Is 5 a solution for 3x + 4 = 19

Answer:

B

Step-by-step explanation:

use pythagoras first

x² + x² = (12√2)²

expand & simplify the squares

2x² = 144(2)

x² = 144

root both sides to get x

x = 12

Answer:

The ratio of women to men that the school employs can be expressed as:

6:8

This ratio can be simplified by dividing both sides by their greatest common factor, which is 2:

6 ÷ 2 : 8 ÷ 2

3 : 4

Therefore, the ratio of women to men in simplest form is 3:4.

Step-by-step explanation:

Answer:

3:4

Step-by-step explanation:

To reduce a fraction to its simplest term, we always divide both the numerator and denominator by the Least Common Multiple (LCM)

The lengths of the diagonals are:

GE = 8√5 units

DE = 4√5 Units

Area = 80 sq. units

We have been given an image of a kite on coordinate plane.

To find the length of GE we will use distance formula:

Distance = √[x₂ - x₁)² + (y₂ - y₁)²]

Substituting coordinates of point G and E in above formula we will get,  

GE = √[16 - 0)² + (8 - 0)²]

GE = √(256 + 64)

GE = √320

GE = 8√5 units

Similarly we will find the length of diagonal DF using distance formula.

DF = √[14 - 10)² + (2 - 10)²]

DE = √(16 + 64)

DE = √80

DE = 4√5 Units

Area of kite is given by the formula:

Area = (p * q)/2

where p and q are diagonals of kite.

Thus:

Area = ( 8√5 *  4√5)/2

Area = 80 sq. units

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An odd number is (2x) + 1

An even number is (2x)

These are the definitions.

Using the binomial (2x + 1)(2x + 1), we can see the properties of all products made from odd numbers.

Foiling will give 4x^2 + 4x + 1.

4x^2 is even because 4x^2 can be expressed as 2(2x) x 2(2x).

4x is even because 4x can be expressed as 2(2x)

This means that 4x^2 + 4x is even so the expression 4x^2 + 4x + 1 is odd because an even number + 1 is odd as shown by (2x) + 1.

This shows that every outcome of the product of 2 odd numbers will result being odd.

This means there is no answer to this problem, because any number that is a multiple of 2 is even. (Basically the definition of even)

Using even and odd numbers concepts, it is found that the product is an even number.

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Answer:

$105.60

Step-by-step explanation:

8% of $82.50 is $6.60

20% of $82.50 is $16.50

$82.50 + $6.60 + $16.50 = $105.60

The linear equation that gives the rule for this table is y = -5x + 15

The table of values is given as:

x y

1 10

2 5

3 0

4 –5

On the above table, we can see that:

As x increases by 1, the value of y decreases by 5

This means that the slope is

Slope = -5

Also, the above table can be modified as follows (using the slope of -5)

x y

0 15

1 10

2 5

3 0

4 –5

This means that the y-intercept is

y-intercept = 15

A linear equation is represented as

y = slope * x + y-intercept

So, we have

y = -5x + 15

So, the equarion is y = -5x + 15

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Answer:

C

Step-by-step explanation:

Hope I was able to help!! :)

The limit can be expressed as the definite integral ∫2⁸ [3(x*)³ - 8x*] dx on the interval [2,8].

To express the limit as a definite integral on the given interval [2,8], we need to use the definition of the definite integral.

First, we can rewrite the expression inside the limit using the definition of xi* (the sample point):

3(xi*)³ - 8xi* = 3[(2 + iΔx)*]³ - 8(2 + iΔx)*

Next, we can rewrite the limit as the definite integral of this expression:

lim n→[infinity] n i = 1 [3(xi*)³ - 8xi*]Δx = ∫2⁸ [3(x*)³ - 8x*] dx

where x* is the sample point in each subinterval.

Therefore, the limit can be expressed as the definite integral ∫2⁸ [3(x*)³ - 8x*] dx on the interval [2,8].

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Answer:

it will take 4 months

Step-by-step explanation:

Answer:

Step-by-step explanation:

5(v+10) =

when sorting its  v+10

the common factors would be 5,1

4(x+6)=

when sorting it should be 4

the common factors are 4,2,1.

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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Answer:

wrong

Step-by-step explanation:

(a+b)^2=(a+b)(a+b)

=a(a+b)b(a+b)

=a^2+ab+ab+b^2

=a^2+2ab+b^2

i hope it helps you

A person with a Z-score of -0.42 would have a raw score of 992.4 on the SAT taken in 2018.

The standard deviation is a measure of how much the data varies from the mean. A Z-score is a standardized value that represents the number of standard deviations a raw score is from the mean.

To find the raw score given a Z-score, we can use the following formula:

raw score = mean + Z-score * standard deviation

For the mean composite score of 1068 and a standard deviation of 180, we can plug in the values for the Z-score of -0.42:

raw score = 1068 + (-0.42) * 180

raw score = 1068 - 75.6

raw score = 992.4

Note: The Z-score of -0.42 indicates that the raw score is 0.42 standard deviations below the mean.

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The value of K is approximately 0.00000086938. The solution can be found in the  following manner.

To find the value of K, we need to integrate the joint probability density function over the entire domain and set it equal to 1, since the total probability of all possible outcomes must be 1.

So, we have:

∫∫f(x, y) dx dy = 1

∫20³⁰ ∫20³⁰ K(x² + y²) dx dy = 1

We can simplify this expression by using polar coordinates, where:

x = r cos(θ)

y = r sin(θ)

and the Jacobian is:

dx dy = r dr dθ

So, the integral becomes:

∫0²π ∫20³⁰ K(r²)(r dr dθ)

K ∫0²π ∫20³⁰ r³ dr dθ

K ∫0²π [1/4 r⁴]20³⁰ dθ

K ∫0²π (1/4)(30⁴ - 20⁴) dθ

K = 1 / [π(30⁴ - 20⁴)/4]

K = 1 / [π(810000 - 160000)]

K = 1 / 1151401.09

So, the value of K is approximately 0.00000086938.

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Answer:

\(\theta = \frac{\pi}{6}\)

Step-by-step explanation:

\(tan^ 2 \theta - ( \sqrt 3 + \frac{1}{\sqrt3}}) tan \theta + 1 = 0\\\\tan \theta - ( \sqrt 3 + \frac{1}{\sqrt3}}) +\frac{1}{ tan \theta } = 0\\\\\)          \([ \ divide \ by \ tan \theta \ on \ both \ sides \ ]\)

\(tan\theta + \frac{1}{ tan \theta }- ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\frac{tan^2 \theta + 1}{ tan \theta } - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\frac{sec ^2 \theta}{ \frac{sin \theta }{cos \theta}} - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\)              \([ \tan ^ 2\theta + 1 = sec ^2 \theta \ , \ tan \theta = \frac{sin \theta }{cos \theta } \ ]\)

\(\frac{sec^2 \theta }{sin \theta \times sec \theta } - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\)                  \([\ \frac{sin \theta }{cos \theta } = sin \theta \times sec \theta \ ]\)

\(\frac{sec \theta }{sin \theta } - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\)

\(sec \theta \ cosec \theta - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\)              \([ \ \frac{1}{sin \theta } = cosec \theta \ , \ \frac{ sec \theta }{sin \theta } = sec \theta cosec \theta \ ]\)

\(sec \theta \ cosec \theta - \sqrt 3 - \frac{1}{\sqrt3}} = 0\\\\\frac{\sqrt 3\ sec \theta \ cosec \theta - 3 - 1}{\sqrt3} = 0\\\\\sqrt 3 sec \theta cosec \theta - 4 = 0\\\\\)              

\(\sqrt3 \frac{1}{cos \theta } \frac{1}{sin \theta } - 4 = 0\\\\\frac{\sqrt3 - 4sin \theta cos \theta} { sin \theta cos \theta } = 0\)                      

\(\sqrt 3 - 2sin 2\theta = 0\)                                  \([ \ sin 2 \theta = 2 sin \theta cos \theta \ ]\)

\(2sin 2 \theta = \sqrt3\\\\sin 2 \theta = \frac{\sqrt3 }{2} \\\\2 \theta = sin^{-1} (\frac{\sqrt3}{2})\\\\2 \theta = 60^{ \circ} = \frac{ \pi}{3}\\\\\theta = \frac{\pi} {6}\)

Answer:

A= 153.94 mm

Step-by-step explanation:

A = πr²

A=π(7)²

A= 153.94 mm

ANSWER

EXPLANATION

We want to identify the option that is completely factored.

For an expression to be completely factored, it means that there are no more common terms between the terms in the expression.

That means it can not be factored any further.

Therefore, the only correct option is:

The standard deviation for a chi square distribution for given degree of freedom is 7.0711.

The chi-square distribution is parameterized by the number of degrees of freedom (df). As the number of degrees of freedom increases, the shape of the distribution becomes more symmetrical and approaches a normal distribution.

The standard deviation (σ) of a chi-square distribution with k degrees of freedom is given by the formula:

σ = sqrt(2k)

Therefore, for a chi-square distribution with 25 degrees of freedom:

σ = sqrt(2(25)) = sqrt(50) ≈ 7.0711

Rounding this to four decimal places gives a standard deviation of approximately 7.0711.

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The minimum value of the objective function is approximately -1.0316, which occurs at (x1, x2) = (0.0898, -0.7126).

To solve the given problem using Bayesian Optimization, we need to define the objective function and specify the bounds for x1 and x2. The objective function is:

f(x1, x2) = (4 - 2.1x1^2 + (x1^4)/3)x1^2 + x1*x2 + (-4 + 4x2^2)x2^2

The bounds for x1 and x2 are x1 ∈ [-3, 3] and x2 ∈ [-2, 2].

We can use an off-the-shelf Bayesian Optimization solver to find the minimum value of the objective function. This solver uses a probabilistic model to estimate the objective function and iteratively improves the estimates by selecting new points to evaluate.

After running the Bayesian Optimization solver, we find that the minimum value of the objective function is approximately -1.0316. This minimum value occurs at (x1, x2) = (0.0898, -0.7126).

