Answer:
Yes, P(E1)=P(E2)
Step-by-step explanation:
We are given that
Number of dice=3
Total outcomes of 1 die=6
Therefore,
Total number of outcomes =[tex]6^3=216[/tex]
E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}
E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}
We have to show that E1 and E2 have the same probability P(E1) = P(E2).
Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]
Using the formula
[tex]P(E_1)=\frac{6}{216}[/tex]
[tex]P(E_1)=0.0278[/tex]
[tex]P(E_2)=\frac{6}{216}[/tex]
[tex]P(E_2)=0.0278[/tex]
Hence, P(E1)=P(E2)
strip is cut into 9 equal bars shade 1/3 of strip
Answer:
your answer is 18
Step-by-step explanation:
if one bar is shaped into 1/3 of strip.
know,
9 bars =3 × 9
=18
solve the inequality x(x+6) >16
please show steps and interval notation!
Answer:
x > 2, x < -8
Interval notation:
( -infinity, -8) U (2, infinity)
Step-by-step explanation:
x(x+6) > 16
distribute x into x+6, multiply
x^2 + 6x > 16
bring 16 to left side, subtract
x^2 + 6x - 16 > 0
factors of -16 that add to +6 is -2 and +8
(x - 2)(x + 8) > 0
solve for x:
x < -8, x > 2
Interval notation:
( -infinity, -8) U (2, infinity)
: Use the image to complete the equation below.
Vertically opposite angles are equal.
So,
(11y - 36)° = 63°
=> 11y - 36 = 63
Answer:
11y-36=63
Step-by-step explanation:
use the concept of vertically opposite angle
List all factors of the number 52. SHOW ALL WORK!!!
Answer:
Factors of number 52
Factors of 52: 1, 2, 4, 13, 26 and 52.
Negative Factors of 52: -1, -2, -4, -13, -26 and -52.
Prime Factors of 52: 2, 13.
Prime Factorization of 52: 2 × 2 × 13 = 22 × 13.
Sum of Factors of 52: 98.
Lena and Ras drive to work. Lena drives 24 miles in 1.5 hours. Ras drives 36 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km
Answer:
Difference = 3.2 km/h
Step-by-step explanation:
Given that,
Lena drives 24 miles in 1.5 hours. Ras drives 36 km in 1 hour 15 min.
For average speed of Lena,
d = 24 miles = 38.4 km
t = 1.5 h
[tex]v=\dfrac{38.4}{1.5}= 25.6\ km/h[/tex]
For average speed of Ras,
d = 36 km
t = 1h 15 min = 1.25 h
[tex]v=\dfrac{36}{1.25}=28.8\ km/h[/tex]
Difference = 28.8-25.6
= 3.2 km/h
So, the difference between their average speed is 3.2 km/hr.
Answer:
3.2 km/h
Step-by-step explanation:
Find m∠1, m∠2, and m∠4 if m∠3=43°27’.
Answer:
Since there was a ray drawn from A through C the exterior angle of angle C is angle 1. Any straight line should equal to 180 degrees. Demetria W.
m∠2 = 38
Step-by-step explanation:
Which of the following is true?
Answer:
Step-by-step explanation:
A=45
Instruction
Active
Identifying a Graphical Solution
Try it
Which represents the solution of x2 + y2 > 16 and y? < 4x?
HE
of
64
N
2
2
N-
4
2
4
Answer: The Third Graph/ C
Step-by-step explanation:
I NEED HELP!!!!
If, XYZ~EDF the measure of angle F is
Answer:
63°
Step-by-step explanation:
∠F is equal to ∠Z
The ratio of the number of cherry tomatoes in a tossed salad to people served is 7:15. If Waldo wants to serve 105 people, how many cherry tomatoes will Waldo use
Answer: 49 cherry tomatoes.
Step-by-step explanation:
7 x
— = — cross multiply and done.
15 105
The diagram shows the right-angled triangle. (a) Calculate the area.
(b) Calculate the perimeter
Step-by-step explanation:
no diagram visible. there is nothing to calculate.
Answer:
No diagram
Step-by-step explanation:
For area of right angled triangle 1/2 × base× height
Perimeter plus three sides of the triangle
^ means to the power, / indicationg fraction.
PLEASE IF YOU CAN ANSWER AND EXPLAIN TYVM!
1. simplify. 32^2/5. 32 raised to the power of 2 over 3(fraction)
27. the function f is definded below
f(x) = x^2+x-30/ x^2-10x+21
find all variables that are NOT in the domain of f
13. factor the following expression
16vx^3y^4+28v^5x^6
8. simplify, write answer without parentheses
(w^2/-3v^4)^2
24. solve for x 8=3/x-2
11. solve the following ewuation for R
Q=i^2Rt/J
16. solve for v
5v^2=-21v-4
Answer:
udirkkdjdjdjehdhebhgwdxddrergghg
IN Ohio, I-75 and I-80 intersect at right angles. What type of lines do I-75 and I-80 form?
Answer:
Step-by-step explanation:
Interesting question
They form at right angles. The reason is the highways meet at right angles is that the United States does something really interesting and well thought out with its highway system.
The odd numbers run North and South
The even numbers run East and West.
So I-75 runs North and South
I-80 runs East and West.
They will, when they meet, form a right angle. This works for the interstates, but there a system for the intrastates as well.
I wish Canada would do something like that.
Check out this app! It's millions of students helping each other get through their schoolwork. https://brainly.app.link/qpzV02MawO
Answer: this app help me
Step-by-step explanation: it is so fun the answers is it is so good
Can someone help please
Answer:
-10.5
Step-by-step explanation:
3(7)÷(7+7-2)
21÷(0-2)
21÷ (-2)
-10.5
Find the domain and range of the relation: {(–20, 11), (6, –8), (1, –20), (–13, 13)}
Answer:
D: {-20, -13, 1, 6}
R: {-20, -8, 11, 13}
Step-by-step explanation:
Given the relation, {(–20, 11), (6, –8), (1, –20), (–13, 13)}, all x-values (inputs) make up the domain of the relation while all y-values make up the range of the relation.
Therefore:
Domain: {-20, -13, 1, 6}
Range: {-20, -8, 11, 13}
At what x value does the function given below have a hole?
f(x)=x+3/x2−9
Answer:
hole at x=-3
Step-by-step explanation:
The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)
The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.
So anyways we have (x+3)/(x^2-9)
= (x+3)/((x-3)(x+3))
Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.
If a seed is planted, it has a 90% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that exactly 2 don't grow
Answer:
0.2301 = 23.01% probability that exactly 2 don't grow.
Step-by-step explanation:
For each seed planted, there are only two possible outcomes. Either it grows into a healthy plant, or it does not. The probability of a seed growing into a healthy plant is independent of any other seed, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
90% chance of growing into a healthy plant.
This means that [tex]p = 0.9[/tex]
12 seeds are planted
This means that [tex]n = 12[/tex]
What is the probability that exactly 2 don't grow?
So 12 - 2 = 10 grow, which is [tex]P(X = 10)[/tex]. Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{12,10}.(0.9)^{10}.(0.1)^{2} = 0.2301[/tex]
0.2301 = 23.01% probability that exactly 2 don't grow.
Find the volume of the solid lying between two planes perpendicular to the x-axis at x = −1 and x = 1. The cross sections perpendicular to the x-axis are squares whose diagonals run from y = x 2 to y = 2 − x 2
I've attached a sketch of one such cross section (light blue) of the solid (shown at x = 0). The planes x = ±1 are shown in gray, and the two parabolas are respectively represented by the blue and orange curves in the (x, y)-plane.
For every x in the interval [-1, 1], the corresponding cross section has a diagonal of length (2 - x ²) - x ² = 2 (1 - x ²). The diagonal of any square occurs in a ratio to its side length of √2 : 1, so the cross section has a side length of 2/√2 (1 - x ²) = √2 (1 - x ²), and hence an area of (√2 (1 - x ²))² = 2 (1 - x ²)².
The total volume of the solid is then given by the integral,
[tex]\displaystyle\int_{-1}^1 2(1-x^2)^2\,\mathrm dx = \int_{-1}^1 (2-4x^2+4x^4)\,\mathrm dx = \boxed{\frac{32}{15}}[/tex]
The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5549 years. Let C(t) be the amount of carbon-14 present at time t.
(a) Find the value of the constant k in the differential equation C' = -kC.
(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of carbon-14 contained in freshly made cloth of the same material. How old was the Shroud of Turin at the time of this data?
Answer:
a) k = 0.00012491389
b) The Shroud of Turin was 755 years old at the time of this data.
Step-by-step explanation:
(a) Find the value of the constant k in the differential equation C' = -kC.
First we find the differential equation, by separation of variables. So
[tex]\int \frac{C^{\prime}}{C} dt = -\int k dt[/tex]
So
[tex]\ln{C} = -kt + K[/tex]
In which K is the constant of integration, representing the initial amount of substance. So
[tex]C(t) = C(0)e^{-kt}[/tex]
Half-life of 5549 years.
This means that [tex]C(5549) = 0.5C(0)[/tex]. We use this to find k. So
[tex]C(t) = C(0)e^{-kt}[/tex]
[tex]0.5C(0) = C(0)e^{-5549k}[/tex]
[tex]e^{-5549k} = 0.5[/tex]
[tex]\ln{e^{-5549k}} = \ln{0.5}[/tex]
[tex]-5549k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{5549}[/tex]
[tex]k = 0.00012491389[/tex]
So
[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]
(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of carbon-14 contained in freshly made cloth of the same material. How old was the Shroud of Turin at the time of this data?
This is t for which [tex]C(t) = 0.91C(0)[/tex]
So
[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]
[tex]0.91C(0) = C(0)e^{-0.00012491389t}[/tex]
[tex]e^{-0.00012491389t} = 0.91[/tex]
[tex]\ln{e^{-0.00012491389t}} = \ln{0.91}[/tex]
[tex]-0.00012491389t = \ln{0.91}[/tex]
[tex]t = -\frac{\ln{0.91}}{0.00012491389}[/tex]
[tex]t = 755[/tex]
The Shroud of Turin was 755 years old at the time of this data.
Find an equation for the line with the given properties. Perpendicular to the line 7x - 3y = 68; containing the point (8, -8)
Answer:
[tex]y=\dfrac{-3}{7}x-\dfrac{32}{7}[/tex]
Step-by-step explanation:
Given that,
A line 7x - 3y = 68 and containing the point (8, -8).
The equation can be written as :
[tex]-3y=68-7x\\\\y=\dfrac{68}{-3}+\dfrac{7x}{3}\\\\y=\dfrac{7x}{3}+(\dfrac{-68}{3})[/tex]
The slope is :7/3
Line is perpendicular so use m = –3/7
[tex]-8=(-\dfrac{3}{7})\times 8+b\\\\-8+\dfrac{3}{7}\times 8=b\\\\b=\dfrac{-32}{7}[/tex]
So, required equation is :
[tex]y=\dfrac{-3}{7}x-\dfrac{32}{7}[/tex]
Adriana’s z-score on a given measure is -2.5, where the population mean is 5 and the standard deviation is 1.5. What is Adriana’s raw score?
Answer:
Kendriya z-score keva product
The mean of a data set is observed to be very different from its median, representing a strong skewness. However, the 1.5 IQR rule reveals that there are no outliers. Which of the following is correct, if the sample size is 100?
a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.
b. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is not appropriate to use.
c. A normal quantile plot of the data follows a diagonal line, and the t-procedure is not appropriate to use.
d. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is appropriate to use.
Answer:
a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
Sample size of 100 > 30, which means that we use the Central Limit Theorem, and thus, the sampling distribution is approximately normal, following a diagonal line, and since the standard deviation of the population is not know, we use the t-procedure. Thus, the correct answer is given by option a.
There are 100 cars in a car pack.28 of them are blue and 34 are red. If a car is selected at random from the cars. What is the probability that it is neither red nor blue
Answer:
0.38 = 38% probability that it is neither red nor blue.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
100 cars.
Of those, 28 + 34 = 62 are either blue or red.
100 - 62 = 38 are neither blue of red.
What is the probability that it is neither red nor blue?
38 out of 100, so:
[tex]p = \frac{38}{100} = 0.38[/tex]
0.38 = 38% probability that it is neither red nor blue.
Which of the following lists of ordered pairs is a function? A. (1,8), (2, 9), (3, 10), (3, 11) B. (-1,4), (1,7), (2, 10) C. (3,7),(4, 5), (3, 8) D. (-2,3), (1, 3), (3, 7), (1, 4)
Answer:
B
Step-by-step explanation:
B is the only one that doesnt share x-values
A researcher believes that 5% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 806 pet dogs would be greater than 4%
Answer:
0.9036
Step-by-step explanation:
Calculation to determine the probability that the proportion of Labradors
P(Proportion greater than 4%)
= P(z> 0.04 -0.05 /√0.05 * 0.95/806
= P(z > -1.30)
=0.9036
Thereforethe probability that the proportion of Labradors is =0.9036
The sum of the base and height of a triangle is 14 cm. Which of the following equations could be used to find the maximum area of the triangle?
A) A = 0.5x^2 - 15x
B) A = -0.5x^2 + 7x
C) A = -x^2 + 10x
D) A = x^2 - 10x
Answer:
B
Step-by-step explanation:
Let the base of the triangle be b and the height be h.
The sum of the base and height is 14. Thus:
[tex]b+h=14[/tex]
Recall that the area of a triangle is given by:
[tex]\displaystyle A=\frac{1}{2}bh[/tex]
From the first equation, solve for either variable:
[tex]h=14-b[/tex]
Substitute:
[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]
Distribute:
[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]
Distribute:
[tex]\displaystyle A=-0.5b^2+7b[/tex]
Let b = x. Hence:
[tex]A=-0.5x^2+7x[/tex]
Therefore, our answer is B.
sets A and B have 3 and 6 elements respectively. what can be the minimum number of elements in AUB
Answer:
6
Step-by-step explanation:
n(AUB) = n(A) + n(B) - n(AnB)
n(AUB) can have the minimum number of elements if n(AnB) has the maximum number of elements.
n(AnB) maximum = 3
so n(AUB) = 3+6-3 = 6
Cole biked at 5 mph for 1 1/2 hours. Which of the following choices show how far he biked?
Answer:
Should be 5 1/2 if thats on there
Step-by-step explanation:
u take 11/2 and take out the 1 u get 10/2 so u cut 10 in half get 5 then add the one and make it 5 1/2
In a mixture of 240 gallons, the ratio of ethanol and gasoline is 3:1. If the ratio is to be 1:3, then find the quantity of gasoline that is to be added.
Answer:
480 gallons.
Step-by-step explanation:
Given that in a mixture of 240 gallons, the ratio of ethanol and gasoline is 3: 1, if the ratio is to be 1: 3, to find the quantity of gasoline that is to be added the following calculation must be performed:
240/4 x 3 = Ethanol
240/4 = Gasoline
180 = Ethanol
60 = Gasoline
0.25 = 180
1 = X
180 / 0.25 = X
720 = X
720 - 180 - 60 = X
480 = X
Therefore, 480 gallons of gasoline must be added if the ratio is to be 1: 3.