State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Rotation symmetry is also called mirror symmetry.

Determine whether each infinite geometric series diverges or converges.

The series converges.

If the series converges, state the sum. 4+2+1+ . . .

The sum of the infinite series is 8

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=4\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{2}{4}=\frac{1}{2}[/tex]

Since , [tex]\vert r\vert < 1[/tex]  , the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{4}{1-\frac{1}{2} } =\frac{4}{\frac{1}{2} }=8[/tex]

The sum of the infinite series is 8

What is an infinite geometric series?

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The total change in the stock market from the beginning of the day to the end of the day is 89.75 points.

Here, we are given that the stock market goes down 30 1/2 points at the beginning of the day.

30 1/2 can be written as-

{(30*2) + 1}/2 = 61/2

Further it is given that the stock market goes up by 120 1/4 points at the end of the day.

120 1/4 can be written as-

{(120*4) + 1}/4 = 481/4

Thus, the total change in the stock market will be-

481/4 - 61/2

= 481/4 - 122/4

= 359/4

or 89.75

Thus, the total change in the stock market from the beginning of the day to the end of the day is 89.75 points.

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The eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.

According to the give question.

We have a sequence 1/2, 1/4, 1/8, 1/6, 1/32

Since, the first term of the given sequence is 1/2.

The second term of the given sequence is 1/4.

The third term of the given sequence is 1/8.

Here, we can see that the numerator of each term is same i.e. 1. But the denominator is changing by power or 2. For the first term it is 2^1, for the second term it is 2^2, for the third term it is 2^3 and so on.

Therefore, the gneral formula for finding the nth term of the given sequence is given by

[tex]T_{n} = \frac{1}{2^{n} }[/tex]

So, the eighth term of the given sequence is 1/2^8 = 1/256.

Hence, the eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.

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After 6 weeks of training, Jorge will have run the equivalent of 13.5 races.

When two quantities, expressions, or numbers have the same value, they are said to be equal. An equivalent quantity can be expressed in a variety of ways, such as by a bar or an equivalent symbol. Because they can relate to it in their everyday lives, children find this topic to be particularly engaging for a variety of reasons.

A common or logical equivalency between several values or quantities can also be referred to as the equivalent. Equivalence is comparable to equality but distinct from it.

1 race = 20 miles

Lets assume he doesn't runs on Sunday and Thursday, thus

Miles he runs a week = (Monday + Tuesday + Friday) + ( Wednesday +Saturday)

1 week = (7 + 7 + 7) + (12 + 12)

           = 45 miles

If he runs for 6 weeks then

6 week's run = 6 × 45

                      = 270 miles

If 1 race is of 20 miles then in 6 weeks he would have ran  

= 270/20

= 13.5 races

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Answer:

32

Step-by-step explanation:

Sorry for not neat explanation but i hope u understand

Answer:

32?

Step-by-step explanation:

when i did it with a Pythagorean theorem calculator i got 32

============================================

Explanation:

x = length of the red and purple lunch box

y = length of the blue lunch box

volume = length*width*height

The volume expression for the red and purple lunch box is x*7.5*4 = 30x

Set this equal to the stated volume 300 cubic inches, and solve for x.

30x = 300

x = 300/30

x = 10

The red and purple lunch box has length of 10 inches.

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

The blue lunch box has volume of

length*width*height = y*8*3 = 24y

Set this equal to 300 and solve for y

24y = 300

y = 300/24

y = 12.5

The blue lunch box has length of 12.5 inches

Therefore the blue lunch box is longer and is longer by 12.5-10 = 2.5 inches.

The slope of the line containing (4,2) and (4,-3) is Infinity.

The slope of a straight line can be written as follows,

m = [tex](y_{2} -y_{1} ) / (x_{2} -x_{1} )[/tex]                  equation1

The line is containing the points  (4,2) and (4,-3). So, we can write

[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = 2 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = 4 .

On substituting the values of variables in equation1, we will get

m = ( (-3)-(2) ) / ( (4)-(4) ) = (-6/0) = Infinity

As the slope of a line is Infinity, so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing (4,2) and (4,-3) is Infinity.

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An equation that models the balance y after x​ months is; y = -130x + 1900

From the given parameters, we can form a table of values as;

Month    Balance

0              1900

3              1510

5              1250

Now, the formula for slope between two coordinates is;

m = (y2 - y1)/(x2 - x1)

At first coordinate, we have;

m = (1510 - 1900)/(3 - 0)

m = -390/3 = -130

At second coordinate;

m = (1250 - 1510)/(5 - 3)

m = -260/2

m = -130

Now, the formula for equation in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, equation is;

y = -130x + 1900

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Complete question is;

Zachary purchased a computer for ​$1,900 on a payment plan. 3 months after he purchased the​ computer, his balance was ​$1,510. 5 months after he purchased the​ computer, his balance was ​$1,250 What is an equation that models the balance y after x​ months?

the two lines have the same slope and different y-intercept, which means that the lines are parallel.

Two linear equations:

y = a*x + b

y = c*x + d

Are parallel only if both have the same slope, which means that c = d, and the y-intercepts are different.

And are perpendicular if the slope of one of the lines is equal to the opposite of the inverse of the other slope, so:

a = -1/c

Now, our linear equations are:

3x + 2y = 6

y = (-3/2)*x + 5

We can write both of these in the slope intercept form:

3x + 2y = 6

2y = 6 - 3x

y = (6 - 3x)/2 = 3 - (3/2)*x

y = -(3/2)*x + 3

So the two lines have the same slope and different y-intercept, which means that the lines are parallel.

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The given sequence is geometric, with common ratio = 1.5

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 10, 15, 22.5, 33.75,....

Here, 15/10 = 22.5/15 = 33.75/22.5 = 1.5

Since the given sequence follows the required condition for a sequence to be geometric, it is the one.

Hence, The given sequence is geometric, with common ratio = 1.5

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Answer:

7x - 35

Step-by-step explanation:

This states the product of (5 less than x) and (7). Five less than x can be written as (x - 5), and 7 is just 7. The product of (x-5) and 7 is 7x - 35.

Hope this helped :)

f (9) =  - 5/2 is the output for the given input .

How can you tell whether a function is linear or not?

f(x)= (2/9)x - (9/2)

Put x = 9    ⇒   (2/9) * 9 - (9/2)

                ⇒   2 - 9/2

                ⇒  -5/2

Therefore f (9) =  - 5/2

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From 125 yards, a marksman hit 55.6 of the targets last year, which is equal to (55.6 × 100)% that is 5560%

A percentage (from Latin: per centum, "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A percentage is a dimensionless (pure) number; it does not have a unit of measurement.

A percentage is a fraction or a ratio in which the full number is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of a possible 100. It is written as 30/100 in fraction form and 30:100 in ratio form.

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Full question

Rewrite the decimal in the sentence below as a percentage.

From 125 yards away, a marksman hit 55.6 of the targets last year.

Answer:

9 degrees

Step-by-step explanation:

Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .

Distance Formula is used to calculate distance between two given points.

the distance between points A(a,b,c) and B(x,y,z) is given by [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2} }[/tex]

Mid point formula the mid point M(m₁,m₂,m₃) between the points  A(a,b,c) and B(x,y,z) is given by M(m₁=[tex]\frac{a+x}{2}[/tex],m₂=[tex]\frac{b+y}{2}[/tex],m₃=[tex]\frac{c+z}{2}[/tex])

To calculate the distance between the points D(0,0,0) and E(1,5,7) we will use distance formula.

Substituting the values in Distance formula we get

d=[tex]\sqrt{(1-0)^{2}+(5-0)^{2}+(7-0)^{2} }[/tex]

=[tex]\sqrt{1^{2} +5^{2} +7^{2} }[/tex]

=[tex]\sqrt{1+25+49}[/tex]

=[tex]=\sqrt{75} \\ 5\sqrt{3}[/tex]

to determine the midpoint M we will use mid point formula.

Substituting the values of the given points in the mid point formula we get

mid point = [tex](\frac{0+1}{2} ,\frac{0+5}{2} ,\frac{0+7}{2} )[/tex]=(1/2,5/2,7/2)

Therefore , Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .

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Answer: 70,464 people

Step-by-step explanation:

         We will write an equation to help us solve. Note that a percent divided by 100 becomes a decimal and that "of" means multiplication in mathematics. Let x be the number of people who will support the measure.

96% of 73,400 voters will support the local measure.

(0.96)(73,400) = x

70,464 people = x

When two sides are provided without an angle measurement, such as a = 13m and b = 17m , we can create an infinite number of obtuse triangles.

As an example:

How many different obtuse triangles can we make if our side lengths are 13m and 17m, and our angle value ranges from 90 to 360 degrees?

Make a triangle with sides of 13m and 17m metres, a 120 degree angle, and a third side that can be protractored to the length you desire. You've constructed a triangle.

We may create a whole different triangle that is identical to this one by altering the third side's length and angle.

You must always remember to select the side lengths and angles. It's hinted that you could choose another course of action. There are an infinite amount of distinct triangles that can be created by using the same angles.

Thus, we can make an infinite number of triangles by employing a single angle and a single side length.

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Answer:

[tex]{ \tt{ {x}^{2} + 6x + 2 = 0}} \\ { \tt{ {x}^{2} + 6x = - 2 }}[/tex]

- Add the square of the half of the sum on either sides:

[tex]{ \tt{ {x}^{2} + 6x + ( { \frac{6}{2}) }^{2} = - 2 + {( \frac{6}{2}) }^{2} }} \\ \\ { \tt{ {x}^{2} + 6x + 9 = - 2 + 9}} \\ { \tt{ {(x + 3)}^{2} = 7}} \\ { \tt{x + 3 = \sqrt{7} }} \\ { \tt{x = - 3 \pm2.648}} \\ { \tt{x = ( - 3 \pm \sqrt{7} )}}[/tex]

The slope of the line passing through the pair of points, (0 , 0) and (5 , -3), is -3/5.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:

m = (y2 - y1)/(x2 - x1)

where m is the slope

x1 and y1 are the coordinates of one point

x2 and y2 are the coordinates of the 2nd point

Given two points in the line, (0 , 0) and (5 , -3), plug in the values to the formula for the slope.

m = (y2 - y1)/(x2 - x1)

m = (-3 - 0)/(5 - 0)

m = -3/5

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The perimeter of a circle with an area of 36 square units is 21.29 units.

For a circle with a radius R, the area is given by the formula:

A = pi*R^2

And the perimeter is given by:

P = 2*pi*R

Where pi = 3.14

In this case the area is A = 36 square units, then the radius is given by:

36 = 3.14*R^2

R = √(36/3.14) = 3.39 units.

Replacing that in the perimeter equation we get:

P = 2*3.14*3.39 units = 21.29 units.

The perimeter of a circle with an area of 36 square units is 21.29 units.

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Answer:

1. 7.8

2. -1/5

3. -16.2

4. -25/8

Step-by-step explanation:

-

Answer:

7.8

-0.2

-16.2

-3.125

I really hope it helps

ps: from ultra instinct Giga Chad

Answer:

One way you could do it is to do a Systematic Sample \textbf{Systematic Sample} Systematic Sample and go to every other house in the neighborhood and ask their opinion.

Step-by-step explanation:

[tex]f(x)=x^2-3x+20\\\\f(5)=(5)^2-3(5)+20\\\\f(5) = 25-15+20\\\\f(5)=\boxed{30}[/tex]

Based on the interest rates available to Michael, the option that would allow him to pay the least interest is B. 18-month loan with a 3.50% annual simple interest rate

The interest on the first option is:
= (7.25% x 12,000) x 12/12months in year

= $870

Interest on second loan:

= (3.5% x 12,000) x 18 / 12 months in year

= $630

Interest on third loan:

= (3.75% x 12,000) x 24/12 months in year

= $900

Interest on fourth loan:

= (2.75% x 12,000) x 36/12  months in year

= $990

In conclusion, the 18-month loan with a 3.50% annual simple interest rate gives the lowest rate.

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the bacterial cell is 6.25*10 times smaller than the amoeba cell.

To find how many times smaller is the bacterial cell than the amoeba cell, we need to take the quotient between the amoeba cell's length and the  bacterial cell's length

We know that:

bacterial cell's length = 4*10^(-6) m

amoebas cell's length. = 2.5*10^(-4) m

The quotient gives:

Q = ( 2.5*10^(-4) m)/(4*10^(-6) m) = (2.5/4)*(10^(-4)*10^6) = 0.625*10^(-4 + 6)

Q = 0.625*10^2

Now we want this in scientific notation, so we need to have a digit in the left fo the decimal point, so we can rewrite this as:

Q = 0.625*10^2 = 6.25*10^1 = 6.25*10

Then the bacterial cell is 6.25*10 times smaller than the amoeba cell.

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The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. Never can one preclude the other. The two events are mutually exclusive if they cannot occur at the same time.

What pairs of occurrences can never coexist?

What are some examples of mutually exclusive events?

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Since the distribution is symmetric, the mean and the median of the distribution are equal.

When a distribution is symmetric, the mean and the median are equal. From the dot plot in this problem, the distribution is uniform(as all outcomes are equally as likely, that is, they have the same frequency in the dot plot), and symmetric, hence the the mean and the median of the distribution are equal.

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The volume of the cone as shown in the diagram is 192 cm²

Diameter in the question is given as 16cm

We need to find the radius of the cone to find the volume of cone which is half of the diameter = 16/2 = 8 cm

The height of the cone as given in the question is 3cm

The volume of the cone =1/3  (πr²h)

We are told to use the value of pi as 3 so we are not using 3.14 or 22/7 as the value of pie

Volume = 1/3  ( 3 × 8² × 3)

= 1/3  ( 9× 64)

  = 1/3  (576)

         = 192 cm²

Hence, the volume of the cone as shown in the diagram is 192 cm²

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Using proportions, it is found that the deducted amounts each year are given as follows:

The tax rates are missing, and they are given as follows:

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

Considering that a year has 52 weeks, her yearly salary is given as follows:

52 x 570 = $29,640.

Considering the tax rate, the deducted amount for Social Security is given by:

0.0620 x 29640 = $1,837.68.

Considering the tax rate, the deducted amount for Medicare is given by:

0.0145 x 29640 = $429.78.

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The solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is n = -2

In this question,

We have been given a rational equation.

[tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex]

We need to find the solution of given rational equation.

First we simplify the LHS of given equation.

[tex]\frac{2}{n} +\frac{n+2}{n+1}\\\\=\frac{2(n+1)+n(n+2)}{n(n+1)} \\\\=\frac{2n+2+n^2+2n}{n^2+n}\\\\ =\frac{n^2+4n+2}{n^2+n}[/tex]

So, given equation would be,

[tex]\frac{n^2+4n+2}{n^2+n}=\frac{-2}{n^2+n}[/tex]

Here, the denominator is same on the both sides.

⇒ n² + 4n + 2 = -2

⇒ n² + 4n + 4 = 0

⇒ (n + 2)² = 0

⇒ n + 2 = 0

⇒ n = -2

We need to check above solution.

so, substitute n = -2 in LHS of given equation.

[tex]\frac{2}{-2} +\frac{-2+2}{-2+1}\\\\=-1+0\\\\=-1[/tex]

Now, substitute n = -2 in RHS of given equation.

[tex]\frac{-2}{-2^2-2}\\\\=\frac{-2}{4-2}\\\\= \frac{-2}{2} \\\\-1[/tex]

For n = -2, LHS = RHS

Therefore, the solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is        n = -2

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