Answer:
Solution
V=πr2h=π·32·8≈226.19467
Step-by-step explanation:
Scott is reading two books at the same time to prepare for a report he is writing. So far, he has read 407 of the total number of 557 pages, which is Three-fifths of the shorter book and StartFraction 5 Over 6 EndFraction of the longer book. Which system of equations can be used to determine the total number of pages in the shorter book, x, and the total number of pages in the longer book, y?
Answer:
The system of equations are
x+y=557
[tex]\frac35x+\frac56 y=407[/tex]
The total pages in shorter book is 245
The total pages in longer book is 312
Step-by-step explanation:
Given that,
Scott has read 407 of the total number of 557 pages, which [tex]\frac35[/tex] of the shorter book and [tex]\frac56[/tex] of longer book.
Total number of pages of shorter book be x and longer book be y.
Then,
[tex]\frac35[/tex] page of the shorter book [tex]=\frac35 x[/tex]
[tex]\frac56[/tex] pages of the longer book = [tex]\frac56y[/tex]
So, he has read [tex]=\frac35x+\frac 56y[/tex]
Total number of pages of both book is = x+y
According to the problem,
x+y=557.........(1)
[tex]\frac35x+\frac56 y=407[/tex].......(2)
We can write equation (2) as
[tex]\frac35x+\frac56 y=407[/tex]
[tex]\Rightarrow \frac{18x+25y}{30}=407[/tex]
[tex]\Rightarrow {18x+25y}=407\times 30[/tex]
[tex]\Rightarrow {18x+25y}=12,210[/tex]......(3)
Now 18 times of equation (1) subtract from equation (3)
18x+25y=12210
18x+18y=10026
- - -
_______________
25y-18y=12,210-10,026
⇒7y=2,184
[tex]\Rightarrow y=\frac{2184}{7}[/tex]
⇒y= 312
Plug y=312 in equation (1)
x+312=557
⇒x=557-312
⇒x=245
The total pages in shorter book is 245
The total pages in longer book is 312
The system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is
3 / 5 x + 5 / 6 y = 407
x + y = 557
How to model a system of equation?Scott has read 407 of the total number of 557 pages, which is 3 / 5 of the shorter book and 5 / 6 of longer book.
x = number of pages in the shorter book
y = number of pages in the longer book
Therefore, the system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is as follows;
3 / 5 x + 5 / 6 y = 407
x + y = 557
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kira has a rope that is 5 meters long. she cuts a piece that is 1.51 meters long. how long is the remaining piece of rope
Answer:
3.49
Step-by-step explanation:
5-1.51=3.49
Answer:
3.49 meters long
Step-by-step explanation:
5-1.51 = 3.49
- If you need this further explained please let me know. I would be glad to help.
2 + y = 11
Solve the equation.
Answer:
the answer is 9
Step-by-step explanation:
Find the probability of this event. Enter the answer as a fraction in simplest form, as a decimal to the nearest hundredth, and as a percent to the nearest whole number. You choose a movie CD at random from a case containing 4 comedy CDs, 5 science fiction CDs, and 7 adventure CDs. The CD is not a comedy.
Answer:
0.75 is the probability of selecting a CD that is not comedy.
Step-by-step explanation:
We are given the following in the question:
Number of comedy CD = 4
Number of science CD = 5
Number of adventure CD = 7
Total number of CD,n = 16
We have to find the probability for selecting a random CD that is not comedy.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
P( Non-Comedy CD) =
[tex]=\dfrac{\text{n(Non-Comedy)}}{n}\\\\=\dfrac{5+7}{16} = \dfrac{12}{16}=\dfrac{3}{4}= 0.75 = 75\%[/tex]
Thus, 0.75 is the probability of selecting a CD that is not comedy.
25 POINTS FOR FIRST ANSWER
ANSWER ASAP PLZ
1 is union so all all the numbers inside the circles:
{8,9,14,15,16,17}
2 is intersection so the numbers where the circles cross each other
{14,17}
3. A’ is any number not included with A
There are 10 total numbers.
7 are not associated with A
Probability would be 7/10 = 0.70
Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over a specified amount of sick leave minutes. Assuming that the company wishes no more than 5 percent of all employees to get a cash payment, what should the required number of minutes be?
