Ann average speed for the entire walk was 1 mile per hour.
Time (hours) Distance from Home (miles)
0 0
1 2
2 4
3 6
4 5
5 4
6 3
7 2
8 1
9 0
1. When Ann was walking, how far away from her house did she get?Ann walked for three hours, covering a distance of 6 miles, the furthest she had walked from her house.
2. When did Ann make her lunch break?
At 4 hours, Ann took a break for lunch.
3. What time did Ann arrive at her house?
After the nine-hour mark, Ann went back home.
4. What was Ann's average walking speed for the first three hours?
The total distance Ann walked during the first three hours of her walk (6 miles) divided by the time required to complete that distance can be used to determine her average pace (3 hours). She moved at an average speed of 2 miles per hour for the first three hours.
5. What was the average pace of Ann's walk?During the entire trek, Ann travelled a total of 9 miles (since she returned to her starting point). It took 9 hours to travel the entire trip. She walked at a mile an hour on average for the entire distance.
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PLEASE HELP ME!!!!!!!! I WILL GIVE POINTS
The most accurate comparison is that a gamma ray has more energy than a radio wave because it has a shorter wavelength and higher frequency.
How do radio waves and gamma rays compare?The most energetic and high frequency particles are gamma rays. On the other side, radio waves are the EM radiation types with the lowest energies, longest wavelengths, and lowest frequencies.
All electromagnetic radiation travels in a vacuum at the speed of light (c), which is the same for all electromagnetic radiation types, including microwaves, visible light, and gamma rays.
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O RATIOS, PROPORTIONS, AND PERCENTS Solving a word problem on proportions using a unit rate Suppose that 18 inches of wire costs 72 cents. At the same rate, how much (in cents ) will 13 inches of wire cost?
13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.
Determine the number of costTo solve this word problem on proportions using a unit rate, we need to first find the unit rate for the cost of the wire. The unit rate is the cost per one inch of wire.
We can find this by dividing the cost by the number of inches:
Unit rate = 72 cents / 18 inches = 4 cents per inch
Now that we have the unit rate, we can use it to find the cost of 13 inches of wire.
We simply multiply the unit rate by the number of inches:
Cost = 4 cents per inch × 13 inches = 52 cents
Therefore, 13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.
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Question 1 1 pts Use the following functions to evaluate each expression f(x) = 1 x + 2 \
g(x) = 3x + 7 a.) f (g(-2)) = [ Select] b.) g (f (1)) = [Select ]
So, the final answers are:
a.) f(g(-2)) = 1/3
b.) g(f(1)) = 8
Question 1: Use the following functions to evaluate each expression f(x) = 1/(x + 2) and g(x) = 3x + 7.
a.) f(g(-2)) = f(3(-2) + 7) = f(1) = 1/(1 + 2) = 1/3
b.) g(f(1)) = g(1/(1 + 2)) = g(1/3) = 3(1/3) + 7 = 1 + 7 = 8
So, the final answers are:
a.) f(g(-2)) = 1/3
b.) g(f(1)) = 8
In summary, to evaluate the expression f(g(x)) or g(f(x)), we need to first find the value of the inner function and then substitute it into the outer function. This process is called function composition. It is important to follow the order of operations and simplify the expression as much as possible.
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find measure of tyk pls hellllllp
The measure of angle TYK is given as follows:
46º.
What are complementary angles?Two angles are defined as complementary if the sum of their measures is of 90º.
In this problem, we have that angle Y is an angle of 90º, which is then divided into two angles, given as follows:
44º.TYK.Then 44 and TYK are complementary angles, and thus the measure of angle TYK is given as follows:
m < TYK + 44 = 90
m < TYK = 90 - 44
m < TYK = 46º.
(the angle addition postulate is also applied for the complementary angles in this problem, as the sum of the two smaller smaller angles combined is of 90º).
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Which expressions are equivalent?
The equivalent expression to the given one is:
y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²
Which expressions are equivalent?We start with the expression:
y⁸*y³*x⁰*x⁻²
Remember the exponent rule for products of powers with the same base, it says that we can write:
xᵃ*xᵇ = xᵃ⁺ᵇ
So we just add the two exponents.
Using exponent rules, we can rewrite the product as
y⁸*y³*x⁰*x⁻² = y³⁺⁸*x⁰⁻² = y¹¹*x⁻²
That is the equivalent expression.
Then we can write:
y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²
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Find the slope-intercept form of the equation of the line that passes through the point P and makes angle 0 with the positive x-axis.
P = (5.4) theta = 30 deg
A. y = (sqrt(3))/3 * x - ((5sqrt(3))/3 - 4)
B. y = (sqrt(3))/3 * x + ((12sqrt(3))/3 - 5)
c. y = sqrt(3) * x - (5sqrt(3) + 4)
D. y = 1/3 * x + ((5sqrt(3))/3 + 12)
The slope-intercept form of the equation of the line that passes through the point P (5, 4) and makes an angle, θ = 30°, with the x-axis is the option A.
A. y = ((sqrt(3))/3)·x - ((5·sqrt(3))/3 - 4)
What is the slope-intercept form of linear equation?The slope-intercept form of linear equation is an equation of the form; y = m·x + c, where;
m = The slope of the graph of the equation
c = The y-intercept of the graph of the equation.
The point through which the line passes, P = (5, 4)
The angle θ the line makes with the positive x-axis = 30°
The slope of the line = The tangent of the angle the line makes with the positive x-axis, therefore;
(y - 4)/(x - 5) = tan(30°) = 1/√3
y - 4 = (x - 5)/√3 = (x - 5)/√3 × (√3/√3) = (x - 5)·√3/3
y = (x - 5)·√3/3 + 4
The above equation can be converted into the slope-intercept form of a linear equation; y = m·x + c by simplifying the equation and rearranging the equation, into the required form;
y = (x - 5)·√3/3 + 4
y = (√3/3)·x - 5·√3/3 + 4 = (√3/3)·x - (5·√3/3 - 4)
y = (√3/3)·x - (5·√3/3 - 4)
The equation in slope-intercept form, is therefore;
A. y = (sqrt(3))/3)·x - (5·sqrt(3))/3 - 4)
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Modified Portfolio - The Trigonometry of Temperatures and then comvert the final aubmision he PDF (Dewhload an a fat er print as a pal and aubmit in Rartfolio teffeeratures int the gines city. * Mater
In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.
It seems like there are a lot of typos and irrelevant information in this question, making it difficult to understand what is being asked. However, I will do my best to provide an answer based on the key terms provided.
In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.
For the final aubmision, it is important to make sure that your work is accurate and complete before converting it to a PDF. This will ensure that your modified portfolio is professional and easy to understand.
Once you have completed your work, you can download it as a PDF and submit it in your portfolio. This will allow you to keep a record of your work and show your understanding of trigonometry and teffeeratures.
I hope this helps! If you have any further questions, please feel free to ask.
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Quadratic Equations, Ques Find the zero (s) of the following function. f(t)=t^(2)+7t+12
The zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.
To find the zeros of a quadratic function, we can either factor the equation or use the quadratic formula. In this case, we can easily factor the equation to find the zeros.
First, we need to find two numbers that multiply to give us 12 and add to give us 7. These numbers are 3 and 4.
Next, we can rewrite the equation using these numbers:
[tex]f(t) = t^(2) + 7t + 12 = (t + 3)(t + 4)[/tex]
Now, we can set each factor equal to zero and solve for t:
[tex]t + 3 = 0 -> t = -3[/tex]
[tex]t + 4 = 0 -> t = -4[/tex]
So, the zeros of the function are -3 and -4.
In conclusion, the zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.
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A toy factory makes an average of 528 toys during a 12-hour shift when it is operating during
its 2-month long busy season. The same factory averages 304 toys during an 8-hour shift
during the remainder of the year.
How many more toys does the factory produce in an hour during the busy season than during
the regular season?
Blank more toys per hour
Answer:
6
Step-by-step explanation:
First, we need to calculate the average number of toys produced per hour during the busy season and the regular season.
During the busy season, the factory operates for 2 x 30 = 60 days or 60 x 12 = <<2*30=60>>720 hours.
The average number of toys produced during this time is 528 toys per 12-hour shift, or 528/12 = <<528/12=44>>44 toys per hour.
During the regular season, the factory operates for the rest of the year, which is 12 - 2 = 10 months, or 10 x 4 = 40 weeks, or 40 x 5 = <<1045=200>>200 days, or 200 x 8 = <<200*8=1600>>1600 hours.
The average number of toys produced during this time is 304 toys per 8-hour shift, or 304/8 = <<304/8=38>>38 toys per hour.
The difference between the average number of toys produced per hour during the busy season and the regular season is:
44 - 38 = <<44-38=6>>6 toys per hour.
Therefore, the factory produces 6 more toys per hour during the busy season than during the regular season. Answer: 6.
Answer:
To calculate the number of more toys the factory produces in an hour during the busy season than during the regular season, we can divide the difference between the two shifts by the total hours of each shift:
More toys per hour = (528-304)/(12-8) = 224/4 = 56 toys per hour
Find the area of the shaded segment of the circle.
The area of shaded region is 0.15 ft².
What is the area of the shaded region?
The area of the shaded region is calculated by subtracting the area of the triangle from the area of the entire sector.
The angle subtended by the sector is calculated as;
θ = ¹/₂ (55⁰)
θ = 27.5⁰
The area of the triangle is calculated as;
A₁ = ¹/₂r² sinθ
where;
r is the radiusA₁ = ¹/₂ x 4² sin(27.5)
A₁ = 3.69 ft²
Area of the sector is calculated as;
A_t = θ/360 x πr²
A_t = ( 27.5 / 360) x π x 4²
A_t = 3.84 ft²
Area of shaded region = 3.84 ft² - 3.69 ft² = 0.15 ft².
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A locker requires a three-digit code to open the lock. The code must contain one letter and two numbers, and no letter or number can be repeated. You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is
.
If a code is chosen at random, the probability that it has a letter that immediately follows an odd number is
.
If a code is chosen at random, the probability that D is in the code but is not in the first position is
.
The probability that this really contains a letter just after an odd number is one-half. D's likelihood of being in the program but not at the first place is 1/4.
What is the likelihood?A possibility which deals with the possibility of random occurrences is referred to as probability. All occurrences must have a chance of occuring at least once, or 1.
Describe probability with an example.The possibility or possibility of an incident occurrence is known as probability. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of coin flipping and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.
You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is (8, 16, 20, and 24)
If a code is chosen at random,
The probability that it has a letter that immediately follows an odd number (1/8, 1/6, 1/3, 2/5, 2/3)
= 1/2
If a code is chosen at random,
The probability that D is in the code but is not in the first position (1/8, 1/6, 1/3, 2/5, 2/3)
= 1/4
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2. Express the following decimal fractions as a sum of fractions. The denominator should be a power of 10. a)0,32 b)3,003 c)13, 134 d)5,2303
Answer:
a) 0.32 = 32/100 = 8/25
b) 3.003 = 3 + 3/1000 = 3000/1000 + 3/1000 = 3003/1000
c) 13.134 = 13 + 134/1000 = 13000/1000 + 134/1000 = 13134/1000
d) 5.2303 = 5 + 2303/10000
Andy has $1,000 in an account. The interest rate is 15% compounded annually.
To the nearest cent, how much will he have in 2 years?
He will have $1322.5 in 2 years.
What is Compound Interest?Compound Interest is the interest calculated on the principal and the interest accumulated over the previous period. It is also the interest-based on the initial principal amount and the interest collected over the period of time.
The formula is A = P(1 + r/n)^nt
Where A = Amount compounded annually
P = Principal = $1000
r = Rate of interest = 15%
n = Number of times interest is compounded per year
t = Time in years
So, A = 1000(1 + 15%/1)^1*2
A = 1000(1 + 0.15)^2
A = 1000(1.15)^2
A = 1000(1.3225)
A = $1322.5
Therefore, the amount he will have in 2 years is $1322.5
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Question 7(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 12 inches and height of 8 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 12 squared times 8
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 8 squared times 12
The answer is V equals 355 over 113 times 6 squared times 8.
What is the volume of the cylinder?
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder, and h is the height of the cylinder.
Alternatively, the volume of a cylinder can be found by multiplying the area of the base (πr²) by the height (h).
The correct method to calculate the number of cubic units of cake batter needed to fill the mold is:
[tex]V = \pi r^2h[/tex], where r is the radius and h is the height of the cylinder.
The diameter of the cake mold is 12 inches, so the radius is half of that, which is 6 inches.
Therefore, the volume of the cake batter needed is:
V = (355/113) x 6² x 8
V = (355/113) x 36 x 8
V = 904.96 cubic inches
So the answer is: V equals 355 over 113 times 6 squared times 8.
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Heather decides to make monthly payments into her savings account in the amount of $75 paying 3.6% compounded monthly for 5 years. Use FV=P((1+i)n−1i)
to determine the amount Heather will have in her savings account after the 5 year period.
Responses
$29,922
$4,922
$4,500
$492
Answer:
First Option, (A) $29,922.
Step-by-step explanation:
To calculate the future value of Heather's savings account after 5 years, we can use the formula for compound interest:
FV = P((1+i)^n - 1)/i
where:
FV = future value
P = principal (the initial amount Heather deposits)
i = interest rate per period (monthly in this case)
n = number of periods (months in this case)
P = $75 (the amount of Heather's monthly payments)
i = 3.6% / 12 = 0.003 (the monthly interest rate, calculated by dividing the annual interest rate by 12)
n = 5 x 12 = 60 (the total number of months in 5 years)
Substituting these values into the formula, we get:
FV = $75((1+0.003)^60 - 1)/0.003
FV = $75(1.21879)/0.003
FV = $29,922.02 (rounded to the nearest cent)
Therefore, Heather will have approximately $29,922.02 in her savings account after the 5 year period. The answer is option A: $29,922.
Add. (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) Simplify your answer as much as possible.
The simplification form of the expression "(z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12)" is = "1/(z+6)".
To add the two fractions, we need to have a common denominator. Since both fractions already have the same denominator of z^(2)+8z+12, we can simply add the numerators together and keep the same denominator.
So, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = (z+2)/(z^(2)+8z+12)
Now, we need to simplify the fraction as much as possible. We can do this by factoring the denominator and seeing if there are any common factors that can be canceled out.
The denominator can be factored as (z+6)(z+2).
So, (z+2)/(z^(2)+8z+12) = (z+2)/(z+6)(z+2)
Now, we can see that there is a common factor of (z+2) in both the numerator and denominator, so we can cancel them out.
So, the final simplified answer is 1/(z+6).
Therefore, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = 1/(z+6).
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jason correctly claims that the equation x2−6x+7=0
has two real solutions. If the discriminant of the equation is D
, which of the following statements about the value of D
supports Jason’s claim?
The discriminant is positive (D = 8), the equation x² - 6x + 7 = 0 has two distinct real solutions, which supports Jason's claim.
What does a quadratic equation's discriminant mean geometrically?The quadratic equation's roots are represented geometrically by the discriminant. The equation has two separate real roots if the discriminant is positive, and as a result, the graph of the quadratic function meets the x-axis twice. The quadratic function's graph crosses the x-axis precisely one time if the discriminant is zero, which indicates that the equation has one real root.
To find the discriminant of the given equation, we can substitute the values of a, b, and c into the formula:
D = (-6)² - 4(1)(7) = 36 - 28 = 8
Since the discriminant is positive (D = 8), the equation x² - 6x + 7 = 0 has two distinct real solutions, which supports Jason's claim.
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The complete question is:
Question content area top Part 1 Challenge A movie theater sends out a coupon for 20% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant. Question content area bottom Part 1 The equation is y enter your response here. (Use integers or decimals for any numbers in the expression).
Answer:
y = 0.8x
Step-by-step explanation:
y = x-0.2x
y=x(1-0.2)
y=x(0.8)
hence y = 0.8x
With these informations you can now do a graph !
Help! I need new dish soap. Which
one is the better price? Should I buy
the Method brand that is $5. 49 for 36
oz. Or the Seventh Generation brand
that is $3. 39 for 25 oz? Use math to solve
The soap from Seventh Generation brand cost less than Method brand.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
The Method brand that is $5. 49 for 36 oz
So, the unit rate of soap
= 5.49 / 36
= $ 0.1525
and, The Seventh Generation brand that is $3. 39 for 25 oz
So, the unit rate of soap
= 3.39/ 25
= $0.1356
So, the soap from Seventh Generation brand is cheaper.
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Adding rational expressions with denominators ax and bx : Basic Subtract. (3)/(4d)-(1)/(6d) Simplify. your answer as much as possible.
The basic subtraction of rational expression simplified is (7)/(12d).
To subtract these rational expressions, we need to find a common denominator. The least common denominator (LCD) of 4d and 6d is 12d. We can then rewrite the expressions with the LCD as the denominator:
(3)/(4d) = (3 * 3)/(4d * 3) = (9)/(12d)
(1)/(6d) = (1 * 2)/(6d * 2) = (2)/(12d)
Now we can subtract the numerators and keep the same denominator:
(9)/(12d) - (2)/(12d) = (9 - 2)/(12d) = (7)/(12d)
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 1:
(7)/(12d) = (7/1)/(12d/1) = (7)/(12d)
So the final answer is (7)/(12d).
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Detamine which pair of functions are not inverse
A.g(x)=2+9
h(x) =1/2x-9
B. g(x)=x-1
h(x)=x+1
C. g(x)=3x-6
h(x)=1/3x+2
D. g(x)=3x+4
h(x)=x-4/3
The pair of functions that are not inverses of each other is (A).
Which of the pair of functions are not inverseTo determine if two functions, g(x) and h(x), are inverses of each other, we need to check if the composition of the two functions, g(h(x)) and h(g(x)), both result in x.
A. g(x) = 2 + 9 = 11, h(x) = 1/2x - 9
g(h(x)) = g(1/2x - 9) = 2 + 9 = 11
h(g(x)) = h(11) = 1/2(11) - 9 = -3/2
Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.
B. g(x) = x - 1, h(x) = x + 1
g(h(x)) = g(x + 1) = (x + 1) - 1 = x
h(g(x)) = h(x - 1) = (x - 1) + 1 = x
Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.
C. g(x) = 3x - 6, h(x) = 1/3x + 2
g(h(x)) = g(1/3x + 2) = 3(1/3x + 2) - 6 = x
h(g(x)) = h(3x - 6) = 1/3(3x - 6) + 2 = x
Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.
D. g(x) = 3x + 4, h(x) = x - 4/3
g(h(x)) = g(x - 4/3) = 3(x - 4/3) + 4 = 3x - 4
h(g(x)) = h(3x + 4) = (3x + 4) - 4/3 = 3x + 8/3
Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.
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If \( \sin \alpha=12 / 13 \), and \( \cos \alpha=5 / 13 \), then \( \tan \alpha=? \) a) \( 5 / 12 \) b) \( 7 / 13 \) c) \( 12 / 5 \) d) \( 13 / 12 \)
The correct answer is c) \( 12 / 5 \).
We can use the relationship between the sine, cosine, and tangent of an angle to find the value of the tangent. The formula is:
\( \tan \alpha = \frac{\sin \alpha}{\cos \alpha} \)
Plugging in the given values for the sine and cosine of alpha, we get:
\( \tan \alpha = \frac{12 / 13}{5 / 13} \)
Simplifying the fraction, we get:
\( \tan \alpha = \frac{12}{5} \)
Therefore, the correct answer is c) \( 12 / 5 \).
In conclusion, if \( \sin \alpha=12 / 13 \), and \( \cos \alpha=5 / 13 \), then \( \tan \alpha=12 / 5 \).
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Assume that the sales of automobiles in Brandon follow a Poisson distribution with a mean of 3 per day.
a. What is the probability that none is sold on a particular day?
b. What is the probability that at least 2 automobiles are sold on a particular day?
c. What is probability that for five consecutive days at least one automobile is sold?
Therefore, the answers are:
a. 0.0498
b. 0.8008
c. 0.7745
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.
a. The probability that none is sold on a particular day can be calculated using the formula:
P(X = 0) = (e^-λ)(λ^0) / 0!
Where λ is the mean and e is the base of the natural logarithm.
Substituting the values, we get:
P(X = 0) = (e^-3)(3^0) / 0!
P(X = 0) = (0.0498)(1) / 1
P(X = 0) = 0.0498
b. The probability that at least 2 automobiles are sold on a particular day can be calculated using the formula:
P(X ≥ 2) = 1 - P(X < 2)
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))
P(X ≥ 2) = 1 - ((e^-3)(3^0) / 0! + (e^-3)(3^1) / 1!)
P(X ≥ 2) = 1 - (0.0498 + 0.1494)
P(X ≥ 2) = 1 - 0.1992
P(X ≥ 2) = 0.8008
c. The probability that for five consecutive days at least one automobile is sold can be calculated using the formula:
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - (e^-3)(3^0) / 0!
P(X ≥ 1) = 1 - 0.0498
P(X ≥ 1) = 0.9502
The probability that for five consecutive days at least one automobile is sold is:
P(X ≥ 1)^5 = 0.9502^5 = 0.7745
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10, 13, 17, 19, 22, 23, 29, 33, 34, 35, 35, 38, 53, 68.
FIND THE Z-SCORES FOR 17, 33, AND 53 FOR THE FIRST DATA SET.
The z-scores for 17, 33, and 53 are -0.82, 0.22, and 1.52, respectively.
To find the z-scores for 17, 33, and 53, we first need to calculate the mean and standard deviation of the data set.
Mean = (10 + 13 + 17 + 19 + 22 + 23 + 29 + 33 + 34 + 35 + 35 + 38 + 53 + 68)/14 = 29.57
Standard deviation = √[(10-29.57)² + (13-29.57)² + (17-29.57)² + (19-29.57)² + (22-29.57)² + (23-29.57)² + (29-29.57)² + (33-29.57)² + (34-29.57)² + (35-29.57)² + (35-29.57)² + (38-29.57)² + (53-29.57)² + (68-29.57)²]/13 = 15.37
Now we can calculate the z-scores using the formula:
z-score = (data point - mean)/standard deviation
Z-score for 17 = (17-29.57)/15.37 = -0.82
Z-score for 33 = (33-29.57)/15.37 = 0.22
Z-score for 53 = (53-29.57)/15.37 = 1.52
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From a pool of six juniors and twelve seniors, four co-captains will be chosen for the football team. How many different combinations are possible if two juniors and two seniors are chosen?
Please help and show work
1 and 3
Step-by-step explanation:
pick one from the junior side and 3 from seniors because the senior is more that the junoir
Answer:
990 different combinations
Step-by-step explanation:
There are 6 juniors and 12 seniors for a total of 16 students
Out of 6 juniors we have to pick 2 juniors
Out of 12 seniors we have to pick 2 seniors
The number of items r that we can pick from a larger set of n items is given by C(n, r) pronounced n choose r.. This is sometimes written as nCr
The formula forC(n, r) is
[tex]\boxed{C(n,r) = \dfrac{n!}{r! (n - r)! }}[/tex]
where n! = n factorial = n x (n-1) x (n-2) x .... x 3 x 2 x 1
We can choose 2 juniors out of 6 juniors in C(6, 2) ways
and
2 seniors out of 12 seniors in C(12, 2) ways
[tex]C(6, 2) = = \dfrac{6!}{ 2! (6 - 2)! }\\\\= \dfrac{6!}{2! \times 4! }\\\\= 15[/tex]
[tex]C(12, 2) = \dfrac{12!}{ 2! (12 - 2)! }\\\\ = \dfrac{12!}{2! \times 10! }\\\\= 66[/tex]
Therefore the total number of ways you can select 2 juniors and 2 seniors from a pool of 6 juniors and 12 juniors
= 15 x 66 = 990
Mr. Morris is a librarian at Eastside Library. In examining a random sample of the library's book collection, he found the following. 737 books had no damage, 67 books had minor damage, and 31 books had major damage. Based on this sample, how many of the 34,000 books in the collection should Mr. Morris expect to have minor damage or major damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Mr. Morris should expect around 3672 books in the collection to have minor or major damage.
What is proportion ?
Proportion is a relationship between two quantities that expresses the fraction of one quantity in terms of the other. In other words, a proportion is a statement that two ratios are equal.
To estimate the number of books in the collection that have minor or major damage, we first need to find the proportion of books in the sample that have such damage. We can then use this proportion to estimate the number of damaged books in the entire collection.
The total number of books in the sample is:
Total number of books = 737 + 67 + 31 = 835
The proportion of books in the sample that have minor or major damage is:
Proportion of damaged books = (67 + 31) / 835 = 0.108
To estimate the number of damaged books in the entire collection, we can multiply the proportion of damaged books by the total number of books in the collection:
Number of damaged books in collection = 0.108 x 34,000 = 3672
Rounding this answer to the nearest whole number, we get:
Therefore, Mr. Morris should expect around 3672 books in the collection to have minor or major damage.
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Find all possible rational zeros for the polynomial fu P(x)=21x^(3)-38x^(2)+44x-10
The possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.
The possible rational zeros of a polynomial function can be determined using the Rational Zero Theorem. This theorem states that if a polynomial function has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In the given polynomial function, P(x)=21x^(3)-38x^(2)+44x-10, the constant term is -10 and the leading coefficient is 21. The factors of -10 are ±1, ±2, ±5, ±10 and the factors of 21 are ±1, ±3, ±7, ±21.
Using the Rational Zero Theorem, the possible rational zeros are:
p/q = ±1/1, ±2/1, ±5/1, ±10/1, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21
Simplifying these fractions gives us the possible rational zeros:
±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21
Therefore, the possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.
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2. For each expression, use the zero product property to determine the values of x for which the expression would equal 0. Expression (x+7)(x-2) x-values (2x + 7)(x-6) (-3x+11)(4x + 18)
Using the zero product property
The values of x for which the expression (x+7)(x-2) equals 0 are x=-7 and x=2.The values of x for which the expression (2x+7)(x-6) equals 0 are x=-7/2 and x=6.The values of x for which the expression (-3x+11)(4x+18) equals 0 are x=11/3 and x=-9/2.Using the zero product property to determine the values of x for which the expressions are equal to zeroTo use the zero product property to determine the values of x for which the expression equals 0, we need to set each factor equal to 0 and solve for x.
(x+7)(x-2) = 0Setting each factor equal to 0 gives us:
x+7 = 0 or x-2 = 0
Solving each equation for x, we get:
x = -7 or x = 2
Hence, the values of x are x=-7 and x=2.
(2x+7)(x-6) = 0Setting each factor equal to 0 gives us:
2x+7 = 0 or x-6 = 0
Solving each equation for x, we get:
x = -7/2 or x = 6
Hence, the values of x are x=-7/2 and x=6.
(-3x+11)(4x+18) = 0Setting each factor equal to 0 gives us:
-3x+11 = 0 or 4x+18 = 0
Solving each equation for x, we get:
x = 11/3 or x = -9/2
Hence, the values of x are x=11/3 and x=-9/2.
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What is the area of the circle? Use pi = 22/7. A. 201 1/7 in2 B. 56 4/7 in2 C. 28 2/7 in2 D. 254 4/7 in2
The correct answer is B. 56 4/7 in². This is determined by multiplying 22/7 by the square of the radius, which is 4 in this case. The answer is equal to 56 4/7 in².
What is area of a circle?The area of a circle is calculated by the formula A=πr2, where r is the radius of the circle. Therefore, to determine the area of a circle, one must know the radius of the circle. Once the radius is known, the area of the circle can be determined by multiplying pi (π) by the radius squared (r2).
The area of a circle is equal to pi multiplied by the square of the radius of the circle. Pi is equal to 22/7, so the area of the circle can be calculated by multiplying 22/7 by the square of the radius. The correct answer is B. 56 4/7 in².
This can be calculated by multiplying 22/7 by the square of the radius, which is 4 in this case. 22/7 multiplied by 4 squared is equal to 56 4/7 in².
To summarize, the correct answer is B. 56 4/7 in2. This is determined by multiplying 22/7 by the square of the radius, which is 4 in this case. The answer is equal to 56 4/7 in².
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When does Percy start to realize the casino is a trap? Use text evidence to support your answer.
Answer:
He realizes the casino is a trap when he found out people from 1977 are in the casino. They wasted five days in the casino.