Answers
Answer:
Domain : (- ∞, - 5), and (3 / 2, ∞),
Range : (∞, 0.4437]
Step-by-step explanation:
Assuming that we want our answer in interval notation, let's start by determining the domain. Remember that the domain can be found where the function is undefined.
Given : f(x) = (2x - 7) / (2x² + 7x - 15)
Alternative Form : (2x - 7) / (x + 5)(2x - 3)
To receive this 'alternative form' we can simply factor the expression 2x² + 7x - 15. See the procedure below,
[tex]\mathrm{Given : 2x^2+7x-15} ,[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups : \left(2x^2-3x\right)+\left(10x-15\right)} ,[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right),\\\mathrm{Factor\:out\:}5\mathrm{\:from\:}10x-15\mathrm{:\quad }5\left(2x-3\right),[/tex]
[tex]x\left(2x-3\right)+5\left(2x-3\right) = \left(2x-3\right)\left(x+5\right) - \mathrm{Factored\:expression}[/tex]
Now let's find the domain using the expression '(x + 5)(2x - 3) = 0.' If the denominator equals 0, the function is considered undefined.
[tex]\mathrm{Given : \left(x+5\right)\left(2x-3\right)=0} ,\\x+5=0:\quad x=-5, 2x-3=0:\quad x=\frac{3}{2}\\\mathrm{The\:solutions\:are: x=-5,\:x=\frac{3}{2}}[/tex]
Knowing these solutions the domain has the intervals (- ∞, - 5), and (3 / 2, ∞). The range is the set of values that correspond to the domain, so in this case the range would be (∞, 42 + 8√17 / 169]. 42 + 8√17 / 169 = (About) 0.4437, so it lies on the interval (∞, 0.4437].
The images below represent the plotted function in two areas. There are 3 curves in this graph.
Related Questions
If you want to go bed a 800 o'clock
at night and set the alarm to get up at
9 in the morning how many hours
sleep would this permt you?
Answers
Answer:
13 hours
Step-by-step explanation:
8:00 plus 4 is twelve ( 12 o'clock )
then you have 9hrs left.
( 4+9=13 )
William drove 35 miles per hour for a total of 105 miles. He drove for x hours.
Which equation and solution below describe the situation?
Answers
Answer:
x=35 hrs
1 hour =105
cross mutiply
105÷35=3
The equation that describes the situation is 35x = 105.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The equations are of various types, such as Trigonometric equations, and quadratic equations.
William drove 35 miles per hour for a total of 105 miles.
The total miles William drove is 105 miles.
The speed at which he drove is 35 miles/ hour.
The total time he drove is given by x hours.
The equation has to be formed for this situation.
Speed is defined as the distance traveled with respect to time.
35 = 105 / x
35x = 105
This equation describes the given situation.
To know more about Equation
https://brainly.com/question/10413253
#SPJ5
One is the additive identity. True or False
Answers
Answer: false
Additive identity - the number 0; when added to any number, the value of the number does not change
( one is multiplicative identity )
Simplify: -8 +2 +3 (-7)
Answers
Answer:
-8/4-21x
Step-by-step explanation:
Distribute inside the parantheses
Divide -8 and 4
Add the two terms
Simplify
8^15÷8^−3 im lost i dont get this whole simply thing at all
Answers
8^15 ÷ 1/8^3 = 8^15 x 8^3=8^18
1.8014399e+16
Step-by-step explanation:
So before you can divide the numbers you have to simplify the exponents. You probably learned P(parentheses) E(exponents) M(multiply) D(divide) A(add) S(subtract.
PEMDAS is important because it shows you what order to so something in. Exponents is before divide so you simplify the exponents and you get 8^15= 3.5184372e+13 and 8^-3 = 0.001953125. So after you simplify the exponents you can now divide themNow (3.5184372e+13) ÷ (0.001953125) = 1.8014399e+16Solve the system of linear equation by substitution. Check your solution. x=6y-7 4x+y=-3
Answers
Answer:
X = -1
Y = 1
Step-by-step explanation:
The solution of the equations x = 6y - 7 and 4x + y = -3 will be (-1, 1).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equation is given below.
x = 6y - 7 ...1
4x + y = - 3 ...2
Simplify the equation, then we have
4(6y - 7) + y = -3
24y - 28 + y = - 3
25y = 25
y = 1
The value of the variable 'x' will be calculated as,
x = 6(1) - 7
x = 6 - 7
x = - 1
The solution of the equations x = 6y - 7 and 4x + y = -3 will be (-1, 1).
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
A snack bar seils scoops of strawberry, chocolate, and
vanilla ice cream. On Monday, the snack bar sold
100 scoops in total of these flavors of ice.cream. The
snack bar sold 3 times as many scoops of chocolate as
it did strawberry and 2 times as many scoops of
vanilla as it did chocolate. How many scoops of
chocolate ice cream did the 'snack bar sell on
Monday?
Answers
Answer:
600/11
Step-by-step explanation:
scoops of
strawberry= x
chocolate= y
vanilla ice cream= z
X+y+z= 100
The snack bar sold 3 times as many scoops of chocolate as it did strawberry
3x= y
X= y/3
and 2 times as many scoops of
vanilla as it did chocolate
2z= y
Z= y/2
X+y+z= 100
Y/3 + y +y/2 = 100
2y + 6y + 3y = 600
11y= 600
Y= 600/11
Evaluate ( z^2 + 4 ) ( z^2 – 5)
Answers
Answer:
z^4-z²-20
Step-by-step explanation:
( z^2 + 4 ) ( z^2 – 5)
z^4+4z²-5z²-20
z^4-z²-20
Find the area of the isosceles triangle.
Answers
Answer:
60in^2
Step-by-step explanation:
Area of a triangle = Height x Base X 1/2
Base = 10
Other 2 sides = 13
Now, let's split the Base into 2 parts.
=> 1 part = 5 and 2 part = 5
We can find the height using Pythagorean theorem
=> Isosceles triangle
=> (1 part of the base)^2 + Height^2 = The Hypotenuse^2 = the longer side of a triangle = 13^2
=> 5^2 + Height ^2 = 13^2
=> 25 + Height^2 = 169
=> 25 - 25 + Height ^2 = 169 - 25
=> Height^2 = 144
=> Height = Square root of 144
=> Height = 12
Area = 12 x 10 x 1/2
=> 12 x 5
=> 60 in^2
So, the Area is 60 in ^2
simplify the expression 3+2^2 / 2+3
Answers
Ans
8 option b.
Step-by-step explanation:
3+4/2+3
=3+2+3
=5+3
=8
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 13.6 reproductions and the population standard deviation is known to be 1.9. If a sample of 189 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.
Answers
Answer:
The confidence interval is [tex]13.4< \mu < 13.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 13.6[/tex]
The standard deviation is [tex]\sigma = 1.9[/tex]
The sample size is [tex]n = 189[/tex]
given that the confidence level is 85% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 85 )\%[/tex]
[tex]\alpha = 0.15[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{\alpha }{2} } = 1.44[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 1.44* \frac{1.9}{\sqrt{189} }[/tex]
=> [tex]E = 0.1990[/tex]
The 85% confidence interval is mathematically represented as
[tex]\= x - E < \mu <\= x + E[/tex]
=> [tex]13.6- 0.1990 < \mu < 13.6+ 0.1990[/tex]
=> [tex]13.4< \mu < 13.8[/tex]
[128 ÷ (6 + 4 – 2)] X 8
Answers
Do parentheses first:
6 +4-2 = 8
Now do brackets:
128/8 = 16
Now multiply:
16 x 8 = 128
The answer is 128
B for brackets
D for division
M for multiplication
A for addition
S for subtraction
2) 200
3) 20
4) 10
5) 170
6) 55plz help i will mark the brainliest
Answers
Answer:
natural numbers - positive integers (whole numbers)
• 1
• 2
• 3
• 4
• 5
whole numbers - a number without fractions
• 10
• 11
• 12
• 13
• 14
rational numbers - a number that can be expressed as the ratio of two integers
• 1/3 or 0.3333...
• 17
• -34
• 25
• -10
integers - a whole number; a value that is not a fraction
• -5
• 49
• 68
• 439
• 35
Write the fraction 2/5 as an equivalent with the given denominator 25
Answers
Answer:
10/25
Step-by-step explanation:
2/5 = x/25
We need to multiply the bottom by 5 to get to 25
5*5 = 25
What we to the bottom, we do the the top
2/5 * 5/5 = 10/25
Answer:
10/25
Step-by-step explanation:
2/5 = x/25
cross multiply
2 • 25 = 50
5 • x = 5x
set equal to each other
5x = 50
divide both sides by 5
x = 10
The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec. How long does it take to reach the ground
Answers
This question is incomplete, the complete question is;
A rocket is launched straight into the air with initial velocity 200 ft/s. Assume the launch is instantaneous. How high will it go, and how long will that take (use time increments of 0.01 seconds)? G= - 32.2 ft/s² , H₀=0 (the ground)
V(t)=V₀ + g t
H(t)= H₀ + V₀ t + ½ g t²
The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec. How long does it take to reach the ground
Answer:
a) maximum height S is 621.12 ft and time taken to reach it is 6.21 sec.
b) The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec,
Time taken to travel t = 24.79 sec
NOW total time taken = 27.55 sec
Step-by-step explanation:
Given that,
initial velocity u = 200 ft/s
acceleration a = 32.2 ft/s²
vertical displacement ( maximum height) S = ?
final velocity at highest point Ц = 0
NOW from the equation of motion
v² - u² = 2as
we substitute
0² - (200)² = 2 (-32.2) × s
s = 621.12 ft
time taken t = (v -u)/a = (0-200)/-32.2
t = (-200) / (-32.2)
t = 6.21 sec
distance traveled by rocket from t=6.21sec to t=9sec
Δt = (9-6.21) = 2.79sec
s = ut + 1/2at²
s = 0 + 1/2(32.2)(2.79)² = 125.32 ft
Remaining distance = 621.12 ft - 125.32 ft = 495.8 ft
Time taken to travel = t = s/v = (495.5ft) / (20 ft/sec)
t = 24.79 sec
NOW total time taken = 2.79sec + 24.79sec = 27.55 sec
Need help with this have no idea how to do it
Answers
Answer:
Step-by-step explanation:
x- intercept, vertex (v) and axis of symmetry, parabola form:x²+bx+c
vertex(h,k)
1- f(x)=(x+3)(x-3) change into parabola formf(x)=x²-9 a=1,b=0 ,c=-9
h=-b/2a=0
k=f(0)=-9
vertex(0,-9) , x intercept is when f(x)=0
(x-3)(x+3)=0 either x-3=0⇒ x=3 or x+3=0 then x=-3
x=3, x=-3 (-3,0) and (3,0)
the x of symmetry is the h of the vertex=0
2-g(x)=(x+1)(x-3)g(x)=x²-2x-3 a=1, b=-2,c=-3
h=-b/2a⇒-(-2)/2(1)⇒h=1
k=f(1)=1²-2(1)-3⇒k=-4
v(1,-4)
x of symmetry=h=1
(x+1)(x-3)=0
x+1=0⇒x=-1 (-1,0)
x-3=0 ⇒x=3 (3,0)
x intercept :-1,3
3-y=-x(x+6) ⇒y=-x²-6x a=-1,b=-6, c=0vertex(-3,9)
x intercept:(0,0) and (-6,0)
axis of symmetry =-3
4-g(x)=2(x-5)(x-1) ⇒ 2x²-12x+10 a=2, b=-12, c=10vertex(3,-8)
axis of symmetry=3
x intercept : (5,0), (1,0)
5) -4x(x+1)⇒-4x²-4x a=-4,b=-4vertex(-1/2,1)
x of symmetry=-1/2
x intercept : (0,0)(-1,0)
6- f(x)=-2(x-3)² ⇒-2x²+12x-18vertex(3,0)
x intercept (3,0)
axis of symmetry = 3
Sarah received a score of 36 points on an exam. The exam consisted of multiple choice questions that were worth 3 points for a correct answer and free response questions that were worth 5 points for a correct answer. If she answered a total of 10 questions correctly, how many of each type of question did she get correct?
Answers
Answer:
Sarah answered 7 multiple choice questions and 3 free response questions correctly.
Step-by-step explanation:
Given that: she has 36 points.
3 points each for the multiple choice question (MCQ)
5 points each for the free response question (FRQ)
To determine how many of each question was answered correctly. Let the number of MCQ she answered be represented by x and FRQ by y.
3x + 5y = 36 ............ 1
Since she answered a total of 10 question, then;
x + y = 10
x = 10 - y ................ 2
Substitute equation 2 into 1,
3(10 - y) + 5y = 36
30 - 3y + 5y = 36
2y = 6
y = 3
Substitute the value of y in equation 2,
x = 10 - y
= 10 - 3
= 7
x = 7, y = 3
Therefore, Sarah answered 7 multiple choice questions and 3 free response questions.
evaluate 1/3(-15+3/2)
Answers
Answer:
-4 1/2
Step-by-step explanation:
1/3(-15+3/2)
1/3(-13 1/2)
1/3(-27/2)
-27/6
-4 3/6
-4 1/2
A three-person committee is chosen at random from a group of 8. How many different committees are possible?
Answers
calculate the weight of a piece of steel to the nearest tenth of a pound. the diameter is 40" and the thickness is 2
Answers
Answer:
2513.3
Step-by-step explanation:
cylinder volume = π[tex]r^{2}[/tex]h
cylinder volume = π [tex]20^{2}[/tex](2)
cylinder volume = 2513.27
cylinder volume = 2513.3
4 times the sum of a number and 8 gives 25
Answers
Answer:
4×(x+8)=25.
use the 4 to multiply the numbers in the bracket.
which is 4x+32=25.
then collect like terms which is...
4x=25-32...
4x=-7.
x=-7/4= -1.75 or -1 whole number 3/4.
What is the quotient of the rational expression below?
Answers
Answer:
first answer
Step-by-step explanation:
Hello, you know that
[tex]\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\cdot \dfrac{d}{c}[/tex]
So, the quotient we need to estimate is
[tex]\begin{aligned}\dfrac{x^2-36}{x+8}\cdot\dfrac{4x+32}{x^2+12x+36}&=\dfrac{x^2-6^2}{x+8}\cdot \dfrac{4(x+8)}{(x+6)^2}\\\\&=\dfrac{4(x-6)(x+6)}{(x+6)^2}\\\\&=\dfrac{4(x-6)}{x+6}\end{aligned}[/tex]
Thank you
SimpifyWhat is x to the power of 3 times x to the power 7?
Answers
Answer:
Here is your solution-
x³ times x⁷
means, x³×x⁷
Here you just have to add the powers as aⁿ×aᵐ=aⁿ⁺ᵐ
x³⁺⁷
x¹⁰
Determine the sum of the arithmetic series: 5+18 +31 +44 + ... 161.
Answers
Answer:
1079
Step-by-step explanation:
Hello,
18-5 = 13
31-18=13
44-31=13
161=5+13*12
So we need to compute
[tex]\displaystyle \sum_{k=0}^{k=12} \ {(5+13k)}\\\\=\sum_{k=0}^{k=12} \ {(5)} + 13\sum_{k=1}^{k=12} \ {(k)}\\\\=13*5+13*\dfrac{12*13}{2}\\\\=65+13*13*6\\\\=65+1014\\\\=1079[/tex]
Thanks
The required sum of the arithmetic series 5+18 +31 +44 + ... 161 is 1079.
Given that,
Arithmetic series: 5+18 +31 +44 + ... 161.
The Sum of the series is to be determined.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values
Here,
From the given series
First term A = 5, Common difference D = 13 and last term L = 161
Last term = An + (n -1)
161 = 5 + (n - 1)13
n - 1 = (161 - 5) / 13
n = 12 + 1
n = 13
Now the sum of an arithmetic series,
S = n /2 (A + L)
S = 13 / 2 (5 + 161)
S = 13 / 2 * 166
S = 13 * 83
S = 1079
Thus, the required sum of the arithmetic series 5+18 +31 +44 + ... 161 is 1079.
Learn more about arithmetic progression here: https://brainly.com/question/20334860
#SPJ2
Binomial (-2x - 8) and trinomial (-3x2 + 4x + 5) are the factors of which of the following polynomials?
Answers
Answer:
5
Step-by-step explanation:
at the mall myla bought a shirt for 25.36$ a hat for 5.09$ and a belt for 11.45$ howe much did she spend altogether?
Answers
25.36+5.09+11.45= 41.9$ intotal
Answer:
41,9
Step-by-step explanation:
25.36+5.09+11.45
A tortoise is walking in the desert. It walks 43.75 meters in 7 minutes. What is it’s speed?
Answers
Answer:
v=0.104167m/s
Step-by-step explanation:
Given:
s=43.75
t=7min
Required:
v=?
Formula:
v=s/t
t in second
Solution:
1min=60s
7min=7*60s=420s
v=s/t
v=43.75m/420s
v=0.104167m/s
Hope this helps ;) ❤❤❤
A steel pipe which was 16.84 feet long, weighed 20.88 pounds what is the weight of one foot of the steel pipe?
Answers
This type of problem is solved using cross multiplication. You know the length (16.84 feet), and the weight (20.88 pounds), of the steel pipe. But what you do not know is the weight of one foot of the steel pipe. Since that is what we are solving for, the weight of one foot of the steel pipe will be our x variable.
This is how I set it up...
16.84 1
——— * ———
20.88 x
I came up with this equation. The length of the pipes I put in the numerator (top), and the weight I put in the denominator (bottom). Since 16.84 feet of a steel pipe weighs 20.88 pounds, 1 foot of a steel pipe weighs x pounds. After you have the equation set up you then move on to cross multiplication.
Step 1: Multiply the top number of the first fraction by the bottom number of the second fraction.
16.84*x= 16.84x
Step 2: Multiply the bottom number of the first fraction by the top number of the second fraction.
20.88*1=20.88
Step 3: Set the answers from step 1 and step 2 equal to each other.
16.84x=20.88
Step 4: Divide 16.88 on both sides so x is by itself.
16.84x 20.88
——— = ———
16.84 16.84
And after you divide on each side you have your answer which should be x=1.24
Negative of (-5) does not exist is true or false
Answers
Answer:
Negative of 5 exists
It continues in the left part of a number line...
Hence the answer is false it does exist
Determine ux and sigma x from the given parameters of e population and sample size.
mu = 86, sigma = 16, n = 64
Suppose a simple random sample of size n = 36 is obtained from a population with mu = 71 and sigma = 6.
A) Describe the sampling distribution of xbar.
B) What is P (xbar > 73)?
C) What is P (xbar 69)?
D) What is P (69.8 < xbar < 72.5)?
1) Choose the correct description of the shape of the sampling distribution of xbar.
A) The distribution is skewed left.
B) The distribution is approximately normal.
C) The distribution is uniform.
D) The distribution is skewed right.
E) The shape of the distribution is unknown.
Find the mean and standard deviation of the sampling distribution of x-.
2) P(x->73) =.
3) P (x- 69) =.
4) P (69.8 < xbar < 72.5) =.
Answers
Answer:
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 86
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 2
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 71
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 1
B) The distribution is approximately normal.
[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]
Therefore, the probability that the sample mean is greater than 73 = 0.0228
[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]
The probability that the sample mean is less than or equal to 69 is 0.0228
[tex]\mathbf{P( 69.8 \leq \overline x \leq 72.5) = 0.8181}[/tex]
Thus, the probability that the sample mean is between 69.8 and 72 is 0.8181.
Step-by-step explanation:
We are to determine the [tex]\mu_{\overline x}[/tex] and [tex]\sigma_x[/tex] from the given parameters of a population and sample size.
Given that :
population mean [tex]\mu[/tex] = 86
population standard deviation [tex]\sigma[/tex] = 16
sample size n = 64
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is equal to the population mean [tex]\mu[/tex]
∴
[tex]\mu_{\overline x}[/tex] = [tex]\mu[/tex] = 86
The standard deviation of the sampling distribution can be computed by using the formula:
[tex]\sigma_{\overline x } = \dfrac{\sigma }{\sqrt{n}}[/tex]
[tex]\sigma_{\overline x } = \dfrac{16 }{\sqrt{64}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{16 }{8}[/tex]
[tex]\mathbf{\sigma_{\overline x } = 2}[/tex]
∴
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 86
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 2
Suppose a simple random sample of size n = 36 is obtained from a population with mu = 71 and sigma = 6.
i.e
sample size n = 36
population mean [tex]\mu[/tex] = 71
standard deviation [tex]\sigma[/tex] = 6
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is equal to the population mean [tex]\mu[/tex]
∴
[tex]\mu_{\overline x}[/tex] = [tex]\mu[/tex] = 71
The standard deviation of this sampling distribution [tex]\sigma_{\overline x}[/tex] can be estimated as :
[tex]\sigma_{\overline x }= \dfrac{\sigma }{\sqrt{n}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{6 }{\sqrt{36}}[/tex]
[tex]\sigma_{\overline x } = \dfrac{6 }{6}[/tex]
[tex]\mathbf{\sigma_{\overline x } = 1}[/tex]
∴
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 71
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 1
A)
The correct option from the given question is:
B) The distribution is approximately normal.
B) What is P (xbar > 73)?
i.e
[tex]P(\overline x >73) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 \times 6 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{12 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > 2 \end {pmatrix}[/tex]
[tex]P(\overline x >73) = 1- P \begin {pmatrix} Z < 2 \end {pmatrix}[/tex]
Using the Excel Function ( =NORMDIST(2) )
[tex]P(\overline x >73) = 1- 0.9772[/tex]
[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]
Therefore, the probability that the sample mean is greater than 73 = 0.0228
C) What is P (xbar ≤ 69)?
i.e
[tex]P(\overline x \leq 69) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{69 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix}Z \leq \dfrac{-2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-2 \times 6 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-12 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq -2 \end {pmatrix}[/tex]
Using the EXCEL FUNCTION ( = NORMSDIST (-2) )
[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]
The probability that the sample mean is less than or equal to 69 is 0.0228
NOTE: This text editor can't contain more than 5000 characters so the last part of the question is attached in the image below.