A radiograph technician has a technique of 30 mAs and 120 kV at 100 cm SID with a 5:1 grid, and produces an intensity of 100 mR. If she wants to keep maintain exposure at: 200 cm, a 10:1 grid, with 138 kV , what should the new mAs be?

Answer:

ML/OP=MK/PN since sides of similar traingle are proportional

17/60=35/PN

PN=35×60/17=123.529=123.6 or 124

The measure of the side PN is 123.5.

Similar triangles are those triangles which has the same shape but different size.

The length of sides and angles are proportional in similar triangles

Given that triangle KLM is similar to triangle NOP.

If two triangles are similar, then their corresponding sides will be proportional.

From the figure,

Corresponding side of LM is PO.

Corresponding side of MK is NP.

Corresponding side of LK is ON.

So LM / PO = MK / NP = LK / ON

17 / 60 = 35 / PN = LK / ON

We need the length of PN.

17 / 60 = 35 / PN

17 × PN = 60 × 35

PN = (60 × 35) / 17

PN = 123.5

Hence the measure of the side of the triangle is PN = 123.5.

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Anime club: 500 - 30y

Computer club: 150 + 20x

*you could use any letter(variable) you like*

There are 1440 ways for 8 people to be seated in a round table if persons A and B must sit next to each other with no rules about their respective position.

There are a few steps to figuring out how many ways 8 people can be seated in a round table if persons A and B must sit next to each other.

Step 1: Consider persons A and B as one unit.

By considering both person A and B as one person, that there are now 7 available chairs to be seated around the table.

Step 2: Calculate the number of ways to arrange these 7 units around the table.

Since it is a round table, the number of ways is (7-1)! = 6! = 720.

Step 3: Consider the fact that person A and B can be arranged in 2 different ways within their unit (either A is on the left and B is on the right, or vice versa).

We have no rules about the sequence of person A and B's sits, then we can consider that they can choose 2 more options about their own position. This means that the total number of ways to seat the 8 people is 720 * 2 = 1440.

So, the answer is that there are 1440 ways for 8 people to be seated in a round table if persons A and B must sit next to each other.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-2}{4 +4} \implies \cfrac{ -2 }{ 8 } \implies - \cfrac{ 1 }{ 4 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -3 = - \cfrac{ 1 }{ 4 } ( x +4) \\\\\\ y-3=- \cfrac{ 1 }{ 4 }x-1\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 4 }x+2 \end{array}}\)

60+90=180

=150

180-150

= -30

brainyest pls

The distance of the jungle gym to swing is 120 feet.

We have given that the diagram

we have to find the distance between jungle gym and swings is,

suppose that x is shorter length then the hypotenuse is 2x and  \(x\sqrt{3}\)

is the longer length

By using the Pythagoras formula we have

The length of CA is,

\(CA=60(2)=120\)

Therefore the distance of the jungle gym to swing is 120 feet.

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Answer:

A. Brand R will be $548.18 cheaper than Brand S edge 2022 just took it.

Step-by-step explanation:

Brand R will be $548. 18 cheaper than Brand S.

Thus, option (a) is correct.

Given:

The APR of credit card is 9.31%.

Total number of years = 10.

To choose the credit card with the lowest lifetime cost for purchasing the freezer, is required to compare the APR (Annual Percentage Rate) of both credit cards.

Let's assume the cost of the freezer is $1000.

Since Brand S takes 18 months to pay off, the interest accrued over this shorter period will be less compared to Brand R, which takes 4 years to pay off.

By comparing the APRs of the credit cards, it is concluded that Brand R will be $548.18 cheaper than Brand S.

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Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

Answer:

256 cm³

Explanation:

\(\sf Volume\:of\:sphere=\dfrac{4}{3} \pi (radius)^3\)

Here given:

Solve for volume:

\(\sf Volume\:of\:sphere=\dfrac{4}{3} \pi (4)^3\)

take π as 3

\(\sf Volume\:of\:sphere=\dfrac{4}{3} (3) (4)^3\)

simplify exponent

\(\sf Volume\:of\:sphere=\dfrac{4}{3} (3) (64)\)

evaluate following

\(\sf Volume\:of\:sphere=4(64) = 256 \ cm^3\)

Answer:

V = 256 cm³

Step by step explanation:

Given that, diameter of the sphere is: 8cm

First, let us find the radius of the sphere:

d = 2 r

8 = 2 r

8/2 = 2r / 2

4cm = r

The formula to find the volume of the sphere:

\(V=\frac{3}{4} \pi r^{3} \\\)

Here,

r ⇒ radius

Let us find it now.

\(V=\frac{3}{4} \pi r^{3} \\\\V=\frac{3}{4} *\pi *4^{3} \\\\V=\frac{768}{4} \\\\V=256cm^{3}\)

The two statements "if it is a triangle, then it has three sides and If it does not have three sides, then it is not a triangle is logically equivalent

A sentence is logically equivalent if the two sentences are true in exactly the same circumstances or false in exactly the same circumstances.

From the question we have two statements

Statement 1: If it is a triangle, then it has three sides.

Statement 2: If it does not have three sides, then it is not a triangle.

Since a triangle only have 3 sides and any contradiction makes the statement false, hence we can conclude that the two statements "if it is a triangle, then it has three sides and If it does not have three sides, then it is not a triangle is logically equivalent

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A membership which would be 26, and 2 people which is 5 for each, therefor ten.

I hope this helps <3

Answer:

Yes the bridge will hold 1 ton

Step-by-step explanation:

16 ounces = 1 pound.

2,000 pounds = 1 ton.

He builds a model of the bridge that is exactly 4 times smaller than the actual bridge

The scale used is:

Model : Actual

1:4

If a test of the model shows that it holds 8,000 ounces, will the bridge hold 1 ton?

The actual bridge can hold :

8000 ounces × 4 = 32,000 ounces

16 ounces = 1 pound.

32000 ounces = x

Cross Multiply

x = 32000/16

x = 2000 pounds

2,000 pounds = 1 ton

Hence, The original bridge = 2000 pounds can hold 1 ton.

Answer:

Sjhdhdnjsuemshusushdj

Step-by-step explanation:

now yte don't do this because then you will be reported and people really want to learn and STEAL THESE ANSWERS pop it's time for my class brb but don't do this if you don't know the answer don't put it in or you will, be reported. Time for P.E and sorry.

Answer:36.36%

Step-by-step explanation:

%change=100 X (final-inital value) divided by initial

Answer:

8

Step-by-step explanation:

If the width of the path is x, then the dimensions of the combined area would be (20 + 2x) × (24 + 2x). Since the combined area is given as 1440, we can equate this with the area of a rectangle with these dimensions.

1440 = (20 + 2x)(24 + 2x)

Expand the brackets

1440 = 480 + 88x + 4x^2

Rearrange the equation, moving the 1440 to the other side so that it is equal to zero

0 = 4x^2 + 88x - 960

Divide by 4 as it is a common factor

0 = x^2 + 22x - 240

Use the quadratic formula

For an equation of the form 0 = ax^2 + bx + c, the quadratic formula is:

\(x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \)

\(x = \frac{ - 22 \pm \sqrt{ {22}^{2} - 4 (1)( - 240)} }{2(1)}\)

\(x = \frac{ - 22 \pm \sqrt{484 + 960} }{2}\)

\(x = \frac{ - 22 \pm \sqrt{1444} }{2}\)

\(x = \frac{ - 22 \pm38}{2}\)

\(x = - 11 \pm19\)

\(x = 8\)

Answer:

=81x^28

Step-by-step explanation:

Answer:

1) 64 and 81

2) a(n) = (n + 2)^2, where n = 1, 2, 3, ...

3) a(25) = (25 + 2)^2 = 27^2 = 729

Answer:

B. 9/41

Step-by-step explanation:

Answer:

Third option: (1, 0), (2, 0), and (–3, 0)

Step-by-step explanation:

The x-intercepts are the points at which the graph of the function crosses the x-axis.

By reading the question, we can see that:

"... crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0)..."

So the x-intercepts are:

(-3, 0)

(1, 0)

(2,  0)

Then the correct option is the third one:

"(1, 0), (2, 0), and (–3, 0)"

Answer: Option 3

Step-by-step explanation: Got it right on Edge

Answer:

Yes

Step-by-step explanation:

If she writes 8 pages a day for 4 days a week, in the first week, she will have already written 32 pages which she would only need one more day.

4 x 8 = 32

32 + 8 = 40

That gives her time to edit and revise :)

Hope this makes sense

By considering the signs and magnitudes of these partial derivatives, we can further analyze the specific impact of changes in the loan duration and interest rate on the monthly payment.

To compute the monthly payment for Alex's home mortgage, we can use the formula provided:

\(M(p, r, t) = pr(1+r)^t / ((1+r)^t - 1)\)

Given the values:

A = 526

B = 21

r = 0.06 (6% interest rate per year)

t = B * 12 (converting years to months)

Substituting the values into the formula, we have:

\(M = 526 * 0.06 * (1 + 0.06)^(21 * 12) / ((1 + 0.06)^(21 * 12) - 1)\)

Using a calculator to evaluate the expression, we get the monthly payment, correct to 2 decimal places.

(b) To compute M(1,000, 4, 0.004, 120), we can use the same formula with the given values:

M = 1000 * 0.004 * (1 + 0.004)^(4 * 120) / ((1 + 0.004)^(4 * 120) - 1)

Using a calculator to evaluate the \(M = 1000 * 0.004 * (1 + 0.004)^(4 * 120) / ((1 + 0.004)^(4 * 120) - 1)\), we get the value of M, correct to 2 decimal places.

Interpretation: The value of M represents the monthly payment required to amortize the loan over the given period, taking into account the principal amount, interest rate, and duration. It provides a measure of the amount that needs to be paid each month to gradually pay off the loan.

(c) To discuss how the monthly payment for Alex's home mortgage is affected by changes in the duration of his loan and the interest rate charged, we can use the concept of total differential.

Let's denote the monthly payment as M and the variables that affect it as t (duration of the loan) and r (interest rate). We can express the differential of M as follows:

dM = (∂M/∂t) dt + (∂M/∂r) dr

The partial derivatives (∂M/∂t) and (∂M/∂r) represent the rate of change of M with respect to t and r, respectively.

By considering the signs and magnitudes of these partial derivatives, we can further analyze the specific impact of changes in the loan duration and interest rate on the monthly payment.

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Answer:

23.75y+25

Step-by-step explanation:

multiply everything turn the fraction into a decimal add them together add the 5y at the end

Answer:

  (a)  A two column table with five rows. ... The second column, y, has the entries, 2, 2, 2, 2

Step-by-step explanation:

You want to know which table shows a relation with zero slope.

When a graph has zero slope, it is a horizontal line. Every y-value is the same.

The table demonstrating zero slope will have all y-values the same:

  The second column, y, has the entries, 2, 2, 2, 2

Answer:y=-10

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Well, now that I found out the prices per ounce, it has to be option B. Here is my reasoning:

Option A, when you do 2.98÷15.5, you get 0.19225...

Option B, is a different story. When you do the same process, it amazingly comes out to 0.1785...(this means that Option B is 0.2 cents (rounded) cheaper per unit, then Option A.

So its option B

Your welcome.

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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(a) x_n = (1 + 0.1 - h/1000)^n * x_0, given x_0 = 1000 and h = 20. (b) Sequence terms are always non-negative. (c) Equilibrium is maintained when h = 10 for x_0 = 1000.

(a) The expression for x_n in terms of n, given x_0 = 1000 and h = 20, is x_n = (1 + 0.1 - h/1000)^n * x_0.  The population count after n years, x_n, is obtained by multiplying the previous year's count, x_{n-1}, by the growth factor (1 + 0.1 - h/1000) and multiplying it recursively for n years.

(b) No, the terms in the sequence generated by the expression found in (a) will never be negative. The factor (1 + 0.1 - h/1000) is always greater than or equal to 0, ensuring a positive population count.  Since the growth factor is always greater than or equal to zero, the terms in the sequence will never be negative.

(c) To determine a value for h such that the population with x_0 = 1000 remains at equilibrium, we set x_n = x_0. By substituting the given values and solving the equation (1 + 0.1 - h/1000)^n * 1000 = 1000, we find h = 10. At equilibrium, the population count remains constant over time. By setting x_n = x_0 and solving the equation, we find that h = 10 is the value at which the population remains at equilibrium when x_0 = 1000.

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