Using ratio and proportions, Jacob has mixture with stronger basil taste
Ratios and ProportionRatio can be defined as a comparison between two or more numbers that shows their sizes in relation to each other. A ratio often compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Proportion can be defined as equality of two ratios. Two equivalent ratios are always in proportion. Proportion is an equation or statement that shows that the two ratios or fractions are equivalent.
In this case, we can compare the ratio and determine which will have a stronger basil taste.
Lupita mixed 2 tsp of basil for 3tsp of oregano
The ratio of basil to oregano = 2/3 = 0.67
Jacob mixed 4 tsp of basil for 5 tsp of oregano
The ratio of basil to oregano = 4/5 = 0.8
Comparing the ratios, Jacob ratio is higher compared to Lupita and makes Jacob have the strong basil taste.
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16. john buys a cake at a bakery and a hammer at a hardware store. if there are five hardware stores and three bakeries, in how many different combinations of stores can he purchase the cake and the hammer?
15 different combinations can be used by John to buy the cake and the hammer.
Given,
John buys a cake at a bakery and a hammer at a hardware store
Number of hardware shops = 5
Number of bakeries = 3
We have to find the combinations of stores he can purchase;
Here,
5 hardware shops; H₁, H₂, H₃, H₄, H₅
3 bakeries; B₁, B₂, B₃
Now,
The combinations be like;
B₁ ; (H₁, H₂, H₃, H₄, H₅)
B₂ ; (H₁, H₂, H₃, H₄, H₅)
B₃ ; (H₁, H₂, H₃, H₄, H₅)
That is,
3 bakeries and 5 hardware shops
= 3 x 5
= 15
Therefore,
John can buy the cake and hammer in 15 different combinations.
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in how many ways can we seat 6 people at a round table if john and sam insist on sitting next to each other? (two seatings are equivalent if one is a rotation of the other.)
If John and Sam insist on sitting next to each other , then 6 people can sit at a round table in 48 ways .
In the question ,
it is given that ,
John and Sam insist to sit together ,
we have to find the number of ways , we can sit 6 people at a round table
the number of people = 6 people
there is no head of the table ,
So, first person is just a place marker so there are really only 5 people whose positions matter.
But since John and Sam are tied together, they are the equivalent of one person.
that means there are only 4 people.
= 4! × 2 ways ...because it could be (John , Sam) or (Sam, John) ,
= 48 ways .
Therefore , 6 people can sit in 48 ways .
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ASAP!!!
Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
5 units
12 units
16 units
25 units
The perimeter of the triangle ABC is 12 units. Hence, option (B) is correct.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given right angle triangle,
The vertices are A(-3, 2), B(-3, -1) and C(1, -1)
The distance between AB = 3,
And the distance between BC = 4
To find the distance of AC, use Pythagoreans theorem,
AC² = AB² + BC²
= 3² + 4²
= 9 + 16
AC² = 25
AC = 5
The perimeter of triangle ABC = AB + BC + AC
= 3 + 4 + 5
= 12
The perimeter of the triangle ABC is 12 unit.
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what is the commission
The commission amount is $60 with the rate at 8% of earned sales amount $750.
What is the percentage?
Percentage means one part of every cent or hundred. And it is represented by symbol '%'.
Given that sales = $750 ,
and the commission rate is 8% .
Now to find the commission , we find 8% of $790
= 750 x 8 / 100
= 6000 / 100
= $60
Therefore, the commission amount is $60 with the rate at 8% of earned sales amount $750.
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consider the initial value problem take the laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. denote the laplace transform of by . do not move any terms from one side of the equation to the other (until you get to part (b) below). help (formulas) solve your equation for . take the inverse laplace transform of both sides of the previous equation to solve for .]
Initial value that take the LaPlace transform of both sides of the given differential equation to create the corresponding algebraic equation is [tex]y(t) = 3t + sin4t + 3cos4t[/tex]
What is The Laplace transform?In terms of its usefulness in resolving physical issues, the Laplace transform is an important transform that is probably second only to the Fourier transform. The Laplace transform is especially helpful in solving linear ordinary differential equations, such as those that arise in the analysis of electronic circuits.
