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Work Shown:
Given info
P(A) = 7/20
P(A∩B)=49/400
P(B) = unknown
--------------------
P(A∩B) = P(A)*P(B), assuming A and B are independent events
49/400 = (7/20)*P(B)
(7/20)*P(B) = 49/400
P(B) = (20/7)(49/400)
P(B) = (20*49)/(7*400)
P(B) = (20*7*7)/(7*20*20)
P(B) = 7/20
---------------------
Note how
P(A∩B) = P(A)*P(B)
P(A∩B) = (7/20)*(7/20)
P(A∩B) = (7*7)/(20*20)
P(A∩B) = 49/400
which helps to confirm the answer.
Two shirt screening companies charge a set up fee and a charge for each shirt made.
The table shows the total costs for the company Shirt Express. The total costy (in
dollars) for x shirts made by Shirt Custom is represented by the equation y = 8x + 50
Answer:
The correct option is;
Shirt Express charges less per shirt. For the cost to be the same 74 shirts must be ordered
Step-by-step explanation:
1) The given table for Shirt Express can be used to find the equation of the total cost of each made by Shirt Express as follows;
The rate of change of the function m is given as follows;
[tex]m = \dfrac{y_2 - y_1 }{x_2 - x_1}[/tex]
Therefore, we have;
m = (438 - 353)/(50 - 40) = 8.5
Te equation in slope and intercept form is then y - 438 = 8.5(x - 50)
From which we have;
y = 8.5·x - 8.5×50 + 438 = 8.5·x + 13
y = 8.5·x + 13
Therefore, Shirt Express initially charges 13 per shirt which is less than the 50 Shirt Custom charges
2) the cost to be the same, we equate both shirts equations to get;
8.5·x + 13 = 8·x + 50
0.5·x = 50 - 13 = 37
x = 37/0.5 = 74 shirts
Therefore, for the cost to be the same 78 shirts must be ordered
The difference between a number squared, and that same number is 30. What is the number
Answer:
n^2 = n + 30
n^2 -n -30 = 0
Solving by quadratic formula
numbers equal 6 AND -5
DOUBLE -CHECK
6^2 -6 -30 = 0
36 -6 - 30 = 0 CORRECT
-5^2 - -5 -30 = 0
25 +5 -30 = 0 CORRECT
Two numbers 6 and -5
Step-by-step explanation:
Mr. Johnson hired a contractor to build a small deck on the back of his house. The cost of materials alone added to $678.12. When he received the final bill from the contractor, the total amount charged was $1206.12. Verify the accuracy of this bill if labor amounted to 16.5 hours at $32 an hour
Answer:
Yes, the bill is absolutely accurate
Step-by-step explanation:
Cost of materials= $ 678.12
Final bill amount(given)=$1206.12
Rate= $32 per hour for 16.5 hrs
Total amount for 32 hrs = time * rate = 16.5* 32=$528
Therefore, by the problem ,
Cost of materials+ Total amount for 32 hrs = Final bill amount
= 678.12+ 528
=1206.12
Therefore , the final bill amount is 100% accurate as it completely matches with the given bill amount
What is the sum to 'n' terms of the series √5,√20,√45,√80,.....?
Answer:
Sₙ = √5/2 n (n + 1)
Step-by-step explanation:
Given AP:
√5,√20,√45,√80,...Rewriting as:
√5,√4*5,√9*5,√16*5,...√5, 2√5, 3√5, 4√5,..., n√5Common difference:
d= 2√5 - √5 = √5Sum of n terms:
Sₙ = 1/2n (a₁ + aₙ) =1/2n (√5 + √5 + (n-1)√5) =1/2n (n + 1)√5=√5/2 n (n + 1)Sₙ = √5/2 n (n + 1)
Find the slope that passes through (9, 4) and (7, 7) simplify your answer and write it as a proper fraction, improper fraction, or integer
Answer:
m= =3/2
Step-by-step explanation:
(9,4) (7,7)
m= y2-y1/x2-x1
m=7-4/7-9
=3/-2
=-3/2
What two numbers should you break 10 down to ?
