Answer:
17/25
Step-by-step explanation:
The equation for the probability of two events that are not mutually exclusive is:
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
A = the number is prime
B = the number is prime
The numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Here are the 8 prime numbers that satisfy event A:
3, 5, 7, 11, 13, 17, 19, 23
p(A) = 8/25
Here are the 13 numbers that are greater than 12 that satisfy event B:
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
p(B) = 13/25
Here are the 4 numbers that satisfy both event A and event B:
13, 17, 19, 23
p(A ∧ B) = 4/25
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
p(A ∨ B) = 8/25 + 13/25 - 4/25
p(A ∨ B) = 17/25
The probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/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.
For given question,
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25.
n(S) = 25
Let event A: the number drawn is prime
The prime numbers from 1 to 25 are:
2, 3, 5, 7, 11, 13, 17, 19, 23
So, n(A) = 9
The probability that the number drawn is prime,
[tex]P(A)=\frac{n(A)}{n(S)}\\\\ P(A)=\frac{9}{25}[/tex]
Let event B: the number drawn is greater than 12
So, n(B) = 13
The probability that the number drawn is greater than 12,
[tex]P(B)=\frac{n(B)}{n(S)}\\\\ P(B)=\frac{13}{25}[/tex]
The number drawn is prime as well as greater than 12.
Such numbers are : 13, 17, 19, 23
n(A ∩ B) = 4
So, the probability that the number drawn is prime as well as greater than 12,
[tex]P(A\cap B)=\frac{n(A\cap B)}{n(s)}\\\\ P(A\cap B)=\frac{4}{25}[/tex]
Using the equation P(AUB) = P(A) + P(B) - P(A ∩ B) to find the probability that the number drawn is prime or greater than 12,
[tex]\Rightarrow P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow P(A\cup B)=\frac{9}{25}+ \frac{13}{25} -\frac{4}{25} \\\\\Rightarrow P(A\cup B)=\frac{9+13-4}{25}\\\\ \Rightarrow P(A\cup B)=\frac{18}{25}[/tex]
Therefore, the probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle
⇛L = W + 5
⇛L × W = 150 sq. units
⇛W (W + 5) = 150
⇛W² + 5W = 150
⇛W² + 5W - 150 = 0
⇛[(W - 10) (W + 15)] = 0
⇛W = -10 , 15 (reject negative width)
☞ Width of rectangle is 10 units
☞ Length of rectangle is 15 units
Joes bait shop brought in a gross profit in sales of $4,100.00 in the month of June. During the same month their operating expenses totaled $1990.00. Calculate the net income of the bait shop for the month of June
Answer:
2110
Step-by-step explanation:
4100-1990=2110
g is a trigonometric function of the form g(x)=acos(bx+c)+d
Below is the graph of g(x). The function has a maximum point at (3.5,-4) and a minimum point at (-1,-5)
Find a formula for g(x). Give an exact expression.
9514 1404 393
Answer:
a = 0.5b = π/4.5c = 7π/9d = -4.5Step-by-step explanation:
The value of d is the average of the maximum and the minimum.
d = (-4 +-5)/2 = -9/2 = -4.5
The value of 'a' is the difference between the maximum and d.
a = -4 -(-4.5) = 0.5
The value of b is 2π divided by the period. Here, the half-period is 3.5 -(-1) = 4.5, so ...
b = 2π/9 = π/4.5
The value of c is the value that makes the cosine argument zero at x=3.5.
(π/4.5)(3.5) +c = 0
c = -7π/9
1. Find the HCF of the following numbers by prime factorisation and continued division method10,35,40
Answer:
Step-by-step explanation:
10 = 2*5
35 = 5*7
40 = 2*2*2*5
The number 5 is common to all three factorisations
So the HCF = 5.
Continued division:
10 and 35:
10) 35(3
30
5)10(2
10
0
- so the HCF of 10 and 35 is 5.
10 and 40:
10)40( 4
40
0
So the HCF of 10 and 40 is 10
We found HCF of 10 and 35 is 5 so:
HCF of 10, 35 and 40 is HCF of 5 and 10 which is 5.
i don’t quite get the concept yet and i really don’t wanna bother the teacher again :/ please help
Answer:
they are asking which claims are true vs false
Step-by-step explanation:
I totally get not wanting to bother our teachers again,... (that is why we're here)
m (AB = 20
m<ABD = 140
m (AD = 60
I think they want to know which ones (based on the "graph") are true,...
A shipping container in the shape of a rectangular prism is 60 feet long, 45 feet wide, and 14 feet tall. What is the volume of the shipping container? *
What is the slope of the line that
contains the points (13,-2) and (3.-2)
Points are
(13,-2)(3,-2)[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{3-13}{-2+2}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-10}{0}[/tex]
[tex]\\ \sf\longmapsto m=0[/tex]
About 60% of U.S full-time college students drank alcohol within a one-month period. You randomly select six U.S. full-time college students. Find the probability that the number of U.S. full-time college students who drank alcohol within a one-month period is exactly two.
Answer:
13.82%
Step-by-step explanation:
Here we have proportion of U.S. full time college students= p = 0.60, Random sample = n = 6
Here we apply Binomial distribution .
p ( X =x ) = nCx * px * ( 1 -p) n-x
a) Exactly two.
P ( x = 2 ) = 6C2 * 0.602 * ( 1 -0.60) 6-2
= 0.1382
find the slope of the joining pairs of points (1/a, 1/b) (b,a)
Answer: m = 1/b
Step-by-step explanation: Unfortunately, I can't give you a picture of the slope, but take that formula I gave you and enter it into a graphing calculator and it will show you the slope. I recommend desmos online calculator, good luck
What is the present value of $25,000 to be received in 15 years at an (a) 6.2% interest rate and, (b) 9.6% interest rate? Explain why the present value is lower when the interest rate is higher.
Answer:
With a higher interest rate, you get more money per period, that acuminates.
The Present value is the starting amount... If the final amount is the same in both scenarios, and you get more interest in the second situation, you can start with a lower amount
Step-by-step explanation:
[tex]PV = CF / (1 + r) t[/tex]
pv1 = 25000/(1.062)^15 = $10,140.80
pv2 = 25000/(1.096)^15 = $6,320.94
The lengths of the sides of a triangle arc 3, 4, and 5. If Theta is the measure of the smallest angle of the triangle, what is the
value of tah theta?
(A)4/3
(B)5/4
(C)3/4
(D)3/5
Answer:
C
Step-by-step explanation:
Since they are pythagorian triplets, ABC is a right angled triangle at the angle between the arc 3 and arc 4. Theta is the angle opposite to 3 and hence tan(theta)=3/4
A dodgeball team at Lincoln Elementary School needs a team of 4 in order to compete against other schools. If there are 9 kids that want to be part of the team, how many different ways can you pick a team of 4
Answer:
3 ways
Step-by-step explanation:
Fill in the blanks
To factor the polynomial 3x2–5x - 12, find two numbers whose product is
and
whose sum is
Answer:
Step-by-step explanation:
Ooooooofkfnvkanggkmfifkfkfkdkcknavnhkgnvkic
PLEASE HELP!!!
write an equation in slope-intercept form for the line with y-intercept 1 and slope 4.
Answer:
y = 4x+1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x+1
Answer:
y = 4x + 1.
Step-by-step explanation:
The general slope-intercept form is
y = mx + c where m = the slope and c is the y-intercept.
Solve for x step by step:
2(4x-3)-8=4+2x
Answer:
3
Step-by-step explanation:
2(4x-3)-8=4+2x
8x - 6 - 8 = 4 + 2x
8x - 2x = 4 + 6 + 8
6x = 18
x = 18/6
x = 3
Answer:
[tex]2(4x - 3) - 8 = 4 + 2x \\ 2 \times 4x + 2 \times - 3 - 8 = 4 + 2x \\ according \: to \: bodmas \: first \: \times then + or - \\ so \\ 8x - 6 - 8 = 4 + 2x \\ 8x - 14 = 4 + 2x \\ 8x - 2x = 4 + 14 \\ 6x = 18 \\ x = \frac{18}{6} \\ x = 3 \\ thank \: you[/tex]
There are 25 peanut candies in a bowl. 4 red, 3 orange, 4 yellow, 5 green, 6 blue and 3 brown. what is the probability of randomly choosing a blue candy from the bowl?
Answer:
6/25 or 24%
Step-by-step explanation:
Answer:
6/25, 0.24, or 24% chance
Step-by-step explanation:
Hi there!
We're given that:
⇒ There are 25 peanut candies in total
⇒ 6 out of the 25 candies are blue
To find the probability of randomly choosing a blue candy from the bowl, divide 6 by 25:
6/25 = 0.24 = 24%
I hope this helps!
Can someone help with this please
Answer:
x2 1-
Step-by-step explanation:
Answer:
x ≥ 0
Step-by-step explanation:
Domain of a function is the x values of a function
The graph extends from 0 to positive infinity.
Since the point at x=0 is closed, the graph includes 0
150 is 40% of what number
Step-by-step explanation:
hope it helps youu.........
The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 3 minutes. What cutoff value would separate the 2.5% of orders that take the most time to process?
A) 4.76 minutes
B) 3.52 minutes
C) 10.01 minutes
D) 11.00 minutes
E) 12.00 minutes
look at the image to see the question
9514 1404 393
Answer:
1385.4 yd³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . radius r and height h
For the given radius and height, the volume is ...
V = π(7 yd)²(9 yd) = 441π yd³ ≈ 1385.4 yd³
You work as a residential painter. A customer wants two tables and eight chairs painted using one coat of the same color paint. Each table requires 158
5
8
quarts of paint, and each chair requires 23
2
3
quarts of paint. How many total quarts of paint should you bring to paint this furniture?
Each table requires = 158 quarts paint
Each chair = 23 quarts of paint
Total no. Of coats = 1
Total chairs = 8
Total table = 2
Total paint required = (158×2)+(23×8)
= 500 quarts of paint
Must click thanks and mark brainliest
Arrange the following rational numbers in descending order. 5/8 ,-11/15 , 17/(-24) ,7/12
help pls!!! Classify the following question: “President, vice president, and secretary are being chosen for the Environmental Club. In how many different ways can these three offices be filled from a list of ten members?”
the answer is: combation
Fatima purchased a new mattress when it was on sale. The sale price was 27% less than the regular price. If the sale price was $409, what was the original price? (Round your answer to the nearest dollar).
Answer:
560
Step-by-step explanation:
Let x be the original price
27% off
original price minus discount = new price
x - .27x = new price
.73x = new price
.73x = 409
Divide each side by .73
.73x/.73 = 409/.73
x=560.2739726
To the nearest dollar
x = 560
A phone company offers two monthly plans. Plan A costs $21 plus an additional $0.11 for each minute of calls. Plan B costs $29 plus an additional $0.09 for each minute of calls. A. For what amount of calling do the two plans cast the same? ____minutes B. What is the cost when the two plans cost the same? $____
$121 and $12 ok isn't available in your ma er bishal bishal bishal
I had 180 mL of water in a measuring cylinder.
I added a stone. The reading is now 195 mL.
What is the volume
of the stone?
Answer:
15×10^-6 cubic meter
Step-by-step explanation:
The volume of the stone is, 195-180 = 15 mL
which is, 15×10^-6 m³
Answer:
=15
Step-by-step explanation:
195ml - 180ml
= 15
the first measuring minus with the second measuring will get the volume for the stone
How do I solve |10-5| ?
Answer:
5
Step-by-step explanation:
Subtract
5
from
10
.
|
5
|
The absolute value is the distance between a number and zero. The distance between
0
and
5
is
5
.
5
How many solutions exist for the given equation?
121 x+ 1 =3(4x+1)-2
zero
one
two
infinitely many
Answer: infinitely many
There are nickles and quarters worth $2.20 in total. If there are 28 coins, how many nickels are there?
What is the value of X
A 15
B 21
C 26
D 105
Answer:
B)21
Step-by-step explanation:
∠KN=∠ML
∠KN=90°+15°
=105°
∠ML=105°
5x°=105°
x°=105÷5
x°=21°
Answer:
[tex]5x=90+15[/tex]
Add, 90 + 15 = 105
[tex]5x=105[/tex]
Divide both sides by 5
[tex]\frac{5x}{5}=\frac{105}{5}[/tex]
[tex]x=21[/tex]°
[tex]\textbf{OAmalOHopeO}[/tex]