The initial value-
[tex]y" + 16y = 48t\\y(0)=3,y'(0)=7\\L( f^{n}(t) ) = s^{n}L(f(t)) - s^{n - 1}(f(0)) - s^{n - 2}(f(0)).........................................f^{n - 1} (0)\\[/tex]
By the formula,
[tex]s^{2}Y(s) - sy(0) - y'(0) + 16Y(s) = 48L(t)\\L(t^{n}) = \frac{n!}{s^{n+1} } \\\\On substitutinf the values,\\Y(s)(s^{2} + 16) - 3s - 7 = \frac{48}{s^{2} }\\Y(s)(s^{2} + 16) = \frac{48}{s^{2} } +3s + 7\\Y(s) = \frac{48 + s^{3} -7s^{2} }{s^{2}((s^{2} + 16) }\\Y(s) = \frac{3}{s^{2} } + \frac{4}{(s^{2} + 16} + \frac{3s}{(s^{2} + 16}[/tex]
On taking LaPlae inverse both side,
[tex]Y(t) = L( \frac{3}{s^{2} } ) + L( \frac{4}{(s^{2} + 16)} ) + L( \frac{3s}{(s^{2} + 16)} )\\Y(t) = 3t + sin4t + 3cos4t\\[/tex]
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A triangle has one 42° angle and two 69° angles. Is this triangle scalene?
Step-by-step explanation:
It is not a scalene triangle
because the third angle is 69⁰
Explanation: 180-(69+42)
180-111
69
question content area top part 1 one of the ancient stone pyramids in egypt has a square base that measures 148 m on each side. the height is 126 m. what is the volume of the pyramid?
The ancient stone pyramids in Egypt, which have a square base with a width of 148 meters and a height of 126 meters, have a volume of 9394 square metres.
What is volume?Mathematics uses cubic units to quantify volume, including cubic meters, cubic centimeters, cubic millimeters, etc. Typically, liters and gallons are used to calculate liquid volume. The loudness of a sound is measured by its volume. A container's capacity, or how much it can hold, would be determined by its volume. Cubic units established by the International System of Units are frequently used to express volume. Learn how to easily measure volume.
Here,
Side of the pyramid=148 m
Height of pyramid=126 m
Volume,
=1/2*b*h
=1/2*148*126
=9394 m²
The volume of the ancient stone pyramids in Egypt that has a square base of side 148 m and height 126m is 9394 m².
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Patty has a photograph that is 5 inches wide and 6 inches long. She enlarged each side by the same amount. By how much was the photograph enlarged if the new area is 182 square inches? PLEASE HURRY
I'LL GIVE BRAINLIEST! PLS HELP!!!!
Todd and his friends are painting 5 equal sections of a wall. The wall is 10 feet tall, but its length is unknown. Each section will be a different color, so they need to know the area of each section.
1. Write an expression for the total area of the wall. Explain how you came up with your expression.
2. To find the area of each section, what do you need to do to the total area?
3. Write an expression for the area of each section of the wall.
1. Write an expression for the total area of the wall: 10x
2. The area of each section: 2x ft²
3. The area of each section of the wall: 2x ft²
What is area?A flat (2-D) surface's or an object's shape's overall area is known as its area. On a sheet of paper, draw a square using a pencil. It's a two-dimensional figure. The term "Area" refers to the area that a form occupies on paper.
We use cm² or m² as our units for measuring area. Area is computed by multiplying a shape's length by its breadth.
Given that,
Todd and his friends are painting 5 equal sections of a wall.
The wall is 10 feet.
1. Total area of the wall this is rectangular size wall which length is 'x' (unknown) and width/height is 10 feet.
So, area = length × height
area = 10x
2. To find the area of each section, there are 5 section (each are equal) so area of each section = total area / 5
= 10x /5
= 2x ft²
we divided total area by 5.
3. Now area of each section
= 10x/5
= 2x ft²
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a tortoise and hare are competing in a 1000 meter race. the function f and g are such that f ( t ) represents the tortoise's distance from the finish line (in meters) t seconds after the start of the race and g ( t ) represents the hare's distance from the finish line (in meters) t seconds after the start of the race. if we want to compute the number of seconds needed for the hare to finish the race, which of the following procedures should be used?
o Solve g(t) = 0 for the value of t o Solve f(t) = g(t) for the value of t o Evaluate (1000) o Solve g(1) = 1000 for the value of t o Evaluate (0)
To determine the number of seconds that the hare would finish the race, we solve g(t) = 0, to calculate the value of t.
Linear equation
Linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope of the equation (rate of change) and b is the y intercept (initial value of b).
Given that g (t) represents the hare's distance from the finish line (in meters) t seconds after the start of the race.
Hence the answer is, To determine the number of seconds that the hare would finish the race, we solve g(t) = 0, to calculate the value of t.
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Because sample statistic is a numerical descriptive measure of a sample, every time that we randomly select observations, the sample statistics may be a different value. True False
True, the sample statistics may have a different value for each observation that is randomly chosen since they are a numerical explanatory measure of a sample.
Using sample data, a statistic is a quantitative descriptive measure. A parameter is a quantitative way to describe a population. Since whole populations (N) aren't always possible, we must rely on samples (n) as well as the statistics that can be calculated from them.
The mean, median, & mode, which are utilized at practically all math and statistics levels, are the most well-known forms of descriptive statistics. By summing together all the data set's figures & then dividing the total number of figures, the mean or average can be derived.
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endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. what is the probability that an endure all battery selected at random will last more than 550 hours? a) 0.8944 b) 0.1151 c) 0.8849 d) 0.1056 e) 0.1587 f) none of the above.
The probability that an Endure All battery selected at random will last more than 610 hours is 0.1056.
What is meant by the term normal distribution?A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred . Eventsare approximately normal happen more often than information that are far the mean.
The normal distribution appears as a "bell curve" on a graph.
A probability bell curve is more properly described as the normal distribution.
In a normal distribution, the mean is 0 and the standard deviation is 1. The kurtosis is 3, and there is no skew.All normal distributions are symmetrical.
Natural occurrences frequently resemble the usual distribution.
However, in finance, most price distributions are not fully normal.
How to solve?
Given that μ = 500, σ = 40, for x > 550
z = 550-500/40
z = 1.25
From the normal distribution table, P(z > 1.25) = 1 - P(z < 1.25) = 1 - 0.8944 = 0.1056
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Kennedy has $0.81 worth of pennies and nickels. She has 9 more nickels than pennies. Write a system of equations that could be used to determine the number of pennies and the number of nickels that Kennedy has. Define the variables that you use to write the system of equations.
Answer:
Step-by-step explanation:
kwik trip
Answer:
Let x be the number of pennies, and y be the number of nickels.
1 penny = 0.01 dollar
1 nickel = 0.05 dollar.
The equations that will describe the given problem will be,
0.01 x + 0.05 y = 0.81
y = x + 9
Plugging the second equation into the first gives us,
0.01 x + 0.05(x+ 9) = 0.81
0.06 x + 0.45 = 0.81
0.06 x = 0.36
y = 15
So, Kennedy has 6 pennies, and 15 nickels.
Step-by-step explanation:
Ms. Lopez had some drinking glasses. The ratio of the number of blue glasses to the number of white glasses was 5 : 6. Her children broke 8 blue glasses and the ratio became 13 : 18. How many white glasses did she have?
Answer:
12
Step-by-step explanation:
(5x-8)/6x
the temperature of a duck breast is checked during cooking. according to the operation's policy, the duck breast must be cooked for 16 minutes to allow the internal temperature to reach 165 degrees f. what haccp principle is addressed by cooking the duck breast to 165 degrees f?
The HAACP principle addressed by cooking the duck breast to 165 degrees F is a 'critical limit'.
What is the critical limit?
