one-degree equation is another name for it.A quadratic equation.
A second-order equation is this one. At least one of the variables in quadratic equations needs to be raised to exponent 2.Cubic Formula.
Third-order equation.There should be at least one variable raised to exponent 3 in cubic equations.To know more about the equation, here
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find the slope on the line
Answer:
slope is -3
Step-by-step explanation:
change in y over change in x is -3/1
A ball is thrown vertically upward with an initial velocity of 48 feet per second and started from a height of 8 ft off the ground
A ball is thrown vertically upward with an initial velocity of 48 feet per second from a height of 8 ft off the ground.
How high does the ball reach when thrown upward with an initial velocity of 48 ft/s from a starting height of 8 ft?When a ball is thrown vertically upward with an initial velocity of 48 feet per second and starts from a height of 8 feet off the ground, it reaches a maximum height before falling back down.
The ball's upward motion slows down due to the gravitational pull until it comes to a stop at its maximum height.
At this point, the ball begins to descend, accelerating downward due to gravity. The maximum height the ball reaches can be determined using kinematic equations.
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th eproduct of two consecutive odd integers positive is 77 more than twice the larger. find the intergers please. I cannot set up "product" consecutive integers?
the product is x*(x+2)
To find the two consecutive odd integers, let's set up an equation using the given information. Let x be the smaller odd integer, then the next consecutive odd integer is x+2.
The problem states that the product of these two integers is 77 more than twice the larger integer. In equation form, this can be written as:
x * (x + 2) = 2(x + 2) + 77
Now, let's solve for x:
x * (x + 2) = 2x + 4 + 77
x^2 + 2x = 2x + 81
x^2 = 81
To find the value of x, take the square root of both sides:
√(x^2) = √81
x = 9
So, the smaller odd integer is 9. The next consecutive odd integer is 9 + 2 = 11.
Therefore, the two consecutive odd integers are 9 and 11.
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The two consecutive odd integers are 9 and 11.
How to find consecutive integers?To find the two consecutive odd integers whose product is 77 more than twice the larger, we can set up the following equation:
x * (x + 2) = 2(x + 2) + 77
Here, x represents the first odd integer, and x + 2 represents the second consecutive odd integer. Now, let's solve the equation step by step:
1. Expand the equation: x^2 + 2x = 2x + 4 + 77
2. Simplify the equation: x^2 + 2x = 2x + 81
3. Subtract 2x from both sides: x^2 = 81
4. Take the square root of both sides: x = ±9
Since we're looking for positive integers, x = 9. Therefore, the two consecutive odd integers are 9 and 11.
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Will give crown help
Answer:
(2,-8)
Step-by-step explanation:
(2,-8)
Theo rolls a dice 306 times.
Work out an estimate for the number of times Theo rolls an even number
help with number one please need it right now please
I reallly badly need help
Answer:
You can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
Step-by-step explanation:
The above is a cyclic quadrilateral.
What is a cyclic quadrilateral?A Cyclic quadrilateral is having all the vertices of a quadrilateral ( four sided figure) inside a circle, that is a quadrilateral inscribed in a circle.
To find either x or y, we should note:
The sum of opposite angles of a cyclic quadrilateral is 180° or Angles in opposite segment are supplementary.
Therefore,
2x + 2x + 4= 180
4x = 180 - 4
4x = 176
x = 44°
To find y
3y + 8 + y = 180°
4y = 180 - 8
4y = 172
y = 43°
Therefore, you can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
The Running Aces card team won $548 dollars playing in poker tournaments last year. The winnings were split evenly among the p players.
How much money did each player receive?
Write your answer as an expression.
Since the question doesnt give the amount of players on the team we can just say that each player was given 548/p dollars.
PLEASE PLEASE HELP REALLY QUICK❤️❤️
Answer:
Sorry
Step-by-step explanation:
Sorry I don't know the answer because I haven't learned this yet. Hope you get your answer!
What is actually true of all numbers and variables?
Answer: they are all ideas that are mutally agreed on.
Step-by-step explanation:
My math teacher told me this
Help pls? Let f(x)=x3-3x2+2 and g(x)=x2-6x+11 enter the value of x such that f(x)=g(x)
If both the functions f(x) and g(x) are equal. Then the value of the variable will be 3.
What do you understand by the term y = f(x) ?The term f(x) is used to represent a function of x i.e. a function with only one independent variable ' x '.
The functions are given below.
f(x) = x³ - 3x² + 2 and g(x) = x² - 6x + 11
If both the functions f(x) and g(x) are equal.
f(x) = g(x)
x³ - 3x² + 2 = x² - 6x + 11
Simplify the equation, then we have
x³ - 4x² + 6x - 9 = 0
Then the equation is solved by the calculator, then we have
x = 3
Then the value of the variable will be 3.
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1. When is it best to solve a system of equations using graphing?
2. When is it best to solve a system of equations using substitution?
3. When it is best to solve a system of equations using elimination? When it is
1. You can solve a system of equations using graphs when there are no decimals or fractions in the equations. This can allow you to almost precisely plot a graph, and determine the values of the variables.
2. You can use the substitution method when one (or both) of the equations is already solved for one of the variables.
3. Elimination is best used when the equations are written in the form Ax + B = C, and also when the coefficients are values not equal to 1.
If the objective function is to be maximized and all the variables involved are nonnegative, then the simplex method can be used to solve the linear programming problem. True or False
The simplex method is a widely used algorithm for solving linear programming problems, which involve optimizing a linear objective function subject to linear constraints. False.
However, the simplex method does not explicitly require the variables to be nonnegative in order to find a solution.
The simplex method starts with an initial feasible solution and iteratively improves it by moving along the edges of the feasible region, ultimately reaching the optimal solution. During the iterations, the variables can take any real values, including negative values.
That being said, some variations of the simplex method, such as the dual simplex method, have been developed specifically to handle problems with nonnegativity constraints. These variations can be used when variables are required to be nonnegative.
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