Answer: 0.9887
Step-by-step explanation:
Let p be the probability that flights are on time.
As per given, p =70% = 0.7
Sample size : n = 8
Let x be a binomial variable that represents the number of fights are on time ( i.e. success).
Using binomial formula: [tex]P(X=x) = \ ^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that at least 3 flights are on time = [tex]P(X\geq 3)=1-P(X<3)\\\\=1-[P(X=0)+P(X=1)+P(X=2)]\\\\=1-[^8C_0(0.7)^0(0.3)^8+^8C_1(0.7)^1(0.3)^7+^8C_2(0.7)^2(0.3)^6]\\\\=1-[(0.3)^8+8(0.7)(0.3)^7+\dfrac{8!}{2!6!}(0.7)^2(0.3)^6]\\\\=1-[0.00006561+0.00122472+0.01000188]\\\\=1-0.01129221\\\\=0.98870779\approx\ 0.9887[/tex]
The probability that at least 3 flights are on time = 0.9887
Find constants a , b, and c such that the function
y = ax2 + bx + c satisfies the differential equation y′′ + y′ − 2y = 4x2.
Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
3/4x-2=2/5
Rewrite so there is no fractions
Answer:
15x - 40 = 8
Step-by-step explanation:
3/4x-2=2/5
Multiply each side by 4*5 or 20
20 (3/4x-2=2/5)
15x - 40 = 8
A pancake recipe require 1 2/3 cups of flour to make 20 pancakes and you have 9 cups of flour.
a. How many pancakes can you make with 1 cup of flour?
b. How many pancakes can you make with 9 cups of flour?
C. Do you have enough to make 100 pancakes? Explain
Quantity of flour needed to make 20 pancakes =
[tex] = 1 \frac{2}{3} \: [/tex]
[tex] = \frac{3 \times 1 + 2}{3} [/tex]
[tex] = \frac{5}{3} \: cups \: of \: flour[/tex]
Then , number of pancakes that can be made from 1 cup of floor :-
[tex]20 \div \frac{5}{3} [/tex]
[tex]20 \times \frac{3}{5} [/tex]
[tex] \frac{60}{5} [/tex]
[tex] = 12 \: pancakes[/tex] .
Therefore , 12 pancakes can be made from 1 cup of floor .
Solution (b) :-Number of pancakes that can be made with 1 cup of flour = 12 pancakes
Number of pancakes that can be made with 9 cups of flour :-
= 9 × 12
= 108 pancakes
Therefore , I can make 108 pancakes with 9 cups of flour .
Solution (c) :-Yes , I have enough flour to make 100 pancakes . I say this because :-
With one cup of flour I can make = 12 pancakes
With 9 cups of flour I can make =
= 9 × 12
= 108 pancakes
As I can make 108 pancakes with 9 cups of flour , I can conclude that I have enough flour to make 100 pancakes .
A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.39 pounds, which has a standardized score of 1.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution
Answer:
The number of standard deviation above the mean is [tex] z_o = 1.4607 [/tex]
Step-by-step explanation:
From the question we are told that
The mean weight of ears of corn from each farm is [tex]\mu=1.26[/tex]
The standard deviation of ears of corn from Iowa is [tex]\sigma_1[/tex]
The standard deviation of ears of corn from Ohio is
[tex] \sigma_2= 0.01 + \sigma_1 [/tex]
The weight of a random selected ear of corn from Iowa is x = 1.39 pound
The standardized score is z =1.645
The weight of a random selected ear of corn from Ohio is [tex]x_1 = 1.39\ pound[/tex]
Generally the standardized score of weight of corn from Iowa is mathematically represented as
[tex]z = \frac{ 1.39 - 1.26 }{\sigma_1 }[/tex]
=> [tex] 1.645 = \frac{ 1.39 - 1.26 }{\sigma_1 }[/tex]
=> [tex] \sigma_1 = \frac{ 1.39 - 1.26 }{ 1.64 5}[/tex]
=> [tex] \sigma_1 = 0.0790 [/tex]
Generally the standardized score of weight of corn from Ohio is mathematically represented as
[tex]z_o = \frac{ 1.39 - 1.26 }{\sigma_2 }[/tex]
=> [tex] z_o= \frac{ 1.39 - 1.26 }{0.01 + \sigma_1 }[/tex]
=> [tex] z_o = \frac{ 1.39 - 1.26 }{ 0.089}[/tex]
=> [tex] z_o = 1.4607 [/tex]
Because the value is positive it means that this value represent the number of standard deviation above the mean.
Using the normal distribution, it is found that the weight with respect to the Ohio distribution is 1.46 standard deviations from the mean.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X.For the Iowa farm:
The mean is of 1.26 pounds, hence [tex]\mu = 1.26[/tex].The weight is of 1.39 pounds, hence [tex]X = 1.39[/tex]The standardized score is of 1.645, hence [tex]Z = 1.645[/tex].Then, the standard deviation can be found as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{1.39 - 1.26}{\sigma}[/tex]
[tex]1.645\sigma = 0.13[/tex]
[tex]\sigma = \frac{0.13}{1.645}[/tex]
[tex]\sigma = 0.079[/tex]
In Ohio:
Same mean.Standard deviation 0.01 pound greater, hence [tex]\sigma = 0.079 + 0.01 = 0.089[/tex]Same weight.Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.39 - 1.26}{0.089}[/tex]
[tex]Z = 1.46[/tex]
The weight with respect to the Ohio distribution is 1.46 standard deviations from the mean.
To learn more about the normal distribution, you can check https://brainly.com/question/24663213
3x - 5 = 2x + 10
What’s the value of x
Answer:
x = 3
Step-by-step explanation:
braniest pls
Answer:
x=3
Step-by-step explanation:
-5 +10
+5=15
+5=0
3x, 2x
+2 -2
5x=15
_ _
x=3
uestion 1:
Damon wants to sell his motorcycle that he paid $4,000 for 3 years ago. The motorcycle depreciated (decreased in value) at a constant rate each month over a 3-year period. If x represents the monthly depreciation amount, write an expression that shows how much Damon can sell his motorcycle for today.
Answer:
4,000 -x3
Step-by-step explanation:
x times 3 is equal to the decrease so therefore you take the decrease away form 4/oo
Answer:
3y-x=4,000
Step-by-step explanation:
3 over 5 =nothing over 20
ion even know yet
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Which is true 0.45>0.5
0.45<0.5
4.05=0.45
4.05 <0.45
Answer:
4.05 is greater than 0.45
Which property justifies the statement if y = 7, then 7 = y?
find the measures of angles 1, 2, and 3
x = 33°
Then :-
m∠1 = 33° ( angle x and angle 1 are corresponding angles on a transversal )
Which means :-m∠1 + m∠2 = 90° ( angle 1 and angle 2 are complementary angles )
33 + ∠2 = 90
∠2 = 90 - 33
m∠2 = 57°
Then :-m∠1 + m∠3 = 180° ( angle 1 and angle 3 are a linear pair )
33 + ∠3 = 180°
∠3 = 180 - 32
m∠3 = 147°
Therefore , m∠1 = 33°m∠2 = 57° m∠3 = 147°A cash register contains q quarters. Write an algebraic expression that represents the total amount of money (in dollars).
Answer:
0.25q
Step-by-step explanation:
A cash register is a machine used in small business that sums, display and records the total amount made by each sale. A cash register also has a drawer which is used to store money.
A quarter is a coin in the United States which is 25 cents.
Converting 25 cents to dollars:
100 cents = $1
25 cents = 25 cents × $1 / 100 cent = $0.25
The total amount of money registered = number of quarters × $0.25
The total amount of money registered = q × $0.25 = 0.25q
what are the 3 consecutive integers with a sum of 48
Answer:
15 16 and 17.
Step-by-step explanation:
Hope this helps.
Answer:
15, 16, and 17
Step-by-step explanation:
6th grade math i mark as brainliest
Answer:
16
Step-by-step explanation:
Plz help i only need c im confused lol 6th grade history
Answer:
War
Step-by-step explanation:
Criminals
Jason is only able to work 28 hours a week this month (at $12 an hour) so he is worried that he will be in a bind paying his bills. He has to pay
his rent ($875) and his car payment ($330) with insurance ($130). How miuch will Jason have left over at the end of the month?
Answer:
9
Step-by-step explanation:
28 x 4=112
112 x 12= 1344
1344-875-330-130=9
Answer:
he will have $9 left over
Given m||n, find the value of x.
t
>m
(x+14)
(9x-8)"
Answer:
1st one
Step-by-step explanation:
Answer:
1st one
Step-by-step explanation:
The function C(x)=16x+4,200 represents the cost to produce x number of items. How many items should be produced so that the average cost is less than $40?
Answer:
175
Step-by-step explanation:
HELP ASAP IT'S AN EMERGENCY
Answer:
Last option must be correct because you need to prove three things congruent to give a postulate.In which case you have two sides of each triangle that means it is incomplete.
thus last option is correct.
Please help with this
a. r + (-s) = r - s
b. r - (-s) = r + s
c. -r + (-s) = -r - s
d. -r - (-s) = -r + s
When converting a proper fraction to a decimal is the answer less than or greater than 1
Answer:
Proper and Improper Fractions. Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions. In proper fractions, the numerator is less than the denominator.
Step-by-step explanation:
Help! Now help! ASAP!I’ll make you brainly now please
Answer:
35
Step-by-step explanation:
Answer:
-35 meters
Step-by-step explanation:
He's below sea level, basically saying below 0= sea level.
Then it's basically saying -172+ 137 meters because the shark is going upwards 137 meters, which makes 137 positive. Dude, remember, up is positive and down is negative. So the answer to this problem would be -35 meters because of -172+137=-35. Hope this helped you.
h(x) = x + 1 k(x) = x - 2 (h + k)(2) =
[tex]h(x) = x + 1[/tex]
[tex]k(x) = x - 2[/tex]
_________________________________
[tex](h + k)(x) = h(x) + k(x)[/tex]
[tex](h + k)(x) = (x + 1) + (x - 2) \\ [/tex]
[tex](h + k)(x) = x + 1 + x - 2[/tex]
[tex](h + k)(x) = 2x - 1[/tex]
[tex](h + k)(2) = 2(2) - 1[/tex]
[tex](h + k)(2) = 4 - 1[/tex]
[tex](h + k)(2) = 3[/tex]
_________________________________
And we're done.....♥️♥️♥️♥️♥️
Answer:it’s 5
Step-by-step explanation:
because it is
Simplify and write answer in terms of i as appropriate. *. i^25
Answer:
i
Step-by-step explanation:
Given the complex value i^25, we are to write in terms of i. In complex number:
i² = -1
i^25 =( i²)¹² × i
= (-1)¹² × i
Note that -1 to a negative number will give a positive number hence (-1)¹² = 1
(-1)¹² × i = 1×i
= i
Hence i^25 = i
. 1. Amanda correctly
answered 48 of the 60
questions on a math exam.
What percent of questions did
she answer correctly?
I NEED TO SHOW MY WORK step by step explanation plz
Answer:
80%
Step-by-step explanation:
To find what percent a part is of the whole, divide the part by the whole and multiply by 100%.
part = 48
whole = 60
percent = part/whole * 100%
percent = 48/60 * 100%
percent = 80%
Answer: 80%
Amanda answered 80 % of question correctly.
Given that, Amanda correctly answered 48 of the 60 questions on a math exam.
Percent of question, she answer correctly,
[tex]=\frac{48}{60}*100=\frac{8}{10}*100 =80 [/tex]
Hence, Amanda answered 80 % of question correctly.
Learn more:
https://brainly.com/question/2236179
The perimeter of a playing field for a certain sport is 214 ft. The field is a rectangle, and the length is 41 ft longer than the width. Find the dimensions
The width of the playing field is
(Type an integer or a decimal)
Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
L is the length of the rectangle:
W is the width of the rectangle.
Given
Perimeter = 214feet
If the length is 41 ft longer than the width, then L = 41+W
Substitute L = 41+W into the formula:
P = 2(L+W)
214 = 2(41+W+W)
214 = 2(41+2W)
214 = 82+4W
4W = 214-82
4W = 132
W = 132/4
W = 33 feet
Since L = 41+W
L = 41+33
L = 74 feet
Hence the dimension of the field is 74ft by 33ft
The width of the playing field is 33feet
The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what pattern would you expect in a normal quantile plot of these data?
a. The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be bell-shaped.
b. The histogram would by non-symmetric, and the normal quantile plot would have data points that would be non- linear.
c. The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be non-linear.
d. The histogram would be approximately bell-shaped, and the normal quantile plot would have data points have follow a straight-line pattern.
Answer:
d. The histogram would be approximately bell-shaped, and the normal quantile plot would have data points have follow a straight-line pattern.
Step-by-step explanation:
Since the variable is normally distributed, the histogram of women's height should be approximately bell shaped (if the data was obtained form a random sample).
Again, the variable is normally distributed, therefore, the quantile plot should follow a straight line pattern (a diagonal line to be more precise).
Solve the following: - 8h = -0.36
Answer:
h=0.045
Step-by-step explanation:
What is the solution to 2x-8 <12?
o x<2
O x<3
Ox<10
0x<40
Answer:
x<10
Step-by-step explanation:
i think this is the answer
x<10 is the solution of the inequality 2x-8 <12
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 2x-8<12
Two times of x minus eight less than twelve
x is the variable
We have to find the solution of the inequality
2x<20
Divide both sides by 2
x<10
Hence, x<10 is the solution of the inequality 2x-8 <12
To learn more on Inequalities click:
https://brainly.com/question/28823603
#SPJ7
Express 13/4 as a mixed number
Answer:
3 1/4
Step-by-step explanation:
Answer:
3/1/4
Step-by-step explanation:
Please Mark Brainliest!! Hope this helped!!
After 5.5 hours, Allie had traveled 264 miles. If she travels at a constant speed, how far will she have traveled in 6 hours?
Answer:
288 Miles
Step-by-step explanation:
Solve for x (speed)
5.5x = 264
Divide by 5.5
x = 48
y = 48x
Subsitute 6 hours in for x
y = 48(6)
y = 288
Answer: Allie went 288 miles in 6 hours.
Step-by-step explanation:
First, you must find out how many miles Allie travled in one hour
= 264/5.5
= 48
Next, multiply the quotient by the number of hours to get the answer.
= 48 x 6
= 288
