To the nearest square inch, what is the surface area of the cone?
The image consists of an inverted three-dimensional cone. The diameter of its circular base is 3 inches. The diagonal length from the base to the tip is 4 inches.

Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

[tex]A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2[/tex]

Area 2:

[tex]A\frac{}{2} = ∫(g(x) - f(x))dx[/tex]

[tex]= ∫(x - {(x - 2)}^{2} )dx[/tex]

[tex] = ∫( - {x}^{2} + 5x - 4)dx[/tex]

[tex]= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}[/tex]

[tex] = 2.67 - ( - 0.67) = 3.34[/tex]

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34

Answer:

third and last one

Step-by-step explanation:

im pretty sure those are the answers i used a graphing calculator.

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Answer:

  C and E

Step-by-step explanation:

The rules of exponents apply:

  (a^b)(a^c) = a^(b+c)

__

  [tex]200(10^x)=20\cdot10^1\cdot10^x=\boxed{20(10^{x+1})}\\\\=2\cdot10^2\cdot10^x=\boxed{2(10^{x+2})}[/tex]

These match the 3rd (C) and last (E) choices.

Answer: $3648

Step-by-step explanation:

Firstly, we have to calculate the interest which will be:

= Principal × Rate × Time

= $1600 × 8% × 16

= $1600 × 0.08 × 16

= $2048

Therefore, the amount in the account after 16 years will be:

= Principal + Interest.

= $1600 + $2048

= $3648

Answer:

1

Step-by-step explanation:

When you multiply two quantities under a root, it is just like normal multiplication. 2*18 is 36, which is the perfect square of six. Since this number can be expressed as p/q (where p and q are integers; the values here are 6 and 1), it is rational.

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Answer:

  20

Step-by-step explanation:

As with any evaluation problem, take it step by step according to the order of operations.

The first thing you need to do here is compute a#b.

The given definition can be simplified a bit for evaluation purposes:

  a#b = a²b -ab² = ab(a -b)

Then for a=3 and b=-2, you have ...

  (3)#(-2) = (3)(-2)(3 -(-2)) = -6(5) = -30

Now, you are in a position to evaluate the expression you're asked for.

  [tex]\dfrac{(a\#b)^2}{15-(a\#b)}=\dfrac{(-30)^2}{15-(-30)}=\dfrac{900}{45}=\boxed{20}[/tex]

Answer:

If both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.

Step-by-step explanation:

Since Susan drives north on the 405 Freeway at 50 miles per hour, and two hours after Susan passes under Westminster Blvd, Maria enters the 405 Freeway at Westminster Blvd and heads north at 60 miles per hour, if both cars maintain their average speeds, to determine how long will it take Mary to catch up with Susan the following calculation must be performed:

Hour 1 = 50

Hour 2 = 100

Hour 3 = 150 - 60

Hour 4 = 200 - 120

Hour 5 = 250 - 180

Hour 6 = 300 - 240

Hour 7 = 350 - 300

Hour 8 = 400 - 360

Hour 9 = 450 - 420

Hour 10 = 500 - 480

Hour 11 = 550 - 540

Hour 12 = 600 - 600

Therefore, if both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.

Answer:

f(x) = 3 cos  (2Pi / period value ; x  )+ 2

or see answer using 2 as the period see answer in bold below.

Step-by-step explanation:

cosine function amplitude of 3 is  A = 3

The period is used to find B

You need to show period value as the denominator and work out from there with 2PI as a function numerator to show as 2pi / period can be a data angle

C is the adding value.

Acos (Bx) + C

A = 3

Bx =  2 pi / period

C = + 2

However f 2 is also the period found

then we just plug in 2 to above formula

f(x) = 3 cos  (2Pi / 2 ; x  )+ 2

f(x) = 3cos (x pi) + 2

Answer:

0.1

Step-by-step explanation:

For a density curve, total area = 1

Probability lies in between 0 and 1

The Area of rectangle :

Area = Length * width

Length = 0 - 10 = 10

Area = 1

Hence,

Area = Length * width

1 = 10 * w

1 = 10w

w = 1 /10

w = 0.1

Answer:

0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large consignment of televisions contained 11% defectives.

This means that [tex]p = 0.11[/tex]

Sample of size 237

This means that [tex]n = 237[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.11[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.11*0.89}{237}} = 0.0203[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

P-value of Z when X = 0.11 + 0.03 = 0.14 subtracted by the p-value of Z when X = 0.11 - 0.03 = 0.08. So

X = 0.14

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.14 - 0.11}{0.0203}[/tex]

[tex]Z = 1.48[/tex]

[tex]Z = 1.48[/tex] has a p-value of 0.9306

X = 0.08

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.08 - 0.11}{0.0203}[/tex]

[tex]Z = -1.48[/tex]

[tex]Z = -1.48[/tex] has a p-value of 0.0694

0.9306 - 0.0694 = 0.8612

0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%

Answer:

126 cubic cm

Step-by-step explanation:

6 x 7 x 2 = 84

2 x 3 x 7 = 42

84 + 42 = 126

(i separated the shape to two rectangular prisms)

Answer:

Step-by-step explanation:

X * 3^2 +2 = 47

X * 9 + 2 = 47

9X = 47 - 2

9x = 45

x = 45 : 9

X = 5

Answer:

6

Step-by-step explanation:

.....................

Answer:

6

Step-by-step explanation:

pecentage calculator.what is 75 percent of 8?=6

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Answer:

  A. (1, - 3/2)

Step-by-step explanation:

The coordinate of the midpoint is the average of the endpoint coordinates.

  M = (A +B)/2

  M = ((1, 2) +(1, -5))/2 = (1+1, 2-5)/2 = (2, -3)/2

  M = (1, -3/2) . . . . . matches choice A

Answer:

A. (1, - 3/2)

Step-by-step explanation:

Answer:

..........

Step-by-step explanation:

[tex]\pi[/tex]

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Answer:

  a) r + (r+3) = 68/4 . . . . equation to answer the question

  b) r = 7, r+3 = 10 . . . miles per hour

Step-by-step explanation:

a. The combined speed of the two cyclists is found from the time it takes for them to close the distance between them. The faster cyclist is traveling at (r+3) miles per hour.

  speed = distance/time

  r + (r+3) = 68/4 . . . . an equation to answer the problem

__

b. Solving the above equation helps us answer the question

  2r +3 = 17 . . . simplify

  2r = 14 . . . . . subtract 3

  r = 7 . . . . . . divide by 2

  r+3 = 10

The speeds of the two cyclists are 7 miles per hour and 10 miles per hour.

Answer:

111degrees

Step-by-step explanation:

ArcAC + arcBC = 180

Given theat arcBC = 69degrees

arcAC + 69 = 180

arcAC = 180 - 69

arcAC = 111

Hence the length of minpr arc AC is 111degrees

Answer:

Step-by-step explanation:

Im not sure but i think

452.16/3.14.= 3.14r^2/3.14

144(square root sign) = squarw root sign r^2)

12=r

Answer:

x = 79

Step-by-step explanation:

All triangles have a sum of 180°. Knowing this, we can solve for the unknown angle.

56 + 23 + ? = 180

79 + ? = 180

? = 101

The variable x is known as an exterior angle. That and the angle we just solved for are supplementary meaning they add up to 180°.

101 + x = 180

x = 79

Answer:

79 degrees

Step-by-step explanation:

56 + 23 = 79

I'm assuming all the numbers here mistakenly got copied twice.

Let A(t) denote the amount (in kg) of salt in the tank at time t. The solution starts with 70 kg of salt, so (a) A(0) = 70.

I also assume there is more to the question, so I'll just go ahead and build the differential equation to model this situation, and solve it.

Pure water is flowing into the tank, so no salt is being introduced. The concentration of salt at time t is A(t)/2000 kg/L, and solution is drained from the tank at a rate of 4 L/min, which means salt is being removed at a rate of

(4 L/min) (A(t)/2000 kg/L) = A(t)/500 kg/min = 0.002 A(t) kg/min

Thus the amount of salt (ignoring units now) in the tank changes according to the DE,

dA(t)/dt = -0.002 A(t)

which is easy to solve because it's linear with constant coefficients.

Without going into too much detail:

dA(t)/dt + 0.002 A(t) = 0

exp(0.002t ) dA(t)/dt + 0.002 exp(0.002t ) A(t) = 0

d/dt [exp(0.002t ) A(t)] = 0

exp(0.002t ) A(t) = C

A(t) = C exp(-0.002t )

Given A(0) = 70, solve for C :

70 = C exp(0) = C

Hence

A(t) = 70 exp(-0.002t )

SOLUTION

• -4 = 5(p -2)

 -4 = (5)(p) + (5)(-2)   • Distribute

 -4 = 5p + (-10)

 -4 = 5p - 10

• 5p - 10 = -4

• 5p - 10 + 10 = -4 + 10

  5p = 6

• [tex]\frac{5p}{5} = \frac{6}{5}[/tex]

  p = [tex]\frac{6}{5}[/tex]

Answer: [tex]y=-\frac{1}{3}x[/tex]

Step-by-step explanation:

From the origin we can see to get to the point plotted we have to go down 1 and right three giving us the slope [tex]\frac{-1}{3}[/tex]

These are in the form of y=mx+b

b is the y-intercept and m is the slope

since the y-intercept is 0 b is 0 and isn't need leaving us with y=mx

We can put our slope into the equation giving us the answer in C

The required equation of the line is that passing through the point (3, -1) is y = -x/3.

Given that,
To determine the equation of the line that passes through the origin and a point (3, -1).

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Since the line passes from the origin and a point (3, -1)
So, the slope of the line is given by,
m = (y₂ - y₁) /  (x₂ - x₁)

Substitute the respective values in the above equation,
m = -1 + 0 / 3 - 0
m = -1/3,
Now the point-slope form of the equation of a line is,

y - y₁ = m (x - x₁)
Substitute the respective values in the above equation,
y + 1 = -1/3 (x - 3)
y = -x/3

Thus, the required equation of the line is that passing through the point (3, -1) is y = -x/3.

Learn more about slopes here:

https://brainly.com/question/3605446

#SPJ2

Answers:

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

Explanation:

Any conditional statement is of the form "If P, then Q"

P is the hypothesis, which is the initial set up to lead to the conclusion Q

As an example, the sentence "If it rains, then it gets wet on the road" has P = "it rains" as the hypothesis and Q = "it gets wet on the road" as the conclusion.

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

In short, the format is "If hypothesis, then conclusion".

Answer:

36123.5994797

Answer and explanation:

Multicollinearity happens when multiple independent variables are correlated and therefore it is hard to determine which independent variable has the most impact or is most significantly affecting the dependent variable. This could be a source of confusion as the coefficients become less reliable.

Extreme multicollinearity occurs when there is exaggerated standard errors or increased variance of coefficient estimates.

Answer:

4.7 to nearest tenth.

Step-by-step explanation:

By Pythagoras:

8^2 = x^2 + 6.5^2

x^2 = 8^2 - 6.5^2

x^2 = 64 - 42.25 = 21.75

x = √21.75

= 4.6637

Answer:

5 divided by 1/5

5 x 5/1 = 25, he has 25 servings.