Using the general addition rule, p(F or G) = 0.667.
What is sample space?
In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.
Let,
S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
F = {8, 9, 10, 11, 12, 13}
G = {12, 13, 14, 15}
n(S) = number of elements in set S are 12.
n(F) = 6
n(G) = 4
n(F and G) = common elements in F and G = 2
n(F or G) = n(F) + n(G) - (F and G)
n(F or G) = 6 + 4 - 2
n(F or G) = 8
Now, using the general addition rule,
P(F or G) = P(F) + P(G) - P(F and G)
Here,
P(F) = n(F)/n(S) = 6/12 = 1/2
P(G) = n(G)/n(S) = 4/12 = 1/3
P(F and G) = n(F and G)/n(S) = 2/12 = 1/6
⇒ P(F or G) = 1/2 + 1/3 - 1/6
= 5/6 - 1/6
= 4/6
⇒ P(F or G) = 0.667
Hence, using the general addition rule, P(F or G) = 0.667.
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A and B are two similar solids. 1A А 10 cm The volume of A is 400 cm³. Work out the volume of B. 15 cm B
The volume of solid B is 1350 [tex]cm^{3}[/tex].
What is the volume ratio?
The side length ratio raised to the third power represents the volume ratio for the two solids.
If two solids are comparable, their volumes will have a ratio that is equal to the cube of their corresponding side ratios.
Given that both solids are similar.
The volume of solid A = 400 [tex]cm^{3}[/tex]
height of solid A = 10 cm
height of solid B = 15 cm
the volume of solid B = ?
Now,
volume of solid A/ volume of solid B = (height of solid A)^3/(height of solid B)^3
or, [tex]\frac{400}{x} = \frac{10^{3} }{15^{3} }[/tex]
or, [tex]x = \frac{400*15^{3} }{10^{3}}[/tex]
or, [tex]x = \frac{400*3375 }{1000}[/tex] = 1350
Hence, the volume of solid B is 1350 [tex]cm^{3}[/tex].
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If f(x) = e¹/x then f(x)=
The derivative of f(x) is option A.
What is derivative?
The instantaneous pace at which one quantity changes in relation to another is referred to as a derivative in mathematics.
Main Body:
Since the derivative of [tex]e^{x}[/tex] is just [tex]e^{x}[/tex] , application of the chain rule to a composite function with [tex]e^{x}[/tex] as the outside function means that:
[tex]\frac{dy}{dx} (e^{f(x)} )= e^{f(x) }.f'(x)[/tex]
Now the derivative of 1/x = [tex]\frac{-1}{x^{2} }[/tex]
Hence derivative of f(x) = [tex]-e^{\frac{1}{x} } /x^{2}[/tex].
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Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios. A 2-column table has 3 rows. Column 1 is labeled Silver paints (parts) with entries 3, blank, blank. Column 2 is labeled Green paint (parts) with entries 4, blank, blank. Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check all that apply. 4:5 6:8 5:6 9:12
The ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
Generally speaking, a proportional relationship can be represented by the following mathematical expression:
x = ky
Where:
x represents the silver paints (parts).y represents the green paint (parts).k represents the constant of proportionality.In this context, the constant of proportionality or ratio of the quantity of silver paint (parts) to green paints (parts) can be calculated as follows:
Constant of proportionality (k) = x/y
Constant of proportionality (k) = 3/4
Now, we can determine the equivalent ratios as follows:
Equivalent ratio = 4/5 ≠ 3/4
Equivalent ratio = 6/8 = 3/4 (divide by 2)
Equivalent ratio = 5/6 ≠ 3/4
Equivalent ratio = 9/12 = 3/4 (divide by 3).
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the answer is 6:8 and 9:12
Step-by-step explanation: hope this helped ;D
Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.
The statement which is true about this equation is that: C. The equation has no solution.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.
This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.
From the information provided above, we have this equation:
3(-y + 7) = 3(y + 5) + 6
Opening the bracket, we have the following:
-3y + 21 = 3y + 15 + 6
Next, we would rearrange the equation by collecting like terms as follows:
-3y + 21 = 3y + 21 (no solution)
-3y - 3y = 21 - 21
-6y = 0
y = -0/6
y = 0
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let nn denote the smallest positive integer that is divisible by both 44 and 9,9, and whose base-1010 representation consists of only 44's and 99's, with at least one of each. what are the last four digits of nn?
The last four digits of the number nn are 4944
Given that,
Let nn stand for the lowest positive integer that can be represented in base-1010 using only the numbers 44 and 99, with at least one of each. This number must be divisible by both 44 and 9,9.
The last two digits of n must be divisible by 4 for n to be divisible by 4.
So last digits of n will be 44.
And for divisiblity by 9, sum of all digits of n has to be divisible by 9.
As two digits are fixed and their total is 8, next feasible total will be 45 so 9 can be atleast one time in n.
And as statement says n has to be smallest number n will be 4444444944
So last 4 digits of n are 4944.
Therefore, nn's last four numbers are 4944.
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consider tbe graph of a function that is positive over its entire domain. can the graph have an x-intercept?
The graph whose domain is positive will not have any x - intercept.
What is graph of a function?
At first it is important to know about function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Graph of a function is the set of all points of the form (x, f(x)).
The graph is positive in its entire domain
f(x) > 0 for all x
So the graph will never cut the x axis at any point.
So the graph will not have any x intercept.
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4x−1=3y+5 khan academy
The slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given is a equation of a straight line as -
4x - 1 = 3y + 5
We have the equation as follows -
4x - 1 = 3y + 5
Rearranging the equation -
3y = 4x - 1 - 5
3y = 4x - 6
y = (4/3)x - 2
Refer to the graph attached.
The slope of the line is [m] = 4/3
The [y] intercept is at [c] = -2
Therefore, the slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2
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sec^2 54 - 1, can anyone please help me with question asap
The numeric value of the expression sec²(54º) - 1, using a trigonometric identity, is given as follows:
tan²(54º) = 1.8944.
How to solve the expression using a trigonometric identity?Before applying the trigonometric identity, we have to define the secant and the tangent of an angle, as follows:
The secant of an angle is given by the division of one by the cosine of the angle.The tangent is given by the division of the sine of the angle by the cosine of the angle.The identity that exists between the squares of these measures is given as follows:
tan²(x) + 1 = sec²(x).
Hence, isolating the tangent:
tan²(x) = sec²(x) - 1.
In this problem, the expression is given as follows:
sec²(54º) - 1
Applying the identity, the expression is given as follows:
sec²(54º) - 1 = tan²(54º).
Using a calculator, the numeric value of the expression is given as follows:
tan²(54º) = 1.8944.
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How do you write 11+5(3x-2)-8x in the sum of two terms
The simplified for of the Algebraic expression which is the sum of two terms is 1 + 7x
What is an Algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms which can either be a variable or a constant .
11 + 5(3x - 2) -8x
multiply out the bracket we have,
11 + 15x - 10 -8x
collect like terms and simplify
11 - 10 + 15x - 8x
1 + 7x
In conclusion, the expression 11 + 5(3x - 2) as a sum of two terms is 1 + 7x
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8/5 + 7/3 Please put step by step
Answer:
59/15
Step-by-step explanation:
8/5 + 7/3 Multiply the numerator and denominator by the LCF of the denominator
(3/3) 8/5 + 7/3 (5/5) Multiply
24/15 + 35/15 Add the numerators
59/15
Suppose that 12 inches of wire costs 36 cents. At the same rate, how many inches of wire can be bought for 21 cents?
The amount of wire that can be bought from 21 cents is 7 inches.
It is given in the question that 12 inches of wire costs 36 cents.
We have to find the amount of wire that can be bought from 21 cents.
We will use the unitary method to solve this question.
Amount of wire that can be bought from 1 cent = 12/36 = 1/3 inches
Hence, according to the data given in the question, we can write,
The amount of wire that can be bought from 21 cents = (1/3)*21 = 7 inches.
Unitary method
The unitary method is a mathematical problem-solving technique where the value of a single unit is found out from the value of multiple units prior to finding the necessary result.
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Does the point (-2, 7) lie on the graph of y = -2x+1
The point (-2, 7) is not on the graph of y = -2x + 1
How to determine if the point is on the graph?From the question, we have the following equation
y = -2x + 1
This equation represents the equation of the graph
Also, we have the following points
(-2, 7)
This point implies that
(x, y) = (-2, 7)
Substitute (x, y) = (-2, 7) in the equation y = -2x + 1
So, we have
7 = -2 x -2 + 1
Evaluate
7 = 5
This is false
Hence, the point is not on the graph
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what is the correct postulate to prove these two triangles congruent?
A. SAS
B. ASA
C. SSS
D. AAS
E. HL
720 divided by 50 gives the same answer as x divided by 100
what is the value of X
Answer:
Value of x is 1440
Step-by-step explanation:
According to the question,
720 ÷ 50 gives same answer as x ÷ 100
[tex] \therefore[/tex]
[tex] \rm \implies \dfrac{720}{50} = \dfrac{x}{100} \\ \\ \rm \implies x = \frac{720}{50} \times 100 \\ \\ \rm \implies x = 720 \times 2 \\ \\ \rm \implies x = 1440[/tex]
subtract 5 from 12, then multiply by 4
Answer:
Step-by-step explanation:
(12-5)x4=28
Find the surface area of this cuboid.
4 cm
2 cm
2 cm
Answer:
40 cm²
Step-by-step explanation:
Let,
length ( l ) = 4 cm
Height ( h ) = Width ( w ) = 2 cm
To find : Surface are of cuboid : -
Formula : -
Surface are of cuboid = 2 [ lh + hw + wl ]
Surface are of cuboid
= 2 [ ( 4 )( 2 ) + ( 2 )( 2 ) + ( ( 2 )( 4 ) ]
= 2 [ 8 + 4 + 8 ]
= 2 [ 20 ]
= 2 x 20
= 40 cm²
Editors preparing a report on the economy are trying to estimate the percentage of businesses that plan to hire
additional employees in the next 60 days. They are willing to accept a margin of error of 1% but want 95% confidence.
How many randomly selected employers will they need to contact?
n= (Round up to the nearest integer.)
The number of randomly selected employers that would have to be contacted is 9604
How to solve for the value of nThe confidence level is 95%
1 - 0.95 = 0.05
We have to get the z value at 0.05
0.05/2 = 0.025
Using the standard normal table, the critical value at 0.025 = 1.96
We have to define the probability as P = 50% = 0.5
we have to define q = 1 - 50% = 0.5
The formula that would be used to find the value of n is given as
[tex]n = pq\frac{Zc}{E} ^2[/tex]
These variables used are:
pq = variance of population
E = margin of error = 0.01
critical value = Zc = 1.96
[tex]n = 0.5*0.5 (\frac{1.96}{0.01})^2[/tex]
= 0.25 * 38416
= 9604
Hence the sample space is given as 9604
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PLEASE HELP I WILL GIVE BRAINLIEST
Find x and y
*image is linked below*
The value of x and y in the triangle given are 15 and 4 respectively
Equivalent TrianglesAn Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. The equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.
In the triangle given, we can equate equal sides and find the missing sides on the triangle.
12/18 = y + 12 / 18 + 6
12/18 = y + 12 / 24
2/3 = y + 12 / 24
solve for y
y = 4
Taking another side and solve for x
12 / x = 12 + y / x + 5
but y = 4
12 /x = 12 + 4 / x + 5
12/x = 16 / x + 5
x = 15
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Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm
What is the expression d/3+4
Answer:
d+12/3
Step-by-step explanation:
*= multiply /= fraction ALL OVER= fraction over fraction
find the common denominator-
d/3+4
d/3+3*4/3
combine fractions with the common denominator
d/3+3*4/3 ALL OVER d+3*4/3
multiply
d+3*4/3 ALL OVER d+12/3
algebra 2 please help!
Answer:
The answer is C, I had this same quiz today and I got 100%
PLEASE HELP!!
Solve x^2 – 2x = 15 by applying the quadratic formula.
Answer: The correct answer is x=−3 or x=5
Step-by-step explanation:
Solve for x^2−2x=15 using the quadratic equation
Step 1) Subtract 15 from both sides
x2−2x−15=15−15
x2−2x−15=0
For this equation: a=1, b=-2, c=-15
1x2+−2x+−15=0
Step 2) Use quadratic formula with a=1, b=-2, c=-15
x= (−b±√b2−4ac)/2a
x= (−(−2)±√(−2)2−4(1)(−15))/2(1)
x= (2±√64)/2
x=5 or x=−3
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Which postulate can be used to prove the two triangles are congruent?
Answer:
SAS
Step-by-step explanation:
If two sides and the included and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. The included angle is the angle formed by the two sides.
EF = BC
∠ F = ∠ C
DF = AC
then the two triangles are congruent by the SAS postulate.
Answer:
SAS
Step-by-step explanation:
On triangle one and two, they both start by having a congruent side, then a congruent angle, then another congruent side, thus making these triangles congruent by Side Angle Side.
It can't be AAS because there is only one angle, we know is congruent.
It can't be SSS because there are only two sides, we know are congruent.
It can't be HL because there is no right angle, meaning these aren't right triangles.
Help I need this for my homework
Answer:
6.6
Step-by-step explanation:
you subtract 6.6 from both sides to cancel it out on one side
Hopes this helps please mark brainliest
make y the subject of the formula
k= y^2 + a
Answer:
y = [tex]\sqrt{(k-a)}[/tex]
Step-by-step explanation:
k= y^2 + a
k-a= y^2
y^2 = k-a
y = (k-a)^(1/2)
y = [tex]\sqrt{(k-a)}[/tex]
Answer:
[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]
Step-by-step explanation:
To make y-term as the subject of formula means to solve for y-term. First, subtract both sides by a-term, this’ll at least isolate y².
[tex]\displaystyle{k-a=y^2+a-a}\\\\\displaystyle{k-a=y^2}[/tex]
Everything that you do or add to one of both sides, that side will also be done too. (e.g Suppose we have x + 1 = y. If we add 2 to left then 2 should also be added to right too so we’ll have x + 1 + 2 = y + 2)
Then square root both sides to get rid of the exponents of y-term:
[tex]\displaystyle{\sqrt{k-a}=\sqrt{y^2}}[/tex]
If we substitute y = any numbers, we’ll always get positive result. Therefore, this means that y-term can be any positive or negative values. Hence, write plus-minus to the left side then evaluate the square root of y² to y:
[tex]\displaystyle{\pm \sqrt{k-a}=y}[/tex]
Therefore, the new equation written in term of y is:
[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]
if two numerical variables x and y have a correlation coefficient of 0.90, what percentage of the variation in one variable can be accounted for by the other variable?
The percentage of variation in variable can be accounted for by the other variable is 81%.
What is variation in statistic?
The statistical distance between the values of the observations (data points) is what makes up a measure of variance. There are various ways to measure variation.
What is correlation coefficient?
A statistical indicator of the strength of a linear link between two variables is the correlation coefficient.
The formula of percentage of variation is:
(correlation coefficient × correlation coefficient × 100)%.
Given that the correlation coefficient is 0.90.
Thus the percentage of variation is (0.90 × 0.90 × 100)% = 81%
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assume that blood pressure readings are normally distributed with and a blood pressure reading of 145 or more may require medical attention. what percent of people have a blood pressure reading greater than 145?
0.08891% percent of people have a blood pressure reading greater than 145.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
145) = (145-120)/8 = 25/8.P(x > 145) = P(z > 27/8) = 0.0008891.. = 0.08891%Hence, 0.08891% percent of people have a blood pressure reading greater than 145.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
I think it is y = -3x + 2
Step-by-step explanation:
room attendants at your hotel typically clean one room every 20 minutes. one-fifth of the rooms take 40% longer to clean due to various issues. how much time will it take to clean 175 rooms?
a die is rolled 2 times .what is the probability of getting a number 6 two times. what is the probability of not getting 6 at all?
The probability of not getting 6 at all is 11/36
Define probability.The term "probability" is most commonly used to refer to the likelihood that a specific event (or set of events) will occur, expressed as a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.
Given,
A die is rolled 2 times
6 was on the first roll, but there was no 6 on the second,
6 came up on the second roll but not the first.
2 sixes
A) It is evident that 1/6 of the time you will roll a six.
B) There is a 5/6 chance of not getting a six on a single roll.
1/6x5/6 + 5/6x1/6 + 1/6x1/6
= 5/36 + 5/36 + 1/36
= 11/36
The probability of not getting 6 at all is 11/36
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