Find the directions in the xy-plane in which the function f(x,y) = 15--y has zero change at the point 26.4.13) Expens the directions in term of unit vectors What is the unit vector in a direction of zero change with a positive x-component?

Answer:

17

Step-by-step explanation:

If Rin pulls out 1 blue marble from the bag then total marbles left in the bag now= 18 − 1 = 17

Now Misaki pulls out a marble: Probability of red marble= 3/17

probability of blue marble= 4/17

Answer:17

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

5(x – 10) = 30 – 15x

Distribute

5x -50 = 30-15x

Add 15x to each side

5x+15x – 50 = 30 – 15x+15x

20x-50 = 30

Add 50 to each side

20x-50+50 = 30+50

20x = 80

Divide by 20

20x/20 = 80/20

x =4

Gregs's mom baked 24 cookies, while Vinnie's mom baked 36 cookies. Brad's mom baked twice as much as Greg's mom, resulting in a total of 48 cookies. The total number of cookies that were baked is found by adding the number of cookies that each mom baked:

24 + 36 + 48 = 108.

The cookies can be divided into 3 groups of 36, 4 groups of 27, 6 groups of 18, 9 groups of 12, 12 groups of 9, 18 groups of 6, 27 groups of 4, or 36 groups of 3 cookies. Since there are more than 100 words required, let's talk about the importance of fractions and equivalent ratios.

In conclusion, Greg's mom baked 24 cookies, Vinnie's mom baked 36 cookies, and Brad's mom baked 48 cookies, resulting in a total of 108 cookies. The cookies can be divided into fractions or equivalent ratios to distribute them evenly among the children.

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Using the definition of slope, the points (-2 , 6), (0 , 2), and (1 , 0) are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

m = (y2 - y1)/(x2 - x1)

Getting the slope of each pair of points:

(-2 , 6) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - 6)/(0 - -2)

m = -4/2

m = -2

(0 , 2), and (1 , 0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 2)/(1 - 0)

m = -2/1

m = -2

(-2 , 6) and (1 , 0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 6)/(1 - -2)

m = -6/3

m = -2

Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is equal with each other, then they are collinear.

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Answer:

\(21n^{2} - 35\)

Step-by-step explanation:

\(7n(-2n+5n-5)\)

\(-14n^{2} + 35n^{2} - 35\)

\(21n^{2} - 35\)

Answer:

x = 119°

Step-by-step explanation:

The angle between chord KJ and chord LM is half the sum of the arcs intercepted by the angle and its vertical angle, that is

\(\frac{1}{2}\) (75 + 47)° = 0.5 × 122° = 61°

This angle and x are adjacent angles and sum to 180° , then

x = 180° - 61° = 119°

Step-by-step explanation:

Let Jack's present age be x

Hence, his fathers present age=4x

Jacks age after 5 years= (x+5)

Jacks Fathers age after 5 years= (4x+5)

We know.. that the difference between their ages fives years later is 10.. hence

4x+5-(x+5)=10

4x+5-x-5=10

3x = 10

x= 3.3 years old...

Hence,

Jacks present age = 3.3 years

Fathers present age= 13.2 years...

Hope it helps .. I know that the answer comes in decimals... but the questions' like that..

Answer:

see below

Step-by-step explanation:

length to width ratio is 2

so 5 1/2 ÷ 2 = 11/2 ÷ 2 , simplify  = 11/4 = 2 3/4

6 2/5 *2 = 32/5 *2 = 64/5 =12 4/5

Answer:

.86 square feet.

Step-by-step explanation:

Directions

You have to do this by following directions.

1, Go one circle to your right. Make it the top circle.

2, Drop a perpendicular from the circle you've just been directed to.

3. Draw until you hit the center of the circle below the circle you started your line from. You should get a square.

Find the area of the square.

Each side of the square is 2 feet. You get that because the side of the square = 2 radii -- one radii from the two circles in the center.

Area Square = s^2

Area Square = 2 * 2

Area Square = 4

Find the are of the circles

The 4 central circles that are touching (2 to the left and 2 to the right)  are each are 1/4 of a full circle. 4 * 1/4 circle Area = 1 full circle.

Area = pi * r^2 = 3.14 * 1^2 = 3.14

Find the area of the star

Area of the star = area of square - area of circle.

Area of the star = 4 - 3.14

Area of the star = .86 sqr feet

The nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

To find a nonzero vector orthogonal to the plane through the points P, Q, and R, we can use the cross product of two vectors that lie in the plane.

Let's find the vectors PQ and PR, which can be found by subtracting the coordinates of P from the coordinates of Q and R:

PQ = Q - P = (-2, 1, 3) - (1, 0, 1) = (-3, 1, 2)

PR = R - P = (4, 2, 5) - (1, 0, 1) = (3, 2, 4)

Next, we'll take the cross product of these two vectors to find a vector orthogonal to the plane:

n = PQ x PR =

[(1)(4) - (2)(2), (2)(-3) - (3)(1), (3)(3) - (2)(-2)]

= [-8, -8, -12]

This vector is orthogonal to the plane through the points P, Q, and R. To make it a nonzero vector, we can scale it to have magnitude 1:

n = [-8, -8, -12] / sqrt((-8)^2 + (-8)^2 + (-12)^2) = [-8/13, -8/13, -12/13]

So, the nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

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The answer to the question is (a) the coefficient of determination.

The coefficient of determination, denoted as R-squared (R²), represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model. It is a statistical measure that indicates the goodness of fit of the regression line to the observed data. R-squared ranges from 0 to 1, where 0 indicates no linear relationship between the variables, and 1 indicates a perfect fit. In simpler terms, R-squared tells us how well the independent variable(s) can predict the dependent variable. It is commonly used to evaluate the strength and reliability of a regression model and understand the percentage of variability in the dependent variable that can be accounted for by the independent variable(s). #spj11

R-squared to assess the goodness of fit in a regression model. It quantifies the proportion of the dependent variable's variability that can be explained by the independent variable(s). R-squared ranges from 0 to 1, with higher values indicating a better fit. Is R-squared an indicator of the regression line's accuracy? Understand how R-squared provides insights into the relationship between variables and helps evaluate the predictive power of your model.

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Answer:

1. C) \(3.6 \, \textrm{cm}\)

2. A) \(4\sqrt{10}\)

Step-by-step explanation:

Utilize the Pythagorean Theorem for both problems:

\(a^2+b^2=c^2\)

where \(a\) and \(b\) are the right triangle's legs (short sides adjacent to the right angle) and \(c\) is its hypotenuse.

1) Form an equation using the above formula.

\(8.7^2 + x^2 = 9.4^2\)

Next, isolate x.

\(x^2 = 9.4^2 - 8.7^2\)

\(x = \sqrt{9.4^2 - 8.7^2}\)

Finally, plug the square root into a calculator and round the result to get:

C) \(3.6 \, \textrm{cm}\)

2) Form an equation using the Pythagorean Theorem.

\(6^2 + x^2 = 14^2\)

Next, isolate x.

\(x^2 = 14^2 - 6^2\)

\(x^2 = 196 - 36\)

\(x^2 = 160\)

\(x = \sqrt{160}\)

Finally, use prime factorization to simplify the square root.

\(x = \sqrt{10 \cdot 16\)

\(x = \sqrt{(2 \cdot 5) \cdot 2^4}\)

\(x = 2^2 \sqrt{2 \cdot 5}\)

A) \(4\sqrt{10}\)

The equation that represents the average of the x-intercepts for f(x) is given by: \(x = (x1 + x2) / 2\)

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

For instance, \(3x + 5 = 14\) is an equation in which \(3x + 5\) and 14 are two expressions that are separated by the 'equal' sign.

The equation that represents the average of the x-intercepts for f(x) is given by:\(x = (x1 + x2) / 2\)
where x1 and x2 are the x-intercepts of the quadratic function f(x).

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The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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First find the center, then graph all the points that are at a distance of R units from that center.

A circle of radius R is the set of all points that are at a distance R from a given point (the center of the circle).

So to graph it, we need to know these two things, radius and center.

Once we do, first we graph the center on the coordinate plane.

Once we find the center, we can find all the poiints that are at a distance of R units from our center, so we need to graph these. Once we do, we will have the graph of our circle on the coordinate plane.

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Answer:

Point-slope form of equation of a line that passes from (-1,3) and (0,0) is given as y-3=-3(x+1).

Slope-intercept form of equation is given as y=-3x.

Step-by-step explanation:

In the question, it is given that the line passes from (-1,3) and (0,0).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

Step 1 of 2

Passing point of line is (-1,3).

