The probability of event X is 30%. The probability of event Y is 40%. If events X and Y are mutually exclusive, what is the probability of event X or Y
The probability of event X or Y is P = 0.7, or, in percentage form, the probability is 70%.
How the get the probability of event X or Y?
First, two events are mutually exclusive if these events can't happen at the same time.
This means that if happens X, with a 30% of probability, then Y can't happen.
If happens Y, with a 40% of probability, then X can't happen.
Then the probability of X or Y (the probability that one of these two events happens, not both) is just the addition of the two individual probabilities.
Then we have:
P(X or Y) = 0.3 + 0.4 = 0.7
Or, in percent form, we get:
P(X or Y) = 70%
The probability of event X or Y is just 70%.
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A board of directors consists of fourteen men and six women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women
Answer:
probability of all the four women chosen over people needed in a committee=4 over 4 =1
a^4 b^2÷4a^3 b^-2
[tex] {a}^{4} {b}^{2} \div 4 {a}^{3} {b}^{ - 2} [/tex]
A square sandbox has sides of length 9 ft and a depth of 1 ft. If sand costs $5 / cubic foot, how much will it cost to fill the sandbox with sand?
The cost spent on fill the box with sand is 405$.
According to the statement
we have given a square sandbox with length 9 ft and depth of 1 ft.
and the rupees of sand per cubic ft is $5
then
Now, we have to find the volume of sandbox with the given length and depth.
So, for this purpose we use Volume formula
V = (a)^3
V = 9*9*1
V = 81 cubic feet
And the cost of sand per cubic feet is $5.
then
The cost of sand for 81 cubic per feet is calculate by multiplication formula then
Total cost of sand = 81*5
Total cost of sand = 405$
So, The cost spent on fill the box with sand is 405$.
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What are relative advantages and disadvantages of the algebraic notations of viete and harriot?
Generally speaking, Harriot's notation was clearer than Viète's, which made it simple for him to connect Viète's identities.
Harriot made significant contributions to the theory of equations and developed a more straightforward notation for algebra.
The employment of special notation is algebra's most evident characteristic. Variables are the symbols that are used to represent numbers.
A symbolic system known as notation is used to represent mathematical concepts and objects.
The primary components of notation are letters, symbols, figures, and signs. Notation can be made using symbols, characters, numbers, or a combination of these, such as the factorial symbol.
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Can someone help me with these problems pleaseeee!!
Answer:
I have wrote just answer.
Write as a decimal the number that is exactly halfway between 1 100 and 1 10
Answer:
605
Step-by-step explanation:
We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.
110 + 1/2(1100 - 110) Subtract what is in the parentheses
110 + 1/2(990) Find 1/2 of 990
110 + 495
604
Simplify the expression
The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
[tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18} \\\\=\frac{(x +3)(x +4)}{x-3} .\frac{(x-3)(x-3)}{2(x+3)(x-3)} =\frac{x+4}{2}[/tex]
The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2
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Solve for x in the diagram below.
Answer:
x = 20
Step-by-step explanation:
x°
2x°
(x + 10)°
little box on the bottom left means this is a right angle which is 90°
add up all the angles and make it equal to 90°
( x° + 2x° + (x + 10)° ) = 90°
4x + 10 = 90
4x = 80
x = 20
Since we can see the "square" at the bottom left corner of the angle, the square indicates that the angle is a right angle (which measures 90°).
We can also see three smaller angles forming the right angle. Therefore, the sum of the measure of the smaller angles = 90°.
According to the diagram, the measures of the smaller angles are x°, 2x°, and (x + 10)° respectively. Then we get the following equation:
[tex]\implies x + 2x + (x + 10) = 90\°[/tex]
Step-2: Solving the equation obtained in step-1Here, we had the equation: [tex]\underline{x + 2x + (x + 10) = 90\°}[/tex]
[tex]\implies x + 2x + x + 10 = 90\°[/tex] [tex]\text{(Ope} \text{ning the parentheses)}[/tex]
[tex]\implies 4x + 10 = 90\°[/tex] [tex]\text{(Combining like terms)}[/tex]
[tex]\implies 4x + 10 - 10 = 90 - 10[/tex] [tex]\text{(Subtracting 10 on both sides)}[/tex]
[tex]\implies 4x = 80[/tex] [tex]\text{(Simplifying both sides)}[/tex]
[tex]\implies \dfrac{4x}{4} = \dfrac{80}{4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Dividing 4 on both sides)}[/tex]
[tex]\implies \boxed{x = 20}[/tex] [tex]\text{(Simplifying both sides)}[/tex]
Therefore, the value of x, in the diagram provided, is 20.
Which equation is equivalent to
f(x) = 16x4 -81 = 0?
✓(4x² +9)(4x² - 9) = 0 ✓
COMPLETE
Select all of the zeroes of the function.
O
2/3
DONE
The equivalent equation is (4x² + 9)(4x² - 9) and the zero's are x =± 3 / 2 and x = ± 3 / 2i
How to find equivalent equation?The equivalent equation can be found by factoring. Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
Therefore,
f(x) = 16x⁴ - 81 = 0
Hence,
9 × 9 = 81
4x² × 4x² = 16x⁴
Therefore,
16x⁴ - 81 = (4x² + 9)(4x² - 9)
Hence,
The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).
The zero's of the function are as follows:
4x² = 9
x² = 9 / 4
x =± 3 / 2
4x² = -9
x² = - 9 / 4
x =√-9 / 2
x = ± 3 / 2i
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in this triangle, cosA/cosB =
AB = 4.24
BC= 3
AC = 3
<C 90deg.
Answer:
1
Step-by-step explanation:
[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]
A
B
C
D
LO
-5
Y
A'
В'
O
D'
Which rule describes the translation?
(x, y)
(x-8, y - 3)
(x, y)
(x-3, y + 8)
C
(x, y) → (x + 8, y − 3)
O (x, y) → (x + 3, y + 8)
Answer:
C. (x,y) ⇒ (x + 8, y − 3)
Step-by-step explanation:
See attached image.
what is the length of side s of the square shown below
Hello,
an other method
Pythagorean theorem :
x² + x² = 6²
2x² = 36
x² = 36/2
x² = 18
x = √18 (and not -√18 because x ≥ 0)
x = √(9 × 2)
x = √(3² × 2)
x = 3√2
Answer A
WILL MAKE BRAINLIEST!!
Find the correct angle measure for angle b in each figure.
_1. 52°
_2. 27°
_3. 32°
_4. 98°
please help find the answer
Answer:
[tex]AC = \bf 4.13 \space\ cm[/tex]
Step-by-step explanation:
Using Pythagoras's theorem:
[tex]\boxed {a^2 = b^2 + c^2}[/tex],
where:
a ⇒ hypotenuse (AC, ? cm)
b, c ⇒ the two other sides of the triangle (AB = 2.2 cm, BC = 3.5 cm),
we can find the length of AC.
[tex]AC^2 = AB^2 + BC^2[/tex]
⇒ [tex]AC^2 = (2.2)^2 + (3.5)^2[/tex]
⇒ [tex]AC = \sqrt{(2.2)^2 + ((3.5)^2}[/tex]
⇒ [tex]AC = \sqrt{17.9}[/tex]
⇒ [tex]AC = \bf 4.13 \space\ cm[/tex]
My fruit basket contain apples and oranges.The ratio apples to oranges is 3:8.When I remove one apple the ratio changes to 1:3 .How many apples are in the basket
The number of apples in the basket are; 24 apples
How to simplify simultaneous equations?Let there be X number of apples and Y number of oranges.
Thus by the given ratio we can say that;
x/y = 3/8 -----(1)
(x — 1)/y = 1/3
3x — 3 = y ----(2)
Substitute 3x - 3 for y in eq 1 to get;
x/(3x - 3) = 3/8
8x = 9x - 9
9x - 8x = 9
x = 9
Thus;
y = 3(9) - 3
y = 24 apples
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Select the correct equation.
The focus and directrix of a parabola are shown. What is the equation of the parabola?
Check the picture below, so the parabola looks more or less like that one, with a "p" distance of 2 units that is positive, whilst the vertex, which is always half-way between the focus point and the directrix is where you see it there, thus
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=-1\\ k=2\\ p=2 \end{cases}\implies 4(2)( ~~ x-(-1) ~~ )~~ = ~~(y-2)^2\implies 8(x+1)=(y-2)^2 \\\\\\ x+1=\cfrac{1}{8}(y-2)^2\implies \boxed{x=\cfrac{1}{8}(y-2)^2-1}[/tex]
Answer: UR WELCOME
Step-by-step explanation: ANSWER ON EDMENTUM
Based on an 8-hour day, the number of hours worked in a hospital food service department was 55,267/yr., and the total number of hours paid was 59,995/yr. The actual number of productive FTEs was:
That year FTE was 26.
