Find the sum of a finite geometric series.

The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the length of the outer triangle. This process is continued until three triangles are inscribed in the first triangle. The sum of the perimeters of all four triangles is ______ inches.

Answer:

Step-by-step explanation:

If we had a division problem that read "16 divided by 8 equals 2", the 8 would be outside the division sign, the 16 would be under the division sign, and the 2 would be sitting on top of the division sign.  The 8 is called the divisor, the 16 is called the dividend, and the 2 is called the quotient.

The answer you want, then, is "dividend"

The number by which another number is divided is called a divisor. This applies to many mathematical operations, including division, multiplication, and calculations involving exponents, such as in scientific notation.

A number by which another number is to be divided is called a divisor. When we consider a division operation, we usually think of it as a 'dividend' divided by a 'divisor' equals a 'quotient'. If you take an example of 16 ÷ 4 = 4, here, 16 is the dividend (the number being divided), 4 is the divisor (the number that divides the dividend), and the resulting 4 is the quotient (the result of the division).

Similarly, this concept can be applied to complex mathematical operations such as multiplication and division in scientific notation or logarithmic expressions. For example, in scientific notation, when you want to divide two numbers, you divide the numbers out front and subtract the exponents.

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Answer:

The center is at 2

Step-by-step explanation:

The spread is only from 0 to 5.

There are two clusters (one at 0-2 and one at 4-5)

The peak is at 5 not at 8

Answer:

oh i did this one the answer is B.

Answer:

0

Because -2/3x-1=2-2/3x

-2/3x+2/3x=2+1

0=3

and that's wrong, so there is no solution.

ANSWER

A. 0

EXPLANATION

The first equation is

2x + 3y = 6

The second equation is

y=-2/3x-1

Let us rewrite the first equation in slope-intercept form.

3y =-2x+ 6

[tex]y = - \frac{2}{3} x + 2[/tex]

We can see that both equations has the same slope,

[tex] m = - \frac{2}{3} [/tex]

but different y-intercepts.

This implies that the two lines do not intersect because they are parallel.

Therefore the system has no solution.

Answer:

C, 1/2 of the time.

Step-by-step explanation:

all the seconds added together is 90. 45 is half of 90, so half the time the light will be green, the cars will have a 50% chance of coming up to a green light.

Answer:

C.

Step-by-step explanation:

The range of the given data is $48.50, i.e. option D.

The range is defined as a relation between a set of inputs having one output each.

We have,

The prices of the 10 most popular truck tires,

i.e.

$249.99, $239.99, $236.99, 223.99, 221.99, $219.99, $219.99, $212.49, $207.49, $201.49.

Now,

Arrange the given data in the ascending form,

i.e.

$201.49, $207.49, $212.49, $219.99, $219.99, $221.99, $223.99, $236.99, $239.99, $249.99.

Now,

We have,

The Greatest and the smallest number,

i.e.

Greatest number = $249.99

Smallest number = $201.49

So,

The range = Greatest number - Smallest number

i.e.

The range = $249.99 - $201.49 = $ 48.50

So,

The range of the given data is $48.50.

Hence, we can say that the range of the given data is $48.50, i.e. option D.

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Answer:

the second one would be more effective because $800*12 will cost a lot more than $650+2 months penalty if u leave

The following integers from least to greatest are as follows:

0, -2, -4, -5, -6

Answer:

-6, -5, -4, -2, 0

Step-by-step explanation:

Find them on the number line and read them from left to right.

__

You can also enter the numbers into a spreadsheet and use the 'sort' function.

_____

The key understanding here seems to be that negative numbers with a larger magnitude are smaller or less than negative numbers with a smaller magnitude:

-6 is less than -5

And all negative numbers are less than zero or any positive numbers.

Answer:

  22.6°

Step-by-step explanation:

Since all three sides of the right triangle are given, you can use any of the trig ratios to find the angle. I choose to use the tangent.

  tan(A) = BC/AC = 5/12

Then the inverse trig function tells you ...

  A = arctan(5/12) = 22.6°

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

Option B.

Step-by-step explanation:  

we know that

If a ordered pair is a solution of the system of inequalities

then

the ordered pair must satisfy both inequalities of the system

Verify each case

Case A) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2< -3[/tex] ----> is not true

therefore

The ordered pair is not a solution of the system A

Case B) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2> -3[/tex] ----> is true

Inequality 2

[tex]-2 \geq \frac{2}{3} (3)-4[/tex]

[tex]-2\geq -2[/tex] ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2<-3[/tex] ----> is not true

therefore

The ordered pair is not a solution of the system C

Case D) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2>-2[/tex] ----> is not true

therefore

The ordered pair is not a solution of the system D

Answer:

i think it is b as well! on edg

Step-by-step explanation:

Answer:

a. [tex]A\geq B[/tex]

Step-by-step explanation:

[tex]sin\frac{\pi }{2} =1[/tex]

and

[tex]cos(-\pi )=-1[/tex]

Answer:

Sin (pi/2) > Cos (-pi)

Step-by-step explanation:

Sin (pi/2) = 1

Cos (-pi)  -1

Answer:

6.4 m

Step-by-step explanation:

We have 2 expressions here.  The first one is the fact that r = y.  That's one of 2 equations.  The second one involves whats' left after cutting off certain lengths of each color string.  We cut 2.5 m from red, we cut 3.8 m from yellow.  We know that what's left of red is 1.5 times the length of what's left of yellow.  What's left of red is r - 2.5; what's left of yellow is y - 3.8.  We know that r = 1.5y, so filling that in with our corresponding expressions gives us

r - 2.5 = 1.5(y - 3.8)

Distribute to get

r - 25 = 1.5y - 3.2

Now from the first expression, r = y, so fill in y for r to get an equation in one variable:

y - 2.5 = 1.5y - 3.2

Combine like terms:

-.5y = -3.2 and divide to get

y = 6.4

Check it to make sure it works.  What's left of red should be 1.5 times the length of what's left of yellow and y = 6.4:

What's left of red: 6.4 - 2.5 = 3.9

What's left of yellow: 6.4 - 3.8 = 2.6

1.5 x 2.6 = 3.9, just like it should!

Answer:

4 yards. The radius is half the diameter of the circle and the length of one point of the circle to the center of the circle.

Step-by-step explanation:

Final answer:

The diameter of a prize wheel with a radius of 2 yards is calculated by multiplying the radius by 2, resulting in a diameter of 4 yards.

Explanation:

Akash, a contestant on a game show, gets to spin a prize wheel with a radius of 2 yards. The diameter of a circle is twice the length of its radius. Therefore, to find the prize wheel's diameter, we simply need to multiply the radius by 2.

Calculating Diameter:

Diameter = 2 × Radius
Diameter = 2 × 2 yards
Diameter = 4 yards

The prize wheel's diameter is 4 yards.

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 3y = 4 into this form

Subtract 2x from both sides

3y = - 2x + 4 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex], hence

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (- 2, 15) into the partial equation

15 = - 3 + c ⇒ c = 15 + 3 = 18

y = [tex]\frac{3}{2}[/tex] x + 18 → B

The equation of the line that passes through (-2, 15) and is perpendicular to 2x + 3y = 4 is y = 3/2x + 18.

Option B is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

To find the equation of the line that is perpendicular to 2x + 3y = 4, we need to first find its slope.

We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:

2x + 3y = 4

3y = -2x + 4

y = (-2/3)x + 4/3

So the slope of line 2x + 3y = 4 is -2/3.

Now,

Since we want a line that is perpendicular to this line, we know that its slope will be the negative reciprocal of -2/3, which is 3/2.

Now we have the slope and a point (-2, 15) that the line passes through.

We can use the point-slope form to write the equation:

y - 15 = 3/2(x + 2)

Simplifying:

y - 15 = 3/2x + 3

y = 3/2x + 18

Thus,

The equation of the line that passes through (-2, 15) and is perpendicular to 2x + 3y = 4 is y = 3/2x + 18.

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Answer:

y = 178.3 ft

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan27° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{350}[/tex]

Multiply both sides by 350

350 × tan27° = y, hence

y = 178.3

Answer:

  27

Step-by-step explanation:

If the slope of f(x) is no less than 3, then the value of f(9) can be no less than 27.

  f(x) ≈ f(4) +f'(x)·(x-4)

  f(9) = 12 +3(9 -4) = 27 . . . . . for f'(x) = 3.

For larger numbers of f'(x), f(9) will be larger.

We want to find the minimum possible value of f(9) given that:

We will see that the smallest value that f(9) can take is 27.

We know that the derivate of f(x) gives the slope to the tangent line to the graph of f(x) in a given point where it is evaluated.

If this slope is positive, the function is increasing. So if we want to find the minimum value for f(9), then we need to take the smallest slope possible (knowing that it is positive).

Then we must use f'(x) = 3

Now, we can integrate this to get:

f(x) = 3*x + b

Where b is a constant of integration, to find the value of b, we can use the fact that f(4) = 12, then:

12 = f(4) = 3*4 + b

12 = 12 + b

12 - 12 = 0  = b

Thus the equation is just:

f(x) = 3*x

Now we can evaluate this in x = 9 to get:

f(9) = 3*9 = 27

The smallest value that f(9) can take is 27.

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Answer:

4) reflexive property of congruence

5) SAS theorem

6) property of Congruent triangles

Step-by-step explanation:

Given:

In ΔXYZ, line YW ⊥ XZ

Also XW≅ZW

Now

4) by reflexive property of congruence that states that any line,object or figure is congruent to itself

hence YW≅YW

5) By SAS theorem that states that if the two corresponding sides and the angle between those sides of two triangles are congruent then the two triangles are said to be congruent.

Hence ΔWXY≅ΔWZY

6) By property of Congruent triangles that states that if two triangles are congruent then their corresponding sides are also congruent.

Hence XY≅ZY !

Answer:  the answer is a

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

2a. The block of wood has the shape of a rectangular prism.  The log has the shape of a cylinder.

2b. Density is mass divided by volume.  We know the mass, but we need to find the volume.

Volume of a rectangular prism is:

V = whl

where w is the width, h is the height, and l is the length

V = (18)(10)(8)

V = 1440 in³

So the density is:

d = 46.65 lbs / 1440 in³

d = 0.0324 lb/in³

2c.  Volume of a cylinder is:

V = πr²h

where r is radius and h is height.

The circumference is C = 2πr, so r = C / (2π).

r = 25.12 / (2*3.14)

r = 4.00

V = 3.14 (4.00)² (21)

V = 1055.04 in³

So the density is:

d = 39.25 lb / 1055.04 in³

d = 0.0372 lb/in³

2d.  The block is less dense than water; the log is more dense than water.  So he should make the boat out of the block.

Answer:

189°

Step-by-step explanation:

∠UPR = ∠UOP + ∠POQ + ∠QOR = 81° + 56° + 52° = 189°

Answer:

I think it is 25.

Step-by-step explanation:

Answer with explanation:

Population Mean = 25

Standard Deviation =2.5

[tex]Z_ {Score} =\frac{5}{100}\\\\Z_ {Score} =0.05\\\\Z_{0.05}=0.5199[/tex]

Let ,Margin of error= m

 And, Sample Population = n  

[tex]m=Z_{0.05} \times \frac{\sigma}{\sqrt{n}}\\\\ m=0.5199 \times \frac{2.5}{\sqrt{25}}\\\\m=0.5199 \times 0.5\\\\m=0.25995[/tex]

m= 0.2599 × 100%

m=25.99%=26%

Option A: 25=Margin of error

Answer:

first name the triangles

triangle 1=triangleABC

triangle2=trianglePQR

therefore,SSS:sideAB of ABC=sidePQ of PQR

Answer:

-7+6i

Step-by-step explanation:

On the Cartesian x-y plane, a point is located by giving the ordered pair of its coordinates. A point in this position on the x-y plane would have coordinates (-7, 6). That is, it is located 7 units to the left of the vertical axis, and 6 units above the horizontal axis.

The complex plane is similar in many ways, but each point represents a single number (not a pair of numbers). That single number has two parts: a real part and an imaginary part. The real part is measured by the real axis, a horizontal axis that looks very much like the x-axis of a Cartesian plane. The imaginary part is measured against the imaginary axis, a vertical axis that looks very much like the y-axis of a Cartesian plane.

Just as an ordered pair locates a point on the Cartesian plane, a complex number with a real part and an imaginary part locates a point on the complex plane. The imaginary part is identified by the "i" multiplier. (In some fields of study, notably Electrical Engineering, "j" is used instead of "i", because "i" has a different meaning.)

Here, your point is 7 units left of the imaginary axis, so has a real part of -7. It is 6 units above the real axis, so has an imaginary part of 6. When both parts are written together, the number is written -7+6i.

Comparing this form to a+bi, we find a=-7, b=6.

Final answer:

Option B, a one-time bonus of 10% of a worker’s annual salary, is not an example of exponential growth or decay because it does not involve a percentage change being applied repeatedly over time to a changing base amount.

Explanation:

The question asked is: Which of the following is not an example of exponential growth or decay? The options are: A. a t-shirt shrinks by 2% after each wash, B. a one time bonus of 10% of a worker’s annual salary, C. a yearly pay increase of 3% each year, D. a savings account growing by 3% each year. To answer this, we must recognize that exponential growth or decay refers to processes that grow or decrease at a rate proportional to their current size. This means the amount of increase or decrease changes over time, as it is a percentage of an ever-changing base amount.

