The probability that the mean is less than 1,998 milliliters is 0.11%
To solve this problem, it is important to understand the normal probability distribution and the central limit theorem
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean μ and standard deviation σ , the z-score of a measure X is given by:
Z = (X -μ) / σ
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p value, we get the probability that the value of the measure is greater than X.
Central Limit theorem
The Central Limit Theorem establishes that, for a random variable X, with mean and standard deviation σ, a large sample size can be approximated to a normal distribution with mean μ and standard deviation δ = σ /√n
In this problem, we have that:
μ = 2000, σ = 18
If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1998 milliliters
So n =100,
δ=18/√100 = 1.8
This probability is the p value of Z when X = 1998. So
Z = (X -μ) / σ
By the Central Limit Theorem
Z = (X -μ) /δ
Z = (1998 -2000) / 1.8
Z = -1.11 has a p-value of 0.0011
So, 0.11% probability that the mean is less than 1998 milliliters.
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Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let x represent the number
of slushies sold.
a. Write a linear function for cost.
C(x) =
Write a linear function for revenue.
R(x)=
c. Find C(50). Show your work.
• Write C(50) as an (x, y) coordinate point. ——-
• Write a sentence that explains the meaning of the point in the context of the problem.
D. Find R(50).
Represent R(50) as an (x, y) coordinate point. ———
Write a sentence that explains the meaning of the point in the context of the problem?
e. If the students sell 50 slushies, do they make a profit? Use mathematical work to help explain your answer. Complete the sentence below.
If the students sell 50 slushies, do they make——- a profit? Because——-
F. How many slushies do the students need to sell to break even? Use complete sentences to explain your problem solving strategy and your conclusion.
G. How many slushies do the students have to sell to make a profit of $1250? Use complete sentences to explain your problem solving strategy and your conclusion.
The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
What is a function?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable
solution:
The linear function:
C(x) = 1.25x + 500
For revenue function:
R(x) = 3.50x
R(50) = 3.50(50)
= $175
Using the C(x) and revenue function we can find the number of slushies and profit.
Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
Hence the linear and revenue functions are C(x) = 1.25x + 500 and R(x) = 3.50x
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X 2.3.PS-17
Question He
Peter says, "If you subtract 16 from my number and multiply the difference by -6, the result is -66." What is Peter's
number?
Peter's number is?
Peter's number is 27
Step-by-step explanation:
You would need to multiply -6 with 11 to get -66. 11+16=27 this 27-16=11 so 11×(-6)=-66.
Xavier downloaded 40 songs last week including 14 jazz songs . what percent of Xavier's downloads were jazz songs
Answer:
35%
Step-by-step explanation:
Xavier downloaded 40 songs last week,
14 of them were jazz songs.
Therefore, [tex]\frac{14}{40}[/tex] of Xavier's downloads were jazz songs.
In order to convert it into a percentage, we need to multiply 100 to the fraction.
We get [tex]\frac{1400}{40}[/tex], which is equal to 35%.
I would appreciate it if you mark my answer as brainliest.
What is the slope of a line perpendicular to the line whose equation is 6x+y=-5
Answer:
It would have a slope of a positive 6x
Step-by-step explanation:
Since the slope of the equation shown is -6x, we would just find the opposite which is -6x
Tommy earned $62.40 in interest after 4 years on a principal of $400. His simple interest rate is 3.9%. Jane
earned $66.60 in interest after 3 years on a principal of $600. Her simple interest rate is 3.7%. Which bank would you rather
use, Tommy's or Jane's? Explain your reasoning.
Answer:
I would rather use Jane's bank because she earned more interest in a shorter amount of time. Jane's bank has a higher simple interest rate of 3.7%, which means she earned more money in a shorter amount of time than Tommy did with his 3.9% rate.
if you mix 3 ounces of blue paint and 2 ounces of yellow paint and decided to make 20 ounces how much of the yellow paint will there be?
8 ounce of yellow color required.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
if you mix 3 ounces of blue paint and 2 ounces of yellow paint.
So, we have the composition ratio as 2:3
Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.
Thus, yellow = 2/5 x 20= 8 ounce
Blue= 3/5 x20 = 12 ounce
Hence, 8 ounce of yellow color required.
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suppose a student repeats a measurement two times and then calculates the standard deviation. because the standard deviation is small, the student reports that their experiment was extremely precise. is the student's conclusion appropriate?
The student's conclusion is not appropriate or no, because there were not enough measurements to use standard deviation.
Given:
suppose a student repeats a measurement two times and then calculates the standard deviation. because the standard deviation is small, the student reports that their experiment was extremely precise.
standard deviation:
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
To find standard deviation :
σ = x - μ / z
But here sample mean and proportion , z score not given so there are not enough measurements to use standard deviation.
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What is the correct factorization of the following quadratic expression: x² - 7x - 60
a. (x-12) (x + 5)
b. (x+12) (x - 5)
c. (x-10) (x+6)
d. (x+10) (x-6)
a study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86. 1. state the decision rule for 0.05 significance level: h0: rho ≤ 0; h1: rho > 0 (round your answer to 3 decimal places.) 2. compute the value of the test statistic. (round your answer to 2 decimal places.) 3. can we conclude that the correlation in the population is greater than zero? use the 0.05 significance level.
The decision rule is reject H(0) if t>1.714, test statistic t is 7.157 and Yes, we can conclude that the correlation in the population is greater than zero.
In the given question,
A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86.
n=20, r = 0.86
The decision rule for α=0.05 significance level:
H(0): P ≤ 0
H(1): P > 0
Degree of freedom(df) = n-2
Degree of freedom(df) = 20-2
Degree of freedom(df) = 18
This is the right tailed test using the t table.
Critical Value: [tex]t_{\alpha /2}[/tex], df = [tex]t_{\alpha /2}[/tex] = 1.714
(a) The decision rule is reject H(0) if t>1.714.
(b) Test statistic is t
t= r√(n−2)/√(1–r^2)
t= 0.86*√(20 -2)/√(1-(0.86)^2)
t= 0.86*√18/√(1-0.7396)
t= 0.86*4.243/√0.2604
t= 3.65/0.51
t= 7.157
Test statistic = 7.157
(c) We have to conclude that the correlation in the population is greater than zero.
Yes, we can conclude that the correlation in the population is greater than zero.
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Enter the numerator and denominator of a fraction in simplest form that is equivalent to 0. 941941.
Answer:
The answer is 941/1000.
Step-by-step explanation:
The simplified decimal is 0.941 and the 1 is in the thousandth place.
Hope this helped!
an information technology company claims that a certain model of laptops have mean battery capacity of 5 hours. a consumer report firm wants to show that the actual mean is smaller than the company claims. what should be the null and alternative hypotheses?
The null and alternative hypotheses are-
Null hypothesis H₀; μ ≤ 9Alternative hypothesis Hₐ: μ > 9Explain the formulation of Hypotheses?The null and alternate hypothesis must be formulated as two opposed and mutually excluding hypotheses for hypothesis testing.
This alternative hypothesis is a statement that contradicts the null and is the assertion that a sample research seeks to demonstrate. This null hypothesis can be accepted that represents the declaration of equality, the generally accepted presumption about the population.The intended relationship between the variables must be stated first. In order for researchers to determine whether such a hypothesis is true or untrue, it must also be able to be tested and falsified. Third, it must be consistent the with corpus of information already in existence. Last but not least, it should be said as briefly and simply as possible.A specific laptop model's battery has a typical life of more than 9 hours, according to the claim.
For this assertion, we form:
Null hypothesis H₀; μ ≤ 9
Alternative hypothesis Hₐ: μ > 9
The assertion is represented by the alternative hypothesis in this right-tailed test.
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What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14, ...
Answer:
0.36
0.26
0.16
0.06
the answers doesn't come in -
Which system of equations is equivalent to this system?5x=10=3(x+y) and x+7=3x+y
The system of equations is equivalent to this system is 2x = 3y - 10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given the equation as;
5x + 10 = 3(x+y)
x+7=3x+y
Solving the equation as;
5x + 10 = 3(x+y)
5x + 10 = 3x+ 3y
combine the like terms;
2x = 3y - 10
The system of equations is equivalent to this system is 2x = 3y - 10
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what is the rate of change for y=2x+100
Answer: rate of change = 2
Step-by-step explanation:
g assuming a linear relationship between x and y, the larger r-square value is, the larger the absolute value of the coefficient of correlation
In the domain of finance, an R-Squared value above 0.7 is typically seen as indicating a high level of correlation, whereas one below 0.4 indicates a low level of correlation.
What is correlation?A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.
The strength of the association is measured by the sample correlation coefficient, or r. The statistical significance of correlations is also examined.
For describing straightforward links between data, correlations are helpful. Consider a dataset of campgrounds in a park in the mountains as an illustration. You're interested in finding out if the height of the campsite—how high up the mountain it is—and the summer's typical high temperature are related.
Hence, In the domain of finance, an R-Squared value above 0.7 is typically seen as indicating a high level of correlation, whereas one below 0.4 indicates a low level of correlation.
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The odds in favor of Michael Jordan making a free throw were 21:4. Find the probability of Michael Jordan missing a free throw.
Give answer as a decimal rounded to the nearest hundredth.
The probability that he will miss is 25%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
The odds in favor of Michael Jordan making a free throw were 21:4.
Total number of throw is 21+4 = 25
The number of time he will miss is 4
So the probability that he will miss is 4/25 = 0.25
Hence, the probability that he will miss is 25%.
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A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are
C(x) = 75,000 + 60x and p(x) = 300 - x/30, 0 ≤ x ≤ 9000.
A) Find the maximum revenue.
B) Find the maximum profit, the productionlevel that will realize the maximum profit, and the price the company should charge for each television set.
C) If the government decides to tax the company $5 for each set it produces, how many sets should the company manufacture each month to maximize its profit What is the maximum profit What should the company charge for each set?
A) The maximum revenue is $__________ .
B) The maximum profit is $____________ when __________ sets are manufactured and sold for $________ each.
C) When each set is taxed ate $5 , the maximum profit is $________ when ______ sets are manufactured and sold for $__________ each.
A) The maximum revenue is 450000$
B) The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each
C) When each set is taxed at $55, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.
A)p(x)=300−(x/20),
revenue R(x)=p*x
revenue R(x)=300x -(x2/20)
for maximum revenue dR/dx =0 ,
=>300-(2x/20)=0
=>x/10=300
=>x=3000
maximum revenue = R(3000)=300*3000 -(30002/20)
maximum revenue = R(3000)=450000$
B) profit =revenue -cost
profit P(x)=300x -(x2/20)-72000-60x
profit P(x)=240x -(x2/20)-72000
for maximum cost dP/dx =0
240 -(2x/20)=0
x=240*10
x=2400
p(2400)=300−(2400/20)=180
profit P(2400)=240*2400 -(24002/20)-72000 =216000
The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each
c)
profit =revenue -cost -tax
profit P(x)=300x -(x2/20)-72000-60x-55x
profit P(x)=185x -(x2/20)-72000
for maximum cost dP/dx =0
185-(2x/20)=0
x=185*10
x=1850
p(1850)=300−(1850/20)=207.5
profit P(1850)=185*1850 -(18502/20)-72000
profit P(1850)=99125$
When each set is taxed at $55, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.
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calculate 1001 base two +1011 base two
question the range for a list of measurements equals the greatest measurement minus the least measurement. the two lists of measurements, x and y , combined consist of 30 measurements with a range of 25. what is the range for the measurements in list x ? (1) the range for the 12 measurements in list y is 20. (2) list x consists of 18 measurements.
The statements are insufficient to answer the question.
What is measurement?
Measurement is the quantification of an object's or event's attributes for comparison with other objects or events. Measurement, in other words, is the process of determining how large or small a physical quantity is in comparison to a basic reference quantity of the same kind.
So we are given 2 lists, x and y and we are given the
1. The total number of measurements is 30. x(n) + y(n) = 30.
2. Largest measurement - Smallest Measurement = 25
But we are not told the number of measurements in either x or y. We also don't know whether the largest of smallest measurement of the combined range belongs to x or y.
We need to find the largest measurement of x and the smallest measurement of x for our answer.
1)The range for the 12 measurements in list y is 20.
Okay so we know that y has 12 measurements, therefore x has 18. And we know the y(largest) - y(smallest) = 20 INSUFFICIENT
2) List x consists of 18 measurements.
We are told that x consists of 18 elements. We already figured this out in Statement 1 as well. It again does not tell us anything further. INSUFFICIENT DATA
Hence, the statements are insufficient to answer the question.
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A movie theater has a seating capacity of 159. The theater charges $5.00 for children, $7.00 for students,
and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was S
1140, How many children, students, and adults attended?
Answer:12
Step-by-step explanation:
Match each item with the correct unit price.
1. 78 cents each 20 for $1.56
2. 40 cents each 2 for one dollar
3. $1.05 each 5 at $3.90
4. 7.8 cents each $3.78 for 6
5. 63 cents each 1 for $1.58
1. 20 for $1.56 = A. 7.8 cents each
2. $3.78 for 6 =B. 63 cents each
3. For one dollar =C. 40 cents each
4. 5 at $3.90 = D. 78 cents each
5. for $1.58 = E. $1.05 each
1. 20 for $1.56
Since cost of 20 items = $1.56
So, cost of 1 item = 1.56/20
=$0.078
1 dollar = 100 cents
So, $0.078= 0.078 × 100
=7.8 cents.
2. $3.78 for 6
Since cost of 6 items = $3.78
So, cost of 1 item = 3.78/ 6
=$0.63
1 dollar = 100 cents
So, $0.63 = 0.63 × 100 =63 cents.
3. 2 1/2 for one dollar
Cost of 2 1/2 = 5/2 = $1
So, cost of 1 item = 1/5/2
= 2/5
1 dollar = 100 cents
So, $2/5 =2/5 × 100
=40 cents.
4. 5 at $3.90
Since cost of 5 items = $3.90
So, cost of 1 item = 3.90/5
=$0.78
1 dollar = 100 cents
So, $0.78 = 0.78 × 100
=78 cents.
5. 1 1/2 for $1.58
Cost of 1 1/2 = $1.58
So, cost of 1 item = 1.58/3/2
= 1.05
Thus,
1. 20 for $1.56 =A. 7.8 cents each
2. $3.78 for 6=B. 63 cents each
3. or one dollar =C. 40 cents each
4. 5 at $3.90 = D. 78 cents each
5. for $1.58 = E. $1.05 each
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A rectangle yas area 3 square feet and with 1/2 foot. what is the length of the rectangle
Answer:
6ft
Step-by-step explanation:
3 divided by 1/2 = 6
someone please help, thank you.
Step-by-step explanation:
it seems the questions 8., 9. and 10. demonstrate exactly what is the asked via variables in 11., 12. and 13.
you only need to apply the principles of equal angles of crossing lines again.
11.
to be parallel
50 + (x + 30) = 180
x + 80 = 180
x = 100.
12.
135 = 2y + 15
120 = 2y
y = 60
13.
70 = 4x - 10
4x = 80
x = 20
14.
yes, because
142 + 38 = 180°
15.
yes, because
112 + 68 = 180°
16.
no, because
146 + 44 = 190° <> 180°
17.
to be parallel, angle 1 = angle 2
88 = 2x
x = 44
18.
to be parallel, angle 1 = angle 3
88 = 2x + 10
2x = 78
x = 39
You and a friend start running from the same location. Your distance d (in miles) after t minutes is d(t) = ⅕t. Your friend starts running 10 minutes after you. Your friend's distance f is given by the function f(t) = d(t - 10). Describe the transformation from the graph of d to the graph of f.
Answer: 23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
Regan is making a square garden in her back yard with an area of 25ft² What factors could be the length and width of her garden
The required length and width of the square garden is 5ft.
Given that,
Regan is making a square garden in her backyard with an area of 25ft² length and width of the garden is to be determined.
The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
here,
According to the question, l = w
Area of the garden = 25
l × w = 25
l × l = 25
l = 5
Thus, the required length and width of the square garden is 5ft.
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what is the common ratio for this geometric sequence? 3,12,48,192
Answer: r=4
Step-by-step explanation:
12/3 = 4
48/3 = 4
192/48 = 4
Factorize a²+ b²-c²-d² - 2ab-2cd
Answer:
(a-b+c+d)(a-b-c-d) answer of the following questoin
On a print-out of these slope fields, sketch for each three solution curves to the differential equations that generated them. Then complete the following statements: For the slope field in figure 1. a solution passing through the point (0.-1) has slope. For the slope field in figure 1. a solution passing through the point (-2.2) has slope. For the slope field in figure 2. a solution passing through the point (1.-3) has slope For the slope field in figure 2. a solution passing through the point (0.4) has a slope.
Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.
What is slope field?A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.
Here,
For figure 1 slope field=
[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}[/tex]
For figure 2 slope field=
[tex]\frac{dy}{dx} = xy-3\\[/tex]
For figure 1 a solution passing through the point (0,-1)
therefore,
slope=
[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2[/tex]
so slope comes out to be negative
For figure 1 a solution passing through the point (-2,2)
[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30[/tex]
so slope comes out to be negative
For the slope field in figure 2. a solution passing through the point (1.-3)
[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6[/tex]
so slope comes out to be negative
[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3[/tex]
so slope comes out to be negative.
Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.
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identify the most appropriate test to use for the following situation: a national computer retailer believes that the average sales are greater for salespersons with a college degree. a random sample of 14 salespersons with a degree had an average weekly sale of $3542 last year, while 17 salespersons without a college degree averaged $3301 in weekly sales. the standard deviations were $468 and $642 respectively. is there evidence to support the retailer's belief?
99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
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two cars leave towns kilometers apart at the same time and travel toward each other. one car's rate is kilometers per hour less than the other's. if they meet in hours, what is the rate of the slower car?
The rate of the slower car is 152 km/hr.
Given:
two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours.
Let x be the rate of slower car.
We have two cars heading towards each other. They start 340 km apart and meet up 2 hours later. This means that they are traveling:
340 / 2 = 170 km/hr towards each other.
If the two cars were traveling the same speed, they'd both be going:
170 / 2 = 85 km/hr
We know that one car is traveling 18 km/hr faster than the other car. One way we can account for this is to ± 9 km/hr to the average speed:
85 ± 9 = 94 , 76 km/hr
rate of slower car x = 84 - 9 * 2
x = 76 * 2 km/hr
= 152 km/hr
Therefore The rate of the slower car is 152 km/hr.
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Full question:
two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours, what is the rate of the slower car?