The line and circle intersect at the point (4, 7).
Given the line equation: 4x + 7y = 65
Substituting the coordinates of the point (4, 7) into the equation:
4(4) + 7(7) = 16 + 49 = 65
The point (4, 7) satisfies the equation of the line.
Now let's consider the equation of the circle centered at (0, 0) with radius 8:
The equation of a circle centered at (h, k) with radius r is given by:
(x - h)² + (y - k)² = r²
The equation of the circle is x² + y² = 8²
x^2 + y^2 = 64
Substituting the coordinates of the point (4, 7) into the equation:
4² + 7² = 16 + 49 = 65
The point (4, 7) satisfies the equation of the circle as well.
Since the point (4, 7) satisfies both the equation of the line and the equation of the circle, we can conclude that the line and circle intersect at the point (4, 7).
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If $4.50 will buy 3 bus tickets, how many bus tickets can be bought with $18?
Answer:
12 Bus Tickets
Step-by-step explanation:
18 / 4.50 = 4 x 3 Bus tickets = 12 Tickets
What is the definition of a tangent in math
Answer:
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. ... The word "tangent" comes from the Latin tangere, "to touch".
Step-by-step explanation:
A straight line touching a curve at a single point without crossing it there is tangent.
Consider a market served by a monopolist, Firm A. A new firm, Firm B, enters the market and, as a result, Firm A lowers its price to try to drive Firm B out of the market. This practice is known as
Predatory pricing. Predatory pricing occurs when a dominant firm intentionally sets its prices below the cost of production or below its competitors' prices in order to eliminate competition and deter new entrants into the market.
In this scenario, Firm A, the monopolist, engages in predatory pricing by reducing its prices in response to the entry of Firm B into the market. The aim is to make it financially difficult for Firm B to survive and eventually force it out of the market. By lowering its prices, Firm A hopes to attract customers away from Firm B and regain its monopoly power.
Predatory pricing is considered an anti-competitive practice and is often illegal in many jurisdictions. It can harm competition, limit consumer choice, and lead to higher prices in the long run. Regulatory bodies and competition authorities closely monitor such practices and may take legal action against firms found engaging in predatory pricing.
Overall, predatory pricing is a strategy employed by dominant firms to protect or strengthen their market position by driving out competitors. However, it is important for regulators to enforce antitrust laws to ensure fair competition and protect the interests of consumers and smaller market players.
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Sky zone charges a flat fee of $15 plus $6 per person to jump for one hour. if Gabe was charged $75 at Sky Zone, how many people, p, did he pay for?
Answer:
10 people--------------------------------
As per information given, the equation for total cost for p people is:
C = 6p + 15, where C- total cost, p - number of peopleSubstitute 75 for C and solve for p:
75 = 6p + 156p = 75 - 156p = 60p = 10Gabe paid for 10 people.
There are 10 people, p, did he pay for.
Now, We get;
the equation for total cost for p people is:
C = 6p + 15,
where C- total cost,
And, p - number of people
Hence, Substitute 75 for C and solve for p:
75 = 6p + 15
6p = 75 - 15
6p = 60
p = 10
Thus, There are 10 people, p, did he pay for.
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What is the value of 3.5 (11) + 1.9 (11) + 1.6 (11)
40
77
4,096
9,317
Step-by-step explanation:
the joint pdf of x and y is f(x,y) = x y, 0 < x < 1; 0 < y < 1. are x and y independent?
Since the joint pdf \(\(f(x,y)\)\) cannot be expressed as the product of the marginal pdfs \(\(f_X(x)\) and \(f_Y(y)\),\)we conclude that x and y are not independent.
What is the determination of independence?
The determination of independence refers to the process of assessing whether two or more random variables are statistically independent of each other. Independence is a fundamental concept in probability theory and statistics.
When two random variables are independent, their outcomes or events do not influence each other. In other words, the occurrence or value of one variable provides no information about the occurrence or value of the other variable.
To determine whether x and y are independent, we need to check if the joint probability density function (pdf) can be expressed as the product of the marginal pdfs.
