Answer:
a = 16
b = 8z
Step-by-step explanation:
Expanding the given expression, we get:
(4y + z)^2 = (4y + z) × (4y + z)
= 16y^2 + 8yz + z^2
Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:
a = 16
b = 8z
Therefore, the value of a is 16 and the value of b is 8z.
A cat darts around a room chasing a ball. The cat first travels along the vector −1, 2 and then chases the ball along the vector 2, 6 − . The cat darts after the ball 1.5 times along the vector 4, 3 . This is where the cat catches the ball and chews on it. What vector describes the cat’s final position? Show all your work.
To find the cat's final position, we need to add up all the vectors representing the cat's movements.
The cat first travels along the vector −1, 2.
Next, the cat chases the ball along the vector 2, 6 − , which we can write as (2, 6) − (0, 1) = (2, 5).
Then, the cat darts after the ball 1.5 times along the vector 4, 3, which we can write as 1.5(4, 3) = (6, 4.5).
Finally, the cat's position after catching the ball is the sum of all these vectors:
(-1, 2) + (2, 5) + (6, 4.5) = (7, 11.5)
Therefore, the vector describing the cat's final position is (7, 11.5).
help mif with dis math probles pwees
For this above box plot prompt, the answer are given below.
What is the explanation for the response?Part A
From the box plots, we can see that the Red Team has the least variability and spread of times, followed by the Blue Team and then the Green Team.
The Red Team's box is the smallest, indicating that their times are more tightly clustered together.
Blue Team:
Q1: 75
Q2: 82
Q3: 87
IQR: 12
Upper fence: Q3 + 1.5IQR = 87 + 1.512 = 105
There are no outliers
Green Team:
Q1: 70
Q2: 75
Q3: 80
IQR: 10
Upper fence: Q3 + 1.5IQR = 80 + 1.510 = 95
There is one outlier at 90
Red Team:
Q1: 80
Q2: 83
Q3: 87
IQR: 7
Upper fence: Q3 + 1.5IQR = 87 + 1.57 = 98.5
There are no outliers
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It is claimed that 75% of puppies are house-trained by the time they are 6 months old. To investigate this claim, a random sample of 50 puppies is selected. It is discovered that 42 are house-trained by the time they are 6 months old. A trainer would like to know if the data provide convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The standardized test statistic is z = 1. 47 and the P-value is 0. 708. What conclusion should be made using the Alpha = 0. 05 significance level?
Because the P-value is greater than Alpha = 0. 05, there is convincing evidence that 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is not convincing evidence that 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old
The conclusion should be made using the Alpha = 0. 05 significance level is because the P-value is greater than Alpha = 0.05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The correct answer is B.
The given null hypothesis is that 75% of puppies are house-trained by the time they are 6 months old. The alternative hypothesis is that greater than 75% of puppies are house-trained by the time they are 6 months old.
The test statistic is a z-score, which is calculated by subtracting the hypothesized proportion (0.75) from the sample proportion (42/50 = 0.84), dividing by the standard error of the sample proportion, and then standardizing with respect to the standard normal distribution. The resulting z-score is 1.47.
The P-value is the probability of observing a test statistic as extreme or more extreme than the calculated z-score, assuming the null hypothesis is true. A P-value of 0.708 means that there is a 70.8% chance of observing a sample proportion as extreme or more extreme than 0.84, assuming that 75% of puppies are house-trained by the time they are 6 months old.
Since the P-value is greater than the significance level (alpha) of 0.05, we fail to reject the null hypothesis. In other words, there is not convincing evidence to suggest that greater than 75% of puppies are house-trained by the time they are 6 months old.
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2. A scientist placed 100 bacteria in a petri dish. The number of bacteria triples every 12 hours. What is the equivalent hourly rate?
Let's call the initial number of bacteria in the petri dish as $N_0 = 100$. After 12 hours, the number of bacteria triples, which means there are now $3N_0$ bacteria. After another 12 hours, the number of bacteria triples again, which means there are now $3(3N_0) = 9N_0$ bacteria.
We can see a pattern here that after every 12 hours, the number of bacteria is multiplied by 3. Let's calculate the number of bacteria after 1 hour:
$\sf\implies\:N_1 = N_0 \times 3^{1/12}$
After simplifying:
$\sf\implies\:N_1 = 100 \times 3^{1/12}$
Using a calculator, we can find that $\sf\:3^{1/12} \approx 1.1548$. Therefore:
$\sf\implies\:N_1 \approx{\boxed{115.48}}$
So the equivalent hourly rate at which the number of bacteria is increasing is approximately 15.48% per hour.
In general, if the number of bacteria triples every $t$ hours, the equivalent hourly rate can be calculated as:
$\sf\implies\:r = 3^{1/t} - 1$
where $r$ is the hourly rate expressed as a decimal.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
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How do you solve the cube root function of x²/³ = 16?
The cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
The given function is x³=16.
Here, the given function can be written as
[tex]x=\sqrt[3]{16}[/tex]
[tex]x=\sqrt[3]{2\times2\times2\times2}[/tex]
[tex]x=\sqrt[3]{2^3\times2}[/tex]
[tex]x=2\sqrt[3]{2}[/tex]
Therefore, the cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
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"Your question is incomplete, probably the complete question/missing part is:"
How do you solve the cube root function of x³=16.
Greg, Harry and Ian share their electricity bill in the ratio 2:4:5.
how much dies each of them pay when their electricity bill are 1) 110$ 2) 165$ 3) 352$
pls answer quickly
The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:
1) $20, $40, $50
2) $30, $60, $75
3) $64, $128, $160
1. How much do they pay for a $110 electricity bill?To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.
Total bill: $110
The total ratio is 2+4+5=11.
Greg's share: (2/11) * $110 = $20
Harry's share: (4/11) * $110 = $40
Ian's share: (5/11) * $110 = $50
Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.
2. How much do they pay for a $165 electricity bill?Total bill: $165
The total ratio is still 2+4+5=11.
Greg's share: (2/11) * $165 = $30
Harry's share: (4/11) * $165 = $60
Ian's share: (5/11) * $165 = $75
Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.
3. How much do they pay for a $352 electricity bill?Total bill: $352
The total ratio remains the same: 2+4+5=11.
Greg's share: (2/11) * $352 = $64
Harry's share: (4/11) * $352 = $128
Ian's share: (5/11) * $352 = $160
Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.
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find the angle between the vectors. (round your answer to two decimal places.) u = (4, 3), v = (5, −12), u, v = u · v
The angle between u and v is approximately 104.66 degrees. To find the angle between two vectors u and v, we can use the dot product formula:
cos(theta) = (u · v) / (||u|| ||v||)
where ||u|| and ||v|| are the magnitudes of u and v, respectively.
First, let's compute the dot product of u and v:
u · v = [tex](4)(5) + (3)(-12) = 20 - 36 = -16[/tex]
Next, we need to find the magnitudes of u and v:
[tex]||u||[/tex] = sqrt([tex]4^2[/tex] + [tex]3^2[/tex]) = 5
[tex]||v||[/tex] = sqrt([tex]5^2[/tex] + (-12[tex])^2[/tex]) = 13
Now we can substitute these values into the formula for cos(theta):
cos(theta) = [tex](-16) / (5 * 13) = -0.246[/tex]
To find the angle theta, we take the inverse cosine of cos(theta):
theta = [tex]cos^-1[/tex](-0.246) = 104.66 degrees
Therefore, the angle between u and v is approximately 104.66 degrees.
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The diagonal of rectangle ABCD is 42. 3 cm, and it forms an angle of 53° with the shorter side AD of the rectangle
Using trignometric functions the shorter side AD has length a ≈ 25.75 cm and the longer side AB has length b ≈ 34.25 cm.
In the given scenario, we have a rectangle with sides AD and AB. The length of AD is represented as 'a' and is approximately 25.75 cm, while the length of AB is denoted as 'b' and is approximately 34.25 cm. The diagonal AC of the rectangle has a length of 42.3 cm and forms an angle of 53° with AD.
To find the lengths of sides a and b, we can utilize trigonometric functions, specifically cosine and sine. Since we have the length of the diagonal AC and the angle it forms with AD, we can set up the following equations:
cos(53°) = a/42.3
sin(53°) = b/42.3
By rearranging the equations, we can solve for a and b:
a = 42.3 * cos(53°) ≈ 25.75 cm
b = 42.3 * sin(53°) ≈ 34.25 cm
By substituting the given values into the equations, we can determine that the length of AD (a) is approximately 25.75 cm, and the length of AB (b) is approximately 34.25 cm.
These calculations allow us to find the side lengths of the rectangle based on the given information about the diagonal length and angle. Understanding trigonometric relationships enables us to solve geometric problems involving angles, sides, and diagonals in various shapes and configurations.
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Find the radius of the circle with equation x² + y² = 12²
Answer:
The equation of a circle with center (a,b) and radius r is given by:
(x - a)² + (y - b)² = r²
Comparing this to the equation x² + y² = 12², we can see that the center of the circle is (0,0) and the radius is 12. Therefore, the radius of the circle is 12 units.
4+5x > 19
how to do
Answer:
x>3
Step-by-step explanation:
i assume you're solving for x so,
1) rearrange terms,
5x+4>19
2)subtract 4 from both sides
5x+4-4>19-4
3) Simplify
5x>15
4) divide both sides by 5, because they are same factor
\frac{5x}{5} > \frac{15}{5}
5) Finally, the answer is
x>3
Complete parts a through c for the given function. 2 f(x) = xº(x-2) on [ -2,2] O A. The local minimum/minima is/are at x = and there is no local maximum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. The local maximum/maxima is/are at x = and the local minimum/minima is/are at x = (Use a comma to separate answers as needed. Type integer or simplified fractions.) C. The local maximum/maxima is/are at x = 1 and there is no local minimum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O D. There is no local maximum and there is no local minimum. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum is at x= and there is no absolute minimum. (Use a comma to separate answers as needed. Type integers or simplified fractions.) B. The absolute maximum is at x = and the absolute minimum is at x= 11. (Use a comma to separate answers as needed. Type integer or decimals rounded to two decimal places as needed.) O C. The absolute minimum is at x= and there is no absolute maximum. (Use a comma to separate answers as needed. Type integers or simplified fractions.)
The absolute maximum occurs at x = -2 and the absolute minimum occurs at x = 0 and x = 2 and The absolute maximum is at x = -2 and the absolute minimum is at x = 0, 2.
a. The local minimum is at x=2 and there is no local maximum.
b. The local maximum is at x=1 and the local minimum is at x=-2 and x=2.
c. The absolute maximum is at x=0 and the absolute minimum is at x=2.
(Note: To find the absolute maximum and minimum, we need to evaluate the function at the critical points and endpoints of the interval. The critical points are x=0 and x=2, and the endpoints are x=-2 and x=2. The absolute maximum is the largest value among these, which is f(0)=0. The absolute minimum is the smallest value among these, which is f(2)=-4.)
Given the function f(x) = x²(x - 2) on the interval [-2, 2]:
A. To find the local minima and maxima, we need to take the first derivative and find its critical points.
f'(x) = 3x² - 4x
Solving for x, we get x = 0 and x = 4/3.
However, x = 4/3 is not within the interval [-2, 2], so the only critical point within the interval is x = 0.
There is a local minimum at x = 0, and no local maximum. Therefore, the answer is:
A. The local minimum is at x = 0 and there is no local maximum. (Type an integer or a simplified fraction.)
B. For the absolute maximum and minimum, we need to evaluate the function at the endpoints and the critical point within the interval.
f(-2) = (-2)²(-2 - 2) = 16
f(0) = (0)²(0 - 2) = 0
f(2) = (2)²(2 - 2) = 0
The absolute maximum occurs at x = -2 and the absolute minimum occurs at x = 0 and x = 2. The answer is:
B. The absolute maximum is at x = -2 and the absolute minimum is at x = 0, 2. (Use a comma to separate answers as needed. Type integers or simplified fractions.)
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There are 30 chocolates in a box, all identically shaped. There are 5 filled with coconut and 10 filled with caramel. The other 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. What is the probability of selecting a caramel chocolate both times? Are the events of selecting a caramel chocolate on your first pick and selecting a caramel chocolate on your second pick indipendent or dependent? Round to three decimal places
The probability of selecting a caramel chocolate both times is approximately 0.103.
The events of selecting a caramel chocolate on each pick are dependent since the probability of the second pick depends on the outcome of the first pick.
First, we need to calculate the probability of selecting a caramel chocolate on the first pick, which is 10/30 or 1/3. After eating the first chocolate, there will be 29 chocolates left in the box, and 9 of them will be caramel-filled. So, the probability of selecting a caramel chocolate on the second pick, given that the first pick was a caramel chocolate and it was eaten, is 9/29.
To find the probability of selecting a caramel chocolate both times, we need to multiply the probabilities of the two events together, since they are independent:
P(caramel and caramel) = P(caramel on first pick) * P(caramel on second pick | first pick was caramel)
= (1/3) * (9/29)
= 0.103 or 0.1034 rounded to four decimal places.
Therefore, the probability of selecting a caramel chocolate both times is approximately 0.103.
The events of selecting a caramel chocolate on the first pick and selecting a caramel chocolate on the second pick are dependent events since the probability of selecting a caramel chocolate on the second pick changes based on what was selected on the first pick.
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All the 4-digit numbers you could make using seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8
Using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
To create a 4-digit number using these seven square tiles, we have to consider the following:
- The first digit cannot be 2 because then the number would only have three digits.
- We can choose any of the remaining six tiles for the first digit, which means there are 6 choices.
- We can choose any of the seven tiles for the second digit, which means there are 7 choices.
- We can choose any of the remaining six tiles for the third digit, which means there are 6 choices.
- We can choose any of the remaining five tiles for the fourth digit, which means there are 5 choices.
Therefore, the total number of 4-digit numbers we can make is:
6 x 7 x 6 x 5 = 1260
So, using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
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A rectangle garden measuring 13 m x 50 m it’s a have a gravel pathway of constant with built all around it. There is enough gravel to cover 80 meters. Answer and equality that represents all possible with (w) in meters of the pathway?
The width of the gravel pathway is 7 meters.
The length of the rectangular garden is 50m and the width is 13m. Let's assume the width of the gravel pathway to be w meters.
The length of the rectangular garden including the two widths of the pathway would be 50+2w meters, and the width including the two widths of the pathway would be 13+2w meters.
The area of the rectangular garden including the pathway is the product of the length and the width:
(50+2w)(13+2w)
We can now set up an equation using the area of the garden and the amount of gravel available:
(50+2w)(13+2w) - 50*13 = 80
Simplifying this equation gives:
4w^2 + 126w - 3196 = 0
This is a quadratic equation that we can solve for w using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 4, b = 126, and c = -3196.
Plugging in these values and solving for w gives:
w = 7 or w = -22.75
Since the width of the pathway cannot be negative, the only valid solution is w = 7.
Therefore, the width of the gravel pathway is 7 meters.
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Which function is increasing and has a domain of (1,infiniti)?
A. F(x) = log(x - 1) + 2
B. F(x) = -log(x - 2) + 1
C. F(x) = -log(x - 1) + 2
D. F(x) = log(x - 2) + 1
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
To determine the increasing function with the specified domain, let's analyze each option:
A. F(x) = log(x - 1) + 2
This function is increasing because the logarithm of a positive number is always increasing. The domain is (1, infinity), which matches the requirement.
B. F(x) = -log(x - 2) + 1
This function is decreasing because the negative sign in front of the logarithm inverts the increase. The domain is (2, infinity), which does not match the requirement.
C. F(x) = -log(x - 1) + 2
This function is also decreasing because of the negative sign in front of the logarithm. The domain is (1, infinity), which matches the requirement, but the function is not increasing.
D. F(x) = log(x - 2) + 1
This function is increasing because the logarithm of a positive number is always increasing. However, the domain is (2, infinity), which does not match the requirement.
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
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solve the triangle.
angle C = 16°
angle c = 32
angle b = 92
Find angle B, a, and A
Answer:
Step-by-step explanation:
To solve the triangle, we can use the law of sines and the fact that the sum of the angles in a triangle is 180 degrees.
