Answer:
Center = (7, - 5)
Radius = 3
Step-by-step explanation:
\( {x}^{2} + {y}^{2} + 14x - 10y + 65 = 0 \\ {x}^{2} + 14x + {y}^{2} - 10 + 65 = 0 \\ ( {x}^{2} + 14x + {7}^{2}) - {7}^{2} + ({y}^{2} - 10y + {5}^{2}) \\- {5}^{2} + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 - 25 + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 + 40= 0 \\ (x + 7)^{2} + (y - 5)^{2} - 9= 0 \\ (x + 7)^{2} + (y - 5)^{2} = 9 \\ (x + 7)^{2} + (y - 5)^{2} = {3}^{2} \\ equating \: it \: with \: \\ (x - h)^{2} + (y - k)^{2} = {r}^{2} \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3\)
What is the circumference?
7 ft
Answer:
C = 7π
Step-by-step explanation:
Diameter: 7 feet
Formula: C = πd (Circumstance = π × Diameter)
C = 7π
which expression fails to compute the area of a triangle having base b and height h (area is one-half base time height)?
The expression fails to compute the area of a triangle having base b and height h is (1.0 /2.0)*b*h.
Therefore the answer is A.
The correct expression to compute the area of a triangle having base b and height h is (1/2) * b * h, or equivalently, 0.5 * b * h.
Expression A is incorrect because it uses floating-point division, which may result in round-off errors or inaccuracies in the computation.
Expression B is the correct expression because it uses integer division and the division by 2 is clear.
Expression C is also correct because it uses floating-point division and the division by 2.0 is clear.
Therefore, both expressions B and C are correct, and expression D is a correct equivalent form of B and C.
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--The question is incomplete, answering to the question below--
"which expression fails to compute the area of a triangle having base b and height h (area is one-half base time height)?
A. (1.0 /2.0)*b*h
B. (1 /2)*b*h
C. (b*h)/2.0
D. 0.5*b*h"
a conveyor belt carries supplies from the first floor to the second floor, which is 12 feet higher. the belt makes a 60 angle with ground. how far does the supplies
Therefore, the supplies travel approximately 6.928 feet horizontally on the conveyor belt.
To determine how far the supplies travel horizontally on the conveyor belt, we can use trigonometry.
Given that the second floor is 12 feet higher and the belt makes a 60-degree angle with the ground, we can consider the vertical distance (rise) as the opposite side and the horizontal distance (run) as the adjacent side of a right triangle.
Using the trigonometric function tangent (tan), we can calculate the horizontal distance:
tan(60 degrees) = opposite/adjacent
tan(60 degrees) = 12 feet/run
Rearranging the equation to solve for run:
run = 12 feet / tan(60 degrees)
run ≈ 12 feet / 1.732 (rounded to three decimal places)
run ≈ 6.928 feet (rounded to three decimal places)
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Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? A.The margin of error does not change. B.The margin of error increases. C.The margin of error decreases. (d) If the sample size is 17,what conditions must be satisfied to compute the confidence interval? A.The sample must come from a population that is normally distributed and the sample size must be large. B.The sample data must come from a population that is normally distributed with no outliers. C.The sample size must be large and the sample should not have any outliers.
Here we are required to compare the results with the effect of increasing the confidence level on the margin of error. The answer to this comparison is option (B). The margin of error increases with an increase in the level of confidence.
If the sample size is 17, the condition that must be satisfied to compute the confidence interval is the option (B). The sample data must come from a population that is normally distributed with no outliers. What is a Confidence Interval?
A confidence interval is a statistical measure that informs us of the degree of uncertainty that lies in a particular statistic, such as the mean or the proportion, and allows us to make conclusions about a population using sample data. The margin of error is the range of values around the sample statistic within which we are confident that the true population parameter will fall, given a certain level of confidence.
Conclusion: Therefore, The margin of error increases with an increase in the level of confidence, and the sample data must come from a population that is normally distributed with no outliers if the sample size is 17.
