Solve for x 3:21=x:16

The value of the given sine function is √3/2, so the correct option is 2nd.

Given that an function Sin (-5π/3) we need to evaluate the expression,

To evaluate the trigonometric function sine of the angle (-5π/3), we can use the periodicity of the sine function.

Since the sine function has a period of 2, the sine of any given angle is equal to the sine of that angle plus or minus any multiple of 2.

To find an equal angle inside the main range (between -π and π), we can add 2 to the angle (-5/3).

Once adding 2:

(-5π/3) + 2π = (-5π/3) + (6π/3) = π/3

Now we can evaluate the sine of π/3, which is a commonly known angle. The sine of π/3 is √3/2.

Therefore, sin(-5π/3) = sin(π/3) = √3/2.

Hence the correct option is √3/2

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Interpreting the scatterplot, it is found that the correct option is:

Springside weakens the correlation shown in the scatterplot.

Springside weakens the correlation shown in the scatterplot.

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The number of the cups of honey has she collected will be 52 and 2/3 cups.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Gerrie collects honey from a few beehives.

She scoops out the honey with a small jar that holds 1/3 of a cup.

Over the last two weeks, Gerrie has filled this jar 158 times.

1 small jar = 1/3 cup

But we have done this for 158 times. Then we have

158 small jar = 158 x 1/3 cups

158 small jar = 52 and 2/3 cups

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$67.50

Step-by-step explanation:

The amount of each of three checks is 67.5, 135 and 202.5 respectively

Given:

let

amount of smallest check = c

Amount of larger check = 2 × c

= 2c

Amount of largest check = (c + 2c)

= 3c

Amount revived = 50

Total deposit = 355

Total amount in the account = amount of smallest check + Amount of larger check + Amount of largest check

50 + 355 = c + 2c + 3x

405 = 6c

c = 405 ÷ 6

c = 67.5

Therefore,

amount of smallest check = c

= 67.5

Amount of larger check = 2 × c

= 2c

= 2(67.5)

= 135

Amount of largest check = (c + 2c)

= 3c

= 3(67.5)

= 202.5

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(C) 31 is the population size, n, when the sum of the squares of the differences between each value and the population mean is 806 and if the population standard deviation is 26.

The spread of a data distribution is measured by standard deviation. The average distance between each data point and the mean is measured. Whether the data are being treated as a population unto itself or as a sample of a broader population will affect the standard deviation calculation algorithm.

In the event that the data are viewed as a population in and of itself, we divide by the number of data points and If there are less data points in the sample than there are in the total population, we divide by one fewer than the total number of data points.

We require mean to be the point estimate of the unknown population mean in order to build a confidence interval for a single unknown population mean when the population standard deviation is known. The solution can be seen on the attached image.

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Question correction:

The sum of the squares of the differences between each value and the population mean is 806. If the population standard deviation is 26, the population size n is:

Group of answer choices

A. 32

B. 30

C. 31

D. 26

Mathematical operations are used to represent the relationship between variables

The results of the operations are 8 and 254

The operation is given as:

a * b = 4a^2 - b

(a) 2 * 8

This means that:

a = 2

b = 8

So, we have:

2 * 8 = 4 * 2^2 - 8

Evaluate the exponents

2 * 8 = 4 * 4 - 8

Multiply

2 * 8 = 16 - 8

Subtract

2 * 8 = 8

(b) 2 * 8 * 2

In (a), we have:

2 * 8 = 8

So, the operation becomes

2 * 8 * 2 = 8 * 2

This means that:

a = 8

b = 2

So, we have:

8 * 2 = 4 * 8^2 - 2

Evaluate the exponents

8 * 2 = 4 * 64 - 2

Multiply

8 * 2 = 256 - 2

Subtract

8 * 2 = 254

Hence, the results of the operations are 8 and 254

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Answer:

\((x - 3)^{2} + (y + 4)^{2} = 4\)

Step-by-step explanation:

Center is at (3, -4)  and the radius is 2

\((x - 3)^{2} + (y + 4)^{2} = 4\)

Answer:

The first thing you need to do is open the bracket

4(b-6)+19

=4b -24 +19

collect like terms

4b=24 -19

4b =5

divide both sides by 4

4b/4=5/4

b=5/4 or 1.25

The answer is (b) 5.

The Euclidean distance between two points in a Cartesian coordinate system can be calculated using the distance formula:

The Euclidean distance formula, as its name suggests, gives the distance between two points (or) the straight line distance. Let us assume that

(x1,y1) (x2,y2) are two points in a two-dimensional plane. Here is the Euclidean distance formula.

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the Euclidean distance between location A(x-coordinate 9, y-coordinate 16) and location B (x-coordinate 6, y-coordinate 12).

Given the coordinates of location A (9, 16) and location B (6, 12), we can substitute the values into the distance formula:

Distance = √((6 - 9)² + (12 - 16)²)

= √((-3)² + (-4)²)

= √(9 + 16)

= √25

= 5

Therefore, the Euclidean distance between location A and location B is 5.

The correct answer is b. 5.

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Answer:

Y=3X+3

Step-by-step explanation:

Y=mx+b

m=3

when x=2 and y=3 b=3

To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.

The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.

For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.

The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.

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The importance and advantage of using graph representation when organizing your data are that it makes data presentable, summarizing, better way of comparison of data.

An organized diagram or pictorial representation of the relationship between values or data is referred to as a graph. it is a a diagram that depicts a variable's variation in comparison to that of one or more other variables, such as a series of points, lines, line segments, curves, or areas.

The following are the three advantages of graphs:

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Answer:

fg(×)=22fx

Step-by-step explanation:

I hope it help

1.  A consequence of committing a Type I error is falsely rejecting a true null hypothesis.

2. A consequence of committing a Type II error is failing to reject a false null hypothesis.

a. A consequence of committing a Type I error is falsely rejecting a true null hypothesis.

In the given context, it would mean concluding that the AAA proportion of driver error causing fatal accidents is inaccurate (rejecting the null hypothesis) when it is actually accurate.

b. A consequence of committing a Type II error is failing to reject a false null hypothesis. In the given context, it would mean failing to conclude that the AAA proportion of driver error causing fatal accidents is inaccurate (failing to reject the null hypothesis) when it is actually inaccurate.

To determine if the AAA proportion is accurate, a hypothesis test can be conducted using the given sample data. The null hypothesis (H0) would state that the AAA proportion is accurate (54%), while the alternative hypothesis (Ha) would state that the AAA proportion is inaccurate.

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By using simultaneous linear equation the results obtained are-

Number of small boxes = 6 and number of large boxes = 3

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Let the number of small boxes purchased be x, and the number of large boxes purchased be y.

Each small box has 200 nails and each large box has 600 nails.

Total number of nails = 3000
\(200x +600y = 3000\\200(x+ 3y)=3000\\x + 3y = \frac{3000}{200}\\x + 3y = 15\) .............. (1)

The contractor bought twice as many small boxes as large boxes

So,

\(x = 2y\\x - 2y = 0............(2)\)

The equations are solved graphically. The graph has been attached.

From the graph, it can be said that the two lines meet at (6, 3)

So x = 6, y = 3

Number of small boxes = 6 and number of large boxes = 3

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Answer:

5.3

Step-by-step explanation:

Stare at the triangle for a bit. And try to add another one sharing the unmarked angle. You end up with an equilateral triangle. It means \(\sqrt7\) is half the hypotenuse, At this point,

For each pair of fractions, following fraction is larger

a) 5/6 > 5/7

b) 2/9 < 5/9

c) 3/4 < 9/10

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given,

Fraction:

a) 5/6 or 5/7

Taking LCM,

LCM = 42

5/6 × 7/7

35/42

5/7 × 6/6

30/42

5/6 > 5/7

b) 2/9 or 5/9

They have same denominator,

So,

2/9 < 5/9

c) 3/4 or 9/10

Taking LCM:

LCM = 20

3/4 ×5/5

15/20

9/10 × 2

18/20

3/4 < 9/10

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Answer:

Y=.833x-2

Step-by-step explanation:

correct y intercept and rise over run  gives you the slope.

Answer:

x=1y

Step-by-step explanation:

Answer:

.018 Kg/cm^3

Step-by-step explanation:

\(p = m \div v \\ \)

Density (P) is equal to the mass (9.9g) divided by volume (.55cm^3)

\( = 9.9 \div .55\)

= 18g/cm^3

=.018kg/cm^3

The density with given mass and volume is 18 g/cm³.

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

Given that, a gold earring has a volume of 0.55 cubic centimeters and a mass of 9.9 grams.

We know that, density =Mass/Volume

Density = 9.9/0.55

= 18 g/cm³

Therefore, the density with given mass and volume is 18 g/cm³.

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4.84 HP is the amount of work energy used.

Given info,

A helicopter is lifting an 800-pound unit at a rate of 200 feet per minute.

1 horsepower = 550 foot-pounds per second

⇒ 800 x 200 = 160,000 foot-pounds per minute

                      = 160,000/60 foot pounds per second.

Horsepower = 160,000/60 * 550 = 428/33

                                                       = 4.848 HP

Therefore, the horsepower of work energy used is 4.84 HP

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1. Inside the spherical shell (r < R), the potential is given by V(r, θ) = ∑[(2l + 1)σ₀/(2ε₀\(R^{2l+1}\))] * (\(r^l\)) * \(P_l\)(cosθ).

2. Outside the spherical shell (r > R), the potential is given by V(r, θ) = ∑[σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^l\)) * \(P_l\)(cosθ).

3. The electric field inside the shell is E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(r^l\)) * \(P_l\)(cosθ) * ∇r

4. The outside the shell is E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^{l+2}\)) * \(P_l\)(cosθ) * ∇r.

To solve the given problem, let's go through the steps:

1. Boundary Conditions:

Inside the sphere (r < R), the potential must be finite, so we set the coefficients \(A_l\) = 0 for all l.

