Answers
Answer:
[tex] \frac{1}{2} \times 21.6 \times 5.9 = 63.72[/tex]
The area of this triangle is 63.72 square feet.
Related Questions
Factor 8X squared + 10x + 2
Answers
Answer:
2(4x + 1)(x + 1)
Step-by-step explanation:
Given
8x² + 10x + 2 ← factor out 2 from each term
= 2(4x² + 5x + 1)
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 1 = 4 and sum = + 5
The factors are + 1 and + 4
Use these factors to split the x - term
4x² + x + 4x + 1 ( factor the first/second and third/fourth terms )
= x(4x + 1) + 1 (4x + 1) ← factor out (4x + 1)
= (4x + 1)(x + 1), thus
4x² + 5x + 1 = (4x + 1)(x + 1) and
8x² + 10x + 2 = 2(4x + 1)(x + 1) ← in factored form
All regular polygon:
A. Have four sides
B.Have an even number of sides
C.are symmetrical
D.are the same size
Answers
C. Are simmetrical
ExplanationA. is false because only quadrilaterals have 4 sides
B. is false because polygons like equilateral triangle and regular pentagon have an odd number of sides
D. A polygon doesn't have an unique size. It changes every time, cause we can decide its size
Answer: The answer is C. are symmetrical.
Step-by-step explanation: There is a line of symmetry, which is a line where one half of the polygon is a mirror image of the other side. This means that even if a polygon has 5 sides, for example, then it would still be symmetrical.
Solve the following equation. Then place the correct number in the box provided. Leave answer in terms of a mixed number. 7x - 2 < 10
Answers
Answer:
[tex]\huge \boxed{x<\frac{12}{7}}[/tex]
Step-by-step explanation:
First thing you do is add by 2 from both sides of equation.
[tex]\displaystyle 7x-2+2<10+2[/tex]
Simplify.
[tex]\displaystyle 10+2=12[/tex]
[tex]\displaystyle 7x<12[/tex]
Divide by 7 from both sides of equation.
[tex]\displaystyle \frac{7x}{7}<\frac{12}{7}[/tex]
Simplify, to find the answer.
[tex]\displaystyle\huge\boxed{ x<\frac{12}{7}}[/tex], which is our answer.
The inequation 7x - 2 < 10 is x < 12/7.
What are inequalities and it's types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The inequation 7x - 2 < 10 is,
7x < 12.
x < 12/7.
learn more about inequalities here :
https://brainly.com/question/28823603
#SPJ5
Charles owed 390$ to his friend. On the first day Charles paid his friend 12$. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?
Answers
Mr. Olaffsen opened a sandwich shop and a smoothie stand in his neighborhood. The following table and equation show function f, representing Mr. Olaffsen's profit, in dollars, x months since opening the sandwich shop. x 1 2 3 4 5 6 7 f(x) 12,000 15,500 18,000 19,500 20,000 19,500 18,000 The following table and equation show function g, representing Mr. Olaffsen's profit, in dollars, x months since opening the smoothie stand. x 1 2 3 4 5 6 7 g(x) 9,300 12,000 14,100 15,600 16,500 16,800 16,500 Select the true statement. A. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,000. B. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,200. C. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,500. D. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700.
Answers
Answer: the difference between the max is 3200.
Step-by-step explanation:
20000-16800= 3200
The difference between the max is 3200.
What is the difference?Subtract the smaller of the two numbers from the larger of the two numbers to find the difference between them. The difference between the two numbers is the sum's product. For instance, you could calculate the difference between 100 and 45 as follows: 100 - 45 = 55.
Given
20,000 - 16,800 = 3200
therefore, The difference between the max is 3200.
To know more about differences refer to :
https://brainly.com/question/148825
#SPJ2
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = -16t^2 + 6t +4. Round your answer to the nearest hundredth.
Answers
Answer:
t = 0.722 seconds
Step-by-step explanation:
Given in the question that an equation
h = -16t² + 6t + 4
here h is the height
t is the time
To solve this question we need to substitute height with zero because at ground level height is zero
h = 00 = -16t² + 6t + 4
a = -16
b = 6
c = 4
Formula to use
t = -b±√(b²-4ac) / 2a
Plug values in the formula
t = -6 ± √36-4(-16)(4) / 2(-16)
t = 6±2√73 / 32
t = 6+2√73 / 32 or t = 6-2√73 / 32
t = 0.722 or t = -0.347
since time can't be in negative so we reject t = -0.347
The probability that Ashley drives faster than the speed limit (event A) is 0.34, and the probability that he gets a speeding ticket (event B) is 0.22. The probability that he drives faster than the speed limit, given that he has gotten a speeding ticket, is 1. Are events A and B dependent or independent? A. dependent B. independent C. insufficient data D. depends on the other events in the sample space
Answers
The correct answer between all
the choices given is the first choice or letter A. I am hoping that this answer
Answer: Option 'A' is correct
Step-by-step explanation:
Since we have given that
A be the event that Ashley drives faster than the speed limit.
P(A)=0.34
B be the event that he gets a speeding ticket.
P(B)=0.22
Probability that he drives faster than the speed limit, given that he has gotten a speeding ticket i.e.
P(A|B)=1
but for A and B to be independent ,
P(A).P(B)= P(A and B)
0.34×0.22=0.0748
but,
[tex]P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}\\\\1=\dfrac{P(A\cap B)}{0.22}\\\\0.22=P(A\cap B)[/tex]
So, P(A∩B) does not satisfy the condition.
Hence, A and B are not independent events.
Option 'A' is correct as they are dependent events.
Given: NQ is an altitude of △MNP
Prove: Sinm/m = Sinp/p
PLEASE HELP ASAP any answers appreciated I am completely stuck on this
Answers
Answer:
Statement: Reason:
ΔNQM and ΔNQP are right triangle Definition of a right triangle
SinM = h/p and SinP = h/m Definition of sine ratio
p sin M = m sin P Substitution property of equality
p sin M / pm = msinP / pm Division property of equality.
Mr. Harmin is sitting in his office on the third floor of a building. He is at an elevation of 30 feet in relation to street level. Mr. Ehrig is in the parking garage at an elevation of –35 feet, and Mrs. White is in the parking garage at an elevation of –25 feet in relation to street level.
Which statements are true? Check all that apply.
A) Mr. Harmin is closest to street level.
B) Mr. Ehrig is at the lowest elevation.
C) Mrs. White is closest to street level.
D) Mr. Harmin is closer to street level than Mrs. White.
E) Mrs. White is at the highest elevation.
Answers
Answer:
B and C are true.
The statement (B) Mr. Ehrig is at the lowest elevation, and statement (C) Mrs. White is closest to street level are correct.
What is elevation?The distance up or down a specified point of comparison, most often a reference spherical geometry, a mathematical model of the Earth's sea level as an equipotential gravitational surface, determines a physical location's elevation.
We have:
Mr. Harmin is sitting in his office on the third floor of a building.
He is at an elevation of 30 feet in relation to street level.
Mr. Ehrig is in the parking garage at an elevation of –35 feet, and Mrs. White is in the parking garage at an elevation of –25 feet in relation to street level.
From the above data we can say Mr. Ehrig is at the lowest elevation which is -35 and Mrs. White is closest to street level which is 25 feet
Thus, the statement (B) Mr. Ehrig is at the lowest elevation, and statement (C) Mrs. White is closest to street level are correct.
Learn more about the elevation here:
https://brainly.com/question/481548
#SPJ2
find the value of the trigonometric function sin (t) if sec t = -4/3 and the terminal side of angle t lies in quadrant II
Answers
Answer:
[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]
Step-by-step explanation:
By definition we know that
[tex]sec(t) = \frac{1}{cos(t)}[/tex]
and
[tex]cos ^ 2(t) = 1-sin ^ 2(t)[/tex]
As [tex]sec(t) = -\frac{4}{3}[/tex]
Then
[tex]sec(t) = -\frac{4}{3}\\\\\frac{1}{cos(t)} =-\frac{4}{3}\\\\cos(t) = -\frac{3}{4}[/tex]
Now square both sides of the equation:
[tex]cos^2(t) = (-\frac{3}{4})^2[/tex]
[tex]cos^2(t) = \frac{9}{16}\\\\[/tex]
[tex]1-sin^2(t) =\frac{9}{16}\\\\sin^2(t) =1-\frac{9}{16}\\\\sin^2(t) =\frac{7}{16}\\\\sin(t) =\±\sqrt{\frac{7}{16}}[/tex]
In the second quadrant sin (t) is positive. Then we take the positive root
[tex]sin(t) =\sqrt{\frac{7}{16}}[/tex]
[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]
The value of sin(t) = √7/4 because sine is positive in Quadrant II.
First, recall that sec(t) is the reciprocal of cos(t):
sec(t) = 1/cos(t)
Given: sec(t) = -4/3, so:
cos(t) = -3/4
Since angle t lies in Quadrant II, cosine is negative, and sine is positive. Use the Pythagorean identity:
sin²(t) + cos²(t) = 1
Substitute cos(t):
sin²(t) + (-3/4)² = 1
sin²(t) + 9/16 = 1
Solve for sin²(t):
sin²(t) = 1 - 9/16
sin²(t) = 16/16 - 9/16
sin²(t) = 7/16
Take the square root of both sides:
sin(t) = √(7/16) = √7/4
Since we are in Quadrant II, sine is positive:
sin(t) = √7/4
What is the answer?
Answers
Answer:
x ≤ - 4
Step-by-step explanation:
Given
3 - x ≥ 2x + 15 ( add x to both sides )
3 ≥ 3x + 15 ( subtract 15 from both sides )
- 12 ≥ 3x ( divide both sides by 3 )
- 4 ≥ x, hence
x ≤ - 4
3 - x is greater than equal to 2 X + 15
3 is greater than equal to 3X + 15
- 12 is greater than equal to 3 x
- 4 is greater than equal to x
hence x b - 4 - 4 is greater than x
which graph represents y= square root x?
Answers
[tex]y=\sqrt{x}[/tex] is the square root function. The graph of this function has been attached below. As you can see, this is in fact a function it passes the Vertical Line Test for Functions that establishes that if a vertical line intersects a graph at most one point, then this is a function. From the square root function we know:
The domain of the function is the set of all nonnegative real numbers. The range of the function is the set of all nonnegative real numbers. The origin [tex](0,0)[/tex] is an intercept of the graph. The graph increases on the interval [tex](0, \infty)[/tex].Answer:
b on edge
Step-by-step explanation:
Simplify square root 72 minus 3 times square root 12 plus square root of 192
A. 6 square root 2 plus 2 square root 3
B. 12 square root 2 plus 2
C. 14 square root 2
D. 8 square root 3 minus square root 1
Answers
Step-by-step explanation:
hope it helps you!!!!!!!
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
√72-3×√12+√192
As we have
[tex]\sqrt{72}=6\sqrt{2}[/tex]
[tex]\sqrt{12}=6\sqrt{2}[/tex]
[tex]\sqrt{192}=8\sqrt{3}[/tex]
So, our equation becomes
[tex]6\sqrt{2}-3\times 2\sqrt{3}+8\sqrt{3}\\\\=6\sqrt{2}-6\sqrt{3}+8\sqrt{3}\\\\=6\sqrt{2}+2\sqrt{3}[/tex]
Hence, Option 'A' is correct.
What is the answer pls?
Answers
:) Hope this answers your question :)
In rectangle ABCD, if the coordinates of A are (0, 0) and of C are (r, s), find the coordinates of B.
Answers
ANSWER
B(r,0)
or
B(0,s)
EXPLANATION
In rectangle ABCD, the coordinates of A are (0, 0) and of C are (r, s).
When we name the triangle in a clockwise direction.
Then B must bear the y-coordinate of A and bear the x-coordinate of C.
This gives us (r,0)
When we name the triangle in an anticlockwise direction.
Then B must bear the x-coordinate of A and bear the y-coordinate of C.
This gives us (0,s)
Without graphing predict weather the function y= (1/2)x shows exponential growth or decay. Justify your predictions
Answers
Answer:
The base of the exponential function is 0.5 which is between 0 and 1 and thus this is an exponential decay function.
Step-by-step explanation:
Exponential equations are usually in the form;
[tex]y=ab^{x}[/tex]
where;
a is the initial value, that is the value of y when x is 0,
b is the growth or decay factor and also the base of the exponential function
If b>1, then it is an exponential growth function and the values of y keep getting bigger.
if 0<b<1, then it is an exponential decay function and the y values keep getting smaller as x increases.
In the function given;
[tex]y=(\frac{1}{2})^{x}[/tex]
The base of the exponential function is 0.5 which is between 0 and 1 and thus this is an exponential decay function.
In order to justify our prediction, we can simply obtain the graph of the function and check on how x and y vary.
From the attachment below we can see that the values of y become increasingly smaller as the values of x increases in magnitude which justifies our predictions.
The function y = [tex](1/2)^x[/tex] represents an exponential decay because the base (1/2) is a fraction less than 1.
The function y = [tex](1/2)^x[/tex] represents an exponential decay model because it is in the form y = [tex]a^x[/tex] where a is a fraction between 0 and 1 (0 < a < 1).
An exponential decay function describes a situation where the quantity decreases over time, and the rate of decrease slows down as the quantity gets smaller.
In contrast, if a were greater than 1, it would represent exponential growth, indicating that the quantity increases over time, and the rate of increase accelerates as the quantity grows larger.
So, since (1/2) is less than 1, the function shows exponential decay.
Write 0.6 as a fraction.
A) 1 3
B) 2 3
C) 3 7
D) 3 9
Answers
Answer:
All of them are wrong, the answer is 3/5
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
0.6 = 6 / 10 = 3 / 5
Tina raised the number 3 to a power and then added 19 to the result .She obtained the sum 100. To what power did she raise 3 ?
Answers
Answer:
3^4, she raised it to the 4th power
Step-by-step explanation:
3^x+19=100
-19
3^x=81
We can make a table now to find what power of three = 81
Powers of three table
3^1=3 3^2=9 3^3=27 3^4=81
The power she raised the number to is 4.
What is equationThis is a mathematic expression or statement often used to represent word problems.
To solve this question, we need to write an equation to represent this problem.
[tex]3^x + 19 = 100\\ [/tex]
The equation above represents the problem.
Let's solve for x
[tex]3^x + 19 = 100\\ [/tex]
collect like terms
[tex]3^x = 100 - 19\\ 3^x = 81\\ [/tex]
[tex]3^x = 81\\ x = 4[/tex]
What we did above is that how many power are we going to raise 3 to give us 81 and the answer is 4 times.
learn more about equations here;
https://brainly.com/question/13729904
Seiki is planning her workout at her gym. She wants to spend more than 40 minutes exercising. Her workout plan includes 20 minutes lifting weights and the rest of the time on three different cardio machines. She wants to spend the same amount of time on each cardio machine. How many minutes should Seiki spend on each cardio machine?
Answers
Answer:
Assuming that Seiki wants to be as close to 40 minutes are possible (to the nearest minute), She would want to spend 7 minutes on each of the 3 cardio machines
Step-by-step explanation:
With Seiki wanting to spend at least 40 minutes exercising and spending 20 minutes lifting weights, she needs to spend at least 20 more minutes on her cardio. If we are looking for a number that is divisible by 3, that would mean that she would spend 21 minutes exercising.
Seiki should spend at least 10 minutes on each cardio machine after her 20-minute weightlifting session to meet continuous exercise and weekly cumulative goals, therefore surpassing her minimum of 40 minutes of exercise and aligning with health recommendations.
Time Allocation For Cardio Machines
Seiki wants to spend more than 40 minutes exercising, with 20 minutes devoted to lifting weights and the rest on three different cardio machines. To calculate the time she should spend on each cardio machine, we first deduct the weightlifting time from the total minimum exercise time.
This leaves us with more than 20 minutes for cardio (40 minutes total - 20 minutes of weights = 20+ minutes for cardio).
Since she wants to spend the same amount of time on each machine, we divide the remaining time by three. Let's assume Seiki decides on the minimum of 21 minutes for cardio to exceed the 40 minutes total.
So, 21 minutes divided by three cardio machines equals seven minutes per machine.
However, to align with the recommendations for sessions to be continuous for 10 minutes or more and the goal of a cumulative total of 150-300 minutes from at least three days a week, Seiki should aim for at least 10 minutes on each machine.
This would translate to at least a total of 30 minutes on cardio machines, bringing her workout to a minimum of 50 minutes (20 minutes of weights + 30 minutes of cardio).
Remember, these calculations are based on the minimum requirements, and Seiki can adjust her workout duration on the cardio machines to suit her fitness goals and available time.
Subtract 7x2 + 4x - 9 from 5x2 + 10x - 5. Express the result as a trinomial in descending
degree order.
Answers
Answer:
2x^2-6x-4
Step-by-step explanation:
(7x2 + 4x - 9)
-(5x2 + 10x - 5)
=
7x^2-5x^2=2x^2
4x-10x=-6x
-9-(-5)=-4
thus, your answer is 2x^2-6x-4
Convert the function into standard form. Show your work. y-2=-3(x+4)^2
Answers
Answer:
y = -3x² - 24 x + 50
Step-by-step explanation:
y - 2 = - 3(x+4)²
y - 2 = -3(x²+8x+16)
y - 2 = -3x² -24x +48
y = -3x² - 24 x + 50
ANSWER
The standard form is
.
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
EXPLANATION
The given function is
[tex]y - 2 = - 3(x + 4)^{2} [/tex]
The standard form is given by
[tex]y =a {x}^{2} + bx + c[/tex]
We expand to obtain:
[tex]y - 2 = - 3( {x}^{2} + 8x + 16)[/tex]
We expand the parenthesis to obtain:
[tex]y - 2 = - 3 {x}^{2} - 24x - 48[/tex]
Group the similar terms to obtain:
[tex]y = - 3 {x}^{2} - 24x - 48 + 2[/tex]
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
The standard form is
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
PLZZZZZ HELP!!!
The graph shows two lines, A and B.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points)
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
Answers
Answer:
Part A: 1 solution
Part B: x = 3, y = 4
Step-by-step explanation:
Lines A & B intersect one time, meaning there is only one pair of x and y values that will make the two equations equalThey intersect at x = 3, and y = 4what is the missing reason in the proof
Answers
Answer:
SSS Congruence Theorem
Step-by-step explanation:
sss congruence theorem. you can get this answer by marking all the givens.
Colin and Brian were playing darts. Colin scored 139 Brian scored 53 more than Colin. What was their combined score?
Answers
Answer
Their combined score is 331 points
Explanation
Determine each person's score
Collin score: 139
Brian: 139 + 53 = 192
Add the scores together
139 + 192 = 331
Colin scored 139 points and Brian scored 53 points more than Colin, which is 192 points. Adding Colin's and Brian's scores gives a combined score of 331 points.
Explanation:In the game of darts, Colin and Brian scored different points. We know that Colin scored 139 points. As per the information given, Brian scored 53 points more than Colin. So, to find out how many points Brian scored, we can add 53 to Colin's score of 139, which gives us 192 points for Brian.
To find out the combined score of Colin and Brian, we simply add Colin's score to Brian's score. So, 139 (Colin's score) plus 192 (Brian's score) equals 331.
Therefore, the combined score of Colin and Brian is 331 points.
Learn more about Adding Scores here:https://brainly.com/question/29000462
#SPJ3
suppose the radius of a circle is 8 units. what is its circumference
Answers
Answer:
[tex]\large\boxed{C=16\pi\approx50.24}[/tex]
Step-by-step explanation:
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
r - radius
We have r = 8. Substitute:
[tex]C=2\pi(8)=16\pi[/tex]
[tex]\pi\approx3.14\to C\approx(16)(3.14)=50.24[/tex]
Answer:
50.24 units
Step-by-step explanation:
Hope this helps!
What is the area of the base of a cylinder with a volume of 174π in.3 and a height of 12 inches? 1. Apply the formula for the volume of a cylinder: V = Bh 2. Substitute the known measures into the formula: 174π = B(12) 3. Apply the division property of equality: 174π 12 = B 12 12 The area of the base of the cyclinder is π in.2.
Answers
ANSWER
The area of the base is 14.5π in²
EXPLANATION
The volume of a cylinder is given by
[tex]Volume =base\:area \times height[/tex]
Or
V=Bh
It was given that the volume of the cylinder is 174π in³.
The height was given as 12 inches.
We substitute to get,
174π=12B
Divide both sides by 12 to get:
B=14.5π in²
Hence the area of the base is 14.5π in²
Answer:
14.5
Step-by-step explanation:
A store sells a television for $1000. Customers can choose to receive a 10% discount and pay it off with a loan at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years no interest. If the customer plans to pay it off in 3 years, which option is better
Answers
Answer:
Second option
Step-by-step explanation:
Option 1:
1. Original cost: 90% * 1000 = $900
2. Interest: A = P(1 + rt), A = amount, P = original amount, r = rate, t = years
Plug in: A = 900(1 + 0.05*3)
Multiply + add: A = 900(1.15)
Multiply: A = $1035
Option 2: $1000
So, paying full price upfront will save more money if all goes to plan.
Destiny has one round window that is 20 inches in diameter. What is the circumference and area of the window?
Answers
Answer:
The Circumference is 62.80, The Area is 100 inches squared
Step-by-step explanation:
Diameter is 20 so the Radius is half of thats.
D=20 In
R=10 in
Circumference is diameter multipied by pi
so you multiply 20 by 3.14 and you get 62.80 inches
To Find Area you have to multiply the radius times it self. so 10×10 whoch equals 100.
so the area is 100 inches squared.
Which transformation(s) can be used to map one triangle onto the other? reflection only translation only dilation, then translation rotation, then translation rotation then dilation
Answers
Answer:
reflection only
rotation, then translation
Step-by-step explanation:reflection only rotation, then translation
Answer:
Transformation which can be used for mapping of one triangle to another are;
Only translationRotation then dilation.Step-by-step explanation:
Given information:
We need to map one triangle to another ;
Hence, for mapping of one triangle to another,
The transformation which can be used from the given options are;
Only translationRotation then dilation.For more information visit;
https://brainly.com/question/4618918?referrer=searchResults
At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 35 years old, with a standard deviation of 10 years.
If you were to take a sampling of 10 employees, what is the probability your mean age will be at least 37? Round to the nearest percent.
Answers
Answer:
P =26%
Step-by-step explanation:
In this problem we have the ages of all new employees hired during the last 10 years of normally distributed.
We know that the mean is [tex]\mu = 35[/tex] years and standard deviation is [tex]\sigma = 10[/tex] years
By definition we know that if we take a sample of size n of a population with normal distribution, then the sample will also have a normal distribution with a mean
[tex]\mu_m = \mu[/tex]
And with standard deviation
[tex]\sigma_m = \frac{\sigma}{\sqrt{n}}[/tex]
Then the average of the sample will be
[tex]\mu_m = 35\ years[/tex]
And the standard deviation of the sample will be
[tex]\sigma_m =\frac{10}{\sqrt{10}} = 3.1622[/tex]
Now we look for the probability that the mean of the sample is greater than or equal to 37.
This is
[tex]P({\displaystyle{\overline {x}}}\geq 37)[/tex]
To find this probability we find the Z-score
[tex]Z = \frac{{\displaystyle{\overline{x}}} -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{37 -35}{\frac{10}{\sqrt{10}}} = 0.63[/tex]
So
[tex]P({\displaystyle{\overline {x}}}\geq 37) = P(\frac{{\displaystyle{\overline {x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}\geq\frac{37-35}{\frac{10}{\sqrt{10}}}) = P(Z\geq0.63)[/tex]
We know that
[tex]P(Z\geq0.63)=1-P(Z<0.63)[/tex]
Looking in the normal table we have:
[tex]P(Z\geq0.63)=1-0.736\\\\P(Z\geq0.63) = 0.264[/tex]
Finally P = 26%
To find the probability that the sample mean age of 10 employees is at least 37, we can use the Central Limit Theorem and standardize the sample mean. The probability is approximately 2.28%.
Explanation:To solve this problem, we need to use the Central Limit Theorem, which states that the sample mean of a large enough sample size will be approximately normally distributed regardless of the shape of the population distribution.
In this case, the mean age of new employees is normally distributed with a mean of 35 and a standard deviation of 10. We want to find the probability that the sample mean age of 10 employees is at least 37.
To find this probability, we first need to standardize the sample mean using the formula z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Using this formula, we have z = (37 - 35) / (10 / sqrt(10)) = 2 * sqrt(10).
From a standard normal distribution table, we can find that the probability of getting a z-score less than 2 * sqrt(10) is approximately 1 - 0.0228 = 0.9772. However, we want the probability of getting a sample mean at least 37, so we subtract this probability from 1 to get 1 - 0.9772 ≈ 0.0228.
Therefore, the probability that the sample mean age of 10 employees will be at least 37 is approximately 2.28%.