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Kaitlyn loves to shop at discount stores. She bought a scarf for $5.90, some thread for $2.09 and a squirt gun for her brother for $11.97. How much did she spend?
Answer:
$19.96.
Step-by-step explanation:
Add $5.90+$2.09+$11.97
One factor of f (x ) = 5 x cubed 5 x squared minus 170 x 280 is (x 7). what are all the roots of the function? use the remainder theorem.
The roots of the function f(x) = 5x³ + 5x² - 170x + 280 are 2, 4 and -7
How to determine the roots of the function?The function is given as:
f(x) = 5x³ + 5x² - 170x + 280
Factor out 5 in the function
f(x) = 5(x³ + x² - 34x + 56)
One of the roots is x + 7.
So, we have:
f(x)/(x + 7) = 5(x³ + x² - 34x + 56)/(x + 7)
Factor the expression on the right-hand side
f(x)/(x + 7) = 5((x - 2)(x - 4)(x + 7))/(x + 7)
Cancel out the common factors
f(x) = 5((x - 2)(x - 4)(x + 7)
Set the function to 0
5((x - 2)(x - 4)(x + 7) = 0
Divide through by 5
(x - 2)(x - 4)(x + 7) = 0
Expand
x - 2 = 0 or x - 4 = 0 or x + 7 = 0
Solve for x
x = 2, or x = 4 or x = -7
Hence, the roots of the function f(x) are 2, 4 and -7
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Find p(0), p(1) and p(2) for the polynomial P(t) = 2 + t + 2t²-t³
p(0)=2
p(1)=2+1+2-1=4
p(2)=2+2+8-8=4
A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light thin cords 1.50 m long.If a minor earthquake occurs, how many swings per second will these fixtures make?
The light fixtures will make approximately 0.914 swings per second during a minor earthquake in San Francisco.
To determine the frequency of the swings per second for the light fixtures, we need to use the formula for the period of a pendulum, which is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the length of the pendulum is given as 1.50 m, and the mass of the bulb is given as 2.35 kg. We can assume that the shade and cord add negligible mass to the system. The acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the values, we get:
T = 2π√(1.50/9.8)
T ≈ 1.093 seconds
The frequency of the swings per second is the reciprocal of the period, so:
f = 1/T
f ≈ 0.914 Hz
It's important to note that this is an approximation, and the actual frequency may vary depending on factors such as the amplitude of the oscillations and the specific characteristics of the earthquake.
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Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.
Answer:
Is this an incomplete question?
Answer:
this isnt a question???
Step-by-step explanation:
Find the area of the circle. Use 3.14 for T. d = 4 m A = [?] m² A = πr² Enter
Step-by-step explanation: I hope this helps.
Answer:
I don't know how to solve for any of the values so please help me!!
samantha used craft wire to make the design shown. she first made the smaller quadrilateral. then she enlarged the smaller quadrilateral to make the larger quadrilateral, using a scale factor that extended the 6-centimeter side by 3 centimeters. what total length of craft wire did samantha use for both quadrilaterals?
The total length of craft wire used by Samantha is 10x + 9
What is the scale factor?
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Let's call the length of the smaller quadrilateral's 6-centimeter side "x".
Then the length of the corresponding side in the larger quadrilateral would be 6+3=9 centimeters, since the scale factor is 3.
To find the total length of craft wire used, we need to add up the lengths of all the sides in both quadrilaterals.
The smaller quadrilateral has four sides, each with a length of x.
The larger quadrilateral also has four sides, but only one of them has a different length (9 cm), while the other three sides are simply 3 times longer than the corresponding sides in the smaller quadrilateral.
So the total length of craft wire used by Samantha is:
4x + 9 + 3x + 3x + 3x
Simplifying this expression, we get:
10x + 9
Hence, the total length of craft wire used by Samantha is:
10x + 9
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a+sign before the blank (Example: −300 ). If you answer is zero, enter " 0 ". (b) Discuss the value of the portfolio with and without the European put options. The lower the stock price, the 3 beneficial the put options. The options are worth nothing at a stock price of $ 3. There is a benefit from the put options to the overall portfolio for stock prices of $
The sign before the blank is "+" (Example: +300). (b) The value of the portfolio with European put options increases as the stock price decreases, providing a protective benefit to the overall portfolio.
