Mrs. Booth is trying to building a pool with the following dimensions:
4x^2 +15
8x^2 + 10
8x^2
The following polynomial represents the perimeter of the pool, ax^2 + bx + c. Find the values of a, b, and c that represent
the perimeter of the perimeter of the pool
Answers
The values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.
Step 1: Add the three dimensions together to find the total length of one side of the perimeter:
(4x^2 + 15) + (8x^2 + 10) + (8x^2) = 20x^2 + 25
Step 2: Since the perimeter has 4 equal sides (it's a rectangle), multiply the total length of one side by 4:
Perimeter = 4(20x^2 + 25) = 80x^2 + 100
Now, compare the perimeter polynomial with the general form ax^2 + bx + c:
80x^2 + 100 = ax^2 + bx + c
From this comparison, you can see that:
a = 80
b = 0 (since there is no term with x)
c = 100
So, the values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.
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Related Questions
PLEASE HELP ASAP!!!! A ball is thrown up in the air from the top of a 48 ft. building. The height of the ball, h(t), after t seconds is given by the equation h(t) = -16t2 + 32t + 48 1) What is the maximum height of the ball? 2) At what time does the ball reach the maximum height? 3) For how long is the ball above the ground? 4) When does the ball hit the ground? Explain your solutions for this context.
Answers
Answer:
1) h(max) = 64 ft
2) t = 1 s
3) t(in air) = 3 s
4) just after 3 s
Step-by-step explanation:
The height f the ball is:
h(t) = -16*t² + 32*t + 48
Maximum height is when V(y) = 0
D(h)/dt = V(y) = -16*2*t + 32
V(y) = 0 -32*t + 32 = 0
2) t = 1 s time to reach maximum height
Plugging this value in equation h(t) = -16*t² + 32*t + 48
h(max) = -16*(1)² + 32*(1) + 48
1) h(max) = 16 + 48 = 64 ft
3) In equation h(t) = -16*t² + 32*t + 48
when h(t) = 0 we find time of the ball in air
16*t² - 32*t - 48 = 0 a second degree equation solving for x
x₁,₂ = 32 ± √( (32)² + 4*48*16) / 32
x₁,₂ = (32 ± 64 )/32
we dismiss negative x ( negative time)
x₂ = 32 + 64 /32
x₂ = 3 s
4) the ball hit the ground just at 3 scond after its thrown
The ball is 3 s in the air ( touch the ground just in that moment)
Solve the following system of equations using substitution (Enter your answer as an ordered pair, including the parentheses and comma.)
-3x+6y=12
2y=x+4
Answers
The system of equations has infinite solutions, both equations represent the same line.
How to solve the system of equations?
Here we have the following system of equations:
-3x+6y=12
2y=x+4
And we want to solve this by substitution, first, we can rewrite the first equation as:
-3x + 3*(2y) = 12
Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:
-3x + 3*(x + 4) = 12
Now we can solve this for x.
-3x + 3x + 12 = 12
12 = 12
So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).
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A machine that fills cereal boxes is supposed to be calibratedso that the mean fill weight is 12 oz. Let μ denote the true mean fill weight. Assumethat in a test of the hypotheses H0 : μ =12 versus H1 : μ≠ 12, the P-value is 0.4a) Should H0 be rejected on thebasis of this test? Explain. Check all that are true.NoYesP = 0.4 is not small.Both the null and the alternate hypotheses are plausible. The null hypothesis is plausible and the alternate hypothesis isfalse.P = 0.4 is small.
Answers
No, We cannot reject the null hypothesis H0: μ = 12 based on the given P-value of 0.4.
Should H0 be rejected on the basis of this test?Since the P-value is 0.4, which is not small, we cannot reject the null hypothesis H0: μ = 12 at the significance level α = 0.05.
The P-value is the probability of observing a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true. In this case, a P-value of 0.4 means that the observed test statistic is not very unusual under the assumption that the true mean fill weight is 12 oz.
Therefore, we do not have sufficient evidence to reject the null hypothesis and conclude that the machine is not calibrated to produce boxes with an average fill weight of 12 oz.
In summary, we cannot reject the null hypothesis based on the given P-value of 0.4. Therefore, the answer is "No" to the question "Should H0 be rejected on the basis of this test?"
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Don invests $12,000 into an account that pays 8.25% simple interest. How much interest does his account earn after 4 years?
Answers
Answer:
$3960
Step-by-step explanation:
Given parameters:
Principal = $12,000
Simple interest = 8.25%
Time = 4yrs
Unknown:
Interest earned = ?
