If rectangle has its base on the x-axis and its upper two vertices on the parabola y= 12 -x², the largest area the rectangle is 32 square units and dimensions are 2 and 8 units.
To find the largest area of the rectangle, we can start by considering the coordinates of the upper two vertices on the parabola y = 12 - x². Let's denote the x-coordinate of one vertex as "a". The corresponding y-coordinate can be found by substituting this value into the equation:
y = 12 - a²
Since the base of the rectangle lies on the x-axis, the length of the base is given by 2a.
Now, let's calculate the area of the rectangle in terms of "a":
Area = base * height = 2a * (12 - a²)
To find the maximum area, we need to take the derivative of the area function with respect to "a" and set it equal to zero:
d(Area)/da = 2(12 - a²) - 2a(2a) = 24 - 2a² - 4a² = 24 - 6a²
Setting this equal to zero:
24 - 6a² = 0
6a² = -24
a² = 4
a = 2
Now,
Area = 2(2)(8)
Area = 4 * 8 = 32
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suppose 60% of the banks in switzerland are private organizations. if a sample of 469 banks is selected, what is the probability that the sample proportion of private banks will be greater than 65% ? round your answer to four decimal places.
The probability that the sample proportion of private banks will be greater than 65% is 0.1548.
Given that 60% of banks in Switzerland are private organizations.
If a sample of 469 banks is selected, we need to find the probability that the sample proportion of private banks will be greater than 65%.
Let p be the proportion of private banks in a sample of 469 banks.
Then
q = 1 - p
= 1 - 0.6
= 0.4 (as the percentage of private banks is given to be 60%)
Sample size, n = 469
We are to find the probability that the sample proportion of private banks will be greater than 65%.
That is, we need to find P(p > 0.65).
We use the normal distribution for finding probabilities associated with proportions.
We can use the formula as follows:
z = (p - P) / √[PQ/n],
where P is the population proportion (given as 0.6),
Q = 1 - P
= 0.4, and
n = 469
Putting all the given values in the above formula, we get;
z = (0.65 - 0.6) / √[0.6 × 0.4 / 469]
z = 1.0182
P(p > 0.65) = P(z > 1.0182)
Using the standard normal table, we get; P(z > 1.0182) = 0.1548
Therefore, the probability that the sample proportion of private banks will be greater than 65% is 0.1548 (rounded to four decimal places).
Hence, the answer is 0.1548.
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Solve the inequality
x - 4/5 > 1/5
x - 4/5 > 1/5
+4/5 +4/5 add 4/5 on each sides, 4/5s will cancel on the left side.
__________ solve for 1/5 + 4/5, which is 1.
x > 1, is the final answer.
hope this helps :)
Answer:
x>1
Step-by-step explanation:
how do you solve this??
Answer:
4x+50=90 being complementary
4x=90-50
x=40/4=10
value of x=10°
Answer: 10
Step-by-step explanation:
50-90= 40
40/4 = 10
A statistical analysis of the wait (in minutes) at the checkout line of a certain supermarket yields the probability distribution in the table. What is the probability of waiting more than 5 minute
?
The probability of waiting more than 5 minutes at the checkout line of a certain supermarket is 0.35.
This can be calculated by adding the probabilities of waiting 6 minutes (0.10) and 7 minutes (0.25).
The probability distribution table shows that the probability of waiting 0 minutes is 0.50, the probability of waiting 1 minute is 0.20, the probability of waiting 2 minutes is 0.10, and the probability of waiting 3 minutes is 0.05. The probability of waiting more than 5 minutes is the sum of the probabilities of waiting 6 minutes, 7 minutes, and so on. The probability of waiting 6 minutes is 0.10, and the probability of waiting 7 minutes is 0.25. Therefore, the probability of waiting more than 5 minutes is 0.10 + 0.25 = 0.35.
In other words, there is a 35% chance that a customer will wait more than 5 minutes at the checkout line of this supermarket.
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The year-end balance sheet of Star Inc. shows total assets of $6,617 million, operating assets of $5,253 million, operating liabilities of $2,822 million, and shareholders' equity of $2,950 million.
The company's year-end net operating assets are:
$9,39 million
$5,253 million
$2,431 million
$8,075 million
None of these are correct.
If the year-end balance sheet of Star Inc. shows total assets of $6,617 million, operating assets of $5,253 million, operating liabilities of $2,822 million, and shareholders' equity of $2,950 million, the company's year-end net operating assets are $2,431 million. Therefore, the correct answer is option C, $2,431 million.
Net operating assets refer to the difference between operating assets and operating liabilities. In this case, the operating assets of Star Inc. are $5,253 million, and the operating liabilities are $2,822 million. Therefore, the year-end net operating assets are:
Net operating assets = Operating assets - Operating liabilities
Net operating assets = $5,253 million - $2,822 million
Net operating assets = $2,431 million
Therefore, the correct answer is option C, $2,431 million.
