Answer:
p(A) + p(B)
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome. The probability of an event happening or another is the sum of the individual probabilities.
As such, if A and B are two events, the probability of occurrence of either A or B is given as
= p(A) + p(B)
where p(A) and p(B) are the probabilities of A happening and B happening respectively.
if x = 2 and y=1 then prove that (x-y)²=x²-2xy+y²
Answer\Step-by-step explanation:
0≤(x − y)^2 ⟹ 0≤x^2−2xy+y^2
⟹ 2xy≤x^2+y^2
⟹ xy≤ x2+y2\2
⟹ xy≤ x^2+y^2
since the clearly nonnegative real x^2+y^2
clearly satisfies x^2+y^2\2 ≤x^2+y^2.
The proof of the quadratic equation (x-y)²=x²-2xy+y² is given.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
Quadratic equation
(x-y)²=x²-2xy+y²
To prove the equation:
We substitute the value and see if LHS = RHS.
In the LHS,
LHS = (x-y)²
LHS = (2-1)²
LHS = 1
In the RHS,
RHS = x²-2xy+y²
RHS = 4 - 4 + 1
RHS = 1
LHS = RHS
Therefore, the theorem (x-y)²=x²-2xy+y² is proved.
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The area of one face of a cube is 25 square centimeters. What is the volume, in cubic centimeters, of the cube?
Answer:
125 cubic cm
Step-by-step explanation:
Length^2 = 25 so each side length is 5cm
5^3 = 125 cubic cm
Elena had $50 in the bank on Monday. She had $56 on Tuesday. What was the percent of increase from Monday to Tuesday?
A.100 fish
B.40 fish
C.60 fish
D.80 fish
Answer:
c
Step-by-step explanation:
50% of 25% of a number x is
A- one eighth of X
B- half of X
C- one fourth of X
D- three fourth of X
Answer:
The word "of" in mathematical terms means multiplication. The word "is" means equal. This would be translated into 50% x 25% x X = or 0.50 x 0.25 x X =. 0.50 times 0.25 = 0.125. Putting 0.125 into a fraction, it would be 125/1000. Simplify this fraction to get 1/8. So, the answer would be A.
Jenee has a package of 30 cards. There are 5 orange cards
and 25 yellow cards.
If she randomly picks 6 cards, what is the best prediction
for how many cards should be orange?
Answer:
1/2 is the best prediction for the number of orange cards that Jenee could get
Step-by-step explanation:
Hope this helps :D
If it does help could I get brainliest?
Write an equation of the line in point-slope form that passes through the given points.
(1,5) and (-5,4)
Answer:
y-5=1/6(x-1)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-5)/(-5-1)=-1/-6=1/6
slope is 1/6
y-y1=m(x-x1)
y-5=1/6(x-1)
x^2 and -x^2 for x =-3
Answer:
9 and -9
Step-by-step explanation:
x^2:
all you have to do is (-3)^2 = -3 * -3 = 9
-x^2:
this would be -(-3)^2
the order of operations says to do exponents first, so you would have:
-(9) or -9
What is the product of (2x-4)^2
Answer:
( 4x^2 -16x +16)
Step-by-step explanation:
The rule is the
the first term squared + (the first term * second term * 2) + second term^2
What is the y-intercept of the line?
Answer:
y=1/2x+2
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
y intercept is 2
and slope is rise /run
taking points (0,2) and (2,3)
we get slope= 3-2/2-0=1/2
we know the eqaution is y=mx+b where m is the slope and b the y intercept
so y=1/2x+2 which is A/ the first one
if my answer helps please mark as brainliest
8. Which of the following Mathematical expressions is equivalent to a cubed of a number x increased by
ten" ?
A. 3x + 10
B. 10x3
C. x3 – 10
D. x3 + 10
Answer:
B
Step-by-step explanation:
Why is it reasonable to use the same units to describe circles and measure of angles?
Answer:
The more familiar unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°.
Explanation:
The unit circle, or trig circle as it's also known, is useful to know because it lets us easily calculate the cosine, sine, and tangent of any angle between 0° and 360° (or 0 and 2π radians)
A hexagon can be divided into 4 non-overlapping triangles. Which is the sum of the interior angles of a hexagon?
Answer:
12
Step-by-step explanation:
4 time 3 =12
Calcula el área de los rombos.
Answer:
xbxbkzkdkdjd
Step-by-step explanation:
bz va yJnzz
Which expression is equivalent to 7m + 5 + 6 + 3m?
A. 13m + 8
B. 10m + 11
C. 4m + 11
D. 4m + 8
PLEASE HELP ASAP
Answer:
B.10m + 11
....................
what is ask in the problem
todos los numeros naturales son enteros
Answer:
si, todos los números naturales son enteros
If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor
of 3, what is the equation of the new function?
O A. g(x) = x²
O B. g(x) = (3x)2
C. g(x) = 3x2
O D. g(x) = (3x)2
Answer:
g(x)=(1/3x)² .................
A math teacher was frustrated at the number of students leaving their graphing calculator behind in her classroom at the end of class without a way to locate the student. A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.
Required:
What would be a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators?
Answer:
The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.
This means that [tex]n = 50, \pi = \frac{32}{50} = 0.64[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 - 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.4652[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 + 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.8148[/tex]
The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).
Solve 12 - 4x = 44. Find the value of X
Answer:
x = -8
Step-by-step explanation:
We have the expression 12 - 4x = 44 and are asked to find the value of x.
To solve this, we need to isolate x, or get it by itself.
12 - 4x = 44
Subtract 12 from both sides :
-4x = 32
Divide -4 from both sides :
x = -8
please help with my math homework
Answer:
sorry for that
Step-by-step explanation:
image is so unclear can't even read
A rapid strep test is often given in a clinical setting so that, if needed, antibiotics can begin as soon as possible. Researchers at Cochrane.org evaluated the effectiveness of rapid strep tests and found that one type had a sensitivity (ability to correctly detect people with strep) of 85.4% and a specificity (ability to correctly identify people who do NOT have strep) of 95%
Fill in the following chart, assuming that you have a group of 10,000 people, 15% of whom actually have strep throat.
Patient is given a rapid strep test
Result is positive Result is negative totals
Has strep throat
Does not have strep
Totals 10,000
For a population of patients similar to those described in the stem of this problem, use the chart find each of the following probabilities. Write you answer as an abbreviated probability statement with your answer to four decimal places without using a percent symbol. For example, P(strep) = 0.15
A) The probability that a randomly chosen patient has strep throat and tests positive
B) The probability that a randomly chosen patient tests positive for strep throat.
C) The probability that a randomly chosen person actually has strep throat, given that they have tested positive.
Answer:
Follows are the responses to this question:
Step-by-step explanation:
Follows are the table to this question:
[tex]positive \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ negative \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ total[/tex]
[tex]\text{strep value} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1281\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 219 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1500 \\\\[/tex]
[tex]\text{not the strep value} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 425 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8075 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8500 \\\\ \text{total} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1706 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8294 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10000 \\\\[/tex]
In point a:
[tex]P( \text{step and positive test}) = \frac{1281}{10000}=0.1281[/tex]
In point b:
[tex]P(\text{positive test}) =\frac{1706}{10000} =0.1706[/tex]
In point c:
[tex]P \text{(strep | positive test)} =\frac{1281}{1706} =0.7509[/tex]
Please help this is due today!
Answer:
a. True
b. True
c. False
d. False
e. Both
Step-by-step explanation:
a. Explanation: each triangle is composed of three interior angles and three sides which can be of the same length or different lengths
b. Explanation: isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees
c. Explanation: The sum of the measures of the angles is always 180 degrees so that means it is not possible.
d. Explanation: exterior angles of a triangle is greater than either of the measures of the remote interior angles so This is a fundamental result in absolute false because its Interior does not depend upon the Angles
e. Explanation: Eh, There's really no explanation for this So, It's both.
Help pls asap I really need help this is confusing
What is the growth?
What is figure 0?
Y=( )X+( )
Can someone help me too those answers I have no clue
Answer:
Figure 0 = 67 Square Units
Step-by-step explanation:
Its correct, I took the test!
Help plsssssssssssssssssssssss
Answer:
Okay, whats your question?
Step-by-step explanation:
Evaluate the expression when c=2 and y=-6.
-c+by
0
Х
?
Answer:
-38
Step-by-step explanation:
-c + 6y
= -(2) + 6 (-6)
= -2+(-36)
= -2 - 36
= -38
(b)
In how many months will Rs 4800 amount to Rs 5760 at 2 paisa per rupee per
month?
Answer:
This amount will be reached in 1 year and 2 months, that is, in 14 months.
Step-by-step explanation:
Given that 1 paisa is 1 cent of a rupee, at an increase of 2 paisa per rupee per month we are talking about an interest of 2% per month, which annualized is equal to 24% per year (12 x 2).
Thus, given that the initial amount is Rs $ 4800, to determine the period of time in which said interest will take the amount to Rs $ 5760 it is necessary to perform the following calculation:
4800 x 1.02 x X = 5760
4896 x X = 5760
X = 5760/4896
X = 1.17
Thus, this amount will be reached in 1.17 years, with which to calculate the number of months the following calculation must be performed:
1 = 12
0.17 = X
0.17 x 12 = X
2 = X
Thus, this amount will be reached in 1 year and 2 months, that is, in 14 months.
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1051 and a standard deviation of 194. Scores on the ACT test are normally distributed with a mean of 19 and a standard deviation of 4.7. It is assumed that the two tests measure the same aptitude, but use different scales.
Required:
a. If a student gets an SAT score that is the 62-percentile, find the actual SAT score.
b. What would be the equivalent ACT score for this student?
c. If a student gets an SAT score of 1563, find the equivalent ACT score.
Answer:
The answer is "1110, 20.4, and 31.408"
Step-by-step explanation:
For point a:
Given:
[tex]\to mean\ ( \bar{x})=1051\\\\\to standard \ deviation \ (\sigma)=194\\\\\to P(Z<=z)=0.62\\\\\to z=0.3055\\[/tex]
Calculating the SAT score:
[tex]=1051+0.3055 \times 194 \\\\ =1110.267 \approx 1110[/tex]
For point b:
Given:
[tex]\to mean \ \bar{x}=19\\\\ \to standard \ deviation \ (\sigma) =4.7\\\\[/tex]
Calculating the equivalent ACT score:
[tex]=19+0.3055 \times 4.7 \\\\ =20.43585 \approx 20.4[/tex]
For point c:
[tex]\to SAT \ Score =1563\\\\\to z=\frac{(1563-1051)}{194}= \frac{512}{194}=2.64\\\\[/tex]
Calculating equivalent ACT score:
[tex]=19+2.64 \times 4.7 \\\\=31.408[/tex]
Multiply. Write your answer in simplest form. 1/9 x 3/10
Answer:
1/30
Step-by-step explanation:
When you multiply fractions, you just muliply across,
1*3= 3
9*10= 90
you now have 3/90 but you have to simplify, we know 3 goes into 3 and it also goes into 90 equally
3/3= 1
90/3= 30
So your answer is 1/30!!
I hope this helps!!!!!!!!!!!
Can the triangles be proven similar by AA?
Question options:
A)
No, similar triangles cannot contain a pair of parallel lines.
B)
Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
C)
Yes, because || .
D)
No, the triangles contain no angles marked congruent.
Answer:
No, similar triangles cannot contain a pair of parallel lines. Yes, because || . Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
Step-by-step explanation:
Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
What is similarity?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Both triangles are similar as,
∠QUR ≅ ∠TUS (vertical angles)
∠R ≅ ∠S (alternate interior angles).
So, By AA similarity criteria triangles are similar.
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