defined on the specified domain D. 17. f(x, y) = x2 + y2; D = {(x, y): 0 < x <1,0 < y < 1} -

Answer:

6.1

Step-by-step explanation:

we will name the length in front of the angle , y :

tan(71°)≅2.904= y ÷2

⇒ y=  5.8

and we know that

c = \(\sqrt{2^{2} + y^{2} }\)

then  

c = 6.14

and if we round it to the nearest tenth :

c = 6.1

The percentage increase in the winner's check for the U.S. Open Golf Championship from 1895 to 2019 was approximately 4.33% per year. If the winner's prize continues to increase at the same rate, it would be around $11,655,984.98 in 2044.

To calculate the percentage increase per year in the winner's check, we need to find the annual growth rate. We can use the formula for compound interest to do this. The initial prize in 1895 was $150, and the final prize in 2019 was $2.25 million (or $2,250,000).

First, we find the total number of years between 1895 and 2019: 2019 - 1895 = 124 years.

Next, we calculate the percentage increase using the compound interest formula:

Percentage Increase = ((Final Amount / Initial Amount)^(1 / Number of Years) - 1) * 100

Percentage Increase = ((2,250,000 / 150)^(1 / 124) - 1) * 100 ≈ 4.33%

Now, to find the prize money in 2044, we need to use the compound interest formula again. The number of years from 2019 to 2044 is 25 years.

Final Amount = Initial Amount * (1 + Percentage Increase)^Number of Years

Final Amount = 2,250,000 * (1 + 0.0433)^25 ≈ 11,655,984.98

Thus, if the winner's prize continues to increase at the same rate, it will be approximately $11,655,984.98 in 2044.

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The determinant of the coefficient matrix of the given system is zero, indicating that the system does not have a unique solution.

The determinant of a matrix is a scalar value that provides important information about the matrix. In the given system, the coefficient matrix is:

[-3 0 -2]

[ 9 0 5]

[ 6 0 -12]

To find the determinant, we can use various methods, such as cofactor expansion or row reduction. In this case, we can simplify the matrix by performing row operations. Notice that the second row is three times the first row, and the third row is two times the first row. Therefore, the determinant of the coefficient matrix will be zero because the rows are linearly dependent.

When the determinant of a coefficient matrix is zero, it implies that the system of equations is dependent or inconsistent. Geometrically, the equations represent planes in three-dimensional space. A determinant of zero means that the planes are parallel or coincident, resulting in infinitely many solutions or no solution at all. In this case, the system is dependent, and the equations are not sufficient to determine a unique solution for the variables x, y, and z.

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's' and 't' represent free parameters that can take on any real values.

In the given system of equations:

x1 - x2 + 4x3 = -4

6x1 - 5x2 + 7x3 = -5

3x1 - 39x3 = 45

To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:

Step 1: Write the augmented matrix for the system:

[1 -1 4 | -4]

[6 -5 7 | -5]

[3 0 -39 | 45]

Step 2: Perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 6R1

R3 = R3 - 3R1

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 3 -51 | 57]

Step 3: Perform additional row operations to further simplify the matrix:

R3 = R3 - 3R2

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 0 0 | 0]

Step 4: Write the system of equations corresponding to the row-echelon form:

x1 - x2 + 4x3 = -4

x2 - 17x3 = 19

0 = 0

Step 5: Express the variables in terms of a parameter:

x1 = s

x2 = 19 + 17s

x3 = t

where s and t are parameters.

Therefore, the solution to the system is:

[x1] = [s]

[x2] = [19 + 17s]

[x3] = [t]

In the provided solution format:

[x1] = [s] []

[x2] = [19 + 17s] + s []

[x3] = [t] [__]

Here, 's' and 't' represent free parameters that can take on any real values.

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Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

-2x that's the answer, I think

Step-by-step explanation:

Yung negative 4 I subtract mo sa positive 9x ang sagot ay 5x kase may negative sign yung 4 kaya kailangan mong I subtract then yung 5x I subtract mo ata ulit sa negative 7 ang sagot ay - 2 yan na Explanation ko.

Pero di ako sure dyan but I hope it helps

The probability that an orange weighs more than 17 oz is 0.1587.

The probability that an orange weighs more than 17 oz is 0.1587. This value can be calculated using the Z-score formula, which is used to calculate the probability of an event occurring. The formula is as follows:

Z = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

In this case, the Z-score is (17 - 14) / 2 or 1.5. We can find the probability using the Z-score table, which gives us 0.1587, the probability that an orange weighs more than 17 oz.

The Z-score formula is useful for determining the probability of an event occurring when the data follows a normal distribution. Knowing the mean and standard deviation, we can calculate the likelihood of a certain outcome occurring. In this case, the probability that an orange weighs more than 17 oz is 0.1587.

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Answer:

1×42

2×21

3×14

6×7

Answer (assuming that the equation can be written in point-slope form):

\(y-8 = -5(x+\frac{1}{2} )\)

Step-by-step explanation:

Use the point-slope formula, \(y-y_1 = m (x-x_1)\) , to write the equation of the line in point-slope form. Substitute values for the \(m\), \(x_1\), and \(y_1\) in the formula.

Since \(m\) represents the slope, substitute -5 in its place. Since \(x_1\) and \(y_1\) represent the x and y values of one point the line intersects, substitute the x and y values of (-0.5, 8) into the formula as well. Remember that we can convert -0.5 to a fraction: \(-\frac{1}{2}\). So, substitute \(-\frac{1}{2}\) for \(x_1\) and 8 for \(y_1\). This gives the following answer and equation:

\(y-8 = -5(x+\frac{1}{2} )\)    

The interest rate your friend is charging you for the $20,000 loan is 20% per year.

The simple interest is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that;

The Principal P = $20,000

Accrued amount A = $40,000

Elapsed time t = 5 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate r:

\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)

Converting r decimal to R a percentage

Rate R = 0.2 × 100%

Rate r = 20% per year

Therefore, the interest rate is 20% per year.

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2) Ans;

\(\frac{( - 19) - ( - 7)}{5 - ( - 9) - 10} \\ \\ \frac{ - 19 + 7}{5 + 9 - 10} \\ \\ \frac{ - 12}{4} = - 3\)

4) Ans;

\(( - 3)^{3} + \frac{12}{4 - 2} \\ \\ - 27 + \frac{12}{2} \\ \\ - 27 + 6 = - 21

\)

I hope I helped you^_^

We need 32 rows in the truth table that would use to evaluate a logical statement in five variables.

It is TRUE.

Now, According to the question:

A truth table provides a method for mapping out the possible truth values in an expression and to determine their outcomes. The table includes a column for each variable in the expression and a row for each possible combination of truth values.

A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q).

The formula to calculate the number of rows is equal to 2ⁿ, where n is the number of basic statement letters involved.

Number of rows = 2ⁿ

If the number of variables in a truth table is 5, then the number of rows = 2⁵

2⁵ = 2×2× 2× 2× 2

= 32

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Answer:

They'll need to see 12 movies together before they pay the same amount.

Let the number of movies be x

Based on the question given, the equation for Jaycie will be:

= 27 + (6 × x)

= 27 + 6x

The equation for Clarie will be:

= 8.25 × x

= 8.25x

Then, the equation to solve the question will be:

27 + 6x = 8.25x

Collect like terms

27 = 8.25x - 6x

2.25x = 27

x = 27/2.25

x = 12

They will see 12 movies together.

Answer:

3 cups per batch

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

What is 9 divided by 3.... 3 ok so that is your answer. Hope this helped you!! Give brainliest..

Answer:

9x + 6

Step-by-step explanation:

5x + ( x + 6 ) + 3x

= 5x + 3x + x + 6

= 9x + 6

Answer:

5.99 or 6 dollars

Step-by-step explanation:

100 divided by 16.67

The probability that the sweet is a cherry sweet is given as follows:

p = 4/11.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probability that it is an apple sweet is 2/11, and the ratio of apple sweets to pear sweets is 2: 5, hence the probability of a pear sweet is given as follows:

p = 5/11.

Then the probability that the sweet is a cherry sweet is given as follows:

p = 1 - (5/11 + 2/11)

p = 1 - 7/11

p = 11/11 - 7/11.

p = 4/11.

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Answer:

k = 1\(\frac{1}{4}\)  or 5/4

Step-by-step explanation:

5k = 5 + k

4k = 5

k = 5/4

The length of Raj's piece of string is 12x units.

To determine the length of Raj's piece of string, we need to find Kiki's third-longest piece.

Looking at the line plot or list of lengths provided, we can identify the third-longest length of Kiki's pieces.

Let's assume Kiki's third-longest piece has a length of x units.

According to the problem, Raj's piece of string is 12 times as long as Kiki's third-longest piece.

Therefore, the length of Raj's piece of string would be 12 × x units.

We can only express it as 12x units, where x represents the length of Kiki's third-longest piece.

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Answer:

37

Step-by-step explanation:

To find the average, you need to add all the numbers in the set and divide that value by the total amount of numbers there are,

We already know that the average of the set of temperatures is 40,

Since there are 5 different days with temperatures, multiply 40 by 5,

40 × 5

= 200

200 is what all the temperatures should equal once they are added up,

Now add 40, 39, 44, and 40 together,

40 + 39 + 44 + 40

= 163

Now subtract 163 from 200,

200 - 163

= 37

Therefore the temperature that was recorded on the fifth day was 37f.