Answer:
The required amount of minutes is 5796.05 minutes
Step-by-step explanation:
Here, since we have that the sick leave is given as 1 minute per hour worked per month and
The amount of unused sick leave is uniformly distributed between 0 and 480
Therefore, there are 481 employees, counting from 0 to 480 with 0 included
Where the company wishes no more than 5% of all employees get cash payment then we have
Total number of minutes = 1 to 481 = 115921 minutes
Therefore, we have 5% of 115921 = 5796.05 minutes
The balance amount of minutes = 115921 minutes - 5796.05 minutes
= 110124.95 minutes.
Jose scores 544 points in his math test. He needs at least 650 to get an A, write and solve the minimum number of points Jose needs to score on the remaining test,n, in order to get an A
Answer:
The correct answer is x [tex]\geq[/tex] 106, where x is the marks score by Jose in his remaining test, n.
Step-by-step explanation:
Jose scored 544 points in his math test.
Jose needs minimum of 650 points to get an A.
Let Jose scores x in the remaining test, n.
Jose needs to score an A. So, to reach 650 points, Jose need to score a minimum of 650 - 544 = 106 points.
Thus the value of x must be greater than of equal to 106, in his remaining test, n, to ensure that Jose gets an A.
⇒ x [tex]\geq[/tex] 106.
3/4 of the students at Timber Elementary play sports. Of those students, 1/5 of them play soccer. What fraction of the students at Timber Elementary play soccer?
Answer:
3/20 of the students play soccer
Step-by-step explanation:
1. Divide the amount of students that play sports, 3/4 by the amount of those that play soccer, 1/5
2. 3/4 divided by 1/5= 3/20
Answer:
3/20
Step-by-step explanation:
6. 1 point Mark only one oval. Not biased Bias 7. 2 points Mark only one oval. 26 oz 27 oz 28 oz A town has 15,000 registered voters. A random sample of 200 voters finds that 100 are in favor of a new dog park. How many are likely to vote for the dog park?
Answer:
About 7,500 registered voters are expected to vote for the new dog park.
Step-by-step explanation:
- A town has 15,000 registered voters.
- A random sample of 200 voters shows that 100 voters are in favour of a new dog park.
How many registered voters are likely to vote for the dog park?
The laws of probability allows us to extrapolate and use the proportion of randomly sampled registered voters that vote for a new dog park to calculate the actual number of registered voters that will vote for a new dog park.
Proportion of randomly sampled registered voters that voted for a new dog park
= (100/200) = 0.50
Proportion of overall registered voters that will vote for a new dog park will also be 0.50.
Number of likely registers voters that'll vote for a new dog park = 0.50 × 15,000 = 7,500
Hope this Helps!!!
Approximately 7,500 registered voters are likely to vote for the new dog park
To determine how many of the 15,000 registered voters in a town are likely to vote for a new dog park based on a random sample, follow these steps:
First, find the proportion of voters in the sample who are in favor of the dog park. In this case, 100 out of 200 voters are in favor.Calculate the proportion: [tex]\frac{100}{200} = 0.5[/tex] or 50%.Apply this proportion to the entire population of registered voters:Multiply the total number of registered voters by the proportion: 15,000 * 0.5 = 7,500.Therefore, approximately 7,500 registered voters are likely to vote for the new dog park.
A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accomodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and * may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost
Answer: They must hire 12 Counselors and 18 Aides
Step-by-step explanation: The most important factor here is the fact that they need to minimize hiring costs. The math camp can afford to hire up to 45 members of staff and can as well run properly with 30 members of staff.
The camp must have at least 10 aides (simply put, any number above 10 will do). Also they may have up to 3 aides for every 2 counselors, that is the ratio of counselor to aide has been given as;
2 : 3
If the math camp decides to hire the minimum required in order to minimize cost, they would be hiring 30, and that would be divided according to the following ratio;
(Counselor):
30 x 2/5 = 12
(Aide):
30 x 3/5 = 18
Hence they would be hiring 12 counselors at a cost of
2400 x 12 = 28800
And 18 Aides at a cost of
1100 x 18 = 19800
Therefore the total (minimum) cost of hiring staff is $48,600
The problem is a mathematical optimization problem, solved using systems of inequalities. The camp's optimal hiring strategy can be obtained by satisfying a set of constraints and minimizing a cost function.
Explanation:This problem can be solved using systems of inequalities in mathematics. Let's let C represent the number of counselors and A represent the number of aides. Here are the constraints you need to consider:
The camp can accommodate up to 45 staff members: C + A ≤ 45 The camp needs at least 30 staff members to run properly: C + A ≥ 30 They must have at least 10 aides: A ≥ 10 The camp may have up to 3 aides for every 2 counselors: A ≤ (3/2)C
Also, keep in mind that the camp wants to minimize costs, and the average monthly salary is $2400 for counselors and $1100 for aides, so you need to minimize the total cost function: 2400C + 1100A. By solving this system of inequalities and minimizing the cost function, the camp will have an optimal hiring strategy.
