Isabel stacked two wooden blocks as shown. What is the total volume of the stacked blocks?

A. 60 cm3
B. 35 cm3
C. 96 cm3
D. 156 cm3

Answer:

the rate at which the height of the box is decreasing is -0.0593 cm/s

Step-by-step explanation:

Given the data in the question;

Constant Volume of a rectangular box with a square base = 500 cm³

area of the base increases at a rate of 6 cm²/sec

so change in the area of the base with respect to time dA/dt = 6 cm²/sec

each side of the base is 15 cm long

so Area of the base = 15 cm × 15 cm = 225 cm²

the rate at which the height of the box is decreasing = ?

Now,

V = Ah

dv/dt = 0 ⇒ Adh/dt + hdA/DT = 0

⇒ dh/dt = -hdA/dt / A

we substitute

dh/dt = [ -( 500 / 225 ) × 6 ] / 225

dh/dt = [ -(2.22222 × 6)  ] / 225

dh/dt = [ -13.3333 ] / 225

dh/dt = -0.0593 cm/s

Therefore, the rate at which the height of the box is decreasing is -0.0593 cm/s

Answer:

a) 0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.

b) 0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.

c) 0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.

Step-by-step explanation:

We have the mean during an interval, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

During the 20th century the mean number of the major hurricanes to strike U.S mainland per year was 0.6.

This means that [tex]\mu = 0.6[/tex]

Find the probability that the number of major hurricane to strike U.S mainland in any any give year is:

a) Exactly one

This is P(X = 1). So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293[/tex]

0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.

b) At most one

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.6}*0.6^{0}}{(0)!} = 0.5488[/tex]

[tex]P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293[/tex]

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5488 + 0.3292 = 0.878[/tex]

0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.

c) More than one

This is:

[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.878 = 0.122[/tex]

0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.

Answer: no solution

Step-by-step explanation:

Answer:

Area= 90

Step-by-step explanation:

triangle area: (b x h) / 2

(12 x 15) / 2

(180) / 2

a= 90

Answer:

14.75

Step-by-step explanation:

x = 1*1*0.5 = 0.5

y = 1.5*1.5 = 2.25

g = ((2.5+1.5)\2) * 2 = 4

t = 4*2 = 8

total = 0.5 +2.25 +4 +8  - 14.75

Answer:

y = 1.0535(4.9512)^x

It can be considered a viral video

Step-by-step explanation:

Using the exponential regression calculator, the regression model obtained is :

y = 1.0535(4.9512)^x

Using the model, we can determine if a video can be considered viral ;

Number of days, x = 10

y = 1.0535(4.9512)^10

y = 1.0535(8853290.1338)

y = 9,326,941.15

Hence, video will receive way over 3 million reviews, a review of about 9,326,941, hence, it can be considered a viral video.

Answer:

3 1/5

Step-by-step explanation:

Answer:

x = 2.2

Step-by-step explanation:

2(x+4)+6 = 12x-8

Use distribution property

2x+8+6 = 12x-8

Combine like terms

2x+14 = 12x-8

Subtract 14 from both sides

2x = 12x-22

Subtract 12x from both sides

-10x = -22

Divide both sides by negative 10

x = 2.2 or x = 11/5 in fractions.

Hope this helps

Answer:

3.6 * 10^-4

Step-by-step explanation:

36000x10^-8

The number must be between 1 and 10

36000.

Move the decimal 4 places to the left, so add 4 to the exponent

3.6 * 10^(-8+4)

3.6 * 10^-4

Answer:

the scientific notation of

[tex] 36000×10^{-8}=36000/100000000=3.6×10^{4}/10^{-8}[/tex]

[tex]=3.6×10^{4-8}=3.6*10^{-4}[/tex]

Answer: 9.82cm

Step-by-step explanation:

Answer: (-30,30)

Step-by-step explanation:

f = -3,3, -3 times 10 = -30 and 3 times 10 = 30 etc

Answer: 105

Step-by-step explanation:

28% es 0.28 en decimal

28% de 375 es 375 x 0.28

375 x 0.28 = 105

Answer:

105

Step-by-step explanation:

[tex]\frac{y}{375} :\frac{28}{100}[/tex]

y × 100 = 28 × 375

100y = 10500

100y ÷ 100 = 10500 ÷ 100

y = 105

Answer:

sin β = sin(36.87) ≈ -0.73733168456

Step-by-step explanation:

The small angle in a 3-4-5 triangle is 36.87 and when you put that into a calculator you are left with roughly -0.73733168456.

