Answer:
P(one number is a multiple of 4 and the other is a multiple of 6) = 1/18
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Desired outcomes:
One multiple of 4 and one multiple of 6.
2 possible outcomes: (4,6) or (6,4)
Probability:
2 outcomes out of 36, so:
[tex]p = \frac{2}{36} = \frac{1}{18}[/tex]
Then
P(one number is a multiple of 4 and the other is a multiple of 6) = 1/18
If Roger were 32 years older, he would be three times as old as he is now. How old is
Roger?
Answer:
16
Step-by-step explanation:
Set up the equation ->
x+32=3x
(you can get this easily by writing the equation down as you read the problem)
--> revisiting x+32=3x
-x on both sides to isolate the number and put the like terms together
We are left with 32=2x
Divide 2 on both sides, and you will get x (his current age) --> x=16
Roger is currently 16 years old.
Answer:
16
Step-by-step explanation:
3x = 32 + x
2x = 32
x = 16
3.3 A circle has a radius of 12cm. An angle of 3.2 radians is subtended at the centre by an arc. Calculate the length of the arc. (3)
Answer:
S = 38.4 centimeters.
Step-by-step explanation:
Given the following data;
Radius, r = 12 cmAngle = 3.2 radsTo find the length of the arc of a circle;
A full circle measures an angle of 360 degrees.
π = 180°
So; Angle, A = 360° = 2π
Therefore, a full circle is equal to 2π in terms of radians (rads).
Also, the circumference (the length of an arc) of a circle is equal to 2πr or Ar.
Mathematically, the length of the arc of a circle is given by the formula;
S = rA
Where;
S is the length of the arc.A is the angle measured in radians.Substituting into the formula, we have;
S = 12 * 3.2
S = 38.4 centimeters.
A boy's mother was 32 years old when he was born. Let a represent the boy's age and m represent the mother's age.
Complete the table using the relationship between a and m.
PLEASE ANSWER!!!!
see the picture attached
A triangle is rotated 90º about the origin. Which rule describes the transformation?
Solve the equation for all values of xx.
−3x(x−3)(x 2 +16)=0
Answer:
x = 0 or x = 3
Step-by-step explanation:
-3x(x-3)(x^2+16)=0
3x = 0
x-3 = 0
x^2+16 =0 (not possible with real numbers)
x = 0, x= 3
Hence,
x = 0 or x =3
Feel free to mark this as brainliest :D
In a class of 5 , there are 3 students who have done their homework. If the teacher 2 chooses 2 2 students, what is the probability that none of them have done their homework?
Answer:
2 over 5
Step-by-step explanation:
This means out of 5 students only three did their work so 5-3=2
And the number of students who did their work over the total number of students in the class to find the probability
The probability that none of them have done their homework is 0.57%
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We are given that there are 3 students who have done their homework.
If the teacher 2 chooses 2 students, then;
Total no. of Outcomes= 5
Students who did their homework = 3
Students who didn't do their homework is 5-3 = 2
Probability of no. of students who haven't done their homework.
P(e)= 2/5
Thus P(students who haven't done homework) P(e)=0.57%
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One month Ivanna rented 7 movies and 9 video games for a total of $80. The next month she rented 5 movies and 3 video games for a total of $34. Find the rental cost for each movie and each video game.
Answer:
each movie costs $2.75, each video game costs $6.75
Step-by-step explanation:
x = movies, y = video games
7x + 9y = 80
5x + 3y = 34
simplified to
x = 11/4 , y = 27/4
write the following decimal number in word 0.969?
Answer:
nine hundred sixty
nine thousandths
Step-by-step explanation:
n-1 increased by 110%
Answer:
2.1n-2.1
Step-by-step explanation:
The increase is
1.10 (n-1)= 1.1n -1.1
Add this to the original amount
(n-1) + 1.1n - 1.1
2.1n-2.1
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
f(x) = −16x2 + 24x + 16
what is the vertex
Answer:
VERTEX: (0.75,25)
Step-by-step explanation:
the vertex will be at [-b/2a, f(-b/2a)]
−16x2 + 24x + 16
4(-4x^2 + 6x +4)
a = -4, b=6,c=4
-6/-8 = 3/4
f(3/4) = 25
Alonzo finish history assignment and 5/8 hours then he completed his math assignment and 1/3 hours what was the total amount of time allowed to spend doing these two assignments
Step-by-step explanation:
The answer is 5/8 + 1/3
Answer = 5*3 /(8*3) +8/24 =23/24
Answer = 23/24
7
10 points
A6-sided die is rolled. Find P(3 or 5).
O 1
1
36
2
2
1
3
3
6
Answer:
I think the answer is 1/3
Step-by-step explanation:
1/6+1/6
=2/6=1/3
Answer:
1/3
Step-by-step explanation:
The possible outcomes are 1,2,3,4,5,6
The good outcomes are 3 and 5 = 2 good outcomes
P(3 or 5) = number of good outcomes / total outcomes
= 2/6 = 1/3
Wilbur spent $27 on a magazine and some notepads. If the magazine cost $3 and
each notepad cost $3, then how many notepads did he buy?
A) 11
B) 9
C) 8
D)12
Answer:
d 12
Step-by-step explanation:
27-3=24÷3=12 do the mathssssss
Answer:
If it was 11, it would be 33 dollars which is over the total so its not a.
It can't be b because that would be 27, and that would be on just notebooks not magazine
24 is correct because he baught one magazine so + 3 which is the total so it is C
Step-by-step explanation:
Plz help, fill in the blanks in order
Use a calculator to find the mean of the data. {21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
Answer:
The mean of the data is 21.41
Step-by-step explanation:
To find the mean of a data set you must...
Add up all data values to get the sum
Count the number of values in your data set
Divide the sum by the count
The mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have a data set:
{21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
As we know from the definition of the mean:
The mean can be calculated using the formula:
Mean = sum of the data set/number of the data in the data set
Mean = 471/22
Mean = 21.409 ≈ 21.41
Thus, the mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
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Q25 A train travelling at a speed of 30km/h crosses a bridge 25m long in 12 sec. How long will it take to overtake a another train 25m long travelling at 20km/hr? option given 1. 72 sec 2. 74 sec 3. ,75 sec or data insufficient.
Answer:
WHAT
Step-by-step explanation:
Can I get help with this? Easy points!
9514 1404 393
Answer:
maximum: 0minimum: -16Step-by-step explanation:
A graphing calculator can quickly show you the boundaries of the feasible region, and can calculate the values of the objective function.
Mr. Johnson took up an appointment with Nestle Ghana as an accountant with an annual salary of $164 million. as part of his appointment, he was promised a yearly increment of $24 million. Mr Johnson got promoted to chief accountant after six years of work with an annual salary of $300 million and yearly increment of$36 million.
calculate a) Mr. Johnson's salary in the tenth year of service.
b). Mr. Johnson's total earnings at the end of the tenth year of service.
Answer:
300 million(1+ 36 million) y
Step-by-step explanation:
A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is:_______
a. 0.9545.
b. 0.9332.
c. 0.0668.
d. 0.4332.
Answer:
0.9545
Step-by-step explanation:
Given that :
Mean = 300
Standard deviation, σ = 18
Sample size, n = 144
Zscore = (x - mean) ÷ σ/√n
At score, x = 297
Zscore = (297 - 300) / (18/12) = - 2
P(Z< - 2) = 0.02275
At score, x = 303
Zscore = (303 - 300) / (18/12) = 2
P(Z< 2) = 0.97725
P(Z < 2) - P(Z < - 2) = 0.97725 - 0.02275 = 0.9545
The probability that the sample mean will be between 297 to 303 is 0.9545.
We have given that ,A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken.
Mean = 300
Standard deviation, σ = 18
Sample size, n = 144
We have to find the probability that the sample mean will be between 297 to 303
Therefore we use the formula of Z score.
What is the formula of Z score?[tex]Zscore = \frac{ (x - mean)}{\sigma/\sqrt n}[/tex]
At the score, x = 297
Zscore = (297 - 300) / (18/12) = - 2
P(Z< - 2) = 0.02275
At score, x = 303
Zscore = (303 - 300) / (18/12) = 2
P(Z< 2) = 0.97725
Therefore we get,
P(Z < 2) - P(Z < - 2) = 0.97725 - 0.02275 = 0.9545
Therefore,the probability that the sample mean will be between 297 to 303 is 0.9545.
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HELP ME PLS!!!!!
Which of the following is | 5-12i |?
A) -√119
B) √119
C) −13
D)13
Answer:
D) 13
[tex]\sqrt{169} = 13[/tex]
Step-by-step explanation:
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
Step-by-step explanation:
An arithmetic sequence is of the form:
[tex]A_n = A_{n-1} + d[/tex]
While a geometric sequence is of the form:
[tex]A_n = A_{n-1}*r[/tex]
notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.
In fact, the pattern is kinda easy to see.
The first term is:
A₁ = 2
the second term is:
A₂ = -10
notice that:
A₂/A₍ = r = -10/2 = -5
The third term is:
A₃ = 50
the quotient between the third term and the second term is:
A₃/A₂ = 50/-10 = -5
Whit this we can already conclude that the n-th term of our sequence will be:
[tex]A_n = A_{n-1}*(-5)[/tex]
Then the summation will be something like:
[tex]\sum_{n = 1} A_n = A_1 + A_2 + A_3 + ... = 2 - 10 + 50 - ...[/tex]
We can write:
[tex]A_n = A_{n-1}*(-5) = (A_{n-2}*(-5))*(-5)) = A_1*(-5)^{n-1} = 2*(-5)^{n-1}[/tex]
Then the summation is just:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
There are about 320 million people living in the United States. Of these, how many would you predict wear corrective lenses?
Answer:
243840000 people
Step-by-step explanation:
The total sample size = 1000
Samole proportion of those who wear corrective lenses :
p = x / n ; n = sample size
p = 762 / 1000 = 0.762
To predict the number of people who wear corrective lenses :
Total population * p
320,000,000 * 0.762
= 243840000 people
Answer:
243840000
Step-by-step explanation:
does anyone know how to do this help please
Answer:
[tex]\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}[/tex]
Step-by-step explanation:
A quadratic function is given to us . And we need to fill out the table by using the function . The given function is ,
[tex]\rm\implies y = x^2+x - 6 [/tex]
Here we need to substitute the different values of x , to get the different values of y.
Put x = -3 :-
[tex]\rm\implies y = 3^2-3-6\\ [/tex]
[tex]\rm\implies y = 9 - 3 - 6 \\[/tex]
[tex]\rm\implies y = 0 [/tex]
Put x = -2 :-
[tex]\rm\implies y = 2^2-2-6\\ [/tex]
[tex]\rm\implies y = 4 -2-6\\[/tex]
[tex]\rm\implies y = -4 [/tex]
Put x = -1 :-
[tex]\rm\implies y = -1^2-1-6\\[/tex]
[tex]\rm\implies y = 1 -1-6 \\[/tex]
[tex]\rm\implies y = -6 [/tex]
Put x = 1 :-
[tex]\rm\implies y = 1^2+1-6\\ [/tex]
[tex]\rm\implies y = 2 -6[/tex]
[tex]\rm\implies y = -4[/tex]
Put x = 2 :-
[tex]\rm\implies y = 2^2+2-6\\ [/tex]
[tex]\rm\implies y = 4 +2-6\\ [/tex]
[tex]\rm\implies y = 2[/tex]
Put x = 3 :-
[tex]\rm\implies y = 3^2+3-6\\ [/tex]
[tex]\rm\implies y = 9 +3-6\\ [/tex]
[tex]\rm\implies y = 6 [/tex]
Final table :-
[tex]\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}[/tex]
What is 10+2
Please I need help
Answer: 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Check the picture below
5 times a number less than 50 is 250 what is the number
Answer:
x = -40
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
50 - 5x = 250
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 50 on both sides: -5x = 200[Division property of Equality] Divide -5 on both sides: x = -40The circumference of a
square orchard is 1600
meters. How many square
meters does the orchard
cover? How many hectares
9514 1404 393
Answer:
160,000 m²16 haStep-by-step explanation:
The side length of a square is 1/4 of the perimeter, so the side length of the square orchard is (1600 m)/4 = 400 m.
The area of a square is the square of the side length, so the area of the orchard is (400 m)² = 160,000 m².
A hectare is 10,000 m², so the area of the orchard in hectares is ...
16·(10,000 m²) = 16 ha
Write functions for each of the following transformations using function notation. Choose a different letter to represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction.
translation of a units to the right and b units up
reflection across the y-axis
reflection across the x-axis
rotation of 90 degrees counterclockwise about the origin, point O
rotation of 180 degrees counterclockwise about the origin, point O
rotation of 270 degrees counterclockwise about the origin, point O
please use this format:
T(x, y) = (x + 6, y)
T<6, 0>(x, y) = (x + 6, y)
T6, 0(x, y) = (x + 6, y)
Answer:
[tex](a)\ T_{a,b} =(x +a,y+b)[/tex]
[tex](b)\ F_{y\ axis} = (-x,y)[/tex]
[tex](c)\ F_{x\ axis} = (x,-y)[/tex]
[tex](d)\ R_{o,90^o} = (-y,x)[/tex]
[tex](e)\ R_{o,180^o} = (-x,-y)[/tex]
[tex](f)\ R_{o,270^o} = (y,-x)[/tex]
Step-by-step explanation:
Solving (a): Translate a units right, b units up
When a function is translated a units right, the number of units will be added to the x coordinate
When a function is translated b units up, the number of units will be added to the y coordinate.
So, we have:
[tex]T_{a,b} =(x +a,y+b)[/tex]
Solving (b): Reflect across y-axis
When a function is translated across the y-axis, the x coordinate gets negated.
So, we have:
[tex]F_{y\ axis} = (-x,y)[/tex]
Solving (c): Reflect across x-axis
When a function is translated across the x-axis, the y coordinate gets negated.
So, we have:
[tex]F_{x\ axis} = (x,-y)[/tex]
Solving (d): 90 degrees rotation counterclockwise
When a function is rotated 90 degrees counterclockwise, the y-coordinates gets negated and then swapped with the x-coordinate.
So, we have:
[tex]R_{o,90^o} = (-y,x)[/tex]
Solving (e): 180 degrees rotation counterclockwise
When a function is rotated 180 degrees counterclockwise, the coordinates are negated.
So, we have:
[tex]R_{o,180^o} = (-x,-y)[/tex]
Solving (f): 270 degrees rotation counterclockwise
When a function is rotated 270 degrees counterclockwise, the x-coordinates gets negated and then swapped with the y-coordinate.
So, we have:
[tex]R_{o,270^o} = (y,-x)[/tex]
This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
А
B
C D F
Frequency | 5
10
15
3
2
Find the probability that a student earns a
grade of A, B, or C.
p = [?]
Enter a decimal rounded to the bearact hundredth
Answer:
30/35=85.71%
Step-by-step explanation:
Observations with A,B,C: 30
Total Observations: 35
[tex]\frac{30}{35} =\frac{6}{7} =.8571[/tex]
Answer:
.86
Step-by-step explanation:
although 30/35 is .8571 the question is asking to round to the nearest hundredth. therefore, the answer would be .86
Which shows the numbers Nine-tenths, 0.3, 0.8, Five-tenths, and Two-tenths in order from least to greatest?
Answer:
[tex]\frac{2}{10}, 0.3, \frac{5}{10},0.8,\frac{9}{10}[/tex]
Step-by-step explanation:
Given
[tex]\frac{9}{10}, 0.3, 0.8,\frac{5}{10}, \frac{2}{10}[/tex]
Required
Order from the least
We have:
[tex]\frac{9}{10}, 0.3, 0.8,\frac{5}{10}, \frac{2}{10}[/tex]
Express all as decimal
[tex]0.9, 0.3, 0.8,0.50, 0.20[/tex]
Rearrange from least
[tex]0.20, 0.3, 0.50,0.8,0.9[/tex]
Express converted numbers as fractions
[tex]\frac{2}{10}, 0.3, \frac{5}{10},0.8,\frac{9}{10}[/tex]