The joint pdf of \(x\) and \(y\) is given as:
\(\[ f(x,y) = xy, \quad 0 < x < 1, \quad 0 < y < 1 \]\)
To determine the marginal pdfs, we integrate the joint pdf over the range of the other variable. Let's start with the marginal pdf of x
\(\[ f_X(x) = \int_{0}^{1} f(x,y) \, dy \]\[ = \int_{0}^{1} xy \, dy \]\[ = x \int_{0}^{1} y \, dy \]\[ = x \left[\frac{y^2}{2}\right]_{0}^{1} \]\[ = x \left(\frac{1}{2} - 0\right) \]\[ = \frac{x}{2} \]\)
Similarly, we can calculate the marginal pdf of y:
\(\[ f_Y(y) = \int_{0}^{1} f(x,y) \, dx \]\[ = \int_{0}^{1} xy \, dx \]\[ = y \int_{0}^{1} x \, dx \]\[ = y \left[\frac{x^2}{2}\right]_{0}^{1} \]\[ = y \left(\frac{1}{2} - 0\right) \]\[ = \frac{y}{2} \]\)
Since the joint pdf \(\(f(x,y)\)\) cannot be expressed as the product of the marginal pdfs\(\(f_X(x)\\)) and \(\(f_Y(y)\)\), we conclude that x and y are not independent.
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Which property should Remus use to solve the equation below? 7 q = 49 division property of equality addition property of equality subtraction property of equality identity property of equality.
Answer:
Division Property
Step-by-step explanation:
He needs to divide both sides by 7 to find the value of q
The division property of equality should Remus used to solve the given equation and this can be determined by using the given data.
Given :
Equation is \(7q = 49\).
The following steps can be used in order to determine the property that Remus use to solve the given equation:
Step 1 - Write the given equation.
\(7q = 49\)
Step 2 - The arithmetic operations can be used in order to evaluate the given equation.
Step 3 - Using the division property of equality the value of 'q' can be determined.
\(q = \dfrac{49}{7}\)
\(q = 7\)
Therefore, the correct option is A).
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Which choice shown describes
A)
vertical angles
B)
congruent angles
C)
complementary angles
D)
supplementary angles
Answer: supplementary angles
Step-by-step explanation: add them both you get 180
what is the slope or the line going through (0,0) (6,8) A: -6/8 B: -3/4 C: 3/4 D: 8/6
Start at (0,0). To get to the other point, you must move up 8 units and move to the right 6 units.
slope = rise/run = (change in y)/(change in x) = 8/6
Or you could use the slope formula
m = (y2-y1)/(x2-x1)
m = (8-0)/(6-0)
m = 8/6
Normally I would reduce, but your teacher has decided not to.
8/6 reduces to 4/3 when you divide both parts by 2.
i-Ready
Ron is paid $1,500 every month plus an additional $100 bonus for every tractor he sells, 2. Which equation represents the total amount of money, y, Ron makes each
month?
PLEASE ANSWER ASAP!
Answer: y= 100x +1500
Step-by-step explanation:
The 1500 value never changes, so it doesn’t need a variable
The 100 value will change based on how many he sells, so it needs a variable
Answer:
its the first one.
Step-by-step explanation:
the 1500 stays the same so it would be 100×how ever many tractors so 100z+1500
Which geometric construction depicts a plane?
Answer:
Letter C does
Step-by-step explanation:
Because A is a line, B is a line segment, and D is a ray.
Answer:
Letter C
Step-by-step explanation:
1. A is a line,
2. B is a line segment,
3. D is a ray.
i need your help plz say fast
What is the distance from 10 to 0?
A. 10, because [10] = 10
B. 10, because 1101 = -10
C. 0. because [10] = 0
D. -10, because 10] = -10
-
Answer:
A. 10, because [10] = 10
(this is right if the brackets mean absolute value)
Answer:
Step-by-step explanation:
A. 10, because [10] = 10
(this is right if the brackets mean absolute value)
Please help with 19 and 20 find domain and range
List the steps to calculate the slope/rate of change using a calculator.
A right triangle has a leg of length 13 yards and a hypotenuse of length 23 yards. Find the length of the other leg.
Answer:
the length of the other leg is 4sqrt(24) yards. This can also be simplified as 8sqrt(6) yards.
Step-by-step explanation:
Let's use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the legs (the other two sides).
