Write down all the whole numbers that
are between 20 and 45
and
have a difference of 3 between their digits.
I

By the AA (Angle-Angle) similarity postulate, we can conclude that △lmn ∼ △opn.

To complete the proof that △lmn ∼ △opn:

1. Given: l and m are parallel to o and p (lm ∥ op).
2. Reason: When a transversal crosses parallel lines, alternate interior angles are congruent (angle l ≅ angle o).

Therefore, by the AA (Angle-Angle) similarity postulate, we can conclude that △lmn ∼ △opn.

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The quotient of the given problem using laws of exponents is; 6 * 10⁰

We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.

This is;

(30 * 10⁻²⁴)/(5 * 10⁻²⁴)

Now, we can break this down into like terms to get;

(30/5) * (10⁻²⁴/10⁻²⁴)

= 6 * 1

Now, 1 can also be written as;

10⁰ = 1

Thus, the solution of the given problem is; 6 * 10⁰

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Answer:

x=3/4

Step-by-step explanation:

Given:

f(x) = x-1

g(x) = 2x²+3

Evaluate composite functions:

f(g(x)) = f(2x²+3) = (2x²+3)-1 = 2x²+2

g(f(x)) = g(x-1) = 2(x-1)²+3 = 2(x²-2x+1)+3 = 2x²-4x+2+3 = 2x²-4x+5

Set expressions equal to each other and solve for x:

2x²+2 = 2x²-4x+5

2 = -4x+5

-3 = -4x

3/4 = x

x = 3/4

Therefore, the value of x=3/4 satisfies both composite functions

The smallest possible whole number is 2 after how many years will the amount due reach $46,000 or more.

The smallest possible whole number answer of after how many years will the amount due reach $46,000 or more if a loan of $28,000 is made at 6.75% interest, compounded annually.

we'll use the calculator provided on the platform.

\(A=P(1+r/n)^(nt)\)

A = $46,000,

P = $28,000,

r = 6.75%

= 0.0675,

n = 1,

t = years

Let's substitute all the given values in the above formula:

\(46,000 = 28,000 (1 + 0.0675/1)^(1t)\\ln(1.642857) = t * ln(2.464286)\\ln(1.642857)/ln(2.464286) = t\\1.409/0.9048 = t\\1.5576 = t\)

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The rate of growth of revenue when 420 units have been sold is R'(420) = R'(350)..

Revenue from selling x units = R(x). Also, sales are increasing at a rate of 70 per day. That means if x units are sold today, then tomorrow, the units sold would be (x + 70) units. Rate of increasing sales = 70 per day. Now, when 420 units have been sold:

Initial units sold = x = 420 - 70 = 350 units

Total units sold = 420 units

Number of units sold today = 420 - 350 = 70 units

Now, Revenue generated from 350 units of the item = R(350)

Revenue generated from 420 units of the item = R(420)

Rate of growth of revenue when 420 units have been sold = R'(420)\

From the definition of the derivative:

R'(x) = lim_ {h→0} {R(x+h) - R(x)}/{h}

R'(420) = lim_ {h→0} {R(420+h) - R(420)}/{h}

R(420) = R(350 + 70) = R(350) + R'(350) * (70)And, R(420 + h)

= R(350 + 70 + h) = R(350) + R'(350) * (70 + h), Using these equations,

R'(420) = lim_ {h→0} {R(350) + R'(350) * (70 + h) - R(350) - R'(350) * (70)}/{h}

= lim_ {h→0} {R'(350) * h}/{h}

= R'(350)

Thus, the rate of growth of revenue when 420 units have been sold is R'(420) = R'(350).

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12x + 288y = 0 -->(i) x + 192y = 0

=> 12(x + 192y) = 0 × 12

=> 12x + 2304y = 0 -->(ii)

(12x + 288y) - (12x + 2304y) = 0 - 0

=> 12x + 288y - 12x - 2304y = 0

=> - 2016y = 0

=> y = 2016

12x + 288y = 0

=> 12x + 288 × 2016 = 0

=> 12x + 580608 = 0

=> 12x = - 580608

=> x = 48384

28 minutes later, when the car arrived at the second office, it had been traveling at speed of 60 miles per hour. The driver of the car received a ticket for going above the 60 mph limit; the office went over the limit.

Given ,

Distance = 30 miles

Time = 28mins

Determine the speed exceeds the limit:

speed = distance /time

speed = 30 miles / 28 minute

speed = 30 miles /28 minute x 60 minutes/1 hour

speed = 64 mph

The speed actually exceed the limit.

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Answer:

Translation

Step-by-step explanation:

Translation as the x and y are both being moved over the plane.

Answer:

The graph of the function starts high ends low

Step-by-step explanation:

I put the equation into Desmos

Answer:

I hope this help :)

Step-by-step explanation:

radius: 2.459

diameter: 38

circumference: 119.381

but if you're looking for a more appropriate answer I would round radius and circumference.

Answer:

steps below

Step-by-step explanation:

radius: 19/2 = 9.5 ft

diameter: 19 ft

circumference: 2 x 3.14 x 9.5 = 59.66 ft²

The change in volume (dv) is equal to 1221.45 cm³ if the radius of the sphere changes from 18 cm to 18.3 cm.

The change in the volume of the sphere can be represented by the following formula;

dV = 4πr²(dr)

Here dV is the change in the volume, r represents the radius and dr represents the change in the radius of the sphere.

As the radius of this sphere changes from 18 cm to 18.3 cm, we first calculate the change in radius by subtraction;

change in radius = 18.3 - 18 = 0.3 cm

Now substituting the values in the equation;

dV = 4π(18²)(0.3)

dV = 4π(324)(0.3)

dV = 4π(97.2)

dV = 1221.45

Therefore, the change in the volume of the sphere is 1221.45 cm³

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The correct pairing is (2) velocity and m/s , weight is a scalar quantity measured in newtons (N), not kilograms (kg)

Weight is the force experienced by an object due to gravity and is measured in newtons, not the unit of mass which is kilograms.

Velocity is a vector quantity that measures the rate at which an object changes its position. It is defined as the displacement of an object divided by the time taken and is measured in meters per second (m/s).

Speed is the magnitude of velocity and is also measured in meters per second (m/s). It represents how fast an object is moving regardless of its direction. Speed is a scalar quantity, not a vector quantity.

Acceleration is a vector quantity that measures the rate of change of velocity. It is defined as the change in velocity divided by the time taken and is measured in meters per second squared (m/s^2).

Acceleration represents how quickly an object's velocity is changing. Therefore, the correct pairing is (2) velocity and m/s.

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The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.

Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%

In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:

The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.

The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation

Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.

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We can use the conditional proof rule in propositional logic. By assuming r as a premise and using logical deductions, we can derive p. This will allow us to conclude r → p.

To prove the conclusion r → p using the premises P → q and rq, we employ the conditional proof rule. This rule allows us to assume a premise and use it to derive another statement within a subproof. In this case, we assume r as a premise and aim to derive p.

1. Assume r (conditional proof assumption)

2. Since rq is a premise, we can use simplification to obtain q.

3. Using modus ponens, we apply the premise P → q and the assumption P to derive q.

4. Now, using modus ponens again, we apply the premise r → q and the assumption r to derive q.

5. By simplification, we extract p from the premise rq.

6. Having derived p within the subproof, we can now conclude r → p using the conditional proof rule.

By employing the conditional proof rule and logical deductions based on the given premises, we have successfully derived the conclusion r → p from the premises P → q and rq.

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The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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The value of β is approximately 0.0505.

To calculate β, we also need the value of the population proportion (p) under the alternative hypothesis. Let's calculate β for the given conditions.

a) When p = 0.18:

Using the given information, we have:

H0: p ≤ 0.15

H1: p > 0.15

α = 0.05

n = 129

To calculate β, we need to determine the critical value corresponding to the significance level α and the null hypothesis H0. Since the alternative hypothesis is one-sided (p > 0.15), we will use the z-test.

The critical value for a one-sided test at α = 0.05 is z = 1.645.

Next, we calculate the standard error (SE) using the null hypothesis proportion p0 = 0.15 and the formula:

SE = sqrt((p0 * (1 - p0)) / n)

SE = sqrt((0.15 * (1 - 0.15)) / 129) ≈ 0.033

Now, we can calculate β using the formula:

β = 1 - Φ(z - (p1 - p0) / SE)

where Φ is the cumulative distribution function of the standard normal distribution.

β = 1 - Φ(1.645 - (0.18 - 0.15) / 0.033)

Using a standard normal distribution table or a calculator, we find that Φ(1.645) ≈ 0.9495.

β = 1 - 0.9495 ≈ 0.0505

Therefore, when p = 0.18, β is approximately 0.0505.

b) When p = 0.22:

Using the same process as above, we have:

H0: p ≤ 0.15

H1: p > 0.15

α = 0.05

n = 129

The critical value for a one-sided test at α = 0.05 is still z = 1.645.

SE = sqrt((0.15 * (1 - 0.15)) / 129) ≈ 0.033

β = 1 - Φ(1.645 - (0.22 - 0.15) / 0.033)

Using a standard normal distribution table or a calculator, we find that Φ(1.645) ≈ 0.9495.

β = 1 - 0.9495 ≈ 0.0505

Therefore, when p = 0.22, β is also approximately 0.0505.

In both cases (a and b), the value of β is approximately 0.0505.

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Initially, when a bank has a required reserve ratio of 20%, and no excess reserves, if $10,000 is deposited into the bank, the bank will be required to hold 20% of the deposit as required reserves, which amounts to $2,000.

The remaining $8,000 can be used to make loans or acquire additional assets, such as bonds.

The required reserve ratio is the percentage of deposits that a bank is required to hold in reserve, either in cash or on deposit with the Federal Reserve Bank. The required reserve ratio is set by the Federal Reserve and is used as a tool to regulate the money supply and control inflation.

When a bank receives a deposit, it must keep a portion of that deposit in reserve to ensure that it has enough cash on hand to meet the demands of its customers who wish to withdraw their money.

In this scenario, the bank will hold $2,000 in reserves and can use the remaining $8,000 to make loans or acquire additional assets. This process is known as the money multiplier effect, where the original deposit is multiplied through the banking system as it is loaned out and deposited into other accounts. The money multiplier effect can be used to increase the money supply and stimulate economic growth.

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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Answer:

A linear function has a constant rate of change. A nonlinear function does not

Also, Lnear functions show a straight line when they are graphed and nonlinear functions don't.

My advice is to graph it and look at the points.

Good luck! Pls give brainliest!

Answer:

See Picture & I hope this helps!:)

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

I hope this is correct, if it is wrong please feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.

Answer:

\(24000\) ft³

Step-by-step explanation:

The formula for a rectangular prism's volume is \(V=\frac{1}{3}lwh\), where \(V\), \(l\), \(w\), and \(h\) are the prism's volume, length, width, and height, respectively. In this case, we are given that \(l=30\), \(w=40\), and \(h=60\). We also know that we are solving for \(V\). Therefore,

\(V=\frac{1}{3}lwh\)

\(V=\frac{1}{3}*30*40*60\) (Substitute given values into equation)

\(V=24000\) (Simplify)

Hope this helps!

Answer:

A) 50

Step-by-step explanation:

1. Calculate the cost of one cubic meter

\(20/4 = 5\)

2. Determine the amount

(10)(5) = $50

Hope this helps

Answer:

$16.99

Step-by-step explanation:

what i did first was add the .25 and .75 together to get a whole dolor and then add it to the 9 to make 10 then add the 5 to get 15 and from there i would add the 1.99 to get 16.99

In general, football athletes are weightier in comparison to their baseball counterparts.

This is predominantly due to the fact that football necessitates greater physical power and bulk for defensive maneuvers such as tackling and blocking. Contrarily, baseball places greater emphasis on quickness, dexterity, and the ability to coordinate hand movements with visual perception.

If your friend's weight is 180 pounds, it is probable that their weight falls within the expected range for a baseball player's weight. The weights of baseball players may differ, as some players with a lighter build concentrate on agility while others who are heavier excel at strength-based hits.

A football player weighing 180 pounds would probably be considered comparatively lightweight in football, especially when compared to players in the offensive and defensive lines.

The most suitable sport for your friend would ultimately rely on their specific interests, abilities, and physical characteristics.

Opting for baseball could be a wiser decision if their focus pertains to a sport that highlights nimbleness, swift movement, and adeptness in coordinating hands and eyes. If their preference is for a sport that involves physical contact and demands strength and mass, football may be a more suitable option.

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An appropriate ending to the alternative hypothesis is less than 8 hours. The alternative hypothesis would be: The average amount of sleep students at their school get per night is less than 8 hours.

The alternative hypothesis is a statement used in statistical inference experiment which is contradictory to the null hypothesis and denoted by Ha or H1. In hypothesis testing, an alternative hypothesis is a statement that a researcher is testing.

The alternative hypothesis could take one of three forms, depending on the context of the test:

Which alternative hypothesis we use (< or > or ≠) is sometimes called the direction of the test. Which direction we choose depends on the context of the test.

In this case, it is suspected that students at the school are getting less than 8 hours of sleep on average, so that is the alternative hypothesis.

Ha: The average amount of sleep students at their school get per night is less than 8 hours.

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Answer:

1/6

Step-by-step explanation:

There is a 1/12 chance of rolling a 10 and a 1/12 chance of rolling a 8.

Add them together and you get 2/12 which is the same as 1/6