A national health survey weighed a sample of 490 boys aged 6-11 and found that 67 of them were overweight. They weighed a sample of 530 girls aged 6-11 and found that 66 of them were overweight Conduct a hypothesis test to determine whether the proportion of overweight kids aged 6-11 among boys is greater than the proportion of overweight kids aged 6-11 among girls? Use level of significance 10%.

The expression can be rewritten as a single logarithm as:

ln|sin x| + ln|cot x| = ln(|sin x||cot x|) = ln|cos x|

This is possible because logarithm function is a monotonically increasing function, meaning that if a > b then log(a) > log(b) and log(a*b) = log(a) + log(b) that's why we can add the two logarithms.

The result is simplified by combining the absolute values of the sin and cot functions into a single term. The absolute value is removed since the product of two positive numbers is always positive. The final result is ln|cos x|, which is the natural logarithm of the product of the sine and cotangent of x.

It is important to note that the cotangent function is defined as 1/tan(x) so that cot(x) = 1/tan(x) and cot(x) is only defined for x where sin(x) is not equal to 0.

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The area of the triangle whose base is 4 unit and height is 2 unit is 4 square units .

To calculate the area of a triangle, we multiply the base by the height and divide the result by 2 .

Base of triangle = 4 units

Height of triangle = 2 units

Area of triangle = ( Base of triangle * Height of triangle ) / 2

Area of triangle = ( 4 * 2 ) / 2

Area of triangle = 8 / 2

Area of triangle = 4 square units

Therefore, the area of the triangle is 4 square units .

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The value of the expression (8.4 × 10^-3) × (7 × 10^-2) is 5.88 × 10^-4.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

The expression is given as:

(8.4 × 10^-3) × (7 × 10^-2)

= 0.0084 × 0.07

= 0.000588

= 5.88 × 10^-4

The value of the expression is 5.88 × 10^-4.

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(i) AB = BA but neither A nor B is 0 nor I, and A ‡ B:

Let's consider the following matrices:

A = [[1, 0],

[0, 0]]

B = [[0, 1],

[0, 0]]

To verify the conditions:

AB = [[1, 0],

[0, 0]] * [[0, 1],

[0, 0]] = [[0, 1],

[0, 0]]

BA = [[0, 1],

[0, 0]] * [[1, 0],

[0, 0]] = [[0, 0],

[0, 0]]

As we can see, AB = BA, and neither A nor B is the zero matrix or the identity matrix. Also, A is not equal to B.

(ii) AB + BA:

Let's consider the following matrices:

A = [[1, 0],

[0, 0]]

B = [[0, 1],

[1, 0]]

To verify the condition:

AB + BA = [[1, 0],

[0, 0]] * [[0, 1],

[1, 0]] + [[0, 1],

[1, 0]] * [[1, 0],

[0, 0]]

lua

Copy code

    = [[0, 1],

       [0, 0]] + [[0, 1],

                  [1, 0]]

    = [[0, 2],

       [1, 0]]

(iii) AB = AC but B ‡ C, and the matrix A has no zero entries:

Let's consider the following matrices:

A = [[1, 1],

[0, 1]]

B = [[1, 0],

[0, 1]]

C = [[1, 1],

[0, 2]]

To verify the condition:

AB = [[1, 1],

[0, 1]] * [[1, 0],

[0, 1]] = [[1, 1],

[0, 1]]

AC = [[1, 1],

[0, 1]] * [[1, 1],

[0, 2]] = [[1, 3],

[0, 1]]

As we can see, AB = AC, but B is not equal to C, and the matrix A has no zero entries.

(iv) AB = 0 but neither A nor B is 0:

Let's consider the following matrices:

A = [[1, 0],

[0, 0]]

B = [[0, 1],

[0, 0]]

To verify the condition:

AB = [[1, 0],

[0, 0]] * [[0, 1],

[0, 0]] = [[0, 1],

[0, 0]]

As we can see, AB = 0, and neither A nor B is the zero matrix.

(v) AB = I but neither A nor B is I:

Let's consider the following matrices:

A = [[0, 1],

[1, 0]]

B = [[0, 1],

[1, 0]]

To verify the condition:

AB = [[0, 1],

[1, 0]] * [[0, 1],

[1, 0]] = [[1, 0],

[0, 1]]

As we can see, AB = I, and neither A nor B is the identity matrix.

