The ratio of arc length to circumference is the same as the ratio of

The invention that made the rise of the personal computer possible is the microchip (option C).

The computer, as we know it today, is the result of a series of innovations and contributions by many people over several decades. It is difficult to attribute its invention to a single person. Charles Babbage - an English mathematician and inventor who designed the first mechanical computer, the Difference Engine, in the early 19th century.

Here,
The invention that made the rise of the personal computer possible is microchips (option C). Microchips, also known as integrated circuits, are tiny electronic circuits consisting of miniaturized transistors and other components on a small silicon wafer. Microchips allowed the production of smaller, faster, and more powerful computers, making it possible for personal computers to becoming widely available and affordable. While cellular telephones and DVRs have had their own impact on technology, they did not play a significant role in the development of personal computers. Vacuum tubes, on the other hand, were used in the earliest electronic computers but were eventually replaced by transistors and then microchips.

Thus, the invention that made the rise of the personal computer possible is the microchip (option C).

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For this case we have that the perimeter of the figure is given by the sum of the lengths of the sides, that is:

[tex]14 + 18 + 3 + 4 + 3 + 4 + 3 + 4 + (14-9) + (18-12) = 64[/tex]

Thus, the perimeter of the figure is 64 centimeters.

Now, we find the area of the figure:

We have that by definition, the area of a rectangle is given by:

[tex]A = a * b[/tex]

Where:

a and b are the sides of the rectangle

We have 4 vertical rectangles from left to right:

[tex]A_ {1} = 14 * (18-12) = 14 * 6 = 84 \ cm ^ 2\\A_ {2} = (3 + 3 + 3) * 4 = 9 * 4 = 36 \ cm ^ 2\\A_ {3} = (3 + 3) * 4 = 6 * 4 = 24 \ cm ^ 2\\A_ {4} = 3 * 4 = 12 \ cm ^ 2[/tex]

Thus, the total area is[tex]A_ {t} = 156 \ cm ^ 2[/tex]

Answer:

The perimeter of the figure is 64 centimeters.

[tex]A_ {t} = 156 \ cm ^ 2[/tex]

Question:

Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?

There are 15 cups in a gallon

Answer:

The expression to find the number of cups of water she drinks in a week is:

[tex]\frac{15\ cups}{1\ gallon} \times \frac{0.5\ gallons}{1\ day} \times \frac{7\ days}{1\ week}[/tex]

Solution:

Given that,

1 gallon = 15 cups

[tex]\frac{15\ cups}{1\ gallon}[/tex]

Katrina drinks 0.5 gallons of water per day

1 day = 0.5 gallons

[tex]\frac{0.5\ gallons}{1\ day}[/tex]

Find the number of cups of water she drinks in a week

1 week = 7 days

[tex]\frac{7\ days}{1\ week}[/tex]

Thus the expression to find the number of cups of water she drinks in a week is:

[tex]\frac{15\ cups}{1\ gallon} \times \frac{0.5\ gallons}{1\ day} \times \frac{7\ days}{1\ week}[/tex]

Answer:

-1/6

​

Step-by-step explanation:

(−9,8) and (−21,10)

−21−(−9)

10−8  

Plug in.  

−21+9

10−8

​  

The negative of a negative is a positive.  

−12

2

​  

Add/Subtract.  

−  

6

1

​

A positive divided by a negative is a negative.Cancel the common factor of 2.

Final answer:

The slope of the line that passes through the points (-9, 8) and (-21, 10) is calculated using the slope formula and is -1/6.

Explanation:

The slope of a line that passes through two points (x1, y1) and (x2, y2) is calculated using the formula:

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

For the points (−9, 8) and (−21, 10), the slope can be calculated as follows:

m = (10 - 8) / (−21 - (−9))

m = 2 / (−12)

m = −1/6 (which is the slope in simplest form).

Therefore, the slope of the line that passes through the points (−9, 8) and (−21, 10) is −1/6.

Answer:

around $6000 the real answer is $5253.5

Step-by-step explanation:

Answer:

Jill's feet are 17 feet from the balloon.

Step-by-step explanation:

The situation is sketched in the figure attached.

The from the ground to the balloon, the distance from Jack to Jill, and the distance from the balloon to Jill's feet forms a right triangle.

The Pythagorean Theorem says the sum of the squares of the sides of the  right triangle is equal to the square of its hypotenuse [tex]x[/tex]:

[tex](8ft)^2+ (15ft)^2 = x^2[/tex]

simplifying we get

[tex]64ft^2+225ft^2=x^2[/tex]

[tex]289ft^2= x^2[/tex],

and take the square root of both sides to get:

[tex]x = \sqrt{289ft^2}[/tex]

[tex]\boxed{x = 17ft.}[/tex]

Thus, Jill's feet are 17 feet from the balloon.

Answer:

$14.8

Step-by-step explanation:

There is a mistype in the question. It should say: ... si cada uno de ellos hicieron una contribución de dieciseis pesos...

So if everybody contributes $14, they make a total of 14*x, where x denotes the number of students. In this scenario, $4 are left, calling y to the cost of the trip, then:

14*x = y - 4 (eq. 1)

In the other scenario, everybody contributes $16 and $6 are in excess, so

16*x = y + 6 (eq. 2)

subtracting eq. 1 to eq. 2:

16*x - 14*x = y + 6 - (y - 4)

2*x =  y + 6 - y + 4

2*x = 10

x = 10/2 = 5

Replacing this value in eq. 1:

14*5 = y - 4

70 + 4 = y

y = $74

If every student pays: 74/5 =  $14.8, then they would get altogether the exact cost of the trip

Answer: multiply it

Step-by-step explanation:

Answer:

4x / 4 ≤ 25 / 4

x ≤ 6.25

For the first box:  0, 5.25, 3, 6 1/4

5x + 6 - 6 > 21 - 6

5x / 5 > 15 / 5

x > 3

For the second box:  7 3/4, 20, 5.25, 6 1/4

Answer:

Left side: 0, 5.25, 3, 6 1/4

Right side: 7 3/4, 20, 5.25, 6 1/4

Step-by-step explanation:

Plugging everything in should be true to both inequalities.

Answer:

It will take 27.19 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

[tex]A=Pe^{rt}[/tex] , where

∵ Steve deposits $1250 in an account

∴ P = 1250

∵ The account paying 3.4% annual interest compounded continuously

∴ r = 3.4%

- Change it to decimal by dividing it by 100

∴ r = 3.4 ÷ 100 = 0.034

∵ The account balance will reach to $3150.5

∴ A = 3150.5

- Substitute The values of A, P and r in the formula above to find t

∵ ​[tex]3150.5=1250e^{0.034t}[/tex]

- Divide both sides by 1250

∴  ​[tex]2.5204=e^{0.034t}[/tex]

- Insert ㏑ to both sides

∴ ​[tex]ln(2.5204)=ln[e^{0.034t}][/tex]

- Remember that [tex]ln(e^{n})=n[/tex]

∵  [tex]ln(e^{0.034t})=0.034t[/tex]

∴ ​ln(2.5204) = 0.034t

- Divide both sides by 0.034

∴ 27.18875 = t

∴ t ≅ 27.19

It will take 27.19 years

The probability of not getting a odd number is 1/2

Answer:

1/2

Step-by-step explanation:

Ur chances are 1 out of 2 bc there are even and there are odd numbers.

Hope this helps!

Answer:

n = 1/5 or 0.2

Step-by-step explanation:

Given

127/n = 635

Cross multiply

127 = n x 635

Divide both sides by 635

127/635 = n x 635/635

Divide both the numerator and denominator by 127.

We have

1/5 = n

n = 1/5 or

n = 0.2

Answer:

100mm

Step-by-step explanation:

Perimeter is the size of the outer part of the figure. And in this figure, we have a triangle and a semicircle joined together.

Formulae for finding the perimeter of a circle is 2πr, and since it's a semicircle, we divide the answer by 2. Where π is 3.14

2(3.14)(16)/2

50.24

Adding the other parts

50.24+40

90.24

Rounding up to the nearest hundred, we have the number between 0 and 100. 90 is closer to 100 than 0.

Hence, the answer is 100

The total number of digits used to write all the integers from 1 to 12 are 15.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

Given that, Rena wrote all the integers from 1 to 12.

So, the integers from 1 to 12 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Here, 1 to 9 are single digits

10, 11 and 12 has two digits

Thus total number of digits = 9×1+3×2

= 9+6

= 15

Therefore, the total number of digits are 15.

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The total number of digits Rena wrote is:

[tex]\[\boxed{15}\][/tex]

To find the total number of digits Rena wrote when she wrote all the integers from 1 to 12, we need to consider each range of numbers separately based on their digit counts.

1. Single-digit numbers (1 to 9):

  - There are 9 single-digit numbers.

  - Each single-digit number contributes 1 digit.

  - Total digits from 1 to 9:

[tex]\[ 9 \times 1 = 9 \][/tex]

2. Two-digit numbers (10 to 12):

  - There are 3 two-digit numbers: 10, 11, and 12.

  - Each two-digit number contributes 2 digits.

  - Total digits from 10 to 12:

[tex]\[ 3 \times 2 = 6 \][/tex]

Adding the digits from both ranges gives us the total number of digits:

[tex]\[9 + 6 = 15\][/tex]

Thus, the total number of digits Rena wrote is:

[tex]\[\boxed{15}\][/tex]

Answer:

0.0548

Step-by-step explanation:

The distribution of life span for a certain type of battery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour.

To find the the probability that a selected battery will have a life span of at most 2.1 hours, we need to first determine the z-score for x=2.1 hours using

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

We substitute the values to get:

[tex]z = \frac{2.1 - 2.5}{0.25} = - 1.6[/tex]

We read read -1.6 from the standard normal distribution table to get:

P(X≤2.1)=0.0548

The probability that the selected battery will have a life span of at most 2.1 hours is 0.0548.

Given information:

The life span of a battery is the amount of time the battery will last.

The distribution of life span for a certain type of battery is approximately normal with a mean of 2.5 hours and a standard deviation of 0.25 hours.

The z-value for the probability that the selected battery will have a life span of at most 2.1 hours will be calculated as,

[tex]z=\dfrac{x-\mu}{\sigma}\\z=\dfrac{2.1-2.5}{0.25}\\z=-1.6[/tex]

Now, use the standard normal distribution table or curve to get the value of required probability as,

[tex]P(x=2.1)=0.0548[/tex]

Therefore, the probability that the selected battery will have a life span of at most 2.1 hours is 0.0548.

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Answer:

x = 2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

12-4x-x=2

Combine like terms

12 -5x =2

Subtract 12 from each side

12-5x-12 =2-12

-5x = -10

Divide each side by -5

-5x/-5 = -10/-5

x =2

Answer:

the correct answer for 28 is 5*b

5b

Answer: The two point questions are 45, while the four point questions are 5.

Step-by-step explanation: We shall start by assigning letters to the unknown variables. Let the first type of question be called a and the second type of question be called b.

If the final exam is made up of 50 questions, that means

a + b = 50

Also if some questions are two points while others are four points and the total score for all of them is 110 points, then

2a + 4b = 110

(That is, we assume that a is the two point question and b is the four point question, so total score equals 110)

We now have a pair of simultaneous equations

a + b = 50 ————(1)

2a + 4b = 110 ——-(2)

From equation (1), we shall make a the subject of the equation,

hence let a = 50 - b

Substitute for the value of a in equation (2)

2a + 4b = 110

2(50 - b) + 4b = 110

100 - 2b + 4b = 110

By collecting like terms we now have

4b - 2b = 110 - 100

2b = 10

Divide both sides of the equation by 2

b = 5

Now substitute for the value of b into equation (1)

a + b = 50

a + 5 = 50

Subtract 5 from both sides of the equation

a = 45.

Therefore the two point questions are 45, while the four point questions are 5

**A quick check would show the following results ; 2(45) + 4(5) = 90 + 20 = 110.**

There are 45 questions worth 2 points each and 5 questions worth 4 points each on the 110-point final exam consisting of 50 questions.

Let's call the number of 2-point questions "x" and the number of 4-point questions "y." We can set up a system of equations to represent the information given:

1. The total number of questions is 50:

  x + y = 50

2. The total number of points is 110:

  2x + 4y = 110

Now we have a system of two equations with two variables:

1. x + y = 50

2. 2x + 4y = 110

We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method:

First, let's multiply the first equation by 2 to make it easier to eliminate x:

1. 2(x + y) = 2(50)

2x + 2y = 100

Now we have the following system of equations:

1. 2x + 2y = 100

2. 2x + 4y = 110

Now, subtract the first equation from the second equation to eliminate x:

(2x + 4y) - (2x + 2y) = 110 - 100

This simplifies to:

2y = 10

Now, divide both sides by 2 to solve for y:

2y/2 = 10/2

y = 5

So, there are 5 questions worth 4 points each (4-point questions), and we can find the number of 2-point questions by substituting the value of y back into one of the original equations (e.g., the first equation):

x + 5 = 50

Now, subtract 5 from both sides to solve for x:

x = 50 - 5

x = 45

So, there are 45 questions worth 2 points each (2-point questions).

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Answer:

237.09m

Step-by-step explanation:

Let's use the tan rule to find the length of the adjacent side.

Tan rule is given as

[tex]Tan \theta=\frac{Opposite \ side}{Adjacent \ side}\\[/tex]

[tex]\theta[/tex]=67° , and Adjacent length is given as 100m.

We therefore need to find the length of the adjacent side.

[tex]Tan\theta=\frac{X}{100}\\Tan 67\textdegree=\frac{X}{100}\\X=Tan \ 67\textdegree \times 100\\X=235.58m[/tex]

To find height of the rock, we add X value to transit height=[tex]235.58+1.5=237.09m[/tex]

*See pic for graphic illustration

The height of the rock formation is approximately [tex]230\ meters[/tex].

Given:

[tex]\text{Distance from the base of the rock formation to the transit, d = 100\ m}[/tex]

[tex]\text{Angle of elevation, \( \theta = 67^\circ \)}[/tex]

[tex]\text{Height of the transit above the ground, \( h = 1.5 \) m}[/tex]

Let [tex]\( H \)[/tex] denote the height of the rock formation.

First, we need to find the vertical distance from the transit to the top of the rock formation using the tangent function:

[tex]\[ \tan(\theta) = \frac{H - h}{d} \][/tex]

Substitute the given values:

[tex]\[ \tan(67^\circ) = \frac{H - 1.5}{100} \][/tex]

Calculate [tex]\( \tan(67^\circ) \)[/tex]

[tex]\[ \tan(67^\circ) = 2.281 \][/tex]

Now, solve for [tex]\( H -1.5 \)[/tex]

[tex]\[ 2.281 = \frac{H - 1.5}{100} \][/tex]

Multiply both sides by [tex]100[/tex] to solve for [tex]\( H -1.5 \)[/tex]

[tex]\[ 2.281 \times 100 = H - 1.5 \][/tex]

[tex]\[ 228.1 = H - 1.5 \][/tex]

Add 1.5 to both sides to solve for [tex]\( H \)[/tex]

[tex]\[ H = 228.1 + 1.5 \][/tex]

[tex]\[ H = 229.6 \][/tex]

[tex]\[ H = 230\ m \][/tex] (Round to the nearest meter)

Answer:

Step-by-step explanation:

Area = Length* height

= 4w³ * (5w² - 3w - 4)

 = 4w³*5w² - 4w³*3w - 4w³*4

= 20w⁵ - 12w⁴ - 16w³

Solution:

The given pyramid has 3 lateral triangular side

The figure is attached below

Base of triangle = 12 unit

Find the perpendicular

By Pythagoras theorem

[tex]hypotenuse^2 = opposite^2 + adjacent^2[/tex]

Therefore,

[tex]opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8[/tex]

Find the lateral surface area of 1 triangle

[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base[/tex]

[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48[/tex]

Thus, lateral surface area of 3 triangle is:

3 x 48 = 144

Thus lateral area for the pyramid with the equilateral base is 144 square units

Answer:

  five and eight hundredths

Step-by-step explanation:

I was taught to reserve the word "and" to mark the decimal point when the number has a fraction. The integer part is "five." The fractional part is "eight hundredths." Together, the word form might be ...

  five and eight hundredths.

