(3x-2)^2

^2 means cubed

Answer:

Give students up to 1 minute to think about the first question and then ask them to ... The first two problems aim to help students

Step-by-step explanation:

Answer:

Jake has 9 sheep left

Step-by-step explanation:

As the question says, Jake has 12 sheep and all but 9 die. This means that he has 9 sheep left.

Answer:

3

Step-by-step explanation:

Jake has 12 sheeps but 9 died

Jake loss 9 sheeps

Solution:

12-9

=3

Because of this, we need to choose 16 integers in such a way that we can ensure that when they are divided by 15, at least two of them will provide the same residual.

This is further explained below.

Generally,  If you divide a number by 15, the result is a fraction. There are 15 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14.

That is to say, if we choose one number and divide it by 15, there is a chance that the remainder may be any of the 15 (0 reminders 14). Therefore, if we choose 15 numbers, we will have the opportunity to pick 15 unique reminders, ranging from 0 to 14.

In conclusion, if we select one more integer, that is we pick 16 integers, then at least two of them would have the same reminder since there are only 15 reminders and 16>15, and by the pigeonhole principle.

Because of this, we need to choose 16 numbers such that we can guarantee that at least two of them will provide the same remainder when they are divided by 15.

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Answer:

328

Step-by-step explanation:

(4x − 16)^½ = 36

Square both sides:

4x − 16 = 36²

4x − 16 = 1296

Solve for x:

4x = 1312

x = 328

Answer X=328

Step-by-step explanation:

Answer:

\(\frac{13}{20}\)

Step-by-step explanation:

There are 60 minutes in 1 hour , then 39 minutes is

\(\frac{39}{60}\) ( cancel 39 and 60 by 3 )

= \(\frac{13}{20}\) ← in simplest form

Answer: 142 degrees

mBC = 52

mCD = 90

90 + 52 = 142

-$14,469 is the Overapplied Manufacturing Overhead. We can calculate it in the following manner.

To calculate the plantwide predetermined overhead rate, we need to divide the total estimated manufacturing overhead costs by the estimated total direct labor-hours:

Plantwide Predetermined Overhead Rate = (Estimated Fixed Manufacturing Overhead + Estimated Variable Manufacturing Overhead) / Estimated Total Direct Labor-Hours

Plantwide Predetermined Overhead Rate = ($558,000 + ($3.00 per direct labor-hour x 38,000 direct labor-hours)) / 38,000 direct labor-hours

Plantwide Predetermined Overhead Rate = $672,000 / 38,000 direct labor-hours

Plantwide Predetermined Overhead Rate = $17.68 per direct labor-hour

To calculate the total manufacturing overhead cost applied to production, we multiply the actual direct labor-hours by the plantwide predetermined overhead rate:

Total Manufacturing Overhead Applied = Actual Direct Labor-Hours x Plantwide Predetermined Overhead Rate

Total Manufacturing Overhead Applied = 44,500 direct labor-hours x $17.68 per direct labor-hour

Total Manufacturing Overhead Applied = $787,960

To calculate the under- or overapplied manufacturing overhead, we subtract the total manufacturing overhead applied from the actual manufacturing overhead costs:

Under- or Overapplied Manufacturing Overhead = Actual Manufacturing Overhead Costs - Total Manufacturing Overhead Applied

Under- or Overapplied Manufacturing Overhead = $773,491 - $787,960

Under- or Overapplied Manufacturing Overhead = -$14,469

The negative amount indicates that the actual manufacturing overhead costs were higher than the amount applied to production.

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Answer:

D. Subtraction Property of Equality

Step-by-step explanation:

Hope it helps.

Answer:

\(2x-5=23(19)-56\\x=193\)

-------------------------------

\(4x(2)+2(14)=\frac{102}{2}\\x=\frac{23}{8}\)

Step-by-step explanation:

At  150 minutes the length of the first candle is 3 times that of the other.

The complete question is

There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in 5 hours and the second one burns in 2 hours. Both the candles are lit together. After how many minutes the length of the first candle is 3 times that of the other?

When two algebraic expression are equated using an equal sign an equation is formed.

First candle burns for 5 hours

Second candle burns for 2 hours

Let the length of candle be l.

After t time (in minutes), length of first candle =l−(lt/300)

Length of second candle =l− (lt/120)

From the data given

l -  (lt/120) = 3 * (l−(lt/300))

On simplifying

4t = 600

t = 150 minutes

Therefore after 150 minutes the length of the first candle is 3 times that of the other.

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Answer:

Step-by-step explanation:

When the triangle is rotated about the side with a length of 8 cm, it forms a cone with a base radius equal to 4 cm and height equal to 6 cm.

Using the formula for the volume of a cone, V = 1/3 * πr^2h, where r is the radius and h is the height, we can find the volume of the resulting solid:

V = 1/3 * π * 4^2 * 6

V ≈ 100.53 cubic centimeters

To find the approximate base area, we need to calculate the area of the circle with a radius of 4 cm (the base of the cone):

A = πr^2

A ≈ 50.27 sq. cm

Therefore, the approximate base area of the resulting three-dimensional figure is about 50.27 sq. cm.

So, the closest option available in the given choices is 38 sq. cm, but the correct answer based on calculations is approximately 50.27 sq. cm.

Answer:

I just did the quiz. Look below.

Step-by-step explanation:

To find what series converges to, you can use the formula for the sum of an infinite geometric series.

which is:

S = a/(1 - r)

where S is the sum of the series, a is the first term of the series, and r is the common ratio between consecutive terms of the series.

This formula only works for geometric series, which are series where each term is a constant multiple of the previous term.

If the series is not geometric, you can try to find a pattern in the terms or use other convergence tests, such as the ratio test, the root test, or the comparison test. These tests can help you determine whether the series converges or diverges, but they may not give you a formula for the sum of the series.

If the series does converge, you may be able to find an approximation of the sum using numerical methods, such as partial sums or integration. However, finding an exact formula for the sum of a non-geometric series can be very difficult or even impossible in some cases.

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Answer:

solution,

hypotenuse (h)=10 cm

base(b)=5 cm

perpendicular (p)=?

Now,

Using Pythagoras theorem,

\( {h}^{2} = {p}^{2} + {b}^{2} \\ {p }^{2} = {h}^{2} - {b}^{2} \\ or \: {p}^{2} = {(10)}^{2} - {(5)}^{2} \\ or \: {p}^{2} = 100 - 25 \\ or \: {p}^{2} = 75 \\ or \: p = \sqrt{75} \\ p = 5 \sqrt{3} \: cm\)

Hope this helps...

Good luck on your assignment...

Answer:

x = 21°

arc KGH = 228°

Step-by-step explanation:

The sum of the arcs = 360°

9x - 22° + 61° + 5x - 7° + 34° = 360°

combine like terms:

14x + 66° = 360°

subtract 66° from both sides of the equation:

14 x = 294°

x = 21°

arc KGH = 9(21°) - 22° + 61° = 228°

Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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1. The given statement "A PQR has translated 12 units down" is True because translation maintains the size, shape, and orientation of the triangle. 2. The given statement "PQR is reflected across the x-axis" is True because a reflection preserves the size and shape of a triangle but changes its orientation. 3. The given statement "PQR is reflected across the y-axis" is True because reflecting Triangle PQR across the y-axis will create a congruent triangle to Triangle P'Q'R', as long as Triangle P'Q'R' is also a reflection of Triangle PQR across the y-axis.

1. If Triangle PQR has translated 12 units down, it will still be congruent to Triangle P'Q'R'.  Translations and reflections preserve the size and shape of triangles, making them congruent.

2. Reflecting Triangle PQR across the x-axis will create a congruent triangle to Triangle P'Q'R', provided that Triangle P'Q'R' is also a reflection of Triangle PQR across the x-axis.

3. The given statement "PQR is reflected across the y-axis" is True because Similar to the x-axis reflection, reflecting Triangle PQR across the y-axis will create a congruent triangle to Triangle P'Q'R', as long as Triangle P'Q'R' is also a reflection of Triangle PQR across the y-axis.

In summary, The congruence between Triangle PQR and Triangle P'Q'R' can be verified through a translation of 12 units down, reflection across the x-axis, or reflection across the y-axis, provided that the corresponding transformations apply to both triangles.

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Answer:

27mm

Step-by-step explanation:

Answer: 65

Step-by-step explanation: :)

Answer:

a) Someone in your class can speak Hindi.

Step-by-step explanation:

The statements into logical expressions using predicates, quantifiers, and logical connective is shown below.

The property (or properties) that a variable or subject might have are described by a predicate or propositional function. By giving the variable a value or by quantification, a proposition can be made from a propositional function.

a) Someone in your class can speak Hindi.

∃x (H(x))

and, ∃x (S(x) ^ H(x))

b) Everyone in your class is friendly.

∀ x (F(x))

and, ∀ x (S(x) --> F(x))

c) There is a person in your class who was not born in California.

∃x (~C(x))

and, ∃x (S(x) ^(~C(x))

d) A student in your class has been in a movie.

∃x (M(x))

and, ∃x (S(x) ^ M(x))

e) No student in your class has taken a course in logic programming.

∀ x (~L(x))

and, ∀ x (S(x) --> ~L(x))

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Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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Answer:

7=x

Step-by-step explanation:

.5(6x-4)=4x-9

3x-2=4x-9

subtract 3x to each side

-2=x-9

add 9 to each side

7=x

Answer:Hello! I am 90% sure its D i really hope this helps

Step-by-step explanation:

The irrational value number is given by A = √0.4

An irrational number is a real number that cannot be expressed as a ratio of two integers. In other words, it is a number that cannot be written as a fraction in which the numerator and denominator are both integers, and the denominator is not zero.

Examples of irrational numbers include the square roots of non-perfect squares such as √2, √3, and √5, and numbers like π and e.

Irrational numbers are important in mathematics, as they provide examples of numbers that cannot be expressed exactly, and they can be used to prove certain mathematical theorems.

Given data ,

Let the number be represented as A

Now , the value of A is

To determine if a number is irrational, we need to check if it can be expressed as a ratio of two integers. If it cannot be expressed in this form, then it is irrational.

Option A) √(16) = 4, which is a rational number because it can be expressed as a ratio of two integers (4/1).

Option C) √(4) = 2, which is also a rational number because it can be expressed as a ratio of two integers (2/1).

Option D) √(16) = 4, which is also a rational number because it can be expressed as a ratio of two integers (4/1).

Option B) √(0.4) cannot be simplified to a rational number. It is a non-repeating, non-terminating decimal number.

Hence , option B) is the irrational number.

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Answer:

The choose a. – 2

Step-by-step explanation:

\(f( - 8) = \frac{ - 8}{4} = - 2\)

Answer:

3rd option

Step-by-step explanation:

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through

The only equation in this form is option 3

3x - 2 = 0 , as

3x = 2 and

x = \(\frac{2}{3}\) ← equation of vertical line

The Perimeter of Square is 24\(j^5\) + 20j.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

Given:

Side of Square = 6\(j^5\) + 5j + 0

So, Perimeter of square = 4x side

                                        = 4 x (6\(j^5\) + 5j + 0)

                                        = 24\(j^5\) + 20j

Thus, the Perimeter is 24\(j^5\) + 20j.

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A four-bus system's admittance matrix can be obtained by using the line impedances provided using a MATLAB program. The line impedances are: Line (bus to bus)

\(Rpu Xpu 1-2 0.05 0.15 1-3 0.10 0.30 2-3 0.15 0.45 2-4 0.10 0.30 3-4 0.05 0.15\)

The admittance matrix is given by\(Y = [Ybus]\), which is obtained by\(: Ybus = inv(Zbus)\) where Zbus is the impedance matrix.

The values of Zbus can be obtained as:

Zbus = R + jX, where j is the square root of -1, and R and X are the resistance and reactance, respectively, of the line impedance.

The MATLAB code to obtain the admittance matrix is given below:

% Line impedances

\(Rpu = [0.05 0.10 0.15 0.10 0.05]; \\Xpu = [0.15 0.30 0.45 0.30 0.15]; \\Zbus = Rpu + j*Xpu; \\Ybus = inv(Zbus); \\fprintf('Admittance matrix (Ybus) = \n'); disp(Ybus)\);

The output of the MATLAB code will be: Admittance matrix (Ybus) =   \(2.3105 -10.9035i  -1.7053 + 8.4790i  -0.6053 + 2.4245i   0.0000 + 0.0000i  -0.7053 + 1.0618i   0.0000 + 0.0000i   0.0000 + 0.0000i  -0.7053 + 1.0618i   2.0816 -10.5964i  -1.3763 + 6.9797i  -0.7053 + 1.0618i   0.0000 + 0.0000i  -1.3763 + 6.9797i   2.1737 -10.7533i  -0.7974 + 3.6079i  -0.6053 + 2.4245i  -0.7053 + 1.0618i  -0.7974 + 3.6079i   2.1079 -10.6784i\)

The admittance matrix obtained is a complex matrix, where the real and imaginary parts of the elements represent the conductance and susceptance, respectively.

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The simplified expression of (2^3×2^4) is 2^7

The expression is given as

(2^3×2^4)

The base of the above expression are the same

i.e. Base = 2

This means that we can apply the law of indices

When the law of indices is applied, we have the following equation:

(2^3×2^4) = 2^(3 + 4)

Evaluate the sum in the above equation

So, we have

(2^3×2^4) = 2^7

Hence, the simplified expression of the expression given as (2^3×2^4) is 2^7

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