Answer:
P(E)=1/2
Step-by-step explanation:
Total numbers=6
Numbers greater than or equal to 4= 3(4,5,6)
P(E)= favourable outcomes/total outcomes
P(E)=3/6
=1/2
Answer:
4/6
Step-by-step explanation:
probability of rolling a num greater than or equal to 4 = 4/6
=2/3
Solve the equation
34=7r-8
Answer:
r = 6
Step-by-step explanation:
34 = 7r - 8
+8 . +8
42 = 7r
__ . __
7 . 7
6 = r
b) In a box of 10 oranges, 3 are bad. If two oranges are drawn at random one after the other
without replacement, find the probability that
(i)both are good
(ii)one is good and the other is bad
Answer:
Step-by-step explanation:
Let A,B, and C be the respective events that the first, second, and third drawn orange is good.
Therefore, probability that first drawn orange is good, P(A)=
15
12
The oranges are not replaced.
Therefore, probability of getting second orange good, P(B)=
14
11
Similarly, probability of getting third orange good, P(C)=
13
10
The box is approved for sale if all the three oranges are good.
Thus, probability of getting all the oranges good =
15
12
×
14
11
×
13
10
=
91
44
=0.48
Therefore, the probability that the box is approved for sale is 0.48
Answer:i
i) 7/15
ii) 7/15
Step-by-step explanation:
total: 10
good: 7
bad: 3
i) both are good
p(both good) = 7/10 * 6/9 = 42/90 = 7/15
ii) one good & one bad
p(first good & second bad) = 7/10 * 3/9 = 21/90 = 7/30
p(first bad & second good) = 3/10 * 7/9 = 21/90 = 7/30
p(one good & one bad) = 7/30 + 7/30 = 14/30 = 7/15
Write an expression to represent the area of the following figure.
X - 12
х
Your answer:
4x - 48
4x - 24
x² - 12
Answer:
[tex] x^2 - 12x [/tex]
Step-by-step explanation:
The given rectangle had a length (l) of (x - 12), and a width (w) of x.
Area of rectangle = [tex] l * w [/tex]
Therefore, the expression representing the are if the given rectangle is:
[tex] Area_{rectangle} = (x - 12)*x [/tex]
[tex] Area_{rectangle} = x*x - 12*x [/tex]
[tex] Area_{rectangle} = x^2 - 12x [/tex]
The expression for the area = [tex] x^2 - 12x [/tex]
The width of a rectangle measures (4.4d - 4.3) centimeters, and its length
measures (7.60 +4.7) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
Answer:
p = 8.8d + 16
Step-by-step explanation:
P=2(l+w)
p = 2((4.4d - 4.3) + (7.60 +4.7))
p = 8.8d + 16
Peter weighs 156 pounds, but he would like to wrestle in a lower weight
class. He loses 4 pounds one week, gains back 2 pounds the next, loses 5
pounds the third week and loses 3 pounds the fourth week. How much does
Peter weigh now?
Answer:
146 pounds
Step-by-step explanation:
He starts at 156 pounds.
1st week: He loses 4 pounds, indicating 156 - 4, or 152.
2nd week: He gains 2 pounds, indicating 152 + 2, or 154.
3rd week: He loses 5 pounds, indicating 154 - 5, or 149.
4th week: He loses 3 pounds, indicating 149 - 3, or 146.
Which equation shows a slope of -5 and a y-intercept of (0,1) ?
Answer:
y = -5x + 1
Step-by-step explanation:
Y= mx +b
m = slope
b = y-intercept
y = -5x + 1
Answer:
y = -5x + 1
Step-by-step explanation:
Seeing the words "slope" and "y-intercept," I jump immediately to the slope-intercept form of the equation of a straight line: y = mx + b.
Here we have m = -5 and b = 1:
y = -5x + 1
Why is the product of 1/4 times 1/5 less than each factor
The value of the number falls as the denominator rises, and the product of 1/4 and 1/5 is smaller than each factor.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The complete question is:
Why is the product of 1/4×1/5 less than each factor
It is given that:
Two fractions are given:
1/4 = 0.25
1/5 = 0.20
1/5 < 1/4
The product of the two fractions: 1/4 and 1/5
= (1/4)(1/5)
= 1/20
Because the value of the number falls as the denominator rises, the product of 1/4 and 1/5 is smaller than each factor.
