Find the measure of the exterior angle. (hint: find x first, then plug it in to the exterior angle)

Answer:

Step-by-step explanation:

the answer is "downward". If you say "why", it is because of the degree coefficient.

in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.

Answer:

25

Step-by-step explanation:

Let the age of Thomas be x.

Huilan is 11 years older than Thomas,

Huilan = x + 11

The sum of their ages is 61.

x + x + 11 = 61

2x + 11 = 61

2x = 61 - 11

2x = 50

x = 50/2

x = 25

Hence,

Thomas's age is 25.

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:

y=7

Step-by-step explanation:

-3(-3)-y=2

9-y=2

9-2=y

y=7

Please mark as brainliest

The BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.

Given:

1 ≤ x ≤ 3

we know x is between 1 and 3 so the best estimate is 2 even though the answer could also be 3 but that will be skewed.

1 ≤ 2 ≤ 3 is the best estimate.

Therefore the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.

Learn more about the average rate and function here:

https://brainly.com/question/28744270

#SPJ1

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)

Learn more about FIFO and LIFO inventory methods at brainly.com/question/24938626

#SPJ1

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

The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The given triangle is a right-angled triangle

As Z² = X²+Y²

So sin (x) = 60/68=0.88

and sin(y) = 32/68=0.47

Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.

Learn more about  Trigonometric Functions, by the following link.

brainly.com/question/24349828

#SPJ1

The area of left over wrapping paper is 380 square inches

The given dimensions are:

The surface area of the box is calculated as

Surface area = 2(lw + lh + wh)

This gives

Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches

The surface area of the wrapping paper is calculated as

Wrapper = lw

This gives

Wrapper = 2 * 3 = 6 square feet

Express the area in square inches

Wrapper = 864 square inches

The area left is the difference between the areas calculated above

i.e.  Amount left = Wrapper - Box

So, we have

Amount left = 864 square inches - 484 square inches

= 380 square inches

Hence, the amount left is 380 square inches

Read more about surface areas at

https://brainly.com/question/76387

#SPJ1

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 correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6

Information given in the question

f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity

This is written as (x + 6) / ( x² - 9x + 18 )

factorizing the denominator gives

(x + 6) / {( x - 6)( x - 3)}

In the denominator

At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:

f(x) is decreasing for all x < 6: contains  x = 3 and result to a higher value

f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing

f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4

Therefore the correct option is f(x) is increasing for all x > 6

Learn more on polynomial functions here:

https://brainly.com/question/29241065

#SPJ1

The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.

The average rate of change shows the slope line over the stated interval.

We can find the average rate of change by dividing the change in y-values by the change in x-values.

Year        No. of cars sold

                in (hundreds)

2000                 45

2002                 51

2004                53

2006                60

2008                77

The total number of cars sold between 2002 and 2006 = 16,400

The number of cars sold in 2002 = 5,100

The number of cars sold in 2006 = 6,000

The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)

OR:

Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)

Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)

Total change in y-values = 900 (6,000 - 5,100)

Total change in x-values = 4 (2006 - 200)2

Average rate of change = 225 (900/4)

Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.

Learn more about the average rate of change at https://brainly.com/question/8728504

#SPJ1

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.

Answer:

64

Step-by-step explanation:

119+89+145=353-289=127+74+88
^
64

Answer:

m∠D = 54°

Step-by-step explanation:

The sum of the measures of the interior angles of a triangle is 180°.

The sum of the measures of an interior angle and its corresponding exterior angle is 180°.

With this knowledge, we can construct the equation:

50° + (3x + 18)° + (180 - (8 + 8x))° = 180°

and solve for x.

50° + (3x + 18)° + (180 - 8 - 8x)° = 180°

(50 + 18 + 180 - 8)° + (3x - 8x)° = 180°

240° - 5x° = 180°

5x° = 240° - 180°

5x° = 60°

x° = 12°

Now, we can solve for m∠D by plugging in the x value that we solved for.

m∠D = (3x + 18)°

m∠D = 3(12)° + 18°

m∠D = 36° + 18°

m∠D = 54°

Answer:

1/4

Step-by-step explanation:

rise/run                                          you can count it but it doesn't always work

If you want to know the mathematical way of doing it it's:

m(slope) = y2-y1/x2-x1                 Choose any two points I chose (-4,5) & (0,6)

m = 6-5/0-(-4)                               Then subtract 6 - 5 and 0-(-4)  

m = 1/4

Answer:

[tex]y=x+1[/tex]

Step-by-step explanation:

I am assuming that, given the nature of the curve, you know what a derivative is, and you know how to compute the derivative of the ratio of two functions.

[tex]f'(x) = \frac1{(\sqrt x)^2}[(2x+0)\sqrt x-(x^2+1)(\frac1{2\sqrt x})][/tex]

Could be rewritten in a nicer form? Probably, do we care? No, let's just evaluate it for [tex]x=1[/tex]:

[tex]f'(1)=\frac11 [(2)(1)-(1+1)\frac12]=1[2-1]=1[/tex]

We're almost done. We got the point, we have the slope, we can rewrite the tangent line as

[tex]y-y_0=f'(x_0)(x-x_0)\\y-2=1(x-1) \rightarrow y=x+1[/tex]

Answer:

C______________4_⁴________

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

To learn more about Variation from the given link

https://brainly.com/question/25215474

#SPJ9

The missing x and y values in the ordered pair of the equation are:

x = 1

y = -4

Given the ordered pair (x, y) of an equation, y = mx + b, we can find their values by plugging in the given value of either of the x or y coordinates to find the other coordinate value.

The ordered pairs of y = -2x + 4 are given as:

(4, y) and (x, 2)

To find the value of y, substitute x = 4 into the equation y = -2x + 4:

y = -2(4) + 4

y = -8 + 4

y = -4

The value of y is -4.

To find the value of x, substitute y = 2 into the equation y = -2x + 4:

2 = -2x + 4

2 - 4 = -2x

-2 = -2x

-2/-2 = x

1 = x

x = 1

Learn more about ordered pairs of an equation on:

https://brainly.com/question/25837325

#SPJ1

Number lines are significant because they depict numbers as they appear in daily life.

What is number line?

A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa.

Research has revealed that number lines are crucial because they foster sound mental number sense and arithmetic procedures.

They assist in providing a mental approach for addition and subtraction. Number lines are crucial, we can all agree on that.

Number lines are significant because they depict numbers as they appear in daily life.

Primarily because they make it possible for negative integers to be represented in a meaningful fashion.

The ability to display all real numbers, even enigmatic irrational numbers such π, -π, √2, -√ 2, etc., was a secondary but no less significant result.

Hence, number lines are significant because they depict numbers as they appear in daily life.

To know more about the number line, click on the link

https://brainly.com/question/24644930

#SPJ1

Answer:

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

The stack of paper will have the height of 1048576 papers

The first cut will produce 2 papers, the second cut will produce 4 papers, the third cut will produce 8 papers and the fourth cut will produce 16 papers.

If you examine the stages of cut and the number of papers, the relationship between them is:

1st cut: number of papers = 2¹ = 2  

2nd cut: number of papers = 2² = 4

3rd cut: number of papers = 2³  = 8

4th cut: number of papers = 2⁴  = 16

nth cut: number of papers = 2ⁿ

So if the  process is repeated 20 times, the number of papers will be:

Number of paper = 2²⁰ = 1048576

Therefore, the stack of paper will be as high as 1048576 papers

Learn more about height on:

https://brainly.com/question/12446886

#SPJ1

Answer:

  8

Step-by-step explanation:

You want the period of a sinusoidal function that has a graph with peaks at x=1 and x=9.

The period is the difference between x-values where the function repeats itself. Typically, we can determine the period from corresponding recognizable features of the graph.

Here, the graph has peaks at x=1 and x=9. The period is the difference between these x-values:

  period = 9 - 1 = 8

The period of the function is 8 units.

__

Additional comment

In more formal terms, the period p of a function is the smallest value of p such that f(x -p) = f(p).

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.

Learn more about rates of change:

https://brainly.com/question/8728504

#SPJ1

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

Learn more about tangent here:

https://brainly.com/question/6617153

#SPJ1

complete question

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

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.

To learn more about inequality link is here

brainly.com/question/28823603

#SPJ1

Answer: 33577

Step-by-step explanation:

3x3x5x7x7 = 2205

The artist will take 5 hours to decorate 25 clay pots.

Given,

Number of pots to be decorated in 3 hours =40

Number of pots he decorated in 3 hours =[tex]\frac{3}{8}*40=3*5=15[/tex]

So, the artist took 3 hours to decorate 15 pots instead of 40 pots.

It means to decorate 1 pot he took time=[tex]\frac{Total time}{Number of pots decorated} =\frac{3}{15} =\frac{1}{15} hour[/tex]

So, to decorate 25 pots he need time,

[tex]time=\frac{1}{5}*25= 5 hours[/tex]

Thus, the artist need 5 hours to decorate 25 clay pots.

To learn more about fractions refer here

https://brainly.com/question/18271414

#SPJ9

1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.

Given the expression in the question;

( 5 + 2i ) / 4i

To simplify, multiply the numerator and denominator by the conjugate of 4i

( 5 + 2i ) / 4i

( 5 + 2i ) × i / 4i × i

( 5 + 2i )i / 4ii

Apply distributive property

( 5i + 2ii ) / 4ii

Not that i × i = i² = -1

( 5i + 2i² ) / 4i²

( 5i + 2( -1 ) ) / 4( -1 )

( 5i - 2 ) / -4

( -2 + 5i ) / -4

Split the fraction

-2/-4 + 5i/-4

1/2 - 5i/4

Therefore, the simplified form is 1/2 - 5i/4.

Learn more about conjugate of expressions here: https://brainly.com/question/27932423

#SPJ1