Points A, B and C make the triangle triangle ABC and are at the coordinates A(- 4, 3) , B(- 48, 17) and C(22, - 53) . Point D is the midpoint of BC and AD is a median of triangle ABC . What is the equation of the median in standard form?

PLEASE HELP ASAP

Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:

a) 60,466,176.

b) 5,961,600.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with n1, n2, ...  ways to be done, each thing independent of the other, the number of ways they can be done is N=n1*n2*n3*....

Item a:

No restrictions, hence, for each of the five characters, there are 36 outcomes, hence n1=n5=36.

Then, the possible number of passwords is:

N=36^5=60,466,176

Item b:

The letters and the digits have to be alternated, hence:

Starting with a letter n1=n3=n5=36, n2=n4=10.

Starting with a digit n1=n3=n5=10, n2=n4=36.

Then, the possible number of passwords is:

N=36^3*10^2+10^3*36^2=5,961,600.

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Answer: The distributive property is a property where there is a coefficient/number, that is being multiplied to a group of numbers enclosed in parentheses. The coefficient can be distributed/multiplied to the numbers in the parentheses individually or after solving the expression in it.

Step-by-step explanation:

You can spot when the distributive property is used when you see a number in front of a group of numbers, such as these examples (in bold):

1. 4(5 + 6) = 46 , in this problem you can solve 5+6 before multiplying it by 4, or multiply 4*5 and 4*6 and then add it.

2. 2(x-3) = 12 , in this situation x is the unknown variable so you must distribute the 2 individually, so the result would look like: (2*x) + (2*-3) -> 2x - 6 = 12

Answer:

A - The exponent of 3 is 7/9.

Step-by-step explanation:

The expression 3^(7/9) can be read as "3 to the power of 7/9".
This means that the number 3 is being multiplied by itself 7/9 times.

For example
3^(2/3) can be written as cube root of 3, cube root of 3 is equal to 3^(1/3) .

When the exponent of an expression is a fraction, it can be written in radical form, with the denominator of the fraction as the index of the radical. However, it's not true in this case as the index is not 9 but 7.

So, the correct answer is A - The exponent of 3 is 7/9.

Answer:

B

Step-by-step explanation:

Irrational numbers are real numbers that cannot be written as a ratio of integers. They have decimal expansions that neither terminate nor become periodic.

Example: π , √2 , √3 are irrational numbers.

The equation to represented the situation of drop the price of each item $5 at the end of each week until the item sells as used by the manager of the clothing store is

Information given in the problem include

the managers drop the price of each item $5 at the end of each week

until the item sells

let c represent the cost of the item at the beginning

;et x represent the number of weeks

let y represent the cost at the end of each week

The equation is modeled as follows

the present cost c will drop by $5 each week

c - $5x

The cost after the drop that is at the end of the week

y = c - $5x

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The store location for which  % of the data lies between $19,371.18 and $22.295.48 is location C

You should be aware that Standard deviation explains the relation of data with mean.

For normal distributions, 68% of the data lies under one SD from the mean. Two standard deviations is within  95%, and three standard deviations would take up to 99%.

This implies that on taking (mean + SD) and (mean - SD), 68% of data would cover these two numbers.

Add and subtract SD from the mean to check which location will give $19,371.18 and $22.295.48.

For location A, we have

M-SD=23,124.70-1553.43=21,571.27

M SD = 23,124.70 + 1,553.43 = 24,678.4

For location B, we have

M - SD = 24,842.18 - 1,617.20 = 23,224.98

M + SD = 24, 842.18 + 1,617.20 = 26,459.38

For location C, we have

M - SD = 20,833.33 - 1,462.15 = 19,371.18

M + SD = 20,833.33 + 1,462.15 = 22,295.48

This implies the store location is C

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Correct question:

The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.

For which store location does 68% of the data lie between $19,371.18 and $22,295.48?

If the owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. The location that 68% of the data lie between $19,371.18 and $22,295.48 is: A. Location C.

