Find an equation for the nth term of the arithmetic sequence. -15, -6, 3, 12, ...

an = -15 + 9(n + 1)
an = -15 x 9(n - 1)
an = -15 + 9(n + 2)
an = -15 + 9(n - 1)

Answer:

B) ∫₂⁵ ∜x dx

Step-by-step explanation:

The factor is 3/n, so b − a = 3

The expression under the radical is 2 + 3k/n, so a = 2.  Therefore, b = 5.

The function is f(x) = ∜x.

Plugging into a definite integral:

∫₂⁵ ∜x dx

Answer:

9

Step-by-step explanation:

Number of tulips per row has to be a factor of the number of available tulips.

Red tulips: 45 = 3×3×5

Yellow tulips: 63 = 3×3×7

Highest no. of tulips each row is 9 (3×3 = 9)

The sale price of a black coat is $ 2.4 less than sale price of a blue coat

Solution:

Given that,

Bluecoat usually cost $48 but it's on sale for 25% off

Cost price of blue coat = $ 48

Discount = 25 %

Therefore, discount price is given as:

Discount price = 25 % of 48

[tex]Discount\ price = 25 \% \times 48\\\\Discount\ price = \frac{25}{100} \times 48\\\\Discount\ price = 0.25 \times 48\\\\Discount\ price =12[/tex]

Thus sales price is given as:

Sales price = cost price - discount price

Sales price = 48 - 12

Sales price = 36

Thus sales price of blue coat is $ 36

Black coat is really cost $56 but it's on sale for 40%

Cost price of black coat = $ 56

Discount = 40 %

Therefore, discount price is given as:

Discount price = 40 % of 56

[tex]Discount\ price = 40 \% \times 56\\\\Discount\ price = \frac{40}{100} \times 56\\\\Discount\ price = 0.4 \times 56\\\\Discount\ price =22.4[/tex]

Thus sales price is given as:

Sales price = cost price - discount price

Sales price = 56 - 22.4

Sales price = 33.6

Thus sales price of black coat is $ 33.6

How much less is the sale price of a black coat in the sale price of a blue coat

Sales price of blue coat - sales price of black coat = 36 - 33.6 = 2.4

Thus sale price of a black coat is $ 2.4 less than sale price of a blue coat

Answer:

2.40

Step-by-step explanation:

Answer: the 32nd term is - 3

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 15.6

d = 15 - 15.6 = 14.4 - 15 = - 0.6

n = 32

The explicit formula for the arithmetic sequence is

Tn = 15.6 - 0.6(n - 1)

We want to determine the value of the 32nd term, T32. Therefore,

T32= 15.6 - 0.6 (32 - 1)

T32 = 15.6 - 18.6

T32 = - 3

Answer:    [tex]\dfrac{12}{13}[/tex]

Step-by-step explanation:

Let A = he known the answer then A' = he guess the answer.

B = he answered it correctly

As per given , we have

[tex]P(A)=\dfrac{3}{4}\ \ ,\ \ P(A')=\dfrac{1}{4}[/tex]

[tex]P(B|A)=1[/tex]

[tex]P(B|A')=\dfrac{1}{4}[/tex]

By Bayes theorem , we have

[tex]P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A')P(A')}\\\\ P(A|B)=\dfrac{1\times\dfrac{3}{4}}{1\times\dfrac{3}{4}+\dfrac{1}{4}\times\dfrac{1}{4}}\\\\= \dfrac{12}{13}[/tex]

The probability that the student knows the answer given that he answered it correctly is  [tex]\dfrac{12}{13}[/tex] .

Answer:

EC = 1 ft

Step-by-step explanation:

DE // BC and AC and AD are transversal lines

∴ ∠E≅∠C  ⇒ corresponding angles are congruent

  ∠D≅∠B  ⇒ corresponding angles are congruent

 ∠A≅∠A   ⇒ Reflexive property

∴Δ ADE is similar to ΔABC  by AA postulate

So, The corresponding sides are in proportion.

[tex]\frac{AC}{AE} = \frac{AB}{AD}[/tex]

AE = 4 ft , AD = 8 ft , AB = 8 + 2 = 10 ft

AC = AE * AB/AD = 4*10/8 = 40/8 = 5 ft

EC = AC - AE = 5 - 4 = 1 ft

So, the Length of EC = 1 ft.

The equation after the sum symbol is written in terms of ar^k-1

A = 12 and r = 0.7

To see if it converges use the formula a /1-r, if the answer is greater than 1 it converges, if it’s less than 1 it diverges

12 / 1 - 0.7 = 12/0.3 = 40

The answer C. Converges, 40

Answer:

No, it is not.

Step-by-step explanation:

The set [tex] C = \mathbb{N} \times \mathbb{N}[/tex] contains every ordered pair of Natural numbers, while B only contains those pairs in which both values in each entry are the same. Therefore, C is a bigger set than B, but B is not equal to C because for example C contains [tex][1] \times [2] [/tex] and B doesnt because 1 is not equal to 2.

Answer:

B. This is an example of causation because the application of fertilizer caused the plant to improve its leaf color.

Answer:

B

Step-by-step explanation:

Answer:  B. [tex]\dfrac{1}{98}[/tex].

Step-by-step explanation:

Given : A hat contains four red marbles, two blue marbles, seven green marbles, and one orange marble.

Total marbles = 4+2+7+1 = 14

P(Blue)= [tex]\dfrac{2}{14}=\dfrac{1}{7}[/tex]

P(Orange) = [tex]\dfrac{1}{14}[/tex]

if we randomly select two marbles , then the probability of selecting  one will be orange and one will be blue marble =  P(Blue) x P(Orange)  [both events are independent]

[tex]=\dfrac{1}{7}\times\dfrac{1}{14}=\dfrac{1}{98}[/tex]

Hence, the probability that one will be orange and one will be blue is  [tex]\dfrac{1}{98}[/tex].

Therefore , the correct answer is  B. [tex]\dfrac{1}{98}[/tex].

Answer:

Step-by-step explanation:

Answer: I’m pretty sure $86

Step-by-step explanation:

If I’m correct it would just be $1,204 divided by 14 pairs of shoes.

9 pairs of jeans and 12 shirts were sold on each day.

Let x be the number of jeans sold and y be the number of shirts sold. From the given information, we can form two equations:

25x + 18y = 441 (equation 1)

20x + 20y = 420 (equation 2)

Multiplying equation 2 by 5, we get 100x + 100y = 2100. Subtracting this equation from equation 1, we get -75x - 82y = -1659. Solving this equation, we find that x = 9 and y = 12.

Therefore, 9 pairs of jeans and 12 shirts were sold on each day.

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Answer:

Definition: Two sets are equal if they contain the

same elements. I.e., sets A and B are equal if

∀x[x ∈ A ↔ x ∈ B].

Notation: A = B.

Recall: Sets are unordered and we do not distinguish

between repeated elements. So:

{1, 1, 1} = {1}, and {a, b, c} = {b, a, c}.

Definition: A set A is a subset of set B, denoted

A ⊆ B, if every element x of A is also an element of B.

That is, A ⊆ B if ∀x(x ∈ A → x ∈ B).

Example: Z ⊆ R.

{1, 2} ⊆ {1, 2, 3, 4}

Notation: If set A is not a subset of B, we write A 6⊆ B.

Example: {1, 2} 6⊆ {1, 3}

Answer:

Part a: The transformation matrix is the clockwise rotation matrix of π/4.

Part b: The hyperplane would move towards the mean of class 1.

Part c: The distance will remain in the Euclidean Space  due to the rotation transformation only.

Step-by-step explanation:

As the complete question is not available, the question is searched online and a reference question is obtained which has 3 parts as follows:

Part a:

The decision boundary  after transformation coincides with the line x1 = x2, the two class means must lie on a line that is normal to the decision boundary, i.e. on x1 = −x2. This implies that the transformation matrix Γ is a clockwise rotation transformation of π/4, given as

                                               [tex]\Gamma=\left[\begin{array}{cc}\frac{\sqrt{2}}{2}&\frac{\sqrt{2}}{2}\\\frac{-\sqrt{2}}{2}&\frac{\sqrt{2}}{2}\end{array}\right][/tex]

Part b:

If the prior probability of class 0 was increased after transformation, then the decision boundary of BDR would still have the same normal as before,  i.e.,[tex]w=(1/\sqrt{2},-/\sqrt{2})^T[/tex], but move toward the mean of class 1.

