The invention that made the rise of the personal computer possible is the microchip (option C).
Who invents the computer?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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What is the rate of change for the equation y = 4x +60?
The rate of change is .
The slope represents the rate of change. Then the rate of change will be 4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
y = 4x + 60
The slope is 4 and the y-intercept is 60.
The slope represents the rate of change. Then the rate of change will be 4.
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The rate of change in the equation y = 4x + 60 is 4, which is the coefficient of x. This means for each unit increase in 'x', 'y' will increase by 4 units.
Explanation:In mathematics, the rate of change in an equation like y = 4x + 60 is represented by the coefficient of the variable x. This is because, in such an equation which is in the form of y = mx + b (a standard linear equation), 'm' represents the rate of change or the slope of the line.
So, in your specific equation y = 4x + 60, the rate of change or slope is 4. This means that for each increment of 1 in 'x', 'y' will increase by 4 units. This value - 4 - is your rate of change in this case.
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x2 + y2 + 12x + 2y – 1 = 0
Answer:
This question would be related to slopes so the answer is [tex]y=-\frac{7}{2}x+\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope-Intercept\:form\:of}\:\\x2+y2+12x+2y-1=0:\quad y=-\frac{7}{2}x+\frac{1}{4}[/tex]
[tex]\mathrm{Domain\:of\:}\:-\frac{7}{2}x+\frac{1}{4}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Range\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Parity\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{Neither\:even\:nor\:odd}[/tex]
[tex]\mathrm{Axis\:interception\:points\:of}\:\\-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{14},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:\frac{1}{4}\right)[/tex]
[tex]\mathrm{Inverse\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad -\frac{4x-1}{14}[/tex]
[tex]\mathrm{Slope\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad m=-\frac{7}{2}[/tex]
Hope this helps you!
Have a good night!
if 2a+b=3,find the value of 8a³+b³+18ab
Answer:
531.
Step-by-step explanation:
Let's assume 2(1) + 1 = 3
a = 1 and b = 1
Now we can plug that in
8(1)^3 + (1)^3 + 18(1)(1)
Then we need to multiply together
8^3 + 1^3 + 18
Then do the powers
512 + 1 + 18
Then add them together
531
Hope this helped!
Answer:
27
Step-by-step explanation:
A sum of cubes factors as
a³ + b³ = (a + b)(a² - ab + b²)
Factor the sum of cubes 8a³ + b³
8a³ = (2a)³, thus
8a³ + b³
= (2a)³ + b³
= (2a + b)(4a² - 2ab + b²)
We now have the right side as
(2a + b)(4a² - 2ab + b²) + 18ab ← substitute 2a + b = 3
= 3(4a² - 2ab + b²) + 18ab
= 12a² - 6ab + 3b² + 18ab ← collect like terms
= 12a² + 12ab + 3b² ← factor out 3 from each term
= 3(4a² + 4ab + b²) ← perfect square
= 3(2a + b)² ← substitute 2a + b = 3
= 3 × 3²
= 3 × 9
= 27
Step by step please :)
Answer:
Step-by-step explanation:
a) (5,5) ; (10,6); slope = 1/5
(x1,y2); (x2,y2)
y-y1 = m (x-x1)
[tex]y-5=\frac{1}{5}*(x-5)\\\\y-5=\frac{1}{5}*x-\frac{1}{5}*5\\\\y-5=\frac{1}{5}x-1\\y=\frac{1}{5}x-1+5\\\\y=\frac{1}{5}x+4[/tex]
d) (√2,7) ; (√2,-7)
(x1,y1) ; (x2,y2)
[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-7-7}{\sqrt{2}-\sqrt{2}}\\\\=\frac{-14}{0}=0[/tex]
Equation: y =7 or y = -7
A circle has a diameter of 30 yd. What is it’s circumference?
Use 3.14 for PIE, and don’t your answer.
