A student on the track team runs 45 minutes each day as a part of her training. She begins her workout by running at a constant rate of 8 miles per hour for 푎 minutes, then slows to a constant rate of 7.5 miles per hour for 푏 minutes. Which equation describes the relationship between the distance she runs in miles, 퐷, and her running speed, in miles per hour?

Step-by-step explanation:

You want to know how the squeeze theorem applies to help you find the limit of f(x) is zero as x approaches zero.

The short of it is that you have ...

  f(x) = [messy finite function] × [function that cleanly approaches 0 at x=0]

The zero product rule tells you that the product of any finite value and 0 is zero, so the limit of this product is 0 at x=0.

The graph in the attachment shows the "function that cleanly approaches 0" in red. When multiplied by the "messy finite function", the result is the blue curve. You can see that the result is a function that has a limit of 0 at x=0.

Here, we'll decompose f(x) into two parts:

Messy finite function

The numerator sine function factor of f(x) gets increasingly messy as x approaches zero, due to the cosine term it contains. We can define ...

  [tex]g(x)=\sin(1+\cos(\pi x^{-3}))[/tex]

Because this is a sine function, its value is always in the range |g(x)| ≤ 1.

Function cleanly approaching zero

The remaining factors of f(x) need to be rearranged a bit to make a function that obviously approaches zero at x=0. We do that by factoring ∛x from the denominator and rearranging the leading fraction.

  [tex]h(x)=\dfrac{e\dfrac{-1}{13+x^{-2}}\sqrt{3x^4+5x^6}}{(x+x^{1/3})(3+\arctan\sqrt{7+x^{-8}})}\\\\=-e\dfrac{x^2}{13x^2+1}\cdot\dfrac{x^2\sqrt{3+5x^2}}{x^{1/3}(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}\\\\h(x)=-e\dfrac{x^{11/3}\sqrt{3+5x^2}}{(13x^2+1)(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}[/tex]

Recognizing that the arctangent term will approach π/2 as x→0, this can be (more or less) directly evaluated at x=0 to give ...

  [tex]h(0)=-e\dfrac{0\cdot\sqrt{3}}{1\cdot1\cdot(3+\dfrac{\pi}{2})}=0[/tex]

The sign of h(x) will be opposite the sign of x. The graph of h(x) is shown in red in the attachment.

As h(x) approaches zero, the product ...

  f(x) = g(x)·h(x)

approaches zero. This is the essence of the squeeze.

Starting from our description of g(x) above, we can multiply both sides of the inequality by the positive value |h(x)| to get ...

  |g(x)| ≤ 1 . . . . . . . . . . the range of the sine function

  |h(x)|·|g(x)| ≤ |h(x)|·1 . . . . . . multiply by |h(x)|

Simplifying, this is ...

  |f(x)| ≤ |h(x)| . . . . true for all x

So, the limit is ...

  [tex]\displaystyle \lim_{x\to0}|f(x)|\le\lim_{x\to 0}|h(x)|\\\\\lim_{x\to0}|f(x)|=0[/tex]

The attachment illustrates this nicely, showing that the oscillating f(x) has its amplitude limited by h(x), which approaches zero.

__

Additional comments

The limit of x^-8 is positive infinity as x approaches zero. This means the arctangent function argument is positive infinity as x approaches zero, so the function value is π/2. The sign of x is irrelevant.

We cannot tell if the fraction following "e" in this function is supposed to be an exponent. The two typeset versions of f(x) seem to show "e" as a multiplier, not the base of an exponential term. Even if an exponential term is what is intended, that term would approach 1 at x=0, so the conclusion here remains unchanged.

The function which results from the reflection of the given function; f(x) = 3^x is; f(x) = 3^(-x).

It follows from the task content that the function given is; f(x) = 3^x.

The function in discuss is reflected across the y-axis, hence, it follows from transformation rules that the resulting function involves multiplying x by -1 as follows;

f(x) = 3^(-1×x)

f(x) = 3^(-x).

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The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

x - 2y = -2

To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.

