The probability that a student takes art, given that the student takes music is 10.8%
In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.
For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."
Two events, A and B, are independent if
P(A ∣ B)=P(A)
P(A).P(B) = P(A ∩ B)
In the given question there are independent events.
Given:-
P(A) = Student takes both art and music = 0.9
P(B) = Student takes music = 0.12
P(A ∩ B) = student takes art, given that the student takes music
Thus by using the formula we get,
P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%
The probability that a student takes art, given that the student takes music is 10.8%
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From the diagram below, if AC =40, CD=10, and DB=8, then what would be the length of AB?
The length of AB would be 38 units
How to determine the length AB?The attached image represents the missing piece in the question
Considering the triangle BCD;
Calculate the length BC using the following Pythagoras theorem
BC^2 = CD^2 + BD^2
This gives
BC^2 = 10^2 + 8^2
Evaluate
BC^2 = 164
Considering the triangle CBA;
Calculate the length AB using the following Pythagoras theorem
AB^2 = AC^2 - BC^2
This gives
AB^2 = 40^2 - 164
Evaluate
AB^2 = 1436
Take the square root
AB = 38 (approximated)
Hence, the length of AB would be 38 units
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What is the volume of the sphere shown below with a radius of 9? OA. 108 cu. units B. 972* cu units OC. 2916 cu units D. 1458, cu units
The volume of the sphere shown below with a radius of 9 is 3052.08 cubic units
Volume of a sphereThe formula for calculating the volume of a sphere is expressed as;
V = 4/3πr³
where
r is the radius of the sphere
Substitute
V = 4/3π(9)³
V = 4/3(3.14)*729
V = 3052.08 cubic units
Hence the volume of the sphere shown below with a radius of 9 is 3052.08 cubic units
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A trader sold 100 boxes of a $8.00 per box, 800 boxes at $6.00 per box and 600 boxes at $4.00 per box .find the average selling price per box
The average selling price per box is $5.33
What is the average selling price?The core value of a set of data is expressed as the average of a list of variables. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. The average of a specific set of numerical data is also known as the mean in statistics.
Average = Sum of Values/Number of Values
The total selling price of all boxes=(8*100)+(800*6)+(600*4)
=$8000
Total number of boxes=100+800+600
=1500
Average selling price per box=8000/1500=$5.33
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HELPPPP PLEASEEE ASAPP!! The population of a small farming community is declining at a rate of
7% per year. The decline can be expressed by the exponential
equation P=C (1-0.07), where P is the population after t years and
C is the current population. If the population was 8500 in 2004, when
will the population be less than 6000?
Answer:
365/8500*7=0.30058823529411-0.07/100*7=0.9951
A Venn diagram is shown below: What are the elements of (A n B) ‘ ?
The elements of (A n B)' are ( 3, 4 , 5 ,6). Option A
How to determine the setThe elements of this set (A n B) explains the common elements of both sets without repetition
Set A = 3, 4
Set B = 5, 6
A n B = 1, 2
(A n B)' = Is the elements both A and B in common but is not found in the universal set
(A n B)' = ( 3, 4 , 5 ,6)
Thus, the elements of (A n B)' are ( 3, 4 , 5 ,6). Option A
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You were painting a room in your house. Unfortunately, you lost the lid to the 5 gallon bucket of paint, but you only used half of the paint. You want to save the paint, so you plan on transferring it to a new container. The new container is shaped like a rectangular prism. If there are originally 1,155 cubic inches of paint in the 5 gallon bucket, is your container big enough to fit the paint that is left over? Remember that half the paint is left in the bucket.
Answer:
bro wuts da answer am so lost yo
Answer: It's my understanding that the answer would be the last one - No, the container is not large enough.....new container is 960 cubic inches. I saw this answer marked on another website but not how to find the answer.
Step-by-step explanation:
Last years freshman class at big state university totaled 5,305 students of those 1258 received a merit scholarship to help offset tuition costs their freshman year.the amount received was n(3456, 478) if the full cost was 4250 what percentage of students receive a merit scholarship did not receive enough to cover full tuition
Using the normal distribution, it is found that 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for the amounts are given as follows:
[tex]\mu = 3456, \sigma = 478[/tex]
The proportion is the p-value of Z when X = 4250, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4250 - 3456}{478}[/tex]
Z = 1.66
Z = 1.66 has a p-value of 0.9515.
Hence 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.
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A population of a particular yeast cell develops with a constant relative growth rate of 0.4425 per hour. The initial population consists of 3.1 million cells. Find the population size (in millions of cells) after 3 hours. (Round your answer to one decimal place.)
The exponential function is often used to model the growth or decay of a population
The population size of the yeast cell after 3 hours is 6.24 million
The given parameters are:
a = 3.1M --- initial number of cells
r = 0.4425 per hour --- rate
The nth term of an exponential function is:
f(n) = a(1+r)^n-1
After 3 hours; n = 3
So, we have:
f(3) = a(1+r)^3-1
Substitute values for a and r
f(3) = 3.1 (1+0.4425)^3-1
f(3) = 3.1 ( 1.4425)^2
f(3) = 6.24
Hence, the population size of the yeast cell after 3 hours is 6.24 million.
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I set off on a 15 miles cycle ride at a speed of 10mile per hour. how long does the ride take me
The ride takes 1.5 hours for a speed of 10 miles per hour.
What is speed?The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.
A body's speed can be defined as how quickly it is going. The equation for a given body's speed can be written as,
Speed=Distance/Time
According to the question,
Speed=10 miles per hour
Distance=15 miles
Time=[tex]\frac{15}{10}[/tex]=1.5 hours
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Graph a system of equations to solve Log(-5.6x+1.3)=-1-x
From least to greatest the solutions are:
By seeing where the curves intercept, we conclude that the solutions are:
(0.22, -1.22) and (-2.12, 1.12)
How to solve the system of equations?
Here we just need to graph the equations:
y = log(-5.6*x + 1.3)
y = -1 - x
And see in which points the curves intercept.
The graph can be seen below:
There we can see that the intersections (and solutions) are the points:
(0.22, -1.22) and (-2.12, 1.12)
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2x − 4y = 40,
−x + 2y = −20
Find x and y intercept
Answer:
The x and y intercept are (20,0)
Step-by-step explanation:
2x-4y=40—eqn1
-x+2y=-20—eqn2
Make x the subject of eqn2
-x=-20-2y
x=20+2y
plug this into eqn 1
2(20+2y)+4y=40
40+4y+4y=40
8y=40-40
y=0
plug y=0 into eqn2
-x+2(0)=-20
-x=-20
x=20
Ted has 45 apples he give his one friend 20 apples how many apples do ted have left
A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.
Which system of linear equations represents the beverage sales on Saturday?
Answer:
There are two equations and two variables, so this is a system of linear equations.
c + h = 360
4c = h
Step-by-step explanation:
Answer:
The linear equations would be c = 4h and 1.5c + 2h = 360.
Step-by-step explanation:
First we have to create a table for our data.
c = total number of cold beverages sold.
h = total number of hot beverages sold.
The total cost of both beverages sold -
1.5c + 2h = 360
The amount of cold beverages -
c = 4h
Now we just need to substitute the second equation to the first one.
1.5 * (4h) + 2h = 360
= 6h + 2h = 360
= 8h = 360
= h = 45
Now we need to find the value of c.
c = 4* 45 = 180
Therefore 180 cold beverages were sold and 45 hot beverages were sold.
But the linear equations would be c = 4h and 1.5c + 2h = 360.
Hope this helped! :D
Student Name:
Lesson Number: 22
4th Proportion
Directions:
Complete the following constructions. Leave all construction arcs on your paper.
a
Math Assignment
Level: 1007
b
1 Given a, b, and c, the length of three segments. Find the fourth proportional.
Find the fourth proprtional to r, s, and t.
The fourth proportionals are bc/a and st/r
How to determine the fourth proportional?Segments a, b and c
Let the fourth segment be x.
So, we have the following equivalent ratio
a : b = c : x
Express as fraction
a/b = c/x
Make x the subject
x = bc/a
Segments r, s and t
Let the fourth segment be x.
So, we have the following equivalent ratio
r : s = t : x
Express as fraction
r/s = t/x
Make x the subject
x = st/r
Hence, the fourth proportionals are bc/a and st/r
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A country specializes in agricultural production—in particular, pineapples and coconuts. last year, its economy was operating efficiently at point a. to capitalize on its favorable climate for growing these fruits, the country decides to build some islands near its coast to use for growing pineapples and coconuts. which ppc represents the change that results from this decision?
The country will achieve a blue PPC.
What is Production Possibilities Curve (PPC)?
The Production Possibilities Curve (PPC) Sometimes called the production possibilities frontier (PPF) is a model used to show the tradeoffs associated with allocating resources between the production of two goods. The PPC can be used to illustrate the concepts of scarcity, opportunity cost, efficiency, inefficiency, economic growth, and contractions.
Due to the increase in resources of the country, the production capacity for both pineapple & coconut will increase as a result country's PPC will shift rightward/forward. And the country will achieve blue PPC.
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if sin x =
[tex] - \frac{ \sqrt{3} }{2} [/tex]
and cos x >0 find the value of x. pls an pls answer i will mark him or her brainlest. pls
Step-by-step explanation:
sin^-1√-3/2=300°
cos300°=0.5
Sarah has 15 naira and bobo has 39 naira .how much must Sarah give to bobo so that bibo shall have 5 times as much as Sarah
Please help! will give 14 points and brainliest!
Answer:
EF = 22 , AB = 1
Step-by-step explanation:
the midsegment of a trapezoid is equal to half the sum of the parallel bases
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) ← substitute values
x + 6 = [tex]\frac{1}{2}[/tex] (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction
2x + 12 = 3x - 4 ( subtract 3x from both sides )
- x + 12 = - 4 ( subtract 12 from both sides )
- x = - 16 ( multiply both sides by - 1 )
x = 16
Then
EF = x + 6 = 16 + 6 = 22
Similarly
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) , that is
x + 3 = [tex]\frac{1}{2}[/tex] (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction
2x + 6 = 6x + 2 ( subtract 6x from both sides )
- 4x + 6 = 2 ( subtract 6 from both sides )
- 4x = - 4 ( divide both sides by - 4 )
x = 1
Then
AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1
the Royal fruit company produces two types of fruit drinks the first type is 45% pure fruit juice and the second type is 95% pure fruit juice. the company is attempting to produce a fruit drink that contains 55% pure fruit juice how many pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 55% pure fruit juice
Answer:
first type: 144 pints
second type: 36 pints
Step-by-step explanation:
So let's try to interpret the given information. So the first thing to know is how to calculate x%, to calculate this, you simply multiply the number by x/100, which is what x is in decimal form.
So let's just start off by assigning variables to each brand, with the variable representing the amount of pints. Let's say "x" is the amount of pints of the first brand, and "y" is the amount of pints of the second brand.
The next thing to do is make equations using the given information. So we want a fruit drink that is 55% pure fruit juice, and it's 180 pints. So to find what 55% is, we multiply by 55/100 or 0.55. This means that 55% is 0.55(180) = 99. So using the given information this means that 99 pints is pure fruit juice in the mixture. This comes from mixing the first two brands, so that means if we take the pure fruit juice from the first brand and add it to the second brand we get 99, and remember we are given the information that 45% of the first brand is pure fruit juice and the second is 95%, this means that 0.45x is pure fruit juice in the first brand and 0.95y is pure fruit juice in the second brand. This sets up the following equation: [tex]99 = 0.45x + 0.95y[/tex]
The second equation to set up is using the total amount of pints. x represents how much is from the first brand, and y represents how much is from the second brand. Since the mixture consists of these two brands, and the mixture is 180 pints we can form the equation: [tex]180 = x+y[/tex]
The last step is to solve the systems of equations using the two equations we formed. This can be done via substitution. We simply need to solve for either x or y, in the total amount of pints equation and then substitute it into the pure fruit juice equation. In this example I'll solve for x
Original Equation:
[tex]180 = x+y[/tex]
Subtract y from both sides
[tex]180-y=x[/tex]
So now that we solved for y in terms of x we can substitute this into the pure fruit juice equation, so that we're only dealing with one variable.
Original Equation:
[tex]99 = 0.45x + 0.95y[/tex]
Substitute 180-y as x
[tex]99 = 0.45(180-y) + 0.95y[/tex]
Distribute the 0.45
[tex]99=81-0.45y+0.95y[/tex]
Add like terms
[tex]99=81+0.5y[/tex]
subtract 81 from both sides
[tex]18=0.5y[/tex]
Divide both sides by 0.5 (same thing as multiply by 2)
[tex]36=y[/tex]
This means we have to use 36 pints of the second brand. We can substitute this into either equation to solve for x, but it's easier to substitute into the total pints equation since there are no coefficients (technically a 1 in front, but it's kind of be ignored for now), so it's pretty straightforward to solve for x
Original Equation:
[tex]180=x+y[/tex]
Substitute 36 as y
[tex]180=x+36[/tex]
Subtract 36 from both sides
[tex]144=x[/tex]
This means 144 pints from the first brand and 36 from the second
Look at this triangle.
A
Work out length BC.
13 cm
8 cm
B
С
In the given triangle, the length of BC is 10.25 cm
Solving a right triangle
From the question, we are to determine the length BC
The triangle is a right triangle, then we can write that
/AB/² = /AC/² + /BC/² (Pythagorean theorem)
From the given information,
/AB/ = 13 cm
/AC/ = 8 cm
Putting the parameters into the equation, we get
13² = 8² + /BC/²
169 = 64 + /BC/²
/BC/² = 169 - 64
/BC/² = 105
/BC/ = √105
/BC/ = 10.25 cm
Hence, the length of BC is 10.25 cm
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Can some one help !!???
Answer:
Yes
Step-by-step explanation:
I need the volume of that figure
Answer:
708π in³ = 2224.25 in.³
Step-by-step explanation:
The composite solid is made up of a cone, a cylinder, and a half sphere.
Recall the volume formulas:
cone: πr²h/3
cylinder: πr²h
sphere: 4πr³/3
half sphere: (1/2) × 4πr³/3
We need to find teh heoght of the cone. The slant height is 10 in. The radius is 6 in. We can use the Pythaogorean theorem to find the height of the cone.
h = √(10² - 6²) = 8
total volume = π(6 in.)²(8 in.)/3 + π(6 in.)²(13 in.) + (1/2) × 4π(6 in.)³/3
total volume = π(96 in.³ + 468 in.³ + 144 in.³)
total volume = 708π in³ = 2224.25 in.³
Help me with this problems
Answer:
its easy
Step-by-step explanation:
you should change all into degrees
Sir yesuba withdrew a sumof money from the bank he gave 3/8 of it to his son and 1/4 to his daughter if he had gh600 left, how much did he take form the bank
Sir Yesuba took Rs 1600 from the bank.
Concept : Addition and subtraction from an unknown quantity which can be calculated easily using variables.
Given: The Amount given to son = 3/8x
The Amount given to daughter = 1/4x
Money left = Rs 600
Let the amount taken by him be equal to Rs x.
The Amount given to son = 3/8x
The Amount given to daughter = 1/4x
x - (3/8x + x/4) = 600
x- x/8 = 600
7x/8=600
x= Rs1600
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10 divided by 34352 rounded to the nearest tenth
Answer: 0
Step-by-step explanation:
Answer:
34352.0
Step-by-step explanation:
help me please, you gonna be my hero
The rate of change of the relationship is 6/5
Rate of change of a lineThe rate of change of a line is also known as the slope of the line. The formula for calculating the slope of a line is expressed as:
Slope =y2-y1/x2-x1
Given the coordinate points (-3,-2) and (2, 4). On substituting;
Slope = 4-(-2)/2-(-3)
Slope =4+2/2+3
Slope = 6/5
Hence the rate of change of the relationship is 6/5
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please help solve inequality question c
The solution to the given inequality is; x ≥ -9/4 or x ≥ 1
How to solve Inequality problems?
We want to solve the inequality;
(4x² + 5x - 9)/(x² - x - 6) ≥ 0
Let us factorize both numerator and denominator to get;
4x² + 5x - 9 = (4x + 9)(x - 1)
Similarly, x² - x - 6 when factorized gives;
x² - x - 6 = (x + 2)(x - 3)
Thus, we now have;
[(4x + 9)(x - 1)]/[(x + 2)(x - 3)] ≥ 0
Multiply both sides by [(x + 2)(x - 3)] to get;
(4x + 9)(x - 1) ≥ 0
Thus;
(4x + 9) ≥ 0 or (x - 1) ≥ 0
Thus;
x ≥ -9/4 or x ≥ 1
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In sunlight, a vertical stick 6 ft tall casts a shadow 2 ft long. At the same time a nearby tree casts a shadow 14 ft long. How tall is the tree? Round to the nearest tenth.
Answer:
42.0 ft
Step-by-step explanation:
let t be the height of the tree.
At the same time ,the measure of something
and its shadow are proportional .
Then
[tex]\frac{2}{6} =\frac{14}{t}[/tex]
Then
2t = 6 × 14
Then
2t = 84
Then
t = 84/2
Then
t = 42
Therefore the tree is 42 ft tall
Which is equivalent to (3/125)*?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads:}[/tex]
[tex]\large\textbf{Which is equivalent to }\rm{\bf \dfrac{3}{125}}\large\textbf{ ?}[/tex]
[tex]\huge\textbf{Solving for your fraction:}[/tex]
[tex]\mathbf{\dfrac{3}{125}}[/tex]
[tex]\mathbf{= \dfrac{3\times2}{125\times2}}[/tex]
[tex]\mathbf{\approx \dfrac{3 + 3}{125 + 12{5}}}[/tex]
[tex]\mathbf{= \dfrac{6}{250}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{6}{250}}}\huge\checkmark[/tex]
[tex]\large\text{By the way, they are a lot more fractions that are equivalent to}\\\large\text{the given equation (}\rm{\dfrac{3}{125}}\large\text{) but we only labeled one that is the very}\\\large\text{first fraction that is equal to it. }[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]The functions fand g are defined as follows.
g(x) = -2x³-5
f(x) = -2x-3
Find f(5) and g (-2).
Simplify your answers as much as possible.
ƒ (5) = 0
8 (-2) =
믐
X S
2.
?
Answer:
f(x) = -2x - 3
g(x) = -2x³ - 5
f(5) = -2(5) - 3
f(5) = -10 - 3
f(5) = -13
g(-2) = -2(-2)³ - 5
g(-2) =-2(-8) - 5
g(-2) = 16 - 5
g(-2) = 11