In this problem, one leg has a length of 13 yards, and the hypotenuse has a length of 23 yards. Let's call the length of the other leg x.
Using the Pythagorean theorem, we get:
23^2 = 13^2 + x^2
Simplifying and solving for x, we get:
x^2 = 23^2 - 13^2
x^2 = 384
x = sqrt(384)
x = sqrt(16 * 24)
x = 4sqrt(24)
Therefore, the length of the other leg is 4sqrt(24) yards. This can also be simplified as 8sqrt(6) yards.
A tennis ball has a diameter of about 3 inches. What is the approximate volume of the cylindrical container if it holds three tennis balls? A. About 64 in³ B. About 27 in³ C. 108 in³ D. 82 in³
The approximate volume of the given cylindrical container which has 3 balls is 63.62 in³, under the condition that tennis ball has a diameter of about 3 inches. Then, the required answer is 64 in³ which is Option A.
Now
The volume of a tennis ball is approximately
\(4/3 * \pi * (diameter/2)^{3}\)
=\(4/3 * \pi * (1.5)^{3}\)
= 14.137 in³.
Therefore, 3 balls are present in the container.
The diameter of a tennis ball = 3 inches,
Radius = 1.5 inches.
The height of the cylindrical container can be evaluated by multiplying the diameter of a tennis ball by three
Now, three tennis balls are kept on top of each other.
Then, the height of the cylindrical container
3 × 3 = 9 inches.
The radius = 1.5 inches.
The volume of a cylinder = \(V = \pi * r^2 * h\)
Here,
V = volume,
r = radius
h = height.
Staging the values
\(V = \pi * (1.5)^{2} * 9\)
= 63.62 in³.
The approximate volume of the given cylindrical container which has 3 balls is 63.62 in³, under the condition that tennis ball has a diameter of about 3 inches. Then, the required answer is 64 in³ which is Option A.
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Sally’s employer pays for 38% of her annual health insurance premium of $4,350.00. Sally pays the remaining balance by having it deducted in equal amounts from her 26 paychecks throughout the calendar year. How much will Sally have deducted from each paycheck? a. $63.58 b. $103.73 c. $137.75 d. $207.46
Answer:
B. 103.73
Step-by-step explanation:
which equation has the solution x=4: 4x=20 x/2=8 x+8=3x x =x+5/2
Answer:
x+8=3x
Step-by-step explanation:
4x=20
4x/4=20/4
x=5
The solution to the first equation is x=5.
x/2=8
2(x/2)=2(8)
x=16
The solution to the second equation is x=16.
x+8=3x
x+8-x=3x-x
8=2x
8/2=2x/2
x=4
The solution to the third equation is x=4.
x=x+5/2
x-x=x+5/2-x
-x=5/2
x=-5/2
The solution to the fourth equation is x=-5/2.
The equation x+8=3x has the solution to x=4.
Step-by-step explanation:
4x = 20
x = 20/4 = 5
x/2 = 8
x = 8 x 2 = 16
x + 8 = 3x
8 = 3x - x
8 = 2x
8/2 = x
4 = x
x = x + 5/2
2x = 5/2
x = 5/2 x 2
x = 5
from a point 100m from a building the angles of elevation to the top and the bottom of a flagpole atop the building are 54.5 degrees and 51.8 degrees. how tall is the flagpole?
From a point 100m from a building the angles of elevation to the top and the bottom of a flagpole atop the building are 54.5 degrees and 51.8 degrees. Therefore, the height of the flagpole is 125.6m.
we can use the trigonometric ratios of Sine, Cosine, and Tangent.
First, we need to draw a right triangle with the given information.
The triangle will have two sides:
the 100m side and the side to the flagpole. We can use the angle of elevation of 54.5 degrees to calculate the side of the triangle opposite the flagpole.
To do this, we use the Tangent ratio and solve for the side opposite the flagpole (the height of the flagpole):
Tangent(54.5) = Height/100
Height = 100*Tangent(54.5)
Height = 100*1.256
Height = 125.6m
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What is the Y and x intercept of 9X-6Y= 72
Answer: The y-intercept is -12
The x-intercept is 8
Step-by-step explanation: Factor out 3
Divide all by 3 to simplify.
