The number of lattes sold daily for two coffee shops is shown in the table:


Lattes
55
52
50
47
68
48
53
53


Based on the data, what is the difference between the median of the data, including the possible outlier and excluding the possible outlier?

Answer:

The shaped is being reflected.

Answer: Reflection

Step-by-step explanation:

When we look at the picture, the two rectangles QRST and Q'R'S'T' appears as the mirror images of each other , also the corresponding sides and angles are congruent.

The transformation that create a mirror image of the figure is known as reflection. It is a rigid transformation because it produces congruent shapes.

Therefore, the transformation maps rectangle QRST to rectangle Q'R'S'T' is reflection.

Answer:

First Image: [tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

Step-by-step explanation:

We have the following functions:

[tex]P(w)=\frac{1}{2}w+1[/tex]

Here, P(w) represents the number of paintings Jenny completes in w weeks.

J(y)  = Number of weeks per year.

Since, J(y) is the number of weeks spent per year in painting, in order to calculate the paintings completed in a year we substitute w = J(y) in the above equation. So the equation becomes:

[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

This composite function would represent number of paintings Jenny completes in a year.

p[J(y)] = 1/2 . J(y) + 1 or the first image is the correct answer!

I took the test and ended up getting it right.

Good luck! I hope you have an awesome day!

Answer:

$4 per pound

Step-by-step explanation:

To find how much one pound of cashew nuts cost you have to use money over unit.

So money/unit, in this problem the money is 32 and the unit is 8.

So 32/8, now you divide 32 by 8 to get the price for one pound.

32 divided by 8 is 4

So $4 per pound

Answer:

The total cost of one pound is $4.

Step-by-step explanation:

[tex]\Large\textnormal{First, you divide the numbers from left to right to find the answer.}[/tex]

[tex]\displaystyle 32\div8=4[/tex]

[tex]\displaystyle \frac{8}{8}=1[/tex]

[tex]32\div4=8[/tex]

[tex]\displaystyle \frac{32}{8}=4\times1=4[/tex]

[tex]\Large \boxed{4}[/tex], is the correct answer.

I hope this helps you and have a wonderful day!

Answer:

(4,3)

Step-by-step explanation:

asoming 4 is x and 5 is y down 2 turns 5 into 3

Start at the point (4,5). Moving 2 units down decreases the y-coordinate by 2, thus bringing you to the new point (4,3). Draw a graph to visualize this better.

In the context of a grid in Mathematics, the first quadrant is where both x and y coordinates are positive. The given point starts at (4,5). If you move 2 units down, it means you are reducing the y-coordinate by 2 units. So, starting at (4,5) and moving 2 units down would land you at a new point, which will be (4,3).

To visualize this, you may want to draw a graph on an x-y axis and plot the points (4,5) and (4,3) to see how the position change looks.

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Answer: 359 ft

Step-by-step explanation:

Whenever you have a problem like this, you must first make an assumption that the building (in this case the lighthouse) is perpendicular to the ground (or sea).  This allows you to create a right triangle (see attached image).

The angle of depression is the angle from an imaginary perpendicular line passing through the top of the building.  Since that imaginary line is parallel to the ground (or sea), you can use alternate interior angles to place that angle in the triangle.

NOTE: BOTH angle of elevation and angle of depression are placed in the lower corner of the triangle. Don't let the names confuse you!

Now you can use trigonometry to solve ....

In the given problem, we have the side OPPOSITE of the given angle (24°) and need the side ADJACENT to the angle, so we will use tan to solve for x.

[tex]tan\ \theta=\dfrac{opposite}{adjacent}\\\\\\tan\ 24^o=\dfrac{160}{x}\\\\\\\rightarrow x=\dfrac{160}{tan\ 24^o}\\\\\\\rightarrow x=359.4\\\\\\\rightarrow x\approx 359[/tex]

Answer:

Step-by-step explanation:

x=1, y=-1

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

y = 2x² - 6x + 3 → (1)

y = x - 2 → (2)

Since both equations express y in terms of x we can equate the right sides, that is

2x² - 6x + 3 = x - 2 ( subtract x - 2 from both sides )

2x² - 7x + 5 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × 5 = 10 and sum = - 7

The factors are - 2 and - 5

Use these factors to split the x- term

2x² - 2x - 5x + 5 = 0 ( factor the first/second and third/fourth terms )

2x(x - 1) - 5(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(2x - 5) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]

Substitute these values into (2) for corresponding values of y

x = 1 : y = 1 - 2 = - 1 ⇒ (1, - 1)

x = [tex]\frac{5}{2}[/tex] : y = [tex]\frac{5}{2}[/tex] - 2 = [tex]\frac{1}{2}[/tex]

Solutions are (1, - 1) and ( [tex]\frac{5}{2}[/tex], [tex]\frac{1}{2}[/tex] )

Answer:

The one that is not equivalent is 7x^3

Step-by-step explanation:

7x^3= 7 * x*x*x

4x+3x = 7x = 7*x

(4+3)x = (7)x = 7*x

7x= 7*x

Answer:

7x^3

Step-by-step explanation:

All of the following are equivalent except 7x^3.

7x^3 = 7x^3

4x+3x = 7x

(4+3)x = 7x

7x = 7x

[tex]h(6)=3\cdot6-4=14[/tex]

Answer:

a. 14 is your answer.

Step-by-step explanation:

h(x) = 3x - 4

h(6) = ?

Plug in 6 for x: x = 6

h(6) = 3(6) - 4

Remember to follow PEMDAS. First, multiply, then subtract:

h(6) = (3 * 6) - 4

h(6) = (18) - 4

Simplify:

h(6) = 18 - 4

h(6) = 14

a. 14 is your answer.

~

For this case we must find an expression equivalent to[tex]6 ^ {- 3}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, we can rewrite the given expression as:

[tex]6 ^ {3} = \frac {1} {6 ^ 3}[/tex]

This is equivalent to:

[tex](\frac {1} {6}) ^ 3[/tex]

Answer:

Option D

Answer:

The correct answer option is D. ( 1 / 6 ) ^ 3.

Step-by-step explanation:

We are given the following expression and we are to determine whether which of the given answer options is equivalent to this:

[tex] 6 ^ { - 3 } [/tex]

Rewriting this as a fraction to get:

[tex] \frac { 1 } { 6 ^ 3 } [/tex]

Therefore, the correct answer option is D. ( 1 / 6 ) ^ 3.

Answer:

Step-by-step explanation:

[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\ on\ a\ line\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\======================================[/tex]

[tex]\text{We have the points:}\ (2,\ -2)\ \text{and}\ (1,\ -6).\\\\\text{Substitute:}\\\\m=\dfrac{-6-(-2)}{1-2}=\dfrac{-4}{-1}=4\\\\y-(-2)=4(x-2)\\\\y+2=4(x-2)[/tex]

Answer:

[tex]\large\boxed{y-8=\dfrac{5}{7}(x-4)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope [tex]m=\dfrac{5}{7}[/tex] and the point [tex](4,\ 8)[/tex].

Substitute:

[tex]y-8=\dfrac{5}{7}(x-4)[/tex]

Answer:

[tex] 2 ^ { \frac { 5 } { 2 } [/tex]

Step-by-step explanation:

We are given the following expression which we are to find its simplest form:

[tex] \frac { 4 ^ { \frac { 5 } { 4 } } \times 4 ^ { \frac { 1 } { 2 } } } { 4 ^ { \frac { 1 } { 2 } } }[/tex]

Cancelling the like terms to get:

[tex] 4 ^ { \frac { 5 } { 4 } } [/tex]

[tex] 2 ^ { 2 .\frac { 5 } { 4 } } = 2 ^ { \frac { 5 } { 2 } } [/tex]

[tex] 2 ^ { \frac { 5 } { 2 } [/tex]

Answer:

B

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

If Erin has 9 more shells than Jamie, then 27 minus 9 would be equivalent to the amount of shells Jamie has.

This can be represented by:

[tex]27-9=j[/tex]

Which can be rewritten as:

[tex]27=j+9[/tex]

by adding 9 to both sides.

To solve, subtract 9 from 27.

[tex]27-9=18[/tex]

Jamie has collected 18 shells.

Answer:

C. 27=j+9; Jamie collected 18 shells.

Step-by-step explanation:

First, you do is switch sides.

[tex]\displaystyle j+9=27[/tex]

Then, you subtract 9 from both sides.

[tex]\displaystyle j+9-9=27-9[/tex]

Simplify, to find the answer.

[tex]\displaystyle 27-9=18[/tex]

Therefore, Jamie got collected of 18 shells.

[tex]\huge \boxed{18}[/tex], which is our answer.

The correct answer is C.

Answer:

sqrt( 146)

Step-by-step explanation:

To find the distance between two points, we use the formula

d = sqrt( ( y2-y1)^2 + (x2-x1)^2)

Where (x1,y1) and (x2,y2) are the two points.

(–9, 0) and (2, 5).

Substituting into the equation

d = sqrt( (5-0)^2 + (2- -9)^2)

d = sqrt( ( 5^2 + (2+9)^2)

      sqrt( ( 5^2 + (11)^2)

   = sqrt( 25+121)

  = sqrt( 146)

The distance between the two points is sqrt(74)

Final answer:

The distance between the points (–9, 0) and (2, 5) in the Cartesian plane is approximately [tex]\sqrt{146}[/tex] units.

Explanation:

To find the distance between two points in the Cartesian plane, we can use the distance formula.

The distance formula is:

distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}[/tex]

Using the given points (–9, 0) and (2, 5), we can plug in the values:

distance = [tex]\sqrt{((2 - (-9))^2 + (5 - 0)^2)}[/tex]

distance = [tex]\sqrt{((11)^2 + (5)^2)}[/tex]

distance = [tex]\sqrt{(121 + 25)}[/tex]

distance = [tex]\sqrt{146}[/tex]

So, the distance between the points (–9, 0) and (2, 5) is approximately [tex]\sqrt{146}[/tex] units.

Answer:

For [tex]x^x > 500,000[/tex]  [tex]x=7[/tex]

For [tex]x^{(-x)} > 500,000[/tex]  [tex]x=-7[/tex]

Step-by-step explanation:

We need to find the smallest positive whole number that satisfies the inequality:

[tex]x^x > 500,000[/tex]

We tested with x = 6

[tex]6^6=46,656[/tex]

[tex]46,656 > 500,000[/tex]

Inequality is not met because [tex]46,656 < 500,000[/tex]

We test with the following integer x = 7

[tex]7^7=823,543[/tex]

[tex]823,543 > 500,000[/tex]

Then the smallest positive integer that will make [tex]x^x > 500,000[/tex] is 7

Inequality is met.

In the same way the largest negative integer that will make [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse [tex]7^{-(-7)}=823,543[/tex]

Answer:

Smallest positive integer value for [tex]x^x>5000[/tex] is,

x = 7,

Largest negative integer value for [tex] x^{-x} >500000[/tex] is,

x = -8

Step-by-step explanation:

If [tex]x^x>500000[/tex]

∵ If x is a positive integer then the possible values of x = 1, 2, 3, 4, 5, 6, 7.....

Case 1 : If x < 7,

[tex]x^x < 500000[/tex]

Case 2 : If x ≥ 7,

[tex]x^x > 500000[/tex]

Hence, smallest positive integer value of x is 7.

Now, if [tex]x^{-x}>500000[/tex]

∵ If x is negative integer then the possible value of x = -1, -2, -3, -4,.....

Case 1 : if x is odd negative integer,

[tex]x^{-x} < 50000[/tex]

eg : -1, -3, -5, -7,...

Case 2 : If x is even negative integer then there are further two cases,

(i)  x is more than or equal to -6,

[tex]x^{-x} < 500000[/tex]

eg x = -6, -4, -2,

(ii) x is less than -8,

[tex]x^{-x} > 50000[/tex]

eg : x = -10, -12, -14,...

Hence, the largest negative integer value that will make [tex]x^{-x}> 500000[/tex] is x = -8.

Answer:

x=4

Step-by-step explanation:

AB + BC = AC

AB= 6x, BC= x-5, AC= 23

Substituting what we know

6x + x-5 = 23

Combine like terms

7x -5 = 23

Add 5 to each side

7x-5+5 =23+5

7x = 28

Divide each side by 7

7x/7 = 28/7

x=4

Answer:

Last option: Translate each point of the graph of h(x) 3 units left.

Step-by-step explanation:

There are some transformations for a function f(x). The following is one of these transformations:

If [tex]f(x+k)[/tex], then the function is shifted "k" units to the left.

Given the function  [tex]h(x)=log_6(x)[/tex] and the function  [tex]m(x)=log_6(x+3)[/tex], you can notice that the function m(x) is the function h(x) but shifted left 3 units.

Therefore, you could graph the function m(x) by translating each point of the graph of the function h(x) 3 units left.

This matches with the last option.

Answer:

Last option (D) Translate each point of the graph of h(x) 3 units left.

Answer:

See Below.

Step-by-step explanation:

I'm going to take the equation to be

y = x3 + 2x2 + 3x + 6

That is, the first term is a typo

make 2 groups. Put brackets around both groups.

group 1: x^3 + 2x^2   Take out the common factor of x^2

group 1: x^2(x + 2)

group 2: 3x + 6       Take out the common factor of x^2

group 2: 3(x + 2)

Now put the two groups together

Cubic = group 1 + group 2

Cubic = x^2 (x + 2) + 3(x + 2)

Now take out the common factor of x + 2

Cubic = (x + 2) (x^2 + 3)

Answer:

all her patients patients with no cavities

patients younger than 18

every patient with braces

Step-by-step explanation:

when a sample is selected in a manner that some elements, in this case patients, of population have higher or lower probability of sampling then that sample is biased.

From given case, all the following are biased samples

all her patients patients with no cavities

patients younger than 18

every patient with braces

because they are non-random sample of a population in which all other elements were not equally likely to be chosen!

The dentist should avoid biased sampling methods.

The biased samples in this case would be:

1. All her patients: This would only include the dentist's current patients, which may not be representative of the entire population.
2. Patients with no cavities: This would only include a specific subset of patients who do not have cavities, which may not be representative of the entire population.
3. Patients younger than 18: This would only include patients below the age of 18, which may not be representative of the entire population.

It is important to have a random and representative sample in order to make accurate conclusions about the population's flossing habits.

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Answer:

[tex]7 \times {3}^{n - 1} [/tex]

Step-by-step explanation:

using form:

[tex]a \times {r}^{n - 1} [/tex]

where a: starting number

where r: common ratio (in this case each next term is 3 times previous term)

The nth term of the sequence 7, 21, 63, 189,... is given by the explicit rule an = 7 × 3(n-1), which applies to a geometric sequence with a common ratio of 3.

To find an explicit rule for the nth term of the sequence 7, 21, 63, 189,..., we notice that each term is three times the previous term. This indicates that the sequence is geometric with a common ratio of 3. The first term of the sequence (a1) is 7.

To find the nth term of a geometric sequence, the formula is an = a1 × r(n-1) where r is the common ratio. Plugging in the values for our sequence, we get the nth term as an = 7 × 3(n-1).

This gives us the explicit rule for the nth term of the given sequence, which allows us to calculate any term in the sequence based on its position, n.

Where an represents the nth term of the sequence and an-1 represents the previous term.

For example, if we want to find the 5th term of the sequence, we can use the formula:

a5 = a4 * 3 = 189 * 3 = 567

Answer:

= 9x³+ 0x²+0x -52....

Step-by-step explanation:

Descending powers means you start with highest power and then decrease.

In this expression the highest power is 3. We do not have any variable with power 2 and 1. So we will write it as:

9x³ -  52

= 9x³+ 0x²+0x -52....

Answer:

4x - y = 7.

Step-by-step explanation:

We substitute for x and y and see if they fit.

4x - y = 7

4(2) - 1 = 7

So it is the first line.

Answer: First option.

Step-by-step explanation:

To find which line contains the point (2,1), we can substitute the coordinates into each equation of the line provided in the options:

First option:

[tex]4x-y=7\\4(2)-1=7\\7=7[/tex]

It contains the point (2,1)

Second option:

[tex]2x+5y=4\\2(2)+5(1)=4\\9\neq 4[/tex]

It does not contain the point (2,1)

Third option:

[tex]7x-y=15\\7(2)-1=15\\13\neq15[/tex]

It does not contain the point (2,1)

Fourth option:

[tex]x+5y=21\\2+5(1)=21\\7\neq 21[/tex]

 It does not contain the point (2,1)

Answer:

B

Step-by-step explanation:

x² + 8x + 7 = 0

x²+x+7x+7=0

x(x+1)+7(x+1)=0

(x+1)(x+7)=0

Either x=-1or x=-7.

Answer:

$10d

Step-by-step explanation:

The unit price is $d per pound. It is a dollar amount divided by the number of pounds. If you multiply the unit price by pounds, then the units work out like this:

$/lb * lb = $

When you multiply the unit price in dollars per lb by lb, you get dollars.

In your case:

$d/lb * 10 lb = $10d

That value of the nuts is $10d.

Answer:

x^2  +  y^2  = 4

Step-by-step explanation:

The center-radius form (formally called the standard form) of a circle is

(x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.

So if we replace (h,k) with (0,0) since the center is the origin and r with 2 since the radius is 2 we get:

(x-0)^2+(y-0)^2=2^2

Let's simplify:

x^2  +  y^2   = 4

Answer:  24/4=D

Step-by-step explanation:

24LEGS/4LEGS=6DOGS

Answer:

4d=24

Step-by-step explanation:

4(dogs)=24 legs

so the answer is 6 dogs (in case you need it)

Answer:

1.3 repeating or 4/3

Step-by-step explanation:

if you take 24 and divide it by 18 this is the answer you receive

hey! the value of y is 57

Answer:

45 meters

Step-by-step explanation:

If x represents the seconds after the launch, then the time of launch is when x=0 so you just need to solve for h(0)

h(0) = -5(1)(-9)

h(0) = 45

Answer:

45 m

Step-by-step explanation:

At the time of launch, the time x = 0

Substitute x = 0 into h(x)

h(0) = - 5 (0 + 1)(0 - 9) = - 5(1)(- 9) = - 5 × - 9 = 45