The rate at which the temperature is dropping is 6t 5t2 degrees Celsius per hour t hours after sundown. How much had the temperature decreased between sundown and 3 hours after sundown

The height of the monument is 30 meters.

We have,

Let's assume the height of the monument is "h" meters.

From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.

In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.

The opposite side of the angle of depression is the height of the monument, which is "h" meters.

Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.

Therefore, the opposite sides are equal in length.

By setting up the equation:

h = 30

Thus,

The height of the monument is 30 meters.

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Answer: 21

Step-by-step explanation:

arc AC = 2b

3x + 9 = 2(3x - 1.5)

3x + 9 = 6x - 3

solve for x

6x - 3x = 9 + 3

3x = 12

x = 4

substitute in the 2 equations

3 (4) - 1.5 = 10.5

which means that if we substitute in the second equation we should get 21

3(4) + 9 = 21

so arc AC= 21 degrees

We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

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Answer:  Choice C)  David should buy 5 packages of buns and 6 packages of hot dogs.

========================================================

Explanation:

Focus on the hot dog buns for now

1 package = 12 hot dog buns

2 packages = 24 hot dog buns  (multiply both sides by 2)

3 packages = 36 hot dog buns (multiply original equation by 3)

We can see that the multiples of 12 are being listed. So we have

12, 24, 36, 48, 60, 72, 84, ...

as the possible number of hot dog buns we could get if we buy 1,2,3... packages.

The possible number of hot dogs we can get are

10, 20, 30, 40, 50, 60, 70, 80, ...

which are multiples of 10. Simply add 10 to each item to get the next one.

--------------------------------

Considering these two sets

12, 24, 36, 48, 60, 72, 84, ...

10, 20, 30, 40, 50, 60, 70, 80, ...

what is the lowest common multiple? That would be 60 since it is found in both lists and it is the smallest in common.

The LCM of 12 and 10 is 60.

If he wanted 60 hot dog buns, then 60/12 = 5 packages of buns is what he needs.

If he wanted 60 hot dogs, then he needs 60/10 = 6 packages of hot dogs.

Therefore, David should buy 5 packages of buns and 6 packages of hot dogs. The answer is choice C.

--------------------------------

Side note: a different way to find the LCM is to multiply 10 and 12 to get 10*12 = 120. Then we divide by the GCF 2 getting 120/2 = 60.

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer:

5b+4

Step-by-step explanation:

1/2(20b-10b+8)

By distribution, (10b-5b+4)= 5b+4

Answer:

they pay $x*35.25

Step-by-step explanation:

this is the answer

Answer:

i'm answer is letter b 16. 5675

Answer:

At the time the ball was thrown, it was 8 feet above the ground.

h'(x) = -32x + 64 = 0, so x = 2

The ball reaches its maximum height after 2 seconds.

• We assume here that the auto drives at 40 mph for 4 hours.

• Then, it stops and then drives for 2 hours at 10 mph.

• We need to find the total miles the auto drove.

• To answer this question, we need to know that we have a constant rate at each part of the driving of the auto: in the first part, it drove at a constant speed of 40 mph. In the second part, it drove at a constant speed of 10 mph.

• We can say that the total distance for the first part is:

• d1 = 40 miles/hour * 4 hours ---> ,d1 = 160 miles.

• In the second part:

• d2 = 10 miles/hour * 2 hours ---> ,d2 = 20 miles.

• Then, the total miles it went was:

• ,d1 + d2 = 160 miles + 20 miles = 180 miles.

• The auto drove for 180 miles.

•

•

Answer:

The answer is 28

Step-by-step explanation:

because you just multiply 7×4

Answer: It would be True

The difference between the total amount of bags of box tops collected by 4th grade to 5th grade is 2 (1/16). Option D

The given parameters that will help us to get the difference are

The fractions,  

We shall be solving the fractions in pars then later we find the difference.

[4 3/12 +5 5/16 +3 3/8} -  {3 1/4 +4 1/2 + 3 1/8}  

Simplify by find the  LCM of each side

[12{12+15+18}/48 ] - {10 (2+4+1)/8

Simplify to get

12 (45/48)   - 10[7/8]

subtracting the fractions to have

2 [45 - 42]/48

Making it more simpler to get

2 1/16

Therefore the difference between the two fractions is 2 1/16

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Answer:

45

Step-by-step explanation:

Answer:

c.

y = StartFraction 7 Over 9 EndFractionx + StartFraction 17 Over 9 EndFraction

Step-by-step explanation:

Answer:

1.542425 or 4

Step-by-step explanation:

Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

Probability is defined as the measurement of the likelihood of an outcome. It is mathematically expressed as:

The selected outcome here is the number of members classified under boot camp.

