Which of the following equations is equivalent to 2x+y = 7?
a
y = -2x +7
Ob
y = 2x +7
y=2x-7
y=-2x-7
Od

Answer:6,760,000

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

For the triangle, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles of a triangle.

The correct option (d): a ≈ 14.9, C ≈ 24.1, B ≈ 104.9.

We have,

A = 51° (angle opposite side a)

b = 14

c = 6

Using the Law of Sines, we have:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting the given values, we get:

a/sin(51°) = 14/sin(B) = 6/sin(C)

To find angle B, we can use the equation:

sin(B) = (b * sin(A))/a

sin(B) = (14 * sin(51°))/a

Now, let's calculate the values using the options:

a) No triangles possible: This option can be eliminated since the given side lengths satisfy the triangle inequality.

b) a ≈ 14.9, C ≈ 28.1, B ≈ 100.9:

Using the equation sin(B) = (14 * sin(51°))/a, we find sin(B) ≈ (14 * sin(51°))/14.9 ≈ 0.725.

Taking the arcsin of 0.725, we find B ≈ 46.3°.

c) a ≈ 11.2, C ≈ 24.1, B ≈ 104.9:

Using the equation sin(B) = (14 * sin(51°))/a, we find sin(B) ≈ (14 * sin(51°))/11.2 ≈ 1.022.

Since the sine value cannot exceed 1, this option can be eliminated.

d) a ≈ 14.9, C ≈ 24.1, B ≈ 104.9:

Using the equation sin(B) = (14 * sin(51°))/a, we find sin(B) ≈ (14 * sin(51°))/14.9 ≈ 0.725.

Taking the arcsin of 0.725, we find B ≈ 46.3°.

Therefore, the correct answer is option (d): a ≈ 14.9, C ≈ 24.1, B ≈ 104.9.

To know more about Law of Sines refer here:

https://brainly.com/question/17289163#

#SPJ11

The οnly sοlutiοn is sinθ = 0, θ = kπ, where k is any integer.

Trigοnοmetric functiοns are mathematical functiοns that relate tο the angles and sides οf a right-angled triangle.  These functiοns can be used tο calculate the relatiοnships between the sides and angles οf a triangle.

1a) Using inverse tangent functiοn,

θ = tan^{-1}(-2/3) ≈ -0.93 + kπ οr 2.21 + kπ, where k is any integer.

1b) Using cοsine functiοn,

\(2cos^{2}\theta - 1 = 0\)

\(cos^{2}\theta= 1/2\)

cοsθ = ±√(1/2) = ±1/√2

Sο, θ = π/4 + kπ/2 οr 3π/4 + kπ/2, where k is any integer.

1c) Rearranging the equatiοn, we get

\(sin^{2}\theta - 6sin\theta- 7 = 0\)

Using the quadratic fοrmula,

sinθ = [6 ± √(36 + 28)]/2 = 3 ± √19

Since -1 ≤ sinθ ≤ 1, the οnly sοlutiοn is

sinθ = 3 - √19

\(θ = sin^{(-1)(3 - \sqrt{19})} \approx 0.47 + 2k\pi\) οr π - 0.47 + 2kπ, where k is any integer.

1d) Factοring οut sinθ frοm the equatiοn, we get

sinθ(cοsθ - 7) = 0

Sο, either sinθ = 0 οr cοsθ = 7. Since -1 ≤ sinθ, cοsθ ≤ 1, the οnly sοlutiοn is

cοsθ = 7 has nο real sοlutiοn, sο the οnly sοlutiοn is

sinθ = 0

θ = kπ, where k is any integer.

To learn mοre about trigonometric functions visit the link:

https://brainly.com/question/25618616

#SPJ1

The probability of scanning the items in order of price, given a random order, depends on the number of orderings. The probability that the items are scanned in order of price is 1/n!.

To determine the probability of scanning the items in order of price, we need to consider the number of possible orderings that satisfy the condition and divide it by the total number of possible orderings.

Let's assume there are 'n' items with distinct prices. If the items are scanned in order of price, it means that the lowest-priced item must be scanned first, followed by the second lowest-priced item, and so on.

The total number of possible orderings of 'n' items is given by n!. However, since we want the items to be scanned in a specific order, only one ordering satisfies the condition. Therefore, the number of possible orderings that satisfy the condition is 1.

Thus, the probability of scanning the items in order of price is 1/n!.

To know more about probability visit -

brainly.com/question/31182920

#SPJ11

The equation of circles that have a diameter of 12 units and a center that lies on the y-axis is (x-0)² + (y-3)² = 6²

The standard form for finding the equation of a circle is expressed as;

(x-a)² + (y-b)²=r²

where;

(a, b) is the center of the circle

r is the radius of the circle

Given the following diameter = 12 units

radius = 12/2 = 6 units

If the centre lies on the y-axis, the center will be at (0, 3)

Substituting into the formula, we will have (x-0)² + (y-3)² = 6² equivalent to x²+ (y-3)² = 36

Hence, the equation of circles that have a diameter of 12 units and a center that lies on the y-axis is (x-0)² + (y-3)² = 6²

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

To find the expected number of sixes appearing on three die rolls, we can calculate the probability of rolling a six on each individual roll and then multiply it by the number of rolls.

The probability of rolling a six on a single roll of a fair die is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a six.

Since the rolls are independent events, we can multiply the probabilities together to find the probability of rolling a six on all three rolls:

(1/6) * (1/6) * (1/6) = 1/216

Therefore, the probability of rolling a six on all three rolls is 1/216.

To find the expected number of sixes, we multiply the probability by the number of rolls:

Expected number of sixes = (1/216) * 3 = 1/72

So, the expected number of sixes appearing on three die rolls is 1/72.

To know more about probability click here: brainly.com/question/31828911

#SPJ11

Answer

APY = 4.39 %

Step-by-step explanation

Compound interest formula

where

• A: final amount (value of the account after t years)

• P: principal (amount of money invested)

• r: interest rate (APR), as a decimal

• n: number of times interest applied per year

• t: time in years

Substituting, P = $1400, r = 0.043 (= 4.3/100), n = 365 (compounded daily means 365 times per year), we get:

APY formula

Substituting with the before mentioned values, we get:

The stationary distribution (vector) π can be found as (C/A)ci / (co + ao).

The Ehrenfest urn problem can be generalized such that it considers m urns and n particles. The dynamics proceeds by randomly picking a particle of the first type, picking a particle of the second type, and then exchanging the two. This can only happen provided they are in different urns. Random picking is uniform over particles of that type.

There are two types of assets, dollars and stocks, in this model of a simple financial market, where there are m traders who have total assets.

Suppose that the total number of dollars in the market is C and the total number of stocks is A.

For simplicity, assume that ao + co ≤ min{A, C}.

The processes c = {ck}k ∈ N and a = {ak}k ∈ N evolve randomly, and the trader may not buy or sell at all on some time steps.

In spite of that, c is a Markov chain and the stationary distribution (vector) π can be found. The reason c is a Markov chain is that it satisfies the Markov property, which states that the future state of a process depends only on the present state and not on its history.

A Markov chain is therefore defined by its state space, which in this case is {0, 1, ..., A + C}, and its transition probabilities.

The transition probabilities for this model are given as follows:

P(i, i + 1) = min{ci, A − ai} / ACP(i, i − 1) = min{ai, C − ci} / C ( where i is the present state of the system)

For the stationary distribution (vector) π, we can use the balance equations as follows:

π(i) P(i, i + 1) = π(i + 1) P(i + 1, i)     [for i = 0, 1, ..., A + C − 1 ]

This can be used to obtain the balance equations that are needed to find π(0), π(1), ..., π(A + C).

The solution is given by:

π(i) = (C/A)ci / (co + ao) for i = 0, 1, ..., min{A, C}.

Therefore, the stationary distribution (vector) π can be found as (C/A)ci / (co + ao).

Learn more about : Statistics - https://brainly.com/question/31270186

#SPJ11

Step-by-step explanation:

mx=n

⟹x=mn

Since m and n are both negative, x=mn will be positive.

Hence, the solution of mx=n will be a positive number.

other sulotion :-

9.75 ft is the answer

\(By \: Pythagoras \: Theorem, \\ \boxed{ {hyotenuse}^{2} = {base}^{2} + {height}^{2} } \\ \\ here \\ hypotenuse = 12ft \\ base = 7 ft\\ height = x\ \\ \\ \ {12}^{2} = {7}^{2} + {x}^{2} \\ \implies144 = 49 + {x}^{2} \\ \implies {x}^{2} = 144 - 49 \\ =95 \\ x = \sqrt{95 } \\ = 9.75 ft\\ \\ \\ \)

Answer:

y=49/9

Step-by-step explanation:

Distribute 3 with 3y and -5

3 times 3y is 9y

3 times -5 is -15

So the equation now looks like this:

9y-15=34

Add 15 on both sides:

9y=49

Divide 9 on both sides

So y=49/9

Since there is no common value to divide by y is 49/9

If you want the decimal version it is 5.44=> (=> meaning continuing forever)

Hope this helps!

More variability in watching TV. b. Clare's estimate of 1.2 hours for homework is likely closer to the actual mean value.

Based on the information provided, it seems that there is more variability in how much time students spend watching TV rather than doing homework.

To determine which estimate is likely to be closer to the actual mean value for all the students at their school, we need to consider the variability of the data.

Learn more about variability

brainly.com/question/15078630

#SPJ11

Answer:

that not a thing

Step-by-step explanation:

Answer:

m = 2

Step-by-step explanation:

to find the slope you must find (rise)/(run)

the rise is how much it goes up

the run is how much it goes to the right

in this case

it goes up 2 for every 1 to the right

so

(2/1) or just 2 is the slope

The quotient of an expression of signs decimal numbers is positive:

= 0.16.

The correct option is B.

There is one key notion when dividing any negative integer by another: the negative signs cancel out. This is unique to this situation. A positive number divided by such a negative number equals a negative number. As a result, you can't divide any two numbers as well as expect a positive result. In general, negative and positive numbers behave differently.

For

a. 2.5 / -9.56

dividing the numbers we get:

= -0.26

For

b. -1.7 / -10.06

dividing the numbers we get:

= 0.16

For

c. -0.3 / 9.44

dividing the numbers we get:

= -0.03

For

d. -9.34 / 0.55

dividing the numbers we get:

= -16.98

To know more about Negative Integer Division visit:

https://brainly.com/question/11444421

#SPJ9

I understand that the question you are looking for is:

Which expression of signed decimal numbers has a positive quotient?

a. 2.5 / -9.56

b. -1.7 / -10.06

c. -0.3 / 9.44

d. -9.34 / 0.55

Answer:

M = 0

Zero Slope (slope of 0)

Step-by-step explanation:

If the line is going in a straight line like this it is a slope of 0

If its a undefined slope it will stay in a line going up and down

Answer:

0

Step-by-step explanation:

To find the gradient of any line it is best to use the formula to find it:

\(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

where \(y_{2}\) is one of the give value and the other is going to be the other value given.

If you substitute it:

\(m=\frac{1-1}{2--2} = \frac{0}{4}\)

which equals to 0 so no gradient

:) Hope it helps

The exponential function for this problem is defined as follows:

y = 0.5(2/3)^x + 2.

An exponential function is defined as follows:

y = a(b)^x + c.

In which:

From the graph of the function, the horizontal asymptote is at y = 2, hence the parameter c is given as follows:

c = 2.

When x increases by 1, y is multiplied by 2/3, hence the parameter b is given as follows:

b = 2/3.

When x = 0, y = 2.5, hence the parameter a is obtained as follows:

a + c = 2.5.

a + 2 = 2.5

a = 0.5.

Meaning that the function is defined as follows:

y = 0.5(2/3)^x + 2.

More can be learned about exponential functions at https://brainly.com/question/30113628

#SPJ1

Answer:

D Keisha did not make a mistake

Step-by-step explanation:

Where the above are given,

(a) MLE of β: (nα + y₁ + y₂ + ... + yn)/n

(b) MLE of E(Y): (nα + y₁ + y₂ + ... + yn)/n

Maximum Likelihood Estimation (MLE) is   a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood function based on observed data.

(a) The MLE of β can be found by   maximizing the likelihood function. The likelihood function for  a gamma distribution is given by  -

L(β;  y₁, y₂, ..., yn) = (1/β^nαΓ(α))ⁿ * exp(-( y₁ + y₂ + ... + yn)/β)

Taking the logarithm of the likelihood function (log-likelihood) to simplify the calculations  -

log L(β;  y₁, y₂, ..., yn) =   n*log(1/β) + nα*log(β) - n*logΓ(α) - ( y₁ + y₂ + ... + yn)/β

To find the MLE of β, we differentiate the log-likelihood with respect to β, set it equal to zero, and solve for β  -

d/dβ(log L(β;  y₁, y₂, ..., yn)) = -n/β + nα/β² + ( y₁ + y₂ + ... + yn)/β² = 0

Simplifying the equation -

-n/β + nα/β^2 + ( y₁ + y₂ + ... + yn)/β² = 0

Multiplying through by β²

-nβ + nα + ( y₁ + y₂ + ... + yn) = 0

Rearranging  whave

nβ = nα + ( y₁ + y₂ + ... + yn)

Finally, solving for β -

β = (nα +  y₁ + y₂ + ... + yn)/n

Therefore, the MLE of β is (nα +  y₁ + y₂ + ... + yn)/n.

(b) The MLE of E(Y), the expected value of Y, is simply the MLE of β.

So, the MLE of E(Y) is (nα +  y₁ + y₂ + ... + yₙ)/n.

Learn more about MLE:
https://brainly.com/question/30513452
#SPJ4

Answer:

Step-by-step explanation:

4x = 80 - x          {Vertically opposite angles are equal}

Add 'x' to  both sides

4x + x = 80

5x = 80

Divide both sides by 5

x = 80/5

x = 16

∠DEA = 4x = 4*16 = 64

∠BEC = 80 - x = 80 - 16 = 64

∠DEA  +  ∠AEB = 180    {linear pair}

64 + ∠AEB = 180

∠AEB = 180 - 64

∠AEB = 116

∠CED = ∠AEB  {Vertically opposite angles}

∠CED = 116

The exponential function that best models the data is:  P(t) = 0.164 * e^(0.0887t)

To determine the exponential function that best models the data, we need to use the general form of an exponential function:

P(t) = P0 * e^(kt)

where P0 is the initial population, k is the growth rate, and t is time in minutes.

We can use the given data to solve for P0 and k.

At t = 10, P(t) = 283, so we have:

283 = P0 * e^(k*10)

Similarly, we can write equations using the other data points:

395 = P0 * e^(k*20)
809 = P0 * e^(k*40)
1,589 = P0 * e^(k*60)
3,177 = P0 * e^(k*80)
6,417 = P0 * e^(k*100)

We can solve for P0 by dividing the equations for P(t) at different time points:

395/283 = e^(k*20) / e^(k*10)
809/395 = e^(k*40) / e^(k*20)
1,589/809 = e^(k*60) / e^(k*40)
3,177/1,589 = e^(k*80) / e^(k*60)
6,417/3,177 = e^(k*100) / e^(k*80)

Simplifying these equations, we get:

e^(k*10) = 395/283
e^(k*20) = 809/395 * (395/283)^-1
e^(k*40) = 1,589/809 * (809/395)^-1 * (395/283)^-2
e^(k*60) = 3,177/1,589 * (1,589/809)^-1 * (809/395)^-3 * (395/283)^-3
e^(k*80) = 6,417/3,177 * (3,177/1,589)^-1 * (1,589/809)^-4 * (809/395)^-6 * (395/283)^-4
e^(k*100) = (6,417/3,177)^-1 * (3,177/1,589)^-5 * (1,589/809)^-10 * (809/395)^-15 * (395/283)^-10

Now we can solve for k by taking the natural logarithm of each equation and solving for k:

k = ln(395/283) / 10
k = ln(809/395 * (395/283)^-1) / 20
k = ln(1,589/809 * (809/395)^-1 * (395/283)^-2) / 40
k = ln(3,177/1,589 * (1,589/809)^-1 * (809/395)^-3 * (395/283)^-3) / 60
k = ln(6,417/3,177 * (3,177/1,589)^-1 * (1,589/809)^-4 * (809/395)^-6 * (395/283)^-4) / 80
k = ln((6,417/3,177)^-1 * (3,177/1,589)^-5 * (1,589/809)^-10 * (809/395)^-15 * (395/283)^-10) / 100

After calculating k for each equation, we find that the values are approximately equal to 0.0887.

Therefore, the exponential function that best models the data is:

P(t) = 0.164 * e^(0.0887t)

where P(t) is the bacteria population in thousands at time t in minutes.

Visit here to learn more about exponential function brainly.com/question/29287497

#SPJ11

Answer:

-8

Step-by-step explanation:

Answer:

the correct answer is A. 70°

Answer: a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Refer to  https://brainly.com/question/20131783 for full question

Use the formula:

As per given:

l = 12 feet, r = 10 feet

Answer:

the answer is 35 and 38 because 35+38 is 73 and when u subtract 35 from 38, you get 3.

Step-by-step explanation:

Answer:

9 times as many, the answer would be number 4

Step-by-step explanation:

Because when you subtract 8 from 72 you get 64 meaning the jar holds 64 more worms than the cup.

Answer:

the best is equations is 72:8=1

Step-by-step explanation: