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10 points. please help ​

Answer:

54

Step-by-step explanation:

The correct answer is B.

The notation f(3) = 1 means that the value of the function f at input 3 is 1. In the context of a sequence described by a function, this means that the third term in the sequence has a value of 1.

A function is a mathematical object that takes one or more inputs, performs a specific operation on them, and produces an output. It describes a relationship between two sets of values, often referred to as the domain and the range. Functions are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.

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Answer:

∠ C ≈ 73.7°

Step-by-step explanation:

using the sine ratio in the right triangle

sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AT}{CT}\) = \(\frac{48}{50}\) , then

∠ C = \(sin^{-1}\) ( \(\frac{48}{50}\) ) ≈ 73.7° ( to the nearest tenth )

Answer:

The boat will travel 16 miles in 1 hour (B)

Step-by-step explanation:

Find unit rate

32/2

Which is 16

and therefore 16/1

The work done by the force field on the particle moving along the given helix is 60π units of work.

To find the work done by the force field F on the particle that moves along the helix r, we use the formula:

W = ∫ F · dr

where · denotes the dot product, and dr is the differential displacement vector along the path of the particle.

First, we need to calculate dr. Since the particle moves along the helix r, we can write:

dr = dx i + dy j + dz k

where dx, dy, and dz are the differentials of x, y, and z with respect to t, respectively. We have:

dx = -2sin(t) dt

dy = 2cos(t) dt

dz = 5 dt

Therefore, we can write:

dr = (-2sin(t) i + 2cos(t) j + 5k) dt

Next, we need to calculate F · dr. We have:

F · dr = (6x i + 6y j + 2k) · (-2sin(t) i + 2cos(t) j + 5k) dt

= -12sin(t) + 12cos(t) + 10 dt

Finally, we can integrate F · dr over the interval 0 ≤ t ≤ 2π to obtain the work done by the force field F on the particle that moves along the helix r:

W = ∫ F · dr = ∫ (-12sin(t) + 12cos(t) + 10) dt

= [-12cos(t) + 12sin(t) + 10t]0\(^(2π)\)

= (-12cos(2π) + 12sin(2π) + 10(2π)) - (-12cos(0) + 12sin(0) + 10(0))

= 20π

Therefore, the work done by the force field F on the particle that moves along the helix r is 20π.

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Answer:

Step-by-step explanation:

wwwwwwwwwwwwwwwwwwwwwwwww

Answer:

Absolute Value

Step-by-step explanation:

– The distance a number is from the zero on a number line. (Absolute value is always positive). Acute Angle - An angle with a measure > than 0° and < 90˚. Acute Triangle– A triangle that has all three angles that are acute.

4x² − 9y² + 16x + 18y = 29 Complete the square and write in standard form: (x + 2)²/3 - (y - 1)²/4/3 = 1

First, let's rearrange the equation:

4x² + 16x - 9y² + 18y = 29

To complete the square for the x-terms, we add and subtract (16/2)² = 64 to the equation:

4(x² + 4x + 4) - 9y² + 18y = 29 + 4(4)

Next, let's complete the square for the y-terms by adding and subtracting (18/2)² = 81 to the equation:

4(x² + 4x + 4) - 9(y² - 2y + 1) = 29 + 4(4) - 9(1)

Simplifying further, we get:

4(x + 2)² - 9(y - 1)² = 12

Dividing both sides by 12, we obtain the standard form:

(x + 2)²/3 - (y - 1)²/4/3 = 1

From the standard form, we can identify that the conic section is an ellipse. The center of the ellipse is (-2, 1). To find the vertices, we can use the formula a = √(4/3) and b = √(4/3). The distance from the center to each vertex is a = √(4/3) in the x-direction and b = √(4/3) in the y-direction. The foci can be found using the formula c = √(a² - b²).

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The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:

P(x=0) = (p^5)*(q^0) = p^5

In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.

For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.

To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

The correct question is:

A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective

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The answer fam is.........

0.169

58.9%

1.77

6/5

the total interest earned on Anne's retirement account over the last 30 years is $299,323

To calculate the total interest earned, we need to subtract the total amount deposited from the current value of the account. Anne has been depositing $200 at the end of each month for 30 years, which amounts to a total deposit of $200 * 12 months * 30 years = $72,000.

The current value of the account is $371,323. Therefore, the total interest earned can be calculated as $371,323 - $72,000 = $299,323.

Hence, the total interest earned on Anne's retirement account over the last 30 years is $299,323.

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Answer: n = 17

Step-by-step explanation:

2n + 3n -5 = 90

5n - 5 = 90

5n = 85

n = 17

Answer:

n = 19°

Step-by-step explanation:

The tiny square in the corner of the big angle shows that it is a right angle. Right angles have a measure of 90°. So the two angles labelled added together make a 90° angle.

2n + 3n - 5 = 90

Combine like terms.

5n - 5 = 90

Add 5.

5n = 95

Divide by 5.

n = 19

Answer:

I don't know sorry.

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

A= - 48

B= 6

-48/6

= 8

Negative x Negative = Positive

Negative x Positive = Negative

Positive + Positive = Positive

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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The probability is approximately 0.0682 or 6.82%.

To calculate the probability that the three marbles selected will be the same color, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes = C(12, 3) = 220

(Here, C(n, r) represents the combination of n objects taken r at a time.)

Number of favorable outcomes:

If we select 3 blue marbles, there are C(5, 3) = 10 ways to choose them.

If we select 3 white marbles, there are C(4, 3) = 4 ways to choose them.

If we select 3 red marbles, there are C(3, 3) = 1 way to choose them.

So, the total number of favorable outcomes is 10 + 4 + 1 = 15.

Therefore, the probability that the marbles selected will be the same color is:

P(Same color) = favorable outcomes / total outcomes

= 15 / 220

= 3 / 44

≈ 0.0682 (rounded to four decimal places)

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Therefore , the solution of the given problem of inequality comes out to be correct option is A  $5.00w + $3.80a < $63.00 and w + a < 15 .

Just without the equal sign, a mathematical inequality is a connection or a collection of variables. Equilibrium is typically followed by equity. Inequality happens when two values are not equal. Differences exist between equation and inequality. It was decided to utilize the most prevalent symbol when the parameters are not identical or equivalent ().

Here,

Given :

They are limited to a combined 15 hours in the two parks.

A total of $63 can be spent on food and beverages by purchasing $5 in concessions at the water park and

$3.80 in concessions at the amusement park.

Let w be the water park and a be the amusement park:

So,

=> w + a < 15

and

=> $5.00w + $3.80a < $63.00

thus , correct option is A.

Therefore , the solution of the given problem of inequality comes out to be correct option is A  $5.00w + $3.80a < $63.00 and w + a < 15 .

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Given:

The statement is

\((1+i)^2=2i\)

To prove:

The given statement \((1+i)^2=2i\).

Solution:

We have,

\((1+i)^2=2i\)

Taking LHS, we get

\(LHS=(1+i)^2\)

\(LHS=(1)^2+2(1)(i)+(i)^2\)         \([\because (a+b)^2=a^2+2ab+b^2]\)

\(LHS=1+2i+(-1)\)         \([\because i^2=-1]\)

On further simplification, we get

\(LHS=1+2i-1\)

\(LHS=2i\)

\(LHS=RHS\)

Hence proved.

Answer:

P - 6 = (-5)

P = (-5) + 6

p = 1

c. 1,256 m³ is the approximate volume of the sphere.

The approximate volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere. In this case, the diameter of the sphere is given as 10m.

The radius of the sphere is half of the diameter, so the radius would be 10m/2 = 5m.

Plugging the radius value into the formula, we get V = (4/3)π(5m)^3. Simplifying further, we have V = (4/3)π(125m^3).

Calculating the value, V = (4/3)π(125m^3) ≈ 1,256 m³.

Therefore, the approximate volume of the sphere is approximately 1,256 m³.

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Answer:

2

Step-by-step explanation:

we replace x with -3

f(-3)=2(-3)+8

f(-3)=-6+8

f(-3)=2

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Using the unit circle:

Answer:

The second reason is incorrect.

It should be "Transitive Property of Congruence"

Answer:

Reason 2 ( got it correct on my test)

Step-by-step explanation:

The reason must justify its corresponding statement.

Answer: Width = 3.4 meters, Length = 6.4 meters

Step-by-step explanation:

If the width is \(w\), then the length is \(w+3\).

\(w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4\)

Answer:

Step-by-step explanation:

Question (1)

From the table showing arithmetic sequence,

First term of the sequence = 18

5th term of the sequence = -10

Explicit formula of an arithmetic sequence,

\(T_{n}=a+(n-1)d\)

For 5th term,

-10 = 18 + (5 -1)d

-10 = 18 + 4d

4d = -28

d = -7

Therefore, explicit formula for the table will be,

\(T_n\) = 18 + (n - 1)(-7)

    = 18 - 7n + 7

    = 25 - 7n

\(T_n=25-7n\)

Recursive formula → \(T_n=T_{n-1}+d\)

                                 \(T_n=T_{n-1}-7\)

Question (2),

From the table attached,

First term of the geometric sequence = 6

5th term = 96

Recursive formula of a geometric sequence = \(a(r)^{n-1}\)

Here a = first term

r = common ratio

For 5th term from the table,

96 = \(6(r)^{5-1}\)

r⁴ = 16

r = \(\sqrt[4]{16}\)

r = 2

Therefore, explicit formula will be,

\(T_n=6(2)^{n-1}\)

Recursive formula will be,

\(T_n=T_{n-1}\times (r)\)

\(T_n=2\times T_{n-1}\)

Answer:

2(2x - 3)(x^2 -4)

Step-by-step explanation:

the second one

Answer:

4

Step-by-step explanation:

m = 4

Answer:

I DONT KNOW IM VERY SORRY PLEASE GIVE ME 5 STARS I WOULD REALLY APPRECIATE IT...

Step-by-step explanation:

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-10-3(7-x)=

answer: -31+3x  that's what he gave me I hope I have helped you.