Location A:

Mean -Standard Deviation

=23,124.70-1553.43

=21,571.27

Mean + Standard Deviation  

= 23,124.70 + 1,553.43

= 24,678.4

Location B:

Mean -Standard Deviation = 24,842.18 - 1,617.20

Mean -Standard Deviation  = 23,224.98

Mean + Standard Deviation  

= 24, 842.18 + 1,617.20

= 26,459.38

Location C:

Mean - Standard Deviation  

= 20,833.33 - 1,462.15

= 19,371.18

Mean + Standard Deviation  

= 20,833.33 + 1,462.15

= 22,295.48

Therefore the correct option is C.

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The complete question is:

The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.

Location A Location B Location C Location D

Mean = 23,124.70

SD = 1,553.43 Mean = 24,842.18

SD = 1,617.20 Mean = 20,833.33

SD = 1,462.15 Mean = 21,432.82

SD = 1,512.10

For which store location does 68% of the data lie between $19,371.18 and $22,295.48?

The required percentage of teachers who teach math but not English is 21%. Option B is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Total teachers = 104
A number of teachers teach math but not English = 22

Percentage = 22 / 104 × 100%
Percentage = 21%

Thus, the required percentage of teachers who teach math but not English is 21%. Option B is correct.

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The required equation -3x + 3y = 6 can pair with x - y= -2 to create a consistent and dependent system.

The equation is given in the question, as follows:

x - y = - 2

First, we have to convert the standard form of the equation to slope-intercept form.

As per the question, we have

x - y = -2

Subtract x from both sides of the equation,

x - y - x = -2 - x

- y = -2 - x

Divide -1 by both sides of the equation,

y = x + 2

Comparing it with the slope-intercept form y = mx + b, we get

Slope m = 1, y intercept b = 2

Considering option (B),

-3x + 3y = 6

Add 3x on both sides of the equation,

-3x + 3x + 3y = 6 + 3x

3y = 3x + 6

Divide both sides by 3 of the equation,

y = x + 2

Comparing the slope-intercept form

m = 1 and y-intercept = 2

Hence, the correct answer would be an option (C).

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Answer: x > -11

Step-by-step explanation:

3x + 7 > 2x - 4

First, we can simplify the right side of the equation by combining like terms:

3x + 7 > 2x - 4

then we can subtract 2x from both sides of the equation:

3x + 7 - 2x > -4

This gives us:

x+7 > -4

then we can add 4 to both sides of the equation:

x + 7 + 4 > 0

This gives us:

x + 11 > 0

then we can subtract 11 from both sides of the equation:

x + 11 - 11 > 0 - 11

This gives us:

x > -11

so the number is greater than -11.

The MAD of the given set of numbers is 4.64.

The mean absolute deviation (MAD) is a variability metric that indicates the average distance between observations and their mean. MAD interprets the data in its original units. Larger values indicate that the data points are further apart from the mean. Lower values, on the other hand, represent data points clustering closer to it. The average absolute deviation is also known as the mean deviation.

The mean absolute deviation is defined in the same way as the standard deviation (SD). While they both measure variability, their calculations differ. Some proponents of MAD have suggested that it replace SD as the primary measure in recent years because it is a simpler concept that is more applicable in real life.

Lets find the mean of given data set:

240+ 225+ 227+ 227+ 228+ 230+ 230+ 231+ 238+ 240

= 2316

⇒ 2316/10 = 231.6

Find the distances of the mean

240 - 231.6 = 8.4

225 - 231.6 = 6.6

227 - 231.6 = 4.6

227 - 231.6 = 4.6

228 - 231.6 = 3.6

230 - 231.6 = 1.6

230 - 231.6 = 1.6

231 - 231.6 = 0.6

238 - 231.6 = 6.4

240 - 231.6 = 8.4

Add the distances

8.4+ 6.6+ 4.6 + 4.6 + 3.6 + 1.6 + 1.6 + 0.6 + 6.4 + 8.4 = 46.4

Divide the sum by the number of data points.

46.4/10 = 4.64

Thus, The Mad of the given set of numbers is 4.64.

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Answer: To help you with this problem, I need to know the discount percentage.

