there is a three term arithmetic sequence with the first term 9. if you add 2 to the second term and 20 to the third term it forms a geometric sequence. what is the smallest number the third term in the geometric sequence could be?

Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.

The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. It can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.

Given data:

The number formed as:

(x²) .(y³).(z)  ...eq 1

Number appeared on screen - 2592

Find the prime factors of 2592.

2592 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3

This can be written as:

2592 = 4² x 3³ x 2 x 3

2592 = 4² x 3³ x 6¹  .....eq 2

comparing eq 1 and 2

(x²) .(y³).(z)  =  4² x 3³ x 6¹  

x = 4, y = 3 and z = 6

Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.

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The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.

The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c

a( b + c ) = ab + ac

Using this property, we can rewrite the expression 2(10+12) as

2( 10 + 12 ) = 2(10) + 2(12)

Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:

2(10+12) = 20 + 24

Simplifying further, we get

2(10+12) = 44

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Answer:

The probability that a randomly selected camper likes to have a cookout will be 0.93.

Step-by-step explanation:

did it already.

Answer:   To solve this problem, we need to find the probability that a randomly selected camper likes swimming or having a cookout, but not both. We can do this by using the formula:

P(S or C, but not both) = P(S) + P(C) - 2P(S and C)

We are given the following probabilities from the Venn diagram:

P(S) = 0.06 (the proportion of the circle labeled S)

P(C) = 0.04 (the proportion of the circle labeled C)

P(S and C) = 0.89 (the proportion of the shared area)

Substituting these values into the formula, we get:

P(S or C, but not both) = 0.06 + 0.04 - 2(0.89)

= 0.10 - 1.78

= -1.68

This is not a valid probability, as probabilities cannot be negative. Therefore, there must be an error in the problem statement or the Venn diagram. Please check the values again and ensure they are correct.

Step-by-step explanation:

A causal study is a study that seeks to determine whether one variable causes another variable.

The independent variable is the variable that is believed to cause the change in the dependent variable, while the dependent variable is the variable that is believed to be influenced by the independent variable.

In a causal study of the effect of shelf placement on sales of a brand of cereal, the independent variable is where the cereal was placed on the shelf. The dependent variable is sales of the cereal.

This is because the sales of the cereal are influenced by where it is placed on the shelf.The answer to the question is sales of the cereal.

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Answer:

x = 13°

Step-by-step explanation:

-> all angles of triangle add up to 180°

-> right angle = 90°

-> GIVEN: 90° and 23°

90° + 23° + (6x-11) = 180°

6x-11 = 67°

6x = 78°

[tex]\frac{6x}{6} =\frac{78}{6}[/tex]

x = 13°

Answer:22

Step-by-step explanation:

h + i3 = ?

19 + 1X3 = 22

Answer:

h + i3 = 22

Step-by-step explanation:

Given expression,

→ h + i3

→ h + 3(i)

Now we have to use,

→ i = 1

→ h = 19

Let's simplify the expression,

→ h + 3(i)

→ 19 + 3(1)

→ 19 + 3

→ 22 => {final answer}

Hence, the solution is 22.

Answer:

yes you're right!

Step-by-step explanation:

-6 equals c because the quadratic formula is [tex]ax^2+bx+c=0[/tex].

to apply the formula, we would end up with [tex]\frac{-(-2)±\sqrt(-2)^2-4*3(-6)}{2(3)}[/tex] as our answer

once we simplify, we're left with [tex]x=\frac{2±2\sqrt{19}}{6}[/tex]

we break the equations into two to separate the positive sign's answer from the negative sign's answer, so we'll have [tex]x=\frac{2+2\sqrt{19} }{6}[/tex] and [tex]x=\frac{2-2\sqrt{19} }{6}[/tex]

isolate the variable to get our solution, [tex]x=\frac{1±\sqrt{19} }{3}[/tex]

The type of transformation that occurred in each object are:

1) Rotation

2) Translation

3) Reflection

4) Translation

There are different types of transformations of objects such as:

Translation: Translation is said to occur when we slide a figure in any direction.

Reflection: Reflection is said to occur when we flip a figure over a line.

Rotation: Rotation is said to occur when we rotate a figure a certain degree around a point.

Dilation: Dilation is said to occur when we enlarge or reduce a figure.

1) The given transformation is rotation because the original object was clearly rotated.

2) The given transformation is said to be translation because the object just changed position.

3) The transformation that occurred is said to be a reflection because it is a mirror image.

4)  The given transformation is said to be translation because the object just changed position.

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The probability that the second smallest integer from a set of six distinct integers is picked at random is the same as the probability that the first smallest is 1.

This can be expressed mathematically as:

P(second smallest) = P(first smallest).

The probability of the first smallest integer is the number of combinations that result in the first smallest number divided by the total number of possible combinations of six distinct integers.

For example, if we have six distinct integers in a set, A, B, C, D, E, and F, the probability of A being the first smallest is the number of combinations that result in A being the smallest divided by the total number of combinations.

The combinations that result in A being the smallest are {A, B, C, D, E, F}, {B, A, C, D, E, F}, {C, A, B, D, E, F}, and so on. That’s a total of 6 combinations out of the total possible number of combinations, which is 6 x 5 x 4 x 3 x 2 x 1 = 720.

Therefore, P(first smallest) = 6/720 = 1/120. Similarly, the probability of the second smallest number being the same is also 1/120.

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Answer:1 and 0

Step-by-step explanation:

If x=0 and y=0

?=0

if x=1 and y=1

?=1

if  x=2 and y=2

?=1

if x=3 and y=3

?=1

if x=4 and y=4

?=1

if x=5 and y=5

?=1

Answer:772

Step-by-step explanation:

SA=PH+2b

SA=(10+8+10+8)(17)+2(8x10)

SA=772

Answer:

Step-by-step explanatin

multiply all of them

None of these options

Option A

Conversion of measurement of Metres to Centimetres can be done by multiplying the number by 100

1 metre = 100 centimetres

5.2 metres = 520 centimetres

Option B

Conversion of measurement of Metres to Decametres can be done by multiplying the number by 0.1

1 metre = 0.1 decametres

5.2 metres = 0.52 decametres

Option C

Conversion of measurement of Metres to Decimetres can be done by multiplying the number by 10

1 metre = 10 decimetres

5.2 metres = 52 decimetres

Option D

Conversion of measurement of Metres to Kilometres can be done by multiplying the number by 0.001

1 metre = 0.001 kilometres

5.2 metres = 0.0052 kilometres

Therefore,

5.2 metres = 520 centimetres

5.2 metres=  0.52 decametres

5.2 metres= 52 decimetres

5.2 metres= 0.0052 kilometres

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Answer:

No, q=15 is not a solution to the inequality.

Step-by-step explanation:

As given, q=15. So, substituting is the best way to solve this problem.

Step 1: Substitute

[tex]\frac{15}{5}=3[/tex]

[tex]15-20=-5[/tex]

Step 2: Substitute values into inequality

[tex]3 < -5[/tex]

Equation is false since 3 is a bigger value than -5.

Hope this helps ya!

The distance between the two points (-8,-1) and (-8,4) is 5 units.

The distance formula is a mathematical formula used to find the distance between two points in a two-dimensional or three-dimensional coordinate system.

The distance between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be found using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, the two points are (-8, -1) and (-8, 4). Therefore, we can substitute the values into the formula:

d = √((-8 - (-8))² + (4 - (-1))²)

= √(0² + 5²)

= √(25)

= 5

Therefore, the distance between the two points is 5 units, so the answer is (B) 5.

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Answer:L x b

              98ft x 56ft =5488

                                  =5488 / $3.75= $1463.47

Step-by-step explanation: Play ground is more like a rectangle so we use the formula for the rectrectangle to get total area . A=Lxb

Divide  the total with the cost since it say each per sqr feet

A=lxb

98x56=5488

5488/3.75= 1463.47

Answer: A and C

Step-by-step explanation:

angles in a triangle add up to 180

180 - 30 = 150

other two angles must add up to 150 and two of the angles have to be the same.

Since one is already 30, one of the others have to also be 30 or both of the others have to be the same.

A and C both add up to 150 and both of them have one angle repeating

The smallest two-digit prime number that is not an emirp is 11.

An emirp is a prime number that, when its digits are written in reverse order, becomes another prime number. In this way, 73 is an emirp because when its digits are reversed, we get 37, which is also a prime number.

To answer this question, we must examine each of the two-digit prime numbers and verify whether or not they are emirps.

Let's begin by listing all of the two-digit prime numbers:

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

We must now test each of the above prime numbers to see whether they are emirps by reversing their digits and then testing if the new number is also prime.

We do not need to examine the primes in reverse order since, if a number is a two-digit prime, its reverse will also be a two-digit number.

Let's start by checking whether 11 is an emirp or not by reversing its digits.11 reversed becomes 11, which is the same number. Since 11 is a prime number, it is not an emirp.

Therefore, 11 is the smallest two-digit prime number that is not an emirp.

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We can expect approximately 90 mosquitoes in the trap at the end of the 13-week mosquito season.

Based on the given data, we can observe that the number of mosquitoes is increasing over time, and the increase is not constant. So, it would be unreasonable to continue counting individual mosquitoes after a certain point.

To estimate the number of mosquitoes at the end of the 13-week mosquito season, we can assume that the rate of increase remains constant over time. Using this assumption, we can find the average increase in mosquitoes per week, which is the difference between the number of mosquitoes in the last week and the number in the first week, divided by the number of weeks:

Average increase = (27 - 8) / 3 = 6.33

Then, we can use this average increase to estimate the number of mosquitoes in the 13th week:

Number of mosquitoes in the 13th week = 27 + 6.33 × 10 = 90.3

Since we cannot have a fraction of a mosquito, we can round this estimate to the nearest whole number.

Therefore, we can expect approximately 90 mosquitoes in the trap at the end of the 13-week mosquito season.

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The shaded region of the provided number is 214.5 yards, according to the given statement.

A rectangular shape is an illustration of a trapezoid with proportionate and matched opposite sides. It has four sides, four 90-degree borders, and is shaped like a rectangular. Any shape with only two sides is said to be rectangular.

Calculating Area by Subtracting Area from Two as well as More Regions: To determine the area for combined figures consisting of basic forms that overlap, deduct the area of the unshaded figure from the total area to obtain the area of the shaded region.

For illustration, let's calculate the size of the shaded section in the provided picture.

It is clear from the provided picture that a triangular and a rectangle have overlapped. We must deduct the triangular area from the size of the parallelogram in order to determine the area about the shaded figure. Area of the shaded figure =

Area of the rectangle −

Area of triangle

=l×b−12×b×h

=22×11−12×11×5

=214.5yd2

Hence, the area of the shaded figure is 214.5yd2

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The ship is about 65.6 meters away from the base of the lighthouse.

What is tangent function ?

Tangent is one of the three primary trigonometric functions, along with sine and cosine. In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

The tangent function is denoted by "tan" and is defined mathematically as:

tan(theta) = opposite / adjacent

where theta is the angle, opposite is the length of the side opposite the angle, and adjacent is the length of the side adjacent to the angle.

According to the question:
We can use trigonometry to solve this problem. Let's draw a right triangle with the lighthouse at the top, the ship at the bottom, and the line connecting them as the hypotenuse. The angle of depression of 26° is the angle between the hypotenuse and the horizontal line passing through the lighthouse. We know the height of the lighthouse is 32 meters.

Let x be the distance between the ship and the base of the lighthouse, which is the adjacent side of the angle of depression. Then we can use the tangent function:

tan(26°) = opposite / adjacent

We know the opposite side is the height of the lighthouse, which is 32 meters. Solving for x:

x = opposite / tan(26°)

x = 32 / tan(26°)

x ≈ 65.6 meters

Therefore, the ship is about 65.6 meters away from the base of the lighthouse.

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Answer:

f(x) = x ³ shifted 4 units to the right will be g(x) = f(x-4) = (x - 4)³

Step-by-step explanation:

If a function f(x) is shifted right 4 units every x coordinate will become x - 4

g(x)  = f(x - 4) = (x - 4)³

The x-intercepts of the graphed function are:

(-2, 0), (-1, 0), (1, 0), and (2, 0)

For any function, we define the x-intercepts as the values of x such that y= 0, when we have a graph we can identify these values as the values of x at which the graph intercepts the x-axis.

Remember that the x-axis is the horizontal one, then, we can look at the graph and identifty the 4 x-intercepts, these are at the values of x:

x = -2

x = -1

x = 1

x = 2

Writting them in point notation, these are (-2, 0), (-1, 0), (1, 0), and (2, 0)

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The probability that 2 red balls and 2 blue balls are taken from the box is 3/7. This can be expressed mathematically as [tex](8C2 * 8C2) / (16C4) = 3/7[/tex].

To better understand this probability, let's look at an example. Say there are 8 red balls and 8 blue balls in the box. This can be represented as:

R = 8, B = 8

We want to determine the probability of taking 2 red balls and 2 blue balls out of the box. To do this, we need to calculate the total number of ways of selecting 4 balls from the box (16 balls in total) and then calculate the total number of ways of selecting 2 red and 2 blue balls out of the box.

The total number of ways of selecting 4 balls from the box can be expressed as (16C4). This is calculated by dividing the number of ways of selecting 4 balls out of 16 (16!) by the number of ways of arranging those 4 balls in any order (4!):

[tex](16C4) = 16! / 4! = 1820[/tex]

The total number of ways of selecting 2 red and 2 blue balls out of the box can be expressed as (8C2 * 8C2). This is calculated by multiplying the number of ways of selecting 2 red balls out of 8 (8C2) by the number of ways of selecting 2 blue balls out of 8 (8C2):

[tex](8C2 * 8C2) = 8C2 * 8C2 = 28[/tex]

The probability of taking 2 red balls and 2 blue balls out of the box is then the ratio of the number of ways of selecting 2 red and 2 blue balls out of the box (28) to the total number of ways of selecting 4 balls from the box (1820):

P(2 red balls, 2 blue balls) = 28 / 1820 = 3/7

In conclusion, the probability of taking 2 red balls and 2 blue balls out of a box containing 8 red balls and 8 blue balls is 3/7.

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The magnitude of the resultant force is given by:

|F| = [tex]sqrt((-7)^2 + 0^2) N|F| = 7 N[/tex]The direction of the resultant force is given by:

[tex]θ = tan^-1(0/-7)θ = tan^-1(0) = 0[/tex]

Therefore, the magnitude of the resultant force is 7 N, and its direction is along the negative x-axis.

1. Cartesian vector expression for five forcesThe five forces acting along the edges of a pentagon plate ABC are shown below:Force acting on AB = (6i + 6j) NForce acting on BC = (8i + 4j) NForce acting on CD = (-5i + 10j) NForce acting on DE = (-10i - 8j) NForce acting on EA = (4i - 12j) N2.

Cartesian vector expression of the resultant force of these five forcesThe resultant force acting on the pentagon plate ABC can be determined by finding the vector sum of the five forces. The cartesian vector expression of the resultant force can be found as follows:[tex]F = F1 + F2 + F3 + F4 + F5F = (6i + 6j) N + (8i + 4j) N + (-5i + 10j) N + (-10i - 8j) N + (4i - 12j) N= (-7i + 0j) N[/tex]

Therefore, the cartesian vector expression of the resultant force is (-7i + 0j) N.3. Magnitude and direction of the resultant forceThe magnitude and direction of the resultant force can be determined by using the cartesian vector expression of the resultant force obtained in the previous step.

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The values as per similarity of traingles is x=4 and y=10.

Since ABC and DEF are similar triangles, their corresponding sides are proportional.

That is,

AB/DE = AC/EF = BC/DF

Substituting the given values, we get:

9/6 = 18/10 = (4x-1)/y

Simplifying this expression, we can solve for x and y:

9/6 = (4x-1)/y

Cross-multiplying, we get:

27y = 6(4x-1)

27y = 24x - 6

Substituting y = 10/3, we get:

(27)(10/3) = 24x - 6

90 = 24x - 6

96 = 24x

x = 4

Therefore, the value of x is 4.

9/6 = (4x-1)/y

Substituting x = 4, we get:

9/6 = (4(4)-1)/y

9/6 = 15/y

Cross-multiplying, we get:

9y = 90

y = 10

Therefore, the value of y is 10.

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The 99% confidence interval for the true population mean textbook weight is (38.11, 39.89) ounces.

We can find the standard error (SE) by using the formula:

SE = σ/√n

Where

σ = population standard deviation = 2.8 ounces

n = sample size = 41

SE = 2.8/√41

SE = 0.436

Now we can find the confidence interval by using the formula:

CI = x ± z*SE

Where

x = sample mean = 39 ounces

z* = the z-value corresponding to the level of confidence of 99 percent

The z-value corresponding to the level of confidence of 99 percent can be found using the z-table or calculator. It is found to be 2.576.

CI = 39 ± 2.576*0.436

CI = (38.11, 39.89)

Therefore, we can say that we are 99% confident that the true population mean textbook weight is between the interval (38.11, 39.89) ounces.

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Answer:21924 different ways

Step-by-step explanation:

There are 29 choices for the blue ribbon, 28 for the red and 27 for the yellow. If you multiply 29x28x27 you get 21924

If there are 29 horses competing in the show. then there are 21,084 ways can the blue, red, and yellow ribbons be awarded.

           Ribbons are awarded to horses. Therefore, we will use the multiplication rule of probability to find the total number of ways in which the blue, red, and yellow ribbons can be awarded.

       Multiplication Rule of Probability If there are 'm' ways of doing one thing and 'n' ways of doing another thing, then there are 'm*n' ways of doing both things.

       Multiplication Rule of Probability formula:

                A total number of ways of doing both things = m*n

      To find the total number of ways in which the blue, red, and yellow ribbons can be awarded to horses,

we need to multiply the number of ways of giving each ribbon.

        Blue ribbons can be awarded to 29 horses.

        Red ribbons can be awarded to 28 horses.

        Yellow ribbons can be awarded to 27 horses.

The multiplication rule of the probability formula will be applied to get the total number of ways of awarding blue, red, and yellow ribbons to horses.

 A total number of ways of awarding blue, red, and yellow ribbons = Number of ways of awarding blue ribbons × Number of ways of awarding red ribbons × Number of ways of awarding yellow ribbonsTotal number of ways of awarding blue, red, and yellow ribbons

                          = 29 × 28 × 27

 The total number of ways of awarding blue, red, and yellow ribbons

                          = 21,084

 Therefore, there are 21,084 ways in which the blue, red, and yellow ribbons can be awarded to horses.

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Based on the provided information The seller received a fee of $122.

The term "commission" describes the payment made to the staff member after they successfully complete a job, which is frequently marketing a predetermined quantity of goods or services. Selling goods or services is difficult. Sales and marketing professionals must contend with fierce rivalry.

The commission rules are defined by the following piecewise function:

c(p) = 0.10p, if p ≤ 1,000

c(p) = 0.15p - 50, if 1,000 < p ≤ 1,500

c(p) = 0.20p - 125, if p > 1,500

a. If the profit is $1,500, the commission rate is calculated using the second rule:

c(1,500) = 0.15(1,500) - 50 = 175

The commission rate is $175 / $1,500 = 0.1167, or approximately 11.67%.

b. If the profit is $900, the commission rate is calculated using the first rule:

c(900) = 0.10(900) = 90

The commission rate is $90 / $900 = 0.10, or 10%.

c. To find the commission on a car sold for a $970 profit, we need to determine which rule applies. Since 970 is less than 1,000, we use the first rule:

c(970) = 0.10(970) = 97

The commission on a car sold for a $970 profit is $97.

d. The profit on the car sale is calculated as follows:

profit = selling price - purchase price = $33,200 - $32,090 = $1,110

To determine the commission, we need to identify the appropriate rule based on the profit amount. Since $1,110 is greater than $1,500, we use the third rule:

c(1,110) = 0.20(1,110) - 125 = 122

The commission paid to the salesperson is $122.

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Answer:

8 7/15

Step-by-step explanation:

4/5 and 2/3 need to a a common denomenator

4/5*3 and 2/3*5 = 12/15 and 10/15 so 5 12/15 + 2 10/15= 7 22/15= 8 7/15

Answer:

79

Step-by-step explanation:

Using the formula

A=wl

Solving forl

l=A

w=5056

64=79m

To find area, you multiply the width by the length [tex]( \text{A} = \text{L} \times \text{W})[/tex]. Here, it is asking for the length, giving the area of the pool and the width. With this information, you can inverse operation ( division) to find the length of the pool. So:

[tex]5056 \div 64 = 79[/tex]

This tells us that the length of the pool is 79 meters. To check this answer, multiply 64 and 79. If it's equivalent to 5056, the given area, then 79 is indeed the length of the pool.

[tex]64 \times79 = 5056[/tex].

Thus, the length of the pool is 79 m.