A supermarket normally sells 20 eggs for £2.60. In a sale, the cost of the eggs is reduced by 30%. Work out how much 180 eggs cost in the sale. Give your answer in pounds (£).​

By applying the unitary method, counting 67 colonies on a plate with 1ml of the 1:1,000,000 dilution indicates that 67,000,000 bacteria were present in 1ml of the original sample.

The unitary method is a mathematical technique that involves finding a unit value and using it to solve problems. In this case, we need to determine the number of bacteria present in 1ml of the original sample.

The dilution factor represents the ratio of the volume of the original sample to the volume of the diluted sample. In this case, the dilution factor is 1:1,000,000, which means that 1ml of the original sample was diluted with 1,000,000ml of a diluent solution to obtain 1ml of the diluted sample. Therefore, the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample.

Now, let's use the colony count to determine the number of bacteria in the diluted sample. We are told that 67 colonies were counted on the plate with 1ml of the 1:1,000,000 dilution. This means that each colony represents the growth of a single bacterium in the diluted sample. Therefore, the number of bacteria in the diluted sample is 67.

Using the unitary method, we can now determine the number of bacteria in 1ml of the original sample. We know that the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample. Therefore:

Number of bacteria in original sample = Dilution factor x Number of bacteria in diluted sample

Number of bacteria in original sample = 1,000,000 x 67

Number of bacteria in original sample = 67,000,000

So, the answer is that 67,000,000 bacteria were present in 1ml of the original sample.

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The triangle ABC has sides of length a = 106.5, b = 126, and c = 162, and angles A = 83.3, B = 43, and C = 53.7. Additionally, we have A₁ = 32.7, A₂ = 32.7, and C₁ = 8.2.

To solve the triangle ABC, we can use the Law of Cosines and the Law of Sines.

First, we can use the Law of Cosines to find the length of side a, which is opposite angle A:

a² = b² + c² - 2bc cos(B)

a² = (126)² + (162)² - 2(126)(162) cos(43)

a = 106.5

Next, we can use the Law of Sines to find angle A:

sin(A) / a = sin(B) / b

sin(A) = (a sin(B)) / b

A = 83.3

To find angle C, we can use the fact that the angles of a triangle add up to 180:

C = 180 - A - B

C = 53.7

Next, we can use the given relationship between angles A₁ and A₂ to find their values:

A₂ = A₁ = 2C₁

A₁ + A₂ + C₁ = 180

A₁ + 2A₁ + A₁/2 = 180

5.5A1₁ = 180

A₁ = 32.7

A₂ = 32.7

C₁= 8.2

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The distance between point D and E is 17.89 units

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

d=√((x2 – x1)² + (y2 – y1)²).

d = √ (11-3)² + 13-(-3)²

d = √ 8²+ 16²

d = √ 64 + 256

d = √320

d = 17.89 units

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Answer:

the logistic function that models the population of this species as a function of time is P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t)).

Step-by-step explanation:

We can use the logistic growth equation to model the population of this species as a function of time:

P(t) = K / (1 + A * e^(-r * t))

Where:

P(t) is the population at time t

K is the carrying capacity of the environment

A is the initial population as a proportion of the carrying capacity (A = P(0)/K)

r is the growth rate of the population

We are given that the initial population A is 350/7000 = 0.05 (since the carrying capacity is 7000). We are also given that after 5 years the population has grown to 900. So we can use this information to find the growth rate r:

P(5) = 900 = K / (1 + A * e^(-r * 5))

We also know that the carrying capacity K is 7000. Substituting these values, we get:

900 = 7000 / (1 + 0.05 * e^(-r * 5))

Multiplying both sides by the denominator and simplifying, we get:

1 + 0.05 * e^(-r * 5) = 7.777...

Subtracting 1 from both sides, we get:

0.05 * e^(-r * 5) = 6.777...

Dividing both sides by 0.05, we get:

e^(-r * 5) = 135.555...

Taking the natural logarithm of both sides, we get:

-ln(135.555...) = -r * 5

Solving for r, we get:

r = 0.1682...

Now that we have the growth rate r, we can use the logistic growth equation to find the function that models the population as a function of time:

P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t))

Therefore, the logistic function that models the population of this species as a function of time is P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t)).

The probability that Machine A filled a randomly selected bottle, given that it is defective, is 2/3 or approximately 0.67.

Let's define the subsequent events:

A: Machine A filled the bottle.

A': The bottle wasn't mechanically filled A (i.e. filled by machine AC).

D: the bottle is defective.

The chance that a randomly selected bottle was filled by machine A, assuming that it is broken, is known as P(A|D). The Bayes theorem provides us with:

P(A|D) = P(D|A)P(A) / P(D)

The following three terms on the right-hand side must be calculated:

P(D|A): the probability that a bottle is flawed given that machine A filled it. 10% of the bottles filled by machine A are reported to be faulty. so P(D|A) = 0.1.

