the world had been harmed by a widespread z-virus which already turned 10% of the world's population into zombies (i.e., the probability that an individual in the world was affected by the z-virus is 10%). scientists then invented a test kit which would return a positive result with 98% probability if a tested subject was infected by z-virus and a negative result with 88% probability if the tested subject was not infected by z-virus. if the test kit returned a negative result, what is the probability that the tested subject was actually affected by z-virus?

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

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Answer:

-6 and 7

Step-by-step explanation:

I hope this helps!

Answer:

7 and -6

Step-by-step explanation:

7 x -6 = -42

7 - 6 = 1

Answer:

610000

Step-by-step explanation:

Srry i misread that i thought it said round to the nearest thousandth f

After rounding the number to the nearest thousand we get 609635.783

Here,

The given number to round nearest thousand is 609635.782852

What is rounding off of a number?

Rounding off means a number is made simpler by keeping its value intact but closer to the next number.

Now,

In rounding off a number nearest thousand we can write a number up to 3 decimal places

So after rounding 609635.782852 to the nearest thousands we get,

609635.783

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The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.

The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.

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Answer:

942.48

Step-by-step explanation:

C) f is decreasing for x<0 because f′(x)<0 for x<0. , we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of f is f′(x)=x2−a2=(x−a)(x+a).

This implies that f′(x)<0 when x<−a or x>a. From the derivative, we can deduce that f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of the function f is f′(x)=x2−a2=(x−a)(x+a), where a is a positive constant. This means that the derivative is negative when x<−a or x>a. We can use this information to determine the behavior of the function. Since the derivative is negative when x is less than zero, we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

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False. To calculate a percent increase, the portion is not the missing element. The portion refers to the initial or original value, while the missing element is the final or increased value.

The formula for calculating a percent increase is:

Percent Increase = (Final Value - Initial Value) / Initial Value * 100

In this formula, the initial value is the portion that represents the starting or original value. The final value is the missing element, as it represents the increased or final value after the increase.

By subtracting the initial value from the final value, we obtain the difference between the two. Dividing this difference by the initial value gives us the relative increase as a decimal or fraction. Multiplying by 100 converts it into a percentage, representing the percent increase.

Therefore, the portion in calculating a percent increase is the known value or initial value, while the missing element is the final value that we are trying to determine or find.

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Answer:

C. 1 point

Step-by-step explanation:

Before her third turn = -2 points

During her third turn = 8 points

During her fourth turn = -10 points

during her fifth turn = 5 points

How many points did Emma have at the end of her fifth turn?

Total points Emma has at the end of her fifth turn = -2 + 8 -10 + 5

= 1 point

Total points Emma has at the end of her fifth turn = 1 point

C. 1 point

Answer:

3rd one

Step-by-step explanation:

12

Answer:

11, 43, 80

Step-by-step explanation:

A second number is 10 more than three times a first number

The third number is 14 more than six times the first number

The sum of the three numbers is 134. What are the three

numbers?

call the first number " x "

call the second number " y "

call the third number " z "

now represent the given information algebraically

y - 10 = 3x

manipulate for the problem:

y = 3x +10

z - 14 = 6x

manipulate for the problem:

z = 6x +14

x + y + z =134

now use substitution to form one equation

x + y + z = 134

x + 3x + 10 + 6x + 14 = 134

simplify and solve by inverse operations:

10x + 24 = 134

10x = 110

x = 11

now substitute back into to find the answer to the problem

y= 3x + 10

y = 3 * 11 +10

y = 43

z = 6x + 14

z = 6 * 11 + 14

z = 80

Answer: 25.00$

Step-by-step explanation:50.00 take away 50% from it you have 25$

Answer:

$25

Step-by-step explanation:

It would be 25 because half of 50 is 25.

Answer:

240, 241, 242

Step-by-step explanation:

Use x, x+1, and x+2 to express the three consecutive numbers.

Set up an equation: x + x+1 + x+2 = 723.

Solve for x.

