Julia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M.

Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees.

Which best describes the accuracy of Julia’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º.
Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Answer:

12<n​

Step-by-step explanation:

11+n+9+3n<9n-3n-4​

Combine like terms

20+4n<6n-4​

Subtract 4n from each side

20+4n-4n<6n-4n-4

20 < 2n-4

Add 4to each side

20+4 < 2n-4+4

24 < 2n

Divide by 2

12<n​

The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Answer:

60x36x120

Step-by-step explanation:

Because the scale factor is 1:12, you multiply the dimension of the building by 12.

The conversion of 27cm to inch is 10.63 inches.

A centimeter is a metric unit of measurement equal to one-hundredth of a meter. It is commonly used in many countries for measuring small distances, such as the length of an object or the height of a person. One centimeter is equal to 0.3937 inches.

To convert 27 centimeters to inches, we can use the following formula:

1 inch = 2.54 centimeters

Therefore, to convert 27 centimeters to inches, we can divide 27 by 2.54:

27 cm ÷ 2.54 = 10.63 inches (rounded to two decimal places)

So, 27 centimeters is approximately equal to 10.63 inches.

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Answer:8x3=24

Step-by-step explanation:

8 across the x axis and

3 across the y axis

8x3=24

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

Take the cube root of both sides. That way, you'll get rid of the ³ next to x and leave x by itself

\(\large\boldsymbol{\rm{x=\sqrt[3]{13} }}\)

done !!

⊰________________________________________________________⊱

The fraction of the occupied apartments is 9/10.

In mathematics, a fraction is a symbol for a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

Given that,

Total apartments in the building = 200.

Also,

The number of apartments leased by realtor = 180

The fraction of the apartments which is occupied by realtor

= number of apartments leased /Total apartments

= 180 / 200

= 18 / 20

= 9 / 10

The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.

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Answer:

Step-by-step explanation:

5+3x/4 = 7/12

[(5*4)+3x]/4 = 7/12

(20+3x)/4 = 7/12

20+3x = 7/12*4

20+3x = 7/3

3x = 7/3 - 20

3x = [7-(20*3)]/3

3x = (7-60)/3

3x = -53/3

x = -53/3/3/1 ( reciprocal )

x = -53/3*1/3

x= -53/9

The 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481

How to calculate confidence interval?

First, calculate sample proportion by divide number people who favored candidate by number of sample. So:
\(\pi\) = 450 / 1,000 = 0.45

Then we use the formula for confidence interval

\(\pi\) ± \(z\sqrt{\frac{\pi (1-\pi )}{n}}\)

In which z is z score that has a p value of \(1 - \frac{\alpha }{2}\)

For 95% confidence interval z is the value of Z that has a p value of \(1 - \frac{0.05}{2}\) = 0.975, so z = 1.96

After we have \(\pi\) value and z value then put it in the formula. So:

= 0.45 ± \(1.96\sqrt{\frac{0.45(1-0.45)}{1000} }\)

= 0.45 ± 0.0308

= 0.419, 0.481

Thus, the 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481

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a) To find the moment generating function (MGF) for x, we use the formula:

M(t) = E(e^(tx))

where E denotes expected value. Since x has a probability density function (PDF), we integrate the expression e^(tx) times the PDF over all possible values of x to find the expected value:

M(t) = ∫ e^(tx) f(x) dx

where f(x) is the given PDF for x. Substituting the given PDF, we get:

M(t) = ∫ e^(tx) (2/3) x^2 dx    (from x = 0 to x = 1)

Evaluating the integral, we get:

M(t) = (2/3) ∫ e^(tx) x^2 dx

We can use integration by parts twice to evaluate this integral, or we can look it up in a table of integrals to find:

M(t) = (2/3) (2/(t^3)) (e^t - 1 - t)

Therefore, the moment generating function for x is:

M(t) = (4/(3t^3)) (e^t - 1 - t)

b) To compute the first moment, we differentiate the MGF once with respect to t and evaluate at t = 0:

E(x) = M'(0) = (4/(3t^4)) (te^t - 3e^t + 3)

Evaluating at t = 0, we get:

E(x) = 1

Therefore, the first moment of x is 1.

To compute the second moment, we differentiate the MGF twice with respect to t and evaluate at t = 0:

E(x^2) = M''(0) = (4/(3t^5)) ((t^2 + 2t) e^t - 4te^t + 6e^t)

Evaluating at t = 0, we get:

E(x^2) = 2

Therefore, the second moment of x is 2.

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Answer:

69

Step-by-step explanation:

that is what it is

Answer:

The answer should be 984

Step-by-step explanation:

There are 17,576,000 different license plates possible if a plate consists of three digits followed by three letters.

To calculate the number of different license plates possible, we need to consider the number of options for each character position.

For the three-digit part, there are 10 options for each digit (0-9). Therefore, there are 10 × 10 × 10 = 1,000 different possibilities for the three digits.

For the three-letter part, assuming we have an alphabet with 26 letters (A-Z), there are 26 options for each letter. Therefore, there are 26 × 26 × 26 = 17,576 different possibilities for the three letters.

To find the total number of different license plates, we multiply the possibilities for the digits and the possibilities for the letters together:

1,000 (possibilities for the digits) × 17,576 (possibilities for the letters) = 17,576,000.

So, there are 17,576,000 different license plates possible if a plate consists of three digits followed by three letters.

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Answer:

T = 4.0 s

Step-by-step explanation:

The period of a simple pendulum is given by

\(period = 2\pi \sqrt{ \frac{l}{g} } \)

where l = length of the pendulum

= 4 m

g = acceleration due to gravity

= 9.8 m/s^2

\(period = 2\pi \sqrt{ \frac{(4 \: m)}{(9.8 \: \frac{m}{ {s}^{2} } )} } = 4.0 \: s\)

Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

Answer:

75 ft

Step-by-step explanation:

for perimeter you're adding the outside of the shape

so you'd add 30 ft+9 ft+9 ft+9 ft+9 ft+9 ft, which equals 75 ft

Answer:

m<a = 44°

Step-by-step explanation:

Left triangle:

95 + 39 + x = 180

x = 46

Right triangle:

46 + 90 + a = 180

a = 44

To write this distance in scientific notation, we can express it as:

\(1.08\) × \(10^8 km\)

Distance refers to the physical length or space between two objects or points, measured typically in units such as meters, kilometers, miles, etc.

Light travels at a constant speed of approximately 299,792,458 meters per second (m/s) in a vacuum. To convert this speed to kilometers per minute, we can use the following steps:

Multiply the speed of light in meters per second by the number of seconds in one minute:

299,792,458 m/s × 60 seconds/minute = 17,987,547,480 m/minute

Convert this distance from meters to kilometers by dividing by 1,000:

17,987,547,480 m/minute ÷ 1,000 = 17,987,547.48 km/minute

Therefore, light travels approximately 17.99 million kilometers per minute.

To find out how far light travels in 6 minutes, we can multiply the distance it travels in one minute by 6:

17,987,547.48 km/minute × 6 minutes = 107,925,284.88 km

To write this distance in scientific notation, we can express it as a number between 1 and 10 multiplied by a power of 10:

107,925,284.88 km = 1.0792528488 × \(10^8 km\)

Rounding this to two significant figures gives:

\(1.08\) × \(10^8 km\)

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The soda left in the bottle is 0.4 liters in a 2-liter bottle.

Let’s understand this with the concept of Ratio.

How does ratio work?

When two objects are related using numbers or amounts, the relationship is known as a ratio.

Initially, we are given that the bottle is 2 liters. From that, Sergio poured ⅘ of the soda.

So, the soda left is the initial quantity- the final quantity

= 2(initial quantity) - ⅘*2(final quantity)

=2 - 1.6= 0.4 liter

So finally, the soda left in the 2-liter bottle is 0.4 liter.

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Answer:

1

Step-by-step explanation:

because 1/2 time 1 = 1/2

Mixed number is the combination of the whole number and the proper fraction. One is integer and other is fraction in a mixed number. When you multiply a mixed number by another mixed number the product is equal to the another mixed number. For exact same mixed number, when you multiply a mixed number by one  number the product is equal to the mixed number.

Mixed number is the combination of the whole number and the proper fraction. One is integer and other is fraction in a mixed number. As it is the combination of two types of number thus it is known as mixed number.

Mixed number are used to count the whole and part of a thing together.

For example five and a half of a thing can be written as,

\(5+\dfrac{1}{2} =5\dfrac{1}{2}\)

Now when a mixed number is multiplied by the another mixed number the product of both is a another mixed number.

For example let multiply 2 and a half with 3 and a half. The result is,

\(2\dfrac{3}{2} \times3\dfrac{3}{2} =\dfrac{7}{2} \times \dfrac{9}{2}\)

\(2\dfrac{3}{2} \times3\dfrac{3}{2} =\dfrac{63}{4}\)

\(2\dfrac{3}{2} \times3\dfrac{3}{2} =15\dfrac{3}{4}\)

Thus when you multiply a mixed number by another mixed number the product is equal to the another mixed number.

If the product should be equal to the given mixed number thus it need to be multiplied by the one. Thus when you multiply a mixed number by one  number the product is equal to the mixed number.

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Answer:

7 :))

Step-by-step explanation:

The point that partitions segment AB in a 1:4 ratio is \(P = \left(-1, -\frac{2}{5}\right)$\).

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

\($\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$\)

and

\($\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$\)

Using the distance formula, we can find the lengths of AP, PB, and AB:

\(AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}\)

Substituting these into the section formula, we have:

\($\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$\)

Therefore, the point that partitions segment AB in a 1:4 ratio is \(P = \left(-1, -\frac{2}{5}\right)$\).

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There are 2475 ways to place 10 identical red balls and 10 identical blue balls into 4 distinct urns, given the condition for the first urn.

We want to place 10 identical red balls and 10 identical blue balls into 4 distinct urns with the condition that the first urn has at least 1 red ball and at least 2 blue balls.

Step 1: Place the minimum number of balls in the first urn.
Let's place 1 red ball and 2 blue balls in the first urn. Now we have 9 red balls and 8 blue balls left to distribute.

Step 2: Use the stars and bars method to distribute the remaining balls.
For the remaining 9 red balls, we will use the stars and bars method. There are 3 urns left to place the balls, so we will have 2 "bars" to divide them. In total, we have 9 stars (red balls) and 2 bars, so there are C(11, 2) ways to distribute the red balls, where C(n, k) represents combinations.

If the first urn has no red balls, then we need to place all 10 red balls into the other 3 urns, and the blue balls can go into any of the 4 urns. There are 3^10 ways to place the red balls and 4^10 ways to place the blue balls, so there are 3^10 * 4^10 ways to violate the condition in this way.

If the first urn has exactly 1 red ball and fewer than 2 blue balls, then we need to place the other 9 red balls and the remaining blue balls into the other 3 urns. There are 3^9 ways to place the red balls, and (4 choose 2) * 3^8 ways to place the blue balls (since we need to choose 2 of the remaining 3 urns to put the blue balls in). So there are 3^9 * (4 choose 2) * 3^8 ways to violate the condition in this way.

For the 8 blue balls, we also use the stars and bars method. Again, there are 3 urns left, so we will have 2 "bars" to divide them. We have 8 stars (blue balls) and 2 bars, so there are C(10, 2) ways to distribute the blue balls.

Step 3: Calculate the total ways to distribute the balls.
Since the ways to distribute red balls and blue balls are independent, we multiply the number of ways to distribute the red balls by the number of ways to distribute the blue balls.
Using the principle of inclusion-exclusion, the total number of ways to place the balls into the urns that satisfy the condition is:

4^20 - 3^10 * 4^10 - 3^9 * (4 choose 2) * 3^8

= 2,922,821,387,520 - 3,486,784,401,920 - 312,491,796,480

= 123,544,189,120
Total ways = C(11, 2) * C(10, 2) = 55 * 45 = 2475

So, there are 2475 ways to place 10 identical red balls and 10 identical blue balls into 4 distinct urns, given the condition for the first urn.

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Step-by-step explanation:

focus(p) is on the x axis= -1

vertex=(0,0)

parabola equation----- (y-h)^2 =4p(x-k)

(h, k)=(0,0)

(y-0)^2 =4(-1)(x-0)

|

|

|

y^2 = -4x

that is the answer

Answer:

I believe it is true! :)

Step-by-step explanation:

The radio host can play one song from each of 3 CDs by a single artist where the first CD includes 12 songs, the second CD includes 14 songs, and the third CD includes 13 songs in 2,184 number of ways.

This is a combination problem. The number of ways the radio host can play can be obtained by the number of ways the radio host can select 1 song from 12 songs in first CD, 1 song from 14 songs in second CD and 1 song from 13 songs in third CD. That is,

The total number of ways = 12C1 × 14C1 × 13C1

As nC1 = n

The total number of ways = 12 × 14 × 13

=  2,184

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