Which of the following points lie in the solution to the following system of inequalities y less than or equal to x -5 and y greater than or equal to -x-4
(-5,2)
(5,-2)
(-5,-2)
(5,2)
Answers
The point that lies in the solution to the system of inequalities is (5,-2). The correct answer would be an option (B).
What is inequality?An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The system of inequalities is given in the question, as follows:
y ≤ x -5 and y ≥ -x-4
Since the required point is to satisfy the system of inequalities.
Then the graph attached below represents a solution to the system of inequalities.
Point A (-5,2) does not lie in the solution to the system of inequalities.
Point B (5,-2) lies in the solution to the system of inequalities.
Point C (-5,-2) does not lie in the solution to the system of inequalities.
Point D (5,2) does not lie in the solution to the system of inequalities.
Therefore, the point that lies in the solution to the system of inequalities is (5,-2).
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Related Questions
state the next terms in the sequence of number 8, 4, 2, 1 -1/2
Answers
The next term in the sequence of number 8, 4, 2, 1, 1/2 is 1/4
How to determine the next term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
The sequence of number 8, 4, 2, 1 -1/2
Express properly
The sequence of number 8, 4, 2, 1, 1/2
The above definitions imply that we simply divide the previous term by 2 to get the current term
Using the above as a guide,
Next term = (1/2)/2
Evaluate
Next term = 1/4
Hence, the next term is 1/4
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The three graphs represent the progress of three runners in a 500-meter race.
The red solid line represents runner A. The purple dotted line represents runner B.
The blue dashed line represents runner C.
Options: Runner A, Runner B, Runner C, 0, 20, 55, 90.
Answers
The answers include the following:
Runner B ran at a constant rate throughout the race.Runner C stopped running for a while and it occurred between 20 to 55.Runner A also sprinted at different speeds.Runner A won the race.What is Speed?This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.
From the graph, we can deduce that Runner A won the race because it attained a greater distance when compared to the time for all the other runners.
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A= (x| x es un mes del año ayúdeme a resolver no le entiendo
Answers
The elements of the set A are given as follows:
A = {January, February, March, April, May, June, July, August, September, October, November, December}.
How to obtain the elements of the set A?The set A in the context of this problem is defined as follows:
A = {x | x is a month of the year.}
Hence the set A is composed by 12 elements, which are all the months of an year, as follows:
A = {January, February, March, April, May, June, July, August, September, October, November, December}.
TranslationThe problem asks for all the elements of the set A, given as follows:
A = {x | x is a month of the year.}
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Which represents the solution to the inequality 5.1(3+2.2x)>-14.25-6(1.7x+4)?
X=<-2.5
x>2.5
(-2.5,~)
(-~,2.5)
Answers
Step-by-step explanation:
Hope it helps :) #CarryOnLearning
A local high school has 1,152 students with 391 freshmen, 351 sophomores, 208 juniors, and 202 seniors. What is the
relative frequency of sophomores at this high school?
Answers
The relative frequency of sophomores at this high school is 39/128.
How to find the relative frequency?
Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).
We are given that;
Total students=1152
Freshmen=391
Sophomores=351
Juniors=208
Seniors=202
Now, to find frequency of sophomores
=number of sophomores/total number of students
=351/1152
=117/384
=39/128
Therefore, the relative frequency will be 39/128.
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Which one of the following items is not necessary in preparing a statement of cash flows?
O Determine the cash provided by operations
O Determine cash from financing and investing activities
O Determine the cash in all bank accounts
Determine the change in cash
Answers
The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
What is meant by statement cash flows?In financial accounting, a cash flow statement, often called a statement of cash flows, is a financial statement that breaks down the analysis into operating, investing, and financing operations. It illustrates how changes in balance sheet accounts and income effect cash and cash equivalents.
A cash flow statement lists all of an organization's cash inflows from current operations and outside investment sources. The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
Functionally speaking, cash flows are categorized according to the nature of the underlying transaction. The statement's main goal is to give pertinent details about the agency's cash inflows and outflows during a given time period.
Therefore, the correct answer is option d) Determine the change in cash.
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What is the size, in degrees, of the missing angle?
45
65°
Answers
Explanation
Triangle angle Theorem: The total of the three interior angles in any triangle is 180 degrees.
Thus, 180 - 45 - 65 = 70 degrees
A hole in a steel plate has a diameter of 1.166 cm
at 23.00 ∘C
At what temperature is the diameter of the hole equal to 1.164 cm
?
will give brainliest
Answers
So here we have a hole in a steel plate with a diameter of 1.166 cm. So we need to find the temperature at what temperature is the diameter of full equal to 1.165 cm. So you're given is D. I. That is equal to initial diameter. That is equal to 1.166 cm. and temporary Germany shirt temperature is equal to 23°C and DF is equal to 1.165 m. This is the final diameter. So you only need to find the value of P. F. So we know that whole diameter very nice linearly with And nature. So here we can say DFS equal to D. I multiplied by one plus alpha. They're dirty. Yeah, I'll find that coefficient of thermal expansion. So here we can say it this is for steel And the value of alpha is equal to 13, multiplied by 10, raised to -6. So D F. Is equal to B. I multiplied plus the I'm multiplied by alpha, multiplied by delta T. So here we can see it D F minus D. I. That is the initial final diameter minus initial diameter divided by D. I. Alpha. That is equal to delta P. So this will be where to tell 30. That is equal to -6.59717. multiplied by 10° to -5 divided by And there's do -6. So here the key Is equal to -65.9717 degree. So here P f minus T I is equal to minus 65.9717 degree. The T.F will be equal to 23 -65.9717. So therefore final temperature that this T.F is equal to -42.8717 degrees Celsius. So therefore this is the answer to the question. So here we can say hands, final temperature Is equal to -42.8717°C.
please thank you mwaaaaaaaaaaaaa
Answers
The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is 301.44 square inches.
What is perimeter and area enclosed in circle?
A circle is also defined by two properties: area and perimeter. The formulas for both the measures of the circle are given by; Area of a circle = πr². The perimeter of a circle = 2πr.
Let's call the center of the circle O and the endpoint of the arc A. Let's also call the endpoint of the chord that defines the segment B. Then we have an isosceles triangle OAB, where OA = OB = 24 inches.
1) The perimeter of the segment is equal to the length of the arc plus the length of the chord. To find the length of the arc, we can use the formula:
Arc length = (Ф / 360) * 2πr,
where Ф is the measure of the angle in degrees, r is the radius (which is 24 inches in this case), and π is pi.
In this case, the measure of the angle is 60°, so the length of the arc is:
Arc length = (60 / 360) * 2π * 24 inches
Arc length = (1/6) * 2π * 24 inches
Arc length = 4π inches
To find the length of the chord, we can use the formula:
Chord length = 2r * sin(Ф/2), where r is the radius and Ф is the measure of the angle in radians.
First, we need to convert the angle measure from degrees to radians:
60° = 60 * (π / 180) radians = π / 3 radians
Now, we can find the length of the chord:
Chord length = 2 * 24 * sin(π / 6)
Chord length = 24 * 2 * sin(π / 6)
Chord length = 24 * √3 inches
Finally, we can add the length of the arc and the chord to find the perimeter:
Perimeter = 4π + 24 * √3
Perimeter = 4π+41.57
Perimeter = 54.13 inches
2) To find the area of the segment, we can use the formula:
Area = (Ф/ 360) * πr², where Ф is the measure of the angle in degrees and r is the radius.
In this case, the measure of the angle is 60°, so the area of the segment is:
Area = (60 / 360) * π * 24² square inches
Area = (1/6) * π * 576 square inches
Area = 96π square inches
Area = 301.44 square inches
So, The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is301.44 square inches.
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What are the slopes and lengths?
Answers
Answer:
KL - slope 6/5 , length 7.8
LM - slope -5/6 , length 7.8
MN - slope 6/5 , length 7.8
NK - slope -5/6 , length 7.8
Step-by-step explanation:
square :3
_____
which two integers is between /-83
Answers
The two integers that are between -83 and +83 are -82 and +82.
What is integers ?
In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.
There are multiple pairs of integers that are between -83 and 83.
Here are two examples:
-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -50 0 50 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -75 0 75 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.
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A scientific model is used to predict the average global high
temperature on earth by anaylizing the data from previous
years. In 1940, the temperature was 55° F However, the
temperature has grown to 59.5° F in 1990.
A) Find an equation in the form T = ax + b, where x is the
number of years since 1940 and T is the average gobal high
temperture on Earth.
Answers
Answer:
chapter 1
Step-by-step explanation:
That are a valid decomposition of c (x )such that c equals f ring operator g g (x )equals x squared f (x )equals cube root of x plus 1 end root g (x )equals x squared plus 1 f (x )equals cube root of x g (x )equals x plus 1 f (x )equals cube root of x squared end root g (x )equals cube root of x plus 1 f (x )equals x squared
Answers
By using the composition of functions, we can find valid decompositions of c(x) using f(x) = [tex](x+1)^{1/3}.[/tex] and g(x) = x²
A function is a rule that takes an input value and produces an output value.
One way to do this is to use the composition of functions. The composition of two functions f(x) and g(x) is denoted as f(g(x)). This means that we first apply g(x) to the input, and then apply f(x) to the output of g(x). In other words, we first evaluate g(x), and then plug that result into f(x) to get the final output.
Using this concept, let's look at the first set of functions. We are given
=> c(x) = f ◦ g (x) = (x²) f(x) = [tex](x+1)^{1/3}.[/tex]
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x², and f(x) = [tex](x+1)^{1/3}.[/tex] This is a valid decomposition of c(x).
Similarly, in the second set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x² + 1.
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x² + 1, and [tex](x+1)^{1/3}.[/tex] This is also a valid decomposition of c(x).
In the third set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x + 1, and f(x) = [tex](x^2)^{1/3}=x^{2/3}[/tex]
This is another valid decomposition of c(x).
Finally, in the fourth set of functions, we have
=> c(x) = f ◦ g (x) = x² g(x) = [tex](x+1)^{1/3}[/tex], and f(x) = [tex]x^{2/3}[/tex].
This is yet another valid decomposition of c(x).
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Parallelogram ABCD is a rhombus. Side BC = 5cm and segment AO = 3.8cm
What is the measure of angle d₁°?
What is the tangent ratio of angle c₂?
Answers
Answer:
Let's call angle d₁ "θ". To find θ, we can use the Pythagorean theorem. The segment AO is the hypotenuse of a right triangle with sides BC/2 and AC/2 (since the rhombus is a parallelogram, opposite sides are equal).
AC/2 = (BC/2) / tan(θ)
So:
tan(θ) = AC/2 / (BC/2)
Plugging in the values we have:
tan(θ) = 3.8 / (5/2) = 3.8 / 2.5 = 1.52
Therefore,
θ = tan^(-1)(1.52) = 55.23°
The tangent ratio of angle c₂ is simply the tangent of the angle:
tan(c₂) = tan(90° - θ) = tan(90° - 55.23°) = tan(34.77°) = 1.52
So the tangent ratio of angle c₂ is 1.52.
Step-by-step explanation:
Solve the equation. 15 - 2x = -4(x + 1) + 9
Answers
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
x = -5
Step-by-step explanation:
15 - 2x = -4(x+1) + 9
-4(x+1) can be distributed and simplified to -4x - 4
15 - 2x = -4x - 4 + 9
15 - 2x = -4x +5
-2x + 4x = 5 - 15
2x = -10
x = -5
Answer:
[tex]x=-5[/tex]
Step-by-step explanation:
Given
[tex]15-2x=-4(x+1)+9[/tex]
Simplify the right side by applying the distributive property.
[tex]15-2x=(-4*x)+(-4*1)+9[/tex]
[tex]15-2x=-4x-4+9[/tex]
Add [tex]-4[/tex] and 9.
[tex]15-2x=-4x+5[/tex]
Add [tex]4x[/tex] to both sides of the equation.
[tex]15-2x+4x=5[/tex]
Add [tex]-2x[/tex] and [tex]4x[/tex].
[tex]15+2x=5[/tex]
Subtract [tex]15[/tex] from both sides of the equation.
[tex]2x=-10[/tex]
Divide both sides of the equation by [tex]2[/tex].
[tex]x=-5[/tex]
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You randomly draw once from this deck of cards.
4 6
1 6 9 4
8
1
1
2 6 7
What is the probability of not drawing an even number? Write your
answer as a fraction.
9
5
Answers
Answer:why not
Step-by-step explanation:that sa prrety nice ask
Answer: 5/8
Step-by-step explanation:
The probability of not drawing an even number can be calculated by finding the number of odd numbers in the deck and dividing by the total number of cards. In this deck, there are 5 odd numbers: 1, 1, 1, 7, and 9. The total number of cards is 8. Therefore, the probability of not drawing an even number is 5/8. The answer is written as a fraction as 5/8.
A. 188.5in²
B. 94.25in²
C. 133.5in²
D. 149.25in²
Answers
Answer:B
Step-by-step explanation:
area of triangle is (10*11)/2=55
area of semicircle is
[tex]d=2r\\r=10/2=5\\s=\pi r^{2} /2=25\pi /2=39.25\\39.25+55=94.25[/tex]
What are the line segments in this rectangle?
a rectangle with the vertices labeled Q, R, S, and T
Answers
Answer:
qr rs st qt are the line hope it helped
someone help me please
Answers
The value of summation of ( x-2)² is 973
What is summation?A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.
if
x (x-2) ( x-2)²
15 13 169
13 11 121
13 11 121
4 2 4
19 17 289
12 10 100
6 4 16
5 3 9
14 12 144
Therefore the summation of (x-2)²
= 169+121+121+4+289+100+16+9+144 = 973
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Answer:answer
Step-by-step explanation:
The value of summation of ( x-2)² is 973
There are 32 computers in a computer lab—some are laptops, and some are desktops. If there
are 8 more laptop computers than desktop computers, how many of each type of computer are
in the lab?
Answers
Answer:
There are 12 desktop computers and 20 laptop computers.
Step-by-step explanation:
32:2=16
8:2=4
16-4=12
16+4=20
PLEASE HELP; BEEN STUCK ON THIS PROBLEM FOR A WHILE:
Answers
Answer:
been a while, so I'd check w someone else too, but hope this helps
Step-by-step explanation:
it is expected that over the next 10 years,the speed of personal computer will double every 18 months.calculate how much faster the speed of personal computer will be in 6 years time compared to now
Answers
Answer: Since the speed of personal computers is expected to double every 18 months, we can use exponential growth to calculate the increase in speed over time. We can start by finding the growth factor, which is equal to 2 raised to the power of the number of doublings. In this case, the number of doublings over 6 years can be calculated as follows:
6 years / 1.5 years = 4 doublings
So the growth factor is:
2^4 = 16
This means that the speed of personal computers will be 16 times faster in 6 years compared to now.
Step-by-step explanation:
Question 4 (10 points)
(03.06 MC)
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points
Answers
The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.
Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³
Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³
The volume of this cylinder is 1.5 times that of the cone
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Solve the given initial-value problem.
y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) =
1
2
, y'(0) =
5
2
, y''(0) = −
11
2
the values for the first 3 derivatives derivatives of y are 1/2, 5/2, -11/2 respectively
Answers
The given differential equation:
y''' − 2y'' + y' = 2 − 24ex + 40e5x,
y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2
Therefore, the next solution is 13/2
Differential Equation:
In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.
Now,
Given differential equation is
y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ ------------ (1)
Auxiliary equation is m³ - 2m² +2m = 0
Now,
m(m² - 2m +2) = 0
⇒ m(m-1)² = 0
Therefore, m = 0,1,1
Therefore,
[tex]y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}[/tex]
Now, we have to find the particular solution by method of undetermined coefficient.
[tex]y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}[/tex]
⇒ [tex]y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}[/tex]
⇒ [tex]y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}[/tex]
⇒ [tex]y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}[/tex]
Putting these values in differential equation (1), we get:
y'''(0) = 13/2
Complete Question:
Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2
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2. Чему равна разность? Сравните результаты.
Answers
Answer:
[tex] \frac {3}{8} + \frac{2}{8} = \frac{5}{8} = 1 \frac{3}{8} [/tex]
[tex] = \frac{5}{ \\ 8} = 1 \frac{3}{8} [/tex]
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.4 mmHg (millimeters of mercury) for a sample of size 686 and a sample standard deviation 5.5 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 90% confidence.
What is the 90% confidence interval to estimate the population mean? Round your answer to one decimal place.
Answers
Answer:
{30.1,30.7}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{90\%}=30.4\pm1.645\biggr(\frac{5.5}{\sqrt{686}}\biggr)\\\\CI_{90\%}\approx30.4\pm 0.3\\\\CI_{90\%}=\{30.1,30.7\}[/tex]
Thus, we are 90% confident that the true amount of mmHg that is lowered will be between 30.1 and 30.7 mmHg.
Write this ratio as fraction in lowest terms. 8.64 to 37.76
Answers
The ratio 8.64 : 37.76 as a fraction will be 27/118.
What precisely is ratio?
Ratios and proportions are typically described using fractions. When a fraction is presented as a:b, a ratio is shown, whereas a percentage suggests that two ratios are equal. In this case, a and b can be any two numbers. The ratio and proportion are two essential notions that serve as a foundation for understanding other concepts in mathematics and science.
In our daily lives, we apply the notion of ratio and proportion, such as in business when dealing with money or in cooking.
As a consequence, when b is greater than zero, the ratio specifies the connection between two variables, such as a:b. The 2:4 ratio, for example, is written as 2:4 = 1:2.
Now,
Given ratio is 8.64 : 37.76
we can write this as 8.64/37.76
=864/3776
=432/1888
=216/944
=54/236
=27/118
Hence,
The ratio 8.64 : 37.76, as a fraction will be 27/118.
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helpppp ASAP.
1. What is the height of the cone? Explain how you found the height. (4 points)
2. Now that you have the height of the cone, how can you solve for the slant height, s? (3 points)
3. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. (3 points)
Answers
1. The height of the cone is, 22.18 mm.
2. The slant height is, 28.14 mm.
3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
The volume of cone V = (1/3)πr²h
Given that,
The volume = 8792 mm³
1. by using the formula to solve for h,
we get h = (3V)/(πr²).
Plugging in the values given,
we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.
Therefore, the height of the cone is approximately 22.18 mm.
2. it is known that, from the Pythagoras theorem
s² = h² + r²,
where s is the slant height, h is the height, and r is the radius.
Plugging in the values we found in part 1,
we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².
Taking the square root of both sides, we get s ≈ 28.14 mm.
Therefore, the slant height is approximately 28.14 mm.
3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.
Using the value we found in part 2,
the length of the slant height is approximately 28.14 mm.
Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.
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Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]
Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 80 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.33?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's
approach and calculations.
(Enter your answer as a number accurate to 4 decimal places.)
Answers
The probability that the sample proportion is less than 0.33 is approximately 0.7422.
How to model sample proportion?The sample proportion of first-time customers can be modeled by a normal distribution with mean p, the true proportion of first-time customers, and standard deviation [tex]\sqrt{\frac{p(1-p)}{n}}[/tex], where n is the sample size.
In this case, p = 0.32, n = 80, and we want to find [tex]P(\hat{p} < 0.33)[/tex].
The standardized version of [tex]\hat{p}[/tex] is given by:
[tex]z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Substituting the values, we get:
[tex]z = \frac{0.33-0.32}{\sqrt{\frac{0.32(1-0.32)}{80}}} \approx 0.6579[/tex]
Using a standard normal distribution table (or a calculator or statistical software), we find that the probability of z being less than 0.6579 is approximately 0.7422.
Therefore, the probability that the sample proportion is less than 0.33 is approximately 0.7422.
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