The probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75
How to find the geometric probability?When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:
E = favorable eventS = total sample spaceThen:
[tex]P(E) = \dfrac{A(E)}{A(S)}[/tex]
where A(E) is the area/volume/length for event E, and similar for A(S).
For this case, we're given that:
We want to get probability for a randomly chosen point in square to be in the blue region.The diagram is attached below.The favorable space is the blue shaded region.
The total sample space is the area of the considered square.
Let we take:
E = event of choosing point in the blue shaded region
Now, we have:
Area of blue region = Area of triangle with base = height = 8 inches + Area of right sided triangle which has base of 4 inch (look it upside down), and height of 8 inches
Area of blue region = [tex]\dfrac{1}{2} \times (8 \times 8 + 4 \times 8) = 48 \: \rm in^2[/tex]
Area of the square of sized 8 inches = 64 sq. inches.
Thus, we get:
[tex]P(E) = \dfrac{A(E)}{A(S)} = \dfrac{48}{64} = \dfrac{3}{4} = 0.75[/tex]
Thus, the probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75
Learn more about geometric probability here:
https://brainly.com/question/24701316
what are the x- intercepts of the graph that represents y=(x+1)(x+5)
Answer:
x= -1 and x= -5
Explanation
y=(x+1)(x+5)
set both equations equal to 0
x+1=0 and x+5=0
subtract each constant from the appropriate side
x= -1 x=-5
PLEASE PLEASE PLEASE HELP ME YALL‼️‼️‼️‼️‼️
There are four boys in a class of ten students. Four students are to be randomly selected
(without replacement) to help in the lunch line. Determine the probability that all four
students are boys.
Answer:
Hi .. im happy to help
answer is 0.033
Step-by-step explanation:
P = C(4,4)÷C(10,4)
P = 1 ÷ 30
[tex]p = \frac{1 }{30} [/tex]
p = 0.033
someone pleaseee helppppp
find the hcf by prime factorization method of 18 and 24
Answer:
6
Step-by-step explanation:
Prime factorization of 18 = 2 × 3 × 3
Prime factorization of 24 = 2 × 2 × 2 × 3
Common factors of 18 and 24 = 2 × 3 = 6
HCF (18,24) = 6
Which person is not living within their means?
A. Joyelle set aside money for emergency funds by limiting her thing
entertainment costs for a few months.
B. Bill earns a high salary, so he contributes the maximum allowed to
his IRA each year.
C. Ella maxed out all three of her credit cards but pays the minimum
balance each month.
O D. Dmitri earns $1000 a month and spends $800 on rent, groceries,
and other expenses.
The person that is not living within their means is Ella who has maxed out all three of her credit cards but pays the minimum balance each month.
What does it mean when a person is living above their means?If a person is living above their means, the person is spending more money than they have. A person living above their means would most likely borrow in order to afford their lifestyle. A person living above their means would have no amount of savings.
To learn more about credit cards, please check: https://brainly.com/question/14716152
Please answer this order of operations question
-8 - (-2 + 7)2
Answer:
-18
Step-by-step explanation:
= -8 - (-2 +7) x 2
= -8 - 5 x 2
= -8 - 10
= -18
The current temperature is 48°F. It is expected to drop 1.5°F each hour.
Which equation can be used to find in how many hours, h, the temperature will be 36°F?
A) 36 + 48h = 1.5
B) 48 – 1.5h = 36
C) 48 + 1.5h = 36
D) 36 - 1.5h = 48
Answer:
B
Step-by-step explanation:
please someone help i will give brianliest
Answer:
the answer is 16
Step-by-step explanation:
look at the photo
solve pls brainliest
Answer:
Simplify the radical by breaking the radicand up into a product of known factors.
Exact Form:
3
√
75
5
Decimal Form:
0.84343266
…
Answer:
[tex]\frac{27}{125}[/tex]
Step-by-step explanation:
[tex](\frac{3}{5})^{3}[/tex] is [tex]\frac{3^{3}}{5^{3}}[/tex]
[tex]3^{3} = 27[/tex] and [tex]5^{3} = 125[/tex]
[tex]\frac{27}{125}[/tex]
Find of 14. 3/7
A. 3
B. 5
C. 6
D. 2
Answer:
C. 6.
Step-by-step explanation:
3/7 of 14
= 3*14/7= 42/7
= 6.
Find the values of x and y. State which theorem(s) you used.
Answer:
3x+45=180
3x=180-45
x=135/3
x=45
(y-4)=45
y=45+4
y=49
Answer:
x=45° and y=49° (180°in a straight line, co-interior angles add up to 180°)
Step-by-step explanation:
There are 180° in a straight line so 180°-45=135, 135=3x
135 divided by 3= 45, so x=45°, then because co-interior angles always add up to 180°, 45+ the missing angle=180, 180-45=135, so the angle next to angle (y-4) is 135°.
Then, solving the equation u have 135+(y-4)=180 because there are 180° in a straight line.
The equation ends up as y=49°
Isaiah decides to launch a model rocket to demonstrate parabolic motion. Given x stands for time and y stands for height in feet, find the equation for his rocket if it launches at 5 seconds, lands at 11 seconds, and is at 80 feet after 10 seconds. Explain in one sentence how you created your equation.
The parabolic motion is an illustration of a quadratic function
The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
How to model the function?Given that:
x stands for time and y stands for height in feet
So, we have the following coordinate points
(x,y) = (5,0), (11,0) and (10,80)
A parabolic motion is represented as:
y =ax^2 + bx + c
At (5,0), we have:
25a + 5b + c = 0
c= -25a - 5b
At (11,0), we have:
121a + 11b + c = 0
Substitute c= -25a - 5b
121a + 11b -25a - 5b = 0
Simpify
96a + 6b = 0
At (10,80), we have:
100a + 10b + c = 80
Substitute c= -25a - 5b
100a + 10b - 25a -5b = 80
75a -5b = 80
Divide through by 5
15a -b = 16
Make b the subject
b = 15a + 16
Substitute b = 15a + 16 in 96a + 6b = 0
96a + 6(15a + 16) = 0
Expand
96a + 90a + 96 = 0
This gives
186a = -96
Solve for a
a = -16/31
Recall that:
b = 15a + 16
So, we have:
b = -15 * 16/31 + 16
b =-240/31 + 16
Take LCM
b =(-240 + 31 * 16)/31
[tex]b =256/31
Also, we have:
c= -25a - 5b
This gives
c= 25*16/31 - 5 * 256/31
Take LCM
c= -880/31
Recall that:
y =ax^2 + bx + c
This gives
y = -16/31x^2 + 256/31x - 880/31
Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
Read more about parabolic motion at:
https://brainly.com/question/1130127
For a sphere with a radius of 8 cm, find the volume of the sphere. Write each answer as an exact value or as a number rounded to the nearest tenth.
Answer:
V≈2144.66cm³
Step-by-step explanation:
GUYS PLS HELP
What kind of
drawing is this
figure?
A. A triangle
B. A perspective drawing
C. A cylinder
D. A net
B: A perspective drawing
Answer:
B. perspective drawing.
Step-by-step explanation: perspective drawings can be inspirational drawing and can be imagined and created to be like anything and can be anything.
Pick the biggest number.
A0.193 B0.26 C0.6 D0.308
Answer:
Hello fellow Human! ^ω^
The answer is option D. 0.308
Step-by-step explanation:
We are going to Compare the digits starting with the greatest place value.
The Number 0.193 Is not the biggest number. However, 0.193 is bigger than 0.26 and 0.60.The number 0.193 is smaller than the number 0.308.
Therefore, the answer is Option D. 0.308
Hope this helps!
Have an Awesome Friday!
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the lengths of the prisms vary. It cost $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum length of the prism is highest length of the hexagonal prism
The maximum length of each prism is 8.0 cm
How to determine the maximum length of each prism?The surface area of the hexagonal prism is calculated using:
A = 6al + 3[tex]\sqrt[/tex]3 a^2
Where:
a represents the edge length; a = 4 cm
l represents the length (or height) of the prism
The surface area costs $0.04 per square centimeter.
So, we have:
C = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
The maximum cost is $11.
So, the equation becomes
11 = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
Substitute 4 for a
11 = 0.04 * [6 * 4l + 3[tex]\sqrt[/tex]3 * 4^2]
Evaluate the products and exponents
11 = 0.04 * [24l + 48[tex]\sqrt[/tex]3]
Divide both sides by 0.04
275 = 24l + 48[tex]\sqrt[/tex]3
Subtract 48[tex]\sqrt[/tex]3 from both sides
24l = 275 - 48[tex]\sqrt[/tex]3
Evaluate the difference
24l = 191.9
Divide both sides by 24
l = 8.0
Hence, the maximum length of each prism is 8.0 cm
Read more about surface areas at:
https://brainly.com/question/6613758
Answer:
275, 7.99
Step-by-step explanation:
i got it right
and please get me too branliest
Pls help I need to know how much the penny will be by the end
Answer:
Day 1: $.01
Day 2: $.02
Day 3: $.04
Day 4: $.08
Day 5: $.16
Day 6: $.32
Day 7: $.64
Day 8: $1.28
Day 9: $2.56
Day 10: $5.12
Day 11: $10.24
Day 12: $20.48
Day 13: $40.96
Day 14: $81.92
Day 15: $163.84
Day 16: $327.68
Day 17: $655.36
Day 18: $1,310.72
Day 19: $2,621.44
Day 20: $5,242.88
Day 21: $10,485.76
Day 22: $20,971.52
Day 23: $41,943.04
Day 24: $83,886.08
Day 25: $167,772.16
Day 26: $335,544.32
Day 27: $671,088.64
Day 28: $1,342,177.28
Day 29: $2,684,354.56
Day 30: $5,368,709.12
A fuel tank is in the shape of a right circular cylinder. The radius of the base and height of the tank are
10
feet and
25
feet, respectively. Due to safety measures, the tank can be filled to only
80
%
of its capacity.
If
100
cubic feet of fuel are equal to
2. 78
gallons, what is the maximum number of whole gallons of fuel the tank can contain due to safety measures?
The maximum number of whole gallons of fuel the tank can contain due to safety measures is 174.584 gallons
Volume of a cylinderv = πr²hr = radius
h = height
Therefore,
r = 10 ft
h = 25 ft
The tank can only be 80% filled due to safety measures. Therefore,
v = 3.14 × 10² × 25
v = 3.14 × 100 × 25
v = 3.14 × 2500
v = 7850 ft³
80% capacity of 7850 ft³ is as follows:
80 / 100 × 7850 = 628000 / 100 = 6280 ft³
100 ft³ = 2.78 gallons
6280 ft³ = ?
cross multiply
maximum number of whole gallons = 6280 × 2.78 / 100 = 17458.4 / 100 = 174.584 gallons
Therefore, the maximum number of whole gallons of fuel the tank can contain due to safety measures is 174.584 gallons
learn more on cylinder here: https://brainly.com/question/1780981
Need help with b please and thank you (lots of points)
Answer:
17.34 years
Step-by-step explanation:
The equation you wrote in the first part of the problem can be solved for the value of t that makes the population be 5000.
[tex]P(t)=\dfrac{10000}{1+11.5e^{-0.1408614477t}}[/tex]
Setting this equal to 5000 and multiplying by the denominator, we have ...
[tex]5000=\dfrac{10000}{1+11.5e^{-0.1408614477t}}\\\\5000+57500e^{-0.1408614477t}=10000\\\\e^{-0.1408614477t}=\dfrac{5000}{57500}\qquad\text{subtract 5000, divide by 57500}\\\\-0.1408614477t = \ln{\dfrac{1}{11.5}}=-\ln(11.5)\qquad\text{take logs}\\\\t=\dfrac{\ln(11.5)}{0.1408614477}\approx17.3386[/tex]
For the population to reach 5000, it will take about 17.34 years.
_____
Additional comment
The value -0.14086... is the natural log of the ratio 1818/2093. This means the "exact answer" is ln(11.5)/(ln(2093) -ln(1818)), an irrational number.
A graphing calculator can answer the question easily.
A dartboard is divided into 20 sectors. Each sector is worth a point value from 1 to 20 and has shaded regions that double or
triple this value. A sector is shown below. Find the areas of the entire sector, the double region, and the triple region. Round
your answers to the nearest hundredth.
in
triple
double
The area of the entire sector is about
square inches.
The area of the double region is about
square inches.
square inches.
The area of the triple region is about
The area of each sector is the amount of space on the sector
The area of the entire region is 6.89The area of the double region is 0.75The area of the triple region is 0.46The area of the entire sectorThe area of a sector is calculated as:
A = (1/2) × r^2θ
For the entire sector, we have:
θ = π/10
r = 6.625
So, we have:
A = (1/2) × 6.625^2 × π/10
Evaluate the product
A = 6.89
The area of the double regionFor the double region, we have:
θ = π/10
r = 6.25
So, we have:
A = Complete sector - (1/2) × r^2θ
A = 6.89 - (1/2) × 6.25^2 × π/10
Evaluate the difference
A = 0.75
The area of the triple regionFor the triple region, we have:
θ = π/10
R = 4.125
r = 3.75
So, we have:
A = (1/2) × R^2θ - (1/2) × r^2θ
A = (1/2) × 4.125^2 × π/10 - (1/2) × 3.75^2 × π/10
Evaluate the difference
A = 0.46
Hence, the area of the triple region is 0.46
Read more about sector areas at:
https://brainly.com/question/16736105
Abby practiced her horn for 3/4 of an hour every day for 12 days?
a) How many hours did she practice in those 12 days?
b) How many minutes did she practiced in those 12 days?
Answer:
9 hours, 540 minutes
Step-by-step explanation:
12 x 0.75 = 9
Given that x is an acute angle and cos x=2√5÷5,find without using mathematical tables or a calculator , tan(90-x)°.
Answer: 2
Step-by-step explanation:
Rachel has half the amount of money that Melanie has.
Melanie has $12 less than 3 times the amount that Kim has.
Let k represent the amount. of money kim has.
(A) write an expression that represents the amount of money that Melanie and Kim has. (two separate expressions)
(B) if kim has $20, how much money does Melanie and Rachel have?
EXPLAIN UR WORK
Let the amount of money Kim has be k then,
ATQ,
The amount of money Melanie has
⇢3k - $12The amount of money Rachel has
⇢3k-$12/2 = 1.5k - $6Given that,
Kim has $20,
so,
The amount of money Melanie has
⇢3k - $12 = 3 x $20 -$12 = $48The amount of money Rachel has
⇢ 1.5k - $6 = 1.5 x $20 -$6 = $24There are 250 wolves in a national park. the wolf population is increasing at a rate of 16% per year. write an exponential model to represent the situation. use the model from problem 1 to determine how long it will take the wolf population in the national park to reach 1000. round the answer to the nearest hundredth.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill[/tex]
[tex]A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}[/tex]
Cole is buying a new rain barrel to help with watering his garden. The rain barrel is shaped like a right circular cylinder. What is the volume of the rain barrel if it is 26 inches tall and has a diameter of 22 inches? Use straight pi equals 3.14.
A right circular cylinder diameter 22 inches and a height of 26 inches.
V equals_(blank)_ inches cubed
Round to the nearest hundredth if necessary. Type your numerical answer (without units) below.
Answer:
[tex]V = 9878.44 in^3[/tex]
Step-by-step explanation:
The volume of a cylinder, is essentially base multiplied by height. Think of it like this, you are taking a flat 2D circle and extending it in 3rd dimension by a length 'h'.
[tex]V = base * h[/tex]
The base here is the circle area, and the height is the amount you extended that 2d circle in the 3rd dimension.
The area of a circle is [tex]\pi r^2[/tex]. If we put that into our equation we get the volume of a cylinder.
[tex]V = \pi r^2 *h[/tex]
Now applying that to the question; Firstly, we are given the diameter, which is 22 inches. We need radius, to actually put it in the equation. The diameter is essentially 2 multiplied by the radius. That means to get the radius we divide the diameter by 2, giving us 11 inches. Next we are given how tall it is, 26 inches; that is the height.
[tex]r = 11in\\h = 26in[/tex]
Plug these values into the equation.
[tex]V = 3.14(11in)^2 * 26in[/tex]
Calculate this, and you get [tex]V = 9878.44 in^3[/tex]
Find the slope of the line.
PLS HELP I AM SO BEHIND
Answer:
-1
Step-by-step explanation:
Follow the example below and Good Luck!!!
Answer:
-6/5
Step-by-step explanation:
The slope of the line is the ratio of "rise" to "run". That is, it is the ratio of the vertical change between two points to the horizontal change between those points.
__
Here, two points are marked, (-1, 2) and (4, -4). Either by counting grid squares or by subtracting coordinates, we find the vertical change (rise) from the first point to the second to be (-4 -2) = -6 units. The horizontal change (run) from the first point to the second is (4 -(-1)) = 5.
The slope is the ratio of these values:
slope = rise/run = -6/5
A triangular bandana has an area of 38 square inches. The height of the triangle is 9
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.
Answer:
Base=8.4 inches
Step-by-step explanation:
Area of triangular bandana is 38sq inches
Height of triangle is 9 inches
Area of ∆ =½×b×h
38=½×b×9
38×2=b×9
76/9=b
b=8.4 inches
A toy car launches off a ramp with a height of 6 feet with an upward velocity of 10 feet per second. The function h = -16t^2 +10t +6 gives the height in feet of the car after t seconds. After how many seconds does the car land on the ground?
On factoring, the value of t is 1. This shows that the car will land on the ground after 1 sec.
Solving quadratic functionsQuadratic functions are functions having a leading degree of 2.
Given the function height in feet of the car after t seconds expressed as
h = -16t^2 +10t +6
The height of the car on the ground is zero, hence:
16t^2 -10t -6 = 0
8t^2 - 5t - 3 = 0
Factorize the quadratic function
8t^2 - 5t - 3 = 0
On factoring, the value of t is 1. This shows that the car will land on the ground after 1 sec.
Leearn more on functions here: https://brainly.com/question/10439235
LAY
STOP
Solve using the Zero Product Property.
15. The height of a football after it has been kicked from the top of a hill can be modeled
by the equation h= 2(-2-4t) (2t - 5), where h is the height of the football in feet
and tiltihe time in seconds. How long is the football in the air?
A
A. t=2.5 seconds
B.
B. t=-0.5 seconds
с
C. t=1.5 seconds
Answer:
A
Step-by-step explanation:
how long is the ball in the air ?
that is the same as asking : after how many seconds will the ball hit the ground (= reach the height of 0) ?
so, that means we need to find the zero solution of h(t).
at what t is h(t) = 0 ?
when at least one of the factors is 0 :
2(-2 - 4t)(2t - 5)
we have 3 factors
2 : can never be 0.
(-2 -4t) : can only be 0 for negative t, which does not make sense in our scenario (we cannot go back in time, only forward).
(2t - 5) : is 0 when 2t = 5 or t = 2.5
so, A is the right answer.
FYI : the starting height (on the hill) is given by t = 0 :
2(-2 - 0)(0 - 5) = 2×-2×-5 = 20 ft
Elsa drove 737 miles in 11 hours.
At the same rate, how many miles would she drive in 13 hours?
Answer:
871 miles
Step-by-step explanation:
737/11= 67
67 x 13= 871