the graph below shows a proportional relationship between x and y. what is the constant of proportionaliy y/x​

Larry has a 0.12 chance of hitting the inner bullseye and thus, his probability of winning is also 0.12.

His probability of hitting the outer bullseye is 0.31, thereby resulting in a winning likelihood of 0.19 when subtracting 0.12.

Pia holds a 0.13 likelihood for hitting the inner bullseye, estimating her overall probability of securing victory as 0.01 - being 0.13 after deducting 0.12. Moreover, her potential of hitting the outer bullseye stands at 0.35, rendering a probability of success to be 0.22 when considering the 0.13 deduction.

Lastly, Carina's chances of making it to the inner bullseye stand at 0.25, indicating a probability of attaining triumph at 0.13 - following a subtraction of 0.12 from 0.25. On top of that, her possibility of striking the outer bullseye rests at 0.49, resulting in an odds of conquering the game as 0.24 after subtracting 0.25.

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To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.

(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.

df/dx = df/dg * dg/dx

df/dx = cos(g(x)) * (2x)

(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.

dg/dx = dg/df * df/dx

dg/dx = 2f(x) * cos(x)

Hence, the derivatives are:

(a) d/dx(f(g(x))) = cos(g(x)) * (2x)

(b) d/dx(g(f(x))) = 2f(x) * cos(x)

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Answer:

In the first equation x is the same as 3 or -8

while in the second one x is within the range of -8 and 3

Step-by-step explanation:

X²+5x-24=0

p=-24

s=5 (8,-3)

(X²+8x)-(3x-24)=0

x(x+8)-3(x+8)=0

(x-3)(x+8)=0

x-3=0 x+8=0

X=3 x=-8

these are the solutions for both equationsbut in equation 2 it will be

-8≤≤

The statement is true as in statistics, the variance (Var) of a random variable is a measure of the spread or dispersion of its values.

For a random sample X₁, X₂, ..., Xn with mean μ and standard deviation δ, the variance of the sample is defined as,

Var(X) = (1/n) × Σ(Xᵢ - μ)²

where Σ denotes the sum from i = 1 to n.

In this case, since the sample has mean μ and standard deviation δ, we can rewrite the variance formula as.

Var(X) = (1/n) × Σ(Xᵢ - u)²

By definition, the standard deviation δ is the square root of the variance, δ = √Var(X).

Therefore, squaring both sides of this equation, we get,

δ² = Var(X)

Therefore, it is true that the variance of a random sample X₁, X₂, ..., Xn with mean μ and standard deviation δ is equal to δ².

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Answer:

y<3

Step-by-step explanation:

It is  y<3 because all areas below y=3 are shaded.

In addition, the line y=3 is dotted, which means it is not part of the inequality (i.e. strict inequality).

If it had been a full line, then it would be y<=3.

Answer:

its 847>×+18 enjoy hope it work

Answer:

133.78684807256

Step-by-step explanation:

step 1: We need the assumption that 44.1 is 100% since it is our output value

step 2: We need to represent the value we seek in x

step 3: From step 1, it follows that 100% = 44.1

step 4: In the same vein x% = 59

step 5: This give us a pair of simple equations:

100% = 44.1 (1)

x% = 59 (2)

step 6: by simplify dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have

\( \frac{100}{x} = \frac{44.1}{59} \)

step 7: Taking the inverse (or reciprocal) of both sides yields

\( \frac{x}{100 } = \frac{59}{44.1} \)

= x = 133.78684807256

Therefore, 59 is 133.78684807256% of 44.1

Answer:

need to find the area of the circular dining room table which has a radius of 3 feet of each person sitting at the table needs about 2 feet of space how many people will fit at the table 3 feet of each person sitting at table needs about two feet of space than about five people will fit at the table

Answer:

A. 6x^{2}+6y^{2}=144

Step-by-step explanation:

Answer:

 2xy4 • (11x2 + 14xy + 17)

Step-by-step explanation:

(((22•(x3))•(y4))+((28•(x2))•(y5)))+(2•17xy4)

(((22•(x3))•(y4))+((22•7x2)•y5))+(2•17xy4)

 (((2•11x3) • y4) +  (22•7x2y5)) +  (2•17xy4)

5.1     Pull out like factors :

  22x3y4 + 28x2y5 + 34xy4  =   2xy4 • (11x2 + 14xy + 17)  

Trying to factor a multi variable polynomial :

5.2    Factoring    11x2 + 14xy + 17

Final result :

 2xy4 • (11x2 + 14xy + 17)

Answer:

6.5

Step-by-step explanation:

For the given transformation of the graph of the function f(x)= -10(x- 2 )² to the graph of g(x) = -2 ( x- 2 )² , dilation is vertical compression compare to parent function.

As given in the question,

Given parent function is :

f(x) = -10 ( x- 2 )²

After transformation the graph of parent function converts to :

g(x) = -2 ( x- 2 )²

      = (1/5) [-10 ( x- 2 )² ]

      = ( 1/5) f(x)

( 1/ 5 ) is less than 1.

Here constant is in between 0 and 1.

