solve the equation z2 z 1 = 0 for z = (x,y) by writing (x,y)(x,y) (x,y) (1,0) = (0,0)

Answer:

it is probably 70° of the triangle

Kaeya need to save at least $600 for a trip. She ha already saved $45. She plan to save $35 per week she will need 16 week to completely save money for her trip.

Kaeya need to save at least $600 for a trip

She has already saved $45.

so she now has to save 600 - 45 = $555

She plan to save $35 per week

So she have to save 555/35 no of weeks to collect the remaining no of money for her trip

= 555/35

= 15.85

≈ 16 weeks

Therefore, she will need 16 week to completely save money for her trip if  she need to save at least $600 for a trip.

Savings are the funds that remain after subtracting a person's consumer spending from their disposable income during a specific time period. Savings, then, is what's left over after all bills and commitments have been fulfilled for an individual or household.

Cash or cash equivalents (such as bank deposits) are used to store savings since they carry no danger of loss but also offer very low returns. Savings can increase through investing, but doing so involves putting money at risk.

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The volume v of the solid obtained by rotating the region bounded by the curves y = x + 1, y = 0, x = 0, x = 5 about the x-axis is 215π/3.

We have to determine the volume v of the solid obtained by rotating the region bounded by the curves about the specified line.

The line is y = x + 1, y = 0, x = 0, x = 5; about the x-axis.

The volume of the solid disk is;

V = [tex]\int\limits^a_b A(x) \, dx[/tex], where A(x) = π(radius)^2

So, V = [tex]\pi\int\limits^{5}_{0} (x+1)^2 \, dx[/tex]

Now simplifying the value of (x + 1)^2 as x^2 + 2x + 1. So

V = [tex]\pi\int\limits^{5}_{0} (x^2+2x+1) \, dx[/tex]

Now integrating

V = [tex]\pi \left(\frac{x^3}{3}+\frac{2x^2}{2}+x\right)^{5}_{0}[/tex]

V = [tex]\pi \left[\left(\frac{5^3}{3}+\frac{2(5)^2}{2}+5\right)-\left(\frac{0^3}{3}+\frac{2(0)^2}{2}+0\right)\right][/tex]

V = [tex]\pi \left[\left(\frac{125}{3}+\frac{50}{2}+5\right)-\left(0+0+0\right)\right][/tex]

V = π(125/3 + 25 + 5)

V = π(125/3 + 30)

V = π(125 + 90)/3

V = 215π/3

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Strategy should be, choosing purse A if number of days is less than 10,if it is more than 10 , he should choose purse B.

If there are 10 days, he can choose any of the purse.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given,

Genie provides friend two purses,

Purse A and Purse B

Graph of Growth in amount to number of days is given.

By the graph,

Intersection point is on 10th day

Till 10th day Amount of purse A is grows more than amount of purse B.

After 10th day amount of purse B starts growing more than amount of purse A

Let no. of days be x

If x < 10, he should choose purse A.

If x > 10 he should choose purse B.

If x = 10, he can choose any purse.

Hence, Friend should choose purse A if number of days is less than 10.

Friend should choose purse B if number of days is greater than 10.

If number of days is 10, he can choose any of the purse.

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Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.

The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.

When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.

Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.

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Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.

The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.

When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.

Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.

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The function sin(x-y)/cosec(x+y)=sin²x-sin²y

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to prove that sin(x-y)/cosec(x+y)=sin²x-sin²y

Using the identity cosecx=1/sinx

We get sin(x-y)/cosec(x+y)=sin(x-y)sin(x+y)

We know sin(x+y)=sinxcosy+cosxsiny

sin(x-y)=sinxcosy-cosxsiny

Now sin(x-y)sin(x+y)=(sinxcosy-cosxsiny)(sinxcosy+cosxsiny)

=sin²xcos²y-cos²xsin²y

=sin²x(1-sin²y)-(1-sin²x)sin²y

=sin²x-sin²xsin²y-sin²y+sin²xsin²y

=sin²x-sin²y

Hence, we proved that sin(x-y)/cosec(x+y)=sin²x-sin²y

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The larger cup can hold 144.51 in³ more water than the smaller cup.

The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:

V = 3.14r²h/3

V = 1.0472r²h.

For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:

V = 1.0472 x 2² x 3

V = 12.57 in³.

For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:

V = 1.0472 x 5² x 6

V = 157.08 in³.

Then the difference is of:

157.08 - 12.57 = 144.51 in³.

The cones are given by the image presented at the end of the answer.

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Let's call the time it takes the fair maiden to sew the border of the tapestry "t". So, her sister can sew the border in t/2 hours.

Working together, they can sew the border in t + t/2 = 1.5t hours.

Since we know the fair maiden can sew the border in 6 hours, we can substitute this into the equation to find t:

6 + 6/2 = 1.5t

Simplifying the right side of the equation:

6 + 3 = 1.5t

9 = 1.5t

Dividing both sides of the equation by 1.5:

t = 6

So the fair maiden can sew the border in 6 hours and her sister can sew the border in 6/2 = 3 hours.

Working together, it would take them 6 + 3 = 9 hours to sew the border of the tapestry.

Answer:

0.0000000045, 0.0000097 and 0.000167 isthe acending order

The geometric mean of two or more numbers is the same as their average. In this case, we have the numbers 48 and 12.

[tex]\dfrac{48+12}{2}=\dfrac{60}{2}=30[/tex]

Hence, the geometric mean of 48 and 12 is 30. Let me know if you have any questions, thanks!

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

This is the symmetric equation of the line that passes through the point P and is parallel to the vector .

What is symmetric equation?

A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:

x = -2 + 0t

y = 1 + 2t

z = 0 - 3t

where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:

d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v

So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:

(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t

x + 2 = -2t

y - 1 = 2t

z + 3 = 3t

Rearranging the above equations, we get:

x = -2 - 2t

y = 2t + 1

z = 3t - 3

Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

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x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

This is the symmetric equation of the line that passes through point P and is parallel to the vector.

What is the symmetric equation?

A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:

x = -2 + 0t

y = 1 + 2t

z = 0 - 3t

where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:

d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v

So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:

(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t

x + 2 = -2t

y - 1 = 2t

z + 3 = 3t

Rearranging the above equations, we get:

x = -2 - 2t

y = 2t + 1

z = 3t - 3

Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

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The polynomial 5s2 + 5s - 30 can be factored as (s + 6)(s - 5). This is done by finding two numbers whose product is -30 and whose sum is 5. They are -6 and 5.

The factored representation of the polynomial 5s2 + 5s - 30 can be found by factoring. First, we need to find two numbers whose product is -30 and whose sum is 5. This can be done by trial and error or by using the Fundamental Theorem of Algebra. When these two numbers are found, the polynomial can be factored as (s + 6)(s - 5). To factor the polynomial, we can use the factor theorem. This states that if a and b are factors of a polynomial, then (x-a) and (x-b) are factors of the polynomial. In our case, a=6 and b=-5. So, the polynomial can be written as (s + 6)(s - 5). We can then use the distributive property to expand the polynomial and verify that it is the same as the original polynomial.

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Answer:

3/10 or 0.3

Step-by-step explanation:

(9/15)(5/10)

= (3/5)(1/2)

  3x1=3 and 5x2=10

= 3/10 or 0.3

m = 4

13=2m+5

-5 -5 subtract 5 from both side

8=2m

8/2=2m/2 divide both side by 2

4=m

There is no value of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by 7.

For d=7, we can see that:

3² - 1 = 8 is divisible by 7, but 5² - 1 = 24 is not divisible by 7.

For larger values of d such as 11, 13, 77, and 1001, we can use a similar approach to see if there are any values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. However, finding an exact value of n for larger values of d may be difficult without using more advanced mathematical methods.

In general, the number of values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by a given integer d will depend on the properties of the numbers 3, 5, and d. For example, if d is a prime number that is not a divisor of either 3 or 5, it is likely that there are only a few values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d.

However, if d is a composite number or a divisor of either 3 or 5, there may be more values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. Whether there are finitely or infinitely many such n will depend on the specific values of 3, 5, and d.

