Answer:
Size of |E n B| = 2
Size of |B| = 1
Step-by-step explanation:
I'll assume both die are 6 sides
Given
Blue die and Red Die
Required
Sizes of sets
- [tex]|E\ n\ B|[/tex]
- [tex]|B|[/tex]
The question stated the following;
B = Event that blue die comes up with 6
E = Event that both dice come even
So first; we'll list out the sample space of both events
[tex]B = \{6\}[/tex]
[tex]E = \{2,4,6\}[/tex]
Calculating the size of |E n B|
[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]
[tex]|E n B| = \{2,4,6\}[/tex]
The size = 3 because it contains 3 possible outcomes
Calculating the size of |B|
[tex]B = \{6\}[/tex]
The size = 1 because it contains 1 possible outcome
A regression analysis between sales (y in $1000) and advertising (x.in dollars) resulted in the following equation: ỹ= 30,000 + 4x
The above equation implies that an:________
a. increase of $l in advertising is associated with an increase of $4 in sales.
b. increase of $4 in advertising is associated with an increase of $4000 in sales.
c. increase of $1 in advertising is associated with an increase of $34,000 in sales.
d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Answer:
Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Step-by-step explanation:
Given the equation of regression analysis is given as:
[tex]y= 30,000 + 4x[/tex]
where [tex]x[/tex] is the cost on advertising in Dollars.
and [tex]y[/tex] is the sales in Thousand Dollars.
To find:
The correct increase in sales when there is increase in the advertising cost.
Solution:
Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.
Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].
Initial sales
[tex]y= 30,000 + 4x[/tex] ....... (1)
After increase of $1 in advertising cost, final cost:
[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]
Subtracting (2) from (1) to find the increase in the sales:
[tex]y'-y=30004+4x-30000-4x = 4[/tex]
The units of sales is Thousand Dollars ($1000).
So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]
So, correct answer is:
d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Use the following cell phone airport data speeds (Mbps) from a particular network. Find the percentile corresponding to the data speed 4.9 Mbps.
0.2 0.8 2.3 6.4 12.3 0.2 0.8 2.3 6.9 12.7 0.2 0.8 2.6 7.5 12.9 0.3 0.9 2.8 7.9 13.8
0.6 1.5 0.1 0.7 2.2 6.1 12.1 0.6 1.9 5.5 11.9 27.5 0.6 1.7 3.3 8.3 13.8 1.3 3.5 9.8
14.6 10.1 14.7 11.8 14.8
Answer:
Thus percentile lies between 53.3% and 55.6 %
Step-by-step explanation:
First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N
where n is the ordinal rank of the given value
N is the number of values in ascending order.
The data in ascending order is
0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3
1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5
Number of observation = 45
4.9 lies between 3.3 and 5.5
x*n = 24 observation x*n = 25 observation
x*45= 24 x*45= 25
x= 0.533 x= 0.556
Thus percentile lies between 53.3% and 55.6 %
Assume that random guesses are made for multiple-choice questions on a test with choices for each question, so that there are n trials, each with probability of success (correct) given by p. Find the probability of no correct answers
Complete Question
Assume that random guesses are made for 7 multiple-choice questions on a test with 5 choices for each question, so that there are n=7 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct answers.
Answer:
The probability is [tex]P(X = 0 ) = 0.210[/tex]
Step-by-step explanation:
From the question we are told that
The number of trial is n = 7
The probability of success is p = 0.20
Generally the probability of failure is
[tex]q = 1- 0.20[/tex]
[tex]q = 0.80[/tex]
Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure
Then the probability is mathematically represented as
[tex]P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^{0} * q^{n- 0}[/tex]
[tex]P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^{0} * (0.8)^{7- 0}[/tex]
Here [tex]\left 7} \atop {}} \right. C_0 = 1[/tex]
=> [tex]P(X = 0 ) = 1 * 1* (0.8)^{7- 0}[/tex]
=> [tex]P(X = 0 ) = 0.210[/tex]
PLEASE SOLVE THE ABOVE PROBLEM you’ll get 43 POINTS
heya friend
0.2
0.2**10/10
=2/10
in 2/10 2 and 10 are integers
and 10 is not zero
so it is sacrificed
hope this helps u
Answer:
0.2
0.2**10/10
=2/10
in 2/10 2 and 10 are integers
10 is not 0
Step-by-step explanation:
Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (3x2 − 2y2)i + (4xy + 4)j
In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means
[tex]\dfrac{\partial f}{\partial x}=3x^2-2y^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=4xy+4[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y)=x^3-2xy^2+g(y)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=-4xy+\dfrac{\mathrm dg}{\mathrm dy}=4xy+4\implies\dfrac{\mathrm dg}{\mathrm dy}=8xy+4[/tex]
But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.
In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.
A vector field can be described as:
[tex]F = <P,Q>[/tex]
It is conservative if:
[tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}[/tex]
In this problem, the field is:
[tex]F = <3x^2 - 2y^2, 4xy + 4>[/tex]
Then:
[tex]P(x,y) = 3x^2 - 2y^2[/tex]
[tex]\frac{\partial P}{\partial y} = -4y[/tex]
[tex]Q(x,y) = 4xy + 4[/tex]
[tex]\frac{\partial Q}{\partial x} = 4y[/tex]
Since [tex]\frac{\partial P}{\partial y} \neq \frac{\partial Q}{\partial x}[/tex], the field is not conservative.
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On a map 1 cm represents 4.5km. What is the actual distance between two towns which are 4cm apart on the map?
Answer:
18km
Step-by-step explanation:
1cm:4.5km/4cm then get the answer as 18km
1 cm represents [tex]4.5[/tex] km. To find the actual distance between two towns that are 4 cm apart on the map, we can use the scale ratio.
Since 1 cm represents [tex]4.5[/tex] km, we can calculate the actual distance by multiplying the map distance with the scale ratio. Map distance: 4 cm Scale ratio: 1 cm represents [tex]4.5[/tex] km Actual distance = Map distance × Scale ratio Actual distance[tex]= 4 cm × 4.5[/tex] km/cm Actual distance[tex]= 18 km[/tex]
Therefore, the actual distance between the two towns is18 [tex]18[/tex] km. Using the given scale, 1 cm on the map corresponds to[tex]4.5[/tex]km in reality. As the towns are represented as 4 cm apart on the map, the actual distance between them is [tex]18[/tex]km.
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In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?
Answer:
a
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
b
[tex]P( X >0.025 ) = 0.99379[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.10[/tex]
The sample size is [tex]n = 100[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]
=> [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]
=> [tex]SE =0.03[/tex]
The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]
Generally [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]
From the z-table
[tex]P(Z < 2.6 ) = 0.99534[/tex]
[tex]P(Z < 2.4 ) = 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as
[tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]
[tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]
From the z-table
[tex]P (Z > -2.5 ) = 0.99379[/tex]
Thus
[tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]
1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident
Answer:
math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.
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Michelle is 7 years older than her sister Joan, and Joan is 3 years younger than their brother Ryan. If the sum of their ages is 64, how old is Joan?
16
22
18
19
Answer:
(C) 18
Step-by-step explanation:
We can create a systems of equations. Assuming [tex]m[/tex] is Michelle's age, [tex]j[/tex] is Joan's age, and [tex]r[/tex] is Ryan's age, the equations are:
[tex]m = j + 7[/tex]
[tex]j = r-3[/tex]
[tex]m+j+r = 64[/tex]
We can use substitution, since we know the "values" of m and j.
[tex](j+7)+(r-3)+r = 64\\(j+7)+(2r-3)=64\\2r + j + 4 = 64\\2r + j = 60\\\\[/tex]
[tex]r = 21, j = 18[/tex]
So we know that Joan is 18 years old.
Hope this helped!
[tex]4x - 2x = [/tex]
Answer:
2x
Step-by-step explanation:
These are like terms so we can combine them
4x-2x
2x
Answer:
2x
Explanation:
Since both terms in this equation are common, we can simply subtract them.
4x - 2x = ?
4x - 2x = 2x
Therefore, the correct answer should be 2x.
A person collected $700 on a loan of $600 they made 5 years ago. If the person charged simple interest, what was the rate of interest? The interest rate is %. (Type an integer or decimal rounded to the nearest hundredth as needed.)
Answer:
Rate= 3 1/3%
Or Rate= 3.33%
Step-by-step explanation:
Final amount collected= $700
Initial amount given out= $600
Interest made= Final amount - initial amount
Interest made= $700-$600
Interest made= $100
Type of interest rate = simple
Number of years = 5
PRT/100= interest
R=(100*interest)/(PT)
R= (100*100)/(600*5)
R= 10000/3000
R= 10/3
R= 3 1/3%
Or R= 3.33%
ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information
Answer: B. Always
Explanation:
Two points always create a line. The correct answer is option B.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, the two points always create a line. The correct answer is option B.
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Can someone please help me?
Negative Integers are :
Less than zeroTo the left of zero on a number line.Original price of a soda: $800 tax 7% selling price: $
Answer:
$856
Step-by-step explanation:
Find 7% of $800 and then add it to $800
34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles.
Required:
Construct a binomial distribution using n= 0.6 and p=0.34
Answer:
solution below
Step-by-step explanation:
The question says 6 working mother's were selected so n = 6 not 0.6
We are expected to find
P(X = 0,1,2,3,4,4,6)
1. When x = 0
6C0*(0.34)⁰*(0.66)⁶
= 1 *1* 0.827
= 0.0827
2. When X = 1
6C1*(0.34)¹*(0.66)⁵
= 6 x 0.34 x 0.252
= 0.2555
3. When X = 2
6C2*(0.34)²*(0.66)⁴
= 15 x 0.1156 x 0.1897
= 0.3289
4. When x = 3
6C3*(0.34)³*(0.66)³
20 x 0.039304 x 0.2875
= 0.2599
5. When X = 4
6C4*(0.34)⁴*(0.66)²
= 15 x 0.01336 x 0.4356
= 0.8729
6. When x = 5
6C5*(0.34)⁵*(0.66)¹
= 6 x 0.0045 x 0.66
= 0.01782
7. When x = 6
6C6*(0.34)⁶*(0.66)⁰
1 x 0.0015 x 1
= 0.0015
will rate you brainliest
Answer:
A
Step-by-step explanation:
f(x)→g(x)
(0, 0) → (3, -4)
Therefore it increases it x-axis from 0 to 3
And decreases in y-axis from 0 to -4
Select the correct graph.
Answer:
Graph 1
Step-by-step explanation:
The only graph that could be possible would be graph 1.
As you can see the function x = 2t - 4 is linear, and the only graph that consists of a linear line would be the first graph.
5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution
Answer:
C. Infinitely many solutions
Step-by-step explanation:
First, simplify the second equation by dividing it by 2
2y = 6x + 2
y = 3x + 1
Now, we can see that both equations are the same, both y = 3x + 1.
Since they are the same line, this means that there are infinitely many solutions.
So, the correct answer is C.
I will rate you brainliest Select the best description of what the LCM of a set of polynomials is. a.It is the quotient of all the factors of the polynomials. b.It is the common numerator of a rational expression. c. It is the product of the prime factors that are either unique to or shared by the polynomials. d. It is all the polynomials in the set.
Answer:
C. It is the product of the prime factors that are either unique to or shared by the polynomials.
Step-by-step explanation:
LCM of polynomials is:
=> Finding the factors of all the numbers and variable in the expression
=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.
So, C is the correct answer.
The LCM of a set of polynomials is the product of the prime factors that are either unique to or shared by the polynomials.
What is LCM of polynomial?To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.
Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.
Factorizing 4a2 - 25b2 we get,
(2a)2 - (5b)2, by using the identity a2 - b2.
= (2a + 5b) (2a - 5b)
Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get
= 3a(2a + 5b)
L.C.M. is 3a(2a + 5b) (2a - 5b)
According to the question
The LCM of a set of polynomials is
is the product of the prime factors that are either unique to or shared by the polynomials.
(from above example we can see that )
Hence, It is the product of the prime factors that are either unique to or shared by the polynomials.
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Simplify the following expression.X^1/3 * X^1/5
Answer:
[tex] X^{\frac{8}{15}} [/tex]
Step-by-step explanation:
[tex] X^\frac{1}{3} \times X^\frac{1}{5} = [/tex]
To multiply two powers with the same base, write the base and add the exponents.
[tex] = X^{\frac{1}{3} + \frac{1}{5}} [/tex]
[tex] = X^{\frac{5}{15} + \frac{3}{15}} [/tex]
[tex] = X^{\frac{8}{15}} [/tex]
f(x) = x^2 + 2x + 1, then for what values of x, f(x)=f(x+2) step by step plz
Answer:
x = -2
Step-by-step explanation:
given f(x) = x² + 2x + 1
f(x+2) = (x+2)² + 2(x+2) + 1
= x² 4x+4+2x+4+1
= x² + 6x + 9
for f(x) = f(x+2), simply equate the two expressions and solve for x
f(x) = f(x+2)
x² + 2x + 1 = x² + 6x + 9 (x² terms cancel out)
2x + 1 = 6x + 9 (subtract 1 from both sides)
2x = 6x + 9 - 1
2x = 6x + 8 (subtract 6x from both sides)
2x - 6x = 8
-4x = 8 (divide both sides by -4)
x = 8 / (-4)
x = -2
Point A is at (2, -8) and point C is at (-4, 7).
Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.
Answer:
(-2, 2)
Step-by-step explanation:
Given:
Point A is at (2, -8) and point C is at (-4, 7)Difference of coordinates:
Δx = 2 - (-4) = 6Δy = - 8 - 7 = - 15The ratio of AB to AC is 2:1. So:
AB = 2*AC/3 and BC = AC/3Then coordinates of point B should be 2/3 from the point A:
x = 2- 6*2/3 = 2 - 4 = -2y = - 8 - (-15)*2/3 = -8 + 10 = 2So point B has coordinates of (-2, 2)
(x+1)(x−1)(x−5)=0 HELP
Answer:
x³ - 5x² - x + 5
Step-by-step explanation:
(x+1)(x-1)(x-5) = 0
fisrt step:
(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1
then:
(x+1)(x-1)(x-5) = (x²-1)(x-5)
(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5
Please help. I’ll mark you as brainliest if correct!
Answer: x= -1, z=2, y= -4
Step-by-step explanation:
System of equations:
-5x - 4y - 3z= 15 +
-10x + 4y + 6z= 6
-15x + 3z = 21 ------> 3 (-5x + z) = 7.3
-5x + z = 7
now,
-10x + 4y + 6z= 6
2(-5x + z) + 4y + 4z = 6
14 + 4y + 4z = 6
7 + 2y + 2z = 3
2y + 2z= -4
y+z=-2
Now we were using the equation: 20x + 4y + 4z = -28
20x + 4(y+z) = 20x -8= - 28
20 x = -20
x= -1
With this we can find y and z
X=-1
-5x + z = 7
z= 2
y+z=-2
y=-4
Finally we have: x= -1, z=2, y= -4
I hope this can help you.
Thank you
Reading a Tape Measure
Measure the green bar using the provided image of a tape measure
Answer:
3 inches
Step-by-step explanation:
The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.
PLS HELP:Find the side length, C.
Round to the nearest tenth.
Answer:
[tex]\huge\boxed{c = 14.9}[/tex]
Step-by-step explanation:
Using Cosine Rule
[tex]c^2 = a^2 + b^2 -2abCosC[/tex]
Where a = 11 , b = 7 and C = 110
[tex]c^2 = (11)^2+(7)^2-2(11)(7)Cos 110[/tex]
[tex]c^2 = 121+49-154 (-0.34)\\c^2 = 170+52.7\\c^2 = 222.7[/tex]
Taking sqrt on both sides
c = 14.9
Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42 . Find their ages. Use whole numbers.
Answer: Jake is 9 and his dad is 33.
Step-by-step explanation: 9x3=27+6=33 9+33=42
Answer:
Jake is 9 and Jake's dad is 33
Step-by-step explanation:
To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake
J+D=42
3J+6=D
Solve by substitution
FIND THE VALUE OF NT
PLEASE HELP ASAP :(
Answer:
NT = 14 units
Step-by-step explanation:
In this question we will apply the theorem of intersecting chords.
Two chords MY and TN are intersecting each other inside a circle at a point H.
Theorem states,
MH × HY = TH × HN
12(x) = 8(x + 2)
12x = 8x + 16
12x - 8x = 16
4x = 16
x = 4
Therefore, measure of chord NT = NH + HT
= 8 + (x + 2)
= x + 10
= 4 + 10
= 14 units
The number of weekly hours spent on a smart device varies inversely with the person's age. If a 20-year-old person spends 52 hours on their smart device each week, how many hours does a 50-year-old person spend on their smart device?
Answer:
20.8 hours
Step-by-step explanation:
Given that hours (h) varies inversely with age (a) then the equation relating them is
h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation
To find k use the condition h = 52 when a = 20, thus
52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )
1040 = k
h = [tex]\frac{1040}{a}[/tex] ← equation of variation
When a = 50, then
h = [tex]\frac{1040}{50}[/tex] = 20.8 hours
Find the values of x which satisfy the following inequation:
x3 – x² <12x
Answer:
x< -3 and 0 < x < 4
Step-by-step explanation:
x^3 – x² <12x
Subtract 12x from each side
x^3 -x^2 - 12x< 0
Factor
x( x^2 -x-12) <0
Factor
x( x-4) ( x+3) < 0
Using the zero product property
x=0 x=4 x=-3
We have to check the signs regions
x < -3
-( -) (-) < 0 True
-3 to 0
-( -) (+) < 0 False
0 to 4
+( -) (+) < 0 True
x>4
+( +) (+) < 0 False
The regions this is valid is
x< -3 and 0 < x < 4