Answer:

i

Step-by-step explanation:

Answer:

did you forget a picture?

Step-by-step explanation:

if you did, either add it in the comments, or make a new question

Answer:

first one on top to the left

Step-by-step explanation:

Answer: B) (x - 5)(x + 4)

Step-by-step explanation:

we’re looking for x intercepts at x = 5 and x = -4

x - 5 = 0; x = 5

x + 4 = 0; x = -4

(x - 5)(x + 4) is your answer

Answer:

10 inches

Step-by-step explanation:

Half of the circle is 5 inches. the other half will be 5, which added together makes 10

Answer:

I think D

Hope this helps!!

Answer:

1

Step-by-step explanation:

x is 1 and y is 1 and the total is three so 1

Answer:

(x-8.5)2=81.25

We want to describe the system of equations by analyzing the graph. We will see that the correct option is:

"The blue line represents the equation 2x -3 y = -6, and the solution to the system of equations is (–6, –2)."

We know that the equations are:

y = (-1/3)*x - 4

2x - 3y = -6

Notice that the y-intercept of the first equation is -4, and the line that intercepts the y-axis at -4 is the red line. So the red line represents the equation y = (-1/3)*x - 4, while the blue line represents the other equation.

Also, remember that the solution of a system of equations is given by the point where the graphs of the equations intercept, here, we can see that the lines intercept at (-6, -2), so the solution of the system is (-6, -2)

Then the correct option is:

The blue line represents the equation 2x-3y=-6, and the solution to the system of equations is (–6, –2).

If you want to learn more, you can read:

https://brainly.com/question/9351049

Answer:

a:The blue line represents the equation 2x-3y=-6 , and the solution to the system of equations is (–6, –2).

Step-by-step explanation:

The surface area is B

Answer:

324 cm^3

Step-by-step explanation:

Volume = l x w x h / 2

V = 12 x 6 x 9 / 2

V = 648 / 2

V = 324 cm^3

Answer:

V = 324 cm³

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = area of triangular end × length

A of triangle = [tex]\frac{1}{2}[/tex] × 6 × 9 = 3 × 9 = 27 cm² , then

V = 27 × 12 = 324 cm³

Answer:

A quadrilateral.

Step-by-step explanation:

A quadrilateral has four sides and four angles. For example, a square is a quadrilateral because it has four sides and angles.

Answer:

The maximum of the parabola lands at (2,5).

The coordinates of the turning point of the parabola whose equation is y=-x²+4x+1 are (2, 5)

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points.

The equation of Parabola is y=-x²+4x+1

The turning point (vertex) is the point where the derivative is equal to zero.

y=-x²+4x+1

Differentiate the equation

dy/dx=-2x+4

Now equate dy/dx with zero

dy/dx=0

-2x+4=0

-2x=-4

x=2

Now put x value in the equation

y=-(2)²+4(2)+1

y=-4+8+1

y=5

Hence the coordinates of the turning point of the parabola whose equation is y=-x²+4x+1 are (2, 5)

To learn more on Coordinate System click:

https://brainly.com/question/4726772

#SPJ2

Answer:

Ed's answer of [tex]\frac{3}{8}[/tex] is correct because he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer.

Step-by-step explanation:

To solve for m in [tex]\frac{2}{3}m=\frac{1}{4}[/tex] you want to isolate m by dividing by [tex]\frac{2}{3}[/tex] on both sides, therefore he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer of [tex]\frac{3}{8}[/tex], and his answer is correct.

Answer:

Yes.

Step-by-step explanation:

The diameters are the same so the radii are the same also.

The volume of both is  3.14r^2h.

The radius r and height h is the same for both cylinders.

The volume = 3.14 * 5^2 * 19 = 1491.5 in^3.