1. A weather balloon that contains 540 m' of helium springs a leak and empties in 60 seconds. Suppose that the volume of helium in the balloon as a function of time is given by V(t)=540 (1-t÷60)^3 (a) the average rate of change of volume during the 60 seconds it takes to empty. (b) the volume of the balloon after 40 seconds. (c) the instantaneous rate of change of the volume at 40 seconds. ​

The blue shaded portion on the top left side is described as forming lines pass through (6, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion W. D.

To graph the system of inequalities y ≥ 1/3x - 2 and y ≤ -4x - 2, we will plot the lines corresponding to each inequality and shade the region that satisfies both inequalities.

First, let's graph the line y = 1/3x - 2.

We can find two points on this line and connect them with a straight line:

Using (6, 0):

y = 1/3(6) - 2

y = 2 - 2

y = 0

So we have the point (6, 0).

Using (0, -2):

y = 1/3(0) - 2

y = -2

So we have the point (0, -2).

Plotting these two points and drawing a line through them, we get a line labeled as Line 1.

Next, let's graph the line y = -4x - 2 using the same process:

Using (0.5, 0):

0 = -4(0.5) - 2

0 = -2 - 2

0 = -4

So we have the point (0.5, 0).

Using (0, -2):

-2 = -4(0) - 2

-2 = -2

So we have the point (0, -2).

Plotting these two points and drawing a line through them, we get a line labeled as Line 2.

Now, we need to shade the region that satisfies both inequalities.

The shaded region will be the region where Line 1 is above Line 2.

Based on the given descriptions of the shaded portions W, X, Y and Z we can determine the correct option.

The blue shaded portion on the top left side is described as forming when lines pass through (0.5, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion X.

The blue shaded portion on the left side is described as forming when lines pass through (0.5, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion Y.

The blue shaded portion on the bottom left side is described as forming when lines pass through (6, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion Z.

Based on this information, we can determine the correct option:

A. X

B. Y

C. Z

D. W

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Answer:

140 words

Step-by-step explanation:

If Tim can read 28 words per minute and we are trying to find how many words he can read in five minutes, we simply have to multiply 28 x 5 = 140 and we got our answer.

Answer:

  f(x) = 5^x -2

Step-by-step explanation:

You want the equation for the graph attached.

The graph has a horizontal asymptote for negative values of x, and rises rapidly for positive values of x. This suggests an exponential function.

The graph of the parent exponential function will pass through the point (0, 1), which is 1 unit above the horizontal asymptote. Here, the horizontal asymptote is y = -2, and the graph passes through (0, -1).

This tells us the graph is vertically translated down 2 units and not translated horizontally at all. (Horizontal translation is equivalent to a vertical scale factor. The lack of it tells us the vertical scaling is 1.)

The parent exponential function b^x rises b units above the horizontal asymptote when the value of x is 1. Here, the function rises to +3 from the asymptote of -2 at x=1, so the base of the exponential is 3-(-2) = 5.

The equation for the graph is ...

  f(x) = 5^x -2

Confirmation is shown in the attachment.

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Answer:

Step-by-step explanation:

You want to know the slope and intercept of the linear equation that results from taking the logarithm of y = 4(1.4^x).

The applicable rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a^b) = b·log(a)

The log of the given equation is ...

  y = 4·1.4^x

  log(y) = log(4·1.4^x)

  log(y) = log(4) +log(1.4^x)

  log(y) = log(4) + x·log(1.4)

In slope-intercept form, this is ...

  log(y) = mx +b

  log(y) = log(1.4)·x +log(4)

Comparing equations, we see ...

  m = log(1.4)

  b = log(4)

__

Additional comment

The line representing log(y) is shown in the attachment, along with verification that its slope and intercept are as found above.

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The ticket price that maximizes revenue is $8.50.

Let x be the ticket price in dollars

Let y be the attendance.

We are given two points: (12, 20000) and (11, 24000).

Using the point-slope formula, we can find the equation of the line:

y - 20000 = (24000 - 20000)/(11 - 12) * (x - 12)

y = -4000x + 68000.

Revenue R is equal to the product of price and attendance: R = xy.

Substituting y = -4000x + 68000, we get:

R = x(-4000x + 68000)

R = -4000x^2 + 68000x.

