In right triangle XYZ, the tangent of acute angle X is 4. What is the secant of angle X?

The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission if each boat has a failure rate of 1 failure per 100 hoursis 99.5%. Hence, the correct option is (A).

To determine the probability of mission success, we'll need to calculate the probability of failure for each boat and then use the binomial probability formula.

Here are the steps:

1. Calculate the probability of failure for each boat during the 20-hour mission: Since each boat has a failure rate of 1 failure per 100 hours, the probability of failure for each boat in 20 hours is 20/100 = 1/5 or 0.2.

2. Calculate the probability of success for each boat: The probability of success for each boat is 1 - probability of failure = 1 - 0.2 = 0.8.

3. Use the binomial probability formula to find the probability of at least 11 boats operating successfully:
P(X ≥ 11) = 1 - P(X ≤ 10), where X is the number of successful boats.

4. Calculate P(X ≤ 10) using the binomial probability formula:

P(X ≤ 10) = ∑[C(16, k) × (0.8)^k × (0.2)^(16-k)], where k ranges from 0 to 10, and C(16, k) is the binomial coefficient or the number of ways to choose k successes from 16 boats.

5. Calculate 1 - P(X ≤ 10) to get the probability of mission success.

After performing the calculations, the probability of mission success is found to be approximately 99.5%, which corresponds to option A.

So, the probability of mission success, given that at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission and each boat has a failure rate of 1 failure per 100 hours, is approximately 99.5%.

Hence, option (A) is correct.

Read more about probability: https://brainly.com/question/13604758

#SPJ11

The range of the given function is the set of all possible output values, or the set of all y-values that the function can produce. The answer is option B. {-1, 3, 4, 6}

How to locate the set encapsulates the function's range?\(\{(2,4),(-3,3),(1,6),(4,-1)\}\) ?

To find the range of a function, we need to determine all possible output values of the function. In other words, we need to find the set of all second elements (y-values) in the given set of ordered pairs.

The given set of ordered pairs is: {(2,4),(-3,3),(1,6),(4,-1)}

The second elements (y-values) in each of the ordered pairs are: 4, 3, 6, -1

As a result, the set of these numbers constitutes the function's range:

Range = {4, 3, 6, -1}

Option B lists these values in a set, so it is the correct answer:

B. {-1, 3, 4, 6}

To know more about  range of a function visit

https://brainly.com/question/21027387

#SPJ1

Answer:

x = -7

Step-by-step explanation:

\(-3x+7=8\) subtract 7 on both sides

\(-3x=21\) divide -3 into both sides

\(x=-7\)

To check

-3(-7) = 21 + 7=28

Answer:

The answer is D(f-g)

Step-by-step explanation:

Profit minus expenses

Answer:

D

Step-by-step explanation:

The profit can be defined as (cost of production) - (revenue) and since the cost is defined as g(x) = x^2 and the revenue is f(x) = 4x+1. The profit can be defined as \((f-g) = (4x+1)-x^2 = -x^2+4x+1\). After 2 months you can calculate the profit by simply plugging in 2 as x. This gives you the equation: \((f-g) = (4(2) + 1) - 2^2 = 9-4 = 5\$\)

Answer:

onse sec and ill help

Step-by-step explanation:

In order to cross the bridge, the seven cars can form groups of four to cross the bridge in 35 combinations.

The process of combination is used to calculate in how many ways seven cars can form groups of four in order to cross the bridge.

Combination formula is given by:

\(nCr = n!/ (n! * (n-r)!)\)

The number of combinations of seven cars taken four at a time can be given by the equation:

C(7,4) = 7!/(4! * (7-4)!)

C(7.4) = 5040/(24*6) = 5040/144 = 35.

Therefore, the seven cars can cross the bridge in groups of four in 35 different combinations.

Learn more about combination here brainly.com/question/3901018

#SPJ4

-1/7, since parallel lines have equal slopes.

Answer:

2

Step-by-step explanation:

The answer is a- 2

Answer: 13

Step-by-step explanation:

Answer:

If you want step by step I will show you

0.8

The largest possible volume for the rectangular box is approximately 160.57 cubic inches. Let x be the side of the square base and h be the height of the rectangular box.