Thus, the value of the number falls as the denominator rises, and the product of 1/4 and 1/5 is smaller than each factor.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
Find the difference. Enter your answer in the box below as a fraction, using
the slash mark ( 1 ) for the fraction bar.
Answer:
2/17
Step-by-step explanation:
Given, [tex] \frac{16}{17} - \frac{14}{17} [/tex], to find the difference, first look for the common denominator of both fractions.
Common denominator of both fractions is 17.
Divide the common denominator by the denominator of each fraction, then multiply the result by its numerator and solve as follows:
[tex] \frac{1(16) - 1(14)}{17} [/tex]
[tex] \frac{16 - 14}{17} [/tex]
[tex] \frac{2}{17} [/tex]
The answer is 2/17
[tex] \frac{16}{17} - \frac{14}{17} [/tex] = 2/17
A triangle has sides with lengths of 5x - 7, 3x - 4, and 2x - 6. What is the perimeter of triangle?
Answer:
10x -17
Step-by-step explanation:
The perimeter is the sum of the side lengths:
P = (5x -7) +(3x -4) +(2x -6)
Grouping like terms can make simplification easier:
P = 5x +3x +2x -7 -4 -6
P = 10x -17
What is a simplified expression for the perimeter
of the polygon?
✓ 5x2 + 2y2 + 12x + 5y
If x = 3 cm and y = 2 cm, what is the perimeter of
the polygon?
State whether the data described below are discrete or continuous, and explain why. The weights of dogs (in pounds) at a dog show
A. The data are discrete because the data can take on any value in an interval.
B. The data are discrete because the data can only take on specific values.
C. The data are continuous because the data can only take on specific values.
D. The data are continuous because the data can take on any value in an interval.
Answer: D. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation: When distinguishing between quantitative variables, they could be classed as either discreet or continuous. This difference between a discreet and continuous variable lies in whether the variable has a finite number of values or not. When a variable can only take up a certain number of values usually while numbers within a certain interval, then such varibak eis said to be finite. On the other hand variables which can take up any value within an interval are said to be continuous as they can take up an uncountable number of values within an interval. When weight is being recorded, it could take up an infinite number of values including decimal within an interval making it difficult to ascertain the number of possible values within the interval.
question what is 2√8+√8=
Answer:
6√2Step-by-step explanation:
[tex]2\sqrt{8}+\sqrt{8}\\\\\mathrm{Add\:similar\:elements:}\:2\sqrt{8}+\sqrt{8}=3\sqrt{8}\\\sqrt{8}=2\sqrt{2}\\\\=3\times\:2\sqrt{2}\\\\=6\sqrt{2}[/tex]
Write an equivalent expression by distributing the "-−" sign outside the parentheses:
-(4s+8.5)
Answer: -4s-8.5
Step-by-step explanation:
-(4s+8.5)
you need to change all the signs in the parentheses that is after a negative (-) sign.
-4s-8.5
since the signs of 4s and 8.5 are all positive (+), we need to change it to its opposite which is negative (-)
Hope this helps!! :)
Please let me know if you have any question
Four times the sum of a number and 2 is 26
4(x + 2) = 26
(x + 2) = 26/4
x + 2 = 6.5
x = 4.5
There are n machines in a factory, each of them has defective rate of 0.01. Some maintainers are hired to help machines working. Using Poisson approximations to answer the following questions and explain why we can use Poisson approximation.
(a) If one maintainer is responsible for 20 machines, what’s the probability that machines go defective and cannot be repaired on time?
(b) If three maintainers are responsible for 80 machines, what’s the probability that machines go defective and cannot be repaired on time?
(c) Assume n=300, then at least how many maintainers are required such that the probability machines cannot be fixed on time is less than 0.01?
Answer:
a) 1 - ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k!
b) 1 - ∑^(80x/d)_k=0 ((e^-λ) × λ^k) / k!
c) ∑²⁰ˣ_k=0 (3^k)/k! = 0.99e³
Step-by-step explanation:
Given that;
if n ⇒ ∞
p ⇒ 0
⇒ np = Constant = λ, we can apply poisson approximation
⇒ Here 'p' is small ( p=0.01)
⇒ if (n=large) we can approximate it as prior distribution
⇒ let the number of defective items be d
so p(d) = ((e^-λ) × λ) / d!
NOW
a)
Let there be x number of repairs, So they will repair 20x machines on time. So if the number of defective machine is greater than 20x they can not repair it on time.
λ[n0.01]
p[ d > 20x ] = 1 - [ d ≤ 20x ]
= 1 - ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k!
b)
Similarly in this case if number of machines d > 80x/3;
Then it can not be repaired in time
p[ d > 80x/3 ]
1 - ∑^(80x/d)_k=0 ((e^-λ) × λ^k) / k!
c)
n = 300, lets do it for first case i.e;
p [ d > 20x } ≤ 0.01
1 - ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k! = 0.01
⇒ ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k! = 0.99
⇒ ∑²⁰ˣ_k=0 (λ^k)/k! = 0.99e^λ
∑²⁰ˣ_k=0 (3^k)/k! = 0.99e³
Find the maximum rate of change of f(x; y) = 4y p x at the point (4,1) and the direction in which it occur
Answer:
16p
Direction: positive/upward direction
Step-by-step explanation:
First, the function is f(x,y) = 4ypx
At the point where x=4 and y=1, the maximum rate of change of the function f(x,y) is
4(1)p(4) = 16p
The direction in which it occurs is the positive(upward) direction
The label on William's muffin said that one serving provided 11 grams of protein, which is 22% of the recommended daily
amount. What is the total recommended daily amount of protein?
Answer: 50 grams
Step-by-step explanation:
11=0.22 a
A =50
When interest is compounded annually, the amount of money accumulated in one year is the same under either a simple or compound interest scenario.
a) true
b) false
Answer:
a) true
Step-by-step explanation:
In case when the interest is compounded on an annually so the amount of money that is accumulated in year 1 would remain the same if there is a simple interest or compound interest situation.
Therefore the given case should be true and hence, the same is to be considered
hence, the correct option is a. true
A circular arc has measure 8 cm and is intercepted by a central angle of 2.3 radians. Find the radius of the circle. Do not round any intermediate computations, and round your answer to the nearest tenth.
Answer:
3.5 cm
Step-by-step explanation:
Given the question:
A circular arc has measure 8 cm and is intercepted by a central angle of 2.3 radians. Find the radius of the circle. Do not round any intermediate computations, and round your answer to the nearest tenth.
Central angle in radian (θ) = 2.3 radian
Length of arc (s) = 8cm
Recall:
Length of arc (s) = radius (r) × central angle (θ)
8cm = radius × 2.3 rad
radius = 8 / 2.3
Radius = 3.478 cm
Radius = 3.5 cm
What is the probability that a randomly selected day of a leap year (with 366 possible days) is in February?
Answer:
0.0792
Step-by-step explanation:
Probability is the likelihood that an event is going to occur. The formula for probability is:
Probability = number of favorable outcomes / total number of outcomes.
Normally in a year there are 365 days and in the month of February there are 28 days but during a leap year there are 366 days in the year and 29 days in the month of February.
Probability that a selected day of a leap year is in February = 29 / 366 = 0.0792
The probability that a selected day of a leap year falls in February is 0.0792
Question DEF will be reflected across a line such that all of vertices of triangle D’E’F are in quadrant II. What line of reflection is used to form triangle D’E’F’?
The line of reflection is
A. y = 0
B. x = 0
C. y = x
D. y = -x
Answer:
i think the answer is b by far
Answer:B
Step-by-step explanation : DEF will be reflected across a line such that all of vertices of triangle D’E’F are in there own quadrant ways. The line of reflection is used to form triangle D’E’F’.
The line of reflection is (B. x = 0 )
Find the root(s) of the equation x2 = 169? A) x = ±13 B) x = ± 13 C) x = 13 D) x = 13
Answer:
We have this equation:
[tex]x^2 = 169[/tex]
What we do is a square root on both sides, so we get:
[tex]\sqrt{x^2}=\sqrt{169}[/tex]
[tex]x = \sqrt{169}[/tex]
And now, we calculate the square root, remember tehre are always two results when the root index is even:
[tex]\bold{x_1 = 13}[/tex]
[tex]\bold{x_2 = -13}[/tex]
As 13 * 13 = (-13)*(-13)
Answer:
I guess both A and B since they have the same exact answer: ±13
Step-by-step explanation:
The square root of any positive number is both the positive (+) version of the root and the negative (-) version of the root.
169 is a perfect square and its positive square root is 13, but you must also include its negative square root, -13, so the roots of this equation are ±13.
That means both answer choices A and B are correct, since they are exactly the same.
Pls help fast What is this number's most specific set name √144 A. Natural B. Whole C. Integer D. Rational E. Irrational
Answer:
C. Integer
Step-by-step explanation: Since the square root of 144 could either be -12 or 12, so it is an integer.
Change 33 feet to yards
Answer: 11 yds
Step-by-step explanation: 1 yd=3 ft
Answer:
11 yards is the correct answer
Step-by-step explanation:
a yard = 3 feet
33/3 = 11 yards
Can someone help me with this please anyoneeeeee
Answer:
michelle made more money
Step-by-step explanation:
If m∠NLO = 41° and m∠NLM = 88°, what is m∠OLM?
Answer:
47°
Step-by-step explanation:
Given that m<NLO = 41°, and m<NLM = 88°, according to angle addition postulate, m<OLM + m<NLO = m<NLM
Therefore, subtracting m<NLO from both sides will give us:
m<OLM = m<NLM - m<NLO
m<OLM = 88° - 41°
m<OLM = 47°
How do I solve for (2√5−√3)^2?
Answer:
[tex]23-4\sqrt{15}[/tex]
Step-by-step explanation:
So we want to simplify:
[tex](2\sqrt5-\sqrt3)^2[/tex]
Note that this is in the format:
[tex](a-b)^2[/tex]
And we know that this is the same as:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Let 2√5 be a and let √3 be b. Thus:
[tex](2\sqrt5-\sqrt3)^2\\=(2\sqrt5)^2-2(2\sqrt5)(\sqrt3)+(\sqrt3)^2[/tex]
Simplify:
[tex]=(4(5))-4(\sqrt5)(\sqrt3)+(3)\\=20-4\sqrt{15}+3\\=23-4\sqrt{15}[/tex]
And this cannot be simplified any further.
Classify the groups below. Do they list repeating decimals, terminating decimals, or irrational numbers? 12,1/2, 34.2, and 4/5
Answer:
terminating decimals
Step-by-step explanation:
All of the fractions (4/5, 1/2) can go into 100 so they are all termination
and 34.2 is a terminating decimal.
12 is also terminating
The sum of two numbers is 48. Their difference is 38. Find the numbers.
Answer:
43 and 5
Step-by-step explanation:
Let's let the two unknown numbers be a and b.
Their sum is 48, therefore:
[tex]a+b=48[/tex]
And their difference is 38. In other words:
[tex]a-b=38[/tex]
We now have a system of equations. To solve, we can use substitution. First, add b to both sides in the second equation:
[tex]a=38+b[/tex]
Substitute this into the first equation:
[tex](38+b)+b=48[/tex]
Combine like terms:
[tex]2b+38=48[/tex]
Subtract 38 from both sides:
[tex]2b=10[/tex]
Divide both sides by 2:
[tex]b=5[/tex]
So, one of the numbers is 5.
The sum of them is 48. Therefore, the other number is 48-5 or 43.
So, our two numbers are 43 and 5.
And we're done!
Answer:
5 and 43
I hope this helps!
Write the decimal number as a binary number
26
Answer:
26 as a binary number is 11010