Peter bought 8 lemons for $6. Each lemon was the same price.
What was the cost of 1 lemon?

Answer:

2/3

Step-by-step explanation:

We know that 0.6 is part of the 1/3 family.

1/3 would be equal to 0.333...

2/3 would be equal to 0.666...

3/3 would equal to 1

Alternatively, we know that anything out of 9 or 99 would be a repeating decimal. Simply take 6 and divide it by 9:

6/9 = 0.666

We can then simplify the fraction by dividing both top-bottom by 3:

6/9 = 2/3

Answer:

Step-by-step explanation:

Given the expression (8x² −15x)−(x² −27x) = ax² +bx, we are to determine the value of b-a. Before we determine the vwlue of b-a, we need to first calculate for the value of a and b from the given expression.

On expanding the left hand side of the expression we have;

= (8x² −15x)−(x² −27x)

Open the paranthesis

= 8x² −15x−x²+27x

collect the like terms

= 8x²−x²+27x −15x

=  7x²+12x

Comparing the resulting expression with ax²+bx

7x²+12x =  ax²+bx

7x² = ax²

a = 7

Also;

12x = bx

b =12

The value of b - a = 12 - 7

b -a = 5

Hence the value of b-a is equivalent to 5

The value of b minus a is 5

Since the expression is

\((8x^2 -15x)-(x^2 -27x) = ax^2 +bx\)

Here we have to expand the left-hand side of the expression so it should be like

\(= (8x^2 -15x)-(x^2 -27x)\\\\= 8x^2 -15x-x^2+27x\\\\= 8x^2-x^2+27x -15x\\\\= 7x^2+12x\)

Now

\(7x^2+12x = ax^2+bx\\\\7x^2 = ax^2\)

a = 7

Also;

12x = bx

b =12

So,

The value of b - a = 12 - 7

b -a = 5

Hence the value of b-a should be 5

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The solutions to the system of equations f(x) = x² + x - 6 and g(x) = -2x² - 2x + 12 are (-3, 0) and (2, 0). So, correct option is 1.

To graph the functions f(x) and g(x) using a calculator, we can enter the equations into the calculator's graphing function and choose an appropriate window to display the graph. Once the graphs are displayed, we can look for the points of intersection to find the solution to the system of equations.

Using a graphing calculator, we can see that the graphs of f(x) and g(x) intersect at two points: (-3, 0) and (2, 0). These points represent the x-coordinates of the solutions to the system of equations.

To verify that these points are indeed the solutions, we can substitute each of them into both equations and check that they satisfy both equations simultaneously.

For point (-3, 0):

f(-3) = (-3)² + (-3) - 6 = 0

g(-3) = -2(-3)² - 2(-3) + 12 = 0

Therefore, (-3, 0) is a solution to the system of equations.

For point (2, 0):

f(2) = 2² + 2 - 6 = 0

g(2) = -2(2)² - 2(2) + 12 = 0

Therefore, (2, 0) is also a solution to the system of equations.

The point (0, -6) and (0, 12) are not the points of intersection and (-6, 12) is not a solution to the system of equations.

Therefore, the answer is option 1.

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Answer:

The answer is

6x²+x-2

.Step-by-step explanation:

The probability that exactly 3 residents in the survey have adequate earthquake supplies is 0.2824. The probability that more than 3 residents have adequate earthquake supplies is 0.4643. The probability that at least 3 residents have adequate earthquake supplies is 0.8177. The probability that between 2 and 4 residents have adequate earthquake supplies is 0.8126.

In this problem, we are dealing with a binomial distribution, where each resident in the survey can be considered as a Bernoulli trial with a success probability of 0.28 (the proportion of residents in Ventura County with adequate earthquake supplies). Let's calculate the probabilities for each part.

a. To find the probability of exactly 3 residents having adequate earthquake supplies, we use the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the success probability. Plugging in the values, we have P(X = 3) = (8 choose 3) * (0.28)^3 * (1-0.28)^(8-3) ≈ 0.2824.

b. To find the probability of more than 3 residents having adequate earthquake supplies, we need to calculate the probabilities of having 4, 5, 6, 7, and 8 residents with adequate supplies and sum them up. P(X > 3) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8). Using the same formula as before, we can calculate each term and sum them to get P(X > 3) ≈ 0.4643.

c. To find the probability of at least 3 residents having adequate earthquake supplies, we need to calculate the probabilities of having 3, 4, 5, 6, 7, and 8 residents with adequate supplies and sum them up. P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8). We can use the binomial probability formula to calculate each term and sum them to get P(X ≥ 3) ≈ 0.8177.

d. To find the probability of having between 2 and 4 residents (including both 2 and 4) with adequate earthquake supplies, we calculate the probabilities of having 2, 3, and 4 residents with adequate supplies and sum them up. P(2 ≤ X ≤ 4) = P(X = 2) + P(X = 3) + P(X = 4). Using the binomial probability formula, we can calculate each term and sum them to get P(2 ≤ X ≤ 4) ≈ 0.8126.

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Answer:

A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

There are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

To determine the number of ways to award first, second, and third prizes in a contest with 950 contestants, we can use the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of contestants and r is the number of prizes to be awarded (in this case, 3).

Using this formula, we get:

P(950, 3) = 950! / (950 - 3)!

= 950! / 947!

= 950 × 949 × 948

= 853,818,600

Therefore, there are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

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Answer:

its 10 bro calm down ok chill

Answer:

10

Step-by-step explanation:u have 5 and add 5 more

Answer:

c < -1

Step-by-step explanation:

-3c - 8 > -5

Add 8 to both sides.

-3c > 3

Divide both sides by -3. REMEMBER: in an equality, when dividing by a negative, flip the inequality sign.

c < -1.

The expression in spherical coordinates is r² · sin² α - 6 · r · cos α + 4 = 0.

In this question we must transform an expression in rectangular coordinates, whose equivalent expression in spherical coordinates by using the following transformation:

f(x, y, z) → f(r, α, γ)

x = r · sin α · cos γ, y = r · sin α · sin γ, z = r · cos α

If we know that x² + y² + 2² - 6 · z = 0, then the equation in spherical coordinates is:

(r · sin α · cos γ)² + (r · sin α · sin γ)² + 4 - 6 · (r · cos α) = 0

r² · sin² α · cos² γ + r² · sin² α · sin² γ - 6 · r · cos α + 4 = 0

r² · sin² α - 6 · r · cos α + 4 = 0

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Answer:

22.9504 pounds

Step-by-step explanation:1 pint = 1.0432 pounds so multiply that by 22 and you get 22.9504 pounds

Answer:

22 pints = 22 pounds

Step-by-step explanation:

There is 1 pint in a pound so your answer would be..

22 pounds

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

We discovered that a10 = 207 after answering the presented question using arithmetic progression.

What is Arithmetic Progression?

Arithmetic Progression (AP) is a numerical series in which the difference between any two consecutive integers is a constant value. Arithmetic Sequence is another name for it.

Solution:

9,15,25..............

15-9 = 6

25-15 = 10

a4 - 25 = 14 => a4 = 39

a5-39 = 18 => a5 = 57

a6-57 = 22 => a6 = 79

a7-79 = 26 => a7 = 105

a8 - 105 = 30 => a8 = 135

...

...

...

a10 - 169 = 38 => a10 = 207

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Answer:

The Four Virtues of Ethical Sport Ethics in sport requires four key virtues: fairness, integrity, responsibility and respect.

Step-by-step explanation:

hope this helps

Different starting lineups can be created - 120+60+120=300. A certain college team has on its roster 4 centers, 5 guards, 5 forwards, and one individual (x) who can play either guard or forward.

1. A lineup without x is an example. You must decide.

It can be made as -

2C5 × 2C3× 1C4 = 10× 3×4 = 120 ways

2. Consider starting lineups with guard x. You must decide.

1C5×2C3×1C4 = 5×3×4 = 60 ways

3. Think about lineups where x is the forward. You must decide.

2C5×1C3×1C4 = 10×3×4 = 120 ways.

Therefore, total number different lineups is - 120+60+120=300.