9x - 6y = 72 is equivalent to
3x - 2y = 24
At this point, you can substitute 0 for x and solve for y
3(0) -2y = 24. -2y/-2 = 24/-2
y = -12
And substitute 0 for y and solve for x.
3x -2(0) = 24. 3x/3 = 24/3
x = 8
OR Change to slope intercept form:
y = mx + b. b is the y intercept.
-2y = -3x + 24. Solve for y.
Divide all by-2
y = 3x/2 - 12.
The y-intercept is -12
To find the x-intercept, substitute 0 for y and solve for x.
0 = 3x/2 -12 Add 12 to both sides.
12 = 3x/2. Multiply both sides by 2/3
8 = x
The x-intercept is 8
20= -x + (x squared)
solve for x
In one particular suburb 30 families own a boxer. If there are 50 families that own a dog in general then what percentage of dog owners have a boxer. Round your answer to the nearest whole number if necessary.
Answer:
60%
Step-by-step explanation:
Do 30/50
What are the domain and range of the function F(x) = |x| * 0.015, for x > 0 (sale)
F(x) = |x| *0.005, for x < (return)
Domain: For sales, x > 0 (positive values); for returns, x < 0 (negative values).
Range: F(x) ≥ 0 (non-negative values).
The given function is defined as follows:
For x > 0 (sale): F(x) = |x| * 0.015
For x < 0 (return): F(x) = |x| * 0.005
The domain of the function is the set of all possible input values, which in this case is all real numbers. However, due to the specific conditions mentioned, the domain is restricted to positive values of x for the "sale" scenario (x > 0) and negative values of x for the "return" scenario (x < 0).
Therefore, the domain of the function F(x) is:
For x > 0 (sale): x ∈ (0, +∞)
For x < 0 (return): x ∈ (-∞, 0)
The range of the function is the set of all possible output values. Since the function involves taking the absolute value of x and multiplying it by a constant, the range will always be non-negative. In other words, the range of the function F(x) is:
For x > 0 (sale): F(x) ∈ [0, +∞)
For x < 0 (return): F(x) ∈ [0, +∞)
In conclusion, the domain of the function F(x) is x ∈ (0, +∞) for sales and x ∈ (-∞, 0) for returns, while the range is F(x) ∈ [0, +∞) for both scenarios.
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please help me solve this and ad how you did it as well thank you
Answer:14.42
How to get it:Use Pythagorean Theorem to solve this problem. Since a squared plus b squared =c squared and we have an and c we can work backwards. Start by squaring 17 (17x17) which would be 289. Then do 9 squared (9x9) to get 81. Subtract 289-81 to get 208, square root this for your answer 14.4222 round to 14.42. You can check this by doing 14.4222 squared plus 9 squared then square root it and you should get approximately, but not exactly 17.
Please help!! 13 points, will mark brainliest!! How to calculate \(cos (x)=\frac{6}{15}\)?
I'm doing a trig question; trying to find angle XYZ, and I think the formula for the answer is C = \(\frac{A}{H}\), which as stated in the title, I think in this situation is \(Cos(x)=\frac{6}{15}\).
I don't know what I'm doing wrong, or if I've done the whole question wrong, but no scientific calculators will give me an answer because it says Cos is already defined. I know for sure the answer isn't 0.4, which was a guess I made. The entire question is attached below.
Answer:
66.4°
Step-by-step explanation:
Let ∠XYZ be x°.
Given the adjacent side, XY, and the hypotenuse side,YZ, we use cosine.
\( cosθ= \frac{adj}{hyp} \\ cosx° = \frac{6}{15} \)
To find the value of x°, take the inverse of cosine.
\( x°\\ = cos^{ - 1} (\frac{6}{15} ) \\ = 66.4° \: (1 \: d.p.)\)
Thus, ∠XYZ= 66.4°
*Given 2 sides, we can find the measure of an angle in a right- angled triangle by taking the inverse of the trigonometry function.
Answer:
0;0;2;9;8;4
Step-by-step explanation:
(2)^(3)
36.481;2.5
-3*(-2/3)-1
8;1;2;9;0;4
0;0;2;9;8;4
what is the probability that the waiter will earn a total of less than $450 in tips when he waits on 40 parties (round answer to 4 decimal places)?
The probability that the waiter will earn less than $450 in tips when he waits on 40 parties is 0.2364. This means that there is a 23.64% chance that the waiter will make less than $450 in tips.
The probability that the waiter will earn less than $450 in tips when he waits on 40 parties can be calculated using the binomial distribution. The binomial distribution is used to calculate the probability of success in a series of independent events. In this case, the probability of success is the probability that the waiter will earn less than $450 in tips.The number of independent events, or trials, is 40, since the waiter will serve 40 parties. The probability of success for each trial is the expected average tip amount divided by the total amount of tips the waiter is trying to earn. The expected average tip amount is $11, and the total amount of tips the waiter is trying to earn is $450, so the probability of success for each trial is 0.024.Using the binomial distribution formula, the probability that the waiter will earn less than $450 in tips when he waits on 40 parties is 0.2364. This means that there is a 23.64% chance that the waiter will make less than $450 in tips.
\(p = (n! / (x! * (n-x)!) * p^x * (1-p)^(n-x))\)
where
n = 40 (number of parties)
x = 450 (desired tip amount)
p = 0.1 (probability of earning a tip of $10)
p = (40! / (450! * (40-450)!) * 0.1^450 * (1-0.1)^(40-450))
p = 0.2364
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Lily withdrew 2/5 of her savings from the bank. She spent $ 420 of it and
had $ 28 left. How much was her total savings in the bank at first?
Choose the correct simplification of (6x − 5)(2x2 − 3x − 6). 12x3 28x2 21x 30 12x3 − 28x2 − 21x 30 12x3 28x2 − 21x 30 12x3 − 28x2 − 21x − 30.
The correct simplification of (6x − 5)(2x2 − 3x − 6) is 12x^3 - 28x^2 - 21x + 30.
To simplify the expression (6x - 5)(2x^2 - 3x - 6), we first need to distribute the terms inside the parentheses. And then using the distributive property, we multiply each term of the first expression (6x - 5) by each term of the second expression (2x^2 - 3x - 6) and combine like terms. The simplified expression is obtained by multiplying the coefficients and adding the exponents of like terms. Therefore, the correct simplification is 12x^3 - 28x^2 - 21x + 30.
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let f and g have continuous first and second derivatives everywhere. if f(x) ≤ g(x) for all real x, which of the following must be true?
If f (x) < g(x) for all real 1; The expression that must be true is I f'(x)sg'(x) for all real x II. f'(x)≤g'(x) for all real x III. f(x)dx ≤ [8(x)dx is option D. I and II only
How did we determine which is true?I. f(x) and g(x) have continuous first and second derivatives everywhere, so by the mean value theorem, there exists a point c in the interval (a, b) such that f'(c) = (f(b) - f(a)) / (b - a) and g'(c) = (g(b) - g(a)) / (b - a). Since f(x) < g(x) for all x, we have f(b) - f(a) < g(b) - g(a), so f'(c) < g'(c), and thus, f'(x) < g'(x) for all x.
II. f(x) and g(x) have continuous first and second derivatives everywhere, so by the mean value theorem, there exists a point c in the interval (a, b) such that f''(c) = (f'(b) - f'(a)) / (b - a) and g''(c) = (g'(b) - g'(a)) / (b - a). Since f'(x) < g'(x) for all x, we have f'(b) - f'(a) < g'(b) - g'(a), so f''(c) < g''(c), and thus, f''(x) < g''(x) for all x.
III. This statement is not necessarily true. The definite integral of f(x)dx is equal to the area between the curve and the x-axis, and the definite integral of g(x)dx is equal to the area between the curve and the x-axis. The definite integral of a function does not depend on the value of the function at each point, but on the overall shape of the curve, so it is not guaranteed that f(x)dx ≤ g(x)dx just because f(x) < g(x) for all x.
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The complete question goes thus:
Let f and g have continuous first and second derivatives everywhere. If f (x) < g(x) for all real 1; which of the following must be true? I f'(x)sg'(x) for all real x II. f'(x)≤g'(x) for all real x
III. f(x)dx ≤ [8(x)dx
(A) None
(B) I only
(C) III only
(D) I and II only
(E) I, II, and III