Answer:
$2.7
Step-by-step explanation:
Let the price of one apple be x
and the price of one orange y
Hence ;
One apple and 3 oranges would cost:
x + 3×y = $5.10----------------------------(1)
One apple and 5 oranges would cost;
x + 5×y = $7.50--------------------------(2)
Subtracting eqn (1) from (2), we have :
x-x + 5y -3y = 7.5- 5.1
2y = 2.4
y = $1.2
From eqn(1)
x + 3y = $5.10
x= $5.10-3($1.2) = $5.10-$3.6 = $1.5
Hence x=$1.5 and y= $1.2
We are required to find the cost of one apple and one orange, hence :
x+y = $1.5+$1.2= $2.7
What’s the correct answer for this?
Answer:
C: x = 10
Step-by-step explanation:
PO = QR (so having equal central angles)
Now
4x-11 = 2x+9
4x-2x = 9+11
2x = 20
Dividing both sides by 2
x = 10
Answer:
x=10
Step-by-step explanation:
2x+9=4x-11
-2x -2x
9=2x-11
+11 +11
20=2x
:2 :2
x=10
The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.25 and P(B | A2) = 0.05. (a) Are A1 and A2 mutually exclusive? They mutually exclusive. How could you tell whether or not they are mutually exclusive? P(B | A1) ≠ P(B | A2) P(A1) + P(A2) = 1 P(A1 ∩ A2) = 0 P(A1) ≠ P(A1 | A2) P(A2) ≠ P(A2 | A1) (b) Compute P(A1 ∩ B) and P(A2 ∩ B). P(A1 ∩ B) = P(A2 ∩ B) = (c) Compute P(B). (d) Apply Bayes' theorem to compute P(A1 | B) and P(A2 | B). (Round your answers to four decimal places.) P(A1 | B) = P(A2 | B) =
Answer:
(a) [tex]A_1[/tex] and [tex]A_2[/tex] are indeed mutually-exclusive.
(b) [tex]\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}[/tex], whereas [tex]\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}[/tex].
(c) [tex]\displaystyle P(B) = \frac{9}{100}[/tex].
(d) [tex]\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}[/tex], whereas [tex]P(A_1 \; |\; B) = \displaystyle \frac{4}{9}[/tex]
Step-by-step explanation:
(a)[tex]P(A_1 \; \cap \; A_2) = 0[/tex] means that it is impossible for events [tex]A_1[/tex] and [tex]A_2[/tex] to happen at the same time. Therefore, event [tex]A_1[/tex] and [tex]A_2[/tex] are mutually-exclusive.
(b)By the definition of conditional probability:
[tex]\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}[/tex].
Rearrange to obtain:
[tex]\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}[/tex].
Similarly:
[tex]\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}[/tex].
(c)Note that:
[tex]\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}[/tex].
In other words, [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive. Since [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive and mutually-exclusive at the same time:
[tex]\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}[/tex].
(d)By Bayes' Theorem:
[tex]\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}[/tex].
Similarly:
[tex]\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}[/tex].
Using probability concepts, along with conditional probability and Bayes Theorem, it is found that:
a) [tex]P(A1 \cap A2) = 0[/tex], thus yes, A1 and A2 are mutually exclusive.
b) The probabilities are: P(A1 ∩ B) = 0.05, P(A2 ∩ B) = 0.04.
c) The probability of event B is: P(B) = 0.09.
d) The probabilities are: P(A1|B) = 0.5555 and P(A2|B) = 0.4445.
-----------
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
P(B|A) is the probability of event B given that A. [tex]P(A \cap B)[/tex] is the probability of both A and B. P(A) is the probability of A.-----------
Bayes Theorem:
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
-----------
Item a:
Two events A and B are mutually exclusive if they cannot happen together.Since [tex]P(A1 \cap A2) = 0[/tex], yes, it can be said that events A1 and A2 are mutually exclusive.Item b:
Using conditional probability.
A1 and B:
[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]
[tex]0.25 = \frac{P(A1 \cap B)}{0.2}[/tex]
[tex]P(A1 \cap B) = 0.25(0.2) = 0.05[/tex]
A2 and B:
[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]
[tex]0.05 = \frac{P(A1 \cap B)}{0.8}[/tex]
[tex]P(A1 \cap B) = 0.8(0.05) = 0.04[/tex]
Item c:
P(B) is given by:
[tex]P(B) = P(A1 \cap B) + P(A2 \cap B) = 0.05 + 0.04 = 0.09[/tex]
Item d:
Applying Bayes Theorem
[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.25(0.2)}{0.09} = 0.5555[/tex]
[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.8(0.05)}{9} = 0.4445[/tex]
A similar problem is given at https://brainly.com/question/22428992
A city has a total budget of $10 million per year. It brings in $3.5 million per year
in revenues other than property taxes. Therefore, the city must generate $6.5
million in property taxes to balance its budget. The net assessed valuation of all
property in that city is $825 million. What is the percent tax rate necessary to
generate the $6.5 million? Only use two decimal places and do not round.
Answer:
0.78%
Step-by-step explanation:
The percentage tax rate required is t such that ...
825t = 6.5 . . . . . milliions of dollars
t = 6.5/825
As a percentage, ...
t = 6.5/825 × 100% = 0.7878...% ≈ 0.78%
_____
Comment on rounding
Ordinarily, this value would be rounded to 0.79%. Property tax rates are often expressed in mils, or dollars per thousand. In that form, the tax rate would be 7.88‰ when rounded to two decimal places.
Simplify –2x3y × xy2.
Question 1 options:
A)
–3x4y3
B)
–2x4y3
C)
–2x3y4
D)
–12x4y3
Answer: B. -2x^4y^3
Step-by-step explanation:
Multiply the variables by each other.
-2x^3 * x = -2x^4
y * y^2 = y^3
Answer:
B) -2x4y3
Step-by-step explanation:
Cuanto es 1× -1× es x o no?
Answer:
[tex]1^x[/tex] is always 1, so [tex]1^x-1^x=0[/tex]
es0
dame grasias
si soi nuevo
Find the value of x needed to make the equation below true.
Step-by-step explanation:
[tex]5(2x - 4) = 2(4x + 2) \\ 10x - 20 = 8x + 4 \\ 2x = 24 \\ x = 12[/tex]
Mrs. Beverly brought two quarts of juice to class.
How many cups of juice could she pour for the students?
Answer:
8
Step-by-step explanation:
1 quart=4 cups so 4x2=8
The sum of x and it’s opposite is always zero?
Answer:
1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies
2) Now let's consider any real number a no matter positive or negative we will have that:
[tex]a-a =0[/tex]
Or in the other case:
[tex]-a -(-a) =-a +a=0[/tex]
So then we can conclude that the expression is a general rule and is true
Step-by-step explanation:
For this case we can verify if the following expression is true or false:
The sum of x and it’s opposite is always zero?
If we want to proof this we need to show that for any number is true.
1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies
2) Now let's consider any real number a no matter positive or negative we will have that:
[tex]a-a =0[/tex]
Or in the other case:
[tex]-a -(-a) =-a +a=0[/tex]
So then we can conclude that the expression is a general rule and is true
72 candies are devided between ahmad, zara and bilal in the ratio 3:4:5,find the number of candies that each person will receive
Answer:
6*3 = 18 candies - Ahmad
6*4 = 24 candies - Zara
6*5 = 30 candies - Bilal
Step-by-step explanation:
3+4+5= 12 parts
72 : 12 = 6 candies is one part
6*3 = 18 candies - Ahmad
6*4 = 24 candies - Zara
6*5 = 30 candies - Bilal
Water flows from the bottom of a storage tank at a rate of r(t) = 400 − 8t liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 30 minutes.
______ Liters.
Answer:
Step-by-step explanation:
Just integrate r(t) with respect to t
Integrate r(t) dt = 400t -(4t^2)/2 + C
= 400t -4t^2 + C
where C is a constant
then replace the above answer with 30 and 0, then do subtraction for both answers
hence the amount of water flows during first 30 mins is
= {400*30 - 4*(30)^2 + C} - {400*0 - 4*(0)^2 + C}
= 12000 - 3600
= 8400 liters
The amount of water that flows from the tank during the first 30 minutes is 8,400Liters.
Based on the information definite integral will be use to find the amount of water.
Using this formula
[tex]\int_{a}^{b} r(t) dt\\\\\\Where:\\r(t)=400-8t\\\\\\ \int_{a}^{b} r(t) dt\ = \int_{0}^{30} (400-8t) dt\\\\\\\\ \int_{a}^{b} r(t) dt\ = (400t-8t^2/2)_{0}^{30}\\\\\\\\ = (400t-4t^2)_{0}^{30}\\\\\\\\=(400\times30)-4(30)^2\\\\\\=12,000-4(900)\\\\\\=12,000-3,600\\\\\\=8,400\ liters\\[/tex]
Inconclusion the amount of water that flows from the tank during the first 30 minutes is 8,400Liters.
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Another question (sorry)
Answer:
19.99
Step-by-step explanation:
First you would multiply .44 by 16 to get 7.04
then you would add 12.95 to get 19.99
The augmented matrix of a system of equations has been transformed to an equivalent matrix in​ row-echelon form. Using​ x, y, and z as​ variables, write the system of equations corresponding to the following matrix. If the system is​ consistent, solve it.
left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 2 3rd Column 2 2nd Row 1st Column 0 2nd Column 1 3rd Column negative 3 3rd Row 1st Column 0 2nd Column 0 3rd Column 1 EndMatrix Start 3 By 1 Table 1st Row 1st Column 4 2nd Row 1st Column 9 3rd Row 1st Column negative 2 EndTable right bracket
1 2 2
0 1 −3
0 0 1
4
9
−2
Which of the following system of equations corresponds to the given​ matrix?
A.
x plus 2 y plus 2 zx+2y+2z
equals=44
y minus 3 zy−3z
equals=99
z
equals=minus−22
B.
2 x plus 2 y2x+2y
equals=44
negative 3 y−3y
equals=99
z
equals=minus−22
C.
2 x plus 2 y plus 4 z2x+2y+4z
equals=1
negative 3 y plus 9 z−3y+9z
equals=1
minus−z
equals=1
D.
x
equals=44
2 x plus y2x+y
equals=99
2 x minus 3 y plus z2x−3y+z
equals=minus−22
Select the correct choice below and fill in any answer boxes in your choice.
A.
The solution set is
StartSet nothing EndSet{}.
​(Type an ordered​ triple.)
B.
The solution is the empty set.
Answer: The system of equations is:
x + 2y + 2 = 4
y - 3z = 9
z = - 2
The solution is: x = -22; y = 15; z = -2;
Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.
The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a Row Echelon Form, which satisfies the following conditions:
There is a row of all zeros at the bottom of the matrix;The first non-zero element of any row is 1, which called leading role;The leading row of the first row is to the right of the leading role of the previous row;For this question, the matrix is a Row Echelon Form and is written as:
[tex]\left[\begin{array}{ccc}1&2&2\\0&1&3\\0&0&1\end{array}\right][/tex][tex]\left[\begin{array}{ccc}4\\9\\-2\end{array}\right][/tex]
or in system form:
x + 2y + 2z = 4
y + 3z = 9
z = -2
Now, to determine the variables:
z = -2
y + 3(-2) = 9
y = 15
x + 30 - 4 = 4
x = - 22
The solution is (-22,15,-2).
Find the perimeter of the figure 35 in. 34 in. 70 in. 84 in.
Answer:
p=8in+8in+12in+7in
=35 in
Answer:
35
Step-by-step explanation:
what should be add to 7 3/5 to get 18
Answer:
[tex]10\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]7\frac{3}{5} + x = 18\\[/tex]
transformation : [tex]7\frac{3}{5} = \frac{(5*7) + 3}{5} = \frac{38}{5}[/tex]
[tex]\frac{38}{5} + x = 18\\\\x = 18 - \frac{38}{5} = \frac{(5*18) - 38}{5} = \frac{52}{5}[/tex]
[tex]\frac{52}{5} = 10\frac{2}{5}[/tex]
Answer:
[tex]10\frac{2}{5}[/tex]
Step-by-step explanation:
What should be add to [tex]7\frac{3}{5}[/tex] to get [tex]18[/tex] ?
[tex]18-7\frac{3}{5}=\\ \\=17\frac{5}{5}-7\frac{3}{5}\\\\\\=(17-7)+(\frac{5}{5}- \frac{3}{5})\\ \\=10+\frac{2}{5}\\ \\=10\frac{2}{5}[/tex]
What factoring method should be used to factor a polynomial with four terms?
Answer:
The easiest way to factor it is to use grouping.
Step-by-step explanation:
you look at only two terms at a time to see if any techniques become apparent.
The grouping factoring method should be used to factor a polynomial with four terms.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The simplest method to factor a polynomial with four or more parts is to use grouping. With this approach, you evaluate just two terms at once to determine whether any methods stand out.
Therefore, the grouping factoring method should be used to factor a polynomial with four terms.
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What 4 1/2 meters equal to
Answer:
4 1/2 meters is equal to 4.5
Step-by-step explanation:
This is the correct answer to 4 1/2 meters. :)
Mr. Patel is photocopying lab sheets for his first period class. A particle of toner carrying a charge of 4.0 * 10^9 C in the copying machine experiences an electric field of 1.2 * 10^6 N/C as it’s pulled toward the paper. What is the electric force acting on the toner particle?
Answer:
4.8 * 10^15 Newton
Step-by-step explanation:
Electric field is electric force created by a unit charge. Mathematically it is defined as
Electric field = electric force /charge in coulomb _____(1)
given
Electric field = 1.2 * 10^6 N/C
charge = 4.0 * 10^9 C
substituting above value in equation 1 we have
1.2 * 10^6 N/C = electric force/4.0 * 10^9 C
=> 1.2 * 10^6 N/C * 4.0 * 10^9 C = electric force
=> electric force = 4.8 * 10^15
Thus, electric force acting on the toner particle is 4.8 * 10^15 Newton
17 large and blue, 3 small and blue, 8 large and red, 12 small and red, how many large or blue
Answer:
28 are large or blue.
Step-by-step explanation:
In this case they ask us how many are big or blue, that is, either of the two characteristics are valid, they tell us the following things in the statement:
17 large and blue, that is, 17 comply with what they ask us, since they are blue or large.
3 small and blue, that is 3 since they are blue, and we must take them into account.
8 large and red, you have to add 8 more because there are 8 large ones here.
12 small and red, none of them meet the requested characteristics, that is, they are in total:
17 + 3 + 8 = 28
28 are large or blue.
What is the sum of V-2 and V-18?
Answer:
=2v−20
Step-by-step explanation:
Let's simplify step-by-step.
v−2+v−18
=v+−2+v+−18
Combine Like Terms:
=v+−2+v+−18
=(v+v)+(−2+−18)
=2v+−20
Answer:
=2v−20
A sphere has a diameter of 14 ft. Which equation finds the volume of the sphere?
V=4/3(7)^3
V=4/3 3.14(7)^3
V=4/3(14)^3
V=4/3 3.14(14)^3
Given that y varies directly with x, use the values specified to write a
direct variation equation relating y to x.
x = -19, y = 190
Use your answer to find x when y = -9.
Answer:
(a)y=-10x
(b)x=0.9
Step-by-step explanation:
If y varies directly with x, we write:
[tex]y \propto x\\y=kx$ where k is the constant of proportionality.\\If $x = -19, y = 190\\190=-19k\\$Divide both sides by -19\\k=190 \div -19\\k=-10\\[/tex]
Therefore, a direct variation equation relating y to x is:
(a)y=-10x
(b)When y=-9
Substituting y=-9 into the equation obtained in (a) above
[tex]-9=-10x\\$Divide both sides by -10$\\x=-9\div -10\\x=0.9\\$Therefore, when $ y=-9, x=0.9[/tex]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. The graph cross the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10
Step-by-step explanation:
→Looking at the line as it increases, you can see that it intersects at the point of (0, 5) on the y-axis.
→The line on the graph is increasing from the point where x = -10, and stops at x = 2.
→The line then stays constant (basically meaning it doesn't increase/decrease, making it a horizontal line), strting from x = 2, to x = 10.
Looking at the points above, you can determine that the correct answer is "B. The graph cross the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10."
a bag contains 8 red balls and 6 green balls. michelle randomly draws 3 balls from the bag. she does not replace the balls after each draw. what is the probability that she draws 2 red balls and 1 green ball
Answer:
Red balls 2/14
Green balls 1/14
Step-by-step explanation:
I hope that helped.
The following table shows a proportional relationship between www and zzz.
www zzz
181818 222
454545 555
818181 999
Write an equation to describe the relationship between www and zzz.
Answer:
z=1/9w
Step-by-step explanation:
Equation w = 9z best describes the proportional relationship between w and z.
Data has been given
w = 18 45 81
z = 2 5 9
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.
Clearly from the data as z increases w increases so it implies w is directly proportional to z.
w ∝ z
w = kz - - - - - - (1)
Where k is proportionality constant.
From data put w = 18 and z = 2
18=k*2
k=18/2
k=9
put k in equation w =kz
w = 9z
It shows that w is directly proportional to z by the constant of proportionality 9.
Thus equation w = 9z best describes the proportional relationship between w and z.
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please help plzzzzzzzzzzzzzzzzzzzz
Answer: C,D are true
Step-by-step explanation:
Answer:
Step-by-step explanation:
C and D are both true the rest are false
which of the following questions are identities? Check all that apply
Answer:
all I see is a black image
question is attached
Answer:
The centroid is 1/3 of the vertical distance between QV
QV = 3 x VT = 3 x 5 = 15
QT = 15-5 = 10
If the terminal ray of β lies in the fourth quadrant and sin (β) = -√3/3 determine cos(β) in simplest form.
I really appreciate your help, please help.
Thank you
God bless
Answer:
cos(β) = √6/3
Step-by-step explanation:
Given β lies in the fourth quadrant and sin (β) = -√3/3
we know that the trigonometry formula
sin²(β)+cos²(β) = 1
cos²(β) = 1- sin²(β)
cos²(β) = 1- ( -√3/3)²
= [tex]1-\frac{3}{9} } } =\frac{6}{9}[/tex]
cos(β) = √6/9 = √6/3
we Know that β lies in the fourth quadrant so cos(β) is Positive
cos(β) = √6/3
5. A cyclist and bike have a total mass of 102 kg and a speed of 17 m/s.calculate the kinetic energy?
Answer:
14739
Step-by-step explanation:
1/2mv^2
1/2*105*17*17
=14739
Use long division to find quotient below
the answer is in the photos
