(b) How many different groups of children can be chosen from a class of 18 children if the class contains one set of twins who must not be separated?
​

Answer:

D. 120

Step-by-step explanation:

Array formula: A (n, p) = n! / (n -p)!

At where:

 n = Total number of elements in the set.

p = Quantity of elements per arrangement

A (5.5) = 5! / (5-5)! = (5x4x3x2x1) / 0!

By definition: 0! = 1

Then: 120/1 = 120

Answer:

Step-by-step explanation:

Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation

V ' ( t ) = − 26400 e^− 0.49 t .

t = time (in days)

.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:

V'(6) = − 26400 e− 0.49 (6)

V'(6) = -26400e-2.94

V'(6) = -26400×-0.2217

V'(6) = $5852.88

V'(6) = $5,853 to nearest dollars

V'(6) = 585300cents to nearest cent

To get v(6), we need to get v(t) first by integrating the given function as shown:

V(t) = ∫−26400 e− 0.49 t dt

V(t) = -26,400e-0.49t/-0.49

V(t) = 53,877.55e-0.49t + C.

When t = 0, V(t) = $170,000

170,000 = 53,877.55e-0 +C

170000 = 53,877.55(2.7183)+C

170,000 = 146,454.37+C

C = 170,000-146,454.37

C = 23545.64

V(6) = 53,877.55e-0.49(6)+ 23545.64

V(6) = -11,945.63+23545.64

V(6) = $11,600 (to the nearest dollars)

Since $1 = 100cents

$11,600 = 1,160,000cents

Answer:

The GDP gap is 9 % when there is 4.5 % unemployment.

Step-by-step explanation:

The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:

[tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex]

The GDP gap at a given increase in unemployment can be estimated by the following expression:

[tex]\frac{g}{u} = r[/tex]

[tex]g = r\cdot u[/tex]

Where:

[tex]r[/tex] - GDP gap-unemployment increase rate, dimensionless.

[tex]u[/tex] - Increase in unemployment rate, measured in percentage.

[tex]g[/tex] - GDP gap, measured in percentage.

If [tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex] and [tex]u = 4.5\,\%\,unemp.[/tex], the GDP gap is:

[tex]g = \left(\frac{2\,\%\,GDP}{1\,\%\,unemp.} \right)\cdot (4.5\,\%\,unemp.)[/tex]

[tex]g = 9\,\%\,GDP[/tex]

The GDP gap is 9 % when there is 4.5 % unemployment.

Answer:

equation: y = 3x + 14

number of coins after 30 months: 104 coins

Hope this helps :)

An equation is formed of two equal expressions. The number of coins that will be with Deandre after a period of 30 months is 104 coins.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it is given that in the initial phase Deandre saves 14 coins. While he adds 3 coins each month. Therefore, the equation that will represent the number of coins that Deandre will have after a period of x months can be written as,

y = 14 + 3x

where y is the number of coins and x is the number of months.

After a period of x=30 months, the number of coins that will be with Deandre can be written as,

[tex]y = 14 + 3x\\\\y = 14 + 3(30)\\\\y = 104[/tex]

Thus, the number of coins that will be with Deandre after a period of 30 months is 104 coins.

Learn more about Equation:

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Answer:

N(L) = 20

The expected number of left handed people is 20.

Step-by-step explanation:

Given;

Percentage of left handed people P(L) = 10%

Total number of selected people N(T) = 200

The Expected number of left handed people N(L) is;

N(L) = Total number of selected people × Percentage of left handed people/100%

N(L) = N(T) × P(L)/100%

Substituting the given values;

N(L) = 200 × 10%/100%

N(L) = 200 × 0.1

N(L) = 20

The expected number of left handed people is 20.

Answer:5. 291503

Step-by-step explanation:

√28

2√7

5. 291503

Answer:

24024 are the total number of ways of choosing 4 campsites out of 14.

Step-by-step explanation:

We are given that there are a total of 14 campsite out of which 4 campsites are to be chosen.

It is a simple example of selection problem.

Number of ways to choose the first campsite = 14

Now, one campsite is chosen, 13 campsites are left.

Therefore,

Number of ways to choose the second campsite = 13

Now, one more campsite is chosen, 12 campsites are left.

Therefore,

Number of ways to choose the third campsite = 12

Now, one more campsite is chosen, 11 campsites are left.

Therefore,

Number of ways to choose the fourth campsite = 11

So, total number of ways for choosing 4 campsites out of 14:

14 [tex]\times[/tex] 13 [tex]\times[/tex] 12 [tex]\times[/tex] 11 = 24024

Hence, answer is 24024.

Answer:

Degree: 4; Type: quartic; Leading coefficient: 1

Step-by-step explanation:

Answer:

Jomo Kenyatta

Step-by-step explanation:

Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.

Answer:

Jomo Kenyatta

Step-by-step explanation:

took the test

Answer:

Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = $ 1,264,000

Total start-up amount required, according to the details provided in the question = $1,264,000

Step-by-step explanation:

- Hay 1000 m² de espacio de almacén para construir a $ 42 por m². Dinero total requerido = 1000 × 42 = $ 42,000.

- Hay 6000 m² de espacio de acceso pavimentado para construir a $ 32 por m². Dinero total requerido = 6000 × 32 = $ 192,000.

- Compra de servidores de última generación para revisar los autobuses antes de comenzar sus recorridos. Costo total = $ 630,000.

- Se necesita comprar equipo especial para revisar los neumáticos. Costo = $ 400,000.

Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = 42000 + 192000 + 630000 + 400000 = $ 1,264,000

¡¡¡Espero que esto ayude!!!

English Translation

- There is 1000 m² of warehouse space to construct at $42 per m². Total required money = 1000 × 42 = $42,000

- There is 6000 m² of paved access space to construct at $32 per m². Total money required = 6000 × 32 = $192,000

- Purchase of state-of-the-art servers to check the buses before starting their tours. Total Cost = $630,000

- Purchase of special equipment is needed to check the tires. Cost = $400,000

Total start-up amount required, according to the details provided in the question = 42000 + 192000 + 630000 + 400000 = $1,264,000

Hope this Helps!!!

Answer:

2.87 = AC

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opp / hyp

sin 35 = AC /5

5 sin 35 = AC

2.867882182= AC

To the nearest hundredth

2.87 = AC

Answer:

4 : 3

Step-by-step explanation:

16 : 12 can be simplified by 4 to get 4 : 3

Answer:

[tex]4:3[/tex]

Step-by-step explanation:

[tex]16 : 12[/tex]

The common highest factor of the ratio is 4.

Simplify the ratio.

[tex]16 \div 4:12 \div 4[/tex]

[tex]4:3[/tex]

Answer:

Step-by-step explanation:

When the time is 3:40pm

(a)The angle between the two hands in standard position is drawn and attached below.

(b)Now, each hour = 30 degrees

Therefore, the angle between 3 and 8 in an anticlockwise movement

= 7 X 30 =210 degrees

Stating the angle as a negative angle, we have:

[tex]210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ[/tex]

Answer:

The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.

Step-by-step explanation:

The question is incomplete:

The probability distribution is:

x   P(x)

0   0.30

1    0.40

2   0.20

3   0.06

4   0.04

The mean can be calculated as:

[tex]M=\sum p_iX_i=0.3\cdot 0+0.4\cdot 1+0.2\cdot 2+0.06\cdot 3+0.04\cdot 4\\\\M=0+0.4+0.4+0.18+0.16\\\\M=1.14[/tex]

(pi is the probability of each class, Xi is the number of topping in each class)

The standard deviation is calculated as:

[tex]s=\sqrt{\sum p_i(X_i-M)^2}\\\\s=\sqrt{0.3(0-1.14)^2+0.4(1-1.14)^2+0.2(2-1.14)^2+0.06(3-1.14)^2+0.04(4-1.14)^2}\\\\s=\sqrt{0.3(-1.14)^2+0.4(-0.14)^2+0.2(0.86)^2+0.06(1.86)^2+0.04(2.86)^2}\\\\ s=\sqrt{0.3(1.2996)+0.4(0.0196)+0.2(0.7396)+0.06(3.4596)+0.04(8.1796)}\\\\s=\sqrt{0.3899+0.0078+0.1479+0.2076+0.3272}\\\\ s=\sqrt{ 1.0804 }\\\\s\approx 1.04[/tex]

Answer:

mean: 1.14; standard deviation: 1.04

Step-by-step explanation:

Answer:

D. 32 sq. unit s

Step-by-step explanation:

4×18/2=32

Answer:

Type of error: Run-on(comma splice).

Best revision to fix it: Adding a semicolon after beginners .

Explanation:

A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.

In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:

'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'

Answer:

Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.

What type of error is present in the underlined sentence?

✔ run-on

Which is the best revision to fix the error?

✔ adding a semicolon after instrument

Step-by-step explanation:

Answer:

AT least 14 classrooms to hold the total number of students

Step-by-step explanation:

Since  we don't know the numer of girls in the school, let's call it "x".

What we know is that the number of girls plus the number of boys gives the total number of students. This is:

x + 129 = Total number of students

Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:

"5/8 of the school's population are girls" as:

0.625 (x + 129) = x

then we solve for "x":

0.625 x + 0.625 * 129 = x

0.625 * 129 = x - 0.625 x

80.625 = x (1 - 0.625)

80.625 = 0.375 x

x = 80.625/0.375

x = 215

So now we know that the total number of students is: 215 + 129 = 344

and if each classroom can hold 25 students, the number of classroom needed for 344 students is:

344/25 = 13.76

so at least 14 classrooms to hold all those students

◇Given :-

The denominator of a fraction is increased by a number and numerator will be doubled

To find

We have to find the required number or fraction

[tex]\underline{\bigstar{\sf\ \ Solution:-}}[/tex]

Now let us consided as the number be a

Then

The given fraction is 5/9

[tex]:\implies\sf \dfrac{5\times 2}{9+a}= 1\\ \\ \\ :\implies\sf \dfrac{10}{9+a}=1\\ \\ \\ :\implies\sf 10= 1(9+a)\\ \\ \\ :\implies\sf 10-9=a\\ \\ \\ :\implies\sf 1=a [/tex]

Answer:

The recurrence relation for aₙ is  aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8

Step-by-step explanation:

Solution

Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.

Ternary sequence is sequence with each of digits either 0, 1 or 2.

Now

Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.

Let us first find few initial values of aₙ

For n = 1

a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.  

This 1-digit sequence can be either 0 or 1 or 2.

Thus,

a₁ = 3

For n =2

a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.

This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.

here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)  

But one of these 9 sequence there are consecutive 0's .... (00)  

So we eliminate this one sequence.

So, a₂ = 8

Now

let us find the recurrence relation

Fir n ≥ 3

aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.

For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2

Let assume the 1st digit of this n - digit ternary sequence is 1.  

Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.

For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1

So,

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.

Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.

So  

If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:

aₙ-1 + aₙ -1 = 2aₙ -1

For the second case: if 1st digit of this n - digit ternary sequence is 0

If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,

If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.

So there are 2 choices for 2nd digit.  

After this there are more n-2 digits.  

Then

For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them  

For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.

Now,

The total number of sequence in this case is given as:

2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)

Hence  

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3

Now,

The recurrence relation for aₙ is shown below:

aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3

With the initial conditions as a₁ =3; a₂ = 8

Question Correction

Evelyn packed this box with 1 inch cubes. Which expression does not show how Evelyn can find the volume of the box?

Answer:  

(C) 2 + 3 + 6

Step-By-Step Explanation

In the diagram,  

Volume  = Height X Length X Width

= 6 X 2 X 3

=36 cubic units

Consider the options:

(A)6+6+6+6+6+6 =36 cubic units

(B) 2 X 3 X 6 =36 cubic units

(C) 2 + 3 + 6 = 11 cubic units

(D) 6 X 6 =36 cubic units

Out of the option, that which is not equivalent to 36 cubic units is:

(C) 2+3+6

Therefore, it does not show how Evelyn can find the volume of the box.

Answer:

2+3+6

Step-by-step explanation:

i just did it

Complete question is;

A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.

a. P(A ∩ B).

b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.

Answer:

A) 0.4

B) 0.4

Step-by-step explanation:

We are given;

P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8

A) To solve this question, we will use the the general probability addition rule for the union of two events which is;

P(A∪B) = P(A) + P(B) − P(A∩B)

Making P(A∩B) the subject of the equation, we have;

P(A∩B) = P(A) + P(B) − P(A∪B)

Thus, plugging in the relevant values, we have;

P(A∩B) = 0.7 + 0.5 - 0.8

P(A∩B) = 0.4

B)The probability that the lifeline usage amount is exceeded in exactly one of the two months can be described in terms of A and B as:

P(A but not B) + P(B but not A) = P(A∩B') + P(B∩A')

where;

A' is compliment of set A

B' is compliment of set B

Now,

P(A∩B') = 0.7 − 0.4 = 0.3

P(B∩A') = 0.5 − 0.4 = 0.1

Thus;

P(A but not B) + P(B but not A) = 0.1 + 0.3 = 0.4

Answer:

A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.

Answer:

22.11 miles per gallon

Step-by-step explanation:

1 km = 0.621371 miles

1 litre = 0. 264172 gallon

Given

Mileage of car =  9.4 Milometers per liter of gasoline

Mileage of car = 9.4 Km/ litres

now we will use 0.621371 miles for Km and 0. 264172 gallon for litres

Mileage of car = 9.4 * 0.621371 miles/ 0. 264172 gallon

Mileage of car = 9.4 * 2.3521 miles/ gallon

Mileage of car = 22.11  miles/ gallon

Thus, 9.4 Km/litres is same as 22.11 miles per gallon.

Answer:1260

Step-by-step explanation:

Kissing has 7 letters, and there are 2 paris of the same letter.

[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260

Answer:

False

Step-by-step explanation:

from *millermoldwarp*

"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."

hopes this helps

Answer:false

Step-by-step explanation:

Answer: 35%

Step-by-step explanation:

If no is 10, 10 x 0.65 = 6.5. OR

10 - 35% of 10 = 6.5

  Multiplying by 0.65 is the same as decreasing by 35%

Let the number is 'a' and percentage decrease is 'b',

Expression for the given statement will be,

a × 0.65 = a - (b% of a)

[tex]0.65a=a(1-\frac{b}{100})[/tex]

[tex]0.65=1-\frac{b}{100}[/tex]

[tex]\frac{b}{100}=1-0.65[/tex]

[tex]b=100(0.35)[/tex]

[tex]b=35[/tex]

    Therefore, Multiplying by 0.65 is the same as decreasing by 35%.

Learn more about the Algebraic expressions for the statements here,

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Option D is the correct answer.

Answer:

D. ∠B and ∠C are congruent.

Step-by-step explanation:

Since, ∠A and ∠B are supplementary.

Therefore,

∠A + ∠B = 180°.....(1)

Since, ∠A and ∠C are supplementary.

Therefore,

∠A + ∠C = 180°.....(2)

From equations (1) & (2)

∠A + ∠B = ∠A + ∠C

=> ∠B = ∠C

Hence, ∠B and ∠C are congruent.

Step-by-step explanation:

Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.

The Wronskian of them functions be

W = (y1y2' - y1'y2)

y1 = (e^x)/2 = y1'

y2 = (xe^x)/2

y2' = (1/2)(x + 1)e^x

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.

Answer:

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Step-by-step explanation:

Answer:

r = -10*cos(t)

Step-by-step explanation:

To write the rectangular equation in polar form we need to replace x and y by:

[tex]x=r*cos(t)\\y=r*sin(t)[/tex]

Replacing on the original equation, we get:

[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]

Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:

[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]

Answer:

[tex]x=8[/tex]

[tex]y=24[/tex]

Step-by-step explanation:

3x+2y=72

If y=3x, we plug it into our equation and get:

3x+2×3x=72

3x+6x=72

9x=72

Divide both sides by 9

x=8

Answer:

x = 8

Step-by-step explanation:

3x + 2y = 72

Put y as (3x), and solve for x.

3x + 2(3x) = 72

Multiply 2(3x).

3x + 6x = 72

Add like terms 3x and 6x.

9x = 72

Divide 9 into both sides and isolate x.

x = 72/9

x = 8

The value of x is 8.