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Equivalent to the original implication, "if you win the lottery, then you will be rich," are statements (d), (h), (j), and (1). Equivalent to the converse of the implication are statements (b), (e), (i), and (k).

The original implication states that winning the lottery leads to being rich. The equivalent statements are those that express the same relationship, while the converse of the implication reverses the order of the events.

Equivalent to the original implication:

(d) You will be rich if you win the lottery.

(h) You will be rich only if you win the lottery.

(j) If you are rich, you must have won the lottery.

(1) You will win the lottery if and only if you are rich.

Equivalent to the converse of the implication:

(b) Either you don't win the lottery or else you are rich.

(e) You will win the lottery if you are rich.

(i) Unless you win the lottery, you won't be rich.

(k) If you are not rich, then you did not win the lottery.

Not equivalent to either the implication or its converse:

(a) Either you win the lottery or else you are not rich.

(c) You will win the lottery and be rich.

(f) It is necessary for you to win the lottery to be rich.

(g) It is sufficient to win the lottery to be rich.

These statements do not capture the exact relationship between winning the lottery and being rich or its converse.

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The calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

A manager of a sports club maintains data about the main sport in which members participate and their ages.

To verify if there is a connection between the age of a member and their sport preference, a test of independence is performed on 651 sports club members who were randomly selected at a 5% level.200 Words:

Test of independence: Test of independence is a statistical method that helps to determine if there is a connection between two groups, and if there is, what is the magnitude of the relationship.

A test of independence is performed using the chi-square statistic.

The null hypothesis in this test is that there is no relationship between the two group S.

We will use a chi-square test to determine whether there is a connection between the age of the member and the sport in which they participate.

Hypotheses:

Null hypothesis: There is no link between the age of a member and the sport in which they participate.

Alternate hypothesis: There is a relationship between the age of a member and the sport in which they participate.

Level of significance = 5%.

Step 1: Prepare the contingency table for observed values

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  25  30  20  10  15 20-29 years  20  50  35  30  25 30-39 years  15  40  40  35  30 40-49 years  10  35  25  25  20 Over 50 years  5  15  10  15  10

Step 2: Calculate the marginal frequencies.

Age  Basketball  Football  Hockey  Soccer  Other Total Under 20 years  25  30  20  10  15 100 20-29 years  20  50  35  30  25 160 30-39 years  15  40  40  35  30 160 40-49 years  10  35  25  25  20 115 Over 50 years  5  15  10  15  10 55 Total 75  170  130  115  100 651

Step 3: Compute the expected frequencies.

The predicted frequency for each group is (row total) * (column total) / total number of observations.

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  11.5  26.1  19.9  17.7  15 20-29 years  30.9  70.1  53.4  47.5  40.1 30-39 years  30.9  70.1  53.4  47.5  40.1 40-49 years  21.3  48.2  36.8  32.7  27.6 Over 50 years  9.4  21.4  16.4  14.6  12.3

Step 4: Calculate the test statistic:

We will use a chi-square test statistic to determine whether the null hypothesis should be accepted or rejected.

Chi-square test formula is:χ2 = Σ (Observed frequency – Expected frequency)2 / Expected frequency.

Degrees of freedom = (Number of rows – 1) * (Number of columns – 1)

χ2 = (25-11.5)2 / 11.5 + (20-30.9)2 / 30.9 + (15-30.9)2 / 30.9 + (10-21.3)2 / 21.3 + (5-9.4)2 / 9.4 + (30-26.1)2 / 26.1 + (50-70.1)2 / 70.1 + (40-70.1)2 / 70.1 + (35-48.2)2 / 48.2 + (15-21.4)2 / 21.4 + (20-19.9)2 / 19.9 + (35-53.4)2 / 53.4 + (40-53.4)2 / 53.4 + (25-36.8)2 / 36.8 + (10-16.4)2 / 16.4 + (15-14.6)2 / 14.6 + (15-32.7)2 / 32.7 + (25-27.6)2 / 27.6 + (10-12.3)2 / 12.3χ2 = 15.16

Degrees of freedom = (5-1) * (4-1) = 12

Step 5: Determine the p-value:

The p-value is determined by looking up the chi-square value and the degrees of freedom in the chi-square table.

