Which is a greater angle of rotation? 720° or 6π radians? Explain how you know.

Answer:

7

Step-by-step explanation:

derivate of 7x = 1(7)x⁰, or 7

derivate of 4 is 0

derivative of 7x + 4 = 7

Considering the given system of equations, it is found that:

\(|Ay| = \left|\begin{array}{cc}-8&1\\-6&-1\end{array}\right|\)

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the system is:

-8x+y=-6

3x-2y=-1

In matrix form, it is given by:

\(\left[\begin{array}{cc}-8&1\\3&-2\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-6\\-1\end{array}\right]\)

To find the matrix |Ay|, we replace the y coefficients of 1 and -2 by the results of -6 and -1, hence:

\(|Ay| = \left|\begin{array}{cc}-8&1\\-6&-1\end{array}\right|\)

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Answer:

C. (-8 -6 3 -1)

Step-by-step explanation:

EDG

Answer:

x = (66.50 - 4y) / 3

Step-by-step explanation:

Given that:

Amount had = $70

Change collected = $3.50

Total amount spent = $(70 - 3.50) = $66.50

Total amount used for purchasing prawn and fish:

Kg of fish = 4

Kg of prawn = 3

1 kg prawn will cost, x

If 1 kg of fish = y

(Total amount spent - cost of 4 kg fish) / Number of kg of prawn

($66.50 - 4y) / 3

x = (66.50 - 4y) / 3

Answer: 6(x+1)^2

Step-by-step explanation:

1. Find the GCF. Because you know the equation is 6x^2+12x+6, you can see that the coefficients, 6 and 12, are all factors of 6. To make factoring easier, factor out 6 from all the coefficients, which leaves you with 6(x^2+2x+1)

2. Factor the equation in the parentheses. If you have learned your perfect squares, then you know that x^2+2x+1 is (x+1)^2 because x^2+2x+1 = (x+1)(x+1) (you can foil that out if you want to check). Once finished with this, it leaves you with 6(x+1)^2

The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

What is dilation?

A dilation is a transformation that creates an image that has the same shape as the original but is larger.

• An enlargement is a dilation that produces a larger image.

• A reduction is a dilation that produces a smaller image.

• A dilation expands or contracts the original figure.

A dilation is a stretch or a shrink in the size and location of a figure or point.

The scale factor in a dilation is the amount by which the figure is stretched or shrunk.

The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,

k, the location of the center of dilation, \((x_0,y_0)\) is

\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)

Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

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The researcher's approach is known as stratified random sampling, where the population is divided into age groups and a random sample is chosen from each group before combining them into a single sample.

This is known as a stratified random sampling technique. Stratified random sampling involves dividing the population into distinct subgroups or strata based on certain characteristics, such as age groups in this case. The researcher then selects a random sample from each stratum, ensuring representation from each subgroup. Finally, the samples from each stratum are combined to form a single sample that represents the entire population.

The purpose of using stratified random sampling is to ensure that each subgroup is adequately represented in the final sample. By dividing the population into strata and selecting random samples from each, the researcher can obtain a sample that reflects the diversity of the population's characteristics, such as age distribution. This approach helps to minimize sampling bias and improve the accuracy of the sample's representation of the overall population.

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The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔABC and ΔLMN, we have

AB = LM = 8 cm

∠B = ∠M = 90°

AC = LN = 12 cm

The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate.

The triangles ΔFGH and ΔLMN are similar triangles, then we have

x / 12 = 4 / 8

x / 12 = 1 / 2

x = 12 / 2

x = 6 cm

The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.

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Susan needs to use a length of 20 feet for the floor of her treehouse.

In the scale drawing, the ratio of 2.5 inches to 3 feet represents the relationship between the actual measurements and the scaled measurements. To find the length of the floor in feet, we can set up a proportion using the given scale. Since 2.5 inches corresponds to 3 feet, we can write the proportion as follows:

2.5 inches / 3 feet = x inches / 20 feet

To solve for x, we cross-multiply and divide:

2.5 inches * 20 feet = 3 feet * x inches

50 inches * feet = 3x inches * feet

50 = 3x

Dividing both sides by 3:

50 / 3 = x

x ≈ 16.67

Therefore, the length of the floor in inches is approximately 16.67 inches. However, since we need the answer in feet, we round it to the nearest whole number, which is 17 feet. Therefore, Susan must use a length of 17 feet for the floor of her treehouse.

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6.29117647059

This is the answer

Answer: 6.29117647059

Step-by-step explanation:

divide the problem :)

Answer:

f(4) = 13

Step-by-step explanation:

f(4) = 2(4)+5
f(4) = 13

Answer:

13

Step-by-step explanation:

f ( x ) = 2x + 5

To find : f ( 4 )

f ( 4 ) = f ( x )

Here,

x = 4

So,

f ( 4 ) = 2 ( 4 ) + 5

        = 2*4 + 5

        = 8 + 5

f ( 4 ) = 13

Answer:

You would need 9 liters of pure acid and 72 liters of 10% acid to make a mixture of of 81 liters of 20% acid.

Step-by-step explanation:

See attached picture.

\(\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =118 \end{cases}\implies \begin{array}{llll} s=\cfrac{(118)\pi (20)}{180}\implies s=\cfrac{118\pi }{9} \\\\\\ s\approx 41.19~cm \end{array}\)

Answer:

  0.253 m/s

Step-by-step explanation:

You want to know the horizontal component of motion of a passenger riding a Ferris wheel when they are 1/27 of the way around the circle and their rate of rise is 0.06 m/s.

The wheel makes one revolution in 27 minutes, so the angular displacement is changing at the rate of (360°)/(27 min) = 13 1/3°/min.

After 1 minute, the passenger is following a path that has an angle of elevation of 13 1/3°.

The ratio of vertical speed to horizontal speed will be the tangent of the angle of elevation:

  Vv/Vh = tan(13 1/3°)

Then the horizontal speed will be ...

  Vh = Vv/tan(13 1/3°) = (0.06 m/s)/0.237004

  Vh ≈ 0.253 m/s

The passenger's horizontal motion is about 0.253 m/s.

Probability to get the sum of numbers on dices at least 11 is 1/12.

Probability is the ratio of the favorable number of cases to the total number of cases.

A dice has 6 sides

There are a pair i.e. 2 dices.

So the total number of cases here = 6*6 = 36

Now the sum of the numbers on dices is at least 11, i.e. it is either 11 or 12.

11 is possible when the pairs are like below:

(6,5) and (5,6) only

12 is possible when the pair is (6,6)

So the number of favorable case = 2+1 = 3

Hence the required probability is = 3/36 = 1/12

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There are 15890700 different selections to win at lotto at a certain state.

To find the number of different selections that are possible, you can use the combination formula. The combination formula is:

C(n , r) = n! / (r! × (n - r)!)

where C(n , r) represents the number of combinations, n represents the total number of items, and r represents the number of items being chosen at a time.

In this case, n is 50 and r is 6, so the number of different selections is:

C(50 , 6) = 50! / (6! × (50 - 6)!) = 50!/6!44! = 15890700

Therefore, there are 15890700 different selections that are possible.

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Answer:

A

Step-by-step explanation:

we should first find the value of x.

Answer:

C

Step-by-step explanation:

(x-a)^2=5

x-3=root of 5

x= root of 5 +3

Answer:

x=-11

Step-by-step explanation:

The population of the study is club members who were asked whether they preferred a new sauna or new steam room

Yes, there are diminishing returns to labor in the given production function.

There are diminishing returns to labor in the given production function. As more units of labor (L) are added while holding capital (K) constant, the increase in output (y) becomes smaller and smaller. This is indicative of diminishing marginal product of labor.

When the wage rate (w) is 1 and the capital (K) is fixed at 64, the profit-maximizing choice of labor (L) can be found by equating the marginal product of labor (MPL) to the wage rate. In this case, MPL = 12L^2K.

Setting MPL = w, we have 12L^2K = 1. Substituting K = 64, we get 12L^2 * 64 = 1. Solving for L, we find L ≈ 0.0917.

The profit-maximizing output level (y) can be calculated by substituting the values of L and K into the production function. Thus, y = 4L^3K = 4(0.0917)^3 * 64 ≈ 0.026.

The maximized profit can be determined by subtracting the total cost (TC) from the total revenue (TR). Since the fixed cost is given as 64, TC = 64 + wL = 64 + 1(0.0917) ≈ 64.092. TR is the product of the output level and the price, which is 0.026 * 3 = 0.078.

Profit = TR - TC ≈ 0.078 - 64.092 ≈ -63.014.

Diminishing returns to labor imply that as more labour is employed while holding other factors constant, the incremental increase in output becomes smaller. In the given production function, this phenomenon is observed. In the short run, with a fixed capital level of 64, we determine the profit-maximizing choice of labour (L) when the wage rate (w) is 1. By equating the marginal product of labour (MPL) to the wage rate, we find L ≈ 0.0917. Substituting this value into the production function, we calculate the profit-maximizing output level as y ≈ 0.026. The maximized profit is determined by subtracting the total cost (TC) from the total revenue (TR), resulting in a profit of approximately -63.014. This analysis helps understand the relationship between input choices, output levels, and profit optimization in the short run.

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Answer:

A. 8

Step-by-step explanation:

Sydney is 8 miles far from the airplane if the plane took off at a 15° angle to the ground and flew in Sydney's direction option (A) 8 miles is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

It is given that:

A plane took off at a 15° angle to the ground and flew in Sydney's direction.

She is standing at a point 25 miles from the point where the plane took off. If the plane has traveled 20 miles in the air

From the data we can draw a triangle:

From the diagram:

a + b = 25 miles

a = 20 cos(15)

h = 20 sin (15)

As we know, Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle that is equal to the sum of the squares of the other two sides.

Using Pythagoras theorem:

x = √(h² + b²)

x = √((20 sin15)² + (25 - 20 cos15)²)

After solving:

x = 7.68 miles

or

x = 8 miles

Thus, Sydney is 8 miles far from the airplane if the plane took off at a 15° angle to the ground and flew in Sydney's direction option (A) 8 miles is correct.

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9514 1404 393

Answer:

  y = -1/2x +4

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis, at y=4.

The slope is found by following the line to the right until it meets another grid line crossing point. That is 2 units to the right and down 1 unit.

The slope is ...

  m = "rise"/"run" = -1/2

Then the slope-intercept equation is ...

  y = mx + b . . . . . slope m, y-intercept b

  y = -1/2x +4

Answer:

idontknow which is becausw i dont speak a lot of englisj do

Step-by-step explanation:

i dont understan you is just ames yoy writibg

Answer:

13

Step-by-step explanation:

khan

A graph which represent the solution to the inequality 0.75 is less than the product of a number and −1.5 is: B. number line with open circle on point on negative 0.5 with arrow shaded left.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Let the variable n represent the unknown number. Therefore, translating the word problem into an inequality, we have the following:

0.75 < -1.5 × n

Next, we would find the solution to this given inequality in order to determine its graph:

0.75 < -1.5n

0.75 + 1.5n < 0

1.5n < -0.75

Dividing both sides of the inequality by 1.5, we have:

n < -0.75/1.5

n < -0.5

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if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

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Answer:

The exponent of the first term must have twice the value of the exponent of the second term.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Neither.

It is a complex number. The - sign is the culprit. sqrt(-144) = i * sqrt(144) = 12 i

The "i" is an imaginary representation for the square root of -1. It is a definition for sqrt(-1). So a new category of number has been created. The ancients would have been profoundly surprised to learn that such a thing existed.

Answer:

Step-by-step explanation:

according to the question equation is

3i-71

-4i

Answer:

3i - 7i = (3-7)i = -4i

so -4i.