The sign before the blank is "+" (Example: +300).
(b) The value of the portfolio with European put options increases as the stock price decreases. The put options provide a protective benefit to the portfolio, as they allow the holder to sell the stock at a predetermined price (strike price).
When the stock price is below the strike price, the put options become valuable as they enable the investor to sell the stock at a higher price than the market value. However, if the stock price is above the strike price, the put options have no value and do not contribute to the portfolio's overall worth.
Therefore, the benefit of the put options is realized when the stock price is below the strike price, and it diminishes as the stock price rises above the strike price.
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Please help me with this problem
Answer:
1.price(dollars) and soccer ball
2.y=30 and x=5
3. I think 5 or 30
Step-by-step explanation:
pa follow po
pa brainlest po
pa heart and 5 star
an square has an area of 54 sq in . the length of each side is the same but not a whole number
Answer:
Answer = 13.5
Step-by-step explanation:
A square has 4 sides
54 / 4 = 13.5
The side of the square will be 7.34 inches.
What is an area?A square is a quadrilateral having all the sides equal to each other and the sum of the angles will be 360 degrees. The area is defined as the space occupied by the shape in a two-dimensional plane.
Given that a square has an area of 54 sq in . the length of each side is the same.
The side of the square will be calculated as below:-
Area of square = Side²
54 = Side²
Side = √54
Side = 7.34 inches.
Therefore, the side of the square will be 7.34 inches.
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Relational operators allow you to ____________ numbers.
a. add
b. multiply
c. compare
d. average
e. none of these
Relational operators allow you to compare numbers. The correct option for the given statement is C.
Compare is an operation that compares two values. Operators are special characters that represent the calculation or comparison in a program. The relational operator is one of the operator types used in programming.
Relational operators are mostly used for comparison. They are used to check whether one value is greater than the other, less than the other, equal to the other, or not equal to the other. Relational operators are primarily used in conditional statements or loops.
The relational operators are:
< (less than)
(greater than)
<= (less than or equal to)
= (greater than or equal to)
== (equal to)
!= (not equal to)
These operators return a boolean value, which is either true or false, depending on the result of the comparison, when used in a program.
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(x-3)2 = 4x
Which of the following is a value of x that satisfies the equation above?
Answer:
x=-3
Step-by-step explanation:
Answer:
x = -3
Step-by-step explanation:
2(x - 3) = 4x
2x - 6 = 4x
2x - 4x = 6
-2x = 6
x = -3
I hope this helps you :)
GIVING BRAINLY TO THE RIGHT PERSON
a store sold 54 t-shirts and 33 sweatshirts yesterday what is the ratio of the number of T-shirts sold to the number of sweatshirts
18:11
11:7
11:18
7:11
Answer:
18:11
Step-by-step explanation:
33÷3=11
54÷3=18
so its 18:11
hope it helped! :D
\(\large\huge\green{\sf{Answer:-}}\)
ratio= 54 t shirt/33 sweatshirt
ratio= 54/33
ratio= 18/11
Which graph represents the function f(x) = |x|– 4?
Answer:
It is graph C
Step-by-step explanation:
Answer: Graph C
Step-by-step explanation: On Edge
wwwwwwwwwwwwwwwweeemem2lm;2rnwejtnrjqktnqrjtnij;tnq43i;ntlhqrntbjqnlrjkebtgqrejtglqrjtnhtnhftkhkntiltnoeiqhtknefiothefwntbqotq43uhi413hto3u so it is 12
Answer: Ehhhhhhh
Hello?
Oof
find the missing side. Round your answer to the nearest tenth.
Answer:
1) 14.7cm
2)13.7cm
Soh Cah Toa
Sin. Cos. Tan.
1) we have a opposite and adjacent so we're going to use tan.
48÷Tan(73)=14.6750
2) we have the hypotenuse and the adjacent so we use cos.
40×cos(70)=13.6808
Which equation represents a line which is parallel to the line y = -7/2x-3
You do not have the options listed, but I will tell you what the line needs:
[] A parallel line will need the same slope.
- The slope is our m in y = mx + b
[] What will this be for our problem:
- \(y=\frac{-7}{2}x-3\)
- Our slope is \(\frac{-7}{2}\)
[] So what will the line look like:
- \(y=\frac{-7}{2}x +?\)
- Since you do not have the options listed, I cannot tell you the answer, but I can tell you the answer will have a slope of \(\frac{-7}{2}\)
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
solve:
-2(6)^x=-432
Answer:
x = 3
Step-by-step explanation:
1) Divide both sides by -2.
\(6^x=\frac{-432}{-2}\)
2) Two negatives make a positive.
\(6^x=\frac{432}{2}\)
3) Simplify \(\frac{432}{2}\) to 216.
\(6^x=216\)
4) Convert both sides to the same base.
\(6^x=6^3\)
5) Cancel the base of 6 on both sides.
x = 3
\(\huge\text{Hey there!}\)
\(\huge\textbf{Equation:}\)
\(\mathbf{-2(6)^x = -432}\)
\(\huge\textbf{DIVIDE -2 to BOTH SIDES:}\)
\(\mathbf{\dfrac{-2(6^x)}{-2} = \dfrac{-432}{-2}}\)
\(\huge\textbf{SIMPLIFY IT!}\)
\(\mathbf{6^x = 216}\)
\(\huge\textbf{Solve for the current exponent:}\)
\(\mathbf{6^x = 216}\)
\(\huge\textbf{Log them:}\)
\(\mathbf{Log \ 6^x = log = 216}\)
\(\huge\textbf{Take the log to both of the sides:}\)
\(\mathbf{x \times log (6) = log(216)}\)
\(\huge\textbf{Convert it:}\)
\(\mathbf{x = \dfrac{log(216)}{log(6)}}\)
\(\huge\textbf{SIMPLIFY IT!}\)
\(\mathbf{x = 3}\)
\(\huge\textbf{Answer:}\)
\(\huge\boxed{\mathsf{x = 3}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)Please help me solve this practice SAT question!
Answer:
t=5
Step-by-step explanation:
∵ (t,17) lies on (x,y) plane y=x²-3x+7,t>0
∴ 17=t²-3t+7
t²-3t+7-17=0
t²-3t-10=0
t²-5t+2t-10=0
t(t-5)+2(t-5)=0
(t-5)(t+2)=0
t=5,-2
t>0
so t=5
(L2) A circle that contains a polygon so that it passes through each vertex of the polygon is a(n) _____ circle.
(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.
A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.
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Simplify the following expression: 7n (-3+ 6n) - 2n (3 + 7n)
Answer:
=28n2−27n
Step-by-step explanation:
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $2; if the number of spots showing is 6 you win $4, and if the number of spots showing is 1,2, or 3, you win nothing. Let X be the amount that you win.
What is the Expectation of X and Variance of
The variance of X is -10/9.
To calculate the expectation and variance of the random variable X, we first need to determine the probabilities associated with each possible outcome.
The possible outcomes are:
- If the number of spots showing is 4 or 5, you win $2.
- If the number of spots showing is 6, you win $4.
- If the number of spots showing is 1, 2, or 3, you win nothing.
The probability of each outcome can be determined by considering that a fair die has 6 equally likely outcomes.
The probabilities are as follows:
- P(X = $2) = P(4 or 5) = 2/6 = 1/3
- P(X = $4) = P(6) = 1/6
- P(X = $0) = P(1, 2, or 3) = 3/6 = 1/2
Now we can calculate the expectation:
E(X) = ($2) * P(X = $2) + ($4) * P(X = $4) + ($0) * P(X = $0)
= (2/3) * $2 + (1/6) * $4 + (1/2) * $0
= 4/3 + 2/6
= 8/6 + 2/6
= 10/6
= 5/3
≈ $1.67
Therefore, the expectation of X is approximately $1.67.
