10. Determine whether the following represents an identity.

cos x sin x tan x + cos²x = 1

Answer:

Step-by-step explanation:

v = 1/3 (area of base) (height)

v = 1/3 (1/2*6*8) (7)

v = 1/3 (24) (7)

v = 8 (7)

v = 56 square inches

The numbers in order are 7, 8, 9, 11, 11, and 11.

Mode:

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all

Here we have to arrange the number in order.

Range:

The difference between the lowest and highest values.

Pu the six numbers in order from small to large.

7,8,9,11,11,11

So the median of the number is = (9 + 11) /2

= 10

The mode of these numbers is = 11

As 11 is three times in the series.

The range of the numbers is = 11-7 =4

Therefore the order is 7, 8, 9, 11, 11, 11.

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Step-by-step explanation:

I assume you need the slope-intercept form

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

since we have the slope and a point, we can start with the point-slope form

y - y1 = a(x - x1)

"a" is again the slope, (x1, y1) is a point on the line

so, we have

y - -7 = 3(x - -4)

y + 7 = 3(x + 4) = 3x + 12

and from there now the final equation :

y = 3x + 5

The answer that 12 times 1/3 will equal to -4 to 0, solving an equation.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

So the equation 12(x)-4 = 0

⇒12*x =4

⇒x=4/12

⇒x = 1/3

Hence, the equation will be solved and the number will be 1/3.

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The difference between the record high and low temperatures for this state is 118 degrees Fahrenheit or 118°F

Given that,

104 f is the highest temperature ever recorded in a particular US state. The state's all-time low temperature is -14 f.

To find : The difference between the record high and low temperatures for this state.

Difference can be calculated as

Difference equals to highest temperature minus lowest temperature in the state

Difference = 104 -(-14)

= 104+14=118°F

Therefore, The difference in temperature between the state's record high and low readings is 118 degrees Fahrenheit, or 118°F.

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Answer: 8.3

Step-by-step explanation:

50/6= 8.3

$144104.88 Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.

Given that,

For the next 20 years, Bill intends to contribute the maximum $2,000 each year to his individual retirement account (ira).

We have to find how much will Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.

We know that,

The worth of repeated payments at a specific future date, less a specified refund rate or a discount rate, is known as the future annuity value. The annuity amount increases with the discount rate.

According to the information provided, Future Value of Annuity equals:

FV= A×[(1+r)ⁿ-1]/r

Here,

A is periodic payment

r is rate per period

FV is future value

n is number of period

FV=2000×[(1+0.12]²⁰-1]/0.12

FV=2000×72.05244

FV=$144104.88

Therefore, $144104.88 Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.

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The answer is:  " - 1,458 ".

Step-by-step explanation:
We are asked to simplify: " -2(3²)³ " ; into standard form.

Take note of the 'order of operations'—by using the mnemonic:
 "Please Excuse My Dear Aunt Sally."

  in which:
_______
Parentheses, if they occur, take top priority.
then :
Exponents, if they occur, take second priority.
then :

Multiplication—and/or:
Division—if they occur; take third priority; yet, multiplication does not necessarily take priority over division.  Rather, multiplication and/or division, if Either occurs, take the next priority—in the order in which they occur from the far left of the expression to the end.
then :
Addition—and/or:
Subtraction—if they occur; take the last priority; yet, addition does not necessarily take priority over subtraction.  Rather, addition and/or subtraction, if Either occurs, take the last priority—in the order in which they occur from the far left of the expression to the end.
____

Our given expression:  " -2(3²)³ " ;  is the same as:
  " - 2* (3²)³ " ;   We have parentheses, exponents, and multiplication;

 So; we need to find the value of:  " (3²)³ " ;  

and multiply that value by -2 ;

 So, let's start with calculating:  " (3²)³ " ;

Method 1)
 " (3²)³ = (3* 3)³ = 9³ = 9 * 9 * 9 = (9 * 9) * 9 = 81 * 9 = 729 " .