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The value of [tex]\frac{\sqrt{12}}{\sqrt{10}}\cdot \frac{\sqrt{5}}{\sqrt{6}}[/tex] is closest to the whole number 1.

What is multiplication?

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

An expression,

[tex]\frac{\sqrt{12}}{\sqrt{10}}\cdot \frac{\sqrt{5}}{\sqrt{6}}[/tex].

Simplifying,

{(√2 × √6) / (√2 × √5)} × √5/ √6

= 1.

Therefore, the value is 1.

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No, you're incorrect. The tournament lasted from 12:15pm to 4:00pm, which is a duration of 3 hours and 45 minutes. So, the tournament lasted less than 4 hours.

To calculate the duration, you subtract the start time from the end time:

4:00pm - 12:15pm = 3 hours and 45 minutes

Therefore, the tournament lasted for 3 hours and 45 minutes, which is less than 4 hours.

Here's a step-by-step breakdown of the calculation:

Start by calculating the number of whole hours between the start and end time.

4:00pm - 12:15pm = 3 hours

Next, calculate the number of remaining minutes.

4:00pm - 12:15pm = 45 minutes

So the total duration of the tournament was 3 hours and 45 minutes, which is less than 4 hours.

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The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

Substituting the parameters, we have:

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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Answer:12(x+18)

Step-by-step explanation:

As per the FIFO algorithm, there have been a total of 13 page faults.

The FIFO algorithm is a page replacement strategy used in operating systems to manage the allocation of memory frames to pages.

For the given reference string of

=> 1, 2, 3, 4, 5, 3, 4, 1, 6, 7, 8, 7, 8, 9, 7, 8, 9, 5, 4, 5, 4, 2

with four-page frames, we can see that there will be multiple page faults. Initially, all four frames are empty, so there will be four page faults as the first four pages are brought into memory.

Then, when page 5 is needed, the oldest page in memory, page 1, is replaced leading to another page fault.

As the reference string continues, there are several page faults that occur as pages are replaced

By the end of the reference string, there have been a total of 13 page faults.

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The value of x in the triangle is 75°

Triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angles in a triangle is 180°. Also the sim of angles on a straight line is also 189°

One of the triangle theorem is that the exterior angle of a triangle is equal to the sum of the opposite angles.

Therefore with this, we can say that

120= 57+x

collect like terms

120-57 = x

x = 75°

therefore the value of x in the triangle is 75°

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Writing the function P = 35(1.3)^t in the form P(0)e^{kt}, the value of k = log(1.3) and P(0) = 35.

The function is P = 35(1.3)^t

At t = 0, P = 35, so P(0) = 35

P = 35e^{kt} .................Equation 1

P = 35(1.3)^t .................Equation 2

Now dividing the equation, we get

P/P = 35e^{kt}/35(1.3)^t

1 = e^{kt}/(1.3)^t

Multiply by (1.3)^t on both side, we get

1.3^t = e^{kt}

Now taking log of both side, we get

log [1.3^t] = log[e^{kt}]

Using the formula log[m^n] = n logm

t log(1.3)= kt loge

t log(1.3)= kt

Divide by t on both side, we get

k = log(1.3)

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On average, an atom's nucleus has a density of 2.31017 kg/m³.

According to nuclear density, the ratio of mass to volume inside an atom's nucleus determines its density. The nuclear density is highly high because the atomic nucleus makes up the majority of an atom's mass despite being relatively small in relation to the rest of the atom.

On average, an atom's nucleus has a density of 2.31017 kg/m³. Nuclear density is what causes this. It is the same for all nuclei since it is independent of the mass or size of the nucleus.

The nucleus is particularly dense because to its high mass and small size. A penny's worth of material would weigh more than 30 million tons if it had the same density as an atom's nucleus.

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The total surface area painted black is 12.6 sq. feet.

The surface area of a cone with height h and circumference of the base c can be calculated using the formula:

A = πr^2 + πrs,

where,

r = the radius of the base

s = the slant height.

We can find the radius of the base by dividing the circumference by 2π:

r = c / (2π)

  = 8π / (2π)

r = 4.