The probability of attending the boot camp therefore is:

We know from probability that:

The probability of non-attendance of the boot camp therefore is:

The probability that an attendee does not attend a boot camp is 0.7829

Answer:

B) 49,062.5 ft²

Step-by-step explanation:

The area of a circle can be found using the following equation:

A(c) = πr²

Note:

A(c) = Area of circle

π = pi = 3.14

r = radius

The diameter of the circle is given to you. To find the radius, simply divide the diameter by 2:

Diameter/2 = Radius

Radius = 250/2 = 125

Next, plug in 125 into the Area formula for circle for r:

A(c) = πr²

A(c) = π(125)²

A(c) = π * 15625

A(c) = 3.14 * 15625

A(c) ≈ 49062.5

B) 49,062.5 ft² is your answer.

~

Answer:

Length = 10 cm

Width = 10-2 = 8 cm

Step-by-step explanation:

Area formula (L)(W)

80 = 10(x-2)

80 = 10x - 20

Add 20 to both side

100 = 10x

x= 10

Length = 10 cm

Width = 10-2 = 8 cm

The sample space for the two mornings at the stop light would be D. {red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}.

In probability theory, the sample space constitutes the collection of all potential results that could ensue from an experiment. Symbolized by S, it encompasses every plausible outcome that can arise when such a test is conducted.

The sample space would therefore be :
{red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}

This includes all the possible lights that could be seen on the two mornings by Julie.

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Answer:

Step-by-step explanation:

The answer is B

Answer:

\(\huge\boxed{x=15;\ y=4}\)

Step-by-step explanation:

Proportion:

\(\dfrac{x}{18}=\dfrac{5}{6}\qquad|\text{cross multiply}\\\\(x)(6)=(18)(5)\\\\6x=90\qquad|\text{divide both sides by 6}\\\\\huge\boxed{x=15}\)

\(\dfrac{y}{5}=\dfrac{12}{x}\)

substitute x = 15:

\(\dfrac{y}{5}=\dfrac{12:3}{15:3}\\\\\dfrac{y}{5}=\dfrac{4}{5}\qquad|\text{cross multiply}\\\\(y)(5)=(5)(4)\\\\5y=20\qquad|\text{divide both sides by 5}\\\\\huge\boxed{y=4}\)

a) Horizontal Velocity = 12 units per second

b) Vertical Velocity = 6 units per second

c) Speed = 6sqrt(5) units per second

The parametric equations x = 4t^2 + 4t , y = 3t^2 + 2

To find the horizontal velocity, we need to take the derivative of the x equation with respect to time t

dx/dt = 8t + 4

So, when t = 1, the horizontal velocity is

dx/dt = 8(1) + 4 = 12 units per second

Therefore, the horizontal velocity is 12 units per second

To find the vertical velocity, we need to take the derivative of the y equation with respect to time t

dy/dt = 6t

So, when t = 1, the vertical velocity is

dy/dt = 6(1) = 6 units per second

Therefore, the vertical velocity is 6 units per second

To find the speed, we need to use the Pythagorean theorem

speed = sqrt((dx/dt)^2 + (dy/dt)^2)

Substituting the values we found earlier, we get

speed = sqrt((12)^2 + (6)^2) = sqrt(180) = 6sqrt(5) units per second

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Answer:

This is not a function

Step-by-step explanation:

Assuming that the line in question is parallel with the y axis, by using the line test we can see that the line is not a function. The line test is where you draw straight lines going vertically over the graph and if the lines touch the figure in question more than once that means it's not a function.

This can also be proved by imagining there are 2 different points on the line in question. Since the line is straight vertically that means that the points will share the same x value for different y values, which makes it not a function

Answer:

This is not a function.

Step-by-step explanation:

The questioned parallel line within the y-axis does not meet the requirements to be a function. The line test, as the other person stated, is a test where lines are drawn over the points to determine if the graph / model is, or is not a function. Doing so in this process, if the lines touch the same point more than once, that means the graph is not a function.

Answer:

Listen don't use this site

Step-by-step explanation:

They are using people to make money

Answer:

Answer is B

Step-by-step explanation:

P(x<2) - P(x<-2) = .9772 - .0228 = .9544

= 95%

Answer:

Larger number is 618.5

Step-by-step explanation:

=> a = b + 1

=> a - b = 1

Now,

=> a² - b² = 1236

=> (a + b)(a - b) = 1236

=> (a + b)(1) = 1236

=> (a + b) = 1236

Now,

a + b = 1236

=> b + 1 + b = 1236

=> 2b = 1235

=> b = 617.5

=> a = 618.5