Mathematics High School

Find the sum of the geometric sequence. (7 points) 1 divided by 3, 2 divided by 3, 4 divided by 3, 8 divided by 3, 16 divided by 3

Answers

Answer 1

The sum of the geometric sequence is 31/3

How to determine the sum?

The sequence is given as:

1/3, 2/3, 4/3, 8/3, 16/3

The sum of the sequence is;

Sum = 1/3+ 2/3+ 4/3+ 8/3+ 16/3

Evaluate

Sum = 31/3

Hence, the sum of the geometric sequence is 31/3

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Related Questions

15. When x = -3, what is the value of
|4x²| − 2x − (9 − |−3x|)

(A)0
(B) 12
(℃) 30
(D) 42

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Solving for your equation:}[/tex]

[tex]\mathbf{|4x^2| - 3x - (9 - |-3x|)}[/tex]

[tex]\mathbf{= |(4)(9)|-(2)(-3)-(9-|(-3)(-3)|)}[/tex]

[tex]\mathsf{= |36| - (2)(-3)- (9 - |(-3)(-3)|)}[/tex]

[tex]\mathbf{=36 - (2)(-3) - (9 - |(-3)(-3)|)}[/tex]

[tex]\mathbf{= 36 -(-6) - (9 - |(-3)(-3)|)}[/tex]

[tex]\mathbf{= 42 - (9 - |(-3)(-3)|)}[/tex]

[tex]\mathbf{= 42 - (9 - |9|)}[/tex]

[tex]\mathbf{= 42 - (9 - 9)}[/tex]

[tex]\mathbf{= 42 - (0)}[/tex]

[tex]\mathbf{= 42 - 0}[/tex]

[tex]\mathbf{= 42}[/tex]

[tex]\huge\textbf{Notice that your equation kept getting}\\\huge\textbf{getting smaller and smaller?}\\\\\\\huge\textbf{That's because we kept solving as we got}\\\huge\textbf{closer to your result and we got there}\\\huge\textbf{sooner than we thought :)}[/tex]

[tex]\huge\textsf{ANYWAY!}[/tex]

[tex]\huge\textsf{Therefore, the answer is: \boxed{\mathsf{Option\ D. 42}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Jun Wei is a bus driver who earns $ 1600 per month while Lixin is a manager who earns $ 6800 per
month. In 2012, Jun Wei donated a total of $ 1200 to charitable organisations while Lixin donated a
total of $4500 to charitable organisations. Who donated a higher percentage of his or her annual
income to charitable organisations?

Answers

Answer:

Jun Wei donated a higher percentage than Lixin

calculate it by multiplying monthly salary by 12 then divide the total donated to total earned for both people... you Will Find 6.25 % for Jun Wei but for Lixin You Will get 5.51%

i hope this helps u :)

thank u

Convert 8125 g into kilograms (kg) and grams (g).

Answers

Answer:

8125 x 10^-3

= 8.125

8125 g

= 8.125 kg

Step-by-step explanation:

First, note that g is the same as grams and kg is the same as kilograms. Thus, when you are asking to convert 8125 g to kg, you are asking to convert 8125 grams to kilograms.

A gram is smaller than a kilogram. Simply put, g is smaller than kg. In fact, a gram is "10 to the power of -3" smaller than a kilogram.

Since a gram is 10^-3 smaller than a kilogram, it means that the conversion factor for g to kg is 10^-3. Therefore, you can multiply 8125 g by 10^-3 to get 8125 g converted to kg.

Here is the answer with the math showing you how to convert 8125 g to kg by multiplying 8125 by the conversion factor of 10^-3.

Answer:

8.125kg and 8125g

Step-by-step explanation:

1kg=1000g

write an equivalent expression.
4 + m

Answers

umm maybe m+4 try that cause it’s equivalent

Find (in radians) for an
angle having an arc length of
23 and a radius of 15.
?
0 = ² radians
Enter

Answers

By using the concept of circumference and all known inputs, we conclude that an arc length of 23 and a radius of 15 is equal to 23/15 radians.