Circumference of the circle = 94.2 yd
Solution:
Given data:
Diameter of the circle = 30 yd
The value of π = 3.14
To find the circumference of the circle:
Circumference of the circle = πd
Substitute the diameter value in the formula, we get
Circumference of the circle = 3.14 × 30
= 94.2
Circumference of the circle = 94.2 yd
If the volume of the pyramid shown is 216 in 3, what is the area of its base?
Answer:
Step-by-step explanation:
volume =1/3×base area×height
216=1/3× A×6
base area=216/2=108 in²
Answer:
Here is the answer
Step-by-step explanation:
108 in squared
or D
Hi I just have a question what is 23+4189
Answer:
4,212
Step-by-step explanation:
Step 1: Add
23 + 4189
4,212
Answer: 4,212
3. In a carnival game, players are given three darts and throw them at a set of balloons on a wall.
Suppose there are eight balloons on the wall. Five of the eight balloons have slips of paper in
them that say 'Winner' while three of the eight balloons have slips of paper that are blank.
Suppose you pop a balloon with each of your three darts. If all three balloons have 'Winner'slips,
you win the grand prize. If all three balloons have blank slips, you win the consolation prize.
What is the probability that:
a) you win the grand prize?
b) you win the consolation prize?
The chances of winning the grand prize in this game are approximately 0.089, whereas the chances of winning the consolation prize are 0.01.
Explanation:The subject of this question is Probability, which is a branch of Mathematics. To calculate the probability, we'll need to determine the total number of outcomes and the count of the favorable outcomes.
a) To win the grand prize, all three balloons popped have to have 'Winner' slips. The probability of each dart hitting such a balloon will decrease as the total number of balloons decreases. First dart probability would be 5/8 (5 'Winner' balloons out of 8 total), the second one 4/7 (as one 'Winner' balloon is already popped), and 3/6 for the third. Multiply these probabilities together to get the overall probability: (5/8) * (4/7) * (3/6) = 0.089 (rounded to the third digit).
b) Similarly, for the consolation prize, we would have to hit all three balloons with blank slips. The process is equivalent, resulting in a probability of (3/8) * (2/7) * (1/6) = 0.01 (rounded to the third digit).
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The length of a certain rectangle is 15cm more than three times its width. If the perimeter of the rectangle is 94cm, what is the area.
Answer:
Step-by-step explanation:
Let w be the width
Length = 3w +15
Perimeter = 94 cm
2*(length + width) = 94
2*(3w+15 + w) = 94
2*( 4w + 15) = 94
4w + 15 = 94/2
4w +15 = 47
4w = 47 -15
4w = 32
w = 32/4
w = 8 cm
Length = 3w +15 = 3*8 + 15 = 24 +15 = 39
Length = 39cm
Area = length * width = 39*8 = 312
Area = 312 cm²
The area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]
Step 1
Let's denote the width of the rectangle as w cm.
According to the problem, the length of the rectangle is [tex]\( 15 \)[/tex] cm more than three times its width. So, the length [tex]\( l \)[/tex] can be expressed as [tex]\( 3w + 15 \)[/tex]cm.
The perimeter P of a rectangle is given by:
[tex]\[ P = 2(l + w) \][/tex]
Given that the perimeter of the rectangle is [tex]\( 94 \)[/tex] cm, we can write the equation:
[tex]\[ 94 = 2((3w + 15) + w) \][/tex]
Step 2
Now, let's solve for [tex]\( w \)[/tex]:
[tex]\[ 94 = 2(4w + 15) \]\[ 94 = 8w + 30 \]\[ 8w = 94 - 30 \]\[ 8w = 64 \]\[ w = \frac{64}{8} \]\[ w = 8 \][/tex]
Step 3
Now that we have found the width of the rectangle to be [tex]\( 8 \)[/tex] cm, we can find its length:
[tex]\[ l = 3w + 15 \]\[ l = 3(8) + 15 \]\[ l = 24 + 15 \]\[ l = 39 \][/tex]
Step 4
Now that we have the width [tex]\( w = 8 \)[/tex] cm and the length [tex]\( l = 39 \)[/tex] cm, we can calculate the area A of the rectangle:
[tex]\[ A = l \times w \]\[ A = 39 \times 8 \]\[ A = 312 \][/tex]
So, the area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]
Write each repeating decimal using bar notation.
5.313131
0.999
2.010101
26.993993
Answer:
1) 5.313131 put the bar over the first 31
2)0.999 put the bar over the first 9
3)2.010101 put the bar over the first 01
4)26.993993 put the bar over the first 993
Step-by-step explanation:
Four times a divided by two equals 5.2
Initial equation:
4a / 2 = 5.2
Multiply both sides by 2:
4a = 10.4
Divide both sides by 4:
a = 2.6
Hope this helps!! :)
Answer:
Step-by-step explanation:
2.6 becuase 4a/2= 5.2
4a=10.4
a=2.6
This is so confusing I don't understand how to do it!
Answer:
494 square feet
494 ft^2
Step-by-step explanation:
Trapezoid:
(20 + 32) ÷ 2 ) × 3
52 ÷ 2 ) × 3
26 × 3
= 78
Rectangle:
32 × 13 = 416
Add:
78 + 416 = 494
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
15 mm
Not drawn to scale.
What is the surface area of the prism?
Answer:
The answer should be 45
Step-by-step explanation:
To get the whole are you would have to multiply the lenght with the Width and then take that answer and multiply it with the height
BUT
because you want the surface area, it would be just the lenght and width
15x3=45
so 45 is your answer.
Write the explicit formula for the geometric sequence
The formula [tex]3(4^{n-1})[/tex] represents the geometric sequence.
Step-by-step explanation:
Step 1:
The value of [tex]a_{n}[/tex] is dependent on the value of n.
So n is independent while [tex]a_{n}[/tex] is dependent on n i.e. the value of [tex]a_{n}[/tex]depends on the value of n.
Step 2:
We substitute the values of n in the functions to check which function satisfies the values of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} = -4(3)^{n-1} = -4 (3^{3}) = -108.[/tex] This does not equal the value of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} = 4(3)^{n-1} =-4 (3^{3}) = 108.[/tex] This does not equal the value of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} =3(-4)^{n-1} = 3 (-4^{3}) = -192.[/tex] This does not equal the value of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} =3(4)^{n-1} = 3 (4^{3}) = 192.[/tex] This equals the value of [tex]a_{n}[/tex].
So the fourth formula represents the geometric sequence.
Which of these absolute values is the greatest?
A.
|140|
B.
|-104|
C.
|104|
D.
|-204|
When doing absolute value, negatives will always be positive.
Option A's absolute value is 140.
Option B's absolute value is 104.
Option C's absolute value is also 104.
Option D's absolute value is 204.
Therefore, the option with the greatest absolute value would be D. |-204|
Answer:
A because is positive and highlights numbers
Which of the following describes how to translate the graph y = 1xl to obtain the graph of y = lx - 11 - 1?
1)1 unit left and 1 unit down
2)1 unit left and 1 unit up
3)1 unit right and 1 unit down
4)1 unit right and 1 unit up
Please help
Answer:
3)1 unit right and 1 unit down
Step-by-step explanation:
The parent function is
[tex]y = |x| [/tex]
This is the base of the absolute value functions.
It has its vertex at the origin.
The transformed function is
[tex]y = |x - 1| - 1[/tex]
This absolute value function has its vertex at (1,-1).
This means the parent function has been shifted 1 unit right and 1 unit down to obtain the transformed function.
If the length of a pool is 8 more than twice the width and the total area is 960 square feet, find the length and width of the rectangular landscape element.
Answer:
l=48, w=20
Step-by-step explanation:
Let the width of the pool be w feet, then the length will be:
[tex]l = 2w + 8[/tex]
The area of the pool is 960 square feet.
This means that:
[tex]w(2w + 8) = 960[/tex]
Expand and rewrite in standard form to get:
[tex]2 {w}^{2} + 8w - 960 = 0[/tex]
[tex] {w}^{2} + 4w - 480 = 0[/tex]
[tex]{w}^{2} + 24w - 20w- 480 = 0[/tex]
[tex]{w}(w+ 24) - 20(w + 24) = 0[/tex]
Factor to get:
[tex](w+ 24)(w - 20) = 0[/tex]
[tex]w = - 24 \: or \: w = 20[/tex]
We discard the negative value because magnitude is positive.
This means
[tex]l = 2 \times 20 + 8 = 48[/tex]
can someone pls answer this question for me
Answer:
the height is 3
the with is also 3 because
1.5+1.5=3
What is the mad of this set 0,3,6,9,11,13,14
Answer:
When I calculated this I got: 4.2857142857143 but I don't know if that's the correct answer.
Step-by-step explanation:
Combine the like terms to simplify the polynomial. Show any work. Put your answers in standard form.
(5x^4-3x^3+2x^2-15x+27)+(7x^4+5x^3-x^2+8x-13)
Answer:
12x⁴ + 2x³ + x² - 7x + 14
Step-by-step explanation:
(5x^4-3x^3+2x^2-15x+27) + (7x^4+5x^3-x^2+8x-13)
(5+7)x⁴ + (-3+5)x³ + (2-1)x² + (-15+8)x + (27-13)
12x⁴ + 2x³ + x² - 7x + 14
The probability
The number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3,5,8, and 9 is _. The probability that both the first digit and the last digit of the three-digit number are even numbers is _.
Probability of distinct 3-digits is 1/6.
Probability of both the first digit and the last digit are even numbers is 1/5.
Step-by-step explanation:
Given set of numbers {1,2,3,5,8,9} = 6
Total number of 3-digits can be formed = 6[tex]\times[/tex]5[tex]\times[/tex]4 = 120.
Probability of the three-digit numbers with distinct digits :
The number of 3-digit numbers with distinct digits = (6[tex]\times[/tex]5[tex]\times[/tex]4) / (3[tex]\times[/tex]2[tex]\times[/tex]1) = 20.
P(distinct 3-digits) = no. of distinct 3-digits / Total no.of 3-digits
⇒ 20/120
⇒ 1/6
Probability that both the first digit and the last digit of the three-digit number are even numbers :
The even numbers in the set are 2 and 8 = 2 possibilities.
The number of 3-digits with 1st and 3rd digit are even = (2[tex]\times[/tex]6[tex]\times[/tex]2) = 24.
P(1st and 3rd digits even)= no. of 1st and 3rd digit even/Total no. of 3-digits.
⇒ 24/120
⇒ 1/5
abby buys 4 pencils and 2 erasers for $3.58. Micheal buys 1 pencil and 6 erasers for $2.49
what is the cost of 1 pencil and 1 eraser ?
Answer:
1 pencil = $0.75
1 eraser = $0.29
Step-by-step explanation:
4p+2e=3.58 1p+6(0.29)=2.49
1p+6e=2.49 1p+1.74=2.49
p=2.49-6e 1p=0.75
4(2.49-6e)+2e=3.58 p=0.75
9.96-24e+2e=3.58
9.96-22e=3.58
-22e=-6.38
e=0.29
what is the probability of rolling a 4 on a single sided die and then rolling a 6?
Answer:
If it is a six-sided die then it has the probability of 1/6 or .16
Step-by-step explanation:
Find the missing angle measure below:
Answer:
81
Step-by-step explanation:
ANGLES in a TRIANGLE add up to 180
In the Triangle you have 65 and 34
Add them together = 99
Subtract the total from 180
180 - 99 = 81
Answer:
81 degrees
Step-by-step explanation:
The angles of the triangle always add up to 180.
SO you'd do 65+34 which equals 99.
