how many different rational numbers between $\dfrac{1}{1000}$ and $1000$ can be written either as a power of $2$ or as a power of $3$, where the exponent is a (possibly negative) integer?

Answer:

All systems have 2 real solutions.

Step-by-step explanation:

there are X and Y unknowns.

If the sample correlation coefficient of x and y is r = 0, x and y are independent. Thus, option C is the answer.

The coefficient of correlation measures the statistical relationship between two variables. It is denoted by "r". The value lies between - 1 and + 1.

When r is 1 it means there is a perfect positive correlation. When r is -1 it means there is a perfect negative correlation. When r is 0 it means there is no correlation.

Thus, the two variables are independent. There is no linear relationship between the two variables. Change in one variable has no impact on another variable.

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a = 18°

we have opposite angles =>

=> 6a + 11 = 2a + 83

6a - 2a = 83 - 11

4a = 72

a = 72 : 4

a = 18°

Answer:

All the given measurements of the right triangles are correct

Step-by-step explanation:

Check the three diagram and determine the three sides of the right triangle that correspond to Pythagoras triple.

For the first triangle:

12² + 5² should be equal to  13²

144 + 25  =  13²

169 = 13²

Thus, 5, 12 and 13 corresponds to three sides of right triangle.

For second diagram;

24² + 7² should be equal to 25²

576 + 49 = 25²

625 = 25²

Thus, 7, 24 and 25 corresponds to three sides of right triangle.

For third diagram;

3² + 4² should be equal to 5²

9 + 16 = 5²

25 = 5²

Thus, 3, 4 and 5 corresponds to three sides of right triangle.

Answer:

The 90% confidence interval, C.I = (0.693, 0.7307)

Step-by-step explanation:

Catalysts 1 and catalyst 2 have the following statistical data;

Catalyst 1

The number of batches in the sample, n₁ = 12

The average yield by the 12 batches of catalyst 1, \(\overline x_1\) = 85

The sample standard deviation, s₁ = 4

Catalyst 2

The number of batches in the sample, n₂ = 10

The average yield, \(\overline x_2\) = 81

The standard deviation, s₂ = 5

F-test = s₂²/s₁² = 5²/4² = 1.5625

The degrees of freedom, df = n₁ + n₂ - 2

∴ df = 12 + 10 - 2 = 20

The critical-t at 90% confidence level = 1.725

The F-test < The critical-t, we pool the variance

The 90% confidence interval with the assumption of equal variance is given as follows;

\(The \ 90\% \ confidence \ interval= \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times (s_p) \times \sqrt{\dfrac{1^{2}}{n_{1}}+\dfrac{1^{2}}{n_{2}}}\)

\(s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}\)

Therefore;

\(s_p\) = √((12 - 1)×4² + (10 - 1)×5²)/(12 + 10 - 2)) ≈ 4.48

Therefore, we get;

\(C.I. = \left (85- 81 \right )\pm 1.725 \times 4.48 \times \sqrt{\dfrac{1}{12}+\dfrac{1}{10}}\)

The 90% confidence interval, C.I = 0.693 < μ₁ - μ₂ < 7.307 = (0.693, 0.7307).

For each x in the interval 0 ≤ x ≤ 5, the shell at that point has

• radius = 5 - x, which is the distance from x to x = 5

• height = x ² + 2

• thickness = dx

and hence contributes a volume of 2π (5 - x) (x ² + 2) dx.

Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:

\(\displaystyle 2\pi \int_0^5 (5-x)(x^2+2)\,\mathrm dx=2\pi\int_0^5 (10-2x+5x^2-x^3)\,\mathrm dx=\boxed{\frac{925\pi}6}\)

Answer: your slope would be -0.375

Sothe non-parametric equation of the plane with the given normal vector and passing through the point (5, -6, 0) is: -5x + 6y + 6z + 61 = 0

In order to find the non-parametric equation of the plane, we need the normal vector and a point on the plane. The normal vector is given as (-5, 6, 6), and a point on the plane is (5, -6, 0).

The non-parametric equation of a plane is given by:

Ax + By + Cz = D

where (A, B, C) is the normal vector and (x, y, z) is a point on the plane. We can substitute the values into the equation to find the values of A, B, C, and D.

(-5)(x - 5) + (6)(y + 6) + (6)(z - 0) = 0

Expanding this equation:

-5x + 25 + 6y + 36 + 6z = 0

-5x + 6y + 6z + 61 = 0

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Answer:

The chain is around 11 feet in length.

Step-by-step explanation:

Area of a circle = π × r²

380 ft² = π × r²

121 ft² = r²

11 ft = r

Answer:

112

Step-by-step explanation:

3y^2 + 7y + 2

if y = 5, then 3(5^2) + 7(5) + 2

= 3(25) + 35 + 2

= 75 + 37

= 112

The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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The correct option is A. The unique solution is x1 = -1 and x2 = -1/2.

Given, the system of equation is,-4x1 + 8x2 = 122x1 - 4x2 = -6

We can write the given system of equation in the form of AX = B where, A is the coefficient matrix, X is the variable matrix and B is the constant matrix.

Then, A = [−4 8 2 −4], X = [x1x2] and B = [12−6]

Now, we will find the determinant of A.  |A| = -4(-4) - 8(2)

|A| = 8

Hence, |A| ≠ 0.Since, the determinant of A is not equal to zero, we can say that the system of equation has a unique solution.Using inverse matrix, we can find the solution of the given system of equation. The solution of the given system of equation is,x1 = -1, x2 = -1/2

Therefore, the correct option is A. The unique solution is x1 = -1 and x2 = -1/2.

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Taking the profit for every bucket of popcorn and every ticket sold, the linear inequality that represents their goal is 6x + 8y ≥ 5000, as further explained below.

A linear inequality is an inequality in which two expressions or values are not equal and are connected by an inequality symbol such as >, <, ≥, or ≤. A linear inequality can have one or more variables, and it defines a range of values that satisfy the inequality.

Now, to solve the question, let x be the number of popcorn buckets sold and y be the number of movie tickets sold. The profit from selling x popcorn buckets would be 6x and the profit from selling y movie tickets would be 8y. To represent the total amount of profits required to reach the goal of $5,000, we can use the following inequality:

profit from popcorn + profit from tickets ≥ goal

6x + 8y ≥ 5000

This means that the total profits from selling popcorn and movie tickets combined should be at least $5,000. Note that this inequality assumes that there are no other costs or expenses associated with selling the popcorn and tickets.

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Answer:

A

Step-by-step explanation:

\(8y - 3 > 10y + 21 \\ - 24 > 2y \\ y< - 12\)

$5 for 1 shirt

y = cost

x = number be shirts

10y = 2x

5y = x

Answer:i need to know what youre trying to find first

Step-by-step explanation:

The Total surface of triangular prism  is 112 inches.

To calculate the surface area of a triangular prism, you need the measurements of the base and the height of the triangular faces, as well as the length of the prism.

The given measurements are;

Base ; 5 inches and  4 inches

height is 8 inches

Length of the prism is 2 inches.

To find the total surface area, we sum up the areas of all the faces:

Total surface area = area of triangular  faces + area of rectangular faces + area of lateral faces.

area of triangular faces = 5 inches × 4 inches = 20 inches.

area of the two faces = 20 ×2 =40

Area rectangular faces = 5 inches × 8 inches/ 2 = 40 inches.

Area of lateral faces = 8 inches ×2 = 16 square inches

for the two lateral faces is 16 × 2 = 32 square inches.

Total surface area = 40 square inches + 40 inches + 32 square inches = 112 square inches.

The Total surface of triangular prism  is 112 inches.

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Answer:

W'(1,0), X'(2,2), and Y'(4,-3)

Explanation:

In the graph, the coordinates of the vertex of triangle WXY are:

• W(-5, 2)

• X(-4, 4)

• Y(-2, -1)

After a translation by the rule below:

The coordinates of the image W'X'Y' are calculated below:

The coordinates of the image are W'(1,0), X'(2,2), and Y'(4,-3).

(-5 , 6) 5x + y = 10

                             ⤸

y = 5.6 * 5x = 10

I. move the expression to the right

y = 10 + 5.6 * 5x

II. reorder the terms

The property of real numbers illustrated by the equation -(2t - 11) = 11 - 2t is the commutative property of addition.

Given that an expression we need to determine which property does it follow,

The commutative property of addition states that the order of numbers can be changed without affecting the result when adding them together. In other words, for any real numbers a and b, the sum of a and b is the same regardless of the order in which they are added.

In the given equation, we can observe that the terms on both sides of the equation involve addition and subtraction. By rearranging the terms, we can rewrite the equation as 11 - 2t = -(2t - 11).

This shows that the terms 11 and 2t have been swapped in their positions without altering the equality of the equation. This swap of terms demonstrates the commutative property of addition.

So, the commutative property of addition is illustrated in the equation -(2t - 11) = 11 - 2t by the interchangeability of the terms without affecting the solution or outcome.

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Answer:

1/20

Step-by-step explanation:

3/10 - 1/4

First, convert the fractions to a common denominator:

3/10 *2/2 = 6/20

1/4 * 5/5 = 5/20

Now put them back into the equation and solve:

6/20 - 5/20 = 1/20

Another way to do this:

3/10 - 1/4

Convert the fractions into decimals:

3/10 = 0.3

1/4 = 0.25

substitute back into the equation and solve:

0.3 - 0.25 = 0.05

convert back into fractions:

0.05 = 1/20

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Distance between two points can be determined by distance formula. So, the distance between the points (11 , -19) and (-13 , -19) is equals to the 2 units .

Distance is equal to the square root of the sum of the difference in coordinates values the square of. The Distance Formula is a derived from the Pythagorean Theorem. Distance formula for determining the distance between two points is written as,

\(d= \sqrt{(x_2-x_1)²+(y_2-y_1)²}\)

where, d --> distance

( x₁ , x₂) --> coordinates of first point

(y₁ , y₂) --> coordinates of second point

We have, coordinates of two points as (11 , -19) and (-13 , -19). So, x₁ = 11, x₂ = -13 , y₁ = -19, y₂ = -19

The distance between the points (11 , -19) and (-13 , -19),

\(d = \sqrt{( -13 -(-11))² + ( -19 -(-19))²} \\ \)

=> d = √(- 13 + 11)² + ( -19 + 19)²

=> d = √4 + 0

=> d = 2 units

Hence, required distance is 2 units.

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Answer:

c (2,0) and (-2,0) I hope ot helps

Using the area of a rectangle, the total floor area to be tiled = area of the dinning room + area of the lounge floor = 32 m²

The area of rectangle = (length)(width).

Total floor area to be tiled = area of the dinning room + area of the lounge floor

Total floor area to be tiled = (4)(5) + (3)(4)

Total floor area to be tiled = 20 + 12

Total floor area to be tiled = 32 m²

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If sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².

As given in the question,

In triangle ABC,

AB = Perpendicular side

BC = Base

AC = Hypotenuse

sinx = 0.6

AB = 12

sinx = AB / AC

⇒0.6 = 12/AC

⇒AC = 12 /0.6

⇒ AC = 20

Using Pythagoras theorem,

AB² + BC² = AC²

⇒ BC² = 20² -12²

⇒BC = 16

Area of ΔABC = (1/2)× AB×BC

                       = (1/2)×12×16

                       = 96 units²

Therefore, if sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².

The complete question is:

If sin x = 0.6 and AB = 12 as shown in the diagram , what is the area of ΔABC ?

a. 96 units²

b. 28.8 units²

c. 31.2 units²

d. 34.6 units²

e. 42.3 units²

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Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

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

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