what is the rate of change of the linear function that has a graph that passes through the points (2, 9) and (-1, 3)

The correct answer is A. 73 books

Explanation:

The first step to find the answer is to know the total volume/space in the bookcase. This can be calculated by using the formula v (volume) = h (height) x l (length) x w (width) or multiplying the three sides given because this is the formula for a cuboid and most bookcases have this shape.

v (volume) h x l x w

v = 36 in x 24 in x 12 in

v =  10368 in

According to this, the total volume of the shelf is 10368 in. The next step is to calculate the volume of 1 book. This can be found using the same process and formula.

1.5 in x 11 in x 8.5 in = 140.25 in

Finally, to know how many books can fit in the bookshelf divide the total volume of the bookshelf into the volume of one book.

10368 ÷ 140.25 = 73.9

Thus, the total books that can be fit in the bookshelf is 73

Answer:

Distance = √52

Step-by-step explanation:

Given:

First point = (6,9)

And y = 5

So,

x = 0

Second point = (0,5)

Find:

Distance

Computation:

Distance = √(x1 - x2)² + (Y1 - Y2)²

Distance = √(6 - 0)² + (9 - 5)²

Distance = √ 36 + 16

Distance = √52

Answer:

y = 3x + 26

Step-by-step explanation:

Plug in the slope and the given point into the equation, y = mx + b

Solve for b (y intercept)

8 = 3(-6) + b

8 = -18 + b

26 = b

Now, plug this into the equation with the slope:

y = 3x + 26 will be the equation

Answer:

y=3x+26

Step-by-step explanation:

We can start by writing this line in point-slope form.

Point-slope form is:

y-y1=m(x-x1)

This is where m is the slope

x1 and y1 are the x and y coordinates of a given point on a line.

With the given info, we are able to write the following equation:

y-8=3(x-(-6))

y-8=3(x+6)

We can now simplify that to slope-intercept form which is y=mx+b

m is slope and b is y-intercept in this form.

y-8=3(x+6)

Distribute

y-8=3x+18

Add 8 to both sides.

y=3x+26

Hi there! :)

Answer:

[tex]\huge\boxed{18 units}[/tex]

Subtract point F from point G to solve for the distance:

12 - (-6) = 18 units.

Answer:

A. the reduction of variance

Step-by-step explanation:

If the p bakue gets smaller, the smaller the p- value the stronger the evidence that we can or we should totally reject and not accept the null hypothesis.

Id the p value is lower, the result is trumpeted as significant, but if higher,it is not significant.

So Smaller p-values indicate more evidence in support of the the reduction of variance

Answer:

xy-y^2/x

Step-by-step explanation:

you factor the expression and reduce the gcf 3:

(x-y)*(x+y)/x *y/x+y

reduce the expression with x+y:

x-y/x*y

calculate the product:

y*(x-y)/x

remove parenthesis:

xy-y^2/x

Answer:

Step-by-step explanation:

Given data : 2x , x , 2x - 11 , x - 3

Mean = 4

N ( number of items ) = 4

Σx = 2x + x + 2x - 11 + x - 3

To find : value of x

Finding the value of x

We know that ,

Mean = [tex] \sf{ \frac{Σx}{n} }[/tex]

plug the values

⇒[tex] \sf{4 = \frac{2x + x + 2x - 11 + x - 3}{4} }[/tex]

Collect like terms

⇒[tex] \sf{4 = \frac{6x - 14}{4 }}[/tex]

Apply cross product property

⇒[tex] \sf{6x - 14 = 16}[/tex]

Move 14 to right hand side and change it's sign

⇒[tex] \sf{6x = 16 + 14}[/tex]

Add the numbers

⇒[tex] \sf{6x = 30}[/tex]

Divide both sides of the equation by 6

⇒[tex] \sf{ \frac{6x}{6} = \frac{30}{6} }[/tex]

Calculate

⇒[tex] \sf{x = 5}[/tex]

Hope I helped!!

Best regards!!!

Answer: 15

Step-by-step explanation: To evaluate an expression, we plug the value of the variable into the expression and simplify.

Since we have 7 - 2x and x is -4, we have 7 - 2(-4).

