Answer:
[tex]P(X=3)\approx27\%[/tex]
Step-by-step explanation:
Use the binomial distribution
[tex]\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\\\\P(X=3)=\binom{4}{3}(0.52)^3(1-0.52)^{4-3}\\\\P(X=3)=\frac{4!}{3!(4-3)!}(0.52)^3(0.48)^1\\ \\P(X=3)=0.26996736\\\\P(X=3)\approx0.27\\\\P(X=3)\approx27\%[/tex]
Therefore, the probability that exactly 3 students out of 4 randomly chosen students have brown hair is about 27%
Four circles, each with a radius of 2 inches, are removed from a square.
Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square?
(16 – 4π) in.2
(16 – π) in.2
(64 – 16π) in.2
(64 – 4π) in.2
Given:
Given that the radius of the circle is 2 inches.
We need to determine the area of the remaining square.
Area of a square:
Given that each circle has a radius of 2 inches.
Then, the diameter of each circle is 4 inches.
Hence, the side length of the square is 2 × 4 = 8 inches.
The area of the square is given by
[tex]A=s^2[/tex]
[tex]A=8^2[/tex]
[tex]A=64[/tex] [tex]in^2[/tex]
Thus, the area of the square is 64 square inches.
Area of the four circles:
The area of one circle is given by
[tex]A=\pi r^2[/tex]
Substituting r = 2, we have;
[tex]A=4\pi[/tex]
Thus, the area of one circle is 4π in²
The area of 4 circles is 4 × 4π =16π in²
Hence, the area of the 4 circles is 16π in²
Area of the remaining square:
The area of the remaining square is given by
Area = Area of the square - Area of four circles.
Substituting the values, we get;
[tex]Area=64-16\pi[/tex]
Thus, the area of the remaining square is (64 - 16π) in²
Hence, Option c is the correct answer.
Answer:
C. (64 – 16π) in.2
Step-by-step explanation:
Find the product of (x + 3)(x - 3).
x^2 - 6x + 9
x^2 + 6x + 9
x^2 + 9
x^2-9
Step-by-step explanation:
So the question is easy ....the thing that you need to do is just to multiply the expression and organize the like terms....okay so lets solvee..
[tex](x + 3)(x - 3)[/tex]
Solution,
[tex] = x(x - 3) + 3(x - 3)[/tex]
[tex] = {x}^{2} - 3x + 3x - 9[/tex]
[tex] = {x}^{2} - 9[/tex]
Find the measure of each angle in the problem. MG contains point T.
A. 100 and 80
B. 95 and 85
C. 50 and 40
D. 60 and 120
Answer:
A
Step-by-step explanation:
the angles are adjacent angles on a straight line and sum to 180°, so
5x + 4x = 180
9x = 180 ( divide both sides by 9 )
x = 20
then
∠ MTQ = 5x = 5 × 20 = 100°
∠ GTQ = 4x = 4 × 20 = 80°
If you shift the exponential parent function, f(x) = 2^x , right 2 units, what is the equation of the new function?
Answer:
[tex]g(x)=2^{x-2}[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: [tex]f(x)=2^x[/tex]
Translated 2 units right: [tex]g(x)=f(x-2)=2^{x-2}[/tex]
We know the rule for shifting right(x is changed)
f(x) —» f(x-a)So
here
For a =2
f(x-2)[tex]\sf 2^{x-2}[/tex]Need help in math ASAP
pls help this is urgent
aiden’s teacher tells him that the values in the table represent a proportional relationship.
x y
1 5
2. 10
3. 15
Based on the table, Alden claims that in order for a coordinate point to be in the proportional relationship, both the
x-coordinate and y-coordinate must be integers.
Determine a coordinate point that proves that Alden's claim is false.
Enter the x-coordinate in the first response box.
Enter the y-coordinate in the second response box.
Answer:
Step-by-step explanation:
im passing this concept trust me the answer is 12
Please help! I asked this question the other day and nobody even looked at it. I need help!!!!
A forest fire has been burning for several days. The burned area, in acres, is given
the equation y = (4, 800) • 2d, where d is the number of days since the area of the
fire was first measured.
Complete the following table:
Answer:
you gotta show a picture of the table in order for us to know what's missing from it
When d = -1, the value of y is 300 acres means that the area burned in the fire was 300 acres. When d = -3, the value of y is 1.17 acres means that the area burned in the fire was only 1.17 acres three days
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
we can use the given equation y = (4,800)2^d and substitute the values of d in the table to get the complete table.
Now the equation y = (4,800)2d for d when y = 4,800 and then subtract 7 from that value.
(4,800)2d = 4,800
2d = 1
d = 0.5
The fire had burned for 12 hours, before it measured 4,800 acres.
To determine the area the fire had burned a7 days before this measurement, we will then substitute d = -6.5 into the equation:
y = (4,800)2(-6.5) ≈ 0.00025 acres
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helpppppppppppppppp 88 points
Answer:
20 in²
Step-by-step explanation:
Divide the shape into two rectangles (see attached image)
Area of a rectangle = width × length
Area of rectangle 1
⇒ area = 2 × 3
= 6 in²
Area of rectangle 2
⇒ area = (5 - 3) × 7
= 2 × 7
= 14 in²
Total area
Total area = area of rectangle 1 + area of rectangle 2
= 6 + 14
= 20 in²
Area of vertical rectangle:-
LB5(2)10in²Area of horizontal rectangle
LB5(5-3)5(2)10in²Total:-
10+1020in²You and your sister have been saving and decide to buy a Playstation 5 together. You need $500 to
buy the Playstation. Together you have $850 saved up. Since you have more money, you contribute
50% of your savings and your sister contributes 75% of hers toward the $500 cost. How much do each
of you have saved individually?
a. Write a system of equations in standard form to model this situation
b. Solve this system of equations using eliminations
According to the information given, we have that:
a) The system of equations is given by: x + y = 850, 0.5x + 0.75y = 500.
b) You has saved $550 and your sister has saved $300.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: The amount you have saved up.Variable y: The amount your sister has saved up.Item a:
Together you have $850 saved up, hence:
x + y = 850.
You contribute 50% of your savings and your sister contributes 75% of hers toward the $500 cost, hence:
0.5x + 0.75y = 500.
Item b:
From the first equation, we have that:
x = 850 - y
Replacing on the second:
0.5(850 - y) + 0.75y = 500
0.25y = 75
y = 75/0.25
y = 300
x = 850 - y = 550.
You has saved $550 and your sister has saved $300.
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Solve the equation. 4y = 12
Answer:
y = 3Step-by-step explanation:
Given equation:
4y = 12To solve the equation, the L.H.S must be equivalent to the R.H.S. To prove that L.H.S is equivalent to R.H.S, we have to know the value of "y".
The value of the y variable can be found by isolating the variable from its coefficient. In this equation, the y-variable can be isolated by dividing both sides by four. This cancels the coefficient, isolating the y-variable on one side of the equation.
⇒ 4y = 12⇒ 4y/4 = 12/4 (Dividing both sides by 4)Once the y-variable has been isolated, we can simplify the other side of the variable. The expression/variable/number obtained, on the other side of the equation, is the value of the y-variable.
⇒ y = 12/4 (Isolating the y-variable)⇒ y = 3 (Simplifying the R.H.S)Therefore, the value of y is 3.
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Hey there!
4y = 12
DIVIDE 4 to BOTH SIDES
4y/4 = 12/4
SIMPLIFY IT!
y = 12/4
y = 3
Therefore, the answer should be: y = 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Please help me on this!
Answer:
B. f(x) = 176x + 10,580
Step-by-step explanation:
The y-intercept is about 10,580.
The slope is about 176
You can get the slope by subtracting 10925-10600 and then dividing the answer by 2
Cost of a CD: $23.50
Markup: 63%
Discount: 50%
Which equation is true? 9x2 – 25 = (3x – 5)(3x – 5) 9x2 – 25 = (3x – 5)(3x 5) 9x2 – 25 = –(3x 5)(3x 5) 9x2 – 25 = –(3x 5)(3x – 5).
Answer:
9x² - 25 = (3x - 5)(3x + 5)
Step-by-step explanation:
(a + b)(a - b) = a² - ab + ab - b² = a² - b²
a² - b² = (a + b)(a - b)
Find the quotient
5,103 divided by 54
Answer:
94.5 is your answer bc u have to divide to get your answer for your thing
I need help with number 8….
Pls help
The equation properties are:
The distributive propertyThe associative property.The associative property.How to determine the properties?
The equations are given as:
3 * (6 + 2) = 3 * 6 + 3 * 25 * (7 * 8) = (7 * 5) * 85 * 3 * 7 = 7 * 3 * 5The distributive property of an equation states that:
a * (b + c) = ab + ac
This means that 3 * (6 + 2) = 3 * 6 + 3 * 2 is represented by the distributive property.
The associative property of an equation states that:
a * (b * c) = (a * b) * c
This means that 5 * (7 * 8) = (7 * 5) * 8 and 5 * 3 * 7 = 7 * 3 * 5 are represented by the associative property.
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The diagram shows a solid cylinder made of metal.
The metal has a mass of 800 kg.
Calculate the density of the cylinder in kg/m³.
Round to 1 dp.
4 m
12 m
Answer:
1.3kg/m^3
Step-by-step explanation:
Volume of cylinder=πr^2h
V=πx4^2x12
V=192π
192π=603.186m^3
Density=Mass/volume
D=800/603.186
D=1.3
PLEASE SOMEONE HURRY I NEED THE ANSWER PLS
7. After washing your hands there are 300 bacteria on your right hand. The amount of bacteria on each of
your hands is doubling each hour. When will the amount of bacteria on your right hand exceed 2000?
A) 2 hours
B) 2½ hours
C) 3 hours
D) 3½ hours
Answer: maybe c?
Step-by-step explanation:
Uh, 300+300 = 600
600+600= 1200
1200+ 1200= 2400
Help please..........................................................
Answer:
A) YXWZ
Step-by-step explanation:
W) 57.4*10^4 = 574 000
X) 5.11*10^5 = 511 000
Y) 0.17*10^6 = 170 000
Z) 7.3*10^5 = 730 000
Y, X, W, Z: A
can someone help me with this question? Thank you!
Answer:
See the attachment!
Bobby has a party while his parents are away for the weekend. Bobby estimated that if his 9 friends hep him to clean the house, they will finish in time if they start 8 hours before his parents return. But after only two hours of cleaning, Bobby's parents call and say they are just two hours from home. How many more friends does Bobby need to call to help finish cleaning in time.
Bobby will need additional 20 friends to help finish cleaning in time.
Rate at which Bobby and his 9 friends are workingThe rate at which Bobby and his 9 friends are cleaning the house is determined as follows;
10 person ------> 8 hours
1 person -------->?
= 10 x 8 = 80 hours/person
When the parents are 2 hours from the house, Bobby will more friends working at the same rate to complete it in 2 hours time.
During this period Bobby and his friends have worked for 2 hours remaining 6 hours.
New rate;
10 person ------> 6 hours
1 person -------->?
1 person = 10 x 6 hrs = 60 hours per person
Total persons that will do the same work in 2 hours2 = 60/x
x = 60/2
x = 30 persons
Thus, Bobby will need additional 20 friends to help finish cleaning in time.
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Ruby owns a small business selling bagels. She knows that in the last week 4
customers paid cash, 10 customers used a debit card, and 74 customers used a credit
а
card.
If next week, she is expecting 1600 customers, about how many would you expect to
pay with cash? Round your answer to the nearest whole number.
Answer:
73 people
Step-by-step explanation:
4/10/74=88
1600/88=18.18
18.18 x 4= 73
18.18 x 10= 182
18.18 x 74= 1345
Answer: 73
Step-by-step explanation:
The mean shoe size of the students in a math class is 7. 5. Most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9. What is the standard deviation of the shoe size data for the math class? 1. 5 2. 7 3. 0 3. 8.
Answer: 1.5
Step-by-step explanation:Let the standard deviation of the shoe size be represented by ' ' and the mean shoe size be represented by ' = 7.5'. Also, the sizes of the shoe be represented by ' '. So, . Hence, the standard deviation of the shoe size data for the math class is 1.5.
30 points see picture below
Answer:
6912cm³
Step-by-step explanation:
volume is equal to length multiplied by width multiplied by height so if we multiply the three it will give us a volume of 6912cm³
Answer:
a) 6912 cm³
b) 192 cm³
Explanation:
Volume of rectangular prism = Length × Width × Height
Part A
Here Volume: 32 × 72 × 3 = 6912 cm³
∴ The volume of the chocolate slab is 6912 cm³.
Part B
total volume ÷ total students = 6912 ÷ 36 = 192 cm²
Each student receives 192 cm³ of chocolate.
Find the value of x.
Answer:
x= 20
Step-by-step explanation:
The total amount of degrees in a triangle is 180. The equation we can pull from this is x+x+30+110= 180. Now we can simplify and combine like terms. x+x= 2x. 30+110 is 140. Now move the constant, 140 to the right. 180-140 is 40. Lastly, divide x and 40 by 2 to get the final answer of 20.
If a job has salary of $470 a week, how much would it pay for a year
Answer:
$22560
step 1
$270 × 4month
=$1880 for a month
step 2
$1880×12months
= $22560
HEEEEELPPPPP Please help, last question will mark brainliest
Answer:
B
Step-by-step explanation:
y+1>2(x-2)
distribute the right side
y+1>2x-4
minus 1 on both sides
y>2x-5
slope is 2/1
y intercept is -5
> means dotted line and shaded in to the left
:)
a toll box has 10 screwdrivers and 6 wrenches Bella puts 8 more wrenches in the toolbox how many more wrenches are in the toolbox
Answer: There are 4 more wrenches in the toolbox than the screwdrivers.
Step-by-step explanation: Add the 6 wrenches Sid put in the toolbox with the 8 wrenches Bella added to get 14 wrenches in total. Then, subtract the 10 screwdrivers from the 14 wrenches to get 4 wrenches.
2 + 5^2 / (30 - 5) + 3
2 + 5^2 / (30 - 5) + 3 = 6
---
Hope this helps! :)
Q5 A and B
Unsure of how to go about this.
Thanks :)
Answer:
Step-by-step explanation:
the given angle measurments are x, (x + 18), and 2(x - 5)
knowing that the angles add up to 180, you can write the equation:
x + (x + 18) + 2(x - 5) = 180
Then you solve the equation
so our equation is:
x + x + 18 + 2(x - 5) = 180
*combine like terms
2x + 18 + 2(x - 5)
*distribute the 2
2x + 18 + 2x - 10
* combine like terms
4x + 8 = 180
* subtract 8 from both sides
4x = 172
* divide both sides by 4
x = 43
so knowing that x is 43, we can plug that in to the original given angle measurements:
the top angle which was x + 18 becomes 43 + 18, or 61
the bottom right angle was 2(x - 5), now it's 2(43 - 5) or 2(38) which is 76
and the other one was x so it's 43 degrees
We can check our work by adding them together.
61 + 76 + 43 = 180
they equal 180 as the angles of a triangle should.
Note: most of these numbers should have degree symbols, but I don't know how to type that.
