From a population with a variance of 529, a sample of 289 items is selected. What is the margin of error at 95% confidence? a. 1.353 b. 2.652 c. 17 d. 23

The determinant of the given matrix [ 1 0 3 2 4 6 5 -1 3] is 0. Determinants of matrices are numerical values that can be calculated through different methods like expansion and elimination.

For the given matrix C, we can use the elimination method to find the determinant as follows:

Step 1: Subtract row 1 multiplied by the value in row 2 column 1 (i.e., 2) from row 2 and row 3 in order to get a zero in row 2 column 1 and row 3 column 1. This gives us the matrix:

[1 0 3
0 4 0
0 -1 -12]

Step 2: Multiply row 3 by -1 and add it to row 2 in order to get a zero in row 2 column 3. This gives us the matrix:

[1 0 3
0 4 -12
0 -1 -12]

Step 3: Subtract row 1 multiplied by the value in row 3 column 1 (i.e., 0) from row 3 in order to get a zero in row 3 column 1. This gives us the matrix:

[1 0 3
0 4 -12
0 -1 0]

Step 4: Multiply row 3 by -1 and add it to row 2 in order to get a zero in row 2 column 2. This gives us the matrix:

[1 0 3
0 4 0
0 -1 0]

Step 5: The determinant of the matrix C is calculated as:

det(C) = 1(4(0)-0(-1)) - 0(0(0)-0(-1)) + 3(0(-1)-4(0))
= 0 - 0 + 0
= 0
Therefore, the determinant of the given matrix [ 1 0 3 2 4 6 5 -1 3] is 0. It means that the matrix is singular, i.e., it does not have an inverse.

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Curl(F(x, y, z)) = (5x^4 - 3y^2)k; curl(F (-1,4,2)) = -191k; This vector field is not irrotational.

To find the curl of the vector field F = (x^5, y^3, z^2),

we need to calculate the cross-product of the del operator and F

(where del = gradient).

Therefore, curl(F(x, y, z))= ∇ × F(x, y, z)=| i        j       k |  ∂/∂x  ∂/∂y  ∂/∂z|x^5   y^3    z^2|

= (0 - 0)i - (0 - 0)j + (5x^4 - 3y^2)k

= (5x^4 - 3y^2)k

The curl at the point (-1,4,2) is, curl(F (-1,4,2))

= (5(-1)^4 - 3(4)^2)k= -191k

We can check if this vector field is irrotational or not by calculating the curl of F again, but this time using the partial derivative theorem instead of the del operator.

If curl(F) = 0, then the vector field is irrotational.

curl(F(x, y, z)) = (2z - 0)i + (0 - 5y^2)j + (3y^2 - 4x^4)k

Since curl(F) is not equal to 0, this vector field is not irrotational.

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Answer:

542

Step-by-step explanation:

-3, 2, 7, 12

-3 + x = 2 x = 5

2 + x = 7 x = 5

7 + x = 12 x = 5

If you want to find the 3rd term in the sequence and you start with the first number, then you do this:

-3 + (2 * 5) = -3 + (10) = 7

The same goes for the 110th term:

-3 + (109 * 5) = -3 + (545) = 542

The formula to find the nth term is:

f(n) = n(0) + (n-1) * 5

Suppose n(0) = -3 then

f(110) = -3 + {(110-1) * 5}

f(110) = -3 + {(109) * 5}

f(110) = -3 + (545) = 542

You can simplyfy f(n) = n(0) + (n-1) * 5

f(n) = n(0) + (n-1) * 5

f(n) = n(0) + (5n-5)

f(n) = n(0) + 5n - 5

f(110) = -3 + (5 * 110) - 5

f(110) = -3 -5 + (550)

f(110) = - 8 + 550

f(110) = 542

Answer:

Domain: -3<=x<4

Range:-1<=y<-3

(can I get brainliest please)

Answer:

range: [-3,-1) domain: [4,-3); idrk know the second one srry.

Step-by-step explanation:

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's define some terms:

Let's find the domain:

   For log(x),

           ⇒ the only inputs that are accepted are nonnegative and nonzero

               ⇒ therefore: Domain is (0, ∞)

Now let's find out the range:

    The biggest constraint of the output is log(x)

         ⇒ however log(x) has a range of (-∞,∞)

             ⇒ therefore the entire equation's range is

                      (-∞,∞)

Answer:

Hope that helps!

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Answer:

its B

Step-by-step explanation:

hopefully this helps.

Answer:  2/3

Step-by-step explanation:

Since the line is going through the origin it slope will use the formula  y/x = k where k is the slope. So you can use any point on the number line to determine the slope.

use the point (3,2)  using the formula y/x = k   divide the y by x.

k = 2/3

Answer: 0.67

Step-by-step explanation:

Look at the points (3,2), (6,4), and (9,6)

Answer:

I guess that you want to model the elevation of Lake Sam Rayburn.

During the summer, it is 165 ft above the sea level (the sea level is our position 0ft).

