Which conic section is formed when a plane intersects the central axis of a double-napped cone at a 90° angle?



circle


ellipse


hyperbola


parabola



Answer: A

Answer:

im sorry this makes absolutely no sense

Step-by-step explanation:

There are 15 different possible outcomes when Hudson spins both spinners in his board game.

To determine the total number of possible outcomes when Hudson spins both spinners, you need to multiply the number of outcomes on the first spinner (Walk, Run, Stop) by the number of outcomes on the second spinner (Monday, Tuesday, Wednesday, Thursday, Friday).

Step 1: Determine the number of outcomes on the first spinner. There are 3 outcomes: Walk, Run, and Stop.

Step 2: Determine the number of outcomes on the second spinner. There are 5 outcomes: Monday, Tuesday, Wednesday, Thursday, and Friday.

Step 3: Multiply the number of outcomes from both spinners. 3 outcomes on the first spinner multiplied by 5 outcomes on the second spinner equals 15 total possible outcomes.

So, there are 15 different possible outcomes when Hudson spins both spinners in his board game.

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An angle of 0 radians is an angle along the positive x-axis of the unit circle. Its terminal point is (1, 0).

The tangent of 0 radians is defined as the ratio of the y-coordinate to the x-coordinate of the terminal point, which is 0/1 = 0.

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To emphasize the difference between the cost per doctor visit for each of the three plans, you can change the scale on the y-axis to either 0–100 or 25–40 and adjust the interval of the y-axis to count by 5s.

To emphasize the difference, you can consider the following adjustments to the graph:

1. Change the scale on the y-axis to 0–100. This adjustment will give a wider range for the costs, making it easier to see the differences between the three plans.

2. Alternatively, change the scale on the y-axis to 25–40. This change will focus more on the specific cost range that the three plans fall into, magnifying the differences between them.

3. Change the interval of the y-axis to count by 5s. This alteration will increase the number of increments on the y-axis, giving a more detailed view of the cost differences between the plans.

4. On the other hand, changing the interval of the y-axis to count by 20s might not be the best option. It will decrease the increments on y-axis and make it harder to visualize the cost differences between the plans.

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To find the surface area C of the birdhouse, we need to find the area of each face and add them together.

First, let's find the area of the square base:

Area of base = side^2 = 16^2 = 256 in^2

Next, let's find the area of each triangular face:

Area of each triangular face = 1/2 * base * height

Since the base is 16 in and the slant height is 10 in, the height can be found using the Pythagorean theorem:

height^2 = slant height^2 - base^2/4

height^2 = 10^2 - 16^2/4

height^2 = 100 - 64

height^2 = 36

height = 6

So the area of each triangular face is:

1/2 * 16 * 6 = 48 in^2

There are four triangular faces, so the total area of the triangular faces is:

4 * 48 = 192 in^2

Finally, we add the area of the base and the area of the triangular faces to find the total surface area:

256 + 192 = 448 in^2

Therefore, the surface area of the birdhouse is 448 square inches, which is closest to option A: 262 in^2.

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The answer is: ∠N ≈ 33°

To find ∠N in ΔLMN, we can use the Law of Cosines which states that c² = a² + b² - 2abcos(C), where c is the side opposite angle C.

In this case, side LM (m) is opposite angle ∠N, side LN (n) is opposite angle ∠L, and side MN (x) is opposite the unknown angle.

So, we can write:
m² = n² + x² - 2nxcos(82°)

Substituting the given values:
x² = 35² + 59² - 2(35)(59)cos(82°)

Solving for x, we get:
x ≈ 64.27

Now, using the Law of Sines which states that a/sin(A) = b/sin(B) = c/sin(C), we can find ∠N:

sin(∠N)/35 = sin(82°)/64.27

sin(∠N) ≈ 0.5392

∠N ≈ sin⁻¹(0.857) ≈ 32.6344°

Therefore, ∠N ≈ 33° to the nearest degree.

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Based on the information provided, James would have 20 different waffle options.

Since each waffle cone can hold two scoops of ice cream and James must choose a different flavor for each scoop, we can approach this problem by using the multiplication principle of counting.

There are 5 different ice cream flavors to choose from for the first scoop, and 4 different flavors remaining for the second scoop. This is because James must choose a different flavor for each scoop.

