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Answer:

rational : square root of 81, 7/16, square root of 36

irrational : pi, square root of 48, square root of 120

Step-by-step explanation:

Step-by-step explanation:

All the explanation in the photo

The given numbers are arranged in the appropriate column according to the divisibility rules as below:

Divisibility by 3:

1128, 5004, 2235, 4002, 7134, 5661, 9120, 2088, 9999

Divisibility by 6:

1128, 5004, 4002, 7134, 9120, 2088

Divisibility by 9:

5004, 5661, 2088, 9999

The divisibility rule for the numbers 3, 6, and 9 are:

For 3 - If the sum of the digits of the given number is divisible by 3, then the number is divisible by 3.

For 6 - If the number is divisible by both 2 and 3, then the number is divisible by 6.

For 2 - If the last digit of the number is 0, 2, 4, 6, or 8 then the number is divisible by 2.

For 9 - If the sum of the digits of the number is divisible by 9 then the number is divisible by 9.

The given numbers are:

1128, 5228, 1124, 2101, 5004, 1750, 2235, 6625, 4002, 3122, 7134, 5661, 4445, 9120, 7886, 2088, 9457, 9999

Divisible by 2:

If the last digit of the number is 0, 2, 4, 6, or 8 then the number is divisible by 2.

So, such numbers in the given list are:

1128, 5288, 1124, 5004, 1750, 40002, 3122, 7134, 9120, 7886, 2088

Divisible by 3:

If the sum of the digits of the given number is divisible by 3, then the number is divisible by 3.

So,

1128 - 1 + 1 + 2 + 8 = 12; Divisible by 3

5228 - 5 + 2 + 2 + 8 = 17

1124 - 1 + 1 + 2 + 4 = 8

2101 - 2 + 1 + 0 + 1 = 4

5004 - 5 + 0 + 0 + 4 = 9; Divisible by 3

1750 - 1 + 7 + 5 + 0 = 13

2235 - 2 + 2 + 3 + 5 = 12; Divisible by 3

6625 - 6 + 6 + 2 + 5 = 19

4002 - 4 + 0 + 0 + 2 = 6; Divisible by 3

3122 - 3 + 1 + 2 + 2 = 8

7134 - 7 + 1 + 3 + 4 = 15; Divisible by 3

5661 - 5 + 6 + 6 + 1 = 18; Divisible by 3

4445 - 4 + 4 + 4 + 5 = 17

9120 - 9 + 1 + 2 + 0 = 12; Divisible by 3

7886 - 7 + 8 + 8 + 6 = 29

2088 - 2 + 0 + 8 + 8 = 18; Divisible by 3

9457 - 9 + 4 + 5 + 7 = 25

9999 - 9 + 9 + 9 + 9 = 36; Divisible by 3

Thus, the numbers divisible by 3 are:

1128, 5004, 2235, 4002, 7134, 5661, 9120, 2088, 9999

Divisible by 6:

If the number is divisible by both 2 and 3, then the number is divisible by 6.

So, the numbers divisible by both 2 and 3 are:

1128, 5004, 4002, 7134, 9120, 2088

Divisible by 9:

If the sum of the digits of the number is divisible by 9 then the number is divisible by 9.

5004 - 5 + 0 + 0 + 4 = 9;

5661 - 5 + 6 + 6 + 1 = 18;

2088 - 2 + 0 + 8 + 8 = 18;

9999 - 9 + 9 + 9 + 9 = 36;

Only these numbers are divisible by 9. They are:

5004, 5661, 2088, 9999

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Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer:

145

Step-by-step explanation:

angles in a pentagon add up to equal 540

Hence, 110 + 90 + 80 + 115 + v = 540

( note that we just created an equation that we can use to solve for v )

We now solve for v using the equation created

110 + 90 + 80 + 115 + v = 540

step 1 combine like terms

110 + 90 + 80 + 115 = 395

we now have 395 + v = 540

step 2 subtract 395 from each side

540 - 395 = 145

395 - 395 cancels out

we're left with v = 145

The measurements are;

a. 4 inches = No

b. 15 inches = Yes

c. 23 inches = Yes

d. 5 inches =  Yes

e. 25 inches = Yes

f. 10 inches = Yes

Jose in this problem draws a triangle, ABC.

We know the length of two sides of the triangle:

AB = 10 inches

BC = 15 inches

The length of the third side in a generic triangle can be calculated using the cosine theorem:  

\(\alpha = \sqrt{b^2 + c^2 - 2bc cos \alpha }\)

where;

Looking at the formula, we observe that:

- The maximum value for  is obtained for α = 180 degrees, so that cos α = -1 .

In this case, the length of the missing side  (AC, in this case) is

\(AC = \sqrt{10^2 + 15^2 - 2*10*15 *-1 }\)

AC = 25 inches

- The minimum value for α is obtained for 180 degrees , for which cos α= 1;

\(AC = \sqrt{10^2 + 15^2 - 2*15*10*1}\)

AC = 5 inches

Hence, the length must be between 5 and 25 inches.

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The complete question:

Jose draws ABC. AB has a length of 10 inches and BC has a length of 15 inches.

Determine whether each measurement could be the length of AC.

Choose Yes or No for each measurement.

a. 4 inches Yes : No

b. 15 inches Yes : No

c. 23 inches Yes : No

d. 5 inches Yes : No

e. 25 inches Yes : No

f. 10 inches Yes : No

Answer:

$79.98-$75.02=$04.96

Answer:

$04.96 is right answer am I right or wrong hope I am right

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box.

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box. In general, more metal is required for larger, thicker boxes. One must first calculate the box's volume in order to determine how much metal is required. The box's length, width, and height can be multiplied together to get this. The thickness of the metal must next be determined. The total amount of metal required can be estimated by multiplying the volume of the box by the thickness of the metal once the volume and thickness of the metal have been established. For instance, consider a box with dimensions of 6 inches long, 6 inches wide, and 6 inches high and a metal thickness.

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90 mm Hg is Zigg's mean arterial pressure.

Here's the formula for calculating MAP: MAP = (CO x SVR) + CVPR

where:

CO stands for cardiac output (measured in liters per minute).

SVR stands for systemic vascular resistance (measured in mm Hg/L/min).

CVPR stands for central venous pressure (measured in mm Hg).

Now, let's get started with the calculation of MAP.

First, let's calculate CO (cardiac output): CO = HR x SV

where:

HR is heart rate (measured in beats per minute).

SV is stroke volume (measured in milliliters per beat).

CO = 140 bpm x 95 mlCO = 13300 ml/minCO = 13.3 L/min

Next, we need to calculate SVR (systemic vascular resistance).

The formula for calculating SVR is: SVR = (MAP - CVP) / CO

where:

MAP is mean arterial pressure (measured in mm Hg).

CVP is central venous pressure (measured in mm Hg).

CO is cardiac output (measured in liters per minute).

Since we don't have CVP in this question, let's assume it to be zero.

SVR = (MAP - 0) / 13.3 L/minSVR = MAP / 13.3 L/min

Now, we can rearrange the above equation to calculate

MAP:

MAP = SVR x 13.3 L/minMAP = 60 mm Hg (diastolic pressure) + 1/3 (systolic pressure - diastolic pressure)MAP = 60 mm Hg + 1/3 (150 mm Hg - 60 mm Hg)MAP = 60 mm Hg + 30 mm HgMAP = 90 mm Hg

Therefore, Ziggy's mean arterial pressure (MAP) is 90 mm Hg.

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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Answer:

23

Step-by-step explanation:

x + x + 1 + x + 2 + x + 3 + x + 4 = 110

5x + 10 = 110

x = 20

4th number = x + 3

20 + 3 = 23

The 50th term is 290.

It is a sequence where there is a common difference between each consecutive term.

Example:

12, 14, 16, 18, 20 is an arithmetic sequence.

We have,

-4, 2, 8, 14,

This is an arithmetic sequence.

First term = a = - 4

Common difference.

d = 2 - (-4) = 6

d = 8 - 2 = 6

Now,

The nth term = a + (n -1)d

So,

n = 50

a = -4

d = 6

50th term.

= -4 + (50 - 1) 6

= - 4 + 49 x 6

= - 4 + 294

= 290

Thus,

The 50th term is 290.

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The complete question:

What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?

Answer:

A

Step-by-step explanation:

\( \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) \)

\( \sin( \alpha ) \cos( \alpha) = \frac{1}{2} \sin( 2\alpha ) \)

Answer:

The answer is A.Cos 57.

Step-by-step explanation:

Took the test..

In Aunt Jennifer's pumpkin pie recipe, the amount of pumpkin, flour, and sugar that needs to be added is based on the initial quantity of 500 grams of pumpkin.

The recipe does not provide specific ratios or proportions for the amounts of flour and sugar in relation to the pumpkin. To accurately determine the quantities of flour and sugar required, we would need additional information from the recipe, such as the desired texture, taste, or other ingredients.

Different recipes may have varying ingredient ratios to achieve different results, so without further details, we cannot provide specific measurements for the flour and sugar.

To create a pumpkin pie, it is recommended to follow a reliable recipe that provides precise measurements and instructions for all ingredients. This will ensure the best results in terms of taste, texture, and consistency.

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Step-by-step explanation:

Sum of the interior angles of a hexagon is 720°

117 + 146 + 93 + 129 + 113 + R = 720

598 + R = 720

R = 122°

NORAL follows a hyperbolic path.

Equation of hyperbola; x²/6400 + y²/33600 = 1

Given,

The coordinates where the two NAROL transmitters are located = (-200, 0) and (200, 0)

The distance from receiver to these transmitters = 160 miles

We have to find the standard form of the hyperbola that the receiver sits on ;

Here,

The transmitters behave as foci of the hyperbola.

The center of hyperbola; (h, k) = (0, 0)

The distance from center to focal point,

c = 200

Square both sides

c² = 40,000

The distance from the receiver to the transmitters  is given as:

2a = 160

Divide both sides by 2

a = 80

Square both sides

a² = 6400

We have:

b² = c² - a²

This gives

b² = 40000 - 6400

b² = 33600

The equation of a hyperbola is:

(x - h)²/a² + (y - k)²/b² = 1

So, we have:

(x - 0)²/6400 + (y - 0)²/33600 = 1

Therefore,

The equation of the hyperbola is:

x²/6400 + y²/33600 = 1

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The result of the Fourier Transform (Ω) X ( Ω ) of the signal x() = ((−1)−(+1))cos(200) is

x(t) = 1/(2π) ∫[-j∞, j∞] (s/(s^2 + 4π^2f0^2) + (s + 2/T)/(s^2 + 4π^2f0^2)) e^{st} ds

Given that the signal x()=((−1)−(+1))cos(200)  

The Fourier transform (Ω) X (Ω) is given by;

X (Ω) = ∫[-∞, ∞] x(t) e^{-jΩt} dt

Taking Laplace transform of the signal x(t);

x(t) = (−1)^(t/T)cos(2πf0t)

= cos(2πf0t) - 2cos(2πf0t)u(-t/T)

The Laplace transform of the first term is L(cos(2πf0t)) = s/(s^2 + 4π^2f0^2)

The Laplace transform of the second term is given by

L(cos(2πf0t)u(-t/T)) = (s + 2/T)/(s^2 + 4π^2f0^2)  

which is derived using partial fraction decomposition

Hence, the Laplace transform of the signal is given by

X(s) = L{x(t)}

= s/(s^2 + 4π^2f0^2) + (s + 2/T)/(s^2 + 4π^2f0^2)

Taking inverse Laplace transform of X(s) we have;

x(t) = 1/(2π) ∫[-j∞, j∞] X(s) e^{st} ds

= 1/(2π) ∫[-j∞, j∞] (s/(s^2 + 4π^2f0^2) + (s + 2/T)/(s^2 + 4π^2f0^2)) e^{st} ds

After solving this integral we will get the result of the Fourier Transform (Ω) X ( Ω ) of the signal x() = ((−1)−(+1))cos(200).

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To find the length of an arc of a circle, we need to use the formula:

Arc length = (central angle/360°) x 2πr

where r is the radius of the circle.

In this case, the central angle is 100°, and the radius is 15 in. So we can plug in these values and simplify:

Arc length = (100/360) x 2π(15)

Arc length = (5/18) x 30π

Arc length = 50/3 π or approximately 52.36 in.

Therefore, the length of a 100° arc for a circle with a 15 in. radius is approximately 52.36 inches.

Answer:

x = 10.2

Step-by-step explanation:

To find x, use Cosine

Cosine = \(\frac{adjacent}{hypothenuse}\)

⇒ Cosine 22 = \(\frac{x}{11}\)

Cosine of 22 is 0.93

⇒ 0.93 =  \(\frac{x}{11}\)

Multiply 11 on both sides:

⇒ 0.93 x 11 = \(\frac{x}{11}\) x 11

⇒ 10.23

Round to the nearest tenth:

10.23 ⇒ 10.2

x = 10.2

Match the Data Visualisation terms as follows:

1. Numpy: Working with arrays and matrices.

2. Bar chart: Representing categorical data with rectangular bars.

3. Pip: Package installer for Python.

4. S: Statistical library for Python.

The following are the meanings of the given terms:

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Answer:

140x+420

Step-by-step explanation:

7(x+3)20

=140x+420

Answer:

14x+420

Step-by-step explanation:

7(x+3)(20)

=140x+420

Answer:

mx(1 - 2) + y(m + 2n)

Step-by-step explanation:

mx - 2mx + my + 2ny

mx(1 - 2) + y(m + 2n)

Hope it helps.

Answer:

The interest is $1512 and the amount is $1519.

Step-by-step explanation:

: Convert interest rate of 7200% per month into a rate per year. Then Convert 3 months into years. Next Find an interest by using the formula, where I interest, P is total principal, i is the rate of interest per year, and t is the total time in years. Lastly, Find an amount by using the formula.

Interfaces can hold member variables - True

A variable that is connected to a particular object and available to all of its methods is known as a member variable. Although member variables can be declared in interfaces, they are inherently public, static, and final. However, these variables must be inherently final, public, and static without any keyword declaration.

This means that one may only specify constants within interfaces. Interfaces cannot be used to specify instance variables. An interface in Java is a group of abstract constants and methods that classes can use to implement them. Member variables, which are constants since they must be initialised and cannot be altered by implementing classes, can also be declared in an interface.

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The equation that amounts y in dollar after x years is y=P(1+0.02)ˣ

Simple Interest (S.I) is defined as method of calculating the interest amount for some principal amount of money.

The all amount repaid at the end of the borrowing period is indicated by the letter (A).

A = P(1 + RT)

A = Total amount

P = Principal amount or the initial loan amount

R = Rate of interest (per annum)

T = Time (in years)

The equation for the given data can be expressed as

y=P(1+n)ˣ

to find the value of n (rate of interest);

Putting initial values, we get

P=$1200

x=1yr

y=$1224

1224=1200(1+n)

1224/1200-1=n

n=0.02

Hence, the equation that amounts y in dollar after x years is y=P(1+0.02)ˣ.

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The general solution to the given differential equation is z(t) = C1*\(e^{(3t)}\) + C2*\(e^{(-3t)}\)

The given differential equation is a second-order linear homogeneous differential equation, which can be written as:

z'' + z' - 9z = 0

To find the general solution, we first need to solve the characteristic equation:

\(r^2\) + r - 9 = 0

By factoring or using the quadratic formula, we find the roots r1 and r2:

r1 = 3
r2 = -3

Since we have two distinct real roots, the general solution of the differential equation is:

z(t) = C1 * \(e^{(r1t)}\) + C2 * \(e^{(r2t)}\)
z(t) = C1 * \(e^{(3t)}\) + C2 * \(e^{(-3t)}\)

where C1 and C2 are arbitrary constants determined by initial conditions.

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F(x) = x! × x² - 2² + 3²

F(5) = 5! × 5² - 2² + 3²

F(5) = 120 × 25 - 4 + 9

F(5) = 3.000 - 4 + 9

F(5) = 2.996 + 9

F(5) = 3.005

I hope this helps

Answer:

In standard form -3x⁵ + x³ + 4x² - 8x

Step-by-step explanation: