Answer:
The events are independent.
The probability of showing heads on both toss is equal to 1/2
Step-by-step explanation:
The sample space for this experiment consists of 2⁴= 16 sample points, as each toss can result in two outcomes we assume that the events are equally likely.
Two events are independent in the sample space if the probability of one event occurs, is not affected by whether the other event has or has not occurred.
In general the k events are defined to be mutually independent if and only if the probability of the intersection of any 2,3,--------, k equals the product of their respective probabilities.
P (A∩B) = P(A). P(B)
P (A∩B) = 1/2. 1/2= 1/4
Head Tail
P(E1)= 1/2 ---------- Coin 1 H,H T,H
1/4 1/4
P(E2)= 1/2 --------------- Coin 2 H, H H,T
1/4 1/4
So the events are independent.
The probability of showing heads on both toss is equal to 1/2
The sample space for this experiment consists of 2⁴= 16 sample points, out of which eight will have heads on both toss.
Or in other words ( 1/4* 1/4) = 2/4 = 1/2
(Algebra)
Plz help me ASAP!! I’ll be so grateful!
Answer:
y > 1
Step-by-step explanation:
-2(7 + y) > -8(y + 1)
-14 -2y > -8y -8
-2y +8y > -8 +14
6y > 6
6y/6 > 6/6
y > 1
Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ(x) = 2x2 + 4x – 16 C ƒ(x) = x2 – 2x – 8 D ƒ(x) = 2x2 – 4x – 16
Answer:
D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]
Step-by-step explanation:
Any parabola is modelled by a second-order polynomial, whose standard form is:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.
In addition, a system of three linear equations is constructed by using all known inputs:
(-2, 0)
[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)
(4, 0)
[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)
(0,-16)
[tex]c = -16[/tex] (Eq. 3)
Then,
[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)
[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)
(Eq. 3 in Eqs. 1 - 2)
[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)
[tex]a = 4 + 0.5\cdot b[/tex]
Then,
[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)
[tex]64 + 12\cdot b = 16[/tex]
[tex]12\cdot b = -48[/tex]
[tex]b = -4[/tex]
The remaining coeffcient is:
[tex]a = 4 + 0.5\cdot b[/tex]
[tex]a = 4 + 0.5\cdot (-4)[/tex]
[tex]a = 2[/tex]
The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.
Answer:
D ƒ(x) = 2x2 – 4x – 16
Step-by-step explanation:
the difference of 8 and 2, added to x"
Answer:
see below
Step-by-step explanation:
Difference is subtract
(8-2)
Then add this to x
(8-2) +x
6+x
PLEASE HELP !!! (5/5) -50 POINTS-
Answer:
at least one solution
Step-by-step explanation:
Consistent solutions have at least one solution, but may have more than one solution. Intersecting lines and Lines that are the same are consistent solutions
Answer:
[tex]\boxed{Atleast\ one \ Solution}[/tex]
Step-by-step explanation:
A consistent system of equations have at least one solution. It can be more than that. There are no compulsions.
Cancel the common factor of the numerator and the denominator and write specified expression
Step-by-step explanation:
Hello,
I hope you mean to cancel the common factor that exists in numerator and denominator,right.
so, Let's look for the common factor,
here, the expression is,
=4(x-2)/ (x+5)(x-2)
so, here we find the common factor is (x-2)
now, we have to cancel it. And after cancelling we get,
=4/(x+5)
Note:{ we cancel the common factor if the common factors are in multiply form.}
Hope it helps
What is the difference? Complete the equation. -1 2/5 - (-4/5) = ?
Answer:
First convert them which will be
-7/5 - (-4/5)
so when you subtract a negative number from negative number they actually subtract ex = -4-(-2) = -2
so its simply 7/5-4/5 then add a negative sign
so
3/5
now add negative sign so
-3/5
The ages of some lectures are 42,54,50,54,50,42,46,46,48 and 48.Calculate the:
(a)Mean Age.
(b)Standard deviation.
Answer:
The mean age is 48
The standard deviation is 4
Step-by-step explanation:
The answer is, (a) mean age is 48.
(b) standard deviation is 4.
What is a mean age?Average age of the population calculated as the arithmetic mean.Another parameter determining the average age of the population is the median age.What does standard deviation of age mean?In general, the standard deviation tells us how far from the average the rest of the numbers tend to be, and it will have the same units as the numbers themselves. If, for example, the group {0, 6, 8, 14} is the ages of a group of four brothers in years, the average is 7 years and the standard deviation is 5 years.How do you find the mean age?To find the mean add all the ages together and divide by the total number of children.
Learn more about mean age and standard deviation here:
https://brainly.com/question/475676
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Find the Vertical asymptotes of the graph of f
[tex]f(x) = \frac{x + 2}{ {x}^{2} - 4}[/tex]
Answer:
x = 2 and x = -2
Step-by-step explanation:
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
vertical asymptotes are x = 2 and x = -2
Sherina wrote and solved the equation. x minus 56 = 230. x minus 56 minus 56 = 230 minus 56. x = 174. What was Sherina’s error?
Answer:
subtracting 56 instead of adding (or adding wrong)
Step-by-step explanation:
She wrote ...
x - 56 = 230
x - 56 - 56 = 230 -56 . . . . correct application of the addition property*
x = 230 -56 . . . . . . . . . . . . incorrect simplification
Correctly done, the third line would be ...
x -112 = 174
This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...
x - 56 + 56 = 230 + 56 . . . using the addition property of equality
x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides
__
There were two errors:
1) incorrect strategy --- subtracting 56 instead of adding
2) incorrect simplification --- simplifying -56 -56 to zero instead of -112
We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.
_____
* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.
Answer:
D: Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
I got a 100% on my test.
I hope this helps.
Find the length of AB¯¯¯¯¯¯¯¯ A. 19.56 B. 51.86 C. 42.99 D. 34.98
Answer:
Apllying cos on the triangle
cos(angle)= Base/ Hyp
cos(34)= 29/ AB
AB= 29/0.8290
AB=34.98
Step-by-step explanation:
The length of AB is 34.98 units which the correct answer would be an option (D).
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
Given that ΔABC
∠C = 90°
Here base = BC = 29 units and hypotenuse = AB
To determine the length of AB
Apply the cosine on the given right triangle
⇒ cos(θ) = Base/hypotenuse
⇒ cos(34) = 29/ AB
∴ cos(34°) = 0.8290
⇒ 0.8290 = 29/ AB
⇒ AB= 29/0.8290
⇒ AB = 34.98 units
Hence, the length of AB is 34.98 units
Learn more about Trigonometric functions here:
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Ax + By = C for x. plz sove
Answer:
[tex]\boxed{\boxed{ x=\frac{C-By}{A}; A\neq 0}}[/tex]
Step-by-step explanation:
[tex]Ax+By=C\\\\Ax+By-By=C-By\\\\Ax=C-By\\\\\frac{Ax=C-By}{A}\\\\\boxed{ x=\frac{C-By}{A}; A\neq 0}[/tex]
Hope this helps.
The expression −50x+100 represents the balance, in dollars, of a bank account after x months. What is the rate of change, in dollars per month, of the bank account balance?
Answer:
-50
Step-by-step explanation:
Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)
-50(0)+100 (0,100) Y₂-Y₁/X₂-X₁ 50-100/1-0
Rate of change per month = -$50
write a letter to your friend in Ghana stating your experience in your presentation school in nigeria
Answer:
hi Ghana how are you doing I am fine here. I really miss u and my friends in the old.U know what in Nigeria this school is really awesome and fantastic we have a swimming pool here and we can go to trip and we can have many things here I really loved this school.
at starting I was not have any friends and know I have many friends. But I really miss u this is what about our . Come to my house I can show you my school it is very near to my house .
Ur friend
writ ur name
If x = -1 then how much is 2x - 1
a) 1
b) -3
c) -2
hurry please need to turn in 10 min
Answer: -3
Step-by-step explanation: 2x = -2 then you subtract 1 from that which is the same as adding negative one so -2 - 1 or -2 + -1 = -3
What is the answer, what are the steps to solve this, and what do the parts of the equation represent?
Step-by-step explanation:
Just sub 4 into where n is
what should be added to 66.778 get 78.2
Answer:
11.422
Step-by-step explanation:
[tex]78.2 - 66.778 \\ = 11.422[/tex]
(12x^(2)+x-35)-:(4x+17)
Answer:
(3x-5)(4x+7) / 4x + 17
Step-by-step explanation:
Rewrite the division as a fraction
12 x ^2 + x-35 / 4x+17
Factor by grouping
(3x-5)(4x+7) / 4x + 17
Hope this was the answer you were looking for
What is the rate of change from x = 0 to x = pi over 2 ? (6 points) trig graph with points at (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4)
Answer: [tex]\dfrac{8}{\pi}[/tex] .
Step-by-step explanation:
We know that the rate of change of function f(x) from x=a to x= b is given by :-
[tex]k=\dfrac{f(b)-f(a)}{b-a}[/tex]
The given points on graph : (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4).
The rate of change from x = 0 to x = pi over 2 will be :-
[tex]\dfrac{0-(-4)}{\dfrac{\pi}{2}-0}=\dfrac{4}{\dfrac{\pi}{2}}[/tex] [By using points (0, -4) and (pi over 2, 0) ]
[tex]=\dfrac{8}{\pi}[/tex]
Hence, the rate of change from x = 0 to x = pi over 2 is [tex]\dfrac{8}{\pi}[/tex] .
At a sale, dresses were sold for $39 each. This price was 65% of a dress's original price. How much did a dress originally cost?
Answer:
Hey there!
We can write the equation:
0.65x=39
x=60
The dress originally sold for 60 dollars.
Hope this helps :)
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Social Activity Education Above Average Average Below Average College 30 20 10 High School 20 40 90 Grade School 10 50 130 Using 0.05 as the significance level, what is the critical value for the test statistic
Answer:
9.488
Step-by-step explanation:
The critical value is found by first assessing which statistical test should be used.
We are interested in investigating relationship between social activity and education so chi-square test would be appropriate.
We have 3 rows and 3 columns. The degree of freedom for chi-square critical value is (r-1)(c-1)=(3-1)(3-1)=2*2=4
Chi-square critical value(0.05,4)= 9.488
What is the result of question?
Answer:
B
Step-by-step explanation:
x can not be greater than (1,325-270)/26 because $270 is fixed for the rental
Can someone do this assuming that it is infinite and as well as assuming it's not infinite? Thanks!
Answer:
see below
Step-by-step explanation:
4,7,12,19
We are adding 3,5,7,9..... each time
The sequence is not arithmetic because we are not adding a constant. It is not geometric since we are not multiplying by a constant term each time
There is no common difference or common ratio.
The explicit formula is
an =n^2 +3
The recursive formula is
(n+1)^2 +3 - (n^2 +3)
n^2 +2n+1+3 - ( n^2+3)
2n+1
a sub(n+1) = a sub( n) + 2n+1
The 10th term
an = n^2 +3
Let n=10
an = 10^2+3
= 100+3
= 103
summation
see image
since the numbers are increasing and greater than 1 the sum does not exist
The chart shows a certain city's population by age. Assume that the selections are independent events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.
Answer:
0.000014
Step-by-step explanation:
The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:
City X's Population by Age
0-24 years old 33%
25-44 years old 22%
45-64 years old 21%
65 or older 24%
In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:
P(A and B) = P(A) * P(B)
probability that the first 2 are 65 or older
Let A be the event that the first 2 are 65 or older
The probability of 65 or older 24% i.e. 0.24
So the probability that first 2 are 65 or older is:
0.24(select resident 1) * 0.24(select resident 2)
P(A) = 0.24 * 0.24
= 0.0576
P(A) = 0.0576
probability that the next 3 are 25-44 years old
Let B be the event that the next 3 are 25-44 years old
25-44 years old 22% i.e. 0.22
So the probability that the next 3 are 25-44 years old is:
0.22 * 0.22* 0.22
P(B) = 0.22 * 0.22 * 0.22
= 0.010648
P(B) = 0.010648
probability that next 2 are 24 or younger
Let C be the event that the next 2 are 24 or younger
0-24 years old 33% i.e. 0.33
So the probability that the next 2 are 24 or younger is:
0.33 * 0.33
P(C) = 0.33 * 0.33
= 0.1089
P(C) = 0.1089
probability that last is 45-64 years old
Let D be the event that last is 45-64 years old
45-64 years old 21% i.e. 0.21
So the probability that last is 45-64 years old is:
0.21
P(D) = 0.21
So probability of these independent events is computed as:
P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)
= 0.0576 * 0.010648 * 0.1089 * 0.21
= 0.000014
The sum of two polynomials is 10a^2b^2-8a^2b+6ab^2-4ab+2 if one addend is -5a^2b^2+12a^2b-5 what is the other addend
Answer:
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Step-by-step explanation:
The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]
[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Answer:
A
Step-by-step explanation:
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
First find the critical points of f :
[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]
[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]
so the point (1, 0) is the only critical point, at which we have
[tex]f(1,0)=-7[/tex]
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]
Find the critical points of g :
[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]
[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]
[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]
where n is any integer. We get 4 critical points in the interval [0, 2π) at
[tex]t=0\implies f(10,0)=155[/tex]
[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]
[tex]t=\pi\implies f(-10,0)=235[/tex]
[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]
So f has a minimum of -7 and a maximum of 299.
7 less than the quotient of a number and 3 is 5. Find the number.
Answer:
The answer is 36
Step-by-step explanation:
Let the number be x
7 less than the quotient of a number and 3 is written as
[tex] \frac{x}{3} - 7[/tex]The result is 5
So we have
[tex] \frac{x}{3} - 7 = 5[/tex]Move - 7 to the right side of the equation
That's
[tex] \frac{x}{3} = 7 + 5[/tex][tex] \frac{x}{3} = 12[/tex]Multiply both sides by 3 to make x stand alone
We have
[tex]3 \times \frac{x}{3} = 12 \times 3[/tex]We have the final answer as
x = 36Hope this helps you
How to evaluate this help me out so lost?
Answer:
5443
Step-by-step explanation:
Order of Operations: BPEMDAS
Always left to right.
Step 1: Add 68 and 5042
68 + 5042 = 5110
Step 2: Add 5110 and 333
5110 + 333 = 5443
And we have our answer!
List the sides in order from the largest to the smallest. A. XY, YW, WX B. XY, WX, YW C. WX, YW, XY D. WX, XY, YW
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]
[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]
= 1.1489
XW : XY ≈ 1.15 : 1
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]
XY : WY = 1 : 0.7342
XW : XY : WY = 1.15 : 1 : 0.7342
Therefore, WX > XY > WY
Option (D). will be the correct option.
Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?
Answer:
Step-by-step explanation:
First we start with 12 pounds
On Monday, she and her friends eat 4 pounds. So we have 8 now.
On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.
On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15
On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.
On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.
On Saturday, her mom gives her one more pound. 2 + 1 = 3.
On Sunday, she finally has 3 pounds.
Answer:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
A study of 200 computer service firms revealed these incomes after taxes: Income After Taxes Number of Firms Under $1 million 102 $1 million up to $20 million 61 $20 million or more 37 What is the probability that a particular firm selected has $1 million or more in income after taxes
Answer:
The probability that a particular firm selected has $1 million or more in income after taxes is 49%.
Step-by-step explanation:
We are given a study of 200 computer service firms revealed these incomes after taxes below;
Income After Taxes Number of Firms
Under $1 million 102
$1 million up to $20 million 61
$20 million or more 37
Total 200
Now, the probability that a particular firm selected has $1 million or more in income after taxes is given by;
Total number of firms = 102 + 61 + 37 = 200
Number of firms having $1 million or more in income after taxes = 61 + 37 = 98 {here under $1 million data is not include}
So, the required probability = [tex]\frac{\text{Firms with \$1 million or more in income after taxes}}{\text{Total number of firms}}[/tex]
= [tex]\frac{98}{200}[/tex]
= 0.49 or 49%
The probability that a particular firm selected has $1 million or more in income after taxes is 0.49 or 49%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
A study of 200 computer service firms revealed these incomes after taxes:
Income After Taxes Number of Firms Under
$1 million 102
$1 million up to $20 million 61
$20 million or more 37.
Then the total event will be
Total event = 102 + 37 +61 = 200
The probability that a particular firm selected has $1 million or more in income after taxes will be
Favorable event = 37 + 61 = 98
Then the probability will be
[tex]\rm P = \dfrac{98}{200} \\\\P = 0.49 \ or \ 49 \%[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
