2x - (-4x + 5b). x = 2. b = -5

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:

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

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:

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

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:

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

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:

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

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

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The image of the polygon after the rotation is added as an attachment

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

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

The location of point G is

G = (3, -1)

To rotate about point G, we start by subtracting the points from G

So, we have

[(1, 0), (2, 0), (0, 2) and (2, 2)] - (3, -1)

This gives

(-2, 1), (-1, 1), (-3, 3) and (-1, 3)

The rule is 90 degrees clockwise rotation

This is represented as

(x, y) ⇒ (y, -x)

So, we have

(-2, 1), (-1, 1), (-3, 3) and (-1, 3) ⇒ (1, 2), (1, 1), (3, 3) and (3, 1)

Next, we plot (1, 2), (1, 1), (3, 3) and (3, 1)

See attachment for the image of the transformation

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Answer:

1) y = -1x+-1 and 2) y = -1x+-1

Step-by-step explanation:

Slope Intercept Form: y = mx+b (m is slope and b is y-intercept)

1) 8x+8y=-8

8y = -8x+-8

y = -1x+-1

2) 3x+3y =-3

3y = -3x+-3

y = -1x+-1

The amount of coverage that you will have on the contents of your home would be = $68,750

The total amount of money that was insured for the house = $125,000

The percentage of insurance that was left for the contents of the house = 55% of insurance.

That is;

= 55/100 × $125,000

= 6875000/100

= $68,750.

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Answer:

The polynomial that represents the difference of 12x^3+7x+3 and 3x^7+4x is 12x^3-3x^7+7x-4x.

Answer:

below

Step-by-step explanation:

[ 2.13 * 13   +  2.34 * 12  +  3.00 * 17 ] / ( 13 + 12 + 17) = 2.54 GPA

The value of A n (B U C) = {q, s, w, y} for the given sets.

A set is a clearly defined group of things in mathematics. We may define several operations on sets and look at their attributes, unlike numbers. An operation in set theory is a task that involves combining different sets in order to create a new set with unique attributes.

The set containing all elements shared by sets A and B is the intersection of the two sets.

The given sets are:

U= {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C= {v,w,x,y,z}

The value of (B U C) depicts all the terms in B and C:

(B U C) = {q, s, y, z, v, w, x}

The value of A n (B U C) depicts all the common terms in set A and B U C:

A n (B U C) = {q, s, w, y}

Hence, the value of A n (B U C) = {q, s, w, y} for the given sets.

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Answer:     b = 82°

To solve for angle b, calculate using the given angles and the straight angle theorem.

The straight angle theorem is a rule that says all straight lines are 180°.

Since the angle formed by XY is a straight line, it is also equal to 180°.

XY is divided into three separate angles, a, b and c.

If we add a, b, and c, it will equal to 180°.

XY = a + b + c                              XY is the sum of a, b, and c.

180° = 46° + b + 52°                     Substitute what we know.

To solve for b using this equation, isolate.

180° - 46° = 46° + b + 52° - 46°   Subtract 46° on both sides.

134° = b + 52°

134° - 52° = b + 52° - 52°             Subtract 52 on both sides.

82° = b                                         Keep the variable on the left.

b = 82°                                         Final answer.

Therefore, angle b is 82°.

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Answer:

1st one

Step-by-step explanation:

Answer: A. (2/5,-3)

Step-by-step explanation:

in order to find the solution to the set of equations, you need to find one variable first, lets fing y first

10x+3y=-5

10x = -5 - 3y

x = (-5 -3y)/10

substitute this in for x in the other equation

-5((-5 - 3y)/10) -4y = 10

(25 + 15y)/10 -4y = 10

25/10 + 15y/10 -4y = 10

make all fractions on the left side

25/10 + 15y/10 - 40y/10 = 10

combine

25/10 -25y/10 = 10

multiply both sides by 10 to get rid of the denominator

25 - 25y = 100

combine like terms

-25y = 75

divide

y = -3

plug y into the first equation to find x

10x + 3(-3) = -5

10x -9 = -5

10x = 4

x = 4/10

simplify

x = 2/5

hope this helps!

The range of value for d is d ≥ 1

Inequality, In mathematics is a statement of an order relationship. Greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Greater than is >

Greater then or equal to is ≥

less than <

less then or equal to ≤

d + 5≥ 6

add the additive inverse of 5 to both sides

d+5+(-5) ≥ 6+(-5)

d ≥ 6-5

d ≥ 1

therefore the range of value of d is d ≥ 1

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The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.

A simple random sample is a type of probability sampling method used in statistics, where each member of a population has an equal chance of being selected for the sample.

In other words, in a simple random sample, every possible sample of a given data will have has an equal probability of being selected from the population.

Here we have

A statistics class has 10 graduate and 40 undergraduate students.

We want to randomly sample 10% of the students in the class.

Even though one graduate student and four undergraduate students are selected at random, the percentage selecting both categories is the same.

