Answer:
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) The probability of drawing exactly one blue marble = 0.46875
Step-by-step explanation:
Complete Question
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.
To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.
Probability of drawing a blue marble = P(B) = (3/8)
Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)
- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625
- Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)
= (3/8) × (3/8) = (9/64) = 0.140625
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
Hope this Helps!!!
what is the constant of proportionality (in miles per hour) based on the table? (can you please help me)
Answer:
45 ( please label me brainliest)
Step-by-step explanation:
The constant of proportionality is a factor that describes a linear relationship between two variables. In the context of a car's speed, it can be found by dividing the distance covered by the time taken, giving a result in miles per hour.
Explanation:
The constant of proportionality is a factor used to describe quantities that have a linear relationship. It is the ratio between two directly proportional variables. For example, if the speed of a car increases proportionally with the time spent driving, the constant of proportionality would be the rate the car is moving in miles per hour (mph). It can be found in simple linear equations with the form y = mx + b, where m is the constant of proportionality.
In your case, if you are given a table of values displaying a linear relationship, the constant of mathrm{proportionality} in mph can be found by selecting any two corresponding values (for time and distance in this case), and calculating the rate by dividing the distance covered in miles by the time taken in hours.
This rate (in miles per hour) is your proportionality constant, assuming that the relationship is indeed linear. Therefore, if one assumes the speed remains constant and acceleration is nil, then the speed of the car (in mph) is the constant of proportionality in this context.
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What shapes can the composite figure be decomposed into? Select two options.
A hexagon.
a rectangle and a triangle
a rectangle and two triangles
a square and two triangles
two rectangles
two trapezoids
The composite figure can be decomposed into:
C. a rectangle and two triangles
F. two trapezoids.
What is a Composite Figure?A composite figure is a figure that is formed by two or more shapes, or a figure that can be decomposed into two or more shapes.
The composite figure in the diagram be be broken down into either two trapezoids or a rectangle and two triangles.
Therefore, the shapes that the composite figure can be decomposed into are:
C. a rectangle and two triangles
F. two trapezoids.
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Angles J X M, M X N, and N X P form a straight line. Angle M X N is a right angle.
Which statement is true about ∠JXM and ∠NXP?
Answer:
∠JXM and ∠NXP are complementary
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
[tex]m\angle JXM+m\angle MXN+m\angle NXP=180^o[/tex] ----> form a straight line
we have
[tex]m\angle MXN=90^o[/tex]
substitute
[tex]m\angle JXM+90^o+m\angle NXP=180^o[/tex]
[tex]m\angle JXM+m\angle NXP=180^o-90^o[/tex]
[tex]m\angle JXM+m\angle NXP=90^o[/tex]
Remember that
Two angles are complementary, if their sum is equal to 90 degrees
therefore
∠JXM and ∠NXP are complementary
Answer:The answer is A, I got it right
Step-by-step explanation:
Two bicyclists left at 11:30 AM for a ride. Rider A traveled at a constant rate of 12 mph at a
bearing of N 47° E, stopping at 1:30 PM. Rider B traveled until 3:00 PM, biking at a constant rate
of 9 mph at a bearing of S 62° E. Determine the distance between the two bicyclists.
Answer:
32.8 miles
Step-by-step explanation:
The total time travelled by rider A is 2 hours. If his speed was 12 mph, the distance travelled is 2 * 12 = 24 miles.
The total time travelled by rider A is 3 hours and 30 minutes (so 3.5 hours). If his speed was 9 mph, the distance travelled is 3.5 * 9 = 31.5 miles.
The angle that they make, as rider A was in the direction N 47 E and the rider B was in the direction S 62 E, is equal to 180 - 47 - 62 = 71°
With these values (two distances and a angle between then, we can use law of cosines to find the distance between the bicyclists:
c^2 = a^2 + b^2 - 2ab*cos(angle)
c^2 = 24^2 + 31.5^2 - 2*24*31.5*cos(71)
c^2 = 1075.99
c = 32.8 miles
The distance between the two bicyclist is 32.8 miles
The calculation is as follows:The total time travelled by rider A is 2 hours.
In the case when his speed was 12 mph,
So, the distance travelled is 2 (12) = 24 miles.
Now
The total time travelled by rider A is 3 hours and 30 minutes i.e. 3.5 hours).
In the case when his speed was 9 mph, the distance travelled is 3.5 (9) = 31.5 miles.
Now the direction is
= 180 - 47 - 62
= 71°
Now the distance is
[tex]c^2 = a^2 + b^2 - 2ab\times cos(angle)\\\\c^2 = 24^2 + 31.5^2 - 2\times 24\times 31.5\times cos(71)\\\\c^2 = 1075.99[/tex]
c = 32.8 miles
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4c = 3 what does c equal?
