Here are five number cards.
19
13
10
14
22
Two of the five cards are picked at random.
Work out the probability that the total of the two numbers is more than 32
Answers
19 , 14
14, 19
18,22
22, 19
13,22
22,13
14, 22
22,14
That is 8 ways
Total number of permutations of 2 cards from 5
= 5P2
= 5!/3!
= 20
So required probability
= 8/20
= 2/5.
The probability that the total of the two numbers is more than 32 = [tex]\frac{2}{5}[/tex]
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
What is the formula of combination?[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
For given question,
We have been given five number cards.
Two of the five cards are picked at random.
Using combination formula the possible number of outcomes would be,
[tex]^5C_2\\\\=\frac{5!}{2!(5-2)!} \\\\=10[/tex]
So, n(S) = 10
Let event A : the total of the two numbers is more than 32
A = {(19, 14), (19, 22), (13, 22), (14, 22)}
So, n(A) = 4
Using the formula for probability,
[tex]\Rightarrow P(A)=\frac{n(A)}{n(S)} \\\\\Rightarrow P(A)=\frac{4}{10}\\\\\Rightarrow P(A)=\frac{2}{5}[/tex]
Therefore, the probability that the total of the two numbers is more than 32 = [tex]\frac{2}{5}[/tex]
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Related Questions
guys help how do i do fings like
63+__=100
I did this 6+_=10 and it’s 4
And 3 + _=0 abs it’s 3 so I thought it was 43 but it’s wrong help
Answers
Answer:
63+37=100 there you go
that the answer
Answer:
37
Step-by-step explanation:
To find out what the missing number is, you can subtract the known number (63) from the sum (100). 100 - 63 = 37.
deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. This value should always be positive.
1. In tossing one coin 10 times, what are your chances for tossing a head? a tail?: When I tossed one coin 10 times, I got heads 4 times and I got tails 6 times.
2. In tossing one coin 100 times, what are your chances for tossing a head? a tail?: I got heads 55 times and tails 45 times when I tossed one coin 100 times.
3. In tossing one coin 200 times, what are your chances for tossing a head? a tail?: When I flipped one 200 times, I got heads 92 times, and tails 108 times.
4. What is the deviation for 10 tosses?: 0.1
5. What is the deviation for the 100 tosses?
6. What is the deviation for 200 tosses?
7. How does increasing the total number of coin tosses from 10 to 100 affect the deviation?
8. How does increasing the total number of tosses from 100 to 200 affect the deviation?
Answers
When a coin is tossed ten times, the probability of getting a head will be 1/2.
How to solve the probability?In probability, one can either get a head or a tail. Therefore, when a coin is tossed ten times the probability of tossing a head will be:
= 5/10 = 1/2
In tossing one coin 100 times, the chances for tossing a head will be:
= 1/2 × 100 = 50
In tossing one coin 200 times, the chances for tossing a head will be:
= 1/2 × 200
= 100
In conclusion, the deviation for 10 tosses is 0.1
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3 . Which graph represents a function?
Answers
Answer:
There is no graph....
Step-by-step explanation:
But I believe this is the graph you are talking about
Therefor Graph D represents a function.
need help with all of these questions you see on the top. there the red squares. please someone smart. this is one of the problems I need to finish this tonight.
Answers
Let's consider the information given:
Volume: 678.24 yd³radius: 6 yd[tex]\pi[/tex] = 3.14Let's consider what we want to find:
HeightLet's consider how the: ⇒ volume, radius, height ⇒ are related
[tex]Volume = \pi *(radius)^2*height[/tex]
Let's Solve:
[tex]678.24=3.14 *(6)^2*height\\height=6_.yd[/tex]
Answer: 6 yd
Hope that helps!
calculate the 12% simple interest of R10000 in a year
Answers
Answer:1.4.
Step-by-step explanation:
Find the volume of the sphere.
Answers
Answer:
V = 4/3 πr³
Step-by-step explanation:
Find the volume of the sphere
since there is no data, I mean you are looking for the formulaThe formula for the volume of a sphere is V = 4/3 πr³.
Answer:
volume of sphere is the capacity it has. It is the space occupied by the sphere. The volume of sphere is measured in cubic units, such as m3, cm3, in3,
if sin x =cos 60° what is the value of x
Answers
Answer:
the answer is 30
Step-by-step explanation:
cos60=1/2=>sinx=1/2=>x=30
mean: _.5
Median: 5._
Answers
Answer: Mean=4.5
Median=5.5
Step-by-step explanation:
MEAN= Add all of the numbers together then divide by 18 to get 4.5
Median=To find the median, first order your data. Then calculate the middle position based on n, the number of values in your data set. If n is an odd number, the median lies at the position (n + 1) / 2. If n is an even number, the median is the mean of the values at positions n / 2 and (n / 2) + 1. This should get you 5.5
A book rests on a table. The force of gravity pulls down on the book with a force of 25 newtons. What prevents the book from accelerating downward at 9. 8 m/s2?.
Answers
Answer:
the table is pressing back on the boom with its own force which is greater than gravity
A pedestrian sees a cat stuck in the tree that is 40.4 feet tall and calls 911. A fire truck
arrives and sends a fireman up in a rescue lift to save the cat. If the rescue lift is ascending at
a 45° angle of elevation, how far must the rescue bucket reach to save the cat?
Answers
Answer:
the cat should be about 6 or 7 inches away
Step-by-step explanation:
I'm sorry if I was wrong I hope I help
Answer:
57.3 feet
Step-by-step explanation:
Make a right angle triangle. Angle is 45 degrees
hight is 40.4 which is opposite to this angle, that means it's opposite side. And the distance of the bucket to rescue cat is hypotenuse, that's what we are looking for.
apply trig ratio
Sinθ = opposite leg/ hypotenuse
[tex] \sin( 45) = \frac{40.4}{x} \\ x = \ \frac{40.4}{ \sin(45) } \\ x = 57.275 \\ x = 57.3[/tex]
WILL MARK BRAINLIST!!! PLS HELP QUICK!!
Find the least number which must be subtracted from 1381 so as to get a perfect square number. Also find the square root of the square number so obtained.
Answers
Answer:
12.
Square root = 37,
Step-by-step explanation:
40^2 = 1600
35^2 = 30 * 40 + 25 = 1225
So the requred square is between 35 and 40
38^2 = 1444
37^2 = 1369 - so its this one.
Required difference = 1381 - 1369 = 12.
ok ok ok ok ok ok ok
Answers
Answer:
3: equally likely
4: likely
Step-by-step explanation:
Question 3:
the spinner has 1, 2, 3, 4, 5, 6
2, 4, 6 are all even number which is 3 / 6 = 1 / 2
so half a chance can be odd or half even possibility of landing
Question 4:
- 13 yellow
- 4 green
- 3 blue
total marbles: 13 + 4 + 3 = 20
yellow / total = 13 / 20
which is more than half of the marbles are yellow
factor completely
2c^3-22c^2+48c
Answers
Answer:
2c(c - 3)(c - 8)
Step-by-step explanation:
Hello!
Factor:
2c³ - 22c² + 48c2c(c² - 11c + 24)Think: What two numbers multiply to 24, and add up to -11?
Answer: -8 and -3
Split up the -11c into -8c and -3c:
2c(c² - 8c - 3c + 24) (factor each pair)2c( c(c - 8) - 3(c - 8)) 2c(c - 3)(c - 8)evaluate sin 315 without a calculator
Answers
Answer:
-0.7071.
Step-by-step explanation:
The value of function sin 315 is -1/2.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Sin 315 degrees can be found by using the unit circle.
The unit circle is a circle with the radius of one centered at the origin of a coordinate plane.
Every point on the unit circle is a point that is one unit away from the origin.
The unit circle is used to help find the exact values of the trigonometric functions at specific angles.
The angle 315 degrees is in the fourth quadrant of the unit circle, so the x-coordinate is negative and the y-coordinate is negative.
Using the x-coordinate, we can calculate the sine to be -1/2.
Hence, the value of function sin 315 is -1/2.
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HELP PLEASE I already asked this question but no one answerd PLEASE!!!
Answers
Answer:
i say the second one
im sorry if this is wrong
and if this is a test someone is going to report you
Step-by-step explanation:
A square coaster has a side length of 512 feet on each side.
What is the area of the coaster?
Enter your answer as a fraction in simplest form by filling in the boxes.
Answers
Answer:
A square is a 2D figure with four equal straight sides and four right angles. This means the length and width will be the same, which are both 512.
512 x 512 = 262144 ft2
Step-by-step explanation:
Have a great rest of your day
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Given a+b=7 and a-b=3, find the following.
2^a*2^b
Answers
Answer:
a = 5
b = 2
Step-by-step explanation:
You can use system of equations on this.
what fraction of a dollar is 7 dimes and 8 pennies
Answers
Answer:
78/100 or if simplified 39/50
Step-by-step explanation:
Add together the 70 cents and 8 pennies to get 78 cents. One dollar is 100 cents so you automatically get the fraction 78/100 and you can simplify by dividing it by 2 in order to get 39/50.
Write the equation of the line that is perpendicular to the graph of y=1/2x +6, and whose y-intercept is (0,-2).
Answers
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so we're really looking for the equation of a line whose slope is -2 and passes through (0 , -2)
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{-2}(x-\stackrel{x_1}{0}) \\\\\\ y+2=-2x\implies y=-2x-2[/tex]
The spinner shown is spun 5 times. What is the probability that you will spin white exactly 3 times?
Answers
Answer:
3 / 5
Step-by-step explanation:
Total = 5
Probability of spinning white exactly 3 = 3 / 5
Finding the surface area
Answers
Answer: so you do length times width times height and then you divide by two
Step-by-step explanation:
The village basket shop has two types of basket available.One type holds 2 meals and one holds 4 meals.There are 25 basket in the shop, and they can hold a total of 70 meals How many baskets are there that hold 4 meals? help me ASAP
Answers
Using a system of equations, it is found that there are 10 baskets that hold 4 meals in the shop.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given by:
Variable x: Number of baskets that hold 2 meals.Variable y: Number of baskets that hold 4 meals.There are 25 baskets in the shop, hence:
x + y = 25 -> x = 25 - y
They can hold a total of 70 meals, hence:
2x + 4y = 70
2(25 - y) + 4y = 70
2y = 20
y = 10
There are 10 baskets that hold 4 meals in the shop.
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Jill is weighing between two job offers. Job offer 1, would pay her a base salary of
$58,000 with an increase of $3,000 per year. Job offer 2, would pay $53,000 with an
increase of $3500 per year. At which year would both jobs have an equal pay? (Note that
it would only happen at that year)
Answers
Answer:
a 230 metersa 230 metersa 230 metersa 230 metersa 230 metersa 230 metersa 230 meters
A container of orange juice has a pH of 3.3. Find the concentration of hydronium ions in the milk.
pH = -log[H30+]
Answers
The concentration of the hydronium ions in the milk is 5.011×10⁻⁴ if the container of orange juice has a pH of 3.3.
What is pH value?The pH of a solution is a measurement of the concentration of hydrogen ions in the solution, as well as its acidity or alkalinity. Normally, the pH scale ranges from 0 to 14.
We have:
A container of orange juice has a pH of 3.3.
The pH value = 3.3
[tex]\rm pH = -log[H_3O^+][/tex]
[tex]\rm 3.3 = -log[H_3O^+][/tex]
Removing log:
[tex]\rm 10^{-3.3}=[H_3O^+][/tex]
[tex]\rm [H_3O^+] = 5.011\times10^{-4}[/tex]
Thus, the concentration of the hydronium ions in the milk is 5.011×10⁻⁴ if the container of orange juice has a pH of 3.3.
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The shopkeeper agrees to give him a total discount of $70, but charges $9 for every pen. what is the maximum number of pens he can buy now?
Answers
To determine the maximum number of pens he can buy, we need to consider the total discount of $70 and the cost of each pen, which is $9.
Assume he buys an "x" number of pens.
The total discount he receives can be calculated by multiplying the number of pens by the cost of each pen:
$9x
Based on, the shopkeeper agrees to give him a total discount of $70, so we have the equation:
$9x = $70.
To determine the maximum number of pens he can buy, we need to solve for "x".
Dividing both sides of the equation by $9:
x = $70 / $9.
x= 7.77.
Therefore, the maximum number of pens he can buy is 7.
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Use the Law of Sines to find the missing angle of the triangle.
Find m∠B to the nearest tenth.
Answers
Answer:
m∠B = 70.0° (nearest tenth)
Step-by-step explanation:
Sine Rule for Angles
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Given:
a = 13c = 19A = 40°Substituting the given values into the formula to find m∠C:
[tex]\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}[/tex]
[tex]\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}[/tex]
[tex]\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)[/tex]
[tex]\implies \sf m \angle C=69.96086904^{\circ}[/tex]
Interior angles of a triangle sum to 180°
[tex]\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}[/tex]
[tex]\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}[/tex]
[tex]\implies \sf m \angle B=70.03913...^{\circ}[/tex]
Therefore, m∠B = 70.0° (nearest tenth)
pls answer i neend this done
Answers
Answer:
The correct answer is D) -15, 15
Step-by-step explanation:
(-)15^2 = 225
Therefore, x^2 = 225 = (-)15^2
Answer:
It is (D) -15,15
Explantion:
The square root of 225 is 15
Solve the simultaneous equations
2x - y = 6
3x + y = 14
Answers
Answer:
x = 4
y = 2
Explanation:
2(4) = 8 - 2 = 6
3(4) = 12 + 2 = 14
2x - y = 6 —(1)
3x + y = 14 —(2)
Make y in (2) the subject:
y = 14 - 3x —(3)
Substitute (3) into (1):
2x - (14 - 3x) = 6
2x - 14 + 3x = 6
5x - 14 = 6
5x = 6 + 14
5x = 20
x = 20 / 5
x = 4
Substitute x = 4 into (2):
3(4) + y = 14
12 + y = 14
y = 14 - 12
y = 2
ANS : x = 4, y = 2
PLSSS HELPPPPP 20 POINTS!!!!!!!!!!! HELP HELP!!!!! PLSSSSS
Answers
Answer:
A. For sure
Step-by-step explanation:
Product of 12 => 12x
is greater than => [tex]\geq[/tex]
24
so 12x [tex]\geq[/tex] 24
Answer:
c. 12x > 24
Step-by-step explanation:
Only one choice has the "greater than" symbol. It is C.
A number is the variable x.
The product of 12 and a number is 12 × x which is written simply as 12x.
12x is greater than 24.
The symbol for "greater than" is >.
Answer: c. 12x > 24
9. how many small cubes aside 4 cm can be filled in a rectangular box with an internal dimension of 1.6 dm long. 1.4 dm and 1.2 dm high?
pls pasagot ayan nalang kailangan ko po pls
appreciate it ko kung kahit wala nang solution basta pls sagot lang po
Answers
[tex] \small \blue{\boxed{{\colorbox{white}{42}}}} [/tex]
that's my answer