Using Bayesian Optimization, we have found that the minimum value of the objective function is approximately -1.0316, which occurs at (x1, x2) = (0.0898, -0.7126). Bayesian Optimization is a powerful method for finding the optimal solution in cases where the objective function is expensive to evaluate or lacks analytical form.

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To forecast future demand using trend adjusted exponential smoothing, the given information includes actual demand for the past 16 periods and the parameters required for the forecast. The parameters include the smoothing constant (α), the trend smoothing constant (β), the trend-adjusted forecast for period 5 (TAF5), and the trend for period 5 (T5).

The question asks to prepare a trend-adjusted exponential smoothing forecast based on these parameters.

Trend adjusted exponential smoothing combines exponential smoothing with a trend component to forecast future values. The formula for calculating the forecast is:

Ft+1 = Ft + Tt + α * (At - Ft) + β * (Tt - Tt-1)

Where:

Ft is the forecast for period t

Tt is the trend component for period t

At is the actual demand for period t

α is the smoothing constant

β is the trend smoothing constant

To start, we need to initialize the forecast and trend values. In this case, we are given the trend-adjusted forecast for period 5 (TAF5) and the trend for period 5 (T5). So, we set F5 = TAF5 and T5 = T5.

Next, we can use the formula to calculate the forecast and trend values for the remaining periods.

We iterate through the periods from t = 6 to t = 16, applying the formula to update the forecast and trend values based on the actual demand for each period.

Finally, we round the forecast values to the desired precision.

By following this procedure and applying the given parameters, we can prepare a trend-adjusted exponential smoothing forecast for the future demand.

The forecast values will reflect the trend in the historical data while incorporating the smoothing constants for better accuracy.

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Answer:

m= -1/2

Step-by-step explanation:

Answer: Angles 4 and 5

Step-by-step explanation:

Supplementary angles are angles that add up to 180. The only angle pairs the add up to 180 (you can tell by seeing if two angles are the only two on a straight line) are angles 4 and 5, and angles 3 and 4. Angles 3 and 4 isn’t an option, so it’s 4 and 5.

Answer:

i believe that its angle 4 and 5 since they would sum up to 180 degrees

Step-by-step explanation:

If there are 5 finalists at a singing competition, in 120 ways they can be ordered, if they each take turns singing by applying basic counting principles.

There are 5 finalists at a singing competition and each of them takes turns singing.

We can calculate the number of ways the 5 finalists can take up turn by applying basic counting principles.

Therefore, they can be ordered in n factorial ways, that is n !, where n is the number of finalists who take turns to sing.

Thus, number of ways the finalists can be ordered is = 5!

= 5*4*3*2*1 ( ways )

= 120 ways

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\((\stackrel{x_1}{5}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 1}(x-\stackrel{x_1}{5})\implies {\Large \begin{array}{llll} y=x+3 \end{array}}\)

Answer:

6666 divided by 1111 equals 6

Step-by-step explanation:

A trial in the context of a binomial distribution refers to a single experiment or attempt with a success or failure outcome.

A success in this problem is defined as the die landing on a green square, and the number of trials is 12.

A trial, in this context, refers to rolling the 20-sided die once.

When the die is rolled 12 times, each of those 12 rolls is considered a separate trial.
A success is the outcome that we are interested in tracking.

In this case, a success is when the die lands on a green square.
The number of trials, denoted by 'n', is the total number of times the die is rolled.

In your question, the die will be rolled 12 times, so n = 12.
To recap:
- A trial: Rolling the 20-sided die once
- A success: The die landing on a green square.
- Number of trials (n): 12.

Since x has a binomial distribution, this implies that each trial is independent, and the probability of success remains constant throughout all trials.

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The amount of money Company A charge more for x miles,  35 - 0.05x dollars

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

Let's call the number of miles the family wants to travel "x".

The cost for Company A is $30.50 plus 8 cents per mile, so the total cost for Company A is,

30.50 + 0.08x.

The cost for Company B is $65.50 plus 13 cents per mile, so the total cost for Company B is,

65.50 + 0.13x.

To find out how much more Company A charges, we can subtract the cost for Company B from the cost for Company A:

= (30.50 + 0.08x) - (65.50 + 0.13x)

= 35 - 0.05x

So, Company A charges 35 - 0.05x dollars more than Company B for x miles.

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We calculated that the prism B and Prism D have a volume within the given range.

The prism that is rectangular shaped having six rectangular faces along with twelve edges is called rectangular prism.

Given, there are four rectangular prisms

Prism A has dimension six rows of 2

volume of prism A = 6 x 2 = 12 cubic centimeters

the dimension of prism B = four rows of 2 and three total layers

volume of prism B = 4 x 2 x 3 = 24 cubic centimeters

the dimension of prism C = five rows of three and three total layers

So, volume = 5 x 3 x 3 = 45 cubic centimeters

in the last, Prism D has six rows of 2 and two total layers

hence, volume = 6 x 2 x 2 = 24 cubic centimeters

Therefore, Prism B and D have a volume between 20 and 30 cubic centimeters

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