an experiment consists of rolling two fair dice and adding the dots on the two sides facing up assuming each simple event is as likely as any other find the probability that the sum of the dots is greater than 2
Answer:
35/36
Step-by-step explanation:
Sample space = S
n(S) = 36
Event of obtaining sum greater than 2, = A
Event of obtaining sum less than 2, B =( 1, 1)
n(B) = 1
Probability of obtaining sum less than 2, P(B) = n(B)/n(S) = 1/36
n(A) = 36 - 1 = 35
∴ Probability of obtaining sum greater than 2, P(A) = n(A)/n(S) = 35/36
A spring with a mass of 5 Kg has natural length 0.5m. A force of 35.6 N is required to maintain it stretched to a length of 0.5m. If the spring is stretched to a length of 0.5m and released with initial velocity 0, find the position of the mass at any time t. Here damping constant is zero.
Answer:
Step-by-step explanation:
Planes A and B intersect. Vertical plane B intersections horizontal plane A at line k. Line k contains points Y and Z. Line m intersects line n at point W. Which describes the intersection of line m and line n? point W point X point Y point Z
Answer:
It's point W!!!
Step-by-step explanation:
Have a great day :)
Find the value of x.
x = [?]
Answer:
25°
Step-by-step explanation:
[tex]55 \degree = \frac{1}{2} \bigg \{(100 \degree + 35 \degree) - x \bigg \} \\ 55 \degree \times 2 = 135 \degree - x \\ 110 \degree = 135 \degree - x \\ x = 135 \degree - 110 \degree \\ \huge \red{ \boxed{ x = 25 \degree}}[/tex]
Construct a simulation model to estimate the average profit per unit. What is a 95% confidence interval around this average
Answer:
The answer is not complete. But you can use a spreadsheet to construct a simulation model to estimate the average profit per unit of a set of data.
Step-by-step explanation:
To calculate the Expected value of profit, we use:
Selling price - Expected value of different costs
Selling price is Total Cost * Probability
Confidence Interval
A Confidence Interval is a range of values that someone can be sure the true value lies in.
To calculate the confidence interval, we use the formula x ± z * S/√n
Where S is the standard deviation
n is the number of observations
x is the mean
z is the chosen z value
3. One morning, the elevator in Emilio's apartment building was out of order. When he walked down the stairs from
his apartment to the ground floor, he counted 252 steps. Emilio lives on the 14th floor. How many steps are
between each floor?
A 10
C 22
B 18
D 32
Answer:
Number of steps per floor= 18 steps
Step-by-step explanation:
he counted 252 steps. Emilio lives on the 14th floor.
The number of steps between the ground floor and the fourteenth floor.
Let's bear in mind that there 14 floors .
Number of steps per floor= total steps/floor
Number of steps per floor= 252/14
Number of steps per floor= 18 steps
The ratio of a quarterback’s completed passes to attempted passes in 2:5. If he attempted 20 passes he completed. Round to the nearest whole number if necessary
The Brazilian free-tailed bat can travel 99 miles per hour. After sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. How long before these bats cover an area of 80,000 square miles? Use π = 3.14
Answer: 1.6 hours.
Step-by-step explanation:
Ok, the speed of the bats is 99mph.
Here we can think this situation as a circle where the radius is growing at a speed of 99mph.
We assume that the initial radius is r = 0, and we can write the equation of the radius as a linear equation that depends on the time t.
r(t) = 99mi/h*t
First, let's find the radius that we need:
The area of a circle is:
A = ´pi*r^2
If we want A = 80,000 mi^2 we have:
80,000 mi^2 = 3.14*r^2
r = √(80,000 mi^2/3.14) = 159.6 mi
So the radius must be 159.6 miles.
Now, we know that the speed at which the radius increases is 99miles per hour, and we also know that:
Distance = Speed*Time.
in this case:
Distance = 159.6 mi
Speed = 99mi/h
Time = is the thing we want to find.
159.6mi = 99mi/h*T
T = 159.6mi/99mi/h = 1.6 hours.
