Captain michael has a ship, the h.m.s. khan. the ship is two furlongs from the dread pirate william and his merciless band of thieves. the captain has probability \dfrac{2}{3} 3 2 ​ start fraction, 2, divided by, 3, end fraction of hitting the pirate ship. the pirate only has one good eye, so he hits the captain's ship with probability \dfrac{1}{3} 3 1 ​ start fraction, 1, divided by, 3, end fraction. if both fire their cannons at the same time, what is the probability that both the pirate and the captain hit each other's ships?

Answer:

I can't see!

Step-by-step explanation:

The integers of option (a), (c) are prime numbers.

Here are the solutions to the given questions:

(a)Since 157 is only divisible by 1 and itself, it is a prime number. Thus, 157 is a prime number.

(b)We need to determine whether 9831 is a prime number or not.  The number 9831 is divisible by 3, because the sum of its digits is divisible by 3. Therefore, 9831 is not a prime number.

(c)The given number, 9833, is only divisible by 1 and itself. Therefore, 9833 is a prime number.

(d) We need to determine whether the given number is prime or not. By factoring, we get:

55511111=11 times 41 times 12167

The given number is not a prime number.

(e)The given number is equal to 2 raised to the power 13 multiplied by 17, as below:

2^{13}-1=(2^7+1)(2^6+1)-1=(128+1)(64+1)-1=129times 65-1=8384

Since 8384 is not a prime number, therefore 2216,090−1 is not a prime number.

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Answer:

C. 98

Step-by-step explanation:

If you add all of his previous test scores and go through the list of numbers you get C.98 as the answer. I added all of his test scores plus 98 which equals 630 divided by 7 (because if he got a 98 there would be 7 test scores) you would get 90 or an A average.

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Explanation:

Let x be the next test grade. It ranges from 0 to 100, inclusive of both endpoints.

The original set {87,92,90,84,88,91} becomes {87,92,90,84,88,91,x} after adding on that score.

We have 7 scores now. We find the average by adding up those seven scores and dividing by 7.

average = (sum of the scores)/(number of scores)

average = (87+92+90+84+88+91+x)/7

average = (532+x)/7

We want the average to be 90 or higher, so we would then have these steps

\(\text{average} \ge 90\\\\\frac{532+x}{7} \ge 90\\\\532+x \ge 90*7\\\\532+x \ge 630\\\\x \ge 630-532\\\\x \ge 98\\\\\)

This means Edgar must score a 98 or higher on the seventh test in order for his overall average to be 90 or higher.

In other words, the lowest test score he can get is a 98.

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Extra info (optional section):

Let's say Edgar gets the highest score possible.

So he gets x = 100

This would mean

average = (87+92+90+84+88+91+x)/7

average = (532+x)/7

average = (532+100)/7

average = 632/7

average = 90.2857 which is approximate

We can see that his overall average would stick to 90 if the teacher is rounding to the nearest whole number.

If 400 baht is shared between A and B; A gets 240 baht while B gets 160 baht.

A linear equation is a polynomial with a degree of one. The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let x represent the amount of money that A gets and y represent the amount of money that B gets.

400 Baht is been divided between A and B, hence:

x + y = 400    (1)

Also; twice A's share may equal three times B's share, hence:

2x = 3y

2x - 3y = 0     (2)

From both equation 1 and 2:

x = 240, y = 160

A gets 240 baht while B gets 160 baht.

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The correct option is B• "The LP has multiple optimal solutions". Because  feasible region, intersects with the objective function in multiple points.

The given linear programming (LP) problem consists of two constraints and two decision variables, x1 and x2. The objective function to be minimized is x1 + 2x2.

To determine the nature of the LP problem, we need to analyze its feasible region and objective function.

The first constraint, x1 + x2 ≤ 4, defines a region in the xy-plane that lies below the line x1 + x2 = 4. The second constraint, x1 - x2 ≥ 5, defines a region that lies to the right of the line x1 - x2 = 5. The feasible region is the intersection of these two regions.

By analyzing the feasible region, we can determine the potential optimal solutions. Since the feasible region is a bounded region, there are finite points within it. The objective function, x1 + 2x2, represents a straight line in the xy-plane with a positive slope. As long as this line intersects the feasible region, there will be multiple points of intersection, each representing a potential optimal solution.

Therefore, the LP problem has multiple optimal solutions because there are multiple points of intersection between the objective function and the feasible region.

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Answer:

9 : 25

Step-by-step explanation:

Given the ratio of the sides of 2 similar equilateral triangles = a : b , then

the ratio of their areas = a² : b²

Given ratio of sides = 3 : 5 , then

ratio of areas = 3² : 5² = 9 : 25

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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Answer:

Step-by-step explanation:

Hence, the surface area of a triangular pyramid is 140 square units.

Answer:

10 girls

Step-by-step explanation:

The critical value for chi-square test decreases as the size of the sample increases.

As sample size increases, absolute differences become a smaller and smaller proportion of the expected value

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Answer:

10√3/3

Step-by-step explanation:

To get x we will use the SOH CAAH TOA trigonometry identity

Given

Angle = 60 degrees

Hypotenuse = x

Opposite = 5

Sin theta = opposite/hypotenuse

Sin 60 = 5/x

x = 5/sin 60

x = 5/(√3/2)

x = 5 * 2/√3

x = 10/√3

Rationalize

x = 10/√3 * √3/√3

x = 10√3/3

hence the length of the side x in simplest radical form is 10√3/3

Step-by-step explanation:

The domain of a quadratic is All Reals however the function is only increasing on the interval (-2, ♾️)

Therefore the domain is (-2, ♾️). The function is also one to one since only one. x value maps to one y value.

\(y = (x + 2) {}^{2} \)

Swap x and y

\(x = (y + 2) {}^{2} \)

\( \sqrt{x} = y + 2\)

\( \sqrt{x} - 2 = y\)

Let y=f^-1(x)

\(f {}^{ - 1} (x) = \sqrt{x} - 2\)

The domain here is [0, ♾️)

It won't be all reals since we can not graph the square root of a negative number on a cartisean coordinate plane

Answer:

When x is 12, \(5-(\frac{x}{3})=1\)

Step-by-step explanation:

\(5-(\frac{x}{3} )\)

Insert the given value of x:

\(5-(\frac{12}{3} )\)

Simplify the expression. Divide 12 by 3:

\(5-4\)

Simplify subtraction:

\(1\)

:Done

Answer:1

Step-by-step explanation:

True. The Span(S) equals the intersection of all subspaces of V that contain S.

The span of a set S of vectors in a vector space V is the smallest subspace of V that contains S. On the other hand, the intersection of all subspaces of V that contain S is the largest subspace of V that contains S. These two concepts are complementary to each other.

To see that span(S) equals the intersection of all subspaces of V that contain S, we need to show that each set is a subset of the other.

The span(S) is a subset of the intersection of all subspaces of V that contain S. This is because every subspace that contains S must contain all linear combinations of the vectors in S, which is precisely the span of S. Span(S) is contained in every subspace of V that contains S, and therefore, it is also contained in their intersection.

The intersection of all subspaces of V that contain S is a subset of span(S). This is because the span of S is a subspace of V that contains S, so it is also one of the subspaces that intersect to form the intersection of all subspaces of V that contain S.

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The measurement of <B is 121 degree.

The sum of a triangle's three internal angles is 180 degrees, as stated by the angle sum Property of a triangle.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.

Given:

let the measure of <A be x.

So, m<G= x- 9

and, m<B = 4x- 15

Using Angle Sum Property

m<A+ m<B+ m<G= 180

x+ 4x- 15 + x- 9 = 180

6x - 24 = 180

6x = 180+ 24

x= 204/6

x= 34

So, m<A = 34

m<B= 4(34) - 15 = 121

and, m<G = 34 - 9= 25 degree.

Hence, the measure of <B is 121 degree.

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Answer:

What is the question from Solving inequalities unit portfolio task 2-3?

Step-by-step explanation:

Comment it down below and I will solve it! :D

The required values of the given scale images are as follows:

a. x = 17.5, b. x = 16.67, and x = 5.

a. As we know that scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

As per the given figure a, we can be written as:

35/x = 18/9

35 × 9 = 18x

x = (35 × 9)/18

x = 17.5

b. As per the given figure b, we can be written as:

x/10 = 15/9

x = (15 × 10)/9

x = 150/9

x = 16.67

c. As per the given figure c, we can be written as:

x/2 = 15/6

x = (15 × 2)/6

x = 5

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Here we want to study the relation between the exponents in a polynomial function and the "odd" property of functions.

We will see that Dimetri is correct.

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

We start by defining an odd function as a function such that:

f(-x) = -f(x).

Now, let's see a simple function with only odd exponents.

f(x) = a*x  (the exponent is 1, so it is odd).

if we evaluate this in x = 1, we get:

f(1) = a

If we evaluate this in x = -1, we get:

f(-1) = a*-1 = -a

Then this is odd.

Now let's see a more general case and why Dimetri is correct.

For the rule of signs, when we multiply 2 negative numbers, the product is positive.

So always that we have an even exponent on a negative number, the outcome will be positive.

This does not happen for odd exponents, because we can't separate all the products in groups of 2, thus if we take the odd exponent of a negative number, the outcome is negative.

Then for functions with only odd exponents, the outcome for evaluating the function in a given input is exactly the opposite of evaluating the same function with the opposite input.

This means that the function is odd.

Again, note that this only happens if the function only has odd exponents.

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Answer:

The answer is 6y :)

Have an amazing day!!

Please rate and mark brainliest!!!

Answer:

C is the correct answer

Answer:

5q²(3p² + 5q)

Step-by-step explanation:

15p²q² + 25q³ ← factor out 5q² from each term

= 5q²(3p² + 5q)

Hey there!

15p²q² + 25q³

= 5q²(3p² + 5q)

Just factorise the common factors out. In this case, the common factors are :- 5q².

Hope it helps ya!

Answer:

b

Step-by-step explanation:

The 34992÷81

=Answer is 432

Answer:

b

Step-by-step explanation:

Answer:

So, the step1 is correct.

Step-by-step explanation:

The expression is

\((6 x^3 + 8 x^2 - 7 x)-(2x^2 + 3)(x- 8)\\\\(6 x^3 + 8 x^2 - 7 x) - (2x^3 - 16 x^2 + 3 x - 24)\\\\6 x^3 + 8 x^2 - 7 x - 2 x^3 - 16 x^2 + 3 x - 24\\\\4 x^3 - 8 x^2 - 4 x - 24\)

So, the step 1 is correct.

Answer: Dog show 1 was a dog show for smaller dogs while dog show 2 was a dog show for larger dogs.

Step-by-step explanation:

Answer:

1. $50+$20x

2. 3 hours

3. $170

Step-by-step explanation:

I am not gonna explain so, don't ask.

The number of regions created when constructing a Venn diagram with three overlapping sets is 8.

In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.

When three sets overlap, there are different combinations of elements that can be present in each region.

For three sets, the number of regions can be calculated using the formula:

Number of Regions = 2^(Number of Sets)

In this case, since we have three sets, the formula becomes:

Number of Regions = 2^3 = 8

So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.

Each region represents a unique combination of elements belonging to different sets.

These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.

Therefore, the correct answer is 8.

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