Outside the sphere (r > R), the potential must match the potential of a point charge at the center of the sphere, so we set \(B_l\) = σ₀ / (2l + 1) for all l.

2. Maxwell's Equation and Boundary Conditions:

Using the equation ∇²V = -ρ/ε₀, where ε₀ is the permittivity of free space, and ρ is the charge density, we have ∇²V = 0 outside the sphere (r > R) and ∇²V = -σ₀/ε₀ inside the sphere (r < R).

Applying the appropriate boundary conditions, we find that \(B_l\) = (2l + 1)σ₀/(2ε₀\(R^{2l+1}\)) for all l.

3. Potentials:

Using the expressions for the constants obtained in step 2, the potentials inside and outside the sphere are:

Inside (r < R): V(r, θ) = ∑[(2l + 1)σ₀/(2ε₀\(R^{2l+1}\))] * (\(r^l\)) * \(P_l\)(cosθ)

Outside (r > R): V(r, θ) = ∑[σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^l\)) * \(P_l\)(cosθ)

4. Electric Fields:

The electric field can be obtained from the potential using the relation E = -∇V.

Outside the sphere (r > R): E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^{l+2}\)) * \(P_l\)(cosθ) * ∇r

Inside the sphere (r < R): E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(r^l\)) * \(P_l\)(cosθ) * ∇r

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Answer:

Here, the given expression is,

62 % of 45

  ( 1 % =  )

  ( Dividing 62 by 100 )

Hence, Option A and C are correct

Answer:

\(23^{o}\) and \(23^{o}\)

Step-by-step explanation:

An isosceles triangle has two of its sides and angles to be equal. Let each of the unknown equal angles be represented by x. Since one of its angles measures  134°, then;

x + x +  134° = \(180^{o}\)

2x + 134° = \(180^{o}\)

2x = \(180^{o}\) - 134°

    = 46

x = \(\frac{46}{2}\)

  = \(23^{o}\)

x = \(23^{o}\)

The other angles that could be in the isosceles triangle are \(23^{o}\) and \(23^{o}\).

By applying the algebra concept, it can be concluded that Leona ordered 25 boxes of pens.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

We have this information:

The price of a box of pens = $8

The price of a box of rubber bands = $4

Total order = 30 boxes

Total payment = $220

Let p symbolize the number of pens and r symbolize the number of rubber bands. Now we have the following equations:

p + r = 30 ....................... (1)

8p + 4r = 220 ............... (2)

To find the value of p and r, we can do it by simplifying the first equation as follows:

p + r = 30

r = 30 - p

Then we can substitute this value into the second equation:

         8p + 4r = 220

8p + 4(30 - p) = 220

8p + 120 - 4p = 220

                 4p = 220 - 120

                      = 100

                   p = 100/4

                      = 25 boxes of pens

So we can calculate the value of r as well:

r = 30 - p

 = 30 - 25

 = 5 boxes of rubber bands

Thus, it can be concluded that Leona ordered 25 boxes of pens.

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Step-by-step explanation:

since the both angles are the same, this is an isoceles triangle (both legs AC and AB have the same length).

that means

3x - 15 = x + 33

2x = 48

x = 24 = BC

Answer:

Option (A)

Step-by-step explanation:

Function 'f' given in the graph is differentiable with a tangent at x = 3.

Since, slope of the function = value of the differentiated function at a point

Tangent at a point x = 3 is passing through two points (3, 4) and (1, 5).

Slope of the function passing through \((x_1,y_1)\) and \((x_2,y_2)\) is,

Slope = \(\frac{y_2-y_1}{x_2-x_1}\)

          = \(\frac{5-4}{1-3}\)

          = \(-\frac{1}{2}\)

Therefore, value of f'(3) will be equal to \(-\frac{1}{2}\)

Option (A) will be the answer.

Tangent lines are lines that touches a curve at a point, without running over the curve.

The value of f'(3) is -1/2

From the figure, the line tangent to the graph passes through (5,3) and (1,5)

Next, we calculate the slope of the line using:

\(\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

So, we have:

\(\mathbf{m = \frac{5-3}{1-5}}\)

\(\mathbf{m = \frac{2}{-4}}\)

Simplify

\(\mathbf{m = \frac{1}{-2}}\)

Rewrite as:

\(\mathbf{m = -\frac{1}{2}}\)

The line also passes through (3,4) and (1,5)

So, the slope of the line is:

\(\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

So, we have:

\(\mathbf{m = \frac{5-4}{1-3}}\)

\(\mathbf{m = \frac{1}{-2}}\)

Rewrite as:

\(\mathbf{m = -\frac{1}{2}}\)

The calculated slope is -1/2

This means that:

\(\mathbf{f'(3) = m}\)

Substitute \(\mathbf{m = -\frac{1}{2}}\)

\(\mathbf{f'(3) = -\frac{1}{2}}\)

Hence, the value of f'(3) is -1/2

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