Using the normal distribution and the central limit theorem, it is found that there is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
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. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 62 mph, hence [tex]\mu = 62[/tex].Standard deviation of 5 mph, hence [tex]\sigma = 5[/tex].Sample of 50 cards, hence [tex]n = 50, s = \frac{5}{\sqrt{50}} = 0.7071[/tex]The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 1 subtracted by the p-value of Z when X = 66, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{66 - 62}{0.7071}[/tex]
[tex]Z = 5.66[/tex]
[tex]Z = 5.66[/tex] has a p-value of 1.
1 - 1 = 0.
There is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
A similar problem is given at https://brainly.com/question/24663213
y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence relation that the coefficients must satisfy
Let
[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots[/tex]
Differentiating twice gives
[tex]\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots[/tex]
[tex]\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n[/tex]
When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.
Substitute these into the given differential equation:
[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0[/tex]
Then the coefficients in the power series solution are governed by the recurrence relation,
[tex]\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}[/tex]
Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.
• If n is even, then n = 2k for some integer k ≥ 0. Then
[tex]k=0 \implies n=0 \implies a_0 = a_0[/tex]
[tex]k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}[/tex]
[tex]k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}[/tex]
[tex]k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]
It should be easy enough to see that
[tex]a_{n=2k} = \dfrac{a_0}{(2k)!}[/tex]
• If n is odd, then n = 2k + 1 for some k ≥ 0. Then
[tex]k = 0 \implies n=1 \implies a_1 = a_1[/tex]
[tex]k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}[/tex]
[tex]k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}[/tex]
[tex]k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}[/tex]
so that
[tex]a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}[/tex]
So, the overall series solution is
[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)[/tex]
[tex]\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}[/tex]
Find the surface area of this cuboid
Answer:
62
Step-by-step explanation:
SA=2(5x2)+2(5x3)+2(3x2)
SA=20+30+12
SA=62
3. Sarah has a goal to save $81.84 for a new gan
If she has 12 weeks to save the money, how much does she need
to save each week?
Answer:
93.84
Step-by-step explanation:
I think I'm not sure
The length of a rectangle is three times its width. if the area of the rectangle is 75 in2, find its perimeter.
Answer:
40 in
Step-by-step explanation:
For a width of w, the length is 3w and the area and perimeter are ...
A = LW = (3w)(w) = 3w^2
P = 2(L+W) = 2(3w +w) = 8w
We are given the area, so we can find w to be ...
75 in^2 = 3w^2
25 in^2 = w^2 . . . . . divide by 3
5 in = w . . . . . . . . . square root
Then the perimeter is ...
P = 8w = 8(5 in) = 40 in
helpppp pleaseeeee✋
Answer:
5 x 3 = 15 / 4 x 8 = 32 / 6 x 1.5 = 9
Step-by-step explanation:
Answer:3,8,3/2
Step-by-step explanation:
1) 5*x=15
X=15/5=3
2) 4*x=32
X=32/4=8
3)
6*x=9
X=9/6=3/2
PLS HELP ASAP
x^2 - 4x-1=0
Solve using formula
Answer:
Your answer would be x=2±√5
Step-by-step explanation:
please help.. no links
Use Pythagorean theorem,
[tex]29^2 = 21^2 + x^2 \\\\\implies x^2 = 29^2 -21^2 \\\\\implies x^2 = 400\\\\\implies x = \sqrt{400} = 20[/tex]
Can someone answer this for me
Answer:
s=4
Step-by-step explanation:
area of square is side*side
so that means s*s=16
so s = 4
I need to find out the answer for this problem...
Answer:
where is the problem to solve. please tell me
Write an equation with slope of -2 and goes through the point (-3,7)
Answer:
y = -2x + 1
Step-by-step explanation:
Substitute the slope and the given point into y = mx + b and solve for "b".
y = mx + b
7 = -2(-3) + b
7 = 6 + b
1 = b the y-intercept is 1
The equation of the line is y = -2x + 1
4. Suppose you have a map of Charlotte where 2
inches equals 4 miles. On the map, the distance
from your house to school if 3.5 inches. How
many miles is this?
Andrew invests $9000
What are you asking?
evaluate 6^2 - (9 divided by x) when x = 3
Answer:
33
Step-by-step explanation:
Se mezcla café del tipo A de 6 €/kg con café del tipo B de 4,5 €/kg para obtener una mezcla de 60 kg a 5 €/kg. ¿Cuántos kilogramos de café debemos tomar de cada tipo?
9w=8w-5
[tex]9w=8w-5[/tex]
Answer:
9w=8w-5
collect like terms
9w-8w=-5
w=-5
Multiply & Divide Fractions Task Card # 29
3
4
Beverly walks for exercise
mile every day: How far does
she walk each week?
Answer:
I dont understand what you're saying, but im thinking 7 miles?
Write the equation of the circle centered at (10, – 4) that passes through (14, 12).
Answer:
(x -10)² +(y +4)² = 272
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
The center is given as (h, k) = (10, -4). We can find the value of r² using the "passes through" point coordinates:
(14 -10)² +(12 -(-4))² = r² = 16 +256 = 272
Then for the given center and the value of r² we found, the equation is ...
(x -10)² +(y +4)² = 272
What is the equation of this line?
y= 1/2+2
y = 2x + 2
y= 1/2x-2
y = 2x - 2
HELP ME PLEASEEE ILL GIVE BRAINLIEST
Answer:
y=2x-2
You use rise/run in this problem
The homeowners association for a residential community is selecting a committee of 7. There are 24 candidates for positions. How many possible committees can be formed?
Answer: 168
Step-by-step explanation:
Times the two numbers together to get the combinations.
24x7=168
Possible number of committees formed is equals to 3.
What is number?
" Number is defined as the arithmetic value which represents the count of any given quantity."
According to the question,
Total number of candidates for positions = 24
Number of candidate selected for 1 committee = 7
Total possible number of committees = [tex]\frac{24}{7}[/tex]
= 3.428
≈ 3 committees (approximate)
As one committee is formed by 7 candidates , it can not be in decimals or fractions.
Hence, possible number of committees formed is equals to 3.
Learn more about number here
https://brainly.com/question/17429689
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Help please!!!!
Find the measure of the angle indicated
Answer:
x = 6
Step-by-step explanation:
Because we have parallel lines, we can use alternate angles are equal. Therefore, we know that 11x-6 = 10x.
Minus 11 from both sides, and we get -6 = -x, so x = 6
A company makes 110 bags. 30 of the bags have buttons but no zips. 23 of the bags have zips but no buttons. 23 of the bags have neither zips nor buttons. How many bags have zips on them?
Well, 30+23+23 = 76 which means there are only a total of 76 bags that are accounted for. 110-76 = 34 bags which we do not know if they have zips or not. If we assume they have zips, that would be 34+23 bags with zips which is 57 bags.
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Answer:
E
Step-by-step explanation:
Like and give 5 star rating
Please take a look at the picture
Answer:
I think it'
is A and B
Step-by-step explanation:
hope hwlps
Write each decimal as a percent. 1. 0.74
4. 0.617 =
Write each percent as a decimal. 6. 68%
9. 175% =
2. 0.15 =
5. 0.834 =
7. 34% =
10. 200% =
3. 0.09 =
8. 58.5% =
Answer:
1. 0.74 = 74%
4. 0.617 = 61.7
6. 68% = 0.68
9. 175% = 1.75
2. 0.15 = 15%
5. 0.834 = 83.4%
7. 34% = 0.34
10. 200% = 2.00
3. 0.09 = 9%
8. 58.5% = 0.585
Step-by-step explanation:
Second Graph problem! Can anybody please help me out with this? (Almost done for today) (Algebra graph problem)
Answer:
x = -2
Step-by-step explanation:
The expression f(x) = 1 corresponds to the point on the graph that is 1 unit above the x-axis. You can locate that horizontal line and see where it intersects the graph. That point of intersection is 2 grid squares to the left of the y-axis, where x = -2.
f(-2) = 1
x = -2
how do i rewrite -2/3x+2y=-7 in slope intercept form?
Answer:
y=1/3x-7/2
Step-by-step explanation:
First get the 2y by itself by adding 2/3x to both sides. Then subtract both sides by 2.
Multiply.
3 1/2 times 2 2/3
Answer:
Step-by-step explanation:
1. Un restaurant ofrece 14 entradas, 8 platos principales y 7 postres. ¿De cuántas formas un cliente puede ordenar una comida?