P(A): the previous probability that machine A filled a bottle. There are just two machines, both of which fill bottles., P(A) = P(A') = 0.5.

P(D): the slight possibility that a bottle is flawed. The law of total probability can be used to calculate this:

P(D) = P(D|A)P(A) + P(D|A')P(A') = 0.1 x 0.5 + 0.05 x 0.5 = 0.075

Now we can plug in the values:

P(A|D) = 0.1 x 0.5 / 0.075 = 2/3

Therefore, the probability that Machine A filled a randomly selected bottle, given that it is defective, is 2/3 or approximately 0.67.

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We have to multiply numerator and denominator to 3/3 to make 6/6.

A fraction represents a part of a whole.

We have to convert the fraction three by three to six by six.

The given fraction is 3/3

Three by three

3 is the numerator and 3 in the denominator.

We have to make it 6/6.

To do this we have to multiply numerator and denominator by 2

3/3×2/2

Three by three times of two by two.

We get six divide by six

6/6

We know that the value of 3/3 is equal to one and the value of 6/6 is one.

So the fraction 3/3 and 6/6 are equivalent fractions.

Hence, we have to multiply numerator and denominator to 3/3 to make 6/6.

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Complete question

How to make 3/3 to 6/6 ratio?

(7+3/2)^3

Answer: 614.125

To round to the nearest whole number it would be 614

hope this helped =)

The expected value for playing roulette if you bet $15 on red is $6.32

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

The expected value for playing roulette if you bet $15 on red can be calculated as follows:

There are 18 red compartments out of a total of 38 compartments (18 red + 18 black + 2 neither red nor black).

Therefore, the probability of the ball landing on red is 18/38 or 9/19.

If the ball lands on red, you win $15 in addition to keeping your original $15 bet. So your total payout is $30.

If the ball does not land on red, you lose your $15 bet.

Using the formula for expected value, we can calculate the expected value of betting $15 on red as:

Expected value = (probability of winning * payout for winning) - (probability of losing * amount lost)

Expected value = (9/19 * $30) - (10/19 * $15)

Expected value = $270/19 - $150/19

Expected value = $120/19

Therefore, the expected value for playing roulette if you bet $15 on red is $6.32

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The system of equations has only one solution and is the point (1, 1)

Here we have the graph of a system of equations, where we can see that both of them are linear equations.

Whenw e have a graph of a system, the solutions are all the points where the graphs of the equations intercept.

On the given graph, we can see that the two lines intersept at the point (1, 1)

So we have only one solution and is the point (1, 1)

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The standard deviation of the portfolio may increase or decrease, depending on the weightings of the portfolio holdings. after she adds security Y

The portfolio standard deviation as a result of revealing how reliable an investment's earnings are, mean serves as a risk indicator. Because it reveals that the earnings are extremely unstable and fluctuating, a high standard deviation in a portfolio denotes significant risk.

The statistical measure of market volatility used to determine how widely prices deviate from the average price is called standard deviation. The standard deviation will show a low number, which denotes little volatility if prices move within a small range of prices.

The term "standard deviation" (or " σ") refers to a measurement of the data's dispersion from the mean.

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Donald  has a higher three-game series score.

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

here, we have,

Given that :

BRUCE :

score (x) = 500

League average (m) = 620

Standard deviation (σ) = 20

DONALD:

score (x) = 520

League average (m) = 625

Standard deviation (σ) = 25

Take standardized score of both Bruce and Donald

BRUCE:

Zscore = (x - m) / σ

Zscore = (500 - 620) / 20

Zscore = - 120 / 20

Zscore = - 6

DONALD:

Zscore = (x - m) / σ

Zscore = (520 - 625) / 25

Zscore = - 105 / 25

Zscore = - 4.2

Bruce's standardized score is lesser Than Donald's.

Hence, Donald has a higher three-game series score.

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The Cartesian Equation of the given parametric equation is written below

: x^2 + y^2=4

To eliminate the parameter t and find the Cartesian equation, we can use the trigonometric identity: cos^2(t) + sin^2(t) = 1. We can rearrange the given equations to get:

x(t) = 2cos(t)

y(t) = 2sin(t)

Dividing both sides of each equation by 2, we get:

cos(t) = x/2

sin(t) = y/2

Squaring both equations and adding them, we get:

cos^2(t) + sin^2(t) = (x/2)^2 + (y/2)^2

Using the identity, we can simplify the right-hand side to get:

1 = (x/2)^2 + (y/2)^2

Multiplying both sides by 4, we get the Cartesian equation:

x^2 + y^2 = 4

This is the equation of a circle with radius 2 centered at the origin. The domain of this equation is all real numbers, and the range is from -2 to 2 (inclusive) in both the x and y directions, represented as [-2,2].

In summary, the Cartesian equation of the given parametric equations is x^2 + y^2 = 4, with domain of all real numbers and range of [-2,2].

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The solution of the system of equations is c = 10 and d = 7.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

A system of equations,

c+d=17  {equation 1}

c-d=-3  {equation 2}

Adding both the equation,

we get,

c + d + c - d = 17 + 3

2c = 20

Divide by 2,

we get,

c = 10 and d = 7.

Therefore, c = 10 and d = 7.

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The value of the distance BC across the lake to the nearest foot is 463 ft.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

Extend the segment AB and draw a perpendicular line from B to C.

From the figure we see that:

tan (42) = y / 325 + x

y = tan (42) (325 + x)

Also, tan (70) = y / x

y = tan(70) x

Equating the values of y together we have:

tan (42) (325 + x) = tan(70) x

x = 158.430

Now,

cos (70) = 158.430/h

h = 463.2 ft

Hence, the value of the distance BC across the lake to the nearest foot is 463 ft.

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Solution in da attachment!! :)

The value of x in this figure is equal to: D. 5.

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

Sum of interior angles = 180 × (5 - 2)

Sum of interior angles = 180 × 3

Sum of interior angles = 540°.

112 + 7x + 5 + 6x + 2 + 10x - 8 + 4x + 24 = 540°.

27x = 135

x = 135/27

x = 5.

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x=-1/2 and  x=-3 are the zeros of the function y =2x²+7x+3

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given function is y= 2x²+7x+3

Factor out the equation

2x²+6x+x+3

2x(x+3)+(x+3)

(2x+1)(x+3)=0

So the roots we get

2x+1=0

x=-1/2 is one  zero and x=-3 is another zero.

Hence, x=-1/2 and  x=-3 are the zeros of the function y =2x²+7x+3

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The stores do not form similar rectangles, as the ratios between the equivalent side lengths are different.

Similar polygons are polygons that share these two features presented as follows:

To observe if the rectangles are similar for this problem, we must observe if the side lengths of Store B and of Store A have the same ratio, as follows:

Different ratios, hence not similar.

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Answer:

t = 9

Step-by-step explanation:

We know that 1/3 of t is 3, so to find t, we have to multiply 3 x 3 because we want to find 3/3 or 1 of t. When we multiply 3 x 3, we get t = 9

OR

We could also solve it like this-

1/3 × t = 3

1/3 goes to the other side so it becomes: [tex]t = \frac{3}{1/3} \\[/tex]

Then, it become multiplication so: [tex]t = 3 * 3/1[/tex]

So t is 9

Hope this helps!

Using equations, the time for the main engine 14.4 seconds and 21.6 seconds for the auxiliary engine

Let's call the time each engine takes to consume its allotted fuel supply as "t₁" for the main engine and "t₂" for the auxiliary engine.

From the first piece of information, we know:

t₁ = (2/3)t₂

From the second piece of information, we know that the combined fuel consumption time for both engines is 36 seconds:

t₁ + t₂ = 36

Now we can substitute the first equation into the second:

t₁ + (2/3)t₂ = 36

Combining like terms:

t₂ = 21.6

Finally, substituting t₂ back into the first equation:

t₁ = (2/3)(21.6) = 14.4

So the main engine alone could be fired for 14.4 seconds and the auxiliary engine alone could be fired for 21.6 seconds.

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The explicit solution of the given differential equation is [tex]& y=[c(1+\sqrt{x})-1]^2[/tex]

Solution of the Differential Equation :

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable)

We employ the approach of variable separation to discover the answer to the differential equation. By splitting the equation into two halves, we can find a solution. We integrate both sides after moving all of the equations involving the y variable to one side and all of the equations involving the x variable to the other side.

⇒[tex](\sqrt{x}+x) \frac{d y}{d x} & =(\sqrt{y}+y) \\[/tex]

⇒[tex]\frac{d y}{\sqrt{y}(1+\sqrt{y})} & =\frac{d x}{\sqrt{x}(1+\sqrt{x})}[/tex]

Put [tex]$\sqrt{y}=u \quad \sqrt{x}=v$[/tex]

⇒[tex]& \frac{1}{2 \sqrt{y}} d y=d u \frac{1}{2 \sqrt{x}} d x=d v \\[/tex]

⇒[tex]& \frac{d y}{\sqrt{y}}=2 d u \frac{d x}{\sqrt{x}}=2 d v[/tex]

By substituting,

⇒[tex]& \int \frac{7 d u}{1+u}=\int \frac{2 d v}{1+v} \\[/tex]

⇒[tex]& \ln (1+u)=\ln (1+v)+\ln c \\[/tex]

⇒[tex]& \ln (1+u)=\ln [c(1+v)] \\[/tex]

⇒[tex]& (1+u)=c(1+v) \\[/tex]

⇒[tex]& (1+\sqrt{y})=c(1+\sqrt{x}) \\[/tex]

⇒[tex]& \sqrt{y}=c(1+\sqrt{x})-1 \\[/tex]

⇒[tex]& y=[c(1+\sqrt{x})-1]^2[/tex]

Therefore, the explicit solution of the given differential equation is [tex]& y=[c(1+\sqrt{x})-1]^2[/tex]

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The supplement of angles 2.68, 2.79, 1.79, 2.04, 0.34 are 1.32, 1.21, 1.21, 1.96, 2.66 radians respectively.

The supplement of an angle is defined as the difference between π radians (180 degrees) and the given angle. If the measure of an angle is "x" radians, then its supplement is calculated as π - x radians.

The supplement of an angle represents the smallest angle that when added to the original angle.

Supplement of 2.68 radians: π - 2.68 = 1.32 radians

Supplement of 2.79 radians: π - 2.79 = 1.21 radians

Supplement of 1.79 radians: π - 1.79 = 1.21 radians

Supplement of 2.04 radians: π - 2.04 = 1.96 radians

Supplement of 0.34 radians: π - 0.34 = 2.66 radians

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___________The given question is incomplete, the complete question is given below:

find the supplement of each of the following angles measured in radians: 2.68 is supplementary to_____, 2.79 is supplementary to_____, 1.79 is supplementary to_______, 2.04 is supplementary to______, 0.34 is supplementary to_______.

Answer:

108+x=108 or x=108-108

x=72

x+y=108

y=108

x+88-88=108-88

x=92

88+y=88

if my answer is helpful comment

16 cookies were oatmeal

How long do cookies with oats last? The cookies can last up to two weeks when kept in an airtight container. The cookies may be frozen and kept for two months. But, these cookies taste best when they are still warm from the oven!

Keep crisp cakes in a jar with such a loose-fitting cover for cookies which will be consumed within a day or two; keep soft sweets in a jar with a close cover. Wax paper should be placed between the layers of cookies that are exceptionally soft, delicate, iced, or adorned. Many cookies may be frozen.

To find the number of oatmeal cookies, take the total number of cookies and multiply by the fraction that were oatmeal

24 * 2/3 = 48/3 = 16

16 cookies were oatmeal

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a) The coefficient of variation (CV) for Brand A, is equals to the 2.8%.

b) The coefficient of variation (CV) for Brand B, is equals to the 2.0%.

c) Brand B, is more consistently produces tablets as advertised.

We have comparing data of consumer groups of vitamin C tablets of two brands. Tablets for each group were selected randomly. Data from above table, For brand A :

Tablets contains the quantity of vitamin C = 500 mg

Sample mean = 250

Standard deviation = 7

For brand B :

Tablets contains the quantity of vitamin C = 250 mg

Sample mean = 500

Standard deviations = 10

Cofficient of variation, CV is statistical parameter and it is the ratio of the standard deviation to the mean. Formula is, Coefficient of Variation (CV)

= (Standard Deviation/Mean) × 100.

a) To calculate the coefficient of variation (CV) for Brand A = (7/250 )×100

= 2.8%

b) To calculate the coefficient of variation (CV) for Brand B = (10/500 )×100

= 2.0%

c) As we see, Cofficient of variation of advertising for brand B is less than brand A. So, Brand B more consistently produces tablets as advertised.

Hence, required brand is brand B.

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Complete question:

consumer interest group is comparing two brands of vitamin C. One group advertises that its tablets contain 500 mg of vitamin C. The other advertises that its tablets contain 250 mg of vitamin C. Tablets for each group were selected randomly. The table above shows the results.Vitamin C Content (mg) Brand A (500 mg) x = 250s = 500Brand B (250 mg) x = 500s = 10

a) Calculate the coefficient of variation (CV) for Brand A (1point)

b) Calculate the coefficient of variation (CV) for Brand B (1 point)

c) Which brand more consistently produces tablets as advertised? (2 points) d) Explain your answer to c) above. (1 point)

Answer: Let's call the first integer "x". Then, the second integer would be x + 1, and the third integer would be x + 2.

According to the problem, the sum of the first and the third integer is 8 more than the second integer:

x + (x + 2) = (x + 1) + 8

Simplifying the left side of the equation:

2x + 2 = x + 9

Subtracting x from both sides:

x + 2 = 9

Subtracting 2 from both sides:

x = 7

So the first integer is 7, the second integer is 8, and the third integer is 9. These are three consecutive integers that satisfy the condition in the problem.

Step-by-step explanation:

The area of the composite figure is 203 square km

The complete question is added as an attachment

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

Area of the figure = Sum of the areas of the individual shapes

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

Area of the figure = 3 * 4 + 12 * 6 + 17 * 7

Evaluate the expression

Area of the figure = 203

Hence, the area is 203 square km

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