Step-by-step explanation:

The solution to the radical equation is 2/5

From the question, we have the following radical equation

6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y

Complete the equation

So, we have the following representation

6√y² − 22y + √16 + 4 = 4y

Evaluate the radicals

The equation becomes

6y - 22y + 4 + 4 = 4y

So, we have

6y - 22y + 8 = 4y

Evaluate the like terms

So, we have the following

20y = 8

Divide both sides by 20

y = 2/5

Hence, the solution is 2/5

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Answer:

Answer:

I have graphed it and attached an image in the explanation.

Step-by-step explanation:

5x - 3y = 7 is in slope intercept form is y = 5/3x - 7/3

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

You can utilize two different versions of a line's general form to figure out its equation.

These are the formulas:

1) (y - y1) = m (x – x1), the Point-Slope Formula

2) The formula for slope-intercept, y = mx + b

The form you use depends on the information you are provided at the beginning, as the names suggest.

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Answer:

Step-by-step explanation:

y axis range is 35

1.  The average rate of range for 3 to 4 days is -3.9.

2. Approximate rate of range for 3 days is 34.8.

Adding a very small increment, for example, can help us approximate the instantaneous rate of change at x = a.

The instantaneous rate of change is equal to the slope of the tangent line at a given location. The slope of secant lines can be used to calculate the slope at a point as each secant line's "run" gets closer to zero (the slope of the tangent line).

You can find the instantaneous rate of change of a function by computing the derivative at a specific point and then entering the point's x-value.

The speed at which that function changes right now.

IROC = f(a + 0.001) - f(a) / 0.001 f(a) = 0.1

1.

[tex]$$\begin{aligned}& \text { A.R.C }=\frac{\mathrm{A}(4)-\mathrm{A}(3)}{4-3} \\& \mathrm{~A}(4)=100(0.5)^{\frac{4}{15}} \\& \mathrm{~A}(4)=83.12378 \\& \mathrm{~A}(3)=100(0.5)^{\frac{3}{16}} \\& \mathbf{A}(3)=87.05505\end{aligned}$$A. R. C $=\frac{83.12378-87.05505}{1}$$$=-3.93127$$A. R. $\mathrm{C}=-3.9$[/tex]

2. it can be obtained by takibg derivative with respect 't';

[tex]$\mathrm{A}^{\prime}(\mathrm{t})=100\left(\frac{\mathrm{t}}{15}\right)(0.5)^{\left(\frac{t}{15}\right)-1}$\\rate of change in 3 days:$$\begin{aligned}& \mathrm{A}^{\prime}(3)=100\left(\frac{3}{15}\right)(0.5)^{\left(\frac{3}{15}\right)-1} \\& \mathrm{~A}^{\prime}(3)=34.82202\end{aligned}$$Approximate rate of change;$$\mathrm{A}^{\prime}(3) \approx 34.8$$[/tex]

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The table that represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery used will be:

Cream cheese Cheesecake

1. 11

2. 22

3. 33

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the bakery can make 44 cheesecakes for every 4 blocks of cream cheese. This will be Illustrated as:

= 44 / 4

= 11 cheesecake per cheese.

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Negative 1 (StartFraction x over 4 EndFraction) + three-fourths 12 StartFraction negative x + 3 over 4 EndFraction = 12One-fourth (x + 3) = 12 is the equivalent equation.

An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equal sign (=). Equations are used to describe relationships between unknown values, such as the relationship between the circumference and diameter of a circle. Equations can also be used to solve for unknown values, such as the area of a triangle.

These three equations are equivalent to Negative one-fourth (x) + three-fourths = 12. The first equation is the original equation, while the second and third equations are equivalent forms of the original equation. In the second equation, the negative one-fourth (x) has been moved to the other side of the equation, and in the third equation, the negative one-fourth (x) has been multiplied by one-fourth.

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The statements about the functions are true A. f(x) = 1/2ˣ

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

We are given that On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1.

When evaluated in zero we have:

f(0) = 2(1/2)^0 = 2

So it crosses through the point (0, 2).

And when evaluated in x = 1, then

f(1) = 2(1/2)^1 = 1

Then it also passes through (1, 1).  It goes crosses the y-axis at (0, 14) and goes through (1, 5) and (2, 2).

The answers are A, D, and E

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Answer:a,d,e

Step-by-step explanation:

i took the test

Answer:  -1/10

Step-by-step explanation:

a) Una deuda total de $ 4837.65 en un período de amortización debe ser pagada en seis trimestres.

b) Se requiere aproximadamente 42 trimestres para pagar la misma deuda.

En este problema tenemos dos casos de préstamos bajo un modelo de interés compuesto, léase un caso acumulativo de intereses en el tiempo, en función de períodos definidos. La persona que recibe el préstamo se hace acreedora de una deuda, la cual debe ser amortizada en el tiempo. Ahora, bien, el modelo de interés compuesto se describe bajo la siguiente fórmula:

D' = D · (1 + r / 100)ˣ

Donde:

a) Si sabemos que D = 1500, r = 5 y x = 24, entonces:

D' = 1500 · (1 + 5 / 100)²⁴

D' = 4837.65

La persona debe pagar una deuda total de $ 4837.65 en un período de amortización de seis trimestres (nótese que un año tiene cuatro trimestres).

b) Es preciso determinar el período equivalente para una tasa de interés compuesta anual de 12 %, esto es:

D' = D · (1 + r /100)ˣ

㏒ (D' / D) = x · ㏒ (1 + r / 100)

㏒ D' - ㏒ D = x · ㏒ (1 + r / 100)

x = (㏒ D' - ㏒ D) / [㏒ (1 + r / 100)]

x = (㏒ 4837.65 - ㏒ 1500) / [㏒ (1 + 12 / 100)]

x = 10.332 años (aprox. 42 trimestres)

El período de amortización es de aproximadamente 42 trimestres.

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Match the word to its definition or symbol.

1. ∈                                            element

2. { }                                           braces representing a set with no elements

3. C                                            subset

4. {whole numbers]                  finite set

5. ∅                                           symbol for the empty set or null set

6. A set limited by definition - infinite set

7. ∉                                            not an element

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form.

Curly brackets are typically used to represent sets.

Sets with a finite/countable number of members are referred to as finite sets. Due to their ability to count, finite sets are often referred to as countable sets.

A set with an infinite number of elements is one that cannot be numbered. Any set that has no last element is said to be infinite Set

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The correct graph is the last one, positive at the left,  and positive at the right, when x is positive.

A relation from set A to set B is a function if every element of set Aonly one image in set B.It is a subset of A×B.The set of elements in Athat are plugged into the function  is called the domain. The set of images of the elements in A, a subset of B is called the range of the function f.

Here,

Given : Let's analyze our function, first we know that the parent cubic function:

We want to see which one of the given graphs is the graph of the function: f(x) = (1/2)*x^3

g(x) = x^3

Is positive for positive values of x and positive for positive values of x, then the graph is below the horizontal axis at the left, and above the horizontal axis at the right.

The graph below the horizontal Axis at left and above the horizontal axis at the right.

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Answer:

X = -50

Y = -30

Step-by-step explanation:

To find the value of Y and X, we can solve a system of equations. One way to do this is by substitution.

From the first equation:

10 + 5Y = X

We can substitute the value of X from the second equation:

10 + 5Y = 40 + 10Y

Then, we can subtract 10Y from both sides:

10 = 40 + Y

Finally, we can subtract 10 from both sides:

Y = -30

Now that we have the value of Y, we can substitute it back into either equation to find the value of X:

X = 10 + 5Y

X = 10 + 5(-30)

X = -50

So the solution is:

X = -50

Y = -30

Answer:

(x,y)=(-20,-6)

Step-by-step explanation:

Answer:

2/6 +2/6= 4/6 and 4/6 reduced down is 2/3

Step-by-step explanation:

hope this helps

The derivative of f at (a, b) is the gradient vector [4a - b, -a].

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

f(x, y) = 2x^2 − xy

The two-variable function f(x, y) = 2x^2 - xy is differentiable at any point (a, b) if its partial derivatives exist and are continuous at that point.

This is represented as

∂f/∂x = 4x - y

∂f/∂y = -x

The derivative of f at (a, b) can be calculated by evaluating the partial derivatives of f at (a, b):

∂f/∂x(a, b) = 4a - b

∂f/∂y(a, b) = -a

Hence, the derivative of f is [4a - b, -a].

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