How to determine the central angle of an arc

According to the statement, arc length (s) and radius (r) are given:

s = 23, r = 15

The central angle (θ), in radians, is determine by dividing the former by the latter:

θ = s/r

θ = 23/15 rad

By using the concept of circumference and all known inputs, we conclude that an arc length of 23 and a radius of 15 is equal to 23/15 radians.

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Please help me with this geometry question, Im pretty sure you need to use Sas congruence rule

Answers

The information about SAS Congruence is illustrated below.

How to illustrate the information?

The complete information wasn't found. Therefore, an overview will be given. SAS congruence simply means that two triangles are congruent.

This implies that the sides of the triangles are equal. The rule states that if two sides and the angles if one triangle are equal to two sides and included in another triangle, then the triangles are congruent.

For example, given AC = PQ, BC = RQ and angle C = angle P. Then according to SAS, ABC = QRP.

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Polygon abcd has the following vertics: a( -3, 3) b (5, 5) c (5, -4 ), d (-3 -4). caculate the area of the polygon

Answers

Analytic geometry (polygon in the coordinate system).

Mark the point on the coordinate system and draw the polygon (attachment).

This is the trapezoid.

The formula of an area of a trapezoid:

[tex]A=\dfrac{a+b}{2}\cdot h[/tex]

a, b - the lengths of the parallel sides

h - the height

Substitute:

[tex]a=9,\ b=7,\ h=8\\\\A=\dfrac{9+7}{2}\cdot8=\dfrac{16}{2}\cdot8=8\cdot8=64[u^2][/tex]

[tex]\huge\boxed{A=64u^2}[/tex]

Identify the range of the function shown in the graph.

Answers

Answer:

D. 0≤y≤5

Step-by-step explanation:

The range refers to how far on the y axis a function exists on a graph. This function starts at y=0 and ends at y=5, meaning you can find a point on the function for any y-level between 0 and 5. So y is greater than or equal to 0, and is less than or equal to 5.

A: A function with a range of all real numbers goes both up and down infinitely, however this function does not go up and down infinitely so we can rule out A.

B: If y>0, the function would start above y-level 0 and go up infinitely, however this graph does not display that so we can rule out B as well.

C: C is the domain of the graph, which is how far left and right the function exists.

Evaluate: −5−(x+y)2, where x=3 and y=6

Answers

Answer: -23

Step-by-step explanation:

-5-2x-2y

-5-2(3)-2(6)

-5-6-12 = -23

In the figure, ∠ABD = 50° and ∠BCD = 60°.
Calculate ∠ADC and ∠ADO.

Answers

Answ

Step-by-step explanation:

Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6 meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.

What is the distance between points M and N?

meters

Answers

The distance between points M and N according to the task content is; 9.8 meters.

What is the distance between points M and N?

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.

Answers

The statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial function:

[tex]\rm f(x) = x^{3}+2x^{2}-5x-6[/tex]

The function is a cubic function and the graph of the cubic function will be a curve.

As we can see in the graph, f(x) grows larger as x approaches negative infinity. f(x) also becomes closer to infinity as x does.

Thus, the statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

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QT=
Help me please thanks:)

Answers

The length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

By intersecting chords theorem:

QM×QL = QJ×PQ

10×8 = QJ(QJ/4)

4×80 = QJ²

QJ = 4√20 units

Thus, the length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.

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Question 5 of 10
If f(x)=3x-2 and g(x)=x+1, find (f+g)(x).
OA. 4x²-1
OB. +3x+1
OC. +3x-1
OD. 2x+3

Answers

Answer: 4x-1

Step-by-step explanation:

[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=3x-2+x+1\\\\=\boxed{4x-1}[/tex]

Please help me asap!!!!!!!

Answers

D because the answer is 7.94 so it would be closest to 8

On a coordinate plane, solid circles appear at the following points: (negative 5, negative 3), (negative 4, negative 4), (negative 2, 2), (1, 3), (1, negative 2), (2, 1), (5, negative 4).
Which ordered pair can be removed so that the resulting graph represents a function?

