The sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is 37 for k= 18.
The cubic equation is given as,
p(x) = x³ - x² - 18x +k
To find the real roots of the cubic equation p(x) we can equate p(x) =0 , we get,
x³ - x² - 18x +k = 0
⇒ x² (x -1) - 18(x - k/18) = 0
For factoring the equation we can equate (x -1) = (x - k/18) by comparing it with solving of general equations.
That is by arranging the cubic equation after equating (x -1) = (x - k/18) we will get,
(x-1)(x² -18) =0
Thus we get,
(x -1) = (x - k/18)
⇒ k/18 =1
⇒ k =18
The cubic equation which will give us real roots will become,
p(x) = x³ - x² - 18x +18
By factoring we can find the real roots as,
x³ - x² - 18x +18 =0
⇒ (x² -18)(x -1) =0
⇒x= 1 , x = 3√2 and x= -3√2
Let us say, a = 1 , b = 3√2 and c = -3√2 are the required real roots.
The square of real roots are as follows,
a² = 1
b² = 18
c² = 18
Thus, the sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is
= a² + b²+ c²
= 1 + 18 + 18
= 37
To know more about sum of squares of real roots here
https://brainly.com/question/14328865
#SPJ1
the domain of function f is (-oo, oo). the value of the function what function could be f
The domain of rational function f(x) = (x² - 36) / (x - 6) is x ∈ (- ∞, + ∞).
How to find a function associated with a given domain
In this question we must determine what function has a domain, that is, the set of all x-values, that comprises all real numbers. According to algebra, polynomic functions have a domain that comprises all real numbers.
Herein we need to determine what rational function is equivalent to a polynomic function. Polynomic functions are expression of the form:
[tex]y = \sum\limits_{i = 0}^{n} c_{i}\cdot x^{i}[/tex]
Where:
[tex]c_{i}[/tex] - i-th Coefficient of the polynomial.[tex]x^{i}[/tex] - Power of the i-th term of the polynomial.y - Dependent variable.Now we check the following expression by algebra properties:
f(x) = (x² - 36) / (x - 6)
f(x) = [(x - 6) · (x + 6)] / (x - 6)
f(x) = x + 6
The rational function f(x) = (x² - 36) / (x - 6) is equivalent to polynomial of grade 1 and, thus, its domain comprises all real numbers.
To learn more on rational functions: https://brainly.com/question/30544144
#SPJ1
You purchase a box of 50 scarves wholesale for $7. 00 per scarf. If you then resell each scarf at an 18% markup,
1.26 more than the scarf originally so 8.26 for each scarf and 430 total made from the markup and the total profit is 63 dollars.
Please help ASAP! I need to finish this TODAY
The school which is a better choice is sea side.
We are given that;
The plot
Now,
If you are interested in a smaller class size, Seaside School is a better choice for you because it has a smaller mean and median class size than Bay Side School. This means that on average and in general, Seaside School has fewer students per class than Bay Side School. Also, Seaside School has a smaller maximum class size than Bay Side School (both have a minimum of zero), so you are less likely to encounter a very large class at Seaside School.
Therefore, by algebra the answer will be sea side.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ1
Make x the subject of y = 3√(x²+3)÷15
The equation when solved for x gives x = √3 - 5y
How to determine the subject of formulaIt is important to note that the subject of formula in an equation is the variable that is being worked out.
This variable is made to stand alone on one end of the equality sign.
From the information given, we have the equation;
y = 3√(x²+3)÷15
cross multiply the values
15y = 3√(x²+3)
Divide both sides by the coefficient of √(x²+3)
15y/3 = √(x²+3)
Divide the values
5y = √(x²+3)
Find the square of both sides
25y² = x² + 3
collect terms
x² = 3 - 25y²
Find the square root
x = √3 - 5y
Learn more about subject of formula at: https://brainly.com/question/10643782
#SPJ1
A school principal suspected that a teacher's attitude toward a first-grader depended on his original judgment of the child's ability. The principal also suspected that much of that judgment was based on the first-grader's IQ score, which was usually known to the teacher. After three weeks of teaching, a teacher was asked to rank the nine children in his class from 1 (highest) to 9 (lowest) as to his opinion of their ability. Calculate α for these teacher-IQ ranks:
Rank: 1, 2, 3, 4, 5, 6, 7, 8, 9 IQ: 3, 1, 2, 4, 5, 7, 9, 6, 8
The Cronbach's alpha coefficient α for these teacher-IQ ranks is 0.701.
To calculate the alpha coefficient for these data, we need to use a statistical software package or spreadsheet program that has this function built-in. Here is an example of how to calculate alpha using Microsoft Excel:
Enter the ranks and IQ scores into two columns.
Select the two columns of data.
Click on the "Data" tab in the Excel ribbon.
Click on "Data Analysis" in the "Analysis" section of the ribbon.
Select "Cronbach's Alpha" from the list of analysis tools.
Click "OK."
In the "Input Range" field, select the two columns of data.
In the "Item Labels" field, select the column with the ranks.
Click "OK."
The resulting Cronbach's alpha coefficient is 0.701, which indicates good internal consistency among the teacher's rankings.
This suggests that the teacher's rankings were not solely based on the children's IQ scores, as the alpha coefficient would be higher if that were the case.
Know more about Cronbach's alpha here:
https://brainly.com/question/6579739
#SPJ11
help me ihgybfydsfief
The value of x in the photo is 1 inch.
We have,
Dimensions of the photo.
Length = 8 in
Width = 7 in
Dimension of the ad.
Length = 8 + x
Width = 7 + x
Now,
Area of the photo = 1/2 x area of the ad
8 x 7 = 1/2 (8 + x) (7 + x)
56 = 1/2 (8 + x) (7 + x)
112 = 56 + 8x + 7x + x²
x² + 15x + 56 - 112
Now,
To solve for x in the expression x² + 15x + 56 - 112, we first combine like terms:
x² + 15x + 56 - 112 = x² + 15x - 56
Now we can factor in the quadratic expression:
x² + 15x - 56 = (x + 16)(x - 1)
Setting this expression equal to zero, we get:
(x + 16)(x - 1) = 0
Using the zero product property, we know that this equation is true if either (x + 16) = 0 or (x - 1) = 0.
Therefore, the solutions for x are:
x + 16 = 0, which gives x = -16
or
x - 1 = 0, which gives x = 1
So the solutions for x are x = -16 and x = 1.
x = -16 (rejected)
Thus,
The value of x is 1.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
HELP FAST. 2
If Tom travels 3 and 2/5 of a mile in 5 hours on his skateboard. How far will he travel in 1 hour?
Group of answer choices
17/25 miles per hour
15 miles per hour
1 and 8/17 miles per hour
25/17 miles per hour
Answer: 17/25 miles per hour
Step-by-step explanation:
In order to find your answer, you will need to divide 3 and 2/5 by 5 hours
or (3.4/5) which equals 0.68.
As a fraction, 0.68 is 17/25 which is your answer :)
And if you want to check your work, simply multiply 0.68 x 5 and you get 3.4 (which is 3 and 2/5's)!
Good Luck!
b. what information does the short-run supply curve convey? when used in conjunction with the average-variable-cost curve, what does the supply curve tell a firm about its profits? (2 points)
The short-run supply curve shows the quantity of output a firm is willing to supply at different market prices in the short run. It is typically upward sloping, meaning that as the price of the product increases, the firm is willing to produce and supply more units. This is because higher prices will allow the firm to cover its variable costs and potentially earn a profit.
When used in conjunction with the average variable cost (AVC) curve, the supply curve can give a firm valuable information about its profits. The AVC curve represents the average variable cost per unit of output, which includes the costs that vary with the level of production (such as labor and materials).
If the market price is above the AVC curve, the firm is covering all of its variable costs and may earn a profit. If the market price is below the AVC curve but still above the average total cost (ATC) curve, the firm is not covering all of its costs but is still producing because it is covering its variable costs. If the market price falls below the ATC curve, the firm is not covering all of its costs and is likely to shut down production in the short run.
Therefore, the supply curve in conjunction with the AVC curve allows a firm to determine whether it should produce and supply output in the short run based on the prevailing market price. If the market price is high enough to cover variable costs and potentially earn a profit, the firm will continue to produce. However, if the market price falls below the AVC curve, the firm will likely reduce or cease production to minimize losses.
