How do you use index notation?

The solution for x on the diagram is given as follows:

x = 111.

The angle measures in this problem are given as follows:

x and (x - 42)º.

They are on the same side relative to the transversal line, and between the two parallel lines, hence they are classified as consecutive interior angles.

Consecutive interior angles are supplementary, as the sum of their measures is of 180º, hence the value of x is obtained as follows:

x + x - 42 = 180

2x = 222

x = 222/2

x = 111.

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The equation for a hydraulic lift can be used to calculate the force on each mass.  F1 = F2

m2 = 210 kg

Using the equation for a hydraulic lift, the force on each mass can be calculated.

F1 = F2

(m1 x g) x (d1/d2) = (m2 x g)

(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)

210 kg = m2 x 9.8 m/s2

m2 = 210 kg/9.8 m/s2

m2 = 21.43 kg

m2 = 210 kg (rounded up)

The equation for a hydraulic lift can be used to calculate the force on each mass.  F1 = F2

(m1 x g) x (d1/d2) = (m2 x g)

Plug in the given values:

(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)

Solve for m2:

m2 = 210 kg/9.8 m/s2

m2 = 21.43 kg

m2 = 210 kg (rounded up)

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By examining the truth table, we can determine the two expressions are equivalent and it is possible for one of them to be true and the other false.

Given two Boolean expressions, it is possible for one of them to be true and the other false if they are not equivalent. For example, consider the two expressions: φ ∧ (ψ ∨ θ) and (φ ∧ ψ) ∨ (φ ∧ θ).

It is possible to construct a truth table for these two expressions, which shows all possible combinations of truth values for φ, ψ, and θ, along with the corresponding truth values for the two expressions.

Boolean logic is a branch of mathematical logic that deals with binary operations (i.e., true or false values) and is often used in computer science. One of the basic operations in Boolean logic is the logical conjunction (denoted by ∧), which represents the and operator. For example, if φ and ψ are two propositions, then φ ∧ ψ is true if and only if both φ and ψ are true.

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Answer:

7 boxes of pencils and 5 boxes rubbers.

Step-by-step explanation:

Since LCM (10,14) = 70, that means that the minimum number of each you must buy is 70. So it's 7 boxes of pencils ( 10 each ) and 5 boxes of rubbers ( 14 each ).

The solution to the system of equation -3x = 2y - 34 and 3y = 13 + 5x     is x = 4 and y = 11

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Given the equations:

-3x = 2y - 34

multiply the equation by 3:

-9x = 6y - 102

-9x - 6y = -102      (1)

And:

3y = 13 + 5x    

multiply the equation by 2:

6y = 26 + 10x

-10x + 6y = 26         (2)

To solve by elimination method, add equation 2 and 1 to get:

-19x = -76

x = 4

Put x = 4 in the equation:

-3x = 2y - 34

-3(4) = 2y - 34

2y = 22

y = 11

The solution to the equation is x = 4 and y = 11

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Answer:not sure

Step-by-step explanation:

Answer:

See explanation and examples below.

Step-by-step explanation:

The probability that an event (desired outcome) will occur is the quotient of the number of ways the event can occur (desired outcomes) and the total number of possible outcomes.

For example, consider a die. A die is a 6-faced cube with numbers 1 through 6 on its faces.

The total number of possible outcomes is 6 since it can land with any face with numbers 1 through 6 facing up.

What is the probability if getting a 5?

Here the desired outcome is a 5. There is only one desired outcome since only 1 face has a 5. The total number of possible outcome is 6.

p(5) = 1/6

The probability of getting a 5 is 1/6.

Another example:

A spinner has 4 sections of equal size.

1 section is red.

1 section is blue.

1 section is green.

1 section is yellow.

What is the probability of landing on red?

Desired outcome: landing on red

Number of desired outcomes: 2

Total number of possible outcomes: 4

p(red) = 1/4

Using the same spinner, what is the probability of landing on yellow or green?

Landing on the green section or landing on the yellow section are both desired outcomes, so the number of desired outcomes is 2.

The total number of outcomes is 4.

p(yellow or green) = 2/4 = 1/2

Answer:

a

Step-by-step explanation:

Answer: 17

Step-by-step explanation: 3.4 can go into 57.8 seventeen times. 3.4 x 17 is 57.8. Therefore, 57.8 divided by 3.4 is 17.

Check the picture below.

[tex]\cfrac{x}{1225}=\cfrac{2035}{2950}\implies \cfrac{x}{1225}=\cfrac{407}{590}\implies x=\cfrac{(1225)(407)}{590}\implies x=\cfrac{99715}{118}~ft[/tex]

now, we know your strolling speed is 200 ft per minute or 200 ft per 60 seconds, so how long for that distance above?

[tex]\begin{array}{ccll} feet&seconds\\ \cline{1-2} 200&60\\[1em] \frac{99715}{118}&y \end{array}\implies \cfrac{200}{ ~ \frac{99715}{118}~ } =\cfrac{60}{y}\implies \cfrac{200}{1}\cdot \cfrac{118}{99715}=\cfrac{60}{y} \implies \cfrac{4720}{19943}=\cfrac{60}{y} \\\\\\ 4720y=(19943)(60)\implies y=\cfrac{(19943)(60)}{4720}\implies y\approx 254~seconds[/tex]

To find the distance DE across a river using indirect measurement, you can use the Angle-Angle (AA) Congruence Theorem.

A jogging path runs along the river from point C to point E ,passing through point A.

To find the distance DE across a river using indirect measurement, you can use the Angle-Angle (AA) Congruence Theorem.

This theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are congruent. In this scenario, you can measure the angles at A in both triangles ABC and ADE, and if they are congruent, you can conclude that the triangles are congruent by AA Congruence Theorem.

Knowing that ABC and ADE are congruent, you can use the Side-Side-Side (SSS) Congruence Theorem to find that their corresponding sides are congruent.

In particular, you can conclude that AB = AD, BC = DE, and AC = AE, which means that DE can be found by simply measuring AC and subtracting AB.

Therefore, we can use the Angle-Angle (AA) Congruence Theorem.

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The value of XY in the given trapezoid is 30 ft

A quadrilateral with at least one pair of parallel sides is called a trapezoid.

Given that, a trapezoid WXYZ we need to find XY,

We need that,

Midsegment of a trapezoid = M = 1/2 (b1 + b2), where b1 and b2 are parallel sides,

Therefore,

35 = (xy + 4xy/3) / 2

70 = 7xy / 3

210 = 7xy

xy = 30

Hence, the value of XY is 30 ft

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Answer:

3.4 in²

Step-by-step explanation:

Information we must know:

1) Find the area of the circle

2) Find the area of the square around the circle

3) Subtract!

Have a lovely day :)

Answer:

3.4 in²

Step-by-step explanation:

We can solve for the area of the blue portion of this figure by subtracting the area of the circle (the area that is NOT blue) from the area of the surrounding square.

First, we can solve for the area of the square using arithmetic.

In this problem, the side length is twice the radius ([tex]r[/tex]) of the circle (given as 2 in), since the circle is circumscribed inside the square, meaning that it touches the square at all 4 midpoints of its sides.

[tex]\textrm{side length} = 2r[/tex]

[tex]\textrm{side length} = 2(2 \, \textrm{in})[/tex]

[tex]\textrm{side length} = 4 \, \textrm{in}[/tex]

Now we can solve for the area of the square using the formula:

[tex]\textrm{Area}_\square = \textrm{side length}^2[/tex]

[tex]\textrm{Area}_\square = (4 \, \textrm{in})^2[/tex]

[tex]\textrm{Area}_\square = 16 \, \textrm{in}^2[/tex]

Next, we can solve for the area of the circle using the formula:

[tex]\textrm{Area}_\circ = \pi r^2[/tex]

Remember that the radius of the circle was given as 2 in.

[tex]\textrm{Area}_\circ = \pi (2 \, \textrm{in})^2[/tex]

[tex]\textrm{Area}_\circ = 4\pi \, \textrm{in}^2[/tex]

Finally, we can solve for the area of the blue portion of the figure by subtracting the area of the circle from the area of the square.

[tex]\textrm{Area}_{\textrm{blue}} = A_\square - A_\circ[/tex]

[tex]\textrm{Area}_{\textrm{blue}} = 16 \, \textrm{in}^2 - 4\pi \, \textrm{in}^2[/tex]

If we plug this into a calculator, we approximately get:

3.4 in²

The height of the kite from the ground is 54ft

Information involves angles of elevation that can be solved using the trigonometric ratios of sine.

The question reads that a geometry student is flying a

kite with 120-ft of string and their

hand 4-ft from the ground

The height is found by  sin30 = h+4/120

Making h the subject of the relationship

h+4 = 120 * 0.5

h= 60-4

Therefore the height of the kite is 54ft

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The solution to x, when the equations au = a and av =b are satisfied, will be x = [0 0].

Given that u = [2 -3] and v = [4 2] satisfy the equations au = a and av = b, we need to find a solution to the equation ax = b.

Let's express the matrix an as a column vector of its columns: a = [a1 a2]. Now, we have the following equations:

a*u = a

[a1 a2] * [2 -3] = [a1 a2]

This yields two equations:

2a1 - 3a2 = a1

2a1 - 3a2 = a2

Simplifying these equations, we get:

a1 = 3a2 ...(1)

a2 = 2a1 ...(2)

Substituting equation (2) into equation (1), we have:

a1 = 3(2a1)

a1 = 6a1

Solving for a1, we find a1 = 0.

Substituting this value back into equation (2), we have:

a2 = 2(0)

a2 = 0

Therefore, a solution to x is x = [0 0].

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Histogram is a visual representation of data distribution and a stem and leaf plot provide individual values in a set.

Pros of a histogram:

Cons of a histogram:

Pros of a stem-and-leaf plot:

Cons of a stem-and-leaf plot:

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The required value of w in the given expression is 1, as per the given conditions.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The question seems to be incomplete, assume that the given expression 8w + 5 = 13
So

8w + 5 = 13
simplify

8w = 13 - 5
w = 8 / 8
w = 1

Thus, the required value of w in the given expression is 1, as per the given conditions.

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Total number of ways to paint rooms is 19,740.

We can solve this problem using the combinatorics. First, we choose the color for the living rooms, which can be done in 3*2 = 6 ways (yellow, red, or purple). Then, we choose the colors for the remaining 10 rooms.

Case 1 : living room is yellow and red

Then remaining colors are 3 yellow, 4 red, 3 purple

number of ways to paint living room = 2

number of ways to pain bedroom = 10!/(3! 4! 3!)

So number of ways = 2 * 10!/(3! 4! 3!) = 8400

Case 2 : living room is yellow and purple

Then remaining colors are 3 yellow, 5 red, 2 purple

So number of ways = 2 * 10!/(3! 5! 2!) = 5040

Case 3 : living room is red and purple

Then remaining colors are 4 yellow, 4 red, 2 purple

So number of ways = 2 * 10!/(4! 4! 2!) = 6300

Total number of ways = 8400 + 5040 + 6300 = 19,740

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The plastic cylinder will take 18 cubic inches of sand to fill it.

Let 'r' and 'h' be the radius and height of the both cylinder and cone, then the ratio of the volume of the cylinder to the volume cone can be calculated as given below

=> Volume of cylinder: Volume of cone

=> πr²h : 1/3 πr²h  

=> 1: 1/3  

=> 3: 1

Ratio of volume of a cylinder to the volume of a cone = 3: 1  

which means the volume of the cone is one-third of the volume of the cylinder

Given that

It takes 6 cubic inches of colored sand to fill a plastic cone.  

The volume of the cone = 6 cubic inches

It is also given that cylinder has the same base and height as the cone

As we know the volume of the cone is one-third of the volume of the cylinder

Volume of cone = (1/3) × Volume of cylinder

=> Volume of cylinder = 3 × Volume of cone

Volume of the given cylinder = 3 × 6 cubic inches  

= 18 cubic inches

Therefore,

The plastic cylinder will take 18 cubic inches of sand to fill it.

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Answer:

see bleow

Step-by-step explanation:

supplementary simply means angle 1+ which angle =180

so angle 2 & 4 are supplementary.

if angle 1 = 124, then angle 4 = angle 2 = 180-124 =56

angle 3 = angle 1 =124

The solutions that match the given differential equation are a)y=0 and b)y=2x.

The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.

In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.

Therefore, the general solution to this differential equation is y = c1 + c2x.

y=0 is a solution of the differential equation since it satisfies the equation when plugged in.

y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.

y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.

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The number is: 9.

The number we are trying to find consists of two digits, with the units digit being 9.

So, let's call the number x. The number would be 10x + 9.

Next, we add 9 to the number, and the digits are interchanged. This means the number becomes 10 + x.

Now, we have two equations:

By comparing the two equations, we can deduce that x = 10 + x - 9.

So, the original number was 9, and after adding 9, it became 10 + 9 = 19, which has its digits interchanged.

Complete Question:

"A number consists of two digits, with the units digit being 9. If 9 is added to the number, its digits are interchanged. Find the number."

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How frequently and how long is the system in use function

A system's reliability can be used to gauge how well it is operating and performing. It considers both the system's software and hardware components. This includes how long the system can function without experiencing any issues, how frequently it bounces back from a crash or failure, and how rapidly it reacts to information or service demands. The frequency and length of any system outages, as well as how quickly and dependably the system recovers from failure, must all be determined in order to assess a system's reliability. The user experience should also be taken into account because people may assess the reliability of a system based on how fast and effectively it answers to their requests. In order to determine a system's reliability with precision,

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The complete question is

reliability is measured as the amount of time the system is running and functioning properly. this includes the system’s hardware and software. What is the correct question for the statement above. How frequently and how long is the system in use function ?

Answer: CDB

Step-by-step explanation: Congruent angles are angles that are identical to each other. For a more in-depth explanation, Congruent angles are basically when two angles "have the same shape and size, or if one has the same shape and size as the mirror image of the other". Out of the choices given, CDB is the most identical to BAC. If you rotate CDB with your mind, you'll notice that you get BAC.

The histogram in question is a visual representation of the weights of guinea pigs. It indicates that the median weight is located in the interval between 250 and 300.

This is determined by first looking at the shape of the histogram. The histogram is approximately symmetrical, meaning that the median is going to be located in the middle of the data points. When looking at the intervals listed in the histogram, the interval between 250 and 300 is the middle interval, thus indicating that the median weight falls in this range.

In addition, the peak of the histogram is located in this interval, which further confirms that the median weight falls in the interval between 250 and 300. Overall, the interval between 250 and 300 contains the median guinea pig weight.

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The probability that all tosses produce different outcomes is 1.666

Probability;

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Number of toss of dice = 3 times

Number of ways to throw one dice that shows different results = 6 × 5 × 4 × 3 = 360 ways

The total number of throw results = 6³ = 216

Now,

The probability that each throw will result in a different result;

Number of ways / Total number of throws = 360 / 216 = 1.666

The probability that each toss will result in a unique outcome is 1.666

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The solution to the quadratic equation x² + 4x + 4 = 0 is x = -2 and x = -2

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The standard form of a quadratic equation is:

y = ax² + bx + c

Where a, b and c are constants

Given the quadratic equation:

x² + 4x + 4 = 0

x² + 2x + 2x + 4 = 0

x(x + 2) + 2(x + 2) = 0

(x + 2)(x + 2) = 0

x + 2 = 0; and x + 2 = 0

x = -2 and x = -2

The solution to the quadratic equation is x = -2 and x = -2

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Answer:

m = 5/4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0, -3) (4, 2)

We see the y increase by 5 and the x increase by 4, so the slope is

m = 5/4

The required money that Taha paid more than lowan is £0.6, as per the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Taha buys one fish, a portion of peas, and pickled onion.
taha paid = 2.70 + 0.45 + 0.25
= £3.40

Lowan buys a portion of rice, a sausage, and a bread roll.

Total money lowan to pay
= 0.90 + 1.60 + 0.30
= £2.80

Money Taha pays more than lowan = 3.40 - 2.80
                                                      = £0.6

Thus, the required, money that Taha paid more than lowan is £0.6, as per the given condition.

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The probability of flipping 1 head in a fair coin flip is 0.5. The probability of flipping t heads in a row is [tex]0.5^{t}[/tex]. To win the game, you need to flip t heads after flipping t tails, so the probability of winning the game is ([tex]0.5^{t}[/tex])².

The probability of flipping heads in a fair coin flip is 0.5, meaning that the chance of getting heads on any given flip is 50%. If you have flipped t tails and now need to flip t heads in a row to win the game, then the probability of flipping t heads in a row is [tex]0.5^{t}[/tex].

To win the game, you need to flip t heads after t tails, so the overall probability of winning the game is ([tex]0.5^{t}[/tex])², which is the probability of flipping t heads multiplied by the probability of flipping t tails. In other words, the chance of winning the game is the product of the individual probabilities of each coin flip outcome. The probability of winning the game decreases as the number of heads you need to flip in a row increases.

To simplify the answer, let's assume that you need to flip t=3 heads in a row to win the game after flipping t=3 tails

The probability of flipping one head is 0.5, so the probability of flipping 3 heads in a row is (0.5)³ = 0.125.

The probability of flipping one tail is also 0.5, so the probability of flipping 3 tails in a row is (0.5)³ = 0.125.

The probability of winning the game, which is flipping 3 heads after flipping 3 tails, is (0.125)² = 0.015625.

So, the probability of winning the game is approximately 0.016, or 1.56%.

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Answer:

52.9 inches.

Step-by-step explanation:

Let's call the current height of the corn stalks as "h". Then the increase in height will be 0.058 * 50 = 2.9 inches.

So, h = 50 + 2.9 = 52.9 inches.