The p-value is the probability of obtaining a result as extreme as or more extreme than the calculated value if the null hypothesis is true.

We will use a 5% level of significance.

Since the calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

There is evidence to suggest that the age of a member is related to the sport in which they participate.

In other words, the age of a member and their sport preference are not independent.

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If the mean of a set of data is 4.11 and its standard deviation is 3.03. the z score for a value of 10.86 is: 2.23.

Using this formula to find the z-score

z-score  =  Value - Mean / Standard deviation

Where:

Value = 10.86

Mean = 4.11

Standard deviation = 3.03

Let plug in the formula

z-score  =  10. 86 - 4.11 / 3.03

z-score  =  6.75 /3.03

z-score = 2.227

z- score = 2.23

Therefore the z-score is 2.23.

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The correct answers are:

Mapping of Regular Entity Types.

Mapping of Binary 1:1 Relationship Types.

Mapping of Weak Entity Types.

Mapping of N-Ary Relationship Types.

Mapping of Single-Valued Attributes.

The steps of ER-to-relational mapping algorithm are as follows:

Mapping of Regular Entity Types.

Mapping of Binary 1:1 Relationship Types.

Mapping of Binary 1:N Relationship Types.

Mapping of Binary M:N Relationship Types.

Mapping of Multivalued Attributes.

Mapping of Composite Attributes.

Mapping of Derived Attributes.

Mapping of Weak Entity Types.

Mapping of N-Ary Relationship Types.

Mapping of Single-Valued Attributes.

ER-to-relational mapping algorithm is a process of converting ER model into relational model. The ER-to-relational mapping algorithm is the process of converting the ER schema into the relational model.

However, the correct answers are:

Mapping of Regular Entity Types.

Mapping of Binary 1:1 Relationship Types.

Mapping of Weak Entity Types.

Mapping of N-Ary Relationship Types.

Mapping of Single-Valued Attributes.

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Answer: Invertible

Step-by-step explanation:

If inverse of a function exists, then the function is said to be invertible. A unique value exits for each given input.

Inverse of a function can be obtained by expressing the given function in terms of y and then replace y by x.

To find the expected number of each animal type treated by the veterinarian, we will multiply the percentage distribution by the total number of animals treated in a month.

Total animals = 230

Dogs: 61% * 230 = 0.61 * 230 = 140.3 (approximately 140)
Cats: 22% * 230 = 0.22 * 230 = 50.6 (approximately 51)
Livestock: 8% * 230 = 0.08 * 230 = 18.4 (approximately 18)
Birds: 6% * 230 = 0.06 * 230 = 13.8 (approximately 14)
Other: 3% * 230 = 0.03 * 230 = 6.9 (approximately 7)

So, the expected number of each animal type treated is:
Dogs: 140
Cats: 51
Livestock: 18
Birds: 14
Other: 7

The correct answer is C) Animal type Dogs Cats Livestock Birds Other Expected 140 51 18 14 7

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer:x=2+2√3 OR x=2−2√3

Step-by-step explanation: The answer is too long to write down. For complete step-by-step, go to mathpapa algebra calculator and type in your question. It would be a bit too long and difficult to write down.

Hope this helps

BRAINLIEST please?

The probability of winning $1000 a day for life is approximately 5.245 x 10^-11 and the probability of winning $1000 a week for life is approximately 1.07 x 10^-8. The probability of winning the jackpot ($1000 a day for life) is 1/(60^5 * 4), while the probability of winning $1000 a week for life is 1/(60^5).

In the Florida Lottery Cash4Life game, a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. The jackpot prize is $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. If just all five numbers match the winning numbers, the player will win $1000 a week for life.
To determine the probability of winning $1000 a day for life, we can use the formula for the probability of independent events: P(A and B) = P(A) x P(B)

(a) To win the jackpot of $1000 a day for life, the player needs to match all five numbers and the Cash Ball. There are 60 options for each of the five numbers and 4 options for the Cash Ball. The total number of possible outcomes is 60^5 (60 choices for each of the five numbers) times 4 (for the Cash Ball). So the probability of winning the jackpot is 1/(60^5 * 4). (b) To win $1000 a week for life, the player needs to match only the five numbers, without considering the Cash Ball. The total number of possible outcomes for this scenario is 60^5. Therefore, the probability of winning $1000 a week for life is 1/(60^5).

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Answer:

6xl2 + 223x - 113

Step-by-step explanation:

Answer:

Emily's claim is correct that with 12 skewers which can hold 5 shrimp each, there will be 15 leftovers.

Step-by-step explanation:

Given that:

Total number of shrimp contained in the bag of Emily = 75

Number of skewers available = A dozen

A dozen means 12.

Therefore, there are 12 number of skewers available.

Each skewer can have = 5 number of shrimp

Total number of shrimp on the 12 skewers = 12 \(\times\) 5 = 60

Total number of leftover = Total number of shrimp in the bag - Total number of shrimp on the 12 skewers = 75 - 60 = 15

Therefore, Emily's claim is correct that with 12 skewers which can hold 5 shrimp each, there will be 15 leftovers.

Answer:

\(14in^2\)

Step-by-step explanation:

Volume of a rectangluar prism = Length x Width x Height

Volume, Length, and Width is given now we can solve for Height, y

\(V = l * w * h\)

\(3in^3 = 1in * 1in* h\)

\(h = 3in\)

Surface area of a rectangular prisim is A = 2(wl +hl +hw)

A = \(2(1in * 1in + 3in * 1in + 3in * 1in)\\2(1 in^2+ 3 in^2+ 3in^2)\\2(7in^2)\\14in^2\)

Hope this helps!

Brainliest is much appreciated!

Answer:

40°

Step-by-step explanation:

Answer:

21 cm.

Step-by-step explanation:

The sum of the two longest sides is given as 41 cm:

(x+1) + (x+2) = 41

Simplifying the left side:

2x + 3 = 41

Subtracting 3 from both sides of the equation :

2x = 38

Dividing both sides by 2:

x = 19

In the big picture(at least of the triangle), the length of the shortest side is 19 cm, and the lengths of the other two sides are 20 cm and 21 cm.

Hope it helped!

The inequality that represents the problem is x < 100 which means that Britney wants to spend less than $100 at restaurants  in June.

Inequality:

In math, inequality defines the non equal relationship between the expression.

Given,

Britney sets a limit on how much money she can spend at restaurants during the month of June. She divides the total amount evenly among the 5 times she expects to go to restaurants. Britney determines she should spend less than $20 each time.

Here we need to find the inequality that refers the given problem.

Let x represent how much Britney wants to spend at restaurants in June.

Here we know that, the number of time she goes in the restaurant is 5.

And the amount limit for each time is less than $20.

So, it can be written as,

=> x/5 < 20

While we solve the inequality then we get

=> x < 100

Therefore, Britney wants to spend less than $100 at restaurants in June.

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According to the ADA, the maximum slope for a wheelchair ramp is 1/12. Given the dimensions of the ramp built by the Glen Head Boys Club for a local school, we can calculate the height of the ramp at point B. The height of the ramp at point B is approximately 16.7 inches

Explanation:

To calculate the height of the ramp at point B, we need to use the formula:

Height = Length of Ramp × Slope

From the diagram, we can see that the length of the ramp is 26 feet or 312 inches. The slope of the ramp is 1/12, as per the ADA guidelines.

Therefore, the height of the ramp at point B can be calculated as follows:

Height = 312 × (1/12)

= 26

So, the height of the ramp at point B is 26 inches. However, we need to round the answer to the nearest tenth of an inch, as per the question.

Rounding the answer to the nearest tenth of an inch, we get:

Height at Point B = 26 ÷ 12

= 2.1667 feet

= 26.0 inches (rounded to the nearest tenth of an inch)

Hence, the height of the ramp at point B is approximately 16.7 inches, rounded to the nearest tenth of an inch.

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