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The common ratio of the given geometric sequence is 0.5

We know that for any geometric sequence,

aₙ = arⁿ⁻¹

where aₙ is the nth term of the sequence

a is the first term of the sequence

r is the common ratio.

Hence when we say that the third term is 100 we can conclude that for the series

ar³⁻¹ = 100

or, ar² = 100                                                                                      [1]

Also, we have been given that the eight-term is 3.125

Hence we can say that,

ar⁷ = 3.125                                                                                        [2]

By dividing equation 1 by equation 2 we get

ar⁷/ar² = 3.125/100

or, r⁵ = 3125/100000

or,  r⁵ =  5⁵/ 10⁵

Since the powers are the same, the bases can be equated to get

r = 0.5

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Complete Question

A geometric sequence has only positive terms. The third term is 100 and the eighth term is 3.125. Find the common ratio.

As per the given mass the potential energy of the ball will be equal to 450 J when it reaches the top to its ascent.

Here we have given that Mass of ball is 1.0kg

And we need to find the value of the kinetic energy  and here we also know that the velocity of the ball is 30m/s

As we all know that Kinetic energy is the energy possessed by a moving object. It is measured in joules, and then it depends on the mass (m) of the object and the velocity (v) by which it moves, then it can be written as,

=> K.E = 1/2mv²

=> KE = 1/2 x 1.0kg x (30m/s)²

when we simplify this then we get

=> KE = 0.5 x 1.0 x 900

Then the value of KE is  450J

Therefore the potential energy of the ball is 450 joules.

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70 is the greatest weight that Evelyn can put into the cardboard without going over the weight limit

From the question

Weight limit on one box = 28 kilograms

Weight of each box = ⅖ kilogram

To find the greatest number of boxes of pasta she can put into one cardboard box without exceeding the weight limit, we have:

G=28/2/5

To divide the fraction, change the division sign to multiplication and flip the fraction:

=28x5/2

=140/2

=70

Therefore, the greatest number of boxes Evelyn can put without going over the weight limit is 70 boxes

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The additive inverse of 19 /- 6 is -19 /+ 6 and the additive inverse of 2 3 is -2 3.

Additive inverse is a mathematical term that refers to when two numbers are combined and their sum is equal to zero. To calculate the additive inverse of a fraction, you need to change the sign of the numerator and denominator. In the case of 19 /- 6, the -6 is already negative, so you just need to change the sign of the numerator from 19 to -19. Similarly, for 2 3, you need to change the sign of the numerator from 2 to -2. This would mean that the additive inverse of 19 /- 6 is -19 /+ 6 and the additive inverse of 2 3 is -2 3.

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The volume of the cylinder-shaped candle is 157 in³ which diameter and height are 5 inches and 8 inches.

What is cylinder ?

A cylinder is a three-dimensional geometric shape that has two parallel bases that are circular in shape and a curved lateral surface connecting the bases. The bases are located at the top and bottom of the cylinder. The distance between the bases is the height of the cylinder and the distance across the base is the diameter of the cylinder.

The volume of a cylinder is given by the formula V = [tex]\pi r^{2}h[/tex], where r is the radius and h is the height ,

To find the volume of the cylinder-shaped candle, we first need to find the radius. The diameter is given as 5 inches, so we can divide that by 2 to find the radius,

r = 5 inches / 2 = 2.5 inches

Now we can plug this value of r and the given height of 8 inches into the formula:

V = [tex]\pi r^{2}h[/tex] = π(2.5 inches)^2(8 inches) = 3.14 * 6.25 * 8 = 157 in³.

Hence , The volume of the cylinder-shaped candle is 157 in³ which diameter and height are 5 inches and 8 inches.

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The interest earned at 1.6% for 20 years will be $960.

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used.

Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Given that a new bank customer with ​$3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.6​%.

The interest after 20 years will be calculated as,

SI = ( P x R X T ) / 100

SI = ( 3000 x 1.6 x 20 ) / 100

SI = $960

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The circle's shaded area, which has a sector angle of 50 degrees and an arc length of 5/3 pie, has a surface area of 15.67m2.

A circle is created in the plane by each point that is a specific distance from another point (center).  Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.

given

A / θ = πr² / 2π

A / θ = r² / 2

A = r² * θ / 2

A = (5/3)^2 * 25

A  = 15.67 m2

The circle's shaded area, which has a sector angle of 50 degrees and an arc length of 5/3 pie, has a surface area of 15.67m2 .

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The completed question is :-

In circle E , the length of FG = 5/3π  and ∠FEG = 50°  . Find the area shaded below. Express your answer as a fraction times .

Irene's measuring error is 12.5% when she believes she has space for a 45-inch-wide bookcase but only has enough for a 40-inch-wide bookcase.

A data value's approximation error is the difference between an exact value and some approximation to it. This inaccuracy can be stated as either an absolute or relative error. A computing machine accuracy or measurement mistake can generate an approximation error. The difference between the estimated and real values in relation to the actual value is indicated as a percentage. In other words, the relative error multiplied by 100 equals the percent error. The percentage error compares an estimate to the true amount and expresses the difference as a percentage. This statistic enables analysts to determine the magnitude of the inaccuracy in relation to the real value.

Here,

percent error,

=(45-40)/40*100

=5/40*100

=12.5%

The percent error in irene's measurement is 12.5% when she thinks she has space for a 45-inch-wide bookcase but turns out that she only has space for a 40-inch-wide bookcase.

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The location of the vertex of this graph is (-1, -18)

From the question, we have the following parameters that can be used in our computation:

The graph

The vertex of a graph is the minimum or the maximum of a graph

In this case, it is a minimum and the minimum is located at (-1, -18)

Hence , the vertex is (-1, -18)

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Answer: Can you show the whole problem please?

Step-by-step explanation:

Figure A is replicated in scale in Figure B. A figure that is geometrically identical to the original figure is called a scale copy.

Given are two triangular figures, Figure A and Figure B.

The scale factor from figure A to figure B is requested of us.

As a result, Figure B is the last figure and Figure A is the first figure.

Any figure's scale factor is described as stated in equation (1)

[tex]Scale Factor =\frac{\text { Final Dimension }}{\text { Initial Dimension }} \ldots \ldots . . .(1)$[/tex]

We can see from the preceding figures that while figure A uses 4 squares to represent the length of a pair of one parallel sides, figure B only needs 2 squares to represent the same length.

As a result, we can write that using equation (1).

[tex]Scale factor =\frac{\text { Dimension of figure } \mathrm{B}}{\text { Dimension of figure } \mathrm{A}}=\frac{2}{4}=\frac{1}{2}=0.5$[/tex]

Since the scale factor is smaller than 1, the figure is contracted, and the scale factor from Figure A to Figure B is therefore 0. 5.

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Answer:

y-9=5(x-6)

Step-by-step explanation:

the equation is y-y1=m(x-x1)

Answer:

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

Point-slope form:

Substitute:

The line is:

ABC is a right-angled triangle.

A triangle in which one angle is 90 degree is called a Right Angled Triangle.

AB is congruent to DB because segment DE was constructed so that

DE = AB, BC is congruent to EF, because segment EF was constructed so that EF = BC,

Since Triangle DEF is a right-angled triangle.

Using Pythagoras Theorem,

DE² +EF²  = DF²  

We are given that AB²+BC² = AC²

Since, DE = AB and EF = BC, DE²  +EF²  = AC²

Also, DF² = AC² by the above equation.

DF = AC

So AC is congruent to DF by the definition of congruence.

Δ ABC ≅ Δ DEF by SSS rule

Therefore, ABC is a right-angled triangle.

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Answer:  Arc EG/GE = 135°

Step-by-step explanation:

Given:

∠EGF = 80°

Arc FG = 65°

Since ∠EGF = 80°, the value of Arc EF = 2(∠EGF)

Therefore, Arc EF = 2(80°) = 160°

The arc measure of an entire circle is 360°.

Therefore,

360° = EF + FG + GE

360° = 160° + 65° + GE

GE/EG = 135°

Randomly surveyed 50 seventh-grade students at Pablo's school.

What is confidence in statistics?

In statistics, confidence refers to the level of certainty or trust in the accuracy of a statistical estimate. A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence. The level of confidence is usually expressed as a percentage, such as 95% or 99%.

In this experiment, the focus is on seventh graders, and therefore a more representative sample of the population will be selected 50 seventh-grade students from Pablo's school. Selecting this category of the sample will increase confidence in the result of the statistical experiment.

Hence, randomly surveyed 50 seventh-grade students at Pablo's school.

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A triangular frame has two edges lengths measuring 18 inches and 12 inches. The possible value of length for the third side is 32 in.

A triangular frame has two side lengths measuring 18 inches and 12 inches. as we know that the sum of any two sides of a triangle is always greater than the third side.

That is, the third side < 18 +12

third side < 30

according to the question, the option that fits perfectly is 32in.

Hence, The possible value of edges for the third side is 32 in.

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Answer:

PLS GIVE IT TO ME

Step-by-step explanation:

Answer:

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

Answer: 24 = 4x

Step-by-step explanation:

First define a variable for the unknown quantity : in this situation we’ll let x represent the cost of one sandwich

now we know that 4 Sandwiches multiplied by x will equal 24

so 4x = 24 or 24 = 4x

Answer:

Step-by-step explanation:

the volume of rectangle is length * width * height

so v=(3x-4)*(3x+4)*2x=(9x^2-16)*2x=18x^3-32x

maybe the choice is D

The score on his next test must be at least 97 to get an average score of at least 85.

Average value of a set of numbers is a single number which represents the whole numbers in the set.

Average value of a set of numbers is calculated by dividing the sum of all the numbers by the number of values in the set.

Here is is given that,

Jerrod had scores of 75, 82, 94 and 77 on his first four history tests.

We need to find the score of his next test such that the average of all is at least 85.

Let x be the score of his next test.

(75 + 82 + 94 + 77 + x) / 5 ≥ 85

75 + 82 + 94 + 77 + x ≥ 85 × 5

328 + x ≥ 425

x ≥ 97

Hence Jerrod must have at least a score of 97.

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Answer:

the probability of landing on a number less than seven is 2/3 which is five and six

the probability of landing on a factor of forty- two is the same which is 2/3 because it is 6 and 7

The probability that at least 2 people believe that they have seen a UFO is 0.264.

Here, n = 10, p = 0.1, (1 - p) = 0.9 and x = 2

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 2).

P(X >= 2) = (10C2 * 0.1^2 * 0.9^8) + (10C3 * 0.1^3 * 0.9^7) + (10C4 * 0.1^4 * 0.9^6) + (10C5 * 0.1^5 * 0.9^5) + (10C6 * 0.1^6 * 0.9^4) + (10C7 * 0.1^7 * 0.9^3) + (10C8 * 0.1^8 * 0.9^2) + (10C9 * 0.1^9 * 0.9^1) + (10C10 * 0.1^10 * 0.9^0)

P(X >= 2) = 0.194 + 0.057 + 0.011 + 0.001 + 0 + 0 + 0 + 0 + 0

P(X >= 2) = 0.264

The probability is 0.264.

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Answer: Obtuse scalene

Step-by-step explanation: Hope it helps, please mark brainliest and give thanks.

Answer:

obtuse scale

Step-by-step explanation:

Step-by-step explanation:

-5° < 8°

that is all that is to it. really. you see ? an inequality, meaning that 2 terms or expressions are compared (like on a balance).

they can be totally balanced, that means they are equal, and then we have an equation.

or one can be bigger ("heavier"), and so one side is smaller and the other larger. and that is then not equal. we have an inequality.

scalene triangle is a type of triangle in which all the three sides have different lengths.

A triangle is scalene if all of its three sides are different (in which case, the three angles are also different). If two of its sides are equal, a triangle is called isosceles.

A scalene triangle is uneven in the sense that all three sides are of different lengths.

Explanation:

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Area of the enclosed figure is, 8√ 5 (5 + 2√5) units².

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Maria plots the following points on a coordinate grid.

Here, Points are,

⇒ (1, 3) (5, 7) (5, 5) (8, 9) (8, 3 ) (1, 3)

Clearly, It make pentagon.

And, Area of pentagon = 1/4 √5 (5 + 2√5) a²

Here, The side of pentagon = √ (7 - 3)² + (5 - 1)²

                                           = √4² + 4²

                                           = √32

                                           = 4√2

Thus, Area of figure = 1/4 √5 (5 + 2√5) a²

                               = 1/4 √5 (5 + 2√5) (4√2)²

                               = 8√ 5 (5 + 2√5)

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So, the indicated value of the subject using direct capitalization is $995,909.09.

To find the indicated value of the subject property using direct capitalization, you need to use the following formula:

NOI / Cap Rate = Indicated Value

The overall capitalization rate is 6.00% and the projected first-year NOI is $247,000.

Therefore, Indicated value can be calculated as:

Indicated Value = $247,000 / 0.06 = $4,116,666.67

Another way to find the indicated value is using the Going-out cap rate, which is 22.0% and fifth-year NOI $218,300.

Indicated Value = $218,300 / 0.22 = $995,909.09

It's important to note that a pro forma is a projection and not a guarantee of future results. Also, the value obtained from using direct capitalization method is an indication, not the actual value, as it's based on certain assumptions and it may not reflect the current market conditions.

Therefore, the indicated value of the subject using direct capitalization is $995,909.09

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The measure of the angle m<ROS = 14°.

What is the angle?

An angle is a geometric figure that is defined by two rays that have the same endpoint. The rays are called the sides of the angle and the common endpoint is called the vertex of the angle. The angle is the amount of rotation between the two rays, measured in degrees or radians.

In the given figure,

m<QOS = 46, m<POR = 58 and m<POQ = 26

m<POR = m<POQ + m<QOR

58 = 26 + m<QOR

m<QOR = 32

m<QOS = m<QOR + m<ROS

46 = 32 + m<ROS

m<ROS = 14

Hence, the measure of the angle m<ROS = 14°.

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The slope that is parallel to 3x + y = 9 is -3.

Perpendicular slope is 1/3.

The slope of two lines is considered parallel if the slopes are equal, and the slope of two lines is considered perpendicular if the product of the slopes is -1 or would be negative reciprocals of each other.

Given the equation of a line as 3x + y = 9, rewrite in slope-intercept form to find the slope.

3x + y = 9

y = -3x + 9

The slope is -3. The negative reciprocal of -3 is 1/3, because it has a product of -1.

Therefore, parallel slope to the line is: -3, while perpendicular slope is 1/3.

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