Abigail invested $29,000 in an account paying an interest rate of 2.1% compounded continuously

Answer:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]

Step-by-step explanation:

From the given information;

The total number of beads  = 10 + 8 + 11 = 29

To choose k beads out 29 beads, let assume that [tex]t_k[/tex] be the no. such that:

[tex]t_k = ( ^{29}_{k}) \ \ \ where; k =0,1,2,3,....,29[/tex]

∴

The sequence [tex]\{ t_k\}^{29}_{k=0} = (^{29}_{k})[/tex]

The generating function for [tex]\{ a_k \}^n_{k=0}[/tex] is:

[tex]G(x) = a_o +a_1x +a_2x^2 +...+a_nx^n[/tex]

[tex]G(x) = \sum \limits ^{n}_{k=0} \ a_k x^k[/tex]

For the sequence above;

[tex]G(x) = \sum \limits ^{29}_{k =0 } (^{29}_{k}) x^k[/tex]

By applying binomial series [tex](1+x)^n = \sum \limits ^n_{k=0} ( ^n_k) x^k[/tex]

Thus:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]

Answer:

The cost of 2 quintal of rice is $10,000.

Step-by-step explanation:

To determine the cost of 2 quintals of rice, knowing that 90 kilos of said product is worth $ 4,500, it is first necessary to establish the equivalence between quintals and kilograms. In this regard, a quintal is equivalent to 100 kilograms, so 2 quintals are equivalent to 200 kilos.

Now, to determine the cost per kilogram of rice, the following calculation is required:

4,500 / 90 = X

50 = X

Therefore, 1 kilogram of rice costs $ 50. Thus, since 200 x 50 equals 10,000, 2 quintals of rice will cost $ 10,000.

Answer:

19

Step-by-step explanation:

15z-14z=12+7

z=19

Answer:

7x7

Step-by-step explanation:

its base (length) and width is 7.

Answer:

I believe it to be C

Step-by-step explanation:

Answer:

Step-by-step explanation:

.90-.35=.55

200/.55=364 bags i think

Elvira sells a total of 364 bags to earn a profit of $200 and this can be determined by using the unitary methods.

Given :

The following steps can be used to determine the total number of bags she sells to earn the profit of $200:

Step 1 - First find the total profit she earns to sell one bag.

= 0.90 - 0.35

= $0.55

Step 2 - Now, using the unitary method find the total number of bags she sells to earn a profit of $200 If she earns a profit of $0.55 to sell one bag.

[tex]=\dfrac{200}{0.55}[/tex]

= 363.63 [tex]\approx[/tex] 364 bags

She sells a total of 364 bags to earn a profit of $200.

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Answer:

1 unit to the right of 0

Step-by-step explanation:

Well if you distribute the - into the (-1) than you should get a positive becuase -1*-1 is positive 1. So it would be right next to 0 to the right.

Answer:

67.5%

Step-by-step explanation:

Answer:

The  estimate the proportion of college students who drive cars with manual transmissions with 90% confidence is  

      [tex]0.171 <  p <  0.297 [/tex]  

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  124

    The population proportion p =  0.06

     The number of cars with manual transmissions is  k =  29

From the question we are told the confidence level is  90% , hence the level of significance is    

      [tex]\alpha = (100 - 90 ) \%[/tex]

=>   [tex]\alpha = 0.10[/tex]

Generally the sample proportion is mathematically represented as

       [tex]\^ p = \frac{ 29 }{124 }[/tex]

=>   [tex]\^ p = 0.234[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.645 [/tex]  

Generally the margin of error is mathematically represented as  

     [tex]E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]

=>   [tex]E =   1.645  * \sqrt{\frac{0.234 (1- 0.234 )}{124} } [/tex]

=>   [tex]E =  0.063  [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\^ p -E <  p <  \^ p +E[/tex]

=>  [tex]0.234  - 0.063  <  p <  0.234  + 0.063 [/tex]

=>  [tex]0.171 <  p <  0.297 [/tex]  

Answer:

1.22 meters aprx.

Step-by-step explanation:

This is talking about meters right. If it is 1.22 would be your answer.

Answer: $4 senior, $7 child

Step-by-step explanation:

(3s + 9c = 75)

8s + 5c = 67

Answer:

you have it right! 3x - 4= 23

Answer: 3x-4 = 23

Step-by-step explanation:

Cos ik

Answer:

D) The vectors point in opposite directions.

Step-by-step explanation:

got it right on edge :)

see graph below

Given vectors u = (-2,1) and v =( 4, -2) represents the vectors point in opposite directions.

"Vectors is a quantity which gives us both magnitude and direction of the given quantity."

According to the question,

Given vectors u(-2,1) and v(4,-2) represented on the graph.

From the graph we conclude that given vectors u and v

Does not form obtuse angle of approximately 93° , 96° or 127°.

The vector 'u(-2,1)' is in second quadrant and v(4,-2) is in fourth quadrant.

Second quadrant and fourth quadrant are in opposite direction.

Hence, we conclude the vectors point in opposite directions.

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Answer:

x= 1

y= -2

Step-by-step explanation:

1. y+3x=1 subtract 3x from both side to get y= 1-3x

2. Put the new found y value in the equation

3x-4(1-3x)=11

3. Distribute the 4

3x-4+12x=11

4. Add 4 to both sides

3x+12x=15

5. Add the x's

15x=15

6. Solve for x

x=1

7. Plug in the x in the y equation y= 1-3x

y=1-3(1)

8. Solve for y

y= -2

The solution to the system of equations is x = 1 and y = -2.

To solve the system of equations using substitution, we need to solve one of the equations for one variable in terms of the other variable and then substitute that expression into the other equation. Let's solve the second equation for y and then substitute it into the first equation:

Given system of equations:

3x - 4y = 11

y + 3x = 1

Step 1: Solve the second equation for y:

y = 1 - 3x

Step 2: Substitute the value of y from equation (2) into equation (1):

3x - 4(1 - 3x) = 11

Now, let's solve for x:

3x - 4 + 12x = 11

Combine like terms:

15x - 4 = 11

Step 3: Solve for x:

15x = 11 + 4

15x = 15

x = 15 / 15

x = 1

Step 4: Now that we have the value of x, we can find y using equation (2):

y = 1 - 3(1)

y = 1 - 3

y = -2

So, the solution to the system of equations is x = 1 and y = -2.

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Answer:

I believe it is D

Step-by-step explanation:

The entire equation y=nx-d means that d is the fee Kyle pays the school. SO that means that nx is the amount of money he earns from the people attending a yoga class.

Term nx represents the total money Kyle collects from people attending the class.

" Linear equation in one variable represents straight line and it is a equation in one variable in which degree of the given variable is equals to one. General form is written as ax + b =0."

According to the question,

x represents fees paid by each person for yoga class.

Condition is Kyle has to pay a fee for the use of gym.

It mean gym fees would be deducted from her earned fees from yoga class.

Therefore , d represents gym fee.

n represents number of people comes for yoga class.

From the given condition it is a linear equation in one variable,

Therefore, nx represents amount Kyle collects from people attending the class.

Hence, Option (D) is the correct answer.

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Answer:

I love cookies too.

Answer:

me depending on what kind of math it is

Step-by-step explanation:

Answer:

275n + 1000 = 2700

They will go 6 days on vacation.

Step-by-step explanation:

Given that the Carter family wants to go on vacation with a budget of $ 2700, of which $ 1000 will be used exclusively for food, and for each day of stay $ 275 will be spent, the formula to obtain the number of days they can spend on vacation is following:

1000 + 275n = 2700

275n = 2700 - 1000

n = 1700/275

n = 6.18

Therefore, with this amount, the Carters will be able to spend 6 days on vacation, and they will have money left over.

Answer:

Option (2)

Step-by-step explanation:

Formula to get the surface area of a sphere is,

Surface area = 4πr²

Here 'r' = Radius of the sphere

We have to calculate the surface area of a sphere with radius r = 9 inches.

By substituting the value of r in the formula,

S = 4π(9)²

Therefore, Option (2) will be the correct option.

Answer:

Answer:

124 mph (200 km/h) (for a small plane) .  621 mph (1.000 km/h) (airliner) .  1243 mph (2.000 km/h) (jet) .

Step-by-step explanation:

Answer:

2nd option is the correct answer

Step-by-step explanation:

[tex]m \angle 1 > m \angle 3 \: \& \: m \angle 1 > m \angle 7 \\ [/tex]

According to the Exterior Angle Theorem, the true statement should be considered as the option b.

The exterior angle theorem defined that at the time when a triangle's side should be extended, the resultant exterior angle formed should be equivalent to the sum of the measures of the two opposite interior angles of the triangle.

So based on this, we can say that the option b is correct.

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Answer:

X=5

Step-by-step explanation: