Find the next four terms of the arithmetic sequence 16,24,32

Answer: lb=48

l(l-8)=48

l^2–8l=48

l^2–8l-48=0

l^2–12l+4l-48=0

l(l-12)+4(l-12)=0

l=12inches &

b=12–8=4inches

Step-by-step explanation:

If you fix a point on the curve in the given interval, and revolve that point about the \(x\)-axis, it will trace out a circle with radius given by the function value \(y\) for that point \(x\). The perimeter of this circle is then \(2\pi(8\sqrt x) = 16\pi \sqrt x\).

The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].

So, the surface area is given by the definite integral

\(\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}\)

A function which could be the function graphed above "On a coordinate plane, a curve starts in quadrant 2 and crosses the y-axis and goes into quadrant 1. The curve opens down and to the right" is: D. f(x) = √(x + 4).

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

This ultimately implies that, there are four (4) major types of quadrants in any graph and these include the following:

In this scenario, we would use an online graphing calculator to plot all of the given functions in order to determine the function that was graphed, which we can logically deduce that it is function f(x) = √(x + 4).

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Complete Question:

Which could be the function graphed below?

On a coordinate plane, a curve starts in quadrant 2 and crosses the y-axis and goes into quadrant 1. The curve opens down and to the right.

f(x) = √(x - 5) + 1

f(x) = √(x - 2)

f(x) = √x

f(x) = √(x + 4)

If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training

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.

Velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

According to the quantity equation (MV = PQ), changes in the money supply (M) will lead directly to changes in the price level (P) if velocity (V) and real GDP (Q) remain constant. However, velocity is not necessarily constant over time and can be influenced by various factors.

Velocity represents the rate at which money circulates in the economy, indicating how quickly money is used to facilitate transactions. It is influenced by factors such as changes in consumer and business behavior, technological advancements, financial innovation, and shifts in confidence and trust in the economy.

Changes in velocity can occur due to several reasons. For example:

Changes in Transaction Patterns: Shifts in consumer preferences or business practices can alter the frequency and speed of transactions, affecting how money circulates and influencing velocity.

Financial Innovation: Advancements in payment systems, such as the rise of electronic transactions, online banking, or mobile payments, can potentially impact the velocity of money by facilitating faster and more efficient transactions.

Confidence and Economic Stability: Changes in economic conditions, inflation expectations, or financial stability can influence people's willingness to hold money, affecting velocity.

Monetary and Fiscal Policies: Changes in monetary policy, such as interest rate adjustments or changes in the money supply, can indirectly affect velocity by influencing borrowing and spending behavior.

While changes in velocity can occur independently of changes in the money supply, they can also be related. For instance, if the money supply increases without a corresponding increase in the demand for money (velocity decreases), it can put upward pressure on prices. On the other hand, if velocity increases due to changes in transaction patterns or increased economic activity, it can offset the impact of changes in the money supply on prices.

Overall, velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

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This is not the correct answer.

1. 2.30 is not even close to the point given in the number line.

2. My guess for the correct answer would be 0.23 because in between 0.2 and 0.3 is 0.25, so the best answer would be 0.23.

The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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The total worth of shares that he has is 24000$

To calculate earnings per share, take a company's net income and deduct preferred dividends from it. Divide the total by the average number of outstanding common shares.

Given Sergio purchased 2000 shares at four dollars each

the cost price of shares is 4$ each

Therefore total shares worth he has  = 2000 * 4

                                                             = 8000 $

He now expects the stock to triple in value by the end of next year.

total amount of shares he owns = 8000 * 3

                                                      = 24000$

Therefore, the total amount of shares he owns is 24000$

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We can find the coordinates of the point that partitions a line segment into a ratio of 1 to 5 by using the formula:

(x, y) = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and r is the ratio of the distance from the starting point to the point of interest, to the total distance of the line segment. In this case, r = 1/(1 + 5) = 1/6.

We know the coordinates of the two endpoints of the line segment:

(x1, y1) = (-10, 9)

(x2, y2) = (-4, 3)

So, we can substitute these values into the formula and find the coordinates of the point that partitions the line segment into a ratio of 1 to 5:

(x, y) = (-10 + (1/6) * ((-4) - (-10)), 9 + (1/6) * (3 - 9))

= (-10 + (1/6) * (-6), 9 + (1/6) * (-6))

= (-10 -1/6, 9 -1)

= (-10/6 -1/6, 3/2 -1)

= (-16/6, 3/2 -1)

= (-8/3,-1/2)

So, the coordinates of the point on the directed line segment from (-10, 9) to (-4, 3) that partitions the segment into a ratio of 1 to 5 is (-8/3,-1/2)

It is important to notice that this point is a vector and not a point in the Cartesian plane

Answer:

28.05$

Step-by-step explanation:

The game got a discount of 15%.
New price is   (30$) ( 0.85 )  =  25.5$   (since the discount is 15% you only pay for the 85% of the original price)

Then an increase of 10%. this is:
New price:   25.5$ (1.10) = 28.05

New price is 28$ with 5 cents

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

The equation for temperature 67, gives the time as 4.8 hours.

What is amplitude?

A sound is a type of energy that is created when objects vibrate. For it to spread, a medium is needed. As a result, sound cannot travel in a vacuum because there is nothing for the sound waves to travel through. The object's back-and-forth movement creates the sound. Sound vibration is the name for this. Additionally called oscillatory motion. Oscillation describes the regular rhythmic back-and-forth movement.

We know that the general equation of a sine wave is:

\($$y(t)=A \{Sin}(W(t-C))+D$$\)

where,

A- Amplitude

D = Average of Max(y) and Min(y);

\(W=\frac{2 \pi}{\text { Period }}\)

C - Phase shift on y(axis)

Part a)

Given Max T= 94 and Min T = 66

Hence,

D = (Max+Min)/2 = 80

A = Max - D = 94-80= 14

Since period is 24 hours, so W = 2\pi/24 = \pi/12

Thus the function till now is:

\(T(t)=14Sin(\frac{\pi}{12}(t-C))+80\)

Given low temperature occurs at 3 AM so,

T(3)=66

Solving this we get C = 9

Hence,

\(T(t)=14Sin(\frac{\pi}{12}(t-9))+80\)

Part b)

Given Max T= 58 and Average = 45

Hence,

D = 45

A = Max - D = 58-45= 13

Since the period is 24 hours, so W = \(2\pi/24 = \pi/12\)

Thus the function till now is:

\(T(t)=13Sin(\frac{\pi}{12}(t-C))+45\)

Given high temperature occurs at 5 PM so,

T(17)=58

Solving this we get C = 11

Hence,

\(T(t)=13Sin(\frac{\pi}{12}(t-11))+45\)

The temperature at 4 AM is:

\(T(4)=13Sin(\frac{\pi}{12}(4-11))+45 = 32.44\)

Part c)

Given Max T= 86 and Min T = 64

Hence,

D = (Max+Min)/2 = 75

A = Max - D = 86-75= 11

Since period is 24 hours, so W = 2\pi/24 = \pi/12

Thus the function till now is:

\(T(t)=11Sin(\frac{\pi}{12}(t-C))+75\)

Given average temperature occurs at 8 AM so,

T(8)=75

Solving this we get C = 8

Hence,

\(T(t)=11Sin(\frac{\pi}{12}(t-8))+75\)

Now,

We need to find t such that T(t) = 67.

\(67=11Sin(\frac{\pi}{12}(t-8))+75\)

\(\Rightarrow t=4.88945 \approx 4.89 hours\)

Hence, The equation for temperature 67, gives the time as 4.8 hours.

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The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

44

Step-by-step explanation:

180-96=84

180-128=52

52+84=136

180-136=44

Answer:

D

Francisco spent 3 hours, 10 minutes playing his violin

Explanation:

Given that:

Francisco practised playing his violin for

2 hours on Sunday

5/6 hours on Monday

The total number of time he spends playing his violin is obtained by adding the number of hours he spends each day.

This is 3 hours, 10 minutes.

The measure of angle D is 45°

Similar triangles have the same corresponding angle measures and proportional side lengths. When two triangles are similar, the corresponding angles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

To know the corresponding angles

side AC is corresponding to side EF, therefore angle D is congruent to angle A

angle D = 45°

OR , we can use the sum of angles In a triangle , which is 180°

angle D = 180 -( 72+63)

= 180 - 135

= 45°

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9514 1404 393

Answer:

  A = 108.78°

  a = 11 mi

  b = 7 mi

Step-by-step explanation:

The sum of angles in a triangle is 180°, so the third angle is ...

  A = 180° -38.71° -32.51°

  A = 108.78°

__

The remaining sides can be found from the law of sines.

  a/sin(A) = c/sin(C)

  a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896

  a ≈ 11 mi

  b = sin(B)·11.163896 ≈ 0.625379 × 11.163896

  b ≈ 7 mi

Answer:

see explanation

Step-by-step explanation:

look photo

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

The given pair of angles form linear pair, therefore their sum is equal to 180°

that is :

\(\qquad \sf  \dashrightarrow \:2(x - 26) + 3x + 2 = 180\)

\(\qquad \sf  \dashrightarrow \:2x - 52 + 3x + 2 = 180\)

\(\qquad \sf  \dashrightarrow \:5x - 50 = 180\)

\(\qquad \sf  \dashrightarrow \:5x = 230\)

\(\qquad \sf  \dashrightarrow \:x = 46 \degree\)

Have a great day ~

Answer:

C. AC~= DF, FB~=CB

Step-by-step explanation:

In order use HL theorem you have to have two right triangles, which it's marked that you do. HL stands for Hypotenuse-Leg. So in order to use Hypotenuse-Leg you have to know that the hypotenuses are congruent on the two triangles and also a leg is the same on the two triangles. AC and DF are the two hypotenuse. And FB and CB are legs. You need those two congruent segment pairs in order to use HL theorem.

Answer:

=$21075

Step-by-step explanation:

Given data

Earnings =$415 per hour

Commission =5%

Sales =$89500

Time =40 hours

Let us find the commission

5/100*89500

0.05*89500

=4475

Let us find the amount earned in 40 hours

40*415

=16600

Total

=16600+4475

=21075

Answer:

x + 93 = 124

Step-by-step explanation:

4x = x + 93  {Vertically opposite angles are equal}

Subtract 'x' from both sides

4x - x = 93

3x = 93

Divide both sides by 3

x = 93/3

x = 31

x + 93 = 31+ 93 = 124

Answer:

kl is a volume with sides that are equal

If the point K  is over -9 and L is over 15 then the value of KL is 24.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

A number line is a horizontal line that has equally spread number increments.

On the number line K is over -9 and L is over 15

We need to find the distance of KL.

KL=OL-OK

Where the OL is 15 and OK is -9.

Now plug in these values in KL

KL=15-(-9)

When minus and minus are multiplied we get positive.

=15+9

Add fifteen and nine we get twenty four.

=24

Hence, if the point K  is over -9 and L is over 15 then the value of KL is 24.

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The points that lie on the same plane is coplanar points.

A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalisation of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.

For points to be parallel then the points must arrange in the form that the distance between the points should be same apart, vertically.

So, the points are not parallel.

If any geometric shape, such as a line or point, lies on the same plane, that shape is said to be coplanar. They are referred to as non-coplanar if not.

Thus, the given points are coplanar

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A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!

Answer:

1 and 3, 2 and 4, 1 and 2, 3 and 4

5 and 7, 6 and 8, 5 and 6, 7 and 8

Step-by-step explanation:

The course of the airplane relative to true north is 094°, and the ground speed is 344.2 km/h.

The horizontal and vertical component of the airspeed is calculated as follows;

Vx = 300 cos(30) = 259.8 km/h

Vy = 300 x sin(30) = 150 km/h

The horizontal and vertical component of the wind velocity is calculated as follows;

Vx = 50 cos(60) = 25 km/h

Vy = 50 sin(60) = 43.3 km/h

To find the resultant velocity, we can add the x and y components separately:

Vx = 259.8 km/h  +  25 km/h = 284.8 km/h

Vy = 150 km/h  +  43.3 km/h  = 193.3 km/h

The magnitude of the resultant velocity is calculated as;

V = √(284.8² + 193.3²)

V = 344.2 km/h

The direction of the resultant velocity is calculated as;

θ = arc tan (193.3/284.8)

θ = 34.2⁰

The resultant direction to true north is calculated as;

track = 34.2 + 60 = 94.2°

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Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.

To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.

Let's denote the length of the actual tank as "x".

According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.

So, we can set up the following proportion:

1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)

Cross-multiplying and solving for x, we get:

x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm

The actual tank is 1620 cm long.

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Answer:

Area of sector bounded by angle = 100.37 ft² (Approx.)

Step-by-step explanation:

Given:

Radius of a circle = 12 feet

Arc angle θ = 80°

Find:

Area of sector bounded by angle

Computation:

Area of sector bounded by angle = [θ/360][πr²]

Area of sector bounded by angle = [80/360][(3.14)(12)²]

Area of sector bounded by angle =[0.22][(3.14)(144)]

Area of sector bounded by angle = [0.22][452.16]

Area of sector bounded by angle = 100.37 ft² (Approx.)