Answer:
5
Step-by-step explanation:
Answer:
perhaps 2 and 5 depending on what you are asked to do
Step-by-step explanation:
10 can be broken down into 2 and 5 if you are looking for prime factors.
Area of a circle- pls pls pls help me- I'll give Brainly answer and big points.
Answer: The answer is 12.57 because the formula is The area of a circle is pi times the radius squared (A = π r²). Hope this helps.
Step-by-step explanation:
simplify (x)^3(-x^3y)^2
Answer:
[tex] {x}^{3} \times {x}^{6y } = {x}^{3 + 6y} [/tex]
Answer: x^9 y^2
the way it works is you need to multiply the x's then answer
¿Cuál propiedad de los números complejos se muestra a continuación?
(2+31)+(5 - 41)=(5-41)+(2+31)
A asociativa
B distributiva
C inverso aditivo
D conmutativa
Answer:
D) conmutativa
Step-by-step explanation:
Propiedad conmutativa: Cuando se suman o multiplican dos números, la suma o el producto es el mismo independientemente del orden en que
los números se suman o multiplican.
Se da como:
a + b = b + a
a × b = b × a
Propiedad distributiva: La suma de dos números por un tercer número es igual a la suma de cada número sumado por el tercer número. Se da como:
a × (b + c) = (a × b) + (a × c)
Propiedad asociativa: Se da como:
a + (b + c) = (a + b) + c
a × (b × c) = (a × b) × c
Propiedad inverso aditivo: Se da como
a + (-a) = 0
if band practice is 4:00p.m how many min do i have to untill band practice if its 3:40
Answer:
20 minutes
4:00 - 3:40 = 20 minutes
Answer:
20 minutes
Step-by-step explanation:
The number of rainbow smelt in Lake Michigan had an average rate of change of −19.76 per year between 1990 and 2000. The bloater fish population had an average rate of change of −92.57 per year during the same time. If the initial population of rainbow smelt was 227 and the initial population of bloater fish was 1,052, after how many years were the two populations equal? The linear function that models the population of rainbow smelt is y1 = −19.76x + 227, where x = the years since 1990 and y1 = the number of rainbow smelt. The linear function that models the population of bloater fish is y2 = . The linear equation that determines when the two populations were equal is –19.76x + 227 = –92.57x + 1052 . The solution is x = years.
Answer:
x= 11.33 years
Step-by-step explanation:
Y1= −19.76x + 227
Y2= = –92.57x + 1052
Y1 = Y2
–19.76x + 227 = –92.57x + 1052
Collect like terms and Simplify
-19.76x + 92.57x = 1052 - 227
72.81x = 825
Divide both sides by 72.81
x= 825 / 72.81
=11.33 years
Therefore,
x= 11.33 years
The solution for x is 11.33 years.
Given,
The linear function that models the population of rainbow smelt is[tex]y_{1} = -19.76x + 227[/tex]
The linear function that models the population of bloater fish is [tex]y_{2} =-92.57x + 1052[/tex]
Since, According to the question,
[tex]y_{2}=y_{1}[/tex]
[tex]-19.76x + 227 =-92.57x+1052[/tex]
On solving for x
[tex]-19.76x + 92.57x = 1052 - 227[/tex]
[tex]72.81x = 825[/tex]
Divide both sides by 72.81
[tex]x= \dfrac{825}{72.81}[/tex]
[tex]x=11.33 \ years[/tex]
Hence the solution for x is 11.33 years.
For more details follow the link:
https://brainly.com/question/11897796
What is the speed of a sailboat traveling 120m in 60s?
A sailboat traveling 120m in 60s is 20.
Find the surface area and volume for the following composite figure.
Step-by-step explanation:
volume = lbd + πr²h
l = 12 , b = 7 , d = 4 , r = 3 and h = 10
V = 336 + 90π
surface area = [2(lb + ld + bd) - πr²] - [2πrh + πr²]
= 320 - 9π - 60 - 9π
= 260 - 18π
Find the measure of b. A. 80 B. 70 C. 40 D. 20
Answer:
40°
Step-by-step explanation:
e = 20°
d = 20°
c = 140°
b = 40°
If one angle in the circle is 20° then the measure of b is 40°.
What is alternate exterior angle?Alternate exterior angles are those angles which are formed when two parallel lines are intersected by a transversal line and angle formed outside is known as alternte exterior angles.
How to find angle?When we observe the angles then we can say that d and 20° angles are alternate exterior angles. We can say that b=2d.So we have to put the value of d in the above formula to get the value of b.
b=2*20
=40°
Hence if one angle in the circle is 20° then the measure of b is 40°.
Learn more about alternate exterior angles at https://brainly.com/question/2398628
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please do the steps solve the equation for d: 1/6d-8=5/8 2. Solve the equation for x: 3x-4+5x=10-2z 3. Solve the equation for c: 7(c-3)=14 4. Solve the equation for m: 11(m/22+3/44)=87m+m 5. Solve the equation for k: ck+5k=a
Step-by-step explanation:
1. 1/6d - 8 = 5/8
1/6d -8 + 8 = 5/8 + 8
1/6d = 69/8
1/6d / 1/6 = 69/8 / 1/6
d = 51.75 or [tex]51\frac{3}{4}[/tex]
2. 3x - 4 + 5x = 10 - 2z
8x - 4 = 10 - 2z
8x - 4 + 4 = 10 - 2z + 4
8x = 14 - 2z
8x / 8 = (14 - 2z) / 8
x = [tex]\frac{14 - 2z}{8}[/tex]
3. 7(c - 3) = 14
7(c - 3) / 7 = 14 / 7
c - 3 = 2
c - 3 + 3 = 2 + 3
c = 5
4. 11(m / 22 + 3 / 44) = 87
m / 22 + 3 / 44 = 87 / 11
m / 22 + 3 / 44 = 348 / 44
m / 22 = 345 / 44
m = 172.5
5. ck + 5k = a
k(c + 5) = a
k = [tex]\frac{a}{c+5}[/tex]
Which of the following are identities? Check all that apply.
Answer:
b
Step-by-step explanation:
thats funny i just did that
Answer: check all the answers except cos(x+y)+cos(x-y)=cos^2 x-sin^2 y
Step-by-step explanation:
took the test and hopefully mine was the same as the image above
what property is 16=16
Find the measure of b. A. 105 B. 100 C. 75 D. 80
Answer:
B 100.
Step-by-step explanation:
The measure of the angle opposite to the 100 degree angle = 180 - 100 = 80 degrees (The opposite aNGLES IN A CYCLIC QUADRILATERAL are supplementary).
S0 b = 180 - 80 = 100 degrees (adjacent angles are supplementary).
Answer:
B
Step-by-step explanation:
im smart
3/2y-3+5/3 z when y =6 and z= 3
Answer:
Step-by-step explanation:
Plug in the value of y & z in the expression
[tex]\frac{3}{2}y-3+\frac{5}{3}z=\frac{3}{2}*6-3+\frac{5}{3}*3\\\\\\=3*2 - 3 + 5 *1\\\\\\= 6 - 3 + 5\\\\\\= 3 + 5\\\\\\= 8[/tex]
Answer: 11
Step-by-step explanation:
If y=6 and z=3 then your problem will look like this : 3/2(6) - 3 + 5/3(3)
Put both 6 and 3 over 1 to turn them into a fraction and then multiply
3/2 multiplied by 6/1 is 18/2 which reduces to 9
5/3 multiplied by 3/1 is 15/3 which reduces to 5
Then your problem will look like this : 9 - 3 + 5
Follow order of operations and add and subtract from left to right
9 - 3 is 6 and 6 + 5 is 11
So your answer is 11
A model of an airplane is 19 in. long. The actual plane is 152 ft. long. What is the scale of the model?
Answer:
1 in : 8 ft or 1 : 96
Step-by-step explanation:
The scale is the ratio of model dimensions to actual dimensions:
19 in : 152 ft = 1 in : 8 ft = 1 in : 96 in = 1 : 96
__
The scale can be expressed in mixed units as 1 in : 8 ft, or it can be expressed as the pure ratio 1 : 96.
if 3x+5/x-=16, what is x?
Answer:
x=5, x= 1/3
Step-by-step explanation:
Answer :
[tex]x = \frac{1}{3} \\ x = 5[/tex]
my liTTLE COUSIN needs help cAN someone answer this for her? thx bebe!!! : Kyle has run 7 laps around the track. If he plans to run 15 laps, how many more laps must he run?
Answer:
8
Step-by-step explanation:
15-7= 8
Answer:
8 laps
Step-by-step explanation:
We know that Kyle has already run 7 laps, and that he wants to run 15 laps. To find the answer, we need to think, "How much more is 15 than 7?" To find the answer, we simply can do 15 - 7 = 8 laps.
What is the range of the following set of measurements?
"24.35 cm, 22.51 cm, 20.98 cm, 20.98, 30.33 cm, 30.98 cm"
The range is
cm.
Answer:
The range is 10 cm.
Step-by-step explanation:
The range of a set is the difference of the largest and smallest values of the set. Looking at the data, we see that 30.98 cm is the largest value and 20.98 is the smallest value so the range is 30.98 - 20.98 = 10 cm.
Answer:
The answer is
10 cmStep-by-step explanation:
To calculate the range in a given set of data subtract the lowest observation from the highest observation
From the question
The highest measurement = 30.98 cm
The lowest measurement = 20.98 cm
So the range is
30.98 cm - 20.98 cm
We have the final answer as
10 cmHope this helps you
how to do this question plz answer me step by step plzz plz
Answer:
adult cost £7, child cost £2
Step-by-step explanation:
let a represent an adult and c a child , then
2a + 3c = 20 → (1)
a + 4c = 15 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate a
- 2a - 8c = - 30 → (3)
Add (1) and (3) term by term to eliminate a, that is
- 5c = - 10 ( divide both sides by - 5 )
c = 2
Substitute c = 2 into either of the 2 equations and evaluate for a
Substituting into (2)
a + 4(2) = 15
a + 8 = 15 ( subtract 8 from both sides )
a = 7
The cost of an adult ticket is £7 and a child ticket is £2
round 5.659 to the nearest hundredth
Answer:
Your answer will be 5.66
In the triangle below y=? Round to the nearest tenth
Answer:
y = 51.3°Step-by-step explanation:
To find y we use tan
tan∅ = opposite/ adjacent
From the question
8 is the adjacent
10 is the opposite
Substitute the values into the above formula
That's
[tex] \tan(y) = \frac{10}{8} [/tex]
[tex]y = \tan^{ - 1} ( \frac{10}{8} ) [/tex]
y = 51.34019
We have the final answer as
y = 51.3 to the nearest tenthHope this helps you
The Sides of regular octagon T are three time the length of the sides of regular octagon G
Answer:
According to the statement, the equation is :
Sides of regular octagon T= 3 × the length of sides of regular octagon G
The required equation is x = 3y
Where x is the length of the sides of the octagon T and y is the length of the side of the octagon G.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 5 - 9 is an equation.
We have,
Sides of regular octagon T = x
Sides of regular octagon G = y
Now,
The equation of the sides of regular octagon T is three times the length of the sides of regular octagon G can be written as:
x = 3y
Thus,
The equation is x = 3y.
Learn more about equations here:
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For k= -3 and n= -4, -K2 - (9k – 3n) + 6n=
(Simplify your answer.)
Answer: -(-3)2-(9(-3)-3(-4))
6+27-12
Step-by-step explanation:
Two negatives make a positive and a negative times a positive is negative
в коком году родился пушкин
Answer:
May 26, 1799
Step-by-step explanation:
y=-3x + 4; y=-3x + 40
Is it parallel or perpendicular