For each sample given in questions 2 - 4, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house. Sample: The days of the week the students in your math class ordered food during the past week. Sample: The daily high temperatures for the capital cities of all 50 U.S. states over the past year.

The length=12cm and width=8cm of the rectangle.

What is area of rectangle?

   The territory a rectangle occupies inside its four sides or limits is known as its area. A rectangle's sides determine its area. Basically, the area formula is equal to the rectangle's product of its length and width.

Here length = l ans width = w.

The length of rectangle is 4 cm less than twice its width.

=> l = 2w - 4

Then area of rectangle A= 96 sqaure centimeters.

=> A = l*w

=> 96 = (2w-4)w

=> 96= 2\(w^{2}\)-4w

=>  2\(w^{2}\)-4w = 96

=>  2\(w^{2}\)-4w-96=0

=> \(w^{2}\)-2w -48 =0

=> \(w^2\)-8w+6w-48=0

=> w(w-8)+6(w-8)=0

=> (w+6)(w-8)=0

=> w= -6,8

Then width w = 8 cm

Now l = 16-4 =12 cm.

Therefore the length = 12cm and width=8 cm.

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Answer:

the answer is b

Step-by-step explanation:

Answer:

→To combine the two functions, you have to multiply them together, like so:

h(x) · s(x)

→This can also be shown as:

\((103)(1.03)^x^-^1\)

The reason as to why you would multiply the two functions together, and not add, is because of the words accrues. Based on the information given, the interest amount of money, which is $103, accrues, which basically means that the money will increase in a pattern, over time. In addition, when a world problem involves a bank and money, multiplication is usually occurring.

The total amount of money Christina will have in her bank account as interest accrues after she deposits her $103 is g(x) = (103)(1.03)^(x-1).

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

Christina has $103 earned from babysitting saved at home, and the amount is modeled by the function,

\(h(x) = 103\)

She reads about a bank that has savings accounts that accrue interest according to the function,

\(s(x) = (1.03)^{(x-1)}\)

This function means that the interest amount is 3% in value per year in which x represent the number of years.

Now the total amount of money she will have in her bank account as interest accrues will be equal to the product principal and interest rate.

Let the amount of money she will have in her bank account as interest accrues is represented by function g(x). Thus,

\(g(x) = (103)(1.03)^{(x-1)}\)

Thus, the total amount of money Christina will have in her bank account as interest accrues after she deposits her $103 is.

\(g(x) = (103)(1.03)^{(x-1)}.\)

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Answer:

E.

the product of seven and the difference of b minus two

Step-by-step explanation:

Answer:179.5

Step-by-step explanation:

(C)

Given data:

The given inequalities.

The graph of the given inequalities is shown below.

b 35 is the answer sorry if I'm worng

The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

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Answer:

it's a

Step-by-step explanation:

we subtract 9 from the 30 in the other side. that makes 21

3x ≤ 21

x≤7

that means any answer possible is below 7.

srry if bad quality

Answer:

It’s c. -37 and -3

Step-by-step explanation:

Answer:

(x - 8)² + (y - 15)² = 9

Step-by-step explanation:

Assuming you want the equation.

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (8, 15 ) and r = 3 , then

(x - 8)² + (y - 15)² = 9

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer: 85.1

Step-by-step explanation:

Answer:

Bro perpendicular is when the lines are connected in the form you know

This line I and j are parallel to each other so the answer Is 2

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

equilateral:  E

scalene:  F

isosceles:  G

Step-by-step explanation:

equilateral = all sides are equal

scalene = no sides are equal

isosceles = two sides are equal

Given the equation,

Let us pick 5 points starting from x = 0 to x = 4

Having picked from point x = 0, let us solve for the corresponding y-values.

When x = 0,

So when x = 0, y = 0

When x = 1

So when x = 1, y = -1.375

When x = 2,

So when x = 2, y = -11

When x = 3

So when x = 3, y = -37.125

When x = 4

So when x = 4, y = -88.

Let us now plot the graph

Answer:

Step-by-step explanation:

Right cylinder

Solve for volume

V=πr2h

Answer:

Solution,

\(f(x) = - 4 {x}^{2} + 5x \\ f(6) = - 4 \times {6}^{2} + 5 \times 6 \\ \: \: \: \: \: \: = - 4 \times 36 + 30 \\ \: \: \: = - 144 + 30 \\ \: \: \: - 114\)

hope this helps.

Good luck on your assignment..

Answer:

-114

Step-by-step explanation:

To find f(6), you need to plug in the value in parentheses wherever there is an x in the equation.

f(x) = -4x + 5x

f(6) = -4(6) + 5(6)

f(6) = -4(36) + 30

f(6) = -144 + 30

f(6) = -114

The answer is -114.

Answer:

A group of five people are at a restaurant, the bill comes and is $50, the bill is split evenly amongst the five people, each person pays $10 which is the same as gaining -$10 which is the answer to the expression

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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The frictional force acting on the cylinder is F= (4.0N)i when a fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n.

Given that,

A fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n. The cylinder has a radius of 0.10 m, a mass of 10 kg, and rolls smoothly on the horizontal surface.

We have to find what is the cylinder being frictionally forced by.

We know that,

To ensure that the angular acceleration is positive, we make the unorthodox decision to treat the clockwise sense as positive (as is the linear acceleration of the center of mass, since we take rightward as positive). Applying the linear form of Newton's second law results in

(12 N)−f=Ma

Therefore, f=−4.0 N.

The friction force is discovered to point rightward with a magnitude of 4.0 N, or, in contrast to what we thought when formulating our force equation,

F= (4.0N)i

Therefore, The frictional force acting on the cylinder is F= (4.0N)i when a fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n.

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The height of the cone in discuss as required to be determined is; 16.38 cm.

Since the height of the cone is three times the length of the diameter of its base;

h = 3d;

d = h/3

Therefore, radius,

r = d/2

r = h/3 ÷ 2

multiply by the reciprocal of 2

r = h/3 × 1/2

r = h / 6.

Volume of a cone, V = (1/3) πr²h

128 = (1/3) × (22/7) × (h³/36)

h³ = 4398.55

h = 16.38 cm.

Ultimately, the height of the cone is; 16.38 cm.

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Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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The depth of the lake is 500 meters.

According to the question

Acceleration = 10 m/s²

Time = 10 sec

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

The distance covered in a certain time of accelerated motion:

D  =  (1/2) × A × T²

Distance covered= (1/2) (Acceleration) (Time squared) .

The question gives us the acceleration and the time.

Let's plug them into the formula.

Distance = (1/2) (10 m/s²) (10 sec)²

= (5 m/s²) (100 sec²)

= 500 meters.

The depth of the lake is 500 meters.

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Prostate cancer is a type of cancer that develops in the prostate gland.Symptoms of Prostate CancerProstate cancer is usually asymptomatic during the early stages.

The patient with localized prostate cancer will exhibit no specific symptoms. Hence, a Prostate cancer is a type of cancer that develops in the prostate gland, which is located beneath the bladder and is responsible for producing a fluid that nourishes and transports sperm.What is prostate cancer?The prostate is a gland in the male reproductive system located below the bladder and in front of the rectum. It surrounds the urethra, the tube that carries urine from the bladder, through the prostate, and out of the body. The prostate gland produces a milky fluid that forms part of the semen that transports sperm out of the body. Prostate cancer is a type of cancer that develops in the prostate gland.Symptoms of Prostate CancerProstate cancer is usually asymptomatic during the early stages. Later stages of prostate cancer can result in urinary problems and other symptoms. They are:Difficulty in urinatingWeak urine stream or flowDiscomfort in the pelvic region or when urinatingPain in the back, hip, or pelvisBlood in the urine or semenIn conclusion, localized prostate cancer may not exhibit any specific symptoms, which makes it important to get routine screenings for the condition.

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After 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.

What is eRDPML?

The Electronic Recreational Dive Planner Multi Level, or simply eRDPml, is a novel programme created by PADI to help you correctly plan your dives. FOR MANY. An electronic version of the PADI dive tables may be more convenient for certain divers than having to recall how to use them.

If a diver exits the water at 1:30 pm after a 35-minute dive to 19 metres utilising the eRDPML, he will be in pressure group P.

At 2:20 PM, he returns to the ocean. His surface interval is 50 minutes, according to this. A diver in pressure group P switches to pressure group G after 50 minutes.

He will then be in pressure group S if he stays at 17 metres for another 25 minutes. Go to the Surface Interval Mode to find out how long must be spent above the surface before the third dive.

After the second dive, join the pressure group S and start the third dive at a depth of -15 metres for 38 minutes.

33 minutes are determined to be the necessary surface interval. A 33 minute surface interval after the second dive places the diver in pressure group K before the third dive, completing the dive profile.

Hence, after 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.

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