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The circumference of a circle is 16 pi ft.
What's the radius
Answer:
2.54648 ft
Step-by-step explanation:
r = 8/π (ft.) Therefore, the radius of the circle when its circumference is 16 feet is r ≈ 2.54648 ft. C = 2 (3.14159) (2.54648) ft :)
Suppose the supply function for a certain item is given by S(q)= (q+6)2 and the demand funtion is given by D(q)= (1000)/(q+6).
A. Find the point at which supply and demand are in equilibrium?
B. Find the consumer's surplus?
C. find the producer's surplus?
Answer: The equilibrium point is where; Quantity supplied = 100 and Quantity demanded = 100
Step-by-step explanation: The equilibrium point on a demand and supply graph is the point at which demand equals supply. Better put, it is the point where the demand curve intersects the supply curve.
The supply function is given as
S(q) = (q + 6)^2
The demand function is given as
D(q) = 1000/(q + 6)
The equilibrium point therefore would be derived as
(q + 6)^2 = 1000/(q + 6)
Cross multiply and you have
(q + 6)^2 x (q + 6) = 1000
(q + 6 )^3 = 1000
Add the cube root sign to both sides of the equation
q + 6 = 10
Subtract 6 from both sides of the equation
q = 4
Therefore when q = 4, supply would be
S(q) = (4 + 6)^2
S(q) = 10^2
S(q) = 100
Also when q = 4, demand would be
D(q) = 1000/(4 + 6)
D(q) = 1000/10
D(q) = 100
Hence at the point of equilibrium the quantity demanded and quantity supplied would be 100 units.
A. The point at which supply and demand are in equilibrium is [tex]q=4[/tex].
B. The consumer's surplus is 178.16 .
C. The producer's surplus is 66.6 .
Given,
The supply function for a certain item is,
[tex]S(q)= (q+6)^2[/tex]
The demand function is,
[tex]D(q)= \dfrac{1000}{ (q+6)}[/tex]
Now we know that the supply and demand are in equilibrium where the supply and demand functions are equal.
So for equilibrium,
[tex]S(q)= D(q)[/tex]
[tex](q+6)^2=\dfrac{1000}{q+6}[/tex]
[tex](q+6)^3=1000[/tex]
[tex]q+6=\sqrt[3]{1000}[/tex]
[tex]q+6=10[/tex]
[tex]q=4[/tex]
Hence the point is [tex]q=4[/tex], at this point supply and demand are in equilibrium.
At equilibrium the supply is [tex](4+6)^2=100[/tex] and demand is also 100.
so, [tex](q^*,p^*)[/tex] is [tex](4,100)[/tex]
Now, the consumer's surplus will be,
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=\int\limits^4_0 {\dfrac{1000}{q+6} } \, dq -4\times 100[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=1000[log10-log6]-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=1000[1-0.778]-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=1000\times 0.22184-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=221.84-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=178.16[/tex]
Now, the producer's surplus will be,
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=400-\int\limits^{4}_0(q+6)^2dq[/tex]
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=400-\frac{1}{3} [1000-0][/tex]
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=\dfrac{200}{3}[/tex]
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=66.66[/tex]
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What is the product of – 7.2 x -3?
A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10% more than the number of shoppers the day before. What is the total number of shoppers that visited the mall in the first 7 days?
Answer:
193 shoppers
Step-by-step explanation:
2nd 120 +12
3rd 132+13.2
4rd 145.2+ 14.52
5th 159.72+15.972
6th 175.692 +17.5692
7th 193.2612
Shota built a time travel machine, but he can't control the duration of his trip. Each time he uses the machine he has a 0.80.80, point, 8 probability of staying in the alternative time for more than an hour. During the first year of testing, Shota uses his machine 202020 times. Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour? Round your answer to the nearest hundredth.
Answer:
0.99 probability that at least one trip will last less than an hour
Step-by-step explanation:
For each time that the machine is used, there are only two possible outcomes. Either it lasts more than an hour, or it does not. The probability of a trip lasting more than an hour is independent of other trips. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
0.8 probability of lasting more than one hour.
So [tex]p = 0.8[/tex]
20 trips
So [tex]n = 20[/tex]
Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour?
Either all the trips last for more than an hour, or at least one does not. The sum of the probabilities of these outcomes is decimal 1. So
[tex]P(X = 20) + P(X < 20) = 1[/tex]
We want P(X < 20). So
[tex]P(X < 20) = 1 - P(X = 20)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 20) = C_{20,20}.(0.8)^{20}.(0.2)^{0} = 0.0115[/tex]
[tex]P(X < 20) = 1 - P(X = 20) = 1 - 0.0115 = 0.9885[/tex]
0.9885 probability that at least one trip will last less than an hour
Rouding to the nearest hundreth.
0.99 probability that at least one trip will last less than an hour
The painting by itself is a rectangle with length 20 cm and width 16 cm. The painting and frame together form a larger rectangle with length 25 cm and width 20 cm Find the area of the frame.
Answer:
The area of frame is 180 square meters.
Step-by-step explanation:
We are given the following in the question:
Dimension of rectangular painting:
Length, l = 20 cm
Width, w = 16 cm
Dimension of frame:
Length, L = 25 cm
Width, W = 20 cm
We have to find the area of frame.
Area of rectangle =
[tex]A = l\times w[/tex]
Area of frame =
[tex]A-a\\=(L\times W)-(l\times w)\\=(25\times 20)-(20\times 16)\\=180\text{ square meters}[/tex]
Thus, the area of frame is 180 square meters.
What is the area of the parallelogram?
Answer:
A=Bh
the area of a parallelogram is base times height
Find the arc length of the partial circle.
Answer:
[tex]11[/tex]
Step-by-step explanation:
[tex] \frac{90}{360} \times 2 \times \pi \times 7 \\ \frac{1}{4} \times 2 \times \frac{22}{7} \times 7 \\ = 11[/tex]
Answer:
11
Step-by-step explanation:
[tex] = \frac{1}{2} \pi \: r \\ = \frac{1}{2} \times \frac{22}{7} \times 7 \\ = \frac{1}{2} \times 22 \\ = 11[/tex]
You are throwing darts at a dart board. You have a chance of striking the bull's-eye each time you throw. If you throw 3 times, what is the probability that you will strike the bull's-eye all 3 times?
Answer:
Correct answers is
[tex] \frac{1}{216} [/tex]
Step-by-step explanation:
Given: The chances of striking the bull's-eye each time of throw =\frac{1}{6}
Since, if we throe dart on dart board , each event will be independent of the other.
Then, If we throw 3 times, what is the probability that we will strike the bull's-eye all 3 times is given by :-
[tex]p(strike \: bulls \: eye \: ) = \frac{1}{6} x \frac{1}{6} x \frac{1}{6} = \frac{1}{216} [/tex]
Hence, the probability that we will strike the bull's-eye all 3 times is 1/216
Answer:
1/216
Step-by-step explanation:
2 + 2 x 2
plz help me it hard
Answer:
There is no way. Its 6.
Step-by-step explanation:
2 x 2 is 4
4 +2 is 6
When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units
Answer:
r=1/π
Step-by-step explanation:
Area of the circle is defined as:
Area = πr²
Derivating both sides
[tex]\frac{dA}{dr}[/tex]=2πr
[tex]\frac{dA}{dt}[/tex] = [tex]\frac{dA}{dr}[/tex] x [tex]\frac{dr}{dt}[/tex] = 2πr[tex]\frac{dr}{dt}[/tex]
If area of an expanding circle is increasing twice as fast as its radius in linear units. then we have : [tex]\frac{dA}{dt}[/tex] =2[tex]\frac{dr}{dt}[/tex]
Therefore,
2πr [tex]\frac{dr}{dt}[/tex] = 2 [tex]\frac{dr}{dt}[/tex]
r=1/π
Answer:
r = 1/π
Step-by-step explanation:
Here we have
Area of a circle given as
Area = πr²
Where:
r = Radius of the circle
When the area of the circle is expanding twice as fast s the radius we have
[tex]\frac{dA}{dt} =2 \times \frac{dr}{dt}[/tex]
However,
[tex]\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}[/tex] and
[tex]\frac{dA}{dr} = \frac{d\pi r^2}{dr} = 2\pi r[/tex]
Therefore, we have
[tex]\frac{dA}{dt} =2 \times \frac{dr}{dt} = 2\pi r \times \frac{dr}{dt}[/tex]
Cancelling like terms
[tex]1= \pi r[/tex]
Therefore, [tex]r = \frac{1}{\pi }[/tex].
Susan owns a home that is worth $128,318.74, a 2005 truck worth $10,615.00, and has investments that total $4,459.16. Susan owes $93,987.74 on her mortgage, $2,874.46 in student loans, and $1,214.92 on her credit card. What is Susan's Net Worth?
Answer:
Net worth is defined as:
Assets - Liabilities.
Assets are what you own.
Liabilities are what you have to pay.
So, home + truck + investments are assets.
Likewise, mortgage + student loans + credit cards are liabilities.
Doing the math, Susan's net worth is
Assets - Liabilities
$143,392.90 - $98,077.12 =
$45,315.78
Susan's net worth is $45,315.78
Good luck!
Susan's net worth is calculated by subtracting her total liabilities (mortgage, student loans, and credit card debt) from her total assets (home, truck, and investments). Therefore, Susan's net worth is $45,315.78.
Explanation:The question is about calculating Susan's net worth. Net worth is calculated by subtracting the total liabilities from total assets. In Susan's case, her assets include her house, truck, and investments, which total to $143,392.90 ($128,318.74 for the house, $10,615.00 for the truck, and $4,459.16 for her investments). Her liabilities include her mortgage, student loans, and credit card debt, which sums up to $98,077.12 ($93,987.74 for the mortgage, $2,874.46 for the student loans, and $1,214.92 for the credit card debt). To calculate Susan's net worth, subtract total liabilities from total assets. Therefore, Susan's net worth is $45,315.78 ($143,392.90 - $98,077.12).
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1: Mr. Alter bought a block of fudge that weighed 75 pounds. He cut the fudge into 6 equal pieces. What was the weight of each piece of fudge? A 930 pounds B 830 pounds C 307 pounds D 730 pounds
Answer: The weight of each piece of fudge is 12.5 pounds
Step-by-step explanation: To find how much each piece of fudge weighs simply divide 75 by 6 to get the equal weight for 6 pieces.
75/6 = 12.5 pounds per piece.
What is 2+2 if you add it agin anthem add it
Answer:
4
Step-by-step explanation:
Hope this helped :)
Answer:
it is 9
Step-by-step explanation:
because 2+2=4+2=6+2=9
Two sides of a triangle measure 5 in. and 12 in. Which could be the length of the third side?
To determine the possible length of the third side in a triangle with sides measuring 5 in. and 12 in., we need to check if the sum of the given sides is greater than the length of the third side.
Explanation:In a triangle, the length of any side must be less than the sum of the lengths of the other two sides. Therefore, to determine the possible length of the third side, we need to check if the sum of the given sides is greater than the length of the third side.
Let the third side be denoted as 'x'.
For a triangle with sides measuring 5 in. and 12 in., the possible length of the third side must satisfy the inequality:
5 + 12 > x
17 > x
Therefore, any length less than 17 in. is a valid possibility for the third side.
Final answer:
The length of the third side of the triangle must be greater than 7 inches but less than 17 inches, following the triangle inequality theorem. If considering a right triangle, the hypotenuse would measure exactly 13 inches according to the Pythagorean theorem.
Explanation:
Based on the question about the lengths of the sides of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given that two sides of the triangle measure 5 inches and 12 inches, the length of the third side must be greater than 7 inches (12 - 5) but less than 17 inches (12 + 5).
This is because the third side must be long enough to reach between the ends of the other two sides to close the triangle, but can't be so long that it would stretch beyond both ends if laid out straight. In the context of a right triangle, such as described by the Pythagorean theorem, we could consider that if the triangle were right-angled, then using the given sides as legs, the length of the hypotenuse would actually be exactly 13 inches, as 5² + 12² = 13².
A manufacturer of a new medication on the market for Alzheimer's disease makes a claim that the medication is effective in 65% of people who have the disease. One hundred eighty individuals with Alzheimer's disease are given the medication, and 115 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 65% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.
Answer:
[tex]z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309[/tex]
[tex]p_v =P(z<-0.309)=0.379[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65
Step-by-step explanation:
Data given and notation
n=180 represent the random sample taken
X=115 represent the adults with the medication was effective
[tex]\hat p=\frac{115}{180}=0.639[/tex] estimated proportion of adults with the medication was effective
[tex]p_o=0.65[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that true proportion is less than 0.65.:
Null hypothesis:[tex]p \geq 0.65[/tex]
Alternative hypothesis:[tex]p < 0.65[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
[tex]p_v =P(z<-0.309)=0.379[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65
Answer:
H0: p = 0.65
Ha: p < 0.65
Sample proportion = 115 / 180 = 0.6389
Test statistics
z = - p / sqrt( p( 1 -p ) / n)
= 0.6389 - 0.65 / sqrt ( 0.65 * 0.35 / 180)
= -0.31
Critical value at 0.05 level = -1.645
Since test statistics falls in non-rejection region, do not reject H0.