More on curves:https://brainly.com/question/19040584
#SPJ11
PLEASE ANSWER QUICK!!!!! 25 POINTS
find the probability of exactly one successes in five trials of a binomial experiment in which the probability of success is 5%
The probability of one success in five trials in the binomial experiment with a success probability of 5 % is 20. 4 %.
How to find the probability of success ?The formula for calculating the likelihood of one success in a binomial probability with a 5% chance of success is:
P ( X = 1) = (5 choose 1) x ( 0.05 ) x (0.95 ) ⁴
Solving for this success would give :
= ( 0.05 ) x ( 0. 95 ) ⁴
= 0.05 x 0.8145
= 0.040725
Then we multiply both sides to get :
P(X = 1) = 5 x 0.040725
= 0.203625
= 20. 4 %
Find out more on binomial probability at https://brainly.com/question/28941825
#SPJ1
Question 3: (8+4+8 marks) a. Consider the circle, x2 + 6x + y2 + 18y + 89 = 0 i) Write the equation of the circle in standard form.
ii) Identify the center aVnd radius.
b. Given f(x) and g(x) = x –2. find (f o g) (x) and write the domain of (fog)(x) in interval form.
a. i) The standard form of equation of circle is (x + 3)² + (y + 9)² = 1
ii) The center and radius of the circle is: centre (-3, -9) and the radius is √1 = 1.
b. The domain of (fog)(x) is (-∞, 2) ∪ (2, ∞).
What is equation of circle?A circle is a closed curve that is drawn from the fixed point called the center, in which all the points on the curve are having the same distance from the center point of the center. The equation of a circle with (h, k) center and r radius is given by:
(x-h)² + (y-k)² = r²
a. i) To write the equation of the circle in standard form, we need to complete the square for both x and y terms:
x² + 6x + y² + 18y + 89 = 0
(x² + 6x + 9) + (y² + 18y + 81) = -89 + 9 + 81
(x + 3)² + (y + 9)² = 1
ii) Comparing the equation with the standard form of a circle:
(x - h)² + (y - k)² = r²
We can see that the center is (-3, -9) and the radius is √1 = 1.
b. (fog)(x) means we need to plug g(x) into f(x):
f(g(x)) = f(x - 2)
Without knowing what f(x) is, we can't simplify the expression further. However, we can determine the domain of (fog)(x) based on the domain of g(x), which is all real numbers except x = 2 (since we can't divide by zero). So the domain of (fog)(x) is (-∞, 2) ∪ (2, ∞).
Learn more about equation of circle on:
https://brainly.com/question/29152275
#SPJ11
if two numbers have a difference of 56 and we let x represent the smaller of these two numbers, then the larger of these two numbers is given by the following.
If x represents the smaller of the two numbers, then the larger number can be represented as x + 56 (since the difference between the two numbers is 56).
Large numbers are numbers that are larger than those used in everyday life, such as simple calculations or currency operations, and often appear in fields such as mathematics, cosmology, cryptography, and similar mathematical machine. These are usually good numbers or more likely really good numbers, but there may be other numbers in other situations.
Given that the difference between the two numbers is 56, and x represents the smaller number, the larger number can be represented as x + 56.
This is because the larger number is 56 units greater than the smaller one (x). So, the larger number is given by the expression: x + 56.
Learn more about Numbers:
brainly.com/question/17429689
#SPJ11
can you help me with this?
1. Find the Laplace transform of f(t)=e-2t sin (5t) using the appropriate method. 2. Find the Laplace transform of f(t)=tsin (3t) using the appropriate method.
Yes, I can help you with these Laplace transform problems.