Method 2)
Note the multiplication property of exponents:
 (aᵇ)ᶜ = a⁽ ᵇ *ᶜ ⁾ ;

As such:   "  (3²)³ =  3⁽²*³⁾ = 3⁶ " ;

                             =  3 * 3 * 3 * 3 * 3 * 3 ;          

                             =  (3 * 3) * 3 * 3 * 3 * 3 ;

                            =   9 * 3 * 3 * 3 * 3 ;

                             =   (9 * 3) * 3 * 3 * 3 ;

                            =   (27) * 3 * 3 * 3 ;

                             =   (27)  *  (9)* 3 ;\

                             =  27 * 27 ;              

            ₁

             ₄  

              2 7
          *  2  7  
           ¹ 1 8 9          

        ⁺_5 4    
          7   2  9

                          =  729
____

Now,  multiply 729 by -2 ;

{Note that a negative value, when multiplied by a positive value, results in a negative value.}\

      ₁

      7 2 9

*       -   2      
-  1 4 5 8 ;  which is our answer to:  " -2(3²)³ " ; written in   standard form.

The answer is:  " - 1,458 ".

____

Hope this is helpful to you.

Best of luck to you!
____

Answer: 23456789ol.09876

Step-by-step explanation:

Answer:

x-intercept is 5

y-intercept is -3

Step-by-step explanation:

For the x-intercept:

[tex]3x - 5(0) = 15[/tex]

[tex]3x = 15[/tex]

[tex]x = 5[/tex]

For the y-intercept:

[tex]3(0) - 5y = 15[/tex]

[tex] - 5y = 15[/tex]

[tex]y = - 3[/tex]

Answer:

Y intercept= -3

x-intercept = 5

Step-by-step explanation:

So you would want to get your y alone for it to be in slome intercept form (y=mx+b) so you would:

1. Subtract 3x from both sides to get -5y= -3x+15

2. then you would divide each side by -5 to get y= [tex]\frac{3}{5}[/tex] x -3

And since in slope intercept form, b= the y-intercept, The y-intercept =-3 and to find the x-intercept you would have to solve for y=0 in your new-found equation.

sorry if this was long

The value of y so that WX ⊥ YZ is y = 4 .

In the question ,

it is given that

the line WX is perpendicular to line YZ

and the end points of WX is W(2,-3) and X(-4,9)

and the end points of YZ is Y(5,y) and Z(-1,1) .

let the slope of line WX = m₁

and slope of line YZ = m₂ .

we know that when two lines are perpendicular , then

m₁ * m₂ = -1

m₁ = (9-(-3))/(-4-2)

and m₂ = (1-y)/(-1-5)

Substituting the values of m₁ and m₂ in the equation m₁ * m₂ = -1  ,

we get

(9-(-3))/(-4-2) * (1-y)/(-1-5) = -1

(9+3)/(-6) * (1-y)/(-6) = -1

12/(-6) * (1-y)/(-6) = -1

-2* (1-y) = 6

-2 + 2y = 6

2y = 6+2

2y = 8

y = 4

Therefore , the value of y is = 4 .

The given question is incomplete , the compete question  is

Given W(2, -3) X(-4, 9) Y(5, y) and Z(-1, 1) . find the value of y so that WX ⊥ YZ ?

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The probability that the sample mean is greater than 105 is 0.0384.

A simple random sample is a subset of persons chosen at random from a bigger collection. It is the process of randomly selecting a sample.

A simple random sample is a population subset chosen at random. Each member of the population has a precisely equal probability of being selected in this sampling approach, reducing the likelihood of selection bias.

Random sampling ensures that the results received from your sample are close to what would have been achieved if the full population had been measured.

The population mean is  μ =100.

The population standard deviation is σ= 20.

n=50 is the sample size

Let [tex]\bar{x}[/tex] be the mean of the sample

The chance that the sample mean is greater than 105 is then given by :

P( [tex]\bar{x}[/tex]>105)=1-P( [tex]\bar{x}[/tex]≤105)

=1-P(( [tex]\bar{x}[/tex]-μ)/(σ/√n) ≤ (105-100)/(20/√50))

=1-P(z≤1.77)

=1-0.96164

=0.03836≈0.0384

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The complete question is:

"According to a survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. a. What is the probability that the sample mean is more than 105? (Round answer to 4 decimal places.)"

Answer:

[tex]\frac{1}{120}[/tex]

Step-by-step explanation:

To solve such a problem you need to simulate a situation in which this could happen in three picks and then make sure your equation takes into account that all three picks take place at the same time. One such situation could look like this:

1) At the start, the probability of picking one rotten apple with one pick is 2 out of 16 which 2/16.

2) After picking the first apple you have 15 apples left of which only 1 is rotten. So the chance to pick the second rotten apple is 1/15.

3) After you picked the second rotten apple you want the third one in the set to be good. As you are left with 14 apples of which all 14 are good, the probability of picking a good one is 14/14.

