Answers
Given:
In ΔABC, ∠C = 90°, ∠A = 50° and AB = 3 unit.
To find the value of BC.
Formula:
By Trigonometric Ratio we get,
[tex]sin \ \theta=\frac{opposite}{Hypotenuse}[/tex]
Now,
With respect to θ = 50°, AB is the hypotenuse and AB is the opposite side.
So,
[tex]sin \ 50^{\circ}=\frac{BC}{AB}[/tex]
[tex]sin \ 50^{\circ}=\frac{BC}{3}[/tex]
[tex]BC = 3 \times sin 50^{\circ}[/tex]
[tex]BC = 2.298 = 2.3[/tex] (approx)
Hence,
The value of BC is 2.3 units.
Related Questions
A certain drug is used to treat asthma. In a clinical trial of the drug, 23 of 277 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 10% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below.
a. What is test statistic?
b. What is p-value?
c. What is the null hypothesis, and what can we conclude about it?
d. Decide whether to reject the null hypothesis?
e. What is the final conclusion?
Answers
Answer:
a) The test statistic is z=-0.94
b) The p-value is 0.1736
c) The null hypothesis is [tex]H_0:p=0.10[/tex], we can conclude that, if the result is not significant at 0.01 level, we fail to reject the null hypothesis
d) We fail to reject the null hypothesis at 0.01 significance level.
e) We do not have sufficient evidence to reject the claim that, less than 10% of the treated subjects experienced headaches.
Step-by-step explanation:
The test statistic is defined by:
[tex]Z=\frac{\hat p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]
It was given that, 23 of 277 treated in the clinical trial of the drug subjects experienced headaches.
This means that:
[tex]\hat p=\frac{23}{277}\approx 0.083[/tex] and n=277
The claim is that, less than 10% of treated subjects experienced headaches. This means:
[tex]p_0=\frac{10}{100}=0.1[/tex]
We substitute the values into the formula to obtain:
[tex]Z=\frac{0.083-0.1}{\sqrt{\frac{0.1(1-0.1)}{277} } }[/tex]
The test statistics becomes:
[tex]Z=-0.94[/tex]
b) From the normal distribution table, the p-value corresponds to Z=-0.94 .
Since this is a left-tailed test, the p-value corresponds to area under the normal curve that is to the left of z=-0.94
P(Z<-0.94)=0.173609.
c) Since the claim is that, less than 10% of treated subjects experienced headaches, the null hypothesis is
[tex]H_0:p=0.10[/tex]
The alternate hypothesis will be:
[tex]H_1:p\:<\:0.10[/tex]
This implies that, the result is not significant at 0.01 alpha level.
d) We need to compare the p-value to the significance level. If the significance level is greater than the null hypothesis, we reject the null hypothesis.
Since 0.01<0.1736, we fail to reject the null hypothesis.
d) Conclusion: There is no enough evidence to reject the claim that, less than 10% of treated subjects experienced headaches.
Answer:
(a)Test statistic[tex]z_{score}=-0.94[/tex]
(b) p-value=0.1736
(c)Null hypothesis,
[tex]H_0:p=0.10[/tex]
(d)[tex]\alpha>p[/tex], we reject the null hypothesis.
(e)We have experimental values to reject the claim.
Step-by-step explanation:
Given information;
n=277
Significance level [tex]\alpha[/tex]=0.01
By normal distribution,
[tex]z_{score}=\frac{\widehat{p}-p_0}{\frac{\sqrt {p_0(1-p_0)}}{n}}[/tex]
[tex]\widehat{p}=\frac{23}{277}=0.83[/tex]
[tex]p_0=10[/tex]%=0.1
On substitution,
[tex]z_{score}=\frac{{0.83}-0.1}{\frac{\sqrt {0.1(1-0.1)}}{277}}[/tex]
Test static,
[tex]z_{score}=-0.94[/tex]
b)From the table normal distribution,
for,[tex]z_{score}=-0.94,[/tex]
[tex]P(z<-0.94)=0.173609[/tex]
(c)Null hypothesis,
[tex]H_0:p=0.10[/tex]
Alternate hypothesis,
[tex]H_1:p<0.10[/tex]
It implies result is not significant at
[tex]\alpha=0.01[/tex]
(d) On compare value if
[tex]\alpha>p[/tex], we reject the null hypothesis.
