(Calculator Active) Find the volume of the solid whose base is the region bounded by the parabola x^2 = 4y and the line y = 2, and each plane section perpendicular to the x-axis is an equilateral triangle.
o 1.131 o 7.838 o 0.980 o 5.226

Answer:

B (2.72, 1)

Step-by-step explanation:

The equation is y = 2.72x is in slope intercept form y = mx + b

since there is no b (y-intercept), b = 0

So you could rewrite the equation y = 2.72x + 0

You're first point is b which is 0 on the y axis.

From the 0 you are going to do the slope, which is m.

The slope is 2.72. Since it is positive you will go up 2.72 and right 1.

Angles 6 and 8 are adjacent, they are Linear pair οf angles.

Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.

Angles 1 and 4 are not adjacent, they are vertically opposite.

Angles 5 and 8 are not adjacent, they are vertically opposite.

Angles 6 and 8 are adjacent, they are Linear pair οf angles

Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.

Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles

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In the original equation, x is a variable, hence f(x). If that term in the parenthesis changes, such as to 0 or -2, we will plug in that number in place of the current variable.

f(0) = 4(0)^2 + 3 = 0 + 3 = 3

f(-2) = 4(-2)^2 + 3 = 4(4) + 3 = 16 + 3 = 19

Hope this helps! :)

Step-by-step explanation:

When you multiply or divide both sides of an inequality by a negative, you swap the inequality. You had less than or equal? Now it'll be greater than or equal.

Answer:

flip the sign

Step-by-step explanation:

You just flip the sign...

for example: \(-x < 2\implies x > -2\)

But why is this happening? So let's just analyze the initial inequality we started with: \(-x < 2\)

As you can see here, the x values are negated, or in other words they become negative. So even though -5 is less than 2, it becomes -(-5) which cancels the negative and it becomes 5, this of course makes the inequality false.

The opposite occurs with positive values, the positive value becomes negative, thus any positive value will satisfy this inequality, since it becomes a negative number.

For example 10 is not less than 2, but the negative sign will make it -10, thus making the inequality true.

Even though negative values will cancel out, there are still some negative values that satisfy this equation. Since -1 becomes 1, it satisfies this equation, but once it becomes less than or equal to -2, it becomes false. This is because it becomes a positive value. Thus the equation really just means x must be greater than -2.

I could've used something more abstract, but I wanted to give a specific example so it might be a bit easier to understand.

Answer:

I think answer C

Step-by-step explanation:

You can display how many toothbrushes were distributed each month on the dot plot :)

Have an amazing day!!

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Answer:

= 4.116 × 10^9

Step-by-step explanation:

Hope this helps! Mark me BRAINLIEST, if possible.

The lengths that could be the length of the third side are any values less than 12 feet, the value of 12 feet itself, and any values greater than 2 feet.

To determine which lengths could be the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that the lengths of the two sides are 5 feet and 7 feet, we can evaluate the following possibilities for the length of the third side:

The third side is less than the sum of the two given sides: If the third side is less than 5 + 7 = 12 feet, it can be a valid length.

The third side is equal to the sum of the two given sides: If the third side is equal to 5 + 7 = 12 feet, it can be a valid length, forming a degenerate triangle.

The third side is greater than the difference between the lengths of the two given sides: If the third side is greater than |5 - 7| = 2 feet, it can be a valid length.

Based on these conditions, the possible lengths for the third side are:

Less than 12 feet

Equal to 12 feet

Greater than 2 feet

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Answer:

8x + x^2

Step-by-step explanation:

See attached image

Cot θ is equal to 1/2.

To find cot θ, we need to use the given information:

csc θ = √(5/2)

tan θ = 0

We can use the reciprocal identities and the Pythagorean identity to find cot θ.

Reciprocal Identity:

csc θ = 1/sin θ

Pythagorean Identity:

\(sin^2\) θ + \(cos^2\)θ = 1

Given that csc θ = √(5/2), we can find sin θ:

1/sin θ = √(5/2)

sin θ = 2/√5

Using the Pythagorean identity, we can find cos θ:

\(sin^2\) θ + \(cos^2\) θ = 1

\((2/√5)^2\)+ \(cos^2\) θ = 1

4/5 + \(cos^2\) θ = 1

\(cos^2\) θ = 1 - 4/5

\(cos^2\)θ = 1/5

cos θ = ±√(1/5)

Now, we can find cot θ:

cot θ = cos θ / sin θ

Since tan θ = 0, it means that sin θ is not equal to 0, as tan θ = sin θ / cos θ. Therefore, we can use the positive value of cos θ.

cot θ = (√(1/5)) / (2/√5)

cot θ = (√5/√5) / (2/√5)

cot θ = 1/2

Therefore, cot θ is equal to 1/2.

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Answer:

because red is colour which attracts more

Answer:

1/15

Step-by-step explanation:

Total number of marbles: 3 + 4 + 1 + 2 = 10

First pick:

p(red) = 3/10

Now there are a total of 9 marbles.

Second pick:

p(blue) = 2/9

Overall probability:

p(red then blue) = 3/10 * 2/9 = 6/90 = 1/15

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

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To evaluate dy for the given values of x and dx, we can use the formula:

dy = (∂y/∂x)dx

Where (∂y/∂x) represents the partial derivative of y with respect to x.

First, let's find the partial derivative of y with respect to x: ∂y/∂x =\(√3(2x)/2 = √3x\)

Now we can plug in the given values of x and dx into the formula to find dy: dy = \((√3x)(-0.1) = -0.1√3\)

Therefore, when x = 1 and dx = -0.1, the value of dy is \(-0.1√3.\)

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Answer:

ok so lets right this is slope intercept form

y=mx+b

ok so first we have to find how much it goes up by ok so loking at it it goes up one for every one over so just 1 so

y=(1)x+b

then we have to see where it is on the graph at zero x 23 can see it 3

y=x+3

Hope This Helps!!!

If the city worker released the statement that 60% of dairy city's 3,000 homes are in violation of city codes , then the City Worker's statement is an example of : (d) Statistical Inference .

The Statistical Inference involves making generalizations about a population based on a sample.

In this case, the city worker has taken a sample of 200 homes out of the total 3,000 homes in Dairy City, and based on that sample, the City Worker is making an inference about the proportion of homes in violation of city codes for the entire population of Dairy City.

The statement is not a census as a census would involve collecting data from every single unit in the population, in this case every single home in Dairy City.

The given question is incomplete , the complete question is

A city worker inspected 200 homes in dairy city. during that inspection, 120 homes were found to violate one or more city codes. the city worker released a statement that 60% of dairy city's 3,000 homes are in violation of city codes.

The City Worker's statement is an example of :

(a) Census

(b) An experiment

(c) Descriptive Statistics

(d) Statistical Inference

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The Kermack and McKendrick model of an epidemic proposes that the population can be divided into three classes: healthy, sick, and dead. The total population remains constant in size, except for deaths due to the epidemic. The model is kxy, where k and l are positive constants. The equations are based on the assumptions that healthy people get sick at a rate proportional to the product of x and y, and sick people die at a constant rate l.

The given model consists of three variables: x(t), y(t), and z(t), representing the number of healthy, sick, and dead people, respectively, in a population. The model has two assumptions:

1. Healthy people get sick at a rate proportional to the product of x and y (kxy).
2. Sick people die at a constant rate l.

We are given the following system of equations:

dx/dt = -kxy
dy/dt = kxy - ly
dz/dt = ly

Now, our goal is to reduce this third-order system to a first-order system that can be analyzed by our methods.

First, we notice that the total population N is constant except for deaths due to the epidemic, so we have:

N = x(t) + y(t) + z(t)

Since the total population remains constant (ignoring deaths due to the epidemic), we have:

dN/dt = dx/dt + dy/dt + dz/dt = 0

Substituting the given equations into the equation above, we get:

(-kxy) + (kxy - ly) + ly = 0

Notice that the terms involving kxy and ly cancel each other out. As a result, the system of equations is already reduced to a first-order system:

dx/dt = -kxy
dy/dt = kxy - ly

Now you can analyze this first-order system using the appropriate methods for first-order differential equations.

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Answer: 2

Step-by-step explanation:

To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.

Adding 5 to both sides of the inequality, we get:

x ≥ 2

This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.

The resulting graph looks like this:

     ------•-------------------------------->

           2

The shaded region on the right of 2 represents all the values of x that make the inequality true.

Answer:

110

Step-by-step explanation:

Substitute x = 4 and y = 7

20 + 2 (3y - 4x)

= 20 + 2 [(3 x 7) - (4 x 4)]

= 20 + 2 (21 - 16)

= 20 + 2 (5)

= 22 (5)

= 110

Answer:

30 (always use .P.E.M.D.A.S.)

Step-by-step explanation:

20+2(3y-4x)

20+2(21-16)

20+2(5)

20+10

30

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

It would be $20 per each hour

Step-by-step explanation:

Divide  480  by  24 .

Answer:

$20/ hour

Step-by-step explanation:

Divide $480/ 25

The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.

Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute

1. Convert the speed from kilometers to meters per hour

36 km/hr = 36 x 1000 m/hr

2. Calculate the circumference of the wheel

Circumference of wheel = Diameter x π

Circumference of wheel = 50 cm x 3.14 = 157 cm

3. Calculate the number of revolutions per minute

Number of revolutions per minute = (Speed in m/hr) / (Circumference of wheel in cm)

Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute

The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.

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A;

5 + 2.5xx = AA

B;

20 + 0.5xx = BB

A: 5 + 2.5 • 11

B: 20 + 0.5 • 11

A = 32.5

B = 25.5

Answer:

B

Step-by-step explanation:

I THINK B

Answer:

The answer is (8x20)-(8x1)

Answer:

-21

Step-by-step explanation:

put in -3 where x is

-3^2  9

-9-12 = -21

Answer:

-21

Step-by-step explanation:

We know that  \(f(x)=-x^2-12\)  and we also know that \(f(x)=f(-3)\). Therefore, you will have to substitute x with -3.

Calculations:

\(f(x)=-x^2-12\)  

\(f(-3)=-(-3)^2-12\)

\(-9-12=-21\)

Statment b. If you buy groceries for $50, then you PIBP for them is equal to $50 is always true.

PIBP stands for "price paid in buyer's perspective," which means the amount that the buyer pays to purchase a product or service. In this case, if you buy groceries for $50, then your PIBP for them is indeed $50 since that is the price you paid as the buyer.

Option a is incorrect because PISP stands for "price in seller's perspective," which means the value the seller receives in exchange for a deal they own. Option c is incorrect because PIBP stands for "price paid in buyer's perspective," not "value in use." Option d is incorrect because PIBP and PISP can change around a cycle of ownership depending on the negotiation and agreement between the buyer and seller.

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n = 37, and tenth term = 18

Given progression,

36, 34, 32, ...

The sum of the first n terms is 0

First term(a1) = 36

The common difference (d)= 34-36 = -2,

The formula of the sum of the first n term is,

\(Sn = \frac{n}{2} [2a_{1} + (n - 1)d]\)

substitue the values Sn= 0, a1= 36, d= -2 in the above equation to find n

\(0\)= \(\frac{n}{2} [2(36) + (n-1) (-2)]\)

\(0 = \frac{n}{2}[72- 2n+ 2]\)

\(0 = \frac{n}{2}[74 - 2n]\)

\(74 - 2n = 0\)

\(2n = 74\)

\(n = \frac{74}{2}\)

\(n = 37\)

n = 37

The formula for finding the nth term(10th term):

\(a_{n} = a1 + (n - 1)d\)

n = 10, a1 = 36, d = -2

\(a_{10} = 36 + (10-1)(-2)\)

\(a_{10} = 36 + 9(-2)\)

\(a_{10} = 36 - 18\)

\(a_{10} = 18\)

\(a_{10}\) = 18

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the correct option is b

The estimate value of the standard deviation of the population ( manufacturing process) is 0.125..

The standard deviations is estimated to be one fourth of the sample range (as most of data values are within two standard deviations of the mean).

We have given that,

A sample of manufacturing process.

Sample size, n = 5

Mean of sample ranges = 0.50

we have to calculate the estimate of standard deviations of population.

thus , we estimate the standard deviations as fourth of the mean of the sample ranges is

S = Mean of sample ranges/4

=> S = 0.50/4

=> S = 0.125

Hence, the standard deviation of the population is estimated as 0.125..

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We get the value of angle Q in the triangle PQR as 155 °.

We are given a triangle PQR.

We are also given that:

∠ P = 110 °

∠ R = 15 °

Now, we need to find ∠ Q.

We know that sum of the angles of a triangle = 180 °

This is called the angle sum property of a triangle.

So, we get that:

∠ P + ∠ Q + ∠ R = 180 °

Substituting the given values, we get that:

110 ° + ∠ Q + 15 ° = 180 °

125 ° + ∠ Q = 180 °

∠ Q = 180 ° - 125 °

∠ Q = 155 °

Therefore, we get the value of angle Q in the triangle PQR as 155 °.

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Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time

A measurement of statistical dispersion, or the spread of the data, is the interquartile range (IQR). It is described as the variation between the data's 75th and 25th percentiles. The fourth spread, middle 50%, midspread, or H-spread1 are further names for the IQR.

The dataset is displayed using a box plot, which is a standardized method based on the five-number summary of the minimum, maximum, sample median, and first and third quartiles

The box plot displays measurements made from data acquired from interviews with 20 people on how long they waited at a drive-through restaurant window.

Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time.

A data set is divided into quartiles to calculate the IQR (Interquartile Range), which is a measure of variability. The first quartile (Q1) is subtracted from the third quartile (Q3) to determine it.

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Given :

The price of a sandwich is $5.50 more than the price of a smoothie, which is d dollars

so, the expression :

d + 5.5 represents : The price of of a sandwich