A critical limit is a value to which a biological, chemical or physical factor must be controlled to prevent food safety hazards. These are the conditions under which potential hazards can be controlled, reduced, or eliminated. They are monitored by observation or measurement, such as measuring the temperature of food storage to avoid spoilage.
Critical limits are based on factors such as:
Temperature, Humidity, Moisture level, pH, Water activity (Aw), Time, Salt concentration, and Preservatives.
Production processes that fail to stay within the bounds of the critical limits must be stopped or the products must be discarded.
Hence the answer is critical limit.
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mr banda is buying chocolate bars and hot chips for his students who scored meets and masters on the semester exam. chocolate bars cost $1.1 you each and hot chips 0.40 each Mr banda spent $87 on buying 130 chocolate bars and hot chips. how many chocolate bars did Mr banda buy?
The number of chocolate bars which Mr Banda bought is equal to 50 chocolate bars.
How to determine the number of chocolate bars?In order to determine the number of chocolate bars and the number of hot chips that Carter bought, we would have to write a system of linear equation and assign variables to the number of chocolate bars and number of candies respectively, and then translate the word problem into algebraic equation as follows:
Let the x indicate the number of chocolate bars.Let the y indicate the number of hot chips.Since chocolate bars cost $1.1 each and hot chips 0.40 each and Mr Banda spent $87 on buying 130 chocolate bars and hot chips, we would have the following system of linear equation:
1.1x + 0.40y = 87 ......equation 1
x + y = 130 ......equation 2
From equation 2, we have:
y = 130 - x ......equation 3
Substituting equation 3 into equation 1, we have:
1.1x + 0.40(130 - x) = 87
1.1x + 52 - 0.4x = 87
0.7x + 52 = 87
0.7x = 87 - 52
0.7x = 35
x = 35/0.7
x = 50 chocolate bars.
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use the same regression results where you already found r square and other results for this regression. what is the standard error for the estimated slope of the regression line? answer to four decimal places.
A regression model can only predict values that are lower or higher than the actual value. As a result, the only way to determine the model's accuracy is through residuals.
What is regression ?
Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the relationship between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).
The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).
Based on a line of best fit, linear regression determines the linear relationship between two variables.
The slope of a straight line used to represent linear regression thus indicates how changing one variable affects changing another..
In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept. Regression without linearity.
Hence, A regression model can only predict values that are lower or higher than the actual value.
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a family decides to have children until it has three chil-dren of the same gender. assuming p(b)5p(g)5.5, what is the pmf of x5the number of children in the family?
The pmf of X = the number of children in the family is
1/4 + 3/8 + 3/8 =1
It is given that,
a family decides to have children until it has three children of the same gender i.e. BBB or GGG.
X can take the values {3,4,5}
and we know that
P(X = 3) + P(X = 4) + P(X = 5) = 1
We will find each term one by one,
P(X = 3) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*2
= [tex]\frac{1}{8}[/tex] * 2
P(X = 3) = [tex]\frac{1}{4}[/tex]
P(X = 4) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*6
= ([tex]\frac{1}{16}[/tex]) * 6
P(X =4) = [tex]\frac{3}{8}[/tex]
P(X = 5) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*12
= ([tex]\frac{1}{32}[/tex])* 12
P(X = 5) = [tex]\frac{3}{8}[/tex]
Therefore the pmf equation implies,
[tex]\frac{1}{4} + \frac{3}{8} + \frac{3}{8}[/tex] = [tex]\frac{32}{32}[/tex] = 1.
The probability mass function (pmf) is also called a probbility function or frequency which characterizes the distribution of a discrete random variable. It is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.
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I need help its hard pls
A stock loses 2.9 points on Monday but gains 6.4 points on Tuesday. What is the stock's overall change in points over the two days?
Answer:
3.5 Points
Step-by-step explanation:
Change means how many more points did you gain. 6.4 - 2.9= 3.5
The stocks overall change in points over the two days is 3.5 points.
the scores on a standardized test are normally distributed with a mean of 100 and standard deviation of 20. what test score is 1.5 standard deviations below the mean?
The 1.5 standard deviations below the mean implies that the Z-score value will be equal to -1.5.
The test score 70 is 1.5 standard deviations below the mean .
We have given that,
The Score standardized test are Normally distributed,
Mean ,μ = 100
Standard deviations, s.d = 20
we have to calculate test score is 1.5 standard deviations below mean.
so, Z- score = -1.5
This is the z-score formula or z-score equation.
Z = (x − μ )/σ
Where, Z--> z-score
x---> the value in question
μ--> mean of the distribution
σ --> standard deviation of the distribution
plugging all known the value in formula
-1.5 = (x- 100)/20
=> -1.5 × 20 = x - 100
=> x = -30 + 100 = 70
So, 70 is the test score that is 1.5 standard deviations from the mean.
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A census was conducted at a school. All of the students were asked how
many cars their family owns. The results are below.
Number of Cars 0 1 2 3
Probability 0.005 0.120 0.125 0.500 0.250
For the questions below enter the value only. Round to the nearest hundredth, if necessary.
1. What is the expected number of cars?
2. What is the standard deviation?
1. The expected number of cars is given as follows: 2.87.
2. The standard deviation of the number of cars is given as follows: 0.94.
How to obtain the expected value and the standard deviation of a discrete distribution?The discrete distribution is given from the table in this problem, as follows:
P(X = 0) = 0.005.P(X = 1) = 0.12.P(X = 2) = 0.125.P(X = 3) = 0.5.P(X = 4) = 0.25.The expected value is given by the sum of each outcome multiplied by it's probability, as follows:
E(X) = 0 x 0.005 + 1 x 0.12 + 2 x 0.125 + 3 x 0.5 + 4 x 0.25 = 2.87.
The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, as follows:
S(X) = sqrt((0-2.87)² x 0.005 + (1-2.87)² x 0.12 + (2-2.87)² x 0.125 + (3-2.87)² x 0.5 + (4-2.87)² x 0.25) = 0.94.
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Perimeter of sector is 4 times of its radius what is the radian measurre?
The radian measures of the central angle of the sector is 2
Given,
In the question:
Perimeter of sector is 4 times of its radius .
To find the radian measures of the central angle of the sector is?
Now, According to the question:
We know:
The perimeter of the circumference is = 2[tex]\pi[/tex]r
If the perimeter of a sector is 4 times its radius.
then, the arc measure of the sector is (4r-2r) → 2r
So, if 2×[tex]\pi[/tex] radians (full circle) has a length → 2[tex]\pi[/tex]r
X radians → 2× r (the sector)
X=2× r ×(2×[tex]\pi[/tex])/(2[tex]\pi[/tex]r)
X = 2
Hence, The radian measures of the central angle of the sector is 2.
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Solve six times three-sixths equals blank.
Leave your answer as an improper fraction.
thirty-six thirds
eighteen-sixths
eighteen-sixteenths
25 Points
The total cost to rent and drive a car for one day is listed below for two car rental agencies.
Blue Car Rental charges $27.60 to rent a car plus $0.18 per mile driven.
Red Car Rental charges $40.40 to rent a car plus $0.14 per mile driven.
• Write a variable expression that shows the total cost to rent and drive a car for one day at Blue Car Rental. Write a variable expression that shows the total cost to rent and drive a car for one day at Red Car Rental. Define the variable.
• Calculate the total cost at each agency to rent a car for one day and drive it 280 miles. Show all your work.
• Write and solve an inequality that shows how many miles must be driven before the total daily cost at Red Car Rental is less than the total daily cost at Blue Car Rental. Show all your work.
• If Mr. Kao rents a car for one day and drives it 400 miles, which company has a lower total cost?
The variable expression are
y = $0.18x + $27.60 - Blue Car Rentaly = $0.14x + $40.40 - Red Car Rentalcost at each agency to rent a car for 280 miles
y = $78.00 - Blue Car Rentaly = $79.60 - Red Car RentalThe company that has a lower cost for 400 miles
Red Car RentalHow to write the expressionThe required expression is a linear function
A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
Definition of variable to suit the problem
y = output variable (total cost/)
m = slope (cost per mile driven)
x = input variable (number of miles)
c = y intercept (Car Rental charges)
The equation as described in the problem is represented using linear function as as follows
y = $0.18x + $27.60 - Blue Car Rental
y = $0.14x + $40.40 - Red Car Rental
the total cost at each agency to rent a car for one day and drive it 280 miles
y = $0.18x + $27.60 - Blue Car Rental
y = 0.18 * 280 + 27.60
y = $78
y = $0.14x + $40.40 - Red Car Rental
y = 0.14 * 280 + 40.40
y = $79.60
Write and solve an inequality
$0.18x + $27.60 < $0.14x + $40.40
0.18x + 27.60 < 0.14x + 40.40
0.18x - 0.14x < 40.40 - 27.60
0.04x < 12.80
x < 320 miles
Mr. Kao rents a car for one day
y = $0.18x + $27.60 - Blue Car Rental
y = 0.18 * 400 + 27.60
y = $99.60
y = $0.14x + $40.40 - Red Car Rental
y = 0.14 * 400 + 40.40
y = $96.40
comparing the both shows that Red Car Rental has a lower cost
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Zion has scores of 92, 97, 94, and 86 on three math tests. What must his grade be on his next text so he can average test grade is a 91?
The average score is 97
What is average ?
In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or to a value that lies halfway between two extremes.
Let the grade he got on final test be x
The average of all four grades is 91.
So, we have
(92+89+86+x)/4 = 91
⇒x=364−267
= 97
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with the new dough, there were 16 complaints out of 340 pizzas. let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. based on a 95% confidence for the difference of the proportions, what can be concluded?
The correct answer is:
Reject null hypothesis H0, we cannot conclude the proportion of customer complaints is more for the old dough.
As given in the question,
Let us consider proportion of customer complaints with old dough is p₁
And proportion of complaints with new dough is p₂
Difference in proportion of complaints in old and new dough
= p₁ - p₂
Null hypothesis : H0 : p1 ≥ p2
p₁ - p₂ ≥ 0
Alternative hypothesis : Ha : p1 < p2
p1 - p2 < 0
Let 'x' represents the number of complaints
Sample size = n
Sample proportion = x/n
Old dough:
Number of complains with old dough 'x₁' = 6
Number of pizzas with old dough 'n₁' = 385
p₁ = 6/385
= 0.01558
= 0.016
New dough:
Number of complains with new dough 'x₂' = 16
Number of pizzas with new dough 'n₂' = 340
p₂ = 16/340
= 0.04705
= 0.047
Pooled proportion test:
[tex]\bar{p}[/tex] = (x₁+ x₂)/(n₁ + n₂)
= (6 + 16)/(385 + 340)
= 0.0303
= 0.03
1 - [tex]\bar{p}[/tex] = 1 - 0.03
= 0.97
z = (p₁ - p₂)/√[tex]\bar{p}[/tex](1 - [tex]\bar{p}[/tex])(1/n₁ + 1/n₂)
= (0.016 - 0.047)/√(0.03)(0.97)(1/385 + 1/340)
= (-0.031)/ √(0.03)(0.97)(0.0026 + 0.0029)
= - 0.031/√0.00016005
= -0.031 / .01265
= -2.45
It is left tailed test.
p value for the area to the left of the z score using normal distribution table:
p value = 0.007143
Significant level 'α' for 95% confidence level:
= 1 - 0.95
= 0.05
Since 0.05 > 0.0.007143
Reject null hypothesis.
Therefore, reject H0, we cannot conclude the proportion of customer complaints is more for the old dough.
The complete question is :
Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. Based on a 95% confidence for the difference of the proportions, what can be concluded?
Multiple Choice
A. Reject H0, we can conclude the proportion of customer complaints is more for the old dough
B. Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough
C. Do not reject H0, we can conclude the proportion of customer complaints is more for the old dough
D. Reject H0, we cannot conclude the proportion of customer complaints is more for the old dough
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Please help ASAP 100 points and the brainiest
Match the number and nature of the solutions to each equation.
1.2x2 – 6x – 8 a.one rational
2.3x2 – 5x – 3 b.two complex
3.x2 – 14x + 49 c.two irrationals
d.two rationals
Select the equation that most accurately depicts the word problem. The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches.
68 = 9L + 2
68 = L/2 + 2(9)
68 = 2/L + 2/9
68 = 9(L + 2)
68 = 2L + 2(9)
68 = 2(L - 9)
Answer:
68 = 2L + 2(9)
Step-by-step explanation:
Just write down exactly what it says!
The perimeter of a rectangle is 68 inches
68
The perimeter equals twice the length of L inches
68 = (2 × L)
Plus twice the width of 9 inches.
68 = (2 × L) + (2 × 9)
Now just clean up the equation.
68 = 2L + (2 × 9)
68 = 2L + 2(9)
The answer is 68 = 2L + 2(9).
Company f sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable x represent the number of defects on a fat quarter created by company f. The following table shows the probability distribution of x.
By using the concept of expectation, it can be calculated that
a) Probability distribution of Y
P(Y = 0) = 0.63
P(Y = 1) = 0.25
P(Y = 2) = 0.12
b) Mean of Y = 0.49
Standard deviation of Y = 0.6999
c) Mean of selling price = $4.4
Standard deviation of selling price = $0.99
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Suppose x is a random variable with the probability function f(x). suppose
[tex]x_1, x_2, ...., x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1, p_2,...., p_n[/tex] be the corrosponding probabilities.
Expectation is given by the formula
[tex]E(x) = p_1x_1 + p_2x_2 + ... + p_nx_n[/tex]
a)If a fat quarter has more than 2 defects, it cannot be sold and is discarded.
The table for the probability distribution of X is given
P(X [tex]\leq[/tex] 2) = 0.58 + 0.23 + 0.11 = 0.92
For probability distribution of Y
P(Y = 0) = P(X= 0 | X [tex]\leq[/tex] 2) = [tex]\frac{0.58}{0.92}[/tex] = 0.63
P(Y = 1) = P(X= 1 | X [tex]\leq[/tex] 2) = [tex]\frac{0.23}{0.92}[/tex] = 0.25
P(Y = 2) = P(X= 2 | X [tex]\leq[/tex] 2) = [tex]\frac{0.11}{0.92}[/tex] = 0.12
Mean of Y = 0 [tex]\times[/tex] 0.63 + 1 [tex]\times[/tex] 0,25 + 2 [tex]\times[/tex] 0.12 = 0.49
E([tex]Y^2[/tex]) = 0 [tex]\times[/tex] 0.63 + 1 [tex]\times[/tex] 0.25 + 4 [tex]\times[/tex] 0.12 = 0.73
Variance = [tex]0.73 - 0.49^2[/tex] = 0.4899
Standard deviation = [tex]\sqrt{0.4899} = 0.6999[/tex]
b) Here, E(G) = 0.40, V(G) = [tex]0.66^2[/tex]
The fat quarters sell for $5.00 each but are discounted by $1.50 for each defect found.
Selling price = 5 -1.5G
Mean of selling price = 5 - 1.5[tex]\times[/tex] 0.4 = 5 - 0.6 = $4.4
Variance of selling price = [tex]5 - 1.5^2 \times 0.66^2\\[/tex] = $0.9801
Standard deviation of selling price = [tex]\sqrt{0.9801}[/tex] = $0.99
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Complete Question
Company f sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable x represent the number of defects on a fat quarter created by company f. The following table shows the probability distribution of x.
x 0 1 2 3 4 or more
probability 0.58 0.23 0.11 0.05 0.03
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F.
(a) Construct the probability distribution of the random variable Y.
(b) Determine the mean and standard deviation of Y. Show your work.
Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0.40 and 0.66, respectively. The fat quarters sell for $5.00 each but are discounted by $1.50 for each defect found.
(c) What are the mean and standard deviation of the selling price for the fat quarters sold by Company