The average monthly temperature T(m), in degrees Celsius, of a particular city varies according to the model T of m equals 10 times cosine of the quantity pi over 6 times m end quantity plus 5 comma where m represents the months of the year and January begins at m = 0. Between what months will the temperature be below 0°C?

April and August
April and September
May and August
May and September

There is only 1 real zero of the function.

What are Zeros of a Function?

The zeros of a function are the values of the function's variables that fulfil the equation and yield the function's value of 0. The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.

Solution:

As mentioned above,

The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.

So,

We can see that there is only one point where the graph intersects the x-axis.

Therefore, it can be said that there is only 1 real zero of the function.

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Answer:

-2

Step-by-step explanation:

Answer:

y = -2

Step-by-step explanation:

y = 14 - 2(8)

y = 14 - 16

y = -2

The complementary function for the differential equation is ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\). The particular solution for the differential equation is \(Yp(x) = -7e^(^6^x^)\). The general solution for the differential equation is y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) -\(7e^(^6^x^)\).

To find the complementary function for the given differential equation, we assume a solution of the form \(ye(x) = e^(^r^x^)\), where r is a constant to be determined. Plugging this into the differential equation, we get:

\(r^2e^(^r^x^) + 6e^(^r^x^) = 0\)

Factoring out \(e^(^r^x^)\), we obtain:

\(e^(^r^x^)(r^2 + 6) = 0\)

For a nontrivial solution, the term in the parentheses must equal zero:

\(r^2 + 6 = 0\)

Solving this quadratic equation gives us r = ±√(-6) = ±i√6. Hence, the complementary function is of the form:

ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\)

Next, we need to find the particular solution Yp(x) for the differential equation. The particular solution is assumed to have a similar form to the forcing term \(-294x^2^e^(^6^x^).\)

Since this term is a polynomial multiplied by an exponential function, we assume a particular solution of the form:

\(Yp(x) = (A + Bx + Cx^2)e^(^6^x^)\)

Differentiating this expression twice and substituting it into the differential equation, we find:

12C + 12C + 6(A + Bx + Cx^2) = \(-294x^2^e^(^6^x^)\)

Simplifying and equating coefficients of like terms, we get:

12C = 0 (from the constant term)

12C + 6A = 0 (from the linear term)

6A + 6B = 0 (from the quadratic term)

Solving this system of equations, we find A = -7, B = 0, and C = 0. Therefore, the particular solution is:

\(Yp(x) = -7e^(^6^x^)\)

Finally, the general solution for the differential equation is given by the sum of the complementary function and the particular solution:

y(x) = ye(x) + Yp(x)

y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) - \(7e^(^6^x^)\)

This is the general solution to the given differential equation.

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The area of a rectangular carpet that measures 2 1/2 ft by 4 ft is 10 square feet.

Given,Length of rectangular carpet = 2 1/2 ftWidth of rectangular carpet = 4 ftThe area of a rectangle can be given as;Area of rectangle = length × breadthSubstitute the given values in the formula we get;Area of rectangle = 2 1/2 × 4 ftArea of rectangle = 10 sq.ft.Hence, the required area of a rectangular carpet is 10 square feet.

Area of rectangular carpet that measures 2 1/2 ft by 4 ft can be calculated as;We have given,Length of rectangular carpet = 2 1/2 ft Width of rectangular carpet = 4 ft The area of a rectangle can be given as;Area of rectangle = length × breadth Substitute the given values in the formula we get;Area of rectangle = 2 1/2 × 4 ft Area of rectangle = 10 sq.ft.Hence, the required area of a rectangular carpet is 10 square feet.

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Therefore, the distance between points P and Q to the nearest tenth is about 10.6 units.

The Pythagorean Theorem is a mathematical formula that describes the relationship between the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical notation, the theorem can be expressed as: c² = a² + b² where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. The Pythagorean Theorem has many practical applications in fields such as architecture, engineering, physics, and trigonometry. It can be used to solve a wide range of problems involving right triangles, such as finding the distance between two points in a coordinate plane, calculating the height or length of an object, or determining the angle of elevation or depression.

Here,

To find the distance between points P(3, 2) and Q(10, 10), we can use the distance formula or the Pythagorean theorem. Since the prompt asks us to use the Pythagorean theorem, we can create a right triangle with points P and Q as two of its vertices and find the length of the hypotenuse using the theorem.

First, we need to find the lengths of the legs of the right triangle. The horizontal leg is the difference between the x-coordinates of the two points:

leg₁ = 10 - 3 = 7

The vertical leg is the difference between the y-coordinates of the two points:

leg₂ = 10 - 2 = 8

Now, we can use the Pythagorean theorem to find the length of the hypotenuse (c), which is the distance between points P and Q:

c² = leg₁² + leg₂²

c² = 7² + 8²

c² = 49 + 64

c² = 113

c ≈ √113 ≈ 10.6 (rounded to the nearest tenth)

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Answer:

Step-by-step explanation:

Step 1: The general equation of straight line is

     y = mx + c

c = initial value

m = rate of change

Step 2: Initial value c = 20

Step 3: Rate of change

m = \(\frac{y2 - y1}{x2 - x1}\)

Step 4: From the graph, pick two points

x1 = 0, y1 = 20

x2 = 4, y2 = 2

Step 5: By substitution, rate of change m = \(\frac{21-20}{4-0}\)

m = \(\frac{1}{4}\)

Step 6: Equation of the graph

y = mx + c

y = \(\frac{1}{4}x\) + 20

we must evaluate the domain points in the function

x=0

x=1

x=2

x=3

x=4

x=5

x=6

x=7

the points are

now, locate each point on the graph and join with a line

Answer:

D. (z) = (x − 3)¹ – 2​

Step-by-step explanation:

To determine which transformation of the parent square root function will result in the given domain and range, we need to consider the effects of the transformations on the function.

The parent square root function is given by f(x) = √x.

Let's analyze each option and see if it satisfies the given conditions:

A. j(x) = (x + 2)³ + 3

This transformation involves shifting the graph 2 units to the left and 3 units up. However, this does not change the domain of the function, so it does not satisfy the given domain condition.

B. k(x) = (z + 3) – 2

This transformation involves shifting the graph 3 units to the left and 2 units down. Again, this does not change the domain of the function, so it does not satisfy the given domain condition.

C. g(x) = (x − 2)³ + 3

This transformation involves shifting the graph 2 units to the right and 3 units up. However, this does not change the range of the function, so it does not satisfy the given range condition.

D. z(x) = (x − 3)¹ – 2

This transformation involves shifting the graph 3 units to the right and 2 units down. This shift does not affect the domain of the function, but it affects the range. The function z(x) = (x − 3)¹ – 2 starts at y = -2 when x = 3, and it increases as x goes to infinity. Therefore, it satisfies both the given domain and range conditions.

Based on the analysis, the correct transformation that satisfies the given domain and range is option D:

z(x) = (x − 3)¹ – 2

chatgpt

Answer:

122.46 inches ³

Step-by-step explanation:

Volume of a cone = πr²h/3

Pi, π = 3.14

Radius, r = diameter / 2 = 6 inches / 2

= 3 inches

Height, h = 13 inches

Volume of a cone = πr²h/3

= {3.14 * (3 inches)² * 13 inches} / 3

= (3.14 * 9 inches ² * 13 inches) / 3

= 367.38 inches ³ / 3

= 122.46 inches ³

Volume of a cone = 122.46 inches ³

Answer:

20

Step-by-step explanation:

substitute 5 for 'x':

6(5) - 2(5) = 30-10 = 20

The area under the standard normal curve to the left of z = 1.72 is 0.0427. To find the area to the right of z = 1.72, we can subtract the area to the left from 1.

Subtracting 0.0427 from 1 gives us an area of 0.9573. Therefore, the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573.In the standard normal distribution, the total area under the curve is equal to 1. Since the area to the left of z = 1.72 is given as 0.0427, we can find the area to the right by subtracting this value from 1. This is because the total area under the curve is equal to 1, and the sum of the areas to the left and right of any given z-value is always equal to 1.

By subtracting 0.0427 from 1, we find that the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573. This represents the proportion of values that fall to the right of z = 1.72 in a standard normal distribution.

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Answer:

w=10

Step-by-step explanation:

Let original width of pen be w feet.

New width of pen = (w+2) feet

(w+2)×9=108

     w+2=108÷9

            =12

         w=12-2

            =10

Answer:

9(w + 2) = 108

Step-by-step explanation:

A = l * w = 9w

A' = l * w' = 9w' = 9(w + 2) = 108

The original width, w, of the pen was 10 feet. Thus, the original area was 9 * 10 = 90 feet.

The final width was 10 + 2 = 12 feet

12 * 9 = 108

Prove for all real numbers x and y, if

\(x − ⎣x⎦ ≥ y − ⎣y⎦ then ⎣x − y⎦ = ⎣x⎦ − ⎣y⎦.\)

Given :

\(x − ⎣x⎦ ≥ y − ⎣y⎦\)

To Prove :

⎣x − y⎦ = ⎣x⎦ − ⎣y⎦.

Proof :

Let\(A = ⎣x⎦, B = ⎣y⎦, C = ⎣x − y⎦.\)

Since A ≤ x < A + 1,

we have

A − B ≤ x − y < A + 1 − B

This implies that C = ⎣x − y⎦ lies between A − B and A + 1 − B;

that is, A − B ≤ C ≤ A + 1 − B.

But the only integers that lie between A and A + 1 are A itself and A + 1.

Therefore, either

C = A or C = A − 1 or, equivalently,

\(⎣x − y⎦ = ⎣x⎦ or ⎣x − y⎦ = ⎣x⎦ − 1,\)

but in the second case, we have

⎣x⎦ − ⎣y⎦ > x − y, which contradicts the assumption that

\(x − ⎣x⎦ ≥ y − ⎣y⎦.\)

Hence,\(⎣x − y⎦ = ⎣x⎦ − ⎣y⎦\)

for all real numbers x and y, if

\(x − ⎣x⎦ ≥ y − ⎣y⎦.\)

Therefore, the given statement is proved.

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Answer: 12

Step-by-step explanation:

Answer:

1407.4 cm³ to nearest tenth

Step-by-step explanation:

volume of cyclinder =  π r² h , where r is radius and h is the height.

volume = π (8)²  (7)

= 7 (64) π

= 448π

= 1407.4 cm³ to nearest tenth

(a) To find the product of 1/2x-1/4 and 5x^2-2x+6, we can use the distributive property of multiplication:

(1/2x - 1/4)(5x^2 - 2x + 6)

= (1/2x)(5x^2) + (1/2x)(-2x) + (1/2x)(6) - (1/4)(5x^2) + (1/4)(2x) - (1/4)(6)

= (5/2)x^2 - x + 3 - (5/4)x + (1/2)x - (3/2)

= (5/2)x^2 - (3/4)x + 3/2

Therefore, the product of 1/2x-1/4 and 5x^2-2x+6 is (5/2)x^2 - (3/4)x + 3/2.

(b) No, the product of 1/2x-1/4 and 5x^2-2x+6 is not equal to the product of 1/4x-1/2 and 5x^2-2x+6. This is because when we expand both products using the distributive property, we get different expressions:

(1/2x - 1/4)(5x^2 - 2x + 6) = (5/2)x^2 - (3/4)x + 3/2

(1/4x - 1/2)(5x^2 - 2x + 6) = (5/4)x^2 - (7/4)x + 3

So the coefficients of the x^2 and x terms in the two products are different. Therefore, the two products are not equal.

The relation that has the  domain {-3, 4} and the range {0, 1} is B:

{( −3, 1), (4, 0)}

Remember that for any relation, the domain is the set of the inputs and the range is the set of the outputs, and the general notation for a point is (input, output).

Then if the domain is {-3, 4} and the range is {0, 1} the only of the given relations that can be described by these is:

B. {( −3, 1), (4, 0)}

So that is the correct option.

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The given relation can be written as:

y = $5*x + $20

Notice that we have a constant term, thus it is not a proportional relation.

A general proportional relationship can be written as:

y = k*x

Where k is a constant of proportionality.

The given case is:

" A bike rental store charges $20 as a flat fee, plus $5 per hour."

We know that there is a flat fee of $20 plus $5 per hour, so we can write the equation:

y = $5*x + $20

Notice that we have a constant term, thus, it is not a proportional relation.

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Answer:

Jun Wei is incorrect.

Step-by-step explanation:

In this case, Jun Wei is incorrect.

When rounding a number to two decimal places, the general rule is to look at the digit immediately to the right of the desired decimal place. If that digit is 5 or greater, we round up, but if it is less than 5, we round down.

In the given number, 8.395, the third decimal place is 5.

This means we need to round up to 8.40 rather than round down to 8.39.

The notation 8.40 is equivalent to 8.4, as the trailing zero after the decimal point does not change the value of the number.  However, as the number should be rounded to 2 decimal places, the correct notation is 8.40, as 8.4 is rounded to one decimal place.

Answer:

Yes, I agree with Jun Wei's statement that 8.395 is equal to 8.4 when rounded off to 2 decimal places.

Step-by-step explanation:

When rounding off to 2 decimal places, we look at the third decimal place. If it is 5 or greater, we round up the second decimal place by 1. If it is less than 5, we leave the second decimal place as it is.

In this case, the third decimal place of 8.395 is 5, so we round up the second decimal place, which is 9, by 1. Therefore, 8.395 rounds off to 8.4.

Furthermore, Jun Wei's assumption that 8.40 is the same as 8.4 is correct. The trailing zero in 8.40 signifies that it has been rounded off to 2 decimal places. Therefore, 8.40 and 8.4 are equivalent.

Hope it helps!

The appropriate measure of association for two nominal-level variables is lambda.

What do you mean by nominal-level variables?

Nominal variables lack any intrinsic ranking because they are measured at the nominal level. Gender, race, religious affiliation, and college major are a few examples of nominal variables that are frequently evaluated in social science investigations.

According to the options in the given question,

The appropriate measure of association for two nominal-level variables is:

We have the options in the given question,

a.omega.

b.gamma.

c.pre.

d.lambda.

e.alpha.

The option d. lambda is the correct answer to the question.

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The value of the line integral is approximately 34.3333.

To evaluate the line integral, we need to parametrize the line segment C from (1,0,-1) to (3,4,2) with a vector function r(t) = <x(t), y(t), z(t)> for t in [0,1].

We can do this by defining:

for t in [0,1].

Note that when t = 0, r(0) = (1,0,-1), and when t = 1, r(1) = (3,4,2), as desired.

Next, we need to compute the line integral:

∫c x y dx + y²dy + yz dz

Using the parametrization r(t), we have:

and

Substituting these expressions and simplifying, we get:

Therefore, the value of the line integral is approximately 34.3333.

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Answer:

Hello there are only 2 real solutions where x_1 = 11, x_2 = 7, x_3 = 3 and x_1 = 4, x_2 = 7, x_3 = 10

Step-by-step explanation:

Lets begin with arithmetic progression we know that we need some d which we will add to our x_1 to get x_2, so let's write it : x + (x+d) +(x+2d) = 21 and x*(x+d)*(x+2d) = 231 and that should be it.

Answer: The answer is -30 - 45 k

Step-by-step explanation:

Answer:

Appearantly, you forgot to mention the question

Two of them have the same remaining. The proof using the pigeonhole principle is now complete.

When an integer is divided by 4, there are four potential remainders: 0, 1, 2, or 3. Take any set of five numbers as an example.

If at least three of them have the same remainder when divided by 4, then we are done, since two of them will have the same remainder. This is because if three integers have the same remainder, then we can subtract that remainder from all of them, and the resulting three integers will all be divisible by 4, which means that two of them will have the same remainder when divided by 4.

So suppose that at most two of the integers have the same remainder when divided by 4. Then there are at most two integers with remainder 0, at most two integers with remainder 1, at most two integers with remainder 2, and at most two integers with remainder 3. This means that there are at most 8 integers in total, which is a contradiction since we started with 5 integers. Therefore, there must be at least three integers with the same remainder when divided by 4, and hence there are two with the same remainder. This completes the proof by the pigeonhole principle.

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The correct statement is:

1000n log(n³) ∈ (n(log(n))³) x³ + 5x² = (x³)

The symbol "∈" represents "belongs to" or "is an element of." It indicates that the expression on the left-hand side is an element of the set represented by the expression on the right-hand side.

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Answer:

Step-by-step explanation:

amama

Answer:

It will take 0.989 second to attain this speed

Step-by-step explanation:

In this question, we want to calculate the time it will take for the wheel of the machine to attain the given rotational speed

We proceed as follows;

From the question, we can identify the following parameters

Rotational acceleration of the wheel is, α = 180 rad/s^2

Initial spinning rotational speed of the wheel is, ω= 0 rpm

1 rpm = (1/60) revolution per second = 2π * (1/60) rad/s

Thus,

initial rotational speed ωi = 0 rad/s

Final spinning rotational speed ωf of the wheel is, = 1700 rpm =178.02 rad/s

Now, from the equations of motion (for rotational motions),

ωf = ωi + αt

where t is the time taken by the wheel to attain its final rotational speed.

178.02= 0 + 180 * t

t = 178.02/180

t = 0.989 second