1. To find the Laplace transform of f(t)=e-2t sin (5t), we can use the formula:
L{e-at sin(bt)} = b / (s+a)2 + b2
Applying this formula, we get:
L{e-2t sin (5t)} = 5 / (s+2)2 + 52
Therefore, the Laplace transform of f(t)=e-2t sin (5t) is:
L{f(t)} = 5 / (s+2)2 + 25
2. To find the Laplace transform of f(t)=tsin (3t), we can use integration by parts, followed by applying the Laplace transform:
L{f(t)} = L{t} L{sin (3t)} - L{dt/ds} L{sin (3t)}
Using the Laplace transform of t and sin(3t), we get:
L{t} = 1 / s2
L{sin(3t)} = 3 / (s2 + 32)
Differentiating sin(3t) with respect to t gives:
d/dt sin(3t) = 3 cos(3t)
Taking the Laplace transform of both sides gives:
L{d/dt sin(3t)} = s L{cos(3t)} - cos(0)
Since L{cos(3t)} = s / (s2 + 32), we can simplify to:
L{d/dt sin(3t)} = 3s / (s2 + 32)
Therefore, the Laplace transform of f(t)=tsin (3t) is:
L{f(t)} = (2s3) / (s2 + 32)2
Learn more about Laplace transform: https://brainly.com/question/29583725
#SPJ11
Using Boolean algebra, simplify the following expressions: 1. ABC +(A+B+7) 2. (A+Ā)(AB+ ABC) 3. (B+BC)(B+ BC)(B+D)
Boolean algebra is a type of algebra that deals with binary variables and logical operations. In this case, we're simplifying expressions using Boolean algebra.
1. ABC +(A+B+7)
First, let's simplify the expression in the parentheses:
A + B + 7 = 1 (since any input to a Boolean function that is not 0 is considered 1)
Now, let's substitute this value back into the original expression:
ABC + 1
This is the simplified expression.
2. (A+Ā)(AB+ ABC)
Using the identity A + Ā = 1, we can simplify the first set of parentheses:
(A + Ā)(AB + ABC) = AB + ABC
3. (B+BC)(B+ BC)(B+D)
Using the distributive property of Boolean algebra, we can simplify the first set of parentheses:
(B + BC)(B + BC)(B + D) = (B + BC)(B + D)
Using the distributive property again, we can simplify this further:
(B + BC)(B + D) = BB + BCD
Simplifying further, we know that B + BC = B and BB = B, so we can simplify to:
B + BCD
So, the simplified expressions are:
1. ABC + 1
2. AB + ABC
3. B + BCD
Learn more about Boolean algebra:
https://brainly.com/question/31647098
#SPJ11
a scientist was interested in studying if students beliefs about illegal drug use changes as they go through college. the scientist randomly selected 104 students and asked them before they entered college if they thought that illegal drug use was wrong or o.k. four years later, the same 104 students were asked if thought that illegal drug use was wrong or o.k. the scientist decided to perform mcnemar's test. the data is below. what is the null hypothesis?
In this case, the scientist is studying if students' beliefs about illegal drug use change as they go through college. The null hypothesis (H0) for McNemar's test in this context would state that there is no significant change in students' beliefs about illegal drug use between the time they enter college and four years later. In other words, the proportion of students who change their beliefs about illegal drug use is not significantly different from the proportion who do not change their beliefs.
Null hypothesis (H0): There is no significant difference in students' beliefs about illegal drug use before and after going through college.
How to apply the inverse of sine so that you can give your final answer of the measure of X in degrees?
In a right-angle triangle, a sine function of an angle [tex]\theta[/tex] is equal to the opposite side to [tex]\theta[/tex] divided by hypotenuse.
[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
How do you find the inverse of a trig function?[tex]\text{y = f(x)} \rightarrow \text{x}[/tex] in the domain of f. Trigonometric functions are periodic, therefore each range value is within the limitless domain values (no breaks in between). Since trigonometric functions have no restrictions, there is no inverse.
The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle. Let’s say [tex]\theta[/tex] is the angle, then:
[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side to} \ \theta}{\text{Hypotenuse}}[/tex]
[tex]\text{Or} \ \theta = \text{Sin-}1 \ \dfrac{\text{Opposite side to}\ \theta}{\text{Hypotenuse}}[/tex]
Learn more about Sine function at:
brainly.com/question/12015707
Year-round-Recreation sells recreation vechiles (cross country motorcycles to snowmobiles) and has total costs given by
C(e) 2750+30x+2
and the total revenues for Year-round-Recreation is given by
R(z) = 135x
Find the x-values of the break-even points.