Now, because you are interested in ALL those 3 things happening at the same time, you need to multiply the probabilities. So this gives you the answer of:

[tex]\frac{2}{16} *\frac{1}{15} *\frac{14}{14} = \frac{1}{8} *\frac{1}{15} *1 = \frac{1}{120}[/tex]

You can achieve the same result if your picks are in a slightly different order. The result won't change as long as the outcome is the same (set of 2 rotten apples and 1 good apple). So if you first pick a rotten apple (2/16), then you happen to pick a good apple (14 out of 15 left are good so 14/15) and then pick the second rotten apple last (1/14) you will see it's gives the same result because you also end up with 2 rotten and 1 good apples:

[tex]\frac{2}{16} * \frac{14}{15} * \frac{1}{14} = \frac{1}{8} * \frac{1}{15} = \frac{1}{120}[/tex]

Answer:  The correct answer is on Day 39 they both have the same amount (38) of naxvips

Step-by-step explanation:

First, determine the rate of change for each using the formula (end-start/days):

Min-jun:

start=36

end=41

days (constant)=15

Rate=41-36/15=5/15 = 1/3 (increment/day)

Tran:

start=56

end=11

days (constant)=15

Rate=11-56/15=-45/15 = -3 (decrement/day)

Build the table using the rate of change for every 3 days:

DAY    MJ    ROC    TRAN    ROC

33       36       0         56          0       <---Start date

36       37      +1          47          -9

39       38      +1          38          -9     <-----SAME!

42       39      +1          29          -9

45       40      +1          20          -9

48       41       +1           11           -9

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Answer:

10AM on November 21.

Step-by-step explanation:

12am: - 32: November 21.

1am: - 31: November 21.

2am: - 30: November 21.

3am: - 29: November 21.

4am: - 28: November 21.

5am: - 27: November 21

6am: - 26: November 21.

7am: -25: November 21.

8am: -24: November 21.

9am: -23: November 21.

10am: -22 hours (22 hours ago): November 21 - ANSWER IS 10 AM.

11am: - 21: November 21.

12pm: - 20: November 21.

1pm: - 19: November 21.

2pm: - 18: November 21.

3pm: - 17: November 21.

4pm: - 16: November 21.

5pm: - 15: November 21.

6pm: -14: November 21.

7pm: -13: November 21.

8pm: -12: November 21.

9pm:-11: November 21.

10pm: -10: November 21.

11pm: - 9: November 21.

12am: - 8: November 22.

1am: -7: November 22.

2am: -6: November 22.

3am: -5: November 22.

4am: -4: November 22.

5am: -3: November 22.

6am: -2: November 22.

7am: -1: November 22.

8am: CURRENT TIME (RIGHT NOW): November 22 - START FROM HERE.

The value of a and b based on the given table when the number of pairs of tiles is 2 is given by 30 cm and 40 cm respectively.

When,

number of pairs of tiles is 1

Width of each tile = 20 cm

Length of each tile = 30 cm

number of pairs of tiles is 3

Width of each tile = 40 cm

Length of each tile = 50 cm

number of pairs of tiles is 2

Width of each tile, a = 20 cm + width of each tile

= 20 cm + 10 cm

= 30 cm

a = 30 cm

Length of each tile, b = 30 cm + width of each tile

= 30 cm.+ 10 cm

= 40 cm

b = 40 cm

In conclusion, the value of a and b from the above diagram is 30 cm and 40 cm respectively.

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A polynomial function with zeros of -1, -1, 2i is:

f(x) = x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i

We have been given a polynomial function with zeros of -1, -1, 2i

This means, (x + 1), (x + 1) and (x - 2i) are roots of polynomial.

Let f(x) be required polynomial function.

To find a polynomial consider an equation,

f(x) = 0

(x + 1) * (x + 1) * (x - 2i) = 0

(x^2 + 2x + 1) * (x - 2i) = 0

x(x^2 + 2x + 1) - 2i(x^2 + 2x + 1) = 0

x^3 + 2x^2 + x - 2ix^2 - 4ix - 2i = 0

x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i = 0

so, f(x) = x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i

Therefore, a polynomial with zeros of -1, -1, 2i is f(x) = x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i

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Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches Mattie’s house.

The shortest distance between Caroline's and Mattie's house is 10 blocks.

If we assume this as a right angle triangle then height (BA) is 6 blocks long and base (BC) is 8 blocks

long.

Then, the shortest distance between Caroline's and Mattie's house will be the hypotenuse (AC) of this

triangle.

