Answer:
1/80Step-by-step explanation:
This problem brothers is the probability of mutually exclusive events,
Given the sample space of 80 separate events, the probability of of one event happening is
Pr(each event)= [tex]\frac{1}{80}[/tex]
Moise Moliere
Mrs. Johnson has 159 chickens that she puts in shelters at night to keep safe. She places 12 chickens in a shelter
and continues putting this number of chickens in each shelter until she comes to the last one. How many chickens
will Mrs. Johnson put in the last shelter?
3
4
13
11
6
7
8 9 10
14
Back
2 3 4 5
9:3
INTL
Answer: she putz 9 in the last shelter
Step-by-step explanation:
A high school track is shaped as a rectangle with a half circle on either side.Jake plans on running four laps. How many meters will Jake run? Use 3.14 for Pi.
Answer:
if you go around a track one time thats 400 meters but if you go around 4 times thats 1600 meters, you dont need to use 3.14 pi for this " no offense", i do track and field myself and i do the short distance, which is 100 meters and 200 meter but for for long distance runners they go around the track 4- 8 times so it is 1600 meters is ur answer. and when u go around 8 times, thats 3200 meters.
Step-by-step explanation:
Solve the following equation for x.
|x/4+3|<6
Answer:
x<12
Step-by-step explanation:
subtract both sides by -3 because you need to isolate x. then you have x/4<3. now you need to get rid of the 4. so you do the opposite of division and multiply 4 by both sides so you get x<12
Solve using
elimination 5y+3x=9 and 4y-3x=32
Answer:
(x,y)= (-124/27, 41/9)
Step-by-step explanation:
1) Add the equation to eliminate x.
5y+3x=9
4y-3x=32
2) Add 5y and 4y.
5y=9
4y=32 --> 9y=41
3) Get y by itself by dividing 9 on both sides:
y=41/9
4) Substitute Value in the equation 5y+3x=9
5(41/9)+3x=9
5) solve for x
x=-124/27
Step-by-step explanation:
5y + 3x = 9
4y - 3x = 32
using elimination method
subtracting equation 1 from 2 gives
y = -23
substitute to get value of X
5(-23) + 3X = 9
-115 +3x = 9
3x= 124
x = 41.33
find the square root of 12 to the nearest hundredth
Answer:
\sqrt(12) hope this helped.
128 less than a number is 452
Answer:
580
Step-by-step explanation:
"128 less than a number is 452" is represented by:
n - 128 = 452
Solve for 'n':
n - 128 + 128 = 452 + 128 (Addition Property of Equality)
n = 580
Suppose that the functions u and w are defined as follows.
Answer:
- 3 and 3
Step-by-step explanation:
To evaluate (u ￮ w)(- 1), evaluate w(- 1) then use this value to evaluate u(x)
w(- 1) = (- 1)² + 2 = 1 + 2 = 3, then
u(3) = - 3
---------------------------------------------------
To evaluate (w ￮ u)(- 1), evaluate u(- 1) then use this value to evaluate w(x)
u( - 1) = - (- 1) = 1, then
w(1) = 1² + 2 = 1 + 2 = 3
b. Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.) c. Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.) d. Find the expected value of X. (Round your answer to one decimal place.) e. Find the standard deviation of X. (Round your answer to three decimal places.)
Answer:
(a) Probability distribution is prepared below.
(b) The probability that two or fewer heads are observed in three tosses is 0.875.
(c) The probability that at least one head is observed in three tosses is 0.875.
(d) The expected value of X is 1.5.
(e) The standard deviation of X is 2.121.
Step-by-step explanation:
The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.
(a) Find the probability distribution of X.
(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)
(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)
(d) Find the expected value of X. (Round your answer to one decimal place.)
(e) Find the standard deviation of X. (Round your answer to three decimal places.)
Now, firstly the sample space obtained in three tosses of a fair coin is given as;
Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}
(a) The Probability distribution of X is given below;
Number of Heads (X) P(X) [tex]X \times P(X)[/tex] [tex]X^{2} \times P(X)[/tex]
0 [tex]\frac{1}{8}[/tex] = 0.125 0 0
1 [tex]\frac{3}{8}[/tex] = 0.375 0.375 0.375
2 [tex]\frac{3}{8}[/tex] = 0.375 0.75 3
3 [tex]\frac{1}{8}[/tex] = 0.125 0.375 3.375
Total 1.5 6.75
(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.125 + 0.375 + 0.375
= 0.875
(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= 1 - 0.125
= 0.875
(d) The expected value of X = E(X) = [tex]\sum (X \times P(X))[/tex]
= 1.5
(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]
= [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]
= [tex]6.75 - 1.5^{2}[/tex] = 4.5
Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.121.
Given a quadratic function that has solutions at x=4 and x=6 which of the following is one of the linear factors of the function?
A.(x+4)
B.(x-6)
C.(x-2)
D.(x+6)
Answer: THE SOLUTION IS B
x=4 gives the linear factor x-4
x=6 gives the linear factor x-6
Step-by-step explanation:
..
..................