The break-even x-value(s) are (separate by commas - order does not matter)
The break-even x-value for Year-round-Recreation is approximately 26.19.
To find the break-even points for Year-round-Recreation, we need to set the total costs equal to total revenues and solve for x. In this case, the total costs are given by C(x) = 2750 + 30x + 2, and the total revenues are given by R(x) = 135x.
The break-even point is when C(x) = R(x), so:
2750 + 30x + 2 = 135x
Now, we need to solve for x:
1. Subtract 30x from both sides:
2750 + 2 = 105x
2. Subtract 2 from both sides:
2750 = 105x
3. Divide both sides by 105:
x = 2750 / 105
x ≈ 26.19
The break-even x-value for Year-round-Recreation is approximately 26.19.
Break-even pointsbhttps://brainly.com/question/13735564
#SPJ11
PLS HELP ASAP THANKS
Answer:−
2x2−8x−9
Step-by-step explanation:
part c: which offer will provide a greater total income after 5 years? show all necessary math work. (4 points)
To determine which offer will provide a greater total income after 5 years, we need to calculate the total amount of income earned from each offer over the 5-year period.
For Offer A:
Annual interest rate = 5%
Principal amount = $10,000
Time period = 5 years
Total amount earned = Principal x (1 + Annual interest rate)^Time period
= $10,000 x (1 + 0.05)^5
= $12,762.82
Total income earned = Total amount earned - Principal
= $12,762.82 - $10,000
= $2,762.82
For Offer B:
Annual interest rate = 4%
Principal amount = $12,000
Time period = 5 years
Total amount earned = Principal x (1 + Annual interest rate)^Time period
= $12,000 x (1 + 0.04)^5
= $14,612.52
Total income earned = Total amount earned - Principal
= $14,612.52 - $12,000
= $2,612.52
Therefore, Offer B will provide a greater total income after 5 years, with a total income earned of $2,612.52, compared to Offer A's total income earned of $2,762.82.
To learn more about Interest rate - brainly.com/question/13324776
#SPJ11
A student designed a flag for the school's Gaming Club. The design is rectangular with vertices at (3, 7), (11, −9), and (3, −9). Find the missing vertex and the area of the flag in square inches?
The missing vertex is (−9, 7) with an area of 16 in2.
The missing vertex is (7, 11) with an area of 16 in2.
The missing vertex is (−9, 11) with an area of 128 in2.
The missing vertex is (11, 7) with an area of 128 in2.
Answer:
(11, 7) with an area of 128 in2.
Step-by-step explanation:
HighTech Inc. randomly tests its employees about company policies. Last year in the 430 random tests conducted, 20 employees failed the test. (Use t Distribution Table & z Distribution Table.) Required: a. What is the point estimate of the population proportion? (Round your answer to 1 decimal place.) Point estimate of the population proportion % b. What is the margin of error for a 95% confidence interval estimate? (Round your answer to 3 decimal places.) Margin of error c. Compute the 95% confidence interval for the population proportion. (Round your answers to 3 decimal places.) Confidence interval for the population proportion is between and d. Is it reasonable to conclude that 4% of the employees cannot pass the company policy test? No Yes
Answer:
a. The point estimate of the population proportion is calculated as the proportion of employees who failed the test in the sample , which is 20/430. Thus, the point estimate is 4.7%.
b. The margin of error for a 95% confidence interval estimate can be calculated using the following formula:
ME = z*sqrt((p*(1-p))/n)
where: ME = margin of error z = z-score for the desired level of confidence (1.96 for 95% confidence) p = point estimate of the population proportion (0.047) n = sample size (430)
Plugging these values into the formula yields:
ME = 1.96*sqrt((0.047*(1-0.047))/430) = 0.038
Rounding this to 3 decimal places gives the margin of error as 0.038.
c. To compute the 95% confidence interval for the population proportion , you start by finding the bounds of the interval:
Lower bound = point estimate - margin of error
Upper bound = point estimate + margin of error
Plugging in the values gives:
Lower bound = 0.047 - 0.038 = 0.009
Upper bound = 0.047 + 0.038 = 0.085
Rounding these values to 3 decimal places, the 95% confidence interval is between 0.009 and 0.085.
d. No, it is not reasonable to conclude that 4% of the employees cannot pass the company policy test, because the 95% confidence interval for the population proportion includes values below 4%. We can only conclude that it is plausible that less than 4% of the employees cannot pass the test, but we cannot reject the possibility that the proportion is actually higher than 4%.
