**HELP**
Intersecting Line Plots
⭐️VIEW PHOTO⭐️
A line plot for the data is shown in the image attached below.
What is a line plot?In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 3.5 or 3 1/2 because it has the highest frequency of 5.
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Your lawnmower requires 1/3 gallon of gas to cut grass for one hour. you know it will take you 3/4 of an hour to mow the empty lot. You have 5/6 gallon of gas in a gas can in the garage. How long can you cut the grass with this amount of gas?
Therefore, the lawnmower can cut grass for 2.5 hours on 5/6 of a gallon of fuel in the gas can
To find out how long the lawnmower can cut grass with 5/6 of a gallon of gas, we first need to figure out how many gallons of gas the lawnmower will use per hour:
1 hour of grass cutting = 1/3 gallon of gas
1 gallon of gas = 3 hours of grass cutting
So the lawnmower uses 1/3 gallon of gas per hour, which means that 1 gallon of gas will last for 3 hours of grass cutting.
Now we can use this conversion factor to figure out how long 5/6 of a gallon of gas will last:
5/6 gallon of gas * 3 hours of grass cutting per 1 gallon of gas = 15/18 hours of grass cutting
Simplifying this fraction by dividing the numerator and denominator by 3:
15/18=3/6
So 5/6 of a gallon of gas will last for 5/6 of 3 hours, which is equal to 2.5 hours of grass cutting.
As a result, 5/6 of a gallon of gas will last for 5/6 of 3 hours, or 2.5 hours of mowing the lawn.
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Rewrite -3 to the -3 power without exponents
Thus, the statement -3 to the -3 power written without using exponents is -1/27.
Explain about the exponents:A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.
The exponent rules must be understood while performing mathematical calculations or when simplifying complex equations. There are numerous rules, including the multiplication rule, the rule of negative exponents, and the rule of fractional exponents.Given that-
-3 to the -3 power
This can written as:
= (-3)⁻³
Now using the property of exponents,taking reciprocal of the number will remove the negative number.
= (1 /-3)³
= (1)³ / (-3)³
= 1/(-27)
= - 1/ 27
Thus, the statement -3 to the -3 power written without using exponents is -1/27.
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Help please geometry
The area of the shaded region = 30.903 in²
From the attached figure we can observe that the radius of the circle R is r = 6 in.
Using the forula for the area of circle, the area of circle R would be,
A₁ = πr²
A₁ = π × 6²
A₁ = 36π
A₁ = 113.097 in²
So, the diameter would be d = 6 × 2 = 12 in.
The circle R is inscribed in a square.
So, the side length of square is equal to the diameter of the circle.
This means the side length 'a' os square = 12 in.
Using the formula of the area of square,
A₂ = side²
A₂ = a²
A₂ = 12²
A₂ = 144 in²
so, the area of the shaded region would be,
A = A₂ - A₁
A = 144 -113.097
A = 30.903 in²
This is the required area.
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a system of equations is shown. y=3x+2 y=x-2 , Graph the system of equations to show its solution
To graph the two lines, we can plot two points on each line and connect them with a straight line. For y = 3x + 2, we can choose x = 0 and x = 1 to get the points (0, 2) and (1, 5), respectively. For y = x - 2, we can choose x = 0 and x = 1 to get the points (0, -2) and (1, -1), respectively.
In the graph: The red line represents y=3x+2 and the blue line represents y=x-2
Explain the term straight line
A straight line is a geometric figure that extends infinitely in both directions and has no curvature or bends. It is the shortest distance between two points and can be described using various mathematical equations, such as y = mx + b, where m is the slope and b is the y-intercept. Straight lines are used in various fields, including geometry, physics, and engineering, to represent and analyze the relationships between objects or points.
According to the given information
To graph the system of equations y = 3x + 2 and y = x - 2, we can plot the two lines on the same coordinate plane and find the point where they intersect.
First, we can find the point of intersection by setting the two equations equal to each other:
3x + 2 = x - 2
Simplifying, we get:
2x = -4
x = -2
Substituting this value of x back into one of the equations, we get:
y = (-2) - 2 = -4
So the solution to the system of equations is the point (-2, -4).
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create a system of equations that has a solution of (5,-3)
The system of equations that has a solution of (5,-3) is y + 3 = m (x-5).
or
We have the points (5, -3).
