A shipping box has dimensions as shown in the diagram. The red, dashed line represents the longest length of item that will fit inside the box. What is the length of the longest item that will fit inside the shipping box? Enter the correct answer in the box by replacing the values of m and n.

[tex]\frac{1}{15}[/tex] or 6.67%

In practice, the relative frequency of an event happening is the same as the probability that that event happened. In other words, the terms "relative frequency" and "probability" can be used interchangeably.

Now, the probability P(A) of an event A happening is given by;

P(A) = [tex]\frac{number-of-outcomes-in-the-event-A}{number-of-outcomes-in-the-sample-space}[/tex]

From the question;

The event A is the situation of local residents having a post office box. Therefore the;

number-of-outcomes-in-the-event-A = 8   [since only 8 of the local residents have a post office box]

number-of-outcomes-in-the-sample-space = 120 [since there are altogether 120 local residents]

Therefore,

P(A) = [tex]\frac{8}{120}[/tex]

P(A) = [tex]\frac{1}{15}[/tex]

The relative frequency that a local resident does not have a post office box for receiving a mail is therefore, [tex]\frac{1}{15}[/tex]

PS: Sometimes it is much more convenient to express relative frequencies as percentage. Therefore, the result above expressed in percentage gives:

[tex]\frac{1}{15} * 100%[/tex]% = 6.67%

Answer:

(3,0)

Step-by-step explanation:

The graph is a line so it will have an equation with this form:

y = mx+b

m is the slope and b is the y-intercept.

Let's calculate m:

● m = (-32-(-64))/(-9-(-21)) = 8/3

Now replace m with its value and x,y with coordinates of a point.

● -32 = (8/3)*(-9) +b

● -32 = -24 +b

● -32+24 = b

● -8 =b

Solve y = 0

●(8/3)*x+b = 0

● (8/3) *x = 8

● x = 3

The coordinates of the x-intercept are (3,0)

Explanation:

The area of a semicircle is given by ...

  A = πr^2/2

where r is the radius. Here, we're given diameters, so in terms of diameter, the area of a semicircle is ...

  A = π(d/2)^2/2 = (π/8)d^2

__

The area of the semicircle with diameter AC is ...

 white area = (π/8)AC^2

The area of the semicircle with diameter BC is ...

  left semicircle area = (π/8)BC^2

And the area of the semicircle with diameter AB is ...

  right semicircle area = (π/8)AB^2

__

We can use the relationship between the areas to find the shaded area:

  triangle area + left semicircle area + right semicircle area =

     white area + shaded area

Then the shaded area is ...

  shaded area = triangle area + left semicircle area + ...

     right semicircle area - white  area

__

Filling in the values for area from above, we have ...

  shaded area = triangle area+ (π/8)BC^2 +(π/8)AB^2 -(π/8)AC^2

  shaded area = triangle area + (π/8)(BC^2 +AB^2 -AC^2)

From the Pythagorean theorem, we know that ...

  AC^2 = BC^2 +AB^2

Substituting this into the above equation gives ...

  shaded area = triangle area + (π/8)((Bc^2 +AB^2 -(BC^2 +AB^2))

  shaded area = triangle area + 0 . . . . simplify

  shaded area = triangle area

Answer:

exponential decay

Step-by-step explanation:

The function  f(x)=0.85ˣ is a exponential decay.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=0.85ˣ.

The function f of x is equal to zero point eight five to the power of x.

Exponential decay refers to a process in which a quantity decreases over time, with the rate of decrease becoming proportionally smaller as the quantity gets smaller.

The function  f(x)=0.85ˣ is a exponential decay.

Hence, the function  f(x)=0.85ˣ is a exponential decay.

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Answer:

y = 3/8x - 9 + 4/5

Step-by-step explanation:

assuming y = 3/4 (1/2x-12)+4/5

multiply 3/4 and (1/2x - 12)

y = 3/8x - 9 + 4/5

Answer:

Step-by-step explanation:

The LCD here is 120.  Multiplying both terms by 120 and then dividing the result by 120 yields

90(1/2x - 12) + 96           45x - 1080 + 96               45x - 984

-------------------------- = -------------------------------  =  ----------------------

         120                                 120                                 120

Hey there! I'm happy to help!

The IQR is how far apart the first and third quartiles are, which are the middle numbers of the first and second halves of a data set. Let's find some random numbers that are 17 apart. We will use 3 and 20.

Now, we have to create a data set where 3 is the middle number of the first half and 20 is the middle number of the second half. Let's have one with six numbers because that's a good amount I guess. Remember that the data has to be going from least to greatest.

In our first half we will have one number that is smaller than 3 and one bigger than three so that 3 is in the middle. Here's an example of what our first half should look like:

2,3,5

Now, for our second half, we need a number smaller than 20 and one greater than 20 so 20 is the the middle. Here's the second half I've made for you.

16,20,100

So, the data set I've created for you is 2,3,5,16,20,100. However, there are many other possibilities as you've seen.

My answers for your question 1 and 2 are in the explanation I've done, and here's the math that shows that the interquartile range is 17.

You split the data in half.

2,3,5,         16,20,100

Q1 is the middle number of the first, which is 3. Q3 is the middle of the second, which is 20.

You find how far apart they are by subtracting 3 from 20.

20-3=17.

The IQR is 17.

Have a wonderful day! :D

Answer:

Option A)     [tex]\angle F\\[/tex] congruent with  [tex]\angle Q[/tex]

Step-by-step explanation:

There is only information about two sides in each triangle, so there is still the need of a third piece of info which can come from an angle like [tex]\angle F\\[/tex] congruent with  [tex]\angle Q[/tex], which are angles opposite to one of the given sides on each triangle.

Answer:

3

Step-by-step explanation:

Plug in 2 for x:

5-2 - 3

Answer:

3

Step-by-step explanation:

f(x)= 5 - x

f(2) = 5 - 2 = 3

Answer:

6 units squared

Step-by-step explanation:

To solve this problem you can solve for the entire area of the square and subtract the area of the unfilled areas for the area of the shaded region..

Area of entire square is 4*4=16

Now for the sections that are unfilled:

4*3/2= 6

1*1/2= 0.5

2*1 = 2

1*1 = 0.5

2*1/2 = 1

Total area of Unfilled region = 6 + 0.5 + 2 + 0.5 +1 = 10

Area of filled region = 16 - 10 = 6 units squared

Hope this helped!

Answer:

A

Step-by-step explanation:

Since the the value is greater than 1, f(x),g(x), and h(x) are exponential functions.

Answer:

[tex]120\º \text{ and } 240\º[/tex]

or in radians:

[tex]$\frac{2\pi }{3} \text{ and } \frac{4\pi }{3}$[/tex]

Step-by-step explanation:

From the way you wrote, you want to solve the equation

[tex]\sqrt {2 \cos(x)+1}=0[/tex] for [tex]0 \leq x < 360\º[/tex], or in radians [tex][0, 2\pi)[/tex]

[tex]\sqrt {2 \cos(x)+1}=0[/tex]

Square both sides

[tex]2 \cos(x) +1= 0[/tex]

[tex]2\cos(x)=-1[/tex]

[tex]$\cos(x)=-\frac{1}{2} $[/tex]

In the Unit Circle, considering one revolution (interval [tex][0, 2\pi)[/tex]),

the values where [tex]$\cos(x)=-\frac{1}{2} $[/tex]  are in Quadrant II and III.

Once

[tex]$\cos(x)= \frac{1}{2} \text{ for } x = 60\º \text{ in the Quadrant I}$[/tex]

The values where

[tex]$\cos(x)=-\frac{1}{2} $[/tex]   are 120º and 240º.

Answer:

C on edge

Step-by-step explanation:

Answer: Choice A

Step-by-step explanation:

She can only buy 3 pizzas. 14 times 3 is 42. 42 plus 7.50 is 49.50. Another 14 dollars would be over. So 24 SLICES she can afford.