If x = 0, we have:

0 - 2y = -2

y = -2/-2 = 1

if x = 1 then:

1 - 2y = -2

1 + 2 = 2y

3 = 2y

3/2 = y

Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:

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Answer:

Step-by-step explanation:

Find the area of the figure. (Sides meet at right angles.)

1 rettangle on a square

Area Rectangle

(2+2+5)*5=

9*5=

45in²

Area of the Square

5*5=

25in²

sum

45+25=

70in²

Answer:

207  2 hundreds seven ones

Step-by-step explanation:

Answer:8/15 part of rain gauge is filled after 1 hour.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

because the chart matches the scenario

Answer:

A

Step-by-step explanation:

Since the leading coefficient of the function is greater than 0, then it opens upward.

After solving for x in the constructed equation, 97100 bushels were harvested last year.

What is an equation?

Constructing equation to determine no. of bushels.

Bales from the previous year = x + 0.45 x

= 140795 1.45 x

= 140795 X

= 97100 bales

After solving for x in the constructed equation, 97100 bushels were harvested last year.

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Answer:97100

Step-by-step explanation:

The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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The total volume of the tank is 300L.

The volume of a 3D figure is the space that it occupies.

Here, we are given that Yuki adds cleaning solution that is 7/900 of the tank's total volume.

Let the total volume of the tank be V

We know that the cleaning solution required to clean this tank is 2 1/3 L

Firstly, we need to convert this mixed fraction into an improper fraction, Thus, 2 1/3 = (2*3 + 1)/ 3

= 7/3 L

Thus, we can make the following equation,

(7/900)* V = 7/3

V = 7/3 (900/7)

V = 900/ 3

V = 300

Thus, the volume of the tank is 300L.

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Your question was incomplete. Check for full content here-

Yuki works at an aquarium. To clean a tank, she calculates 7/ 900 of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be  2 1/3 L of cleaning solution. What is the total volume of the tank?

Answer:

300L

Step-by-step explanation:

Just did it on Khan academy.

Answer:

1022 minutes

Step-by-step explanation:

Let x be the number of minutes the executive used the phone

There is a base charge of $35 and only minutes greater than 900 min are charged at the rate of $0.40 per minute

So total bill A = 35 + 0.4(x-900)

We know the bill was $83.80

So we can rewrite the equation as

35 + 0.4(x-900) = 83.30

and solve for x

To make it easier for computational purposes

1)  Multiply both sides by 10

[tex]35\cdot \:10+0.4\left(x-900\right)\cdot \:10=83.8\cdot \:10[/tex]

2) Perform individual multiplication

[tex]350+4\left(x-900\right)=838[/tex]

3)  Subtract 350 from both sides

[tex]350+4\left(x-900\right)-350=838-350[/tex]

4)  Simplify

[tex]4\left(x-900\right)=488[/tex]

5) Divide both sides by 4

[tex]\frac{4\left(x-900\right)}{4}=\frac{488}{4}[/tex]

6) Simplify

[tex]x-900=122[/tex]

7) Add 900 to both sides to isolate x

[tex]x-900+900=122+900[/tex]

8) Simplify to obtain x

[tex]x=1022[/tex]

Answer: The executive used the phone for 1022 minutes that month

(a) The change in the tram's elevation (speed) each second is 3 meters/Sec

(b) The total change in temperature of the substance was 160 Celsius.

(a) The tram moves downward 21 meters in 7 second. So, the speed of the tram is 21/7 = 3 meters/Sec, which is the tram’s elevation each second.

We know that, speed = (total distance travel)/(Total travelling time)

(b) The substance was heated by 4 Celsius each hour for 40hours.

Therefore, the total change in temperature is = (4x40) = 160 celcius.

The degree Celsius is the unit of temperature on the Celsius scale, originally known as centigrade scale

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Answer:

(a) The change in the tram's elevation (speed) each second is 3 meters/Sec

(b) The total change in temperature of the substance was 160 Celsius.

Step-by-step explanation:

Answer: 46.5 by 19.5

Step-by-step explanation:

P=perimeter of panel. L=length. W=width

L=3W-12

P=2L+2W

132=2(3W-12)+2W

132=6W-24+2W

132=6W+2W-24

132=8W-24

156=8W

W=19.5

P=2L+2W

132=2L+2(19.5)

132=2L+39

2L=93

L=46.5

46.5 by 19.5

The experimental research conducted by the scientist takes into account the following factors:

a)The change in temperature is the independent variable.

b) The effect of temperature on the chimp's act of aggression is the dependent variable.

c)The dependent variable is continuous.

d)The scale of measurement used to measure the dependent variable is interval.

e) The research method being used here is experimental.

In the above experiment the researcher wants to see the change in the aggression of the chimp when there is a change in temperature in the zoo.

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Answer:

8a-2ab

Step-by-step explanation:

5a-2b+2b+3a-2ab

Simplify 'a'

5a+3a=8a

Simplify 'b'

2b+2b=4b

8a-2ab

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600.

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200.

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600.

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200.

3a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

3b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

3a. Sales commissions per unit is $1.30.

3a. The number of units sold is 14,000 units.

3a. Total sales commission is $18,200.

3a. Fixed portion of sales representatives’ compensation is $14,000.

3a. Total direct selling expense is $18,200.

3b. The total indirect selling expense is $14,000.

Relevant production range = 12,000 to 16,000 units

Production and sales units = 14,000 units

                                                  Average Cost

                                                       per Unit

Direct materials                                $ 7.30

Direct labor                                      $ 4.30

Variable manufacturing overhead  $ 1.80

Direct cost per unit                         $13.40

Fixed manufacturing overhead     $ 5.30

Total manufacturing cost per unit $18.70

Fixed selling expense                   $ 3.80    $53,200 ($3.80 x 14,000)

Fixed administrative expense      $ 2.80     $39,200 ($2.80 x 14,000)

Total fixed costs per unit               $6.60     $92,400 ($6.60 x 14,000)

Variable selling and admin:

Sales commissions                        $ 1.30

Variable administrative expense $ 0.80

Total variable selling and admin per unit = $2.10

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600 ($13.40 x 14,000).

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200 ($5.30 x 14,000).

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600 ($13.40 x 14,000).

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200 ($5.30 x 14,000).

3) Fixed selling expenses =  $53,200 ($3.80 x 14,000)

Advertising expenses = $39,200

Sales Compensation = $14,000 ($53,200 - $39,200)

Sales Commission = $18,200 ($1.30 x 14,000)

Total Salespersons' compensation = $32,200

a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

3a. Sales commissions per unit is $1.30.

3a. The number of units sold is 14,000 units.

3a. Total sales commission is $18,200 (14,000 x $1.30)

3a. Fixed portion of sales representatives’ compensation is $14,000.

3a. Total direct selling expense is $18,200.

3b. The total indirect selling expense is $14,000.

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If we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.

Given that we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour.

We are required to find the number of cups that are needed.

Fraction is the combination of two numbers,one above the division sign and other one below the division sign. The number which is above the division sign is known as numerator and the number which is below the division sign is known as denominator.

Measuring cup=1/3

Number of cups needed in recipe=12+2/3=38/3

Number of cups needed=38/3/1/3

=38 cups

Hence if we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.

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Answer:

k < - 10 or k > 10

Step-by-step explanation:

inequalities of the type | x | > a have solutions of the form

x < - a or x > a , then

3k < - 30 or 3k > 30 ( divide each interval by 3 )

k < - 10 or k > 10

The equation which represents the height of the books is  [tex]s(b)=\frac{5}{4} b[/tex]

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation between two sums of monomials of degree 0 or 1 is known as a linear equation.

The books are stacked one above the other and each book is [tex]1\frac{1}{4}[/tex] inches thick.

So to calculate the total height of the stack we have to multiply the number of books in the stack with the thickness of each book.

The total thickness is represented in the from of a function as

s(b) and the thickness of each book is [tex]1\frac{1}{4}=\frac{5}{4}[/tex] inches

total height=[tex]\frac{5}{4}\times b[/tex]

Therefore the required equation is  [tex]s(b)=\frac{5}{4} b[/tex].