Hence, this is a simple random sample.

Therefore,

The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.

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Mr. Finn's rent in the next 3 years will be £ 833.49

To find the rent, calculate how much it will increase in the first and in the second year by using calculating percentages individually or using the compound interest formula. From the find total rent for next years. Using the total rent in the second year find the rent in 3rd year.

Here we have

The rent paid by Mr. Finn is £700 per month in rent.

His landlord informed him that rent will increase by 5% for the next two years and by 8% after that.

The rent in the 1st year = 700 + 5% of 700

= 700 + (5/100) 700

= 700 + 35 = 735  

In the second year again the rent will increase by 5%

The total rent in the second year = 735 + 5% of 735

= 735 + 36.75 = 771.75

After 2 years, the increment will be 8%

So, The total rent in the 3rd year year = 771.75 + 8% of 771.75

= 771.75 + (8/100) 771.75

= 833.49

Therefore,

Mr. Finn's rent in the next 3 years will be £ 833.49

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Answer:

B. $11

Step-by-step explanation:

At end of 4th year:

[tex]320 {e}^{.03 \times 4} = 360.80[/tex]

At end of 5th year:

[tex]320 {e}^{.03 \times 5} = 371.79[/tex]

Interest earned between end of these two years:

[tex]371.79 - 360.80 = 10.99[/tex]

The individual events are dependent. The probability of the combined event is of:

0.0137 = 1.37%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

As the students are chosen without replacement, the events are dependent.

The parameter values for this problem are given as follows:

N = 72 students, k = 18 seniors, n = sample size of 3.

The probability of three seniors is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,72,3,18) = \frac{C_{18,3}C_{54,0}}{C_{72,3}} = 0.0137[/tex]

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Answer:208 mi

 Step-by-step explanation:

If David rents the car for four days,

that's an up-front costof 4 × 23.95 = $95.80.

The other cost depends on the distance (d) he drives.

The equation for his total cost (C) isC = 0.26d + 95.80If David has needs a budget

of $150, then

150 = 0.26d + 95.80- 95.80 from each side54.20 =

0.26d ÷ 0.26d = 208.5

David can't drive that extra 0.5 mi without going over his budget.He can drive 208 whole miles.

The length of the apothem of the pentagon is 12.96 meters .

What is apothem ?
In geometry, the apothem of a polygon is the distance from the center of the polygon to the midpoint of one of its sides. For a regular polygon (a polygon with all sides and angles equal), the apothem is the perpendicular distance from the center of the polygon to one of its sides.

Explanation:
The formula for the area of a regular pentagon is:

A = (1/2)P × a

where A is the area, P is the perimeter, and a is the apothem.

To solve for the apothem, we need to rearrange the formula and solve for a:

a = (2A) / P

The perimeter of a regular pentagon is given by:

P = 5s

where s is the length of each side.

Substituting the given values, we get:

P = 5s = 5(9.7) = 48.5

A = 315.25

a = (2A) / P = (2 × 315.25) / 48.5 = 12.96

Therefore, the length of the apothem of the pentagon is 12.96 meters (rounded to two decimal places).

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Answer:

Step-by-step explanation:

its 13

y=100000(0.25)^8 exponential decay​ is 1.526.

The formula represents exponential decay with a decay factor of 0.25 and an initial value of 100,000. To evaluate the formula, you can simply substitute 8 for the variable x (since the formula has y in terms of x) and calculate the result:

y = 100000(0.25)^8

y = 100000(0.00001525878906)

y ≈ 1.526

Therefore, the value of y for x = 8 is approximately 1.526. This means that after 8 units of time, the initial value of 100,000 has decayed to around 1.526.

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Answer: 6 3/4 I hope this helps

Step-by-step explanation:

27/4

Convert the improper fraction into a mixed number

6 3/4

Mixed number-A number written as a whole number and a fraction.

Answer: The answer is  (A)

Step-by-step explanation:

Answer:

a. (x-5) meters

b. 390 m²

Step-by-step explanation:

A. We get the equation x²+x-30.

We need to find two factors of 30, which equals 1.
6 and -5 are factors of 30.
Now, we can see that (x-5) and (x+6) are the equations. (x+6) cannot be applied, so the answer is (x-5)

B. We can substitute x with 20, and when we plug it in, we get 390 meters.

Answer:

k = 11.7

Step-by-step explanation:

Constant of Proportionality

When two quantities y and x are proportional to each other, they are related by the proportionality equation
y = kx
where k is known as the constant of proportionality

The y axis is Money earned in $

x axis is time worked in hours

The relationship is y = kx and we are asked to find k

The constant of proportionality for this graph is nothing but the slope of the graph.

Slope can be found by taking any two points on the graph, determining the difference in y values and dividing by the difference in corresponding x values;

Two points have been chosen for us:
(3, 35.1) and (7, 81.9)

Difference in y values = 81.9 - 35.1 = 46.8 (also known as rise)

Difference in x values = 7 - 3 = 4 (also known as run)

Slope = k = rise/run = 46.8/4 = 11.7

Therefore k = 11.7

Answer: k = 11.7

Step-by-step explanation: hope this helps0^0

The correctly matched pairs are mentioned below.

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to match the correct pairs given below.

{ 1 } -

47, 41, 35, 29, 23   →   a{n} = a{1} + (n- 1)d

{ 2 } -

7, -21, 63, -189, 567   →   a{n} = a{1}rⁿ⁻¹

{ 3 } -

[tex]$A = P(1 + 0.025/12)^{12t}[/tex]   →   A = [tex]$P(1 + r/n)^{nt}[/tex]

{ 4 } -

An 18 - month invest on $10 at 5%.   →   A = P[tex]$e^{rt}[/tex]

{ 5 } -

Investments and loans -

Therefore, the correctly matched pairs are mentioned above.

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The value of x from the adjoining figure​ given as pentagon is 85°.

An angle is a geometric figure formed by two rays, or lines, that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees, radians, or other units of angular measurement, and it represents the amount of rotation between the two rays. Angles are often used in geometry, trigonometry, physics, and other fields to describe the orientation of objects and the relationships between them. Some common types of angles include acute angles (less than 90°), obtuse angles (greater than 90°), and right angles (exactly 90°).

Here,

This is a pentagon with sum of angle as 540 degrees.

50+x=180

x=130°

x+80+120+125+130=540

x=540-455

x=85°

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Answer:

Step-by-step explanation:

9w=93w=10

We move all terms to the left:

9w-(93w)=0

We add all the numbers together, and all the variables

-84w=0

w=0/-84

w=0

The set of x-values where f(x) is continuous is all real numbers except x=1, interval notation is (-∞, 1) U (1, ∞).

The function f(x) is a rational function, which is continuous for all x-values except those that make the denominator 0.

Thus, to find the set of x-values where f(x) is continuous, we need to find the values that make the denominator x-1 equal to 0:

x - 1 = 0

x = 1

Therefore, the set of x-values where f(x) is continuous is all real numbers except x=1. We can write this set in interval notation as:

(-∞, 1) U (1, ∞)

which means the set of all x-values less than 1, combined with the set of all x-values greater than 1.

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Answer:

[tex]\frac{3}{x+7}[/tex]

Step-by-step explanation:

[tex]\frac{3x-21}{x^{2} -49}[/tex]

We will start with factoring the numerator, by pulling a 3 out of each term:

3(x - 7)

We will then factor the denominator. As the denominator is a difference of perfect squares (in the form [tex]x^{2} -a^{2}[/tex]), we know that it can be factored in the form (x + a)(x - a), a being the square root of the number given. (In this case, a = 7, because the square root of 49 is 7.)

Our denominator is now:

(x + 7)(x - 7)

And our fraction is now:

[tex]\frac{3(x-7)}{(x-7)(x+7)}[/tex]

As both the numerator and denominator have the term (x-7), they will cancel, leaving us with the simplified expression:

[tex]\frac{3}{x+7}[/tex]

Answer:

slope = 4

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 24 ) and (x₂, y₂ ) = (0, 0 )

m = [tex]\frac{0-24}{0-6}[/tex] = [tex]\frac{-24}{-6}[/tex] = 4

Answer:

Step-by-step explanation:

To determine the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out, we can use the following formula:

n = (Z^2 * p * q) / E^2

where:

n is the sample size we want to determine

Z is the z-score associated with the desired level of confidence (let's assume a 95% confidence level, so Z = 1.96)

p is the estimated proportion of orders that were carry-out (we don't know this yet, so we'll use 0.5 as a conservative estimate)

q is 1 - p (i.e., the estimated proportion of orders that were delivery)

E is the desired margin of error (in this case, 0.04)

Using the given information, we can estimate that the proportion of orders that were carry-out is:

p = 1 - 431/778 = 0.446

Then, plugging in the values into the formula, we get:

n = (1.96^2 * 0.446 * 0.554) / 0.04^2 ≈ 602.25

Rounding up to the nearest whole number, the minimum sample size needed is 603.

Note that I used the formula for sample size calculation based on a finite population, since the total number of orders is known (778). If we used the formula for an infinite population, the result would be very similar (around 604). I calculated this by hand, without using any calculator program, but you could use a calculator or a spreadsheet to perform the calculations more efficiently.

Answer:

y - 7 = 2(x - 4)

Step-by-step explanation:

The equation of the line that goes through the points (4, 7) and (5, 9) is y - 7 = 2(x - 4). To find the equation of the line, you can use the point-slope form of the equation, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a given point on the line. In this case, the given points are (4, 7) and (5, 9), and the slope is m = 2. Therefore, the equation of the line is y - 7 = 2(x - 4).

It can be put as 40 / 100 as a fraction, which if you needed, it can be further simplified to 4 / 10, or even 8 / 20.