The surface area of the base and four sides is:

SA = x² + 4xh

The volume of the rectangular box is:

V = x²h

We want to maximize the volume of the box subject to the constraint that the surface area is 164 square inches. That is  

SA = x² + 4xh = 164

Therefore:h = (164 - x²) / 4x

We can now substitute this expression for h into the formula for the volume:

V = x²[(164 - x²) / 4x]

Simplifying this expression, we get:V = (1 / 4)x(164x - x³)

We need to find the maximum value of this function. Taking the derivative and setting it equal to zero, we get:dV/dx = (1 / 4)(164 - 3x²) = 0

Solving for x, we get

x = ±√(164 / 3)

We take the positive value for x since x represents a length, and the side length of a box must be positive. Therefore:x = √(164 / 3) ≈ 7.98 inches

To find the maximum volume, we substitute this value for x into the formula for the volume:V = (1 / 4)(√(164 / 3))(164(√(164 / 3)) - (√(164 / 3))³)V ≈ 160.57 cubic inches

To leran more about rectangular box, refer:-

https://brainly.com/question/29971591

#SPJ11

Answer:

either d or b???

Step-by-step explanation:

answer is d and b.

they both lie in same line

In the equation f(x) = (x - h)² + k, the value of k represents the vertical shift of the graph, indicating the y-coordinate of the new vertex.

To determine the value of k in the equation f(x) = (x - h)² + k, we need to consider the transformation of the original function f(x) = x².

Comparing the two equations, we observe that the transformation involves shifting the graph horizontally by h units and vertically by k units.

In the original function f(x) = x², the vertex of the parabola is located at the point (0, 0), which means k is 0.

However, when the equation is rewritten in the form f(x) = (x - h)² + k, the vertex is shifted to the point (h, k).

Since the original vertex is (0, 0) and the new vertex is (h, k), it implies that k is the y-coordinate of the new vertex.

For more such questions on graph

https://brainly.com/question/30287521

#SPJ8

The total amount of payment for calls is Rs 648

From the problem, the following information is deduced to help solve the problem

the minimum charge of 175 calls is Rs 180 and Rs 1.50 per calls for additional calls

The total call reading

= present reading - former reading

= 7577 - 5577

= 2000

the number of 175 calls in 2000

= 2000 / 175

= 11 3/7 approximately 12

Total cost of calls

175 calls = Rs 180 + Rs 1.50 * 12

= 180 + 1.50 * 12

= Rs 180

Adding other charges to Rs 180

= 180 * 1.1 + 180 * 1.3 + 180 * 1.2

= Rs 648

Learn more about call charges at:

https://brainly.com/question/30123892

#SPJ1

The life length in hours is exceeded by 95/5% of the light bulbs is 1329 hours.

To find the life length in hours that is exceeded by 95% of the light bulbs, we need to determine the corresponding z-score for the 95th percentile and use it to calculate the value.

Since the distribution is assumed to be normal, we can use the standard normal distribution (z-distribution) to find the z-score. The z-score represents the number of standard deviations an observation is above or below the mean.

To find the z-score corresponding to the 95th percentile, we look for the z-value that corresponds to a cumulative probability of 0.95. This value can be obtained from standard normal distribution tables or using a statistical software/tool.

For a cumulative probability of 0.95, the corresponding z-score is approximately 1.645.

Once we have the z-score, we can calculate the exceeded life length as follows:

Exceeded life length = Mean + (Z-score * Standard deviation)

Exceeded life length = 1000 + (1.645 * 200)

Exceeded life length ≈ 1000 + 329

Exceeded life length ≈ 1329 hours

Therefore, approximately 95% of the light bulbs will have a life length that exceeds 1329 hours.

Learn more about Test statistics here:

brainly.com/question/14128303

#SPJ11

The probability that a high school junior will take less than 135 minutes to complete the SAT exam is 0.5745.

To determine the probability, the standard normal distribution table or calculator is utilized.

The standard normal distribution table, also known as the z-score table, is used to find the probability of a certain z-score or a range of z-scores.

The SAT exam's time is normally distributed, with a mean of 150 minutes and a standard deviation of 25 minutes.The formula for z-score is as follows:

z=(x-μ)/σ

Where x is the time to complete the SAT exam, μ is the mean of the time to complete the SAT exam, and σ is the standard deviation of the time to complete the SAT exam.

To calculate the z-score, the time of 135 minutes is substituted for x, the mean μ of 150 minutes is substituted for μ, and the standard deviation σ of 25 minutes is substituted for σ.The computation is as follows:

z=(135-150)/25= -0.60

Using the standard normal distribution table, the probability of getting a z-score of -0.60 is 0.2743.

To obtain the probability that a high school junior will complete the SAT exam in less than 135 minutes, the area under the standard normal curve to the left of z = -0.60 must be computed. Because the normal curve is symmetrical, the region to the right of z = -0.60 is equal to 1 - 0.2743 = 0.7257.