We conclude at 0.05 level that we fail to support the claim.
Step-by-step explanation:
Amy sold 10 packages of sugar cookies and 2 packages of oatmeal
cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of
oatmeal cookies for $60. What is the price of a pack of sugar cookies and a
pack of oatmeal cookies?
Answer:
sugar cookies -- $4oatmeal cookies -- $8Step-by-step explanation:
Using "s" and "o" to represent the prices of packs of sugar and oatmeal cookies, respectively, we can write the revenue equations as ...
10s +2o = 56
9s +3o = 60
In standard form (with common factors removed), these equations are ...
5s + o = 28
3s + o = 20
Subtracting the second equation from the first, we find ...
(5s +o) -(3s +o) = (28) -(20)
2s = 8 . . . . simplify
s = 4
Substituting into the first equation, we have ...
5·4 +o = 28
o = 8 . . . . . . subtract 20
The price of a pack of sugar cookies is $4; of oatmeal cookies, $8.
The price of a pack of sugar cookies is $4 and the price of a pack of oatmeal cookies is $8.
Let's denote the price of a pack of sugar cookies as s and the price of a pack of oatmeal cookies as o
From Amy's sales, we have the equation:
10s + 2o = 56 (Equation 1)
From Adam's sales, we have the equation:
9s + 3o = 60 (Equation 2)
Let's use the elimination method.
3(10s + 2o) = 3(56)
30s + 6o = 168 (Equation 3)
2(9s + 3o) = 2(60)
18s + 6o = 120 (Equation 4)
Now we subtract Equation 4 from Equation 3 to eliminate o
(30s + 6o) - (18s + 6o) = 168 - 120
12s = 48
s = 4
Now that we have the price of a pack of sugar cookies s=4 we can substitute this value back into either Equation 1 or Equation 2 to find the price of a pack of oatmeal cookies.
Let's use Equation 1:
10(4) + 2o = 56
o = 8
Abu made a profit from his business.He used 1/12 of his profit business to buy a pair of trousers and a shirt costing RM 105.80 and RM 64.20 respectively.If he give 0.2 of the remainder profit to his parents,how much did they receive?
HELP NEEDED ASAP !!!
Answer:
Step-by-step explanation:
105.80 + 64.20 = 170 +57 = 227
= $46
What is the length of the shortest side of a triangle that has vertices at (4, 6), (-2, 0), and (-6, 3)?
A.
B.
C.
D.
Answer:
5
Step-by-step explanation:
Figuring the short side, it becomes a nice 3, 4, 5 triangle
so the short side is 5 units.
Hope this helped
:)
Final answer:
The length of the shortest side of the triangle is the length of side BC, which is calculated to be 5 units using the distance formula.
Explanation:
To find the length of the shortest side of the triangle with the given vertices, we will calculate the length of each side using the distance formula √((x2-x1)² + (y2-y1)²) and then determine the shortest one.
Side AB: [tex]\sqrt{((-2-4)^2 + (0-6)^2)}[/tex] = √(36+36) = √72 ≈ 8.5Side AC: [tex]\sqrt{((-6-4)^2 + (3-6)^2)[/tex]= √(100+9) = √109 ≈ 10.4Side BC: [tex]\sqrt{((-6+2)^2 + (3-0)^2)}[/tex] = √(16+9) = √25 = 5Therefore, the length of the shortest side is the length of side BC, which is 5 units.
Sarah used her calculator to work out the value of a number y .
The answer on her calculator display began.
7.8
Complete the error interval for y.
[......] ≤ y < [......]
The error interval for y is 7.8 ≤ y < 7.9.
Explanation:The error interval is determined by the decimal digits that will determine the value of y. Since the calculator display shows 7.8, y will be between 7.8 and the next smallest number, which will be 7.9. Therefore, the error interval for y is:
7.8 ≤ y < 7.9
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The error interval for y is [7.8, 7.9).
Explanation:To find the error interval for y, we need to consider the decimal place immediately after the given value on Sarah's calculator display. Since the given value is 7.8, we look at the digit after the decimal point, which is 0. If this digit is 5 or greater, we round up the previous digit. In this case, 0 is not greater than 5, so we do not round up. Therefore, the error interval for y is [7.8, 7.9).
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