According to statement
Labor hours worked that year = 55,267
Total number of hours paid that year = 59,995
The total number of hours during the year
8 hours × 5 days × 52 weeks = 2080 hours
Now we find the FTE per year
So, FTE/YEAR = Labour works on that year / total number of hours in year
Substitute the values in it then
FTE/YEAR = 55267/2080
FTE/YEAR = 26
So, That year FTE was 26.
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If you rolled two dice, what is the probability
that you would roll a sum of 9?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
second
first
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3
5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
The probability you will roll a sum of 9 is 1/4.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability you will roll a sum of 9 = total times a sum of 9 is derived / total sample spaces
total times a sum of 9 is derived = (3 + 6) , (6 + 3) , (4 + 5) , (5 + 4) Total sample spaces = 36The probability you will roll a sum of 9 = 4/36 = 1/9
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i dont understand this at all
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What are we solving for?}[/tex]
[tex]\mathsf{56 = w(w + 10) }[/tex]
[tex]\huge\textbf{How are we going to solve for the}\\\\\huge\textbf{equation?}[/tex]
[tex]\mathsf{56 = w(w + 10)}[/tex]
[tex]\mathsf{w(w + 10) = 56}[/tex]
[tex]\mathsf{w(w) + w(10) = 56}[/tex]
[tex]\mathsf{w(w) + 10(w) = 56}[/tex]
[tex]\mathsf{w^2 + 10w = 56}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf 56} to both sides:}[/tex]
[tex]\mathsf{w^2 + 10w - 56 = 56 - 56}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{w^2 + 10w - 56 = 0}[/tex]
[tex]\huge\textbf{Factor the left side of the equation:}[/tex]
[tex]\mathsf{(w - 4)(w + 14) = 0}[/tex]
[tex]\mathsf{(w - 4)\times(w + 14) = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{w - 4 = 0\ or\ w + 14 = 0}[/tex]
[tex]\mathsf{w = 4\ or \ w = -14}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\mathsf w = 4\ or \ \mathsf w = -14}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Consider this quadratic equation.
x2 + 2x + 7 = 21
The number of positive solutions to this equation is
.
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is
Answer:
1 positive solution (and 1 negative)
the greatest solution is about 2.87
Step-by-step explanation:
so, it is
x² + 2x + 7 = 21
x² + 2x - 14 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -14
x = (-2 ± sqrt(2² - 4×1×-14))/(2×1) =
= (-2 ± sqrt(4 + 56))/2 = (-2 ± sqrt(60))/2 =
= (-2 ± sqrt(4×15))/2 = (-2 ± 2×sqrt(15))/2 =
= -1 ± sqrt(15)
x1 = -1 + sqrt(15) = 2.872983346... ≈ 2.87
x2 = -1 - sqrt(15) = -4.872983346...
Damian has 74 m of fencing to build a four-sided fence around a
rectangular plot of land. The area of the land is 342 square meters.
Solve for the dimensions (length and width) of the field.
Answer:
Step-by-step explanation:
Let the length be l and the width be y. We have the following:
l + w = 37
lw = 342
From here, we can find the factor pairs of 342, and see which pair has a sum of 37. Our desired pair is 18 & 19, so the dimensions of the field are 18 by 19 feet.
Given that tanx=14 and sinx is negative, determine sin(2x), cos(2x), and tan(2x). Write the exact answer. Do not round.
By applying trigonometric identities, the value of tan(x) = 14, gives;
[tex]sin(2 \cdot x) = \frac{28}{197} [/tex]
[tex]cos(2 \cdot x) = -\frac{195}{197} [/tex]
[tex]tan(2 \cdot x) = -\frac{28}{195} [/tex]
Which method can be used to find the value of the trigonometric expressions?Given;
tan(x) = 14
sin(x) is negative
By definition, we have;
[tex]sin(2 \cdot x) = \mathbf{\frac{2 \cdot \: tan(x)}{1 + {tan(x)}^{2} }} [/tex]
Which gives;
[tex]sin(2 \cdot x) = \frac{2 \times 14}{1 + {14}^{2} } = \frac{28}{197} [/tex]
Similarly, we have;
[tex]cos(2 \cdot x) = \mathbf{\frac{1- tan(x)^2}{1 + {tan(x)}^{2} }} [/tex]
Which gives;
[tex]cos(2 \cdot x) = \frac{1- 14^2}{1 + {14}^{2} } = -\frac{195}{197} [/tex]
[tex]tan(2 \cdot x) = \mathbf{\frac{sin(2 \cdot x) }{cos(2 \cdot x) } } [/tex]
Which gives;
[tex]tan(2 \cdot x) = \frac{ \frac{28}{197}}{-\frac{195}{197} } = -\frac{28}{195} [/tex]
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Intermediaries who are independent, but agree to cooperate have likely formed a(n) distribution system.
Intermediaries who are independent, but agree to cooperate have likely formed a(n) contractual distribution system.
The most commonplace form of Contractual VMS is Franchising. In franchising, the manufacturer authorizes the distributor to promote its product below the producer's call against some annual license rate. For example, McDonald's, Dominos, Pizza Hut, etc. are all styles of a franchise that might be operating on a contractual foundation.
A form of vertical advertising machine in which unbiased firms at unique degrees of distribution are tied together by using contracts to achieve economies of scale and more income impact.
A vertical advertising system refers to a marketing system that aims to draw and attain organizations running inside the same industry. then again, horizontal advertising and marketing device refers to an advertising and marketing system whereby corporations which can be on equal degree join collectively to advantage economies of scale.
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In the figure shown, line AB is parallel to line CD. Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points) A 65⁰ P 120⁰ R B O
a) ∠PQR=65° (alternate interior angles theorem)
∠PRQ = 60° (linear pair)
x = 55° (angles in a triangle add to 180°)
b) ∠APQ and ∠PQR are congruent alternate interior angles.
Ms. drake invests $1000 at a simple interest rate of 8.5% for 2 years. how much interest will she earn in this time?
Ms. Drake will earn [tex]\$ 170[/tex] in this time from the investment of [tex]\$ 1000[/tex] at a simple interest with rate of interest [tex]8.5\%[/tex]
What is the definition of simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Formula for finding simple interest is [tex]\frac{principal \times rate \ of \ interest \times time}{100}[/tex]
Given principal of Ms. Drake is [tex]\$1000[/tex]
Rate of interest is [tex]8.5 \%[/tex]
Time is [tex]2[/tex] years.
Interest [tex]=\frac{1000 \times 8.5 \times 2}{100}[/tex]
[tex]=\frac{17000}{100}\\=170[/tex]
Therefore, Ms. Drake will earn [tex]\$ 170[/tex] in this time.
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An auditorium with 30 rows of seats has 10 seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, what is the maximum number of students that can be seated for an exam
Answer:
Step-by-step explanation:
380 rows in total
bcs
use sense
which of the following expresses the possible number of positive real solutions for the polynomial equation shown below
The polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.
In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.
To find the solutions, we do as follows:
x³ - 4x² - 7x + 28 = 0,
or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},
or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},
or, (x - 4)(x² - 7) = 0 {Grouping},
or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex]}.
By the zero-product rule, the solutions are:
x - 4 = 0, or, x = 4,
x + √7 = 0, or, x = -√7,
x - √7 = 0, or, x = √7.
Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.
Thus, the polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.
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The complete question is:
"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
x³-4x²-7x+28=0
a. two or zero
b. three or one
c. one
d. two"
Answer:
Two or zero.
Step-by-step explanation:
terrell watched 300 dogs being groomed. He found that 0.35 of the groomed dogs tried to bite the groomer. what percent of dogs did not try to bite the groomer?
The percentage of dogs who didn't try to bite the groomer is; 65%.
What is the percentage of dogs that did not try to bite the groomer?If follows from the task content that the number of dogs is 300 of which, 0.35 faction of the whole tried to bite the groomer.
Hence, the faction that did not try to bite the groomer is; 0.65 which corresponds to 65% when expressed as a percentage.
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18. The area of a right triangle is 30 cm². The length
of one leg of the triangle is 5 cm. What is the
length of the other leg?
(A) 6 cm
(B) 12 cm
(C) 18 cm
(D) 24 cm
Answer:
12
Step-by-step explanation:
The area of a triangle is calculated with the following formula:
[tex]\frac{1}{2} *b*h[/tex] (b: base, h: height (or legs))
We can use this formula to find the length of the other leg:
30 = [tex]\frac{1}{2} *b*h[/tex] multiply both sides with 2 to get rid of fraction
60 = b*h one of the leg's length is given as 5 so
60 = 5*h divide both sides by 5
12 = h is the length of the missing leg.