there are 3 towns, ainsly broking and Cinderford​

The distance between the points M=(-4, 9 ) and L=(-1. 1) in the coordinate plane is [tex]\sqrt{73}[/tex].

Explain Coordinate Plane.

In a plane, a Cartesian coordinate system is a system of a coordinate that designates each point uniquely by a pair of numerical coordinate in a plane, which are the signed distances from two fixed perpendicular oriented lines to the point on the same plane, measured in the same unit of length.

Solution Explained:

Using the distance formula, we have

[tex]\sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2} }[/tex]

Substituting the values using the values of the points

[tex]\sqrt{(-1 + 4) ^{2} + (1 - 9) ^{2} }[/tex]

[tex]\sqrt{(3) ^{2} + (-8) ^{2} }[/tex]

[tex]\sqrt{9 + 64}[/tex]

[tex]\sqrt{73}[/tex]

Hence, the distance between the two points is [tex]\sqrt{73}[/tex]

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The salary is $55100 when [tex]a_n=55100[/tex].

[tex]55100=41900+1100n\\\\13200=1100n\\\\12=n[/tex]

So, her salary will be $55,100 after 12 years.

The salary is $55100  after 12 years.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that construction worker's starting salary is $43,000. Each year she receives a $1100 raise.

Therefore, an = 41,900 + 1100n

An explicit formula of the form an = bn + c to model this situation.

When n = 10,

= 41,900 + 1100n

= 41,900 + 1100(10)

= 41,900 + 11000

= 52,900

when an  = 55,100

Then an = 41,900 + 1100n

55,100 = 41,900 + 1100n

1100n = 55,100 - 41,900

1100n = 13200

n = 13200/ 1100

n = 12

So, her salary will be $55,100 after 12 years.

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Proof:

L.H.S. = A - (B - C)

= A - (B ∩ C'), since A - B = A ∩ B'

= A ∩ (B ∩ C')'

= A ∩ {B' U (C')'}, since (A ∩ B)' = A' U B'

= A ∩ (B' U C)

= (A ∩ B') U (A ∩ C)

= (A - B) U (A ∩ C) = R.H.S.

∴ A - (B - C) = (A - B) U (A ∩ C)

Hence, This completely the proof.

Some properties of set algebra:

1. A U Φ = A, A ∩ Φ = Φ

2. A U U = U, A ∩ U = A

3. A U A = A, A ∩ A = A

4. A U (B U C) = (A U B) U C

5. A ∩ (B ∩ C) = (A ∩ B) ∩ C

6. A U (B ∩ C) = (A U B) ∩ (A U C)

7. A ∩ (B U C) = (A ∩ B) U (A ∩ C)

8. A U A' = U

9. A ∩ A' = Φ

10. (A U B)' = A' ∩ B'

11. (A ∩ B)' = A' U B'

12. A - B = A ∩ B'

13. A - (B ∩ C) = (A - B) U (A - C)

14. A - (B U C) = (A - B) ∩ (A - C)

15. A Δ B = (A - B) U (B - A)

16. A Δ B = B Δ A

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The total number of days for which the food supply will last is 37 days.

Given,

The number of days that the food supply would last is = ?

The number of pounds of grain = 10656 pounds

The number of cattle is = 24 cattle

The number of pounds eaten by each cow each day = 12 pounds.

Therefore if one cow eat 12 pounds a day then 24 cows=

12 × 24 = 288 pounds a day

Therefore if,

288 pounds = 1 day

10656 pounds = 10656/288

= 37 days

Therefore, the number of days that the food supply would last is  37 days.

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The probability of observing an 85°F temperature or higher in Los Angeles during a randomly chosen day in June is 0.266.

We are given information about the temperatures in Los Angeles for the month of June. The average daily high temperature in June in LA is 80°F. The standard deviation in the temperature values is 8°F. The temperatures in June closely followed a normal distribution. We need to find the probability of observing an 85°F temperature or higher in Los Angeles during a randomly chosen day in June. Let the mean, standard deviation, value, z-score, and probability be represented by the variables M, S, X, Z, and P. First of all, we will find the z-score for the given temperature value.

Z = (X - M)/S = (85 - 80)/8 = 5/8 = 0.625

We want to find the probability for Z-values greater than or equal to the calculated z-score. We need to use the z-score table to find the corresponding probability.

P(z ≥ 0.625) = 0.26599

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Answer:

√(16) - √(-2) + √(16) + √(-200) =

8 + 12.7279221 i

The values of the vertical motion modelled by the quadratic function, h(t) = -16·t² + 54·t + 3 of the object are;

The maximum height reached is approximately 48.6 units

The time of flight is approximately 3.4 seconds

A quadratic function is a polynomial of the form y = a·x² + b·x + c, where the value of a is larger than or lesser than 0

First part;

The function, for the vertical motion, h(t) = -16·t² + 54·t + 3, is a quadratic function;

The maximum height is found by using the equation that gives the value of x at the maximum value, which is presented as follows;

At the maximum point, [tex]x = \dfrac{-b}{2\cdot a}[/tex]

From the equation, a = -16, b = 54, c = 3, and x = t, which gives;

[tex]t = \dfrac{-54}{2\times (-16)} = 1.6875[/tex]

The maximum height is therefore;

h(1.6875) = -16 × 1.6875² + 54 × 1.6875 + 3 = 48.6

The time the object is in the air is found using the equation;

h(t) = 0 = -16·t² + 54·t + 3

Using the quadratic formula, [tex]x= \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2 \cdot a}[/tex], we have;

[tex]t= \dfrac{-54\pm \sqrt{54^2 - 4\times (-16)\times 3} }{2 \times (-16)}=\dfrac{27\pm \sqrt{777} }{16}[/tex]

The time of flight is therefore;

[tex]t=\dfrac{27+ \sqrt{777} }{16}\approx 3.4[/tex]

The time of flight is 3.4 seconds

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Answer:

bag A

Step-by-step explanation:

10/1.10=9.09090909091

12/1.38=8.69565217391

6/0.84 7.14285714286

Answer:

Name: TRIANGLE CONGRUENCE THEOREMS COMMON CORE GEOMETRY HOMEWORK REASONING 1. Which picture below that does not contain enough information to prove that AABCADEF? D (4) 2. In the following diagram, we know that AD a BC and 2. Which of the three theorems (ASA, SAS, or SSS) would be used to justify that AMBC ACDA? Explain your choice. 3. An additional theorem could be now stated: If two legs of one right triangle le are equal, respectively, to two legs of another right triangle, then the two right triangles are congruent. Which of the three major theorems (ASA, SAS, or SSS) would this be an extension of? Explain your choice. COMMON CORE GEOMETRY, UNIT a3-EtouDEAN TRIANGLE nor AND Cosstuimoss-Less #3 math instruction, RED HoOK, NY 12571,0 2018

Name: TRIANGLE CONGRUENCE THEOREMS COMMON CORE GEOMETRY HOMEWORK REASONING 1. Which picture below that does not contain enough information to prove that AABCADEF? D (4) 2. In the following diagram, we know that AD a BC and 2. Which of the three theorems (ASA, SAS, or SSS) would be used to justify that AMBC ACDA? Explain your choice. 3. An additional theorem could be now stated: If two legs of one right triangle le are equal, respectively, to two legs of another right triangle, then the two right triangles are congruent. Which of the three major theorems (ASA, SAS, or SSS) would this be an extension of? Explain your choice. COMMON CORE GEOMETRY, UNIT a3-EtouDEAN TRIANGLE nor AND Cosstuimoss-Less #3 math instruction, RED HoOK, NY 12571,0 2018

Step-by-step explanation:

The smallest possible number Hannah could be thinking of will be 351.

And, the largest possible number Hannah could be thinking of will be 355.

Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.

Given that;

Hannah thinks of a whole number.

Rounded to the nearest 10, her number is 350.

And, Rounded to 1 significant figure, her number is 300.

Now,

Since, Hannah thinks of a whole number.

Rounded to the nearest 10, her number is 350.

And, Rounded to 1 significant figure, her number is 300.

Hence, We get;

The smallest possible number Hannah could be thinking of = 351.

And, The largest possible number Hannah could be thinking of = 355.

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Reason:

The x value x = 4 repeats itself. We have the input x = 4 lead to multiple outputs (y = 0 and y = 2) at the same time. This is enough evidence to conclude we do not have a function.

A function is only possible if any given input leads to exactly one output.

If you were to plot these points, then you should note (4,0) and (4,2) fail the vertical line test. To pass the vertical line test, it should be impossible to draw a single vertical line through more than one point.

By finding all the probabilities we will see that the event that is least likely to occur is the one in option D.

Let's find the probability for each event.

A) The probability is computed as the quotient between the outcomes that meet the conditions for the event and the total number of outcomes.

Here the outcomes are {1, 2, 3, 4, 5, 6, 7, 8}

The outcomes that meet the condition (less than or equal to 6) are:

{1, 2, 3, 4, 5, 6}

So 6 outcomes out of 8 meet the condition, the probability here is:

a = 6/8 = 3/4 = 0.75

B) The probability here is 1, as all the outcomes meet the condition of "landing in some color"

C) If there are 100 tickets in total and you have 29, then the probability of winning is:

b = 29/100 = 0.29

D) There are 10 strawberry chews and 50 cherry chows, so the total number of candy is 50 + 10 = 60, and 10 of these are strawberry chews, then the probability of taking one of these is:

d = 10/60  =0.167

So the smaller probability is the one for event D, that is the correct option.

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a) The binomial distribution is suitable to use when:

b) The probabilities are given as follows:

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

The parameters are given by:

The binomial distribution is used when there is a fixed number n of trials, with each trial having only two possible outcomes, success or failure, and trials are independent, that is, the probability of success on any trial is the same.

For item b, the parameter p is obtained as follows:

The sum of all the probabilities is of one, hence:

5 x 0.5p + p = 1

3.5p = 1.

p = 1/3.5

p = 0.2857.

For item i, the probability is obtained as follows:

Hence:

p = (1 - 0.2857)^5 x 0.2857 = 0.0531 = 5.31%.

For item ii, the probability is P(X = 3) when n = 8, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{8,3}.(0.2857)^{3}.(0.7143))^{5} = 0.2428[/tex]

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Answer:

Step-by-step explanation:

5x+30-35

5x-5

Answer:

[tex]5x[/tex] - [tex]5[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

216÷3=72

72 is your answer

Answer:9

Step-by-step explanation:um

Mina uses 17/18 inches of chalk.

What is algebra?

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.

Here, we have

she used 1/3 of a piece of chalk that was originally 2 5/6 inches long.

Now, we have to find how many inches of chalk did she use?

= 1/3 × 2 5/6

= 1/3 × 17/6

= 17/18 inches.

Hence, Mina uses 17/18 inches of chalk.

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Answer:

17/18

Step-by-step explanation:

Example:

120 and 45

10 and 12 can go into 120. 10 can go into 5 and 2, while 12 can go into 3 and 4. 4 can be still divisible, so it would be 2 and 2.

45 is 9x5. 9 can be divisible, so you would turn them into 3 and 3.

The LCM will be the product of the largest multiple of each prime that appears on at least one list. For example, we have a 2, 3, and 5, so I’ll choose the largest multiples of each and find their product. There are three 2's, three 3's, and 5, or 8 x 9 x 5. That would get you 360.

See how you could get that with your problem?

P.S. I don't answer questions directly, instead, I use examples. Feel free to use other suggestions if this one doesn't appeal to you.

Step-by-step explanation:

x + 7 = 11

x + 7 - 7 = 11 - 7

x = 4

Hope this helps! :)

Answer:

[tex]\displaystyle 4[/tex]

Explanation:

Use the inverce of Addition [Deduction (or Subtraction)] to arrive at your answer:

[tex]\displaystyle x + 7 = 11 \hookrightarrow -7 + 11 = x \\ \\ 4 = x[/tex]

I am joyous to assist you at any time.

Answer:

The width of the rectangle should be 8 units.

Calculation of the width:

Since The width of a rectangle is 1 units less than the length. The area of the rectangle is 72 units.

Here we know that

Area = (length) (width)

Here we assume length be x

So, width be = x - 1

So,

(x) (x - 1) = 72

(x + 8) (x - 9)

So, the width should be

= 9 - 1

= 8

hence,

Answer:

I think its false

Step-by-step explanation:

Answer: True i think

Step-by-step explanation: If Nancy is two years older than Mark who is 13, then Nancy would be 15, 15 + 13 equals 28.

The amount that the cell phone owner will pay for the overages is $14.91.

The overage is the difference between the actual usage in minutes and the estimated usage.

For instance, if the plan estimates that the phone usage per year would be 4,000 minutes, but the plan holder uses 4,010 minutes, the extra 10 minutes are regarded as overages.

The opposite of overages is underages.  If underages are part of the phone plan, the plan holder will be refunded accordingly.

Usually, overages attract a variable plan rate per minute.

Fixed charge per month = $35.98

Utilities tax APR = 6.5%

Overages = 40 minutes

Rate per overage minute = $0.35

The total charge for overage = $14 ($0.35 x 40)

Interest on the overages = $0.91 ($14 x 6.5%)

Total payment for the overages = $14.91 ($14 + $0.91)

Thus, for going over the plan by 40 minutes at $0.35 plus an APR of 6.5%, you will pay $14.91 for the overages.

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The larger angle in the straight line is 101°.

What is straight line angle?

   A straight angle in mathematics is one with a sine angle of 180 degrees. Due to the fact that it resembles a straight line, it is called straight. Those angles that make a straight line are known as straight angle pairs. Each angle in this pair adds up to 180 degrees, regardless of how many angles make up the pair. A straight angle in geometry is one that is equal to 180 degrees. It looks like a straight line, hence the name "straight angle." It is an angle, then, whose sides are in the same straight line but opposite to the vertex.

We know that , In straight line angle at any point is 180°.

Here,

=> (14x+3)°+(11x+2)°=180°

=>14x+3+11x+2=180

=>25x+5=150

=>25x=180-5=175

=> x = 175/25 = 7.

Then , 14(7)+3=101° and 11(7)+2=79°.

Hence the larger angle is 101°.

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Step-by-step explanation:

1 have to make number cross the top number n sce

You apply the rule for a pair of parallel angles cut by a line. So that means that 59 degrees equals 2x-15.

59=2x-15

59+15 = 2x

74=2x

x= 37

Answer:

  D.  A triangle with angles measuring 75°, 60°, and 45°​

Step-by-step explanation:

Given various triangle descriptions, you want to know which one describes more than one triangle.

The angles and sides of a triangle satisfy a few different relations:

A. Two sides and the included angle can be used with the Law of Cosines to find the length of the third side. That is, a single triangle is created by these measurements.

B. Sides measuring 4, 8, and 15 do not satisfy the triangle inequality, so no triangle is created by these measurements.

C. Sides measuring 6, 8, and 10 satisfy the triangle inequality, so will create a single triangle. (That triangle is a right triangle.)

D. The given angles total 180°, so could be the angle measures of any number of triangles. At least one side length must be specified in order to completely define a single triangle. These measures create more than one triangle.

The domain of given graph is [-8,8].

The domain of a function is a set of all x values i.e. the numbers for which function is defined. All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range. When viewing a graph, the whole range of numbers from left to right comprise the domain.

As seen from the graph graph is limited from -8 to +8 that means the domain of the graph is [-8,8].

Or it can be written as [tex]-8\leq x \leq 8[/tex]

Therefore, the domain of the function is [-8,8].

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The highest amount that can be charged to your credit account is called credit limit and is therefore denoted as option A.

This is referred to as a type of banking arrangement which involves a customer receiving goods from a store and paying for them over a period of time.

The credit card which is linked to the account is used for such type of transactions and the highest amount that can be charged to it is known as credit limit which is therefore the reason why option A was chosen as the correct choice.

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Answer:

- 42 , - 17

Step-by-step explanation:

(a)

substitute x = 5 into f(x) , that is

f(5) = 5² - 10(5) - 17 = 25 - 50 - 17 = 25 - 67 = - - 42

(b)

substitute x = 0 into f(x)

f(0) = 0² - 10(0) - 17 = 0 - 0 - 17 = - 17