[tex]1. \: (x - y) {2} \\ = {x}^{2} - 2xy + {y}^{2} \\ 2. \: (a + b) ^{2} \\ = {a}^{2} + 2ab + {b}^{2} \\ 3. \: (2x + 3y) ^{2} \\ = {(2x)}^{2} + 2.2x.3y + (3y) ^{2} \\ = {4x}^{2} + 12xy + {9y}^{2} \\ 4.(3x - 2y) ^{2} \\ = (3x) ^{2} - 2.3x.2y + (2y) ^{2} \\ = {9x}^{2} - 12xy + {4y}^{2} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
a) x^2−2xy+y^2
b) a^2 -ab+b^2
c)4x^2+12xy+9y^2
d)9x^2 -12xy+4y^2
Step-by-step explanation:
a) x^2−2xy+y^2
b) a^2 -ab+b^2
c)4x^2+12xy+9y^2
d)9x^2 -12xy+4y^2
We rewrite (x-y)^2 as (x-y) (x-y) to show and always see + sign at start for question a ) and question b)
a) x*x+x(−y)−yx−y(−y) = x^2−2xy+y^2
b) a^2 becomes a^2 -ab as a^2 -ab+b^2
c) As shown in notes attached and this will help you most.
d) the reasons we keep +4y is because -2y becomes -2y-2y and creates a plus.
Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same width but a length that is 5 feet more than its width. If Jack's patio is 120 square feet and Ron's patio is 104 square feet, how many square feet longer is Jack's patio than Ron's?
Answer:
difference in area = 16 ft²
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
Step-by-step explanation:
Jacks rectangular patio
width = a
length = 2a - 1
area = lw
where
l = length
w = width
area = 120 ft²
a(2a - 1)
2a² - a - 120 = 0
(a - 8) (2a + 15)
a = 8 or -15/2
Ron's rectangular patio
width = a
length = a + 5
area = lw
area = 104 ft²
a (a + 5) = 104
a² + 5a -104 = 0
(a + 8) (a - 13)
a = -8 or 13
How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,
120 - 104 = 16 ft²
The value 8 or 13 can be used for a since the width a have to be the same.
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
we choose a sample of size 100 from a population of monthly cable bills having standard deviation $20 If we assume the population mean bill is $65, what is the probability mean of our sample is greater than $70. .
Answer:
0.62% probability that the mean of our sample is greater than $70.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 65, \sigma = 20, n = 100, s = \frac{20}{\sqrt{100}} = 2[/tex]
What is the probability mean of our sample is greater than $70.
This is 1 subtracted by the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{70 - 65}{2}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that the mean of our sample is greater than $70.
g Suppose the company operates mine #1 for x1 days and mine #2 for x2 days. Write a vector equation in terms of v1 and v2 whose solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver. Do not solve the equation.
Answer:
The vector equation in terms of v1 and v2 is x₁v₁ +x₂v₂ = [296 2454]
Step-by-step explanation:
Solution
The aim is to write down a vector equation in terms of v1 and v2, when solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver.
Thus,
Suppose that b = [ 296 2454] is the corresponding vector which is representing the total needed output.
Now,
If the company operates mine 1 for x1 days and mine #2 for x2 days
Then,
The total output becomes x₁v₁ +x₂v₂ which is the same output to b = [296 2454]
Hence, x₁ and x₂ should be satisfactory to the needed vector equation x₁v₁ +x₂v₂ = [296 2454]
So, the vector equation becomes x₁v₁ +x₂v₂ = [296 2454]
The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2.
Required:
a. Estimate at 5% level of significance whether the true average shrinkage percentage U: is greater than 17.5 and write your conclusion.
b. Report the p-value.
Answer:
a) [tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
b) [tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18.4[/tex] represent the sample mean
[tex]s=2.2[/tex] represent the sample standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =17.5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Part a
We want to test if the true mean is higher than 17.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 17.5[/tex]
Alternative hypothesis:[tex]\mu > 17.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
Part b
The p value would be given by:
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
Find the midpoint of (9,2) and (-7,-9)
Answer:
(1,-7/2)
Step-by-step explanation:
The midpoint of (9,2)(-7,-9) is (1,-7/2)
In a game of cards, a bridge is made up of 13 cards from a deck of 52 cards. What
is the probability that a bridge chosen at random contains
6 of one suit, 4 of another, and 3 of another?
Answer:
Probabilty= 4.171. *10^-4
Step-by-step explanation:
bridge is made up of 13 cards
probability that a bridge chosen at random contains
6 of one suit, 4 of another, and 3 of another
Probabilty of 6 = 13C6
Probabilty of 4 = 13C4
Probabilty of 3 = 13C3
Then total= 53C13
Probabilty =( 13C6*13C4*13C3)/53C13
Probabilty=( 1716*715*286)/53C13
Probabilty= 4.171. *10^-4
6q+4-q+5 please right now
Answer:
5q + 9
Step-by-step explanation:
Combine like terms to simplify the expression.
Have a blessed day!
Answer:
7q+9
Step-by-step explanation:
6q+4+q+5
6q+q+4+5
=7q+9
What’s the correct answer for this? Select all the ones that apply
Answer:
A, B and C
Step-by-step explanation:
1) After reflecting the circle over line g, we would come to know that Both are same in size
OR
2) we can also rotate the circle 180° around point C
OR
3) we can also translate the dilated circle so that it's centre is at point b
Find the population mean or sample mean as indicated.
Sample 17, 13, 5, 12, 13
Answer:
13
Step-by-step explanation:
I think
find the circumference of the circle use 3.14 for pi when the radius is 13 cm
Answer:
C =81.64 cm
Step-by-step explanation:
The circumference of a circle is given by
C = 2*pi*r
C = 2 * 3.14 * 13
C =81.64 cm
_______________________________
Radius(r)=13 cm
Circumference of circle=?
Now,
Circumference of circle=2 pi r
=2*3.14*13
=81.64 cm
Hope it helps..
Good luck on your assignment
________________________________
Which is the value of this expression when a = negative 2 and b = negative 3? (StartFraction 3 a Superscript negative 3 Baseline b squared Over 2 a Superscript negative 1 Baseline b Superscript 0 Baseline EndFraction) squared
Answer:
27/8
Step-by-step explanation:
You seem to want to evaluate ...
[tex]\dfrac{3a^{-3}b^2}{2a^{-1}b^0}[/tex]
I like to simplify the expression first, even though the order of operations would have you evaluate it as is.
[tex]=\dfrac{3}{2}a^{-3-(-1)}b^{2-0}=\dfrac{3b^2}{2a^2}[/tex]
Substitute the given values for "a" and "b" and do the arithmetic.
[tex]=\dfrac{3(-3)^2}{2(-2)^2}=\dfrac{3\cdot 9}{2\cdot 4}=\boxed{\dfrac{27}{8}}[/tex]
Show that an implicit solution of 2x sin2(y) dx − (x2 + 10) cos(y) dy = 0 is given by ln(x2 + 10) + csc(y) = C. Differentiating ln(x2 + 10) + csc(y) = C we get 2x x2 + 10 + dy dx = 0 or 2x sin2(y) dx + dy = 0. Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
Answer:
Step-by-step explanation:
[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]
Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.
Problem solved
Solve the problem. When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)
Answer:
73 mph
Step-by-step explanation:
The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).
We have that the model would be:
y = 43.81 - 0.395 * x
We need to solve for x, if y = 15
Replacing:
15 = 43.81 - 0.395 * x
Solving for x we have:
0.395 * x = 43.81 - 15
0.395 * x = 28.81
x = 28.81 / 0.395
x = 72.9
We are asked to round to the nearest number therefore x = 73.
The car will average 15 miles per gallon at the speed of 73 miles per hour.
I need some help please
Answer:
ofn
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since there are 44 average people out of 80. We can do this,
Total students : 600
Checked: 80
Average: 44
Number of averaged throughout the school: 600/80 * 44
l: 7.5 * 44
Thus it is: 330 average students
Use the equation and type the ordered-pairs. y = log 2 x {(1/2, a0), (1, a1), (2, a2), (4, a3), (8, a4), (16, a5)}
Answer:
the answer is 1/2,a0
Step-by-step explanation:
Mel buys a shirt that cost 12.50 and some pairs of socks that are 2.50 each.He pays a total of 27.50$.How many pairs of socks did Mel buy?
Answer:
6
Step-by-step explanation:
Let's call the number of pairs of socks he buys s.
[tex]12.50+2.50s=27.50[/tex]
Subtract 12.50 from both sides:
[tex]2.50s=15[/tex]
Divide both sides by 2.5 to isolate s:
[tex]s=6[/tex]
Hope this helps!
The sum of three consecutive odd numbers is 315 what are the numbers?
Answer:
Search Results
Featured snippet from the web
Which means that the first number is 104, the second number is 104 + 1 and the third number is 104 + 2. Therefore, three consecutive integers that add up to 315 are 104, 105, and 106.
Step-by-step explanation:
Formula to find the number of subsets of a set that has "n" number of elements. 2 raise 1)to the nth power 2)n squared 3)2 times n 4)All of these
Answer:
(A)[tex]2^n[/tex]
Step-by-step explanation:
Given a set with "n" number of elements, the collection of all subsets of the set is referred to as the Power set of the given set.
To find the number of possible subsets of any set, we use the formula: [tex]2^n[/tex]
Take for example the set: A={2,3,4)
A has 3 elements, therefore n=3
The number of possible subsets of A is: [tex]2^3=8$ subsets[/tex]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
6x^2 -2x -6
Step-by-step explanation:
f(x) = 6x^2 -4
g(x) = 2x+2
f(x) - g(x) = 6x^2 -4 - (2x+2)
Distribute the minus sign
6x^2 -4 - 2x-2
Combine like terms
6x^2 -2x -6
Answer:
b
Step-by-step explanation:
6x^2
2x
-4+2=-2
What percentage of the total number of microstates are in one of the three most likely macro states of 100 coins being tossed (49 heads and 51 tails, 50 heads and 50 tails, or 51 heads and 49 tails)
Answer:
Step-by-step explanation:
Idk
