what is the length of AC?

The number of vegetable plates can be made = 120

We know that a combination is nothing but a way of selecting items from a collection. In combination the order of selection does not matter.

We know that a formula for a combination is,

^nC_r = n! / r!(n - r)!

where,  ^nC_r = number of combinations

n = total number of items in the collection

r = number of choosing items from the collection

and n! = n × (n - 1) × (n - 2) × . . . × 1

Here, we have n = 10 and r = 3

Using combination formula,  the total number of plates made:

^10_C_3

= 10! / (3! × (10 - 3)!)

= 10! / (3! × 7!)

= (10 × 9 × 8 × 7!) /( 3! ×7!)

= (10 × 9 × 8) / (3 × 2 × 1)

= (90 × 8) / 6

= 720/6

= 120

Therefore, 120 vegetable plates maybe made

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Answer:

m∠CBD=24

Step-by-step explanation:

The angle measure of m∠CBD = 24°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

AD= 61,

CD= 61,

and m∠ABC= 48°.

The diagram is given in the attached image.

Converse of Angle Bisector Theorem's

If a triangle's interior point is equally spaced from its two sides, that point will be on the angle bisector created by the two line segments.

That means,

angle measure of m∠CBD = 48/2 = 24°.

Therefore,  m∠CBD = 24°.

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The Excel feature that has been updated to let you simultaneously view as many as six statistics about a cell selected in the work area is called the "Quick Analysis Tool."

This tool was first introduced in Excel 2013 and has since been updated in later versions of Excel.

To use the Quick Analysis Tool, simply select the cell or range of cells that you want to analyze. Once selected, a small icon will appear in the bottom right corner of the selection.

Clicking on this icon will open up a menu of options, including formatting, charts, totals, tables, and sparklines.

The "totals" option is where you can find the six statistics about the selected cell or range of cells. These statistics include average, count, numerical count, maximum, minimum, and sum.

By selecting this option, Excel will automatically calculate these statistics and display them in a small table next to your selection.

This feature is particularly useful for quickly analyzing data without having to manually calculate each statistic. It also allows you to easily compare multiple cells or ranges of cells by displaying their statistics side by side.

In addition to the Quick Analysis Tool, Excel also has several other features for analyzing data, including PivotTables and PivotCharts. These tools allow you to summarize and visualize large amounts of data in a variety of ways.

Overall, the Quick Analysis Tool is a powerful and convenient feature that can save time and improve productivity when working with data in Excel.

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Answer:

4/6 = 2/3

Step-by-step explanation:

I know this because she ordered 5/6 of a sack of brown rice and 1/6 of a sack of white rice. Then, I did 5/6 - 1/6 = 4/6, which is also equal to 2/3.

Flying with the wind, a small plane flew 338 mi in 2 h. flying against the wind, the plane could fly only 312 mi in the same amount of time. So, the rate of the plane in calm air is 162.5 mph, and the rate of the wind is 6.5 mph.

Let's use variables to represent the unknowns in this problem:

- Let p represent the rate of the plane in calm air (in miles per hour).
- Let w represent the rate of the wind (in miles per hour).

When the plane is flying with the wind, the combined speed (plane + wind) is (p + w) mph. It flies 338 miles in 2 hours, so we have:

1. (p + w) * 2 = 338

When flying against the wind, the net speed (plane - wind) is (p - w) mph. It flies 312 miles in 2 hours, so we have:

2. (p - w) * 2 = 312

Now, we'll solve the two equations simultaneously. First, divide both sides of each equation by 2:

1. p + w = 169
2. p - w = 156

Next, add the two equations together to eliminate the w variable:

(p + w) + (p - w) = 169 + 156
2p = 325

Now, divide by 2 to find the rate of the plane in calm air:

p = 325 / 2
p = 162.5 mph

Now that we have the rate of the plane, we can find the rate of the wind by substituting the value of p back into either equation 1 or 2. Let's use equation 1:

162.5 + w = 169

Subtract 162.5 from both sides to find w:

w = 169 - 162.5
w = 6.5 mph

So, the rate of the plane in calm air is 162.5 mph, and the rate of the wind is 6.5 mph.

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The probability that a total of four tries will be necessary for both of you to get through is 0.1728.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

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Thus, we can include the conclusion that the length of segment I is a Constructible number.

Given that Let R2 denote the Euclidean plane. Let I ⊂ R2 be the segment connecting the points (0,0) and (1,0). A number a ∈Ris called constructible if a segment of length |a| can be constructed by ruler and We know that segment I connects the points (0, 0) and (1, 0). Therefore, the length of segment I is 1 unit .Constructible Numbers:

A constructible number is a number that can be obtained by starting with a length of 1 and repeatedly using the operations of addition, subtraction, multiplication, division, and the extraction of square roots.What we know is that the length of the segment is 1 unit and we can only use the ruler and compass to construct a number that can be created by using the four basic arithmetic operations and the extraction of square roots. Therefore, the length of segment I is constructible.What we have learned is that a number is said to be constructible if a segment of its length can be constructed by using a ruler and compass only. Since the length of segment I is 1 unit, it is possible to construct it using a ruler and compass only. Therefore, the number 1 is a constructible number. Thus, we can include the conclusion that the length of segment I is a constructible number.

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Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.

As given in the question,

Perimeter of the rectangular area encloses for fencing = 3200 yards

Let 'x' and 'y' be the length and width of the rectangle.

2( x + y ) = 3200

⇒ x + y = 3200/2

⇒y = 1600 - x

Area of rectangular field 'A' = xy

⇒ A = x ( 1600 - x )

⇒ A = 1600x - x²

Differentiate both the side of the equation we get,

dA/dx = 1600 - 2x

For Maximum Area dA/dx = 0

1600 -2x =0

⇒ 2x = 1600

⇒ x= 800 yards

Now, y = 1600 - 800

          = 800 yards

Maximum area = (800) (800)

                        = 640,000 square yards

Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.

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Answer:

hairy ball sack

Step-by-step explanation:

Answer:

[4  -11   1   7   l  -17]

[0  1   -1   -7  l  0]

[3  0  -2   2   l  12]

[4   1   5   3   l   7]

Step-by-step explanation:

This is Finite Math, I got this hehe :)

To find the answer, first you need to understand what R means.

It stands for "row". So R1 means "Row 1".

So: -3R1 + R3 means that you need to multiply -3 by all of the numbers in row 1 and then add all of the numbers in row 3

[0   3   1   -1   l  6]

[0  1   -1   -7  l  0]

[3  0  -2   2   l  12]

[4  1    5   3   l   7]

Then use ^^THAT^^ and apply the next set of instructions.

-4R1 + R4 means that you multiply -4 by all of the numbers in row 1 and then add all of the numbers in row 4:

[4  -11    1   7   l  -17]

[0  1   -1   -7  l  0]

[3  0  -2   2   l  12]

[4   1   5   3   l   7]

By solving a system of equations we will find that the two numbers are 156 and 44.

Let's define x and y as our two numbers. First, we know that the sum is equal to 200, so we can write:

x + y = 200

And we know that the difference is 112, then we can write:

x - y = 112

So we have a system of equations:

x + y = 200

x - y = 112

To solve this we can isolate one of the variables in one of the equations, isolating x on the second one we get:

x = 112 + y

Replacing that on the first equation we get:

112 + y + y = 200

112 + 2y = 200

2y = 200 - 112

2y = 88

y = 88/2

y = 44

Now we can use the equation:

x = 112 + y

x = 112 + 44 = 156

The two numbers are 156 and 44.

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Answer:

2iiej

Step-by-step explanation:

1kejes191828wusnalao

Answer:

The number must also be a multiple of 4,2,1

Step-by-step explanation:

To find the missing number, we need to find the factors of 8

8 = 4*2*1

The number must also be a multiple of 4,2,1

Answer:

1, 2 and 4 (in increasing order)

Step-by-step explanation:

Your number must also be a multiple of 1 (which every single number is), 2 (every even number is a multiple of 8, since 8 is even, it's a multiple of 2), and 4.

Let's think about the factors of 8, or numbers that you can divide evenly into 8 and get a natural number.

These are:

1

2

4

So these three are the numbers that your number's a multiple of.

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Answer: A 18 1/5 - 22 2/5 - 40 1/5

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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Answer:

no money left (0$), but no extra payment either.

Step-by-step explanation:

x = price per kg of crab

y = price per prawn

if he orders the first list, we know $12 will be left on his card, that means the order costs 100 - 12 = $88.

1×x + 4×y = 88

for the second list we know he would have to pay $28 extra, in addition to the $100 in the card.

so, 100 + 28 = $128

2×x + 2×y = 128

x + y = 64

now we have a system of 2 equations with 2 variables. we use one equation to express one variable by the other, and that we use then in the second equation to solve it.

x = 64 - y

(64 - y) + 4y = 88

64 + 3y = 88

3y = 24

y = 24/3 = $8

=>

x = 64 - y = 64 - 8 = $56

so, if he orders 1.5 kg of crab and 2 prawns we get a cost

1.5×56 + 2×8 = 84 + 16 = $100

so, he will not have any money left in the card, but he will not have to pay anything extra either.

The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

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Answer:

Step-by-step explanation:

Dilation about the origin multiplies each coordinate value by the dilation factor.

For dilation factor k, the new coordinates are ...

  (x, y) ⇒ (kx, ky)

Your dilation factor is 3, so the transformation is ...

  (x, y) ⇒ (3x, 3y)

  A(-1, 4) ⇒ A'(-3, 12)

  B(3, 2) ⇒ B'(9, 6)

  C(-2, -2) ⇒ C'(-6, -6)

Answer:

Step-by-step explanation:

The given equation is not instandard form. First standard form is neccesary.

The result is 3x + 108 = 12y which is equal to 12y = 3x + 108

The slope is represented in this form as m (Y = mx + b)

(with b as the initial value)

Therefore, 3 is the slope.

To find its perpendicular slope.

To find it's perpendicular, know that it is the negative reciprocal.

FInally, the slope perpendicular to the line whose equation is 3x - 12y = -108 is \(\frac{1}{-3\\}\)

We know that the equation of the line is in the form \(y=-\frac{2}{3}x+b\). To find b, we can use the fact that (6,-5) lies on the line, meaning that both sides of the equation are equal when x=6 and y=-5.

\(-5=-\frac{2}{3}(6)+b\\-5=-4+b\\b=-1\)

Hence, the equation of the line is \(y=-\frac{2}{3}x-1\), and its graph looks something like follows.

Step by Step Explanation:

Answer:

Step-by-step explanation:

Answer:

simplify?

x^5 Y^5 Z^5

Step-by-step explanation:

Answer: i think its A

Step-by-step explanation: hope this helped

The elements of the complement of set K (K') are {1, 4, 6, 8, 9}.

The elements of the complement of set K (K'), we need to determine all the elements in the universal set that are not in set K.

The universal set, denoted as U, is defined as the set of positive integers less than 10.

The elements in the universal set U are {1, 2, 3, 4, 5, 6, 7, 8, 9}.

Set K is defined as the set of prime numbers.

The prime numbers less than 10 are {2, 3, 5, 7}.

To find the complement of set K (K'), we need to identify all the elements in the universal set U that are not in set K.

K' = U - K

Substituting the values, we have:

K' = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}

Performing the set difference operation, we remove the elements in set K from the universal set U:

K' = {1, 4, 6, 8, 9}

These are the positive integers less than 10 that are not prime numbers.

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Answer:

The order of the matrix D^T × (BE) is 2 × 4

Step-by-step explanation:

In the multiplication of matrix, the number of columns in the first matrix must be equal to the number of rows of the second matrix. The resulting matrix from the product will have the same number of rows as the first matrix and the same number of column as the second matrix. For example, given Matrix A of order (m × n) and Matrix Z of order ( n × k), the product of the two matrices will give a matrix ( say Y) of order (m × k).

AZ = Y

(m x n)(n x k) = (m x k)

Now, From the question,

The order of Matrix B is 4 × 5,

the order of the matrix D is 4 × 2

and the order of the matrix E is 5 × 4.

To determine the order of the matrix D^T × (BE)

First, will find the order of (BE)

Order of BE = (4 × 5) (5 × 4)

Order of BE = (4 × 4)

Hence, the order of matrix (BE) is 4 × 4.

Now, we will determine the order of matrix D^T

D^T means the transpose of matrix D.

The transpose of a matrix is defined as a new matrix whose rows are the columns of the original matrix and the columns of the new matrix are the rows of the original matrix. This means given Matrix A of order (m × n), the transpose of Matrix A (A^T) will have an order of (n × m).

The order of the matrix D is 4 × 2

Hence, the order of the transpose of matrix D (D^T) will be 2 × 4

Now, the order of the matrix D^T × (BE) will be

Order of the matrix D^T × (BE) = (2 × 4) × (4 × 4)

Order of the matrix D^T × (BE) = 2 × 4

Hence, the order of the matrix D^T × (BE) is 2 × 4.

Answer:

D. -1

Step-by-step explanation:

\( \frac{1}{3} (6x - 15) = \frac{1}{2} (10x - 4)\)

Begin by distributing the term outside of the parentheses to each term inside.

\(2x - 5 = 5x - 2\)

Now subtract 2x from each side to isolate the variable.

\( - 5 = 3x - 2\)

Add 2 to each side.

\( - 3 = 3x\)

Divide by 3 to solve for x.

\( - 1 = x\)

The values of the inverse functions are f-¹ (3) = -1 and f-¹ (8) = 7

From the question, we have the following parameters that can be used in our computation:

x   f(x)

-1   3

1     6

2    5

3    7

7   8

Using the above as a guide, we have the following:

f-¹ (x) means that we calculate the value of x from the table when y = x in the function notation

So, we have

f-¹ (3) = -1 and f-¹ (8) = 7

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(a) If there are 4 candidate,  the smallest number of votes that a plurality candidate could have is 33.

(b) If there are 8 candidate,  the smallest number of votes that a plurality candidate could have is 17.

The smallest number of votes that a plurality candidate could have is calculated as follows;

(a) If there are 4 candidate, the number of votes for each candidate;

= 129 / 4

= 32.25

The least number of votes for the plurality candidate = 33

(b) If there are 8 candidate, the number of votes for each candidate;

= 129 / 8

= 16.125

The least number of votes for the plurality candidate = 17

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The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

To find the tangential and normal components of the acceleration vector, we need the velocity vector and the curvature of the path. The tangential component of acceleration (at) represents the change in speed or direction along the path. It is given by the derivative of the velocity vector with respect to time. The normal component of acceleration (an) represents the change in direction perpendicular to the path. It is given by the curvature of the path multiplied by the square of the speed.

In mathematical terms:

at = dV/dt

an = (V^2) / R

where:

V is the velocity vector

t is time

R is the radius of curvature of the path.

The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

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