Please hurry lol I’ll give brainliest

1. Proof that F is injective. Suppose that two different elements in the domain of F have the same image; that is, if x and y are elements of the domain of F and F(x)= F(y). We need to show that x=y. Let F(x) = F(y). This means that y1= x1/ (x1 + x2 + x3) = y1, y2= x2/ (x1 + x2 + x3) = y2 and y3= x3/ (x1 + x2 + x3) = y3.Now adding (1), (2), and (3), we have:y1+y2+y3= x1/ (x1 + x2 + x3) + x2/ (x1 + x2 + x3) + x3/ (x1 + x2 + x3)But this is equal to 1, therefore,x1 + x2 + x3= y1 + y2 + y3 = 1, or, equivalently, y1= 1- y2 - y3x1= (1- y2 - y3)(x1 + x2 + x3) = (1-y2 - y3), x2= y2(x1 + x2 + x3) = y2, and x3= y3(x1 + x2 + x3) = y3Thus, we have constructed an element of the domain of F, with different elements of the domain, that have the same image. Therefore, F is injective.

2. Find the investment directly without appealing to the Inverse Function Theorem. F(x1,x2,x3) = (y1,y2,y3)So, x1= (1- y2 - y3), x2= y2, and x3= y3Thus, the inverse of F is F-1(y1,y2,y3)= ((1-y2-y3),y2,y3)3. The domain of F. The domain of F is the set of all three-tuples, F(x1,x2,x3) where 0 ≤ xi ≤ ∞, and where at least one xi is positive. That is, Dom (F)={(x1,x2,x3)|x1≥0, x2≥0, x3≥0 and (x1,x2,x3)≠(0,0,0)}4. The range of F, which is the domain of F-1. The range of F is the set of all three-tuples, F(y1,y2,y3) where 0 ≤ yi ≤ 1, and where at least one yi is positive.

That is, Rng(F)={(y1,y2,y3)|y1≥0, y2≥0, y3≥0 and y1+y2+y3=1}5.  We have J_f(x) = ∣∣ ∂(y1,y2,y3) /∂(x1,x2,x3) ∣∣= ∣∣ ∂y1/∂x1 ∂y1/∂x2 ∂y1/∂x3 ∂y2/∂x1 ∂y2/∂x2 ∂y2/∂x3 ∂y3/∂x1 ∂y3/∂x2 ∂y3/∂x3 ∣∣= ∣∣ (1 / (x1 + x2 + x3) ) - (x1/ (x1 + x2 + x3)2) - (x1/ (x1 + x2 + x3)2) 0 1 / (x1 + x2 + x3) - (x2/ (x1 + x2 + x3)2) 0 0 1 / (x1 + x2 + x3) - (x3/ (x1 + x2 + x3)2) ∣∣= (1 / (x1 + x2 + x3) )((1 - y2 - y3) (1 - y2 - y3 - y3) - y2 (1 - y2 - y3) - y3(1 - y2 - y3)) = (1 / (x1 + x2 + x3) )((1 - y2 - y3 - y2 + 2y2y3 + y2 - y3 - 2y2y3 + y3 - y2y3 - y3 + y2y3)) = 1 / (x1 + x2 + x3) which is non-zero in the domain of F. Therefore, J_f(x) ≠ 0 when x ∈ Dom (F).

Know more about Inverse Function Theorem:

https://brainly.com/question/31423480

#SPJ11

Answer:

6

Step-by-step explanation:

2+4+7+5+8+10

=36÷6

=6

Answer:

Sorry sis don't know the meaning

Answer:

It is A

Write an equation to represent the total cost, C, as a function of the number, n, of T-shirts

produced.

Step-by-step explanation:

:)

Answer:

Hello!

The answer is 8^18.

Step-by-step explanation:

Answer:

8^12

Step-by-step explanation:

Exponents are confusing at first. You subtract them when dividing, and add them when multiplying, if the base number is the same.

Picture 8 to the 15th as a numerator of:

8x8x8x8x8x8x8x8x8x8x8x8x8x8x8 over a denominator of

8x8x8

To solve that, you'd cancel out 3 of the top 8s and the three bottom 8s, marked in bold to be easier to see. This leaves you with

8^12

Does that help?

Happy to answer questions.

Answer:

x = -5

Step-by-step explanation:

Please write this as y = x^2 + 10x + 25.  Here the coefficients are {1, 10, 25}.

The equation of the axis of symmetry is x = -b/[2a], which here is

x = -10 / [2*1] = -5

Answer:

Distance between the points is 8 miles.

Step-by-step explanation:

Distance between tow points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by,

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between the given points (2, -3) and (2, 5) will be,

Distance = [tex]\sqrt{(2-2)^2+(-3-5)^2}[/tex]

               = 8 units

Since, 1 unit = 1 mile

Therefore, distance between these points will be 8 miles.

Answer:

Let the total charge is y, the number of small arrangements is x.

Total charge will be:

Total charge will be:

Since the total charge is same in both shops, we have:

Solve for x:

Total cost is:

Small arrangements = 3, cost = $86

Answer:

The 2/5th’s bucket is the answer to question one.

for the second one, draw a square or rectangle and divide one of them by 5 (draw 4 lines in it) and fill in two of those lines.

the second fraction, draw another rectangle and draw 3 lines on the inside of it, filling in 3. (you’re creating a visual representation of the fractions. you can also look up ‘3/4 picture’ and ‘2/5 picture’ and copy off the internet.

Step-by-step explanation:

Answer:

The temperature with the highest frequency is 54

Step-by-step explanation:

Given

The above data

Required

The temperature with the highest frequency

The first step, is to plot the stem and leaf plot.

[tex]\begin{array}{cc}{4} & {9\ \ } & {5} & {2\ 4\ 4\ 6\ 8} & {6} & {0\ 1\ } & {7} & {2\ 3\ } \ \end{array}[/tex]

Next, is to identify the leaf with the highest frequency.

The leaf is 4 (with frequency 2)

Next, is to identify the accompanying stem of the leaf

The stem is 5

Hence, the temperature with the highest frequency is 54

Answer:

B

Step-by-step explanation:

edg 2021

Answer:

a) $93, $117.80, $86.80, $68.20

b) $365.80

Step-by-step explanation:

a)

Add 12 hours to each p.m. time to make the subtraction of hours easier.

Also, use decimal numbers to do the subtraction. Remember that 0:30 means 30 minutes which is 0.5 hour, so 7:30 is the same as 7.5 as a decimal.

Monday: 8:00 to 15:30

15:30 - 8:00 = 1.5 - 8 = 7.5 hours

7.5 hours * $12.40/h = $93

Wednesday: 7:30 to 17:00

17:00 - 7:30 = 17 - 7.5 = 9.5 hours

9.5 hours * $12.40/h = $117.80

Friday: 9:00 to 16:00

16:00 - 9:00 = 16 - 9 = 7 hours

7 hours * $12.40/h = $86.80

Saturday: 10:30 to 16:00

16:00 - 10:30 = 16 - 10.5 = 5.5 hours

5.5 hours * $12.40/h = $68.20

b) Add all the daily amounts above.

$93 + $117.80 + $86.80 + $68.20 = $365.80

Answer:

5π

Step-by-step explanation:

just need to find half of the circumference

Answer:

B

Step-by-step explanation:

the notation answer would also be 3.246 × 10-4 i believe :)

The mean of the given probability distribution is 3.4.

To find the mean of a probability distribution, we multiply each value of x by its corresponding probability and then sum them up. Using the provided data:

P(2)    0

P(1)    0.0017

P(2)    0.3421

P(3)    0.065

P(4)    0.4106

P(5)    0.1806

mean = 2(0) + 1(0.0017) + 2(0.3421) + 3(0.065) + 4(0.4106) + 5(0.1806)

     = 0 + 0.0017 + 0.6842 + 0.195 + 1.6424 + 0.903

     = 3.4263

Therefore, the mean of the given probability distribution is approximately 3.4 (rounded to one decimal place).

To learn more about probability distribution: https://brainly.com/question/23286309

#SPJ11

Answer:

B. 1296 m^3

Step-by-step explanation:

To find the volume of a square pyramid, multiply the base by itself twice, then divide the height by 3. After getting both answers, multiply the answers.

In this case, the base is 18.

The height is 12.

First, we must multiply the base by itself twice.

18⋅18 = 324.

Next, divide the height by 3.

12/3 = 4.

Now that we have both answers, we multiply them.

324 ⋅ 4 = 1,296.

Therefore, 1,296 cm^3 is the volume of the square pyramid.

Answer:

Yes, we reject the auto maker's claim.

Step-by-step explanation:

H0 : μ ≥ 20

H1 : μ < 20

Sample mean, xbar = 18 ;

Sample size, n = 36

Standard deviation, s = 5

At α = 0.01

The test statistic :

(xbar - μ) ÷ s /sqrt(n)

(18 - 20) ÷ 5/sqrt(36)

-2 /0.8333333

= - 2.4

Pvalue from test statistic : Pvalue = 0.00819

Pvalue < α

0.00819 < 0.01

Hence, we reject the Null

Answer:

Tony should add $7.70

Step-by-step explanation:

22% = 0.22

0.22 x $35 = $7.70

The covariance Cov(X, Y) can be calculated for the given joint probability density function (pdf) f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1.

To calculate the covariance Cov(X, Y), we need to determine the joint probability density function (pdf) of X and Y and apply the formula for covariance.

First, we need to find the constant k by integrating the joint pdf over its entire range to ensure it integrates to 1 (since it represents a probability density function).

The integral of f(x, y) over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is given by:

∫∫ f(x, y) dy dx = ∫∫ kr² dy dx.

Integrating with respect to y first, we get:

∫[0,1] ∫[0,1] kr² dy dx = k∫[0,1] r² [y=0 to y=1] dx

= k∫[0,1] r² dx

= k[r²x] [x=0 to x=1]

= k(r² - 0)

= kr².

Since the integral of the joint pdf over its entire range equals 1, we have kr² = 1, which implies k = 1/r².

Now, we can calculate the covariance Cov(X, Y) using the formula:

Cov(X, Y) = E[XY] - E[X]E[Y],

where E denotes the expected value.

Since X and Y are continuous random variables with a uniform distribution over the range [0,1], we have E[X] = E[Y] = 1/2.

To calculate E[XY], we integrate the product XY over the range [0,1] for both x and y:

E[XY] = ∫∫ xy f(x, y) dy dx

= ∫∫ xy kr² dy dx

= k∫∫ xyr² dy dx

= k∫[0,1] ∫[0,1] xyr² dy dx.

Integrating with respect to y first, we get:

E[XY] = k∫[0,1] ∫[0,1] xyr² dy dx

= k∫[0,1] [(1/2)xr² [y=0 to y=1]] dx

= k∫[0,1] (1/2)xr² dx

= (k/2)∫[0,1] xr² dx

= (k/2)[(1/3)x³r² [x=0 to x=1]]

= (k/2)(1/3)r²

= (1/2)(1/3)r²

= 1/6r².

Finally, we can calculate the covariance:

Cov(X,Y) = E[XY] - E[X]E[Y]

= 1/6r² - (1/2)(1/2)

= 1/6r² - 1/4.

Therefore, the covariance Cov(X, Y) for the given joint pdf f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1/6r² - 1/4.

Learn more about covariance here:

https://brainly.com/question/32517036

#SPJ11

Answer:

Surface Area: 848.23

Volume: 1727.88

Step-by-step explanation:

I know dis im in 8th grade iz ez!

The important difference to note for the scales of measurement and how they are analyzed is whether they involve ratios, intervals, categories or numbers. The scales of measurement can be divided into four types: nominal, ordinal, interval, and ratio.

Nominal scales use categories or numbers to group data, but these categories or numbers have no inherent order or value. Examples of nominal scales include gender, race, or eye color. Ordinal scales use categories or numbers to group data, but these categories or numbers have a specific order or rank. Examples of ordinal scales include educational attainment, income, or level of agreement on a survey question.

Interval scales use numbers as responses on the scale, but the distance between the numbers is not meaningful. Examples of interval scales include temperature measured in Celsius or Fahrenheit, or IQ scores. Ratio scales use numbers as responses on the scale, but the distance between the numbers is meaningful and there is a true zero point. Examples of ratio scales include height, weight, or income.

In summary, the important difference to note for the scales of measurement and how they are analyzed is whether they involve categories or numbers, and whether the numbers have a specific order or rank, a meaningful distance between them, or a true zero point.

Know more about scales of measurement here:

https://brainly.com/question/13086959

#SPJ11

Answer: C is false

Step-by-step explanation: If B is correct and C is saying otherwise that must mean it's the only false choice :) brainliest would be appreciated :)

Answer:

10

Step-by-step explanation:

use pythagorean theorm

√(8^2+6^2) = 10

The probability of rolling a number less than 3 or an odd number is 3/5 in fraction form.

To compute the probability of rolling a number less than 3 or an odd number, we need to calculate the probability of each event separately and then subtract the probability of their intersection.

The probability of rolling a number less than 3 is 2/10, as there are two numbers (1 and 2) that satisfy this condition out of the ten possible outcomes.

The probability of rolling an odd number is 5/10, as there are five odd numbers (1, 3, 5, 7, and 9) out of the ten possible outcomes.

To compute the probability of their intersection (rolling a number less than 3 and an odd number), we observe that there is only one number (1) that satisfies both conditions.

Therefore, the probability of their intersection is 1/10.

To compute the probability of rolling a number less than 3 or an odd number, we sum the probabilities of each event and subtract the probability of their intersection:

Probability of rolling a number less than 3 or an odd number = (2/10) + (5/10) - (1/10) = 6/10 = 3/5.

Therefore, the probability of rolling a number less than 3 or an odd number is 3/5.

To know more about probability refer here:

https://brainly.com/question/32117953#

#SPJ11

The volume (v) of the solid obtained by rotating the region about y = 6 is approximately 339.02 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 3e^(-x), y = 3, and x = 2 about the line y = 6, we can use the method of cylindrical shells.

First, let's plot the curves and the line of rotation to visualize the region:

    |

       |      y = 3e^(-x)

       |             _______

       |__________|    y = 3

       |     |

       |     |___ x = 2

       |

     y=6|_____________________

We can see that the line y = 6 is above the region bounded by the curves. To find the volume, we will integrate the circumference of each cylindrical shell multiplied by its height.

The height of each cylindrical shell is given by the difference between the line y = 6 and the curve y = 3e^(-x), which is 6 - 3e^(-x).

The radius of each cylindrical shell is given by the distance from the line y = 6 to the x-axis, which is 6 - 0 = 6.

The differential volume element is given by dV = 2πrh dx, where r is the radius and h is the height.

Therefore, the volume of the solid can be obtained by integrating this expression over the range of x from 0 to 2:

V = ∫[0,2] 2π(6 - 3e^(-x))(6) dx

Simplifying the expression:

V = 12π ∫[0,2] (6 - 3e^(-x)) dx

V = 12π ∫[0,2] (6 - 3e^(-x)) dx

V = 12π [6x + 3e^(-x)] evaluated from 0 to 2

V = 12π [(12 + 3e^(-2)) - (0 + 3e^(-0))]

V = 12π (12 + 3e^(-2) - 3)

V = 12π (9 + 3e^(-2))

V ≈ 339.02 cubic units

Therefore, the volume (v) of the solid obtained by rotating the region about y = 6 is approximately 339.02 cubic units.

Learn more about volume here

https://brainly.com/question/27710307

#SPJ11

Answer:

He should buy about 2 quart of stain

Step-by-step explanation:

Find the diagram attached

First we need to find the area of the given ramp

The ramp consists of two identical triangles, a larger and small rectangles

Since area of triangle  = 1/2 * base * height

Area of the identical triangles = 1/2 * 25ft * 25/12 ft (Note that 1ft = 12in)

Area of the 2 identical triangles = 2* 625/24ft² = 625/12 ft²

Area of the large rectangle = Length * Width

Area of the large rectangle = 25 1/12 * 5

Area of the large rectangle = 301/12 * 5

Area of the large rectangle = 1505/12 ft²

Area of the small rectangle = 25/12 * 5

Area of the small rectangle = 125/12 ft²

Area of the figure = 625/12 + 1505/12 + 125/12

Area of the figure = (625+1505+125)/12

Area of the figure = 2255/12

Area of the figure = 187.917

Area of the figure = 187.917ft²

Since  a quarter steam covers a 100' square fee, then;

1 quarter = 100ft²

x = 187.917ft²

Cross multiply

100 * x = 187.917

100x =187.917

x = 187.917/100

x = 1.87917

x ≈ 2

Hence he should buy about 2 quart of stain

The amount of discharge for which the probability of containing at least 1 organism is 0.993 is approximately 0.14 m³.

To find the amount of discharge for which the probability of containing at least 1 organism is 0.993, we can use the Poisson distribution formula. The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

In this case, the concentration of organisms in the ballast water is given as 10 organisms/m³. Let's denote λ as the average rate of occurrence, which is equal to the concentration in this case, λ = 10 organisms/m³.

The Poisson distribution formula is:

P(X ≥ k) = 1 - P(X < k) = 1 - e^(-λ) * (λ^0/0! + λ^1/1! + λ^2/2! + ... + λ^(k-1)/(k-1)!)

We want to find the amount of discharge (let's call it x) for which P(X ≥ 1) = 0.993. Plugging in the values into the formula, we have:

0.993 = 1 - e^(-10) * (10^0/0! + 10^1/1!)

Simplifying the equation, we have:

0.993 = 1 - e^(-10) * (1 + 10)

Now we can solve for e^(-10) using logarithms:

e^(-10) = 1 - 0.993 / (1 + 10)

e^(-10) ≈ 0.0045

Substituting this back into the equation, we have:

0.993 = 1 - 0.0045 * (1 + 10)

Simplifying further, we get:

0.993 = 1 - 0.0045 * 11

Now, let's solve for the discharge amount x:

0.993 = 1 - 0.0495x

0.0495x = 1 - 0.993

0.0495x ≈ 0.007

x ≈ 0.007 / 0.0495

x ≈ 0.14 m³

Therefore, the amount of discharge for which the probability of containing at least 1 organism is 0.993 is approximately 0.14 m³.

Learn more about probability here

https://brainly.com/question/25839839

#SPJ11