Now, The point-slope form of a linear equation is:
(y - y₁) = m (x - x₁)
(y - (-3)) = m (x- 5)
y + 3 = m (x-5)
Now, let the slope m = -2 then
y + 3 = -2(x-5)
y + 3 = -2x + 10
y + 2x + 3 -10 = 0
y + 2x - 7 = 0
Or we can also form the equation as
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Find the area of the composite figure(will mark brainliest)
The area of the composite figure is equal to 278 square inches
How to calculate for the area of the figureThe composite figure can be observed to be made up of two triangles, a rectangle and a parallelogram, so we shall calculate for the area and sum the results to get the total area of the composite figure as follows:
area of top triangle = 1/2 × 8 in × 11 in = 44 in²
area of the side triangle = 1/2 × 9 in × 4 in = 36 in²
area of the rectangle = 11 in × 9 in = 99 in²
area of the parallelogram = 11 in × 9 in = 99 in²
total area of the composite figure = 44 in² + 36 in² + 99 in² + 99 in²
total area of the composite figure = 278 in²
Therefore, the area of the composite figure is equal to 278 square inches
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There are 6 men and 8 women in a book club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.
A) In how many different ways can the committee be selected if exactly one of Mr Lan and Mrs Lan must be on the committee?
B) If a committee is selected at random, find the probability that there are more women than men on the committee, given that Mrs Lan was selected
A)By applying permutation and combination we can select committee in 1782 ways.
B) The probability cannot be determined with the given information, as the calculated probability is greater than 1, which is not possible.
What is permutation and combinationPermutation and combination are two concepts in mathematics that deal with counting the number of possible outcomes or arrangements in a given situation. Permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without regard to the order in which they are chosen.
What is probability?Probability is a measure of the likelihood or chance that an event will occur. It is a number between 0 and 1.
According to the given information:
A) To find the number of ways to select a committee of 5 members, where exactly one of Mr Lan and Mrs Lan must be on the committee, we can use the principle of inclusion-exclusion i.e. Permutation and combination:
First, we find the total number of ways to select a committee of 5 members from 14 members (6 men and 8 women), which is given by:
C(14,5) = 2002
Next, we find the number of ways to select a committee of 5 members that includes both Mr Lan and Mrs Lan, which is given by:
C(12,3) = 220
Note that we choose 3 members from the remaining 12 members after Mr and Mrs Lan have been chosen.
Finally, we subtract the number of committees that include both Mr Lan and Mrs Lan from the total number of committees, since we only want committees that include exactly one of them:
2002 - 220 = 1782
Therefore, there are 1782 different ways to select a committee of 5 members where exactly one of Mr Lan and Mrs Lan must be on the committee.
B) To find the probability that there are more women than men on the committee, given that Mrs Lan was selected, we need to consider the number of committees that satisfy this condition and divide by the total number of committees that include Mrs Lan.
If Mrs Lan is selected, there are two cases to consider:
Case 1: The committee has more women than men.
In this case, we need to select 4 members from the 8 women and 1 member from the 5 men, which can be done in C(8,4) x C(5,1) = 560 ways.
Case 2: The committee has an equal number or more men than women.
In this case, we need to select 3 members from the 8 women and 2 members from the 5 men, which can be done in C(8,3) x C(5,2) = 560 ways.
Therefore, the total number of committees that include Mrs Lan and have more women than men or an equal number of women and men is 560 + 560 = 1120.
The total number of committees that include Mrs Lan is C(13,4) = 715, since we choose 4 members from the remaining 13 members after Mrs Lan has been chosen.
Therefore, the probability of selecting a committee with more women than men or an equal number of women and men, given that Mrs Lan was selected, is:
1120/715 = 1.5664
Note that this probability is greater than 1, which is not possible. Therefore, there is an error in the calculation, and the correct probability cannot be determined with the given information.
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solve this pleasee!!
Thus, the area of the given trapezium is found toe be 37.8 sq. cm.
Explain about the trapezium:A trapezium is a quadrilateral in two dimensions with one pair of parallel sides. The non-parallel sides of a trapezium are referred to as the trapezium's "legs," while the parallel sides are referred to as its "bases." The length of the legs or the measuring of their angles are used to categorise trapeziums.
Given data:
Height PA = 8 cmSide AR = 6.3 cmAs CA = AR; PQ = 6.3 / 2 = 3.15area of trapezium = 1/2(sum of parallel side) * height
area of trapezium = 1/2(PQ + CR)*PA
area of trapezium = 1/2*(3.15 + 6.3)*8
area of trapezium = 1/2*(9.45)*8
area of trapezium = 37.8 sq. cm
Thus, the area of the given trapezium is found toe be 37.8 sq. cm.