Finally, to obtain the region to the left of z = -0.60, 0.7257 must be subtracted from 1:1 - 0.7257 = 0.2743

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

Answer:

Step-by-step explanation:

25-10=15kgs

15+5=20minutes

1/2*15=7.5hrs

7:05-2:00=5:05pm

Step 1:

The formula for the area of a hexagon can also be given in terms of the apothem as,

Area of hexagon

where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.

Step 2:

Length of the sides = 15 cm

Step 3:

Find the Apothem ' a '

Find each angle

Next

Answer:

8397 divided by 27 in partial quotients is 311

Step-by-step explanation:

Answer:

6.4331 × 10 5N

Step-by-step explanation:

Given the following :

Mass (m) of car = 1200kg

Initial Velocity (u) of car = 60 mph

Final velocity = 0 ( comes to rest)

Velocity in m/s = 60 / 2.24 = 26.785 m/s

Time (t) = 0.0500

Using the relation :

Ft = m(v - u)

Where,

v = final velocity ; u = initial velocity ; t = time ; F = force

F*0.05 = 1200(26.785 - 0)

0.05F = 32142.86 - 0

F = 32142.86 / 0.05

F = 642857.14 N

F = 6.43 × 10^5 N

Answer:

=

Step-by-step explanation:

On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

To learn more about postsynaptic membrane visit:

brainly.com/question/14969022

#SPJ11

Answer:

t = 4

Step-by-step explanation:

Substitute the variables with the information provided.

205 = 100 + 12(6) + 5(t) + 7(4) + 5(5) - 8(5)

Simplify

205 = 100 + 72 + 5t + 28 + 25 - 40

20 = 5t

t = 4

This stadium will be demolished and a new one built that can hold 50% more fans. The bigger stadium will hold 86,445 fans

To find out what will be the seating capacity of the new, bigger stadium, you can use the following steps:

Find the 50% of the old stadium’s capacity

Multiply it by 100

Add the product to the old stadium’s capacity to find the capacity of the new stadium

Formula for calculating the new capacity of the stadium:

The new stadium's capacity = Old capacity + 50% of Old capacity

= Old capacity (1 + 50/100)

= Old capacity × 1.5

Using the formula; The new stadium’s capacity will be:

New capacity = Old capacity (1 + 50/100)

New capacity          = 57,630(1 + 0.50)

New capacity = 57,630(1.5)

New capacity = 86,445

Therefore, the new, bigger stadium will hold 86,445 fans.

Learn more about capacity :

brainly.com/question/30490732

#SPJ11

Answer:

12

Step-by-step explanation:

This is a standard subtraction problem, so our equation is:

50 - 38 = 12

So she has 12 pieces of ribbon left

Answer:

12

Step-by-step explanation:

This is a simple subtraction equation.

50-38

=12

Or you could reverse it,

38+12

=50

Answer:

the median is 20 and the mean is 17

Step-by-step explanation:

The statement "A null space is a vector space" is true.

The null space of a matrix, also known as the kernel, is the set of all vectors that, when multiplied by the matrix, result in the zero vector.

Formally, for an m×n matrix A, the null space of A is denoted as null(A) and defined as:

null(A) = {x | Ax = 0}

To prove that the null space is a vector space, we need to show that it satisfies the three fundamental properties of a vector space: closure under addition, closure under scalar multiplication, and the existence of a zero vector.

1. Closure under addition: Let x and y be vectors in the null space of A, i.e., Ax = Ay = 0. We need to show that x + y is also in the null space of A. By adding the two equations, we have:

A(x + y) = Ax + Ay = 0 + 0 = 0

This demonstrates closure under addition.

2. Closure under scalar multiplication: Let x be a vector in the null space of A, i.e., Ax = 0. For any scalar c, we need to show that cx is also in the null space of A. We have:

A(cx) = c(Ax) = c0 = 0

This demonstrates closure under scalar multiplication.

3. Existence of a zero vector: The zero vector, denoted as 0, satisfies A0 = 0, showing that the zero vector is in the null space of A.

Since the null space of a matrix satisfies all the properties of a vector space, we can conclude that the statement "A null space is a vector space" is true.

To know more about null space refer here:

https://brainly.com/question/27959040#

#SPJ11

Answer:

5.98

Step-by-step explanation:

5.28+0.7=5.28+0.70

5.28+0.70=5.98

Answer:

5.98000

Step-by-step explanation: