Each face of a cube has an area of 4 square units. What is the volume of the cube?

Answer:

a)

The angle formed by intersecting chords is half of the sum of the intercepted arcs:

b)

The angle formed by two tangents is the half of the difference of the intercepted arcs:

Answer:

The one in the top right

Step-by-step explanation:

All of the points seem to match the line best, each of the other graphs vary more.

Hey there!

The answer is D

We solve this by multiplying the exponents, and we get 15:

3 x 5 = 15

So, the answer is 2^15

Hope it helps and have a great day!

The dimensions of the garden that minimize the cost are approximately 2.5 feet by 64.8 feet.

To find the dimensions of the garden that minimize the cost, we can use optimization techniques. Let's denote the length of the garden as L and the width as W.

The cost of the brick wall is $60 per foot, and since only one side is enclosed by the brick wall, the cost for that side is 60L. The cost of the metal fence is $40 per foot, and since three sides are enclosed by the metal fence, the cost for those sides is 40(2L + W).

The total cost C is the sum of the costs for the brick wall and the metal fence:

C = 60L + 40(2L + W)

Given that the area of the garden is 162 square feet, we have L * W = 162.

To minimize the cost, we can take the derivative of the cost function with respect to L and set it equal to zero:

dC/dL = 60 + 80 = 0

Solving for L, we find L = 2.5 feet.

Substituting L = 2.5 into the area equation, we get W = 162 / 2.5 = 64.8 feet.

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Answer: 300 kgs.

Step-by-step explanation:

Butter used in last month= 240 kg.

Additional butter used= 25%

Butter used in current month= 240+25%

                                                = 300kg.

A vector field is said to be conservative if it is irrotational and it is path-independent.

A vector field is a field with three components, x, y, and z. To determine if a vector field is conservative, the following steps can be taken:

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Answer:

C

Step-by-step explanation:

If a line is parallel to a side of a triangle and it intersects the other 2 sides then it divides those sides proportionally.

BE is such a line , then

\(\frac{AE}{ED}\) = \(\frac{AB}{BC}\) ( substitute values )

\(\frac{9}{5}\) = \(\frac{9.2}{BC}\) ( cross- multiply )

9 BC = 46 ( divide both sides by 9 )

BC ≈ 5.1 ( to the nearest tenth )

Then

AC = AB + BC = 9.2 + 5.1 = 14.3

The number of days spent or taken by assistant with work efficiency of 2 units per day to do the work alone is equals to the 7.5 days.

We have provide that there is a carpenter and his assistant can do a piece of work.

Number of days taken by both carpenter and his assistant to do a piece of work = 3 days.

Number of days taken by carpenter and to do the same piece of work alone = 5 days.

We have to determine number of taken by assistant and to do the same piece of work alone.

Let the required number of days that the assistant take to do the work alone be 'x days'. As we know, total available work units = LCM (3,5) = 15 units

Ability or efficiency of a person or man is calculated by dividing the total work units to the number of working days spent to do the work.

Now, Ability or efficiency of both carpenter and his assistant work together = 15/5

= 3 units/day

Similarly, Ability or efficiency of carpenter = 15/3

= 5 units/day

So, Ability or efficiency of assistant= 5 - 3 = 2 -(1)

Using efficiency formula, efficiency of assistant

= 15/x --(2)

from (1) and(2), 15/x = 2

=> 2x = 15

=> x = 7.5

Hence, required number of days are 7.5 days.

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Answer:

Step-by-step explanation:

$1.03 x 5 = $5.15

$2.68 x 1 = $2.68

$5.15+$2.68=$7.83

Given the following function:

Let's determine f(x) at x = -2

We get,

Therefore, the answer is 1/4.

The new surface area is (1/4)S, which is equivalent to (1/4) times the original surface area.

Let the original surface area of the figure be S.

If the new surface area is 1/4 of the original, then the new surface area is (1/4)S.

Since the surface area is proportional to the square of the dimensions, we know that the ratio of the new dimensions to the original dimensions must be √(1/4) = 1/2.

Therefore, if the original dimensions were x, y, and z, then the new dimensions must be (1/2)x, (1/2)y, and (1/2)z.

The new surface area can be calculated using the formula for the surface area of the figure with the new dimensions:

New surface area = 2((1/2)xy + (1/2)xz + (1/2)yz)

                  = xy + xz + yz

But we know that the new surface area is (1/4)S, so we have:

xy + xz + yz = (1/4)S

Multiplying both sides by 4 gives:

4xy + 4xz + 4yz = S

Factor out 4:

4(x+y+z)² - 4x² - 4y² - 4z² = S

Substituting the expressions for the new dimensions:

4((1/2)(x+y+z))² - 4((1/2)x)² - 4((1/2)y)² - 4((1/2)z)² = S

Simplifying:

(1/4)(x+y+z)² - (1/4)x² - (1/4)y² - (1/4)z² = (1/4)S

Multiplying both sides by 4 again:

x² + 2xy + y² + 2xz + 2yz + z² - x² - y² - z² = S

Simplifying:

2xy + 2xz + 2yz = S

Substituting (1/2)x, (1/2)y, and (1/2)z for x, y, and z:

2(1/2)(1/2)xy + 2(1/2)(1/2)xz + 2(1/2)(1/2)yz = (1/4)S

Simplifying:

(1/4)xy + (1/4)xz + (1/4)yz = (1/4)S

Therefore, the new surface area is (1/4)S, which is equivalent to (1/4) times the original surface area.

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The point (4, 3) is a viable solution.

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Given:

A basket holds at most 14 pounds of apples and oranges.

There are at least 3 pounds of apples in the basket.

This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges.

That means, we have the system of inequalities,

x + y ≤ 14,

x ≥ 3

Option B and C are discarded.

And y ≥ 0.

Option A is also discarded.

Substituting (4, 3),

x + y ≤ 14,

7  ≤ 14.

Therefore, (4, 3) is a solution.

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The complete question:

A basket holds at most 14 pounds of apples and oranges. There are at least 3 pounds of apples in the basket. This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges. Which point represents a viable solution?

Answer:

7

Step-by-step explanation:

\(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

\(\sqrt{((-1)-6)^{2} +(8-8)^{2} }\)

simplify to get 7 as answer

The distance between (6,8) and (-1,8) is 7.

It is required to find the distance between each points.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

By the use the distance formula to find the distance between (6,8) and (-1,8).

∵The distance between two points is given by

=\(\sqrt{(x_{2}-x_{1} )^{2}+ (y_{2}-y_{1} )^{2} } \\\\\)

Distance between the point (6,8) and origin(-1,8) =

\(\sqrt{(-1-6 )^{2}+ (8-8 )^{2} } \\\\=\sqrt{(-7 )^{2}+ (0 )^{2} }\\\\=7\)

Hence, the distance between (6,8) and (-1,8) is 7.

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Answer:

Step-by-step explanation:

20% of 207.77 = 41.554

1% of 207.77 = 2.0777

21% of 207.77 = 41.554+2.007=43.6317

207.77+43.6317 = 251.4017

Round to 2 decimal places because its money = 251.40

Since the arrival times are independent and uniformly distributed, the probability that a single person arrives in the first hour is 1/10^6. Therefore, the number of people N that arrive in the first hour follows a binomial distribution with parameters n=10^6 and p=1/10^6.

The probability that exactly i people arrive in the first hour is then given by the binomial probability mass function:

P{N=i} = (10^6 choose i) * (1/10^6)^i * (1 - 1/10^6)^(10^6 - i)

Using the normal approximation to the binomial distribution, we can approximate this probability as:

P{N=i} ≈ φ((i+0.5 - np) / sqrt(np(1-p)))

where φ is the standard normal probability density function. Plugging in the values of n=10^6 and p=1/10^6, we get:

P{N=i} ≈ φ((i+0.5 - 1) / sqrt(1*0.999999)) = φ(i - 0.5)

Therefore, an approximation for P{N=i} is given by the standard normal density function evaluated at i-0.5.

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The potential difference between xi = 10 cm and xf = 30 cm in the uniform electric field ex = 2000 v/m can be calculated using the formula: ΔV = Ex * Δx.  Therefore, the potential difference between the two points is 400 volts.

To find the potential difference between two points in a uniform electric field, we can use the formula:

Potential difference (V) = Electric field (E) × Distance (d)

In this case, the electric field (E) is given as 2000 V/m (ex = 2000 V/m). The distance (d) between the two points, xi = 10 cm and xf = 30 cm, is the difference between xf and xi, which is:

d = xf - xi = 30 cm - 10 cm = 20 cm

Now, convert the distance to meters:

d = 20 cm × (1 m / 100 cm) = 0.2 m

Now, we can find the potential difference (V):

V = E × d = 2000 V/m × 0.2 m = 400 V

So, the potential difference between xi = 10 cm and xf = 30 cm in the uniform electric field ex = 2000 V/m is 400 V.

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The standard deviation of the critical path is 6.

To calculate the standard deviation of the critical path, we need to use the concept of variance and consider the activities on the critical path.

The variance of a project or critical path is the sum of the variances of the activities on that path.

Since the variances are given as the squares of the standard deviations, we can square the standard deviations of each activity and sum them to find the variance of the critical path. Finally, we take the square root of the variance to obtain the standard deviation.

Given the standard deviations of the activities on the critical path:

Activity 1: Standard deviation = 1 day

Activity 2: Standard deviation = 3 days

Activity 3: Standard deviation = 1 day

Activity 4: Standard deviation = 4 days

Activity 5: Standard deviation = 3 days

Calculating the variance of the critical path:

Variance = (1^2) + (3^2) + (1^2) + (4^2) + (3^2) = 1 + 9 + 1 + 16 + 9 = 36

Taking the square root of the variance, we find the standard deviation of the critical path:

Standard deviation = √(36) = 6

Therefore, the standard deviation of the critical path is 6.

The correct choice is A. 6.

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The required polynomial f(x) is f(x) = x³ - 3x² - 13x - 21.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial etc. ax+b is a polynomial.

Here,
By the Factor Theorem, we know that:

f(x) = a(x - 7)(x + 1)(x + 3)

where a is a constant.

To find the value of a, we can use one of the given zeros. Let's use x = 7:

0 = f(7) = a(7 - 7)(7 + 1)(7 + 3) = 0

So, a = 0 if f(7) = 0. This makes sense as if x = 7 is a zero of the polynomial, then (x - 7) is a factor of the polynomial.

Now, we can write f(x) as,

f(x) = 0(x - 7)(x + 1)(x + 3) = 0

We can introduce a leading coefficient of 1, and write:

f(x) = a(x - 7)(x + 1)(x + 3) = 1(x - 7)(x + 1)(x + 3)

Expanding this out, we get:

f(x) = (x - 7)(x + 1)(x + 3)

= (x² - 6x - 7)(x + 3)

= x³ - 3x² - 13x - 21

Therefore, the polynomial f(x) is f(x) = x³ - 3x² - 13x - 21.

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It would be 1 by 3

Since [4 -1 0] and [2 1 0] are both 1 by 3, the result should be the same since they match up.

also im learning the same thing right now lol

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5

Answer:

+ 38,000

Step-by-step explanation:

Given that:

Altitude of airplane = 38,000

The altitude of an object such as airplane in this scenario refers to the height of the airplane above sea level. The sea level is represented as a zero point (mid level) such that distance below are negative and those above are positive.

Hence, at an altitude of 38000 feets, altitude of airplane can be represented as +38,000 feets.

The direction of B is opposite to that of i​. The vector B is given by - 3i​.

Given information:A = 3j

​A × B = 9i

A ⋅ B = 12

We need to find vector B. Let's start by using the cross-product of two vectors i.e A × B.

Since we have A × B = 9i^​, we can write A × B = |A| |B| sin(θ)n, where |A| = 3, |B| = B and θ is the angle between vectors A and B.

Therefore, |B| sin(θ) = 9/3

= 3

So, sin(θ) = 1

θ = 90° (θ is in the second quadrant because i and j are perpendicular to each other)

Thus, |B| = 3/sin(90°)

= 3/1

= 3

And, B × A = - (A × B)

B × A = - 9i

Now, |A × B| = |A||B| sin(θ)

9 = 3 × |B|

|B| = 3

The direction of B is opposite to that of i​. Therefore, B = - 3i

The vector B is given by - 3i​.

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Answer:

x=-5 i think

Step-by-step explanation:

Answer: the answer is 2 or C

-8/2 x -3/6

*Always do the recipical*

(-8 x -3) / (2 x 6)

-8 x -3= +24

2 x 6= 12

24/12= 2

The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that the expression is,

-8/2 x -3/6

The expression will be solved as below,

E = (-8 x -3) / (2 x 6)

The numerator will get reciprocal and multiplied to the denominator,

E = 24 / 12

Divide the number 24 by 12 and get the solution,

E = 2

Therefore, the solution of the expression will be 2. The correct option is B.

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Answer:

A is not a right triangle

B is a right triangle

Step-by-step explanation:

A.

6^2 = 36
12^2 = 144.

36 + 144 = 180

15^2 = 225

180 ≠ 225, so it is not a right triangle

----------------------------------------------------------------------------

B.

5^2 = 25

12^2 = 144

25 + 144 = 169

13^2 = 169

169 = 169, so it is a right triangle

The particular solution is:
yp(t) = -sin(4t)

To find a particular solution to the given differential equation y'' + 16y = -16 sin(4t), we will use the method of undetermined coefficients.

First, we will guess the form of the particular solution. Since the right-hand side is a sinusoidal function, our guess for the particular solution will be in the form:

yp(t) = A sin(4t) + B cos(4t)

Next, we need to find the first and second derivatives of yp(t):

yp'(t) = 4A cos(4t) - 4B sin(4t)
yp''(t) = -16A sin(4t) - 16B cos(4t)

Now, we will plug yp(t) and its derivatives into the given differential equation:

-16A sin(4t) - 16B cos(4t) + 16(A sin(4t) + B cos(4t)) = -16 sin(4t)

Simplify the equation:

16B cos(4t) = -16 sin(4t)

Now we can solve for the coefficients A and B:

B = 0 (since there is no cos(4t) term on the right-hand side)
A = -1 (since the coefficient of sin(4t) is -16)

So the particular solution is:

yp(t) = -sin(4t)

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Chen burned 9,912 calories in total from swimming last month.

The quantity of energy that may be used as fuel by our bodies comes in the form of calories, which are a unit of measurement.

By measuring the quantity of heat energy emitted when the meal or drink is burned in a calorimeter, one may quantify the number of calories in various foods and beverages.

We know that Chen burns 354 calories in 1 hour of swimming. So, to find out how many calories he burned in 28 hours, we need to multiply 354 by 28:

Calories burned in 28 hours = 354 calories/hour × 28 hours

= 9,912 calories

Therefore, Chen burned 9,912 calories in total from swimming last month.

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Answer:

\(7-8x+4y=-21\)

Step-by-step explanation:

\(2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21\)

Answer:

\( \huge{ \boxed{ \sf{70}}}\)

Step-by-step explanation:

\( \underline{ \sf{Given}} : \)

\( \sf{ \angle \:FGJ \: = \: 30° \:, } \: \: \angle \: JGH \: = \: 40° \: , \: \angle \: FGH= x\)

Finding the value of x°

\( \sf{ \angle \: FGH= \angle \: FGJ \: + \: \angle \: JGH\:}\)

Plug the values

\( \mapsto{ \sf{x = 40 + 30}}\)

Add the numbers

\( \mapsto{ \sf{x = 70}}\)

The value of x° is 70°

Hope I helped!

Best regards! :D

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