Therefore, the number of different waffle cone options that James has is:

5 x 4 = 20

So, James has 20 different waffle cone options if he chooses a different flavor of ice cream for each scoop.

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We denote triangle ABC, angle A measures 90°, angle B measures 30° and angle C measures 60°.

We apply the cosine of 30 degrees, becuase m(∡A) = 90° and find the hypotenuse of triangle ABC:

cos = (adjacent side) / (hypotenuse)

⇔ cos B = AB/BC ⇔

⇔ cos 30° = 8√3/v ⇔

⇔ √3/2 = 8√3/v ⇔

⇔ √3 • v = 2 • 8√3 ⇔

⇔ v√3 = 16√3 ⇔

⇔ v = 16√3 ÷ √3 ⇔

⇔ v = 16 millimeters

Hope that helps! Good luck! :)

Answer:

Step-by-step explanation:

9 groups with 5 in each equals to

45

Answer: 9 x 5 = 45

Step-by-step explanation:

9

18

27

36

45

54

63

72

81

90

99

108

The first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]

To find the first derivative of g(a), we need to use the power rule and the constant multiple rule.

First, we use the power rule to take the derivative of each term:

[tex]- The derivative of 6x^3 is 18x^2

- The derivative of -9x^2 is -18x

- The derivative of -36x is -36[/tex]

Next, we use the constant multiple rule to combine these derivatives:

g'(a) = 18x^2 - 18x - 36

Therefore, the first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]

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Answer:

274.78

Step-by-step explanation:

Let's call the original price "x".

We know that the price decreased by 31%, so the new price is

100% - 31% = 69% of the original price:

0.69x = 189.6

To solve for x, we can divide both sides by 0.69:

x = 189.6 / 0.69

Simplifying this expression, we get:

x ≈ 274.78

Therefore, the original price was approximately $274.78.

The plane's new velocity is 421.4 mph with a direction of 63.43 degrees relative to the air.

To solve this problem, we need to use vector addition. Let's first draw a diagram to represent the situation.

First, we need to break down the velocity of the plane and the velocity of the wind into their horizontal and vertical components.

The velocity of the plane can be broken down into a horizontal component of 500*cos(135) mph and a vertical component of 500*sin(135) mph.

The velocity of the wind can be broken down into a horizontal component of 60*cos(60) mph and a vertical component of 60*sin(60) mph.

Now, we can add these components together to get the resultant velocity.

The horizontal component of the resultant velocity is 500*cos(135) + 60*cos(60) = -189.28 mph. The negative sign indicates that the velocity is in the opposite direction of the plane's original direction.

The vertical component of the resultant velocity is 500*sin(135) + 60*sin(60) = 374.28 mph.

Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:

|v| = sqrt((-189.28)^2 + (374.28)^2) = 421.4 mph.

Finally, we can find the direction of the resultant velocity using the inverse tangent function:

θ = tan^-1(374.28/-189.28) = -63.43 degrees.

So the plane's new velocity is 421.4 mph with a direction of 63.43 degrees relative to the air.

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Answer:

f(2) = 2

Step-by-step explanation:

We are given
f(x) = x² - 7x + 4

To find f(2), just plug in 2 wherever you see an x and simplify

f(2) = 3 · 2² - 7 · 2 + 4

= 3 · 4 - 7 · 2 + 4

= 12 - 14 + 4

= 2

The probability of choosing a student whose name begins with "K" is 40%.

To find the probability of choosing a student whose name begins with "K," P(K name), we need to calculate the ratio of students with "K" names to the total number of students in the prom committee.
There are 10 students in the prom committee: 7 girls (Kelly, Karri, Michela, Raquel, Rara, Nadya, Neesa) and 3 boys (Rio, Elke, Kevin). Out of these, 4 students have names that start with "K": Kelly, Karri, Kevin, and Elke (note that Elke has been mistakenly included in the boys' list, but we'll consider it as a "K" name).

To find the probability, we'll use the formula:
P(K name) = (number of students with "K" names) / (total number of students)
P(K name) = 4 / 10 = 0.4 or 40%
So, the probability of choosing a student whose name begins with "K" is 40%.

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The probability is that out of 12 customers, 7 will order a non-alcoholic beverage, and the remaining 5 will order an alcoholic beverage.

The likelihood that a client will arrange a non-alcoholic refreshment is given as 48%, which implies that the likelihood that a client will arrange an alcoholic refreshment is (100 - 48) = 52%.

Out of 12 customers, 5 will arrange liquor, which suggests that the remaining clients will arrange a non-alcoholic refreshment. We are able to calculate the number of clients who will arrange a non-alcoholic refreshment as takes after:

Number of clients who will arrange a non-alcoholic refreshment =

Add up to a number of clients - Number of clients who will arrange liquor

= 12 - 5

= 7

Subsequently, out of 12 clients, 7 will arrange a non-alcoholic refreshment, and the remaining 5 will arrange an alcoholic refreshment.

It is critical to note that these calculations are based on the presumption that each client will as it were arrange one refreshment. 

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The rounding method used, the estimated speed of the space shuttle after it has slowed down is 10,200 miles per hour.

To estimate the speed of the space shuttle after it has slowed down, we round each number to the nearest hundred. The speed before the decrease is rounded to 17,600 miles per hour, and the decrease in speed is rounded to 7,400 miles per hour.

Next, we subtract the rounded decrease in speed from the rounded speed before. So, 17,600 - 7,400 = 10,200 miles per hour. This result represents the estimated speed of the space shuttle after it has slowed down.

Rounding to the nearest hundred is a way to approximate the values and make calculations simpler. However, it is important to note that rounding introduces some degree of error, and the actual speed after the decrease may differ slightly from the estimated value.

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To find the sale price of each item, we need to use some basic algebra. Let's call the sale price of each item "x".

First, we need to find the total cost of the table rental for all six friends. Since each friend needs to pay $7.20, the total cost of the table rental is 6 * $7.20 = $43.20.

Next, we need to find the total revenue from selling the items. Each friend sells 3 items, so the total number of items sold is 6 * 3 = 18. The total revenue is the number of items sold multiplied by the sale price, so the total revenue is 18x.

We know that the total profit is $25.20, which is the total revenue minus the total cost of the table rental. So we can set up the equation:

18x - $43.20 = $25.20

Simplifying this equation, we get:

18x = $68.40

Dividing both sides by 18, we get:

x = $3.80

Therefore, the sale price of each item is $3.80.

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The percent error in measuring if the actual length is 4.1 cm and the measured length is 3.9 cm is 4.88%

The error refers to the estimated difference between the measured and actual measurement of an object. Error is mainly of three types systematic errors, random errors, and negligent errors.

Measured length = 3.9

Actual length = 4.1

Error = actual value - measured value

= 4.1 - 3.9

= 0.2

Error percent is the ratio of error to the actual value multiplied by 100

Error percent = [tex]\frac{0.2}{4.1}[/tex] * 100

= 4.88%

Thus, the error percent in the given question comes out to be 4.88%

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i) The light intensity at a depth of 300 feet is approximately 0.131 lumens.

ii)The light intensity of 5 lumens is reached at a depth of approximately 106.6 feet.

iii)The light intensity at the surface of the water is 12 lumens.

The equation given is:

[tex]d= -425log(\frac{I}{12} )[/tex]

where d is the depth in feet, and l is the light intensity in lumens.

i)To find the intensity of light at a depth of 300 feet:

[tex]d= -425log(\frac{I}{12} )[/tex]

[tex]or, \frac{d}{-425}=log(\frac{I}{12})[/tex]

[tex]or, 10^{\frac{d}{-425}}=\frac{I}{12}[/tex]

[tex]or, 12 X 10^{\frac{d}{-425}}=I[/tex]

Given, d= 300 feet. Hence,

[tex]or, 12 X 10^{\frac{300}{-425}}=I[/tex]

or, I = 0.131 lumens (approx.)

ii) We have been given the equation :

[tex]d= -425log(\frac{I}{12} )[/tex]

when I =5 lumens

[tex]d= -425log(\frac{5}{12} )[/tex]

or, d = 106.6 feet (approx.)

iii) For finding the light intensity at the surface of the water d=0

[tex]d= -425log(\frac{I}{12} )[/tex]

Putting d = 0 we get

[tex]0= -425log(\frac{I}{12} )[/tex]

[tex]or, log(\frac{I}{12})=0[/tex]

[tex]or, \frac{I}{12} = 10^0 = 1[/tex]

or, I = 12 lumens

Therefore the light intensity at the surface of the water is 12 lumens.

