Andrea, Ben, Christine, and Doug all live on the same street as their school. The street runs from east to west.Andrea lives 5 1/2 blocks to the west of school.Ben lives 4 blocks to the east of school.Christine lives 2 blocks to the west of school.Doug lives 6 1/2 blocks to the east of school.Use this information to complete the following.Part ARepresent the relative position of the houses on a number line with the school at zero, points to the west represented by negative numbers, and points to the east represented by positive numbers.Part BHow far does Ben live from Andrea? Show how you arrived at your answer using sums or differences.

Step 1 :

We use the Intersecting Chord Theorem which states that :

When two chords intersect each other inside a circle, the products of their segments are equal.

This theorem states that A×B is always equal to C×D

(no matter where the chords are).

From the question, A = 15, B = 12, C = ? , D = 18

Step 2 :

Using the equation, where AB = CD

CONCLUSION :

The value of C = 10 units

The selling price of the item is $55.

The money charged by the auction company is;

The fee paid to the auction company is $2.89

There will be 1,215,450 different random samples of four accounts are possible.

There are two methods to calculate the number of ways a certain event can happen. Both are used in different circumstances, such as, when the order of arrangement does not matter we use the combination and when the order matters we use permutation.

Given,

Population size, N = 75

Sample size, n = 4

We have selected a random sample of 4 accounts in order to learn about the population because these accounts can not be repeated and can be in any order, so we will use combination without repetition. According to this, the number of ways by which n subjects can be chosen from N subjects are given by,

[tex]\frac{N}{n}[/tex] = [tex]\frac{N!}{n!(N-n)!}[/tex]

Therefore, required number of ways are,

= 75!/4!(75-4)!

= 75!/4!*71!

= 75*74*73*72*/4*3*2

=  1,215,450

Hence, There will be 1,215,450 different random samples of four accounts are possible.

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we know that

total blocks=10

total odd prime numbers------> 3,5,7------> 3 numbers

so

Part 1

The probability of picking an odd prime number is

Part 2

total blocks=10

total numbers greater than zero also a perfect square ------>1,4,9---> 3 numbers

so

The probability is

Supposing the rate is:

(a) Converting tho mi/day

Knowing that 1 day = 24 hours

The rate is 48 mi/day.

(b) Finding how many days will it take to reach 14 1/2

14 1/2 is the same as 14.5

Dividing 14.5 by 48:

It will take 0.30 days.

(c) Finding when it will reach the destination.

Knowing the rate is 2 mi/hour, let's find how many hours it will take to reach 14.5 miles.

7.25 hours is 7 hours + 1/4 hour (15 min)

So, let's sum 06 (starting time) + 07 hours + 15 min

01:15 pm.

He will reach her destination at 01:15 pm.

Answer:

- (a) The rate is 48 mi/day.

- (b) It will take 0.30 days.

- (c) He will reach her destination at 01:15 pm.

You can use number line or inequalities to compare the temperatures of this three different cities.

Using number line to compare the temperatures 2.5, -3.5 F and -5 F

Using inequality

The slope of the line graph is -1.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

The slope is rise over run.

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Using (3, -3) and (-2, 2)

Therefore,

x₁ = 3

x₂ = - 2

y₁ = -3

y₂ = 2

Hence,

slope  = 2 + 3 / -2 - 3

slope = 5 / -5

Therefore,

slope = - 1

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Given the graph of a line

As shown the line passes through the point (0, 0)

So, the relation has the form:

We will find the value of k using one point lying on the line

As shown the line passes through the point (4, 14)

So, when x = 4, y = 14

Substitute with x and y into the equation: y = k * x

so,

so, the answer will be option C) y = 3.5x

The probability of an event is determined a follows;

We shall begin with the probability of selecting an even number as shown below;

Next we shall calculate the probability of selecting a number less than 5 as shown below;

The probability of event A OR event B occuring is calculated a follows;

The probability of selecting an even number or a number less than 5 is therefore

The correct answer is option A

Let us represent the premises given:

Then

We can subdivide the argument into substatement

Statement 1: If John is an aardvark then either Charlene has blue eyes or Bob counts

Statement 2: If Charlene has a blue eye then Edna drives a truck

Statement 3: Either John is an aadvark or Dan edits

Statement 4: Moly claims that either Bob counts or Edna drives a truck, but Moly is wrong

Therefor D

The above hypothesis and conclusion can be summarized below as;

Using a truth table calculator, the validity of the above arguments is shown below

Hence, we can conclude that the above is a valid argument.

ANSWER:

STEP-BY-STEP EXPLANATION:

The first thing is to draw the triangle ABC:

We have that the trigonometric cosine ratio is given as follows

You consider each parittion of the axis represents 1 unit.

You can notice that in the given image, the coordinates of the points A, B, C and D are the following:

A(-6,4)

B(-2,1)

C(2,3)

D(-1,-4)

where you have taken into account that point left side of the origin have negative x valuesand points right side have positive x values. Point down side of origin have negative y values and points above origin has positive y values.

In order to prove that the triangles are congruent, we can write the following statements and reasons:

first box in the first row:

statement: BD bisects angle ABC

reason: given

first box in the second row:

statement: angle ABD congruent to angle DBC

reason: A segment bisector divides a segment into two congruent segments.

second box in the second row:

statement: angle ADB congruent to angle BDC

reason: given

third box in the second row:

statement: side AB congruent to side BC

reason: given

Since we have two pairs of congruent angles and one pair of congruent sides that are not between the angles, we can prove the triangles congruent by case AAS.

Solution

The surface area of a Triangular prism is given as;

The volume of a triangular prism is given as;

The ratio of surface area to volume of the triangular prism​

The tangent of an angle, we will follow the steps below

Step 1: Write out the trigonometric ratio to obtain the tangent of an angle

From question 35

Step 2: Apply the tangent ratio

For tan B

Given the vector represented by:

You know that:

By definition, the Component Form of a vector is:

In this case, you only need to multiply the coordinates of "a" by 8, in order to find the Component Form of:

Therefore, you get:

Hence, the answer is:

The final velocity function is given to be:

Thus, we have:

Hence, the initial velocity of the object is 102ft/s

From the graph, we are asked to find the domain and randge./.

First lets know what domain and range.

Domain of a function is the set of values that are allowed is the plug into our function.

The domain and rang of the function written in an inequality form are:

Domain:

-1 < x < 4

Range:

-10 < y < 3

In order to find the value of a composition of functions at x = a, (f º g)(a), we first find the value of g(a), then find the value of f(x) at x = g(a).

(f º g)(a) = f(g(a))

In this problem, the values of f(x) and g(x) are shown in the table, for integer values of x from 0 to 9.

So, we have:

1. (f º g)(8) = f(g(8))

From the table, we see that

g(8) = 4 (value of g(x) in the line corresponding to x = 8)

Then:

f(g(8)) = f(4) = 4 (value of f(x) in the line corresponding to x = 4)

Thus:

2. g(f(3))

f(3) = 8

g(8) = 4

Thus:

3. f(f(1))

f(1) = 6

f(6) = 2

Thus:

4. (g º g)(6) = g(g(6))

g(6) = 7

g(7) = 3

Thus:

So to make equal groups just create the number of groups (divisor, in this case: 4) and insert into that the number of the quotient( in this case: 7)

1) Let's make equal groups for that division since 7 added 4 times is equal to 28:

2) Since 7 x 4 is the same as adding 7 four times, we have above four groups with seven balls that added up yields 28, in each group we have 7 balls.

3) So to make equal groups just create the number of groups (divisor) and insert into that the number of the quotient. Note that this is valid just for exact divisions.

Data

• Small cones (s): $2

• Large cones (L): $3.50

• Total sold (T): $163

• The number of L sold was 12 more than the number of ,s.

Procedure

We have to build a system of equations based on the information given.

• Equation 1:, she sold $163 of small and large cones

• Equation 2: ,the number of L sold was 12 more than the number of ,s.

As we have L isolated in the second equation, it is convenient to use this expression in the first equation to have it in terms of one variable:

Simplifying the parenthesis we get:

As we have two terms with an s we can group in each side of the equation the common terms and simplify them as follows:

Now that we have s, we just have to replace this value in equation 2:

Answer:

• Small snow cones: 22

• Large snow cones: 34

Given the expression :

The answer will be as follows, add the decimal point and two zeros

See the following picture:

Answer

Question 3

Largest number where the sum of the digits is 16 is 862

Question 4

The number between 200 band 400 with 6 more tens than ones is 382

Explanation

We can only use numbers from the digit bank to answer this questions.

Question 3

Largest number where the sum of the digits is 16 is 862

Question 4

A number between 200 and 400 with 6 more tens than ones.

Noting that the tens digit is the second digit from the right in a number and the ones digit is the first number from the right for any number.

So, we are asked to form a number whose second number from the right is 6 more than the first number from the right.

So, we can easily see that

The ones number has to be 2

The tens number has to be 8 (Since 8 is 6 more than 2)

Then, for the third and last number, since the number has to be between 200 and 400, the last number has to be 3.

So, the number between 200 band 400 with 6 more tens than ones is 382

Hope this Helps!!!

Answer:

$8.4

Explanation:

To find how much money you should leave for a tip, we need to find how much is 20% of $42. So, to calculate this, we need to multiply 42 by 20 and then divide by 100, so:

$42 x 20% = 42 x 20 / 100 = 840 / 100 = 8.4

Therefore, the answer is $8.4

1) Let's multiply the second equation by -2, to eliminate x

2x -3y=-11

x+3y = 8

2) Now let's add both equations

2x -3y=-11

-2x-6y = -16

--------------------

-9y = -27

3) Divide both by -9

y=3

4) Plug y=3 into the simpler original equation, to make calculations easier:

x +3y=8

x+3(3) =8

x +9 =8 Subtract 9 from both sides

x = 8-9

x=-1

So, after multiplying it we add both equations to eliminate one variable either x or y.

A horizontal line is in the form

y =

This means the x component changes and the y component stays the same

( -7, 10)

The line is in the form

y = 10

x can be any value

The slope is zero since it is horizontal

The point ( 3,10) is on the line

The equation of the line is y = 10

The y intercept is 10 not -7

Answer

The statement is always true.

Explanation

Since equivalent ratios reduce to essentially the same fundamental ratios, if the numerator of one of the ratios is greater than its denominator, then the numerator of each of the equivalent ratios must be greater than each of their corresponding denominators too.

So, this statement is always true!

Hope this Helps!!!

EXPLANATION

The three numbers are 36, 46 and 56. This is because the only three numbers that have 6 ones and wich are included between 30 and 60 are 36, 46 and 56, no other number can comply that condition.

First box: 10n

2

10n + 2

The area model = 2 (5n + 1)

Thsi can expanded into:

2 (5n) and 2(1)

In the first box:

2 (5n) = 10n

In the second box:

2(1) = 2

In the third box:

2 (5n + 1) = 10n + 2

a. If a friend says his grade is 12 points lower than your grade, it means your grade is greater than his grade, if your grade is represented by x, then the grade of your friend can be found by subtracting 12 from your grade, this can be written as:

b. If x represents your friend's grade instead of yours, then to find your grade you need to add 12 to his grade, it can be represented as:

The correct answers are B. and D.