Use long division to divide.
(x5 + 2x12x² - 5x - 12) = (x² - 3)

The rate of change of the temperature on the time interval is -2°C. This means that, in average, for each hour that passes the temperature decreases by 2 degrees Celcius.

A rate of change is defined as the quotient between the difference in some measure (in this case it will be the difference between the final temperature and the initial temperature) and the time interval in which it happens.

Here we know that:

final temperature = -5°C

Initial temperature = 13°C

And this change goes from 3 P.M. to midnight, so the change happens on an interval of 9 hours.

Then the rate of change of the temperature is:

r = (-5°C - 13°C)/9h = -2°C/h

So for each hour, the temperature decreases by 2°C.

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Answer:

Step-by-step explanation:

x=5

Answer: 33577

Step-by-step explanation:

3x3x5x7x7 = 2205

The height of the stack of paper is 3145.73 in.

Since the Notebook paper is about 0.003 in. thick, and you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times.

Since each piece of paper is halved, that means that the number of paper sheets doubles every time.

So, after halving n times, we would have 2 sheets of paper. Since the thickness of the Notebookpaper is 0.003 in, then the height after cuttin half n times is h = 2ⁿ × 0.003 in.

Since the paper is folded 20 times, n = 20.

So, the height h = 2ⁿ × 0.003 in.

h =  2²⁰ × 0.003 in.

h = 1048576  × 0.003 in.

h = 3145.728 in

h ≅ 3145.73 in

So, the height of the stack of paper is 3145.73 in.

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Answer:

686 cm^2

Step-by-step explanation:

First find the sides

7f = 49

4f = 28

To find a triangle area (right triangle), multiply each side like a rectangle, but divide it by two.

(49*28)/2 = 686

Answer:

67

Step-by-step explanation:

Answer:

Step-by-step explanation:

the side opposite to greater angle is greater.

72>60>48

AB>AC>BC

A=Afton

B=Badeton

C=Capeton

Answer:

See below

Step-by-step explanation:

y = 2x+1     <====  is in form   y = mx + b   where 'm' is the slope

       ....arrange the other into this form

y = 2x-3         <===== this has the same slope as the other line

                          so the two lines are PARALLEL

Answer:

20.4 m

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{total}{count}[/tex]

given mean height of 12 men is 1.70 m , then

[tex]\frac{total}{12}[/tex] = 1.7 ( multiply both sides by 12 to clear the fraction )

total height = 12 × 1.7 = 20.4 m

Answer:

y=7

Step-by-step explanation:

-3(-3)-y=2

9-y=2

9-2=y

y=7

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Answer:

model a is more benfit the other one b/c of by hard working effort from b

Tan of  arc tan x is equal to x when the angle x is 0 degrees

Tangent is the ratio of the side opposite the angle we know or want to know over the side adjacent to that angle, and is sometimes abbreviated as tan.

In a right angle triangle, the formula for tan is as below

Tangent (tan) = opposite / adjacent

Arc tan (tan^(-1)) is the inverse of tan = adjacent / opposite

Arc tan is equal to tan when the angel is zero degree

therefore, tan (tan^(-1) x) = x

when x = 0

tan^(-1) 0 = 0

tan 0 = 0

tan (tan^(-1) 0)

tan (0)

0

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complete question

At what point does tan(tan^-1(x))=x

Answer:

y = 2x + 2

Step-by-step explanation:

(y-y1)/(y2-y1)=(x-x1)/(x2-x1)

(y-6)/(-6-6)= (x-2)/(-4-2)

(y-6)/-12 = (x-2)/-6

y-6 = 2x-4

y = 2x -4 + 6

y = 2x + 2

The perimeter of the shape is 38 total unit.

The perimeter of a shape is a measure of the distance round the boundary or edge of the shape.

The given shape comprises of squares of 1 length each, hence to calculate for the perimeter of the shape, we add up each boundary of 1 unit length which will amount to 39 in total.

Therefore by careful observation, the perimeter of the plane shape is calculated to give us 39 total perimeter length.

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a) The inequality is

P + S + M > 60

b) The solution of the inequality is:

P > 19

Where P is Pedro's age.

c) The oldest brother has more than 21 years-

Let's define the variables:

p = Pedro's age.

S = Sebastian's ae

M = Manuel's age

We know that the sums of their ages is more than 60, then:

P + S + M > 60

This is the inequality.

b) We know that the brother are one year apart, then:

S = P + 1

M = P + 2

replacing that we get:

P + P + 1 + P + 2 > 60

3P + 3 > 60

3P > 60 - 3

3P > 57

P > 57/3 = 19

P > 19

So Pedro has more than 19

c) The oldest brother is 2 years older than Pedro, then:

M > 19 + 2

M > 21

Manuel is more than 21 years old.

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Answer:

C______________4_⁴________

For the two similar cuboids A and B,

surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.

As given in the question,

Given : Two similar cuboids A and B,

Let x , y , and z be the length , width and height of cuboid A

And l, b, h be the length , width , and height of cuboid B.

As both the cuboids are similar their sides are in proportion.

k is the constant of proportionality then,

x= kl , y = kb, z = kh

Surface area of A : Surface area of B = 16 :2

⇒2k²(lb +bh +hl) : 2(lb +bh +hl) = 16 : 2

⇒k² = 16 :2

⇒k = 4 : √2

Now volume of A : Volume of B

= xyz : lbh

= k³lbh : lbh

= k³

=( 4 : √2)³

=64 : 2√2

= 64√2 : 4

= 16√2 : 1

Therefore, for the two similar cuboids A and B,

surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.

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-6t -54  is the expression equivalent to-6(t+9)

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)

Given: -6(t+9)

First, clear the parenthesis by using -6 to multiply t and 9:

-6(t+9) = (-6 x t) + (-6 x 9)

          = -6t + (-54)

          = -6t -54

Therefore, the -6t -54 is equivalent to -6(t+9)

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The algebraic expression that correctly represents the cost of t tickets is 8t , the correct option is (a) .

In the question ,

it is given that

the cost of 1 ticket for the theater is = $8.00

let the number of ticket be = t

so , the cost for t tickets = (cost of 1 ticket ) × ( number of tickets )

Substituting the values of number of tickets and cost of 1 ticket ,

we get ,

cost for t tickets = 8 × t

= 8t

Therefore , The algebraic expression that correctly represents the cost of t tickets is 8t .

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Answer:

Step-by-step explanation:

there are fifty two cards in a deck, of which 26 are black and 26 are red, in addition there are 4 queens, including two of each color.

so:

P(getting red queen) = 2/52

P(getting black card) = 26/52

The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.

Given:

The total no cupcakes = 52,

The no of sprinkled cupcakes = 39,

Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100

Percentage of sprinkled cupcakes = 39 / 52 × 100

Percentage of sprinkled cupcakes = 75%

Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

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The height of the cliff is 7.57m and the time to reach the ground when thrown straight down is 0.814s

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is GRAVITY. In fact, gravity works towards the centre of the Earth.

When an object is moving upward,it is moving against gravity and when it is moving down it is moving with gravity.

from equation of motion

H= ut-1/2gt^2( the object is moving upward)

where h is the height of the cliff and u is the initial velocity and g is acceleration due to gravity

(g=10ms^-2).

therefore h= 8.14×2.41-(1/2×10×2.41)

= 19.62-12.05

h= 7.57m

when the object is thrown Down,

V = u + gt

u will be 0 at top before coming down

V = gt

t= 8.14/10

= 0.814s

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The amount that would be credited,  given the partial payments and the terms, would be $6, 060.61. The balance due would be $19, 939.39.

The terms 2/10 and 1/15 mean that if the buyer pays their bill in 10 days, they get a 2% discount. If they pay in 15 days, they get a 1% discount.

Pete paid on the:

= 27 - 15

= 12 days

This means that the 1 % discount would apply on the $6, 000. The credited amount would be:

= 6, 000 / (1 - 1%)

= $6, 060.61

The balance due would be:

= 26, 000 - 6, 060.61.

= $19,939.39

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The expression that represents the number of tiles on Wendy's kitchen floor is B. 8 × 8t.

An expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, Wendy lays rows of 8 tiles each to cover her kitchen floor.

Let t = the number of rows.

Therefore, the number of tiles on Wendy's kitchen floor will be:

= 8 × 8t.

Therefore, the correct option is B.

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The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:

                                         FIFO          LIFO

Ending inventory          $10,250     $12,800

Cost of goods sold       $17,000     $14,450

FIFO (First-in, First-out) assumes that the physical flow of goods sold depends on the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

Date       Description                      Units   Unit Costs      Total Cost

April 1     Beginning inventory       220          $50             $11,000

April 5    Purchases                        100          $60                6,000

April 10   Purchases                         50          $45                2,250

April 16   Sales                              -300          $80

April 25  Sales                                -20          $95

April 30  Purchases                      200          $40                8,000

Total                                               570                             $27,250

Units sold                                      320

Ending inventory                          250

FIFO:

Ending Inventory = $10,250 (200 x $40 + 50 x $45)

Cost of goods sold = $17,000 ($27,250 - $10,250)

LIFO:

Ending Inventory = $12,800 (220 x $50 + 30 x $60)

Cost of goods sold = $14,450 ($27,250 - $12,800)

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Calculate Ending Inventory And COGS Using FIFO And LIFO Methods For ABC Inc.

At 95% confidence, the z critical value is roughly z = 1.96

You would use a reference table or calculator to determine this value. Unfortunately it's not something that can be easily/quickly found by hand.

If we're trying to estimate the population mean (mu), then we'll use this margin of error formula

E = z*sigma/sqrt(n)

Or if we want to estimate the population proportion (p), then we use this formula

E = z*sqrt(phat*(1-phat)/n)

The confidence interval then spans from (pointEstimate)-E to (pointEstimate)+E. Where "pointEstimate" represents either xbar or phat depending on the context. Other point estimates are possible. We're focusing on these two for now.

xbar estimates mu

phat estimates p

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

An example problem:

A manager at a soda bottling plant wants to know if the contents of the cans are 20 fluid ounces (fl oz) or not. Through past observations, the manager has noted the population standard deviation (sigma) is 1.72 fl oz.

The manager gathers a random sample of 50 cans to test their contents. They find the sample mean is 18 fl oz. Conduct a hypothesis test using a confidence interval at 95% confidence to see if the cans really do have 20 fl oz of drink in them or not.

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

Solution:

Null Hypothesis: mu = 20

Alternate Hypothesis: mu ≠ 20

This is a two-tailed test.

E = margin of error

E = z*sigma/sqrt(n)

E = 1.96*1.72/sqrt(50)

E = 0.47676

L = lower boundary of confidence interval

L = xbar - E

L = 18 - 0.47676

L = 17.52324

L = 17.52

U = upper boundary of confidence interval

U = xbar + E

U = 18 + 0.47676

U = 18.47676

U = 18.48

The 95% confidence interval is approximately (17.52, 18.48)

This is equivalent to writing 17.52 < mu < 18.48 in which we are 95% confidence in saying mu is between those endpoints.

But wait, the hypothesized mu = 20 is not in the interval 17.52 < mu < 18.48, which indicates we must reject the null hypothesis and accept the alternate hypothesis.  

The soda cans do not have 20 fl oz of drink. It appears they have slightly less than 20 fl oz.

The Diameter of the cube would be 3 inches

What is Variation?

A variation is a relationship that exists between a set of values for one variable and a set of values for other variables.

Solution:

We know that,

Horse Power is directly proportional to RPM * Diameter

So, we can write

Horse Power = k * RPM * Diameter

here, k is any constant

From the first case given, we can find the value of k

16 = k * 2 * 120

k = 1/15

Putting the value of k in second case,

30 = 1/15 * 150 * Diameter

Diameter = 3 inches

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How can you stay safe as you evacuate during a flood? Select the three correct answers:

A, C, & D

Moving furniture is not beneficial in a flood situation.

A, C and D

hope this helps!

An inequality of the form |x-al<k so that the inequality has the given solution set (-5,5) is |x|<10.

In the given question,

We have to write an inequality of the form |x-a|<k so that the inequality has the given solution set (-5,5).

We first learn about modulus,

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always positive.

The given set is (-5,5).

For x<(-5,5)

The mean value of x should be between -5 and 5.

-5<x<5

|x|<10

Hence, an inequality of the form |x-a l<k so that the inequality has the given solution set (-5,5) is |x|<10.

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Answer: b

Step-by-step explanation:

Answer:

row-echelon form

Step-by-step explanation:

Matrixes are commonly used to do Gaussian elimination. By reducing the need to manually specify the parameters at each step, this strategy decreases the work required to obtain the solutions. A system of equations equations is solved using the Gauss elimination method. Let's review the definitions of these equation systems. A set of linear equations with numerous unknown components is defined as a system of linear equations. Unknown factors can be found in various equations, as we all know.