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A chemist prepares a sample of hydrogen bromide and finds that it occupies 296 mL at 68°C and 475 Torr. What volume would it occupy at 0°C at the same pressure?
Answer in units of mL.
Here, we want to get the final volume
From the general gas equation, we have it that:
[tex]\dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}[/tex]
From the question, we have it that:
P1 is the initial pressure which is 475 torr
V1 is the initial volume which is 296 mL
T1 is the initial temperature which we have to convert to absolute value by adding 273.15 K ([tex]68 + 273.15 = 341.15 \ \text{K}[/tex])
P2 is the final pressure that is the same as the initial which is 475 torr
V2 is the final volume that we want to calculate
T2 is the final temperature which is 273.15 K (0 degrees Celsius is 273.15 K)
Substituting the values, we have:
[tex]\dfrac{475\times296}{341.15}=\dfrac{475\times V_2}{273.15}[/tex]
[tex]V_2=\cfrac{475\times296\times273.15}{341.15\times475} =\boxed{\bold{237 \ mL}}[/tex]
We could have solved this by using Charles' law that relates temperature to volume (volume is directly proportional to temperature)
y varies directly as a square root of (x-3) y= 16 x=1 find y when x =10
Answer:160
formula:y=kx
16=(16)(10)
=160
Step-by-step explanation:
A resort sells an all-included package for a week-long stay at $2000 per person. It costs $1600 for the resort to operate, so the profit is $400 per package. They sell 300 packages every month. The resort wants to increase the price and they estimate that the number of packages sold will decrease by 5 every time they increase the price by $100. What price will maximize the monthly profit? Find the maximal profit, the number of packages, and their price to get that profit.
The resort should sell a number of 255 packages at a price of $2400 per person to maximize their monthly profit and the maximal profit is $613,400.
What do you mean by maximal profit?Maximal profit refers to the highest level of profit that a business or organization can achieve given certain constraints such as cost, demand, or pricing. It is the point at which a company or business generates the most revenue after accounting for all expenses associated with production and distribution of goods or services. To determine the maximal profit, a business will need to find the optimal balance between costs and revenue, while also taking into account factors such as competition and market demand. This involves analyzing a variety of financial metrics such as revenue, cost of goods sold, gross profit margin, and net profit margin, among others.
Let's begin by defining some variables:
P = price of the package
Q = number of packages sold
R = revenue
C = cost
Profit = revenue - cost
Based on the information given, we can create the following equations:
R = P * Q
C = 1600 + 2000 * Q
Profit = R - C = P * Q - (1600 + 2000 * Q)
We want to find the price that will maximize the monthly profit. To do this, we need to find an expression for profit in terms of P only. We can use the equation for C to substitute Q in the expression for profit:
C = 1600 + 2000 * Q
Q = (C - 1600) / 2000
Profit = P * Q - (1600 + 2000 * Q)
Profit =
Profit = P * ((C - 1600) / 2000) - C + 1600
Now we can find the derivative of profit with respect to P:
dProfit/dP = (C - 1600) / 2000
To find the value of P that maximizes profit, we need to set the derivative equal to 0:
dProfit/dP = 0
(C - 1600) / 2000 = 0
C = 1600
This means that profit is maximized when revenue equals cost, which makes sense. Substituting C = 1600 into the expression for profit, we get:
Profit = P * ((1600 + 2000 * Q - 1600) / 2000) - 1600
Profit = P * Q - 1600
Now we need to find the corresponding values of P and Q. We know that for every increase of $100 in price, there will be a decrease of 5 in the number of packages sold. This means that:
Q = 300 - (P - 2000) / 100 * 5
Substituting this into the expression for profit, we get:
Profit = P * (300 - (P - 2000) / 100 * 5) - 1600
To find the maximum profit, we can take the derivative of this expression with respect to P and set it equal to 0:
dProfit/dP = 300 - (P - 2000) / 20 = 0
P = 2400
This means that the price that will maximize the monthly profit is $2400 per person. To find the corresponding number of packages sold, we can substitute this into the equation for Q:
Q = 300 - (2400 - 2000) / 100 * 5 = 255
Therefore, the resort should sell 255 packages at $2400 per person to maximize their monthly profit. To find the maximal profit, we can substitute these values into the expression for profit:
Profit = 2400 * 255 - 1600 = $613,400.