Answer:

Stefan originally spent $ 110 on the bike and helmet, with which he is making a profit of $ 33.

Step-by-step explanation:

Since Stefan sells Jin a bicycle for $ 125 and a helmet for $ 18, and the total cost for Jin is 130% of what Stefan spent originally to buy the bike and helmet, to determine how much did Stefan spend originally and how much money did he make by selling the bicycle and helmet to Jin, the following calculations must be performed:

130 = 125 + 18

100 = X

100 x (125 + 18) / 130 = X

100 x 143/130 = X

14,300 / 130 = X

110 = X

143 - 110 = 33

Therefore, Stefan originally spent $ 110 on the bike and helmet, with which he is making a profit of $ 33.

Answer:

there's nothing there

Step-by-step explanation:

i don't know what the question is here

The probability that exactly two customers in the sample will default on their payments is 0.9997.

This is a binomial probability problem with n = 5 trials and p = 3% = 0.03 probability of success (default) on each trial.

The probability of exactly two defaults can be calculated using the binomial probability formula:

P(x = r) = nCr * p^r  * q^n-r

where q = 1 - p = 1 - 0.03 = 0.97

P(x = 2) = (5C0 × 0.03⁰ × 0.97⁵⁻⁰) + (5C1 × 0.03¹ × 0.97⁵⁻¹) + (5C2 × 0.03² × 0.97⁵⁻²)

P(x = 2) = 0.9997

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Answer:

0.05, 6x23

Step-by-step explanation:

The correct representation of the given inequality is 6x≥4(2x-1) is x≤2

An inequality is a mathematical statement with an inequality sign and  two mathematical expressions are both sides of the inequality sign. The inequality signs are ≤, ≥, > or <.

Given inequality is 6x≥4(2x-1)

So, 6x≥8x-4

Subtract 6x from both sides ,we get

6x-6x≥8x-4-6x

0≥8x-6x-4

0≥2x-4

Adding 4 on both sides, we get

0+4≥2x-4+4

4≥2x

Multiplying both sides by 1/2, we get

(1/2)×4≥(1/2)×2x

2≥x

x≤2

Hence the correct representation is x≤2.

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Answer:

D: an irregular quadrilateral​

Step-by-step explanation:

def not a rhombus : A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal.

def not a pentagon, cause it's got only 4 sides.

def not a regular quadrilateral which must have 4 equal sides, and 4 equal angles, and its diagonals must bisect each other. Square is the only quadrilateral that satisfies all these conditions.

only D: An irregular quadrilateral is a quadrilateral with four sides that are not regular or the same.

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Step-by-step explanation:

\( \frac{67}{100} \times x = 119.2 \\ x = \frac{11920}{67} = 117.9 = 178\)

Step-by-step explanation:

that's it b is for brings

b compliment is for doesn't bring

To determine which pair of events are independent, we need to check if the probability of their intersection is equal to the product of their individual probabilities. If the two probabilities are equal, the events are independent; otherwise, they are dependent.

Using the probabilities given, we can calculate the probabilities of the individual events:

P(a) = 0.4

P(b) = 0.3

P(c) = 0.2

P(d) = 0.1

We can also calculate the probabilities of the intersections of the events:

P(a ∩ b) = 0.1

P(a ∩ c) = 0.1

P(a ∩ d) = 0.1

P(b ∩ c) = 0.05

P(b ∩ d) = 0.05

P(c ∩ d) = 0.01

Now, we can check the pairs of events for independence:

1. Events a and b:

P(a) * P(b) = 0.4 * 0.3 = 0.12

P(a ∩ b) = 0.1

Since P(a ∩ b) is not equal to P(a) * P(b), events a and b are dependent.

2. Events a and c:

P(a) * P(c) = 0.4 * 0.2 = 0.08

P(a ∩ c) = 0.1

Since P(a ∩ c) is greater than P(a) * P(c), events a and c are dependent.

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3. Events a and d:

P(a) * P(d) = 0.4 * 0.1 = 0.04

P(a ∩ d) = 0.1

Since P(a ∩ d) is greater than P(a) * P(d), events a and d are dependent.

4. Events b and c:

P(b) * P(c) = 0.3 * 0.2 = 0.06

P(b ∩ c) = 0.05

Since P(b ∩ c) is not equal to P(b) * P(c), events b and c are dependent.

5. Events b and d:

P(b) * P(d) = 0.3 * 0.1 = 0.03

P(b ∩ d) = 0.05

Since P(b ∩ d) is not equal to P(b) * P(d), events b and d are dependent.

6. Events c and d:

P(c) * P(d) = 0.2 * 0.1 = 0.02

P(c ∩ d) = 0.01

Since P(c ∩ d) is not equal to P(c) * P(d), events c and d are dependent.

Therefore, none of the pairs of events are independent.

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Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct