A and b are independent events. the probability that a will happen is 1/4 and the probability that b will happen is also 1/4. what is the probability they will both happen?
Answers
1/4*1/4=1/16
For independent events A and B, the probability of both happening is the product of their individual probabilities. In this case, the probability of both A and B happening is 1/16.
Explanation:In the field of probability in mathematics, when dealing with independent events like A and B in your question, the probability of both A and B happening (denoted as P(A AND B)) is calculated by multiplying the probability of A happening (P(A)) by the probability of B happening (P(B)) This is known as the multiplication rule for independent events.
So, if the probability that A will happen (P(A)) is 1/4, and the probability that B will happen (P(B)) is also 1/4, then the probability that both A and B will happen (P(A AND B)) is (1/4) * (1/4) = 1/16.
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Related Questions
put the following equation in slope intercept form: 3x - 2y = 14
Answers
Subtract the x term from both sides and then divide by -3.
A survey was conducted that asked 1011 people how many books they had read in the past year. results indicated that x overbarequals14.8 books and sequals16.6 books. construct a 90% confidence interval for the mean number of books people read. interpret the interval
Answers
First, we need to solve for the margin of error, E.
[tex]E=t_{\frac{\alpha }{2}}\cdot \frac{s}{\sqrt{n}}=1.64\cdot \frac{16.6}{\sqrt{1011}}=0.86[/tex]
The lower bound of the confidence interval is
[tex]LB=\overline{x}-E=14.8-0.86=13.94[/tex]
The upper bound of the confidence interval is
[tex]LB=\overline{x}+E=14.8+0.86=15.66[/tex]
Therefore, the 90% confidence interval is (13.94, 15.66).
We are 90% confident that the interval from 13.94 books to 15.66 books does contain the true value of the population mean number of books people read.
44 points, please answer this question ASAP!
Answers
-10 + -23 = -33
-33 + 8 + 7 + 3 = -15 cents
now divide by the number of changes (5)
-15 / 5 = -3 cents
the mean change is -3 cents
Answer:
-3
Step-by-step explanation:
mean = sum of terms/number of terms
mean = (-10-23+8+7+3)/5
mean = -15/5
mean = -3
4 students ran for class president. In the elction, Mario got 40% of the votes. Jazmyne got 35% of the votes, Arturo got 10%,and Rachel got 60 votes. How many students voted?
Answers
15% = 60 votes
1% = 60 ÷ 15 = 4 votes
100% = 4 x 100 = 400 votes
Answer: 400 students voted
What is the volume of a cylindrical bucket that is 35 cm tall and has a base with a diameter of 21 cm? Use pi= 22/7 and round your answer to the nearest tenth of a cubic centimeter.
Answers
Formula for the volume of a cylinder: [tex]V = \pi r^{2}h [/tex]
Plug in the values and solve[tex] 12,127.5 = \frac{22}{7} * 10.5^2 * 35 [/tex]
The answer is 12,127.5. Hope I helped!
Answer: 12,127.5
Step-by-step explanation:EDGE2021
At the school book sale, Michael bought 3 books for $6. Darnell bought 5 books for $10. Are these rates proportional?
Answers
3 books = $6
1 book = $6 ÷ 3 = $2
Darnell:
5 books = $10
1 book = $10 ÷ 5 = $2
Both Michael and Darnell bought their book at $2/book. The rates are proportional.
Answer Yes, the rate of proportional.
-------------↑-----------------
Michael
_____________________________________________________________
5 for $10 = 10/5 = $2/book
---------------↑-------------------
Darnell
_____________________________________________________________
Yes,they can form a proportion because they are equal
Hope this helps :)
Britany sends between 10 and 20 text messages per day. Each text message costs $0.80. Suppose Britany's cellular bill spans a period of 8 weeks. Which is a reasonable amount that she would spend on text messages on one cellular bill
Answers
The length of a rectangular field is represented by the expression 14x-3x^2+2yThe width of the field is represented by the expression 5x-7x^2+7y How much greater is the length of the field than the width?
Answers
Let A = {the whole numbers} and B = {the integers}. Find A ∩ B.
0
the integers
the whole numbers
the real numbers
Answers
Whole numbers refers to numbers starting from zero to any number, but they do not include negative numbers, fractions and decimals. Integers refers to whole numbers but they also include negative number. The intersection between the two refers to the numbers that are common to the the two of them. Thus, in this case the common numbers are the whole numbers, because whole numbers exist in the two groups.
The answer is WHOLE NUMBERS.
The graph of which function has a minimum located at (4, –3)?
f(x) = x2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = x2 – 4x + 5
f(x) = 2x2 – 16x + 35
Answers
The graph of this function has minimum if a > 0.
Minimum is in point (h; k) where:
[tex]h=\dfrac{-b}{2a};\ k=f(h)[/tex]
[tex]minimum(4;-3)\to h=4;\ k=-3[/tex]
[tex]f(x)=x^2+4x-11;\ a=1 > 0;\ b = 4\\\\h=\dfrac{-4}{2\cdot1}=-2\neq4[/tex]
[tex]f(x)=-2x2+16x-35;\ a=-2 < 0[/tex]
[tex]f(x)=x^2-4x+5;\ a=1 > 0;\ b=-4\\\\h=\dfrac{-(-4)}{2\cdot1}=\dfrac{4}{2}=2\neq4[/tex]
[tex]f(x)=2x^2-16x+35;\ a=2 > 0;\ b=-16\\\\h=\dfrac{-(-16)}{2\cdot2}=\dfrac{16}{4}=4\\\\k=f(4)=2\cdot4^2-16\cdot4+35=2\cdot16-64+35=32-64+35=3\neq-3[/tex]
Answer: Any graph of this functions hasn't a minimum located at (4; -3).
If the coordinates of minimum are (4; 3),
then your answer is f(x) = 2x² - 16x + 35
Answer:
f(x) = 1/2x^2 – 4x + 5 (the third option)
Step-by-step explanation:
On ed :)
Bernice estimated that 69% of 242 is 168. Is her estimate reasonable?
Answers
Since she estimated 69%, you could do either of these options. You could...
A. Divide 242 (or .5) to show how much half off would be, then compare her estimate with half of 242 (121). OR...
B. Simply divide 242 by 69% (.69) and compaor her estimate to the exact amount (166.98).
I hope this helps!
Answer:
D Yes, because her calculation should be 70% of 240.
Step-by-step explanation:
D
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
T.A.=
Answers
Answer: Total area of the given prism is (104 + 16√13) Square inches.
Step-by-step explanation:
By the given diagram,
In the right triangular prism,
The sides of the base ( right triangle ) are 4 inches and 6 inches,
We have to finds : T.A. ( the total area of the prism )
Thus, the total base area of the prism = 2 × ( Area of triangle having base 4 inches and height 6 inches )
= 2× ( 1/2 × 4 × 6 )
= 4 × 6
= 24 square inches,
Let the hypotenuse of the triangles having sides 4 and 6 is x inches, ( shown in the diagram )
Thus, by the given diagram,
[tex]x^2 =4^2+6^2[/tex]
[tex]x^2 = 16 + 36[/tex]
[tex]x^2 = 52[/tex]
[tex]x=2\sqrt{13}[/tex]
Now, the total lateral area of the prism,
= 8×2√13 + 8×4 + 8×6
= 16√13 + 32 + 48
= (16√13 + 80) square inches,
Since, the total area of the given prism (T.A.) = Total base area of the prism(B.A.) + Total lateral area ( L.A.)
= 24 + 16√13 + 80
= (104 + 16√13) Square inches.
The width of a rectangle is 5 inches less than twice the length. The area of the rectangle is 700 square inches. What is the length of the rectangle?
Answers
(2x-5) inches
The area will be given by:
A=length×width
A=x(2x-5)
but
A=700 in²
thus
700=x(2x-5)
700=2x²-5x
this can be written in quadratic form as:
2x²-5x-700=0
solving the quadratic we get:
x=20 or x=-35/2
since the length cannot be negative then:
x=20 in
thus the width will be:
2*20-5
=40-5=35 inches
A system of equations consists of two lines. One line passes through (-1, 3) and (0, 1). The other line passes through (1, 4) and (0, 2). Determine of the system has no solution, one solution, or an infinite number of solutions.
Answers
y = mx + b
Where,
m = (y2-y1) / (x2-x1)
For (-1, 3) and (0, 1):
We look for the value of m:
m = (1-3) / (0 - (- 1))
m = (- 2) / (0 + 1)
m = -2
We look for the value of b:
1 = m (0) + b
b = 1
The line is:
y = -2x + 1
For (1, 4) and (0, 2):
We look for the value of m:
m = (2-4) / (0-1)
m = (- 2) / (- 1)
m = 2
We look for the value of b:
2 = m (0) + b
b = 2
The line is:
y = 2x + 2
The system of equations is:
y = -2x + 1
y = 2x + 2
Answer:
the system has one solution
If f(x)=2x+1 and g(x)=x^2-7, find (f+g)(x)
A. x^2=2x-6
B. 2x^2-15
C. x^2+2x+8
D. 2x^3-6
Answers
(f+g)(x) = 2x + 1 + x^2 - 7
(f+g)(x) = x^2 + 2x - 6
answer
x^2 + 2x - 6
Answer: The correct option is (A) [tex]x^2+2x-6.[/tex]
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=2x+1,\\\\g(x)=x^2-7.[/tex]
We are to find the value of [tex](f+g)(x).[/tex]
We know that
for any two functions p(x) and q(x), we have
[tex](p+q)(x)=p(x)+q(x).[/tex]
Therefore, we get
[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=(2x+1)+(x^2-7)\\\\=2x+1+x^2-7\\\\=x^2+2x-6.[/tex]
Thus, option (A) is CORRECT.
Please help!!!!!!!!!!!!!!
Answers
The graph models the daily high temperature, H(t), in Santiago, Chile, t days after the hottest day of the year. What does the point (0,29) represent?
Answers
The point (0,29) on the graph models the daily high temperature in Santiago, Chile on the hottest day of the year, where '0' represents that hottest day and '29' is the high temperature on that day.
Explanation:The point (0,29) on the graph represents the weather condition in Santiago, Chile on the hottest day of the year. Here, '0' in the pair represents the day which is essentially the hottest day and '29' is the high temperature on that day. It depicts that on this specific day, the highest temperature was 29. The graph is an example of a time series graph, where the changing patterns or trends are displayed over a certain period of time - in this case, the temperature changes across the days following the hottest day of the year.
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please help with math? will give branliest!!
2. A wildlife refuge in South America has howler monkeys and spider monkeys. A biologist working there randomly selected eight adults of each type of monkey, weighed them, and recorded their weights in pounds.
howler monkey: {15, 16, 17, 17, 17, 17, 18, 19}
spider monkey: {12, 13, 13, 14, 14, 14, 16, 16}
(a) Calculate the median each type of monkey.
(b) Calculate the mean for each type of monkey.
(c) Calculate the MAD for each type of monkey.
(d) Calculate the means-to-MAD ratio for the two types of monkeys.
(e) What inference can be made about the weight of both types of monkeys? Explain.
Answer:
Answers
spider 14 14 1
The median of howler monkey is, 17
And, Median of spider monkey is, 14
The mean for the howler monkeys is 17 and the MAD is 0.8571.
The mean for the spider monkeys is 14 and the MAD is 1.1429.
The means-to-MAD ratio is 2.6249.
This means that on average, the number of mean absolute deviations that separate the means is 2.6. This means they are different.
Find the median of data set as;
For howler monkey;
There are 8 number of howler monkey.
Hence, Median is,
= (8/2 + 1)
= 5 th term
= 17
For spider monkey;
There are 8 number of spider monkey.
Hence, Median is,
= (8/2 + 1)
= 5 th term
= 14
To find the mean of the howler monkeys, add all of the data values and divide by 7:
= (15+16+17+17+17+17+18+19)/7
= 119/7
= 17
To find the MAD, subtract each data point from the mean; take the absolute deviation; then average these together:
= (|15-17|+|16-17|+|17-17|+|17-17|+|17-17|+|17-17|+|18-17|+|19-17|)/7
= (2+1+0+0+0+0+1+2)/7
= 6/7
= 0.8571
And, Repeating these processes for the spider monkeys:
Mean:
(12+13+13+14+14+14+16+16)/7
= 98/7
= 14
And, MAD:
= (|12-14|+|13-14|+|13-14|+|14-14|+|14-14|+|14-14|+|16-14|+|16-14|)/7
=(2+1+1+0+0+0+2+2)/7
= 8/7
= 1.1429
To find the means-to-MAD ratio, find the difference in the means and divide it by the larger MAD:
17-14=3;
Hence, We get;
3/1.1429 = 2.6249
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Hal’s sporting Goods had a 1 day sale. The original price of a mountain bike we 325. In a sale it was 276.25. What is the percent decrease for this sale?
Answers
Percentage decrease = 48.75/325 x 100 = 15%
Answer: 15%
Solve by factoring AKA zero product property method. If the equation has no real solutions, write no real solutions.
3. x^2 − 5 + 4 = 0
4. x^2 + 7 + 12 = 0
Answers
[tex]1)\\ x^2-5x+4=0\\ x^2-4x-x+4=0\\ x(x-4)-(x-4)=0\\ (x-4)(x-1)=0\\ Sol=\{1;4\}\\\\ 2)\\ x^2+7x+12=0\\ x^2+3x+4x+12=0\\ x(x+3)+4(x+3)=0\\ (x+3)(x+4)=0\\ Sol=\{-4;-3\} [/tex]
( Please help me, the year is ending and I'm almost at a failing grade): ) An athlete is running along a circular path that has a diameter of 250 yards. The arc traveled by the athlete is 120 degrees. Using 3.14 for (symbol that looks like two Ts that are connected), how many yards did the athlete run? Round the answer to the nearest yard.
Answers
S = R * theta
Where,
R: radius of the circle
Theta: central angle
Substituting values we have:
S = (250/2) * (120) * (3.14 / 180)
S = 261.6666667 yards
Round to the nearest yard:
S = 262 yards
Answer:
the athlete ran:
S = 262 yards
To find the distance an athlete ran on a circular path with a diameter of 250 yards and an arc length of 120 degrees, calculate the arc length using the radius and angle in radians. The athlete ran approximately 262 yards.
To find the distance the athlete ran around a circular path with a given arc length of 120 degrees and a diameter of 250 yards, first, determine the radius of the circle:
Radius (r) = Diameter / 2 = 250 yards / 2 = 125 yards
Convert 120 degrees to radians: 120 degrees × π / 180 = 2π / 3 radians
Calculate the arc length using the formula: Arc Length = Radius × Angle in radians = 125 yards × 2π / 3 = 250π / 3 ≈ 261.8 yards
Therefore, the athlete ran approximately 262 yards.
Shelly is installing a fence around the edge of her property. Her property measures 41 meters by 35 meters. What is the perimeter of Shelly's property?
A.142 m
B.152 m
C.1,420 m
D.1,435 m
Answers
The perimeter of Shelly's property is 152 meter.
Option (B) is correct.
It is required to find the perimeter.
What is rectangle?A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square. A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that:
The Shelly's property is in the shape of rectangle.
Length of property=41 meter
Breadth of property=35 meter
Perimeter of rectangle=2(Length+ Breadth)
Perimeter of rectangle=2(41+ 35)
Perimeter of rectangle=2*76
Perimeter of rectangle=152 meter
Therefore, the perimeter of Shelly's property is 152 meter.
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Calculus question... I need help understanding thanks.
Calculate Гx^3dx
Answers
[tex]\displaystyle\int x^3\,\mathrm dx=\dfrac{x^4}4+C[/tex]
which holds since
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{x^4}4+C\right]=\dfrac{4x^3}4+0=x^3[/tex]
Line Q is represented by the following equation: 2x + y = 11
Which equation completes the system that is satisfied by the solution (3, 5)? (4 points)
x + 2y = 15
x + y = 15
x + y = 8
x − y = 2
Answers
The coordinates are (3,5) where 3 is the x coordinate and 5 is the y coordinate.
If you substitute (3,5) into x + y = 8
you'll get get
3 + 5 = 8 which is true
Answer:
the Answer is x + y = 8 because 3 + 5= 8
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!! What is the simplified form of the expression (3x^7/2)^6 (x^2)^6
A. x^33
B. 3x^29
C. 729x^29
D 729x^33
Answers
Explanation:
Given expression:
[tex](3x^{7/2})^6 (x^2)^6 \\ (3^6x^{42/2})(x^{12}) \\ 729x^{21+12} \\ 729x^{33} \\[/tex]
Which is option (D)
What Is the Measure of Y
41
49
51
61
Answers
_____________________________________________________
→ " y = 41 " .
_____________________________________________________
Explanation:
______________________________________________________
From the "image attached", note that:
"139" and "y" ; together; form a "straight line" ;
→ that is: "139" and "y" are supplementary ;
and by definition; "supplementary angles" add up to " 180 degrees" ;
______________________________________________________
→ y + 139 = 180 ; Solve for "y" ;
Subtract " 139 " from each side of the equation;
to isolate "y" on one side of the equation; & to solve for "y" ;
→ y + 139 − 139 = 180 − 139 ;
to get:
→ y = 41 degrees:
_____________________________________________________
The answer is: " 41 " .
_____________________________________________________
→ " y = 41 " .
_____________________________________________________
Answer:
ITS A.) 41
Step-by-step explanation:
Write the equation of the line going through the point (4,6) that is perpendicular to the lie 3x+6y=12
Answers
6y = - 3x + 12
y = - 1/2x + 2
Since your slope is - 1/2, we take the opposite reciprocal to find the perpendicular slope. Your perpendicular slope is 2.
y = 2x + b
Plug in the point to solve for b and get your final line.
6 = 2(4) + b
6 = 8 + b
6 - 8 = b
- 2 = b
y = 2x - 2 is your perpendicular line
What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 120? A. 720 B. 900 C. 1080 D. 180 E. 360 F. 540
Answers
Sum of the measures of the interior angles of a regular polygon is 180°, using properties of interior and exterior angle and regular polygon.
What is a regular polygon?
A regular polygon is a n-sided polygon in which all sides are of same length and are symmetrically placed about the center.
Properties of interior and exterior angles:
1. The sum of adjacent interior and exterior angle for a polygon is 180°.
2. The sum of exterior angles of a polygon is always equal to 360°.
Here,
Let's consider number of exterior angle=x
given that: each exterior angle measures 120°.
Now, using 2nd property,
x*120 = 180
x = 3
So, total number of exterior angles are = 3
Using 1st property,
each interior angle measures = 180 - 120
= 60°
And total number of interior angle = total number of exterior angle
= 3
So, the sum of interior angles = 3*60
= 180° .
Hence, we reached our answer.
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Write the equation of a line that is parallel to y=-0.75x and that passes through the point (8,0)
Please help
Answers
Answer:
The equation of the line that is parallel to the given is equal to the expressions below:
[tex]\displaystyle \boxed{ y = -0.75(x - 8) \text{ or } y = -0.75x + 6 }[/tex]
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slopeb - y-interceptPoint-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinatey₁ - y coordinatem - slopeStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyley = - 0.75x \\\text{Point } (8, 0) \\[/tex]
Step 2: Find Equation
Recall that a parallel line has the same slope as the one that is given. Therefore, we can define the slope of our parallel line to be m = -0.75:
[Point-Slope Form] Substitute in variables:[tex]\displaystyle y - 0 = -0.75(x - 8)[/tex]Simplify:
[tex]\displaystyle \boxed{ y = -0.75(x - 8) }[/tex]
We can rewrite this form into slope-intercept form as well by expanding:
[tex]\displaystyle y = -0.75(x - 8) \rightarrow \boxed{ y = -0.75x + 6 }[/tex]
∴ we have found the equation of a line that is parallel to the given information.
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Topic: Algebra I
Answer:
what the guy above said
Step-by-step explanation:
What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.
To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.
Question 1 options:
The formula for the surface area of a sphere is 4 x pi x radius^2
The formula for the volume of a sphere is 4/3 x pi x radius^3.
Answers
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²
so
the volume of a sphere=(r/3)*surface area of sphere
therefore
if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere
if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere
if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere
examples
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area
2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area
3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area