Hence, \($x_{1}=-1$\) and

\($$y_{1}=3 \text {. }$$\)

Also, Passing point of line is (0,0).

Hence, \($x_{2}=0$\) and

\($$y_{2}=0 \text {. }$$\)

Substitute the above values to find the slope of line which is given by \($m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$\)

\($$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{0-3}{0-(-1)} \\m &=\frac{-3}{1} \\m &=-3\end{aligned}$$\)

Hence, slope of the line is -3

Step 2 of 3

It is obtained that m=-3

\($y_{1}=3$\)

and \($x_{1}=-1$\)

Substitute the above values in point-slope form of equation given by \($y-y_{1}=m\left(x-x_{1}\right)$\)

\($y-y_{1}=m\left(x-x_{1}\right)$\\ $y-3=-3(x-(-1)$\\ $y-3=-3(x+1)$\)

Hence, point-slope form of equation given as y-3=-3(x+1).

Step 3 of 3

Solve y-3=-3(x+1) to write it as slope-intercept form given by y=mx+c

\($y-3=-3(x+1)$\\ $y-3=-3 x-3$\\ $y=-3 x-3+3$\\ $y=-3 x$\)

Hence, slope-intercept form of equation is given as y=-3x.

Answer:

x = -1/7

y = 6/7

Step-by-step explanation:

factor a 5 out of the first equation to work with smaller numbers:

y - 8x = 2

let y = -6x (derived from the second equation)

substitute:  -6x - 8x = 2

-14x = 2

x = -2/14 or -1/7

find 'y':  y - 8(-1/7) = 2

             y + 8/7 = 14/7

              y = 6/7

Answer:

x = -1/7, y = 6/7

System: \(\left \{ {{5y-40x=10} \atop {y+6x=0}} \right.\)

Step-by-step explanation:

The system of equations would be \(\left \{ {{5y-40x=10} \atop {y+6x=0}} \right.\).

To find out what x and y are, choose one of the equation and solve for y. Then, substitute the result for y into the other equation.

5y - 40x = 10 (Add 40x to both sides)

5y = 40x + 10 (Divide both sides by 5)

y = 1/5(40x + 10) (Multiply 40x + 10 by 1/5)

y = 8x + 2 (Substitute this for y in the other equation.)

8x + 2 + 6x = 0 (Add 8x to 6x)

14x + 2 = 0 (Subtract 2 from both sides)

14x = -2 (Divide both sides by 14)

x = -1/7 (Substitute this for x in the y = 8x + 2)

y = 8(-1/7) + 2 (Multiply -1/7 by 8)

y = -8/7 + 2 (Convert 2 into 14/7; show as a single fraction)

y = (-8 + 14)/7 (Add -8 and 14)

y = 6/7 (The system is solved)

Answer:

1. 24.36

2. Do the same thing (follow the steps in the picture)

Step-by-step explanation:

the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

There are no factors of 24 that are prime numbers. A factor of a number is a whole number that divides that number without leaving a remainder. Prime numbers, on the other hand, are numbers that are divisible only by 1 and themselves, and cannot be expressed as the product of any other numbers.

The prime factors of 24 are 2, 2, and 3. We can factorize 24 as 2 × 2 × 2 × 3 or 2^3 × 3. Here, 2 and 3 are both prime numbers, but they are not factors of 24 in isolation. They are only prime factors of 24 when combined in the manner shown.

This fact highlights an important concept in number theory: the uniqueness of prime factorization. Every composite number can be expressed as a unique product of prime numbers. This fundamental theorem of arithmetic is crucial in many areas of mathematics, including cryptography, where it is used to secure communications and protect sensitive information.

In summary, there are no factors of 24 that are prime numbers. However, the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

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Answer: 10, 911,000,000

Step-by-step explanation:

10,911,000,000 < 11,000,000,000

10,911,000,000 > 10,910,099,999

The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

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(a) The rule for the function is = -280/11 + 187.27, (b) Julia is 409.09 miles west of Denver after having driven for 16 hours, (c) Julia cannot have a negative amount of time, (d) the rule is = 11/280 - 187.27/280 and (e) to construct a graph for , plot the two points (0.25, 170) and (3, 100) and draw a line between them

a) The rule for the function can be determined by finding the slope of the line between the two points (0.25, 170) and (3, 100). The slope is (100-170)/(3-0.25) = -280/11.

Therefore, the rule for the function is = -280/11 + b. To find b, plug in one of the points: 170 = -280/11(0.25) + b. Solving for b gives b = 187.27. Therefore, the rule for the function is = -280/11 + 187.27.

b) The meaning of (16) is Julia's position east from Denver after having driven for 16 hours. To find its value, plug in 16 for in the rule: (16) = -280/11(16) + 187.27 = -409.09. Therefore, Julia is 409.09 miles west of Denver after having driven for 16 hours.

c) The meaning of (-141) is Julia's position east from Denver before she started driving, which does not exist because she cannot have a negative amount of time.

d) To determine a rule, we need to find the inverse of the function. The inverse of a function is found by switching the and variables and solving. So, the inverse = -280/11 + 187.27 becomes = -280/11 + 187.27. Solving it gives = ( + 187.27)/(280/11) = 11/280 - 187.27/280. Therefore, the rule for is = 11/280 - 187.27/280.

e) To construct a graph, the two points (0.25, 170) and (3, 100) and draw a line between them. The slope of the line is -280/11 and the y-intercept is 187.27.

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\((-a+3)(a+4)=-a^2-a+12\).

Hope this helps.

Answer:

-a²-a+12

Step-by-step explanation:

-a²+3a-4a+12

-a²-a+12

Trigonometry's sine, cosine, and tangent ratios link the ratio of a right triangle's sides to each angle.

A subfield of mathematics known as trig studies the correlations between triangles' sides and angles. It entails an investigation of the characteristics and purposes of angles as well as the applications of these ideas to practical issues. Using trigonometric functions like sine, cosine, and tangent—which are described in terms of the lengths of the edges of a right triangle—provides the foundation of trigonometry. These functions can be used to solve a variety of triangle-related problems as well as problems involving other geometric shapes by connecting the lengths of a triangle towards the lengths of its sides. In disciplines like engineering, physics, and astronomy, trigonometry is used extensively in daily life.

"Right" is the word that completes the definition.

Trigonometry's sine, cosine, and tangent ratios link the ratio of a right triangle's sides to each angle.

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Answer:

bro its transition

The system of equations -3x + y = 4 and -9x + 5y = -1 has the solution (-3.5 , -6.5).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations. This is what is called as the solution.

Given two equations in x and y,

-3x + y = 4     (equation 1)

-9x + 5y = -1     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -3x + y = 4     ⇒     y = 3x + 4

-9x + 5y = -1     (equation 2)

-9x + 5(3x + 4) = -1

-9x + 15x + 20 = -1

6x = -21

x = -3.5

Substitute the value of x in equation of y and solve for y.

y = 3x + 4

y = 3(-3.5) + 4

y = -6.5

Hence, the solution to the following system of equations is (-3.5 , -6.5).

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Answer:

(-3.5 , -6.5)

Step-by-step explanation:

The displacement of the particle during 1 ≤ t ≤ 9 is approximately 154.67 meters to the right, while the total distance traveled is 305.33 meters.

To find the distance traveled during 1 ≤ t ≤ 9, we split the integral into two parts based on when the velocity is positive and negative. We have:

∫1^3 |v(t)| dt = ∫1^3 -(t^2 - t - 6) dt = [-t^3/3 + t^2/2 + 6t]1^3 = 6

∫3^9 |v(t)| dt = ∫3^9 (t^2 - t - 6) dt = [t^3/3 - t^2/2 - 6t]3^9 = 299.33

Therefore, the total distance traveled is 6 + 299.33 = 305.33 meters.
Hence the displacement of the particle during 1 ≤ t ≤ 9 is approximately 154.67 meters to the right, while the total distance traveled is 305.33 meters.

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The amount of antifreeze that a radiator can hold depends on the size of the radiator.

Radiators come in different sizes and capacities, and the amount of antifreeze that a radiator can hold can range from less than a gallon to several gallons. In order to determine the exact amount of antifreeze that a particular radiator can hold, you would need to consult the manufacturer's specifications for that radiator or take the radiator to a mechanic who can assess its capacity. Additionally, the amount of antifreeze required may also depend on the make and model of the vehicle that the radiator is installed in.

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Step-by-step explanation:

i hope this helps you somehow