Answers

The ordered pair that can be removed so that the resulting graph represents a function is (1, 3) or (1, -2)

How to determine the points?

The ordered pairs are given as:

(-5, -3), (-4, -4), (-2, 2), (1, 3), (1, -2), (2, 1), (5, -4)

For a set of ordered pairs to represent a function, each x value must point to exactly one y value

From the above ordered pairs, we have:

(1, 3) and (1, -2)

The x value 1 has y values 3 and -2

When one of these pairs is removed, the graph becomes a function

Hence, the ordered pair that can be removed so that the resulting graph represents a function is (1, 3) or (1, -2)

Answers

The smallest possible area of the new rectangle is 52 square units.

In the question, we are given that a rectangle has side lengths of integral value.

We assume the lengths to be x and y units respectively, such that x and y are integers.

In the new arrangement, one pair is increased by 30%, and the other pair is decreased by 20%, such that the new sides are also integers.

We assume a 30% increase in x.

New side = x + 30% of x = x + 30/100 of x = x + 3x/10 = 13x/10.

For this to be an integer, x needs to be a multiple of 10.

Since we are considering the smallest area, we will consider the smallest multiple of 10, that is, 10 itself.

Hence, side 1 = 13 units.

We assume a 20% decrease in y.

New side = y - 20% of y = y - 20/100 of y = y - y/5 = 4x/5.

For this to be an integer, y needs to be a multiple of 5.

Since we are considering the smallest area, we will consider the smallest multiple of 5, that is, 5 itself.

Hence, side 2 = 4 units.

Now, the area of this rectangle is the product of its sides = 13*4 sq. units = 52 sq. units.

Therefore, the smallest possible area of the new rectangle is 52 square units.

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From the diagram below, we can tell that < ADB is congruent to ____.

Select one:

a.
< CBA

b.
< DBC

c.
< C

d.
< A

Answers

Answer:

<CBA

Step-by-step explanation:

<CBA = 90 degrees (given)

<ADB = 90 degrees (given)

Hence They are congruent, so choose A

From the diagram below, we can tell that < ADB is congruent to <CBA.

Here, we have,

given that,

from, the given diagram, we get,

both the triangles ABD and BCA are right angle triangle.

here, we have,

angle D = 90

and angle B = 90

so, we have,

<CBA = 90 degrees (given)

<ADB = 90 degrees (given)

Hence They are congruent, so choose A.

From the diagram below, we can tell that < ADB is congruent to <CBA.

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Select the correct answer.
Simplify the following radical expression.
√48
16√3
4√3
4√2
6√2

Answers

Step-by-step explanation:

[tex] = \sqrt{48} [/tex]

[tex] = \sqrt{16 \times 3} [/tex]

[tex] = \sqrt{ {4}^{2} \times 3 } [/tex]

[tex] = \sqrt{ {4}^{2} } \times \sqrt{3} [/tex]

[tex] = 4 \times \sqrt{3} [/tex]

[tex] = 4 \sqrt{3} [/tex]

The answer is B.

which pair of anglers are alternate exterior angles of parallel lines v and w

Answers

In the image given, a pair of alternate exterior angles is: a° and d°.

What are Alternate Exterior Angles?

The exterior angles that lie opposite sides along the transversal that intersects two parallel lines are said to be alternate exterior angles, which are congruent.

In the image given below, angles a and d lie alternate to each other along the transversal and are also exterior angles.

Therefore, a pair of alternate exterior angles is: a° and d°.

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find the HCF of a²b²-2a+1

Answers

Answer:

Step-by-step explanation:

Just '1'

A sales tax of 7% was added to the $36.00 price of a jacket. What was the total cost of the jacket?
a. $36.70
b. $38.10
c. $36.07
d. $38.52

Answers

Answer:

[tex]\huge\boxed{\sf \$ \ 38.52}[/tex]

Step-by-step explanation:

Marked price = $36.00

Sales tax = 7%

Sales tax in $:

= 7% of marked price

= 7% of $36 [Key: "of" means "to multiply"]

= 7/100 * 36

= 0.07 * 36

= $2.52

Selling price:

= Marked price + sales tax

= $36 + $2.52

= $38.52

[tex]\rule[225]{225}{2}[/tex]

The total cost of the jacket was the amount of $38.52. The correct answer is option (d).

To find the total cost of the jacket after adding a 7% sales tax, we need to calculate the tax amount and add it to the original price.

Calculate the tax amount:

Tax amount = 7% of $36.00

Tax amount = 0.07 × $36.00

Tax amount = $2.52

Add the tax amount to the original price:

Total cost = $36.00 + $2.52

Total cost = $38.52

Thus, the total cost of the jacket was the amount of $38.52.

Hence, the correct answer is option (d).

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The formula used to convert degrees Celsius to degrees Fahrenheit is
F = 0+32.
Convert 59°F to degrees Celsius. Solve the formula for C, and then use it to
convert the temperature.
Which is the correct formula and conversion?
A. C= F-32; conversion: 59°F = 135°C
B. C= (F-32); conversion: 59°F = 15°C
C. C= (F-32); conversion: 59°F = 106°C
OD. C=F-32; conversion: 59°F = 15°C

Answers

Answer:

See below

Step-by-step explanation:

Wrong formula ...and all of your answers are messed up too....

F = 9/5 C + 32

re-arrange to:

C = 5/9 ( F-32)

C = 5/9 (59-32) = 15 ° C

A swimming pool is being filled with water. The diameter of the pool is 27 feet, and the height is 4 feet. Which formula best represents the volume of the pool?
V = pi (13.5) (4)
V = pi (13.5) squared (4)
V = pi (27) (4)
V = pi (27) squared (4)

Answers

The expression that best represents the volume is (b) [tex]V = \pi (13.5)^2 (4)[/tex]

How to determine the volume?

The given parameters are:

Diameter, d = 27

Height, h = 4

Start by calculating the radius using:

r = d/2

This gives

r = 27/2

r = 13.5

The volume is then calculated as:

[tex]V = \pi r^2 h[/tex]

This gives

[tex]V = \pi (13.5)^2 (4)[/tex]

Hence, the expression that best represents the volume is (b) [tex]V = \pi (13.5)^2 (4)[/tex]

Answers

The confidence interval for the mean noise at locations is (127.09,148.51).

Given noise levels at 5 airports=152,154,139,124,120

We have to find the confidence interval for the mean noise and sample mean of the data. We know that mean is the sum divided by the number of items taken.

Mean = sum of X values/n

=137.8 (calculated in figure)

s=[tex]\sqrt{(x-x bar)^{2} /n-1}[/tex]

=[tex]\sqrt{972.8/4}[/tex]

=[tex]\sqrt{243.2}[/tex]

=15.59

t value at 80% confidence level with degree of freedom 4 (5-1) is 1.533.

standard error=t value*s/[tex]\sqrt{n}[/tex]

=1.533*15.59/[tex]\sqrt{5}[/tex]

=10.71

Upper level= Mean + standard error

=137.8+10.71

=148.51

Lower level=Mean - standard error

=137.8-10.71

=127.09

Hence the confidence interval for the true mean noise is (127.09,148.51) and sample mean is 137.8.

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The point-slope form of the equation of line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4(x -8). What is
the slope-intercept form of the equation for this line?
y=1/4 x-12
y= 1/4x-4
y= 1/4x+2
y=1/4 x + 6

Answers

Answer:

y = 1/4x +2

Step-by-step explanation:

The slope-intercept form of the equation for a line can be found by solving the given equation for y. It can be written directly from the slope and the y-intercept.

Solve for y

It is helpful to simplify the equation first, then isolate the y-variable by eliminating non-y terms from that side of the equation.

y -4 = (1/4)(x -8) . . . . . . . given

y -4 = (1/4)x -2 . . . . . . . . eliminate parentheses

y = 1/4x +2 . . . . . . . . . . add 4. This is the desired form

Use given information

Alternatively, you can use the given information to write the slope-intercept equation directly. The slope in the point-slope form is the multiplier outside parentheses. In y-4 = 1/4(x -8), the slope is 1/4.

