An engineer designing a building caculates that the diagonal of a rectangular room measures √23 meters. Which of the following measurements is the best approximation of the lenght of the diagonal ?

Answer:

white: w/80 = 35/100

blue: b/80 = 25/100

red: r/80 = 40/100

Step-by-step explanation:

Answer:

--------------------

The two sides are of same length as radius, hence it is isosceles triangle.

Find the measure x of other two angles using the triangle sum theorem:

The maximum increase in sales that can be sustained assuming no new equity is issued is $11,538.46.

To determine this, we need to consider the company's current financial ratios and constraints. The question states that assets and costs are proportional to sales, and the company maintains a constant 30 percent dividend payout ratio and a constant debt-equity ratio. This means that any increase in sales will result in a proportional increase in assets and costs.

Given the current sales of $77,900, we can calculate the current equity by subtracting the long-term debt from the total equity ($117,000 - $58,000 = $59,000). The net income is calculated by subtracting taxes from the taxable income ($15,300 - $3,213 = $12,087). To maintain the constant dividend payout ratio, the dividends paid would be 30 percent of the net income ($12,087 * 0.3 = $3,626.10). The remaining net income would be added to equity ($12,087 - $3,626.10 = $8,460.90).

Now, let's assume the maximum increase in sales that can be sustained. We know that assets and costs are proportional to sales, so the increase in assets and costs will be proportional as well. If we increase sales by x dollars, then the increase in assets and costs would be 152,000/77,900 * x. The increase in equity would be the net income minus the dividends paid, which is $8,460.90. Setting up an equation, we have (8,460.90 + 152,000/77,900 * x) / (117,000 - 58,000) = 0.3. Solving for x, we find x = $11,538.46. Therefore, the maximum increase in sales that can be sustained without issuing new equity is $11,538.46.

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Answer:

There are 40 multiples of 5.

Step-by-step explanation:

You take 10000 and subtract 8000 = 2000.

Then divide 2000 by 5.

Answer:

Step-by-step explanation:

See attachment

True, the SDLC's planning phase yields a general overview of the company and its objectives. During this initial stage, the project's purpose, scope, and requirements are defined.

True. The planning phase of the Software Development Life Cycle (SDLC) is crucial in determining the direction and scope of the project. During this phase, the project team analyzes the company's goals, objectives, and requirements. This includes identifying the company's strengths, weaknesses, opportunities, and threats (SWOT analysis). The team also determines the feasibility of the project, identifies potential risks, and creates a plan for project execution. The planning phase yields a general overview of the company and its objectives, providing a solid foundation for the rest of the SDLC stages. It is essential to have a well-defined plan during this phase to ensure that the project aligns with the company's objectives and meets the expectations of the stakeholders.

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The concept that relates how much one variable changes as another variable changes is Slope.

Slope is a numerical representation of how inclined a line is with respect to the horizontal. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts changes in y or the vertical axis with changes in x or the horizontal axis.

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Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

We use the format (x, y) to write the coordinates in format XY. Coordinates XY is a coordinate that use in Cartesian coordinate.

What is Cartesian coordinate?

Cartesian coordinate is system to draw a specific location of an unique point in the numerical condition that oriented in the two constant line where the vertical line called ordinate or Y and the horizontal line called abscess or X. The Cartesian coordinate commonly use in architecture or  a design of a certain object that has a certain dilate with its original plan. This design later is use to control the construction process of the original object.

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Answer:

65 in and 39 in respectively

Step-by-step explanation:

Let r be the common ratio; when we multiply both L and R by this common ratio, we'll get the actual length and actual width of the rectangle,  Recalling that the formula for the perimeter of a rectangle is P = 2L + 2R, we get:

2(5r) + 2(3r) = 16r = 208 in

Then r = 208/16 = 13

Thus, the actual length is 5(13 in) and the actual width is 3(13 in.),

or 65 in and 39 in respectively.

As a check, calculate 65 in / 39 in; this comes out to 5:3, as required.

Then

The total expected number of circuit boards with defects out of the 100 made is 2 times the expected number of defective batches, which is:μ = 2 * 0.5 * 2≈ 2.

a. The probability that out of 100 circuit boards made exactly 2 have defects is calculated using the binomial distribution formula:

P(X = k)

= nCk * p^k * (1-p)^(n-k)

where n

= 100, p

= 0.01, and k

= 2. Thus,

P(X = 2)

= 100C2 * (0.01)^2 * (0.99)^98≈ 0.37b.

The probability that out of 100 circuit boards made at least 2 have defects can be calculated using the complement rule

.P(X ≥ 2)

= 1 - P(X < 2)

= 1 - P(X = 0) - P(X = 1)

where n

= 100, p

= 0.01. Thus,

P(X = 0)

= 100C0 * (0.01)^0 * (0.99)^100≈ 0.366P(X = 1)

= 100C1 * (0.01)^1 * (0.99)^99≈ 0.369

Therefore

,P(X ≥ 2) ≈ 1 - 0.366 - 0.369≈ 0.265c.

The expected number of circuit boards with defects out of the 100 made is given by the formula:μ

= n * p where n

= 100 and p

= 0.01. Therefore,μ

= 100 * 0.01

= 1d.

If the circuit boards are made in batches of two, then there are 50 batches of two circuit boards each. The probability that a batch has a defect is 1%. Therefore, the probability that a batch is defect-free is 99%.a. The probability that out of 100 circuit boards (50 batches) at least 2 have defects is calculated using the binomial distribution formula:P(X ≥ 2)

= 1 - P(X < 2)

= 1 - P(X = 0) - P(X = 1)

where n

= 50, p

= 0.01. Thus,P(X = 0)

= 50C0 * (0.01)^0 * (0.99)^50≈ 0.605P(X = 1)

= 50C1 * (0.01)^1 * (0.99)^49≈ 0.324

Therefore,

P(X ≥ 2) ≈ 1 - 0.605 - 0.324≈ 0.071b.

The expected number of circuit boards with defects out of the 100 made can be calculated as follows:For each batch of two circuit boards, either both have a defect or both are defect-free. Therefore, the number of defective circuit boards in each batch follows a binomial distribution with n = 2 and p = 0.01. The expected number of defective circuit boards in each batch is given by the formula:μ = n * pwhere n

= 2 and p

= 0.01.

Therefore,

μ

= 2 * 0.01

= 0.02The expected number of defective batches out of 50 batches is given by the formula:

μ = n * pwhere

n = 50 and

p = 0.01.

Therefore,

μ = 50 * 0.01

= 0.5.

The total expected number of circuit boards with defects out of the 100 made is 2 times the expected number of defective batches, which is:

μ = 2 * 0.5 * 2≈ 2.

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Answer:100-K

Step-by-step explanation:

"100 decreased by a number K" can be written algebraically as:

100 - K

This expression represents the result of subtracting the value of K from 100.

As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.\(f(x)=x^2-2x-10\)  general form to vertex form is y=[\((x-1)^{2}\)-9]

The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.

\(f(x)=x^2-2x-10\)

      = [\((x-1)^{2}\)-9]

Use the form, \(ax^{2} + bx+c\)

a=1

b=2

c=-10

Consider a vertex form of parabola,

\(a(x+d)^{2} + e\)

find the value of d, using the formula d=\(\frac{b}{2a}\)

d=\(\frac{2}{2*(-1)}\)

simplify the right side,

d= -1

find the value of e, using e= \(c-\frac{b^{2} }{4a}\)

e= \(-10\frac{2^{2} }{4*(-1)}\)

simplify the right side,

e= -9

substitute the value of a, d and e into vertex form.

y=  [\((x-1)^{2}\)-9]

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Answer:

The slope is -3.75 or -15/4.

Step-by-step explanation:

The formula for slope is the change in y over the change in x.

To do this, you subtract 7-3 to get you 4 on the bottom of the fraction and -7-8 which is -15.

So pretty much, you get -15/4. :)

Answer:

(0,-10)

Step-by-step explanation:

Using the equation y = mx = b where b is the y-intercept,

we can find that the "b" in y=|3x-10|+1  is -10

So the y-intercept is -10 or at the coordinates (0,-10)

when x = 0, the value of y is 11. This means that the point (0, 11) is on the graph of the function. Since this point lies on the y-axis and is where the graph crosses the y-axis, it represents the y-intercept of the function y = |3x - 10| + 1.

The y-intercept of a function is the point where the graph of the function intersects the y-axis. In other words, it's the point where the value of x is 0.

Given the function y = |3x - 10| + 1, we want to find the y-coordinate when x = 0 to determine the y-intercept.

Substitute x = 0 into the equation:

\(\[y = |3(0) - 10| + 1\]\)

Simplifying within the absolute value:

\(\[y = |-10| + 1\]\)

Since the absolute value of -10 is 10:

\(\[y = 10 + 1\]\[y = 11\]\)

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Answer:

a polygon has 3 or more sides

California has two senators and 53 House seats, it has a total of 55 electoral votes, which is the highest number of electoral college votes any state has.

California has 55 electoral college votes. When it comes to presidential elections, each state's electoral college vote depends on the number of representatives and senators it has. The number of seats in the House of Representatives is determined by the state's population, while every state gets two senators. California has the most representatives with 53 seats in the House of Representatives.California has 53 seats in the House of Representatives. For each of the 435 representatives, their states receive one electoral college vote, plus an additional two electoral votes for each of the two senators that represent their state in the US Senate. California has two senators and 53 House seats, it has a total of 55 electoral votes, which is the highest number of electoral college votes any state has.

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The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

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Answer:

B. at the mall

Step-by-step explanation:

The largest angle formed during his trip is at the mall.

Answer:

36 mins

Step-by-step explanation:

0.5 miles/6 mins = 3 miles/x mins

In order to convert the ratio from 0.5 miles to 3 miles, 0.5 was multiplied by 6. Therefore, to keep the ratio the same, 6 minutes must also be multiplied by 6 to find x. This means the answer is:

3 miles/36 mins

Answer:

y = -1.6x + 4

Step-by-step explanation:

slope (gradient) is given by change in y values divided by change in x values.

slope = (4 - -4) / (0 - 5) = (4 + 4)/ -5 = -8/5. = -1.6.

we only need to pick one point for the equation. we shall choose simplest. that is (0,4).

equation of straight line is:

y - y1 = m (x - x1)

where y1 is the y-coordinate of our chosen point, x1 is x-coordinate of our chosen point, m is the value of the slope (-1.6).

so our equation is

y - 4 = -1.6 (x - 0)

y - 4 = -1.6x

add 4 to both sides:

y = -1.6x + 4

Answer:

28(27)(26) assuming that nobody can get multiple designations.

Step-by-step explanation:

Answer:

A = (1/2 x b x h ) 4 + l^2

= 1/2 x 5 x 8 x4 + 5 x 5

80 + 25

= D. 105 cm2

Answer:

105

Step-by-step explanation:

The 95% confidence interval interpretation is as follows:

The 95% confidence interval means that  we can be 95% confident that the true population mean systolic blood pressure falls within the range (114 mmHg, 120 mmHg).

However, it is important to note that the confidence interval does not tell us with certainty where the true population mean systolic blood pressure lies, only where it is likely to be.

If we obtained a different set of 100 patients, we would likely obtain a different confidence interval. This is because the sample mean and standard deviation used to compute the interval would be different. However, if the new sample is still a representative sample of the same population, we would expect the confidence interval to be similar in width and location.

If we wanted a 99% confidence interval, the interval would be wider. This is because a higher confidence level requires a wider interval to be able to capture the true population mean with a higher degree of confidence.

The exact width of the interval would depend on the sample size and standard deviation used to compute it.

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Answer: All four friends would have to share paying the tip and the total so all of them would pay 1/4 of the bill and 1/4 of the tip

Step-by-step explanation: divide the bill and tip between the 4 friends and you get 1/4 which is how much of the bill and tip that all you and the friends have to pay

Answer: 28 y

Step-by-step explanation: All you really have to do is multiply 7 by 4y. 7(4y) 28y

The solution x(t) of the equation x = rx + x', where r > 0 is fixed, approaches infinity in finite time starting from any initial condition x = 0.

We can solve the differential equation x' = rx + x using separation of variables. Rearranging the equation, we get:

x' - rx = x

This is a linear first-order differential equation with integrating factor e^(-rt). Multiplying both sides by e^(-rt), we obtain:

e^(-rt)x' - re^(-rt)x = e^(-rt)x

Using the product rule for derivatives, the left-hand side becomes:

(d/dt)[e^(-rt)x] = e^(-rt)x'

Substituting this into the equation, we get:

(d/dt)[e^(-rt)x] = e^(-rt)x

This equation can be integrated to obtain:

e^(-rt)x = C

where C is a constant of integration. Solving for x, we get:

x = Ce^(rt)

Since r > 0, the exponential function e^(rt) grows without bound as t approaches infinity. Therefore, the solution x(t) of the differential equation also grows without bound in finite time starting from any initial condition x = 0. This means that x(t) approaches infinity as t approaches a certain finite value, which depends on the value of r.


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Answer:

A) 36 mi

Step-by-step explanation:

Got it right on edge 2021