Suppose that the value of a stock varies each day from $11.82 to $15.17 with a uniform distribution. Find the third quartile, i.e., 75% of all days the stock is below what value?
The third quartile, or the value at which 75% of all days the stock is below, is $14.3325.
Used the formula that states,
the range of the distribution by subtracting the minimum value from the maximum value:
Range = Max value - Min value = $15.17 - $11.82 = $3.35
Given that the stock value follows a uniform distribution from $11.82 to $15.17.
Hence,
Range = $15.17 - $11.82
= $3.35
Now, the uniform distribution is symmetric, and the median (50th percentile) is the midpoint of the range,
Median = (Min value + Max value) / 2
= ($11.82 + $15.17) / 2
= $13.495
Hence, the third quartile (75th percentile);
75th percentile = Median + (0.25 × Range)
= $13.495 + (0.25 × $3.35)
= $13.495 + $0.8375
= $14.3325
To learn more about the third quartile visit:
https://brainly.com/question/9180614
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A professor teaches an undergraduate course in statistics. He uses a lot of sports examples to explain key concepts. He is concerned that this may have biased his instruction to favor male students. To test this, he measures exam grades among women (n = 10) and men (n = 10). The mean score in the male group was 82 ± 4.0 (M ± SD); in the female group, it was 74 ± 8.0 (M ± SD) points. If the null hypothesis is that there is no difference in exam scores, then test the null hypothesis at a .05 level of significance for a two-tailed test. Use denominator of 2.98.
Answer:
The null hypothesis is rejected
Therefore there is sufficient evidence to conclude that the professors teaching method favored the male
Step-by-step explanation:
From the question we are told that
The sample size for each population is [tex]n_1 = n_2 = n = 10[/tex]
The first sample mean is [tex]\= x_1 = 82[/tex]
The second sample mean is [tex]\= x_2 = 74[/tex]
The first standard deviation is [tex]\sigma _1 = 4[/tex]
The second standard deviation is [tex]\sigma_2 = 8.0[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 \ne \mu_2[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{ \frac{ \sigma_1^2}{n_1} + \frac{ \sigma_2^2}{n_2} }[/tex]
=> [tex]SE = \sqrt{ \frac{ 4^2}{10} + \frac{ 8^2}{10} }[/tex]
=> [tex]SE = 2.83[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_1 - \= x_2 }{SE}[/tex]
=> [tex]t = \frac{82 - 74}{2.83}[/tex]
=> t = 2.83
Generally the p-value mathematically represented as
[tex]p-value = 2 P(Z > 2.83)[/tex]
From the z table
[tex]P(Z > 2.83) = 0.0023274[/tex]
So
[tex]p-value = 2 * 0.0023274[/tex]
[tex]p-value = 0.0047[/tex]
Since
[tex]p-value < \alpha[/tex]
Hence the null hypothesis is rejected
Therefore there is sufficient evidence to conclude that the professors teaching method favored the male
amanda has 5 pairs of knee high socks and 5 pairs of crew socks in her drawer.If she picks a pair at random, what is the probability that it is a pair of knee high socks.
Answer:
50%
Step-by-step explanation:
There are a total of 5 + 5 = 10 socks
Knee high socks = 5
=> 5/10 = the probability of getting knee high socks
=> 1/2
=> 50%
Answer:
1/2
Step-by-step explanation:
5 pairs of knee high socks and 5 pairs of crew socks= 10 pairs of socks
P ( knee high) = number of knee high/ total
= 5/10 = 1/2
Solve F(x) for the given domain.
F(x)= x2 + 3x-2
F(-1) =
Jutaານເພະາ
a. -4
b. -6
C. 2.
Answer:
A. -4
Step-by-step explanation:
F(-1) means we must plug the number "-1" in for each x.
F(x) = x^2 + 3x - 2
F(-1) = (-1)^2 + 3(-1) - 2
= 1 - 3 - 2
= -4
Let un be the nth Fibonacci number. Prove that the Euclidean algorithm takes precisely n steps to prove that gcd(un+1, un) = 1.
Answer:
Following are the answer to this question:
Step-by-step explanation:
According to Eucharistic algorithm:
[tex]gcd(un+1,un) = gcd (un+1-un, un)[/tex]
[tex]= gcd (un , un-1)[/tex]
so many recursions following
It was the first two the Fibonacci 1,1 numbers
[tex]gcd(un+1, un) = gcd(1,1) = 1 \\\\ from 1 =1 \text{and euclidean principle} \\\\?gcd (un+1,un ) = 1[/tex]
Simplifica
(3x +5) (x -8)
Determine the value of x
Answer:
3x+4=72-x (congruent triangle side are equal)
3x+x=72-4
4x=68
X=68/4
therefore,X=17 ans
Answer:
x = 17
Step-by-step explanation:
[tex]\because\triangle IJK \cong \triangle PQR.....(given)\\\therefore \angle I \cong \angle P....(cact)\\\therefore m\angle I = m\angle P\\\therefore 3x+4 = 72-x\\\therefore 3x+x = 72-4\\\therefore 4x = 68\\\therefore x = \frac{68}{4}\\\therefore x = 17[/tex]
solve the equation 44-x/5 = x/6 - - - -- - -- - - -- - --- - - -- - - -- -
Answer:
120
Step-by-step explanation:
44 - x/5 = x/6 ⇒ add x/5 to both sidesx/6 + x/5 = 44 ⇒ add up fractions by bringing to common denominator11x/30 = 44x = 44*30/11 ⇒ multiply both sides by 30/11x = 4*30x = 120 ⇒ answerIf f(x) = 5x, what is f^-1(x)
Answer:
f^-1(x) = 1/5 x
Step-by-step explanation:
y = 5x
Exchange x and y to find the inverse
x = 5y
Solve for y
1/5x = y
The inverse is 1/5x
Answer:
[tex]\Large \boxed{f^{-1}(x)=\frac{x}{5} }[/tex]
Step-by-step explanation:
f(x) = 5x
Replace f(x) with y.
y = 5x
Switch variables.
x = 5y
Divide both sides by 5.
[tex]\frac{x}{5} =y[/tex]
What type of number is -16.8.
-Rational number
- Whole number
- Integer number
Answer:
Its an integer number
Step-by-step explanation:
hope this helps✨
graph this function y+6=-3(x+5)
Answer:
Hey there!
It's easier to graph a function in slope intercept form:
y+6=-3(x+5)
y+6=-3x-15
y=-3x-21
So, the slope is -3, and the y intercept is -21.
I'll attach a graph of the function down below
Let me know if this helps :)
PLEASE HELP, I DON'T UNDERSTAND THIS! :(
Divide.
Answer:
first answer
(x+1)(x+2)/2
Step-by-step explanation:
flip the second term and multiply
(x²-4x-5)/(x-2) * (x²-4)/(2x-10)
(x-5)(x+1)/(x-2) * (x+2)(x-2)/2(x-5)
(x+1)(x+2)/2
Fine the length of the side labeled x. Around intermediate values to the nearest tenth. use the rounded values to calculate the next value. round your answer to the nearest tenth.
Answer:
A. 23.6
Step-by-step explanation:
Let the dotted line be y
Then
y/x = sin(50°) ⇒ x = y/sin (50°)and
29/y = tan (58°) ⇒ y = 29/tan (58°)So
x = 29/tan (58°)/sin (50°) ≈ 23.6Correct answer is A. 23.6
Answer:
23.6
Step-by-step explanation:
Evaluate Algebraic Expressions
The classroom is divided into four equal parts. The area of each part is 5.3 meters. What is the are of the classroom?
I think that the answer is 21.2 .I can't say it with confidence but still maybe it will help you
If 2^x=5 what is 2^3^x - 4
Answer: 121
Step-by-step explanation:
If 2^x = 5, what is the value of 2³^×
This can also be re arranged in the form
(2^x)³ - 4
Since 2^x = 5, we now substitute for the value in the expression above.
5³ - 4
= 125 - 4
= 121.
What is the equation in point slope form of the line passing through (0,2) and (1,5)
Start by finding the slope of the line.
m = y2 - y1 / x2 - x1
m = 5 - 2/1 - 0 ⇒ 3/1 ⇒ 3.
So the slope of the line is 3.
This can be used with either one of our two points
to write the equation of the line in point-slope form.
So let's go with the point (0, 2).
Point-slope form is written y - y1 = m(x - x1).
Since we are using the point (0, 2), y - y1 would be y - 2.
"m" would be 3 and x1 would be 0.
So we have y - 2 = 3(x - 0).
A company has 3 mechanics in 8 electricians if an employee is selected at random what is the probability that they are an electrician
Answer:
8/11
Step-by-step explanation:
3 mechanics and 8 electricians = 11 employees total
if one selected at random the possibility of the employee to be an electrician is 8/11
how many kilometres are there in 1 metre
Answer: 0.001 kilometer in 1 meter
Step-by-step explanation:
1 kilometer = 1000 meter
so there are 0.001 kilometer in 1 meter
School a has graduated 1700 students and graduates 50 students each year school b has graduated 600 students but 150 each year how many years will it be before school b has as many graduates as school a
Answer:
11 years
Step-by-step explanation:
t=time
1700+50t=600+150t
The reason we have this equation is because they both have the same time and based on the initial numbers that they have equating the two will give you the exact year and number of students of both school.
PLEASE HELPPPP Using the diagram below, which of the following angle pairs represent vertical angles?
Answer:
DCE and BCA
Step-by-step explanation:
Vertical angles are angles which lie directly opposite each other on intersecting lines. Because of this they are equal, and share the same vertex. Out of these pairs, only DCE and BCA are vertical angles because they lie opposite to each other on the lines FJ and IM, and share a vertex of point C.
Hope this helped!
Use counting to determine the whole number that corresponds to the cardinality of these sets:______. (a) A= (xl x € Nand 20.< x<27)
(b) B=(xixeNandx+1=x)
(c) C={xl xe Nand(x- I)(x - 9) = 0)
(d) D={xlx E N, H X 5 100, and xis divisible by both 5 and 8)
Answer:
Step-by-step explanation:
Cardinality of a set is defined as number of element in a set. It is represented as n(X) where X is any set.
a) Given the set A =(x l x € N and 20.< x<27). According to the set, the set contains the values of natural numbers between 20 and 27. The values are 21, 22, 23, 24, 25 and 26
A = (21, 22, 23, 24, 25, 26)
According to the set A, it can be seen that there are 6 elements in the set, this means n(A) = 6.
b) Given B=(x | xeN and x+1=x)
Since natural numbers starts from 1, the first element in the set is 2 i.e 1+1
The elements of the set B = (2, 3, 4, 4...)
The number of whole number in the set is therefore infinite.
c) For the set C={x l xe N and (x- 1)(x - 9) = 0)
We need to get the root of the equation (x- 1)(x - 9) = 0
x-1 = 0 and x-9 = 0
x = 1 and x = 9
Hence the element C = (1,9)
The number of whole number in the set is n(C) = 2
d) D={xlx E N, H X 5 100, and x is divisible by both 5 and 8)
Given the value of x between 5 and 100, the values of x divisible by 5 = (10, 15, 20, 25, 30, 35, 40, 45, 50 , 55, 60 , 65, 70, 75, 80 85, 90, 95)
values of x divisible by 8 = (16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96)
The total number of elements in both set = 29 i.e n(D) = 29
You have a piggy bank containing a total of 106 coins in dimes and quarters. If the piggy bank contains $17.05, how many dimes are there in the piggy bank? There are how many dimes in the piggy bank.
Answer:
63 dimes
Step-by-step explanation:
Set up a system of equations where d is the number of dimes and q is the number of quarters:
d + q = 106
0.1d + 0.25q = 17.05
Solve by elimination by multiplying the top equation by -0.25 to eliminate q:
-0.25d - 0.25q = -26.5
0.1d + 0.25q = 17.05
Add together and solve for d:
-0.15d = -9.45
d = 63
So, there were 63 dimes in the piggy bank