2. ¿Cuántos grupos de 4 letras se pueden formar con las letras de la palabra TECNICA?
3. ¿Cuántos números de 4 dígitos se pueden formar con los primeros 7 números naturales?
4. ¿Cuántos partidos distintos se pueden realizar dados 5 equipos de futbol?
5. ¿De cuántas formas pueden colocarse los 11 jugadores de un equipo de fútbol teniendo en cuenta que el portero no puede ocupar otra posición distinta de la portería mientras que los otros 10 pueden jugar en cualquier otra posición que no sea portero?
6. En el palo de señales de un barco se puede izar tres banderas rojas, dos azules y cuatro verdes. ¿Cuántas señales distintas pueden indicarse con la colocación de las nueve banderas?
Usando técnicas de conteo, se encuentra que
1. Un cliente puede ordenar una comida de 784 formas.
2. 420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.
3. 840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.
4. 10 partidos distintos se pueden realizar.
5. Pueden colocarse de 3,628,800 formas.
6. 1260 señales distintas pueden indicarse.
Item 1:
La técnica usada es el principio fundamental de conteo, que afirma que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] maneras de seren realizadas, el número total de maneras de ser realizadas es:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
En este problema, [tex]n_1 = 14, n_2 = 8, n_3 = 7[/tex], por eso:
[tex]T = 14 \times 8 \times 7 = 784[/tex]
Un cliente puede ordenar una comida de 784 formas.
Item 2:
El orden es importante, ya que TECN es una palabra diferente de NCET, por lo tanto, la fórmula de permutaciones se usa para resolver este problema.
Fórmula de permutaciociones:
El número de permutaciones de x elementos en un conjunto de n elementos es dada por:
[tex]P_{n,x} = \frac{n!}{(n - x)!}[/tex]
En este problema, 4 letras de 7, enconteces:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
La letra C se repite dos veces, o sea:
[tex]T = \frac{P_{7,4}}{2} = \frac{840}{2} = 420[/tex]
420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.
Item 3:
Permutaciones de 4 dígitos de 7, sin repeticiones, o sea:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.
Item 4:
El orden no es importante, ya que Time 1 x Time 2 es la misma partida de Time 2 x Time 1, por lo tanto, la fórmula de combinaciones se usa para resolver este problema.
Fórmula de combinaciones:
El número de combinaciones de x elementos en un conjunto de n elementos es dada por:
[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]
En este problema, combinaciones de 2 elementos de un conjunto de 5, entonces:
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
10 partidos distintos se pueden realizar.
Item 5:
El número de arreglos de n elementos viene dado por
[tex]A_n = n![/tex]
En este problema, arreglo de 10 elementos, o sea:
[tex]A_{10} = 10! = 3628800[/tex]
Pueden colocarse de 3,628,800 formas.
Item 6:
El número de arreglos de n elementos, con repeticiones de [tex]n_1, n_2, \cdots n_n[/tex] elementos viene dado por
[tex]A_n^{n_1,n_2,\cdots,n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
En este problema, [tex]n = 9, n_1 = 3, n_2 = 2, n_3 = 4[/tex], por eso:
[tex]A_9^{3,2,4} = \frac{9!}{3!2!4!} = 1260[/tex]
1260 señales distintas pueden indicarse.
Un problema similar es dado en https://brainly.com/question/19022577
urgent help now plz i will give brainlest
Answer:
Step-by-step explanation:
First get the (m) which is the gradient by using the formula y2-y1/x2-x1
Pick any random 2 values from the table. I will pick. (1,4) (2,8)
Y2=8 Y1=4 X2=2 X1=1
8-4/2-1 4/1 = 4
Y=4x+c
Help I’m timed!
The graph of an equation with a negative discriminant always has which characteristic?
A: no x-intercept
B:no y-intercept
C: no maximum
D: no minimum
Answer:
a
Step-by-step explanation:
Negative discriminant means that the fucntion has no real roots
so in the quadratic function b^2-4ac if this section is negative there are no real roots, so yes a would be the answer
Bonus: if u want to know.
However, in linear algebra which ofc i know ur not taking there would be something called imangiary roots, or complex roots.