To calculate the variance, we use the formula:
Var(X) = E(X^2) - [E(X)]^2
We can find E(X^2) by calculating the expected value of X^2:
E(X^2) = ($2)^2 * P(X = $2) + ($4)^2 * P(X = $4) + ($0)^2 * P(X = $0)
= 4/3 + 4/6
= 8/6 + 2/6
= 10/6
= 5/3
≈ $1.67
Now we can calculate the variance:
Var(X) = E(X^2) - [E(X)]^2
= 5/3 - (5/3)^2
= 5/3 - 25/9
= 15/9 - 25/9
= -10/9
Therefore, the variance of X is -10/9.
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Solve the given differential equation x^3 y"' - 6y = 0 y(x) = ______ , x > 0
The solution to the given differential equation is:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)
How did we get the value?To solve the given differential equation
\(x^3y'''\ -\ 6y\ =\ 0,\)
we can use the method of power series. Let's assume a power series solution of the form
\(y(x)\ =\ \sum_{n=0}^{\infty} a_nx^n.\)
Differentiating y(x) with respect to x gives:
\(\[y'(x)\ =\ \sum_{n=0}^{\infty} n a_n x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+1) a_{n+1} x^n\]\)
Differentiating again gives:
\(\[y''(x)\ =\ \sum_{n=0}^{\infty} (n+1)na_{n+1}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)a_{n+2}x^n\]\)
Differentiating one more time gives:
\(\[y'''(x)\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)na_{n+2}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n\]\)
Substituting these expressions into the differential equation, we have:
\(\[x^3 \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)
Rearranging the terms and combining like powers of x, we get:
\(\[\sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^{n+3} - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)
Now, let's equate the coefficients of like powers of x to zero:
For n=0:
\(\[(3)(2)(1)a_3 - 6a_0 = 0 \implies 6a_3 - 6a_0 = 0 \implies a_3 = a_0\]\)
For n=1:
\(\[(4)(3)(2)a_4 - 6a_1 = 0 \implies 24a_4 - 6a_1 = 0 \implies a_4 = \frac{1}{4}a_1\]\)
\(For \: n\geq 2:
\[(n+3)(n+2)(n+1)a_{n+3} - 6a_n = 0 \implies a_{n+3} = \frac{6a_n}{(n+3)(n+2)(n+1)}\]
\)
Now we can write the solution as:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{6a_{n-2}}{n(n-1)(n-2)}x^{n+3}\]
\)
Simplifying the series, we get:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_
1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]
\)
Therefore, the solution to the given differential equation is:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)
where a₀ and a₁ are arbitrary constants to be determined based on the initial conditions or boundary conditions given in the problem.
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true or false: if you are given a graph with two shiftable lines, the correct answer will always require you to move both lines.
False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.
In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.
When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.
In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.
However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.
Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.
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A surveyor leaves her base camp and drives 42km on a bearing of 32 degrees. She then drives 25km on a bearing of 154 degrees. How far is she then from her base camp and what is her bearing from it
Answer:
35.7 km and 248.3 °
Step-by-step explanation:
I will attach the diagram to an image to make it easier to understand.
We will use the formula corresponding to the law of cosine
y² = 42² + 28² - (2 * 42 * 25 * cos 58 °)
y² = 2389 - 1112.83 = 1276.17
y = √1276.17
y = 35.72 km
Now, to calculate the surveyor's bearing from her base camp we must use the sine law:
[(Sin 58 °) / y] = [(Sin A) / 42]
Without A = (42 * without 58 °) /35.72
A = sin⁻¹ (0.9971)
A = 85.7 °
Bearing of the surveyor from the base camp = 270 ° - (85.7 ° - 64 °) = 248.3 °