Each side of the square below is 8 inches. A triangle inside of a square. The top of the triangle divides a side of the square into 2 equal parts of 4 inches. The triangle is shaded and the area to the right of the triangle is shaded. What is the probability that a point chosen at random in the square is in the blue region? 0. 25 0. 33 0. 66 0. 75.
Answers
The probability that a point is chosen at random in the square is in the blue region is 0.8.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As we know that the area of the shaded region is the sum of the area of triangle A and the area of triangle B. Therefore, the area of the blue shaded region is,
[tex]\text{Area of shaded region} = (\dfrac{1}{2} \times 8 \times 8) + (\dfrac{1}{2} \times 4 \times 8)[/tex]
[tex]= (32) + (16)\\\\= 48\rm\ in^2[/tex]
The area of the square can be written as,
[tex]\text{Area of Square} = \rm(Side)^2 = 8^2 = 64\ in^2[/tex]
Now, the probability that a point is chosen at random in the square is in the blue region can be written as,
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\[/tex]
[tex]\rm Probability = \dfrac{\text{Area of blue region}}{\text{Area of square}}\\\\Probability = \dfrac{48}{60} = 0.8[/tex]
Hence, the probability that a point is chosen at random in the square is in the blue region is 0.8.
Learn more about Probability:
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Related Questions
A triangle has two sides of length 19 and 15. What is the largest possible whole-number length for the third side?
Answers
Answer:
34? Idek
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
To maximize the length of the third side, which I'll call x, it needs to be the longest side.
So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.
HELPPPPPPP URGENT :L
Answers
Answer:
17.5
Step-by-step explanation:
The area for a triangle is (base*height)/2 this means
(5*7)/2 = 17.5 units^2
Answer:
Step-by-step explanation:
base = b = 5 units
height = h = 7 units
[tex]\bf \boxed{\text{Area of triangle = $\dfrac{1}{2}bh$}}[/tex]
[tex]=\dfrac{1}{2}*5*7\\\\\\=\dfrac{35}{2}\\\\\\= 17.5 \ square \ units[/tex]
what is the area of this figure?
Answers
Answer:
234 square millimeters
Step-by-step explanation:
You want the area of the irregular polygon shown.
CompositionThere are always several ways you can find the area of a figure like this. In the attachment we have shown extensions of the vertical and horizontal lines that will divide the figure into a triangle and two rectangles.
Triangle areaThe triangle has a base of 12 mm and a height of 13 mm. Its area is ...
A = 1/2bh
A = 1/2(12 mm)(13 mm) = 78 mm²
Rectangle areaThe upper rectangle has a width of 8 mm and a length of 14 mm. Its area is ...
A = LW
A = (14 mm)(8 mm) = 112 mm²
The lower rectangle has a width of 4 mm and a length of 11 mm. Its area is ...
A = (4 mm)(11 mm) = 44 mm²
Total areaThe area of the figure is the sum of the areas of its parts:
total area = triangle area + upper rectangle + lower rectangle
total area = 78 mm² + 112 mm² + 44 mm² = 234 mm²
The area of the figure is 234 square millimeters.
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Deondre drops a nickel from a balcony that
is 125 meters in the air. The function
y = -512 + 125 can be used to represent y, the
height of the coin in meters after t seconds.
Write and solve an equation to find the time it
will take for the coin to hit the ground.
Answers
The function [tex]y = -5t^2 + 125[/tex] of the nickel is quadratic function
It will take 5 seconds for the coin to hit the ground
How to determine the time the nickel hits the ground?
The function is given as:
[tex]y = -5t^2 + 125[/tex]
When the nickel hits the ground, the value of the function is:
y = 0
So, we have:
[tex]-5t^2 + 125 = 0[/tex]
Subtract 125 from both sides
[tex]-5t^2 =- 125[/tex]
Divide both sides by -5
[tex]t^2 =25[/tex]
Take the square root of both sides
[tex]t = 5[/tex]
Hence, it will take 5 seconds for the coin to hit the ground
Read more about quadratic functions at:
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what is thecentre and diameter of the circle with equation
[tex]x {2} + {y2} - 2y + 1 = 16[/tex]
Answers
Answer:
The exact value of sin 22.5° using the half-angle formula is √(2 - √2) / 2 or 0.38
Step-by-step explanation:
Let us consider θ = 22.5 º
Therefore, sin2θ = [(1− cos 2θ) / 2] -------(1)
If θ = 22.5° then 2θ is 45°.
On substituting the value of θ in equation (1), we get
sin2 22.5° = [(1− cos (2 × 22.5°)) / 2]
sin2 22.5° = [(1− cos 45°) / 2]
sin2 22.5°= [ [1 - (1 / √2)] / 2 ]
sin2 22.5°= (2 - √2) / 4 [ on simplifying the above RHS value ]
sin 22.5° = [√(2 - √2) / 2]
After substituting the value of √2 as 1.414 in the above equation, we get
sin 22.5°= 0.38
Determine the root of the equation by factoring 3x^2-x-4=0.
I have both of the roots solved, but when I verify it does not come out to a zero. Why is this?
Answers
Answer:
The roots you found should be [tex](3x-4)(x+1)=0[/tex], which shows that [tex]x = \frac{4}{3} \\ x=-1[/tex]
Step-by-step explanation:
You likely messed up when trying to one or both of the roots back into the equation.
A cylinder has a base diameter of 16cm and a height of 20cm. What is its volume in cubic cm
Answers
Answer:320 cubic cm
Step-by-step explanation: if you multiply 16x20m you get 320 cm
Can someone help with me
Answers
Answer:
yes your answer is 45 degree
Answer:
105°
Step-by-step explanation:
There 360° in a circle, so...
360°-150°-105°=105°
check: 150°+105°+105°= 360°
[Answer] 105°
Use the definition of continuity and the properties of limits to show that the function k(x)= √8−x2 2x2−5 is continuous at x = -2
Answers
use the terms 8 , 3x , 3/2 and 4x to complete the expression below so that’s is equivalent to 9x - 12
Answers
Answer:
A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).
») b. The area of the parallelogram is 65 ft2. What is its height? mm th 13 ft 13
Answers
Answer:
Five feet
Step-by-step explanation:
H = A ÷ L
H = 65 ÷ 13
H = 5 ft
Whats the equation of a circle with the center point of 1, -1 and a radius of. 5
Answers
Step-by-step explanation:
For this problem, we need to use the fact that the circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.
This gives us that the equation of the circle is (x-1)^2 + (y-1)^2 = 25.
which of the following fractions is NOT equivalent to the others?
A. 24/36
B. 8/12
C. 12/16
D. 4/6
Answers
Answer:
C
Step-by-step explanation:
Just simplify each possible answer by dividing by the lowest common factor, and find the odd one out.
A. 24/36 = 2/3 (LCF of 12)
B. 8/12 = 2/3 (LCF of 4)
C. 12/16 = 3/4 (LCF of 4)
D. 4/6 = 2/3 (LCF of 2)
Answer:
C
Step-by-step explanation:
if you convert all of the fractions into decimal form the only answer that is not .6667 is c
Solve the equation k^2-6k=11 by completing the square
Answers
Answer:
k = ±2√5 + 3
Step-by-step explanation:
k² - 6k + 9 = 11 + 9(k - 3)² = 20k - 3 = √20k - 3 = ±2√5k = ±2√5 + 3[tex]k=3+2\sqrt5\ or\ k=3-2\sqrt5[/tex]
Step-by-step explanation:
[tex]k^2-6k=11[/tex]
_______________________________________________
Add one term in order to complete the square[tex]k^2-6k+(6\times\frac{1}{2})^2=11+(6\times\frac{1}{2})^2[/tex]
________________________________________________
Calculate[tex]k^2-6k+3^2=11+3^2[/tex]
_________________________________________________
Factor the expression using [tex]a^2\pm 2ab+b^2=(a\pm b)^2[/tex][tex](k-3)^2=11+3^2[/tex]
__________________________________________________
Calculate the power[tex](k-3)^2=11+9[/tex]
___________________________________________________
Calculate the sum or difference[tex](k-3)^2=20[/tex]
______________________________________________________
Split into two equations[tex]k-3=\sqrt{20}\ or\ k-3=-\sqrt{20}[/tex]
________________________________________________________
Move variables to the left side of the equation:[tex](k-3=\sqrt{20})[/tex]
[tex]k=\sqrt{20}+3\\ k=2\sqrt{5}+3[/tex]
____________________________________________________
Move variables to the left side of the equation:[tex](k-3=-\sqrt{20})[/tex]
[tex]k=\sqrt{20}+3\\ k=-2\sqrt{5}+3[/tex]
_____________________________________________________
So far:[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]
_____________________________________________________
Find the union of the solutions[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]
_____________________________________________________
I hope this helps you
:)
1. D=5.9 ft.
calculate the circumference of the circle.
2. D=3.2 ft.
calculate the circumference of the circle.
3. D= 6.1 ft.
calculate the circumference of the circle.
4. R= 3.7 m.
Calculate the circumference of the circle.
5. R=6.2
Calculate the circumference of the circle.
6. R=5.1 Ft.
Calculate the circumference of the circle.
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution ~
As we know, we can calculate the circumference of a circle in terms of its diameter as :
[tex]\qquad \sf \dashrightarrow \:c = \pi d[/tex]
where, c = circumference and d = diameter
And also, circumference of circle is terms of radius (r) is :
[tex]\qquad \sf \dashrightarrow \:c = 2\pi r[/tex]
Now, let's move on to questions ~
First[tex]\qquad \sf \dashrightarrow \:3.14 \times 5.9 [/tex]
[tex]\qquad \sf \dashrightarrow \: \approx18.53 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Second[tex]\qquad \sf \dashrightarrow \:3.14 \times 3.2[/tex][tex] \qquad \sf \dashrightarrow \: \approx10.048 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Third[tex]\qquad \sf \dashrightarrow \:3.14 \times 6.1[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx19.15 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Fourth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 3.7[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2×11.62 \: m[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx23.24 \: m[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Fifth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 6.2[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2× 19.47 \: units[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx38.94 \: m[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Sixth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 5.1[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2×16.01 \: ft[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx \: 32.02m[/tex]
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malamud and mohammed bought the same eight CD's but mohammed bought used CD's so each was half the price malamud paid. if the mean price malamud paid in $16 and the median is $16.50 , what are the mean and median prices for mohammed's CD's?
Answers
Answer: $8 , $8.25
Step-by-step explanation: It says “ half the price ” so half of 16 is ( 8 ) and half of 16.50 is ( 8.25 )
someone explain how to do this please
A: square root of 96
B: square root of 48
C:square root of 16
D:8
Answers
8 squared - 4 squared = 48
The next step is getting the square root of the result. Thus revealing B as the answer.
Answer:
B. Square root of 48
Step-by-step explanation:
Using Pythagorean theorem. A^2 = B^2 + C^2
4^2 + x^2 = 8^2
16 + x^2 = 64
x^2 = 48
x = square root of 48
PLEASE ANSWER ASAP.
A snowball has a diameter of 6 cm.
What is the volume of the snowball?
How long would it take a snowball to melt if it melts at a rate of 1.8 cubic centimeters per minute?
Answers
Answer:
Volume: 37.7cm3
It will melt in 21 minutes.
Step-by-step explanation:
Volume of a sphere: 4/3 x pi x r^2
4/3 X pi x 3^2 = 37.7cm3
37.7/1.8=20.943 minutes
(3.1×10^7)(5.8×10^−4) in scientific notation
Answers
Answer:
[tex]\filldraw (10,0) rectangle ++(3pt,3pt);[/tex]
Manny does not eat 4/9 of his orange at lunch. Josh does not 5/9 of his orange at lunch. How much orange do Manny and Josh have left over?
Answers
The amount of orange that Manny and Josh have leftover after eating lunch is 1.
What are fractions?A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below
How much orange is leftover?Oranges Manny has left = 1 - 4/9 = 5/9
Oranges Josh has left = 1 - 5/9 = 4/9
Oranges they both have left = 5/9 + 4/9 = 1
To learn more about subtraction of fractions, please check: https://brainly.com/question/915789
Please help will give brainlest! locks in 30 min!
Answers
Answer:
1
Step-by-step explanation:
[tex] \tan( \frac{5\pi}{4} ) \times \frac{\pi}{180} = 1.19[/tex]
The question wants in radian, not in degrees since using the unit circle. Hope this helps
Answer:
a) 1
Step-by-step explanation:
Tan 5pi/4: 1
Tan (-5pi/4): -1
Tan 5pi/4 in degrees: tan (225°)
What is the area of the given quadrilateral?
Answers
Answer:
20 square units
Step-by-step explanation:
as its a square, we just add all the sides together. like a+b+c+d..
5+5+5+5=20 units
Length x width= area
So 5x5=25
Hope this helped :)))
Can someone please help me with this
Answers
Definition of a trapezoid: a quadrilateral with one pair of parallel sides
Thus PQRS is a trapezium because Line PQ is parallel to line SR
Hope that helps!
6x + 4 - 8x + 9(4 - x)
-
Answers
Answer:
6x - 8x + 4 + 36 - 9x
= 40 - 11x
6x + 4 - 8x + 36 - 9x
(6x - 8x -9x) + 36
-11x + 36
The area of a circular fountain is 121π square feet.
What is the diameter of the fountain?
Answers
Answer:
22 feet
Step-by-step explanation:
The area of a circle is π · r².
So, step one is to figure out the radius, so taking that equation, we can say π · r² = 121π.
Divide both sides by π to get r² = 121
Then, you take the square root of both sides to leave r = 11.
The diameter is twice as long as the radius, so multiply 11 · 2 to get 22.
The diameter is 22 feet long.
Hello I'm just here to say if a question asks "circle all of the expressions that are equivalent to some type of math question do i pick more than one?
Answers
On a coordinate plane ,the segment with endpoints (10,40) and (70,120) is dilated by a factor of 4/5,with the origin as the center of dilation. What is the length of the resulting segment ?
A-80
B-100
C-112
D-125
Answers
The length of the dilated line segment is 80 units.
What is dilation?Dilation is the increase or decrease in the size of a figure or object.
The segment with endpoints (10,40) and (70,120) is dilated by a factor of 4/5 to get (8, 32) and (56, 96).
The distance between points (8, 32) and (56, 96) is:
[tex]Distance = \sqrt{(96-32)^2+(56-8)^2} =80\ units[/tex]
The length of the dilated line segment is 80 units.
Find out more on dilation at: https://brainly.com/question/10253650
The coach of Darnel's baseball team recorded how many runs the team scored in each game last season. This box plot shows the results. please
Answers
The fraction of the game that Daniel's team scores 2 or more runs is 1/4 of the game.
What are box plots?A box plot is used to study the distribution and level of a set of scores. Scores are distributed into 4 groups. Each group has a value of 25%
The first quartile, is the first line on the box. The first quartile represents 1/4 of the score.
To learn more about box plots, please check: https://brainly.com/question/27215146
Helpp me with my sister's math
Answers
Answer:
the 1/2w +22 one is a binomial
Step-by-step explanation:
a binomial is a equation with one two separate numbers AFTER simplifcation. so "1+1" is not a binomial because its equal to just 2, but "1 + x" is a binomial because its simplifed
Select the set of equations that is NOT equivalent to 8k = 20