Answer:
(x + 12)(x + 2)
Step-by-step explanation:
In order to factorize, we first have to break the term in the middle into two terms which add up to 14 and and multiply to 24.
For this, let's take a look at the factor pairs of 24. We have (1, 24), (2,12), (3, 8), (4, 6).
note that the 2nd pair works. 2 + 12 = 14, 2*12 = 24.
And now we rewrite the expression.
x^2 + 14x + 24
= x^2 + 12x + 2x + 24
Take out common factors as below
= x(x + 12) + 2(x + 12)
Note that (x+12) is a common factor in the 2 added expressions. So we take it out.
= (x+12)(x+2)
Done!!! Hope it helps, and if it does, please mark me brainliest...
Kari plans to sample 20 people of a population that contains 100 students. She wants to determine how many people wake up before 6 a.m. Which sample is the most random?
Answer:
5 students out of each of the 4 homeroom classes (C)
Step-by-step explanation:
Answer:
c 5 students out of each of the 4 homeroom classes
i got it right on edge
$14 is what percent of $70
$14 is about 10% of $70
14 percent of 70 is about 10%
Find the mean median and interquartile for the data set below
17,23,8,5,9,16,22,11,13,15,17,18
mean: 14.5
median: 15.5
innerquartile: 17.5
Answer:
mean = 14.5 ; median = 15.5 ; interquartile = 7.5
Step-by-step explanation:
Given : 17,23,8,5,9,16,22,11,13,15,17,18.
To find : Find the mean median and interquartile for the data set .
Solution : We have given 17,23,8,5,9,16,22,11,13,15,17,18.
First we arrange in ascending order 5 , 8 ,9 ,11, 13, 15, 16 , 17, 17,18, 22, 23,
Mean : [tex]\frac{Sum\ of\ all\ number}{total\ number}[/tex].
Mean : [tex]\frac{5+8+9 +11 +13+ 15+16+17+17+18+ 22+23,}{12}[/tex].
Mean : 14.5
Median : Average of middle two numbers
Median : [tex]\frac{15 + 16}{2}[/tex].
Median : [tex]\frac{31}{2}[/tex].
Median : 15 .5
Interquartile : median of lower half - median of upper half.
Interquartile : [tex]\frac{17 +18}{2}[/tex] - [tex]\frac{9 + 11}{2}[/tex].
Interquartile : 17.5 - 10= 7.5
Therefore, mean = 14.5 ; median = 15.5 ; interquartile = 7.5
The graph of f(x)=x^2 is shown. Use the parabola tool to graph g(x). g(x)=(x-1)^2+2 ..Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Please someone help me.
Answer:
See below.
Step-by-step explanation:
The graph of ƒ(x) = x² is the red parabola in Figure 1.
Step 1. Vertex of g(x)
g(x) = (x – 1)² + 2
The graph of g(x) will be a parabola like that of ƒ(x) translated one unit to the right and two units up.
The vertex of ƒ(x) is at (0, 0), so the vertex of g(x) is at (1, 2). See Figure 1.
Step 2. Calculate two more points
(a) Try x = 0
g(0) = (0 – 1)² + 2 = 1² + 2 = 1 + 2 = 3
So, there is a point at (0, 3).
(b) Try x = 2
The axis of symmetry is a vertical line passing through the vertex at x = 1. We have calculated a point one unit left of the axis (at x = 0), so let's calculate a point one unit to the right, at x = 2.
g(2) = (2 – 1)² + 2 = 1² + 2 = 1 + 2 = 3
So, there are points at (2, 3) and (1,3). See Figure 2.
Step 3. Sketch the graph of g(x)
Draw a smooth curve through the three points. Extend the arms of the parabola vertically so the graph has the same shape as that of ƒ(x).
Your graph should look like the blue parabola in Figure 3.
Answer:
they are correct, here's proof
Find the circumference and area of a circle with a diameter of 10 in. Leave your answers in terms of pi.
Answer:
Circumference of given circle = 10π in
Step-by-step explanation:
Points to remember
Circumference of a circle = 2πr
Where r is the radius of circle
To find the circumference of circle
It is given that diameter of circle d = 10 in
Radius r = d/2 = 10/2 = 5 in
Circumference = 2πr = 2 * π * 5 = 10π in
Therefore the correct answer is circumference = 10π in
The number of hours in a day is measured in the tens
A. True
B. False
Answer:
true
Step-by-step explanation:
took the test
The number of hours in a day is correctly measured in the tens, as a day comprises of 24 hours. This measurement is a human invention rather than a natural observation. Hence true.
The question you've asked is whether the number of hours in a day is measured in the tens. The answer is True. There are 24 hours in a complete day. This measure is not something that naturally exists but rather is a human invention for the purpose of timekeeping. The Babylonians are credited with dividing a circle into 360 degrees, and they chose 24 as it divides neatly into 360, which allows for hours of a reasonable length that can be measured throughout the day. Notably, all days do not have exactly 12 hours of day and 12 hours of night except at the equator, and this occurs every day of the year. Other locations may experience nearly equal amounts of day and night during the equinoxes.
When we say that the number of hours in a day is more than seven hours, we are observing a fact about the number of hours in a day, which is significantly more than seven hours since a full day consists of 24 hours.
identify the conjugate: 7-18i
[tex]\overline{7-18i} = 7+18i[/tex]
Line k passes through the point (1, 5) and is perpendicular to the line y = 3x + 1. Which of the following points does line k also pass through?
Select one:
A. (4, 4)
B. (-2, -5)
C. (3, 6)
D. (9, -1)
Answer:
Option A. (4,4)
Step-by-step explanation:
step 1
Find the slope of the line k
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
[tex]m1*m2=-1[/tex]
The slope of the given line is [tex]m1=3[/tex]
so
The slope of the line k is
[tex]m2*(3)=-1[/tex]
[tex]m2=-\frac{1}{3}[/tex]
step 2
Find the equation of the line k
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{3}[/tex]
[tex]point(1,5)[/tex]
substitute the values
[tex]y-5=-\frac{1}{3}(x-1)[/tex]
step 3
Verify if the line k pass through the given points
Remember that
If the line passes through a point, then the value of x and the value of y of the point must satisfy the equation of the line
Verify each case
case A) (4,4)
[tex]4-5=-\frac{1}{3}(4-1)[/tex]
[tex]-1=-\frac{1}{3}(3)[/tex]
[tex]-1=-1[/tex] ----> is true
therefore
The line k pass through the point (4,4)
case B) (-2,-5)
[tex]-5-5=-\frac{1}{3}(-2-1)[/tex]
[tex]-10=-1[/tex] -----> is not true
therefore
The line k not pass through the point (-2,-5)
case C) (3,6)
[tex]6-5=-\frac{1}{3}(3-1)[/tex]
[tex]1=-\frac{2}{3}[/tex] -----> is not true
therefore
The line k not pass through the point (3,6)
case D) (9,-1)
[tex]-1-5=-\frac{1}{3}(9-1)[/tex]
[tex]-6=-\frac{8}{3}[/tex] -----> is not true
therefore
The line k not pass through the point (9,-1)
Find the volume of the composite solid.
A. 702.00in^3
B. 1218.03in^3
C. 676.01in^3
D. 811.51^3
Answer:
[tex] C.676.01 \: {in}^{3} [/tex]
step-by-step explanation :
The volume of the composite solid = volume of the cuboid + volume of the rectangular pyramid
Volume of the cuboid
[tex] = L \times B \times H[/tex]
where
[tex]L = 9 \: inches \\ B = 9 \: inches \\ H = 5 \: inches[/tex]
By substitution,
[tex] \implies \: V = 5 \times 9 \times 9[/tex]
[tex]\implies \: V = 405 \: {in}^{3} [/tex]
Volume of rectangular pyramid
[tex] = \frac{1}{3} \times base \: area \times height[/tex]
[tex]\implies \: V = \frac{1}{3} \times \:( L \times B ) \times \: H[/tex]
[tex] L = 9 \: inches \\ B = 9 \: inches \\ s= 11 \: inches[/tex]
We use the Pythagoras Theorem, to obtain,
h²+4.5²=11²
h²=11²-4.5²
h=√100.75
h=10.03
By substitution,
[tex]\implies \: V = \frac{1}{3} \times \:( 9 \times 9 ) \times \:10.0374[/tex]
we simplify to obtain
[tex]\implies \: V =271.0098 \: {in}^{3} [/tex]
Hence the volume of the the composite solid
[tex]=676.01\: {in}^{3} [/tex]
Answer:
The correct answer is option C. 676.01 in^3
Step-by-step explanation:
It is given a composite solid.
Total volume = volume of cuboid + volume of pyramid
To find the volume of cuboid
Volume of cuboid = Base area * height
Base area = side * side = 9 * 9
Volume = 9 * 9 * 5 = 405 in^3
To find the volume of pyramid
Before that we have to find the height of pyramid
Height² = Hypotenuse² - base² = 11² - 4.5² = 100.75
Height = √100.75 = 10.03
Volume of pyramid = 1/3(base area * height)
= 1/3(9 * 9 * 10.03) = 271.01 in^3
To find the volume of solid
Volume of solid = volume of cuboid + volume of pyramid
= 405 + 271.01 = 676.01 in^3
Therefore the correct answer is option C. 676.01 in^3
You used a 35% off coupon and purchased a skateboard for $55.25. What was the original price of the skateboard? *
To find the original price of a discounted item, divide the price paid by the percentage paid, in decimal form. In this case, $55.25 divided by 0.65 gives $85, which is the original price of the skateboard.
Explanation:If a skateboard was purchased for $55.25 with a 35% off coupon, then that price represents 65% of the original price (100% - 35% = 65%).
To find the original price, you would take the price paid and divide it by the percentage you paid, in decimal form. In this case, that's 0.65 (65%).
So, the calculation would be $55.25 ÷ 0.65 which gives you approximately $85. This means the original price was $85.
Learn more about Discounted price calculations here:https://brainly.com/question/33685989
#SPJ12
pls help. as soon as possible
Answer:
[tex]new\ lenght=24cm\\new\ width=16cm[/tex]
This will scale the drawing up to larger dimensions.
Step-by-step explanation:
You can observe in the figure that the rectangular drawing has these dimensions:
[tex]length=6cm\\width=4cm[/tex]
The new drawing will be obtained by multplying the dimensions of the original drawing by the scale factor 4.
Therefore, the new dimensions will be:
[tex]new\ lenght=(6cm)(4)=24cm\\new\ width=(4cm)(4)=16cm[/tex]
You can observe that this will scale the drawing up to larger dimensions.
The width of a rectangle is 5 cm less than the length. The perimeter is 38 cm. Find the dimensions of the rectangle
Answer:
Step-by-step explanation:
38=2(5)+2(x ) find X
2x5-10
38-10=28
28/2=14
14/2=7
x =7
so you length is 7
The dimensions of the rectangle are length = 12 cm and width = 7 cm by solving equations of given the width of a rectangle is 5 cm less than the length and the perimeter is 38 cm.
Let's represent the length of the rectangle as "L" and the width as "W".
According to the given information:
The width is 5 cm less than the length, so we can write W = L - 5.
The perimeter of a rectangle is given by the formula P = 2(L + W),
where P is the perimeter, L is the length, and W is the width.
In this case, the perimeter is 38 cm, so we have
38 = 2(L + W).
Now we can use these equations to find the dimensions of the rectangle.
Substitute the value of W from the first equation into the second equation:
38 = 2(L + (L - 5))
Simplify the equation:
38 = 2(2L - 5)
38 = 4L - 10
Add 10 to both sides:
48 = 4L
Divide both sides by 4:
L = 12
Now we can substitute the value of L into the first equation to find the width:
W = L - 5
W = 12 - 5
W = 7
Therefore, the dimensions of the rectangle are length = 12 cm and width = 7 cm by solving equations of given the width of a rectangle is 5 cm less than the length and the perimeter is 38 cm.
Learn more about solving equations here:
https://brainly.com/question/28779093
#SPJ4
What is the value of the expression when X=-1 and y=2
4x^3y^2
Answer: the answer is negative 52 (-52 goes in the box)
Answer is -16
Step-by-step explanation:
Michael hikes 1/4 of a mile every 1/6 of a hour. How far will he hike in 2 hours
To determine how far Michael will hike in 2 hours, we calculate his hiking rate which is 1.5 miles per hour and then multiply by the total time, resulting in a distance of 3 miles hiked in 2 hours.
To find out how far Michael will hike in 2 hours, we need to set up a proportion based on the information that he hikes 1/4 of a mile every 1/6 of an hour. First, we find the rate at which Michael hikes by dividing the distance by the time:
Rate = 1/4 mile / 1/6 hour = (1/4) * (6/1) = 6/4 = 1.5 miles per hour.
Now, to find out how far he will hike in 2 hours, we simply multiply the rate by the total time:
Distance in 2 hours = 1.5 miles/hour * 2 hours = 3 miles.
Therefore, Michael will hike 3 miles in 2 hours.
A line segment has endpoints at (-4,13) and (18,-3.5).
What is the y-coordinate of the midpoint of the line segment?
Answer:
4.75
Explanation:
Make a right triangle
It goes right 22 and down 16.5
Those are the two sides
22^2+16.5^2=h^2
484+272.25=h^2
h=27.5
If it were half, it would go right 11, down 8.25
With hypotenuse being=13.75
Being at (7,4.75)
Hope you get it!
simplify (4^3)^5
-
-
-
-
-
Answer:
[tex]\large\boxed{(4^3)^5=4^{15}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (a^n)^m=a^{nm}\\\\(4^3)^5=4^{(3)(5)}=4^{15}[/tex]
Step-by-step explanation: Here we have the number (4^3)^5.
We can use the relationship: [tex](x^{a} )^{b} = x^{a*b}[/tex]
so our number can be written as: [tex](4^{3}) ^{5} = 4^{3*5} = 4^{15}[/tex].
But you can simplify it further!
we know that [tex]4 = 2^{2}[/tex], then [tex]4^{15} = (2^{2}) ^{15} = 2^{2*15} = 2^{30}[/tex]
What is the solution to the equation log2 (5x - 2) = 3?
From log BNE to BEN
X=2
if you want explaination then ask me
what is x in equation 1-2x=21
See attached pic
x = -10 is your answer
given that f'(x) = 6lnx and f(2) = -3.682, find f(3).
Answer:
If you mean: y =(lnx)
3
then:
dy
/dx = [3(lnx)
Step-by-step explanation:
The value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.
What is integration of a function?Integration is the operation which is used to find the original function from its darivative form.
The differencial function is given that
[tex]f'(x) = 6\ln x[/tex]
Integrate this function, with respect to the x,
[tex]f(x) =\int { 6\ln x} \, dx\\f(x) =6(\int { \ln x} )\, dx\\f(x) =6(x\ln x-\int { 1} \, dx)+C\\f(x) =6(x\ln x-x)+C\\f(x)=6x(\ln x-1)+C[/tex]
The value of function at 2 is,
[tex]f(2) = -3.682[/tex]
Put this value in the above equation as,
[tex]f(2)=6(2)(\ln (2)-1)+C\\-3.682=12(0.6931-1)+C\\-3.682=-3.682+C\\0=C[/tex]
Hence the value of constat is 0. Thus, the value of function at 3 is,
[tex]f(3)=6(3)(\ln (3)-1)+0\\f(3)=18(1.0986-1)\\f(3)=1.7748[/tex]
Hence, the value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.
Learn more about the integration of a function here;
https://brainly.com/question/17200095
plz help me brainliest to whoever answers first.
Answer:B) (8x5)xb
Step-by-step explanation:
Answer: b
Step-by-step explanation:
Study the table below. Label the table as proportional or non-proportional. Explain your reasoning.
Answer:
Proportional
Step-by-step explanation:
If the function is proportional, it will have the following relationship:
f(x) = kx
Let's look at the first one:
-14 = -7k
k = 2
Now let's see if k=2 is true for the rest:
0 = 2(0) True
10 = 2(5) True
16 = 2(8) True
f(x) = 2x. So this is indeed proportional.
f(-5)=?
please help me
Answer:
0
Step-by-step explanation:
Plug in -5 for x.
You get [tex]\frac{4}{5}(-5)+4[/tex]
the 5s cancel and you are left with
[tex]-4+4[/tex]
which is equal to 0.
How to find 2 irrational no.s between 2016 and 2017
You can find two irrational numbers [tex]r,s[/tex] between 0 and 1.
Then, you'll have
[tex]2016 < 2016+r < 2017,\quad 2016 < 2016+s < 2017[/tex]
And both [tex]2016+r[/tex] and [tex]2016+s[/tex] will be irrational, because they are the sum of a rational number (2016) and an irrational number (r or s).
Finally, in order to find two such numbers, you can start with any irrational number, and scale it down until it lies between 0 and 1.
For example, you can start from [tex]\sqrt{2}\approx 1.4142[/tex] and divide it by any integer greater than 2, say that we choose
[tex]r = \dfrac{\sqrt{2}}{7}[/tex]
[tex]s = \dfrac{\sqrt{2}}{4}[/tex]
So, the two irrational numbers between 2016 and 2017 are
[tex]2016 + \dfrac{\sqrt{2}}{7},\quad 2016 + \dfrac{\sqrt{2}}{4}[/tex]
Two irrational numbers between 2016 and 2017 can be found by adding non-repeating, non-terminating decimals to 2016. Examples include 2016.172 and 2016.399.
Explanation:Finding irrational numbers between two given numbers involves knowing that irrational numbers are those which cannot be expressed as a quotient of two integers and have non-repeating, non-terminating decimal expansions. Examples of irrational numbers include the square root of non-perfect squares, pi (π), and 'e' (the base of natural logarithms).
Between two such close numbers (like 2016 and 2017), an easy way to find irrational numbers is to add a non-repeating, non-terminating decimal to the smaller number. For instance, let's use 0.172 and 0.399 (which are derived from the reference numbers provided) and add these to 2016:
2016 + 0.172 = 2016.1722016 + 0.399 = 2016.399Both 2016.172 and 2016.399 are irrational numbers that lie between 2016 and 2017.
Learn more about Irrational Numbers here:https://brainly.com/question/4031928
#SPJ3
Solve for the roots in the equation below.In your final answer. Include each of the necessary steps and calculations. x^3 - 27 =0
ANSWER
x=3
EXPLANATION
The given equation is:
[tex] {x}^{3} - 27 = 0[/tex]
We add 27 to both sides of the equation to get:
[tex] {x}^{3} = 27[/tex]
We write 27 as number to exponent 3.
[tex]{x}^{3} = {3}^{3} [/tex]
The exponents are the same.
This implies that, the bases are also the same.
Therefore
[tex]x = 3[/tex]
The answer is:
The equation has only one root (zero) and its's equal to 3.
[tex]x=3[/tex]
Why?We are working with a cubic equation, it means that there will be three roots (zeroes) for the equation.
To solve the problem, we need to remember the following exponents and roots property:
[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]
[tex](a^{b})^{c}=a^{b*c}[/tex]
So, we are given the equation:
[tex]x^{3}-27=0[/tex]
Isolating x we have:
[tex]x^{3}=27\\\\\sqrt[3]{x^{3}}=\sqrt[3]{27}\\\\x^{\frac{3}{3} }=\sqrt[3]{(3)^{3} }\\\\x^{\frac{3}{3} }=3^{\frac{3}{3} }\\\\x=3[/tex]
Hence, we have that the equation has only one root (zero) and its's equal to 3.
Have a nice day!
In DEF, sin D= 36/39. What is cos E?
Answer:
36/39
Step-by-step explanation:
Answer:
The correct option is C.
Step-by-step explanation:
Given information: In DEF, sin D= 36/39.
In a right angled triangle,
[tex]\sin \theta=\frac{perpendicular}{hypotenuse}[/tex]
[tex]\sin D=\frac{EF}{DE}[/tex]
[tex]\frac{36}{39}=\frac{EF}{39}[/tex]
[tex]EF=36[/tex]
[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]
[tex]\cos E=\frac{EF}{DE}[/tex]
[tex]\cos E=\frac{36}{39}[/tex]
The value of cos E is [tex]\frac{36}{39}[/tex]. Therefore the correct option is C.
Events A and B are independent. Find the missing probability.
P(b)=9/20,p(a|b)=1/5,p(a)=?
Answer:
4/9
Step-by-step explanation:
since they are independent
p(ab)=p(a/b)=p(a)*p(b)
1/5=p(a)*9/20
p(a)=[tex]\frac{\frac{1}{5} }{\frac{9}{20} } = 4/9[/tex]
Given that two events are independent, the probability of one event given the other is the same as the probability of the event itself. Therefore, the probability of event A is 1/5.
Explanation:In probability, the concept of independence plays a crucial role. If two events, A and B, are independent, then the probability of event A occurring, given that event B has already occurred, is the same as the probability of event A.
In your case, P(A|B) = P(A). So, P(A) = P(A|B) = 1/5.
Learn more about Independent Events here:https://brainly.com/question/30905572
#SPJ3
what is the length of the magnitude of the vector (-3,2)
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
Given the vector < a, b > then the magnitude is
[tex]\sqrt{a^2+b^2}[/tex], thus
| (- 3, 2) | = [tex]\sqrt{(-3)^2+2^2}[/tex] = [tex]\sqrt{9+4}[/tex] = [tex]\sqrt{13}[/tex]
The length of the magnitude of the given vector <-3,2> is:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:We know that for any vector of the type: <a,b>
The magnitude of the length of the vector is given by the formula:
[tex]|<a,b>|=\sqrt{a^2+b^2}[/tex] [tex]\sqrt{13}[/tex]
Here we are given the vector as: <-3,2>
i.e. a= -3
and b=2.
This means that the length of the magnotude of the vector is given by:
[tex]|<-3,2>|=\sqrt{(-3)^2+(2)^2}\\\\i.e.\\\\|<-3,2>|=\sqrt{9+4}\\\\i.e.\\\\|<-3,2>|=\sqrt{13}[/tex]
Hence, the answer is: [tex]\sqrt{13}[/tex]
Based on the tree diagram below, what is the probability that a student has lice, given that the student tested positive? Round your answer to the nearest tenth of a percent.
A. 77.5%
B. 65.3%
C. 85.9%
D. 57.7%
Answer: C
MAKE ME BRAINLIEST
Answer with explanation:
Probability that the student is suffering from lice the test shows Positive
[tex]=P(\frac{PT}{L})=0.2632[/tex]
Probability that the student is not suffering from lice and the test shows Positive
[tex]=P(\frac{PT}{N L})=0.0432[/tex]
Abbreviation used
L = Student has lice
N L=Student has no lice
P T=Test shows Positive
Probability that a student has lice, given that the student tested positive
[tex]P(\frac{L}{P})=\frac{P(\frac{PT}{L})}{P(\frac{PT}{L})+P(\frac{PT}{NL})}\\\\P(\frac{L}{P})=\frac{0.2632}{0.2632 +0.0432}\\\\P(\frac{L}{P})=\frac{0.2632}{0.3064}\\\\P(\frac{L}{P})=0.8590[/tex]
In terms of Percentages Required Probability
= 0.8590 × 100
= 85.90 %
Option C
Is the triangle below best described as right, acute, or obtuse? Explain your reasoning
Answer:
Right.
Step-by-step explanation:
It is not smaller or larger than a 90% angle, it is exactly at a 90% angle. Therefore, it is a right triangle.
The triangle above is known as a Right Triangle or as the question says it is a Right.
REASON: It is a Right Triangle because it has a Right angle & Right angles always are 90 degrees.
I HOPE U GOT THE ANSWER!....
Which invention allowed computers to be smaller?
Answer:
laptop/phone
As the computer advanced, transistors were invented. They were smaller and allowed the computers to become smaller than ever. Slowly, the size of the computers decreased as more and more pieces were invented.
Step-by-step explanation:
The invention of transistors allowed computers to be smaller.
What is a computer?A computer is a device that accepts information (in the form of digitalized data) and manipulates it to some result based on a program, software, or sequence of instructions on how the data is to be processed.
The invention of transistors or the computer chips made computers to work smarter than previously.
These computers also were more efficient and more reliable than the computers of the first generation.
The transistor replaced the cumbersome vacuum tube in televisions, radios and computers.
Hence, the invention of transistors allowed computers to be smaller.
Learn more about computers, click;
https://brainly.com/question/21080395
#SPJ5