Estimate the area of the circle equal three decimal 14 round to the nearest hundredth if necessary9

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:

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

Answer:

yesseinafhinks

Step-by-step explanation:

Dividing by 10² is also the same thing as multiplying by 10^-2. In that case, we simply move the decimal places only 2 places back. That would give us 7.516, not 0.7516 (which is 3 times, not 2).

Answer:

Yes, triangle GYK is similar to triangle BAK.

Step-by-step explanation:

The sides of each triangle are proportional to each other.

Take the longest side of each triangle. You are comparing line AK with line KY.

The proportion is 15/25.

Now, take the shortest side of each triangle. You are comparing line KB with GK.

The proportion is 6/10.

To determine if the triangles are proportional, we can see if the two proportions are equal to each other:

15/20=6/10

3/5=6/10

Correct! 3/5 equals to 6/10. Therefore, the two triangles are similar because their sides are proportional.

Hope this helps :)

Answer:

O  Yes!

Step-by-step explanation:

We would check whether the proportionality of their sides is equal

Taking proportionality

= [tex]\frac{6}{10} = \frac{15}{25}[/tex]

Cross Multiplying

6 × 25 = 15 × 10

150 = 150

So, ΔABK is similar to ΔGKY

Answer:

D. 32 sq. unit s

Step-by-step explanation:

4×18/2=32

Answer: There are systems with no solutions, and the graphs may show two regions with no intersections (as you know, the solution set is in the intersection of the sets of solutions for each inequality)

Step-by-step explanation:

Ok, suppose that our system is:

y > x

and

y < x.

This system obviously does not have any solution, because y can not be larger and smaller than x at the same time.

The graph of y > x is where we shade all the region above the line y = x (the line is not included)

and the graph of y < x is where we sade all the region under the line y = x (the line is not included)

So we will look at a graph where we never have a region with the two shades overlapping (so we do not have a intersection in the sets of solutions), meaning that we have no solutions.

Answer: 7000

Step-by-step explanation:

Let the amount invested in 8% account be P1 and the amount invested in 6% account be P2

. If the total amount invested is $20,000 then:

P1+P2=20,000. (Eq. 1)

The interest earned in one year from the 8% account is:

I1=0.08P1

and the interest earned in one year from the 6% account is:

I2=0.06P2

If the total interest earned is $1460, then:

I1+I2=1460

0.08P1+0.06P2=1460

(Eq. 2) From Eq. 1 :

P1=20000−P2

Substituting this into Eq. 2:

0.08 (20000−P2) + 0.06P2 = 1460

1600 − 0.08P2 + 0.06P2 = 1460

0.02P2 = 140

P2 = 140 / 0.02

P2 = 7000

Hence, he invested $7000 at the rate of 6%.

Answer:

1.90.93

2.90.27

Step-by-step explanation:

Answer:

one above correct

Step-by-step explanation:

1st - 90.93

2nd-90.27

Answer:

The amount of interest for this loan is 16.6%.

Step-by-step explanation:

Since Levi will make a purchase for $ 3000 with your credit card, you should explore the two options you have:

-On the one hand, a down payment of $ 1000, with fees of $ 125.

-on the other, a down payment of $ 1,300, with fees of $ 110.

In both cases, the fees are the same, and the interest too. Therefore, to determine the amount of installments and interest, the difference between the down payment of one option and the other must be taken and divided by the difference between the value of the installments of either option.

Thus, the difference of the down payment of 300 (1300 - 1000) must be divided by 15 (125 - 110). This yields a result of 20 (300/15), with which that will be the total of quotas until both have paid the same amount of money.

Thus, given that 1300 + 110 x 20 = 3,500, and that 1000 + 125 x 20 = 3,500, in both cases the total value to be paid is $ 3,500. Since 500 is 16.6% of 3000, the total purchase interest will be 16.6%.

Answer: Option d.

Step-by-step explanation:

Ok, we have 3 urns.

Each urn can give a number between 0 and 9, so each urn has 10 options.

And as the urns are different, the outcome in the first urn does not affect the outcomes in the others, and the same happens for the outcome in the second urn, so the events are independent.

The total number of combinations is equal to the product of the number of options for each event (here each urn is one event)

then the number of combinations is:

C = 10*10*10 = 10^3 = 1000

Then the correct option is d.

Answer:

1). [tex]P'(t) = (-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). (-435.36) dollars per week

Step-by-step explanation:

Weekly price decay of the product is represented by the function,

P(x) = [tex]95000.e^{-0.05x}[/tex]

And the price of the product changes over the period of 't' weeks is represented by,

x(t) = [tex]53+0.95t^2[/tex]

Function representing the rate of change in the profit with respect to the time will be represented by,

1). P'(t) = [tex]\frac{dP}{dx}.\frac{dx}{dt}[/tex]

Since, P(x) = [tex]95000.e^{-0.05x}[/tex]

P'(x) = [tex]95000\times (-0.05).e^{-0.05x}[/tex]

       = [tex](-4750).e^{-0.05x}[/tex]

Since, x(t) = 53 + 0.95t²

x'(t) = 1.9t

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05x}\times (1.9t)[/tex]

By substituting x = 53 + 0.95t²

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05(53+0.95t^2)}\times (1.9t)[/tex]

   P'(t) = [tex](-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). For t = 7 weeks,

P'(7) = [tex](-9025\times 7).e^{-0.05(53+0.95(7)^2)}[/tex]

       = [tex](-63175).e^{-4.9775}[/tex]

       = (-63175)(0.006891)

       = (-435.356) dollars per week

       ≈ (-435.36) dollars per week

Answer:

X<3

Step-by-step explanation:

4x-7 <5

4x < 5+7

4x < 12

X < 12/4

X < 3

Hope this helps..

Good Luck!

Answer:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

Step-by-step explanation:

Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(14.4,1.1)[/tex]  

Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.05[/tex]   (a)

[tex]P(X<a)=0.95[/tex]   (b)

We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64

Using this value we can set up the following equation:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]

And we have:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

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:I believe that it is A but i am not fully sure

Step-by-step explanation:

Answer:

I want to say 9 but im preety sure it's 6

Step-by-step explanation:

you have 54 times to pick it

you have 9 marbles,

54 divided by 9= 6

answer is 6

hope this helped:))))

have a grate dayy

Answer:

1

this is because I see only one marble present which is orange

Answer:

[tex]180[/tex]

Step-by-step explanation:

[tex]6 \times 2 \times 3 \times 5[/tex]

[tex]12 \times 15[/tex]

[tex]=180[/tex]

Steps to solve:

6 * 2 + 3 - 5

~Multiply

12 + 3 - 5

~Add

15 - 5

~Subtract

10

Best of Luck!

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

Corrected Question

Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym 2/3 the distance from Ping's home to Ari's home.  Where is the gym?

Answer:

(D)15th Street and 14th Avenue

Step-by-step explanation:

Ping's Location: (3rd Street, 6th Avenue)

Ari's Location: (21st Street, 18th Avenue)

The gym is at point P which is [tex]\dfrac{2}{3}[/tex] the distance from Ping's home to Ari's home.

That is, Point P divides the line segment in the ratio 2:1.

We use the section formula:

[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]

m:n=2:1, [tex](x_1,y_1)=(3,6), (x_2,y_2)=(21,18)[/tex]

[tex]=\left(\dfrac{2*21+1*2}{2+1}, \dfrac{2*18+1*6}{2+1}\right)\\=\left(\dfrac{45}{3}, \dfrac{42}{3}\right)\\=(15,14)[/tex]

The gym is located at 15th Street and 14th Avenue.

Answer:

9 bags

Step-by-step explanation:

130, 134, 136, 145, 145, 147, 147, 151, 154

9 bags had at least 130 peanuts.

Answer:

3^5

Step-by-step explanation:

becuase 3*3*3*3*3

Answer: 3^5 (3 to the power of 5)

Step-by-step explanation:

3 is multiplied by itself 5 times

To shorten the expression, exponential notation is used and it becomes 3^5, which essentially means three multiplied by itself 5 times

ex. 4^3 equals 4x4x4

Answer:

19305

Step-by-step explanation:

We simply take the percentage of 29700 to find how many people were added.

29700(0.35) = 10395 <== so 10395 people have been added

Subtract it from the current:

28700 - 10395 = 19305 people before.

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:The answer is B

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Cos A = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Where Adjacent = 28, Hypotenuse = 197

Cos A = [tex]\frac{28}{197}[/tex]

Answer:

Option D is correct

Step-by-step explanation:

Applying the cosine theorem for triangle ABC, you would have:

cos (angle BAC) = (BA^2 + CA^2 - BC^2)/(2*BA*CA)

                           = (10^2 + 18^2 - 20^2)/(2*10*18)

                           = 24/360

=> angle BAC = ~86 deg

Hope this helps!

Answer:

Each persons share is 6.03

Step-by-step explanation:

Divide the total cost by the number of students

48.24 / 8

6.03

Each persons share is 6.03

Answer:

$6.03

Step-by-step explanation:

A group of 8 students paid $48.24 for food.

Each of their shares would be divided among the 8 students.

48.24/8=6.03

Each student paid a share of $6.03.

Answer:

1 - c

2 - a

3 - e

4 - d

5 - b

Answer:  c, a, e, d, b

Step-by-step explanation:

1. Angle: (c) A figure consisting of two rays with the same endpoint.

2. Circle: (a) The set of all points in a plane that are a given distance from a point. That distance is called the radius.

3. Point: (e) A location, has no size.

4. Ray: (d) The portion of a line that starts at one point and goes off to infinity.

5. Vertex: (b) A point where two or more rays or "arms" of an angle meet.

Answer:

The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex]

Step-by-step explanation:

The expression is:

[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]

Collect the like terms as follows:

[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]

[tex]=(-a^{2}b+5a^{2}b-a^{2}b-a^{2}b+5a^{2}b+5a^{2}b)+(6ab+6ab+6ab)-(6a-6a-6a)-b-8[/tex]

[tex]=12a^{2}b+18ab+18a-b-8[/tex]

Thus, the final expression is [tex]12a^{2}b+18ab+18a-b-8[/tex]

The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex].

Answer:

The CORRECT answer is B

Step-by-step explanation:

Answer: D

Step-by-step explanation:

To express this number in scientific notation, we want to move the decimal so that it goes past the first nonzero integer. In this case, we would move it to the right 8 times.

6.7×10⁻⁸

The only reason why the 8 is negative is because when you write the scientific notation in standard form, you will need to move the decimal to the left in order to get 0.000000067. Negative means moving to the left. Therefore, 6.7×10⁻⁸ is our correct answer.