Find k if y=3k/2x when f(6)=2

The required, methods have been arranged according to the rank from least precise to most precise.

Ranking the methods of timekeeping from least precise to most precise:

Therefore, methods have been arranged according to the rank from least precise to most precise.

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A mathematical quantity having both direction and magnitude is called a vector.

A vector is a mathematical quantity that has both direction and magnitude. It is often represented graphically as an arrow, where the length of the arrow corresponds to the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Vectors are used in many areas of mathematics and science, including physics, engineering, and computer science. Some common operations performed on vectors include addition, subtraction, dot product, and cross product.

Vectors can also be expressed in various coordinate systems, such as Cartesian, polar, and spherical coordinates, depending on the context and application.

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Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

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A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

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We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

12

Step-by-step explanation:

1st circle - \(1+3+6=10\)

3rd circle - \(6+2+5=13\)

2nd circle is proboably the same way.

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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The rate-of-change of area of triangle is changing when height is 16 cm and base is 12 cm is 30 cm²/min.

We know that the area of a triangle is given by the formula

⇒ A = (1/2)×b×h, where b = length of base and h = height,

We are given that the base is shrinking at a rate of 3 cm/min,

So, we have db/dt = -3 cm/min.

We are also given that the height is increasing at a rate of 9 cm/min,

So, we have dh/dt = 9 cm/min.

We need to find the rate at which the area of the triangle is changing with respect to time (dA/dt), when h = 16 cm and b = 12 cm.

⇒ dA/dt = (1/2)(db/dt)(h) + (1/2)(b)(dh/dt)

Substituting the values,

We get,

⇒ dA/dt = (1/2)×(-3)×(16) + (1/2)×(12)×(9),

⇒ dA/dt = -24 + 54,

⇒ dA/dt = 30 cm²/min

Therefore, the rate at which the area of the triangle is 30 cm²/min.

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The probability mass function of the discrete random variable x is:

p(x = -2) = 1/3

p(x = -1) = 1/6

p(x = 0) = 1/6

p(x = 1) = 1/6

p(x = 2) = 1/3

To determine the value of a, we first need to confirm that the probability mass function satisfies the two conditions of a valid probability mass function:

For this probability mass function, the possible values of x are -2, -1, 0, 1, and 2. Therefore, we can calculate the sum of probabilities as:

p ( x = -2 ) + p ( x = -1 ) + p ( x = 0) + p (x = 1) + p (x = 2)

= \(|(-2)| \times a + |(-1)| \times a + |0| \times a + |1| \times a + |2| \times a\)

= 2a + a + 0 + a + 2a

= 6a

To satisfy the first condition of a valid probability mass function, the sum of probabilities must be equal to 1. Therefore, we can set up the equation:

6a = 1

a = 1/6

Thus, the value of a that satisfies the conditions of a valid probability mass function is a = 1/6. Therefore, the probability mass function of the discrete random variable x is:

p(x = -2) = 1/3

p(x = -1) = 1/6

p(x = 0) = 1/6

p(x = 1) = 1/6

p(x = 2) = 1/3

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To find the missing side of the parallelogram, we need to use the right triangle shown in the coordinate plane. We can see that the height of the parallelogram is 3 units and the base is 8 units.

Therefore, we can use the Pythagorean theorem to find the length of the missing side (which is the hypotenuse of the right triangle).

a^2 + b^2 = c^2

where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

In this case, a = 3 and b = 5 (since the length of the base of the right triangle is 5 units, and we know that the length of the missing side plus the length of the base of the right triangle is 8 units).

So, we can plug in these values to get:

3^2 + 5^2 = c^2

9 + 25 = c^2

34 = c^2

c ≈ 5.83

Therefore, the missing side of the parallelogram is approximately 5.83 units.

2) Now that we know all four sides of the parallelogram (which are all congruent in a parallelogram), we can find the perimeter by adding up the lengths of all four sides.

P = 2a + 2b

where a and b are the lengths of the two adjacent sides of the parallelogram.

In this case, a = 5 (since we just found the length of the missing side to be approximately 5.83), and b = 8 (since we were given the length of the base of the parallelogram).

So, we can plug in these values to get:

P = 2(5) + 2(8)

P = 10 + 16

P = 26

Therefore, the perimeter of parallelogram PQRS is 26 units.

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Answer:

Step-by-step explanation:

A kite is symmetrical about its vertical axis, so

if it is a kite, P is the reflection of  (b,0), so its coordinates are

(-b,0) by reflection about the y-axis.

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

There are 317,520 possible ways the banquet committee can select the appetizers, main courses, and desserts.

To calculate the total number of ways the banquet committee can select the appetizers, main courses, and desserts, we need to use the concept of combinations.

The number of ways to select 4 appetizers out of 7 is given by the combination formula: C(7, 4) = 7! / (4! * (7 - 4)!) = 7! / (4! * 3!) = (7 * 6 * 5) / (3 * 2 * 1) = 35.

Similarly, the number of ways to select 5 main courses out of 9 is C(9, 5) = 9! / (5! * (9 - 5)!) = 9! / (5! * 4!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126.

And the number of ways to select 4 desserts out of 8 is C(8, 4) = 8! / (4! * (8 - 4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70.

To find the total number of ways to select the appetizers, main courses, and desserts, we multiply the number of choices for each category:

Total number of ways = 35 * 126 * 70 = 317,520.

Therefore, there are 317,520 possible ways the banquet committee can select the appetizers, main courses, and desserts.

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The magnitude of the electric field is 1,454,000 N/C and the SI unit for this answer is Newtons per Coulomb (N/C).

a) To find the net electric flux through the Gaussian surface, we can use Gauss's law which states that the electric flux through any closed surface is proportional to the charge enclosed by the surface.

So, \(Φ = q/ε0\), where Φ is the electric flux, q is the charge enclosed by the Gaussian surface, and ε0 is the permittivity of free space.

Since 6.78 pC of charge is enclosed by the Gaussian surface, the electric flux through the surface is \(Φ = (6.78 × 10^-12 C) / ε0.\)

The area of the Gaussian surface is

\((2.16 × 10^-6 m) × (2.16 × 10^-6 m) = 4.6656 × 10^-12 m^2.\)

So, the electric flux through the Gaussian surface is

\(Φ = (6.78 × 10^-12 C) / ε0 = (ε0 × E × 4.6656 × 10^-12 m^2) / ε0\),

where E is the electric field.

Solving for E, we get

\(E = (6.78 × 10^-12 C) / (4.6656 × 10^-12 m^2) = 1.454 × 10^6 N/C.\)

Therefore, the magnitude of the electric field is \(1.454 × 10^6 N/C\) and the SI unit for this answer is Newtons per Coulomb (N/C).

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y=3x+6

Step-by-step explanation:

point 1 (2;12)

point 2 (4;18)

\(m = \frac{y2 - y1}{x2 - x1} \)

\(m = \frac{18 - 12}{4 - 2} \)

\(m = \frac{6}{2} \)

m=3

y=mx+b

sub in a point and gradient

12=3(2)+b

12=6+b

b=6

y=3x+6

The value of the radius that minimizes the amount of Aluminium is 4.64 cm and it gives the local minimum of the function

From the question, the volume of the aluminium is given as

Volume = 200pi cm^3

Rewrite this volume properly using the correct symbols and units

So, we have the following representation

Volume = 200π cm³

Solving further, we make use of the volume of a cylinder (i.e. a can)

The volume of a sphere is represented as

V = πr²h

Substitute Volume = 200π cm³ in

πr²h = 200π

Make h the subject in the above equation

This gives

h = 200π/πr²

Cancel the common factors

h = 200/r²

The surface area of a can is

A = 2πr(h + r)

So, we have

A = 2πr(200/r² + r)

This gives

A = 400π/r + 2πr²

Differentiate the function

This gives

A' = -400π/r² + 4πr

Set the differentiated function to 0

-400π/r² + 4πr = 0

So, we have

-400π/r² = -4πr

Cross multiply

-400π = -4πr³

Divide through by -4π

r³ = 100

Take the cube roots

r = 4.64

Hence, the radius that given minimum material is 4.64 cm

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Answer:

for the first one t (less than or equal to sign)40 degrees Fahrenheit

Answer:

sorry this question is very hard

Answer:

1,3

Step-by-step explanation:

Answer:

(4, 2.5 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\), \(\frac{y_{1}+y_{2} }{2}\) )

Here (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (9, 5) , then

midpoint = ( \(\frac{-1+9}{2}\), \(\frac{2+5}{2}\) ) = ( \(\frac{8}{2}\), \(\frac{7}{2}\) ) = (4, 3.5 )

Answer:

$14.85

Step-by-step explanation:

8.98 + 3.27 + 1.5 = 13.75

13.75 x .08 = 1.1

13.75 + 1.1 = 14.85

Answer:

$14.85

Step-by-step explanation:

8.98 x.08= 0.7184

3.27 x .08= 0.2616

1.50 x .08= 0.12

8.98 + 0.72=  9.70

3.27 + .26= 3.53

1.50 + 12 =1.62

9.70+ 3.53 +1.62 = 14.85

Answer:

A. Rational number

Step-by-step explanation:

The square root of 9 is 3.

To check square 3 or square root 9.

3²=9

√9=3

3 is a rational number.

The answer above is also correct.

Hope this helps!

Answer:

3000

Step-by-step explanation:

The probability that at least one person receives exactly one aces in their 52 cards is 4/52= 1/13

We define the following events:

A: person A receives exactly two aces in their five cards.

B: person B receives exactly two aces in their five cards.

C: person C receives exactly two aces in their five cards.

We need to calculate P(A∪B∪C). According to the principle of inclusion and exclusion:

P(A∪B∪C)= P(A)+P(B)+P(C)-P(A∩B)-P(A∩C)-P(B∩C)+P(A∩B∩C)

Total outcomes is equal to  because there 52 cards and we select 5 of them.

The probability of each event is given by:

P(A)=P(B)=P(C)===0.0399

where the possible outcomes are 2 aces and 3 of the other cards.

Then, the intersections of the events mean that one player gets 2 aces and the other gets 2 aces too.

P(A∩B)=P(B∩C)=P(A∩C)==0.0001

Finally,

P(A∩B∩C)=0 because it is not possible that the three events occur at the same time due to there are only 4 aces.

P(A∪B∪C)= 0.0399+0.0399+0.0399-0.0001-0.0001-0.0001+0

P(A∪B∪C)=0.1194

The probability that at least one person receives exactly two aces in their five cards is 0.1194.

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A company wants to determine which of the two production methods has a shorter completion time. To collect completion time data, one sample of workers is randomly selected, and each worker first uses one method, and then the other method.

The sampling method used for data collection is based on a "within-subject design."The within-subject design, also known as a repeated measures design, is a type of research design in which all participants receive both levels of the independent variable (production methods) in a random order. This design is also known as a repeated-measures design, a within-subjects analysis, or a longitudinal design since it collects data over time and compares each participant's performance to his or her own scores on a different occasion.

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On solving the provided question we can say that by null hypothesis There is insufficient proof to conclude that student attendance has changed.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

This is a z-test for a proportion.

\(H0:p=.34 H1:p not=.34\\\alpha=0.01 ... this is a\\2-tailed test\\critical values are +2.58, -2.58\\p=.34 (given) q=1-p=.66\\p^=.33\\z=(p^-p)/sqrt(pq/n)\\z=(.33-.34)/sqrt(.34*.66/8302)\\z=-.01/.0051961\\z=-1.92\)

1.96 does not fall in the reject region

There is insufficient proof to conclude that student attendance has changed.

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From the diagram of the graph we can see that the transformation that is used is translation of 2 units left and 5 units down.

Given,

In the question:

Figure E is the result of a transformation on Figure D.

To find the which transformation would accomplish this?

Numerous different coordinate systems can be used to describe geometrical figures.

Solution: Figure D → Figure E

E vertex : (-1, -3) (0,0) (2, -1)

D vertex : (1, 2) (2,5) (4,4)

\(X_D\) (-2) → \(X_E\)

\(Y_D (-5)\) → \(Y_E\)

(X-2 , Y - 5)

Hence, From the diagram of the graph we can see that the transformation that is used is translation of 2 units left and 5 units down.

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Answer:

2.25 : 6.75

divide by 0.25

9 : 27

1 : 3

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept.

we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.

x + 2y = 6

2y = -x + 6

y = -x/2 + 6

Answer:

R=5%/year

Step-by-step explanation:

R = 5%/year

Equation:

r = I / Pt

Calculation:

Solving our equation

r = 1400 / ( 7000 × 4 ) = 0.05

r = 0.05

converting r decimal to a percentage

R = 0.05 * 100 = 5%/year

The interest rate required to

accumulate simple interest of $ 1,400.00

from a principal of $ 7,000.00

over 4 years is 5% per year.

Answer:

1) b) r = 7

2) e) 82

Step-by-step explanation:

Progressão aritmética:

Em uma progressão aritmética, a diferença entre termos consecutivos é sempre a mesma, chamada de razão.

O n-ésimo termo de uma PA é dado por, tomando o primeiro termo como referência:

\(a_n = a_1 + (n-1)r\)

Tomando o m-ésimo termo como referência, tem-se que:

\(a_n = a_m + (n-m)r\)

1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é:

\(a_5 = 40, a_9 = 68\). Então:

\(a_n = a_m + (n-m)r\)

\(68 = 40 + 4r\)

\(4r = 28\)

\(r = \frac{28}{4} = 7\)

Então a resposta correta é dada pela alternativa b.

2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a:

O primeiro termo é \(a_1 = 72\) e o oitavo termo é \(a_8 = 107\). Com isso, é possível encontrar a razão.

\(a_n = a_1 + (n-1)r\)

\(107 = 72 + 7r\)

\(7r = 35\)

\(r = \frac{35}{7} = 5\)

Então, o terceiro termo é:

\(a_3 = a_1 + 2r = 72 + 2(5) = 82\)

Logo, a resposta correta é dada pela alternativa e.

Answer:

11 cm

Step-by-step explanation:

The strip of paper is 66 cm and it is folded into 6 different parts. It is used to form a model of a honeycomb cell.

To find the length of one side of the model, all we have to do is divide 66 cm by 6. That is:

66 / 6 = 11 cm

The length of one side of the model is 11 cm.