I NEED HELP NOW
Answer:
3/4
Step-by-step explanation:
The solution of expression 4c = 3 by combining like terms is c = 3/4.
Used the concept of the equation that states,
An equation is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
Given that the equation is,
4c = 3
Now simplify the equation by combining like terms,
4c = 3
Divide both sides by 4,
4c/4 = 3/4
c = 3/4
Therefore, the solution is c = 3/4.
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A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours in the packaging department. The larger lift requires 3 hours in the welding department and 1 in the packaging department. The company has 150 hours/day available in welding and 120 hours/day available in packaging. If the profit is $25 for each small lift and $90 for each large lift, how many of each type should be produced to maximize profits? (1) List your variables (2) List your constraints
Answer:
The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.Below are all the steps explained in detail.The graph is attached.
Explanation:
1. Name the variables:
x: number of smaller liftsy: number of larger lifts2. Build a table to determine the number of hours each lift requires from each department:
Number of hours
small lift large lift total per department
Welding department 1x 3y x + 3y
Packaging department 2x 1y 2x + y
3. Constraints
150 hours available in welding: x + 3y ≤ 150120 hours available in packaging: 2x + y ≤ 120The variables cannot be negative: x ≥ 0, and y ≥ 0Then you must:
draw the lines and regions defined by each constraintdetermine the region of solution that satisfies all the constraintsdetermine the vertices of the solution regiontest the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)4. Graph
See the graph attached.
Here is how you draw it.
x + 3y ≤ 150draw the line x + 3y = 150 (a solid line because it is included in the solution set)shade the region below and to the left of the line2x + y ≤ 120draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)shade the region below and to the left of the linex ≥ 0 and y ≥ 0: means that only the first quadrant is consideredthe solution region is the intersection of the regions described above.take the points that are vertices inside the solutoin region.5. Test the profit function for each vertex
The profit function is P(x,y) = 25x + 90y
The vertices shown in the graph are:
(0,0)(0,50)(42,36)(60,0)The profits with the vertices are:
P(0,0) = 0P(0,50) = 25(0) + 90(50) = 4,500P(42,36) = 25(42) + 90(36) = 4,290P(60,0) = 25(60) + 90(0) = 1,500Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.
Final answer:
To maximize profits from manufacturing boat lifts, define variables as x for small lifts and y for large lifts, and list the constraints from the welding and packaging departments' available hours alongside non-negative production quantities.
Explanation:
To find how many of each type of boat lifts should be produced to maximize profits, first, we need to define our variables and list our constraints.
List your variables
Let x be the number of small lifts.Let y be the number of large lifts.List your constraints
For the welding department: 1x + 3y ≤ 150 (hours/day available).For the packaging department: 2x + 1y ≤ 120 (hours/day available).Non-negative constraint: x ≥ 0, y ≥ 0.These constraints represent the limits on production based on the available hours in each department, whilst also considering that the production of both types of lifts must be a non-negative quantity.
Mae loses 3 points for each wrong answer on a test.
How does her score change if she has 7 wrong answers?
Answer:
Mae will have 21 points at the end of the test.
Step-by-step explanation:
3x7=21
Answer: 21 points
Step-by-step explanation:
If you have if she has seven wrong, and each question makes you lose 3 points. you can 21.
If 5 lessened by 1/2 of a number, the result is equivalent to subtracting 3/4 of the number from 11
Answer:
no lose yo ablo español
What is the product of (3x-9) and 6x↑2-2x+5 Write your answer in standard form.
(a) Show your work.
(b) Is the product of (3x-9) and 6x↑2-2x+5 equal to the product of (9x-3) and 6x↑2-2x+5
Explain your answer.
Answer:
a. [tex]18x^3 -60x^2 + 33x - 45[/tex]
b. No
Step-by-step explanation:
Given:
(3x-9) and [tex]6x^2-2x+5[/tex]
=> the production of them is:
[tex](3x-9)(6x^2-2x+5)[/tex] , we will use distributive law to solve this To do that. we first multiply [tex]6x^2-2x+5[/tex] by 3x then by -9. This is done as follows
= [tex]3x (6x^2-2x+5) - 9(6x^2-2x+5)[/tex] [tex]= (3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)\\\\= (18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)[/tex]
Then Open both brackets
= [tex]18x^3 -6x^2+ 15x -54x^2 + 18x -45[/tex]
After that, we group the same terms
= [tex]18x^3 -(6x^2 +54x^2)+ (15x + 18x) -45[/tex]
= [tex]18x^3 -60x^2 + 33x - 45[/tex]
(b) Is the product of (3x-9) and [tex]6x^2-2x+5[/tex] equal to the product of (9x-3) and [tex]6x^2-2x+5[/tex]
No, let find the product of (9x-3) and [tex]6x^2-2x+5[/tex] , we will use distributive law to solve this as the above example.
= (9x-3)[tex](6x^2-2x+5)[/tex]
= [tex]9x (6x^2-2x+5) - 3(6x^2-2x+5)[/tex]
=[tex](9x * 6x^2 - 9x * 2x + 9x *5) - (3* 6x^2 - 3 * 2x + 3* 5)[/tex]
= [tex](54x^3 - 18x^2+ 45x) - (18x^2 - 6x +15)[/tex]
After that, we open the bracket to find the same terms
= [tex]54x^3 - 18x^2+ 45x -18x^2 + 6x -15[/tex]
= [tex]54x^3 - 18x^2 -18x^2 + 45x + 6x -15[/tex]
= [tex]54x^3 - 36x^2 + 51x -15[/tex]
As you can see [tex]54x^3 - 36x^2 + 51x -15[/tex] ≠[tex]18x^3 -60x^2 + 33x - 45[/tex]
Hope it will find you well.
find angles j and k wishing the triangle
Answer: Angle J= 75 degrees and angle K=40 degrees.
Rewrite the expression using only positive integer exponents.
Answer:
the answer is D) m4/n2
Step-by-step explanation:
(m 2/3 n -1/3) 6
2/3 x 6= 4
-1/3 x 6 =-2
you cannot have a negative exponent in this situation so you would put n -2 on the bottom which makes it positive.
Answer:
Other guy is correct it's D
Step-by-step explanation:
v-3/-10= -4 please answer step by step
Answer:
5
-by-step explanation:
Here are advertised horsepower ratings and expected gas mileage for several 2007 vehicles
as reported by Kelly Blue Book
Vehicle
Horsepower
Gas Mileage (MPG)
Audi A4
200
BMW 328
1230
Buick LaCrosse
200
Chevy Cobalt
Chevy TrailBlazer 291
Ford Expedition
300
GMC Yukon
Honda Civic
Honda Accord
Hyundai Elantra
Lexus IS 350
Lincoln Navigator 300
Mazda Tribute
212
Toyota Camry
158
Volkswagen Beetle 150
This is an incomplete table of horsepower and gas mileage data for various 2007 vehicles. Despite the missing information, it can still be used to analyze patterns, create averages, and compare specific models or power ratings.
Explanation:The presented data appears to be a compilation of horsepower ratings and expected gas mileage (MPG) readings for a variety of 2007 vehicles, as reported by Kelly Blue Book. Unfortunately, the table is incomplete, without consistent information for each listed vehicle, but it can still be analyzed to some extent. You could use this data in mathematics to do things like analyze patterns, create averages, and chart the information in graphical form. For instance, you might look at the relationship between horsepower and gas mileage - perhaps higher horsepower means lower gas mileage, or you might find there's no clear pattern at all. Examples of such analyses might include comparing models from the same manufacturer (like the Honda Civic and Honda Accord), or comparing cars with similar horsepower, like the Audi A4 and Buick LaCrosse both with 200 horsepower.
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Luetta is out shopping and finds a $190 video game that
was marked down by 5%.
How much was the item originally?
Answer:
i think the answer is 38
Step-by-step explanation:
$190 divided by 5% = 38
Tools: calculator
1. Which of the following are statistical
questions? Circle all answers.
M
a) Do you have any pets?
b) What dáy does school get out?
c) How many home runs were hit in
MLB last year?
d) How many goals did each soccer
team score in each game last
season?
e) What was the average number of
home runs hit over the last 10
seasons?
Answer:
c d e?
Step-by-step explanation:
btw I'm not sure :")
Answer:
A,d,e
Step-by-step explanation:
The cost of a car rental is $35 per day plus 19cents per mile. You are on a daily budget of $73. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget.
Answer:
73 ≥ 35+.19 m
Answer:
the answer is 200 miles per day
A bag contains 40 marble 12 red and 16 yellow what is the probability that a blue is randomly seclected
Answer:
Fraction=3/10
Decimal=0.3
Percent=30%
Step-by-step explanation:
First we have to add 12+16 so we can find how many marbles are left
12+16=38
Then, we subtract it from the total number of marbles.the outcome of this operation would be equivalent to the number of blue marbles
40-38=12
There are 12 blue marbles.
Now, the we have to use experimental probability if you are familiar with the term is that the number of outcomes(the blue marbles) must be over the total sample space(total marbles) in a fraction.
Probability=
12/40
Simplify
12/40
6/20
3/10
Probability
Fraction=3/10
Decimal=0.3
Percent=30%
For what real value of $v$ is $\frac{-21-\sqrt{301}}{10}$ a root of $5x^2+21x+v$?
Answer:
v = 7
is the value for which
x = (-21 - √301)/10
is a solution to the quadratic equation
5x² + 21x + v = 0
Step-by-step explanation:
Given that
x = (-21 - √301)/10 .....................(1)
is a root of the quadratic equation
5x² + 21x + v = 0 ........................(2)
We want to find the value of v foe which the equation is true.
Consider the quadratic formula
x = [-b ± √(b² - 4av)]/2a ..................(3)
Comparing (3) with (2), notice that
b = 21
2a = 10
=> a = 10/2 = 5
and
b² - 4av = 301
=> 21² - 4(5)v = 301
-20v = 301 - 441
-20v = -140
v = -140/(-20)
v = 7
That is a = 5, b = 21, and v = 7
The equation is then
5x² + 21x + 7 = 0
Michael is planting a garden in the shape of a right triangle. He wants 4 tickseed plants for each square meter of area. How many tickseed plants does Michael want in his garden?
Please Help Me!
Answer:
336 plants
Step-by-step explanation:
To find the number of tickseed plants that Michael needs to plant in his garden, we have to find the area of the garden first.
We notice that the garden has the shape of a right triangle: so, we have to find the area of the right triangle.
The area of a triangle is given by the formula
[tex]A=\frac{1}{2}bh[/tex]
where
A is the area
b is the length of the base
h is the height of the triangle
From the figure, we see that:
b = 7 m is the length of the base
h = 24 m is the height of the triangle
Therefore, applying the formula, we find the area of the garden:
[tex]A=\frac{1}{2}7\cdot 24 =84 m^2[/tex]
We also know that Michael wants to plant 4 tickseed plants for each square meter of area; therefore, the total number of plants that Michael will plant is 4 times the area of the garden, so:
[tex]N=4A=4\cdot 84=336[/tex]
Answer:
336 tickseed plants
Step-by-step explanation:
Because the length cannot be negative the height of the plane is ___ miles.
????????????????
????????????????
????????????????
????????????????
????????????????
????????????????
????????????????
Look at all the steps above. They lead to a double solution. The symbol
[tex]x=\pm 5[/tex]
means that [tex]x[/tex] can be either positive or negative 5. You can't accept negative values for lengths, so you're left with one option only.
PLEASE PLEASE HELP the question is below
Answer:
D. 66/2
Step-by-step explanation:
If you are trying to figure out what operation to perform first, then follow PEMDAS.
P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
So first we start with what is in parenthesis. Since there are two operations within the parenthesis, we start with the division first since it comes first in PEMDAS. This is why D. 66/2 is our best answer.
Algebra problem! PLEASE help me!!!
Helen deposited $1200 at 5% interest compounded continuously. After 6 years, how much did she have?
(A) $1619.83
(B) $1560
(C) $2410.26
(D) $1608.11
(E) none of these
I got (D), but got it wrong. Would (A) be the correct answer?
Answer:
A
Step-by-step explanation:
X = 1200 × e^(5% × t)
X = 1200 × e(0.05×6)
X = 1200 × e^0.3
X = 1619.830569
The line of symmetry of the parabola whose equation is y = ax^2 -4x + 3 is
x = -2. What is the value of "a"?
A. -2
B. -1
C. -1/2
Answer:
B. -1
Step-by-step explanation:
If we have a parabola whose equation is:
[tex]y=ax^{2} +bx+c[/tex]
The line of symmetry is calculated as:
[tex]x=\frac{-b}{2a}[/tex]
Now, we have the equation [tex]y=ax^{2}-4x+3[/tex] and the line of symmetry is [tex]x=-2[/tex]
Where:
[tex]b=-4\\c=3[/tex]
So, we can replace [tex]b[/tex] by -4 and [tex]x[/tex] by -2 and solve for [tex]a[/tex] using the following equation as:
[tex]x=\frac{-b}{2a}\\-2=\frac{-(-4)}{2a}\\-2(2)a=4\\-4a=4\\a=-1[/tex]
It means that the equation of the parabola is equal to:
[tex]y=-1x^{2}-4x+3[/tex]
Oliver hits a baseball at 3 feet above the ground with an initial speed of 135ft/sec at an angle of 20 degrees with the horizontal.
The outfield wall is 380 feet away and is 15 feet high.
At approximately what height will the ball hit the wall?
A) 3 ft
B) the ball lands in front of the wall
C) the ballet goes over the wall
D) 8 ft
Answer:
Option B) the ball lands in front of the wallExplanation:
1. Find the vertical and horizontal components of the initial velocity
a) Horizontal component:
[tex]v_{0,x}=v_0\times cos(20\º)=135ft/s\times cos(20\º)=126.86ft/s[/tex]
b) Vertical component:
[tex]v_{0,y}=v_0\times sin(20\º)=135ft/s\times sin(20\º)=46.17ft/s[/tex]
2. Find the time when the ball runs 380 feet horizontally:
[tex]x=v_{0,x}\times t\\\\380ft=126.86ft/s\times t[/tex]
[tex]t= (380ft)/(126.86ft/s)=2.995s\approx 3.0s[/tex]
3. Find the height of the ball when the time is 3.0s
[tex]y=y_0+v_{0,y}\times t-gt^2/2[/tex]
y₀ = 3 ftg ≈ 32.174 ft/s²[tex]y=3ft+46.17ft/s\times 3.0s-32.174ft/s^2\times (3.0s)^2/2[/tex]
[tex]y=-3.3ft[/tex]
This result means that the ball does not reach the wall because it has fallen to the ground (when y = 0) before 3.0s.
Need help dumb and bad at this but good and smart at other things !!!
Answer:
The answer is A my dude
Step-by-step explanation:
Answer:
He loses 12 limbs over 4 days (need one more branliest to level up)
Step-by-step explanation:
loses 3 on monday (-3)
loses 3 on tuesday (-3)
see the pattern
Joel is listening to his playlist. Joel selects random play from the user playlist. Joel's has 2 Cardi B songs, 13 Eminem songs, and 5 Beyonce songs on it. What is P (Cardi B or Beyonce)? (Use a fraction, decimal[out only 3 spaces], or percent) *
uh
probably beyonce cuz there more songs on the playlist. what kinda quiz is this
Answer:
uh
probably beyonce cuz there more songs on the playlist. what kinda quiz is this
Step-by-step explanation:
how to factor 3x^2-x-30
Answer:
(x + 3)(3x - 10)
Step-by-step explanation:
[tex]3 {x}^{2} - x - 30 \\ = 3 {x}^{2} + 9x - 10x - 30 \\ = 3x(x + 3) - 10(x + 3) \\ = (x + 3)(3x - 10) \: are \: the \: required \: factors.[/tex]
To factor the expression [tex]3x^2-x-30[/tex], use factoring by grouping. The factored form is (3x + 3)(x - 10).
To factor the expression [tex]3x^2-x-30[/tex], we can use factoring by grouping or the quadratic formula. Let's use factoring by grouping:
Step 1: Multiply the leading coefficient (3) by the constant term (-30) to get -90.
Step 2: Find two numbers whose product is -90 and whose sum is the coefficient of the linear term (-1). In this case, the numbers are -10 and 9.
Step 3: Rewrite the middle term (-x) as the sum of the numbers found in step 2 (-10x + 9x).
Step 4: Group the terms and factor out the greatest common factor from each group (3x(x - 10) + 3(x - 10)).
Step 5: Factor out the common binomial (x - 10) from each group to get the final factored form: (3x + 3)(x - 10).
does 5x+20=4(x+6) have one solution
Answer:
One solution x=4
Step-by-step explanation:
5x+20=4(x+6)
Distribute
5x+20 =4x+24
Subtract 4x from each side
5x -4x +20 = 4x-4x+24
x+20 = 24
Subtract 20 from each side
x+20-20 =24-20
x =4
Use the graph to determine the input value for which f(x) = g(x) is true.
x = 0.5
x = 1
x = 1.5
x = 2
Answer: 1.5
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
A watercolor painting is 19 inches long by 11 inches wide. Ramon makes a border around the watercolor painting by making a mat that adds 2 inches to each side of the length and the width. What is the area of the mat?
The total area of mat without painting is 136 square inches.
The original painting is 19 inches long by 11 inches wide. When Ramon adds a 2-inch border to each side of the painting's length and width, the overall dimensions of the mat become:
Length with border: 19 inches + 2 inches + 2 inches = 23 inches
Width with border: 11 inches + 2 inches + 2 inches = 15 inches
To find the area of the mat, one must calculate the area of the border plus the painting and then subtract the area of the painting:
Calculate the area of the full mat with the painting: 23 inches imes 15 inches = 345 square inches.
Calculate the area of the painting alone: 19 inches imes 11 inches = 209 square inches.
Subtract the area of the painting from the full area to get the area of the mat: 345 square inches - 209 square inches = 136 square inches.