question 5 (10 points)

The meaning of each statement is shown below.

Step-by-step explanation:

Assume that the given statements are

(a) c(0)=0

(b) c(3)=c(8)

(c) c(n)=29

(d) c(13)<c(12)

Let c(t) be the number of customers in a restaurant t hours after 8 A.M.

We need to find the meaning of each given statement.

(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.

(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).

(c) c(n)=29 means the number of customers n hours after 8 A.M is 29.

(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.)

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Answer:3

Step-by-step explanation: 105 divided by 3 is 35 there are 3 groups so 1 ten would go in each group.

Answer:

Step-by-step explanation:Price per pound of strawberries is $-0.31635 and blueberries is $0.6836.

Explanation :

Given data ;

Weight of strawberries required for dessert = 212 lb

Weight of blueberries required for dessert = 112 lb

Total cost spent = $9.50

Let,

Cost of blueberries per pound =x

Cost of strawberries per pound = (x-1)

We know that,

Cost of blueberries for overall weight + Cost of strawberries for overall weight = Total cost spent on fruits.

x(112) + (x-1)212 = 9.50

112x + 212x – 212 = 9.50

324x = 221.5

X = 221.5/324

X = $0.6836

So, (x-1) = $-0.31635

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Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794

Given that ;

Ben is making a dessert that requires 212 lbs of strawberries and 112 lbs of blueberries. Strawberries cost $1 less per pound than blueberries. Ben spent a total of $9.50 on the fruit.

So according to the question get the price per pound of each type of fruit;

Let ' x ' be the price per pound of strawberries and ' y ' be the price per pound of blueberries.

By assuming the following equations;

212x - 112y = 1 → ( I )

212x + 112y = 9.5 → ( II )

By solving above equations ( I ) ( II ) we get;

424x = 10.5

      x = 10.5/424

      x = 0.02476

224y = 8.5

      y = 8.5/224

      y = 0.03794

Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794

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4π/ 5 radians = ?

Then if

π radians= 180°

(4/5)•π radians = 180• 4/5

. = 144

Answer is

4pi/5 radians = 144 degrees

The number of ways that the company can choose four workers is 40920 ways.

From the information, the building company employs 3 laborers 12 joiners 8 electrician 4 plumbers. The total number of workers will be:

= 3 + 12 + 8 + 4

= 27 workers

It should be noted that combination will be used to choose the 4 workers. This is illustrated as

Combination formula

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

where n = 33

r = 4

ⁿCr = n! / ((n – r)! r!)

³³C₄ = 33! / (33 - 4)! 4!

= 33! / 29! 4!

= 33 × 32 × 31 × 30 / 4 × 3 × 2

= 40920 ways

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The general slope intercept form equation of a line is as stated below;

where m is the slope and b is the intercept.

If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.

The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;

So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);

Remember, the point slope form equation of a line is given as;

Substituting the above values, we'll have

Let's open up the parenthesis first, we'll have;

Let's isolate y by adding 7 to both sides of the equation;

The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).

The answer to the question -|4-7|+3  is 0  .

The Absolute Value of x denoted by |x| is the non negative value of , without regarding its sign .

For example the absolute value of -3 will be |-3| = 3 .

and absolute value of |-2| = 2 .

In the question ,

it is given that

the question is -|4-7|+3 .

and we have to find the answer of -|4-7|+3 .

let the answer be "y"

So , y = -|4-7|+3

= -|-3| + 3

On further simplification ,

we get  ,

= -(3) + 3     because |-3| = 3

= -3 +3

= 0

Therefore , The answer to -|4-7|+3  is 0  .

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If Milly knits a scarf that is 1.2 m long then Lotte's scarf be 2.20 in metres.

We will use unitary method to solve this problem.

We know, Milly and Lotte are knitting scarves.

For every 6 cm that Milly knits, Lotte knits 11 cm. This can also be written as,

6 cm Milly knits    ---------------->  11 cm  Lotte knits

1 cm Milly knits    ---------------->  (11/6 ) cm  Lotte knits

We know, 1m = 100cm. So, we can write

120 cm Milly knits    ---------------->  ( 11/6 ) × 120 cm  Lotte knits

120 cm Milly knits    ---------------->  220 cm  Lotte knits

120 cm Milly knits    ---------------->  2.20 m  Lotte knits

Thus, we can conclude that  if Milly knits a scarf that is 1.2 m long then  Lotte knits 2.20 metres scarf .