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Vanessa invests $20,000 in an account at 9.1% interest compounded continuously. Find the total value of the investment after 19 years.
Answer:
Step-by-step explanation:
17.5
Find the surface area of the figure (on photo)
Answer:
208
Step-by-step explanation:
4*4(2)+11*4(2)+11*4(2)=208
Find the small squares.
4^2+4^2=32
4*11*4=176
176+32=208
Simplify (4x3y − 2xy2 + 3xy) + (2x3y − 5xy2 − 3xy).
6x3y − 7xy2
6x3y + 3xy2
6x3y − 7xy2 − xy
6x3y − 7xy2 + 2xy
The expression simplified can be written as:
6x³y -7xy²
The correct option is the first one.
How to simplify the expression?Here we have the following expression:
(4x³y - 2xy² + 3xy) + (2x³y - 5xy² - 3xy)
To simplify it, we need to group the like terms (this is terms with the same variables and correspondent exponents).
Then we can rewrite the expression as:
(4 + 2)x³y + (-2 - 5)xy² + (3 - 3)xy
6x³y -7xy²
That is the expression simplified.
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Answer:
A:6x3y − 7xy2
Step-by-step explanation:
i took the test and got it right
. Keisha's employer deducts 0.2 times
her wages in payroll taxes. How much is
deducted when Keisha earns $132?
You have to find what 0.2 of 132 is
132 x 0.2 = 26.40
The answer [tex]\boxed{\bold{\$26.40}}[/tex]
The buidling is 360 feet tall. On a scale drawing. 2 inch =20 feet. What is the height of the building in the scale drawing?
Which best describes the figure
The best description of the figure would be that it is a C. a square.
How to find the figure type ?To find out the type of figure that we have, it would be best to find the lengths of the sides of the figure. We should find AB, BC, CD, and AD.
We can use the distance formula which is:
D=√ ( x 2 - x1 ) ² + ( y2 - y1) ²
Using this formula, we find that AB, BC, CD, and AD are all a distance of 6 units. This therefore means that this figure is a square because all the sides are equal.
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Full question is:
Which best describes the figure that is represented by the following coordinates?
A(-3, 4), B(3, 4), C(3,-2) and D(-3,-2)
a rectangle
a trapezoid
a square
HELP!!!! 50 POINTS!!!!
Answer:sorryy if this is late but its 2
Step-by-step explanation:
Let m, n, and p be real numbers.
Name the property of equality that the statement illustrates.
m(n-p) = mn - mp
The property of equality that the statement m(n-p) = mn - mp illustrates is (d) the distributive property
Naming the property of equality that the statement illustrates.Given that
m(n-p) = mn - mp
The above property is the distributive property
The distributive property states that
a(b - c) = ab - ac
This case
a = m
b = n
p = c
Substitute the known values in the above equation, so, we have the following representation
m(n-p) = mn - mp
Hence, the property of equality that the statement illustrates is the distributive property
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How many different words consisting of four different letters a,b,c,d,e,p that do not start with the letter p and do not end with the letter b and include the letters c,e
Westville has a land area of 84.4 square miles. In 2015 the population density was 22.5 people per square miles. In 2016, the population was 2,000 people, By how many people did the population of Westville increase between 2015 and 2016?
The population of Westville increased by approximately 99.95 people from 2015 to 2016.
To find the increase in population from 2015 to 2016 in Westville, we need to use the formula:
Increase in population = (Population density in 2016 - Population density in 2015) x Land area
First, we need to find the population density in 2016. To do that, we can divide the population of 2,000 people by the land area of 84.4 square miles:
Population density in 2016 = 2,000/84.4 ≈ 23.69 people per square mile
Next, we can plug in the values into the formula:
Increase in population = (23.69 - 22.5) x 84.4 ≈ 99.95 people
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Felipe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Felipe trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?
Plan A lasts for 2/7 hours or approximately 17.14 minutes, and Plan B lasts for 9/7 hours or approximately 1 hour and 17.14 minutes.
What is an equation example?In algebra, the definition of an equation in its simplest form is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x 5 = 14 is an equation where 3x 5 and 14 are two expressions separated by an equal sign.
Let's say plan A takes x hours and plan B takes y hours.
Based on the given data, we can create two equations:
Monday: 6x + 5y = 7
Tuesday: 2x + 3y = 3
We can solve this system of equations by elimination or substitution.
Eliminating, we can multiply the second equation by two and subtract it from the first equation:
(6x + 5 y) - 2 (2x + 3y) = 7 - 2 (3)
Simplifying this, we get:
2x - y = 1
Using substitution, we can solve an equation in one variable and replace it with another equation:
From the first equation we can solve for x:
6x + 5y = 7
6x = 7-5 years
x = (7-5 years) / 6
Substituting this into the second equation, we get:
2 ((7-5 years) / 6) + 3 y = 3
Simplifying this, we get:
7 y = 9
y = 9/7
Now that we know y, we can substitute it back into both equations to solve for x:
6 x + 5 (9/7) = 7
Simplifying this, we get:
x = 2/7
Therefore, Plan A takes 2/7 hours, or approximately 17.14 minutes, and Plan B takes 9/7 hours, or approximately 1 hour and 17.14 minutes.
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A business owner wants to have the front window of his store painted and is considering two artists for the job. Pete has quoted a flat rate of $60 for the job. Reba's quote is $19 per hour, plus $41 to cover the cost of materials. Depending on how long it takes Reba to paint the window, these two could end up charging the same amount. How long would Reba have to take? How much would it cost?
If the job takes Reba ___hours, the cost would be ___$ with either artist.
HELPPP
If the job takes Reba 1 hours, the cost would be $ 19 with either artist
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let's assume the number of hours that Reba takes to paint the window is h. Then, the total cost of the job with Reba would be:
Total cost with Reba = $19 ( h ) + $41
The total cost with Pete is already given as a flat rate of $60.
We want to find the number of hours that Reba would have to take to charge the same amount as Pete, so we can set the two expressions for the total cost equal to each other and solve for "h":
$ 19 ( h ) + $ 41 = $ 60
Subtracting $41 from both sides, we get:
$ 19 ( h ) = $ 19
Dividing both sides by $ 19, we get:
h = 1
So Reba would have to take 1 hour to charge the same amount as Pete.
To calculate the cost of the job with either artist if it takes Reba 1 hour, we can substitute h=1 into the expression for the total cost with Reba:
Total cost with Reba = $ 19 ( 1 ) + $ 41 = $ 60
Hence , this is the same as the flat rate quoted by Pete, so the cost of the job would be $60 with either artist if it takes Reba 1 hour
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1. A cart moving at 20 m/s is brought to a stop by the force plotted in the force-time graph shown here. Find the impulse and the approximate mass of the cart. Show all your work.
The required value of impulse is 88 N-s and the mass of the cart is 8.8 kg.
How to find the impulse?Newton's Second Law relates an object's acceleration as a function of both the object's mass and the applied net force on the object.
Given data:
The speed of cart is, v = 10 m/s.
We are given the Force-time graph for which the area of the force-time graph will provide the value of impulse. So from the graph, the maximum force is,
F = 22 N
And time interval is,
t = 4.5 s - 0.5 s
t = 4 s
So, the impulse is,
I = Area of graph
I = F × t
I = 22 × 4
I = 88 N-s
Now the standard expression for the impulse as per the impulse-momentum theorem is,
I = ΔP (Change in momentum)
I = m ×( v - u )
Here, u is the final velocity, and since the cart stops finally, then u = 0 m/s. And m is the mass of the cart.
Solving as,
88 = m ×( v - u )
88 = m ×( 10 - 0 )
m = 8.8 kg
Thus, we can conclude that the required value of impulse is 88 N-s and the mass of car is of 8.8 kg.
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A ball is hit from the ground. When the ball has traveled a horizontal distance of d d meters, its height, h , h , in meters, can be modeled by the function h ( d ) = − 1 125 d 2 + d . h ( d ) = − 1 125 d 2 + d . What is the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground? Enter your answer in the space provided.
Answer:
Step-by-step explanation:
when h=0
0=-1125d²+d
1125d²-d=0
d(1125d-1)=0
d=0
or 1125d-1=0
d=1/1125 meters
Binomial Random Variable where n = 10 and probability of success on one trial is 15%. Show formula used. a. Find the probability of exactly 4 successes. b. Find the probability of at most 1 success c. Find the probability of at least 1 success d. Find the probability of more than 1 success e. Find the probability of less than 1 success.
Considering the binomial random variable, the probabilities are:
a. 0.1611
b. 0.8915
c. 0.7588
d. 0.1085
e. 0.0576
How to find the probabilitiesThe binomial distribution formula is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where:
P(X = k) is the probability of getting k successes
n is the number of trials
p is the probability of success on one trial
(n choose k) is the binomial coefficient, which is equal to n! / (k! * (n - k)!)
k is the number of successes we want to find the probability for
Using this formula, we can find the probabilities for the given scenarios:
a. P(X = 4) = (10 choose 4) * 0.15^4 * (1 - 0.15)^(10 - 4) = 0.1611
b. P(X <= 1)
= P(X = 0) + P(X = 1)
= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1)
= 0.8915
c. P(X >= 1)
= 1 - P(X = 0)
= 1 - (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)
= 0.7588
d. P(X > 1)
= 1 - P(X <= 1)
= 1 - (P(X = 0) + P(X = 1))
= 1 - ((10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1))
= 0.1085
e. P(X < 1)
= P(X = 0)
= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)
= 0.0576
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Assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 70 beats per minute and 78 beats per minute
Answer:
We can use the Central Limit Theorem to solve this problem since we are dealing with a sample size greater than 30. The distribution of sample means will be approximately normal with a mean of 74 beats per minute and a standard deviation of 12.5 / sqrt(4) = 6.25 beats per minute.
To find the probability that the mean pulse rate of 4 adult females is between 70 and 78 beats per minute, we need to calculate the z-scores for both values and then use a z-table or calculator to find the area under the normal curve between those two z-scores.
The z-score for 70 beats per minute is:
z = (70 - 74) / 6.25 = -0.64
The z-score for 78 beats per minute is:
z = (78 - 74) / 6.25 = 0.64
Using a standard normal distribution table or calculator, the area between these two z-scores is approximately 0.4115.
Therefore, the probability that 4 adult females have pulse rates with a mean between 70 and 78 beats per minute is approximately 0.4115 or 41.15%.
Find the GCF (Greatest common factor) for the following polynomial equation 24x ^ 9 + 21x ^ 6 = 0
The general common factor (GCF) of the polynomial equation [tex]24x^9 + 21x^6 = 0[/tex] is 3x6, which, after factoring, is the common factor of the coefficients and the terms enclosed in brackets.
We must factor out the common terms from both the coefficients and the exponents in order to determine the GCF (Greatest Common Factor) for the polynomial equation 24x9 + 21x6 = 0.
The first step is to determine the coefficients' common factor, which is 3. The equation can be changed to read:
3(8x^9 + 7x^6) = 0
We now need to determine which term the parenthesized terms have in common the most. Since x is raised to a power in both terms, we may factor out x^6 to obtain:
3x^6(8x^3 + 7) = 0
The greatest common factor of the polynomial equation 24x^9 + 21x^6 = 0 is 3x^6.
We can verify this by dividing both terms in the equation by 3x^6. Doing so gives us:
(8x^3 + 7) = 0
This equation has no common factors, and we cannot factor it further. Thus, the GCF of the original polynomial equation 24x^9 + 21x^6 = 0 is 3x^6
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Dorothy Wagner is currently selling 40 "I ♥ Calculus" T-shirts per day, but sales are dropping at a rate of 4 per day. She is currently charging $7 per T-shirt, but to compensate for dwindling sales, she is increasing the unit price by $1 per day. How fast, and in what direction, is her daily revenue currently changing?
The rate at which her daily revenue is currently changing and the direction of the change is; Her revenue is currently increasing at $12 per day
What is the rate of change of a function?The rate of change of a function is the rate at which the output of the function changes per unit change in the input of the function.
Let x represent the number of days, therefore;
The number of T-shirts Dorothy sells, y = 40 - 4·x
The price at which she sells the T-shirts = 7 + x
Therefore, Dorothy's daily revenue, R(x) = (40 - 4·x) × (7 + x) = 12·x - 4·x² + 280
The rate of change of her daily revenue can be obtained from the derivative of the revenue function as follows;
The rate at which her daily revenue is therefore;
R'(x) = d(R(x))/dx = 12 - 8·x
The rate at which her revenue is changing currently can be obtained from the rate function by plugging in x = 0, as follows;
R'(0) = 12 - 8×0 = 12
Her revenue is changing at a rate of $+12 per day.
The positive value of the rate, 12, indicates that her revenue is increasing at $12 per day
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