The y-intercept is the point where the line crosses the y-axis. Its coordinates always have an x-coordinate of 0. That is, the given point (0, 2) tells you the y-intercept is 2.

Using the slope and intercept in the slope-intercept form, you get the equation you're looking for:

y = mx +b . . . . . line with slope m and y-intercept b

y = 1/4x +2 . . . . . line with slope 1/4 and y-intercept 2

Solve the problems using your graphing calculator. Round all parameter values to
the nearest hundredth. Complete Steps 1-4 in order.

Caleb is training for an upcoming race. He runs a mile every day, keeps track of his
timing, and records his progress.
Day #
1
2
3
4
5
6
7

Run time (min)
8.2
8.1
7.5
7.8
7.4
7.2
7.1

Step 1: Choose the function that best represents the data.
y= 8.36x -0.19
y=-0.19x+8.36
y = 8.36x+0.19
y=0.19x8.36.

Answers

Drawing a scatter plot for the given values on a graphing calculator, we have;

y = -0.19•x + 8.36

How can the function that best represents the data be found?

The values are;

Day; Running time

1; 8.2

2; 8.1

3; 7.5

4; 7.8

5; 7.4

6; 7.2

7; 7.1

Entering the above values in a graphing calculator, we have;

The slope of the line of best fit = -0.19The x-intercept = 45

Therefore;

0 = -0.19 × 45 + y-intercept

0 = -8.36 + y-intercept

y-intercept = 8.36

The equation found using the statistics function for scatter plot on a calculator is therefore;

y = -0.19•x + 8.36

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The__________or_______a value of the function is found at the vortex.

Answers

Answer:

Step-by-step explanation:

n fluid dynamics, a vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow. The distribution of velocity, vorticity, as well as the concept of circulation are used to characterise vortices. Hope that gave you a clue and hope you learned something new.

The minimum or maximum value of a function is found at the vertex.

The vertex represents either the minimum or maximum point on the graph of the function.

If the quadratic function opens upward, the vertex is the minimum point, and if it opens downward, the vertex is the maximum point.

The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic function in the form ax² + bx + c.

Once you find the x-coordinate, you can substitute it back into the function to obtain the corresponding y-coordinate, which represents the minimum or maximum value of the function at the vertex.

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What is the inevitable result of running statistical inference on a random sample rather than on an entire population

Answers

Your question is incomplete. Please read below to find the complete questin.

B. Sampling error is the inevitable result of running statistical inference on a random sample rather than on an entire population.

A sampling mistake is a statistical blunder that occurs when an analyst does now not pick out a sample that represents the entire population of records. As a result, the outcomes found in the pattern no longer constitute the outcomes that would be received from the entire population.

Sampling error takes place when a sample is chosen from the incorrect populace statistics. Non-reaction errors occur when a user reaction is not received from the surveys. it can happen because of the incapacity to contact capability respondents or their refusal to respond.

The maximum generally used measure of sampling errors is referred to as the same old errors (SE). the standard error is a measure of the spread of estimates across the "true fee". In exercise, only one estimate is available, so the same old blunders can not be calculated at once.

What is the inevitable result of running statistical inference on a random sample rather than on an entire population?

A. Standard deviation

B. Sampling error

C. Sampling distribution

D. Stratified sampling

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The table represents the cost of flowers at the Tigerlily Flower Shop.

Cost of Flowers
Quantity
Price
1
$2.00
2
$3.50
3
$5.00
4
$6.50
5
$8.00
6
$9.00

Which graph is the best interpretation of this table?
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 3.5), (3, 5), (4, 6.5), (5, 8), (6, 9).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. A line with positive slope goes through points (2, 4) and (4, 8).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. A curved line with positive slope is on the graph.

Answers

The graph which is the best interpretation of the table given is; On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 3.5), (3, 5), (4, 6.5), (5, 8), (6, 9).

Which graph is the best interpretation of the table?

The table given in the task content is a tabular representation of the quantity and the corresponding prices. On this note, plotting the quantity on the x-axis and the price on the y-intercept with the point descriptions above best represents the graph of the table.