Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean = 246 days and standard deviation 13 days. Complete parts (a) through (1) below
(a) What is the probability that a randomly selected pregnancy lasts less than 242 days?
The probability that a randomly selected pregnancy lasts less than 242 days is approximately (Round to four decimal places as needed)
a
Answers
ANSWER
0.3783
EXPLANATION
The lengths of the pregnancies, X, is normally distributed with a mean of 246 days and a standard deviation of 13 days,
\(X=N(246,13)\)We have to find the probability that a randomly selected pregnancy lasts less than 242 days,
\(P(X<242)=?\)For this, we have to standardize the variable X with the formula,
\(Z=\frac{X-\mu}{\sigma}\)So the probability we have to solve is,
\(P(X<242)=P\mleft(\frac{X-\mu}{\sigma}<\frac{242-\mu}{\sigma}\mright)=P\mleft(Z<\frac{242-246}{13}\mright)=P(Z<-0.31)\)This is equivalent to,
\(P(Z<-0.31)=P(Z>0.31)\)Which is also equivalent to,
\(P(Z>0.31)=1-P(Z<0.31)\)We have to find these equivalences because, usually, normal distribution tables show the probabilities for positive z-scores and to the left of those values - i.e. less than those values. Find z = 0.31 in a z-table,
So, the probability is,
\(P(X<242)=1-P(Z<0.31)=1-0.6217=0.3783\)Hence, the probability that a randomly selected pregnancy lasts less than 242 days is 0.3783.
Related Questions
A proton's mass is estimated to be 1.6726 x 10^-24 and the mass of an electron is estimated to be 9.1093 x 10^-28. How many times larger is the mass of a proton compared to the mass of an electron?
Answers
A proton has a mass of \($$1.6726 * 10^{-24}\) g corresponds to 1.0072766 Atomic Mass Unit
A proton exists 1836.096 times heavier than an electron.
Proton Mass = 938.2720813 \($$MeV/c_2\)
Electron = 0.5109989461 \($$MeV/c_2\)
E : P Ratio = 1 : 1836.15267
What is a proton's mass in AMU?
\($$m_{p\) = mass of a proton (1.007277 AMU)
\($$m_n\) = mass of a neutron (1.008665 AMU)
\($$m_e\) = mass of an electron (0.000548597 AMU)
\($$m_{atom}\) = mass of nuclide (AMU)
A proton has a mass of \($$1.6726 * 10^{-24}\) g corresponds to 1.0072766 Atomic Mass Unit
[AMU, Atomic Mass Unit exists utilized to describe atomic and molecular weights, equivalent to one-twelfth of the mass of an atom of carbon-12].
Whereas, the Electron exists at \($$9.1093 * 10^{-28}\) equaling 0.000548597 AMU.
Electron to Proton Ratio = 1: (0.000548597 / 1.0072766)
= 1836.096
A proton exists 1836.096 times heavier than an electron.
Proton Mass = 938.2720813 \($$MeV/c_2\) (MeV= Mega Electron Volt)
(As per Mass - the energy equivalence principle, energy exists proportional to mass whereby, an electron volt exists also as a unit of Mass. Energy can be converted to Momentum and Mass)
Electron = 0.5109989461 \($$MeV/c_2\)
E : P Ratio = 1 : 1836.15267
Therefore, the correct answer is E : P Ratio = 1: 1836.15267.
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A triangle has an angle ratio of 3:5:10. Find the measure of each angle.
Answers
Answer:
Step-by-step explanation:
let angles be 3x, 5x, 10x
3x+5x+10x=180(angle sum property)
18x=180
x=180/18
x=10
therefore, angles are 3*10=30
5*10=50
10*10=100..
Tia buys 7 packages of muffins. How many muffins does she buy?
A. 39
B. 40
C. 48
D. 56
Answers
Answer:
Probably there are 56 muffins in total
Step-by-step explanation:
This is because based on the choices, the only number that 7 is a factor of is 56
That means there were 8 muffins in each package
Hope this helps!
Write an
exponential model given the two points (8,120) and (9,230).
Answers
The exponential model is:
y ≈ 65.097(1.92)ˣ
To create an exponential model, we can use the general form of an exponential equation, which is given by:
y = abˣ
where:
y is the dependent variable (in this case, the value)
x is the independent variable (in this case, the point on the x-axis)
a is the initial value or the y-intercept when x = 0
b is the base or the rate of change
Using the two points you provided, (8,120) and (9,230), we can substitute these values into the equation and solve for a and b.
Point 1: (8,120)
120 = ab⁸ -- Equation 1
Point 2: (9,230)
230 = ab⁹ -- Equation 2
To solve this system of equations, we can divide Equation 2 by Equation 1:
230/120 = (ab⁹) / (ab⁸)
1.92 = b⁽⁹⁻⁸⁾
1.92 = b
Now, substitute the value of b into Equation 1 to solve for a:
120 = a(1.92)⁸
Simplifying further:
a = 120 / (1.92)⁸
a ≈ 65.097
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evaluate tan 60/ cos 45
Answers
Answer:
0.60922709536
Step-by-step explanation:
not sure if this is what you are looking for????
√6
im putting yall on folks
4
Select all the expressions that are equivalent to
-2(5x - 1) + 7(5x - 1) – 3(-5x + 1)
M. -10x – 1 + 35x - 1 + 15x + 1
P. -10x + 2 + 35x - 7 - 15x - 3
R. (5x - 1)(-2 + 7 - 3)
S. (5x - 1)(-2 + 7 + 3)
T. 40% - 8
V. 10x + 2
Answers
Answer:
The first answer is M. -10x - 1 + 35x - 1 + 15x + 1
maybe
The following stem and leaf plot shows the number of students at the local recreational center each day at PM. A stem and leaf plot is shown. Stem, 1; leaf, 6. Stem, 2; leaf, 2, 2, 5, 6, 6, 6. Stem, 3; leaf, 4, 5, 9. Stem, 4; leaf, 2, 2. Stem, 5; leaf, 0. Stem, 6; leaf, blank. Stem, 7; leaf, 2. Which data set is represented by this plot?
Answers
The data set represented by this plot is: 16, 22, 25, 26, 26, 26, 34, 35, 39, 42, 42, 50, 72.
The given stem and leaf plot shows the number of students at the local recreational center each day at PM.
The stem represents the tens digit of the number of students, while the leaf represents the one's digit.
For example, the first stem and leaf pair "1; 6" represents 16 students.
To determine the data set represented by this plot, we need to combine the stem and leaf values.
We can write each data point as a two-digit number, where the first digit is the stem and the second digit is the leaf.
Then, we list all the data points in ascending order.
1. 16
2. 22, 25, 26, 26, 26
3. 34, 35, 39
4. 42, 42
5. 50
6. (no data)
7. 72
Therefore, the data set represented by this plot is:
16, 22, 25, 26, 26, 26, 34, 35, 39, 42, 42, 50, 72.
We can use this data set to analyze the number of students at the local recreational center each day at PM.
For example, we can calculate the mean, median, and mode to describe the central tendency of the data.
We can also create a histogram or frequency table to visualize the distribution of the data.
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Ariel got a job at a restaurant and needed to purchase black dress pants and red shirts to work there. She found shirts she liked for $7.50 each and pants she liked for $18. She needs at least 2 shirts, at least 2 pairs of pants, and wants to spend no more than $150.
Answers
Ariel got a job at a restaurant and needed to purchase 2 shirts and 2 pairs of pants.
Let's use the variable "x" to represent the number of shirts Ariel buys and "y" to represent the number of pants she
buys.
Then, we can write the following system of inequalities:
2 ≤ x ≤ ∞ (Ariel needs at least 2 shirts)
2 ≤ y ≤ ∞ (Ariel needs at least 2 pairs of pants)
7.50x + 18y ≤ 150 (Ariel wants to spend no more than 150)
Now, we can graph the system of inequalities on a coordinate plane to find the feasible region, which represents all the possible combinations of shirts and pants that satisfy the given constraints.
The feasible region is shaded in the graph below:
graph {(150-7.5 × x)/18}
As you can see from the graph, the feasible region is a quadrilateral with vertices at (0, 8.33), (2, 7), (8, 3), and (25, 0).
This means that Ariel can buy any combination of shirts and pants within this region and still meet her requirements.
To find the optimal solution, we can simply check the corner points of the feasible region and see which combination gives us the most value for our money.
For example, if Ariel buys 2 shirts and 2 pants (i.e., the point (2, 2) on the graph), she will spend:
7.50(2) + 18(2) = 51
This is within her budget of 150 and meets her requirement of at least 2 shirts and 2 pants.
Therefore, the answer is: Ariel should buy 2 shirts and 2 pairs of pants.
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please help giving brainlist
Answers
Answer:
the SSS similarity theorem
Step-by-step explanation:
⇒ It cannot be the SAA similarity theorem as they only share a single common angle
⇒ It cannot be the HL similarity theorem, as the sides are not equal
⇒ It must be the SSS triangles
===========================================================
What is the SSS similarity theorem?It states that :
If the lengths of the corresponding sides of two triangles are proportional, then the two triangles are similar.
============================================================
Let's take the sides in proportion :
⇒ 15/5 = 3 (Hypotenuses)
⇒ 6+3/3 = 9/3 = 3 (Heights)
⇒ 8+4/4 = 12/4 = 3 (Bases)
As the sides are in proportion, the triangles are similar by the SSS similarity theorem.
on a coordinate grid what is the distance of (-2,4) and (5,4)
Answers
Answer:
the distance is 7 units
Step-by-step explanation:
Since the we calculate the distance between (-2,4) and (5,4) and those points have the same y=4 coordinate then they are both part of a horizontal line.
The distance is found by looking at the x-axis.
From -2 to 5 so is form -2 until 0 is (2 )+ (5 )more = 7
2p - 3q - 4r + 6r -2q + p
Answers
2p - 3q - 4r + 6r - 2q + p = 0
2p + p - 3q - 2q - 4r + 6r = 0
3q - 5q + 2r = 0
Which of the following statements about dilations are true? Select all that apply.
Answers
The true statement on dilations are that :
A. Dilations have the same shape as the original shape C. Dilations can be reductions of the original image What are dilations ?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.
Dilation therefore allows for the same shape as the original shape, but it is a reduction of the original shape and so cannot be the same size.
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PLS HELP ASAPHow are radicals and rational exponents related?
Answers
Radicals are also referred to as roots. It is the opposite of exponents.
Exponents are also referred to as power. It is the number of times a number is multiplied by itself.
Rational exponent is an exponent or power that is in the form of fraction.
Example:
2^ 1/2 ( two raised to the power of half).
\(2^{\frac{1}{2}}\)The relationship:
When we relate rational exponent to radicals, the bottom of the rational exponent (denominator of the fraction) is the root while the top of the rational exponent (numerator of the fraction) is the power of the radical.
Example:
\(\begin{gathered} 5^{\frac{2}{3}} \\ =(\sqrt[3]{5})^2 \\ 3\text{ is the cube root while 2 is the exponent (power)} \end{gathered}\)Help please? Does anyone understand this?
Answers
Answer:
15
Step-by-step explanation:
TU is parallel to IJ. So ∠I and ∠T are corresponding angles, and ∠U and ∠J are corresponding angles.
By AA similarity, ΔHTU and ΔHIJ are similar.
Write a proportion:
HT / HI = HU / HJ
Plug in values:
4 / 10 = x / (x + 9)
Cross multiply:
4 (x + 9) = 10x
4x + 36 = 10x
36 = 6x
x = 6
So HU = 6, and HJ = 6 + 9 = 15.
Consider the following cumulative probability distribution.
1 2 3
4
0.09 0.31 0.48 0.65 0.84
5
1
a. calculate a{xs 4). (round your answer to 2 decimal places.)
pox s 4)
p
b. calculate p{x= 3). (round your answer to 2 decimal places.)
p(x = 3)
#
+
e
10
19
34
m
c. calculate p(2 s x s 4). (round your answer to 2 decimal places.)
p(2 5 x 84)
Answers
The solution \(P(x \leq 4),p{x= 3), p(2 \leq * \leq 4)\) is mathematically given as
\(P(2 \leq X \leq 4)=0.84\)P(X=3)= 0.17\(P(2 < =X\leq 4)=0.53\)What is the solution \(P(x \leq 4),p{x= 3), p(2 \leq * \leq 4)\)?Generally, the equation for the Probability of P(X=3) is mathematically given as
b)
\(P(X=3) = P(X \leq 3)-P(X\leq 2)\)
Therefore
\(P(X=3)= 0.65-0.48\)
P(X=3)= 0.17
c)
\(P(2\leq X\leq 4) = P(X\leq 4)-P(X\leq 1)\\\\\\P(2\leq X\leq 4) = 0.84-0.31'\)
\(P(2 < =X\leq 4)=0.53\)
a)
\(P(2\leq X\leq 4)=0.84\)
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Please help i dont understand it. thank you
Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
Answers
Answer:
62.9 square units
Step-by-step explanation:
The area of a composite shape is the sum of the areas of the parts. Here the shape consists of a positive rectangle that has dimensions 8 × 11, together with a negative half circle of radius 8/2 = 4. That is, the area of the half-circle is subtracted from the area of the rectangle, as the problem statement tells you.
__
Rectangle areaThe area of a rectangle is the product of its dimensions:
A = LW = (11)(8) = 88 . . . . square units
Semicircle areaThe area of a semicircle is half the area of a circle, so will be given by the formula ...
A = 1/2πr^2 = 1/2π(4^2) = 8π ≈ 25.1 . . . . square units
Total areaThe area of the figure shown is the difference between the rectangle area and the semicircle area:
total area = rectangle area - semicircle area
total area = 88 -25.1 = 62.9 . . . . square units
x=y-8 7x+2y=16 what is the answer???
Answers
Answer:
x = 0 , y = 8
Step-by-step explanation:
x = y - 8 -----(1)
7x + 2y = 16 --------(2)
Substitute (1) in (2)
7(y - 8) + 2y = 16
7y - 56 + 2y = 16
9y = 72
y = 8
Substitute y in (1)
x = 8 - 8 = 0
Pls help it's urgent!
Answers
Answer:
\({ \bf{this \: is \: a \: set \: of \: combination : }} \\ \\ = { \tt{ {}^{25} {C} _{7}}} \\ = { \tt{480,700}}\)
the regression equation is ŷ = 29.29 − 0.96x, the sample size is 8, and the standard error of the slope is 0.22. what is the test statistic to test the significance of the slope
Answers
The test statistic to test the significance of the slope is approximately -4.364.
To test the significance of the slope in a linear regression model, you can use the t-test. The test statistic for the significance of the slope can be calculated using the formula:
t = (slope - hypothesized_slope) / standard_error_slope
In this case, the regression equation is ŷ = 29.29 - 0.96x, which means the slope is -0.96. Let's assume that the null hypothesis states that the slope is zero (hypothesized_slope = 0).
Given that the standard error of the slope is 0.22, we can substitute the values into the formula to calculate the test statistic:
t = (-0.96 - 0) / 0.22
Simplifying the expression:
t = -0.96 / 0.22
t ≈ -4.364
Therefore, the test statistic to test the significance of the slope is approximately -4.364.
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Which of these expressions is equivalent to:
3x^3 y^5 + 3x^5 y^ 3 − (4x^5 y^3 − 3x^3 y^5)
Answers
The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).
Let's simplify the given expression step by step using the given terms:
Expression:
\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)
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Which expression is equivalent to 28 + 12? A: 4 (7 + 3) B: 4 (24 + 8) C: 7 (4 + 12) D: 7 (21 + 5) YOU GET 30 POINTS IF YOU GET THIS ASAP!
Answers
Answer:
A
Step-by-step explanation:
4(7 + 3)
Apply distributive rule.
4(7) + 4(3)
28 + 12
Answer:
A
Step-by-step explanation:
Let us expand A.
4(7+3) is equal to 4(7)+4(3). This is 28+12.
Hope this helped!
If x = -2, what is y = ?
Answers
In the curve of the sinusoidal curve when x = -2 y = 2
How to find the value y when x = -2 in the curve?A sinusoidal curve, also known as a sine wave, is a type of waveform that is commonly used to describe oscillations or periodic phenomena in various fields such as physics, engineering, mathematics, and electronics.
A sinusoidal curve is a graph of a function that oscillates between an upper value and a lower value, and repeats itself over a period of time.
In order to find the value of y when x = -2, from the x-axis at x = -2 trace it to touch the curve and then trace to the y-axis to get the y value (Check the attached).
Therefore, when x = -2, y = 2
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During a special at the school book fair, each book will cost the same amount of money. Nelly can buy 4 books for $10.95. How much money will she need to buy 6 books?
Answers
Answer:
Nelly will need $16.43.
Step-by-step explanation:
First, you want to find out how much 1 book costs.
Take 10.95 and divide it by 4.
10.95/4=$2.73
Take the 2.73 and multiply it by 6.
6x2.73=16.425
=$16.43
Answer:
16.43 i think
Step-by-step explanation:
so first you divide 10.95 by 4 and get 2.74 so then you times it by 6 and get 16.43
PLEASE HELP FAST!!!!!!!!!!
The formula for the circumference of a circle is: C = 2nr.
C is the circumference and r is the radius. Use 3. 14 as an estimate for t.
Which is the approximate circumference of a circle with a radius of 7 m?
A. 21.98 m
B. 28.26 m
C. 43.96 m
D. 153.86 m
Answers
Answer:
43.96
Step-by-step explanation:
You take the radius of 7 and multiply by 2 then multiply by 3.14
t point) Al voctors and subspoces are in R th check the tive statements besw. A. The orthogonal prepecion y of y onto a suthpace W can sometmes depend on the orthogsnai basis for W used to compufe î. C. for each w and each sefspace W, the vector y−pr0 w
w ( y
˙
) is orthogonat in W : D. If y is in a wabsace W, then the crthoponal peopeton of y ores W is y tselt.
Answers
Orthogonal projection, a concept that involves the rejection of a point on a surface or plane, is a mathematical phenomenon that appears in geometry. It is defined as a linear transformation of a vector space that projects vectors orthogonally onto a subspace such as a plane, line, or another subspace.
When a vector is projected onto a subspace, its orthogonal projection is the vector created by subtracting the projection from the original vector, resulting in the segment that connects the projection to the vector's tail.
a. The orthogonal projection of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute it. The correct answer is A.
b. It is a false statement.
c. For every w and subspace W, the vector y - projw(y) is orthogonal in W. The correct answer is True.
d. If y is in a subspace W, the orthogonal projection of y onto W is y itself. The correct answer is True.
The orthogonal projection of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute it. So, option A is correct. It's possible that the basis of the subspace W is made up of several orthogonal vectors, but any other set of orthogonal vectors that span the subspace would work as a basis.
If w is a vector that lies in the subspace W, the vector y – projw(y) is orthogonal in W. So, option C is correct.
If y is in a subspace W, the orthogonal projection of y onto W is y itself. Therefore, option D is correct.
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Rachel is mailing packages. Each small package costs her $2.60 to send. Each large package costs her$4.10. How much will it cost her to send 3 small packages and 4 large packages?
Answers
Answer:
it would be 14.70
Step-by-step explanation:
Kristina walks from her house, around the park, to the store. She is interested in taking a shortcut through the park to save time. Approximately how far away from her house is the store, if she were to follow the path shown by the dotted line in the graphic below?* HOUSE PARK 80 m 100 m STOR O 134 m O 128 m O 180 m 200 m nal. If a 65 inch television has 1 point
Answers
If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.
How to calculate the distance between her house and the store?To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;
C² = a² + b²
where;
a= 80
b= 100
c= ?
That is;
c²= 80²+100²
= 6400+10000
= 16,400
c = √16400
= 128.1m
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solve for h V=2πr^2h
Answers
Answer: h= V/2πr^2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
If WX is 3 and XY is 9, what is VW?
Answers
By Pythagorean formula and proportion formula, the length of side VW is equal to 6 units. (Right choice: C)
How to use similarity ratios to find the missing length
Herein we find a geometric system formed by two right triangles, in which two side lengths are known (WX, XY) and we need to determine the length of side VW.
Both triangles XVW and XYW are similar, where they share the same internal angles and proportional corresponding pair of sides. Then, the system is represented by following proportion formula:
XV / WX = XY / XV
XV² = XY · WX
XV = √(XY · WX)
If we know that XY = 9 and WX = 3, then the value of XV is:
XV = √27
XV = 3√3
Then, the side VW is found by Pythagorean theorem:
VW = √(WX² + XV²)
VW = √(3² + 27)
VW = 6
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It's takes Mario 1/4 hour to mow mr Harris's lawn. It takes him 3 times as long to mow mrs Carter's . How long does it take Mario to mow mrs Carter's lawn
Answers
Answer:
670
Step-by-step explanation:
First you have to fined the unit rate
1,500/25= 60
a do
300x60= 18,00-98
Harris = 1/4
Carter= 3(Harris) = 3(1/4)
which equal 3/4 hours, which is also equivalent to 45 minutes