Solution:
To solve this problem, we have to use the simple interest formula shown below:
Simple interest = \(\frac{PRT}{100}\)
P is the principal
R is the rate
T is the time
Now insert the parameters and solve;
Simple interest = \(\frac{12000 x 8.25 x 4}{100}\) = $3960
hellllllllllllllllllllllllpppppppppppppppppppppppp
Answers
Answer:
A) 200 students
B) 24
C) 46%
D) 46% are driven by car
Step-by-step explanation:
A slab 150 PCF concrete is to be poured 20 feet above an existing floor at depth of 6 inches at a temp of 90 degrees and a pure rate of 10 feet per hour. what is the expected VERTICAL load? a) 943.333 PSF b) 943.333 PCF c) 150 PSF d) 75 PCF e) 75 PSF
Answers
The correct answer to the question is option d) 75 PCF.
To calculate the expected vertical load, we need to consider the weight of the concrete slab and the additional load due to the concrete's temperature and pouring rate. The weight of the slab can be calculated by multiplying the density of the concrete (150 PCF) by the depth (6 inches) and the area (1 square foot). This gives us a weight of 75 pounds per square foot (PSF).
The temperature and pouring rate do not directly affect the vertical load. The temperature and pouring rate are factors that may affect the structural integrity of the slab or the time it takes for the concrete to fully cure. However, they do not contribute to the actual load borne by the slab itself. Therefore, the correct answer is 75 PCF, as it represents the weight of the concrete slab alone.
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Q.4 What is the difference between price floors and price ceiling? Give example and illustrate graphically in support of your answer.
Answers
A price floor is a law that limits the minimum price at which a good, service, or factor of production can be sold while a price ceiling is a regulation that limits the maximum price at which a good, service, or factor of production can be sold
Price floors are commonly implemented to support producers, while price ceilings are typically put in place to protect consumers from higher prices that might result from shortages or monopolies.
Example of Price Floor:Agricultural subsidies are a common example of price floors. Government price floors ensure that farmers receive a minimum price for their crops.
If the market price of wheat falls below the government-established price floor, the government may buy the excess supply at the guaranteed price, ensuring that farmers are able to make a profit. If there is a price floor, the minimum price is set above the equilibrium price.
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Isosceles trapezoid EFGH has area 80 cm ^2, height 20 cm and legs 22 cm. One of the bases is 5 cm. How long is the remaining base ?
Answers
Answer:
3
Step-by-step explanation:
A = \(\frac{base1 + base2}{2}\) x h Formula
\(\frac{base1 + 5}{2}\) x 20 = 80 Substitution
\(\frac{base1 + 5}{2}\) = 4 Work (divide by 20, multiply by 2, subtract 5)
base1 + 5 = 8
base1 = 3 Solution
a continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n) probability distribution. a. normal b. uniform c. exponential d. poisson
Answers
A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event, is an exponential probability distribution.
The probability density function or pdf of the exponential distribution is given by the formula
\($$f(x) = \begin{cases} \lambda e^{-\lambda x} & \text{for } x \ge 0 \ 0 & \text{otherwise} \end{cases}$$\)
where λ is the rate parameter and e is the natural logarithm base.
The pdf gives the probability distribution of a random variable x, which represents an exponential distribution.
The exponential distribution is a continuous probability distribution that simulates the interval between events with an average occurrence rate that is constant.
In this distribution, the likelihood that an event will occur in the future is independent of when that event occurred in the past
The time interval between customers joining a line, the interval between device failures, or the separation between two places in space are all frequently modeled using the exponential distribution.
The rate parameter, which denotes the average number of events per unit of time or space, is what defines the exponential distribution.
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Please help me I need to finish this :)
Answers
There are 65 chairs set up for a movie. They are arranged into 5 rows. How many chairs are in each row?, don’t answer if u don’t know it
Answers
Answer:
13 chairs in each row
Step-by-step explanation:
divide 65 by 5 to get 13
Answer: 13
Step-by-step explanation: 65 divided by 5
Sonequa has two containers one in the shape of a cylinder and the other in the shape of a cone the two containers of equal radii and equal Heights she investigated the relationship between the volume of the cone and the cylinder by transferring water between the two containers which of the following claims is most likely to be supported using the result of sonequa investigation
Answers
Answer:35
Step-by-step explanation:
The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.
The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.
Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.
So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”
In 1990 Dallas, Texas, had an estimated population of 1,006,877. By 2000 the population had increased. 18 1/20%. What was the estimated population in 2000 for Dallas, Texas? Find the answer to the nearest whole number
Answers
can anyone answer this?
can anyone answer this
An amazing thing happens when you get
honest with yourself and start doing
what you love, what makes you happy.
You stop wishing for the weekend.