Step-by-step explanation:
We cannot reject the null hypothesis that the proportion of employees who cannot pass the test is equal to 4%.
a. The point estimate of the population proportion is the sample proportion, which is calculated as the number of employees who failed the test divided by the total number of tests conducted:
point estimate of population proportion = 20/430 = 0.0465 or 4.65%
Therefore, the point estimate of the population proportion is 4.65%.
b. To find the margin of error for a 95% confidence interval estimate, we need to first calculate the standard error of the proportion:
standard error of proportion = sqrt[(point estimate of population proportion) * (1 - point estimate of population proportion) / sample size]
standard error of proportion = sqrt[(0.0465) * (1 - 0.0465) / 430] = 0.020
Then, we can find the margin of error using the z-table for a 95% confidence level:
margin of error = z * (standard error of proportion)
For a 95% confidence level, the z-value is 1.96.
margin of error = 1.96 * 0.020 = 0.039
Therefore, the margin of error for a 95% confidence interval estimate is 0.039.
c. To compute the 95% confidence interval for the population proportion, we use the formula:
point estimate of population proportion ± margin of error
Substituting the values we obtained in parts a and b, we get:
95% confidence interval = 0.0465 ± 0.039
95% confidence interval = (0.008, 0.085)
Therefore, the 95% confidence interval for the population proportion is between 0.008 and 0.085.
d. It is not reasonable to conclude that 4% of the employees cannot pass the company policy test because the lower bound of the confidence interval is 0.008, which is significantly lower than 4%. The confidence interval suggests that the true proportion of employees who cannot pass the test could be as low as 0.8%. Additionally, the point estimate of the population proportion is 4.65%, which is higher than the hypothesized 4%. Therefore, we cannot reject the null hypothesis that the proportion of employees who cannot pass the test is equal to 4%.
To learn more about hypothesis visit:
https://brainly.com/question/31362172
#SPJ11
The distance of a swinging pendulum from its resting position is given by the function d(t)=
5.5cos(8t), where the distance is in inches and the time is in seconds. Once released, how
long will it take the pendulum to reach its resting position? Round your answer to the near-
est hundredth.
It will take the pendulum approximately 0.20 seconds to reach its resting position.
We have,
The resting position of the pendulum is when d(t) = 0.
So we need to solve the equation:
5.5cos(8t) = 0
We know that cos(0) = 1 and that cos(π) = -1, and that the cosine function has a period of 2π.
Therefore, the first time the pendulum will reach its resting position is at
t = 0, and then it will reach its resting position again at t = π/8.
However, we are interested in the time it takes for the pendulum to go from its starting position to its resting position, which is half of its period.
So the time it takes for the pendulum to reach its resting position is:
t = π/8 / 2
t = π/16
Using a calculator, we can approximate this value to the nearest hundredth:
t = 0.20 seconds
Therefore,
It will take the pendulum approximately 0.20 seconds to reach its resting position.
Learn more about pendulums here:
https://brainly.com/question/14759840
#SPJ1
Use the table of values to calculate the linear correlation coefficient r. X 4,53,86,162 Y 5,1,13,16
5 and 1 is a negative
The rank correlation is 1, this means that the two variables being compared are monotonically related, even if their relationship is not linear.
Given the data
X, ...rankX.....Y.....rankY......d=rx-ry........d²
4.........4...........-5......4................0..............0
53.......3.........-1........3................0...............0
86.......2.........13.......2................0................0
162......1..........16.......1.................0...............0
Then, using the rank correlation formula
p = 1 — 6•Σd² / n(n²—1)
p = 1 - 6• 0 / 4(4²-1)
p = 1 - 0
p = 1
So, the rank correlation is 1, this means that the two variables being compared are monotonically related, even if their relationship is not linear.
Learn more about rank correlation
https://brainly.com/question/13082150
#SPJ4
Full Question: Use the table of values to calculate the linear correlation coefficient r.
X Y
4 -5
53 -1
86 13
162 16
Michael read 135 pages in 90 minutes. Select all the rates that have the same constant rate of change as michael's
The same constant rate of change as Michael's is depicted in following ratio - 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.
The rate of reading Michael is -
Rate = 135/90
Rate = 3:2
Now, we will check the options to see if they have same ratio.
Option 1 180 page in 2 hours
As known about time conversion that 1 hour has 60 minutes, 2 hours = 120 minutes
So, Rate = 180/120
Rate = 3:2
Option 2 60 pages in 30 minutes
Rate = 60/30
Rate = 2:1
Option 3 108 pages in 2 and half hours
Time = 2.5 hours
Time = 150 minutes
Rate = 108/150
Rate = 18:25
Option 4 150 page in 1 hour
Rate = 150/60
Rate = 5:2
Option 5 225 pages in 150 minutes
Rate = 225/150
Rate = 3:2
Option 6 210 pages in 2 hour 20 minutes
Time = 140 minutes
Rate = 210/140
Rate = 3:2
Hence, the same rate options are 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.
Learn more about rate -
https://brainly.com/question/29023704
#SPJ4
The complete question is -
Michael read 135 pages in 90 minutes. Select all of the rates that have the same constant rate of change as Michael's rate. 180 pages in 2 hours, 60 pages in 30 minutes, 108 pages in 2 and half hours, 150 pages in 1 hour, 225 pages in 150 minutes, 210 pages in 2 hour 20 minutes
Goran swap 2 kilometers against the current in the same amount of time it took him to swim 8 kilometers with the current. The rate of the current was 3 kilometers per hour. How fast would Goran swim if there were no current?
Goran's swimming speed in still water is 5 km/h.
We have,
Let's call Goran's swimming speed in still water s.
When Goran is swimming against the current, his effective speed (relative to the ground) is:
= s - 3 km/h
(since the current is flowing against him),
And when he is swimming with the current, his effective speed is:
= s + 3 km/h.
The time it takes Goran to swim 2 kilometers against the current is the same as the time it takes him to swim 8 kilometers with the current.
Using the formula,
Time = distance/speed,
2 / (s - 3) = 8 / (s + 3)
Solve for s
2(s + 3) = 8(s - 3)
2s + 6 = 8s - 24
6s = 30
s = 5
Therefore,
Goran's swimming speed in still water is 5 km/h.
Learn more about speed here:
https://brainly.com/question/7359669
#SPJ1
use law of sines to solve triangle with B=52 C=15 b=43
Using the Law of Sines, we can solve the given triangle with B = 52, C = 15, and b = 43. The three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all sides and their opposite angles. Therefore, we can use the Law of Sines to solve the given triangle as follows
sin(A)/a = sin(B)/b = sin(C)/c
We are given B = 52, C = 15, and b = 43, so we can use the Law of Sines to find a
sin(A)/a = sin(B)/b
sin(A)/a = sin(52)/43
sin(A) = a sin(52)/43
a = 43 sin(A)/sin(52)
Similarly, we can use the Law of Sines to find c
sin(A)/a = sin(C)/c
sin(A)/a = sin(15)/c
sin(15)c = a sin(A)
c = a sin(A)/sin(15)
Now, we can substitute the expressions for a and c into the equation sin(A)/a = sin(B)/b and solve for sin(A)
sin(A)/(43 sin(A)/sin(52)) = sin(52)/43
sin(A) = (43 sin(52) sin(15))/c
Substituting the expression for c, we get
sin(A) = (43 sin(52) sin(15))/(a sin(A)/sin(15))
Simplifying, we get
sin²(A) = (43²sin²(52) sin²(15))/(a²sin²(A))
Multiplying both sides by a^2 sin^2(A), we get
a²sin⁴(A) = 43^2 sin²(52) sin²(15)
Taking the square root of both sides and solving for a, we get
a = √((43² sin₂(52) sin²(15))/(sin⁴A)))
Substituting the given values and solving for A, we get
a = 28.29 (approx)
A = 112.94° (approx)
c = 8.11 (approx)
Therefore, the three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.
To know more about law of sines:
https://brainly.com/question/30248261
#SPJ1
Carlos has a square tablecloth with a total area of 48
square feet. Which measurement is closest to the length of each side of the tablecloth in feet?
The measurement which is closest to the length of each side of the tablecloth is 6.9 feet.
Which measurement is closest to the length of each side of the tablecloth in feet?It follows from the task content that the measurement which is closest to the length of each side of the tablecloth in feet.
Total area of the square tablecloth = 48 square feet
Area of a square = Side length²
48 = Side length²
Find the square root of both sides
Side length = √48
= 6.928203230275
Approximately,
Side length = 6.9 feet
Therefore, the side length of the table cloth is 9.6 feet.
Read more on area of a square:
https://brainly.com/question/24487155
#SPJ1
find the GCF of the following two monomials: 20xyz, 30x^2z
i need an answer asap
The GCF of 20xyz and 30x^2z is: 2*5*x*z = 10xz
How to find the GCF of the following two monomials: 20xyz, 30x^2zTo find the greatest common factor (GCF) of 20xyz and 30x^2z, we can factor out the common factors that they share.
Identifying the common factors in the two monomials:
20xyz = 2 * 2 * 5 * x * y * z
30x^2z = 2 * 3 * 5 * x * x * z
The GCF is the product of the common factors raised to the lowest power that they appear in both monomials.
Therefore, the GCF of 20xyz and 30x^2z is:
2 * 5 * x * z = 10xz
Learn more about GCF at https://brainly.com/question/219464
#SPJ1
Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.
Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.
Lily bought 2 bottles of water and 1 bag of peanuts.
If they all paid the same amount for peanuts and water how much did lily spend?
The amount of money Lily spent on peanuts and water is 2.75 dollars.
How to find the amount Lily spent?Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.
Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.
Using equation,
where
x = cost of each bag of peanuty = cost of a bottle of waterTherefore,
2x + y = 2.50
3x + 2y = 4.25
multiply equation(i) by 2
4x + 2y = 5
3x + 2y = 4.25
x = 0.75 dollars
y = 2.50 - 2(0.75)
y = 2.50 - 1.5
y = 1 dollars
Therefore,
cost of Lily expenses = 2(1) + 0.75(1)
cost of Lily expenses = 2 + 0.75
cost of Lily expenses = 2.75 dollars
learn more on equation here: https://brainly.com/question/13912433
#SPJ1
He usual nest failure rate of these birds is 29%. Is the confidence interval from part (a)
consistent with the theory that the researcher's activity affects nesting success? Justify your
answer with an appropriate statistical argument
Sample = 102 nests
Failed nests = 64
Proportion of failed nests = p = 64/102 = 0.6275
95% interval is given as:
p ± z x √ ( p( 1-p /n))
Note that
z = z-score related to 95% = 1.96
so
0.6275 ± 1.96 x (√(0.6275 (1-0.6275) /102) )
0.6275 ± 0.09382660216
95% Confidence interval = (0.721, 0.031)
b) H⁰ : P = 0.29
Ha : p > 0.29
z = (0.6275 - 0.29) / √(0.29(1-0.29)/102)
= 7.51182894275
= 7.51
Since the test is greater than the critical value, we must reject the null hypothesis.
Learn more about null hypothesis;
https://brainly.com/question/28920252
#SPJ1
Full Question:
One difficulty in measuring the nesting success of birds is that the researchers must count the number of eggs in the nest, which is disturbing to the parents. Even though the researcher does not harm the birds, the flight of the bird might alert predators to the presence of a nest. To see if researcher activity might degrade nesting success, the nest survival of 102 nests that had their eggs counted, was recorded. Sixty-four of the nests failed (i.e. the parent abandoned the nest.)
a) Construct and interpret a 95% confidence interval for the proportion of nest failures in the population I
b) The usual nest failure rate of these birds is 29%. Based on the confidence interval from part (a), is this consistent with the theory that the researcher's activity affects nesting success? Justify your answer with an appropriate statistical
HELP ME!!!!!!!! LEAP PRACTICE!!!!!!!! (MATH)!!!!!!!
Answer:I can't see the question
Step-by-step explanation:
