Answers
Answer:
a) We have an aspect ratio of 4:3
This means that the width of the screen, W, is about 4/3 times the height of the screen, H.
Then we have the equation:
W = (4/3)*H
And the diagonal of a rectangle with width W and height H is:
D = √(W^2 + H^2)
Then if we have a 15 in TV, then we have D = 15 in.
Then we have:
15 in = √(W^2 + H^2)
Now we can use the relation W = (4/3)*H and replace this in the above equation:
15 in = √(((4/3)*H)^2 + H^2)
Now we can solve this for H:
15in = √( (16/9)*H^2 + H^2)
(15in)^2 = (16/9)*H^2 + (9/9)*H^2 = (25/9)*H^2
(9/25)*(15in)^2 = H^2
√( (9/25)*(15in)^2) = H
(3/5)*(15in) = H = 9 in
The height is 9 inches, and the width will be:
W = (4/3)*9in = 12in.
Now let's do the same for a 42 in tv.
We can use the same equation than before, this time we get:
42 in = √(((4/3)*H)^2 + H^2)
We can do the exact same procedure as before, and we will get:
(3/5)*(42in) = H = 25.2 in
Then the width is
W = (4/3)*H = (4/3)*25.2in = 33.6 in
b) Now we do the same, but now we have the relation:
W = (16/9)*H
Then if D is the diagonal, we have the equation:
D = √(W^2 + H^2) = √( ((16/9)*H)^2 + H^2)
This time we can simplify it for any general D.
D^2 = (16/9)^2*H^2 + H^2
D^2 = (256/81)*H^2 + H^2 = (256/81)*H^2 + (81/81)*H^2
D^2 = (337/81)*H^2
(81/337)*D^2 = H^2
√( (81/337)*D^2) = H
(9/18.36)*D = H
Then if we have a 42 in TV, the height is:
(9/18.36)*42in = H = 20.59 in
And the width will be:
W = (16/9)*H = (16/9)*20.59in = 36.60 in
If we have a 60 in TV, we get:
(9/18.36)*60in = H = 29.41 in
And the width will be:
W = (16/9)*H = (16/9)*29.41in = 52.29 in
c) if all the aspect ratios are always exactly 16:9, then no, the width and height should be exactly the same for all the TV with that ratio.
Related Questions
11. Let f(x) = 2x² + 7x + 5
Answers
Answer:
(x+1)(2x+5)
Step-by-step explanation:
f(x) = 2x² + 7x + 5
Factor the expression by grouping. First, the expression needs to be rewritten as 2x²+ax+bx+5. To find a and b, set up a system to be solved.
a+b=7
ab=2×5=10
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 10.
1,10
2,5
Calculate the sum for each pair.
1+10=11
2+5=7
The solution is the pair that gives sum 7.
a=2
b=5
2x²+7x+5 as (2x²+2x)+(5x+5).
(2x²+2x)+(5x+5)
Factor out 2x in the first and 5 in the second group.
2x(x+1)+5(x+1)
Factor out common term x+1 by using distributive property.
(x+1)(2x+5)
What is equivalent to 1/3(x9x + 12) + 4x + 6
Answers
Answer:
1/3(9x+12)+4x+6=x
We move all terms to the left:
1/3(9x+12)+4x+6-(x)=0
Domain of the equation: 3(9x+12)!=0
x∈R
We add all the numbers together, and all the variables
3x+1/3(9x+12)+6=0
We multiply all the terms by the denominator
3x*3(9x+12)+6*3(9x+12)+1=0
Wy multiply elements
9x^2(9+18x(9+1=0
Step-by-step explanation:
Marisol buys 3 notebooks that each cost the same amount and 1 calculator that costs $9. The total cost is $21. How much does each notebook cost?
Answers
Answer: 4 dollars for each notebook
Step-by-step explanation:
21-9= 12
12/3=4
each notebooks costs 4 dollars
Answer:
$4
Step-by-step explanation:
The independent variable is represented by the symbol(s)
1. Y
2. xy
3. Both A and B
4. X
5. None of the above
Answers
Answer:
4
Step-by-step explanation:
because variable is independent
hitunglah luas permukaan balok dengan ukuran sebagai berikut
a. 8 cm × 4 cm × 2cm
B. 8 cm × 3 cm × 4 cm
Answers
jawaban
a. = 112 cm²b. = 136 cm²penjelasan langkah demi langkah( step by step explanation )
Total Luas Permukaan = 2 (Panjang x Lebar + Lebar x Tinggi + Panjang x Tinggi)
a.Luas Permukaan = 2( 8×4 + 4×2 + 2×8 )
= 2 ( 32 + 8 + 16 )
= 2 × 56
= 112 cm²b.Luas Permukaan = 2( 8×3 + 3×4 + 4×8 )
= 2 ( 24 + 12 + 32 )
= 2 × 68
= 136 cm²
Goes through points (-2,-1) and (-3,5)
Help me pleaseeeeeeeeeee
Answers
Answer:
Distance between two points = √37
Step-by-step explanation:
Given:
(-2,-1)
(-3,5)
Find:
Distance between two points
Computation:
Distance = √(x1 -x2)² + (y1 - y2)²
Distance between two points = √(-2+3)² + (-1 - 5)²
Distance between two points = √ 1 + 36
Distance between two points = √37
17. Which is M=9pn solved for p? (1 point)
p = M/n p= M-9n. p= 9n/M. p=M/9n
Answers
B 56
Step-by-step explanation:
If you can buy 4 containers of pudding for $4.20 how much can you buy for $9.45 math problem PARAMETERS
*** 7 STEPS ***
Answers
Answer:
9 containers
Step-by-step explanation:
$4.20 for 4 containers
Form that we can find the cost per container, the unit cost.
$4.20 / 4 containers = $1.05/container
Each container costs $1.05
Now we find the number of containers we can buy with $9.45 by dividing $9.45 by the unit cost.
$9.45/($1.05/container) = 9 containers
Answer: 9 containers
Step-by-step explanation:
Four containers of pudding cost $4.20.
4x = 4.20
x = 1.05
Using this we know that one container of pudding costs $1.05.
Then, divide the maximum amount that you have by the cost of one.
9.45/1.05 = 9
With $9.45, you can buy nine cups of pudding.
In the case that you can buy the four containers in bulk (4 at a time)...
You can only buy 8 containers of pudding (two) because $4.20 only fits into $9.45 twice.
A bicycle wheel makes five rotations. The bicycle travels ft. Find the diameter of the wheel in inches. Use 3.14 for .
Answers
Answer:
[tex]r=\frac{L}{2pi R}[/tex]
Diameter=2r
inches=12*ft
Step-by-step explanation:
You forgot to say how far the bike travels.
Given R rotations, L feet, and a wheel radius of r, then the relationship is
[tex]L=2\pi rR[/tex]
Solving this for r gives
[tex]r=\frac{L}{2pi R}[/tex]
Diameter=2r
inches=12*ft
A circle of a radius r,cm inside a square, so that the circle touches the sides of the square.
a) calculate the area of the shaded region when r=6
Answers
Answer:
30.9 square cm
Step-by-step explanation:
subtract area of circle from area of square
Area of square = 12² or 144
(each side is twice the radius)
Area of circle = 6²π or 113.1
The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. What is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?
Answers
Answer:
The 99 percent confidence interval for the proportion of all employees at the company who own an electric car is (0.0104, 0.0496).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In a random sample of 500 employees, 15 reported owning an electric car.
This means that [tex]n = 500, \pi = \frac{15}{500} = 0.03[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.03 - 2.575\sqrt{\frac{0.03*0.97}{500}} = 0.0104[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.03 + 2.575\sqrt{\frac{0.03*0.97}{500}} = 0.0496[/tex]
The 99 percent confidence interval for the proportion of all employees at the company who own an electric car is (0.0104, 0.0496).
You can find the standard mean error and then use that to find the confidence interval limits.
The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by
Lower limit = 0.0104
Upper limit = 0.0496
The confidence interval is (0.0104, 0.0496) (can include those end points too)
How to find the confidence interval for proportions?Let the sample size be n
Let the interested quantities in the sample be present x times
Let the confidence level be of p%.
Then the level of significance is given by [tex]\alpha = 1 - p/100[/tex]
The standard mean error is calculated by:
[tex]SME = \sqrt{\dfrac{x(n-x)}{n^3}}[/tex]
Then the confidence interval limits can be found by
[tex]CI = \dfrac{x}{n} \pm Z_{\alpha/2}(SME)[/tex]
Using above formula for finding the confidence intervalWe have n = 500, x = 15 and [tex]\alpha = 1 - 0.99 = 0.01[/tex]
Finding the standard mean error:
[tex]SME = \sqrt{\dfrac{x(n-x)}{n^3}}\\\\SME = \sqrt{\dfrac{15 \times 485}{500^3}} \approx 0.00763[/tex]
From the z tables, at [tex]\alpha/2 = 0.01/2 = 0.005[/tex], we get z = 2.5758
Thus, the confidence interval is obtained by
[tex]CI = \dfrac{x}{n} \pm Z_{\alpha/2}(SME)\\\\CI = \dfrac{15}{500} \pm 2.575 \times 0.00763\\\\CI = 0.03 \pm 0.0196[/tex]
Lower limit = 0.0104
Upper limit = 0.0496
Thus,
The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by
Lower limit = 0.0104
Upper limit = 0.0496
The confidence interval is (0.0104, 0.0496) (can include those end points too)
Learn more about confidence interval here:
https://brainly.com/question/16427118
From a point 80 m from the base of a tower, the angle of elevation to the top of the tower is 28°. How tall is
the tower (remember: 3 decimal places)?
The height of the tower is [A] m.
Answers
Answer:
42.537 m
Step-by-step explanation:
Let x = height of tower
tan 28 = x/80
x = 80 tan 28
x = 42.537 m
In the figure, the horizontal lines are parallel and AB = BC = CD. Find JM.
A.15
B.10
C.5
D. 20
Answers
Answer:
By the transversal theorem, if segments on a transversal cut by parallel lines are equal, then similar segments cut by the same parallel lines on another transversal are also equal.
Therefore
JK=KL=LM=5
=>
JM=3*5=15
Step-by-step explanation:
1. A house cost $112,000 in 2010. By the year 2015, the house had a value of $132,000. What was the growth rate as a percent for that 5-year period?
Pls help
A. 6.48%
B. 3.34%
C. 5.23%
D. 2.15%
Answers
Answer:
The growth rate for the period was of 17.86%.
Step-by-step explanation:
To find the growth rate as a percent, we multiply the change by 100, and divide by the initial value.
A house cost $112,000 in 2010. By the year 2015, the house had a value of $132,000.
Change: 132 - 112 = 20
Initial value: 112
Growth rate as a percent:
20*100/112 = 17.86%
The growth rate for the period was of 17.86%.
Answer:b
Step-by-step explanation:
A bucket that has a mass of 20 kg when filled with sand needs to be lifted to the top of a 10 meter tall building. You have a rope that has a mass of 0.4 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 16 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building.
Find the work done lifting the bucket (sand and rope) to the top of the building.
Answers
Answer:
W=2001.24 newton meters
Caution: check units and arithmetic - I often make errors.
Step-by-step explanation:
Work is force times distance.
Denote height by h where h=0 is at ground level.
Denote the mass of the bucket and rope at height h by m(h).
The rate at which the bucket loses mass with height is (20-16)/10=0.4 kg/m
The rate at which the rope between the bucket and the top of the building loses mass is 0.4 kg/m
The initial mass of the bucket and rope is
[tex]m_{0}=20+0.4+0.4(10)=24.4[/tex]
The mass at height h is
[tex]m(h)=24.4-0.8h[/tex]
The force required at height h is
m(h)g
where g is the gravitational acceleration.
g=9.81 meters/sec/sec
The work required is
[tex]\int\limits^b_a {m(h)g} \, dh[/tex]
Where a=0 and b=10
[tex]g\int\limits^b_a {(24.4-0.8h)} \, dh=g(24.4h-0.4h^2)\left \{ {{10} \atop {0}} \right.[/tex]
g(244-40)=204g
W=2001.24 newton meters
graph the linear equation y= -4/9x -4
Answers
Answer:
I used Desmos to graph it
Please help! Will mark brainliest! ASAP
Answers
Answer:
165.00 dollars
Step-by-step explanation:
Eight hundred fifty two thousand, six hundred seventy four and thirty five hundredths in numbers
Answers
Answer:
Number = 857674.35
Step-by-step explanation:
Translating the word problem into a numerical format;
Eight hundred and fifty two thousand = 852,000
Six hundred and seventy four = 674
Thirty five hundredths = 35/100 = 0.35
Now, we would add all of the values together.
Number = 852,000 + 674 + 0.35
Number = 857674.35
Write the word sentences as an equation! Half of a number q is 14.
Answers
Answer:
q/2=14I hope this helped you :)
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
Answer:
y = x + 11
Step-by-step explanation:
The table is showing 4 x and y values. With the question of which equation gives the rule of the table.
To solve, all we have to do is plug in x with the correspondant equation, same goes with y.
y = x + 11 will be the only one that fits mainly because all the other ones gives a higher result.
Answer:
y = x + 11
Step-by-step explanation:
y + 11 = 11
1 + 11 = 12
2 + 11 = 13
3+ 11 = 14
4+ 11 = 15
y is the first row, 1,2,3,and 4
11 is 11 (lol)
x is the answer
your answer is y=x+11
Rick earned 36 extra credit points. Cindy earned e fewer extra credit points than Rick. Write
an expression that shows how many extra credit points Cindy earned.
PLEASE ANSWER
Answers
Answer:
36-e
Step-by-step explanation:
-
13. Jannah purchased flowers to plant in
her garden. She planted 2 flowers in
each of her 5 flower beds plus 8 flowers
around a pond. Write an expression
that shows how many flowers Jannah
planted.
Answers
Answer:
2x5=10+8
Step-by-step explanation:
my answer need to be 20 characters long so I had to write this too
CAN SOMEONE PLEASE HELP ME!!!!!!!!!
Answers
Answer:
12(m +1) > 18m - 3
12m + 12 > 18m - 3
12+3 > 18m - 12m
15 > 6 m.
m < 15/6
m < 2.5
4th option is correct.
Answer:
{m| m < 2.5}
Step-by-step explanation:
m < 2 1/2,m < 2.5 , m ∑ [-∞, 5/2]
hope that helped!
what is the area of 5m, 17m, 8m, and 5m, the shape is a kite
Answers
Answer:
It can't be a kite. A kite has 2 pairs of equal sides.
Step-by-step explanation:
Hi! I am having a hard time with this question. Can anyone help me out? I only need to answer the questions with the red circles
Answers
Explanation: The trig ratios are SohCahToa or Sin(o/h), Cos(a/h), and Tan(o/a).
When A is the reference angle, b is the adjacent side and a is always the hypotenuse (Cah).
When J is the reference angle, j is the opposite side and l is always the hypotenuse (Soh).
When K is the reference angle, k is the opposite side and j is the adjacent side (Toa).
Which table or graph shows the value of y going down as the value of x goes up?
Answers
Answer:
c.
Step-by-step explanation:
12.5(7) + 11.9(8)=?
Answers
Answer:the answer is 182.7
Step-by-step explanation:brainliest please Sans Undertale out
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Evalua la siguiente
expresión algebraica si
X=3 Y=2
3x + 4y =
Answers
Answer:
3x + 4y = 17
Step-by-step explanation:
Espero y te haiga ayudado :)
What number is between 5/2 and the other number In the photo.
Answers
Solve for x in equation x^2-10x25=35
Answers
Answer: b
Step-by-step explanation:
x= 5+√35 and 5-√35