NOW you do 180-99 which equals 81
So you're missing angle would be 81 degrees
What is the answer to 50% of $250
Answer:$125
Step-by-step explanation:
50% of 250
50/100 x 250
1/2 x 250=(1x250)/2=250/2=125
16 store cashiers work average 21 hours per week and paid $8.25 per hour . after store manager hires 2 additionsl cashiers each cashier will be paid .25 more per hour and will work an average of 1.5 fewer hours per week. what will be the change in total amount of money the cashiers are paid each week?
Answer:
The change in total amount of money the cashier are paid each week will be $331.5.
Step-by-step explanation:
16 store cashiers work average 21 hours per week and paid $8.25 per hour.
Now, the store manager hires 2 additional cashiers each cashier will be paid 0.25 more per hour and will work an average of 1.5 fewer hours per week.
Therefore, the two additional cashiers will be paid $8.50 per hour and will work an average of (21 - 1.5) = 19.5 hours per week.
So, the change in the total amount of money the cashiers are paid each week will be (2 × 19.5 × 8.5) = $331.5. (Answer)
Please help me!!! Thank you!!
Answer:
Part A - 4x + 8 dollars
Part B - $45
Step-by-step explanation:
Convert 746% to a mixed number
Answer: 373/50
Step-by-step explanation:
Step 1: convert to a fraction
746% = 746 ÷ 100 = 7.46
7.46 = 373/50
Step 2: Write the number as a fraction of one: 7.46 = 746/100
Step 3: use a common divisor of 2 to reduce the numbers, we have
(746÷2)= 373
(100÷2)=50
when reduced to the simplest form= 373/50
Therefore, 746/ 100 = 373/50 when expressed as a mixed number.
Answer: 373/50
Step-by-step explanation:
Step 1) Since 746% is a percent, it is written over the denominator of 100. So first convert it to a fraction, which would be 746/100.
Step 2) Find the GCF (greatest common factor). In order to find the GCF start by writing all the factors of
100:
1, 2, 4, 5, 10, 20, 25, 50, 100
Step 3) Now test every number there and see if any go into 746. Start at the highest number, which in this case is 100. (Example, ask yourself, “does 100 go into 746? No.” Then try with 50, and continue until you get to a number that goes into 746 evenly.)
Step 4) The GCF from the previous step is 2. So now divide 746 by 2 (answer is 373) and 100 by 2 (answer is 50).
Step 5) Now put 373/50 and that’s your answer! Congratulations you finished it!
question 3 - open up to see pic
(12, 11):
2((12) + 3) - (11) = 7 + (12)
2 • 15 - 11 = 19
2 • 4 = 19
8 [tex]\neq[/tex] 19
(1, 0):
2((1) + 3) - (0) = 7 + (1)
2 • 4 = 8
8 = 8
(-5, 1):
2((-5) + 3) - (1) = 7 + (-5)
2 • -2 - 1 = 2
2 • -3 = 2
-6 [tex]\neq[/tex] 2
Hope this helps.
Brenda invests $4500 in the savings account earning 5.5% interest compounded quarterly. What will the account balance be after seven years?
The account balance will be $6642 after seven years.
Step-by-step explanation:
It is given that, Brenda invests $4500 in the savings account.The interest rate is 5.5% interest compounded quarterly.To find the amount after seven years, a certain formula is used.
Amount = [tex]P( 1+r/n)^{n\times t}[/tex]
where,
P is the principal amount that is invested in the account.
Therefore, P = 4500 dollars.
r is the rate of interest. (r = 5.5 %)
Therefore, r = 5.5/100 = 0.055
n is the number of time the interest is compounded per year which is n= 4.
t is the time period which is t = 7 years.
Now, substituting all the above values in the formula,
Amount = [tex]4500(1+0.055/4)^{4\times 7}[/tex]
⇒ [tex]4500(4.055/4)^{28}[/tex]
⇒ [tex]4500(1.014)^{28}[/tex]
⇒ [tex]4500\times1.4759[/tex]
⇒ 6641.55 (which is approximately equal to 6642)
⇒ 6642 dollars.
The account balance after 7 years is $6642.