Simplifying from here, 2(-4) is -8 so we have 7 - (-8).

Now, remember that a a minus sign followed by a

negative sign turns the two signs into a plus sign.

So 7 - (-8) can be thought of as 7 + (+8) which is 15.

Answer: c

Step-by-step explanation:

Answer:

8n, 40 miles in 5 weeks.

Step-by-step explanation:

given that nate runs 8 miles each week.

Hence in n weeks, he will run

8 miles per week x n weeks

= 8n miles

in 5 weeks, n = 5.

Substituting this into the expression,

8(5) = 40 miles

Answer:

The answer is below

Step-by-step explanation:

a) For a normal model the sample size has to be equal or greater than 30 so that it can be a normal distribution.

b) Given that:

μ = 11.2 minutes, σ = 4.8 minutes, n = 45

The z score determines how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

For x < 10 minutes

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.8/\sqrt{45} }= -1.68[/tex]

Therefore from the normal distribution table, P(x < 10) = P(z < -1.68) =  0.0465

Answer:

a.   [tex]1\,\,\,10^4[/tex]

b.   [tex]1.57\,\,\,10^{-4}[/tex]

c.   [tex]1.2\,\,\,10^{10}[/tex]

d.   [tex]1.72\,\,\,10^{-15}[/tex]

e.   [tex]4.53\,\,\,10^5[/tex]

f.   [tex]5.682\,\,\,10^{14}[/tex]

g.   [tex]8.1\,\,\,10^{-8}[/tex]

h.   [tex]9.04\,\,\,10^{-13}[/tex]

i.   [tex]7.123\,\,\,10^3[/tex]

j.   [tex]4\,\,\,10^{-3}[/tex]

Step-by-step explanation:

Start by recognizing the significant figures of the number in question. the first factor to include in the scientific notation should have a non-zero digit followed by a decimal point, and whatever other significant figures follow. Make sure you count how many places you need to move the decimal point to get to the first significant figure for the quantity. If you moved the decimal point to the left in order to get to the first significant figure, you have to include a positive exponent for the base ten, and that exponent is the number of places you counted. If you moved to the right when moving the decimal point to locate it after the first significant figure, you need to include the negative of the number of places you counted in the exponent of the accompanying base 10.

Answer:

Step-by-step explanation:

f(x) = 5x² - x + 2

Using the remainder theorem

To find the reminder substitute the value of x into the above function and solve

That's

x + 1 = 0

x = - 1

So we have

f(-1) = 5(-1)² - ( - 1) + 2

f(-1) = 5 + 1 + 2

f(-1) = 6 + 2

We have the final answer as

Hope this helps you

Question Completion:

Required:

(a) Calculate the total value of products A, B and C which should be shown in inventory in the statement of financial position.

(b) Explain the difference that changing from a weighted average to FIFO method of inventory valuation is likely to have on an entity's profit or loss.

Answer:

Villandry

a) Total value of products A, B, and C based on:

                      Net realizable    List price

                          Value

                            Shs. ​​               Shs.

Ending value   10,486              12,000

b) The difference that changing from a weighted average to FIFO method of inventory valuation is likely to have on an entity's profit or loss:

The weighted average method of inventory valuation accumulates and assigns cost of inventory based on the weighted average.  This simply means that the cost of goods available for sale is obtained and then divided by the number of goods available for sale.  The average cost obtained is used to value the cost of goods sold and the ending inventory.

On the other hand, the FIFO method assumes that goods that are first to be in the store are the ones that are sold first.  This means that the cost of goods sold is valued at the cost of the first goods that are available for sale and the ending inventory is valued at the cost of newly purchased goods, since they are the ones that are still in stock by the FIFO assumption.

The implication of moving from the weighted average method to the FIFO method is that the FIFO method reflects the cost of newly acquired goods in the ending inventory better than the average cost using the weighted average, especially if prices are rising.

Step-by-step explanation:

a) Data and Calculations:

                Net realizable    List price

                      Shs. ​​               Shs.

Product A ​​​​    3,600 ​​​              5,100

Product B ​​​​    2,900          ​​​    2,800

Product C ​​​​    4,200           ​​    4,100

Valuation     10,700            12,000

Discounted 10,486            12,000

Answer: 504 ways

Step-by-step explanation:

given data:

no of people = 6

no of offices = 3

no of people in each office = 2

solution:

first we need to find the number of ways 6 people can be shared in 2 or pairs as this is a combination problem.

= 6C2

= 15 ways

ways to place a pair of 2 in 3 offices

= 15 * 3

= 45ways.

using the remaining 4 people we have 4C2 = 6 ways

in the remaining 2 offices

6 * 2 = 12ways

withour conditions

= 45 * 12

= 540ways

considering the constraint

= 4C2

= 6ways

shared in 3 offices

= 6 * 3

= 18 ways

remaining 2 offices

= 18 * 2

= 36 ways

Without constraints - With constraints

= 540 - 36

= 504ways

90 ways.

Given:

Six people are to be assigned in three offices, two people per office.

Thinking of this problem from the perspective of offices themselves picking persons, we get this:

Firstly out of 6 person, 2 person are chosen in [tex]^6C_2[/tex] ways.

Secondly, from rest of the 4 persons, 2 people are chosen in [tex]^4C_2[/tex] ways.

Then rest of the 2 persons are chosen from rest persons in [tex]^2C_2[/tex] ways.

Applying law of multiplication for number of ways:

Total number of ways = [tex]^6C_2 \times ^4C_2 \times ^2C_2 = 15 \times 6 \times 1 = 90[/tex]

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Answer:

$2416

Step-by-step explanation:

plug in 5 in the place of t

1500(1.1)⁵

(1.1)⁵ = 1.61051

1.61051 x 1500 = 2415.765

Answer:

4.12 ft

Step-by-step explanation:

because 4+0.12=4.12

Answer:

Let's convert 5.1 ft to inches......we have

5.1 x 12 = 61.2 inches

So

61.2 (1.08) = 66.096 inches

And coverting this to back to ft, we have

66.096/12 = 5.508 ft

Step-by-step explanation:

Answer: the demand function is D(x) = 4000/x + 2

Step-by-step explanation:

Given that

D'(x) = - 4000 / x²

Now d(D(x)/dx = - 4000/x²

so we integrate with respect to x

∫ d(D(x)) = - ∫ (4000/x²) dx = -4000 x⁻¹/-1 + C

⇒ D(x) = 4000/x + C

where C is a constant

Given that; x = 4 and D(x) = 1002

so we substitute

1002 = 4000 / 4 + C

1002 = 1000 + C

C = 1002 - 1000

C = 2

so  D(x) = 4000/x + C ⇒ D(x) = 4000/x + 2

Therefore the demand function is D(x) = 4000/x + 2

Answer: Find answers in the attached documents

Step-by-step explanation:

In this case, we have to use the knowledge of probability and calculate the chance of the event to occur, so we have to:

A) No have problem, because every person can be chosen once or not be chosen at all.

B) The event that everybody has been chosen maximally once is equal to the event that we have chosen the sample without replacement.

So that way, we have to analyze to know how the event will occur, so:

A)In this case we choose the sample with replacement, so the probability that there will be birthday match.

B) Using the formula, we have:

[tex]P=1-P\\=1-\frac{(10^6/10^3)}{(10^6)^{(10^3)}}[/tex]

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Answer:

0.6%

Step-by-step explanation:

1/1639 is 0.0006, and to get the percent from that just move the decimal point twice to the right.

Answer:

Hey there!

The answer is 1/12

1/4(1/3)=1/12

Let me know if this helps :)

Answer:

250 boys

Step-by-step explanation:

We know that the ratio is 9:10 from girls to boys

Take 225 and divide it by 9

225 ÷ 9 = 25

So we know that 25 is a factor of 225

We can the number of boys and multiply it by 25 to get 250

If we put it in the ratio form:

225:250 = 9/10

Check work:

25 x 9 = 225

25 x 10 = 250

Girls :Boys = 9:10

Total girls= 225

9=225

10=10/9×225

=250

NB: It will 250 because 9 is going to cancel 225

The horizontal distance from the origin to the point (1, 4) is 1 unit.

The length along a line or line segment between two points on the line or line segment.

To find the horizontal distance from the origin to the point (1, 4)

we need to find the x-coordinate of the point.

The x-coordinate of the point (1, 4) is 1

1 represents the horizontal distance from the origin to the point.

Therefore, the horizontal distance from the origin to the point (1, 4) is 1 unit.

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Answer:

[tex]\bold{t = f(s) = \dfrac{6.2}{s}}[/tex]

Step-by-step explanation:

Given that distance is 10,000 meter or 6.2 miles.

Time taken is [tex]t[/tex] minutes.

Average speed is [tex]s[/tex] miles/minutes

To find:

Equation to determine time 't' as a function of average speed 's' = ?

t is in minutes and

s is in miles/minute

Solution:

First of all, let us have a look at the formula for Average Speed:

[tex]\text{Average Speed} = \dfrac{\text{Total Distance Traveled}}{\text{Total Time Taken}}\\\Rightarrow \text{Total Time Taken} = \dfrac{\text{Total Distance Traveled}}{\text{Average Speed}}\\[/tex]

Now, we are given that Time, [tex]t[/tex] should be in minutes and

Average speed, [tex]s[/tex] must be in miles per minute

That means, we must have distance in miles.

Putting all the values in above formula.

So, the formula or equation becomes:

[tex]t = \dfrac{6.2}{s}[/tex]

Therefore the equation to find time, [tex]t[/tex] in minutes as a function of Average Speed, [tex]s[/tex] is given as:

[tex]\bold{t = f(s) = \dfrac{6.2}{s}}[/tex]

Answer:

15

Step-by-step explanation:

We can imagine this like a number line.

A------------B--------------------C

The distance from A to B is 10.

The distance from A to C is 25.

This means that the distance from B to C will be [tex]25-10=15[/tex].

Hope this helped!

Answer:

82.4

Step-by-step explanation:

12x+4+8x+20=180

20x+24=180

-24 -24

20x= 156

x= 7.8

Angle 2

4(2*7.8 +5)

4(15.6+5)

4(20.6)

82.4

Answer: Option C.

Step-by-step explanation:

Xmin, Xmax, Ymin, and Ymax represent the minimum/maximum values that X and Y can take.

We know that the scale in Y and X is 10.

This means that each mark in each axis represents 10 units.

Now, let's go to the vertical axis (y-axis)

Counting from the (0, 0) we can count:

4 marks up

4 marks down.

So if each mark represents 10 units, 4 marks are 40 units.

Then the range for Y is {-40, 40}

Now for the horizontal axis.

We can count 3 marks on each side, and with the same reasoning as before, we can find that the range for X is: {-30, 30}

Then we have that:

Xmin = -30

Xmax = 30

Ymin = -40

Ymax = 40

Now, as a point is defined as (X, Y)

This region can be written as:

{Xmin, Xmax} by {Ymin, Ymax}

or, replacing the values:

{-30, 30} by {-40, 40)

So the correct option is C.

C] X min and X max = (-300, 300) and Y min and Y max = (-400, 400)

Xmin, Xmax, Ymin and Ymax denote minimum and maximum values of X and Y respectively.

As x and Y scale are 10 each, the minimum and maximum values can be found by multiplying the units with respective scales.

On X (Horizontal Axis), there are 3 units of line segments each on both left & right sides of origin.

Hence X min & X max = (0 - 300, 0 + 300) = (-300, +300) respectively.

On Y (Vertical Axis), there are 4 units of line segments each on both upwards & downwards sides of origin.

Hence Y min & Y max = (0 - 400, 0 + 400) = ( -400, + 400) respectively.

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Answer:

f(x) = 7/8 + n=0 = 7/8 so the answer you looking for would be: n=0

Answer:

C. AB=CF

Step-by-step explanation:

Since AB is equal to radius of circle,

And CF is the radius of circle,

The correct one is:

Correct answer choice is C. AB=SF

this is the answer to your question x=50

Step-by-step explanation:

3x-2x=50

1x=50

The value of x for the given equation is given as x = 50.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is as below,

3x = 2x + 50

It can be solved as follows,

3x = 2x + 50

=> 3x - 2x = 50

=> x = 50

Hence, the solution of the given linear equation is x = 50.

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