Answer: [tex]\dfrac{11}{36}[/tex]
Step-by-step explanation:
Total outcomes for rolling a pair of six-sided dice n(S)= 6 x 6 =36
Let A be the event that the first die is one and B be the event that the sum of the dice is eight.
A = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)}
P(A)= [tex]=\dfrac{n(A)}{n(S)}=\dfrac{6}{36}[/tex]
B= {(2,6), (6,2), (3,5), (5, 3), (4,4)}
P(B)= [tex]=\dfrac{n(B)}{n(S)}=\dfrac{5}{36}[/tex]
A ∩ B = Ф
P(A ∩ B)=0
P(A or B)= P(A)+P(B)+P(A∩ B)
[tex]=\dfrac{6}{36}+\dfrac{5}{36}+0\\=\dfrac{11}{36}[/tex]
Hence, P(A or B) = [tex]\dfrac{11}{36}[/tex]
Which property is represented below? 12+(8+5)=(12+8)+5
A. Associative property of addition
B. Associative property of multiplication
C. Commutative property of addition
D. Commutative property of multiplication
Help I’m being timed
Answer:
its always the third one
Step-by-step explanation:
Have a good day
Answer:
I would say 32 but I'm not sure
Step-by-step explanation:
How much is 20% off of $90.75?
- {(-3, 3), (1, 1), (0, -2), (1,-4), (5, -1)}
Function?
Answer:
Step-by-step explanation:
It is not a function. (1,1) and (1,-4) are both points on the graph.
A large mixing tank initially contains 1000 gallons of water in which 40 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 5 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 3 pounds of salt per gallon. If img represents the amount of salt in the tank at time t, the correct differential equation for A is:______.
A) dA/dT=3--.005A
B) dA/dT=5--.05A
C) dA/dT=15--.005A
D) dA/dT=3--.05A
E) dA/dT=15+.05A
Answer:
If A(t) represents the amount of salt in the tank at time t, the correct differential equation for A is is dA/dt = 15 - 0.005A
Option C) dA/dt = 15 - 0.005A is the correction Answer
Step-by-step explanation:
Given the data in the question;
If A(t) represents the amount of salt in the tank at time t, the correct differential equation for A is?
dA/dt = rate in - rate out
first we determine the rate in and rate out;
rate in = 3pound/gallon × 5gallons/min = 15 pound/min
rate out = A pounds/1000gallons × 5gallons/min = 5Ag/1000pounds/min
= 0.005A pounds/min
so we substitute
dA/dt = rate in - rate out
dA/dt = 15 - 0.005A
Therefore, If A(t) represents the amount of salt in the tank at time t, the correct differential equation for A is is dA/dt = 15 - 0.005A
Option C) dA/dt = 15 - 0.005A is the correction Answer
If b = -3, find
answer
Answer:
-2
Step-by-step explanation:
[tex](-3)^2+3(-3)-2\\=9-9-2\\=-2[/tex]
Valencia is solving this number riddle using guess and check. What number multiplied by eight is equal to forty? Valencia must find . To use guess and check, Valencia can different numbers by . multiplied by eight is equal to forty.
Answer:
first one is A second on is C third is B fourth is B HOPE THIS HELPS
Answer:
1. A
2.C
3.B
4.B
Step-by-step explanation:toke test
What is the quotient of 9.75÷1.3
Answer:
7.5
You know, you can just use a calculator.
3/8x5/4 Helpppppp pls
Answer:
9/25 or .36
Step-by-step explanation:
5(4n) simplify the equation
1. Simplify by multiplying 5 * 4.
20n
----------
Done by NeighborhoodDealer.
I need to Mach the answers to the questions please help
Answer:
1a. 3y = 18
1b. y + 7 = 18
1c. 2y + 4 = 18
Step-by-step explanation:
In each case, let's take the red boxes to be constant why the the green boxes represents the variable, y.
Thus,
1a. There are only 3 green boxes which gives us 18, therefore, the equation that expresses this would be:
3y = 18
1b. We have 7 red boxes which represents the constant, 7.
We also have 1 green box which represents the variable, y. Therefore, the equation that expresses this would be:
y + 7 = 18
1c. We have 4 red boxes = 4
We have 2 green boxes = 2y
Therefore, we would have:
2y + 4 = 18
blank tens 15 ones = 6 tens 5 ones
Step-by-step explanation:
_x_tens 5 ones=6tens 5 ones
5x=65
x=65/5
x=13
sorry i donot get answer at 15 ones.
Sandra deposited $2,500 into a simple interest account.
She earned $ 75 in interest after 11 year.
Ron deposited $8,000 into an account that has the same interest rate as Sandra’s account.
How much money did Ron earn in interest after 11 year?
Show your work.
Answer:
240$
Step-by-step explanation:
we know that
The simple interest formula is equal to
I=P(rt)
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
Sandra
t = 1 year
I= $75
P= $2,500
r= ?
substitute in the formula above
75=2,500 (r(1))
solve for r
r=75/2,500)
r= 0.03
Convert to percentage form
r= 0.03 * 100 = 3%
Ron
t=1 year
I = ?
P= 8,000
r= 0.03
substitute in the formula of interest
I = 8,000(0.03 *1)
I = $240
~!!!!! PLEASE HELP IM IN 7TH GRADE LEARNING 9TH AND 8TH GRADE MATH !!!!~
QUESTION SORRY ITS SMALL*
Answer:
Taylor charges $5 more than Lucy for 2.5 hours.
Step-by-step explanation:
You need to find how much Taylor charges for 2.5 hours and how much Lucy charges for 2.5 hours.
Taylor:
$15 for first hour and then $10 for each hour r fraction of an hour.
Taylor charges $15 for the first hour.
Then the time remaining is 2.5 hours - 1 hour = 1.5 hours.
The charge for an hour or fraction of an hour after the first hour is $10 per hour.
1.5 hours * $10/hour = $15
Total charge for Taylor: $15 + $15 = $30
Lucy:
Lucy charges according to the function that we are shown.
According to the function, we need the middle equation since that is the one that includes 2.5 hours which is between 2 and 4 hours.
Th function that includes x = 2.5 hours is
f(x) = 10x
Since the number of hours is 2.5, then x = 2.5, and we evaluate the function for x = 2.5.
f(x) = 10x
f(2.5) = 10(2.5)
f(2.5) = 25
Lucy charges $25 for 2.5 hours.
Taylor charges $30. Lucy charges $25.
The difference is $30 - $25 = $5.
Answer: Taylor charges $5 more than Lucy for 2.5 hours.
I have data with 2 independent variables measuring the effectiveness of 3 different antibiotics at different dosages. I don't know if I should use a bar graph or line graph
Which inequality is true if p = 2.8?
Complete question :
Which inequality is true if p = 2.8?
3p < 10.2
13.6 ≤ 3.9p
5p > 17.1
8.5 ≥ 2.5p
Answer:
3p < 10.2
8.5 ≥ 2.5p
Step-by-step explanation:
To obtain the true expression, put p = 2.8 in all the options and choose the true inequality expression :
3(2.8) < 10.2
8.4 < 10.2 ( true)
13.6 ≤ 3.9p
13.6 ≤ 3.9(2.8)
13.6 ≤ 10.92 ( False)
5p > 17.1
5(2.8) > 17.1
14 > 17.1 ( False)
8.5 ≥ 2.5p
8.5 ≥ 2.5(2.8)
8.5 ≥ 7 (True)
Don’t mind the check make but which statement describes the error the student made in simplifying the equation
Answer:
i think A sorry i dont know for suee
1. The ratio of 2h to 30min is
A. 1:15
B. 4:1
C. none of these
Answer:
B. 4:1
Step-by-step explanation:
Since its 2 hours:30 minutes, in hours that is 2:1/2. So then if you want it in whole numbers you just multiply 2:1/2× 2 which would be 4:1.
find the value of each expression when z=1,when z=2 and when z =3. then identify which expression are equivalent. 9z - 4-3z and 2(3z-2) and 9z-4z-3
Answer: the answer is :z^3+5z-7
Step-by-step explanation:
How long would it take the money to triple in value, if it is continuously compounding at 18% ?
Answer:
therefore t = 1.0986122887 0.06 = 18.31 hence to the nearest year, it will it take 18 years for an investment to triple, if it is continuously compounded at 6 % per year.
Step-by-step explanation:
Solve For X. Please add an explanation.
Answer:
Your answer is 2.5
Hope that this is helpful. Vote and like it
The Maryland State Department of Education reports that 12% of the high school students in that state attend private high schools. The University of Maryland wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools. They select a random sample of 450 applications, and find that 46 of those students attend private schools.
The question is incomplete. Here is the complete question.
The Maryland State Department of Education reports that 12% of the high school students in that state attend private high schools. The University of Maryland wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 application on file to estimate the percentage of students applying for admission who attend private schools. They select a random sample of 450 applications, and find that 46 of those students attend private schools. Create and interpret a 95% confidence interval.
Answer and Step-by-step explanation: Th proportion of students that attend private schools in the sample is
[tex]p=\frac{46}{450}[/tex]
p = 0.102
At 95% confidence, z-score is 1.96.
Standard deviation for sample proportion is calculated as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
For this sample, it will be
[tex]\sigma = \sqrt{\frac{0.10(1-0.1)}{450} }[/tex]
[tex]\sigma=\sqrt{0.0002}[/tex]
[tex]\sigma=0.01414[/tex]
Interval is calculated as
p ± zσ
Then
0.102 ± 1.96(0.01414)
0.102 ± 0.028
Interval is 0.074 < p < 0.13
What confidence interval means is that with a certainty of 95%, we are confident that the true population proportion of students who attend private schools are between 0.074 and 0.13.
Express g(x) = x4 + 2x3 − x2 + 4x + 12 as the product of linear and irreducible quadratic terms.
Rachel received 5/8 of the 72 vote cast for class president. How many votes did she receive
Answer: Rachel recieved 45 votes.
Step-by-step explanation: Any easy way to solve this is to has the demonimator equal the total amount of votes. So in the questions, 8 is the denominator and 72 is the total amount of votes. To get from 8 to 72, you need to multiple 8 by 9. And whatever you do to the denominator, you must do to the numerator. So, 5 times 9 equal 45 which is the number of votes Rachel recieved.
Stefani received a loan for $2,000 and now has acquired $720 in interest. If she pays an annual interest of 4.5% on the amount borrowed. how much time has elapsed since Stefani received the loan?
Answer:
8 years.
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4.5%/100 = 0.045 per year,
then, solving our equation
t = 720 / ( 2000 × 0.045 ) = 8
t = 8 years
The time required to
accumulate simple interest of $ 720.00
from a principal of $ 2,000.00
at an interest rate of 4.5% per year
is 8 years.
what phrases describes the expression of 16-y
What phrases describes the expression of 16-y
Answer: -9
Hope this helps~
the mean of four numbers is 9 what is the total of the four numbers?
Answer:
36
Step-by-step explanation:
36/4 = 9 wish this helps!
Choose 5 cards from a full deck of 52 cards with 13values (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 kinds(spade, diamond, heart, and club). Count how many possible ways to geta(a)Two-pairs: Two pairs plus another card of a different value, for example:(b)Flush: five cards of the same suitbutdifferent values, for example: (c)Full house: A three of a kind and a pair, for example: (d)Four of a kind: Four cards of the same value, for example:
Answer:
a) 182 possible ways.
b) 5148 possible ways.
c) 1378 possible ways.
d) 2899 possible ways.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question, we have that:
There are 52 total cards, of which:
13 are spades.
13 are diamonds.
13 are hearts.
13 are clubs.
(a)Two-pairs: Two pairs plus another card of a different value, for example:
2 pairs of 2 from sets os 13.
1 other card, from a set of 26(whichever two cards were not chosen above). So
[tex]T = 2C_{13,2} + C_{26,1} = 2*\frac{13!}{2!11!} + \frac{26!}{1!25!} = 182[/tex]
So 182 possible ways.
(b)Flush: five cards of the same suit but different values, for example:
4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So
[tex]T = 4*C_{13,5} = 4*\frac{13!}{5!8!} = 5148[/tex]
So 5148 possible ways.
(c)Full house: A three of a kind and a pair, for example:
4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).
3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So
[tex]T = 4*C_{13,3} + 3*C_{13.2} = 4*\frac{13!}{3!10!} + 3*\frac{13!}{2!11!} = 1378[/tex]
So 1378 possible ways.
(d)Four of a kind: Four cards of the same value, for example:
4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).
1 from the remaining 39(do not involve the kind chosen above). So
[tex]T = 4*C_{13,4} + C_{39,1} = 4*\frac{13!}{4!9!} + \frac{39!}{1!38!} = 2899[/tex]
So 2899 possible ways.
Last year at Sarah's bakery she sold 38 birthday cakes for $57 per cake . She spent 1/2 of that money on ingredients for baking the cakes . How much money did she spend on ingredients for the cakes ?
Answer:
They are right
Step-by-step explanation:
Because
They
Are !!
2+5x+1/2x^3dx
Answer
Answer:
[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}+C[/tex]
Step-by-step explanation:
I notice you have a dx at the end of the equation, this leads me to believe this is an integral. With no bounds of integration, I will solve for the indefinite integral. I will also interpret your equation as follows:
[tex]\int \:2+5x+\frac{1}{2}x^3dx[/tex]
Sum rule tells us:
[tex]\int \:2dx+\int \:5xdx+\int \frac{1}{2}x^3dx[/tex]
From this we get:
[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}[/tex]
Don't forget to add the constant!
[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}+C[/tex]