Graph of the function g(x) = -2 ( x- 2 )²  is vertically compressed compare to parent graph function f(x) = -10 ( x- 2 )² .

Therefore, for the given transformation of the graph of the function f(x)= -10(x- 2 )² to the graph of g(x) = -2 ( x- 2 )² , dilation is vertical compression compare to parent function.

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The parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3

To create a parametric function that models your location on the Ferris wheel at a given time, we need to come up with equations that describe your horizontal and vertical positions as functions of time.

Let's start with the horizontal position. Since the Ferris wheel rotates counter-clockwise, we know that your position on the wheel will increase as time goes on. We can express this as:

x(t) = 80cos(2πt/120)

Here, t represents time in seconds, and the factor of 2π/120 ensures that the function completes one full cycle (i.e. one trip around the wheel) in 120 seconds, or 2 minutes. The cosine function gives us a smooth, periodic curve that oscillates between -80 and 80, corresponding to your position on either side of the wheel's center.

Next, let's consider your vertical position. We know that you start at a height of 3 feet above the ground, and as the wheel rotates, your height will vary sinusoidally over time. We can express this as:

y(t) = 80sin(2πt/120) + 3

Here, the sine function gives us a smooth, periodic curve that oscillates between 77 and 83 feet (i.e. the radius of the wheel plus or minus 3 feet).

So, putting it all together, our parametric function for your location on the Ferris wheel at a given time t is:

(r(t), θ(t)) = (80cos(2πt/120), 80sin(2πt/120) + 3)

Here, r(t) and θ(t) represent your radial distance from the center of the wheel and the angle you've rotated from the starting position, respectively. This parametric function describes a smooth, periodic curve that traces out your path on the Ferris wheel as it rotates counter-clockwise.

Given the information, we know the Ferris wheel has a radius of 80 feet, the bottom is 3 feet above the ground, it rotates counter-clockwise, and has a period of 2 minutes.

To create a parametric function, we need two equations, one for the x-coordinate (horizontal) and one for the y-coordinate (vertical). Let's denote the time variable as t, measured in minutes.

1. X-coordinate (horizontal position):
Since the Ferris wheel rotates counter-clockwise, we can use the following equation for the x-coordinate:
x(t) = 80 * sin(2π * (t/2))

2. Y-coordinate (vertical position):
To account for the bottom of the Ferris wheel being 3 feet above the ground, we need to add 3 to the vertical equation:
y(t) = 80 * cos(2π * (t/2)) + 3

Now, we have the parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3

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Answer:

84 degrees

Step-by-step explanation:

The series [infinity] xn n! n = 0 converges for all real values of x.

The given series [infinity] xn n! n = 0 is a power series with terms xn n! n. To determine the values of x for which the series converges, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. Let's apply the ratio test to the given series:

lim┬(n→∞)⁡〖|(x(n+1)(n+1)!)/(xn n!)|〗

Simplifying the expression:

lim┬(n→∞)⁡〖|(x(n+1))/(xn)| * 1/(n+1)|〗

As n approaches infinity, the ratio x(n+1)/xn approaches x/x = 1. Additionally, the term 1/(n+1) approaches 0. Therefore, the limit simplifies to:

lim┬(n→∞)⁡〖|1 * 0| = 0|〗

Since the limit is less than 1, the ratio test confirms that the given series converges for all real values of x.

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Answer: Store Z has the best sale price of $28.

Step-by-step explanation:

Here is the complete question:

Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale.

Store X is offering 15% off the price of the shoes.

Store Y is offering $5 off the price of the shoes.

Store Z is offering a discount 1/5 off the price of the shoes.

Which statement about the sale price of these shoes is true?

a. Store X has the best sale price of $20.

b. Store Z has the best sale price of $28.

c. Store Y has the best sale price of $30.

d. Store Z has the best sale price of $7.

Since Store X is offering 15% off the price of the shoes, the price of the shoe at store X will be:

= $35 - (15% × $35)

= $35 - (0.15 × $35)

= $35 - $5.25

= $29.75

Since Store Y is offering $5 off the price of the shoes, the price of the shoe at store Y will be:

= $35 - $5

= $30

Since Store Z is offering a discount off the price of the shoes, the price of the shoe at store Z will be:

= $35 - (1/5 × $35)

= $35 - $7

= $28

Base on the analysis above, Store Z has the best sale price of $28.

The solutions to the given expressions is given below.

To add the rational expressions, we need to have a common denominator, which is 5x in this case. Thus,

12/5x + 3/5x = (12+3)/5x = 15/5x = 3/x

So, the sum of the two rational expressions is 3/x.

To subtract the rational expressions, we need to have a common denominator, which is 9x^2 in this case. Thus,

\(x/9x^2 - 3/9x^2 \\= x/9x^2 - (3x)/9x^2 \\= (x-3x)/9x^2 = -2x/9x^2\\ = -2/x^2\)

So, the difference of the two rational expressions is -2/x².

To subtract the rational expressions, we need to have a common denominator, which is (x-2) in this case. Thus,

\(\frac{7}{(x-2)} - \frac{3x}{(x-2)} = \frac{7-3x}{(x-2)}\)

To combine these two rational expressions, we need to first find a common denominator, which is (x-2)^2. Thus,

\(\frac{7(x-2)}{(x-2)^2} - \frac{3x(x-2)}{(x-2)^2} =\frac{ (7x-14-3x^2)}{(x-2)^2}\)

So, the difference of the two rational expressions is \((7x-14-3x^2)/(x-2)^2\).

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The remainder when a 90-digit number 9999 is divided by 89 is 0, as the result of applying the divisibility rule of 89, which involves reversing the digits of the number and subtracting the smaller from the larger.

To find the remainder when a 90-digit number 9999 is divided by 89, we can use the divisibility rule of 89. The rule states that for any integer n, the number obtained by reversing the digits of n and subtracting the smaller from the larger is divisible by 89.

In this case, we reverse the digits of 9999 to get 9999 again, and subtract the smaller from the larger to get 0. Since 0 is divisible by any number, including 89, the remainder when 9999 is divided by 89 is 0.

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Answer: 1,127 miles

Step-by-step explanation:

450.80/0.40=1,127

Answer:

I guess the two angles have to be equal to 180°, so: 15x+48+5x+12=180

solve it:

20x+60=180

20x=180-60

20x=120

x=6 is the correct answer.

The time length of the warranty should be approximately 1.515 times the mean life of the timepiece. To calculate the time length of warranty so that only 1.9% of the the quartz timepieces will be replaced before warranty expires, we use the formula: P(X ≤ x) = 0.019 Where P(X ≤ x) is the probability of failure before the warranty expires.

Let X be the number of months after purchase before a timepiece fails, and let m be the mean life of a timepiece. Then, the standard deviation of the life of a timepiece is σ = 0.25m (given). Also, the probability that a timepiece fails before the warranty expires is 0.019, which means that the probability of success is 1 - 0.019 = 0.981.

Using the standard normal table, we can find the Z-score such that the area to the left of Z is 0.981. From the table, we find that Z ≈ 2.06 (rounded to two decimal places).Therefore, Z = (x - m) / σ implies

x = σZ + m

≈ 0.515m + m

= 1.515m (since σ = 0.25m and Z = 2.06).

Thus, the time length of the warranty should be approximately 1.515 times the mean life of the timepiece.

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The tennis ball has traveled a horizontal distance of 3.717 m, to the nearest tenth of a metre, when it lands on the ground. Hence, the correct option is (A) 3.7.

The given function is h(d) = -0.12d² +0.22d+1.1.

It models the path of a tennis ball hit from a height of 1.1 m above the ground.

Here, d represents the horizontal distance in meters, and h(d) represents the height in meters.

To find how far the tennis ball travelled horizontally when it lands on the ground, we need to find the value of d when h(d) = 0, because the ball will hit the ground when its height is zero.

Substituting h(d) = 0 in the given function, we get:

0 = -0.12d² +0.22d+1.1

Simplifying, we get: 0.12d² - 0.22d - 1.1 = 0

We can solve this quadratic equation using the quadratic formula, which is given by:

-b ± sqrt(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation.

Here, a = 0.12, b = -0.22, and c = -1.1.

Substituting the values, we get:

d = [0.22 ± sqrt(0.22² - 4(0.12)(-1.1))] / 2(0.12)

Simplifying,

We get:

d = [0.22 ± sqrt(0.5964 + 0.528)] / 0.24d

= [0.22 ± sqrt(1.1244)] / 0.24d

= [0.22 ± 1.0604] / 0.24

We get two values of d as follows:d = 3.717 m, -1.598 m

Since the ball cannot travel a negative distance, the only possible solution is d = 3.717 m.

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a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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Answer:

Yes, it is greater than -4

Step-by-step explanation:

Since 7-7=0, the negatives are less than 0.
Example: -3 is greater than -4 because it’s closer to 0, but it’s not the same with positive numbers, because the ones farther than 0 are bigger

The inequality "N minus 7 greater than negative 4" can be written in mathematical notation as:

N - 7 > -4

To solve for N, we can add 7 to both sides of the inequality:

N - 7 + 7 > -4 + 7

Simplifying, we get:

N > 3

Therefore, the solution to the inequality is:

N > 3

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

Answer:

2

Step-by-step explanation:

2^3= 2*2*2

factors of 8= 1,2,4,8

factors of 2= 1,2

Answer:

9x²+12x+12

a = 9

b = 12

c = 12

Step-by-step explanation:

Factor

9x²+6x-18x-12

9x²-12x-12

a = 9

b = 12

c = 12

Answer:

someone needs to answer this because i dont know

it.

Step-by-step explanation:

he is correctStep-by-step explanation:

Answer:

Step-by-step explanation:

All real numbers from 0-10

The domain of the function that best represents the value of the car concerning the number of years could be All real numbers from 0-10.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We have been given that the graph shows the value of Matt's car over 10 years.

We need to find the domain of the function that best represents the value of the car concerning the number of years.

Therefore, we can see that the value of Matt's car over 10 years decreases linearly.

Domain = {0 1 2 3 4 5 6 7 8 9 10}

Therefore, the domain of the function that best represents the value of the car concerning the number of years could be All real numbers from 0-10.

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