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Mixed methods research tends to be more complex when compared to quantitative and qualitative research respectively. This is because mixed methods research combines both quantitative and qualitative research methods in a single study.

Quantitative research involves the collection and analysis of numerical data, while qualitative research involves the collection and analysis of non-numerical data, such as words, images, and sounds.

Mixed methods research, on the other hand, involves the collection and analysis of both types of data. This requires the researcher to have a deeper understanding of both quantitative and qualitative research methods, as well as the ability to integrate the two types of data in a meaningful way.

Furthermore, mixed methods research often involves the use of multiple data sources, multiple research methods, and multiple levels of analysis. This adds an additional layer of complexity to the research process.

As a result, mixed methods research tends to be more complex than either quantitative or qualitative research alone.

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The polynomial that represents the difference between the cost of distributing by train and the cost of distributing by trucks can be obtained by subtracting the polynomial representing the cost of distributing by trucks from the polynomial representing the cost of distributing by train.

The resulting polynomial will express the difference in costs as a function of the number of tons of product distributed.

The cost of distributing by train is represented by the polynomial -0.09x² + 34x - 100, where x represents the number of tons of product distributed. Similarly, the cost of distributing by trucks is represented by the polynomial -0.047x² + 22x - 175.

To find the difference between the two costs, we subtract the cost of distributing by trucks from the cost of distributing by train:

(-0.09x² + 34x - 100) - (-0.047x² + 22x - 175)

Simplifying the expression, we obtain:

-0.09x² + 34x - 100 + 0.047x² - 22x + 175

Combining like terms, we have:

(-0.09 + 0.047)x² + (34 - 22)x + (-100 + 175)

Simplifying further, we get:

-0.043x² + 12x + 75

Therefore, the polynomial that represents the difference between the cost of distributing by train and the cost of distributing by trucks is -0.043x² + 12x + 75, where x represents the number of tons of product distributed.

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Answer:

I think it's 41°

Step-by-step explanation:

Because the angle represents Tan, by using the inverse of tan and the formula of Opp/Adj, the answer will be 41.08 Which is 41°

I hope This helps! and make me brainliest as you said, PLEASE..

Answer:

16 feet

Step-by-step explanation:

Area of triangle = 1/2(a x b)

A = 1/2(6.4 x 5)

A = 32/2

A = 16 feet

Answer:

7x + 2y + 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

3 + 8x - 2y - x + 1 + 4y

Step 2: Simplify

Increases in CPI for both Turkey and Iran between 2000/2001 and 2008.The CPI in Turkey rose by Percentage increase = ((434 - CPI in 2000) / CPI in 2000) * 100 ,The CPI in Iran rose by Percentage increase = ((CPI in 2008 - 67) / 67) * 100

The CPI in Turkey rose by x% between 2000 and 2008 (x represents the calculated percentage, rounded to one decimal place).

The CPI in Iran rose by y% between 2000 and 2008 (y represents the calculated percentage, rounded to one decimal place).

To calculate the percentage increase in CPI, we need to compare the CPI values in the respective base years with the CPI values in 2008.

For Turkey:

The CPI in Turkey in 2000 was 434 (base year), and in 2008, it was given as the reference. To calculate the percentage increase, we can use the following formula:

Percentage increase = ((CPI in 2008 - CPI in 2000) / CPI in 2000) * 100

Substituting the alues, we have:

Percentage increase = ((434 - CPI in 2000) / CPI in 2000) * 100

For Iran:

The CPI in Iran in 2001 was 312 (base year), and in 2008, it was given as the reference. To calculate the percentage increase, we can use the same formula as above:

Percentage increase = ((CPI in 2008 - CPI in 2001) / CPI in 2001) * 100

Substituting the values, we have:

Percentage increase = ((CPI in 2008 - 67) / 67) * 100

By calculating these expressions, we can find the specific percentage increases in CPI for both Turkey and Iran between 2000/2001 and 2008

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The area inside the ellipse with the equation  can be computed using Green's \($\frac{x^2}{11^2}+\frac{y^2}{7^2}=1$\) theorem. The parametrization of the ellipse is \($x(t) = 11\cos(t)$\), and the area can be written as \($\iint_D dxdy = \frac{1}{2}\oint_{\partial D}(-ydx+xdy)$\).

By substituting the parametrization into the integral, we can calculate the area. To compute the area using Green's theorem, we first need to find the parametrization of the curve \($\frac{x^{2/3}}{6^{2/3}}+\frac{y^{2/3}}{6^{2/3}}=1$\). The parametrization is given by \($x(t) = 6\cos^3(t)$\). By substituting this parametrization into the integral, we can evaluate the area of the interior.

To find the area inside the ellipse, we can use Green's theorem, which relates a double integral over a region to a line integral around its boundary. By parametrizing the ellipse, we can express the area integral in terms of the parametric equations. Substituting the parametrization \($x(t) = 11\cos(t)$\) into the expression for the area, we can simplify the integral and evaluate it to find the area inside the ellipse.

Similarly, to find the area of the interior of the curve \($\frac{x^{2/3}}{6^{2/3}}+\frac{y^{2/3}}{6^{2/3}}=1$\), we need to find a parametrization for the curve. The parametrization \($x(t) = 6\cos^3(t)$\) represents the curve, and by substituting it into the area integral expression, we can compute the area inside the curve.

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A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

The probability of an event happening is represented as a fraction, with the numerator being the number of favorable outcomes and the denominator being the total number of outcomes.

In this case, if the player throws two darts, the probability that both land in a shaded region is equal to the product of the probabilities of each dart landing in the shaded region.

If the shaded region is a circle with radius r and the darts are randomly thrown onto a larger circle with radius R, then the probability of a dart landing in the shaded region is given by:

P = (Area of shaded region) / (Area of larger circle) = (πr^2) / (πR^2)

So, the probability that both darts land in the shaded region is given by:

P = (πr^2 / πR^2) * (πr^2 / πR^2) = (πr^2 / πR^2)^2

Note that the specific values of r and R would depend on the particular game and the dimensions of the object.

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Step-by-step explanation:

$ 11.58 is your answer....

Answer:

$50,290

Step-by-step explanation:

I was earning $47,000 per year until she received a 7% raise at the start of 2019.

Step 1

We find how much 7% raise is

Hence,

7 % of $47,000

= 7/100 × $47,000

= $3290

What will her new salary be?

Her new salary is calculated as:

Last year's salary + 7% raise

= $47,000 + $3290

= $50,290

Her new salary is $50,290

Answer:

1/4

Step-by-step explanation:

use 2 points from the graph (-4,5) and (0,6) and  put them in the distance equation.

(y2-y1)

----------

(x2-x1)

6-5

-------

0-(-4)

1/4

Answer:

So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.

Step-by-step explanation:

The derivative of the function F(x) = x^2 - 1/x + 1 can be found by using the limit definition of the derivative. The derivative is the rate of change of the function at a given point and it is calculated as:

F'(x) = Lim h=0 (x + h)^2 - 1/(x + h) + 1 - (x^2 - 1/x + 1)/h

Expanding the expression inside the limit and simplifying, we get:

F'(x) = Lim h=0 2xh + h^2 - (1 - hx)/(x + h)^2

Using L'Hopital's Rule, we get:

F'(x) = Lim h=0 2x + 2h - (x - 1)/(x + h)^2

As h approaches 0, the limit becomes:

F'(x) = 2x + 2(0) - (x - 1)/x^2 = 2x - (x - 1)/x^2

So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.

Mallory should adjust her consumption of candy and cookies until the marginal utility per dollar for each good is equal, and she has spent all of her income.

Marginal utility refers to the additional satisfaction or benefit that a person receives from consuming one additional unit of a good or service. It is a concept in economics that is based on the idea that the value of each additional unit of a good or service diminishes as a person consumes more of it.

For example, if you are hungry and you eat a slice of pizza, the first slice of pizza may provide a high level of satisfaction or utility. However, as you continue to eat more slices of pizza, the marginal utility of each additional slice decreases. At some point, you may become full and may even start to feel sick if you continue to eat more pizza.

To determine whether Mallory should consume more cookies, more candy, or leave her consumption unchanged, we need to calculate the marginal utility per dollar for each good. This will tell us which good is providing the most additional utility for each dollar spent.

The marginal utility per dollar for candy is calculated as follows:

MUc/Pc = 12 utils / $1 = 12 utils per dollar

The marginal utility per dollar for cookies is calculated as follows:

MUk/Pk = 6 utils / $0.50 = 12 utils per dollar

Since the marginal utility per dollar for cookies and candy is the same (12 utils per dollar), Mallory should consume either more cookies or more candy, or a combination of both, until the marginal utility per dollar for both goods is equal. This means that the last dollar spent on both goods should provide the same additional utility.

Therefore, to maximize her total utility, Mallory should adjust her consumption of candy and cookies until the marginal utility per dollar for each good is equal, and she has spent all of her income.

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Answer:

A =7.02 m^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2)*h where b1 and b2 are the lengths of the bases

A = 1/2 ( 4.5+6.3) * 1.3

A = 1/2(10.8) * 1.3

A =7.02 m^2

The point in spherical coordinates is (2√17, π/3, π).

a) To convert the point from cylindrical coordinates to Cartesian coordinates, we use the following equations:

x = r * cos(theta)

y = r * sin(theta)

z = z

Given the cylindrical coordinates (r, theta, z) = (3, 4π/3, -4), we can substitute these values into the equations:

x = 3 * cos(4π/3)

y = 3 * sin(4π/3)

z = -4

Evaluating the trigonometric functions, we get:

x = 3 * cos(4π/3) = 3 * (-1/2) = -3/2

y = 3 * sin(4π/3) = 3 * (√3/2) = (3√3)/2

z = -4

Therefore, the point in Cartesian coordinates is (-3/2, (3√3)/2, -4).

b) To convert the point from cylindrical coordinates to spherical coordinates, we use the following equations:

r = √(x^2 + y^2 + z^2)

theta = atan2(y, x)

phi = acos(z / r)

Using the Cartesian coordinates (-3/2, (3√3)/2, -4), we can calculate the spherical coordinates:

r = √((-3/2)^2 + ((3√3)/2)^2 + (-4)^2) = √(9/4 + 27/4 + 16) = √(16 + 36 + 16) = √(68) = 2√17

theta = atan2((3√3)/2, -3/2) = atan2(3√3, -3) = π/3 (since the angle is in the second quadrant)

phi = acos(-4 / (2√17)) = acos(-2√17 / √17) = acos(-2) = π

Therefore, the point in spherical coordinates is (2√17, π/3, π).

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Answer:

-16

Step-by-step explanation:

Follow . PEMDAS

plug the numbers in

4*2 =8 and -4*6=24

add both...

-16.

Step-by-step explanation:

4(2)+(-4)(6)

8-24

-16

hope it helps..

Answer:

160 / 5 = 32 miles

Step-by-step explanation:

Answer: BD = 9 units

Step-by-step explanation:

ABQ and CDQ are congruent triangles. That means their angle measures are the same but their lengths may be proportional.

19.2 / 32 = 0.6

15 * 0.6 = 9

So the length of side BD is 9 units.

Answer:

9 units

Step-by-step explanation:

Answer:

The answer is -6 5/8

Step-by-step explanation: First, convert the fraction of 1/4 in 8ths, which would be 2/8, so we are subraction 3/8+2/8 which =5/8. The only whole number is -6, so your answer is -6 5/8. I know the person above did not give a real answer, so I hope this answer helps you.

Answer:

x = 5

Step-by-step explanation:

\(12x = 70 - 2x\)

\(14x = 70\)

\(x = 5\)

Answer:

Here :))

Step-by-step explanation:

Answer:

C. Add 13 to both sides of the equation.

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, m. Add 13 to both sides of the equation:

m - 13 = 24

m - 13 (+13) = 24 (+13)

m = 24 + 13

m = 37

~

Answer:

(7,7)

Step-by-step explanation:

The maximum point in a graph is where the y value is the highest. On this graph, the point (7,7) has the highest y value of 7 of the entire graph, making it the maximum. Hope this helps!

Answer:

pls mark me brainliest

Step-by-step explanation:

5th one i wont be able to do

Step-by-step explanation:

7x-4=21-4=17

11+x=11+0=11

9x=9×0=0

7x-4=7×0-4=0-4=-4

11+x=11+(-2)=11-2=9

9x=9×(-2)=-18

7x-4=7×(-2)-4=-14-4=-18

11+x=11+5=16

9x=9×5=45

7x-4=7×5-4=35-4=31

Please mark as brainliest !!