Using  [tex]x = -b/(2a)[/tex] where a and b are the coefficients from the form ax2 + bx + c]

= - 68000/(2*-4000)

= 8.5.

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We would expect Underwood Motors shares to sell for $4.52 per share and Book value per share is $1,303,000 /total shares outstanding

To find the expected price of Underwood Motors shares, we need to use the price-earnings ratio and the earnings per share (EPS):

Expected price per share = price-earnings ratio x EPS

Expected price per share = 18.32 x 0.247 = 4.52384

So we would expect Underwood Motors shares to sell for $4.52 per share.

To find the book value per share, we can use the formula given:

Book value per share = stockholders' equity / total shares outstanding

Book value per share = $1,303,000 /total shares outstanding

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If wheel on a scooter completes 124 revolutions and travels 22.4 meters then  diameter of the wheel is 57 mm

Each revolution of the wheel covers a distance equal to the circumference of the wheel.

The diameter of the wheel "d".

The distance covered in 124 revolutions is:

distance = 124 x circumference

= 124 x pi x d

= 124 x 3.14 x d

We know that this distance is equal to 22.4 meters, so we can set up an equation:

124 x 3.14 x d = 22.4

Simplifying and solving for d:

d = 22.4 / (124 x 3.14)

d = 0.057 meters

As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters

d = 57 millimeters

Therefore, the diameter of the wheel is approximately 57 mm.

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Answer:

12

Step-by-step explanation:

28 plus 20 equals to 48 and then each divide 4

these are all problems designed to practice the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides, and A, B, C being the corresponding opposite angles.

I

and remember :

sin(90) = 1

a)

4/sin(30) = c/sin(90) = c

4/0.5 = c = 8 cm

b)

17/sin(53) = c/sin(90) = c

c = 21.28630619... cm

c)

6/sin(41) = c/sin(90) = c

c = 9.14551852... cm

The transformation that maps the blue triangle into the orange one is a rotation.

First, a translation only moves the figure (it does not change the orientation), and in the image we can see that the orientations are different, then we can discard the translation.

Similarly with the dilation which only changes the size, we can discard that one too.

Finally, if we do a reflection over a given line the orientation can be changed, but there must be a line of symmetry (the line used for the reflection) between the two figures, that we can't see here.

Then the remaining option is the correct one, this is a rotation.

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Answer:

  y = -4(x +2)² +7

Step-by-step explanation:

You want the equation of the parabola with vertex (-2, 7) that passes through point (-1, 3).

The vertex form of the equation of a parabola is ...

  y = a(x -h)² +k . . . . . . . . vertex (h, k)

We can use (x, y) = (-1, 3) and (h, k) = (-2, 7) to find the value of 'a'.

  3 = a(-1 -(-2))² +7 = a +7

  -4 = a . . . . . . . . subtract 7

Then the vertex form equation for the parabola is ...

  y = -4(x +2)² +7

<95141404393>

The box that depicts the number of dogs at the daycare each day is Box C which shows median of 60. The Option C.

The full data for number of dogs at the daycare each day is:

[tex]47,38,72, 56, 40, 64, 30, 80, 66, 51, 33, 74, 70, 69[/tex]

To get median, we will arrange the numbers in ascending order which is:

[tex]30, 33, 38, 40, 47, 51, 56, 64, 66, 69, 70, 72, 74, 80[/tex]

Since we have an even number of observations (14), the median will be the average of the two middle numbers.

The two middle numbers are 56 and 64. So the median is:

= (56 + 64) / 2

= 120 / 2

= 60.

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The average total cost of producing 5 shirts by the firm is $35.

We can use the following formula to calculate the average total cost (ATC) of producing 5 shirts:

ATC = Total Cost / Quantity

We know that the firm produces 6 shirts at a total cost of $187, so the total cost of producing 5 shirts can be estimated by subtracting the marginal cost of the last shirt from the total cost of producing 6 shirts:

Total Cost of producing 5 shirts = Total Cost of producing 6 shirts - Marginal Cost of the last shirt

                                 = $187 - $12

                                 = $175

Now we can use the formula to find the average total cost of producing 5 shirts:

ATC = Total Cost / Quantity

   = $175 / 5

   = $35

Therefore, the average total cost of producing 5 shirts by the firm is $35.

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317 words can be formed by using all the letters of the word ARRANGEMENT

The solution is: Thabang should receive R240 if they decide to split the money based on hours worked.

Here, we have,

If Thabang worked for three hours and Ndivhu worked for two hours, then the total number of hours worked is five.

To determine the amount Thabang will receive if they decided to share their money according to hours, we need to calculate the proportion of the total hours that Thabang worked and multiply that by the total amount of money earned.

Thabang worked for three out of five hours, which is 3/5 or 0.6 of the total time.

To find out how much money he should receive, we can multiply this fraction by the total amount earned:

0.6 x R400 = R240

Therefore, Thabang should receive R240 if they decide to split the money based on hours worked.

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Answer:

A

Step-by-step explanation:

Negation statements have the word "not" in them or taken out of them.  In this case, not is added to the statement.

The length of AB and CB is 7√2.

Using Trigonometry

cos 45 = B/ H

cos 45 = AD / AB

1/√2 = 7 / H

H = 7√2

Then, CB = AB = 7√2

Now, using Pythagoras theorem in ΔABC

AC² = AB² + CB²

14² =  (7√2)² + CB²

CB² = 196 - 98

CB = 7√2

Thus, the length of AB and CB is 7√2.

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The formula that of h is h = 9k/16t

Joint variation describes a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant.

h is inversely proportional to p and directly proportional to t , therefore

h = k t/p

when h = 9 and t = 64 and p is 4

9 = k 64/4

64k = 36

k = 36/64

k = 9/16

h = 9k/16t

therefore the formula of h interns of k and t is

h = 9k/16t

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Answer:

yes

Step-by-step explanation:

common sense

Answer:

843,75 feet away

Step-by-step explanation:

speed of sound is 1.125 feet per sec

to calculate the distance of the canyon use : distance =(speed of sound ×time)/2

(1,125feet/sec ×1,5sec)/2

=843,75 feet away

Answer:

7.5

Step-by-step

to get this answer you need to multiply 10*75 than divide it by 100

10          0

-----     --------

100        75

The equation of line FG is given as follows:

y = -0.5x - 5.5.

The circle has a center of (1, -1), hence the equation is given as follows:

(x - 1)² + (y + 1)² = r².

Point (-1, -5) is on the circumference of the circle, hence the radius is obtained as follows:

(-1 - 1)² + (-5 + 1)² = r²

r² = 40.

Hence:

(x - 1)² + (y + 1)² = 40.

Applying implicit differentiation, the derivative is given as follows:

2(x - 1) + 2(y + 1)m = 0

2x - 2 +2m(y + 1) = 0

m = (x - 1)/(y + 1)

At x = -1 and y = -5, hence the slope is given as follows:

m = -2/4

m = -0.5.

Hence the equation is given as follows:

y + 5 = -0.5(x + 1).

y = -0.5x - 5.5.

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7/12 is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll

The probability of rolling an even number on the first roll is 3/6 = 1/2, since there are three even numbers (2, 4, 6) out of six possible outcomes.

The probability of rolling a 1 on the second roll is 1/6, since there is only one outcome that will result in a 1.

To find the probability that at least one of these events occurs, we can add their probabilities and subtract the probability that both events occur:

P(even or 1) = P(even) + P(1) - P(even and 1)

Since the events are independent, the probability that both occur is simply the product of their probabilities:

P(even and 1) = P(even) × P(1) = (1/2) × (1/6) = 1/12

Substituting into the formula above, we get:

P(even or 1) = 1/2 + 1/6 - 1/12 = 7/12

Therefore, 7/12 is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll

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Egbert must deposit $19,602.52 as a lump sum in order to have $40,000 in the fund at the end of 10 years.

To calculate the required lump sum deposit, we can use the formula for compound interest:

A = P[tex](1+r/n)^{nt}[/tex]

Where:

A = the future value (desired amount in the fund) = $40,000

P = the initial principal (lump sum deposit we need to find)

r = the annual interest rate in decimal form = 7% = 0.07

n = the number of compounding periods per year = 4 (quarterly compounding)

t = the number of years = 10

Plugging in these values, the formula becomes:

$40,000 = P[tex](1+(0.07/4)^{(4*10)}[/tex]

Simplifying further:

$40,000 = P[tex](1.0175)^{40}[/tex]

Now we can solve for P by dividing both sides of the equation by

P = $40,000 /[tex](1.0175)^{40}[/tex]

Using a calculator to evaluate the expression, we find:

P ≈ $19,602.52

Therefore, Egbert must deposit approximately $19,602.52 as a lump sum in order to have $40,000 in the fund at the end of 10 years.

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355.2

i use my notebook and showed my work by doing 3.7x8x12 which is equal to 355.2

The given expression, rewritten by factoring out the greatest common factor is 2y(x³ + 4x - 2x² - 8)

The given expression factored completely is (2xy - 4y)(x² + 4)

From the question, we are to rewrite the given expression by factoring out the greatest common factor and also by factoring completely

The given expression is

2x³y + 8xy - 4x²y - 16y

The greatest common factor is the expression that is common t each of terms in the given expression

The greatest common factor is 2y

Factoring out the greatest common factor

2x³y + 8xy - 4x²y - 16y

2y(x³ + 4x - 2x² - 8)

Factoring the expression completely

2x³y + 8xy - 4x²y - 16y

2xy(x² + 4) - 4y(x² + 4)

(2xy - 4y)(x² + 4)

The complete factoring of the expression is (2xy - 4y)(x² + 4)

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The required length of the segments are found as :

AB = 3.16

AC = 5.1

BC = 5.66

Perimeter = 13.92

A perimeter is  described as a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

We make use of the distance formula:

Distance = √ ((x2 - x1)² + (y2 - y1)²

segment AB:

x1 = 1, y1 = 5

x2 = 4, y2 = 4

= √ ((4 - 1)² + (4 - 5)²

= √ (9 + 1)

= √ (10)

= 3.16

Segment AC:

x1 = 1, y1 = 5

x2 = 0, y2 = 0

= √ ((0 - 1)^2 + (0 - 5)^2)

= √ ((-1)^2 + (-5)^2)

= √ (1+ 25)

=√ (26)

= 5.1

Segment BC:

x1 = 4, y1 = 4

x2 = 0, y2 = 0

= √ ((0 - 4)² + (0 - 4)²

=√ ((-4)² + (-4)²

= √ (16 + 16)

= (32)

= 4 x √(2)

= 5.66

Perimeter = segment AB + segment  AC + segment  BC

Perimeter =  13.92

Perimeter =  13.92

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the complete question is attached in the image:

Answer:

Convert the word problem into equation

Let the number be x

By the problem

7x-13=5x-5

Transport the 5x to lhs and -13 to rhs

7x-5x=13-5

2x=8

x=8/2

x=4

Therefore the number is 4

Step-by-step explanation:

The volume of the prism is 1323 feet³ (cubic feet).

Length= 21 feet.

Width= 9 feet.

Height= 7 feet.

The formula to calculate the volume of rectangular prisms is the following:

[tex]\sf V_{RP} =l*w*h[/tex]; where "l" is the length; "w" is the width, and "h" is the height of the prism.

Check the attached image to see where these values are measured from.

Substitute the variables in the formula by the values on step 1.

[tex]\sf V_{RP} =l*w*h=(21\ feet)*(9\ feet)*(7\ feet)=\boxed{\sf1323\ feet}.[/tex]

The volume of the prism is 1323 feet³ (cubic feet).

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Answer:

The volume of the rectangular prism is 1323 cubic feet.

Step-by-step explanation:

Step 1: Write down the formula for the volume of a rectangular prism:

[tex]\qquad\Large\boxed{\rm{\:\:\:V = l \times w \times h\:\:\:}}[/tex]

Step 2: Substitute the given values for the length, width, and height:

[tex]\qquad\Large\rm{V = 21\: ft \times 9\: ft \times 7\: ft}[/tex]

Step 3: Multiply the numbers together:

[tex]\qquad\Large\rm\implies{V = 1323\: ft^3}[/tex]

Step 4: Write the final answer with the appropriate units:

The volume of the rectangular prism is 1323 cubic feet.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]