how many possible ways are there to match or pair vertices (one-to-one) betweenaandb?

Therefore, the number of ways a student can work 7 out of 10 questions on the exam is 120, which corresponds to option (D).

The number of ways a student can work 7 out of 10 questions on an exam can be calculated using the concept of combinations.

The formula for combinations is given by:

C(n, k) = n! / (k!(n - k)!)

Where n is the total number of items and k is the number of items chosen.

In this case, the student is choosing 7 questions out of a total of 10, so we have:

C(10, 7) = 10! / (7!(10 - 7)!) = 10! / (7!3!)

Simplifying:

10! = 10 * 9 * 8 * 7!

3! = 3 * 2 * 1

C(10, 7) = (10 * 9 * 8 * 7!) / (7! * 3 * 2 * 1)

The 7! terms cancel out:

C(10, 7) = (10 * 9 * 8) / (3 * 2 * 1)

C(10, 7) = 120

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The values of the number expression as a fraction are 1/9, 1/64, and 1/64 respectively after applying the properties of the integer exponent.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The number expression:

After applying the properties of the integer exponent.

A )3⁻²

= 1/9

b)4⁻³

= 1/64

C)2⁻⁶

= 1/64

Thus, the values of the number expressed as a fraction are 1/9, 1/64, and 1/64 respectively after applying the properties of the integer exponent.

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Answer:

66 years old now

bro 60 plus 6

Answer:

66

Step-by-step explanation:

2022 - 6 = 2016

2016 <-> 60

2022 <-> 66

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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Answer:

300

Step-by-step explanation:

2252÷7≈2250÷7

            ≈300

The required radian angle the dog has rotated through is 2.5 radians.

To find the radian angle the dog has rotated through, we can use the formula:

θ = arc length/radius

In this case, the arc length is the distance the dog has traveled, which is the length of the car, 25 feet. The radius is the length of the leash, 10 feet.

θ = 25 feet / 10 feet = 2.5 radians

Therefore, the radian angle the dog has rotated through is 2.5 radians.

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The probability that the vehicle Bob chooses is used or is a car is 0.6

There are 10 new cars, 4 used cars, 12 new trucks, and some used trucks at Bob's Auto Plaza. We are asked to find the probability that the chosen vehicle is used or is a car.

First, we need to find the total number of vehicles at the dealership:

Total number of vehicles = 10 new cars + 4 used cars + 12 new trucks + used trucks

We don't know how many used trucks there are, but we know that there are at least 4 of them (since there are 4 used cars). So the total number of vehicles is at least:

Total number of vehicles = 10 + 4 + 12 + 4 = 30

Now we need to find the number of vehicles that are used or cars. There are 4 used cars, and 10 new cars, for a total of 14 cars. There are also some used trucks, which we don't know the exact number of, but we know that there are at least 4 of them. So the total number of used or car vehicles is at least:

Total number of used or car vehicles = 4 used cars + 10 new cars + 4 used trucks = 18

To find the probability of choosing a used or car vehicle, we divide the number of used or car vehicles by the total number of vehicles:

Probability of choosing a used or car vehicle = Total number of used or car vehicles / Total number of vehicles

Probability of choosing a used or car vehicle = 18 / 30

Divide the numbers

Probability of choosing a used or car vehicle = 0.6

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The given question is incomplete, the complete question is:

At Bob's Auto Plaza there are currently 10 new cars, 4 used cars, 12 new trucks, and used trucks, Bob is going to choose one of these vehices at random te be the Deal of the Month. What is the probability that the vehicle that Bob chooses is used or is a car? Do not round intermediate computations, and round your answer to the nearest hundredth

Answer:

\(y = - 35\)

Step-by-step explanation:

\(y = 7x \\ y = 7( - 5) \\ y = - 35\)

Answer:

148.9ft underwater

Step-by-step explanation:

Substract the ft the submarine dove minus the ft the submarine came up.

Ex. ft of dive-ft of coming up

Which would be 363.5-214.6=

148.9ft

Answer:

$22500

Step-by-step explanation:

principal=$12000

time=15 years

rate=\(12\frac{1}{2}\)

=12*2+1/2

=25/2

=12.5

Interest=PTR/100

=$12000*15*12.5/100

=$2250000/100

=$22500

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Answer: b represents the variable and 42 represents the coefficent.

Step-by-step explanation:

The required  the  parts of the park expression 42b represent

the total price of the bolga basket , b represents the number of bolga basket and 42 represents the cost of each bolga basket.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

Bolga baskets= $42

The expression 42b represents the total price buying b baskets.

According to given question we have

The given statement is

Let the number of bolga basket be b

So, the total price of the bolga basket =42b

The cost of each bolga basket is  $42

Therefore, the required  the  parts of the park expression 42b represent

the total price of the bolga basket , b represents the number of bolga basket and 42 represents the cost of each bolga basket.

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The probabilities for sub-system are as follows: a. Probability = 0.7223, b. Probability = 0.9775, c. Probability = 0.9996.

a. The probability of the sub-system operating as shown is calculated by multiplying the probabilities of each component operating successfully:

Probability = 0.85 * 0.85 = 0.7225

b. If each component has a backup with a probability of 0.85, the probability of the sub-system operating is the complement of both components failing simultaneously. We can calculate it as follows:

Probability = 1 - (1 - 0.85) * (1 - 0.85) = 1 - (0.15 * 0.15) = 1 - 0.0225 = 0.9775

c. If each component has a backup with a probability of 0.85 and a switch that is 98% reliable, the probability of the sub-system operating is the complement of both components failing simultaneously and the switch also failing. We can calculate it as follows:

Probability = 1 - (1 - 0.85) * (1 - 0.85) * (1 - 0.98) = 1 - (0.15 * 0.15 * 0.02) = 1 - 0.00045 = 0.99955

Rounded to 4 decimal places:

a. Probability = 0.7223

b. Probability = 0.9775

c. Probability = 0.9996

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Density is how much matter is contained within a volume. A dense object weighs more than a less dense object that is the same size. An object less dense than water will float on it; one with greater density will sink. The density equation is density equals mass per unit volume or D = M / V. (Hope this helped!)

Answer:

x2 + x - 20.

Step-by-step explanation:

(x-4)(x+5) = x^2-4x+5x-20 = x^2+x-20 = x^2 + x - 20.

Hope This Helped

\(\mathbb{PROBLEM :}\)

\( \tt \: 6. Multiply: ( \times - 4)(x + 5)\)

==========================================

\(\mathbb{ANSWER:}\)

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \underline \color{green}{x2 + x - 20}\)

==========================================

\(\mathbb{SOLUTION:}\)

\( \: \: \: \: \: \: \: \: \tt( \times - 4)( \times + 5)\)

\( \: \: \: \: \: \: \: \: \tt = \: x(x + 5) -4(x + 5)\)

\( \: \: \: \: \: \: \: \: \tt{ = \times 2 + 5 \times 4 \times - 20}\)

\( \: \: \: \: \: \: \: \: \tt{= x2 + x - 20}\)

\( \tt \: So \: possible \: Answer \: is : \underline \green{ \times 2 + \times - 20}\)

==========================================

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︎ CarryOnLearning ૮₍˶ᵔ ᵕ ᵔ˶₎ა

︎︎└─────── °∘❁∘° ───────┘

Answer:

(2m+9)(m-1)

Step-by-Step Explanation:

As per unitary method, the height of the light pole is 3 feet.

The unitary method involves finding the value of one unit and then using it to find the value of another unit. In this problem, we can use the height of Jenny as one unit and her shadow length as another unit. Let's assume that Jenny's height is 1 unit and her shadow length is x units.

Now, we need to find the value of one unit in terms of the height of the light pole. To do this, we can use the fact that the lengths of the two shadows are proportional to the heights of the objects casting the shadows. That is, if the height of the light pole is h units, then we have:

Jenny's height / Jenny's shadow length = Light pole's height / Light pole's shadow length

Substituting the values, we get:

1 / x = h / y

where y is the length of the shadow of the light pole.

We can rearrange this equation to find the value of h in terms of x and y:

h = (x * y) / 1

Now, we can substitute the given values of x and y to find the height of the light pole. If Jenny's shadow is 10 feet long and the shadow of the light pole is 30 feet long, then we have:

h = (1 * 30) / 10 = 3 feet

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A. The speed at which blood is travelling through the plaque-constricted region is approximately 31.62 cm/s. and B. P2 - P1 ≈ -405,431.58 kg/\((m*s^2)\) = -405,431.58 Pa (approximately).

(a) To determine the speed at which blood is travelling through the plaque-constricted region, we can apply the principle of continuity, which states that the flow rate of an incompressible fluid remains constant in a closed system.

The flow rate (Q) is given by the product of the cross-sectional area (A) and the velocity (v): Q = A * v.

Since the flow rate remains constant, we can write:

Q1 = Q2

A1 * v1 = A2 * v2

The cross-sectional area of the artery can be approximated as A = π * \(r^2\), where r is the radius of the artery.

Given that the diameter decreases from 1.16 cm to 0.70 cm, the initial radius (r1) is 0.58 cm (0.58 cm = 1.16 cm / 2) and the final radius (r2) is 0.35 cm (0.35 cm = 0.70 cm / 2).

Using these values, we can find the ratio of the cross-sectional areas:

A1/A2 = (π * \(r1^2\)) / (π * \(r2^2\)) =\((r1^2) / (r2^2).\)

Substituting the given values:

A1/A2 = \((0.58 cm)^2 / (0.35 cm)^2\) ≈ 2.108.

Since the cross-sectional areas are inversely proportional to the velocities, we have:

v2 = (A1/A2) * v1 = 2.108 * 15.0 cm/s ≈ 31.62 cm/s.

Therefore, the speed at which blood is traveling through the plaque-constricted region is approximately 31.62 cm/s.

(b) To determine the pressure change within the plaque-constricted region, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid in a flowing system.

Bernoulli's equation is given by:

P1 + (1/2) * ρ * \(v1^2\) + ρ * g * h1 = P2 + (1/2) * ρ * \(v2^2\) + ρ * g * h2.

Where P1 and P2 are the pressures, v1 and v2 are the velocities, ρ is the density of blood, g is the acceleration due to gravity, h1 is the initial height, and h2 is the final height.

In this case, we can assume that the height remains constant, so the terms ρ * g * h1 and ρ * g * h2 cancel out.

Since we are interested in the pressure change, we can rewrite Bernoulli's equation as:

P2 - P1 = (1/2) * ρ * \((v1^2 - v2^2).\)

Substituting the given values:

\(P2 - P1 = (1/2) * 1050 kg/m^3 * [(15.0 cm/s)^2 - (31.62 cm/s)^2].\\P2 - P1 = (1/2) * 1050 kg/m^3 * [225 cm^2/s^2 - 1000.2244 cm^2/s^2].\)

\(P2 - P1 ≈ (1/2) * 1050 kg/m^3 * (-775.2244 cm^2/s^2).\\P2 - P1 ≈ -405,431.58 kg/(m*s^2) = -405,431.58 Pa (approximately).\)

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Answer:

Step-by-step explanation:

We have

\(f(x) = 6x + 5\)

\(g(x) = 3x\)

To find the value of either of these functions for a specific value of x, simply substitute that value into the corresponding function equation.

\(\bold{f(2)}\)
Substitute x with 2 in 6x + 5
==> \(6\cdot \:2+5=17\)   (Answer)

\(\bold{g(4)}\)
Substitute x with 4 in g(x) = 3x
==> \(3 \cdot4=12\)  (Answer)

\(\bold{f(-2)}\)
Substitute x with -2 in 6x + 5
\(6\left(-2\right)+5=-7\)  (Answer)

\(\bold{g(0)}\)
Substitute x with 0 in g(x) = 3x
==> \(3\cdot0=0\)  (Answer)

\(\bold{f(\frac{1}{2})}\)
Substitute x with \(\frac{1}{2}\) in 6x + 5
==>  \(6\cdot \frac{1}{2}+5 = 3 + 5 = 8\)   (Answer)

\(\bold{g(-4)}\)
Substitute x with -4 in g(x) = 3x
==> \(3\left(-4\right) = -12\)  (Answer)

Answer:

C

Step-by-step explanation:

Given

- 12x - 2(x + 9) = 5(x + 4) ← distribute parenthesis on both sides

- 12x - 2x - 18 = 5x + 20, that is

- 14x - 18 = 5x + 20 ( subtract 5x from both sides )

- 19x - 18 = 20 ( add 18 to both sides )

- 19x = 38 ( divide both sides by - 19 )

x = - 2 → C

Answer:

x=-2

Step-by-step explanation:

-12x-2(x+9)=5(x+4)

-12x-2x-18=5x+20

-14x-5x=20+18

-19x=38

x=38/-19

x=-2

A circle is a curve sketched out by a point moving in a plane. The measure of x is 60°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given that the measure of the arc AC is 120°. Now, as we know, the diameter divides the circle into two equal chords of 180° each. Therefore, the measure of x can be written as,

\(x = {\rm arcAB-arc AC}\\\\x = 180^o-120^o\\\\x = 60^o\)

Hence, the measure of x is 60°.

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Answer:

Step-by-step explanation:

1. no-has decimal

2. yes, simplifies to -2

3. yes

4. yes

5. no-2.1

There are infinite possible values of k.

To find the possible values of k, we need to determine the common factors of the two given polynomials.

Let's denote the first polynomial as P(x) = kx³ + 2x² + 2x + 3 and the second polynomial as Q(x) = kx³ - 2x + 9.

For these polynomials to have a common factor, it means that there exists a polynomial R(x) such that both P(x) and Q(x) can be expressed as the product of R(x) and another polynomial S(x). Mathematically, this can be written as P(x) = R(x) * S(x) and Q(x) = R(x) * T(x).

Since P(x) and Q(x) have a common factor, their common factor must also be a factor of their difference. Therefore, we can compute their difference as follows:

P(x) - Q(x) = (kx³ + 2x² + 2x + 3) - (kx³ - 2x + 9)

= kx³ + 2x² + 2x + 3 - kx³ + 2x - 9

= 2x² + 4x - 6

For P(x) - Q(x) to be divisible by R(x), the remainder should be zero. In other words, 2x² + 4x - 6 should be divisible by R(x).

Now, we need to determine the factors of 2x² + 4x - 6. By factoring this quadratic expression, we get (2x + 6)(x - 1).

Therefore, the possible values of k would be such that (2x + 6)(x - 1) is a factor of both P(x) and Q(x). For this to happen, we need to find the values of x that satisfy (2x + 6)(x - 1) = 0.

Setting each factor equal to zero, we have two possible values of x: x = -3 and x = 1.

Now, substituting these values of x back into the original polynomials, we can solve for k:

For x = -3:

P(-3) = k(-3)³ + 2(-3)² + 2(-3) + 3

= -27k + 18 - 6 + 3

= -27k + 15

Q(-3) = k(-3)³ - 2(-3) + 9

= -27k + 6 + 9

= -27k + 15

For x = 1:

P(1) = k(1)³ + 2(1)² + 2(1) + 3

= k + 2 + 2 + 3

= k + 7

Q(1) = k(1)³ - 2(1) + 9

= k - 2 + 9

= k + 7

Since P(-3) = Q(-3) and P(1) = Q(1), we can conclude that k + 7 = -27k + 15 and k + 7 = k + 7.

Simplifying these equations, we have:

-27k + k = 8

0 = 0

Since the equation 0 = 0 is always true, it means that k can be any real number.

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Answer:

Oh easy...

Step-by-step explanation:

Multiply the numerator on the left by the denominator on the right, and the numerator on the right by the denominator on the left, to solve a proportion. Cross multiplying is the term for this. Simplify the equation, then solve for the variable using the inverse operation, division.

Answer:

0.25 feet for each friend because 2.5/10=0.25

Answer:

0.25 ft.

Step-by-step explanation

You have to divide 2.5 by the amount of friends she has so 2.5/10. Then you would moce the decimal one place forward. You would get 0.25.

Happy to help! Have a great day!

Answer:

C. To make predictions about the values of y for a given​ x-value (I THINK)

Answer:

\(a) x=15\\b) AD\ is\ not\ parallel\ tp BC\)

Step-by-step explanation:

\(As\ we\ know\ that,\\Angle\ D=3x\\Angle\ A=2x\\Angle\ B=90\\Angle\ C=x\\The\ Angle\ Sum\ Property\ Of\ A\ Quadrilateral\ states\ that\ the\ sum\ of\ all\\ the\ interior\ angles\ of\ a\ quadrilateral\ is\ 180.\\Hence,\\ \angle D+ \angle A + \angle B + \angle C=360\\3x+2x+90+x=180\\3x+2x+x=180-90\\6x=90\\x=15\\Hence, x=15\)

\(Hence,\\As\ Angle\ A\ and\ Angle\ B\ are\ co-interior\ angles, if\ they\ are\\ supplementary\ then\ AD \parallel BC.\ Lets\ check\ that\ out.\\Hence,\\Angle\ A=2x=2*15=30\\Angle\ B=90\ [Given]\\Hence,\\As\ 90+30\neq 180,\\Angle\ A +Angle\ B\neq 180\\Hence,\\As\ Angle\ A and\ Angle\ B\ are\ not\ supplementary, AD\ will\ not\ be\ parallel\ to\ CB.\)

The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.

The study is a sample survey, because the population is for it to be practical to record all of the responses.

a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.

b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.

c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.

d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.

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