Aston left his house and ran 4 miles East and then 3 miles north. He then took the diagonal path back home. If he burned 105 calories every mile that he ran, how many total calories did burn on his run

the value of P(X=4,Y=2) is 0.0518.

Given that, X denote the number of Canon SLR cameras sold during a particular week by a certain store.

The probability mass function (pmf) of X is,

X 0 1 2 3 4

PX(x) 0.1 0.2 0.3 0.25 0.15

Let Y denote the number of purchasers during this week who buy an extended warranty.

The value of P(X=4,Y=2) is the probability that 4 cameras are sold and 2 extended warranties are sold in a week.

P(X=4,Y=2)=p(4,2)=P(Y=2|X=4)×P(X=4)

The number of purchasers purchasing the extended warranty can be 0, 1, ……, x.

Here x is cameras are sold.

Assuming that each customer buys at most 1 camera.

Considering that the event “a purchaser buys extended warranty” as “success” and the event “a purchaser does not buy extended warranty” as “failure”.

In that case, all the customers purchasing cameras buy extended is 60%.

The probability of failure is 0.4.

This follows the binomial distribution, where total number of trials is the number of purchasers of camera and x is the probability of success is 0.6.

The probability that 2 out of 4 cameras purchasers buys extended warranty with probability of success 0.6 is,

P(Y=2|X=4)=4C2(0.6)2(0.4)4−2=6×0.36×0.16=0.3456

Given that,

P(X=4)=0.15

Therefore,

P(X=4,Y=2)=P(Y=2|X=4)×P(X=4)=0.3456×0.15=0.0518

Therefore, the value of

P(X=4,Y=2) is 0.0518.

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The additive inverse of 3/2 is -3/2 as the sum of both value is 0 which is additive identity.

An additive inverse of a number is the number that when added to the original number, results in a sum of zero. In other words, it is the opposite of the original number on the number line. In the case of a fraction, the additive inverse is found by multiplying the numerator and denominator by -1. The additive inverse of 3/2 is -3/2 because 3/2 + (-3/2) = 0. This is true for any number in any form, whether it be an integer, a decimal, or a fraction.

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Complete question:

what is additive inverse of 3/2?

Answer:

-6w+49

Step-by-step explanation:

w-7(w-7) <-- Distribute the -7

w-7w+49 <-- Combine like terms

-6w+49

Answer:

4\(x^{2}\)-16x+8

Step-by-step explanation:

4(x - 2)(x - 2) - 8 = 4(\(x^{2}\) - 4x + 4) - 8 = 4\(x^{2}\) - 16x + 16 - 8 = 4\(x^{2}\) - 16x + 8.

Answer:

\(f(x) = 4x^2 -16x + 16\)

Step-by-step explanation:

f(x)=4(x-2)² Simplify.

f(x) = 4x^2 - 16x + 16

Form f(x)=ax²+bx+c.

f(x) = 4x^2 - 16x + 16

Answer:

C. log7 36....................................

The given logarithmic expressions together can be written as log₇ 36

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.

Formulae for logarithmic function are,

LogAB = LogA + LogB

Logₐaᵇ = b

Given that,

= log₇(2 x 6) + log₇3

= log₇ 36

We have the result

log A + log B =  log AB

Here the question is log₇(2 x 6) + log₇3.

Using the property of logarithm we will get,

= log₇(2 x 6) + log₇3

= log₇(2 x 6 x 3)  

= log₇ 36

So,   log₇(2 x 6) + log₇3 = log₇ 36

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The complete expression that gives equivalent values is:

x⁻⁸ . x⁹ = x⁻⁶ . x⁷ = x⁻⁴ . x⁵ = x¹ = x⁻² . x³

From the question, we have the following parameters that can be used in our computation:

x⁻ . x = x⁻ . x = x⁻ . x = x = x⁻ . x

Where the exponents are blank

There is no general answer to this, and one of the possible solutions is as follows:

To start with, we create an expression of the following format:

x⁻ⁿ . xⁿ⁺¹ = x¹

Using the above as a guide, we have the following:

x⁻⁸ . x⁹ = x¹

x⁻⁶ . x⁷ = x¹

x⁻⁴ . x⁵ = x¹

x⁻² . x³ = x¹

So, the equivalent expression is x⁻⁸ . x⁹ = x⁻⁶ . x⁷ = x⁻⁴ . x⁵ = x¹ = x⁻² . x³

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Answer:

7 + 10 + k - 47

Step-by-step explanation:

Just a slight bit late

P(X≥2E(X)) ≤ E(X)/2E(X) = 1/2For minimizing log(h), consider g(x) = log(h(x)) = -x/r + r log(x/r)g'(x) = -1/r + r/x = 0 => x = r=> Minimum value of g(x) = g(r) = -1 - r log(r/e) => Maximum value of h(x) = e^-1 [r/e]^r=> P(X≥2E(X)) ≤ [e^(1/e)/2]^r = (2/e)^r b) import matplotlib.

a) Let h(x) = e^(-x/r) (x/r)^r P(X≥2E(X)) = P(X/2E(X)≥1) ≥ h(X/2E(X)) = e^(-X/2E(X)) (X/2E(X))^r {By Markov's inequality, for any positive r.v. Y and any positive constant c, P(Y≥c)≤E(Y)/c}

So, P(X≥2E(X)) ≤ E(X)/2E(X) = 1/2

For minimizing log(h), consider g(x) = log(h(x)) = -x/r + r log(x/r)g'(x) = -1/r + r/x = 0 => x = r

=> Minimum value of g(x) = g(r) = -1 - r log(r/e)

=> Maximum value of h(x) = e^-1 [r/e]^r=> P(X≥2E(X)) ≤ [e^(1/e)/2]^r = (2/e)^r b) import matplotlib.pyplot as pltimport numpy as npfrom scipy import statsdef markov(r): return (2/e)**rdef gamma(r): return stats.gamma.cdf(2*stats.gamma.mean(r, scale=1), r, scale=1)def main(): lmbda = 1 r = np.linspace(0.5, 15, 1000) plt.plot(r, gamma(r), label='P(X>=2E(X))') plt.plot(r, [(2/e)**i for i in r], label='(2/e)^r') plt.plot(r, [markov(i) for i in r], label="Markov's bound on P(X>=2E(X))") plt.legend(loc="upper left") plt.show()if __name__ == '__main__': main()The overlaid plots are as follows:

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Answer:

Below

Step-by-step explanation:

f(1)    -  2 = a(1) + b

        - 2 = a + b             (1)

f(5)     10 = a (5) + b

          10 = 5a + b            (2)

Multiply first underlined equation by -5  to get

      10 = -5a  - 5b       add this to the second equation (this will eliminate 'a')

      20 = - 4 b       so   b = -5

then the first equation becomes   - 2 = a +  (-5)

             which shows a = 3

so your function is just    f(x) = 3x  -5

Answer:

11c-12a

Step-by-step explanation

Combine like terms

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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Sofie will not make a profit if she sells her scarves for $5 or less.

The maximum profit Sofie can make is $200.

A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line.

According to the given problem,

y = (x - 5)(50 - 2x)

⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)

⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)

⇒ y - (x - 5)(-2x + 50) = 0

⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0

⇒ y - ( -2x² + 50x + 10x - 250) = 0

⇒ y - ( - 2x² + 60x - 250 ) = 0

⇒ y + 2x² - 60x + 250 = 0

⇒ 2x² -60x + y + 250 = 0

⇒ ( 2x² - 60x ) + y + 250 = 0

⇒ 2 ( x² - x) + y + 250 = 0

⇒ 2 ( x² - x) + y + 250 = 0

⇒ 2 ( x² - 30x ) + y + 250 = 0

⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0

⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0

⇒ 2( x - 15 )² + y = -2(-225) - 250

⇒ 2( x - 15 )² + y = 450 - 250

⇒ 2( x - 15 )² + y = 200

⇒ y = -2( x - 15 )² + 200

This equation is in the form of y =  a(x - h)² + k where the vertex of the parabola is (h , k).

Therefore the vertex of the parabola is at (15 , 200)

Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.

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Answer:

hello

4/14 x  5  /14 = 20/196 = 5 / 49

Step-by-step explanation:

Answer:

it's A. 1/3 because yes it's a

Answer:

X=5 y=3

Step-by-step explanation:

Ab=De

4x-2=18

X=5

EF=BC

3y+1=10

y=3

DF=2x+1=11

If the parent function \(\sf y=(1.6)^x\) is translated 5 units up and 9 units to the right, then you should subtract 9 from x and add 5 to the whole function. Thus,

1) translation the parent function \(\sf y=(1.6)^x\) 9 units to the right gives you the function \(\sf y=(1.6)^{x-9}\).

2) translation the function \(\sf y=(1.6)^{x-9}\) 5 units up gives you the function \(\sf y=(1.6)^{x-9}+5\)

Therefore, the correct choice is C

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Answer:

D.

Step-by-step explanation:

The function f gives the temperature in degrees Celsius t hours after midnight.

Therefore, for the temperature at 12:00 AM (exactly midnight), we will have f(0).

For 1:00 AM, 1 hour after midnight, we will have f(1).

And for 12:00 PM (noon), we will have f(12).

We want to find the equation that represents the temperature at 1:30 PM.

1:30 PM is 13.5 hours after midnight or 1.5 hours after noon.

Therefore, the correct statement would be:

f(13.5)=20.

Hence, our answer is D.

Notes:

A and C are not correct because we do not use a colon for function notation. We input numerical values, not time.

Answer:

d

Step-by-step explanation:

Answer:

50.68

Step-by-step explanation:

The higher priced shoes are full price and the lower priced shoes will be 1/2 price

74.99 + 1/2 (68.55)

74.99 + 34.28

109.27

He had 159.95 in credit

159.95-109.27

50.68 in  return

The criterion that is least likely to be used in choosing bins (classes) in a frequency distribution is personal preference or subjective judgment.

When constructing a frequency distribution, it is important to consider objective criteria based on the nature of the data and statistical principles. Common criteria used for choosing bins include the range of the data, the desired number of bins, the shape of the data distribution, and the purpose of the analysis. These criteria help ensure that the bins effectively capture the variation in the data and provide meaningful insights. Personal preference or subjective judgment, on the other hand, may introduce bias and lack objectivity in determining the bin boundaries. It is essential to rely on objective criteria and statistical guidelines to make informed decisions when choosing bins for a frequency distribution.

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Answer:

0.62

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

C is the answer

Step-by-step explanation:

Answer:

The approximate area of Colorado is

369 × 281 = 103,689 square miles

So the population density of Colorado in 2009 was

5,024,748 people / 103,689 square miles = about 48.46 people per square mile

(about 48 people per square mile)

Answer:

1 1/4

Step-by-step explanation:

3 - 1 = 2

2 - 3/4 = 1 1/4

Answer:

y = 2/3x + 4/3

Step-by-step explanation:

you need to know the slope of the line -2x + 3y = -6 because parallel lines have the same slopes

let's put the equation in y=mx+b format (slope-intercept format)

-2x + 3y = -6

add 2x to each side to get:

3y = 2x - 6

divide each side by 3 to get:

y = 2/3x - 2

the equation now shows us the slope is 2/3 and the y-intercept is (0,-2)

now we use y=mx+b again and use the point (-2,0) and the m=2/3 to get the y-intercept ('b' value) of the equation that is parallel:

0 = 2/3(-2) + b

0 = -4/3 + b

b = 4/3

equation would be:

y = 2/3x + 4/3

Answer:

The random process described is a symmetrical random walk.

A symmetrical random walk is a mathematical model that represents a series of steps taken in either a forward (+1) or backward (-1) direction, each with equal probability. Starting from point zero, the process involves taking a certain number of steps. The outcome at each step is independent of previous steps, making it a stochastic process. The key characteristic of a symmetrical random walk is that, on average, the process remains centered around its starting point. This means that over a large number of steps, the expected displacement from the starting point approaches zero.

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The value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

The difference formula in trignometry for the sine funciton is given as,

\(\sin(A-B)=\sin(A)\cos(B) -\cos(A)\sin(B)\)

The trignometric equation given in the problem is,

\(\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)\)

Compare this equation with the above eqution, we get,

\(A=80^o\\B=20^o\)

Thus, this equation can be written as,

\(\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(80-20)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(60)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\dfrac{\sqrt{3}}{2}\)

Hence, the value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

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Answer: w=8/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

20 /3 =2(w+ ( 2 /3 )

20 /3 =(2)(w)+(2)( 2 /3 )(Distribute)

20 /3 =2w+ 4 /3

Step 2: Flip the equation.

2w+ 4 /3 = 20 /3

Subtract 4/3 from each side: 2w+ 4 /3 − 4 /3 = 20 /3 − 4 /3

Divide both sides by 2: 2w/ 2 =16  3 /2

Answer w=8/3

Answer:

w=8/3

Step-by-step explanation:

The approximate volume of the tank is 15714 cubic centimeters.

The volume of a cylinder is the amount of substance that can fill the entire dimension of the cylinder. It can be determined by:

volume of a cylinder = \(\pi\) r^2 h

where r is the radius of the cylinder, and h is the height.

Considering the fish tank,

height = 50 cm

radius = 10 cm

So that,

volume of the cylindrical fish tank =  \(\pi\) r^2 h

                          = 22/7 * 10^2 * 50

                          = 22/7 * 100 * 50

volume of the cylindrical tank = 15714.286

Thus the approximate volume of the fish tank is 15714 cubic centimeters.

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As we can see, the line crosses the x-axis at (-2, 0). If we climb three units up from -2 and then go one unit to the right, we arrive at the next point on the line.

Since we climbed three points and went to the right one point, our slope = 3/1. But, we can reduce that.

Slope = 3/1 = 3

Answer:

The slope is 3.

Step-by-step explanation:

The way to find the slope is to find how many blocks/number it went up and to the side. The number of blocks it went up on the y-axis, in this case, is 3 and it went along the x-axis once. In order to actually find the slope, you need to put the y over the x. So, 3/1 is equal to three, so the slope of this line is 3

Answer:

4.6562707350808111362602485665418‬

Answer:

2 cups

Step-by-step explanation: