Determine whether the sequence an = 2^n-5^n/6^n is convergent. If it is, find its limit.

Answer:

Step-by-step explanation:

Cost = Area Cylinder body* cost * 0.03 cm^3 + Area of 2 lids*cost 0.06 of cm^3

Volume = 300 cm^3

Volume = Base *h  

Volume = pi * r^2 * h = 300

h = 300/(pi * r^2 )

Area material =  2*pi * r * h * 0.03 + 2 pi r^2 * 0.06

Area material = 0.06*pi * r * 300/(pi* r^2) + 0.12 * pi * r^2

dmaterial/dr = (-1)18 r^-2 + 0.12 pi * 2*r

dmaterial/dr = -18 r^-2 + 0.24 pi * r

The minimum occurs when the right side = 0

18/r^2 = 0.24 *pi r

18 = 0.24*pi * r^3

18/(0.24 * pi) = r^3

23.89 = r^3

cube root (23.89) = cuberoot(r^3)

r = 2.88 cm

h = 300/pi * r^2

h = 300/(3.14 * 2.88^2)

h = 11.52

This isn't much of a check but we can try it.

Volume = 3.14 * 2.88^2 * 11.52

Volume = 302.01 which considering all the rounding is pretty close.

Here's a graph that confirms my answer.

The speed of the person located at earth's equator traveling due to rotation is, 1670 km/hr.

The person at equator traveling due to it's rotation will cover one complete round of earth in 24 hours. Hence the distance travelled is the circumference of the earth.

The radius of the earth is, 6 378.1 kilometers.

The circumference can be calculated as, 2×π×R

Using R = 6 378.1 kilometers,

Circumference = 2×π×6 378.1 kilometers

Circumference = 40090.91 kilometers.

The distance traveled = 40090.91 kilometers.

Time taken is 24 hrs.

Hence speed = distance/time

Speed = 40090.91/24

Speed = 1670 km/hr

The speed of the person is 1670 km/hr.

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Answer:

C

Step-by-step explanation:

$101 times 6 is $606...

Answer:

90 is the answer

Step-by-step explanation:

360° / 4= 90°

Amy will choose the second restaurant to purchase pizza. Because the second one is cheaper.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given,

the first restaurant charges a delivery fee of $6 for the entire purchase and $13 per pizza.

The second restaurant has no delivery fee and charges $16 per pizza.

And Amy will choose between two restaurants to purchase pizzas for her party.

The cost of one pizza of the first restaurant:

Cost = delivery fee + price of one pizza

        = $6 + $13

         = $19

The cost of one pizza of the second restaurant:

Cost = delivery fee + price of one pizza

          = $0 + $16

         = $16

And 16< 19

The second restaurant is cheaper.

Therefore, Amy will choose the second restaurant to purchase pizza.

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To eliminate x in the given system of equations, the equation y = x + 8 should be multiplied by 1/3. This multiplication allows us to match the coefficient of x in both equations, simplifying the elimination process.

Let's calculate the reciprocal of the coefficient of x in Equation 2 and determine the number by which Equation 1 should be multiplied to eliminate x:

Equation 1: y = x + 8

Equation 2: y = 3x - 11

The coefficient of x in Equation 2 is 3. The reciprocal of 3 is 1/3.

To eliminate x, we need to multiply Equation 1 by 1/3.

Multiplying Equation 1 by 1/3:

(1/3) * (y = x + 8)

This gives us:

1/3 * y = (1/3) * x + (1/3) * 8

Simplifying:

y/3 = (1/3)x + 8/3

Now, we have two equations:

y = 3x - 11   (Equation 2)

y/3 = (1/3)x + 8/3   (Equation 1, multiplied by 1/3)

By multiplying Equation 1 by 1/3, we have eliminated x from Equation 1.

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The cash price of the bond is $10,898.92.The accrued interest is $315.32.

The cash price of the bond, we need to determine the present value of the bond's future cash flows. The bond has a face value (redeemable at par) of $22,000 and a coupon rate of 5.3%. Since the interest is payable semi-annually, each coupon payment would be half of 5.3%, or 2.65% of the face value. The bond matures on May 12, 2008, and the purchase date is June 07, 2001, which gives a total of 28 semi-annual periods.

Using the formula for present value of an annuity, we can calculate the present value of the coupon payments. The yield is 9.8% compounded semi-annually, so the semi-annual discount rate is half of 9.8%, or 4.9%. Plugging in the values into the formula, we get:

Coupon payment = $22,000 * 2.65% = $583

Present value of coupon payments = $583 * [(1 - (1 + 4.9%)^(-28)) / 4.9%] = $10,315.32

To calculate the present value of the face value, we need to discount it to the present using the same discount rate. Plugging in the values, we get:

Present value of face value = $22,000 / (1 + 4.9%)^28 = $5883.60

Finally, we add the present value of the coupon payments and the present value of the face value to obtain the cash price of the bond:

Cash price = Present value of coupon payments + Present value of face value = $10,315.32 + $5,883.60 = $10,898.92.

Accrued interest refers to the interest that has accumulated on the bond since the last interest payment date. In this case, the last interest payment date was on June 7, 2001, and the purchase date is also June 7, 2001, so no interest has accrued yet.

The accrued interest can be calculated by multiplying the coupon payment by the fraction of the semi-annual period that has elapsed since the last interest payment. Since no time has passed between the last interest payment and the purchase date, the fraction is 0. Thus, the accrued interest is $583 * 0 = $0.

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Hi there!

nickels:19

We know that there is only nickels and dimes in his coin collection..

1.Multiply two terms:

\(10\)·\(10=1.00\)

Then there would be 20 nickels but 1+1=2 not 2.05.

2.Multiply the terms:

\(11\)·\(10=1.10\)

\(19\)·\(5=0.95\)

3.Combine the two terms:

\(1.10+0.95=2.05\)

Therefore, there would be 19 nickels...

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer:

See below

Step-by-step explanation:

You can always plug in x's and solve for y.

There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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Answer:

∠O = 95°

Step-by-step explanation:

since ∠Q = 85°, arc NOP = 2(85°) = 170°

arc PQN = 360° - arc NOP

arc PQN = 360° - 170° = 190°

∠O = 1/2(arc PQN) = 1/2(190°) = 95°

Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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Let the cost of a dozen apples be x and the cost of a loaf of bread be y.As per the given information, a dozen apples and 2 loaves of bread cost $5.76.Thus we can write the first equation as:

12x+2y = 5.76 .....(1)  Half a dozen apples and 3 loaves of bread cost $7.68.Thus we can write the second equation as:6x+3y = 7.68 .....(2)Now, let's solve for the value of y, which is the cost of a loaf of bread, using the above two equations.

In order to do so, we'll first eliminate x. For that, we'll multiply equation (1) by 3 and equation (2) by -2 and then add the two equations. This is given by:36x + 6y = 17.28 .....(3)-12x - 6y = -15.36 .....(4)Adding equations (3) and (4), we get:

24x = 1.92Thus,x = 1.92/24 = 0.08 Substituting the value of x in equation (1), we get:12(0.08) + 2y = 5.76 => 0.96 + 2y = 5.76 => 2y = 5.76 - 0.96 = 4.8Therefore,y = 4.8/2 = $2.40Hence, the cost of a loaf of bread is $2.40.

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Answer:

A= 347.65 B= 43.5

Step-by-step explanation:

A : 347.65

B : 43.5

244.5

+ 1 0 1. 1 5

= 347.65

68.2

- 24.7

= 43.5

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

Step-by-step explanation:

The answer would be 24:600. One student is absent so there are 24 students present. The number of beads is still 600, so the ratio is 24:600 which simplifies to 1:25.

Answer:

The water level is rising at the rate 0.238 cm per second

Step-by-step explanation:

Let the radius and height of water at time t be r and h respectively.

Height of cup =H= 8 cm

Radius of cup = R = 4 cm

By symmetry

\(\frac{r}{h}=\frac{4}{8} \\r=\frac{1}{2}h ---1\)

Volume of water at time t , \(V= \frac{1}{3} \pi r^2 h\)

\(\frac{dV}{dt}=\frac{1}{3}\pi 2r \frac{dr}{dt} h+\frac{1}{3} \pi r^2 \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{3}\pi r (2 \frac{dr}{dt} h+ r \frac{dh}{dt})\)

With 1

\(\frac{dr}{dt}=\frac{1}{2} \frac{dh}{dt}\)

So,

\(\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) (2 (\frac{1}{2} \frac{dh}{dt}h)+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( \frac{dh}{dt}h+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( h+\frac{1}{2}h) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi h(\frac{3h}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi (\frac{3h^2}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{12}\pi 3h^2 \frac{dh}{dt}\)

We are given that Water is poured into a conical paper cup at the rate of 3 cubic centimeters  (cm) per second (s).

We are supposed to find how fast the water level is rising at the instant the water is 4 cm deep.

So,\(\frac{1}{12}\pi 3(4)^2 \frac{dh}{dt}=3\\\frac{dh}{dt}=\frac{3 \times 12}{\pi 3(4)^2 }=0.238\)

Hence the water level is rising at the rate 0.238 cm per second

The radius in terms of height is \(\mathbf{r =\frac 12h}\), while the water level increases at 0.239 cm per second when the height is 4 cm

(a) Radius in terms of height

The given parameters are:

\(\mathbf{h = 8cm}\) --- height

\(\mathbf{r = 4cm}\) --- radius

The above parameters can be written as:

\(\mathbf{r :h =4cm : 8cm}\)

\(\mathbf{r :h =4 : 8}\)

Express as fractions

\(\mathbf{\frac rh =\frac 48}\)

\(\mathbf{\frac rh =\frac 12}\)

Multiply both sides by h

\(\mathbf{r =\frac 12h}\)

(b) How fast the water is rising

The volume of a cone is:

\(\mathbf{V = \frac 13 \pi r^2h}\)

Differentiate with respect to time

\(\mathbf{V' = \frac 13 \pi(2rh\ \frac{dr}{dt} + r^2\frac{dh}{dt})}\)

When the water is 4cm deep, then the radius is 2cm using \(\mathbf{r =\frac 12h}\)

So, we have:

\(\mathbf{V' = \frac 13 \pi(2 \times 2 \times 4\times \frac{dr}{dt} + 2^2\frac{dh}{dt})}\)

\(\mathbf{V' = \frac 13 \pi(16 \frac{dr}{dt} + 4\frac{dh}{dt})}\)

Also, we have:

\(\mathbf{r =\frac 12h}\)

Differentiate with respect to time

\(\mathbf{\frac{dr}{dt} = \frac{1}{2}\frac{dh}{dt}}\)

So, we have:

\(\mathbf{V' = \frac 13 \pi(16 \times \frac{1}{2}\frac{dh}{dt} + 4\frac{dh}{dt})}\)

\(\mathbf{V' = \frac 13 \pi(8\frac{dh}{dt} + 4\frac{dh}{dt})}\)

\(\mathbf{V' = \frac 13 \pi(12\frac{dh}{dt})}\)

Expand

\(\mathbf{V' = 4\pi\frac{dh}{dt}}\)

The volume increases at 3 cm^3 per second.

So, we have:

\(\mathbf{3 = 4\pi\frac{dh}{dt}}\)

Divide both sides by 4

\(\mathbf{0.75 = \pi\frac{dh}{dt}}\)

Divide both sides by pi

\(\mathbf{0.239 = \frac{dh}{dt}}\)

Rewrite as:

\(\mathbf{\frac{dh}{dt} = 0.239}\)

Hence, the water level increases at 0.239 cm per second when the height is 4 cm

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Answer:

\(a) n =\dfrac{c}{d}\\\\\\b) b= 2A -a\\\\c) m_1=\dfrac{Fr^2}{Gm_2}\)

d) z = 10

Step-by-step explanation:

   a)

         \(\sf d = \dfrac{c}{n}\\\\\text{Mulitply the entire equation by 'n',}\\\\n*d=n*\dfrac{c}{n}\\\\nd =c\\\\\text{Now, divide the entire equation by 'd',}\\\\n =\dfrac{c}{d}\)

b)

            \(\sf A = \dfrac{a+b}{2}\\\\\text{Multiply the entire equation by 2,}\\\\2*A = 2*\dfrac{a+b}{2}\\\\2A = a+b\\\\\text{Now subtract 'a' from both sides,}\\\\2A - a = b\\\\\boxed{b=2A - a}\)

c)

               \(\sf F =\dfrac{Gm_1m_2}{r^2}\)

               Multiply the entire equation by r²,

             \(\sf Fr^2=r^2*\dfrac{Gm_1m_2}{r^3}\\\\Fr^2=Gm_1m_2\)

             Divide the entire equation by Gm₂,

            \(\sf \dfrac{Fr^2}{Gm_2}=m_1\\\\\boxed{m_1=\dfrac{Fr^2}{Gm_2}}\)

D) A = 7 ; y =4

Substitute in the equation and find the other number.

          \(\sf A = \dfrac{1}{2}(y+z)\\\\7=\dfrac{1}{2}(4+z)\\\\Multiply \ both \ sides \ by 2,\\\\7*2 = 4 +z\)

             14 = 4 + z

Subtract 4 from both sides,

        14 - 4 = z

               z = 10

The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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Answer:

15-6+10= 19

Step-by-step explanation:

Answer:

19° F

Step-by-step explanation:

This is the answer because:

1) If the temperature fell by 6° F, you would do 15° F -  6° F which equals 9° F

2) And then it rose by 10° F, you would basically add 9° F with 10° F which equals 19° F

3) Finally, the equation is (15° F -  6° F ) + 10° F which equals to 19° F

Hope this helps!

Answer:

10) -1.5

11) 1

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

The bi-weekly job!

Step-by-step explanation:

With a bi-weekly salary, your employer pays you every second week.

Since there are 52 weeks in a year: 52/2 = 26

This means you will get a total of 26 pay checks a year.

26 x 1200 = 31200

Therefore, you earn $31200 a year if you are paid bi weekly.

With a semi-monthly salary your employer pays you twice a month.

Since there are 12 months in a year: 12 x 2 = 24

This means you get a total of 24 pay checks a year.

24 x 1250 = 30000

Therefore, you earn $30000 a year if you are paid semi-monthly.

31200 > 30000

Therefore, you earn more on a bi-weekly salary.

The surface area of the regular pyramid is equal to 1209 m² to the nearest whole number. The first option is correct.

Area of a regular polygon = 1/2 × apothem × perimeter

Area of the hexagon = (1/2 × 8.5√3 × 102) m²

Area of the hexagon = 750.8440 m²

Area of one triangle face = (1/2 × 17 × 9) m²

Area of one triangle face = 76.5 m²

Area of six triangle face = (76.5 × 6) m²

Area of six triangle face = 459 m²

Surface area of the regular pyramid = 750.8440 m² + 459 m²

Surface area of the regular pyramid = 1209.8440 m²

Therefore, the surface area of the regular pyramid is equal to 1209 m² to the nearest whole number. The first option is correct.

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Answer: w=10.35

Step-by-step explanation:

26.9+12+w=49.25

38.9+w=49.25

w=49.25-38.9

w=10.35

Step-by-step explanation:

I hope its help you

Kristen will do both the exercises together, 6 days from now.

We are told that Kristen goes hiking every 3 days and swimming every 2 days.

The day she will do both the exercises together will be the day which is a multiple of the LCM of 2 and 3.

Now, since 2 and 3 are both prime numbers, their LCM (lowest common multiple) will simply be their product, which comes out to be-

LCM (2, 3) = 2 * 3

= 6

Thus, Kristen will do both the exercises on every 6th day.

Thus, if she went for both swimming and hiking today, she will do both the exercises together again 6 days from now.

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Answer:

7 * 4 / 2 = 28/2 = 14

Step-by-step explanation:

You are timed. I will just give you the formula where its multiplying the Diagonals and dividing by 2.

x= -4 w= 1 z= -3 y= 5

This is the answer!

Answer:

It may be 834.5m²……..….…………