If it does not rain, the elevation of the lake decreases by 0.5ft each week.

So if we assume that there is no rain, we can write the elevation fo the lake as a linear relationship with slope equal to -0.5ft and y-intercept equal to 165ft.

L(w) = 165ft - 0.5ft*w

Where w is the number of weeks without rain, if we have 0 weeks without rain, then the level of the lake remains constant at 165ft above sea level,

L(0) = 165ft - 0.

Answer:

5:3

Step-by-step explanation:

So, ratio of girls to boys is 20:12 . You can reduce this ratio, the same way you reduce a fraction. Both numbers have a common fact of 4 , so divide both by 4 . In simplest form, this ratio is 5:3 .

To obtain the vertex of the parabola, we are going to re-write the given parabola equation into its vertex form.

The vertex form of a parabola is given as:

Thus, by completing the square of the given parabola equation, we have:

Comapring this equation with the vertex form of a parabola;

Hence, the vertex of the parabola is:

The focus of a parabola is at the point;

The parabola obtained opens up. An alternative equation for a parabola that opens up is:

We must find the value of a that makes the equation true at any point (x,y).

Suppose x=1;

Hence, the focus of the parabola is:

The directrix is:

Answer: angle A is none of those

Step-by-step explanation:

the sum of all angles in a triangle = 180

one of the triangles is 90

we can form an equation:

90 + (x+69) + (x+39) = 180

90 + 2x + 108 = 180

198 + 2x = 180

2x = 180 - 198

2x = -18

x = - 9

angle A = x+39

substitute x = -9

angle A = -9 + 39 = 30

so angle A is none of those

The future value of an annuity of $500 per year for 12 years, with an interest rate of 5%, can be calculated using the future value of an ordinary annuity formula. The future value is approximately $7,005.53.

To calculate the future value of an annuity, we can use the formula:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the annuity,

P is the annual payment,

r is the interest rate per compounding period,

n is the number of compounding periods.

In this case, the annual payment is $500, the interest rate is 5% (or 0.05), and the number of years is 12. As the interest is compounded annually, the number of compounding periods is the same as the number of years.

Plugging the values into the formula:

FV = $500 * [(1 + 0.05)^12 - 1] / 0.05

= $500 * [1.05^12 - 1] / 0.05

≈ $500 * (1.795856 - 1) / 0.05

≈ $500 * 0.795856 / 0.05

≈ $399.928 / 0.05

≈ $7,998.56 / 100

≈ $7,005.53

Therefore, the future value of the annuity of $500 per year for 12 years, with a 5% interest rate, is approximately $7,005.53.

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Answer:

(x+2)(x+1)(4x+1)(4x-3)

Step-by-step explanation:

(4x² + 5x)² - 5(4x² +5x) - 6

= (4x² + 5x)² - 6(4x² +5x) + 1(4x² +5x) -6

= (4x² + 5x)(4x² +5x -6) +1 (4x² +5x -6)

= (4x²+5x-6)(4x²+5x+1)

= (4x² + 8x - 3x - 6)(4x² + 4x + x +1)

= (4x(x + 2) - 3(x + 2))(4x(x+1) +1(x+1))

= (x+2)(4x-3)(x+1)(4x+1)

answer is 3/4 i hope this helps

Answer:

here, suppose the missing length be X

hy ^2 = (one side square )^2 +(Other side square)^2

29^2= X^2 + 21^2

841 = X^2 + 441

X^2 = 841 - 441

X^2 = 400

X = 20 .........taking square root both side

the value is missing side length is 20 .

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

5.2v - (30 ÷ 6) + 12

9) We need to determine which part of the expression represents a​ quotient?

We know that when we divide one rational expression by another, the result would be termed as 'quotient'.

Here, it is clear that:

(30 ÷ 6) represents the expression part for a quotient.

When we divide 30 by 6, we get the result 5 which would be the quotient of the expression 30 ÷ 6.

10. Which part of the expression represents a product of two​ factors?

We know that when a multiply two number, we get the product. The multiplying numbers are the factors of the product.

For example, 4 × 9 = 36 therefore, 4 and 9 are the factors of 36.

In our case, 5.2v represents a product of two​ factors 5.2 and v. In other words, 5.2 and v are the factors of the product of 5.2v.

Answer:

D

Step-by-step explanation :

Answer:

an=101+13(n−1)

an+1=an+13, a1=101

Answer:

Perimetro = 4 cm + 7 cm + 12 cm

                = 23 cm

Step-by-step explanation:

Step-by-step explanation:

92p = 98

divide both sides by 92

p = 98/92

=49/46

=1.0652173913

The area of the region that lies inside the cardioid (r=1−cosθ) and outside the circle (r=1) is (3π-4)/4.

To find the area of the region that lies inside the cardioid and outside the circle, we need to integrate the area element over the appropriate range of angles.

The equation of the circle is r=1, so its area is π(1)^2=π.

The equation of the cardioid is r=1−cosθ. The cardioid and the circle intersect when 1−cosθ=1, or cosθ=0, which occurs when θ=π/2 and θ=3π/2.

The area of the region inside the cardioid and outside the circle is given by:

A = ∫[0,2π] ∫[0,1−cosθ] r dr dθ

Using the substitution r=1−cosθ, we have:

A = ∫[0,2π] ∫[0, sinθ] (1−cosθ) r dr dθ

= ∫[0,2π] ∫[0, sinθ] (1−cosθ) (1−cosθ) d(\(r^2\)/2) dθ

= ∫[0,2π] ∫[0, sinθ] (1−cosθ)^2/2 dθ dr

= ∫[0,2π] [-cosθ+(1/2)sinθ+(1/4)sin(2θ)] from 0 to π/2 + ∫[π/2,3π/2] [(3/4)-(1/2)cosθ-(1/4)sinθ] dθ + ∫[3π/2,2π] [(1/4)sin(2θ)-(1/2)cosθ-(3/4)] dθ

= (3π-4)/4

Therefore, the area of the region that lies inside the cardioid and outside the circle is (3π-4)/4.

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The rectangular equation formed by eliminating the parameter is d. y = x^3 - 15x^2 + 75x - 125. This equation describes a cubic function with a vertical shift of -125 and zeros at x = 0, x = 5, and x = 10.

To eliminate the parameter in the equation y = t^3 and x = t + 5, we need to solve for t in terms of x. We can do this by rearranging the x equation to get t = x - 5. We can then substitute this expression for t into the y equation to get y = (x-5)^3, which simplifies to y = x^3 - 15x^2 + 75x - 125. Therefore, the rectangular equation formed by eliminating the parameter is d. y = x^3 - 15x^2 + 75x - 125. This equation describes a cubic function with a vertical shift of -125 and zeros at x = 0, x = 5, and x = 10. The answer to this question is d, and it is important to note that this equation was obtained by eliminating the parameter t using the x equation to solve for t in terms of x and substituting that expression into the y equation.

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The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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Answer:

Yes

Step-by-step explanation:

Yes, when you purchase a life insurance policy you will be charged a certain rate but this can change if there are sudden changes in your health or as you get older. In some cases, you may purchase an insurance policy for a certain amount of years in which the rate is guaranteed to remain the same during that time. This type of policy's rate depends on the period of time you choose to be insured but once the time period is over the rate can increase a lot depending on your age and health at that time.

To convert kilometers to miles, you will need to multiply the number of kilometers by a conversion factor.

Converting kilometers to miles is a common unit conversion that can be done easily with a simple formula. Kilometers (km) and miles (mi) are both units of length or distance, but they are used in different countries and contexts.

Identify the number of kilometers you want to convert. For example, let's say you have 10 kilometers. Use the conversion factor of 0.621371 to convert kilometers to miles. This factor represents the number of miles in one kilometer. Multiply the number of kilometers by the conversion factor. In this example, 10 km * 0.621371 = 6.21371 miles.

Round the result to the desired number of decimal places, if necessary. So, to summarize, the formula for converting kilometers to miles is: miles = kilometers * 0.621371. With this formula, you can easily convert any number of kilometers to miles, whether you're working with large distances or small ones.

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About twice as likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers.A 16 or 17-year-old driver has a higher risk of dying every mile they drive compared to operating a vehicle alone. increases by 44% when one of the passengers is under the age of 21. while transporting two passengers who are under 21 in doubles.

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16-year-old driver to crash with two passengers as opposed to with no passengers is about twice as likely.

The complete question is,

According to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?

just as likely

about twice as likely

about three times more likely

about four times more likely

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Answer:

a)  and e)

Step-by-step explanation:

7 * 1/2 = 3.5

3.5 / 2 = 1.75

? = 1.75

a) 2 * 1.75 = 7 * 1/2 (correct!)

b) 7 * 1/2 * 1.75 = 2 (wrong!)

c) 2 * 7 * 1/2 = 1.75 (wrong!)

d) 1.75 * 7 * 1/2 = 2 (wrong! this is the b) backwards)

e) 1.75 * 2 = 7 * 1/2 (correct! this is the a) backwards)

Answer:

5.9

Step-by-step explanation:

Answer:

it is 5.9

Step-by-step explanation:

We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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The required slope (m) is -12 when the points given are (-3, 4) and (-3, -8).

In mathematics, a line's slope, also known as its gradient, is a mathematical expression of the line's steep slopes and orientation.

A line's steeper can be identified by looking at its slope.

The slope was calculated mathematically as "rise over run" (change in y divided by change in x).

So, the slope formula is:
m = y2 - y1/x2 - x1

Now, substitute the values and calculate the slope as follows:

m = y2 - y1/x2 - x1

m = -8 -4/-3+3

m = -12/0

m = -12

Therefore, the required slope (m) is -12 when the points given are (-3, 4) and (-3, -8).

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