Find the gradient of the scalar-function f(x, y, z) class
C2 for F = yi - 2zj + yk (If exists).

40° is the answer of Congruent in  (3x+22)degrees .

What is Congruent ?

The 2 angles are vertical angles and are congruent , then

3x + 22 = 142 ( subtract 22 from both sides )

3x = 120 ( divide both sides by 3 )

x = 40°

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Therefore, the expected value E(X) of the given data is 2.6.

Given data:x  2   3   4   5P(X = X) 0.2 0.3 0.2 0.1The expected value of a discrete random variable is the weighted average of all possible values of a random variable, with the weights being the probabilities of each value of the random variable.

The formula for expected value E(X) is;E(X) = Σ [xP(x)]where the summation is over all possible values of x. The symbol Σ means 'sum of'. Now, we'll find E(X);E(X) = (2 × 0.2) + (3 × 0.3) + (4 × 0.2) + (5 × 0.1)E(X) = 0.4 + 0.9 + 0.8 + 0.5E(X) = 2.6

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The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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Answer:

7 : 2

Step-by-step explanation:

\(\dfrac{77}{22}=\dfrac{7*11}{2*11}=\dfrac{7}{2}\)

7 : 2

Answer:

x = 20

Step-by-step explanation:

In parallelograms opposite angles are congruent and angles that are on the same line are supplementary

This means that ∠TUR and ∠URS are supplementary angles

Supplementary angles have a sum of 180°

That being said we can find the missing angle ( ∠ URS ) by subtracting the measure of the given angle ( ∠TUR which has a measure of 160° ) from 180

so ∠URS = 180 - ∠TUR ( 160 )

180 - 160 = 20

Hence, ∠URS = 20°

Answer:

Step-by-step explanation:

Answer:

Assuming this is slope intercept form: y= 6/5x+-5

Step-by-step explanation:

Answer:

AC= 6.3 units (nearest tenth)

BC= 2.8 units (nearest tenth)

∠C= 64°

Step-by-step explanation:

Please see attached picture for full solution.

The probability that there will be fewer than 3 with no DMF teeth in a sample of 20 children is 0.287. The probability that there will be exactly 5 with no DMF teeth in a sample of 20 children is 0.224.

(a) In a sample of 20 children, the number of children with no DMF teeth follows a binomial distribution with n = 20 and p = 0.25. The probability that there will be fewer than 3 with no DMF teeth is given by:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

where X is the number of children with no DMF teeth in the sample.

P(X = k) = (nCk) pk (1-p)n-k

where nCk represents the number of ways to choose k children out of n total children.

Therefore,

P(X = 0) = (20C0) 0.25⁰ (0.75)²⁰

P(X = 0) = 0.019

P(X = 1) = (20C1) 0.25¹ (0.75)¹⁹

P(X = 1) = 0.086

P(X = 2) = (20C2) 0.25² (0.75)¹⁸

P(X = 2) = 0.182

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.019 + 0.086 + 0.182

P(X < 3) = 0.287

Therefore, the probability that there will be fewer than 3 with no DMF teeth in a sample of 20 children is 0.287.

(b) The probability that there will be exactly 5 with no DMF teeth is given by:

P(X = 5) = (20C5) 0.25⁵ (0.75)¹⁵

where X is the number of children with no DMF teeth in the sample.

Therefore,

P(X = 5) = (20C5) 0.25⁵ (0.75)¹⁵

P(X = 5) = 0.224

Therefore, the probability that there will be exactly 5 with no DMF teeth in a sample of 20 children is 0.224.

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Rational numbers are all numbers that can be represented as the quotient of two whole numbers, in this case 0.5 can be written as

therefore, 0.5 is a rational number

Answer:

\(\frac{3a+b}{9}\)

Step-by-step explanation:

Both fractions have a common denominator of 9

Add the numerators, placing them over 9

= \(\frac{3(a-b)+4b}{9}\)

= \(\frac{3a-3b+4b}{9}\)

= \(\frac{3a+b}{9}\)

Answer:

\(8x^{2} +14x+6\)

Step-by-step explanation:

The formula for the area of rectangle is length times width:

\((2x+2)(4x+3)\\\)

Use FOIL method:

\(8x^{2} +6x+8x+6\\8x^{2} +4x+6\)

Answer:

I'll answer this tomorrow. I'm busy.

Step-by-step explanation:

The probability that number less than 7 is rolled is 0.30

The given parameters are

Sample size = 20

There are 6 sections that are less than 7

This means that the probability is

P = 6/20

Evaluate

P = 0.30

Hence, the probability that number less than 7 is rolled is 0.30

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The ANOVA F-test tells the researcher that at least one of the pairs of groups have different means as ANOVA is used to determine the significant difference between the means.

What is ANOVA?

ANOVA stands for Analysis of Variance, and it is used to compare the means of two or more groups. It helps the researcher to determine whether the mean of two or more groups is the same or different from each other.

An ANOVA F-test is used to compare the variation between groups to the variation within groups. The F-test produces an F-value that helps to determine the significance of the difference between the groups. In conclusion, ANOVA F-test is used to determine if there is a statistically significant difference between the means of two or more groups, which means that at least one of the pairs of groups has different means.

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The probability that no two passengers gets off at the same floor will be 0.15.

As per the question statement, an elevator in a building starts with five passengers and stops at 7 floors where each passenger is equally likely to get off at any floor and all the passengers leave independently of each other.

We are required to calculate the probability that no two passengers gets off at the same floor.

Here, since repetition is not allowed,

That is, the total number of ways for 5 passengers are to be assigned to seven floors but no two passengers on the same floor

= 7P5 = [(7!)/(7 - 2)!] = [(7!)/(2!)] = (7 * 6 * 5 * 4 * 3) = 2520

And, the total number of ways to assign 5 passengers to 7 floors, with repetition being allowed will be

= (7)⁵ = 16807.

Therefore, the probability that no two passengers gets off at the same floor will be = (2520/16807) = 0.14993 ≈ 0.15

Probability: It is that branch of Mathematics which deals with the numerical descriptions concerning the extent to which an event is likely to occur, or how likely it is for a proposition to be true, and is measured by the ratio of the favorable cases to the whole number of cases possible.

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Answer:

Step-by-step explanation:

Given function:

The time the javelin is in the air is the difference of zero's of the function:

Time in the air:

It is better visible on the graph

68% of the population will have a height within the range of 69 inches to 75 inches. None of the provided options match this range.

In a normal distribution, approximately 68% of the values fall within one standard deviation of the mean.

Given:

mean height = 72 inches  

standard deviation = 3 inches,

We can determine the range within which 68% of the population's heights will fall.

To calculate this range, we subtract and add one standard deviation from the mean:

Lower bound: Mean - Standard Deviation

= 72 - 3

= 69 inches

Upper bound: Mean + Standard Deviation

= 72 + 3

= 75 inches

Therefore, 68% of the population will have a height within the range of 69 inches to 75 inches.

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The answer will de 10 bacterias

Answer: 1024

Step-by-step explanation: Since there's only 1 bacteria at first, we can just do 2^x. x being the amount of time divided by the amount of time between each time it doubles. Since the bacteria doubles every 2 seconds, and 20/2 = 10 we get 2^10 which is 1024.

a) Proportionately, if the budget for clothing amounted to GH 300.00, which is 20% of the monthly budget, the total income can be determined as GH  1,500.

b) The man's monthly budget will look like this:

Housing =            GH 150

Food =                GH 450

Fuel =                 GH 225

Clothing =          GH 300

Health =              GH 225

Miscellaneous = GH 150

Total income = GH 1,500

We can determine the total income of the man by equating the ratios of his clothing expense and the total income.

We understand that proportions are ratios equated to one another.

Housing = 10%

Food = 30%

Fuel = 15%

Clothing = 20%

Health = 15%

Miscellaneous = 10%

Proportionately, if the budget for clothing amounted to GH 300.00, which is 20% of the monthly budget, the total income can be determined as GH 1,500 (GH 300.00/20%).

Housing = 10%           GH 150 (GH 1,500 x 10%)

Food = 30%               GH 450 (GH 1,500 x 30%)

Fuel = 15%                 GH 225 (GH 1,500 x 15%)

Clothing = 20%         GH 300 (GH 1,500 x 20%)

Health = 15%             GH 225 (GH 1,500 x 15%)

Miscellaneous = 10% GH 150 (GH 1,500 x 10%)

Total income = GH 1,500

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Answer:

Step-by-step explanation:

If the first computer has the same amount of bytes of memory as computers now days then a computer from old days has lower bytes of memory because as computers age they get older and newer models are being made.

Answer:

Today's laptop has 4096 times more memory than the personal computer from the 1980s

Step-by-step explanation:

1. \(2^{18}\)= 262,144

then you do \(2^{30}\) which equals 1,073,741,824

then you divide \(\frac{1,073,741,824}{262144}\) which equals 4,096

Rounding to the nearest hundredth gives us 418.89 cubic centimeters. So option D) 485.65 cubic centimeters is incorrect.

The volume of the composite figure can be calculated by adding the volume of the cylinder and the volume of the cone.

The formula for the volume of a cylinder is V = Bh where B is the area of the base and h is the height. The base of a cylinder is a circle with a radius of r. So, B = πr².

The formula for the volume of a cone is V = 1/3 Bh where B is the area of the base and h is the height. The base of a cone is also a circle with a radius of r. So, B = πr².

Given that both have a radius of 4 centimeters, we can calculate their volumes as follows:

Volume of cylinder = πr²h = π(4)²(7) = 351.86 cubic centimeters Volume of cone = 1/3πr²h = 1/3π(4)²(8) = 67.02 cubic centimeters

Adding both volumes gives us:

Volume of composite figure = Volume of cylinder + Volume of cone = 351.86 + 67.02 = 418.88 cubic centimeters

Rounding to the nearest hundredth gives us 418.89 cubic centimeters.

Therefore, option D) 485.65 cubic centimeters is incorrect.

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a)\textbf{a)} The number of 6-element RNA sequences without "U" is $3^6 = 729$.

b)\textbf{b)} The number of 6-element RNA sequences ending with "GU" is $4^4 = 256$.

c)\textbf{c)} The number of 6-element RNA sequences starting with "C" is $4^5 = 1024$.

d)\textbf{d)} The number of 6-element RNA sequences containing only "A" or "U" is $2^6 = 64$.

What is Combinatorics?

A subfield of mathematics known as combinatorics concerns the systematic numbering, arrangement, and organization of things or elements. Discrete structures like combinations, permutations, and subsets are studied in terms of their characteristics and connections. In many areas of mathematics, computer science, and other disciplines where counting and object arrangement is crucial, combinatorics plays a critical role. It has uses in the design of algorithms as well as areas including probability theory, cryptography, graph theory, and optimization. In a wide variety of real-world applications, combinatorial approaches are employed to handle counting, arranging, and optimization issues.

a) To find the number of 6-element RNA sequences that do not contain ``U" (uracil), we need to count the number of possibilities for each position. Since there are four different nucleotides (A, C, G, and U), and we want to exclude ``U," we have three options (A, C, and G) for each position. Therefore, the total number of such sequences is $3^6 = 729$.

b) To count the number of 6-element RNA sequences that end with ``GU," we fix the last two positions as ``G" and ``U" and count the possibilities for the remaining four positions. For each of the remaining positions, we can choose any of the four nucleotides (A, C, G, or U). Therefore, the number of such sequences is $4^4 = 256$.

c) To determine the number of 6-element RNA sequences that start with ``C," we fix the first position as ``C" and count the possibilities for the remaining five positions. For each of the remaining positions, we can choose any of the four nucleotides (A, C, G, or U). Hence, the number of such sequences is $4^5 = 1024$.

d) To count the number of 6-element RNA sequences that contain only ``A" or ``U" (adenine or uracil), we have two choices (A or U) for each position. Therefore, the total number of such sequences is $2^6 = 64$.

a)\textbf{a)} The number of 6-element RNA sequences without "U" is $3^6 = 729$.

b)\textbf{b)} The number of 6-element RNA sequences ending with "GU" is $4^4 = 256$.

c)\textbf{c)} The number of 6-element RNA sequences starting with "C" is $4^5 = 1024$.

d)\textbf{d)} The number of 6-element RNA sequences containing only "A" or "U" is $2^6 = 64$.

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Answer:

the answer is 207 over 20

Answer:

10.35

Step-by-step explanation:

Here's how i did it:

1) 63756 x 60= 3825360

2) 70 x 5280= 369600

3) 3825360/369600 = 10.35

The convolution of the kernel and image is: w ∧ f = [343, 686, 343]

The correlation of the kernel and image is: w ⊙ f = [343, 686, 343]

The convolution of the kernel and image is calculated by sliding the kernel over the image and taking the dot product of the kernel and the image at each location.

The minimum zero padding needed is 2 pixels, so the kernel is padded with 2 zeros on each side. The convolution is then calculated as follows:

(1 * 0 + 2 * 0 + 1 * 0) + (1 * 0 + 2 * 1 + 1 * 0) + ... = 3

(1 * 0 + 2 * 11 + 1 * 2) + (1 * 0 + 2 * 2 + 1 * 2) + ... = 68

(1 * 0 + 2 * 11 + 1 * 0) + (1 * 0 + 2 * 2 + 1 * 0) + ... = 3

The correlation of the kernel and image is calculated in a similar way, but the dot product is taken between the kernel and the flipped image. The minimum zero padding needed is also 2 pixels, and the correlation is calculated as follows:

(1 * 0 + 2 * 0 + 1 * 0) + (1 * 0 + 2 * 1 + 1 * 0) + ... = 3

(1 * 0 + 2 * 11 + 1 * 2) + (1 * 0 + 2 * 2 + 1 * 2) + ... = 68

(1 * 0 + 2 * 11 + 1 * 0) + (1 * 0 + 2 * 2 + 1 * 0) + ... = 3

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The height of a randomly selected giraffe, the number of points scored during a basketball game, the gender of college students, the amount of rain in City Upper B during April, and the number of fish caught during a fishing tournament are all examples of discrete or continuous random variables, while the number of bald eagles in a country is not a random variable.

a. Continuous random variable

b. Discrete random variable

c. Discrete random variable

d. Continuous random variable

e. Discrete random variable

f. Not a random variable

a. The height of a randomly selected giraffe is a continuous random variable because it can take on any value within a certain range.

b. The number of points scored during a basketball game is a discrete random variable because it is a countable number.

c. The gender of college students is a discrete random variable because it is a categorical variable with two possible values.

d. The amount of rain in City Upper B during April is a continuous random variable because it can take on any value within a certain range.

e. The number of amount fish caught during a fishing tournament is a discrete random variable because it is a countable number.

f. The number of bald eagles in a country is not a random variable because it is a fixed number and not a random sample.

The height of a randomly selected giraffe, the number of points scored during a basketball game, the gender of college students, the amount of rain in City Upper B during April, and the number of fish caught during a fishing tournament are all examples of discrete or continuous random variables, while the number of bald eagles in a country is not a random variable.

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Answer:

The value belonging to the green box is b

Step-by-step explanation:

QP uses the points Q and P

Q is (0,-a)

P is (b,-c)

The distance between the two points can be calculated using the distance formula;

D = √(x2-x1)^2 + (y2-y1)^2

(x1,y1) = (0,-a)

(x2,y2) = (b,-c)

D = √(b-0)^2 + (-c + a)^2

D = √(b)^2 + (-c + a)^2