Answer:
220 grams.
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:
[tex]\mu = 212, \sigma = 20, n = 22, s = \frac{20}{\sqrt{22}} = 4.264[/tex]
If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?
We have to find the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.88 = \frac{X - 212}{4.264}[/tex]
[tex]X - 212 = 1.88*4.264[/tex]
[tex]X = 220[/tex]
The answer is 220 grams.
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1100 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? Round the answer to the nearest whole number
Answer:
61,925 miles
Step-by-step explanation:
Given :
The p-value of the tires to outlast the were warranty were given in the the question as = 0.96
Checking the normal distribution table, The probability that corresponds to 0.96
from the Normal distribution table is 1.75.
Mean : 'μ'= 60000 miles
Standard deviation : σ=1100
The formula for z-score is given by
: z= (x-μ)/σ
1.75=(x-60000)/1100
1925=x-60000
x=61925
Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.
6th grade math help me please :))
Answer:
b) a coefficientd) a constant1, 2, 4Step-by-step explanation:
Just definitions :)
Hope it helps <3
Elliot’s school has 24 classrooms. Each classroom has seats for 26 students. What is the maximum number of students the school can seat? Multiply to find the answer.
Answer:
24*26= 624 students
hope this helps!
Answer:
624 seats
Step-by-step explanation:
Total classrooms = 24
Each classroom has seats = 26
Total Number of seats = 24*26
=> 624 seats
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. Solve the original equation by solving the new equation
x2y'' + 9xy' - 20y = 0
Answer:
[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's follow the advise and proceed with the substitution
first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t
[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]
Now we can substitute in the equation
[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]
so the new equation is
[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]
the auxiliary equation is
[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]
so the solutions of the new equation are
[tex]y(t)=ae^{2t}+be^{-10t}[/tex]
with a and b real
as
[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]
[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]
hope this helps
do not hesitate if you have any questions
Segu
Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
Answer:
The formula is 10 - 3n
Step-by-step explanation:
For an nth term in an arithmetic sequence
U( n ) = a + ( n - 1)d
Where n is the number of terms
a is the first term
d is the common difference
From the sequence above
a = 7
d = 4 - 7 = - 3
The formula for an nth term is
U(n) = 7 + (n - 1)-3
= 7 - 3n + 3
The final answer is
= 10 - 3n
Hope this helps you.
How do I solve this problem?
Answer:
It would take 1 more mile if he took route Street A and then Street B rather than just Street C.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We use the Pythagorean Theorem to find the length of Street C:
2² + 1.5² = c²
c = √6.25
c = 2.5
Now we find how much longer route A and B is compared to C:
3.5 - (2 + 1.5) = 3.5 - 2.5 = 1
Rationalize the denominator and simplify
Answer:
sqrt(70)/7
Step-by-step explanation:
sqrt(10/7)
sqrt ( a/b) = sqrt(a)/ sqrt(b)
sqrt(10) / sqrt(7)
But we don't leave a sqrt in the denominator, so multiply by sqrt(7) /sqrt(7)
sqrt(10) /sqrt(7) * sqrt(7) / sqrt(7)
sqrt(70)/ sqrt(49)
sqrt(70)/7
Joan conducted a study to see how common binge drinking is on her college campus. She defined "frequent binge drinking" as having five or more drinks in a row three or more times in the past two weeks. Out of 593 students who replied to her survey, 64 fit this criterion. Joan wants to construct a significance test for her data. She finds that the proportion of binge drinkers nationally is 13.1%. The z statistic for this data is __________.
Answer:
z = -1.66
Step-by-step explanation:
Z-statistic:
[tex]z = \frac{X - p}{s}[/tex]
In which X is the found proportion.
p is the mean proportion.
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex] is the standard error for the data.
Out of 593 students who replied to her survey, 64 fit this criterion.
This means that [tex]X = \frac{64}{593} = 0.108[/tex]
She finds that the proportion of binge drinkers nationally is 13.1%.
This means that [tex]p = 0.131[/tex]
Also
[tex]s = \sqrt{\frac{0.131*0.869}{593}} = 0.014[/tex]
The z statistic for this data is
[tex]z = \frac{X - p}{s}[/tex]
[tex]z = \frac{0.108 - 0.131}{0.014}[/tex]
[tex]z = -1.66[/tex]
What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32
Answer:
work is shown and pictured
Answer:
Answer B. (6, 2)
Hope it works!
Step-by-step explanation:
A rectangular box has length 2 inches, width 8 inches, and a height of 10 inches. Find the angle between the diagonal of the box and the diagonal of its base. The angle should be measured in radians.
Answer:
a) diagonal box = 12.9 in
b) diagonal base = 8.2 in
Step-by-step explanation:
w = 8 in
h = 10 in
L = 2 in
required:
a) diagonal of the box
b) diagonal of its base
referring into the attached image
a) the diagonal of the box = sqrt ( w² + h² + L²)
diagonal box = sqrt (8² + 10² + 2²)
diagonal box = 12.9 in
b) diagonal of its base = sqrt ( w² + L²)
diagonal base = sqrt ( 8² + 2²)
diagonal base = 8.2 in
Tickets to a baseball game can be ordered online for a set price per ticket plus a $5.59 service fee. The total cost in dollars for ordering 5 tickets is $108.09. Which linear function represents c, the total cost, when x tickets are ordered
Answer:
c = 20.5x + 5.59
Step-by-step explanation:
c = mx + b
c = mx + 5.59
108.09 = m(5) + 5.59
5m = 102.5
m = 20.5
c = 20.5x + 5.59
Evaluate: .25 (1.2 x 3 - 1.25) + 3.45
The order to us solve is:
ParenthesesMultiplicationSum and subtractionLet's go:
[tex]25(1.2\times 3 - 1.25) + 3.45\\25(3.6-1.25)+3.45\\25\times 2.35 + 3.45\\58.75+3.45\\62.2[/tex]
Therefore, the result is 62.2.
Answer:
4.0375
Step-by-step explanation:
.25(3.6-1.25)+3.45
.25(2.35)+3.45
.5875+3.45
4.0375
HOPE THIS HELPS:)
Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim ||Δ|| → 0 n (4ci + 11) i = 1 Δxi [−8, 6]
Answer:
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
The answer of the above definite integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
Step-by-step explanation:
The given limit interval is
[tex]\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i[/tex]
[tex][a, b] = [-8, 6][/tex]
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
Bonus:
The definite integral may be solved as
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98[/tex]
Therefore, the answer to the integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
which is bigger 1 or
[tex] \frac{19}{9} [/tex]
Answer:
19/9 because it equals to 2.111.. Which is greater than 1
Step-by-step explanation:
By the way if it's right can i get brainliest.
Answer:
1 < 19/9
Step-by-step explanation:
1 vs 19/9
Rewriting 19/9 as 9/9 + 9/9+ 1/9
1 vs 1+1 +1/9
1 vs 2 1/9
1 < 19/9
V(x, y, z) = 5x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.
Answer:
[tex]D_{\vec{v}}V(6,6,5)=48[/tex]
Step-by-step explanation:
You have the following potential function:
[tex]V(x,y,z)=5x^2-3xy+xyz[/tex] (1)
To find the rate of change of the potential at the point P(6,6,5) in the direction of v = i + j - k, you use the following formula:
[tex]D_{\vec{v}}V(x,y,z)=\bigtriangledown V(x,y,z)\cdot \vec{v}[/tex] (2)
First, you calculate the gradient of V:
[tex]\bigtriangledown V(x,y,z)=\frac{\partial}{\partial x}V(x,y,z)\hat{i}+\frac{\partial}{\partial y}V(x,y,z)\hat{i}+\frac{\partial}{\partial z}V(x,y,z)\hat{i}\\\\\bigtriangledown V(x,y,z)=(10x-3y+yz)\hat{i}+(-3x+xz)\hat{j}+(xy)\hat{k}\\\\\bigtriangledown V(6,6,5)=(10(6)-3(6)+(6)(5))\hat{i}+(-3(6)+(6)(5))\hat{j}+((6)(6))\hat{k}\\\\\bigtriangledown V(6,6,5)=72\hat{i}+12\hat{j}+36\hat{k}[/tex]
Next, you replace in the equation (2):
[tex]D_{\vec{v}}V(6,6,5)=(72\hat{i}+12\hat{j}+36\hat{k})\cdot(\hat{i}+\hat{j}-\hat{k})\\\\D_{\vec{v}}V(6,6,5)=48[/tex]
Then, the rate of change of the potential at the point P(6,6,5) in the direction of v, is 48.
Express it in slope-Intercept form
Answer:
Y=1/4x-4
Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25
Jackie built a fence around her garden to keep animals out. The dimensions of the area enclosed by
the fence are shown in the diagram below. What is
the total area, in square feet, enclosed by the fence?
Answer:
the second one
Step-by-step explanation:
We can see that the fence is made by a rectangle and a trapezoid
A1 is the area of the rectangle and A2 is the area of the trapezoid
A1 = 9*12A2= [(1/2)*(18+12)*6)) by adding them we get the second oneDomain and range of T
Answer:
Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.
The domain is all of the x values. Therefore the domain is {-1, 2}.
The range is all of the y values. Therefore the range is {-4, -3, 2}.
We don't use ( ) or [ ] because T is a discrete relation.
What is an equation in point-slope form for the line that passes through the points (4,−1) and (−3,4)? y+4=−57(x+3) y+4=57(x+3) y−4=−57(x+3) y−3=−57(x+4) PLEASE HELP MEEEE
Answer:
Step-by-step explanation:
(4+1)/(-3-4)= -5/7
y + 1 = -5/7(x - 4)
or
y - 4= -5/7(x + 3)
does 6(x + 5) = 6x + 11 , have on solution, infinitely many solutions, or no solutions?
Answer:
no solution
Step-by-step explanation:
hello
[tex]6(x+5)=6x+11\\<=> 6x+30=6x+11\\<=> 30=11[/tex]
this is always false so there is no solution
Let's to expand this equation:
[tex]6(x+5) = 6x+11\\6x + 6\times 5 = 6x + 11\\6x + 30 = 6x + 11[/tex]
Perceive that in two members of equations, we have "6x", so we can to eliminate it. But, when we make it, we have this situation:
[tex]6x + 30 = 6x + 11\\30 = 11[/tex]
How [tex]30 \neq 11[/tex] this is a absurd. Therefore, this equation don't have solutions.
what is the value of 2x+3 if x=1
Answer:
5
Step-by-step explanation:
=> 2x+3
For x = 1
=> 2(1) + 3
=> 2+3
=> 5
Answer:
5
Step-by-step explanation:
2x + 3
Put x as 1 and evaluate.
2(1) + 3
2 + 3
= 5
Bob bought some land costing $15,540. Today, that same land is valued at $45,117. How long has Bob owned this land if the price of land has been increasing at 5 percent per year
Answer:
21.84 years
Step-by-step explanation:
From the compound interest formula;
F = P(1+r)^t .......1
ln(F/P) = tln(1+r)
t = ln(F/P)/ln(1+r) .......2
Where;
F = Final value = $45,117
P = Initial value = $15,540
r = rate = 5% = 0.05
t = time
Substituting the values into equation 2;
t = ln(45117/15540)/ln(1.05)
t = 21.84542292124 years
t = 21.84 years
It will take Bob 21.84 years
pls help help help help
Answer:
D
Step-by-step explanation:
We can plug in the numbers (15, 23, 25, 38, 53) into the equation for x, and see if we get the values given for the number of hits (4, 12, 14, 27, 47)
Fizzy Waters promotes their alkaline water product for everyone on the basis that alkaline water is good for health as it neutralizes acids produced in the body. They boast having a mean alkalinity level of 50 mg/liter. Alkaline water has a higher pH level than regular drinking water and Fizzy Waters claims that its higher Hydrogen content provides better hydration than regular water. To test their claim, you contact Fizzy Waters and they allow you to collect samples from their manufacturing plant to test for yourself. You collect 100 random samples of their alkaline water and find that the mean and standard deviation are y = 32.2mg/liter and 14.4mg/liter. With 99% confidence, is there enough evidence to support their claim that the population mean exceeds 50 mg/liter?
Answer:
The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.
Step-by-step explanation:
First we need to find the z-value for a confidence of 99%
The value of alpha for a 99% confidence is:
[tex]1-\alpha/2 = 0.99[/tex]
[tex]\alpha/2 = 0.01[/tex]
[tex]\alpha = 0.005[/tex]
Looking in the z-table, we have z = 2.575.
Now we can find the standard error of the mean:
[tex]\sigma_{\bar{x} }= s_x/\sqrt{n}[/tex]
[tex]\sigma_{\bar{x} }= 14.4/\sqrt{100}[/tex]
[tex]\sigma_{\bar{x} }=1.44[/tex]
Finding the 99% confidence interval, we have:
[tex]99\%\ interval = (\bar{x} - z\sigma_{\bar{x}}, \bar{x} + z\sigma_{\bar{x}})[/tex]
[tex]99\%\ interval = (32.2 - 2.575*1.44, 32.2 + 2.575*1.44)[/tex]
[tex]99\%\ interval = (28.492, 35.908)[/tex]
The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.
The ratio of sides of 2 similar cubes is 3:4. Larger cube has a volume of 1728 cubic meters. What is the volume of the smaller cube?
Answer:
See steps
Step-by-step explanation:
Volume of cubes is proportional to the cube of the side length.
Using proportions,
Volume of smaller cube / 1728 = (3/4)^3
Cross multiply,
Volume of smaller cube
= 1728 * (3/4)^3
= 1728 * (27/64)
= 729 cubic metres.
Note: all cubes are similar and each has 6 congruent faces.
A jar of sweet contains 5 yellow sweets, 4 red sweets, 8 green sweets, 4 orange sweets and 3 white sweets. Ola chose a sweet at random, what is the possibility that she will pick either a yellow or orange sweet?
Answer:
9/24 or 37.5%
hope this helps :)
Hi,
first thing you must do with a probability problem is to count how many thing you have in your universe.
Here we are dealing with sweets. So let's count : 5 +4+8+4+3 = 24
and there is 5 yellow so probability to pick up a yellow is 5/24
and there is 4 orange so probabilitu to pick up a orange is 4/24
To say : Ola will pick orange or yellow mean if she pick either one of the two sort is good. So you add the proba of each : 5/24 +4/24 = 9/24
and then you must reduce if you can : 9/24 = 3*3 /8*3 = 3/8
So the probability that Ola pick a yellow or orange sweet is 3/8 = 0.375
how many are 15 x 15 ?
Answer:
225
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
Rewrite 19/3 as a mixed number
Answer:
[tex]6\frac{1}{3}[/tex]
Step-by-step explanation:
You can divide 19 by 3 a total of 6 times with a remainder of 1.
Richard has enrolled in a 401(k) savings plan. He intends to deposit $250 each month; his employer does not contribute to his account. How much will be in his account in 20 years?
Answer:
Richard will have $60,000 in his account in 20 years.
Step-by-step explanation:
(1) Multiply $250 x 12
(2) Multiply the answer of $250 x 12 which is 3000 by 20
(3) Final answer would be $60,000
No need of a answer anymore.
Answer:
mean score of class B = 1778/25 = 71.12
Step-by-step explanation:
This was your question : Class A has 12 pupils and class B has 25 pupils. Both classes sit the same maths test. The mean score for class A is 80. The mean score for both classes is 74. What is the mean score (rounded to 2 DP) in the maths test for class B?
mean of class A = Σfx/Σf
mean of class A = 80
Σfx = 80 × 12 = 960
Mean score for both classes = 74
where
b = Σfx of class B
960 + b/37 = 74
cross multiply
960 + b = 2738
b = 2738 - 960
b = 1778
mean score of class B = Σfx/Σf
Σfx = 1778
Σf = 25
Therefore,
1778/25 = 71.12