First, we can find angle A by using the fact that the sum of the angles in a triangle is 180 degrees:
A = 180 - B - C
A = 180 - 92 - 16
A = 72 degrees
Next, we can use the law of sines to find side a:
a/sin(A) = c/sin(C)
a/sin(72) = 32/sin(16)
a = (32*sin(72))/sin(16)
a ≈ 89.4
Finally, we can use the fact that the sum of the angles in a triangle is 180 degrees to find angle B:
B = 180 - A - C
B = 180 - 72 - 16
B = 92 degrees
Therefore, the triangle has angle B = 92 degrees, angle A = 72 degrees, and side a ≈ 89.4.
The hottest day of the year in Buenos Aires, Argentina, on average, is January 7, when the average high temperature is 37° C. The coolest day of the year has an average high temperature of 17° C. Use a trigonometric function to model the temperature in Buenos Aires, Argentina using 365 days as the length of a year. Remember that January 7 is in the summer in Buenos Aires
The temperature in Buenos Aires can be modeled using the equation T(t) = 5 sin(2π(t - 182.5)/365) + 27, where t is the number of days since January 1.
How to model temperature in Buenos Aires?To model the temperature in Buenos Aires using a trigonometric function, we can use the sine function.
First, we need to find the amplitude, period, phase shift, and vertical shift.
Amplitude: The difference between the maximum and minimum temperatures is (37 - 17) / 2 = 10 degrees, so the amplitude is 10/2 = 5 degrees.Period: The period of the function is 365 days, which is the length of a year.Phase shift: January 7 is in the summer, so we want to shift the function to the right by half a year (182.5 days).Vertical shift: The average temperature over the year is (37 + 17) / 2 = 27 degrees, so the vertical shift is 27 degrees.Putting it all together, the equation for the temperature in Buenos Aires as a function of time is:
T(t) = 5 sin(2π(t - 182.5)/365) + 27
Where t is the number of days since January 1 and T(t) is the temperature in degrees Celsius.
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THE PUZZLE
This problem gives you the chance to
Solve and reason abxut equations
A magazine contains a puzzle.
Each symbol represents a
number
>
28
>
24
Different symbols have
different values.
N
42
The sum of each row is given
at the side of the table.
>
36
Try to find out the value for each symbol:
heart-. Spade - 1. Club - 4 diamond
The value for each symbol is: Heart - 9, Spade - 3, Club - 6, Diamond - 8.
How to determine symbol values?To solve the puzzle and find the value for each symbol, we can use the given information.
First, we observe that the sum of each row is provided on the side of the table. Therefore, we can use this information to find the value for each symbol.
Let's assign variables to each symbol: heart (H), spade (S), club (C), and diamond (D).
From the first row, we have H + S + C = 28.
From the second row, we have H + D = 24.
From the third row, we have H + S + C + D = 36.
We can solve this system of equations to find the value for each symbol. By substituting the values, we can deduce that heart (H) is equal to 10, spade (S) is equal to 7, club (C) is equal to 11, and diamond (D) is equal to 14.
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I NEED SERIUOS HELPPP
The regression line equation, can be found to be y = 0.90x - 3.79
How to find the regression equation ?Find the slope using the slope formula :
m = ( 5 x 1944 - 98 x 69 ) / ( 5 x 2580 - 98² )
m = ( 9720 - 6762 ) / ( 12900 - 9604 )
m = 2958 / 3296
= 0.8975
Then find the y - intercept :
b = ( 69 - 0. 8975 x 98) / 5
b = ( 69 - 87. 945) / 5
b = - 18. 945 / 5
= - 3.789
The regression equation is:
y = 0.90x - 3.79
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Please help solve
Use Mean value theorem to prove √ 6a+3
1. Using methods other than the Mean Value Theorem will yield no marks
The Mean Value Theorem can be used to prove that the square root of 6a+31 lies between two values, where one value is equal to the function evaluated at a divided by the square root of 6, and the other value is equal to the function evaluated at a plus one divided by the square root of 6.
Let f(x) = √(6x + 31) and choose any value of a such that a > -31/6.
By the Mean Value Theorem, there exists some c in (a, a+1) such that:
f(a+1) - f(a) = f'(c)
where f'(c) is the derivative of f(x) evaluated at c.
We have:
f'(x) = 3/√(6x+31)
Thus, we can write:
f(a+1) - f(a) = (3/√(6c+31)) * (a+1 - a)
Simplifying, we get:
f(a+1) - f(a) = 3/√(6c+31)
Since a < c < a+1, we have:
a < c
√(6a+31) < √(6c+31)
√(6a+31) < (3/√(6c+31)) * √(6c+31)
√(6a+31) < f(a+1) - f(a)
Therefore, we can write:
f(a) < √(6a+31) < f(a+1)
f(a) = √(6a + 31)/√6
f(a+1) = √(6(a+1) + 31)/√6
Substituting these values, we get:
(√(6a + 31))/√6 < √(6a+31) < (√(6(a+1) + 31))/√6
Simplifying, we get:
√(6a + 31)/√6 < √(6a+31) < √(6a + 37)/√6
Hence, we have shown that the square root of 6a+31 lies between two values, where one value is equal to the function evaluated at a divided by the square root of 6, and the other value is equal to the function evaluated at a plus one divided by the square root of 6.
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Kyra has 2 plates, 2 cups, and 2 bowls. If she chooses one of each randomly, what is the probability that the plate, cup, and bowl she chooses will all be blue?
0.167
0.333
0.125
0.083
The probability is 0.125
To solve this problemThere are a total of 2 × 2 x 2 = 8 possibilities of one plate, one cup, and one bowl that Kyra can select if she has two plates, two cups, and two bowls.
We need to figure out how many combinations fit this requirement because we are interested in the likelihood that all three objects are blue. There are 2 × 2 x 2 = 8 potential color combinations if we assume that each item can be either blue or not blue.
There is only one of these eight color pairings in which all three components are blue. P(all three are blue) = 1/8 = 0.125 is the likelihood that Kyra will select one blue plate, one blue cup, and one blue bowl.
So, the probability is 0.125.
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Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x town chairs is R0 -0.0001 +0.042? + Ofe Curare Per vete te lawn chairs daily a) What is the current daily revenue? b) How much would revenue increase ir 3 lawn chairs were sold each day? c) What is the marginal revenue when 50 lawn chairs are sold daily d) Use the answer from part (c) to estimate R(51), R(52) and R153)
The revenue of the chairs sold as per given R(x) = 0.004x³ -0.04x² +0.6x for different conditions are,
The current daily revenue is $2646.
Increase in revenue for 92 chairs sold every day is $185.16
Marginal revenue is $90.6 per lawn chair for 92 chairs sold every day.
Estimated revenue for R(91), R(92) and R(93) is equal to $2555.4 , $2464.8, and $2374.2 respectively.
Daily revenue from sale of x chairs is,
R(x) = 0.004x³ -0.04x² +0.6x
The current daily revenue can be found by evaluating the function at x = 90,
R(90) = 0.004(90)³ - 0.04(90)² + 0.6(90)
= 2916 - 324 + 54
= $2646
Increase in revenue,
⇒ difference between the revenue from selling 92 lawn chairs and the revenue from selling 90 lawn chairs,
R(92) - R(90)
= [0.004(92)³ - 0.04(92)² + 0.6(92)] - [0.004(90)³ - 0.04(90)² + 0.6(90)]
= 3114.752 -338.56 + 55.2 - 2646
= 2831.16 - 2646
= $185.16
Revenue would increase by$185.16 if 92 lawn chairs were sold each day.
The marginal revenue is the derivative of the revenue function,
R'(x) = 0.012x² - 0.08x + 0.6
Marginal revenue when 90 lawn chairs are sold daily,
we can evaluate the derivative at x = 90,
R'(90) = 0.012(90)² - 0.08(90) + 0.6
= $90.6
When 90 lawn chairs are sold daily, the marginal revenue is $90.6 per lawn chair.
Use the answer from above part to estimate the revenue from selling 91, 92, and 93 lawn chairs daily.
Assume that the marginal revenue is approximately constant in a small interval around 90,
Use the linear approximation,
R(91) ≈ R(90) + R'(90)(1)
= $2646 + $90.6
= $2555.4
R(92) ≈ R(90) + R'(90)(2)
= $2646 + 2($90.6)
= $2464.8
R(93) ≈ R(90) + R'(90)(3)
= $2646 + 3($90.6)
= $2374.2
If 91, 92, and 93 lawn chairs were sold daily,
The estimated daily revenue would be $2555.4 , $2464.8, and $2374.2 respectively.
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The above question is incomplete, I answer the question in general according to my knowledge:
Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x town chairs is
R(x) = 0.004x³ -0.04x² +0.6x .
Currently, Pierce sells 90 lawn chairs daily.
a) What is the current daily revenue?
b) How much would revenue increase if 92 lawn chairs were sold each day?
c) What is the marginal revenue when 90 lawn chairs are sold daily
d) Use the answer from part (c) to estimate R(91), R(92) and R(93)
A farm grew 19.8 tons of wheat in 2013. the farm's wheat output increased by 9.8% from 2013-2014, and by 5.1 % from 2014 to 2015. which expression represents a strategy for estimating the farm's output for 2015?
The expression that represents a strategy for estimating the farm's output for 2015 is 1.153w, where w is the farm's wheat output in 2013.
Let w be the farm's wheat output in 2013. We know that the output increased by 9.8% from 2013 to 2014, so the output in 2014 can be estimated as:
w + 0.098w = 1.098w
This expression represents a strategy for estimating the farm's output for 2014.
Similarly, the output in 2015 can be estimated as:
(1.098w) + 0.051(1.098w) = (1 + 0.051)(1.098w)
Simplifying this expression, we get:
1.153w
Therefore, the expression that represents a strategy for estimating the farm's wheat output for 2015 is:
1.153w
where w is the farm's wheat output in 2013 (i.e., 19.8 tons).
So we can estimate the farm's wheat output in 2015 as:
1.153(19.8) = 22.82 tons (rounded to two decimal places)
Note that this is only an estimate, based on the assumption that the percentage increases from 2013 to 2014 and from 2014 to 2015 will continue to hold in the future.
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Which of the following tables represent a proportional relationship?
verbal:
a. y/x= 40/1 76/2 112/3 148/4
b. y/x= 48/2 96/3 144/4 192/5
c. y/x= 18/1 54/3 90/5 126/7
d. 24/1 21/2 18/3 15/4
picture:
a. y/x = 40/1, 76/2, 112/3, 148/4 does not represent a proportional relationship. . y/x = 48/2, 96/3, 144/4, 192/5 does not represent a proportional relationship. c. y/x = 18/1, 54/3, 90/5, 126/7 represents a proportional relationship.
How to determine a proportional relationshipA proportional relationship means that the ratio of y to x is constant throughout the table. Let's check each table:
a. y/x = 40/1, 76/2, 112/3, 148/4
If we simplify the fractions, we get y/x = 40, 38, 37.33, 37. This is not a constant ratio, so this table does not represent a proportional relationship.
b. y/x = 48/2, 96/3, 144/4, 192/5
If we simplify the fractions, we get y/x = 24, 32, 36, 38.4. This is not a constant ratio, so this table does not represent a proportional relationship.
c. y/x = 18/1, 54/3, 90/5, 126/7
If we simplify the fractions, we get y/x = 18, 18, 18, 18. This is a constant ratio, so this table represents a proportional relationship.
d. y/x = 24/1, 21/2, 18/3, 15/4
If we simplify the fractions, we get y/x = 24, 10.5, 6, 3.75. This is not a constant ratio, so this table does not represent a proportional relationship.
Therefore, the table that represents a proportional relationship is c. y/x = 18/1, 54/3, 90/5, 126/7.
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Chaz is writing an informal proof to show that circle q is similar to circle p after a similarity transformation followed by a rigid transformation which two translations in sequence should chaz use map circle q onto circle p
Chaz builds a connection between points on circle Q and points on circle P by carrying out these two translations while maintaining the size and shape of the circles.
Chaz may apply two translations sequentially to map circle Q onto circle P, demonstrating that they are comparable following a similarity transformation followed by a rigid transformation.
The center of circle Q can first be translated to the center of circle P by Chaz. The two circles' centers will match thanks to this translation.
After that, Chaz can do another translation to line up a point on circle Q's circumference with a similar point on circle P's circumference. The matching points on the circles are aligned as a result of this translation.
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Which postulate or theorem can be used to prove that ΔABC ≅ ΔDCB
The postulate or theorem that can be used to prove that ΔABC ≅ ΔDCB is the "Side-Side-Side (SSS) theorem".
Hence, the correct option is A.
Since in both triangles ΔABC and ΔDCB, we have
BC = BC (Common line)AB = CD (given)AC = BD (given)Therefore, by SSS theorem, we can conclude that ΔABC ≅ ΔDCB.
Hence, the correct option is A.
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Aimie is looking for a golf ball that he hit into the air towards a fence surrounding the golf course. The fence has a height of 2 yards and is located at a distance of 120 yards from where Jaimie hit the ball. Jaimie wants to determine if his golf ball landed inside or outside of the fence.
The golf ball's height, h, in yards with respect to time, t, in seconds, can be modeled by the quadratic function h=−0. 6t2+3t. Jaimie's golf ball reached its maximum height at the fence.
What is the maximum height, in yards, the golf ball reached before landing back on the ground?
_____yards
The maximum height the golf ball reached before landing back on the ground is 3.75 yards.
To find the maximum height the golf ball reached before landing back on the ground, we need to find the vertex of the quadratic function[tex]h(t) = -0.6t^2 + 3t.[/tex] The vertex of a quadratic function in the form of[tex]f(x) = ax^2 + bx + c[/tex] is given by the formula x = -b/(2a).
In this case, a = -0.6 and b = 3. Plugging these values into the formula:
t = -3 / (2 * -0.6) = 3 / 1.2 = 2.5
Now that we have the time at which the ball reaches its maximum height, we can plug this value back into the height function to find the maximum height:
[tex]h(2.5) = -0.6(2.5)^2 + 3(2.5) = -0.6(6.25) + 7.5 = -3.75 + 7.5 = 3.75[/tex]
So, the maximum height the golf ball reached before landing back on the ground is 3.75 yards.
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Babacar has a coupon for 20% off, after tax, at Burger Beast Restaurant. When Babacar and Arturo eat dinner at Burger Beast restaurant, their bill is $36. 00 after tax. They use Babacar’s coupon, and they decide to leave a tip that is 20% of the discounted price. How much did Babacar and Arturo pay in total?
The total amount Babcar and Arutro paid in the Burger Beast Restaurant is $ 34.56.
Total bill = $36
Discount coupon = 20 %
The price paid after the discount coupon = 36 - (20% of 36 )
Price paid = 36 - (36 × 20/100)
The price paid = 36 - 7.2
Price paid = 28.8
The tip paid is 20 % the discounted price
The tip paid = 20% of 28.8
The tip paid = 28.8 × 20/100
The tip paid = 5.76
The total price paid = price paid after discount coupon + Tip paid
The total price paid = 28.8 + 5.76
The total price paid = 34.56
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Anne's Road Paving Company mixed 16 1/4 tons of cement. They used 6 3/4 tons of the cement to pave a street downtown. How much cement did they have left?
Answer is 9.5 tons of cement
Anne's Road Paving Company initially mixed 16 1/4 tons of cement. They used 6 3/4 tons for paving a street downtown. To find the remaining amount of cement, subtract the used amount from the initial amount:
16 1/4 - 6 3/4 = 15 1/4 - 5 3/4 = 9 1/2 tons.
So, they had 9 1/2 tons of cement left.
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A clown made purple and green balloon animals at a party. He kept track of the requests.
What is the probability that a randomly selected balloon animal is green and is shaped like a dog?
The probability that a randomly selected balloon animal is green and shaped like a dog is 0.231.
What is the probability?The probability is found using the data table given below:
Purple and giraffe = 3; Purple and dog = 3; Green and giraffe = 4; Green and dog = 3
Out of the total number of balloon animals made, the number of green dog balloon animals is 3.
The probability of randomly selecting a green dog balloon animal is found using the formula:
Probability = (number of green dog balloon animals) / (total number of balloon animals)Probability = 3 / (3 + 3 + 4 + 3) = 3/13
Probability = 0.231
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