Final answer:
The probability of a pregnancy lasting 309 days or longer is approximately 0.32%. Pregnancies shorter than 266 days are considered premature, which is determined based on the lowest 44% criterion.
Explanation:
The questions deal with calculating probabilities and determining specific values based on a normal distribution of pregnancy lengths, with a mean of 268 days and a standard deviation of 15 days.
a. Find the probability of a pregnancy lasting 309 days or longer.
To find this probability, we first calculate the z-score for 309 days:
Z = (X - μ) / σ = (309 - 268) / 15 ≈ 2.73.
Looking up the z-score of 2.73 in a standard normal distribution table or using a calculator with normal distribution functions, we find the area to the right is approximately 0.0032. This represents the probability of a pregnancy lasting 309 days or longer, which is 0.32%.
b. Find the length that separates premature babies from those who are not premature.
To determine the length of pregnancy that separates the lowest 44% (premature babies), we look for the z-score corresponding to the 44th percentile in a standard normal distribution table, which is approximately -0.15.
Then, we use the formula to find the specific value: X = μ + Zσ = 268 + (-0.15)(15) ≈ 266 days. Therefore, pregnancies shorter than 266 days are considered premature in this context.
find the missing number 1.2 equals 3. what
Match the expressions with the property used to generate 5y + 2y + 6 + 2.
One rejects the null hypothesis only when the:
a. sample mean is larger than the population mean.
b. p value associated with the test statistic is greater than the p level chosen.
c. p value associated with the test statistic is smaller than the p level chosen.
d. sample mean is smaller than the population mean.
3x+4y=-23
2y-x=-19
What is the solution (x,y) to the systems of equations above?
Final answer:
The solution to the system of equations 3x + 4y = -23 and 2y - x = -19, found using the elimination method, is (x, y) = (-61, -40).
Explanation:
To solve the system of equations 3x + 4y = -23 and 2y - x = -19, we can use the method of substitution or elimination. Let's use elimination to find the solution for (x, y).
Multiply the second equation by 2 to align the x terms: 2(2y - x) = 2(-19), which gives us 4y - 2x = -38.
Rewrite the equations to align like terms:
3x + 4y = -23
-2x + 4y = -38
Add the two equations together to eliminate y: (3x - 2x) + (4y + 4y) = -23 - 38, resulting in x = -61.
Substitute x back into the second original equation: 2y - (-61) = -19, which simplifies to 2y + 61 = -19.
Solve for y by subtracting 61 from both sides: 2y = -80, and then dividing by 2 gives us y = -40.
So, the solution to the system of equations is x = -61 and y = -40.
Lucy is making a smoothie by following the recipe below
if m 6 =50 then find m 11
The question about finding the value of m 11 based on m 6 cannot be answered with the information provided. Additional context or a specific formula is needed to make a calculation.
Explanation:It appears that there might be a misunderstanding in the question, as the provided information is not sufficient to determine the value of m 11 based on the value of m 6. The references provided deal with various scientific and mathematical concepts that do not seem directly related to one another and therefore do not give a clear method for calculating m 11 from m 6.
Additional context or information such as a specific formula, sequence, or relationship between m 6 and m 11 would be necessary to provide an accurate answer. Without this information, it's not possible to calculate m 11.
if 30% of the students in Miss World was class like chocolate ice cream then how many students are in her class if 6 students like chocolate ice cream
the movie theater is twice as far from the school as the mall. if the movie theater is to the right of the school, at which location is the movie theater ?
if the input is 3 and the output is 13 what is the function
which term best describes the statement given below?
if a = b and b = c then a= c
Answer:
Syllogism law
Step-by-step explanation:
Given:
a ⇒ b, and b ⇒ c, then a ⇒ c
This is a transitive property and it is also called syllogism law.
For example,
if it rains (a), then the cricket field will be wet (b), this means a ⇒b
If the cricket field wet(b), then the game will be cancelled(c), this means b ⇒c
if it rains (a), then the game will be cancelled(c), this means a ⇒ c
So it is a valid conclusion. This is called syllogism law.
Graph the equation
5x+3y+62=30
Answer:
see below
Step-by-step explanation:
Subtract 62, then divide by -32 to put the equation into intercept form:
... x/(-6.4) + y/(-10 2/3) = 1
This tells you the x-intercept is -6.4, and the y-intercept is -10 2/3. A line through these two points is your graph.
A circle is dropped into parabola y = x 2 . what is the radius of the largest circle that will touch the vertex?
Find an equation of the tangent line to the tangent line to the given curve at the specified point y= ln(x^2-8x+1), (8,0)
What is m? 128° 173° 192° 256°
173 is the answer
The Voyager 2 space probe took 2 years to make its closest approach to Jupiter. How many months did it take Voyager 2 to reach Jupiter? (1 year = 12 months)
Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Check all that apply. The domain is {x| x ≥ 3}. The range is {y| y ≥ –1}. The function decreases over the interval (–∞, 3). The function increases over the interval (–1, ∞). The axis of symmetry is x = –1. The vertex is (3, –1).
Answer:
2,3,6 are true on edg
Step-by-step explanation:
reuben deposits $700 into an account that pays simple interest at a rate of 5% per year. How much interest will he be paid in the first 3 years?
how i describe the algebraic expression of n+4
Answer:
Step-by-step explanation:
One way to put that into words would be "4 added to some number". Another way could be "the sum of some number and 4" or "4 more than some number". They all mean the same thing.
look i know its easy to u but can you help me with this one
The cover of a jacuzzi is a regular pentagon. If the side measures 2.5 feet and the apothem is 1.7 feet, find the area of the lid used to cover the Jacuzzi
The status of a statement is either true or false geometry
What is the principal if the amount is $1056,the time is 4 years,and the rate is 8%?
The principal amount is calculated using the formula for simple interest. By rearranging the formula and inputting the given values for the amount, time, and interest rate, the principal is determined to be $800.
To find the principal if the amount is $1056, the time is 4 years, and the rate is 8%, we can use the formula for simple interest which is:
Amount = Principal + (Principal × Rate × Time)
Rewriting the formula to solve for principal (P), we get:
Principal = Amount ÷ (1 + Rate × Time)
Substituting the given values:
Principal = $1056 ÷ (1 + 0.08 × 4)
Principal = $1056 ÷ (1 + 0.32)
Principal = $1056 ÷ 1.32
Principal = $800
Therefore, the principal is $800.
What are the coordinates of the image of the point (4, 2) after a dilation with a center of (0, 0) and a scale factor of 2? A. (0, 0) B. (2, 1) C. (4, 2) D. (8, 4)
Answer:
Option D (8,4)
Step-by-step explanation:
we know that
The dilation centered at the origin (0,0) is very simple. To find out the image point multiply the scale factor to the x and y-coordinates of the pre-image point.
so
(2*4,2*2) -----> (8,4)
Answer:
D. (8, 4) IS THE ANSWER
me n my dad share the cost of a meal the ratio of 2:3 i payed £52.20 whats the total cost of the meal
Steph Curry makes 9 out of 10 free throws if he free throws 200 shots how many can the expect to get in
Answer:
180 out of 200
Step-by-step explanation:
What is equation for the line or curve of the best fit for the following data?
According to these three facts, which statements are true?
Circle W has center (−3, 0) and radius 8.
Circle V is a translation of circle W, 2 units down.
Circle V is a dilation of circle W with a scale factor of 2.
Select each correct answer. (You can choose more than one).
A. Circle V and circle W are similar.
B. Circle V and circle W have the same center.
C. The radius of circle V is 16.
D. The center of circle V is (−5, 0).
Circle V and Circle W are similar and the radius of Circle V is 16; however, Circle V and Circle W do not have the same center, and the center of Circle V is not (-5, 0), but rather (-3, -2).
Given the information that Circle W has center (-3, 0) and radius 8, and Circle V is a translation of Circle W 2 units down and a dilation with a scale factor of 2, the following statements can be evaluated:
Circle V and Circle W are similar: This statement is true. Both circles maintain their shape after a translation and dilation.Circle V and Circle W have the same center: This statement is false. Translation moves the center of Circle V 2 units down, changing its coordinates.The radius of Circle V is 16: This statement is true. The radius is doubled through the dilation process.The center of Circle V is (-5, 0): This statement is false. The correct center after translation would be (-3, -2).How many triangles can be constructed with angles measuring 80 degrees 80 degrees and 40 degrees
Answer:
None
Step-by-step explanation:
The angles inside a triangle add to 180. If the angles are 80, 80 and 40, then they must add to 180 to form a triangle.
80+80+40 = 200
This can't be a triangle.
For what values of m does the graph of y=mx^2-5x-2 have no x-intercepts
Find the general solution of the given second-order differential equation. 25y'' − 15y' − 4y = 0
Final answer:
To solve the second-order differential equation 25y'' - 15y' - 4y = 0, we find the characteristic equation and its roots, then express the general solution as a linear combination of terms with the found roots as exponents, resulting in [tex]y(t) = C_1e^{-t/5} + C_2e^{4t/5}.[/tex]
Explanation:
We are given a second-order differential equation with constant coefficients: 25y'' − 15y' − 4y = 0. First, we will look for a characteristic equation that arises from this differential equation to find the general solution.
To find the characteristic equation, we substitute [tex]y = e^{rt}[/tex] (where r is a constant) into our differential equation, replacing y'' with [tex]r^2e^{rt}[/tex], y' with [tex]re^{rt}[/tex], and y with [tex]e^{rt}[/tex]. The equation becomes 25r² − 15r − 4 = 0.
Solving for r, we find the roots of the characteristic equation, which are the values of r that satisfy the equation.
Once we have the roots, which we'll call r₁ and r₂, the general solution to the differential equation is [tex]y = C_1e^{r_1t} + C_2e^{r_2t}[/tex], where C₁ and C₂ are arbitrary constants determined by initial conditions.
To find r₁ and r₂, we factor the characteristic equation:
25r² − 15r − 4 = (5r + 1)(5r - 4) = 0. Hence, r₁ = -1/5 and r₂ = 4/5.
Finally, the general solution to the differential equation is [tex]y(t) = C_1e^{-t/5} + C_2e^{4t/5}.[/tex]