So, by applying Pythagoras theorem:

[tex](AC)^{2} = (BA)^{2} = (BC)^{2} = (6)^{2}+(8)^{2}[/tex] = 36+64 = 100

Thus, AC = [tex]\sqrt{100}[/tex] = 10 blocks.

Hence, the shortest distance we can take from Caroline's house to reach Mattie's house is 10 blocks.

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Answer: T is the longest side. T = 62

Step-by-step explanation:

R + S = 118

(57+61)

180-118=62

Given the relation (9,2)(4,5)(7,3)(10,-5), an ordered pair which would result in a relation that is not a function is: (10, 2).

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.

Based on the ordered pairs shown above, we can reasonably infer and logically deduce that (10, 2) is an ordered pair which does not represent a function because the value of "a" has already been mapped to -5.

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Answer:

x=5

Step-by-step explanation:

Because we know the sum of the interior angles should be 180, we can use this to create an equation to solve for x.

60+(7x+3)+(180-20x)=180

Simplify to find that x = 5

If you're confused about where the 180-20x comes from:

The line it lays on is straight, meaning the angle it creates is 180 degrees.

Thus, 180 - known angle = unknown angle.

Answer:

the answer is c, x=5

Step-by-step explanation:

now, if we look at the pic, there is already one angle given.

and we know that sum interior angles of a triangle must be 180;

so the sum of the other two angles is: angle 2 +angle 3=180-60.

now, let's pick any number and put it into x.

first, if we put 15 into x: 7(15)+5=120,

so 180-(120+60)=0. and for there is another angle, it is invalid.

if we put 6: 7(6)+5=47,

180-(60+47)=73.

let's look at the third angle.

for x=6, the angle UBI is 120°. and we also know that the sum of angles on a horizontal line is always 180°, so 180-120=60, and for the third angle is NOT 73°, this one is also invalid.

if x=5: 7(5)+5=40, 180-(60+40)=80.

the angle UBI= 100°, 180-100=80°;

for 80°+60°+40° equals 180°, the answer c is correct.

Answer:

b=1519.87? (If not correct please clarify what sides the 1600 and 500 ft are on. In my answer the 1600 ft was the hypotenuse since it was the longest of the two and it said to find the base of the triangle. This means the 500 ft is the side adjacent to 90 degrees and 1600 ft is the hypotenuse. Sorry if it's not clear!)

Step-by-step explanation:

[tex]500^{2} +b^2=1600^2\\250000+b^2=2560000\\b^2=2560000-250000\\b^2=2310000\\\sqrt{b^2}=\sqrt{2310000}\\ b=1519.87[/tex]

Answer:

side 2 ([tex]b^{2}[/tex]) = 1519.87

OR

hypotenuse ([tex]c^{2}[/tex])= 1676.31

Explanation:

If 1600 ft = hypotenuse and 500 ft = side

[tex]1600^{2}[/tex] = [tex]500^{2}[/tex] + [tex]b^{2}[/tex]

2560000 = 250000 + [tex]b^{2}[/tex]

2560000 - 250000 = [tex]b^{2}[/tex]

2310000 = [tex]b^{2}[/tex]

[tex]\sqrt{2310000}[/tex] = [tex]\sqrt{b^{2} }[/tex]

[tex]b[/tex] = 1519.87

side 2 = 1519.87

OR

If 1600 ft = side 1 and 500 ft = side 2

[tex]1600^{2}[/tex] + [tex]500^{2}[/tex] = [tex]c^{2}[/tex]

2560000 + 250000 = [tex]c^{2}[/tex]

2810000 = [tex]c^{2}[/tex]

[tex]\sqrt{2810000}[/tex] = [tex]\sqrt{c^{2} }[/tex]

[tex]c[/tex] = 1676.31

hypotenuse = 1676.31

Answer:

∴ Shaquana bought 7 candies and 6 pretzels.

Step-by-step explanation:

Suppose all the snacks she bought were candies.

13 × $5 = $65

$65 - $53 = $12

$5 - $3 = $2

$12 ÷ $2 = 6 pretzels

∴ Number of candies Shaquana bought

= 13 snacks - 6 pretzels

= 7 candies

Answer:

6 pretzels and 5 candies

Step-by-step explanation:

Let c be the number of candies and p the number of pretzels.

We can determine the total cost by multiplying the candy price by it's price, $5/candy.  That would be $5*c.  We can do the same for the pretzels:  $3*p.

Thje total spent is:    ($5)c + ($3)p = $53.  Since the $ sign cancels out, let's rewrite this to simplify:   5c + 3p = 53.

We know that c + p = 13

Rearrange this to c = 13-p and then substitute this definition of c in the first equation:

5c + 3p = 53

5(13-p) +3p = 53

65 - 5p + 3p = 53

-2p = - 12

p = 6  Shaquana brought 6 pretzels.

Since c + p = 13, this means she bought 7 candies.

Check to see if this works:

Do 6 pretzels and 7 candies cost $53?

 (6 prezels)*($3/pretzel) =  $18

 (7 candies)*($5/candy) =  $35

               Total                =  $53  YES

Answer:

3043kg

Step-by-step explanation:

30kg

43g

is this right

Negative numbers are sometimes rational numbers. As, this statement is only true in all the following statements.

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them. the system of numbers

Following statements are given,

1. Positive numbers are always rational numbers.

2. Negative numbers are always irrational numbers.

3. Negative numbers are sometimes rational numbers.

4. Negative numbers are always integers.​

According to statement Positive numbers are always rational numbers

As this statement is not always true because though √2 is positive, it is not a rational number.

According to statement Negative numbers are always irrational numbers.

This is also not true as always as -4 is negative and it can be expressed in the form of [tex]\frac{-4}{1}[/tex] , hence it is rational.

According to statement Negative numbers are sometimes rational numbers.  As  it can be both -2 is a negative rational number and -√2 is negative irrational number.

According to statement Negative numbers are always integers.​This is not always true because [tex]\frac{-2}{3}[/tex] is a negative number with a fractional part, hence it is not an integer.

Hence, only 3rd statement is true ,

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Leaping deer company purchased a tractor at a cost of $440,000. The tractor has an estimated residual value of $40,000 and an estimated life of 8 years, or 12,000 hours of operation. The tractor was purchased on January 1, 2015 and was used 2,400 hours in 2015 and 2,200 hours in 2016.

To find out which method of depreciation will produce maximum depreciation, Depreciation expense for 2018 shall be calculated using all methods.

1) Double-declining balance method: Under this method, depreciation is charged to an accelerated rate to the asset by applying double depreciation instead of a regular depreciation rate. This rate is applied to the value of the depreciable assets.

Depreciable Value of Tractor = Gross Value - Salvage Value = $240,000 - $40,000 = $200,000

The regular rate of depreciation = 100% / Life of Tractor = 100% / 8 Years = 12.5%

Double-declining rate of depreciation = Regular rate X 2 = 12.5 % X 2 = 25%

Depreciation expense for 2018 = Depreciable value of tractor X Dobule-decling rate

= $200,000 X 25%

= $50,000

Depreciation expense as per double-declining method = $50,000

2) Straight-line method: Under this method, the value of the depreciable asset is spread over the useful life of the asset evenly.

Depreciation for 2018 = Useful life of Tractor / Useful life

= $200,000 / 8 Years

= $25,000

Depreciation expense as per straight line method = $25,000

3) Units of production method: Under this method, the depreciable value of assets is depreciated with the level of usage with respect to the overall capacity of assets with respect to usage. Hence, more usage shall lead to higher depreciation.

Total hours available during the life of asset = 12,000

Depreciation to be charged for each hour of usage = Depreciable value / Total hours

= $200,000 / 12,000 Hours

= $16.67 per hour

Depreciation for 2018 = Total hours of usage in 2018 X Depreciation per hour

= 3,800 Hours X $16.67

= $63,346

Depreciation under units of production method = $63,346.

Hence, Highest amount of depreciation is produced under units of production method as tractor has been used for more than one-third of its usage hour capacity. As the other two methods do not take into account the level of usage, their depreciation is just based on time. Hence, Depreciation under the unit production method is highest.

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The angular speed is 0.233 radian per second.

What is angular speed?

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ t where θ is the angular displacement, t is the time and ω is the angular speed.

given radius = 24 feet

distance covered = 5.6

First we will find the circumference

= 2πr

=48π

Time = 48π/5.6 = 26.91

Angular speed = 2π/TIME

=2π/26.91

= 0.233

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Answer:

y = -1/5x + 17/5

Step-by-step explanation:

Parallel lines have the same slope as m2 = m1.  Thus, the slope the of second line is -1/5.

We can find the y-intercept by plugging in (2,3) for x and y and our slope:

[tex]3 = -\frac{1}{5}(2)+b\\ 3=-\frac{2}{5}+b\\ \frac{17}{5}=b[/tex]