Part c:

Noting that

[tex]||\bold{T}_x-\bold{T}_y||^2=(x-y)^T \bold{T}^T\bold{T}(x-y)\\||\bold{T}_x-\bold{T}_y||^2=(x-y)^T(x-y)\\||\bold{T}_x-\bold{T}_y||^2=||x-y||^2[/tex]

This indicates that the distance is still the same and is in Euclidean space. This is due to the fact that rotation transformations does not affect the distances between the points.

Answer:

C. The chance to be selected into the sample was the same for all veterinarians

The statement that is NOT correct is D. The sample was a volunteer sample.

The statement that is NOT correct is D. The sample was a volunteer sample.

The given scenario describes a census survey, where questionnaires were sent to all veterinarians treating large animals. In a census survey, every member of the target population is included, so there is no sampling involved. Hence, there is no opportunity for the sample to be a volunteer sample. Therefore, option D is the incorrect statement.

A low response rate, as mentioned in option A, can lead to response bias because the respondents who choose to participate may have different characteristics than those who do not respond. The intended sample, as mentioned in option B, was the target population of veterinarians treating large animals. And option C is correct since all veterinarians on the list had an equal chance of being selected as part of the survey.

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Answer:

3

Step-by-step explanation:

Answer:

a. a × b > 0 ∀ a,b ∈ R : a,b < 0

b. a - a = 0 ∀ a ∈ R

Step-by-step explanation:

a. Let a and b be the numbers. Since it says product of two numbers is greater than zero, we write a × b > 0. Since a and b are real numbers, we write a,b ∈ R where ∈ denotes element of a set and R is the set of real numbers. We then use the connective ∀ which denotes "for all" to join a × b > 0 with a,b ∈ R. So, we write a × b > 0 ∀ a,b ∈ R. Since a and b are negative, we write a,b < 0. We now use the connective : which denotes "such that" to combine a × b > 0 ∀ a,b ∈ R with a,b < 0 to give a × b > 0 ∀ a,b ∈ R : a,b < 0. So, the expression is

a × b > 0 ∀ a,b ∈ R : a,b < 0

b. Let a be the number. Since we are looking for a difference, we write a - a. Since it is equal to zero, we write a - a = 0. Since a is an element of real numbers,R, we write a ∈ R, where ∈ denotes "element of". So, a ∈ R denotes a is an element of real numbers R. We combine these two expressions with the connective ∀ which denotes "for all" to give a - a = 0 ∀ a ∈ R. So, the expression is

a - a = 0 ∀ a ∈ R

The mathematical statements given are translated into logical expressions with predicates, quantifiers, logical connectives, and mathematical operators. The first statement is written as ∀x∀y ((x < 0 ∧ y < 0) → P(x, y)), and the second as ∀x (D(x, x)).

The mathematical statements can be expressed using predicates, quantifiers, logical connectives, and mathematical operators as follows:

For the statement 'The product of two negative real numbers is positive':

Let the predicate P(x, y) represent 'the product of x and y is positive', where x and y are real numbers. Then, the statement can be written as:

∀x∀y ((x < 0 ∧ y < 0) → P(x, y))

This translates to: 'For all real numbers x and y, if x and y are both negative, then the product of x and y is positive.'.

For the statement 'The difference of a real number and itself is zero':

Let D(x, y) be a predicate that states 'the difference of x and y is zero'. Then, the statement can be formulated as:

∀x (D(x, x))

Which reads as: 'For all real numbers x, the difference of x and itself is zero.'.

Therefore,  The first statement is written as ∀x∀y ((x < 0 ∧ y < 0) → P(x, y)), and the second as ∀x (D(x, x)).

Answer:

  65°

Step-by-step explanation:

Since the high is given, it is convenient to use that value with a cosine function to model the temperature. The function will be ...

  T = A + Bcos(C(x-D))

where A is the average temperature, B is the difference between the high and the average, C is π/12, reflecting the 24-hour period, and D is the time at which the temperature is a maximum. "x" is hours after midnight.

We have chosen to use a 24-hour clock with x=16 at 4 pm. Then the value of T at 9 am is ...

  T = 70 +20cos((π/12(9 - 16)) = 70 +20cos(7π/12) ≈ 64.824

The temperature at 9 am is about 65°.

Final answer:

To find the temperature at 9 AM, a sinusoidal function is constructed with an amplitude of 20 degrees, a vertical shift of 70 degrees, and a phase shift adjusted for a high at 4 PM. Plugging in the time value of 9 AM into the function, it is determined that the temperature at 9 AM is approximately the same as the average or midline temperature, which is 70 degrees.

Explanation:

To find the temperature at 9 AM using a sinusoidal function, we first identify essential characteristics of the function. The maximum temperature (high) of 90 degrees occurs at 4 PM (which we'll take as 16 hours on a 24-hour clock) and the average temperature for the day is 70 degrees, which is also the midline of the sinusoidal function. Since this is a typical daily temperature cycle, we assume that the minimum temperature occurs 12 hours after the maximum temperature. Thus, the temperature will have a periodicity of 24 hours. The amplitude of the temperature variation will be the difference between the high temperature and the average temperature (which is 20 degrees in this case).

The sinusoidal function can be written in the form:

T(t) = A · sin(B(t - C)) + D

Where:

C is the phase shift (16 hours for 4 PM)

Using this information, the sinusoidal function for temperature throughout the day is:

T(t) = 20 · sin((2π/24)(t - 16)) + 70

We then plug in t = 9 (for 9 AM), and calculate the temperature:

T(9) ≈ 20 · sin((2π/24)(9 - 16)) + 70

Which gives us, to the nearest degree:

Temperature at 9 AM ≈ 70 degrees.

Since the value of the sine function ranges from -1 to 1, at 9 AM (7 hours before the maximum temperature at 4 PM), the sine value would be negative indicating that the temperature is rising from the minimum towards the average. However, due to the characteristics of sine, the temperature at 9 AM will actually be the same as the temperature at 19 hours (7 PM), which is also 70 degrees.

Answer:

the answer is g21T

Step-by-step explanation:

a3z, b6Y, C9X, d12W, e15V, f18U next step in the series is E. g24t

A mathematical series consists of a pattern in which the next term is obtained by adding the two terms in-front. An example of the Fibonacci number series is: 0, 1, 1, 2, 3, 5, 8, 13, … For instance, the third term of this series is calculated as 0+1+1=2.

1) Arithmetic Sequences.

2) Geometric Sequences.

3) Exponent Sequences.

4) Two-Stage Sequences.

5) Mixed Sequences.

6) Alternating Sequences.

7) Fibonacci Sequences.

8) A Combination of Sequences' Types.

In mathematics, a series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers, but much more generality is possible

You can find the right answer in number series by taking the difference between consecutive pairs of numbers, which form a logical series. In this example, the differences between succeeding pairs of numbers are 1,2, 4, 8, 16, and 32. So, the next difference must be 64.

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Answer: he had 68 cherries in the start

Step-by-step explanation:

In the beginning, Zak had 61 cherries and he gave away 18 cherries to Tim and 18 cherries to Janet.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Cherries are in a bag that Zak possesses. Tim and Janet each received 18 cherries from him. He currently has 25 cherries.

Let's assume the number of cherries Zak had at the start "x".

Zak gave away 18 cherries to Tim and 18 cherries to Janet, so he now has x - 18 - 18 = 25 cherries.

You can solve this equation for x by adding 18 + 18 to both sides, which gives you x = 25 + 18 + 18.

This simplifies to x = 61, so Zak had 61 cherries at the start.

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Answer:

3,604,389

Step-by-step explanation:

Monthly payment P = [tex]\frac{a}{[(1+r)^{n} - 1] / [r(1+r)^{n}] }[/tex]

where a = total loan amount, r = periodic rate, n = number of payment periods

a = 500,000 ; r = 0.12 ; n = (5 x 12) = 60 months

P = [tex]\frac{500000}{[(1+0.12)^{60} - 1] / [0.12 (1+0.12)^{60} ] }[/tex]

P = [tex]\frac{500000}{(896.597) / (107.712)}[/tex]

p = 60,073.151

Total amount paid = 60073.151 x 60 = 3,604,389

Final answer:

Liza will have to pay a monthly amount of P2,997.75 for a loan of P500,000 at a 12% interest rate compounded monthly over 5 years. The total amount paid at the end of the term will be P179,865.

Explanation:

To determine the total sum Liza will pay for a loan of P500,000 with an interest rate of 12% compounded monthly over 5 years, we first need to calculate the monthly payment she would need to make. The problem is essentially asking to find the annuity payment for a present value, which can be calculated using the formula for present value of an ordinary annuity:

PV = PMT * [1 - (1 + r)-n] / r

Where:

PV = Present Value of the annuity (P500,000 in this case)

PMT = Monthly payment

r = Monthly interest rate (12% per year compounded monthly, so 0.12/12 per month)

n = Total number of payments (5 years × 12 months/year = 60 payments)

First, we calculate the monthly interest rate:

r = 0.12 / 12 = 0.01 or 1%

Now, setting up the equation:

500,000 = PMT * [1 - (1 + 0.01)-60] / 0.01

We find that PMT = 500,000 / 166.7916 (Using the present value factor derived from the reference information)

PMT = P2997.752

Therefore, the monthly payment Liza has to make is P2,997.75. To find the total sum paid after 5 years:

Total Sum = Monthly Payment * Number of Payments

Total Sum = P2,997.75 * 60 = P179,865

Answer:

Claire traveled for 9 days.

Step-by-step explanation:

Given:

Total Distance traveled = 701 miles

Distance traveled each day = 80 miles

Distance traveled on last day = 61 miles

We need to find the number of days Claire traveled.

Solution:

Let the number of days Claire traveled be denoted by 'd'.

Now we can say that;

Total Distance traveled is equal to sum of Distance traveled each day multiplied by number of days and Distance traveled on last day.

framing in equation form we get;

[tex]80d+61=701[/tex]

Now Subtracting both side by 61 using Subtraction Property of Equality we get;

[tex]80d+61-61=701-61\\\\80d = 640[/tex]

Now Dividing both side by 80 we get;

[tex]\frac{80d}{80}=\frac{640}{80}\\\\d=8[/tex]

Hence Claire traveled 80 miles in 8 days and 61 miles on last day making of total 9 days of travel.

The probability of having fewer than 4 successes (x < 4) in 8 independent trials with a success probability of 0.6 is 0.1758.

We have,

The binomial probability formula:

[tex]P(x) = (^nC_x) p^x (1-p)^{n-x}[/tex]

Where:

P(x) is the probability of x successes

n is the number of trials

p is the probability of success

nCx is the binomial coefficient, which represents the number of ways to choose x successes from n trials

For the given parameters:

n = 8

p = 0.6

x < 4

For x = 0:

[tex]P(0) = (^8C_0) (0.6^0) (1-0.6)^{8-0}\\= (1) (1) (0.4)^8[/tex]

= 0.0016

For x = 1:

[tex]P(1) = (^8C_1) (0.6^1) (1-0.6)^{8-1}\\= (8) (0.6) (0.4)^7[/tex]

≈ 0.0092

For x = 2:

[tex]P(2) = (^8C_2) (0.6^2) (1-0.6)^{8-2}\\= (28) (0.6^2) (0.4)^6[/tex]

≈ 0.0412

For x = 3:

[tex]P(3) = (^8C_3) (0.6^3) (1-0.6)^{8-3}\\= (56) (0.6^3) (0.4)^5\\= 0.1238[/tex]

Now, sum up these probabilities to find the probability of x < 4:

P(x < 4) = P(0) + P(1) + P(2) + P(3)

≈ 0.0016 + 0.0092 + 0.0412 + 0.1238

≈ 0.1758

Therefore,

The probability of having fewer than 4 successes (x < 4) in 8 independent trials with a success probability of 0.6 is 0.1758.

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Answer:

Step-by-step explanation:

2,2+1,2+1+3,2+1+3+5,...

2,3,6,11,18,27

Answer:

$151,800

Step-by-step explanation:

For the publisher, the expected revenue is $26.40 per copy. For 225,000 copies, the revenue is [tex]225000\times26.40 = 5,940,000[/tex]

The expenses incurred by the publisher are as follows:

Cost of 1 print = $3.75

Cost of 225,000 prints = [tex]225000\times3.75 = 843,750[/tex]

Editing/Design = $27,500

Publicity/Advertising/Administrative = $135,150

Author's fee = 6.5% of retail price per copy for 225,000 copies = [tex]225000\times26.40\times6.5/100= 386,100[/tex]

Total cost = 843,750 + 27,500 + 135,150 + 386,100 = $1,392,500

Let the cost of kelp for copies be k.

Then the total cost = 1,392,500 + k

If the expected profit is 4,092,100, then

Revenue = total cost + profit

5,940,000 = 1,392,500 + k + 4,092,100

5,940,000 = 5,484,600 + k

k = 5,940,000 - 5,484,600 = 455,400

Since Carlita is paying [tex]\frac{1}{3}[/tex] of k, her share of the kelp =

[tex]\frac{1}{3}\times455400 = 151800[/tex]

Carlita will pay $151,800

Answer:

13 square units

Step-by-step explanation:

You could calculate the length of each side using Pythagorean theorem, then use Heron's formula to find the area.  But there's an easier way: find the area of the rectangle that contains the triangle, and subtract the areas of the smaller triangles in the corners.

The area of the rectangle is 4 × 7 = 28.

The area of the upper left triangle is ½(2)(4) = 4.

The area of the upper right triangle is ½(3)(5) = 7.5.

The area of the lower right triangle is ½(1)(7) = 3.5.

So the area of the triangle is:

28 − 4 − 7.5 − 3.5 = 13

Answer:

  L = s^2/(30.25Cd)

Step-by-step explanation:

In accident investigation, the speed of a vehicle can be estimated using a polynomial function that relates speed (s) to the length of skid marks (L). The drag coefficient Cd will depend on the condition of the road surface and tires, but might be expected to be between 0.7 and 0.8.

If the skid marks end in a collision, the length of the marks that might have been made can be estimated using this formula, then that length added to the actual length of marks to estimate the original speed. The speed at the point of collision can be estimated by the damage caused, and/or the movement created.

In the above formula, length is in feet, and speed is in miles per hour.

In Physics, a polynomial function such as[tex]y = -gt^2 + v0*t + h0[/tex] can model an object's motion under gravity. A rational function like P = a / (1 + bQ) can model the relationship between supply and demand in Economics.

In the field of Physics, polynomial functions are often used to model physical phenomena. For example, the motion of an object under the force of gravity can be represented by a second-degree polynomial, or quadratic function. The equation[tex]y = -gt^2 + v0*t + h0[/tex]is an example of a quadratic function modeling free fall, where g represents the acceleration due to gravity, v0 is initial velocity, t represents time and h0 is initial height.

On the other hand, rational functions are used in various fields too. In Economics for instance, it can model situations like the relationship between supply and demand in market equilibrium. A simple model could be P = a / (1 + bQ) where P represents the price, Q is the quantity of good sold, and a, b are constants.

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Answer:

  A. 25% high

  B. 12.5% decrease

Step-by-step explanation:

A. The estimate relative to the actual turnout was ...

  7000/5600 = 1.25

The estimate was 25% high.

__

B. Relative to the previous election, the turnout was ...

  5600/6400 = 0.875 = 1 - 0.125

The percentage decrease from the previous election was 12.5%.