What is the slope of this line?

y=−13x+14

A. -1/3
B. 1/4
C. 1/3

Answer:

The son is 24 and the father is 48

Step-by-step explanation:

If you let x = the age of the child, then the father is 2x old since the father is twice as old as the son. The sum of their ages would be 1x + 2x which simplifies to 3x.

Since the problem gives the total of their ages as 72, we know that 3x = 72.

Dividing both sides by 3, we get x = 24, which we said was the age of the child.

Since the age of the father is 2x, we can say that 2x = 2(24), or 2x = 48 for the age of the father.

Answer:

What fair

Step-by-step explanation:

The data type this function take is int.

Data type is an attribute of a piece of data that instructs a computer how to interpret its value. Example data type is,

In the question, the function is double numbers (int x). The parameter used in this function is int. Even if it try to pass the double value into the function it will take an integer value corresponds to double value and the function always return the data to integer.

Thus, the function only take integer (int) data type.

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The length of the midsegment of the trapezoid is 8 units

Trapezoid

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs.

The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides of the trapezoid and is parallel to the pair of parallel sides.

In this problem

The two non-parallel sides of the trapezoid are AD and BC

Step 1

Find the midpoint side of AD

Let

E the midpoint AD

A ( 2,4 ) D (-2,-1)

Find the x-coordinate of the midpoint AD

\(x = \frac{2-2}{2} = 0\)

Find the y-coordinate of the midpoint AD

\(y = \frac{4 - 1}{2} = 1.5\)

the point E is equal to (0, 1.5 )

Step 2

Find the midpoint side of BC

Let

F the midpoint BC

\(B ( 7,4) C ( 9, -1)\)

Find the x-coordinate of the midpoint BC

\(x = \frac{9+2}{7} = 8\)

Find the y-coordinate of the midpoint BC

\(y = \frac{4 - 1}{2} = 1.5\)

The point F is equal to ( 8 , 1.5 )

Step 3

Find the distance EF

Know that

The formula to calculate the distance between two points is equal to

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

we have

E ( 0 ,1.5) F ( 8, 1.5)

substitute the values

\(d = \sqrt{(1.5 - 1.5)^{2} + (8-0 )^{2} }\)

d = 8 units

Therefore

The length of the midsegment of the trapezoid is 8 units

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Answer:

15 (D)

Step-by-step explanation:

There are 3 15s

it comes up the most

Answer:

Explanation:

15 is the mode because it is shown many times.

Answer:

x = 9

Step-by-step explanation:

To solve these problems, you first set up an equation representing the information given.

6x = x² - 27

This turns into a quadratic equation which you need to factor out.

0 = x² - 6x - 27

You want to choose two numbers that multiply to -27, and add up to -6

0 = (x - 9)(x + 3)

If you're unfamiliar with factoring, you take the opposite sign of the number in the parentheses because it's a shortcut when setting it equal to 0.

x = 9, -3

Since it asks for the positive solution only, the answer is x = 9.

I hope this helps!

Answer:

idk

Step-by-step explanation:

i dont know

The probability that all three children are the same sex, when the first and last children are the same sex, is 1/2.

To compute the probability that all three children are the same sex given that the first and last children are the same sex, we need to consider the possible combinations of sexes.

There are four possibilities: three boys, two boys and one girl, two girls and one boy, or three girls. Since we know that the first and last children are the same sex, the combination of three boys or three girls is favorable.

This means there are two favorable outcomes out of the four possibilities. Therefore, the probability that all three children are the same sex is 2/4 or 1/2.

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Answer:

∠ A = 98°

Step-by-step explanation:

ABCD is a cyclic quadrilateral

its opposite angles sum to 180° , that is

∠ A + ∠ C = 180°

∠ A + 82° = 180° ( subtract 82° from both sides )

∠ A = 98°

Answer:

Step-by-step explanation:

Interchange x and y:  (-6, 8) is the image of (8, -6) after a reflection over y = x.

The image of (8,-6) after a reflection over the line y=x is (-6, 8).

The given coordinate point is (8, -6).

Reflect over the y = x, when you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).

The image of (8,-6) after a reflection over the line y=x is

Reflecting in the line y = x interchanges the x and y coordinates. So, the image of (8, -6) is (-6, 8).

Therefore, the image of (8,-6) after a reflection over the line y=x is (-6, 8).

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Answer:

-8 -8

Step-by-step explanation:

Because it is the most reasonable

Answer:

4,500

Step-by-step explanation:

Answer:

672

Step-by-step explanation:

V=LWH

V=12*7*8

V=672

Answer:

672 ft cubed

Step-by-step explanation:

L x W x H = Area of a Rectangular Prism

12 x 7 x 8 = 672 ft cubed

Answer:

The coterminal angle of -230º is 130º.

Step-by-step explanation:

Coterminal angles are those whose sides start and end at the same point, therefore sharing a common side. To obtain the coterminal angle of a negative angle, 360º must be added to the value of said negative angle. Therefore, the coterminal angle of -230º arises from the following calculation:

-230 + 360 = X

130 = X

Therefore, the coterminal angle of -230º is 130º.

The weekly standard deviation of the stock price calculated from this sample is 42.957

Given info,

Bear Stearns' stock price closed at $98, $103, $58, $29, and $4 over five successive weeks,

To find the weekly standard deviation of the stock price calculated from this sample,

We use,

μ = (98 + 103 + 58 + 29 + 4) / 5

μ = 58.4

The mean of this sample is 58.4

The standard deviation is,

σ = \(\sqrt{\frac{(98-58.4)^2+(103-58.4)^2+(58 - 58.4)^2+(29-58.4)^2+(4-58.4)^2}{(5-1)} }\)

σ = √1845.3

σ = 42.957

Hence, the standard deviation is 42.957

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When a triangle rotated 180 degree counterclockwise, the new coordinates of the triangle would be (3,-1) (-2,-4) and (-5,3)

We know that if we rotate a point P(x, y) with 180 degrees counterclockwise about the origin then the translated point would be P'(-x,-y).

A given triangle having vertice at (-3,1) (2,4) and (5,-3) is rotated 180 degree counterclockwise.

We need to find the coordinates of the rotated triangle.

(-3,1) -> (3, -1)

(2,4) -> (-2, -4)

and (5,-3) -> (-5, 3)

Therefore, after rotation the triangle would have coordinates (3,-1) (-2,-4) and (-5,3)

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Answer:

see explanation

Step-by-step explanation:

Consider the left side

\(\frac{cosA}{1-sinA}\) + \(\frac{cosA}{1+sinA}\)

= \(\frac{cosA(1+sinA)+cosA(1-sinA)}{(1-sinA)(1+sinA)}\)

= \(\frac{cosA+cosAsinA+cosA-cosAsinA}{1-sin^2A}\)

= \(\frac{2cosA}{cos^2A}\) ← cancel cosA on numerator/ denominator

= 2 × \(\frac{1}{cosA}\)

= 2secA

= right side, thus proven

Answer:

B

Step-by-step explanation:

the equation you showed simplified is -20t + 2

b equals that just with a different variable

Answer:

b

Step-by-step explanation:

Answer:

210

Step-by-step explanation:

so first i found out how many shirts each prints in a minute

the first machine produced 15/min

the second produced 20/min

now I added the 2 together and got 35

7,350/35 is 210

Answer:

No.

Step-by-step explanation:

No, Alex is not correct.

760 mm = .760 m    .760 is less than 1.  To change mm to meters you need to move the decimal three places to the left.

Helping in the name of Jesus.

To determine the minimum number of terms we need to add in order to find the sum of the series with an error less than 0.0001, we can use the Alternating Series Estimation Theorem.

The Alternating Series Estimation Theorem is a useful tool for approximating the sum of an alternating series and determining the accuracy of the approximation. An alternating series is a series in which the terms alternate in sign, such as (-1)^n or (-1)^(n+1).

To use the Alternating Series Estimation Theorem, we need to check two conditions. Firstly, we verify that the series is convergent, meaning that the partial sums of the series approach a finite limit as the number of terms increases. If the series is not convergent, this estimation method cannot be applied.

Once we have established that the series is convergent, we can use the theorem to determine the minimum number of terms required to achieve a desired level of accuracy. The theorem tells us that the error in approximating the sum of the series using a partial sum is less than or equal to the absolute value of the first omitted term.

In our case, we want the error to be less than 0.0001. By finding the absolute value of the first omitted term, we can determine how many terms we need to add to the partial sum in order to achieve this desired level of accuracy. This will give us the minimum number of terms required to obtain the sum with an error less than 0.0001.

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The statement that best describes the composition of most foods is: "They contain mixtures of the three energy nutrients, although only one or two may predominate."

Most foods contain mixtures of the three energy nutrients, namely carbohydrates, proteins, and fats. However, the relative proportions of these nutrients can vary significantly from one food to another. In some foods, one or two of these nutrients may predominate, while others may contain relatively equal amounts of all three.

Carbohydrates are a primary source of energy for the body and can be found in various forms such as sugars, starches, and fibers. Foods like grains (e.g., rice, wheat, oats), fruits, vegetables, and legumes tend to be rich in carbohydrates. However, the specific types and amounts of carbohydrates can vary widely.

Proteins are crucial for building and repairing tissues, as well as for various metabolic functions. Foods like meat, poultry, fish, eggs, dairy products, legumes, nuts, and seeds are excellent sources of protein. Again, the protein content in different foods can vary.

Fats, also known as lipids, are an important energy source and provide essential fatty acids. Foods such as oils, butter, avocados, nuts, and fatty meats are high in fats. Like carbohydrates and proteins, the fat content in foods can differ significantly.

It's worth noting that some foods may predominantly consist of one specific nutrient. For example, pure sugar is almost entirely composed of carbohydrates, while pure oil is almost entirely composed of fats. However, most whole foods, such as fruits, vegetables, grains, meats, and dairy products, contain a mixture of these energy nutrients.

Furthermore, a balanced diet typically includes a combination of these nutrients in appropriate proportions. A varied diet that incorporates a range of foods from different food groups helps ensure an adequate intake of carbohydrates, proteins, and fats, along with other essential nutrients required for optimal health.

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Answer: g(x + 4) = (x + 4)² + 9(x + 4)

= x² + 8x + 16 + 9x + 36

= x² + 17x + 52

So, an expression for g(x + 4) in the form a2 + ax + b, where a and b are numbers, is 1x^2 + 17x + 52

Step-by-step explanation:

The divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

Let S be the boundary surface of E with the positive (outward) orientation, and let E be a straightforward solid region. Let F be a vector field with continuous partial derivatives on an open region containing E for each of its component functions. Then

\($\iint_S F \cdot d S=\iint_S F \cdot n d S=\iiint_E div Fdv$\),

where n be the outward normal of S.

Let the given equation be

The sphere S is x² + y² + z² = 1

By using concept,

\($$\iint_S F \cdot n d S=\iint_S\left(2 x+2 y+z^2\right) d S$$\)

Therefore,

\($$F \cdot n=2 x+2 y+z^2$$\)

Given that the sphere S is x² + y² + z² = 1

For S, n will be

\($n=\frac{x i+y j+z k}{\sqrt{x^2+y^2+z^2}}$$\)

After substituting the value of x² + y² + z² = 1

n = x i + y j + z k

Therefore,

F(xi + yj + zk) = 2x + 2y + z²

Consider F = Pi + Qj + Rk

\($& (P i+Q j+R k) \cdot(x i+y j+z k)=2 x+2 y+z^2 \\\)

Px + Qy + Rz = 2x + 2y + z²

By comparing the values, P = 2, Q = 2, R = z

So, F becomes

F = 2i + 2j + zk

By using the definition of Divergence,

\(${div} F=\left(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right) \cdot(2 i+2 j+z k) \\\)

\($& =\frac{\partial}{\partial x}(2 i+2 j+z k)+\frac{\partial}{\partial y}(2 i+2 j+z k)+\frac{\partial}{\partial z}(2 i+2 j+z k) \\\)

= 0 + 0 + 1

div F = 1

By using Divergence Theorem,

\($ \iint_S F \cdot n d S=\iiint_E {div} F d V \\\)

\($& \iint_S\left(2 x+2 y+z^2\right) d S=\iiint_E 1 d V\)

Since \($\iiint_E 1 d V$\) is the volume of sphere with radius 1

\($& \iint_S\left(2 x+2 y+z^2\right) d S=\text { Volume of } E \\\)

\($& =\frac{4}{3} \pi(1)^3=\frac{4}{3} \pi\)

Thus,

\($\iint_S\left(2 x+2 y+z^2\right) d S=\frac{4}{3} \pi$$\)

Therefore, the divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

The complete question is:

Use the Divergence Theorem to evaluate S(2x+2y+z2)dS where S is the sphere x2+y2+z2=1.

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The divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

What is meant by divergence theorem?

Let S be the boundary surface of E with the positive (outward) orientation, and let E be a straightforward solid region. Let F be a vector field with continuous partial derivatives on an open region containing E for each of its component functions. Then

\(\iint_S F \cdot d S=\iint_S F \cdot n d S=\iiint_E d i v F d v\)

where n be the outward normal of S.

Let the given equation be

The sphere S is x² + y² + z² = 1

By using concept,

\(\iint_S F \cdot n d S=\iint_S\left(2 x+2 y+z^2\right) d S\)

Therefore,

\(\mathrm{F} \cdot n=2 x+2 y+z^2\)

Given that the sphere S is x² + y² + z² = 1

For S, n will be

\(n=\frac{x i+y j+z k}{\sqrt{x^2+y^2+z^2}}\)

After substituting the value of x² + y² + z² = 1

n = x i + y j + z k

Therefore,

F(xi + yj + zk) = 2x + 2y + z²

Consider F = Pi + Qj + Rk

\((P i+Q j+R k) \cdot(x i+y j+z k)=2 x+2 y+z^2\)

Px + Qy + Rz = 2x + 2y + z²

By using the definition of Divergence,

= 0 + 0 + 1

div F = 1

By using Divergence Theorem,

\(\begin{aligned}& \iint_S F \cdot n d S=\iiint_E d i v F d V \\& \iint_S\left(2 x+2 y+z^2\right) d S=\iiint_E 1 d V\end{aligned}\)

Since\(\iiint_E 1 d V\)is the volume of sphere with radius 1\($$\begin{aligned}& \iint_S\left(2 x+2 y+z^2\right) d S=\text { Volume of } E \\& =\frac{4}{3} \pi(1)^3=\frac{4}{3} \pi\end{aligned}$$Thus,\iint_S\left(2 x+2 y+z^2\right) d S=\frac{4}{3} \pi\)

Therefore, the divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

Use the Divergence Theorem to evaluate S(2x+2y+z2)dS where S is the sphere x2+y2+z2=1.

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Step-by-step explanation:

The volume =

base area × height

1/2×3.6×2.4 × 6

= 25.92 cm³

Answer:

30 m/s

Step-by-step explanation:

p = mv

momentum = mass × velocity

here the momentum is 60kgm/s

mass is 2kg

substitute in the equation

60 = 2v

v= 30m/s

The straightest lines on a sphere are great circles, which share the same center as the sphere.

A great circle is a circle on a sphere that has the same radius as the sphere and shares its center. It can be thought of as the intersection of the sphere with a plane that passes through its center. Great circles are called "great" because they have the largest possible circumference among all circles on the sphere.

Due to the symmetric nature of a sphere, any line connecting two points on its surface that passes through the center will follow the arc of a great circle. These lines are considered the straightest on the sphere since they are the shortest path between any two points on the sphere's surface.

Examples of great circles include the Equator on the Earth, which divides the sphere into two equal halves, and the lines of longitude that converge at the Earth's poles. Great circles also play an important role in navigation and are used in determining the shortest distance between two points on the Earth's surface.

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The implementation of Boolean function =

a) F = ((A NAND B) NAND (C NAND D)) AND ((A NAND C) NAND (B NAND D))

b) F = (A AND B AND C AND D) NOR (A AND (B NOR C) NOR D)

c) F = (A OR B OR C OR D) NAND ((A OR C) OR (B OR D))

d) F = (A NOR B NOR C NOR D) OR (A NOR C NOR B NOR D)

To implement the Boolean function F(A, B, C, D) = Σ(0,4,8,9,10,11,12,14) using different two-level forms of logic, we'll go through each form step by step:

(a) NAND-AND:

In this form, we'll use NAND gates followed by an AND gate to implement the function.

The expression for F in NAND-AND form is:

F = ((A NAND B) NAND (C NAND D)) AND ((A NAND C) NAND (B NAND D))

Here's a breakdown of the implementation:

The NAND gate produces the complement of the AND operation. So, (A NAND B) means "not (A AND B)."

In this form, the function is expressed as the conjunction (AND) of two NAND gate outputs.

Each NAND gate takes two inputs, and we'll use two NAND gates to handle each term of the sum of products.

(b) AND-NOR:

In this form, we'll use AND gates followed by a NOR gate to implement the function. The expression for F in AND-NOR form is:

F = (A AND B AND C AND D) NOR (A AND (B NOR C) NOR D)

Here's a breakdown of the implementation:

The AND gate produces the logical conjunction of its inputs.

In this form, the function is expressed as the disjunction (OR) of two NOR gate outputs.

Each AND gate takes multiple inputs, and we'll use two AND gates to handle each term of the sum of products.

(c) OR-NAND:

In this form, we'll use OR gates followed by a NAND gate to implement the function. The expression for F in OR-NAND form is:

F = (A OR B OR C OR D) NAND ((A OR C) OR (B OR D))

Here's a breakdown of the implementation:

The OR gate produces the logical disjunction of its inputs.

In this form, the function is expressed as the complement (NAND) of the conjunction (AND) of two OR gate outputs.

Each OR gate takes multiple inputs, and we'll use two OR gates to handle each term of the sum of products.

(d) NOR-OR:

In this form, we'll use NOR gates followed by an OR gate to implement the function. The expression for F in NOR-OR form is:

F = (A NOR B NOR C NOR D) OR (A NOR C NOR B NOR D)

Here's a breakdown of the implementation:

The NOR gate produces the complement of the logical OR operation.

In this form, the function is expressed as the disjunction (OR) of two NOR gate outputs.

Each NOR gate takes multiple inputs, and we'll use two NOR gates to handle each term of the sum of products.

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