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can someone help me on this question?
Answer:
diameter 33
radius 66
area 360
Find the area of the shaded region. Use the pin button on the calculator. Round to the nearest whole number. 14 70°
Answer:
The area is approximately [tex]588cm^2[/tex]
Step-by-step explanation:
Given
See attachment for figure
Required
The area of the shaded region
The shaded region is as follows:
A major segmentA triangleFirst, calculate the area of the major segment using:
[tex]Area = \frac{\theta}{360} * \pi r^2[/tex]
Where
[tex]r = 14[/tex]
[tex]\theta = 360 - 70 =290[/tex]
So, we have:
[tex]A_1 = \frac{290}{360} * 3.14 * 14^2[/tex]
[tex]A_1 = 495.7711[/tex]
Next, the area of the triangle using:
[tex]Area = \frac{1}{2}ab \sin C[/tex]
Where
[tex]a=b=r = 14[/tex]
[tex]C = 70^\circ[/tex]
So, we have:
[tex]A_2 = \frac{1}{2} * 14 * 14 * sin(70)[/tex]
[tex]A_2 = 92.0899[/tex]
So, the area of the shaded region is:
[tex]Area = A_1 + A_2[/tex]
[tex]Area = 495.7711 + 92.0899[/tex]
[tex]Area = 587.8610[/tex]
[tex]Area \approx 588[/tex]
Listed below are the lead concentrations in measured in different traditional medicines Use a 001 significance level to test the contrat mean lead concentration for all such medicines is less than 13 9 Assume that the sample is a simple random sample 5 95 55 8.5 85 14 155 21 45 105 1 ore: GEE Assuming all conditions for conducting a hypothesis fest are met what are the null ang amative hypotheses?
Null hypothesis (H0): The mean lead concentration for all traditional medicines is equal to or greater than 13.9.
Alternative hypothesis (Ha): The mean lead concentration for all traditional medicines is less than 13.9.
The null and alternative hypotheses for the given scenario can be stated as follows:
Null hypothesis (H0): The mean lead concentration for all traditional medicines is equal to or greater than 13.9.
Alternative hypothesis (Ha): The mean lead concentration for all traditional medicines is less than 13.9.
In other words, the null hypothesis assumes that the population mean lead concentration is 13.9 or higher, while the alternative hypothesis suggests that the population mean lead concentration is less than 13.9.
To test these hypotheses, a hypothesis test can be conducted using the given sample data and a significance level of 0.01 (or 0.001 as mentioned)
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Find the unit rate. Enter your answer as a mixed number.
A fertilizer covers 2/3 square foot in 1/4 hour.
The unit rate is
square feet per hour.
the measure of ∠ABD is (0.12x+68)° and the measure of ∠CBD is (0.13x+24)°. Find the value of x.
PLS HELP
ILL GIVE ALOT OF POINTS
Answer:
could you add a form?
Step-by-step explanation:
Answer:
Step-by-step explanatio
which expression is equivalent to (1 cos(x))2tangent (startfraction x over 2 endfraction) )? sin(x) 1 – cos(x) 1 – cos2(x) (1 cos(x))(sin(x))
The expression (1 - cos(x))^2 * tangent(x/2) is equivalent to (1 - cos^2(x))(sin(x)).
We can simplify the expression by using the trigonometric identity: cos^2(x) + sin^2(x) = 1. Rearranging this identity, we have sin^2(x) = 1 - cos^2(x).
Substituting this identity into the expression, we get (1 - cos^2(x))(sin(x)).
Expanding the expression further, we have sin(x) - cos^2(x)sin(x).
Therefore, the expression (1 - cos(x))^2 * tangent(x/2) is equivalent to (1 - cos^2(x))(sin(x)).
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Which of these is an example of qualitative data?
A how many books your classmates read this year
B. your classmates' favorite books
C. how much a book costs at the store
D. how many pages your favorite book has
i think it depends on if you have enough money to buy the books you need so C would be the answer
Write the percent as a fraction and as a decimal.
5% tax
Fraction (simplified) -
Decimal -
Answer:
Fraction = [tex]\frac{1}{20}[/tex] and Decimal = 0.05
Step-by-step explanation:
Percent means, some number over a hundred.
in this case we have 5%
[tex]\frac{5}{100} = \frac{1}{20}[/tex]
and for decimal form we just move the decimal 2 places to the left because our denominator is a 100 and we get 0.05.
Trigonometry, please answer ASAP, Convert the radian measure to degrees.
12
Answer:
687.549 deg
Step-by-step explanation:
12 rad = 687.549 deg
Plz Help me this is already overdue
Answer:
2nd Column: [tex]\frac{39-78}{25-59}[/tex]
3rd Column:[tex]1.56[/tex]
Step-by-step explanation:
2) For this, just follow the formula given underneath the chart.
3) Here, simplify the equation used in the 2nd Column. [tex]\frac{39-78}{25-50} = \frac{-39}{-25} = -1.56[/tex]
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
A
I’m pretty sure it’s A
Answer:
A, sure
mark me as brainliest plz
Hi guys this isn’t about math but it needs to be said if you get a comment answering your question telling you a link they have has the answers DO NOT PRESS IT! Those people are either sex traffickers and trying to get your IP address or trying to get your personal information. Stay safe
Step-by-step explanation:
Dang, that's crazy! Thanks for letting us know! People be warned!
Answer:
FR
Step-by-step explanation:
don’t interact just report ☝️
Simone and Leah are playing a game with dice. What is the probability Simone rolls a 6 and then Leah rolls an odd number?
Answer:
1. 1/6
2. 1/2
Step-by-step explanation:
A dice has 6 sides. So the sample space for this question =
[1,2,3,4,5,6]
1. From the sample space we can see that 6 occurs only once in a dice
So probability of a 6
= 1/6
2. Number of odds = 3 (1,3,5)
Probability Leah rolls an odd number
= Odd/total
= 3/6
= 1/2
Refering to #14, what is the approximate area of the lake where the resort has ownership responsibility? (Round your answer to the nearest hundredths) (Type in answer my F G F ZH = 71°.x=1.3. y = 20.0 . ZH = 71°,x= 3.0, y = 19.8 2H = 71°, x = 18.9, y 6.5 LH = 71°.x 6.5. y 18.9 14 A lakaside resort has ownership responsibility for the lako from each edge of their shoreline to the cantor of the roughly circular lake. The distance hom shore to the center of the lake is 130 meters and the central anglo respresenting the resorts Warship's 50° a What is the approudmate length of shoreline owned by the resort (Round your answer to the nearest hundredma) po in answer m)
The approximate area of the lake where the resort has ownership responsibility is 711.82 meters².
How to calculate the areaArea of sector = (central angle / 360°) * π * radius²
We know that the central angle is 50°, the radius is 130 meters, and π is approximately equal to 3.14.
Plugging these values into the formula, we get:
Area of sector = (50° / 360°) * 3.14 * 130²
Area of sector = 25/72 * 3.14 * 16900
Area of sector = 15750/22
Area of sector = 711.82 meters²
Therefore, the approximate area of the lake where the resort has ownership responsibility is 711.82 meters².
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Can someone help me with this. Will Mark brainliest.
Answer:
3.3
Step-by-step explanation:
Element X decays radioactively with a half life of 11 minutes. If there are 870 grams
of Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 154 grams?
y = a(.5) t/h
Answer:
27.5 minutes
Step-by-step explanation:
Using,
R/R' = 2ᵃ/ᵇ------------------ Equation 1
From the equation,
R = mass of Element X before radioactive decay, R' = mass of element X after radioactive decay, a = Time taken, b = half life.
Given: R = 870 grams, R' = 154 grams, b = 11 minutes.
Substitute these values into equation 1
870/154 = 2ᵃ/¹¹
(870/154)¹¹ = 2ᵃ
Solve for a
2ᵃ = (5.649)¹¹
2ᵃ = 187061.26
Taking the logarithm of both side,
Log2ᵃ = Log(187061.26)
⇒ a = log(187061.26)/log2
a = 8.272/0.301
a = 27.5 minutes
HELP PLSSSSSSDSSSSSSSSSSSSSSSSSSS
Answer:
8 inches.
Step-by-step explanation:
Just count how many units there are between the two points :)
The effectiveness of a blood pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 42.2 for a sample of size 309 and standard deviation 10.7. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level) Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 99% confidence interval for how much the drug will lower a typical patient's systolic blood pressure is approximately (40.6, 43.8).
How to determine the confidence intervalThe formula for calculating the confidence interval is:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
we need to find the critical value associated with a 99% confidence level. Since the sample size is large (n = 309), we can use the z-distribution.
The critical value for a 99% confidence level is approximately 2.576.
Next, we need to calculate the standard error using the formula:
Standard Error = Standard Deviation / √(Sample Size)
Standard Error = 10.7 / √309
Now we can calculate the confidence interval:
Confidence Interval = 42.2 ± (2.576 * (10.7 / √309))
Calculating the values:
Confidence Interval = 42.2 ± (2.576 * 0.609)
Confidence Interval ≈ 42.2 ± 1.570
Therefore, the 99% confidence interval for how much the drug will lower a typical patient's systolic blood pressure is approximately (40.6, 43.8).
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The perimeter of a rectangle is 20m and the length is x m find the
area of the rectangle in terms of x
Answer:
2(x+y)
Step-by-step explanation:
perimeter=20cm
length=x
Take the radius to be y
area of a rectangle=2(length+width)
therefore area of a rectangle=2(x+y)
Aiden works at a lab with a huge circular particle accelerator. It has a diameter of 8 kilometers. What is the accelerator's radius?
Step-by-step explanation:
Diameter = 2x Radius
Radius = 1/2 Diameter
[tex] = \frac{1}{2} \times 8 \\ = 4km[/tex]
Answer:
Hey mate!
The radius is 4kmHere's how:-
Diameter is 2 times the radius.
That means, the radius is half of the diameter.
So, radius equals 8 divided by 2.
Radius is 4cm.
Hope it helps!
If you have any more queries or didn't understand my answer, let me know in the comments so I can help you!
Match the correct term to its definition.
Fomite E. Portal of exit
Vector F. Zoonotic
Reservoir G. Incubation period
Portal of entry
34. _______ Site where infectious agent enters the body
35. _______ Disease transmitted through an animal bite
36. _______ Population or environment in which pathogen lives and reproduces and on which it depends on its survival
37. _______ Inanimate object covered in disease-causing agent
38. _______ Interval between exposure to pathogen and first signs and symptoms of disease
39. _______ Site where infectious agent leaves the body
40. _______ Living insect or animal involved with disease transmission
The words to fill each gap, respectively, are Portal of entry, Vector, Reservoir, Fomite, Incubation period, Portal of exit, Vector.
Diseases InfectionPortal of entry: It refers to the site or pathway through which an infectious agent enters the body of a susceptible host, allowing the agent to establish an infection.
Vector: A vector is a living organism, usually an insect or animal, that transmits disease-causing pathogens from one host to another. It serves as an intermediate carrier of the infectious agent.
Reservoir: Reservoir refers to a population or environment where a pathogen lives and multiplies, serving as a source of infection. The pathogen depends on the reservoir for its survival and can be transmitted from the reservoir to susceptible individuals.
Fomite: A fomite is an inanimate object or surface that becomes contaminated with disease-causing agents, such as bacteria or viruses. These agents can survive on fomites and potentially transmit infection if they come into contact with a susceptible individual.
Incubation period: The incubation period is the interval between exposure to a pathogen and the appearance of the first signs and symptoms of the disease. It represents the time required for the pathogen to replicate and cause noticeable illness in the infected individual.
Portal of exit: It refers to the site or pathway through which an infectious agent leaves the body of an infected individual, allowing it to be transmitted to other hosts. Examples of portals of exit include respiratory secretions, feces, blood, or skin lesions.
Vector: As mentioned earlier, a vector is a living insect or animal that plays a role in transmitting disease. It can acquire the pathogen from an infected host and transmit it to a susceptible individual, potentially causing disease in the process.
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Solve the system using matrices (row operations) S42 – 4y = - 4, = 12. 2 + 3y How many solutions are there to this system? A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 E. Infinitely many F. None of the above If there is one solution, give its coordinates in the answer spaces below. If there are infinitely many solutions, entert in the answer blank for y and enter a formula for a in terms of t in the answer blank for 1. If there are no solutions, leave the answer blanks for 1 and y empty.
The system has infinitely many solutions.
The given system of equations can be represented using matrices and solved using row operations. Let's rewrite the system in matrix form:
[1 -4] [2] = [-4][1 3] [y] [12]To solve this system using row operations, we'll perform elementary operations to transform the matrix into row-echelon form or reduced row-echelon form. Let's proceed with the operations:
1. R₂ = R₂ - R1
[1 -4] [2] = [-4]
[0 7] [y] [16]
2. R₂ = R2/7
[1 -4] [2] = [-4]
[0 1] [y] [16/7]
3. R₁= R₁ + 4R2
[1 0] [2 + 4(16/7)] = [-4 + 4(16/7)]
[0 1] [y] = [16/7]
Simplifying the calculations, we get:
[1 0] [2 + (64/7)] = [-4 + (64/7)]
[0 1] [y] = [16/7]
This system of equations indicates that x = 2 + (64/7) and y = 16/7. Therefore, there are infinitely many solutions to the system.
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5 cups of coffee and 2 bottles of water cost $12 4 cups of coffee and 7 bottles of water cost $15
help plss
Answer:
one cup of coffee costs $2, while one bottle of water costs $1
Step-by-step explanation:
We can represent this using two equations:
Variable x represents cups of coffee, and variable y represents bottles of water.5x + 2y = 12
4x + 7y = 15
Your answer for the value of x and y should be
x = 2
y = 1
Therefore, one cup of coffee costs $2, while one bottle of water costs $1.
what is 7 8/9 written as a decimal
Kendall bought a vase that was priced at $450. In addition, he had to pay 9% sales tax. How much did he pay for the vase?
Answer:
$436
Step-by-step explanation: