3(7 - 2x) - 19 - 5(4- x) = 3(8 - 6x) - 9x + 5(4- x)

The horizontal distance between zack and the water fountain will be 141.05 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Zack is standing at the top of a lookout tower and spots a water fountain below. If the lookout tower is 75 feet tall and the angle of depression is 28°.

Then the horizontal distance between zack and the water fountain is given as,

tan 28° = 75 / x

x = 75 / tan 28°

x = 75 / 0.5317

x = 141.05 feet

The horizontal distance between zack and the water fountain will be 141.05 feet.

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Organizations that build strategic information systems create systems that are paramount to business success. The correct option is(D).

Strategic information systems are those that support the long-term goals and objectives of an organization, aligning the use of technology with the strategic direction of the business. These systems provide a competitive advantage by enabling the organization to achieve its strategic goals and objectives more efficiently and effectively.

They typically involve the integration of different types of information systems, such as transaction processing systems, decision support systems, and executive information systems, to support the decision-making process at all levels of the organization.

By building strategic information systems, organizations can improve their overall performance, enhance their operational efficiency, and gain a competitive advantage in the marketplace.

Such systems can help organizations to better understand their customers, identify new market opportunities, improve supply chain management, and optimize business processes.

In today's rapidly changing business environment, strategic information systems are essential for organizations to remain competitive and achieve long-term success.

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Answer: f(2) = 95/3.

Step-by-step explanation:

To find f'(x), we need to integrate f''(x) once with respect to x:

f'(x) = ∫ f''(x) dx = ∫ (7x + 2) dx = (7/2)x^2 + 2x + C1

where C1 is a constant of integration. To find the value of C1, we can use the initial condition f'(0) = 3:

f'(0) = (7/2)(0)^2 + 2(0) + C1 = C1 = 3

So, we have:

f'(x) = (7/2)x^2 + 2x + 3

To find f(2), we need to integrate f'(x) once more with respect to x:

f(x) = ∫ f'(x) dx = ∫ [(7/2)x^2 + 2x + 3] dx = (7/6)x^3 + x^2 + 3x + C2

where C2 is another constant of integration. To find the value of C2, we can use the initial condition f(0) = 2:

f(0) = (7/6)(0)^3 + (0)^2 + 3(0) + C2 = C2 = 2

So, we have:

f(x) = (7/6)x^3 + x^2 + 3x + 2

Finally, to find f(2), we substitute x = 2 into the expression for f(x):

f(2) = (7/6)(2)^3 + (2)^2 + 3(2) + 2 = 49/3 + 14 = 95/3

Therefore, f(2) = 95/3.

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Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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A good way to sample this population while maintaining the distribution of various sub-populations is by using stratified sampling. In stratified sampling, the population is divided into homogeneous subgroups or strata based on certain characteristics, and then a random sample is selected from each stratum.

To ensure that the distribution of various sub-populations is maintained, the sample should include a proportional representation of individuals from each subgroup. In this case, the subgroups are Asian, Hispanic, and Native American.

Here's how the distribution of the various sub-populations can be maintained in the final sample:

1. Determine the proportion of each subgroup in the population:

  - Asian: 500 / 2000 = 0.25 (25%)

  - Hispanic: 1000 / 2000 = 0.5 (50%)

  - Native American: 500 / 2000 = 0.25 (25%)

2. Calculate the number of samples to be chosen from each subgroup:

  - Asian: 0.25 * 200 = 50 samples

  - Hispanic: 0.5 * 200 = 100 samples

  - Native American: 0.25 * 200 = 50 samples

3. Randomly select the specified number of samples from each subgroup.

By using stratified sampling with the specified proportions, the final sample of 200 individuals will have a distribution that reflects the proportions of Asian, Hispanic, and Native American subpopulations in the overall population.

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Answer:

x = 76/75

Step-by-step explanation:

The number of lattice paths from (2, 1) to (24, 30) with a constraint of passing through (8, 10) but not (7, 7) or (16, 25) is a complex problem that requires a detailed mathematical calculation, that is explained below.

Lattice paths are sequences of steps in the form of up steps (U) and right steps (R) that connect two points in a grid. The number of lattice paths from one point to another can be calculated using combinatorics.

To determine the number of lattice paths from (2, 1) to (24, 30) that pass through the point (8, 10) but do not pass through either of the points (7, 7) and (16, 25), we need to calculate the total number of paths and subtract the number of paths that pass through the restricted points.

Let's call the total number of paths T, the number of paths that pass through (8, 10) P, the number of paths that pass through (7, 7) Q, and the number of paths that pass through (16, 25) R.

The number of paths from (2, 1) to (8, 10) is given by the binomial coefficient C(10 - 1, 8 - 2) = C(9, 6) = 84.

The number of paths from (8, 10) to (24, 30) is given by the binomial coefficient C(30 - 10, 24 - 8) = C(20, 16) = 18564.

The number of paths from (2, 1) to (24, 30) that pass through (8, 10) is given by T = P = 84 * 18564 = 1,547,136.

Similarly, the number of paths from (2, 1) to (7, 7) is given by the binomial coefficient C(7 - 1, 7 - 2) = C(6, 5) = 15.

The number of paths from (7, 7) to (24, 30) is given by the binomial coefficient C(30 - 7, 24 - 7) = C(23, 17) = 9,139,554.

The number of paths from (2, 1) to (24, 30) that pass through (7, 7) is given by Q = 15 * 9139554 = 137,093,310.

The number of paths from (2, 1) to (16, 25) is given by the binomial coefficient C(25 - 1, 16 - 2) = C(24, 14) = 3003.

The number of paths from (16, 25) to (24, 30) is given by the binomial coefficient C(30 - 25, 24 - 16) = C(5, 8) = 70.

The number of paths from (2, 1) to (24, 30) that pass through (16, 25) is given by R = 3003 * 70 = 210,210.

Finally, the number of paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is T - P - Q - R = 1547136 - 137,093,310 - 210,210 = -135,599,384.

The number of lattice paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is zero, as the result is negative.

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The inverse of f is a function which takes any value x and divides it by 4, then adds 7 to the result.

The inverse of a function is the opposite of the original function, meaning that it takes the output of the original function and turns it back into the input. In this case, the original function is f(x)=1/4x+7. To find the inverse, we need to solve for x in the equation, which can be done by subtracting 7 from both sides and then multiplying both sides by 4. This gives us x=(x+7)/4, which is the inverse of the original function. To put it simply, the inverse of f takes any output of the original function, adds 7 to it, and then divides it by 4 to get the original input.

example;

If f(x)=1/4x+7 and x=3, then

f(3) = (1/4)3 + 7

7.75

The inverse of f is f^-1(x) = (x + 7) / 4.

If f^-1(7.75) = (7.75 + 7) / 4, then

f^-1(7.75) = 14.75 / 4

3.6875

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Answer:

200

Step-by-step explanation:

The amount you need to increase your monthly net savings by is C. $200.

Amount to save next year

= Goal - Current savings

= 4,500 - 900

= $3,600

Monthly savings amount

= 3,600 / 12

= $300 per month

Amount to increase savings by

You care already saving $100 so you need to increase by:

= 300 - 100

= $200

Answer:

200

Step-by-step explanation:

Edge 2022

When I looked at the chart I only saw dots plotted on 10 and a 43 ish number I didn't see anything in between  23 and 35 so I'm guessing your answer is 0%

Hope this helped and have an amazing day <3

Answer:

I actually believe it is 50% because the middle box is worth 50% of the plot.

Step-by-step explanation:

Answer:

log(x + 1)inverse function y(x) = e^x + 3 - 4

Answer:

74 yards squared

Step-by-step explanation:

Divide the shape up into 2 3x5 rectangles and one 11x4 rectangle

2(3x5)+11x4=30+44=74

74 yards squared

The decision to use a univariable or multivariable regression model depends on the research question, data availability, model complexity, and goodness of fit.

What is the linear regression equation?

The formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.

When deciding whether to use a univariable or multivariable linear regression model, there are several factors to consider:

Research question: Consider the research question you are trying to answer. If you are interested in understanding the relationship between a single independent variable and a dependent variable, then a univariable regression model may be sufficient. However, if you want to explore the effect of multiple independent variables on a dependent variable, then a multivariable regression model may be more appropriate.

Data availability: Look at the data you have available. If you have only one independent variable that you believe is relevant to your research question, then a univariable regression model may be appropriate. However, if you have multiple independent variables that could potentially influence the dependent variable, then a multivariable regression model may be necessary.

Model complexity: Consider the complexity of the model you want to build. If you are interested in a simple linear relationship between an independent variable and a dependent variable, then a univariable regression model may be sufficient. However, if you believe that there are interactions between multiple independent variables that could affect the dependent variable, then a multivariable regression model may be necessary.

Model fit: Evaluate the goodness of fit of both univariable and multivariable models. Compare the R-squared values of each model to determine which model provides a better fit to the data. A higher R-squared value indicates a better fit between the independent and dependent variables.

Hence, the decision to use a univariable or multivariable regression model depends on the research question, data availability, model complexity, and goodness of fit.

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i would first multiply your 4 so you get 4q-32=7q+5 than add 32 to both sides so ypu get 4q=7q+5+32 than subtract 7q from both sides you should end up with 4q-7q=5+32 which = -3q=37 than divided by -3 to get q =

\( \frac{ - 37}{3} \)

or about -12.33333 going on for ever

Answer:

(4,3)

Step-by-step explanation:

This doesn't even take any math really, just deductive reasoning :)

We know the line segment stretches from one to 15, meaning there are 14 points on the line as there is (1,2,3, etc.)

14/2 obviously equals 7, so just plug it in from there.

12 is too far up on the line to be less than half, so (12, 3) is wrong

^ this goes for (9, 3) as well

7 is literally the halfway marker, so there is no way it could be (7, 3)

Making the answer (4, 3) because not only is it the last one remaining but it makes the most sense, being less than one half of the segment

The position of the particle after t seconds is s(t) = (5/2)\(t^2\) + (2/3)\(t^3\) - (1/12)\(t^4\) + 3t + 10.

To find the position of the particle after t seconds, we need to integrate the acceleration function to obtain the velocity function, and then integrate the velocity function to obtain the position function.

Given:

Acceleration function: a(t) = 5 + 4t - 2\(t^2\)

Initial velocity: v(0) = 3 m/s

Initial displacement: s(0) = 10 m

Integration of the acceleration function gives us the velocity function:

v(t) = ∫[5 + 4t - 2\(t^2\)] dt

v(t) = 5t + 2\(t^2\) - (2/3)\(t^3\) + \(C_1\)

Using the initial velocity v(0) = 3 m/s, we can solve for the constant \(C_1\):

3 = 5(0) + 2\((0)^2\) - (2/3)\((0)^3\) + \(C_1\)

\(C_1\) = 3

Therefore, the velocity function is:

v(t) = 5t + 2\(t^2\) - (2/3)\(t^3\) + 3

Now, we integrate the velocity function to obtain the position function:

s(t) = ∫[5t + 2\(t^2\) - (2/3)\(t^3\) + 3] dt

s(t) = (5/2)\(t^2\) + (2/3)\(t^3\) - (1/12)\(t^4\) + 3t + \(C_2\)

Using the initial displacement s(0) = 10 m, we can solve for the constant \(C_2\):

10 = (5/2)\((0)^2\) + (2/3)\((0)^3\) - (1/12)\((0)^4\) + 3(0) + \(C_2\)

\(C_2\) = 10

Therefore, the position function is:

s(t) = (5/2)\(t^2\) + (2/3)\(t^3\) - (1/12)\(t^4\) + 3t + 10

So, the position of the particle after t seconds is given by the equation:

s(t) = (5/2)\(t^2\) + (2/3)\(t^3\) - (1/12)\(t^4\) + 3t + 10.

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Answer:

x = 2

Step-by-step explanation:

6 ÷ 2 = 3

8 ÷ 2 = 4

4 ÷ 2 = 2

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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Let ages of Seema and her mother be “5x” years and “12x” years respectively.

Difference between ages is 21 years

Hence,

12x - 5x = 21

7x = 21

x = 3

Therefore,

Age of Seema = 5 × 3 = 15 years

Age of her mother = 12 × 3 = 36 years

Ratio of ages after three years = ( 15+3 ) / (36+3 )

= 18 / 39

= 6 / 13

= 6 : 13

2h*0.2

2h is h doubled

20% becomes 0.2

Answer:

The answer is 80°

Step-by-step explanation:

Here, we know that the sum of all interior angles of hexagon is equal to 720°

So,

x + x + 140 + 140 + 140 + 140 = 720

2x + 560 = 720

2x + 560 – 560 = 720 – 560

2x = 160

2x/2 = 160/2

x = 80°

Thus, The value of x is 80°

For Verification

x + x + 140 + 140 + 140 + 140 = 720

80 + 80 + 140 + 140 + 140 + 140 = 720

720 = 720

L.H.S = R.H.S

Hence Verified!

-TheUnknownScientist 72

Tessellation in trapezoid is possible only if it is rotated

see the fig, attached.

But tessellation in parallelogram is possible both rotated and non rotated

see the fig, attached.

A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.

A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.

Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.

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Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

<95141404393>

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

The match of each power of expression with its simplified expression are

(i)  (4⁰)⁻⁹     ⇔  (b) 4⁰  

(ii)  (-4⁹)²    ⇔  (a) (-4)¹⁸

(iii) (4⁶)⁻³    ⇔  (c) 1/4¹⁸

(iv) (4⁻³)⁻³  ⇔   (d) 4⁹.

To simplify these expressions, we use the rule which states that when we have a power raised to another power, we can multiply the exponents.

(i) (4⁰)⁻⁹ = 4⁰, So, (i) matches with Option(b) 4⁰,

(ii) (-4⁹)² = (-4)¹⁸, because 9×2 = 18,

So, (ii) matches with Option (a) (-4)¹⁸.

(iii) (4⁶)⁻³ = (4)⁻¹⁸ = 1/4¹⁸ ,

So, (iii) matches with Option (c) 1/4¹⁸.

(iv) (4⁻³)⁻³ = 4⁹, because -3×-3 = 9,

So, (iv) matches with Option (d) 4⁹.

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The given question is incomplete, the complete question is

Match each power of a power expression with its simplified expression:

(i)   (4⁰)⁻⁹          (a) (-4)¹⁸

(ii)  (-4⁹)²          (b) 4⁰

(iii) (4⁶)⁻³          (c) 1/4¹⁸

(iv) (4⁻³)⁻³        (d) 4⁹

The problem where the professor states that the average age of students in the university is 21 years is an example of statistical inference.

Statistical inference is the process of using data from a sample to make inferences or conclusions about a population. It allows us to draw conclusions about a larger group of individuals or objects based on information from a smaller sample. It is a fundamental part of statistical analysis and is used in many fields, including research, business, and government.

Statistical inference includes two main types: estimation and hypothesis testing.

Estimation: This involves using sample data to make estimates about population parameters. For example, using the sample mean to estimate the population mean or the sample proportion to estimate the population proportion.

Hypothesis testing: This involves using sample data to test a claim or hypothesis about a population parameter. For example, testing the claim that a coin is fair, based on the proportion of heads in a sample of coin flips.

The goal of statistical inference is to use the information from a sample to make informed decisions or predictions about a population. It allows us to draw general conclusions from a specific set of data, and it is an essential tool for making sense of data in many fields.

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The given reflection transformation is a rigid transformation, such that the dimensions are preserved

The statements that are true about the image of triangle ABC following a reflection Bout the the line y = 2·a are;

Reasons:

The given parameters are;

Triangle ΔABC is reflected across the line y = 2·x

Given that a reflection is a rigid transformation, we have;

The distance between two points on a preimage is the same as the distance between the corresponding points on the image;

Therefore;

ΔABC is congruent to ΔRST by Side-Side-Side SSS, rule of congruency, such that we have;

AB ≅ RS, BC ≅ ST, and AC ≅ RT

m∠BAC ≅ m∠SRT

m∠BCA ≅ m∠STR

m∠BAC ≅ m∠SRT

Therefore;

The true statements are;

Therefore;

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Answer:

m a t h  w a y

Step-by-step explanation:

Answer:

1. 15.2*π*10 = 477.522083346

2. (1)/(3)\pi 5.5^(2)12 = 380

4. 7*π*8 = 175.929188601

there did a few

search formulas for each shape

Step-by-step explanation:

The sale price with a 15% discount on an original price of $42 is $35.70.

From the question, we have the following parameters that can be used in our computation:

Original = $42

Discount = 15%

The discount is 15% of the original price, which means the discount amount is:

Discount = 0.15 * $42 = $6.30

To find the sale price, we need to subtract the discount amount from the original price:

Sale Price = Original Price - Discount

Sale Price = $42 - $6.30

Sale Price = $35.70

Hence,, the sale price is $35.70.

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