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Answer: piece of paper or a door

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

30/75 = .4

Answer:

40%

Step-by-step explanation:

Start by doing 30 ÷ 75 which gives you 0.4

0.4 as a percentage is 40%

Find percentage from decimals by moving the decimal place two times to the right.

This situation follows the next exponential decay formula:

where

• a is the initial hairs

• r is the losing rate (as a decimal)

• t is time in years

• y is the remaining hairs

Replacing with a = 1889, r = -0.26 (notice the negative sign) and t = 8, we get:

He will have left about 170 hairs after 8 years

100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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Answer:

I believe all you have to do is click on the crown icon that is near the answer.

Answer: I was looking at someone’s answer and I was trying to find the crown but it wasn’t there so how do I mark them brainliest?

Step-by-step explanation:

The constant 0.2 in the function f(t) = \(460(0.2)^t\)represents the rate of change of the quantity, indicating a continuous decrease at a rate of 20% per month.

In the given function, the term \((0.2)^t\) represents the exponential decay factor. The value of 0.2 indicates that the quantity decreases by 20% with each passing month. This means that after one month, the quantity will be reduced to 20% of its original value, after two months it will be reduced to 20% of the remaining value, and so on. The exponent t represents the number of months. As t increases, the exponentiation causes the quantity to decrease exponentially.

For example, let's consider the initial quantity as 460. After one month, the quantity will be 460 * 0.2 = 92. After two months, it will be 92 * 0.2 = 18.4, and so on. The constant 0.2 acts as a multiplying factor that determines the rate of decrease. The smaller the constant, the faster the quantity diminishes. In this case, the constant 0.2 indicates a relatively rapid decay, as it results in a 20% reduction per month.

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Based on the given side lengths of 3cm, 7cm, and 7.4cm, the triangle is a(n) scalene triangle. In a scalene triangle, all sides have different lengths.

Triangles are described in terms of their sides and angles in geometry. A closed planar three-sided polygon shape with three sides and three angles is known as a triangle. The lengths of the sides of a scalene triangle vary. They are not equal, and the angles have three measurements. However, it still has a 180° angle sum, just like all triangles.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees. As a result, it satisfies the triangle's condition of angle sum.

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Answer: I wish I can help you, But I can't

Step-by-step explanation: lll

Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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Answer:

the answer is 3,680

Step-by-step explanation:

The supply equation is p = -0.05q + 3.15 and the demand equation is p = 0.05q + 2.85. The equilibrium price is $3.00 per gallon, and the equilibrium quantity is 135 billion gallons.

To find the supply and demand equations, we can use the given data points and apply the slope-intercept form of a linear equation, which is p = mq + b, where p is the price and q is the quantity.

First, let's find the slope (m) for the supply equation. We have two points: (133, 3.00) and (152, 3.15). Using the slope formula (m = (y2 - y1) / (x2 - x1)), we get m = (3.15 - 3.00) / (152 - 133) = 0.15 / 19 ≈ 0.0079. Next, we can substitute one of the points into the equation and solve for b: 3.00 = 0.0079 * 133 + b, which gives us b ≈ 2.85. Therefore, the supply equation is p = -0.0079q + 3.15.

Similarly, for the demand equation, using the points (133, 3.00) and (134, 3.15), we find the slope: m = (3.15 - 3.00) / (134 - 133) = 0.15 / 1 = 0.15. Solving for b using the point (133, 3.00), we get b = 2.85. Thus, the demand equation is p = 0.15q + 2.85.

To find the equilibrium price and quantity, we set the supply and demand equations equal to each other: -0.0079q + 3.15 = 0.15q + 2.85. By solving this equation, we find q ≈ 135 billion gallons. Substituting this value back into either the supply or demand equation, we get the equilibrium price p ≈ $3.00 per gallon. Therefore, the equilibrium quantity is 135 billion gallons, and the equilibrium price is $3.00 per gallon.

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Answer:

B, C, and D.

Step-by-step explanation:

1. Finding the midpoint of a portion

2. Drawing an opposite line portion from an offered indicate a given fragment

3. Drawing an opposite line portion through a given point on a given section

4. Drawing a line through a given guide parallel toward a given line

Pls, choose me as brainliest!