You stop merely looking forward to
Special events. You begin to live in each
moment and you start feeling like a
human being. You just ride the wave that
is life, with this feeling of contentment
and joy. You move fluidly, steadily, clam and greateful.
Hope you like it.
Answers
Answer:
Step-by-step explanation:
thanks im an introvert thats obsessed with learning what more is there in life
This is so amazing wow
simplify
15-1/2 (10z + 6) – 25z
plz hurry
Answers
Answer:
-5z -13 is answer
Step-by-step explanation:
=15+−5z+−3+−25
Combine Like Terms:
=15+−5z+−3+−25
=(−5z)+(15+−3+−25)
=−5z+−13
bye
Answer:
-30z+12
Step-by-step explanation:
A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in. If the container holds 1096 cubic feet of shipped goods, what percent is empty?
Answers
As per the volume of a rectangular prism, it is found that 34.76% of the container is empty.
Volume of a rectangular prism
The volume of the rectangle prism is calculated by multiplying the length, breadth and height of the prism.
The formula for the volume of rectangle prism is
V = l x w x h
where
l represents the length
w represents the width
h represents the height
Given,
A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in.
Here we need to find if the container holds 1096 cubic feet of shipped goods, what percent is empty
According to the given question,
Let us consider the length is 30ft, Width is 8ft and Height is 7ft.
Here the value 3ft refers the depth.
That one is also multiplied with the volume.
Therefore, the volume of the container is
=> 8 x 7 x 30
=> 1680
Therefore, the volume of the container is 1680 cubic feet.
So, here we have to percentage of the empty space for that we have to find the difference of them and convert it into percentage,
=> 1680 - 1096
=> 584
The percent of empty space is,
=> x% of 1680 = 584
=> x% = 584/1680
=> x% = 0.3476
=> x = 34.76
Therefore, 34.76% of rectangular prism container is empty.
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b Identify the coefficient and the number of terms in the
following expression.
15x2 + 8
A.) Coefficient: x, number of terms: 1
B.) Coefficient: 2, number of terms: 2
C.) Coefficient: 8, number of terms: 1
D.) Coefficient: 15, number of terms: 2
Answers
Two risky gambles were proposed at the beginning of chapter 14: Game 1: Win $30 with probability of 0.5 Lose $1 with probability of 0.5 Game 2: Win $2000 with probability of 0.5 Lose $1900 with probability of 0.5 How much would you pay (or have to be paid) to take part in either game
Answers
For Game 1:
Expected value = ($30 × 0.5) + (−$1 × 0.5) = $14.50
Therefore, on average, someone playing Game 1 would expect to win $14.50 per game.
For Game 2:
Expected value = ($2000 × 0.5) + (−$1900 × 0.5) = $50
Therefore, on average, someone playing Game 2 would expect to win $50 per game.
The amount someone would pay (or have to be paid) to take part in either game depends on their personal risk tolerance and their preferences for expected value versus potential loss.
If someone is risk-averse, they may be willing to pay a premium to participate in Game 1, as it has a lower potential loss of only $1, and they may be willing to forego the higher expected value of Game 2 for the added security.
On the other hand, someone who is risk-seeking may be willing to pay more to participate in Game 2, as they are willing to take on the higher potential loss of $1900 in exchange for the higher expected value.
Ultimately, the amount someone would pay (or have to be paid) to take part in either game is subjective and depends on their individual risk preferences.
The expected value for Game 1 is $14.50, you would be willing to pay up to $14.50 to participate in the game. For Game 2, with an expected value of $50, you would be willing to pay up to $50 to participate in the game.
To determine how much you would pay or have to be paid to take part in either Game 1 or Game 2, we need to calculate the expected value of each game. The expected value is the average outcome of the game if it were played many times, and it's calculated using the probabilities and potential winnings or losses.
For Game 1, the expected value (EV1) can be calculated as follows:
EV1 = (Win amount x Probability of winning) + (Loss amount x Probability of losing)
EV1 = ($30 x 0.5) + (-$1 x 0.5)
EV1 = $15 + (-$0.50)
EV1 = $14.50
For Game 2, the expected value (EV2) can be calculated similarly:
EV2 = (Win amount x Probability of winning) + (Loss amount x Probability of losing)
EV2 = ($2000 x 0.5) + (-$1900 x 0.5)
EV2 = $1000 + (-$950)
EV2 = $50
Now that we have the expected values, we can determine how much to pay or be paid to take part in each game. Since the expected value for Game 1 is $14.50, you would be willing to pay up to $14.50 to participate in the game. For Game 2, with an expected value of $50, you would be willing to pay up to $50 to participate in the game.
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Simplify the expression -15m + 9m
Answers
Answer:
-6M
Step-by-step explanation:
djdurjjrfjfrjrjrjrf
consider the following binomial experiment: a study in a certain community showed that 5% of the people suffer from insomnia. if there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia? a) 520.00 b) 22.23 c) 50.99 d) 9880.00 e) 49400.00 f) none of the above.
Answers
The number of those who have insomnia has a standard deviation of 22.23.
Given,
People suffer from insomnia = 5%
Total number of people in the community = 10,400
We have to find the standard deviation of the number of people who suffer from insomnia;
Here,
p = 0.05
q = 0.95
n = 10,400
Then,
np = 10400 x 0.05 = 202
Now,
npq = 202 x 0.95 = 494
Standard deviation = √npq = √494 = 22.23
That is,
The standard deviation of the number of people who suffer from insomnia is 22.23
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3.86 x 9.15 = ????
can somebody explain me this question ? <3
Answers
3.86 x 9.15 = 35.319
OR
You could round the numbers first to 1sigfig
3.86 could round to 4
9.15 could round to 9
4 x 9 =36
a committee of four is chosen at random from a group of 6 women and 3 men. find the probability that the committee contains at least one man.
Answers
The probability that the committee contains at least one man is 1 - (probability of selecting only women).
To find the probability, we need to determine the total number of possible committee combinations and the number of combinations with at least one man. There are 9 people (6 women + 3 men) to choose from, and we want to choose a committee of 4.
Total combinations = C(9,4) = 9! / (4!(9-4)!) = 126
Combinations of only women = C(6,4) = 6! / (4!(6-4)!) = 15
To find the probability of at least one man, we'll subtract the probability of selecting only women from 1:
P(at least one man) = 1 - (15/126) = 1 - 0.119 = 0.881
The probability that the committee contains at least one man is approximately 0.881, or 88.1%.
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What is the total length of the tadpoles that are 1/8-inch and 1/4-inch long?
7/8 inches
1 1/8 inches
5/8 inches
3/8 inches
Answers
The dot plot shows the frequency or length of the tadpoles
The total length of the tadpoles that are 1/8-inch and 1/4-inch long is 7/8 inches
How to determine the total length?From the dot plot, we have the following parameters:
3 tadpoles have a length of 1/82 tadpoles have a length of 1/4So, the total length is:
Total = 3 * 1/8 + 2 * 1/4
Evaluate the product
Total = 3/8 + 1/2
Rewrite as;
Total = 3/8 + 4/8
Evaluate the sum
Total = 7/8
Hence, the total length of the tadpoles that are 1/8-inch and 1/4-inch long is 7/8 inches
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I really need help. I dont understand
Answers
Answer:
D
Step-by-step explanation:
An observer stationed 20 m away from a tall
of elevation of the top of the building is 68° and the angle of depression of
its foot is 50 degrees. Calculate the height of the building.
Answers
Answer:
Step-by-step explanation:I don't say you must have to mark my ans as brainliest but my friend if it has really helped you plz don't forget to thank me...
Which table represents a linear function?
Answers
translations can be moved along an vector at any time and still result in the same image true or false ?
Answers
Answer:
True................
Answer:
True
Step-by-step explanation:
are these correct? and what’s the answer for #24?
Answers
The equivalent of 0.85 hectogram (hg) is 850 decigram (dg)
How to determine the conversion?The measure is given as:
0.85 hg
As a general rule:
1 hectogram (hg) = 1000 decigram (dg)
So, multiply both sides of the above equation by 0.85
So, we have:
0.85 * 1 hectogram (hg) = 0.85 * 1000 decigram (dg)
Evaluate the product
0.85 hectogram (hg) = 850 decigram (dg)
Hence, the equivalent of 0.85 hectogram (hg) is 850 decigram (dg)
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What is y in this situation?
Answers
Answer: y would be -5
Step-by-step explanation:
raquel wants to make a rectangular garden with a area of 12m, but using the least amount of fencing. Each has to be a whole (ie not decimals). What will the dimensions of the garden be?
Answers
Answer:
Step-by-step explanation:
The dimensions of the garden will be 4m by 3m. To determine the dimensions of the garden, we need to use the formula A = l x w, where A is the area of the garden (12m), l is the length of the garden and w is the width of the garden.
We can then rearrange the formula to solve for either l or w. We can rearrange the formula to solve for l by dividing both sides of the equation by w: A/w = l.
We know that the area is 12m, so we can substitute 12m for A in the equation. We need to find the dimensions that use the least amount of fencing, so let's set w equal to 3m. We can then substitute 3m for w in the equation and solve for l: 12m/3m = 4m.
Therefore, the dimensions of the garden are 4m by 3m.