Write the equation of the line a) in slope-intercept &
b) in standard form, perpendicular to 3x-y=-5 & passing
through point (3,-2).

a. The probability of no insect contaminants in a 225-gram bar from a brand at the mean contamination level can be found using the Poisson probability formula:

\(P(X = 0) = \frac{ (e^{-λ})(λ^0)}{0!} = \frac{(e^{-14.4})(14.4^0)}{0!}= 0.000000831\)

b. If you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level, the mean number of insect fragments would be one-fifth of 14.4, or 2.88. The probability of no insect contaminants can be found using the Poisson probability formula:

\(P(X = 0) = \frac{(e^-λ)(λ^0)}{0!} = \frac{(e^-2.88)(2.88^0)}{0!} = 0.056032\)

c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, the mean number of insect fragments would be (7 * 28.35/225) * 14.4 = 5.4336.

The probability of consuming one or more insect fragments in more than one bar can be found using the Poisson probability formula and the complement rule:

\($$\begin{aligned}& P(X>1) \\& =1-P(X \hat{a} 1) \\& =1-\left[\left(e^{-} \hat{I}\right)\left(\hat{I}^0\right) / 0 !+\left(e^{-} \hat{I}\right)\left(\hat{I}^1\right) / 1 !\right] \\& =1-\left[\left(e^{-} 5.4336\right)\left(5.4336^0\right) / 0 !+\left(e^{-} 5.4336\right)\left(5.4336^1\right) / 1 !\right] \\& =0.994784\end{aligned}$$\)

d. The probability of contamination more than twice the mean of 14.4 can be found using the Poisson probability formula and the complement rule:

\(P(X > 28.8) = 1 - P(X ≤ 28.8) \\= 1 - ∑(e^-λ)(λ^x)/x!\\ = 1 - 0.999999999999999 \\= 0.000000000000001\)

This probability is extremely small, so it can be considered unusual and not typical variation.

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If the total traveling time is 1 hour 8 minutes f the average speed is 45 km/h.

This is a problem from time and distance. We can solve this equation by following a few steps.

Let's assume the car travel in the city for t minutes and the average speed is v.

According to the question, the car travel outside the city for, (68- t) minutes as 1 hour 8 minutes is equal to 68 minutes.

As per the question, Outside the city, it travels at twice its former speed v.

Now, we can form an equation,  2 (15/t) =  72/(68- t).

Let's simplify the given equation. 30/t = 72/(68- t)

Or, 72t = 30(68- t)                 [cross multiplication]

Or, 72t = 2040 - 30t

Or, 102t = 2040                    [add with +30t both sides]

Or, t = 2040/102    

Or, t = 20                              [dividing by 102 both sides]

Therefore we can conclude that the average speed ( km/h) is (15×60) / 20 = 45 km/h.

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The graph of the solution to the inequality is attached as image to this answer.

The piece-wise defined function h(x) represents different values of y (the output) depending on the value of x (the input). Each interval of x has a different value assigned to it.

In this particular case, the inequality statements define the intervals for x and their corresponding output values.

Let's break it down:

- For values of x that are greater than -3 and less than or equal to -2, h(x) is assigned the value of -1.

- For values of x that are greater than -2 and less than or equal to -1, h(x) is assigned the value of 0.

- For values of x that are greater than -1 and less than or equal to 0, h(x) is assigned the value of 1.

- For values of x that are greater than 0 and less than or equal to 1, h(x) is assigned the value of 2.

Any values of x outside of these intervals are not defined in this piece-wise function and are typically represented as "not a number" (NaN).

For example, if you were to evaluate h(-2.5), it falls within the first interval (-3 < x ≤ -2), so h(-2.5) would be equal to -1. Similarly, if you were to evaluate h(0.5), it falls within the fourth interval (0 < x ≤ 1), so h(0.5) would be equal to 2.

The graph of the piece-wise function h(x) consists of horizontal line segments connecting the specified values of y for each interval, resulting in a step-like pattern.

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Steps:

Add 47.52 to both sides

Divide both sides by 1.16

x= 98

Description:

The first step is to add 47.52 to both sides then simplify it then divide the both sides by 1.16. And your answer will equal as x=98.

Answer: x= 98

Please mark brainliest

Hope this helps.

The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

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

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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Answer:

Linear monomial

Step-by-step explanation:

As here the number of terms is only 8x that is only one hence it is a monomial and as its degree here is 1 hence it is linear.

So it is a linear monomial.

Answer:

it's 166.277

Step-by-step explanation:

i took the test & got it right

Area of the regular hexagon is 166.3 square meter.

A regular hexagon exists comprised of six equilateral triangles.

Area of an equilateral triangle is \($\frac{\sqrt{3}}{4} \cdot s^{2}$\).

Therefore, area of a regular hexagon exists

\($6 \cdot \frac{\sqrt{3}}{4} \cdot s^{2}=3 \sqrt{3} \cdot \frac{s^{2}}{2}$\)

where, s = m exists the length of a side of the regular hexagon.

Area of the regular hexagon is

\($A_{h}=\frac{3 \cdot \sqrt{3} \cdot 8^{2}}{2}$\)

\($=96 \cdot \sqrt{3} \approx 166.3$\) square meter.

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Answer:

4 is the correct answer to your question

Answer:

Step-by-step explanation:

A short web search will turn up the authors of the given titles:

  The Old Man and the Sea - Hemingway

  Huckleberry Finn - Twain

  Moby D.ick - Melville

  1984 - Orwell

  Crime and Punishment - Dostoevsky

Use the formula for the susface area of a sphere with radius r

remember that the radius is

find the radius

replace in the formula for the surface area

Answer:

surface area of rectangular prisms A=2(wl+hl+hw)

surface area of cubes A=\(6a^{2}\)

Step-by-step explanation:

Answer:

The total surface area of a rectangular prism or cube is equal to the sum of the areas of each side.

The area of each side is equal to its length multiplied by its width or A = L x W.

Since the areas of opposite sides are equal, multiple each side area by 2 to obtain the areas of opposite sides.

where:

L = length

W = width

H = height

total area = (2)(L)(W) + (2)(L)(H) + (2)(W)(H)

or simplified:

total area = 2[(L)(W) + (L)(H) + (W)(H)]

Answer: 7:1

Step-by-step explanation:

First off, we see that the contribution was divided into 16 parts (8+5+3). If the tree was $96, 96/16 = $6, so each individual part was $6.

First Person: 3(6) = $18

Second Person: 5(6) = $30

Third Person: 8(6) = $48

We know that after the two friends return the money, the $96 will have been split evenly between all three of them.

96/3 = 32 - each person pays $32 total

Because each person has to pay $32 total, the first person must return $14 and the second person must return $2. This means that the ratio is 14:2 which can be reduced to 7:1.

Person 1: 32-18 = 14

Person 2: 32-30 = 2

Person 3: 48-14-2 = 32. - check to see if we were correct, which we are because after two friends pay 3rd back, their total is also 32 dollars.

Answer:

Step-by-step explanation:

Ukraine wants to join the european union.Due to this Russia realize that if ukraine join the european union then if war started between Ukraine and any other country like Russia it means Ukraine and european union both attack on this country.

1) To determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

2) To determine the surface area and volume of a sphere, we must know the radius of the sphere.

3) The volume of the sphere with a great circle of radius 7 cm is 1436.75 cubic centimeters

4) The area of a regular pentagon with radius 5, and each side of length 6 is 45 square units

To determine the surface area of a right cone:

The formula for the surface area of a right cone is,

A = πr[r + √(h² + r²)]

this means, to determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

To find the surface area and volume of a sphere:

The formula for the surface area of sphere is,

A = 4πr²

and the formula for the volume of sphere is,

V = 4/3 πr³

This means, to determine the surface area and volume of a sphere, we must know the radius of the sphere.

For a sphere with radius r = 7 cm the volume would be,

V = 4/3 * π * 7³

V = 1436.75 cubic centimeters

Now we need to find the area of a regular pentagon with radius 5, and each side of length 6.

The formula for the area of a regular pentagon is:

A = 1/2 × P × a

where 'p' is the perimeter of the pentagon and 'a' is the apothem of a pentagon.

The perimeter of the pentagon is:

P = 5 * side lengths

P = 5 * 6

P = 30 units

We know that an apothem of a regular polygon is a radius of the inscribed circle.

From given dimensions, a = 5 units

so, the area of a regular pentagon would be,

A = 1/2 × 30 × 5

A = 45 square units

Therefore, the area of a regular pentagon is 45 square units

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Answer:

J   29%

Step-by-step explanation:

Monthly rent: $600.

There are 12 months in 1 year, so the total rent she pays in 1 year is

12 × $600 = $7200

We need to find what percent $7200 is of $25,000.

percent = part/whole × 100%

percent = 7200/25000 × 100%

percent = 28.8%

Rounded to the nearest percent, the answer is 29%.

Answer:

0.1998

Step-by-step explanation:

This is a conditional probability question.

We solve this question using Bayes's Theorem of conditional probability.

P(A|B) = [P(B|A) × P(A)] ÷ [(P(B|A) × P(A))+ (P(B|A') × P(A'))]

Based on the information in the question, we have the following values.

Suppose it snows in Greenland once every 27 days.

Probability (it snows) = P(A) = 1/27

= 0.037037037

Approximately = 0.0370

Probability ( it doesn't snow) = P(A') = 1 - 0.0370 = 0.963

Probability ( that when it snow, glaciers grow) = P(B|A) = 26% = 0.26

Probability( that is doesn't snow , glaciers grow) = P(B|A)' = 4% = 0.04

Using the Bayes's Theorem of conditional probability

Probability that it is snowing in Greenland when glaciers are growing is =

P(A|B) = [P(B|A) × P(A)] ÷ [(P(B|A) × P(A))+ (P(B|A') × P(A'))]

= [0.26 × 0.0370] ÷ [(0.26 × 0.0370) + (0.04 × 0.963)]

= 0.00962 ÷( 0.00962 + 0.03852)

=0.00962 ÷ 0.04814

= 0.199833818

Approximately to 4 decimal places ≈ 0.1998

Therefore, probability that it is snowing in Greenland when glaciers are growing is 0.1998

Each of the numbers on the left should be matched with all appropriate number sets on the right as follows:

In Mathematics, there are six (6) common types of numbers and these include the following:

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 6, 12, 1/2, 0.5, √16, -2, etc.

Additionally, -2 can be classified as both a rational number and an integer.

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When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)

First, we shall determine the value of A. Details below:

Quadratic equation is expressed as:

x² - (sum of root)x + product of root

Comparing the above with x² - 11x + 30, we have

x² - 11x + 30 = x² - (sumof root)x + product of root

Product of roots = 30

Thus,

A = 30

Next, we shall determine the value of B. details below:

f(x) = x² + 5

f(2) = 2² + 5

f(2) = 9

Thus,

B = 9

Next, we shall determine the value of C. Details below:

Let

x + 4 = 0

Thus,

x = -4

Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:

Remainder = x² - 2x - 24

Remainder = (-4)² - 2(-4) - 24

Remainder = 0

Thus,

C = 0

Finally, we shall determine value of A/5 + √(B - C). Details below:

A/5 + √(B - C) = 30/5 + √(9 - 0)

A/5 + √(B - C) = 6 + √(9

A/5 + √(B - C) = 6 + 3

A/5 + √(B - C) = 9

Thus, the value of A/5 + √(B - C) is 9 (option B)

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to be honest i dont know all you said was ratio and some colored rings i dont know what im supposed to to that

Answer:

15:8 or 4:15 or 3:15

Step-by-step explanation:

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.

b) To calculate the expected count for the bottom right cell, we can use the formula:

Expected count = (row total x column total) / grand total

The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:

Expected count = (100 x 100) / 300 = 33.33

The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.

c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.

Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Based on the information provided, it is expected that after 18 months, the difference in the cost of the two plants is 240.

By following the sequence provided on the table, let's calculate the cost for each plant:

Plant A: 75, 110, 145, 180, 215, 250, 285, 320, 355, 390, 425, 460, 495, 530, 565, 600, 635, 670.

Plant B: 60, 110, 160, 210, 260, 310, 360, 410, 460, 510, 560, 610, 660, 710, 760, 810. 860, 910

Now, let's calculate the difference in cost:

910 - 670 = 240

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Answer:

Chloe is making a mural. She spends 6 hours designing it.

She paints it during 3 sessions. Each session is the same

number of hours long. In all, Chole spends 24 hours making

the mural.

Step-by-step explanation:

Answer:

Each painting session is 6 hours long

Step-by-step explanation:

You can represent the situation with an equation.

3h+6=24

3h+6/3=24/3

h+2=8

h+2-2=8-2

h=6

Answer:

the answer is 10 im pretty sure

Step-by-step explanation:

Answer: could I see the equtions pls

Step-by-step explanation:

Answer:

are you going to show the equation?

Step-by-step explanation:

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval