Let T(n) denote the nth term of a sequence t. if T(1) = 3, and T(n+1) = T(n) +5 for n>1, what are the first four terms of the sequence

Answer: first one is 12 then second one is 10.5 then the third 9 then the fourth one is 7.5

Step-by-step explanation:

Answer:

252 ft2 (squared)

Step-by-step explanation:

area= a x b

area= 12 x 21

area= 252 ft2 (squared)

Answer:

\(0 \leq P( P_B) \leq 1\)

\(P(P_B) = 0.17\)

Step-by-step explanation:

From the given question:

The probabilities are assigned using the Subjective method.

Let the probability that his roommate will choose rock be  \(P(R_B) = 0.28\)

Let the probability that his roommate will choose scissors be \(P(S_B) = 0.55\)

∴

\(P(R_B) + P(S_B) +P(P_B) = 1\)

\(0.28+ 0.55 + P(P_B) =1\)

\(0.83 + P(P_B) = 1\)

\(P(P_B) = 1 - 0.83\)

\(P(P_B) = 1 -0.83\)

\(P(P_B) = 0.17\)

So;

\(0 \leq P( P_B) \leq 1\)

\(P(P_B) = 0.17\)

The sum of the internal angles of the polygons are

a) The sum is A = 540°

b) The sum is A = 360°

c) The sum is A = 1800°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of the internal angles of a polygon be represented as A

Now , the value of A is

The sum of exterior angle of n polygon is = 360°

Now ,

a)

The number of sides of the polygon = 5 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 5 in the equation , we get

nθ = 180° ( 5 - 2 )

nθ = 180° x 3

nθ = 540°

b)

The number of sides of the polygon = 4 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 4 in the equation , we get

nθ = 180° ( 4 - 2 )

nθ = 180° x 2

nθ = 360°

c)

The number of sides of the polygon = 12 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 12 in the equation , we get

nθ = 180° ( 12 - 2 )

nθ = 180° x 10

nθ = 1800°

Hence , the sum of the internal angles of the polygon is solved

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Answer:

8

Step-by-step explanation:

that's a six tickets for $48 there for F1 tickets we don't know the price of each ticket...divide 48/6

Number of red roses a florist has = 49

Number of white roses a florist has = 63

To find the number of centerpieces with equal number of white and red roses we will find the greatest common factor of both the numbers,

49 = \(7\times 7\)

63 = \(7\times 9\)

GCF of 49 and 63 = 7

Therefore, number of centerpieces = 7

Now divide the total number of red roses by GCF to find the number of red flowers in each centerpiece.

Number of red roses in each centerpiece = 7

Similarly, number of white roses in each centerpiece = 9

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Move it to the left 4 times, move it up once

Answer:

1. c; 2. a; 3. b

Step-by-step explanation:

A(3,-1) translated to (3-4, -1+1)=(-1,0); then reflecting to x=1 (in this case, y doesn't change, and only x value change. x=-1 is 2 unit left side of x=1 line, so new reflected x value would be 2 unit right side of x=1 line, which is 3) gives (3,0).

B(7,1) --> (3,2) --> (-1,2)

C(5,-4) --> (1,-3)--> (1,-3)  

The original price of the snow blower is x = $574.99

Now, According to the question:

Let's know:

What is in a percentage?

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is one of the ways to represent a dimensionless relationship between two numbers; other methods include ratios, fractions, and decimals. Percentages are often denoted by the symbol "%" written after the number.

Boyds hardware just announced a 20% decrease in the price of their snow blower.

Snow blower model sells $459.99

That means that $459.99 is only 80% of the original price.

Since they got a 20% discount.

we can write, using x as the original price,

0.80x = 459.99

x = 459.99/.8

x = $574.99

Hence, The original price of the snow blower is x = $574.99

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One observation (210) given a test at the end of the movie to measure their recall is an outlier because it is above the fence above, as can be seen.

Data should first be arranged as follows in ascending order:

10, 22, 26, 27, 28, 31, 35, 40, 49, 57, 58, 61, 61, 62, 86, 86, 87, 88, 92, 97, 101, 210

There are n = 22 observations. Here n is even. Hence median is the mean of the middle two observations.

Median = (11 + 12) th observation /2 = (58 + 61)/2 = 59.5

We now divide the ordered data equally into two halves. Therefore, there are 11 observations in the lower section and 11 observations in the upper part.

The first quartile now corresponds to the median of the lower half.

Q1 = [(11 + 1)/2] the observation = 6th observation = 31

The third quartile represents the upper half part's median.

Q3 = [(11 + 1)/2] the observation = 6th observation = 87

IQR = Q3 - Q1 = 87 - 31 = 56

Lower fence = Q1 - 1.5 × IQR = 31 - 1.5 × 56 = -53

Upper fence = Q3 + 1.5 × IQR = 87 + 1.5 × 56 = 171

One observation (210) is an outlier since it is above the upper fence, as can be seen.

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Answer:

She has capped 4 correctly and broke 22.

Look at the paper for solution.

She needs a new job.

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The best way to represent histograms is by decreasing to increasing order.

The mean is the arithmetic mean and is calculated by adding a group of numbers and dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Given the values:

50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45

We have that:

(22+24+28+28+30+31+31+32+32+35+36+37+38+41+42+42+44+44+45+46+46+47+47+49+50)/25=37.88.

The average age that a large construction company wants to know is 38.

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Step-by-step explanation:

The given equations are

x2+y3=xy9

⟹xy2y+3x=xy9

⟹3x+2y=9 ........(i) 

x4+y9=xy21

⟹xy4y+9x=xy21

⟹9x+4y=21   ........(ii)  

Now (i)×3⟶9x+6y=27   .....(iii)

Subtracting (iii) from (ii),

−2y=−6⇒y=3.

Putting y=3 in (i),

3x+2×3=9⟹x=1.∴(x,y)=(1,3)

Answer:

i

Step-by-step explanation:

If D be a region bounded by a simple closed path C in the xy-plane, then the centroid of the quarter circle is  (4a/3π , 4a/3π)   .

In the question ,

it is given that D is the region bounded by a simple closed path C in the xy-plane .

the radius of the circle is = "a" ,

let the equation of the circle be x² + y² = a² ,

So , the area of the quarter circle is (A)  = (1/4)*πa²

The coordinate of the centroid x will be :

x = \(\frac{1}{2A} \int\limits x^{2} dy\)

x = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -y^{2} } \, dy\)

Simplifying further ,

we get ,

x = 2/πa² [{a²(a) - a³/3} - 0 ]

x = 2/πa² [a³ - a³/3 ]

x = 4a/3π

The coordinate of the centroid y will be :

y = \(\frac{1}{2A} \int\limits y^{2} dx\)

y = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -x^{2} } \, dx\)

Simplifying further ,

we get ,

y = 2/πa² [{a²(a) - a³/3} - 0 ]

y = 2/πa² [a³ - a³/3 ]

y = 4a/3π

Therefore , the coordinates of the centroid is (4a/3π , 4a/3π) .

The given question is incomplete , the complete question is

Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = \(\frac{1}{2A} \int\limits x^{2} dy\)  ,  y = \(\frac{1}{2A} \int\limits y^{2} dx\) ?  

Find the centroid of a quarter-circular region of radius a.

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Answer:

9 is 3rd -- 8 is last -- 10 is first --

Step-by-step explanation:

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(a) If x = 25 and dy/dt = 3, then dx/dt = 150

(b) If x = 9 and dx/dt = 9, then dy/dt = 3/2

As we have,

y=\(\sqrt{x}\)

So, x=y^2

Now differentiating the above expression with respect to t by using the chain rule

As, \(\frac{dx}{dt}=\frac{dx}{dy} \times \frac{dy}{dt}\)

So, differentiating y^2 with respect to y first.

\(\frac{dx}{dy}=\frac{d}{dy}(y^2)=\frac{1}{2{\sqrt{y}}}\)

Now when we differentiate y with respect to t, then the terms of y will be considered as constant.

We will get it as:

\(\frac{dx}{dt}=\frac{1}{2 \sqrt{9}} \frac{\mathrm{dx}}{\mathrm{dt}} \\\\\Rightarrow\frac{\mathrm{dx}}{\mathrm{dt}} =\frac{1}{2 \times 3} \times 9\\\Rightarrow \frac{\mathrm{dx}}{\mathrm{dt}} =\frac{3}{2}(a)\)

Calculating dx/dt

\(\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dy}}(y^2) \cdot \frac{\mathrm{dy}}{\mathrm{dt}}\\\\\frac{\mathrm{dx}}{\mathrm{dt}}=2y \cdot \frac{\mathrm{dy}}{\mathrm{dt}}\)

As the value of x = 25 and dy/dt = 3.

So, dx/dt = 2*25 *3 = 150

(b)

\(\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dx}}(\sqrt{\mathrm{x}}) \cdot \frac{\mathrm{dx}}{\mathrm{dt}}\\\\\frac{\mathrm{dy}}{\mathrm{dt}} =\frac{1}{2 \sqrt{\mathrm{x}}} \frac{\mathrm{dx}}{\mathrm{dt}}\)

As x = 9 and dx/dt = 9.

So, value of dy/dt will be \(\frac{dy}{dt}=\frac{1}{2{\sqrt{9}}}\times 9=\frac{9}{6}=\frac{3}{2}\)

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Answer:

c. 450

Step-by-step explanation:

i hope It's help...

The length of the line segment AB is 5 units.

Unfortunately, you haven't provided any information about PQ such as its location or any other data to help solve the question.

Therefore, it's impossible to determine the length of PQ using the given options. However, here is an explanation of how to find the length of a line segment using the distance formula, which may help you in solving similar questions in the future.

The distance formula is used to find the distance between two points in a coordinate plane, such as the length of a line segment. The formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where d is the distance, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

To use the distance formula, you first need to find the coordinates of the two points that make up the line segment. Then, substitute these coordinates into the formula and simplify to find the distance.

For example, let's say you have two points: A(1, 2) and B(4, 6), and you want to find the length of the line segment AB. Using the distance formula:

d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5

Remember, the distance formula can be applied to any two points in a coordinate plane to find the distance between them.

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Answer:

C

Step-by-step explanation:

When you add all rentals together you should get 125, after this you see what the problem is asking, in our case, the probability of not renting a drama, as said, our total is 125. When we look at how many dramas have been rented you get 25, simply, you divide 125 by 25, therefore you should get 5, so now, we know that there is a 1/5 possibility for getting it but because its not 5/5.

Thus, there should be 4/5 which is the probability of it not getting chosen.

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

Answer:

The answer is AC = 3.76

Step-by-step explanation:

CohCahToa

Coh: sin(theta) = Opp/Hyp

sin(theta°) = AC/AB

sin(70°) = AC/4

AC = 4*sin(70°)

AC ≈ 3.758770483

AC = 3.76

Answer:

AC = 3.76

Step-by-step explanation:

The opposing side of ∠B needs to be found, where the value of the hypotenuse is given. Take the sin ratio.

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

Answer:

we know that q=-18

So if we see the fraction below it says q/3

We know that q is -18

Therefore, you substitute it in for q and you get

-18/3 which equals -6

Answer:

It will take 5 seconds

The Capital Bank's option with a monthly compounding has a  higher accrued value of $3,849.75

What is accrued value?

The accrued value in this case means accumulated amount after 5 years, in other words, the future value of the investment under each of the two options.

Daily compounding:

FV=PV*(1+r/365)^(365*N)

FV=future value=unknown]

PV=initial investment=$3,475

r=interest rate=1.90%

N=number of years=5

FV=$3,475*(1+1.90%/365)^(365*5)

FV=$3,475*(1+0.0000520547945205479)^1825

FV=$3,475*(1.0000520547945205479)^1825

FV=$3,821.31

Monthly compounding:

FV=PV*(1+r/12)^(12*N)

FV=future value=unknown]

PV=initial investment=$3,475

r=interest rate=2.05%

N=number of years=5

FV=$3,475*(1+2.05%/12)^(12*5)

FV=$3,849.75

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Complete question:

General. Gavin wants to put $3,475 into a savings account when his daughter is born. Examine the account options below to determine which will have a higher accrued value at the end of 5 years.

Community Bank  1.90%   Compounds daily

Capital Bank  2.05%    Compounds monthly

7. Plodd) = 50%

8. Plone-digit number) = 30 percent

9. . P(negative) = 0

11. P(divisible by 6) = 17%

13. P(1 or 30) = 7%

7. The probability of selecting an odd number from 1 to 30 can be found by counting the number of odd numbers in that range, which is 15, and dividing it by the total number of balls, which is 30. Therefore,

Fraction: 15/30

Decimal: 0.50

Percent: 50%

8. The probability of selecting a one-digit number from 1 to 30 can be found by counting the number of one-digit numbers in that range, which is 9, and dividing it by the total number of balls, which is 30. Therefore,

Fraction: 9/30

Decimal: 0.30

Percent: 30%

9. There are no negative numbers in the range from 1 to 30, so the probability of selecting a negative number is 0.

Fraction: 0/30

Decimal: 0

Percent: 0%

11. To be divisible by 6, a number must be divisible by both 2 and 3. There are 15 numbers in the range from 1 to 30 that are divisible by 2, and 10 numbers that are divisible by 3. However, there are only 5 numbers that are divisible by both 2 and 3, which are 6, 12, 18, 24, and 30. Therefore,

Fraction: 5/30

Decimal: 0.17

Percent: 17%

13. The probability of selecting either 1 or 30 is the same as the sum of the probability of selecting 1 and the probability of selecting 30. Since there is only one ball with each of these numbers,

Fraction: 1/30 + 1/30 = 2/30

Decimal: 0.07

Percent: 7%

10. To end in 0, a number must be a multiple of 10, which means it must be one of the numbers 10, 20, or 30. Therefore,

Fraction: 3/30

Decimal: 0.10

Percent: 10%

12.  A two-digit number can be any number from 10 to 30, except for 10 and 30 themselves. Therefore,

Fraction: 18/30

Decimal: 0.60

Percent: 60%

14 The numbers greater than 17 but less than 26 are 18, 19, 20, 21, 22, 23, 24, and 25. Therefore,

Fraction: 8/30.

Decimal: 0.27

Percent: 27%

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Multiple the number of toys bought by c to equal the total spent:

A) 7c = $22.75

B) divide the total spent by the quantity bought:

C = 22.75/7

C = 3.25

Each toy cost $3.75

Answer: a=101 b=79 c=83 d=97

Answer:

a) The sample mean is of 49 and the sample standard deviation is of 11.7.

b) The range of the true mean at 90% confidence level is of 9.62 hours.

c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.

Step-by-step explanation:

Question a:

Sample mean:

\(\overline{x} = \frac{34+40+46+49+61+64}{6} = 49\)

Sample standard deviation:

\(s = sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7\)

The sample mean is of 49 and the sample standard deviation is of 11.7.

b)Determine the range of the true mean at 90% confidence level.

We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 2.0.150

The margin of error is:

\(M = T\frac{s}{\sqrt{n}}\)

In which s is the standard deviation of the sample and n is the size of the sample. So

\(M = 2.0150\frac{11.7}{\sqrt{6}} = 9.62\)

The range of the true mean at 90% confidence level is of 9.62 hours.

(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.

This is the confidence interval, so:

The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.

The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.

The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.