if 4^2x/2x+y =32 and 9^x+y/3^4y = 81 find the value of x and y

Answer:

3/10

3/10

Step-by-step explanation:

0,1,2,3,4,5,6,7,8,9 are in a box

odd primes are 3 and 5 and 7  ( 1 is neither prime nor composite)

There is a total of 10 numbers

P( odd prime) = number of odd primes / total = 3/10

perfect squares greater than 0 are 1,4,9

P( perfect squares) = number of perfect squares / total = 3/10

Answer: 3/10(the first one)

Step-by-step explanation: So, prefect squares are numbers that are divisible by two numbers multiplied by them selves, 1 is 1 x 1 4 is 2 x 2 and 9 is 3 x 3 so 3 numbers out of 10 from 0 to 9 are perfect squares! Hope this helps, 15402256.

To access the first element of an array of integers called "numbers," you can use the expression:
numbers[0]`
This expression uses the array name "numbers" and the index "0" to access the first element.

To access the last element of "numbers," assuming it contains 10 elements, use the expression:

`numbers[9]`

Here, we use the index "9" since arrays are zero-indexed, meaning the last element in a 10-element array has an index of 9.
To access the first element of the array called numbers, we would use the expression "numbers[0]."

To access the last element of the array, assuming it contains 10 elements, we would use the expression "numbers [9]" since arrays are zero-indexed in most programming languages.

To access the last element of the array regardless of its length, we can use the expression "numbers [numbers.length-1]," which subtracts 1 from the length of the array to access the last element.
To access the last element, regardless of its length, use the expression:

'numbers [numbers. length - 1]'

This expression uses the "length" property of the array to find the total number of elements and subtracts 1 to get the correct index for the last element.

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Answer:

x = 6

y = -1

Step-by-step explanation:

i solved the second equation for 'y' to get 'y = 5 - x'

now i substituted that expression into the first equation for 'y'

2x + 7(5 - x) = 5

2x + 35 - 7x = 5

-5x = -30

x = 6

find 'y':

6 + y = 5

y = 5 - 6

y = -1

y=-1 and x=6

followed by the substitution method

The two triangles are congruent, as the Pythagorean Theorem ensures that the hypotenuse of the two triangles will be equal.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

If two triangles have congruent side lengths, the hypotenuse for the two triangles will also be the same, hence the Pythagorean Theorem ensures the congruence of the two triangles.

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Shown & Given:

The dartboard holds 5 in the maximum space.

Known:

Out of 100, it is know that they will hit 5 more than 50 times.

Possible Answers:

55, 66, or 77.

The most likely one is:

66

The possible dimensions of the rectangle are 6 inches by 8 inches, and the answer is D).

What is the area of rectangle?

The area of a rectangle is calculated by multiplying the length of the rectangle by its width. That is:

Area of rectangle = length × width

A = l × w

where A represents the area of the rectangle, l represents its length, and w represents its width.

Let's assume the rectangle has length "L" and width "W". We know that the area of the rectangle is 48 sq. in., so:

L * W = 48

We also know that the perimeter of the rectangle is 28 in., so:

2L + 2W = 28

L + W = 14

Now we can use these two equations to solve for L and W. One approach is to use substitution:

L = 14 - W (from the second equation)

(14 - W) * W = 48 (substituting for L in the first equation)

14W - W² = 48

W² - 14W + 48 = 0

(W - 6)(W - 8) = 0

So the possible values for W are 6 and 8. If W is 6, then L must be 8:

6 * 8 = 48 (the area checks out)

2(6) + 2(8) = 28 (the perimeter checks out)

Therefore, the possible dimensions of the rectangle are 6 inches by 8 inches, and the answer is D).

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The average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.

a) To determine the likely size of the chance error in the average score of 301 for a cluster sample of 1,000 students, we need additional information about the cluster sampling design.

The cluster sampling method involves dividing the population into clusters, selecting a subset of clusters, and then sampling all individuals within the selected clusters.

The likely size of the chance error depends on the within-cluster variability and the between-cluster variability.

Without information about the variability at each level, we cannot accurately estimate the size of the chance error in this specific scenario.

Therefore, we cannot fill in the blank without more details regarding the cluster sampling design and the variability present in the clusters.

b) If a simple random sample of 1,000 students was tested, we can estimate the likely size of the chance error in the average score of 301. Since a simple random sample implies that each student has an equal chance of being selected, we can use the standard error of the mean formula to estimate the size of the chance error.

The standard error of the mean (SE) is calculated as the standard deviation (SD) divided by the square root of the sample size (n):

SE = SD / √n

Given that the SD is 30 and the sample size (n) is 1,000, we can calculate the standard error:

SE = 30 / √1000 = 30 / 31.62 ≈ 0.95

Therefore, the likely size of the chance error in the average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.

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Answer:

\(5\sqrt{2}\)

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

The type of measure that assigns a value to an observation based on a mathematical derivation of multiple measures is known as composite measures.

A composite measure is a type of measure that assigns a value to an observation based on a mathematical derivation of multiple measures. Composite measures are often used when analyzing complex data structures that have many different dimensions or aspects to them. Composite measures are also known as multi-dimensional measures or aggregated measures.

Composite measures are often used in the social sciences, where researchers need to assess many different dimensions of a phenomenon. For example, a researcher might be interested in measuring the overall quality of life in a particular region. To do this, they might use a composite measure that combines information on things like income, education, health, and social status.

Composite measures can be challenging to develop and interpret because they require researchers to make decisions about which dimensions of a phenomenon are most important and how to combine them into a single value. Nevertheless, composite measures can be extremely useful when analyzing complex data structures because they allow researchers to reduce many different dimensions of a phenomenon into a single value.

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

D

Step-by-step explanation:

First find the slope.

\(Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{5-[-9]}{4-[-3]}=\dfrac{5+9}{4+3}\\\\\\=\dfrac{14}{7}=2\)

Point slope form:

y - y1 = m(x -x1)

y -[-9] = 2 (x - [-3])

y +9 = 2 (x + 3)

The probability that at least one major earthquake (Richter scale 6.0 or above) will occur within the next decade in a certain California county is      1 - \(e^(-\lambda)\) ≈ 0.9502.

It can be found using the Poisson distribution. We can assume that the number of major earthquakes occurring in a decade follows a Poisson distribution with a mean of λ = 3, since we are given that on average three major earthquakes occur in a decade.

The probability of no major earthquake occurring in the next decade is \(e^(-\lambda)\) = \(e^(-3)\) ≈ 0.0498. Therefore, the probability of at least one major earthquake occurring in the next decade is 1 - \(e^(-\lambda)\) ≈ 0.9502.

In other words, there is a high probability of at least one major earthquake occurring in the next decade in this particular California county based on the historical average.

However, it is important to note that earthquake occurrences are inherently unpredictable and can vary significantly from historical averages.

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The demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

The demand function is the function

\(Q=a-bP\)

Here, Q is linear demand curve, a factor which influence the demand, b is slope and P is price.

A concert-promoting company has been selling an average of 175 T-shirts at performances for $23 each. Thus, the total selling price is,

\(P=175\times23\\P=4025\)

The company estimates that for each dollar that the price is lowered, an additional 25 shirts will be sold.  Thus, the total number of

\(23=175-25b\\23-175=-25b\\b=\dfrac{152}{25}\\b=6.08\)

Put the values in, the function for X number of shirt and y price,

\(y=175-6.08x\)

Hence, the demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

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The equation for the linear Function that best fits the given data is:y = 152.82x - 7,620.10 (rounded to two decimal places).

Linear regression is a method used to find the line of best fit, which is the line that comes closest to the data points. To find the line of best fit for a set of data, we can use the formula:

y = mx + b, where m is the slope and b is the y-intercept. To find the equation for the linear function that best fits the given data, we need to use this formula.

The first step in using linear regression is to find the slope of the line of best fit. We can do this using the following formula:m = ((nΣxy) - (ΣxΣy)) / ((nΣx²) - (Σx)²), where n is the number of data points, Σxy is the sum of the product of the x and y values, Σx is the sum of the x values, Σy is the sum of the y values, and Σx² is the sum of the squares of the x values.

Substituting the given values into this formula, we get:m = ((6)(34,983) - (21)(36,923)) / ((6)(91) - (21)²)m = (-6,877) / (-45)m = 152.82 (rounded to two decimal places)The second step is to find the y-intercept. We can do this using the following formula:b = (Σy - (mΣx)) / n

Substituting the given values into this formula, we get:b = (34,983 - (152.82)(21)) / 6b = -7,620.10 (rounded to two decimal places)

Therefore, the equation for the linear function that best fits the given data is:y = 152.82x - 7,620.10 (rounded to two decimal places).

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The Reorder Point (ROP) that would provide a stockout risk of 10 percent during lead time is approximately 106 units.

The Reorder Point (ROP) is the inventory level at which a new order should be placed to replenish stock before it runs out. It is determined by considering the lead time and the desired service level, which represents the desired risk of stockouts during that lead time.

In this case, the demand during lead time is normally distributed with a mean of 100 units and a standard deviation of 2 units. The lead time is also normally distributed with a mean of five days and a standard deviation of 2 days.

To calculate the ROP, we need to determine the safety stock, which is the additional inventory held to mitigate the risk of stockouts during lead time. The safety stock is determined based on the desired service level.

Since the stockout risk during lead time is given as 10 percent, the desired service level is 90 percent (100% - 10%). We can find the corresponding z-score for a 90 percent service level using a standard normal distribution table, which is approximately 1.28.

The formula to calculate the safety stock is: Safety stock = z-score * (standard deviation of demand during lead time)

In this case, the safety stock = 1.28 * 2 = 2.56 units.

Finally, the ROP is calculated as: ROP = Mean demand during lead time + Safety stock = 100 + 2.56 = 102.56 units.

Therefore, to achieve a stockout risk of 10 percent during lead time, the ROP would be approximately 102.56 units.

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The maximum oxygen intake for this level and shuttle is given as 28.3 ml/kg/min in the V O subscript 2 Baseline Max column.

According to the provided multistage fitness test reference chart, the maximum oxygen intake for a person who failed to complete the seventh shuttle run in the fifth level would be 28.3 ml/kg/min.

The table given has three columns

Level, Shuttle, and VO2 Baseline Max.

The entries under the Level column range from 4 to 5.

The entries under the Shuttle column range from 2 to 9.

The entries under the V O subscript 2 Baseline Max column range from 26.8 to 32.

The maximum oxygen intake for a person who failed to complete the seventh shuttle run in the fifth level can be found by locating Level 5 and the seventh shuttle run in the Shuttle column.

Therefore, the correct is option B) 28.3 ml/kg/min.

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Answer:

72.5⁰

19.1 ft

Step-by-step explanation:

Picture a right triangle with hypotenuse of 20 ft (length of the ladder), short leg of 6 ft and the missing leg (x) as the height the ladder reaches on the building.  Use the Pythagorean theorem to find the missing leg first, then the angle:

20² = 6² + x²

x² = 20² - 6² = 400 - 36 = 364

x = √364 = 19.1 ft

angle ∅ of elevation of the ladder :

sin∅ = 19.1/20

∅ = sin⁻1(19.1/20) = 72.5⁰

Answer:

m1:m2 = 6:7

y = 7 (Approx.)

Step-by-step explanation:

Given:

Dividing point (3, y)

Two points (9 , 8) , (-4 , 6)

Find:

Ratio

Value of y

Computation:

X = [(m1)(x2) + (m2)(x1)] / [m1 + m2]

3 = [(m1)(-4) + (m2)(9)] / [m1 + m2]

3m1 + 3m2 = -4m1 + 9m2

7m1 = 6m2

m1 / m2 = 6 / 7

m1:m2 = 6:7

Y = [(m1)(y2) + (m2)(y1)] / [m1 + m2]

y = [(6)(6) + (7)(8)] / [6 + 7]

y = [36 + 56] / 13

y = 92 / 13

y = 7.07

y = 7 (Approx.)

Answer:

side A should be about 44cm

Answer:

.1/2

Step-by-step explanation:

is the same as 20÷40

which gives you 1/2

Answer: A: True explanation

The area of the triangle is A = ( 1/2 ) bc

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the area of the triangle be A

Now , the length of the triangle = b

The base of the triangle is = c

And , Let the Triangle be ΔABC , such that

The area of the triangle = ( 1/2 ) x Length x Base

The area of the triangle = ( 1/2 ) ( bc )

On simplifying , we get

The area of the triangle = ( 1/2 )( bc )

Hence , the area of triangle is ( 1/2 )bc

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Yes, it is reasonable to model this scenario using a Markov Chain.

The state space for this Markov Chain can be defined as the number of papers in the pile in the evening. Let's denote the state space as {0, 1, 2, 3, 4, 5+}, where:

0 represents no papers in the pile

1 represents one paper in the pile

2 represents two papers in the pile

3 represents three papers in the pile

4 represents four papers in the pile

5+ represents five or more papers in the pile

The transition matrix for this Markov Chain can be constructed based on the given probabilities. Since there are six possible states, the transition matrix will be a 6x6 matrix.

Let's define the transition probabilities:

When the pile has 0 papers:

P(0 -> 0) = 2/3 (probability that nobody takes the papers)

P(0 -> 1) = 1/3 (probability that someone takes all the papers)

P(0 -> 5+) = 0 (since the pile can't jump directly to 5+ without any papers)

When the pile has 1 paper:

P(1 -> 0) = 1/3 (probability that someone takes all the papers)

P(1 -> 2) = 2/3 (probability that nobody takes the papers)

P(1 -> 5+) = 0

When the pile has 2 papers:

P(2 -> 0) = 1/3

P(2 -> 3) = 2/3

P(2 -> 5+) = 0

When the pile has 3 papers:

P(3 -> 0) = 1/3

P(3 -> 4) = 2/3

P(3 -> 5+) = 0

When the pile has 4 papers:

P(4 -> 0) = 1/3

P(4 -> 5) = 2/3

P(4 -> 5+) = 0

When the pile has 5+ papers:

P(5+ -> 0) = 1 (Mr. Smith takes all the papers)

Constructing the transition matrix T, we have:

T = | 2/3 1/3 0 0 0 0 |

| 1/3 0 2/3 0 0 0 |

| 1/3 0 0 2/3 0 0 |

| 1/3 0 0 0 2/3 0 |

| 1/3 0 0 0 0 2/3 |

| 0 0 0 0 0 1 |

Each element T[i][j] represents the probability of transitioning from state i to state j.

Therefore, the state space for the Markov Chain is {0, 1, 2, 3, 4, 5+}, and the transition matrix is given by T.

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Answer:

The factor used to create the dilation is 3

Step-by-step explanation:

<3333

Answer:

A

Step-by-step explanation:

First off we can see that there are 46 pencils - and 7 students - so we can divide the two

46/7 is not a whole number, so we need to find a number that can be multiplied by 7, and is right below 46.

If you multiply 7 by 6, you get 42, which is the highest you can get with multiply by 7, which is also below 46.

Now that we know that each student gets 6 pencils, we need to find out how many are left.

We can do 46 (total pencils) minus 42 (pencils given) to get a leftover of 4 pencils, so the answer is A.

Answer: the second one because its a virdacal reflection

Step-by-step explanation: it’s sideways all you have to do is find the equation

Answer:

Step-by-step explanation:

Triangle: bh/2 = 8*9/2 = 36 cm²

bottom square: 8*8 = 64 cm²

total surface area: 36*4 + 64 = 208 cm²

The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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1)

Volume of sphere is 113.1 ft³.

Given radius of sphere 3 ft.

Volume of sphere is 4/3× π ×r³

Substitute the value of radius in the formula of Volume of Sphere,

Volume of Sphere= 4/3×π×r³

                             = 4/3×22/7×3³

                             = 4/3×22/7×27

                             = 113.1 ft³

Hence the given sphere has volume of 113.1 ft³ rounded to the nearest tenth.

2)

Volume of cone is 94.3 yd³

Given diameter of base of cone and height of cone.

Diameter of base = 6 yd

Radius = diameter/2

Radius= 3 yd

Height of cone = 10 yd

Volume of cone = 1/3×π×r²×h

r = radius of base of cone

h = height of cone

Substitute the values of radius and height in the formula,

Volume of cone = 1/3×π×r²×h

                          = 1/3×22/7×3³×10

                          = 660/7

                          = 94.3 yd³

Hence volume of cone rounded to the nearest tenth is 94.3 yd³.

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Answer: -1 1/2

Hope it helps :)