.
Which of the following is NOT an arithmetic sequence?

A) 4, 7, 10, 13, 16

B) 1, 2, 3, 4, 5

C) 15, 9, 3, -3, -9

D) 2, 4, 8, 16, 32

Answer:

[tex]cos(x)=\frac{\sqrt{5}}{5}[/tex]

Step-by-step explanation:

we have that

[tex]tan(x)=-2[/tex]

The angle x is in quadrant IV

That means ---> The value of cos(x) is positive and the value of sin(x) is negative

Remember that

[tex]cos^2(x)+sin^2(x)=1[/tex] ----> equation A

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

so

[tex]-2=\frac{sin(x)}{cos(x)}[/tex]

[tex]sin(x)=-2cos(x)[/tex] ----> equation B

substitute equation B in equation A

[tex]cos^2(x)+(-2cos(x))^2=1[/tex]

solve for cos(x)

[tex]cos^2(x)+4cos^2(x)=1[/tex]

[tex]5cos^2(x)=1[/tex]

[tex]cos^2(x)=\frac{1}{5}[/tex]

square root both sides

[tex]cos(x)=\pm\frac{1}{\sqrt{5}}[/tex]

but remember that the value of cos(x) is positive (IV quadrant)

[tex]cos(x)=\frac{1}{\sqrt{5}}[/tex]

simplify

[tex]cos(x)=\frac{\sqrt{5}}{5}[/tex]

At 8 hours of service, the two limousine rental companies charge the same amount.

Step-by-step explanation:

Given,

Initial fee of Executive Limousine rental = $200

Per hour charges of service = $40

Let,

x be the number of hours.

E(x) = 40x+200

Initial fee of Jet Limousine rental = $120

Per hour charges of service = $50

J(x) = 50x + 120

For the charges to be same;

E(x) = J(x)

[tex]40x+200=50x+120\\200-120=50x-40x\\80=10x\\10x=80[/tex]

Dividing both sides by 10

[tex]\frac{10x}{10}=\frac{80}{10}\\x=8[/tex]

At 8 hours of service, the two limousine rental companies charge the same amount.

Keywords: function, addition

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Answer:

The remainder is 64

Step-by-step explanation:

Consider the function [tex]f(x)=x^3+3x^2-51x+91[/tex]

Use synthetic division to divide by x+9

x+9=0, x=-9

divide the given f(x) by -9 using synthetic division

-9               1           3       -51       91

                  0          -9     54        -27              

         --------------------------------------------------

                  1           -6      3         64

The remainder is 64

Answer:

The answer is k=77

Step-by-step explanation:

It is given that n is an integer and greater than 2. Let us simplify k = (n + 2)(n – 2) to k=n^2-4.

In (1) it is stated that k is the product of two primes and in (2) it is stated that k<100. To solve the question we need to consider both cases (1) and (2).

Let say n=9 then k=n^2-4 becomes k=81-4=77. Well, 77 is the product of two prime numbers 7 and 11 (77=7*11). The answer is k=77

Answer:There are 6 matches in each group

Step-by-step explanation:

The first round of the 2010 FIFA World Cup consisted of several groups of four teams each. Within each group, each of the four teams played each other once. Assuming the teams are A, B, C and D.. The way the teams in the group play each other would be

AB, CD first group matches.

AC, BD second group matches.

AD, BC. Third group matches

Therefore, the number of matches in each group would be 6

Answer:

[tex]h=\frac{SA-2s^2}{4s}[/tex]

Step-by-step explanation:

we know that'

The formula to calculate the surface area of a square prism is

[tex]SA=2s^2+4sh[/tex]

where

s is the length of the side of the square base

h is the height of the prism

Solve for h

That means ----> Isolate the variable h

so

subtract 2s^2 both sides

[tex]SA-2s^2=4sh[/tex]

Divide by 4s both sides

[tex]\frac{SA-2s^2}{4s}=h[/tex]

Rewrite

[tex]h=\frac{SA-2s^2}{4s}[/tex]

To find the height of a square prism when given the surface area and base side length, use the formula B. H = (SA - 2s^2) / (4s).

The question asks for a formula that can be used to find the height (h) of a square prism given the surface area (SA) and the side length of the base (s). The surface area of a square prism is calculated using the formula SA = 2s2 + 4sh. To solve for h, we need to re-arrange this equation:

Therefore, the correct formula to find h is B. H = (SA – 2s2) / 4s.

Answer:

The answer to your question is $43.15

Step-by-step explanation:

Current bill = 25, 789 kWh

Previous bill = 25, 350 kWh

Charge = $ 0.0983/ kWh

Process

1.- Subtract the current meter from the previous one

                   25, 789 - 25, 350 = 439 kWh

2.- Find the amount of the bill using a rule of three

                 $0.0983     -----------------   1 kWh

                      x             ----------------   439 kWh

                     x = (439 x 0.0983) / 1

                     x = $ 43.15

Answer:

0.2288

Step-by-step explanation:

This is straightforward.

What we need to do is to divide the number of defective semiconductor chips over the total number of semiconductor chips.

Initially, the total number of semi conductor chips is 119 and the total number of defective semiconductor chips is 28.

After the first selections , we can infer that the total number of semiconductor chips is 118 while the number of defective ones is 27.

Hence on the second drawing, the probability that he will

Select a defective one is 27/118

Answer:

Step-by-step explanation:

cos(c+d)=cos c  cos d-sin c sin d   ...(1)

cos(c-d)=cos  c  cos d+sin c sin d  ...(2)

add (1) and (2)

cos (c+d)+cos (c-d) =2 cos c cos d  ...(3)

put c+d=x

c-d=y

add

2c=x+y

c=(x+y)/2

subtract

2d=x-y

d=(x-y)/2

substitute in (3)

[tex]cos~ x+cos~ y=2 cos (\frac{x+y}{2}) ~cos (\frac{x-y}{2})[/tex]

To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.

To prove the identity cos x + cos y = 2cos((x+y)/2) cos((x-y)/2), we need to show that x+y/2+x-y/2=x and find a similar expression using x+y/2 and x-y/2 that equals y. Once we have these expressions, we can use them to prove the identity.

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Answer:the Vega's cell phone bill for March is $155

Step-by-step explanation:

Let x represent the number of talk time in minutes that the family uses for a month.

Let y represent the number of text messages that the family sends in a month.

Let z represent the total cost of using x talk time and sending y text messages in a month.

The cell phone plan costs $75 per month including taxes and fees. Any minutes over 1,000 cost $1 per minute,and any texts over 400 cost $2 per text. This means that the total cost of x minutes and y texts would be

z = 75 + 1(x - 1000) + 2(y - 400)

z = 75 + x - 1000 + 2y - 800

z = 75 - 1000 - 800 + x + 2y

z = x + 2y - 1725

Because of a family emergency,the family uses 1,050 minutes and 415 texts in March. The total cost would be

z = 1050 + 2(415) - 1725

z = 1050 + 830 - 1725 = $155

Answer:the football team played 25 games in all

Step-by-step explanation:

Let x represent the total number of matches that the football team played.

The football team won 10 matches out of the total number of matches they played. if their win percentage was 40, it means that

10/x × 100 = 40

1000 = 40x

x = 1000/40 = 25

Answer:

Lines 'a' and 'c' are parallel. Line 'b' is non parallel to 'a' and 'c'.

Step-by-step explanation:

Picture is attached with the answer as a solution to it.

In the question it is give that line 'c' only intersect with line 'b' and not with, so the only way that two lines won't intersect here 'a' and 'c' is that lines are parallel. If the lines are not parallel then those lines will definitely meet.

Answer:

11 positive integers can be expressed.

Step-by-step explanation:

Consider the provided information.

The number of possible prime numbers are 5,7,11,and 13.

There are 4 possible prime numbers.

How many positive integers can be expressed as a product of two or more of the prime numbers, that means there can be product of two numbers, three number or four numbers.

The formula to calculate combinations is: [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

The number of ways are:

[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}[/tex]

[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1[/tex]

[tex]^4C_2+^4C_3+^4C_4=6+4+1[/tex]

[tex]^4C_2+^4C_3+^4C_4=11[/tex]

Hence, 11 positive integers can be expressed.

1/2, or one half. since she cuts it into 2.

Answer:

The sprinkler must rotate by an angle of 107.48°.

Step-by-step explanation:

Given:

Area of strawberry patch( in shape of sector)  = 1500 square yards

Radius of circle = 40 yards

To find angle through which the sprinkler should rotate.

Solution.

In order to find the angle of rotation of sprinkler, we will apply the area of sector formula.

[tex]Area\ of\ sector\ = \frac{\theta}{360}\times \pi r^2[/tex]

where [tex]\theta[/tex] is the angle of the sector formed and [tex]r[/tex] is radius of the circle.

Thus, we can plugin the given values to find [tex]\theta[/tex] which would be the angle of rotation.

[tex]1500 = \frac{\theta}{360}\times \pi (40)^2[/tex]

Taking [tex]\pi=3.14[/tex]

[tex]1500 = \frac{\theta}{360}\times \ (3.14) (40)^2[/tex]

[tex]1500 = \frac{\theta}{360}\times 5024[/tex]

Dividing both sides by 5024.

[tex]\frac{1500}{5024} = \frac{\theta}{360}\times 5024\div 5024[/tex]

Multiplying both sides by 360.

[tex]\frac{1500\times 360}{5024} =\frac{\theta}{360}\times 360[/tex]

[tex]107.48=\theta[/tex]

∴ [tex]\theta= 107.48\°[/tex]

Angle of rotation of sprinkler = 107.48°

The strawberry farmer needs the sprinkler to rotate approximately 107.46 degrees to cover the 1500 square yard sector of the circle with a 40-yard radius.

To determine the angle through which the sprinkler should rotate, we first need to find the area of the sector of the circle. The formula for the area of a sector is:

A = 0.5 × r² × θ

where A is the area, r is the radius, and θ is the angle in radians. Here, we know the area A is 1500 square yards and the radius r is 40 yards. Rearranging the formula to solve for θ gives:

θ = (2 × A) / r²

Substituting the given values:

θ = (2 × 1500) / 40²

θ = (3000) / 1600

θ = 1.875 radians

To convert this angle in radians to degrees, we use the conversion factor 180/π:

θ = 1.875 × (180 / π) ≈ 107.46 degrees

Therefore, the sprinkler should rotate through an angle of approximately 107.46 degrees.

Answer:

[tex]P(X\geq 5)=1-P(X< 5)=1-[0.000649+0.00703+0.0343+0.0991+0.1878]=0.6712[/tex]

Step-by-step explanation:

1) Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

2) Solution to the problem  

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=10, p=0.52)[/tex]  

The probability mass function for the Binomial distribution is given as:  

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

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

What is the probability that at least 5 of the students in your study group of 10 have studied in the last week?

[tex]P(X\geq 5)=1-P(X< 5)=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)][/tex]

[tex]P(X=0)=(10C0)(0.52)^0 (1-0.52)^{10-0}=0.000649[/tex]  

[tex]P(X=1)=(10C1)(0.52)^1 (1-0.52)^{10-1}=0.00703[/tex]  

[tex]P(X=2)=(10C2)(0.52)^2 (1-0.52)^{10-2}=0.0343[/tex]  

[tex]P(X=3)=(10C3)(0.52)^3 (1-0.52)^{10-3}=0.0991[/tex]  

[tex]P(X=4)=(10C4)(0.52)^4 (1-0.52)^{10-4}=0.1878[/tex]  

[tex]P(X\geq 5)=1-P(X< 5)=1-[0.000649+0.00703+0.0343+0.0991+0.1878]=0.6712[/tex]

To find the probability that at least 5 of the students in a study group of 10 have studied in the last week, use the binomial probability formula and calculate the respective probabilities for each case. Add these probabilities together to get the final probability.

To calculate the probability that at least 5 of the students in your study group of 10 have studied in the last week, we can use the binomial probability formula. Let's denote the probability that a randomly selected teenager studied at least once during the week as p = 0.52. We want to find P(X >= 5) where X represents the number of teenagers in the study group who studied.

Using the binomial probability formula, P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10). We can calculate each of these individual probabilities using the formula: [tex]P(X = k) = C(n, k) * p^k * (1-p)^(^n^-^k^),[/tex] where C(n, k) is the combination of n items taken k at a time.

Once we have calculated each of these probabilities, we can add them together to find the final probability.

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The term quadratic comes from the word quadrate meaning square or rectangular. Similarly, one of the definitions of the term quadratic is a square. In an algebraic sense, the definition of something quadratic involves the square and no higher power of an unknown quantity; second degree. So, for our purposes, we will be working with quadratic equations which mean that the highest degree we'll be encountering is a square. Normally, we see the standard quadratic equation written as the sum of three terms set equal to zero. Simply, the three terms include one that has an [tex]x^{2}[/tex], one has an x, and one term is "by itself" with no [tex]x^{2}[/tex] or x.

Answer:

Heather pay will be 290 for 40 hours of work.

Step-by-step explanation:

Given:

Amount he gets paid weekly =174

Number of hours of work =24

we need to find the amount of pay for 40 hours of work.

Also Given:

weekly pay is directly proportional to the number of hours.

Framing in equation form we get;

Amount Of Pay ∝ Number of hours of work

Hence Amount of Pay = k × Numbers of hours of work.

where k is constant.

Substituting the values we will find the value of k

[tex]174 = k \times 24\\\\k = \frac{174}{24} = 7.25[/tex]

Now using this we will find the amount of pay when hours of work is 40.

Amount Of Pay = [tex]7.25\times 40 = 290[/tex]

Hence Heather pay will be 290 for 40 hours of work.

Answer:

[tex]a_{n+1}=0.2a_n[/tex] for all n>0, [tex]a_1=16[/tex]

Step-by-step explanation:

Let [tex]\{a_n\}=\{16,3.2,0.64,0.128,\cdots \}[/tex] be the sequence described.

A geometric sequence has the following property: there exists some r (the ratio of the sequence) such that [tex]\frac{a_{n+1}}{a_n}=r[/tex] forr all n>0.

To find r, note that

[tex]\frac{3.2}{16}=\frac{32}{10(16)}=\frac{2}{10}=\frac{1}{5}=0.2[/tex]

Similarly

[tex]\frac{0.64}{3.2}=\frac{64}{10(32)}=\frac{1}{5}=0.2[/tex]

[tex]\frac{0.128}{0.64}=\frac{1}{5}=0.2[/tex]

Thus [tex]a_{n+1}=r a_n=\frac{a_n}{5}=0.2a_n[/tex] for all n>0, and [tex]a_1=16[/tex]

first term = 16

average ratio = 0.2

Answer:

The proper time sequence of the three political parties/movements, from earliest to latest is as follow:

Step-by-step explanation:

Total envelopes: 3 + 1 + 3 + 2 = 9 with a total of 3 green ones.

Probability of picking green first: 3 out of 9 = 3/9 = 1/3

There are 8 envelopes left, with 2 green ones.

Probability of picking a green one is 2 out of 8 = 2/8 = 1/4

There are 7 envelopes left and 1 green one.

Probability of picking green is 1 out of 7 = 1/7

Probability of picking all 3 = 1/3 x 1/4 x 1/7 = 1/84

Answer:

19 revolutions per minute, for model 5.

Step-by-step explanation:

Consider the model shown below:

From the table:

The blade length for model 5 is 148 feet

Also the maximum blade tip speed is 200 miles per hour.

It is given that the tip of the blade travels 0.18 mile per revolution.

To find the number of revolution per hour simply divide the maximum speed of the blade with the revolution.

Number of revolutions per hour = [tex]\frac{200}{0.18}=1111.111[/tex]

We need to find the speed, in revolutions per minute, so divide the obtained revolution per hour with 60.

[tex]\frac{1111.11}{60} =18.52\approx19[/tex]

Hence, 19 revolutions per minute, for model 5.

Final answer:

To determine the speed in revolutions per minute for model 5, we need to know how far the blade tip travels in one minute. This would be divided by 0.18 miles, the distance per revolution, to find the RPM. Without the distance traveled in one minute, we cannot complete the calculation.

Explanation:

To calculate the approximate speed in revolutions per minute for model 5, where the tip of the blade travels 0.18 miles per revolution, we need to find how many revolutions it would complete in one minute. Assuming the tip travels at a constant speed, you would divide the distance it covers in one minute by the distance per revolution.

First, determine the distance traveled by the blade tip in one minute. Since no speed is given for one minute in the question, we cannot provide a direct answer; more information would be needed, such as the distance the blade tip travels in a given time frame. However, if we had information like this, we could proceed with a calculation:

Let's say the tip travels X miles in one minute. You would then divide X by 0.18 miles to find the number of revolutions per minute:

Revolutions per minute (RPM) = Distance in miles per minute / Distance per revolution

RPM = X miles / 0.18 mile

For example, if the tip travels 1.8 miles in one minute, then:

RPM = 1.8 miles / 0.18 mile = 10 RPM

Answer:

Step-by-step explanation:

1. Correct. Corresponding vertices are (A, D), (B, E), and (C, F). The triangle names must list corresponding vertices in the same order. Thus the answer is the one you have chosen.

__

2. Look again. As in the first problem, corresponding vertices are in the same order. Line segment EF is named by the first two vertices in the triangle name, so the corresponding segment is LM, also named by the first two vertices of that triangle's name.

Segment FG is named by the last two vertices of the triangle's name, so the corresponding segment in the other triangle is also named by the last two vertices of the triangle's name: MN. Corresponding segments are proportional, so EF/LM = FG/MN.

__

3. Correct. Segment DB is congruent to itself. The halves of the bisected angle at D are congruent to each other, and the segments DA and DC are shown as congruent. Hence, SAS is an appropriate choice for showing congruence of the triangles.

__

4. The 1:1 ratio of these similar triangles tells you they are congruent, so ...

  AC = EC

  4x -3 = 2x +6 . . . . substitute the given expressions

  2x = 9 . . . . . . . . . . add 3-2x

  EC = 9+6 = 15 . . . substitute for 2x in the expression for EC

The question asks for AE, which is 2 times the length EC, so is ...

 AE = 2·EC = 2·15 = 30 . . . . feet

___

The only indication that the units are feet is that the answer choice with the number 30 has feet as its units. (We should be seeing "(4x-3) feet" as the measure of AC, for example.)

Answer:

On average the carnival gain on each play

= 0.04 dollars

Step-by-step explanation:

Given that a pond contains 100 fish: 78 purple, 21 blue, and 1 silver.

Fish            Purple     Blue          Silver    total

Frequency  78               21                 1    100

Prob          0.78      0.21             0.01      1

Revenue           0.4                0.8            13  

game fee 0.65        0.65            0.65  

Net revenue -0.25      0.15            12.35    

Net Rev*Prob -0.195      0.0315   0.1235   -0.04

Thus we get per player expected net revenue is -0.04

This would be gain for Carnival

Hence On average the carnival gain on each play

= 0.04 dollars

Final answer:

To calculate the carnival's average gain per play, determine the expected payoff for each fish type, subtract the cost to play, and sum these amounts. The carnival gains an average of $0.61 per play.

Explanation:

The student's question involves calculating the average gain for a carnival on each play of a carnival fishpond game. To find this, we need to determine what the carnival earns on average based on the probabilities of catching each type of fish (purple, blue, or silver) and the payoff for each.

Let's calculate the expected profit (gain) per play for the carnival. The probability and payoff for each type of fish are:

Purple fish: Probability = 78/100, Payoff = $0.40

Blue fish: Probability = 21/100, Payoff = $0.80

Silver fish: Probability = 1/100, Payoff = $13.00

The expected payoffs for the carnival from catching each type of fish are:

Purple: 78/100 * $0.40

Blue: 21/100 * $0.80

Silver: 1/100 * $13.00

Subtract the contestant's cost ($0.65) from each expected payoff to find the expected gain. Then, sum these expected gains to find the overall average gain for the carnival.

The carnival's expected gain is:

Expected Gain per Play = (78/100 * $0.40) + (21/100 * $0.80) + (1/100 * $13.00) - $0.65

Calculating:

Expected Gain per Play = ($0.3120) + ($0.1680) + ($0.1300) - $0.65

Expected Gain per Play = $0.61

This calculation shows that on average, the carnival gains $0.61 for each play of the fishpond game.

Y is a bisector of the two sides, so would be half the length of the base.

Y = 36 / 2

y = 18

Answer:

[tex]I_2=9[/tex]

Step-by-step explanation:

We have been told that the ratios are inversely proportional in our given problem. We are asked to find the missing value.

We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where, y is inversely proportional to x and k is the constant of proportionality.

Let us find constant of proportionality using [tex]R_1 = 6[/tex] and [tex]I_1 = 12[/tex] in above equation.

[tex]6=\frac{k}{12}[/tex]

[tex]6*12=\frac{k}{12}*12[/tex]

[tex]72=k[/tex]

Now, we will use [tex]72=k[/tex] and [tex]R_2 = 8[/tex] in our equation to find [tex]I_2[/tex] as:

[tex]8=\frac{72}{I_2}[/tex]

[tex]I_2=\frac{72}{8}[/tex]

[tex]I_2=9[/tex]

Therefore, the value of [tex]I_2[/tex] is 9.

The question is about the mathematical concept of inverse proportionality. The missing value of [tex]I_2[/tex] is found by applying the property of inversely proportional quantities, yielding the result [tex]I_2 = 9[/tex].

In an inverse proportionality relationship, the product of the values in one set is equal to the product of the corresponding values in the other set. This can be represented as:

[tex]\[R_1 \cdot I_1 = R_2 \cdot I_2\][/tex]

Given that [tex]\(R_1 = 6\)[/tex], [tex]\(R_2 = 8\)[/tex], and [tex]\(I_1 = 12\)[/tex], you can solve for [tex]\(I_2\)[/tex]:

[tex]\[6 \cdot 12 = 8 \cdot I_2\][/tex]

Now, simplify the equation:

[tex]\[72 = 8 \cdot I_2\][/tex]

To isolate [tex]\(I_2\)[/tex], divide both sides by 8:

[tex]\[I_2 = \frac{72}{8}\][/tex]

[tex]\[I_2 = 9\][/tex]

So, the value of [tex]\(I_2\)[/tex] is 9. In this inverse proportionality relationship, when [tex]R_1[/tex] is 6, [tex]\(R_2\)[/tex] is 8, and [tex]\(I_1\)[/tex] is 12, [tex]\(I_2\)[/tex] is 9. This means that as one variable increases, the other variable decreases in such a way that their product remains constant.

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Answer:

-48

Step-by-step explanation:

Let me know if you need anything

Answer:

-48

Step-by-step explanation:

next in a row  is always equal previous one multiple by -2

-3*(-2)=6

6*(-2)=-12

-12*(-2)=24

24*(-2)=-48

Good evening ,

Answer:

2x² - 18x + 36

Step-by-step explanation:

2(x-3)(x-6) = 2x²-18x+36.

:)