__

If I were reading this to someone, including myself, I might say it as ...

  "five point oh eight".

_____

Comment on ambiguity

The reason for being particular about marking the decimal point is so you don't get into trouble with something like ...

  1000.13 . . . . . one-thousand and thirteen hundredths

which is different from ...

  1013/100 . . . . one-thousand thirteen hundredths

Some folks will pronounce 1013 as "one-thousand and thirteen." Doing so will get you in trouble in the above situation, where you have 1013/100.

Final answer:

The correct word form of 5.08 is explained as five and eight hundredths.

Explanation:

The correct word form of 5.08 is five and eight hundredths. When writing decimal numbers in words, the digit to the right of the decimal point is read as a whole number followed by the place value of the digit to the right.

In this case, 5.08 is read as five and eight hundredths.

Answer:

1.2

Step-by-step explanation:

He bought= 3 bags

Kg of one bag=1⅖

3×1⅖=1.2 kg

She bought 1.2 kg of beans..

The number of kilograms of beans did she buy will be 4.20 kilograms.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A chef bought 3 bags of beans. Each bag contains 1 ²/₅ kilogram of beans.

Convert the mixed fraction number into a fraction number. Then we have

1 ²/₅ = 1 + 2/5

1 ²/₅ = (5 + 2) / 5

1 ²/₅ = 7/5

The number of kilograms of beans did she buy will be given as,

⇒ 3 x 7 / 5

⇒ 21 / 5

⇒ 4.20 kilograms

The number of kilograms of beans did she buy will be 4.20 kilograms.

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Answer:

D. $500

Step-by-step explanation:

Answer:

Step-by-step explanation:

$500

Answer:

2

Step-by-step explanation:

log4(16)

Rewrite 16 as a power of 4

16 =4^2

log 4(4^2)

We know that log a (b^c) = c log a (b)

2 log 4(4)

We also know that loga (a) =1

2 *1

2

Answer:

The answer is B. 2 on ed.

Step-by-step explanation:

The rectangle with a length of 7 units and a width of 4 units, and with one vertex at the origin (0,0), has been successfully created using the segment tool.

Open the drawing tool or any software that allows you to draw shapes and use the segment tool to begin the construction.

First, mark the origin (0,0) on the canvas as one of the vertices of the rectangle.

Now, move the cursor 7 units to the right from the origin along the x-axis and place a point. This point represents the opposite vertex of the rectangle on the right side.

Next, move the cursor 4 units up from the origin along the y-axis and place another point. This point represents the opposite vertex of the rectangle on the top side.

To complete the rectangle, draw straight lines connecting the following points: (0,0) with (7,0), (7,0) with (7,4), (7,4) with (0,4), and finally, (0,4) back to (0,0).

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Answer:

531.441

Step-by-step explanation:

8.1*8.1*8.1 = Volume of a cube

Answer: C. 2

Step-by-step explanation:

1. combine like terms

-6x + 4 = -8

2. Make x be by itself by subtracting -4 by both sides of the equal sign

-6x = -12

3. Divide both sides by -6, then negatives will cancel out

x= 2

(hope this helped)

Answer:

c. 2

Step-by-step explanation:

simplify:

3x-9x+7-3 = -8

-6x+4 = -8

Subtract 4 from both sides:

-6x = -8 - 4

-6x = -12

Divide both sides by -6:

x = -12/ -6

Answer

x= 2

Answer: 90 mph

Step-by-step explanation:

so if 60 miles in 40 minutes have of 40 is 20 and 40 +20 = 60

so half of 60 is 30. so therefore 90 miles is 60 mins.

Answer:

to be honest i dont know  but i think it is 2400

Step-by-step explanation:

you need to do miles x mins i think i dont knoe try ask your family members