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Answer:

If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.

Absolute Value Calculator: Heron's Calculator

Coterminal Angle Calculator: Graphing Functi...

Step-by-step explanation:

Answer:

No answer

Step-by-step explanation:

An absolute cannot equal a negative number

Answer:

hi how are you . i cant find the answer youre looking for

Answer:

1) 6 ( a - b )

2) x² - 2xy + y²

Step-by-step explanation:

1) 4 ( a - c ) + 2 ( a - b )

First, solve the brackets.

4a - 4c + 2a - 2b

Combine like terms.

6a - 6b

Take the common factor out.

6 ( a - b )

2) x ( x - y ) + y ( y - x )

First, solve the brackets

x² - xy + y² - xy

Combine like terms.

x² - 2xy + y²

Answer:

<3 and <4 are complementary

f is the given profit function whose input is number of cones and output is profit, f(50)=80 tells that $80 profit is made by selling 50 cones of ice cream.

A function is a relation that assigns each element of a set a unique element of another set.

f(x) denotes that function f works on the input values x and give output f(x).

If f is a function and f(x) = x+2, then if we have to check x= 1 , then

f(1) = 1+2 = 3 is the value of the function f at x=1

A La Mode Ice Cream Parlor uses a function f as profit function

The input x is the number of cones it sells and output is profit

f(50) = 85

⇒x = 50 and f(50) = 85

It means that when the parlor sells x = 50 cones , it makes  profit $ f(50) = 85

or On selling 50 cones the profit made is $80

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Answer:

v=-0.5

Step-by-step explanation:

v=2+(-5×0.5)

v=2-2.5

v=-0.5

Answer:

-8 < x < 5

Step-by-step explanation:

-3 < x + 5 < 10

=> Minus 5 in all sides

=> -8 < x < 5

Suppose that y varies directly with x and that y=84 when x=7. What is the value of x when y=108?

when y=84 and when x=7, x to y in proportion is 1:12. Keeping the ratio of x to y at 1 to 12, when y = 108, x = 9.

The size of the angle x in the pentagon is 36 degrees.

A regular pentagon is a polygon with five sides. The angles of a regular polygon is equal to each other.

Therefore,

the sum of angles in a regular pentagon = 540 degrees.

Each angle in a regular pentagon is 540 / 5 = 108 degrees.

The rhombus is inside the pentagon. Opposite angles in a rhombus are equal.

Therefore, the sum of interior angles of a rhombus adds up to 360 degrees

Hence,

108 + 108 + 2y  = 360

where

y is the angle of the rhombus on the x variable.

Therefore,

2y = 360 - 216

2y = 144

y = 144 / 2

y = 72°

Therefore,

x = 108 - 72

x = 36 degrees

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The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2

The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.

It is expressed as;

Given the data in the question;

Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )

Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )

Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )

Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )

Average rate of change = ( 0 + 6 ) / ( 3 )

Average rate of change = 6 / 3

Average rate of change = 2

Therefore, the average rate of change of the function is 2.

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Answer:

Step-by-step explanation:

Convert the first one above:

Apply this to each term of the given expression to get:

The value of n is 89.

Answer:

n = 89

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan double angle identity}\\\\$\tan (A - B)=\dfrac{\tan A - \tan B}{1 + \tan A \tan B}$\\\end{minipage}}[/tex]

Rewrite the tan double angle identity to isolate tanAtanB:

[tex]\implies 1 +\tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}[/tex]

[tex]\implies \tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}-1[/tex]

Therefore:

[tex]\implies \tan 1^{\circ} \tan 2^{\circ}+\tan2^{\circ}\tan3^{\circ}+...+\tan88^{\circ}\tan89^{\circ}[/tex]

[tex]\implies \left(\dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (1 - 2)^{\circ}}-1\right)+\left(\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (2 - 3)^{\circ}}-1\right)+...+\left(\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (88 - 89)^{\circ}}-1\right)[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}-1+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}-1+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-1[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}+\tan 2^{\circ}- \tan 3^{\circ}+...+\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}}{\tan (-1)^{\circ}}-\dfrac{ \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\textsf{Apply the identity}\quad \boxed{ \tan(-x)=-\tan(x)}:[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}}{-\tan 1^{\circ}}+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]

[tex]\implies -1+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]

[tex]\implies \dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-89[/tex]

[tex]\textsf{Apply the identity}\quad \boxed{\tan(90-x)=\cot(x)}:[/tex]

[tex]\implies \dfrac{\cot1^{\circ}}{\tan1^{\circ}}-89[/tex]

[tex]\implies \cot 1^{\circ} \cdot \dfrac{1}{\tan1^{\circ}}-89[/tex]

[tex]\textsf{Apply the identity}\quad \boxed{\dfrac{1}{\tan(x)}=\cot(x)}:[/tex]

[tex]\implies \cot 1^{\circ} \cdot \cot 1^{\circ}-89[/tex]

[tex]\implies \cot^21^{\circ}-89[/tex]

Therefore, n = 89.

The quotient of the triangle side lengths are same as below for different triangle ( please refer attached image for better understanding)-

For ABC - 9/4 or 2.25, 9/6 or 1.5, 6/4 or 1.5

For DEF - 18/8 or 2.25, 18/12 or 1.5, 12/8 or 1.5

For GHI - 27/12 or 2.25, 27/18 or 1.5, 18/12 or 1.5

For JKL - 4.5/2 or 2.25, 4.5/3 or 1.5, 3/2 or 1.5

Quotient in mathematics, can be defined as the result of the division of a number by any divisor.

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First we need to find the 17% of 11,000

The slope between the two pair of points is 3/2. Yes, Dan's productivity is constant.

Number of model are represented on y axis and the hours are represent on x axis.

As we can observe,

One pair of points on the graph is (4,6) and (2,3) and the other pair of points is (6,9) and (0,0)

The slope m between any two points (a,b) and (c,d) can be calculated as,

m = (d-b)/(c-a)

The two points we have are (4,6) and (2,3), so the slope M between them is,

M = (3-6)/(2-4)

M = -3/-2

M = 3/2.

And the slope M' between other two point (6,9) and (0,0) is,

M' = (9-0)/(6-0)

M' = 9/6

M' = 3/2.

As we can see, the slope is same. The slope represents the ratio of number of models and hours. We can conclude that Dan's productivity is constant.

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I f Bill wants to maximize his utility while spending $31 on apple. Bill van buy 10 whole pounds of Apples

given data

Apples cost $3 per pound

Bananas cost $5 per pound

amount Bill has to spend $31

The number of whole apple Bill can buy

Using $31 the number of whole apples this can buy is gotten  dividing the  the total amount by the price of apple per pound.

= amount Bill has to spend $31 / Apples cost $3 per pound

= 31 / 3

= 10.33

Since we are solving for whole pounds of apple Bill can buy 10 whole pounds of apples

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The measure of <5 is 47

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

m<4=5x-42

and m<5=-x+82

as, <4 and <5 are in co- interior angle

<4 + <5 = 180

5x - 42 + (-x + 82) = 180

5x -42 - x + 82= 180

4x +40 = 180

4x = 140

x= 140/4

x= 35

Hence, the measure of <5 = -x+ 82 = -35 + 82 = 47

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1.242 ≤ d ≤ 1.305 is the corresponding interval for the diameter of the washer.

Given that,

Company A makes and sells a washer having a 4-centimeter outer radius. The corporation has decided on a washer with an actual radius in the range of 3.9 ≤ C ≤ 4.1.

Inequality is defined as the connection of an equation having the symbol ( ≤, ≥, <, >) in place of the assignment operator.

Here,

C = 3.14d

Given inequality,

3.9 ≤ C ≤ 4.1

3.9 ≤ 3.14d ≤ 4.1

dividing both sides of the inequality by 3.14,

1.242 ≤ d ≤ 1.305

As a result, the needed matching spacing for the washer's diameter is 1.242 ≤ d ≤ 1.305.

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The hypothesis test is a Left-tailed test and the parameter being​ tested is known as a Population mean.

What is a null and alternative hypotheses?

A null hypothesis predicts no effect between variables while an  alternative hypothesis predict an effect or relationship between variables of the study.

What is the given hypothesis test?

In the question, the given hypothesis test includes "H0​: σ=110" and "H1​: σ<110"

Hence, based on the test above, the hypothesis test is a Left-tailed test and the parameter being​ tested is known as a Population mean.

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