Options A, C, and D all describe situations where the quantity changes by a fixed percentage over time, indicative of exponential growth (or decay, in the case of shrinking). Option A discusses a t-shirt shrinking by 2% after each wash, meaning each time it shrinks, it does so based on its current size, which is a characteristic of exponential decay. Option C talks about a yearly pay increase of 3% each year, and Option D describes a savings account growing by 3% each year; both are examples of exponential growth. Therefore, the answer is Option B, a one-time bonus of 10% of a worker’s annual salary, as it does not describe a situation where the growth rate is applied over time to an ever-changing base amount.

Answer:

x = -0.04166666667

Step-by-step explanation:

2x + 8 * 96 = 0

2x * 96 = -8

x/2 * 96 = -8/2

x * 96 = -4

x = -4/96

x = -0.04166666667

Answer:

198

Explanation:

The way to solve this equation is by using the "X=96" from moving it to the x in the equation witch makes it "2(96) + 6" When the variable is after the letter like 2x it always means multiplying. So when you multiply 2(96) together you get 192, then you would add 6+192 which would equal 198. I hope I helped! :D

Answer:

6.125 minutes per song

Step-by-step explanation:

Unit rates are based on a single unit of something.  Like price per 1 gallon of gas; price for 1 pound of bananas; miles driven per 1 gallon of gas, etc.  What we are looking for in minutes per song.

Use a proportion to solve this with minutes on top and number of songs on the bottom.  We know that 49 minutes = 8 songs, and we want to know how many minutes (x) per 1 song:

[tex]\frac{min}{song}:\frac{49}{8}= \frac{x}{1}[/tex]

Cross multiply to get

8x = 49 so

x = 6.125 minutes per song

The question asked was about finding the average length of songs on a CD. We calculated this by dividing the total length of the CD (49 minutes) by the total number of songs (8), which gives us an average song length of 6.125 minutes.

The subject of the question is average, a fundamental concept in mathematics. In this particular question, we need to find out the average length of the songs on Randall's CD. We know that the total length of his CD is 49 minutes, and he has recorded 8 songs on it. Finding the average involves dividing the total by the number of units.

The steps to find the average length per song are as follows:

Upon carrying out this calculation, we discover that the average length of each song is approximately 6.125 minutes.

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Answer:

if she drove away she would have to drive 14 hours, or if it were i the same direction she would have to drive 2 1/2 hours

Step-by-step explanation:

8 1/4 + 5 3/4 = 14

8 1/4 - 5 3/4 = 2 1/2

Lisa has to drive an extra 2 1/2 hours to get to her aunt's house compared to her uncle's house. This is determined by converting the mixed numbers to improper fractions, subtracting the smaller fraction from the larger one, and simplifying the result.

The subject of this question falls under Mathematics, specifically subtraction of fractions. In this question, Lisa takes 8 1/4 hours to get to her aunt's house and 5 3/4 hours to get to her uncle's house. The time difference is the extra distance she must travel to reach her aunt's house compared to her uncle's house.

So, Lisa has to drive for an extra 2 1/2 hours to get to her aunt's house as compared to her uncle's house.

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The Answer is 7.7

Add all the Shoe size From the second Table

7+7+10+6+9+6+8+7.5+8.5+8=77

77 divide by the number of Shoe size

There are 10 shoe size So,

77/10=7.7

Hope this Help:)

Answer:

7.7

Step-by-step explanation:

The mean (or average) is the sum of the data points divided by the number of data points.

μ = (7 + 7 + 10 + 6 + 9 + 6 +8 + 7.5 + 8.5 + 8) / 10

μ = 77/10

μ = 7.7

Answer:

f(- 2) = 20

Step-by-step explanation:

To evaluate f(- 2) substitute x = - 2 into f(x)

f(- 2) = (- 2)² - 5(- 2) + 6 = 4 + 10 + 6 = 20

The value of the function f(x) = x² - 5x + 6 at x = -2 is 20 after plugging the value of x is -2 in the function.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = x² - 5x + 6

Plug x = -2

f(-2) = (-2)² - 5(-2) + 6

f(-2) = 4 + 10 + 6

f(-2) = 20

Thus, the value of the function f(x) = x² - 5x + 6 at x = -2 is 20 after plugging the value of x is -2 in the function.

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Answer:

162π ft²

Step-by-step explanation:

The surface area (SA) of a sphere is

SA = 4πr² ← r is the radius

Calculate r from the volume, that is

V = [tex]\frac{4}{3}[/tex]πr³ = 972π

Multiply both sides by 3

4πr³ = 2916π ( divide both sides by 4π )

r³ = [tex]\frac{2916\pi }{4\pi }[/tex] = 729

Take the cube root of both sides

r = [tex]\sqrt[3]{729}[/tex] = 9, hence

SA = 4π × 9² = 4π × 81 = 324π