Here, we are required to identify the inequality that describes Jacque's pizza purchase scenario and also the largest number of slices that Jacque can afford

Choice 1 which is ;

Choice 1 which is ;7.50 + 14 P < 60Jacque can afford to buy 30slices of pizza

First,

The inequality which describes the scenario is :

Choice 1 which is ;

And to determine the largest number of slices that Jacque can afford, we have to solve for P first.

However, the question requires that we determine how many slices she can afford to buy,

Jacque can afford to buy 3.75 × 8 slices of pizza.

Jacque can afford to buy 30slices of pizza

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Answer:

A

Step-by-step explanation:

all sides of square is 90degrees

Since AC and BD is the same, when you join the lines together, it will definitely be a square

Answer:

50.24

Step-by-step explanation:

The first step is to find the area of it if it was a whole circle

you get this by squaring the radius

8*8 or 8^2= 64

then, you have to multiply it by 3.14 which gives you

200.96.

Then divide it by 4 to get a quarter of the circle to get the final answer

50.24

Hope this helps, if it does, please give me brainliest, it will help a lot :)

Have a good day

Answer:

    3 > x

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

Step 1: –10 + 8x < 6x – 4

Step 2: –10 < –2x – 4

Step 3: –6 < –2x

Step 4: divide each side by by -2, remembering to flip the inequality

   -6/-2 > -2/-2

    3 > x

Answer:

x < 3

Step-by-step explanation:

−2(5−4x)<6x−4

Use the distributive property to multiply −2 by 5−4x.

−10+8x<6x−4

Subtract 6x from both sides.

−10+8x−6x<−4

Combine 8x and −6x to get 2x.

−10+2x<−4

Add 10 to both sides.

2x<−4+10

Add −4 and 10 to get 6.

2x<6

Divide both sides by 2. Since 2 is >0, the inequality direction remains the same.

x= 6/2

Divide 6 by 2 to get 3.

x= 3

X< 3

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Answer:

(4, 0), (-4, 0), (0, -2), (0, 8)

Step-by-step explanation:

Answer:

  (0, -2), (4, 0), (0, 8), (-4, 0)

Step-by-step explanation:

The y-intercepts are found by solving for y when x=0.

  (y -3)² = 25

  y -3 = ±5 . . . . . take the square root

  y = 3 ± 5 = {-2, 8}

The x-intercepts are found by solving for x when y=0.

  x² +(0-3)² = 25

  x² = 16 . . . . . . . . subtract 9

  x = ±4 . . . . . . . . .take the square root

The y-intercepts are (0, -2) and (0, 8).

The x-intercepts are (-4, 0) and (4, 0).

Answer:

x = $36 , y = $ 838

Step-by-step explanation:

Solution:-

The company makes a profit of $y by selling widgets at a price of $x. The profit model is represented by a parabola ( quadratic ) equation as follows:

                       [tex]y = -x^2 + 72x -458[/tex]

We are to determine the profit maximizing selling price ( x ) and the corresponding maximum profit ( y ).

From the properties of a parabola equation of the form:

                      [tex]y = ax^2 + bx + c[/tex]

The vertex ( turning point ) or maximum/minimum point is given as:

                     [tex]x = -\frac{b}{2a} \\\\x = -\frac{72}{-2} = 36[/tex]

The profit maximizing selling price of widgets would be x = $36. To determine the corresponding profit ( y ) we will plug in x = 36 in the given quadratic model as follows:

                    [tex]y ( 36 ) = - ( 36 )^2 + 72 ( 36 ) - 458\\\\y ( 36 ) = -1296 + 2592 - 458\\\\y ( 36 ) = 838[/tex]

The maximum profit would be y = $838

Answer:

Draw a straight line through these two points (0, 0) and (1, 3).

Step-by-step explanation:

"Proportional relationship" implies line or curve that goes through the origin; there is no "y-intercept" in this case.  

Plot a dot at (0, 0).  Next, move your pencil point 1 unit to the right (you'll end up at (1, 0), and then move it from there up to (1, 3).  Draw a straight line through these two points (0, 0) and (1, 3).

Answer:

The unit rate of change of d with respect to t is 4/3.

The graph should be: (0,0) and (3/4).

Step-by-step explanation:

I got it wrong on khan academy :/

so i went over here and answer it

Answer:

Mean = 30.3

Median = 30

They scored 30 or more points on 11 games.

Step-by-step explanation:

Mean = all the numbers added together divided by 21

636/21 = 30.3

Median is the middle number (the 11th) = 30

Answer:

point a is the maximum

Step-by-step explanation:I took the test

Answer:

f(6) = 24

Step-by-step explanation:

Simply plug the value of 6 into the equation for x.

f(x) = x^2 - 2x

f(6) = (6)^2 - 2(6)

f(6) = 36 - 12

f(6) = 24

Answer: 24

Step-by-step explanation: you can say that 6=x Wichita in this case we would substitute x for 6

6²-2*6=36-12=24

Hope this helps!

Answer:

the 2 equations are on top of each other, they are the same line

which means it is consistent, dependent, infinite

Step-by-step explanation:

the second equation is just 4 times the first equations.

Answer:

242,000 is the present value of the house.

Step-by-step explanation:

Answer:

242,000 represents the value of the house

Step-by-step explanation:

Sine is negative in quadrants 3 and 4, when y < 0.

Tangent is negative for quadrants 2 and 4, when y/x < 0. Basically when x and y differ in sign (one is positive, the other is negative)

The common quadrant mentioned is quadrant 4.

Quadrant 4 has angles that are between 270 degrees and 360 degrees

So we have [tex]270^{\circ} < \theta < 360^{\circ}[/tex]

Answer:

15°

Step-by-step explanation:

∠GOI=150°

∠HOG=30°

∠HIG=30°/2=15°(Circle angle)

Given the value [tex]12b^{5}[/tex] ; the coefficient of b is 12.

The Coefficient is a numerical value or constant which is used to multiply a variable; from the value given above ;

The variable is b ;

The Coefficient = 12 ; the coefficient is the value which is used fo multiply the variable b.

The power is the value to which the variable is raised.

Hence,

The Coefficient is 12 ; it is the value which multiplies the variable 'b' and the power is 5

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Answer:

Step-by-step explanation:

1.

[tex]2x + 8x - 10 + 6[/tex]

Collect like terms

[tex] = 10x - 10 + 6[/tex]

Calculate the sum

[tex] = 10x - 4[/tex]

Factor out 2 from the expression

[tex] = 2(5x - 2)[/tex]

2.

[tex]3(x + 7)[/tex]

Multiply each term in the parentheses by 3

[tex] = 3x + 3 \times 7[/tex]

Multiply the numbers

[tex] = 3x + 21[/tex]

3.

[tex](x + 2)(x - 3)[/tex]

Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )

[tex] = x(x - 3) + 2(x - 3)[/tex]

Calculate the product

[tex] = {x}^{2} - 3x + 2x - 2 \times 3[/tex]

Multiply the numbers

[tex] = {x}^{2} - 3x + 2x - 6[/tex]

Collect like terms

[tex] = {x}^{2} - x - 6[/tex]

Hope this helps..

best regards!!

Answer:  ln5 - ln2 ≈ 0.919

Step-by-step explanation:

[tex]\int\limits^2_1 {\dfrac{2x}{x^2+1}} \, dx\qquad \qquad =\int\limits^2_1 {(x^2+1)^{-1}} \, 2xdx[/tex]

Let u = x² + 1    →    du = 2x

[tex]\text{Then we have:}\quad \int\limits^2_1 {u^{-1}} \, du \qquad =ln|u|\bigg|^2_1[/tex]

Substitute u = x² + 1

[tex]ln|x^2+1|\bigg|^2_1\quad =ln|2^2+1|-ln|1^2+1|\quad = ln|5|-ln|2|[/tex]