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Z-score of 10 is -1.25; Z-score of 20 is 1.25; Z-score of 12 is -0.75; Z-score of 17 is 0.50; and Z-score of 16 is 0.25.

To calculate this, we use the following notations and formulas:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

SD = Standard deviation = Variance^0.5

Z-score = (x - Mean) / SD

Where;

n = number of obsrvations = 5

x = each observation

We now proceed as follows:

Mean = (10 + 20 + 12 + 17 + 16) / 5 = 15

Variance = ((10-15)^2 + (20-15)^2 + (12-15)^2 + (17-15)^2 + (16-15)^2) / (5-1) = 64 / 4 = 16

SD = Variance^0.50 = 16^0.5 = 4

Z-score of 10 = (10 – 15) / 4 = –1.25

Z-score of 20 = (20 - 15) / 4 = 1.25

Z-score of 12 = (12 - 15) / 4 = –0.75

Z-score of 17 = (17 - 15) / 4 = 0.50

Z-score of 16 = (16 - 15) / 4 = 0.25

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The domain of the function given on the graph is basically all numbers which are real and greater than or equal to -3.

Given a graph of a function.

We are required to choose the correct domain of the function from the options.

Function is basically a relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain of that function and the values that we get from the function are known as part of range of that function.

Because the lowest point on x axis on which the curve starts is -3 and it continuously increases, so the domain of the function given on the graph is basically all real numbers which are greater than or equal to -3.

Hence the domain of the function given on the graph is all real numbers which are greater than or equal to -3.

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Question is incomplete as it should include the attached figure.

The intersection is the set of all elements in both sets, so the answer is {-2, 4, 8}.

The union is the set of all elements in at least one of the sets, so the answer is {-2, 0, 3, 4, 5, 6, 8}.

Answer:

A. $0.22 per tortilla

B. $0.19 per tortilla

Step-by-step explanation:

A. All you gotta do is divide the money by the amount of product.

4.40 ÷ 20  = 0.22

B. All you gotta do is divide the money by the product.

8.55 ÷ 45 = 0.19

Therefore, the best pack to spend your money on would be the larger pack  B.

The slope of f is m= -0.05577.

Given : The winning times for the​ 200-meter dash can be approximated by  f(x) = - 0.05577x+146.2 , where x is the year.

To find : The slope of f

Solution : Using slope intercept form a linear function is represented as

y = mx+b

where, m is the slope and b is the y-intercept.

We can write the function as  f(x) = - 0.05577x+146.2

Comparing with slope intercept form,

m= -0.05577 and y-intercept = 146.2

Therefore, The slope of f is m= -0.05577

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There will be an outcome of 16380 times.

What is an outcome?

The football team will play 14 games

and each game can result in one of 2

Hence, the total possible number of outcomes for the season is [tex]2^{14}[/tex].

Now, let us explain

Let the result can be represented by an 'ordered set" i.e. 14- box.

|1|2|3|4|5|6|7|8|9|10|11|12|13|14|

Hence, the first box can be filled in 2 ways.

Similarly, all boxes.

Hence, the total number of cases will be,

2*2*2*2.... 14 times

=  [tex]2^{14}\\[/tex]

=16380 times.

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Answer:

y = 6x + 760

Step-by-step explanation:

In the problem you are given two pairs of numbers. These are both a pair of inputs and outputs, (x, y):

(390, 3100) also,

(490, 3700)

Write an equation by finding and filling in m and b in the following equation:

y = mx + b

To find m, which is the slope of the line, subtract y-y and put that on top. Then subtract x-x and put that on the bottom. See image.

Next, find b by use EITHER pair of numbers to find b.

I used (390, 3100).

see image.

m = 6 and b = 760

Fill these into

y= mx + b

y = 6x + 760

In case they ask, this means each calculator takes $6 to make and it costs $760 to set up your operation even before you have made any calculators.

For the given proportional relationship, it is found that the unit rate is of 1.5 inches per second, and the meaning of the points is given as follows:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality, also called the unit rate.

For this problem, the unit rate is given as follows:

k = 4.5/3 = 1.5/1 = 1.5 inch per second.

The meaning of the points are given by:

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