The slant height can be found using the Pythagorean theorem:

s = √(r² + h²)

  = √(4² + 12²)

  = √(16 + 144)

  = √(160)

s = 12.7279

So the surface area of each cone is:

A = πr² + πrs

= π * 4² + π * 4 * 12.7279

= 3.14 * 4² + 3.14 * 12.7279

= 50.265...

The base and 50% of the lateral surface are painted red, which is a total of 50% + 100% / 2 = 75% of the surface area.

So the total surface area painted black is:

(100% - 75%) * A

= 25% * A

= 25% * 50.265

= 12.566

Rounding to the nearest tenth, the total surface area painted black is 12.6 sq. feet.

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The value of x is 3.

parallel lines are coplanar infinite straight lines that do not intersect at any point.

The lines l and m are the parallel lines.

3x-18+105=180

3x+87=180

Subtract 87 on both sides

3x=180-87

3x=93

Divide both sides by 3

x=31

Hence, the value of x is 3.

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The set S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans  R³

For (x, y, z) ∈ R³, we can find scalars a, b, c for which the equation

(x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4) is true.

We can write above equation (x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4)  as system of equations,

6a - 3b + c = x

7a + 4b - 3c = y

a + 7b + 4c = z

Above system of equations in matrix form as,

[tex]\begin{bmatrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{bmatrix}\begin{bmatrix}a\\b \\c\end{bmatrix}=\begin{bmatrix}x \\y \\z\end{bmatrix}[/tex]

The determinant of coefficient matrix is,

[tex]\left|\begin{matrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{matrix}\right|=360[/tex]

Since the determinant of the coefficient matrix is not zero (it equals 360), the coefficient matrix is invertible.

This means, the system of equations must have solution.

Therefore, S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans  R³

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Answer:

False.

Step-by-step explanation:

8154 = eight thousand one hundred and five four

27 = Two seven.

Now we divide.

8154/27 = 302

Now you get 302 if you divide.

So therefore, its false.

The population of the city in 2023 is 1.6 * 10^6.

The exponential function is a mathematical function that describes the growth of a quantity as a power of another quantity.

In mathematics, the exponential function is used to model a wide range of phenomena including exponential decay, compounding interest, and population growth.

Using the exponential growth model;

P = Poe^rt

P = population at time t

Po = Initial population

r = Population growth rate

t = time

4Po = Poe^rt

If t = 1

4Po/Po = e^r

4 =  e^r

r = ln4

r = 1.4

The population in 2023 is;

P = 88e^1.4 * 7

P = 1.6 * 10^6

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For performing this analysis Brewer can use a method such as a survey for gathering the data.

Brewer would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. He will require a large amount of data to determine this.

This data that he requires can be gathered using the method of survey, and a conclusion can be drawn from the data with the help of statistical analysis and probability analysis.

Surveys can be conducted by email or in an online survey form and can include both open-ended and closed-ended questions to gather both quantitative and qualitative data on the subject.

In this case, the survey can also be conducted by using orthodox methods of gathering data, such as observing people who are going to eat at local restaurants and on campus, although this is not the most ideal method.

Surveys allow the researcher to reach a large number of participants and gather data efficiently and effectively.

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The best way for her to find this data reliably is by using survey's

She can go around campus and survey the other students, and eventually get enough data to find an answer to her question (I also took the test and this answer was right)

have a good day :)

The equation does not hold true, indicating that point C does not lie on line AB.

The equation of line AB can be written in slope intercept form as y = mx + b. The slope of line AB can be found using the equation m = (y2-y1)/(x2-x1). Substituting the coordinates of points A and B into the equation, we get m = (2-4)/(-5-2) = -2/7. The slope-intercept form of this equation is y = -2/7x + b. We can find the value of b by substituting the coordinates of point A into the equation. We get b = 4 + 2/7 = 19/7.

Therefore, the equation of AB in slope-intercept form is y = -2/7x + 19/7. To check whether point C lies on line AB, we must substitute the coordinates of point C into the equation. We get y = -2/7(-1)+19/7 = -2/7 + 19/7 = 17/7. Since the y-coordinate of point C is 8, the equation does not hold true, indicating that point C does not lie on line AB.

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