950.95 written in expanded form

THE CORRECT ANSWER IS 57 CM³

Explanation:

Let's consider the vertical block first, having height 9 cm, length 1 cm, width 5 cm.

Hence the volume of that block = l.w.h = 9×5×1 = 45 cm³

Coming to the horizontal block, having height 4 cm, width 3cm, & length 1 cm.

Hence the volume of that block will be = 4×3×1 = 12 cm²

The total volume of irregular figure = Volume of vertical block + horizontal block = 45+12 = 57 cm³

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Answer:

πr²=22/7×49

=22×7

=154

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The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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Answer:

A) y>=-1

Step-by-step explanation:

The line itself is y=-1, but it is also filled in. Therefore, we are down to either A or C as the right answer

Since (0,0) is a solution to the inequality as indicated by the shade, we know that since y=0 in the origin, 0 is greater than -1, so therefore A is the correct answer.

Answer: 75%

Step-by-step explanation:

Only 9 students have taken fewer than 21 courses

9/12 = 0.75 or 75%

A cylinder with a radius of 6 inches and a height of 5 inches is produced if rectangle ABCD is rotated around line m.

A solid figure is a 3-dimensional shape (length, width, and height) so that it has a volume inside. Examples of solid figures are prism, cylinder, cone, pyramid, and so on.

From the question we get the following information:

- rectangle ABCD

- line m divides side AB into 2, each 6 inches

- the length of side AD and BD is 5 inches

So, when we rotate rectangle ABCD around line m, it will produce a cylinder, with:

- cylinder height = AD = BD = 5 inches

- cylinder diameter = 1/2 AB = 6 inches

To get the best illustration of the problem, we can draw rectangle ABCD and line m.

So the solid figure produces if we rotate rectangle ABCD around line m is a cylinder with a radius of 6 inches and a height of 5 inches.

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Answer: D) cylinder; radius = 6 in.; height = 5 in.

Step-by-step explanation:

Edege 2023

The SI units of the proportionality constant G is Newton \(Kg^{-2} m^2\)

Gravitational force is given by Newton's law of gravitation which states that every particle of matter in the cosmos is drawn to every other particle by a force of attraction that varies directly with the product of their masses and is inversely proportional to the square of the distance or degree of separation from each other.

F = G \($ \frac{m_1 m_2}{r^2}\)

Upon rearranging the terms we get,

G = \($\frac{F r^2}{m_1 m_2}\)

Where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is the length.

Force has the SI units kg · m/s2

The SI units of the proportionality constant G

SI Unit of G = \($\frac{(\text { Newton })\left(\mathrm{m}^2\right)}{\mathrm{kg} ^2}\)

= Newton \(Kg^{-2} m^2\)

Therefore the units are Newton \(Kg^{-2} m^2\)

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Newton's law of universal gravitation is represented by F = G \($ \frac{m_1 m_2}{r^2}\) where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is a length. force has the SI units kg· m/s2. what are the SI units of the proportionality constant G?

The dimensions of the rectangle: length = 15 km and width = 11 km

Let l be the length of rectangle and w be the width of the rectangle.

A rectangle has perimeter 52 km

Using the formula of the perimeter of rectangle we get an equation,

2(l + w) = 52              ............(1)

And its area is 165 sq-km.

Using the formula of the area of rectangle we get an equation,

l * w = 165               ............(2)

From equation (1),

l = 26 - w

Subatitute above value of l in equation (2),

(26 - w) * w = 165  

26w - w² = 165

w² - 26w + 165 = 0

(w - 15)(w - 11) = 0

w = 15     or         w = 11

For w = 15,

l = 26 - 15

l = 11

For w = 11,

l = 26 - 11

l = 15

But as we know, the length of rectangle is always greater than the width,

l = 15 and w = 11 is true .

Therefore, the length of rectangle = 15 km and width of rectangle = 11 km

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Answer:

-a^4b + b^3 - 8c^2

Step-by-step explanation:

Sum of

3a^4b-4b^3+c^2 + 6a^4b+3b^3-6c^2

= 3a^4b + 6a^4b - 4b^3 + 3b^3 + c^2 - 6c^2

= 9a^4b - b^3 - 5c^2

Sum of

6a^4b-4b^3-4c^2 + 2a^4b+4b^3+7c^

= 6a^4b + 2a^4b - 4b^3 + 4b^3 - 4c^2 + 7c^2

= 8a^4b + 3c^2

Subtract

8a^4b + 3c^2 - (9a^4b - b^3 - 5c^2)

= 8a^4b + 3c^2 - 9a^4b + b^3 + 5c^2

= 8a^4b - 9a^4b + b^3 + 3c^2 + 5c^2

= -a^4b + b^3 - 8c^2

The rate at which the distance from the plane to the station is increasing when it has a total distance of 4 miles away from the station is 317.5 mi/h.

A rate in which a certain number of units of the first quantity are compared to one unit of the second quantity is not the same as a unit rate. In other words, we may state that the comparison's second amount is always 1.

Thus, P denotes the plane's location, R denotes the radar's location, and V denotes the point that is vertical to the radar and at the plane's height.

Assume that h is the height of the plane, s is the separation from the radar, and x is the separation from point V.

The plane travels at 480 miles per hour and has a 3 mile height. Ds-480 miles per hour.

dt By Pythagorean theorem,

x² = h² + s²

x² = 3²+s²

x² = 9 + s²

Differentiate implicitly with respect to t.

2x dx/dt = 2s ds/dt + 0

x dx/dt = s ds/dt

Use (1)

dx/dt = \(\frac{dx}{dt} =\frac{\sqrt{x^2-9} }{x}\)

= √7/4 x 480

= 120√7

≈ 317.49

Hence, the distance increasing at the rate of dx/dt is 317.5 mi/h.

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The formula for the number of bacteria at time t is given by N = 10,000e^(0.0173t).

The formula for the number of bacteria at time t can be found using the exponential growth formula. The formula for exponential growth is given by;N = N0ertWhere;N is the number of bacteria after t minutes.N0 is the initial number of bacteria.r is the growth rate.t is the time interval.

To find the formula for the number of bacteria at time t, substitute the given values into the exponential growth formula.N0 = 10,000r = ln2/40 = 0.0173 (since the number of bacteria doubles every 40 minutes, the growth rate is equal to the natural log of 2 divided by 40.)t = t minutesN = 10,000e^(0.0173t)

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The diagrams are shown in the solution.

A rectangle is a quadrilateral with all four interior angles 90°.

(1) The rectangle diagram of 1/2 × 5/6 can be drawn by converting the fractions into integers.

The dimension can be written as:

1/2 : 5/6

Multiply the ratio by 6:

3 : 5

Hence, the rectangle of  1/2 × 5/6 is proportional to 3×5.

The diagram is shown.

Similarly, the diagrams of other rectangles are shown.

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The distance Freya traveled is 320 miles.

We have,

To solve this problem, we need to use the formula:

Speed = Distance/time

First, let's calculate the distance Freya drove from Bournemouth to Gloucester:

distance1 = speed1 x time1

= 50 mph x 2.5 hours

= 125 miles

Next, let's calculate the distance Freya drove from Gloucester to Anglesey:

distance2 = speed2 x time2

= 65 mph x 3 hours

= 195 miles

Finally, we can calculate the total distance Freya traveled by adding the two distances:

Total distance = distance1 + distance2

= 125 miles + 195 miles

= 320 miles

Therefore,

Freya traveled a total of 320 miles.

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Answer: 0.01090566037

Answer: The short answer to this is 0.0109

Answer:

1571in^3

Step-by-step explanation:

Given data

h= 20 in

d= 10 in

r= 10/2= 5 in

V= πr^2h

substitute

V= 3.142*5^2*20

V=3.142*25*20

V=1571 in^3

Hence the volume is 1571in^3

Answer:

Step-by-step explanation:

Answer:

0.069

Step-by-step explanation:

I think you mean 6.9 x 10^-2

This number is in scientific notation. In order to convert it to standard form, you have to do what the exponent is telling you to do. In this case, the -2 means that you are moving the decimal point in 6.9 two spots to the left, since it is negative which means the number is getting smaller.

This equals 0.069

Answer:

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.

The explanatory variables and response variables for this relationship are;

b. Explanatory variable: high school GPA

   Response variable: college GPA

What are explanatory variables?

When it comes to an experiment, a researcher-manipulated variable is an explanatory variable. It acts as a gauge of the transformation the response variable underwent.

Explanatory variables are frequently referred to as predictor variables or independent variables. A response variable is the variable that a researcher is asking a specific question about.

Numerous variables, referred to as explanatory variables, might have an impact on the response variable.

Therefore, the correct option is b, Explanatory variable: high school GPA, Response variable: college GPA.

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Complete question:

College administrators at a small, private college

noticed that students who had higher high school

GPAs tend to have higher college GPAs.

What are the explanatory variable and response

variable for this

relationship?

Explanatory variable: size of college

Response variable: college GPA

Explanatory variable: high school GPA

Response variable: college GPA

Explanatory variable: college GPA

Response variable: high school GPA

Explanatory variable: type of college (public)

Response variable: college GPA

The value of g(4) in the function is -5 which is option b

To find the value of g(4) in the composite function, we need to evaluate the function when x = 4

In the first equation, since x is greater than 4 already, we can't use ot.

Let's proceed to the second equation;

g(x) = -2x + 3, x ≤ 4

Let's put the value x = 4 into the equation;

g(4) = -2(4) + 3

g(4) = -8 + 3

g(4) = -5

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Answer:

x = -2

Step-by-step explanation:

6x - 8 + 3x -3 = -29

9x = - 18

x = -2

Answer:

Step-by-step explanation:

Just like a lot of our other curve transformations

The number with x => (x+2) is the shift in x direction and you take opposite sign so it's been shifted -2 or left 2

bring the 4 to the back of teh equation and it will be +4, that controls the y direction which is +4 or up 4

That would leave a - in the front which means the graph  wil be reflected.

The angle of elevation of Bugs Bunny's climb is approximately 13.8 degrees.

To find the angle of elevation of Bugs Bunny's climb, we can use trigonometry. The angle of elevation can be calculated as the inverse tangent (arctan) of the ratio of the vertical distance (100,100) to the horizontal distance (42,4242).

The angle of elevation (θ) can be found using the formula: θ = arctan(vertical distance / horizontal distance).

In this case, the vertical distance is 100,100 meters and the horizontal distance is 42,4242 meters.

θ = arctan(100100 / 424242)

Using a calculator, we can find the value of the angle of elevation.

θ ≈ 13.8 degrees

Therefore, the angle of elevation is approximately 13.8 degrees.

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Step-by-step explanation:

remember the law of sine :

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

where the sides and the associated angles are always opposite of each other.

and ... the sum of all angles in a triangle is always 180°.

sin(90) = 1.

1.

another right-angled triangle.

500/sin(90) = depth/sin(37)

depth = 500×sin(37)/1 = 300.9075116... m

2.

another right-angled triangle.

the ladder is the Hypotenuse (baseline).

the height of the wall and the ground distance are the 2 legs.

the angle we are looking for is opposite of the wall height.

so, we get

14/sin(90) = 13/sin(elevation) = 14

sin(elevation) = 13/14 = 0.928571429...

angle of elevation = 68.2132107...°

3.

both lines are tangents to the circle. so, both distances (from the starting point J to the touching points K and M) must be equal.

so,

5x - 4 = 2x + 2

3x = 6

x = 2

Step-by-step explanation:

x+2>7

x>7-2

x>5

2x+5>_ 15

2x>_ 15-5

2x>_ 10

2x/2>_ 10/2

x>_5

The correct statement is option (d) Considering a Gaussian GLM with the canonical link, recall that Ể = (XTX)-1X y can be calculated explicitly.

(a) In a GLM with a canonical link function, the likelihood equations can be used to estimate the coefficients of the linear predictor. The residual vector, e = y - û, represents the difference between the observed responses and the predicted means.

(b) In a GLM with a noncanonical link function, the likelihood equations do not necessarily imply that the residuals have mean zero. This means that there may be some systematic error in the model that cannot be explained by the predictor variables.

(c) In a GLM with a canonical link function, an intercept term is needed to ensure that Liſdi = Eiyi. This means that the expected value of the response variable is equal to the linear predictor when all predictor variables are equal to zero.

(d) In a Gaussian GLM with the canonical link, the Fisher Scoring Algorithm can be used to estimate the coefficients of the linear predictor. This algorithm iteratively updates the coefficients using the derivative of the log-likelihood function with respect to the coefficients. The algorithm stops when the change in the coefficients is small.

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Complete Question:

Which one of the following is the correct statement about Newton-Raphson Algorithm?

(a) For a GLM with canonical link function, explain how the likelihood equations imply that the residual vector e = y – û is orthogonal to the column space of X. Here, y and û denote the vectors of the observed responses and the fitted means, respectively.

(b) In a GLM that uses a noncanonical link function, explain why it need not be true that Li Ĝi = Liyi, that is, the residuals need not have mean zero.

(c) Explain why a canonical link GLM needs an intercept term in order to ensure that Liſdi = Eiyi.

(d) Considering a Gaussian GLM with the canonical link, recall that Ể = (XTX)-1X y can be calculated explicitly.

Answer:

c.

Step-by-step explanation:

A. 4 has factors of 1, 2 and 4

B. 6 has factors of 1, 2, 3 and 6

D. 9 has factors of 1, 3 and 9

An informal proof uses specific examples to show that a conjecture is true.

An informal proof is a proof that is written in plain language and is intended to be read by someone who is familiar with the subject matter but not necessarily trained in mathematical rigor or logic. These proofs are usually less formal than formal proofs but are still valid and are often used in textbooks, journals, and other publications.

The main difference between formal and informal proofs is that formal proofs rely on a strict set of rules and symbols, while informal proofs use more everyday language and examples. Informal proofs are often easier to understand than formal proofs because they are written in a more conversational tone and use everyday language and examples that most people are familiar with.

Informal proofs typically use specific examples to show that a conjecture is true. These examples are often drawn from real-world situations or other areas of mathematics and are used to illustrate the key concepts involved in the proof.

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The Wronskian is 2te^t(t - 1).

Let's find the Wronskian of the given functions to determine whether the vectors are linearly independent on (−[infinity], [infinity]) or not.

So, we have the following information:

x₁ = e^tx₂ = t²

First, let's find dx₁/dtx₁ = e^t

Now, let's find dx₂/dtx₂ = 2t

Let's find the WronskianW(x₁, x₂) = |x₁ x₂ dx₁/dt dx₂/dt||e^t t² e^t 2t|= e^t * 2t² - 2te^t = 2te^t(t - 1)

The Wronskian is not equal to 0, therefore, the vectors are linearly independent on (-∞, ∞).

Answer:

The vectors are linearly independent on (-∞, ∞).

The Wronskian is 2te^t(t - 1).

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After 8.5 seconds down the hill, they will be moving at a velocity of 17.19 m/s.

The speed of an object after a certain time can be calculated using the following equation:

v = u + at

Where:v is the final velocity, u is the initial velocity, a is the acceleration of the object, t is the time taken by the object

So, the person is on skis at the top of a 12-degree ski run and starts from rest, which means the initial velocity u is 0 m/s.

The downhill slope creates an acceleration for the person. The acceleration due to gravity is acting down the slope.

The component of gravity along the slope is given by:g = 9.81 × sin (12°) = 2.022 m/s²

Putting all values in the equation:

v = u + atv = 0 + 2.022 × 8.5v = 17.19 m/sTherefore, the person's final velocity after 8.5 seconds down the hill is 17.19 m/s.

After 8.5 seconds down the hill, they will be moving at a velocity of 17.19 m/s.

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