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The equation that can be used to determine the number of people (x) who can go to the amusement park is:

207.50 = 5 + (33.75 × x).

To determine the number of people (x) who can go to the amusement park, we need to create an equation using the given information. We know that they have $207.50 to spend, parking costs $5, and each ticket costs $33.75 per person (including tax).

We can represent the total cost of the trip as the sum of the cost for parking and the cost of the tickets for x number of people. The equation would be:

Total Cost = Cost of Parking + (Cost of Tickets per Person × Number of People)

Since we know the total cost is $207.50, the cost of parking is $5, and the cost of tickets per person is $33.75, we can plug in these values:

207.50 = 5 + (33.75 × x)

This equation can be used to determine the value of the variable x, the number of people who can go to the amusement park. To find the value of x, simply solve the equation by isolating the variable x.

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The length of lm is 10 cm.

To find the length of lm, we need to use the fact that om and oj are both diameters of their respective circles. We can start by finding the radius of each circle:

- The radius of om is half of its diameter, so it's 34 cm.
- The radius of oj is half of its diameter, so it's 27 cm.

Next, we can use the fact that jk is perpendicular to lm to create a right triangle:

- One leg of the triangle is jk, which we know is 8 cm.
- The other leg is half of the difference between the radii of the two circles, since lm connects the two circles. That means the other leg is (34 - 27)/2 = 3.5 cm.

Now we can use the Pythagorean theorem to find the length of lm:

lm² = jk² + (radius difference/2)²
lm² = 8² + 3.5²
lm² = 70.25
lm = 10 cm

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The probability of a paper having exactly 4 errors can be calculated using the binomial probability formula, which is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

In binomial probability formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

n is the number of trials (in this case, the number of papers graded)

k is the number of successes (in this case, the number of papers with exactly 4 errors)

p is the probability of success (in this case, the probability that a paper has an error, which can be calculated by dividing the total number of errors by the total number of papers graded)

p = 80/200 = 0.4

P(X = 4) = (200 choose 4) * 0.4^4 * (1-0.4)^(200-4) ≈ 0.153

Therefore, the probability of picking a paper at random and finding exactly 4 errors is approximately 0.153 or 15.3%.

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The probability of the next coat being sold as a medium navy coat is 11 / 95 when a store sells a coat in three sizes: small, medium, and large. The coat comes in red, navy, and tan.

We need to find the probability that the next coat sold as a medium navy coat. To find the probability we need to find the total number of coats and the number of medium navy coats,

Given data:

Medium navy coat = 22

Total Number of small coats = 18 + 24 +19 = 61

Total Number of medium coats = 21 + 22 + 25 = 68

Total Number of large coats = 19 + 20 + 22 = 61

From the given data the total number of coats is = 61 + 68 + 61 = 190

The probability that the next coat sold as a medium navy coat = a number of medium navy coats / total number of coats.

= 22 / 190

= 11 / 95

Therefore, the probability of the next coat being sold as a medium navy coat is  11 / 95

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The triangles created using the law of sines and the law of cosines for Jumal's approach and Jabari's approach  are attached

The Law of Sines states that the ratio of a sine of an angle to the length of the side facing the angle is the same for the three sides of the triangle.

Jumal's approach

a. The measure of the angle B can be found as follows;

sin(40)/10 = sin(B)/15

B = 15 × arcsine(sin(40)/10) ≈ 74.6°

b. The measure of angle C can be found using the angle sum property of a triangle as follows;

∠C = 180 - (40 + 74.6) = 65.4°

c. The length of the side c is therefore;

sin(40)/10 = sin(65.4)/c

c = sin(65.4) × 10/sin(40) ≈ 14.1

The length of the side c is about 14.1 meters

The triangle can be obtained by using the specified and obtained dimensions as shown in the attached drawing

Jabari's Approach

a. The Law of Cosines indicates; a² = b² + c² - 2·b·c·cos(A)

Therefore;

100 = 225 + c² - 2 × 15 × c × cos(40)

10² = 15² + c² - 23·c

c² - 23·c + 125 = 0

c = (23 ± √(29))/2

c = 14.2 and 8.8

c. Please find attached then possible drawings based on the calculated dimensions, created with MS Word

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Answer:

462

Step-by-step explanation:

1. Start by substituting the value of x and and

2. You then multiply the substituted value in each brace and add 1 and subtract 1 from each bracket respectively

3. After getting your final answer in each bracket multiply them

4. You then get your final answer as 462

The solution of the system of equation

x = 8 and y = 17

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation by substitution method.

Therefore,

y = 49 - 4x

y = 73 - 7x

Hence, using substitution,

73 - 7x = 49 - 4x

73 - 49 = -4x + 7x

24 = 3x

divide both sides of the equation by 3

x = 24 / 3

x = 8

Therefore,

y = 73 - 7(8)

y = 73 - 56

y = 17

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The equation of the function h(x) from the transformation is h(x) = f(x + 1)

From the question, we have the following parameters that can be used in our computation:

The functions f(x), g(x) and h(x)

In the graph, we can see that

Horizontal Shift = 1 unit left

This is represented as

h(x) = f(x + 1)

This means that the transformation of f(x) to h(x) is f(x) is shifted left 1 unit to h(x).

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To evaluate the integral ∫(x^3+4x)/x^4+8x^2+1, we can use the substitution u = x^2 + 1. Then, du/dx = 2x, which means that dx = du/(2x). Substituting these into the integral, we get:

∫(x^3+4x)/x^4+8x^2+1 dx = ∫(1/u)(x^2+1)(x^3+4x)/(2x) du
= 1/2 ∫(u-1)/u^2 du
= 1/2 ∫(u/u^2 - 1/u^2) du
= 1/2 ln|u| + 1/2 (1/u) + C
= 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C

Therefore, the final answer is ∫(x^3+4x)/x^4+8x^2+1 dx = 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C.
Hi! To evaluate the integral, we can rewrite the given expression as follows:

∫((x^3 + 4x) / (x^4 + 8x^2 + 1)) dx

Now, let's use substitution to solve this integral. Let's set:

u = x^2 + 4

Then, the derivative du/dx = 2x. So, dx = du / (2x).

Now, we can rewrite the integral in terms of u:

∫((x^3 + 4x) / (u^2 + 1)) (du / (2x))

Notice that x^3/x and 4x/x simplify, and we are left with:

(1/2) ∫(u / (u^2 + 1)) du

Now we can integrate this expression:

(1/2) * [ln(u^2 + 1) + C]

Now, substitute back x^2 + 4 for u:

(1/2) * [ln(x^2 + 4 + 1) + C] = (1/2) * [ln(x^2 + 5) + C]

So, the evaluated integral is:

(1/2) * [ln(x^2 + 5) + C]

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Partial sums are:

a) limx→∞ S = L
b) The limit does not exist.
c) limx→∞ S = L
d) The limit does not exist.

We need to use the formulas for partial sums and limits of sequences.

First, recall that the nth partial sum of a series is given by:

Sn = a1 + a2 + ... + an

And the limit of a sequence (if it exists) is given by:

limn→∞ an

Now, let's use these formulas to answer the parts of the question:

a) Find lim S as n approaches infinity:

We have:

S = ax = a1 + a2 + a3 + ... + ax

Taking the limit as x approaches infinity, we get:

limx→∞ S = limx→∞ (a1 + a2 + a3 + ... + ax) = limn→∞ Sn

But we know that the series is convergent, so the limit of the partial sums exists and is equal to the sum of the series:

limn→∞ Sn = L

Therefore:

limx→∞ S = L

b) Find lim as x approaches 0:

We have:

S = ax = a1 + a2 + a3 + ... + ax

Taking the limit as x approaches 0, we get:

limx→0 S = limx→0 (a1 + a2 + a3 + ... + ax)

But as x approaches 0, the number of terms in the sum approaches infinity, so this limit does not exist.

c) Find lim S as x approaches infinity:

We have:

S = ax = a1 + a2 + a3 + ... + ax

Taking the limit as x approaches infinity, we get:

limx→∞ S = limx→∞ (a1 + a2 + a3 + ... + ax) = limn→∞ Sn

Again, we know that the limit of the partial sums exists and is equal to the sum of the series:

limn→∞ Sn = L

Therefore:

limx→∞ S = L

d) Find lim as x approaches 100:

We have:

S = ax = a1 + a2 + a3 + ... + ax

Taking the limit as x approaches 100, we get:

limx→100 S = limx→100 (a1 + a2 + a3 + ... + ax)

But as x approaches 100, the number of terms in the sum approaches infinity, so this limit does not exist.

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