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There are 184 plants to put into pots each pot can hold 8 plants how many pots are needed
Answers
Answer:
think 23 pot
Step-by-step explanation:
Answer:
Step-by-step explanation:
23
Is this expression true or false? 5 ÷ 1/9 = 45
Answers
Answer:
False
Step-by-step explanation:
Common sense
Find the volume of the figure.
2.25 m
4
m
2.5 m
no
Answers
Given:
Given that the figure is a triangular prism.
The length of the prism is 4 m.
The base of the triangle is 2.5 m.
The height of the triangle is 2.25 m.
We need to determine the volume of the triangular prism.
Volume of the triangular prism:
The volume of the triangular prism can be determined using the formula,
[tex]V=\frac{1}{2}bhl[/tex]
where b is the base of the triangle,
h is the height of the triangle and
l is the length of the prism.
Substituting b = 2.5, h = 2.25 and l = 4 in the above formula, we get;
[tex]V=\frac{1}{2}(2.5)(2.25)(4)[/tex]
[tex]V=\frac{1}{2}(22.5)[/tex]
[tex]V=11.25 \ m^3[/tex]
Thus, the volume of the triangular prism is 11.25 m³
80% of 25 is equal to what
Answers
Answer:
20
Step-by-step explanation:
Of means multiply and is means equals
80% * 25 = ?
Change to decimal form
.80 *25 =
20
f(-4) in the function f(x) = -2x - 3?
Answers
Answer:
5
Step-by-step explanation:
f(-4) f(x)=-2x-3
f(-4)=-2(-4)-3
f(-4)=8-3
f(-4)=5
Answer:
5
Step-by-step explanation:
you imput -4 for x then you proceed as normal solving the equation
-2(-4) - 3 since two negatives when multiplied make a positive
8 - 3
5
A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor and brings a profit of $2.50. The football uses 3 ounces of foam and 30 minutes of labor and brings a profit of $2. The manufacturer has available 43.5 pounds of foam and 110 labor-hours a week. Use the simplex method to determine the optimal production schedule so as to maximize profits. Show that the geometric method gives the same solution.
Answers
To determine the optimal production schedule to maximize profits, we need to create a linear programming model using the simplex method.
Explanation:To determine the optimal production schedule to maximize profits, we need to create a linear programming model using the simplex method. Let's define our decision variables as follows:
x = number of large basketballs to producey = number of footballs to produceOur objective is to maximize the profit, so our objective function can be written as:
Z = 2.5x + 2y
We have the following constraints:
4x + 3y ≤ 43.5 (foam constraint)20x + 30y ≤ 110 (labor constraint)x, y ≥ 0 (non-negativity constraint)To solve this linear programming problem with the simplex method, we will use a software or calculator that supports linear programming.
14. You are a manager at Dunkin Donuts. Last Friday, your store sold 350 chocolate munchkins, 220 glazed munchkins,
125 powdered munchkins, and 75 jelly munchkins. This week, you are in charge of deciding how much of each
munchkin to make. You are instructed that in all, you need to make 6000 munchkins for the week.
dL
Answers
Answer:
Step-by-step explanation:
The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education.
Savings = β0+∂0 Edu + β1Inc+u
The variable ‘Edu’ takes a value of 1 if the person is educated and the variable ‘Inc’ measures the income of the individual.
Refer to the above model. If ∂0 > 0, _____.
a.
individual with lower income have higher savings
b.
individuals with lower income have higher savings
c.
educated people have higher savings than those who are not educated
d.
uneducated people have higher savings than those who are educated
Answers
Answer:
(C)Educated people have higher savings than those who are not educated
Step-by-step explanation:
The model which is used to determine the annual savings of an individual on the basis of his annual income and education is given below:
[tex]Savings = \beta_0+\delta_0 Edu + \beta_1Inc+u[/tex]
The variable "Edu" takes a value of 1 if the person is educated. The coefficient [tex]\delta_0[/tex] measures the impact of education on a certain individual’s annual savings. If [tex]\delta_0[/tex]>0, it has a positive impact. Therefore, educated people should have higher savings than those who are not educated.
A recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours. Which of the following is a 90% confidence interval for the mean time per week spent listening to the radio? (a) 11.5 +1.676 x 9.2 (b) 11.5 +1.282 x 9.2 (c) 11.5 +1.676 x 9.2/51(d) 11.5 +1.282 x 9.2/V51 (e) 11.4 +1.299 x 9.2/51
Answers
Answer:
90% confidence interval for the mean time per week spent listening to the radio is [tex]11.5 \pm 1.676 \times \frac{9.2}{\sqrt{51} }[/tex] .
Step-by-step explanation:
We are given that a recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours.
Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average amount of time spent listening to music = 11.5
s = sample standard deviation = 9.2 hours
n = sample of students = 51
[tex]\mu[/tex] = population mean per week spent listening to the radio
Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.
So, 90% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.676 < [tex]t_5_0[/tex] < 1.676) = 0.90 {As the critical value of t at 50 degree of
freedom are -1.676 & 1.676 with P = 5%}
P(-1.676 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.676) = 0.90
P( [tex]-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]11.5-1.676 \times {\frac{9.2}{\sqrt{51} } }[/tex] , [tex]11.5+1.676 \times {\frac{9.2}{\sqrt{51} } }[/tex] ]
= [9.34 hours , 13.66 hours]
Therefore, 90% confidence interval for the mean time per week spent listening to the radio is [9.34 hours , 13.66 hours].
Consider the following function. f ( x ) = 1 − x 2 / 3 Find f ( − 1 ) and f ( 1 ) . f ( − 1 ) = f ( 1 ) = Find all values c in ( − 1 , 1 ) such that f ' ( c ) = 0 . (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about Rolle's Theorem? This contradicts Rolle's Theorem, since f ( − 1 ) = f ( 1 ) , there should exist a number c in ( − 1 , 1 ) such that f ' ( c ) = 0 . This does not contradict Rolle's Theorem, since f ' ( 0 ) = 0 , and 0 is in the interval ( − 1 , 1 ) . This does not contradict Rolle's Theorem, since f ' ( 0 ) does not exist, and so f is not differentiable on ( − 1 , 1 ) . This contradicts Rolle's Theorem, since f is differentiable, f ( − 1 ) = f ( 1 ) , and f ' ( c ) = 0 exists, but c is not in ( − 1 , 1 ) . Nothing can be concluded.
Answers
The function f(x) = 1 - x^2/3 has f(-1) = f(1) = 2/3. The derivative f'(x) = -2x/3 equals zero at x=0, which is in the interval (-1, 1). Therefore, this does not contradict Rolle's Theorem.
Explanation:The function given is f ( x ) = 1 - x ^ 2 /3. To find the values f(-1) and f(1), we simply substitute these values into the function. Therefore, f(-1) = 1 - (-1) ^ 2 /3 = 1 - 1/3 = 2/3 and f(1) = 1 - 1^2/3 = 2/3. As you can see, f(-1) = f(1).
Now, to find the value 'c' such that f'(c) = 0, first we need to determine the derivative of the function, f'(x) = -2x/3. Setting this equal to zero gives the equation 0 = -2x/3, which has the solution x = 0. Therefore, f'(c) = 0 at c = 0, which is within the interval (-1, 1).
Finally, regarding Rolle's Theorem which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the interval (a, b) such that f'(c) = 0, our results are consistent with Rolle's Theorem, since f is differentiable, f(-1) = f(1), and a 'c' value exists in the interval (-1, 1) such that f'(c) = 0.
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A circular swimming pool has a radius of 15 feet. The family that owns the pool wants to put up a circular fence that is 5 feet away from the pool at all points. Which is closest to the circumference of the fence they will need?
Answers
Answer: HI
Step-by-step explanation:
Answer:
Wizard123Ambitious
C = 2*pi*radius
radius = 15+5 = 20
C = 2*pi*20 = 40*pi = 125.6
Step-by-step explanation:
Part of a usability study to assess voting machines measured the time on task (TOT) of voters casting ballots (efficiency). Specifically, the data are for the same ballot cast on two different voting machines at the same location (called a precinct). Your job is to perform a "t" test on these data and draw conclusions about which voting machine is better in terms of usability. A few background items:
• The voters (participants/users) are a homogeneous group.
• Voters were randomly assigned to the voting machines.
• Thus, the two groups of voters (one group using the DRE voting machine, and the other using the OptiScan voting machine) have equal variances.
• We have no advance information to indicate that one voting machine will be better than the other. If you need a refresher of the "t" test, read the "t-test description.pdf"
Question1 – What is the null hypothesis in this usability study?
Question 2 – How many degrees of freedom are in each group (the DRE and OptiScan groups)?
Question 3 – Which "t" test should be used – paired, unpaired/equal variance, unpaired/unequal variance?
Question 4 – Should a one-tail, or two-tailed test be used, and why?
Question 5 – What is the t value?
Question 6 – Is the t value significant at the 0.05 level, and why?
Question 7 – Is the t value significant at the 0.01 level, and why?
Question 8 – Considering the combination of the above analysis, and the number of ballots completed, which voting machine has better usability, and why?
Answers
Answer:
See attached file
Step-by-step explanation:
Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on a particular day, one U.S. dollar could purchase 0.8869 Euros, and one Euro could purchase 143.1126 yen. Let fix) represent the number of Euros you can buy with x dollars, and let g(x) represent the number of yen you can buy with x Euros. (a) Find a function that relates dollars to Euros fx)Simplify your answer.) (b) Find a function that relates Euros to yen. gxSimplify your answer.) (c) Use the results of parts (a) and (b) to find a function that relates dollars to yen. That is, find (g o f)(x)-g(fx g(f(x)) Simplify your answer. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) (d) What is g(1000))? g(f(1000)) Type an integer or decimal rounded to one decimal place as needed.)
Answers
Answer:
(a)f(x)=0.8869x
(b)g(x)=143.1126x
(c)g(f(x))=126.9266x
(d)g(f(1000))=126926.6 Yen
Step-by-step explanation:
Given on a particular day
One U.S. dollar could purchase 0.8869 EurosOne Euro could purchase 143.1126 yen(a)If x represents the number of Dollars
Since one can purchase 0.8869 Euro with 1 USD, the function f(x) is a direct relationship where x is dollars and f(x) is in Euros.
f(x)=0.8869x(b)If x represents the number of Euros
Since one can purchase 143.1126 yen with 1 Euros, the function g(x) is a direct relationship where x is Euros and g(x) is in Yen.
g(x)=143.1126x(c)Given:
g(x)=143.1126xf(x)=0.8869xg(f(x))=143.1126(0.8869x)
g(f(x))=126.9266x(d)g(f(1000))
g(f(x))=126.9266xg(f(1000))=126.9266 X 1000 =126926.6 YenConsider the function: y=2x+5
What will be the value of the function when x=10?
Answers
Answer:
y=25
Step-by-step explanation:
10*2=20
20+5=25
Final answer:
When x=10, the value of the function y=2x+5 is 25, found by substituting 10 for x and following the order of operations.
Explanation:
The value of the function y=2x+5 when x=10 can be found by substituting the value of x into the equation. To do this, multiply 2 by 10 and then add 5 to the result:
y = 2(10) + 5
y = 20 + 5
y = 25
Therefore, when x equals 10, the value of the function is 25.
Wheat & Oats Inc. is planning a design for their new line of flavored oatmeal products. They have to choose one of these cylinder containers.
3 cylinders. Figure A has a height of 7 inches and diameter of 4 inches. Figure B has a height of 5.5 inches and radius of 3 inches. Figure C has a height of 10 inches and B = 12.57 inches squared.
It costs the company $0.02 per cubic inch of oatmeal to fill a container. The company does not want the new container to cost more than $2.00 to fill. Which of the proposed container sizes should the company use?
1. Container A
2. Container B
3. Container C
4. None. They all cost more than $2.00.
IF YALL HAVE THIS QUESTION ITS NUMER 1
Answers
Answer:
a) Container A
Step-by-step explanation:
i just did the assignment and that was the correct answer.
Answer:
container a
Step-by-step explanation:
Consider the matrix shown below:
What are the dimensions of A.
Group of answer choices
3 X 4
4 X 3
12
A and B
Answers
Answer:
3 time 4 is 12 a and b is the same
Answer:
Dimensions of matrix:
r × c
r: no. of rows
c: no. of columns
Two angles whose measures add up to 180 degrees are calledTwo angles whose measures add up to 180 degrees are called
Answers
Answer:
they are called supplementary angles
Two angles whose measures add up to 180 degrees are called supplementary angles.
What are angles?
Angles are geometric figures formed by two rays that share a common endpoint called the vertex. The rays are often referred to as the sides or arms of the angle. Angles are typically measured in degrees and are used to quantify the amount of rotation or deviation between the two rays. They are commonly represented by a symbol, such as ∠ABC, where A, B, and C are points on the rays, with the vertex at point B.
The size of an angle is determined by the amount of rotation between the two rays, starting from one ray and ending at the other. A full rotation is equivalent to 360 degrees, and angles are measured counterclockwise from the initial ray. Depending on their measurement, angles can be classified into different types, such as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), and straight (exactly 180 degrees).
When two angles are supplementary, it means that they combine to form a straight angle, which is a straight line measuring 180 degrees. Supplementary angles can be adjacent (sharing a common vertex and side) or non-adjacent, but their sum will always equal 180 degrees. This property is fundamental in geometry and has various applications in solving problems involving angles and shapes.
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akua went shopping and she decided to buy 1.8LBS of apples and 3LBS of strawberries. the apples where on sale for $1.99 per pound and the strawberries cost 2.00 per pound. how much did she spend in total?
Answers
Answer:5
Step-by-step explanation:
Answer: $9.58
Step-by-step explanation: A pound of apples cost $1.99, so you multiply 1.99 and 1.8.(the pounds he got)
1.99x1.8= 3.58 (Cost of 1.8 pounds of apples)
A pound of strawberries cost 2.00, so you multiply 2.00 and 3 (the pounds he got)
2.00x3= $6.00
Add $3.58+$6.00= $9.58
A brownie recipe calls for 1 cup of sugar and 1/2 cup of flour
Answers
Answer:
Uhhhhhhhhhhhhh yes most recipies do call for that
Step-by-step explanation:
have a nice day
What is the volume of the following rectangular prism
Answers
Answer:
7 2/3
Step-by-step explanation:
Multiply 4/3 by 23/4
Description : Ella has a rechangle that has a side with a length of 1/4 foot and a side with a length of 3/4 foot She shaded a model to show that the area of her reciongle is 3/16 square foot Which models represents Ella's rectangle Explain how you know.
Answers
Answer:
What are the models?
Final answer:
Ella's rectangle has a length of 1/4 foot and a width of 3/4 foot. Multiplying these dimensions gives an area of 3/16 square foot, confirming that the model of her rectangle is correct.
Explanation:
The question presents a scenario where Ella has a rectangle with a length of 1/4 foot and a width of 3/4 foot. To find the area of a rectangle, you multiply the length by the width. Thus, the area of Ella's rectangle is calculated as follows:
Area = Length * Width
Area = (1/4) * (3/4)
Area = 3/16 square feet
The model that represents Ella's rectangle should be a scaled shape where the area corresponds to the given sides' lengths. Having a model with these dimensions and affirming that its area is 3/16 square foot simply verifies that the side lengths were used correctly to determine the rectangular area. This applies the concept that the area of a rectangle is a product of its length and width.
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)
Answers
Answer:
In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.
In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.
In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.
Step-by-step explanation:
We have to write the transition matrix M for the population.
We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.
We can write the transition matrix, in which the rows are the actual state and the columns are the future state.
- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. Then, the probability of staying in the same state is 90%.
- For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. Then, the probability of staying in the same state is 80%.
- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. Then, the probability of staying in the same state is 82%.
The transition matrix becomes:
[tex]\begin{vmatrix} &NS&P1&PM\\NS& 0.90&0.08&0.02 \\ P1&0.10&0.80 &0.10 \\ PM& 0.08 &0.10&0.82 \end{vmatrix}[/tex]
The actual state matrix is
[tex]\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right][/tex]
We can calculate the next month state by multupling the actual state matrix and the transition matrix:
[tex]\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right][/tex]
In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.
To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:
[tex]\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right][/tex]
In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.
If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:
[tex]\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right][/tex]
In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.
One month Isabel rented 5 movies and 2 video games for a total of$26 . The next month she rented 3 movies and 8 video games for a total of $53. Find the rental cost for each movie and each video game.
Answers
Answer:
a movie, m is 3
a video game, v is 5.5
Brainliest would be really appreciated. (need it to unlock chat)
Feel free to ask further questions if you feel like it.
Till then, have a nice day
Step-by-step explanation:
I 5m+2v=26
II 3m+8v=53
I 5m+2v=26 devide by 2 on both sides
5/2m+v=13 subtract 5/2m om both sides
v=13-5/2m
Now put this whole thing in the other equation II, replacing the v there
3m+8(13-5/2m)=53 just calculate it
3m+104-20m=53
-17m+104=53 subtract 53 on both sides
-17m+51=0 add 17m on both sides
51=17m devide by 17
3=m
we found m, v is easy
now put m in an equation from the start, let's take equation I here
I 5m+2v=26
5*(3)+2v=26
15+2v=26 subtract 15 on both sides
2v = 11 devide by 2
v = 5.5
So we found m and v, prices for single items. we can proof this when we put m and v into a given equation and the if it equals a true value
m & v in II
II 3m+8v=53
3*(3)+8*(5.5)=53
9+44=53
53=53
Seems legit.
To find the rental cost for each movie and video game, set up a system of equations based on the given information and solve for the variables.
Explanation:To find the rental cost for each movie and video game, we can set up a system of equations based on the given information.
Let's assign variables to represent the rental cost for each movie and video game. Let's use 'm' for the cost of a movie and 'g' for the cost of a video game.
Based on the first month's information, we can write the equation: 5m + 2g = 26
Based on the second month's information, we can write the equation: 3m + 8g = 53
Now we can solve this system of equations to find the values of 'm' and 'g'.
By solving the system of equations, we find that the rental cost for each movie is $4 and the rental cost for each video game is $5.
Learn more about Rental cost for movies and video games here:https://brainly.com/question/22393405
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A study of 178 cases of disease X were identified from a state registry. A total of 220 control subjects were then recruited from random-digit dial procedure. 16 cases had been exposed, compared to only 8 controls. How likely were cases to report an exposure compared with controls
Answers
Answer:
2.47 times more likely.
Step-by-step explanation:
16 out of 178 cases were reported for exposure.
And 8 out of 220 control reported for exposure.
Chances that a case would be reported for exposure = (16/178) = 0.0898876404
Chances that one control would report for exposure = (8/220) = 0.0363636364
Comparing both, how likely were cases to report an exposure compared with controls
= (0.0898876404) ÷ (0.0363636364)
= 2.4719101085 = 2.47 times more likely.
Hope this Helps!!
A student takes a true-false test that has 10 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(Fewer than 3). Round your answer to 2 decimal places.
Answers
Answer:
P(Fewer than 3) = 0.05.
Step-by-step explanation:
We are given that a student takes a true-false test that has 10 questions and guesses randomly at each answer.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 10 questions
r = number of success = fewer than 3
p = probability of success which in our question is probability
that question is answered correctly, i.e; 50%
LET X = Number of questions answered correctly
So, it means X ~ Binom(n = 10, p = 0.50)
Now, Probability that Fewer than 3 questions are answered correctly is given by = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0}+ \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1}+ \binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}[/tex]
= [tex]1 \times 0.50^{10} + 10 \times 0.50^{10} +45 \times 0.50^{10}[/tex]
= 0.05
Hence, the P(Fewer than 3) is 0.05.
To find the probability of the student passing the test with at least a 70 percent, we can use the binomial probability formula. The probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).
Explanation:To find the probability of the student passing the test with at least a 70 percent, we need to find the probability of the student answering 7, 8, 9, or 10 questions correctly out of the 10 questions. Since the student randomly guesses at each answer, the probability of guessing correctly is 0.5. Now we can calculate the probability using the binomial probability formula:
P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
P(X = k) = C(10, k) * (0.5)^k * (0.5)^(10-k), where C(n, r) is the binomial coefficient (n choose r).
Calculating each probability and summing them up, we get P(X ≥ 7) = 0.171875. Therefore, the probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).
Suppose each laptop of a certain type is assigned a series number, which consists of a sequenceof eight symbols: number, letter, letter, letter, number, number, number, number, where aletter is any one of 26 letters and a number is one among 0, 1,. . ., 9. Assume that all series numbers are equally likely.
(a) What is the probability that all symbols are different if one laptop is picked at random with equal probability?
(b) What is the probability that all symbols are different and the first number is the largest among the numbers?
Answers
Answer:
Step-by-step explanation:
There are 5numbers and 3 letters. Each number can be one among the 10 possible.
Each letter is 1 among the 26 available.
a)The number of possible unique serial numbers are
10^5x 26³
The number of 5 number combinations each different (order important) is 5!(10/5)= 30240
The number of 3 letter combinations each different (order important) is 3!(26/3)=15600
The required probability (that all symbols are different if one laptop is picked at random with equal probability) is
15600x3240/ 10^5x 26³=0.2684
b) The first letter must be at least 4 to be largest among the 5 numbers. So the first letter can be one of . 4,5,6,7,8,9..
The number of 5 number combinations each different and starting with 4 (order important) is .
4!=24
The number of 5 number combinations each different and starting with 5 (order important) is .
4!(5/4)= 120
The number of 5 number combinations each different and starting with 6 (order important) is .
4!(6/4)= 360
The number of 5 number combinations each different and starting with 7 (order important) is .
4!(7/4)= 840
The number of 5 number combinations each different and starting with 8 (order important) is
4!(8/4)= 1680
The number of 5 number combinations each different and starting with 9 (order important) is .
4!(9/4)= 3024
Thus, there are
The required probability ( that all symbols are different and the first number is the largest among the numbers) is
15600* 6040/10^5x 26³= 0.0537
An L shaped pool that one part is 8 meters by 6 meters the other part is 12 meters by 6 meters. The whole pool is 4 meters deep.
Answers
Answer: 480 meters. squared
Kim needs to buy 10 pounds of grapes to take to a party. Grapes cost $1.29 per pound. How much will she spend to
purchase 10 pounds of grapes?
Answers
Answer:
$12.90
Step-by-step explanation:
multiply a $1.29 by 10 pounds and you get your answer:)
Answer:
$12.90
Step-by-step explanation
10 x $1.29=$12.90
or
move the decimal 1 time to the right
A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the flow rate be more than 5 gallons per minute (gpm). In an initial study, eight runs were made. The average flow rate was 6.5gpm and the standard deviation was 1.9 gpm. If the mean flow rate is found to meet the specification, the pump will be put into service.
1. State the appropriate null and alternate hypotheses
2. Find the P-value
3. Should the pump be put into service? Explain.
Answers
Answer:
1) We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
2) [tex]df=n-1=8-1=7[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]
3) For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.
Step-by-step explanation:
Data given and notation
[tex]\bar X=6.5[/tex] represent the sample mean
[tex]s=1.9[/tex] represent the sample standard deviation
[tex]n=8[/tex] sample size
[tex]\mu_o =5[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
Part 1: State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
If we analyze the size for the sample is <30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{6.5-5}{\frac{1.9}{\sqrt{8}}}=2.233[/tex]
Part 2: P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=8-1=7[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]
Part d: Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant higher compared to the height of men in 1960 at 1% of signficance.
Part 3
For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.