The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(18Correct,1Correct) b. What is the median giraffe height? 18Correct ft. c. What is the Z-score for a giraffe that is 21 foot tall? 1.5Incorrectd. What is the probability that a randomly selected giraffe will be shorter than 18.6 feet tall? 0.6Incorrecte. What is the probability that a randomly selected giraffe will be between 17.2 and 18 feet tall? 1.042Incorrectf. The 80th percentile for the height of giraffes is 18.5844Incorrect ft.
Answers
Question C:
- The formula for the Z-score is given below:
\(\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ where, \\ \mu=\text{ mean} \\ \sigma=\text{ Standard deviation} \end{gathered}\)- Thus, we can calculate the Z-score as follows:
\(\begin{gathered} \mu=18,\sigma=1,X=21 \\ \\ \therefore Z=\frac{21-18}{1} \\ \\ Z=3 \end{gathered}\)- The Z-score is 3
Question D:
- We need to calculate the Z-score of the height of 18.6ft and then convert the Z-score to probability using a Z-score calculator.
- The Z-score is calculated as follows:
\(\begin{gathered} X=18.6 \\ Z=\frac{18.6-18}{1} \\ Z=0.6 \end{gathered}\)- The probability P(Z < 0.6) is depicted below:
- Thus, the probability of getting a giraffe shorter than 18.6ft is 0.72575
Question E:
- Again, we need to find the Z-scores for both 17.2ft and 18ft and then find the probability:
P(17.2 < Z < 18)
- The Z-scores are gotten as follows:
\(\begin{gathered} Z_1=\frac{17.2-18}{1} \\ Z_1=-0.8 \\ \\ Z_2=\frac{18-18}{1} \\ Z_2=0 \end{gathered}\)- Thus, the probability of obtaining heights corresponding to the above Z-scores is:
- Thus, the probability of getting a giraffe with a height between 17.2 and 18ft tall is 0.28814
Question F:
- The 80th percentile corresponds to 80/100 = 0.8 probability.
- We should find the corresponding Z-score before finding the value of X, using the Z-score formula
- The corresponding Z-score of 0.8 is 0.842
- The value of X is:
\(\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ \\ 0.842=\frac{X-18}{1} \\ \\ Add\text{ 18 to both sides} \\ \\ \therefore X=18+0.842 \\ \\ X=18.842 \end{gathered}\)- The 80th percentile value is 18.842
Related Questions
A ship X sailing with a velocity (21 kmh 052⁰) observes a light fron a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures
i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship.
ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
iii) the distance in km of the ship from the lighthoue when the light.hose is due West of the ship
Answers
i) the original distance when the lighthouse is due West of the ship is 7 km
ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes
iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km
To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:
i) Finding the original distance when the lighthouse is due West of the ship:
The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.
To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:
Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).
ii) Finding the time in minutes when the lighthouse is due West of the ship:
To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:
Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).
To find the time, we can use the formula:
Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).
iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:
We can use the formula for relative velocity to find the distance:
Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)
Using the values we calculated earlier, we have:
Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).
Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.
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\( CHECK \:MY\: PROFILE\\\: PAGE\: AND\: SOLVE \: MY \: QUESTION\: PLS\)
Answers
Answer:
ok
Step-by-step explanation:
Answer:
ok
Step-by-step explanation:
do you mind giving BRAINIEST
have a nice day! :)
318÷53 with a remainder
Answers
Answer:
6
Step-by-step explanation:
318 / 53 = 6
the remainder is 0
24°
Solve for c.
= [?]°
C =
60% C
Enter
![24Solve for c.= [?]C =60% CEnter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/18LkggivbR7cp80IPjukTXssaWPx5XaX.png)
Answers
Answer:
96°
Step-by-step explanation:
You want the value of angle C in the diagram with two parallel lines and a triangle between them.
Angle sum theoremThe sum of angles in a triangle is 180°, so the missing angle in the triangle is ...
180° -60° -24° = 96°
Alternate interior anglesAngle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:
C = 96°
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Help with this Problem Oneo
Answers
Answer:
9 cm
Step-by-step explanation:
ST = 3/4 × 12 = 9 cm
_____
Answer:
9 cm
Step-by-step explanation:
set up a proportion SR/NM=ST/NP, since you know all but one of the lines, sub them into the equation, 15/5=ST/3. solve the side you know to get 3=ST/3, multiply both side by 3 to eliminate the fraction and get the answer, 9=ST.
if you have any questions, leave them in the comments and i will try to answer them, if this helped, pls give brainliest
PLEASE HELP!!!!!!!!!!!!!
Answers
Hope this helps!
Dee Wallace's salary was $61,000 in 2006 and increased to $64,300 in 2009.
What was the annual rate of change in his salary?
Answers
Answer:
$1,100
Step-by-step Explanation:
Dee Wallace's salary in 2006 = $61,000 Dee Wallace's salary in 2009 = $64,300
The salary increased in => 2009 - 2006 = 3yrs
The amount of salary increased = 64,300-61000 = $3,300
The annual change of salary = 3,300/3 = $1,100
Need answers please help
Answers
Answer
Yes, zero is contained in the interval
2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
Answers
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The joint probability model for the number of waiters (X) and chefs (Y) that show up on any given day is given below. X Y 0 1 2 3 0 k 0.01 0.01 0.03 1 0.02 0.04 0.04 0.06 2 0.02 0.01 0.06 0.63 a) What must the value of k be for this to be a valid probability model
Answers
Solution :
Given the Joint Probability distribution is :
Y|X 0 1 2 3 P(y)
0 k 0.03 0.03 0.03 k+0.09
1 0.01 0.02 0.04 0.04 0.11
2 0.01 0.01 0.05 0.72 0.79
P(x) k+0.02 0.06 0.12 0.79 k+0.99
Since we know,
\($\sum \sum P(x_i,y_j) = 1$\)
⇒ k + 0.99 = 1
⇒ k = 1 - 0.99
⇒ k = 0.01
Therefore, the value of k is 0.01
The price of one stock fell $12.50 in five days. How much did the stock’s price change each day (on average)?
Answers
Answer:
-$2.50
Step-by-step explanation:
Since it said that one stock fell $12.50,that means that the $12.50 is negative.Then you have to do -12.50 ÷ 5 which equals -2.50
Hope this helped!
If BD= 4x+3, find x. Round your answer to answer to the nearest tenth if necessary BC= 37CD = x-3
Answers
ok
BD = 4x + 3
BC = 37
CD = x - 3
37 + x - 3 = 4x + 3
37 - 3 - 3 = 4x - x
37 - 6 = 3x
31 = 3x
x = 31/3
That's all
3.6= − a/0.8 − 1.6 − 0.8 a −1.6
Answers
The value of a for the given expression will be -3.31.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 3.6= − a/0.8 − 1.6 − 0.8 a −1.6. The value of a will be calculated as below,
3.6 = − a/0.8 − 1.6 − 0.8 a −1.6
3.6 + 1.6 + 1.6 = -a / 0.8 - 0.8a
6.8 = ( -a - 0.64a ) / 0.8
5.44 = -1.64a
a = -3.31
Therefore, the value of a will be -3.31.
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Find the midpoint of the segment with the given endpoints. (-7,-4) and (3,7)?
Answers
9514 1404 393
Answer:
(-2, 1.5)
Step-by-step explanation:
The coordinates of the midpoint are the average of the end point coordinates:
((-7, -4) +(3, 7))/2 = (-7+3, -4+7)/2 = (-4, 3)/2 = (-2, 1.5)
The coordinates of the midpoint are (-2, 1.5).
What is a formula for the nth term of the given sequence? 18 , 21 , 24
Answers
Answer:
3n+15
Step-by-step explanation:
18, 21, 24
+3. +3
3n
18-3=15
3n+15
Can anyone find the answer to this question
Answers
Answer:
C
Step-by-step explanation:
Each slope down in the graph represents a drink. so the first drink ended at 30 sec and the second one started at 60 sec so he waited 30 sec inbetween.
Can somebody please help?? i’ll give Brainliest to whoever answers first.
There are 625 students in Leon's school. He takes a random sample of 75 students from the entire school population. In the sample, 33
students are planning to attend the end of year picnic.
Based on his data, how many students from the entire school are planning to attend the end of year picnic? Show ALL your work!
Answers
Answer:
The answer is 275 students.
Step-by-step explanation:
In 75 students, 33 students attend.
So the ratio is 33/75.
so multiply with 625.
625 x 33/75 = 275
You have $16 and a coupon for a five dollar discount at a local supermarket one bag of hot Cheetos cost 3 dollars how many bag of Cheetos can you buy
Answers
The number of Cheetos you can buy in the supermarket is 7.
How to find the number of bag of Cheetos bought?You have $16 and a coupon for a five dollar discount at a local
supermarket . One bag of hot Cheetos cost 3 dollars. Therefore, the
number of bag of Cheetos you can buy can be calculated as follows:
Therefore, altogether he has 16 + 5(coupon discount) = 21 dollars to spend
in the super market.
Therefore,
number of Cheetos worth 3 dollars one can buy = 21 / 3
number of Cheetos worth 3 dollars one can buy = 7
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How can seven people share 3 cupcakes equally? (20 pts) quick
Answers
Answer:
You Just have to divide
Step-by-step explanation:
2 1/3
Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 27 cakes. You cannot have more than 13 chocolate cakes. Write a system of inequalities to model this system.Let x = the number of vanilla cakes.Let y = the number of chocolate.
Answers
x = the number of vanilla cakes.
y = the number of chocolate cakes
They need at most 27 cakes means:
x + y ≤ 27 (equation 1)
You cannot have more than 13 chocolate cakes means:
y ≤ 13 (equation 2)
Select the correct answer. Which function represents the inverse function of the function f(x)=x^2 +5
Answers
Answer:
f^(-1)(x) = ±√(x - 5).
Step-by-step explanation:
Replace f(x) with y: y = x^2 + 5.
Swap the x and y variables: x = y^2 + 5.
Solve the equation for y. To do this, we'll rearrange the equation:
x - 5 = y^2.
Take the square root of both sides (considering both positive and negative square roots):
±√(x - 5) = y.
Swap y and x again to express the inverse function:
f^(-1)(x) = ±√(x - 5).
Select ALL the correct answers.
Which shapes have the same volume as the given rectangular prism?
8 cm
15cm
base area = 50 cm
Answers
A.) 15cm 5cm height base area 50 cm
B.) 8cm 5cm height base area 50 cm
C.) 24 cm height base area 50 cm
D.) 18 cm 15 cm height base area 50 cm
Answers
Answer: I think it’s A the cylinder
Step-by-step explanation:
For PLATO users, the answers are the cylinder and the cone, NOT EITHER OF THE PYRAMIDS!!! Your welcome....
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
Find the volume of a sphere with a radius of 12.5cm. (Note: Take the value of π as 3.14.) Round your answer to the nearest thousandth, if necessary.
Answers
The volume of the sphere is approximately 8181.510 cm³.
The volume of a sphere is the amount of space that is enclosed within the surface of a sphere.
It is a measure of the three-dimensional space that is contained within the sphere.
The volume of a sphere is used in a variety of fields, such as physics, engineering, and architecture, to calculate the space enclosed by a sphere or a spherical object, such as a planet or a ball.
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. Substituting r = 12.5 cm and π = 3.14, we get:
V = (4/3) × 3.14 × (12.5 cm)³
V ≈ 8181.51 cm³
The volume of the sphere is approximately 8181.510 cm³.
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HOW TO CHANGE THE PERCENT INTO DECIMAL?
57%= ?
Answers
Answer:
0.57
Step-by-step explanation:
57 / 100 = 0.57
You need to divide the percent by 100
Every plant bloomed in the spring. The simple subject of this sentence is _____.
every
every plant
plant
bloomed
Answers
a simple subject is a person, place or thing
Answer:
plant!!
Step-by-step explanation:
On a map, the scale shown is 1 inch : 5 miles. If
a wildlife refuge is 50 square miles, what is the
area of the refuge on the map?
Use the proportion to solve for x.
1 in. 2
25 mi2
x in. ²
50 mi²
Cross
multiplication
can help!
=
The area of the wildlife refuge is [?] square
inches on the map.
Enter
Answers
Answer:
Step-by-step explanation:
6
In a certain field, the ratio of pigs to sheep is 8 3 . If there are 165 pigs and sheep altogether in a field, how many sheep are there?
Answers
Answer:
440 I think haven't done these questions in a while.
I need help with questions 1,2, and 3. This class is microeconomics
Answers
Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.
What is budget?A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.
What is consumption?Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.
According to the given information:
To draw Ben's indifference curves, we need to plot different combinations of cookies and coffee that give Ben the same level of satisfaction. Since the slope of all his indifference curves is constant at -2, they will be downward-sloping straight lines. We can plot several indifference curves by varying the level of satisfaction they represent. The budget constraint is a straight line that represents all possible combinations of cookies and coffee that Ben can purchase with his $12 budget. The slope of the budget constraint is the ratio of the prices of coffee and cookies, which is 2:1. Ben optimally purchases the point where his budget constraint is tangent to his highest attainable indifference curve. In other words, he maximizes his satisfaction subject to his budget constraint. In the graph above, this point is labeled as "Optimal Consumption." At this point, Ben purchases 2 cookies and 2 coffees, spending $8 on coffee and $4 on cookies, which exhausts his $12 budget.To optimize his consumption, Ben should allocate his budget between cookies and coffee such that the ratio of their marginal utilities equals their prices. In other words, Ben should choose the combination of cookies and coffee where the marginal utility per dollar spent is the same for both goods. At his current consumption level of 3 coffees and 0 cookies, Ben's marginal utility per dollar spent on cookies is 2/2 = 1, and his marginal utility per dollar spent on coffee is 1/4 = 0.25. Since the marginal utility per dollar spent on cookies is higher than that of coffee, Ben should decrease his consumption of coffee and increase his consumption of cookies to achieve the optimal consumption level. He should continue adjusting his consumption until the marginal utility per dollar spent on each good is equal.To know more about budget and consumption visit:
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Factor the expression using the GCF.
16m + 40
Answers
Answer:
8(2m+5)
Step-by-step explanation:
GCF: 8
Factor 8 out of 16 and 40 giving you 2 and 5
DON'T FORGET TO CARRY THE M